1open HolKernel Feedback testutils Parse boolLib mesonLib 2 3local open pairTheory in end 4 5val op$ = Portable.$ 6 7fun M nm tm = 8 let 9 val _ = tprint ("meson "^nm) 10 in 11 require is_result TAC_PROOF (([], tm), MESON_TAC[]) 12 end 13 14fun Mfail nm tm = 15 let 16 val _ = tprint ("meson (expected to fail) "^nm) 17 in 18 require (check_HOL_ERR (fn _ => true)) TAC_PROOF (([], tm), MESON_TAC []) 19 end 20 21 22(*--------------------------------------------------------------------------- 23 * Some of the big formulas are too big for guessing tyvars for. A workaround 24 * is to give explicit constraints. 25 *---------------------------------------------------------------------------*) 26 27val _ = Globals.guessing_tyvars := false; 28val _ = Parse.current_backend := PPBackEnd.raw_terminal 29val _ = temp_remove_termtok {term_name = "O", tok = "O"}; 30val _ = app (ignore o hide) ["irreflexive", "transitive", "one"]; 31 32(* ------------------------------------------------------------------------- 33 * Trivia 34 * ------------------------------------------------------------------------- *) 35 36(* M90: OK *) 37M "T" ���T���; 38 39 40(* M90: OK *) 41M "P \\/ ~P" ���P \/ ~P���; 42 43 44(* ------------------------------------------------------------------------- 45 * Basic existential stuff (bug reported by Michael Norrish) 46 * ------------------------------------------------------------------------- *) 47 48val _ = new_type("num", 0) 49val _ = new_constant("n0", ``:num``) 50val _ = new_constant("n1", ``:num``) 51val _ = new_constant("n2", ``:num``) 52val _ = new_constant("n3", ``:num``); 53 54Mfail "Norrish existential" ���!se:num. ?n:num. f n se se ==> ?m:num. f m n0 n0���; 55 56(* ------------------------------------------------------------------------- 57 * P50 58 * ------------------------------------------------------------------------- *) 59 60val P50 = ���(!x:'a. F0 a x \/ !y. F0 x y) ==> ?x. !y. F0 x y���; 61M "P50" P50; 62 63(* ------------------------------------------------------------------------- 64 * Example from Eric Borm (see long info-hol discussion, September 93). 65 * ------------------------------------------------------------------------- *) 66 67val ERIC = Term 68`!P Q R. !x:'a. ?v w. !y (z:'b). 69 P x /\ Q y ==> (P v \/ R w) /\ (R z ==> Q v)`; 70 71M "ERIC" ERIC; 72 73 74 75(* ------------------------------------------------------------------------- 76 * The classic Los puzzle. (Clausal version MSC006-1 in the TPTP library.) 77 * Note: this is actually in the decidable "AE" subset, though that doesn't 78 * yield a very efficient proof. 79 * ------------------------------------------------------------------------- *) 80 81val LOS = ���(!(x:'a) (y:'a) z. P x y /\ P y z ==> P x z) /\ 82 (!x (y:'a) z. Q x y /\ Q y z ==> Q x z) /\ 83 (!x y. P x y ==> P y x) /\ 84 (!x y. P x y \/ Q x y) 85 ==> (!x y. P x y) \/ (!x y. Q x y)���; 86 87M "LOS" LOS;; 88 89 90(* ------------------------------------------------------------------------- 91 * An equality-free version of the Agatha puzzle. 92 * ------------------------------------------------------------------------- *) 93 94val P55 = 95���lives(agatha) /\ lives(butler) /\ lives(charles) /\ 96 (killed(agatha,agatha) \/ killed(butler,agatha) \/ 97 killed(charles,agatha)) /\ 98 (!x y. killed(x,y) ==> hates(x,y) /\ ~richer(x,y)) /\ 99 (!x. hates(agatha,x) ==> ~hates(charles,x)) /\ 100 (hates(agatha,agatha) /\ hates(agatha,charles)) /\ 101 (!x. lives(x) /\ ~richer(x,agatha) ==> hates(butler,x)) /\ 102 (!x. hates(agatha,x) ==> hates(butler,x)) /\ 103 (!x. ~hates(x,agatha) \/ ~hates(x,butler) \/ ~hates(x,charles)) ==> 104 (?x:'person. killed(x,agatha))���; 105 106M "P55" P55; 107 108 109(* ------------------------------------------------------------------------- 110 * The Steamroller. 111 * ------------------------------------------------------------------------- *) 112 113val P47 = ���((!x:'a. P1 x ==> P0 x) /\ (?x. P1 x)) /\ 114 ((!x. P2 x ==> P0 x) /\ (?x. P2 x)) /\ 115 ((!x. P3 x ==> P0 x) /\ (?x. P3 x)) /\ 116 ((!x. P4 x ==> P0 x) /\ (?x. P4 x)) /\ 117 ((!x. P5 x ==> P0 x) /\ (?x. P5 x)) /\ 118 ((?x. Q1 x) /\ (!x. Q1 x ==> Q0 x)) /\ 119 (!x. P0 x ==> (!y. Q0 y ==> R x y) \/ 120 (((!y. P0 y /\ S0 y x /\ ?z. Q0 z /\ R y z) ==> R x y))) /\ 121 (!x y. P3 y /\ (P5 x \/ P4 x) ==> S0 x y) /\ 122 (!x y. P3 x /\ P2 y ==> S0 x y) /\ 123 (!x y. P2 x /\ P1 y ==> S0 x y) /\ 124 (!x y. P1 x /\ (P2 y \/ Q1 y) ==> ~(R x y)) /\ 125 (!x y. P3 x /\ P4 y ==> R x y) /\ 126 (!x y. P3 x /\ P5 y ==> ~(R x y)) /\ 127 (!x. (P4 x \/ P5 x) ==> ?y. Q0 y /\ R x y) 128 ==> ?x y. P0 x /\ P0 y /\ ?z. Q1 z /\ R y z /\ R x y���; 129 130Mfail "P47" P47; 131 132 133(* ------------------------------------------------------------------------- 134 * Now problems with equality. 135 * ------------------------------------------------------------------------- *) 136 137val P48 = M "P48" 138 ���((a:'a = b) \/ (c = d)) /\ ((a = c) \/ (b = d)) ==> (a = d) \/ (b = c)���; 139 140(* hol90 - tick *) 141 142 143(* ------------------------------------------------------------------------- 144 * More problems with equality. 145 * ------------------------------------------------------------------------- *) 146 147(* hol90 - no *) 148val P49 = Mfail "P49" ���(?x y. !z:'a. (z = x) \/ (z = y)) /\ 149 P a /\ P b /\ ~(a = b) ==> !x:'a. P x���; 150 151val P51 = M "P51" 152 ���(?z w:'a. !x y:'a. F0 x y = (x = z) /\ (y = w)) ==> 153 ?z:'a. !x:'a. (?w:'a. !y:'a. F0 x y = (y = w)) = (x = z)���; 154 155val P52 = M"P52" 156 ���(?z w:'a. !x y. F0 x y = (x = z) /\ (y = w)) ==> 157 ?w:'a. !y. (?z. !x:'a. F0 x y = (x = z)) = (y = w)���; 158 159(*** Too slow 160 161val P53 = 162 ���(?x y. ~(x = y) /\ !z. (z = x) \/ (z = y)) ==> 163 ((?z. !x. (?w. !y. F0 x y = (y = w)) = (x = z)) = 164 (?w. !y. (?z. !x. F0 x y = (x = z)) = (y = w)))���; 165 166 167val P54 = Tactical.prove(GEN_MESON_TAC 168 ���(!y. ?z. !x. F0 x z = (x = y)) ==> 169 ~?w. !x. F0 x w = !u. F0 x u ==> ?y. F0 y u /\ ~ ?z. F0 x u /\ F0 z y���); 170 171 172*****) 173 174(* hol90 - yes? (too slow) *) 175val P55 = 176 ���(?x:'a. lives x /\ killed x agatha) /\ 177 (lives(agatha) /\ lives(butler) /\ lives(charles)) /\ 178 (!x. lives(x) ==> (x = agatha) \/ (x = butler) \/ (x = charles)) /\ 179 (!y x. killed x y ==> hates x y) /\ 180 (!x y. killed x y ==> ~richer x y) /\ 181 (!x. hates agatha x ==> ~hates charles x) /\ 182 (!x. ~(x = butler) ==> hates agatha x) /\ 183 (!x. ~richer x agatha ==> hates butler x) /\ 184 (!x. hates agatha x ==> hates butler x) /\ 185 (!x. ?y. ~hates x y) /\ 186 ~(agatha = butler) 187 ==> killed agatha agatha���; 188 189 190(* ------------------------------------------------------------------------- *) 191(* ------------------------------------------------------------------------- *) 192 193(* hol90 - yes *) 194val P50 = 195 ���(!x:'a. P(a,x) \/ (!y. P(x,y))) ==> ?x. !y. P(x,y)���; 196 197 198(* ========================================================================= *) 199(* 100 problems selected from the TPTP library as a test for MESON_TAC. *) 200(* ========================================================================= *) 201 202(* 203 * These should all work with the default settings, but some are quite slow 204 * (many minutes). 205 * 206 * A few variable names have been primed to avoid clashing with constants. 207 * 208 * Here's a list giving typical CPU times, as well as common names and 209 * literature references. 210 * 211 * BOO003-1 34.6 B2 part 1 [McCharen, et al., 1976]; Lemma d [Overbeek, et al., 1976]; prob2_part1.ver1.in [ANL] 212 * BOO004-1 36.7 B2 part 2 [McCharen, et al., 1976]; Lemma d [Overbeek, et al., 1976]; prob2_part2.ver1 [ANL] 213 * BOO005-1 47.4 B3 part 1 [McCharen, et al., 1976]; B5 [McCharen, et al., 1976]; Lemma d [Overbeek, et al., 1976]; prob3_part1.ver1.in [ANL] 214 * BOO006-1 48.4 B3 part 2 [McCharen, et al., 1976]; B6 [McCharen, et al., 1976]; Lemma d [Overbeek, et al., 1976]; prob3_part2.ver1 [ANL] 215 * BOO011-1 19.0 B7 [McCharen, et al., 1976]; prob7.ver1 [ANL] 216 * CAT001-3 45.2 C1 [McCharen, et al., 1976]; p1.ver3.in [ANL] 217 * CAT003-3 10.5 C3 [McCharen, et al., 1976]; p3.ver3.in [ANL] 218 * CAT005-1 480.1 C5 [McCharen, et al., 1976]; p5.ver1.in [ANL] 219 * CAT007-1 11.9 C7 [McCharen, et al., 1976]; p7.ver1.in [ANL] 220 * CAT018-1 81.3 p18.ver1.in [ANL] 221 * COL001-2 16.0 C1 [Wos & McCune, 1988] 222 * COL023-1 5.1 [McCune & Wos, 1988] 223 * COL032-1 15.8 [McCune & Wos, 1988] 224 * COL052-2 13.2 bird4.ver2.in [ANL] 225 * COL075-2 116.9 [Jech, 1994] 226 * COM001-1 1.7 shortburst [Wilson & Minker, 1976] 227 * COM002-1 4.4 burstall [Wilson & Minker, 1976] 228 * COM002-2 7.4 229 * COM003-2 22.1 [Brushi, 1991] 230 * COM004-1 45.1 231 * GEO003-1 71.7 T3 [McCharen, et al., 1976]; t3.ver1.in [ANL] 232 * GEO017-2 78.8 D4.1 [Quaife, 1989] 233 * GEO027-3 181.5 D10.1 [Quaife, 1989] 234 * GEO058-2 104.0 R4 [Quaife, 1989] 235 * GEO079-1 2.4 GEOMETRY THEOREM [Slagle, 1967] 236 * GRP001-1 47.8 CADE-11 Competition 1 [Overbeek, 1990]; G1 [McCharen, et al., 1976]; THEOREM 1 [Lusk & McCune, 1993]; wos10 [Wilson & Minker, 1976]; xsquared.ver1.in [ANL]; [Robinson, 1963] 237 * GRP008-1 50.4 Problem 4 [Wos, 1965]; wos4 [Wilson & Minker, 1976] 238 * GRP013-1 40.2 Problem 11 [Wos, 1965]; wos11 [Wilson & Minker, 1976] 239 * GRP037-3 43.8 Problem 17 [Wos, 1965]; wos17 [Wilson & Minker, 1976] 240 * GRP031-2 3.2 ls23 [Lawrence & Starkey, 1974]; ls23 [Wilson & Minker, 1976] 241 * GRP034-4 2.5 ls26 [Lawrence & Starkey, 1974]; ls26 [Wilson & Minker, 1976] 242 * GRP047-2 11.7 [Veroff, 1992] 243 * GRP130-1 170.6 Bennett QG8 [TPTP]; QG8 [Slaney, 1993] 244 * GRP156-1 48.7 ax_mono1c [Schulz, 1995] 245 * GRP168-1 159.1 p01a [Schulz, 1995] 246 * HEN003-3 39.9 HP3 [McCharen, et al., 1976] 247 * HEN007-2 125.7 H7 [McCharen, et al., 1976] 248 * HEN008-4 62.0 H8 [McCharen, et al., 1976] 249 * HEN009-5 136.3 H9 [McCharen, et al., 1976]; hp9.ver3.in [ANL] 250 * HEN012-3 48.5 new.ver2.in [ANL] 251 * LCL010-1 370.9 EC-73 [McCune & Wos, 1992]; ec_yq.in [OTTER] 252 * LCL077-2 51.6 morgan.two.ver1.in [ANL] 253 * LCL082-1 14.6 IC-1.1 [Wos, et al., 1990]; IC-65 [McCune & Wos, 1992]; ls2 [SETHEO]; S1 [Pfenning, 1988] 254 * LCL111-1 585.6 CADE-11 Competition 6 [Overbeek, 1990]; mv25.in [OTTER]; MV-57 [McCune & Wos, 1992]; mv.in part 2 [OTTER]; ovb6 [SETHEO]; THEOREM 6 [Lusk & McCune, 1993] 255 * LCL143-1 10.9 Lattice structure theorem 2 [Bonacina, 1991] 256 * LCL182-1 271.6 Problem 2.16 [Whitehead & Russell, 1927] 257 * LCL200-1 12.0 Problem 2.46 [Whitehead & Russell, 1927] 258 * LCL215-1 214.4 Problem 2.62 [Whitehead & Russell, 1927]; Problem 2.63 [Whitehead & Russell, 1927] 259 * LCL230-2 0.2 Pelletier 5 [Pelletier, 1986] 260 * LDA003-1 68.5 Problem 3 [Jech, 1993] 261 * MSC002-1 9.2 DBABHP [Michie, et al., 1972]; DBABHP [Wilson & Minker, 1976] 262 * MSC003-1 3.2 HASPARTS-T1 [Wilson & Minker, 1976] 263 * MSC004-1 9.3 HASPARTS-T2 [Wilson & Minker, 1976] 264 * MSC005-1 1.8 Problem 5.1 [Plaisted, 1982] 265 * MSC006-1 39.0 nonob.lop [SETHEO] 266 * NUM001-1 14.0 Chang-Lee-10a [Chang, 1970]; ls28 [Lawrence & Starkey, 1974]; ls28 [Wilson & Minker, 1976] 267 * NUM021-1 52.3 ls65 [Lawrence & Starkey, 1974]; ls65 [Wilson & Minker, 1976] 268 * NUM024-1 64.6 ls75 [Lawrence & Starkey, 1974]; ls75 [Wilson & Minker, 1976] 269 * NUM180-1 621.2 LIM2.1 [Quaife] 270 * NUM228-1 575.9 TRECDEF4 cor. [Quaife] 271 * PLA002-1 37.4 Problem 5.7 [Plaisted, 1982] 272 * PLA006-1 7.2 [Segre & Elkan, 1994] 273 * PLA017-1 484.8 [Segre & Elkan, 1994] 274 * PLA022-1 19.1 [Segre & Elkan, 1994] 275 * PLA022-2 19.7 [Segre & Elkan, 1994] 276 * PRV001-1 10.3 PV1 [McCharen, et al., 1976] 277 * PRV003-1 3.9 E2 [McCharen, et al., 1976]; v2.lop [SETHEO] 278 * PRV005-1 4.3 E4 [McCharen, et al., 1976]; v4.lop [SETHEO] 279 * PRV006-1 6.0 E5 [McCharen, et al., 1976]; v5.lop [SETHEO] 280 * PRV009-1 2.2 Hoares FIND [Bledsoe, 1977]; Problem 5.5 [Plaisted, 1982] 281 * PUZ012-1 3.5 Boxes-of-fruit [Wos, 1988]; Boxes-of-fruit [Wos, et al., 1992]; boxes.ver1.in [ANL] 282 * PUZ020-1 56.6 knightknave.in [ANL] 283 * PUZ025-1 58.4 Problem 35 [Smullyan, 1978]; tandl35.ver1.in [ANL] 284 * PUZ029-1 5.1 pigs.ver1.in [ANL] 285 * RNG001-3 82.4 EX6-T? [Wilson & Minker, 1976]; ex6.lop [SETHEO]; Example 6a [Fleisig, et al., 1974]; FEX6T1 [SPRFN]; FEX6T2 [SPRFN] 286 * RNG001-5 399.8 Problem 21 [Wos, 1965]; wos21 [Wilson & Minker, 1976] 287 * RNG011-5 8.4 CADE-11 Competition Eq-10 [Overbeek, 1990]; PROBLEM 10 [Zhang, 1993]; THEOREM EQ-10 [Lusk & McCune, 1993] 288 * RNG023-6 9.1 [Stevens, 1987] 289 * RNG028-2 9.3 PROOF III [Anantharaman & Hsiang, 1990] 290 * RNG038-2 16.2 Problem 27 [Wos, 1965]; wos27 [Wilson & Minker, 1976] 291 * RNG040-2 180.5 Problem 29 [Wos, 1965]; wos29 [Wilson & Minker, 1976] 292 * RNG041-1 35.8 Problem 30 [Wos, 1965]; wos30 [Wilson & Minker, 1976] 293 * ROB010-1 205.0 Lemma 3.3 [Winker, 1990]; RA2 [Lusk & Wos, 1992] 294 * ROB013-1 23.6 Lemma 3.5 [Winker, 1990] 295 * ROB016-1 15.2 Corollary 3.7 [Winker, 1990] 296 * ROB021-1 230.4 [McCune, 1992] 297 * SET005-1 192.2 ls108 [Lawrence & Starkey, 1974]; ls108 [Wilson & Minker, 1976] 298 * SET009-1 10.5 ls116 [Lawrence & Starkey, 1974]; ls116 [Wilson & Minker, 1976] 299 * SET025-4 694.7 Lemma 10 [Boyer, et al, 1986] 300 * SET046-5 2.3 p42.in [ANL]; Pelletier 42 [Pelletier, 1986] 301 * SET047-5 3.7 p43.in [ANL]; Pelletier 43 [Pelletier, 1986] 302 * SYN034-1 2.8 QW [Michie, et al., 1972]; QW [Wilson & Minker, 1976] 303 * SYN071-1 1.9 Pelletier 48 [Pelletier, 1986] 304 * SYN349-1 61.7 Ch17N5 [Tammet, 1994] 305 * SYN352-1 5.5 Ch18N4 [Tammet, 1994] 306 * TOP001-2 61.1 Lemma 1a [Wick & McCune, 1989] 307 * TOP002-2 0.4 Lemma 1b [Wick & McCune, 1989] 308 * TOP004-1 181.6 Lemma 1d [Wick & McCune, 1989] 309 * TOP004-2 9.0 Lemma 1d [Wick & McCune, 1989] 310 * TOP005-2 139.8 Lemma 1e [Wick & McCune, 1989] 311 *) 312 313val BOOL = 314���(!(X:'a). equal(X,X)) /\ 315 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 316 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 317 (!X Y. sum(X,Y,add(X,Y))) /\ 318 (!X Y. product(X,Y,multiply(X,Y))) /\ 319 (!Y X Z. sum(X,Y,Z) ==> sum(Y,X,Z)) /\ 320 (!Y X Z. product(X,Y,Z) ==> product(Y,X,Z)) /\ 321 (!X. sum(additive_identity,X,X)) /\ 322 (!X. sum(X,additive_identity,X)) /\ 323 (!X. product(multiplicative_identity,X,X)) /\ 324 (!X. product(X,multiplicative_identity,X)) /\ 325 (!Y Z X V3 V1 V2 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ product(X,V3,V4) ==> sum(V1,V2,V4)) /\ 326 (!Y Z V1 V2 X V3 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(X,V3,V4)) /\ 327 (!Y Z V3 X V1 V2 V4. product(Y,X,V1) /\ product(Z,X,V2) /\ sum(Y,Z,V3) /\ product(V3,X,V4) ==> sum(V1,V2,V4)) /\ 328 (!Y Z V1 V2 V3 X V4. product(Y,X,V1) /\ product(Z,X,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(V3,X,V4)) /\ 329 (!Y Z X V3 V1 V2 V4. sum(X,Y,V1) /\ sum(X,Z,V2) /\ product(Y,Z,V3) /\ sum(X,V3,V4) ==> product(V1,V2,V4)) /\ 330 (!Y Z V1 V2 X V3 V4. sum(X,Y,V1) /\ sum(X,Z,V2) /\ product(Y,Z,V3) /\ product(V1,V2,V4) ==> sum(X,V3,V4)) /\ 331 (!Y Z V3 X V1 V2 V4. sum(Y,X,V1) /\ sum(Z,X,V2) /\ product(Y,Z,V3) /\ sum(V3,X,V4) ==> product(V1,V2,V4)) /\ 332 (!Y Z V1 V2 V3 X V4. sum(Y,X,V1) /\ sum(Z,X,V2) /\ product(Y,Z,V3) /\ product(V1,V2,V4) ==> sum(V3,X,V4)) /\ 333 (!X. sum(inverse(X),X,multiplicative_identity)) /\ 334 (!X. sum(X,inverse(X),multiplicative_identity)) /\ 335 (!X. product(inverse(X),X,additive_identity)) /\ 336 (!X. product(X,inverse(X),additive_identity)) /\ 337 (!X Y U V. sum(X,Y,U) /\ sum(X,Y,V) ==> equal(U,V)) /\ 338 (!X Y U V. product(X,Y,U) /\ product(X,Y,V) ==> equal(U,V)) /\ 339 (!X Y W Z. equal(X,Y) /\ sum(X,W,Z) ==> sum(Y,W,Z)) /\ 340 (!X W Y Z. equal(X,Y) /\ sum(W,X,Z) ==> sum(W,Y,Z)) /\ 341 (!X W Z Y. equal(X,Y) /\ sum(W,Z,X) ==> sum(W,Z,Y)) /\ 342 (!X Y W Z. equal(X,Y) /\ product(X,W,Z) ==> product(Y,W,Z)) /\ 343 (!X W Y Z. equal(X,Y) /\ product(W,X,Z) ==> product(W,Y,Z)) /\ 344 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 345 (!X Y W. equal(X,Y) ==> equal(add(X,W),add(Y,W))) /\ 346 (!X W Y. equal(X,Y) ==> equal(add(W,X),add(W,Y))) /\ 347 (!X Y W. equal(X,Y) ==> equal(multiply(X,W),multiply(Y,W))) /\ 348 (!X W Y. equal(X,Y) ==> equal(multiply(W,X),multiply(W,Y))) /\ 349 (!X Y. equal(X,Y) ==> equal(inverse(X),inverse(Y)))���;; 350 351 352fun MESON _ thms tm = (tm,mesonLib.MESON_TAC (ASSUME BOOL :: thms) ([], tm)); 353val BOOL_FACTS = true 354 355(* hol90 - yes *) 356val BOO003_1 = MESON [BOOL_FACTS] [] ���product((x:'a),x,x):bool���;; 357 358(* hol90 - yes *) 359val BOO004_1 = MESON [BOOL_FACTS] [] ���sum((x:'a),x,x):bool���;; 360 361(* hol90 - yes *) 362val BOO005_1 = MESON [BOOL_FACTS] [] ���sum((x:'a),(multiplicative_identity:'a),multiplicative_identity):bool���;; 363 364(* hol90 - yes *) 365val BOO006_1 = MESON [BOOL_FACTS] [] ���product((x:'a),(additive_identity:'a),additive_identity):bool���;; 366 367(* hol90 - yes *) 368val BOO011_1 = MESON [BOOL_FACTS] [] ���equal((inverse(additive_identity:'a):'a),(multiplicative_identity:'a)):bool���;; 369 370val CAT001_3 = M "CAT001_3" 371 ���(!X:'a. equal(X,X)) /\ 372 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 373 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 374 (!Y X. equivalent(X,Y) ==> there_exists(X)) /\ 375 (!X Y. equivalent(X,Y) ==> equal(X,Y)) /\ 376 (!X Y. there_exists(X) /\ equal(X,Y) ==> equivalent(X,Y)) /\ 377 (!X. there_exists(domain(X)) ==> there_exists(X)) /\ 378 (!X. there_exists(codomain(X)) ==> there_exists(X)) /\ 379 (!Y X. there_exists(compose(X,Y)) ==> there_exists(domain(X))) /\ 380 (!X Y. there_exists(compose(X,Y)) ==> equal(domain(X),codomain(Y))) /\ 381 (!X Y. there_exists(domain(X)) /\ equal(domain(X),codomain(Y)) ==> there_exists(compose(X,Y))) /\ 382 (!X Y Z. equal(compose(X,compose(Y,Z)),compose(compose(X,Y),Z))) /\ 383 (!X. equal(compose(X,domain(X)),X)) /\ 384 (!X. equal(compose(codomain(X),X),X)) /\ 385 (!X Y. equivalent(X,Y) ==> there_exists(Y)) /\ 386 (!X Y. there_exists(X) /\ there_exists(Y) /\ equal(X,Y) ==> equivalent(X,Y)) /\ 387 (!Y X. there_exists(compose(X,Y)) ==> there_exists(codomain(X))) /\ 388 (!X Y. there_exists(f1(X,Y)) \/ equal(X,Y)) /\ 389 (!X Y. equal(X,f1(X,Y)) \/ equal(Y,f1(X,Y)) \/ equal(X,Y)) /\ 390 (!X Y. equal(X,f1(X,Y)) /\ equal(Y,f1(X,Y)) ==> equal(X,Y)) /\ 391 (!X Y. equal(X,Y) /\ there_exists(X) ==> there_exists(Y)) /\ 392 (!X Y Z. equal(X,Y) /\ equivalent(X,Z) ==> equivalent(Y,Z)) /\ 393 (!X Z Y. equal(X,Y) /\ equivalent(Z,X) ==> equivalent(Z,Y)) /\ 394 (!X Y. equal(X,Y) ==> equal(domain(X),domain(Y))) /\ 395 (!X Y. equal(X,Y) ==> equal(codomain(X),codomain(Y))) /\ 396 (!X Y Z. equal(X,Y) ==> equal(compose(X,Z),compose(Y,Z))) /\ 397 (!X Z Y. equal(X,Y) ==> equal(compose(Z,X),compose(Z,Y))) /\ 398 (!A B C. equal(A,B) ==> equal(f1(A,C),f1(B,C))) /\ 399 (!D F' E. equal(D,E) ==> equal(f1(F',D),f1(F',E))) /\ 400 (there_exists(compose(a,b))) /\ 401 (!Y X Z. equal(compose(compose(a,b),X),Y) /\ equal(compose(compose(a,b),Z),Y) ==> equal(X,Z)) /\ 402 (there_exists(compose(b,h))) /\ 403 (equal(compose(b,h),compose(b,g))) /\ 404 (~equal(h,g)) ==> F���; 405 406 407val CAT003_3 = M "CAT003_3" 408 ���(!X:'a. equal(X,X)) /\ 409 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 410 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 411 (!Y X. equivalent(X,Y) ==> there_exists(X)) /\ 412 (!X Y. equivalent(X,Y) ==> equal(X,Y)) /\ 413 (!X Y. there_exists(X) /\ equal(X,Y) ==> equivalent(X,Y)) /\ 414 (!X. there_exists(domain(X)) ==> there_exists(X)) /\ 415 (!X. there_exists(codomain(X)) ==> there_exists(X)) /\ 416 (!Y X. there_exists(compose(X,Y)) ==> there_exists(domain(X))) /\ 417 (!X Y. there_exists(compose(X,Y)) ==> equal(domain(X),codomain(Y))) /\ 418 (!X Y. there_exists(domain(X)) /\ equal(domain(X),codomain(Y)) ==> there_exists(compose(X,Y))) /\ 419 (!X Y Z. equal(compose(X,compose(Y,Z)),compose(compose(X,Y),Z))) /\ 420 (!X. equal(compose(X,domain(X)),X)) /\ 421 (!X. equal(compose(codomain(X),X),X)) /\ 422 (!X Y. equivalent(X,Y) ==> there_exists(Y)) /\ 423 (!X Y. there_exists(X) /\ there_exists(Y) /\ equal(X,Y) ==> equivalent(X,Y)) /\ 424 (!Y X. there_exists(compose(X,Y)) ==> there_exists(codomain(X))) /\ 425 (!X Y. there_exists(f1(X,Y)) \/ equal(X,Y)) /\ 426 (!X Y. equal(X,f1(X,Y)) \/ equal(Y,f1(X,Y)) \/ equal(X,Y)) /\ 427 (!X Y. equal(X,f1(X,Y)) /\ equal(Y,f1(X,Y)) ==> equal(X,Y)) /\ 428 (!X Y. equal(X,Y) /\ there_exists(X) ==> there_exists(Y)) /\ 429 (!X Y Z. equal(X,Y) /\ equivalent(X,Z) ==> equivalent(Y,Z)) /\ 430 (!X Z Y. equal(X,Y) /\ equivalent(Z,X) ==> equivalent(Z,Y)) /\ 431 (!X Y. equal(X,Y) ==> equal(domain(X),domain(Y))) /\ 432 (!X Y. equal(X,Y) ==> equal(codomain(X),codomain(Y))) /\ 433 (!X Y Z. equal(X,Y) ==> equal(compose(X,Z),compose(Y,Z))) /\ 434 (!X Z Y. equal(X,Y) ==> equal(compose(Z,X),compose(Z,Y))) /\ 435 (!A B C. equal(A,B) ==> equal(f1(A,C),f1(B,C))) /\ 436 (!D F' E. equal(D,E) ==> equal(f1(F',D),f1(F',E))) /\ 437 (there_exists(compose(a,b))) /\ 438 (!Y X Z. equal(compose(X,compose(a,b)),Y) /\ equal(compose(Z,compose(a,b)),Y) ==> equal(X,Z)) /\ 439 (there_exists(h)) /\ 440 (equal(compose(h,a),compose(g,a))) /\ 441 (~equal(g,h)) ==> F���; 442 443 444val CAT005_1 = M "CAT005_1" 445 ���(!X:'a. equal(X,X)) /\ 446 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 447 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 448 (!X Y. defined(X,Y) ==> product(X,Y,compose(X,Y))) /\ 449 (!Z X Y. product(X,Y,Z) ==> defined(X,Y)) /\ 450 (!X Xy Y Z. product(X,Y,Xy) /\ defined(Xy,Z) ==> defined(Y,Z)) /\ 451 (!Y Xy Z X Yz. product(X,Y,Xy) /\ product(Y,Z,Yz) /\ defined(Xy,Z) ==> defined(X,Yz)) /\ 452 (!Xy Y Z X Yz Xyz. product(X,Y,Xy) /\ product(Xy,Z,Xyz) /\ product(Y,Z,Yz) ==> product(X,Yz,Xyz)) /\ 453 (!Z Yz X Y. product(Y,Z,Yz) /\ defined(X,Yz) ==> defined(X,Y)) /\ 454 (!Y X Yz Xy Z. product(Y,Z,Yz) /\ product(X,Y,Xy) /\ defined(X,Yz) ==> defined(Xy,Z)) /\ 455 (!Yz X Y Xy Z Xyz. product(Y,Z,Yz) /\ product(X,Yz,Xyz) /\ product(X,Y,Xy) ==> product(Xy,Z,Xyz)) /\ 456 (!Y X Z. defined(X,Y) /\ defined(Y,Z) /\ identity_map(Y) ==> defined(X,Z)) /\ 457 (!X. identity_map(domain(X))) /\ 458 (!X. identity_map(codomain(X))) /\ 459 (!X. defined(X,domain(X))) /\ 460 (!X. defined(codomain(X),X)) /\ 461 (!X. product(X,domain(X),X)) /\ 462 (!X. product(codomain(X),X,X)) /\ 463 (!X Y. defined(X,Y) /\ identity_map(X) ==> product(X,Y,Y)) /\ 464 (!Y X. defined(X,Y) /\ identity_map(Y) ==> product(X,Y,X)) /\ 465 (!X Y Z W. product(X,Y,Z) /\ product(X,Y,W) ==> equal(Z,W)) /\ 466 (!X Y Z W. equal(X,Y) /\ product(X,Z,W) ==> product(Y,Z,W)) /\ 467 (!X Z Y W. equal(X,Y) /\ product(Z,X,W) ==> product(Z,Y,W)) /\ 468 (!X Z W Y. equal(X,Y) /\ product(Z,W,X) ==> product(Z,W,Y)) /\ 469 (!X Y. equal(X,Y) ==> equal(domain(X),domain(Y))) /\ 470 (!X Y. equal(X,Y) ==> equal(codomain(X),codomain(Y))) /\ 471 (!X Y. equal(X,Y) /\ identity_map(X) ==> identity_map(Y)) /\ 472 (!X Y Z. equal(X,Y) /\ defined(X,Z) ==> defined(Y,Z)) /\ 473 (!X Z Y. equal(X,Y) /\ defined(Z,X) ==> defined(Z,Y)) /\ 474 (!X Z Y. equal(X,Y) ==> equal(compose(Z,X),compose(Z,Y))) /\ 475 (!X Y Z. equal(X,Y) ==> equal(compose(X,Z),compose(Y,Z))) /\ 476 (defined(a,d)) /\ 477 (identity_map(d)) /\ 478 (~equal(domain(a),d)) ==> F���; 479 480 481val CAT007_1 = M "CAT007_1" 482 ���(!X:'a. equal(X,X)) /\ 483 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 484 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 485 (!X Y. defined(X,Y) ==> product(X,Y,compose(X,Y))) /\ 486 (!Z X Y. product(X,Y,Z) ==> defined(X,Y)) /\ 487 (!X Xy Y Z. product(X,Y,Xy) /\ defined(Xy,Z) ==> defined(Y,Z)) /\ 488 (!Y Xy Z X Yz. product(X,Y,Xy) /\ product(Y,Z,Yz) /\ defined(Xy,Z) ==> defined(X,Yz)) /\ 489 (!Xy Y Z X Yz Xyz. product(X,Y,Xy) /\ product(Xy,Z,Xyz) /\ product(Y,Z,Yz) ==> product(X,Yz,Xyz)) /\ 490 (!Z Yz X Y. product(Y,Z,Yz) /\ defined(X,Yz) ==> defined(X,Y)) /\ 491 (!Y X Yz Xy Z. product(Y,Z,Yz) /\ product(X,Y,Xy) /\ defined(X,Yz) ==> defined(Xy,Z)) /\ 492 (!Yz X Y Xy Z Xyz. product(Y,Z,Yz) /\ product(X,Yz,Xyz) /\ product(X,Y,Xy) ==> product(Xy,Z,Xyz)) /\ 493 (!Y X Z. defined(X,Y) /\ defined(Y,Z) /\ identity_map(Y) ==> defined(X,Z)) /\ 494 (!X. identity_map(domain(X))) /\ 495 (!X. identity_map(codomain(X))) /\ 496 (!X. defined(X,domain(X))) /\ 497 (!X. defined(codomain(X),X)) /\ 498 (!X. product(X,domain(X),X)) /\ 499 (!X. product(codomain(X),X,X)) /\ 500 (!X Y. defined(X,Y) /\ identity_map(X) ==> product(X,Y,Y)) /\ 501 (!Y X. defined(X,Y) /\ identity_map(Y) ==> product(X,Y,X)) /\ 502 (!X Y Z W. product(X,Y,Z) /\ product(X,Y,W) ==> equal(Z,W)) /\ 503 (!X Y Z W. equal(X,Y) /\ product(X,Z,W) ==> product(Y,Z,W)) /\ 504 (!X Z Y W. equal(X,Y) /\ product(Z,X,W) ==> product(Z,Y,W)) /\ 505 (!X Z W Y. equal(X,Y) /\ product(Z,W,X) ==> product(Z,W,Y)) /\ 506 (!X Y. equal(X,Y) ==> equal(domain(X),domain(Y))) /\ 507 (!X Y. equal(X,Y) ==> equal(codomain(X),codomain(Y))) /\ 508 (!X Y. equal(X,Y) /\ identity_map(X) ==> identity_map(Y)) /\ 509 (!X Y Z. equal(X,Y) /\ defined(X,Z) ==> defined(Y,Z)) /\ 510 (!X Z Y. equal(X,Y) /\ defined(Z,X) ==> defined(Z,Y)) /\ 511 (!X Z Y. equal(X,Y) ==> equal(compose(Z,X),compose(Z,Y))) /\ 512 (!X Y Z. equal(X,Y) ==> equal(compose(X,Z),compose(Y,Z))) /\ 513 (equal(domain(a),codomain(b))) /\ 514 (~defined(a,b)) ==> F���; 515 516 517val CAT018_1 = M "CAT018_1" 518 ���(!X:'a. equal(X,X)) /\ 519 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 520 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 521 (!X Y. defined(X,Y) ==> product(X,Y,compose(X,Y))) /\ 522 (!Z X Y. product(X,Y,Z) ==> defined(X,Y)) /\ 523 (!X Xy Y Z. product(X,Y,Xy) /\ defined(Xy,Z) ==> defined(Y,Z)) /\ 524 (!Y Xy Z X Yz. product(X,Y,Xy) /\ product(Y,Z,Yz) /\ defined(Xy,Z) ==> defined(X,Yz)) /\ 525 (!Xy Y Z X Yz Xyz. product(X,Y,Xy) /\ product(Xy,Z,Xyz) /\ product(Y,Z,Yz) ==> product(X,Yz,Xyz)) /\ 526 (!Z Yz X Y. product(Y,Z,Yz) /\ defined(X,Yz) ==> defined(X,Y)) /\ 527 (!Y X Yz Xy Z. product(Y,Z,Yz) /\ product(X,Y,Xy) /\ defined(X,Yz) ==> defined(Xy,Z)) /\ 528 (!Yz X Y Xy Z Xyz. product(Y,Z,Yz) /\ product(X,Yz,Xyz) /\ product(X,Y,Xy) ==> product(Xy,Z,Xyz)) /\ 529 (!Y X Z. defined(X,Y) /\ defined(Y,Z) /\ identity_map(Y) ==> defined(X,Z)) /\ 530 (!X. identity_map(domain(X))) /\ 531 (!X. identity_map(codomain(X))) /\ 532 (!X. defined(X,domain(X))) /\ 533 (!X. defined(codomain(X),X)) /\ 534 (!X. product(X,domain(X),X)) /\ 535 (!X. product(codomain(X),X,X)) /\ 536 (!X Y. defined(X,Y) /\ identity_map(X) ==> product(X,Y,Y)) /\ 537 (!Y X. defined(X,Y) /\ identity_map(Y) ==> product(X,Y,X)) /\ 538 (!X Y Z W. product(X,Y,Z) /\ product(X,Y,W) ==> equal(Z,W)) /\ 539 (!X Y Z W. equal(X,Y) /\ product(X,Z,W) ==> product(Y,Z,W)) /\ 540 (!X Z Y W. equal(X,Y) /\ product(Z,X,W) ==> product(Z,Y,W)) /\ 541 (!X Z W Y. equal(X,Y) /\ product(Z,W,X) ==> product(Z,W,Y)) /\ 542 (!X Y. equal(X,Y) ==> equal(domain(X),domain(Y))) /\ 543 (!X Y. equal(X,Y) ==> equal(codomain(X),codomain(Y))) /\ 544 (!X Y. equal(X,Y) /\ identity_map(X) ==> identity_map(Y)) /\ 545 (!X Y Z. equal(X,Y) /\ defined(X,Z) ==> defined(Y,Z)) /\ 546 (!X Z Y. equal(X,Y) /\ defined(Z,X) ==> defined(Z,Y)) /\ 547 (!X Z Y. equal(X,Y) ==> equal(compose(Z,X),compose(Z,Y))) /\ 548 (!X Y Z. equal(X,Y) ==> equal(compose(X,Z),compose(Y,Z))) /\ 549 (defined(a,b)) /\ 550 (defined(b,c)) /\ 551 (~defined(a,compose(b,c))) ==> F���; 552 553 554val COL001_2 = M "COL001_2" 555 ���(!X:'a. equal(X,X)) /\ 556 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 557 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 558 (!X Y Z. equal(apply(apply(apply(s,X),Y),Z),apply(apply(X,Z),apply(Y,Z)))) /\ 559 (!Y X. equal(apply(apply(k,X),Y),X)) /\ 560 (!X Y Z. equal(apply(apply(apply(b,X),Y),Z),apply(X,apply(Y,Z)))) /\ 561 (!X. equal(apply(i,X),X)) /\ 562 (!A B C. equal(A,B) ==> equal(apply(A,C),apply(B,C))) /\ 563 (!D F' E. equal(D,E) ==> equal(apply(F',D),apply(F',E))) /\ 564 (!X. equal(apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)),apply(x,apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))))) /\ 565 (!Y. ~equal(Y,apply(combinator,Y))) ==> F���; 566 567 568val COL023_1 = M "COL023_1" 569 ���(!X:'a. equal(X,X)) /\ 570 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 571 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 572 (!X Y Z. equal(apply(apply(apply(b,X),Y),Z),apply(X,apply(Y,Z)))) /\ 573 (!X Y Z. equal(apply(apply(apply(n,X),Y),Z),apply(apply(apply(X,Z),Y),Z))) /\ 574 (!A B C. equal(A,B) ==> equal(apply(A,C),apply(B,C))) /\ 575 (!D F' E. equal(D,E) ==> equal(apply(F',D),apply(F',E))) /\ 576 (!Y. ~equal(Y,apply(combinator,Y))) ==> F���; 577 578 579val COL032_1 = M "COL032_1" 580 ���(!X:'a. equal(X,X)) /\ 581 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 582 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 583 (!X. equal(apply(m,X),apply(X,X))) /\ 584 (!Y X Z. equal(apply(apply(apply(q,X),Y),Z),apply(Y,apply(X,Z)))) /\ 585 (!A B C. equal(A,B) ==> equal(apply(A,C),apply(B,C))) /\ 586 (!D F' E. equal(D,E) ==> equal(apply(F',D),apply(F',E))) /\ 587 (!G H. equal(G,H) ==> equal(f(G),f(H))) /\ 588 (!Y. ~equal(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y))))) ==> F���; 589 590 591val COL052_2 = 592 ���(!X:'a. equal(X,X)) /\ 593 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 594 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 595 (!X Y W. equal(response(compose(X,Y),W),response(X,response(Y,W)))) /\ 596 (!X Y. agreeable(X) ==> equal(response(X,common_bird(Y)),response(Y,common_bird(Y)))) /\ 597 (!Z X. equal(response(X,Z),response(compatible(X),Z)) ==> agreeable(X)) /\ 598 (!A B. equal(A,B) ==> equal(common_bird(A),common_bird(B))) /\ 599 (!C D. equal(C,D) ==> equal(compatible(C),compatible(D))) /\ 600 (!Q R. equal(Q,R) /\ agreeable(Q) ==> agreeable(R)) /\ 601 (!A B C. equal(A,B) ==> equal(compose(A,C),compose(B,C))) /\ 602 (!D F' E. equal(D,E) ==> equal(compose(F',D),compose(F',E))) /\ 603 (!G H I'. equal(G,H) ==> equal(response(G,I'),response(H,I'))) /\ 604 (!J L K'. equal(J,K') ==> equal(response(L,J),response(L,K'))) /\ 605 (agreeable(c)) /\ 606 (~agreeable(a)) /\ 607 (equal(c,compose(a,b))) ==> F���; 608 609 610val COL075_2 = 611 ���(!X:'a. equal(X,X)) /\ 612 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 613 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 614 (!Y X. equal(apply(apply(k,X),Y),X)) /\ 615 (!X Y Z. equal(apply(apply(apply(abstraction,X),Y),Z),apply(apply(X,apply(k,Z)),apply(Y,Z)))) /\ 616 (!D E F'. equal(D,E) ==> equal(apply(D,F'),apply(E,F'))) /\ 617 (!G I' H. equal(G,H) ==> equal(apply(I',G),apply(I',H))) /\ 618 (!A B. equal(A,B) ==> equal(b(A),b(B))) /\ 619 (!C D. equal(C,D) ==> equal(c(C),c(D))) /\ 620 (!Y. ~equal(apply(apply(Y,b(Y)),c(Y)),apply(b(Y),b(Y)))) ==> F���; 621 622 623val COM001_1 = 624Lib.with_flag(Globals.guessing_tyvars,true) 625 Term 626`(!Goal_state Start_state. 627 follows(Goal_state,Start_state) 628 ==> succeeds(Goal_state,Start_state)) /\ 629 (!Goal_state Intermediate_state Start_state. 630 succeeds(Goal_state,Intermediate_state) /\ 631 succeeds(Intermediate_state,Start_state) 632 ==> succeeds(Goal_state,Start_state)) /\ 633 (!Start_state Label Goal_state. 634 has(Start_state,goto(Label)) /\ labels(Label,Goal_state) 635 ==> succeeds(Goal_state,Start_state)) /\ 636 (!Start_state Condition Goal_state. 637 has(Start_state,ifthen(Condition,Goal_state)) 638 ==> succeeds(Goal_state,Start_state)) /\ 639 (labels(loop,p3)) /\ 640 (has(p3,ifthen(equal(register_j,n),p4))) /\ 641 (has(p4,goto(out))) /\ 642 (follows(p5,p4)) /\ 643 (follows(p8,p3)) /\ 644 (has(p8,goto(loop))) /\ 645 (~succeeds(p3,p3)) ==> F`; 646 647val COM002_1 = M "COM002_1" $ 648Lib.with_flag(Globals.guessing_tyvars,true) 649 Term 650`(!Goal_state Start_state. follows(Goal_state,Start_state) ==> succeeds(Goal_state,Start_state)) /\ 651 (!Goal_state Intermediate_state Start_state. succeeds(Goal_state,Intermediate_state) /\ succeeds(Intermediate_state,Start_state) ==> succeeds(Goal_state,Start_state)) /\ 652 (!Start_state Label Goal_state. has(Start_state,goto(Label)) /\ labels(Label,Goal_state) ==> succeeds(Goal_state,Start_state)) /\ 653 (!Start_state Condition Goal_state. has(Start_state,ifthen(Condition,Goal_state)) ==> succeeds(Goal_state,Start_state)) /\ 654 (has(p1,assign(register_j,n0))) /\ 655 (follows(p2,p1)) /\ 656 (has(p2,assign(register_k,n1))) /\ 657 (labels(loop,p3)) /\ 658 (follows(p3,p2)) /\ 659 (has(p3,ifthen(equal(register_j,n),p4))) /\ 660 (has(p4,goto(out))) /\ 661 (follows(p5,p4)) /\ 662 (follows(p6,p3)) /\ 663 (has(p6,assign(register_k,times(n2,register_k)))) /\ 664 (follows(p7,p6)) /\ 665 (has(p7,assign(register_j,plus(register_j,n1)))) /\ 666 (follows(p8,p7)) /\ 667 (has(p8,goto(loop))) /\ 668 (~succeeds(p3,p3)) ==> F`; 669 670 671val COM002_2 = M "COM002_2" $ 672Lib.with_flag(Globals.guessing_tyvars,true) 673 Term 674`(!Goal_state Start_state. ~(fails(Goal_state,Start_state) /\ follows(Goal_state,Start_state))) /\ 675 (!Goal_state Intermediate_state Start_state. fails(Goal_state,Start_state) ==> fails(Goal_state,Intermediate_state) \/ fails(Intermediate_state,Start_state)) /\ 676 (!Start_state Label Goal_state. ~(fails(Goal_state,Start_state) /\ has(Start_state,goto(Label)) /\ labels(Label,Goal_state))) /\ 677 (!Start_state Condition Goal_state. ~(fails(Goal_state,Start_state) /\ has(Start_state,ifthen(Condition,Goal_state)))) /\ 678 (has(p1,assign(register_j,n0))) /\ 679 (follows(p2,p1)) /\ 680 (has(p2,assign(register_k,n1))) /\ 681 (labels(loop,p3)) /\ 682 (follows(p3,p2)) /\ 683 (has(p3,ifthen(equal(register_j,n),p4))) /\ 684 (has(p4,goto(out))) /\ 685 (follows(p5,p4)) /\ 686 (follows(p6,p3)) /\ 687 (has(p6,assign(register_k,times(n2,register_k)))) /\ 688 (follows(p7,p6)) /\ 689 (has(p7,assign(register_j,plus(register_j,n1)))) /\ 690 (follows(p8,p7)) /\ 691 (has(p8,goto(loop))) /\ 692 (fails(p3,p3)) ==> F`; 693 694 695val COM003_2 = M "COM003_2" $ 696Lib.with_flag(Globals.guessing_tyvars,true) 697 Term 698`(!X Y Z. program_decides(X) /\ program(Y) ==> decides(X,Y,Z)) /\ 699 (!X. program_decides(X) \/ program(f2(X))) /\ 700 (!X. decides(X,f2(X),f1(X)) ==> program_decides(X)) /\ 701 (!X. program_program_decides(X) ==> program(X)) /\ 702 (!X. program_program_decides(X) ==> program_decides(X)) /\ 703 (!X. program(X) /\ program_decides(X) ==> program_program_decides(X)) /\ 704 (!X. algorithm_program_decides(X) ==> algorithm(X)) /\ 705 (!X. algorithm_program_decides(X) ==> program_decides(X)) /\ 706 (!X. algorithm(X) /\ program_decides(X) ==> algorithm_program_decides(X)) /\ 707 (!Y X. program_halts2(X,Y) ==> program(X)) /\ 708 (!X Y. program_halts2(X,Y) ==> halts2(X,Y)) /\ 709 (!X Y. program(X) /\ halts2(X,Y) ==> program_halts2(X,Y)) /\ 710 (!W X Y Z. halts3_outputs(X,Y,Z,W) ==> halts3(X,Y,Z)) /\ 711 (!Y Z X W. halts3_outputs(X,Y,Z,W) ==> outputs(X,W)) /\ 712 (!Y Z X W. halts3(X,Y,Z) /\ outputs(X,W) ==> halts3_outputs(X,Y,Z,W)) /\ 713 (!Y X. program_not_halts2(X,Y) ==> program(X)) /\ 714 (!X Y. ~(program_not_halts2(X,Y) /\ halts2(X,Y))) /\ 715 (!X Y. program(X) ==> program_not_halts2(X,Y) \/ halts2(X,Y)) /\ 716 (!W X Y. halts2_outputs(X,Y,W) ==> halts2(X,Y)) /\ 717 (!Y X W. halts2_outputs(X,Y,W) ==> outputs(X,W)) /\ 718 (!Y X W. halts2(X,Y) /\ outputs(X,W) ==> halts2_outputs(X,Y,W)) /\ 719 (!X W Y Z. program_halts2_halts3_outputs(X,Y,Z,W) ==> program_halts2(Y,Z)) /\ 720 (!X Y Z W. program_halts2_halts3_outputs(X,Y,Z,W) ==> halts3_outputs(X,Y,Z,W)) /\ 721 (!X Y Z W. program_halts2(Y,Z) /\ halts3_outputs(X,Y,Z,W) ==> program_halts2_halts3_outputs(X,Y,Z,W)) /\ 722 (!X W Y Z. program_not_halts2_halts3_outputs(X,Y,Z,W) ==> program_not_halts2(Y,Z)) /\ 723 (!X Y Z W. program_not_halts2_halts3_outputs(X,Y,Z,W) ==> halts3_outputs(X,Y,Z,W)) /\ 724 (!X Y Z W. program_not_halts2(Y,Z) /\ halts3_outputs(X,Y,Z,W) ==> program_not_halts2_halts3_outputs(X,Y,Z,W)) /\ 725 (!X W Y. program_halts2_halts2_outputs(X,Y,W) ==> program_halts2(Y,Y)) /\ 726 (!X Y W. program_halts2_halts2_outputs(X,Y,W) ==> halts2_outputs(X,Y,W)) /\ 727 (!X Y W. program_halts2(Y,Y) /\ halts2_outputs(X,Y,W) ==> program_halts2_halts2_outputs(X,Y,W)) /\ 728 (!X W Y. program_not_halts2_halts2_outputs(X,Y,W) ==> program_not_halts2(Y,Y)) /\ 729 (!X Y W. program_not_halts2_halts2_outputs(X,Y,W) ==> halts2_outputs(X,Y,W)) /\ 730 (!X Y W. program_not_halts2(Y,Y) /\ halts2_outputs(X,Y,W) ==> program_not_halts2_halts2_outputs(X,Y,W)) /\ 731 (!X. algorithm_program_decides(X) ==> program_program_decides(c1)) /\ 732 (!W Y Z. program_program_decides(W) ==> program_halts2_halts3_outputs(W,Y,Z,good)) /\ 733 (!W Y Z. program_program_decides(W) ==> program_not_halts2_halts3_outputs(W,Y,Z,bad)) /\ 734 (!W. program(W) /\ program_halts2_halts3_outputs(W,f3(W),f3(W),good) /\ program_not_halts2_halts3_outputs(W,f3(W),f3(W),bad) ==> program(c2)) /\ 735 (!W Y. program(W) /\ program_halts2_halts3_outputs(W,f3(W),f3(W),good) /\ program_not_halts2_halts3_outputs(W,f3(W),f3(W),bad) ==> program_halts2_halts2_outputs(c2,Y,good)) /\ 736 (!W Y. program(W) /\ program_halts2_halts3_outputs(W,f3(W),f3(W),good) /\ program_not_halts2_halts3_outputs(W,f3(W),f3(W),bad) ==> program_not_halts2_halts2_outputs(c2,Y,bad)) /\ 737 (!V. program(V) /\ program_halts2_halts2_outputs(V,f4(V),good) /\ program_not_halts2_halts2_outputs(V,f4(V),bad) ==> program(c3)) /\ 738 (!V Y. program(V) /\ program_halts2_halts2_outputs(V,f4(V),good) /\ program_not_halts2_halts2_outputs(V,f4(V),bad) /\ program_halts2(Y,Y) ==> halts2(c3,Y)) /\ 739 (!V Y. program(V) /\ program_halts2_halts2_outputs(V,f4(V),good) /\ program_not_halts2_halts2_outputs(V,f4(V),bad) ==> program_not_halts2_halts2_outputs(c3,Y,bad)) /\ 740 (algorithm_program_decides(c4)) ==> F`; 741 742 743val COM004_1 = M "COM004_1" $ 744Lib.with_flag(Globals.guessing_tyvars,true) 745 Term 746`(!X. equal(X,X)) /\ 747 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 748 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 749 (!C D P Q X Y. failure_node(X,or(C,P)) /\ failure_node(Y,or(D,Q)) /\ contradictory(P,Q) /\ siblings(X,Y) ==> failure_node(parent_of(X,Y),or(C,D))) /\ 750 (!X. contradictory(negate(X),X)) /\ 751 (!X. contradictory(X,negate(X))) /\ 752 (!X. siblings(left_child_of(X),right_child_of(X))) /\ 753 (!D E. equal(D,E) ==> equal(left_child_of(D),left_child_of(E))) /\ 754 (!F' G. equal(F',G) ==> equal(negate(F'),negate(G))) /\ 755 (!H I' J. equal(H,I') ==> equal(or(H,J),or(I',J))) /\ 756 (!K' M L. equal(K',L) ==> equal(or(M,K'),or(M,L))) /\ 757 (!N O P. equal(N,O) ==> equal(parent_of(N,P),parent_of(O,P))) /\ 758 (!Q S' R. equal(Q,R) ==> equal(parent_of(S',Q),parent_of(S',R))) /\ 759 (!T' U. equal(T',U) ==> equal(right_child_of(T'),right_child_of(U))) /\ 760 (!V W X. equal(V,W) /\ contradictory(V,X) ==> contradictory(W,X)) /\ 761 (!Y A1 Z. equal(Y,Z) /\ contradictory(A1,Y) ==> contradictory(A1,Z)) /\ 762 (!B1 C1 D1. equal(B1,C1) /\ failure_node(B1,D1) ==> failure_node(C1,D1)) /\ 763 (!E1 G1 F1. equal(E1,F1) /\ failure_node(G1,E1) ==> failure_node(G1,F1)) /\ 764 (!H1 I1 J1. equal(H1,I1) /\ siblings(H1,J1) ==> siblings(I1,J1)) /\ 765 (!K1 M1 L1. equal(K1,L1) /\ siblings(M1,K1) ==> siblings(M1,L1)) /\ 766 (failure_node(n_left,or(empty,atom))) /\ 767 (failure_node(n_right,or(empty,negate(atom)))) /\ 768 (equal(n_left,left_child_of(n))) /\ 769 (equal(n_right,right_child_of(n))) /\ 770 (!Z. ~failure_node(Z,or(empty,empty))) ==> F`; 771 772 773val GEO003_1 = M "GEO003_1" 774 ���(!X:'a. equal(X,X)) /\ 775 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 776 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 777 (!X Y. between(X,Y,X) ==> equal(X,Y)) /\ 778 (!V X Y Z. between(X,Y,V) /\ between(Y,Z,V) ==> between(X,Y,Z)) /\ 779 (!Y X V Z. between(X,Y,Z) /\ between(X,Y,V) ==> equal(X,Y) \/ between(X,Z,V) \/ between(X,V,Z)) /\ 780 (!Y X. equidistant(X,Y,Y,X)) /\ 781 (!Z X Y. equidistant(X,Y,Z,Z) ==> equal(X,Y)) /\ 782 (!X Y Z V V2 W. equidistant(X,Y,Z,V) /\ equidistant(X,Y,V2,W) ==> equidistant(Z,V,V2,W)) /\ 783 (!W X Z V Y. between(X,W,V) /\ between(Y,V,Z) ==> between(X,outer_pasch(W,X,Y,Z,V),Y)) /\ 784 (!W X Y Z V. between(X,W,V) /\ between(Y,V,Z) ==> between(Z,W,outer_pasch(W,X,Y,Z,V))) /\ 785 (!W X Y Z V. between(X,V,W) /\ between(Y,V,Z) ==> equal(X,V) \/ between(X,Z,euclid1(W,X,Y,Z,V))) /\ 786 (!W X Y Z V. between(X,V,W) /\ between(Y,V,Z) ==> equal(X,V) \/ between(X,Y,euclid2(W,X,Y,Z,V))) /\ 787 (!W X Y Z V. between(X,V,W) /\ between(Y,V,Z) ==> equal(X,V) \/ between(euclid1(W,X,Y,Z,V),W,euclid2(W,X,Y,Z,V))) /\ 788 (!X1 Y1 X Y Z V Z1 V1. equidistant(X,Y,X1,Y1) /\ equidistant(Y,Z,Y1,Z1) /\ equidistant(X,V,X1,V1) /\ equidistant(Y,V,Y1,V1) /\ between(X,Y,Z) /\ between(X1,Y1,Z1) ==> equal(X,Y) \/ equidistant(Z,V,Z1,V1)) /\ 789 (!X Y W V. between(X,Y,extension(X,Y,W,V))) /\ 790 (!X Y W V. equidistant(Y,extension(X,Y,W,V),W,V)) /\ 791 (~between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)) /\ 792 (~between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)) /\ 793 (~between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)) /\ 794 (!Z X Y W V. equidistant(X,W,X,V) /\ equidistant(Y,W,Y,V) /\ equidistant(Z,W,Z,V) ==> between(X,Y,Z) \/ between(Y,Z,X) \/ between(Z,X,Y) \/ equal(W,V)) /\ 795 (!X Y Z X1 Z1 V. equidistant(V,X,V,X1) /\ equidistant(V,Z,V,Z1) /\ between(V,X,Z) /\ between(X,Y,Z) ==> equidistant(V,Y,Z,continuous(X,Y,Z,X1,Z1,V))) /\ 796 (!X Y Z X1 V Z1. equidistant(V,X,V,X1) /\ equidistant(V,Z,V,Z1) /\ between(V,X,Z) /\ between(X,Y,Z) ==> between(X1,continuous(X,Y,Z,X1,Z1,V),Z1)) /\ 797 (!X Y W Z. equal(X,Y) /\ between(X,W,Z) ==> between(Y,W,Z)) /\ 798 (!X W Y Z. equal(X,Y) /\ between(W,X,Z) ==> between(W,Y,Z)) /\ 799 (!X W Z Y. equal(X,Y) /\ between(W,Z,X) ==> between(W,Z,Y)) /\ 800 (!X Y V W Z. equal(X,Y) /\ equidistant(X,V,W,Z) ==> equidistant(Y,V,W,Z)) /\ 801 (!X V Y W Z. equal(X,Y) /\ equidistant(V,X,W,Z) ==> equidistant(V,Y,W,Z)) /\ 802 (!X V W Y Z. equal(X,Y) /\ equidistant(V,W,X,Z) ==> equidistant(V,W,Y,Z)) /\ 803 (!X V W Z Y. equal(X,Y) /\ equidistant(V,W,Z,X) ==> equidistant(V,W,Z,Y)) /\ 804 (!X Y V1 V2 V3 V4. equal(X,Y) ==> equal(outer_pasch(X,V1,V2,V3,V4),outer_pasch(Y,V1,V2,V3,V4))) /\ 805 (!X V1 Y V2 V3 V4. equal(X,Y) ==> equal(outer_pasch(V1,X,V2,V3,V4),outer_pasch(V1,Y,V2,V3,V4))) /\ 806 (!X V1 V2 Y V3 V4. equal(X,Y) ==> equal(outer_pasch(V1,V2,X,V3,V4),outer_pasch(V1,V2,Y,V3,V4))) /\ 807 (!X V1 V2 V3 Y V4. equal(X,Y) ==> equal(outer_pasch(V1,V2,V3,X,V4),outer_pasch(V1,V2,V3,Y,V4))) /\ 808 (!X V1 V2 V3 V4 Y. equal(X,Y) ==> equal(outer_pasch(V1,V2,V3,V4,X),outer_pasch(V1,V2,V3,V4,Y))) /\ 809 (!A B C D E F'. equal(A,B) ==> equal(euclid1(A,C,D,E,F'),euclid1(B,C,D,E,F'))) /\ 810 (!G I' H J K' L. equal(G,H) ==> equal(euclid1(I',G,J,K',L),euclid1(I',H,J,K',L))) /\ 811 (!M O P N Q R. equal(M,N) ==> equal(euclid1(O,P,M,Q,R),euclid1(O,P,N,Q,R))) /\ 812 (!S' U V W T' X. equal(S',T') ==> equal(euclid1(U,V,W,S',X),euclid1(U,V,W,T',X))) /\ 813 (!Y A1 B1 C1 D1 Z. equal(Y,Z) ==> equal(euclid1(A1,B1,C1,D1,Y),euclid1(A1,B1,C1,D1,Z))) /\ 814 (!E1 F1 G1 H1 I1 J1. equal(E1,F1) ==> equal(euclid2(E1,G1,H1,I1,J1),euclid2(F1,G1,H1,I1,J1))) /\ 815 (!K1 M1 L1 N1 O1 P1. equal(K1,L1) ==> equal(euclid2(M1,K1,N1,O1,P1),euclid2(M1,L1,N1,O1,P1))) /\ 816 (!Q1 S1 T1 R1 U1 V1. equal(Q1,R1) ==> equal(euclid2(S1,T1,Q1,U1,V1),euclid2(S1,T1,R1,U1,V1))) /\ 817 (!W1 Y1 Z1 A2 X1 B2. equal(W1,X1) ==> equal(euclid2(Y1,Z1,A2,W1,B2),euclid2(Y1,Z1,A2,X1,B2))) /\ 818 (!C2 E2 F2 G2 H2 D2. equal(C2,D2) ==> equal(euclid2(E2,F2,G2,H2,C2),euclid2(E2,F2,G2,H2,D2))) /\ 819 (!X Y V1 V2 V3. equal(X,Y) ==> equal(extension(X,V1,V2,V3),extension(Y,V1,V2,V3))) /\ 820 (!X V1 Y V2 V3. equal(X,Y) ==> equal(extension(V1,X,V2,V3),extension(V1,Y,V2,V3))) /\ 821 (!X V1 V2 Y V3. equal(X,Y) ==> equal(extension(V1,V2,X,V3),extension(V1,V2,Y,V3))) /\ 822 (!X V1 V2 V3 Y. equal(X,Y) ==> equal(extension(V1,V2,V3,X),extension(V1,V2,V3,Y))) /\ 823 (!X Y V1 V2 V3 V4 V5. equal(X,Y) ==> equal(continuous(X,V1,V2,V3,V4,V5),continuous(Y,V1,V2,V3,V4,V5))) /\ 824 (!X V1 Y V2 V3 V4 V5. equal(X,Y) ==> equal(continuous(V1,X,V2,V3,V4,V5),continuous(V1,Y,V2,V3,V4,V5))) /\ 825 (!X V1 V2 Y V3 V4 V5. equal(X,Y) ==> equal(continuous(V1,V2,X,V3,V4,V5),continuous(V1,V2,Y,V3,V4,V5))) /\ 826 (!X V1 V2 V3 Y V4 V5. equal(X,Y) ==> equal(continuous(V1,V2,V3,X,V4,V5),continuous(V1,V2,V3,Y,V4,V5))) /\ 827 (!X V1 V2 V3 V4 Y V5. equal(X,Y) ==> equal(continuous(V1,V2,V3,V4,X,V5),continuous(V1,V2,V3,V4,Y,V5))) /\ 828 (!X V1 V2 V3 V4 V5 Y. equal(X,Y) ==> equal(continuous(V1,V2,V3,V4,V5,X),continuous(V1,V2,V3,V4,V5,Y))) /\ 829 (~between(a,b,b)) ==> F���; 830 831 832val GEO017_2 = M "GEO017_2" 833 ���(!X:'a. equal(X,X)) /\ 834 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 835 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 836 (!Y X. equidistant(X,Y,Y,X)) /\ 837 (!X Y Z V V2 W. equidistant(X,Y,Z,V) /\ equidistant(X,Y,V2,W) ==> equidistant(Z,V,V2,W)) /\ 838 (!Z X Y. equidistant(X,Y,Z,Z) ==> equal(X,Y)) /\ 839 (!X Y W V. between(X,Y,extension(X,Y,W,V))) /\ 840 (!X Y W V. equidistant(Y,extension(X,Y,W,V),W,V)) /\ 841 (!X1 Y1 X Y Z V Z1 V1. equidistant(X,Y,X1,Y1) /\ equidistant(Y,Z,Y1,Z1) /\ equidistant(X,V,X1,V1) /\ equidistant(Y,V,Y1,V1) /\ between(X,Y,Z) /\ between(X1,Y1,Z1) ==> equal(X,Y) \/ equidistant(Z,V,Z1,V1)) /\ 842 (!X Y. between(X,Y,X) ==> equal(X,Y)) /\ 843 (!U V W X Y. between(U,V,W) /\ between(Y,X,W) ==> between(V,inner_pasch(U,V,W,X,Y),Y)) /\ 844 (!V W X Y U. between(U,V,W) /\ between(Y,X,W) ==> between(X,inner_pasch(U,V,W,X,Y),U)) /\ 845 (~between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)) /\ 846 (~between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)) /\ 847 (~between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)) /\ 848 (!Z X Y W V. equidistant(X,W,X,V) /\ equidistant(Y,W,Y,V) /\ equidistant(Z,W,Z,V) ==> between(X,Y,Z) \/ between(Y,Z,X) \/ between(Z,X,Y) \/ equal(W,V)) /\ 849 (!U V W X Y. between(U,W,Y) /\ between(V,W,X) ==> equal(U,W) \/ between(U,V,euclid1(U,V,W,X,Y))) /\ 850 (!U V W X Y. between(U,W,Y) /\ between(V,W,X) ==> equal(U,W) \/ between(U,X,euclid2(U,V,W,X,Y))) /\ 851 (!U V W X Y. between(U,W,Y) /\ between(V,W,X) ==> equal(U,W) \/ between(euclid1(U,V,W,X,Y),Y,euclid2(U,V,W,X,Y))) /\ 852 (!U V V1 W X X1. equidistant(U,V,U,V1) /\ equidistant(U,X,U,X1) /\ between(U,V,X) /\ between(V,W,X) ==> between(V1,continuous(U,V,V1,W,X,X1),X1)) /\ 853 (!U V V1 W X X1. equidistant(U,V,U,V1) /\ equidistant(U,X,U,X1) /\ between(U,V,X) /\ between(V,W,X) ==> equidistant(U,W,U,continuous(U,V,V1,W,X,X1))) /\ 854 (!X Y W Z. equal(X,Y) /\ between(X,W,Z) ==> between(Y,W,Z)) /\ 855 (!X W Y Z. equal(X,Y) /\ between(W,X,Z) ==> between(W,Y,Z)) /\ 856 (!X W Z Y. equal(X,Y) /\ between(W,Z,X) ==> between(W,Z,Y)) /\ 857 (!X Y V W Z. equal(X,Y) /\ equidistant(X,V,W,Z) ==> equidistant(Y,V,W,Z)) /\ 858 (!X V Y W Z. equal(X,Y) /\ equidistant(V,X,W,Z) ==> equidistant(V,Y,W,Z)) /\ 859 (!X V W Y Z. equal(X,Y) /\ equidistant(V,W,X,Z) ==> equidistant(V,W,Y,Z)) /\ 860 (!X V W Z Y. equal(X,Y) /\ equidistant(V,W,Z,X) ==> equidistant(V,W,Z,Y)) /\ 861 (!X Y V1 V2 V3 V4. equal(X,Y) ==> equal(inner_pasch(X,V1,V2,V3,V4),inner_pasch(Y,V1,V2,V3,V4))) /\ 862 (!X V1 Y V2 V3 V4. equal(X,Y) ==> equal(inner_pasch(V1,X,V2,V3,V4),inner_pasch(V1,Y,V2,V3,V4))) /\ 863 (!X V1 V2 Y V3 V4. equal(X,Y) ==> equal(inner_pasch(V1,V2,X,V3,V4),inner_pasch(V1,V2,Y,V3,V4))) /\ 864 (!X V1 V2 V3 Y V4. equal(X,Y) ==> equal(inner_pasch(V1,V2,V3,X,V4),inner_pasch(V1,V2,V3,Y,V4))) /\ 865 (!X V1 V2 V3 V4 Y. equal(X,Y) ==> equal(inner_pasch(V1,V2,V3,V4,X),inner_pasch(V1,V2,V3,V4,Y))) /\ 866 (!A B C D E F'. equal(A,B) ==> equal(euclid1(A,C,D,E,F'),euclid1(B,C,D,E,F'))) /\ 867 (!G I' H J K' L. equal(G,H) ==> equal(euclid1(I',G,J,K',L),euclid1(I',H,J,K',L))) /\ 868 (!M O P N Q R. equal(M,N) ==> equal(euclid1(O,P,M,Q,R),euclid1(O,P,N,Q,R))) /\ 869 (!S' U V W T' X. equal(S',T') ==> equal(euclid1(U,V,W,S',X),euclid1(U,V,W,T',X))) /\ 870 (!Y A1 B1 C1 D1 Z. equal(Y,Z) ==> equal(euclid1(A1,B1,C1,D1,Y),euclid1(A1,B1,C1,D1,Z))) /\ 871 (!E1 F1 G1 H1 I1 J1. equal(E1,F1) ==> equal(euclid2(E1,G1,H1,I1,J1),euclid2(F1,G1,H1,I1,J1))) /\ 872 (!K1 M1 L1 N1 O1 P1. equal(K1,L1) ==> equal(euclid2(M1,K1,N1,O1,P1),euclid2(M1,L1,N1,O1,P1))) /\ 873 (!Q1 S1 T1 R1 U1 V1. equal(Q1,R1) ==> equal(euclid2(S1,T1,Q1,U1,V1),euclid2(S1,T1,R1,U1,V1))) /\ 874 (!W1 Y1 Z1 A2 X1 B2. equal(W1,X1) ==> equal(euclid2(Y1,Z1,A2,W1,B2),euclid2(Y1,Z1,A2,X1,B2))) /\ 875 (!C2 E2 F2 G2 H2 D2. equal(C2,D2) ==> equal(euclid2(E2,F2,G2,H2,C2),euclid2(E2,F2,G2,H2,D2))) /\ 876 (!X Y V1 V2 V3. equal(X,Y) ==> equal(extension(X,V1,V2,V3),extension(Y,V1,V2,V3))) /\ 877 (!X V1 Y V2 V3. equal(X,Y) ==> equal(extension(V1,X,V2,V3),extension(V1,Y,V2,V3))) /\ 878 (!X V1 V2 Y V3. equal(X,Y) ==> equal(extension(V1,V2,X,V3),extension(V1,V2,Y,V3))) /\ 879 (!X V1 V2 V3 Y. equal(X,Y) ==> equal(extension(V1,V2,V3,X),extension(V1,V2,V3,Y))) /\ 880 (!X Y V1 V2 V3 V4 V5. equal(X,Y) ==> equal(continuous(X,V1,V2,V3,V4,V5),continuous(Y,V1,V2,V3,V4,V5))) /\ 881 (!X V1 Y V2 V3 V4 V5. equal(X,Y) ==> equal(continuous(V1,X,V2,V3,V4,V5),continuous(V1,Y,V2,V3,V4,V5))) /\ 882 (!X V1 V2 Y V3 V4 V5. equal(X,Y) ==> equal(continuous(V1,V2,X,V3,V4,V5),continuous(V1,V2,Y,V3,V4,V5))) /\ 883 (!X V1 V2 V3 Y V4 V5. equal(X,Y) ==> equal(continuous(V1,V2,V3,X,V4,V5),continuous(V1,V2,V3,Y,V4,V5))) /\ 884 (!X V1 V2 V3 V4 Y V5. equal(X,Y) ==> equal(continuous(V1,V2,V3,V4,X,V5),continuous(V1,V2,V3,V4,Y,V5))) /\ 885 (!X V1 V2 V3 V4 V5 Y. equal(X,Y) ==> equal(continuous(V1,V2,V3,V4,V5,X),continuous(V1,V2,V3,V4,V5,Y))) /\ 886 (equidistant(u,v,w,x)) /\ 887 (~equidistant(u,v,x,w)) ==> F���; 888 889 890val GEO027_3 = M "GEO027_3" $ 891 ���(!X:'a. equal(X,X)) /\ 892 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 893 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 894 (!Y X. equidistant(X,Y,Y,X)) /\ 895 (!X Y Z V V2 W. equidistant(X,Y,Z,V) /\ equidistant(X,Y,V2,W) ==> equidistant(Z,V,V2,W)) /\ 896 (!Z X Y. equidistant(X,Y,Z,Z) ==> equal(X,Y)) /\ 897 (!X Y W V. between(X,Y,extension(X,Y,W,V))) /\ 898 (!X Y W V. equidistant(Y,extension(X,Y,W,V),W,V)) /\ 899 (!X1 Y1 X Y Z V Z1 V1. equidistant(X,Y,X1,Y1) /\ equidistant(Y,Z,Y1,Z1) /\ equidistant(X,V,X1,V1) /\ equidistant(Y,V,Y1,V1) /\ between(X,Y,Z) /\ between(X1,Y1,Z1) ==> equal(X,Y) \/ equidistant(Z,V,Z1,V1)) /\ 900 (!X Y. between(X,Y,X) ==> equal(X,Y)) /\ 901 (!U V W X Y. between(U,V,W) /\ between(Y,X,W) ==> between(V,inner_pasch(U,V,W,X,Y),Y)) /\ 902 (!V W X Y U. between(U,V,W) /\ between(Y,X,W) ==> between(X,inner_pasch(U,V,W,X,Y),U)) /\ 903 (~between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)) /\ 904 (~between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)) /\ 905 (~between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)) /\ 906 (!Z X Y W V. equidistant(X,W,X,V) /\ equidistant(Y,W,Y,V) /\ equidistant(Z,W,Z,V) ==> between(X,Y,Z) \/ between(Y,Z,X) \/ between(Z,X,Y) \/ equal(W,V)) /\ 907 (!U V W X Y. between(U,W,Y) /\ between(V,W,X) ==> equal(U,W) \/ between(U,V,euclid1(U,V,W,X,Y))) /\ 908 (!U V W X Y. between(U,W,Y) /\ between(V,W,X) ==> equal(U,W) \/ between(U,X,euclid2(U,V,W,X,Y))) /\ 909 (!U V W X Y. between(U,W,Y) /\ between(V,W,X) ==> equal(U,W) \/ between(euclid1(U,V,W,X,Y),Y,euclid2(U,V,W,X,Y))) /\ 910 (!U V V1 W X X1. equidistant(U,V,U,V1) /\ equidistant(U,X,U,X1) /\ between(U,V,X) /\ between(V,W,X) ==> between(V1,continuous(U,V,V1,W,X,X1),X1)) /\ 911 (!U V V1 W X X1. equidistant(U,V,U,V1) /\ equidistant(U,X,U,X1) /\ between(U,V,X) /\ between(V,W,X) ==> equidistant(U,W,U,continuous(U,V,V1,W,X,X1))) /\ 912 (!X Y W Z. equal(X,Y) /\ between(X,W,Z) ==> between(Y,W,Z)) /\ 913 (!X W Y Z. equal(X,Y) /\ between(W,X,Z) ==> between(W,Y,Z)) /\ 914 (!X W Z Y. equal(X,Y) /\ between(W,Z,X) ==> between(W,Z,Y)) /\ 915 (!X Y V W Z. equal(X,Y) /\ equidistant(X,V,W,Z) ==> equidistant(Y,V,W,Z)) /\ 916 (!X V Y W Z. equal(X,Y) /\ equidistant(V,X,W,Z) ==> equidistant(V,Y,W,Z)) /\ 917 (!X V W Y Z. equal(X,Y) /\ equidistant(V,W,X,Z) ==> equidistant(V,W,Y,Z)) /\ 918 (!X V W Z Y. equal(X,Y) /\ equidistant(V,W,Z,X) ==> equidistant(V,W,Z,Y)) /\ 919 (!X Y V1 V2 V3 V4. equal(X,Y) ==> equal(inner_pasch(X,V1,V2,V3,V4),inner_pasch(Y,V1,V2,V3,V4))) /\ 920 (!X V1 Y V2 V3 V4. equal(X,Y) ==> equal(inner_pasch(V1,X,V2,V3,V4),inner_pasch(V1,Y,V2,V3,V4))) /\ 921 (!X V1 V2 Y V3 V4. equal(X,Y) ==> equal(inner_pasch(V1,V2,X,V3,V4),inner_pasch(V1,V2,Y,V3,V4))) /\ 922 (!X V1 V2 V3 Y V4. equal(X,Y) ==> equal(inner_pasch(V1,V2,V3,X,V4),inner_pasch(V1,V2,V3,Y,V4))) /\ 923 (!X V1 V2 V3 V4 Y. equal(X,Y) ==> equal(inner_pasch(V1,V2,V3,V4,X),inner_pasch(V1,V2,V3,V4,Y))) /\ 924 (!A B C D E F'. equal(A,B) ==> equal(euclid1(A,C,D,E,F'),euclid1(B,C,D,E,F'))) /\ 925 (!G I' H J K' L. equal(G,H) ==> equal(euclid1(I',G,J,K',L),euclid1(I',H,J,K',L))) /\ 926 (!M O P N Q R. equal(M,N) ==> equal(euclid1(O,P,M,Q,R),euclid1(O,P,N,Q,R))) /\ 927 (!S' U V W T' X. equal(S',T') ==> equal(euclid1(U,V,W,S',X),euclid1(U,V,W,T',X))) /\ 928 (!Y A1 B1 C1 D1 Z. equal(Y,Z) ==> equal(euclid1(A1,B1,C1,D1,Y),euclid1(A1,B1,C1,D1,Z))) /\ 929 (!E1 F1 G1 H1 I1 J1. equal(E1,F1) ==> equal(euclid2(E1,G1,H1,I1,J1),euclid2(F1,G1,H1,I1,J1))) /\ 930 (!K1 M1 L1 N1 O1 P1. equal(K1,L1) ==> equal(euclid2(M1,K1,N1,O1,P1),euclid2(M1,L1,N1,O1,P1))) /\ 931 (!Q1 S1 T1 R1 U1 V1. equal(Q1,R1) ==> equal(euclid2(S1,T1,Q1,U1,V1),euclid2(S1,T1,R1,U1,V1))) /\ 932 (!W1 Y1 Z1 A2 X1 B2. equal(W1,X1) ==> equal(euclid2(Y1,Z1,A2,W1,B2),euclid2(Y1,Z1,A2,X1,B2))) /\ 933 (!C2 E2 F2 G2 H2 D2. equal(C2,D2) ==> equal(euclid2(E2,F2,G2,H2,C2),euclid2(E2,F2,G2,H2,D2))) /\ 934 (!X Y V1 V2 V3. equal(X,Y) ==> equal(extension(X,V1,V2,V3),extension(Y,V1,V2,V3))) /\ 935 (!X V1 Y V2 V3. equal(X,Y) ==> equal(extension(V1,X,V2,V3),extension(V1,Y,V2,V3))) /\ 936 (!X V1 V2 Y V3. equal(X,Y) ==> equal(extension(V1,V2,X,V3),extension(V1,V2,Y,V3))) /\ 937 (!X V1 V2 V3 Y. equal(X,Y) ==> equal(extension(V1,V2,V3,X),extension(V1,V2,V3,Y))) /\ 938 (!X Y V1 V2 V3 V4 V5. equal(X,Y) ==> equal(continuous(X,V1,V2,V3,V4,V5),continuous(Y,V1,V2,V3,V4,V5))) /\ 939 (!X V1 Y V2 V3 V4 V5. equal(X,Y) ==> equal(continuous(V1,X,V2,V3,V4,V5),continuous(V1,Y,V2,V3,V4,V5))) /\ 940 (!X V1 V2 Y V3 V4 V5. equal(X,Y) ==> equal(continuous(V1,V2,X,V3,V4,V5),continuous(V1,V2,Y,V3,V4,V5))) /\ 941 (!X V1 V2 V3 Y V4 V5. equal(X,Y) ==> equal(continuous(V1,V2,V3,X,V4,V5),continuous(V1,V2,V3,Y,V4,V5))) /\ 942 (!X V1 V2 V3 V4 Y V5. equal(X,Y) ==> equal(continuous(V1,V2,V3,V4,X,V5),continuous(V1,V2,V3,V4,Y,V5))) /\ 943 (!X V1 V2 V3 V4 V5 Y. equal(X,Y) ==> equal(continuous(V1,V2,V3,V4,V5,X),continuous(V1,V2,V3,V4,V5,Y))) /\ 944 (!U V. equal(reflection(U,V),extension(U,V,U,V))) /\ 945 (!X Y Z. equal(X,Y) ==> equal(reflection(X,Z),reflection(Y,Z))) /\ 946 (!A1 C1 B1. equal(A1,B1) ==> equal(reflection(C1,A1),reflection(C1,B1))) /\ 947 (!U V. equidistant(U,V,U,V)) /\ 948 (!W X U V. equidistant(U,V,W,X) ==> equidistant(W,X,U,V)) /\ 949 (!V U W X. equidistant(U,V,W,X) ==> equidistant(V,U,W,X)) /\ 950 (!U V X W. equidistant(U,V,W,X) ==> equidistant(U,V,X,W)) /\ 951 (!V U X W. equidistant(U,V,W,X) ==> equidistant(V,U,X,W)) /\ 952 (!W X V U. equidistant(U,V,W,X) ==> equidistant(W,X,V,U)) /\ 953 (!X W U V. equidistant(U,V,W,X) ==> equidistant(X,W,U,V)) /\ 954 (!X W V U. equidistant(U,V,W,X) ==> equidistant(X,W,V,U)) /\ 955 (!W X U V Y Z. equidistant(U,V,W,X) /\ equidistant(W,X,Y,Z) ==> equidistant(U,V,Y,Z)) /\ 956 (!U V W. equal(V,extension(U,V,W,W))) /\ 957 (!W X U V Y. equal(Y,extension(U,V,W,X)) ==> between(U,V,Y)) /\ 958 (!U V. between(U,V,reflection(U,V))) /\ 959 (!U V. equidistant(V,reflection(U,V),U,V)) /\ 960 (!U V. equal(U,V) ==> equal(V,reflection(U,V))) /\ 961 (!U. equal(U,reflection(U,U))) /\ 962 (!U V. equal(V,reflection(U,V)) ==> equal(U,V)) /\ 963 (!U V. equidistant(U,U,V,V)) /\ 964 (!V V1 U W U1 W1. equidistant(U,V,U1,V1) /\ equidistant(V,W,V1,W1) /\ between(U,V,W) /\ between(U1,V1,W1) ==> equidistant(U,W,U1,W1)) /\ 965 (!U V W X. between(U,V,W) /\ between(U,V,X) /\ equidistant(V,W,V,X) ==> equal(U,V) \/ equal(W,X)) /\ 966 (between(u,v,w)) /\ 967 (~equal(u,v)) /\ 968 (~equal(w,extension(u,v,v,w))) ==> F���; 969 970 971val GEO058_2 = M "GEO058_2" $ 972 ���(!X:'a. equal(X,X)) /\ 973 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 974 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 975 (!Y X. equidistant(X,Y,Y,X)) /\ 976 (!X Y Z V V2 W. equidistant(X,Y,Z,V) /\ equidistant(X,Y,V2,W) ==> equidistant(Z,V,V2,W)) /\ 977 (!Z X Y. equidistant(X,Y,Z,Z) ==> equal(X,Y)) /\ 978 (!X Y W V. between(X,Y,extension(X,Y,W,V))) /\ 979 (!X Y W V. equidistant(Y,extension(X,Y,W,V),W,V)) /\ 980 (!X1 Y1 X Y Z V Z1 V1. equidistant(X,Y,X1,Y1) /\ equidistant(Y,Z,Y1,Z1) /\ equidistant(X,V,X1,V1) /\ equidistant(Y,V,Y1,V1) /\ between(X,Y,Z) /\ between(X1,Y1,Z1) ==> equal(X,Y) \/ equidistant(Z,V,Z1,V1)) /\ 981 (!X Y. between(X,Y,X) ==> equal(X,Y)) /\ 982 (!U V W X Y. between(U,V,W) /\ between(Y,X,W) ==> between(V,inner_pasch(U,V,W,X,Y),Y)) /\ 983 (!V W X Y U. between(U,V,W) /\ between(Y,X,W) ==> between(X,inner_pasch(U,V,W,X,Y),U)) /\ 984 (~between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)) /\ 985 (~between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)) /\ 986 (~between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)) /\ 987 (!Z X Y W V. equidistant(X,W,X,V) /\ equidistant(Y,W,Y,V) /\ equidistant(Z,W,Z,V) ==> between(X,Y,Z) \/ between(Y,Z,X) \/ between(Z,X,Y) \/ equal(W,V)) /\ 988 (!U V W X Y. between(U,W,Y) /\ between(V,W,X) ==> equal(U,W) \/ between(U,V,euclid1(U,V,W,X,Y))) /\ 989 (!U V W X Y. between(U,W,Y) /\ between(V,W,X) ==> equal(U,W) \/ between(U,X,euclid2(U,V,W,X,Y))) /\ 990 (!U V W X Y. between(U,W,Y) /\ between(V,W,X) ==> equal(U,W) \/ between(euclid1(U,V,W,X,Y),Y,euclid2(U,V,W,X,Y))) /\ 991 (!U V V1 W X X1. equidistant(U,V,U,V1) /\ equidistant(U,X,U,X1) /\ between(U,V,X) /\ between(V,W,X) ==> between(V1,continuous(U,V,V1,W,X,X1),X1)) /\ 992 (!U V V1 W X X1. equidistant(U,V,U,V1) /\ equidistant(U,X,U,X1) /\ between(U,V,X) /\ between(V,W,X) ==> equidistant(U,W,U,continuous(U,V,V1,W,X,X1))) /\ 993 (!X Y W Z. equal(X,Y) /\ between(X,W,Z) ==> between(Y,W,Z)) /\ 994 (!X W Y Z. equal(X,Y) /\ between(W,X,Z) ==> between(W,Y,Z)) /\ 995 (!X W Z Y. equal(X,Y) /\ between(W,Z,X) ==> between(W,Z,Y)) /\ 996 (!X Y V W Z. equal(X,Y) /\ equidistant(X,V,W,Z) ==> equidistant(Y,V,W,Z)) /\ 997 (!X V Y W Z. equal(X,Y) /\ equidistant(V,X,W,Z) ==> equidistant(V,Y,W,Z)) /\ 998 (!X V W Y Z. equal(X,Y) /\ equidistant(V,W,X,Z) ==> equidistant(V,W,Y,Z)) /\ 999 (!X V W Z Y. equal(X,Y) /\ equidistant(V,W,Z,X) ==> equidistant(V,W,Z,Y)) /\ 1000 (!X Y V1 V2 V3 V4. equal(X,Y) ==> equal(inner_pasch(X,V1,V2,V3,V4),inner_pasch(Y,V1,V2,V3,V4))) /\ 1001 (!X V1 Y V2 V3 V4. equal(X,Y) ==> equal(inner_pasch(V1,X,V2,V3,V4),inner_pasch(V1,Y,V2,V3,V4))) /\ 1002 (!X V1 V2 Y V3 V4. equal(X,Y) ==> equal(inner_pasch(V1,V2,X,V3,V4),inner_pasch(V1,V2,Y,V3,V4))) /\ 1003 (!X V1 V2 V3 Y V4. equal(X,Y) ==> equal(inner_pasch(V1,V2,V3,X,V4),inner_pasch(V1,V2,V3,Y,V4))) /\ 1004 (!X V1 V2 V3 V4 Y. equal(X,Y) ==> equal(inner_pasch(V1,V2,V3,V4,X),inner_pasch(V1,V2,V3,V4,Y))) /\ 1005 (!A B C D E F'. equal(A,B) ==> equal(euclid1(A,C,D,E,F'),euclid1(B,C,D,E,F'))) /\ 1006 (!G I' H J K' L. equal(G,H) ==> equal(euclid1(I',G,J,K',L),euclid1(I',H,J,K',L))) /\ 1007 (!M O P N Q R. equal(M,N) ==> equal(euclid1(O,P,M,Q,R),euclid1(O,P,N,Q,R))) /\ 1008 (!S' U V W T' X. equal(S',T') ==> equal(euclid1(U,V,W,S',X),euclid1(U,V,W,T',X))) /\ 1009 (!Y A1 B1 C1 D1 Z. equal(Y,Z) ==> equal(euclid1(A1,B1,C1,D1,Y),euclid1(A1,B1,C1,D1,Z))) /\ 1010 (!E1 F1 G1 H1 I1 J1. equal(E1,F1) ==> equal(euclid2(E1,G1,H1,I1,J1),euclid2(F1,G1,H1,I1,J1))) /\ 1011 (!K1 M1 L1 N1 O1 P1. equal(K1,L1) ==> equal(euclid2(M1,K1,N1,O1,P1),euclid2(M1,L1,N1,O1,P1))) /\ 1012 (!Q1 S1 T1 R1 U1 V1. equal(Q1,R1) ==> equal(euclid2(S1,T1,Q1,U1,V1),euclid2(S1,T1,R1,U1,V1))) /\ 1013 (!W1 Y1 Z1 A2 X1 B2. equal(W1,X1) ==> equal(euclid2(Y1,Z1,A2,W1,B2),euclid2(Y1,Z1,A2,X1,B2))) /\ 1014 (!C2 E2 F2 G2 H2 D2. equal(C2,D2) ==> equal(euclid2(E2,F2,G2,H2,C2),euclid2(E2,F2,G2,H2,D2))) /\ 1015 (!X Y V1 V2 V3. equal(X,Y) ==> equal(extension(X,V1,V2,V3),extension(Y,V1,V2,V3))) /\ 1016 (!X V1 Y V2 V3. equal(X,Y) ==> equal(extension(V1,X,V2,V3),extension(V1,Y,V2,V3))) /\ 1017 (!X V1 V2 Y V3. equal(X,Y) ==> equal(extension(V1,V2,X,V3),extension(V1,V2,Y,V3))) /\ 1018 (!X V1 V2 V3 Y. equal(X,Y) ==> equal(extension(V1,V2,V3,X),extension(V1,V2,V3,Y))) /\ 1019 (!X Y V1 V2 V3 V4 V5. equal(X,Y) ==> equal(continuous(X,V1,V2,V3,V4,V5),continuous(Y,V1,V2,V3,V4,V5))) /\ 1020 (!X V1 Y V2 V3 V4 V5. equal(X,Y) ==> equal(continuous(V1,X,V2,V3,V4,V5),continuous(V1,Y,V2,V3,V4,V5))) /\ 1021 (!X V1 V2 Y V3 V4 V5. equal(X,Y) ==> equal(continuous(V1,V2,X,V3,V4,V5),continuous(V1,V2,Y,V3,V4,V5))) /\ 1022 (!X V1 V2 V3 Y V4 V5. equal(X,Y) ==> equal(continuous(V1,V2,V3,X,V4,V5),continuous(V1,V2,V3,Y,V4,V5))) /\ 1023 (!X V1 V2 V3 V4 Y V5. equal(X,Y) ==> equal(continuous(V1,V2,V3,V4,X,V5),continuous(V1,V2,V3,V4,Y,V5))) /\ 1024 (!X V1 V2 V3 V4 V5 Y. equal(X,Y) ==> equal(continuous(V1,V2,V3,V4,V5,X),continuous(V1,V2,V3,V4,V5,Y))) /\ 1025 (!U V. equal(reflection(U,V),extension(U,V,U,V))) /\ 1026 (!X Y Z. equal(X,Y) ==> equal(reflection(X,Z),reflection(Y,Z))) /\ 1027 (!A1 C1 B1. equal(A1,B1) ==> equal(reflection(C1,A1),reflection(C1,B1))) /\ 1028 (equal(v,reflection(u,v))) /\ 1029 (~equal(u,v)) ==> F���; 1030 1031 1032val GEO079_1 = M "GEO079_1" $ 1033Lib.with_flag(Globals.guessing_tyvars,true) 1034 Term 1035`(!U V W X Y Z. right_angle(U,V,W) /\ right_angle(X,Y,Z) ==> eq(U,V,W,X,Y,Z)) /\ 1036 (!U V W X Y Z. congruent(U,V,W,X,Y,Z) ==> eq(U,V,W,X,Y,Z)) /\ 1037 (!V W U X. trapezoid(U,V,W,X) ==> parallel(V,W,U,X)) /\ 1038 (!U V X Y. parallel(U,V,X,Y) ==> eq(X,V,U,V,X,Y)) /\ 1039 (trapezoid(a,b,c,d)) /\ 1040 (~eq(a,c,b,c,a,d)) ==> F`; 1041 1042 1043val GRP001_1 = M "GRP001_1" $ 1044 ���(!X:'a. equal(X,X)) /\ 1045 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1046 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1047 (!X. product(identity,X,X)) /\ 1048 (!X. product(X,identity,X)) /\ 1049 (!X. product(inverse(X),X,identity)) /\ 1050 (!X. product(X,inverse(X),identity)) /\ 1051 (!X Y. product(X,Y,multiply(X,Y))) /\ 1052 (!X Y Z W. product(X,Y,Z) /\ product(X,Y,W) ==> equal(Z,W)) /\ 1053 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 1054 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 1055 (!X Y. equal(X,Y) ==> equal(inverse(X),inverse(Y))) /\ 1056 (!X Y W. equal(X,Y) ==> equal(multiply(X,W),multiply(Y,W))) /\ 1057 (!X W Y. equal(X,Y) ==> equal(multiply(W,X),multiply(W,Y))) /\ 1058 (!X Y W Z. equal(X,Y) /\ product(X,W,Z) ==> product(Y,W,Z)) /\ 1059 (!X W Y Z. equal(X,Y) /\ product(W,X,Z) ==> product(W,Y,Z)) /\ 1060 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 1061 (!X. product(X,X,identity)) /\ 1062 (product(a,b,c)) /\ 1063 (~product(b,a,c)) ==> F���; 1064 1065 1066val GRP008_1 = M "GRP008_1" $ 1067 ���(!X:'a. equal(X,X)) /\ 1068 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1069 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1070 (!X. product(identity,X,X)) /\ 1071 (!X. product(X,identity,X)) /\ 1072 (!X. product(inverse(X),X,identity)) /\ 1073 (!X. product(X,inverse(X),identity)) /\ 1074 (!X Y. product(X,Y,multiply(X,Y))) /\ 1075 (!X Y Z W. product(X,Y,Z) /\ product(X,Y,W) ==> equal(Z,W)) /\ 1076 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 1077 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 1078 (!X Y. equal(X,Y) ==> equal(inverse(X),inverse(Y))) /\ 1079 (!X Y W. equal(X,Y) ==> equal(multiply(X,W),multiply(Y,W))) /\ 1080 (!X W Y. equal(X,Y) ==> equal(multiply(W,X),multiply(W,Y))) /\ 1081 (!X Y W Z. equal(X,Y) /\ product(X,W,Z) ==> product(Y,W,Z)) /\ 1082 (!X W Y Z. equal(X,Y) /\ product(W,X,Z) ==> product(W,Y,Z)) /\ 1083 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 1084 (!A B. equal(A,B) ==> equal(h(A),h(B))) /\ 1085 (!C D. equal(C,D) ==> equal(j(C),j(D))) /\ 1086 (!A B. equal(A,B) /\ q(A) ==> q(B)) /\ 1087 (!B A C. q(A) /\ product(A,B,C) ==> product(B,A,C)) /\ 1088 (!A. product(j(A),A,h(A)) \/ product(A,j(A),h(A)) \/ q(A)) /\ 1089 (!A. product(j(A),A,h(A)) /\ product(A,j(A),h(A)) ==> q(A)) /\ 1090 (~q(identity)) ==> F���; 1091 1092 1093val GRP013_1 = M "GRP013_1" $ 1094 ���(!X:'a. equal(X,X)) /\ 1095 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1096 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1097 (!X. product(identity,X,X)) /\ 1098 (!X. product(X,identity,X)) /\ 1099 (!X. product(inverse(X),X,identity)) /\ 1100 (!X. product(X,inverse(X),identity)) /\ 1101 (!X Y. product(X,Y,multiply(X,Y))) /\ 1102 (!X Y Z W. product(X,Y,Z) /\ product(X,Y,W) ==> equal(Z,W)) /\ 1103 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 1104 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 1105 (!X Y. equal(X,Y) ==> equal(inverse(X),inverse(Y))) /\ 1106 (!X Y W. equal(X,Y) ==> equal(multiply(X,W),multiply(Y,W))) /\ 1107 (!X W Y. equal(X,Y) ==> equal(multiply(W,X),multiply(W,Y))) /\ 1108 (!X Y W Z. equal(X,Y) /\ product(X,W,Z) ==> product(Y,W,Z)) /\ 1109 (!X W Y Z. equal(X,Y) /\ product(W,X,Z) ==> product(W,Y,Z)) /\ 1110 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 1111 (!A. product(A,A,identity)) /\ 1112 (product(a,b,c)) /\ 1113 (product(inverse(a),inverse(b),d)) /\ 1114 (!A C B. product(inverse(A),inverse(B),C) ==> product(A,C,B)) /\ 1115 (~product(c,d,identity)) ==> F���; 1116 1117 1118val GRP037_3 = M "GRP037_3" $ 1119 ���(!X:'a. equal(X,X)) /\ 1120 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1121 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1122 (!X. product(identity,X,X)) /\ 1123 (!X. product(X,identity,X)) /\ 1124 (!X. product(inverse(X),X,identity)) /\ 1125 (!X. product(X,inverse(X),identity)) /\ 1126 (!X Y. product(X,Y,multiply(X,Y))) /\ 1127 (!X Y Z W. product(X,Y,Z) /\ product(X,Y,W) ==> equal(Z,W)) /\ 1128 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 1129 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 1130 (!X Y. equal(X,Y) ==> equal(inverse(X),inverse(Y))) /\ 1131 (!X Y W. equal(X,Y) ==> equal(multiply(X,W),multiply(Y,W))) /\ 1132 (!X W Y. equal(X,Y) ==> equal(multiply(W,X),multiply(W,Y))) /\ 1133 (!X Y W Z. equal(X,Y) /\ product(X,W,Z) ==> product(Y,W,Z)) /\ 1134 (!X W Y Z. equal(X,Y) /\ product(W,X,Z) ==> product(W,Y,Z)) /\ 1135 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 1136 (!A B C. subgroup_member(A) /\ subgroup_member(B) /\ product(A,inverse(B),C) ==> subgroup_member(C)) /\ 1137 (!A B. equal(A,B) /\ subgroup_member(A) ==> subgroup_member(B)) /\ 1138 (!A. subgroup_member(A) ==> product(another_identity,A,A)) /\ 1139 (!A. subgroup_member(A) ==> product(A,another_identity,A)) /\ 1140 (!A. subgroup_member(A) ==> product(A,another_inverse(A),another_identity)) /\ 1141 (!A. subgroup_member(A) ==> product(another_inverse(A),A,another_identity)) /\ 1142 (!A. subgroup_member(A) ==> subgroup_member(another_inverse(A))) /\ 1143 (!A B. equal(A,B) ==> equal(another_inverse(A),another_inverse(B))) /\ 1144 (!A C D B. product(A,B,C) /\ product(A,D,C) ==> equal(D,B)) /\ 1145 (!B C D A. product(A,B,C) /\ product(D,B,C) ==> equal(D,A)) /\ 1146 (subgroup_member(a)) /\ 1147 (subgroup_member(another_identity)) /\ 1148 (~equal(inverse(a),another_inverse(a))) ==> F���; 1149 1150 1151val GRP031_2 = M "GRP031_2" $ 1152 ���(!X Y. product(X,Y,multiply(X,Y))) /\ 1153 (!X Y Z W. product(X,Y,Z) /\ product(X,Y,W) ==> equal(Z,W)) /\ 1154 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 1155 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 1156 (!A. product(A,inverse(A),identity)) /\ 1157 (!A:'a. product(A,identity,A)) /\ 1158 (!A. ~product(A,a,identity)) ==> F���; 1159 1160 1161val GRP034_4 = M "GRP034_4" $ 1162 ���(!X Y:'a. product(X,Y,multiply(X,Y))) /\ 1163 (!X. product(identity,X,X)) /\ 1164 (!X. product(X,identity,X)) /\ 1165 (!X. product(X,inverse(X),identity)) /\ 1166 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 1167 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 1168 (!B A C. subgroup_member(A) /\ subgroup_member(B) /\ product(B,inverse(A),C) ==> subgroup_member(C)) /\ 1169 (subgroup_member(a)) /\ 1170 (~subgroup_member(inverse(a))) ==> F���; 1171 1172 1173val GRP047_2 = M "GRP047_2" $ 1174 ���(!X:'a. product(identity,X,X)) /\ 1175 (!X. product(inverse(X),X,identity)) /\ 1176 (!X Y. product(X,Y,multiply(X,Y))) /\ 1177 (!X Y Z W. product(X,Y,Z) /\ product(X,Y,W) ==> equal(Z,W)) /\ 1178 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 1179 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 1180 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 1181 (equal(a,b)) /\ 1182 (~equal(multiply(c,a),multiply(c,b))) ==> F���; 1183 1184 1185val GRP130_1_002 = Mfail "GRP130_1_002" $ 1186 ���(group_element(e_1:'a)) /\ 1187 (group_element(e_2)) /\ 1188 (~equal(e_1,e_2)) /\ 1189 (~equal(e_2,e_1)) /\ 1190 (!X Y. group_element(X) /\ group_element(Y) ==> product(X,Y,e_1) \/ product(X,Y,e_2)) /\ 1191 (!X Y W Z. product(X,Y,W) /\ product(X,Y,Z) ==> equal(W,Z)) /\ 1192 (!X Y W Z. product(X,W,Y) /\ product(X,Z,Y) ==> equal(W,Z)) /\ 1193 (!Y X W Z. product(W,Y,X) /\ product(Z,Y,X) ==> equal(W,Z)) /\ 1194 (!Z1 Z2 Y X. product(X,Y,Z1) /\ product(X,Z1,Z2) ==> product(Z2,Y,X)) ==> F���; 1195 1196 1197val GRP156_1 = M "GRP156_1" $ 1198 ���(!X:'a. equal(X,X)) /\ 1199 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1200 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1201 (!X. equal(multiply(identity,X),X)) /\ 1202 (!X. equal(multiply(inverse(X),X),identity)) /\ 1203 (!X Y Z. equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z)))) /\ 1204 (!A B. equal(A,B) ==> equal(inverse(A),inverse(B))) /\ 1205 (!C D E. equal(C,D) ==> equal(multiply(C,E),multiply(D,E))) /\ 1206 (!F' H G. equal(F',G) ==> equal(multiply(H,F'),multiply(H,G))) /\ 1207 (!Y X. equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X))) /\ 1208 (!Y X. equal(least_upper_bound(X,Y),least_upper_bound(Y,X))) /\ 1209 (!X Y Z. equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z))) /\ 1210 (!X Y Z. equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z))) /\ 1211 (!X. equal(least_upper_bound(X,X),X)) /\ 1212 (!X. equal(greatest_lower_bound(X,X),X)) /\ 1213 (!Y X. equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X)) /\ 1214 (!Y X. equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X)) /\ 1215 (!Y X Z. equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z)))) /\ 1216 (!Y X Z. equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z)))) /\ 1217 (!Y Z X. equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X)))) /\ 1218 (!Y Z X. equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X)))) /\ 1219 (!A B C. equal(A,B) ==> equal(greatest_lower_bound(A,C),greatest_lower_bound(B,C))) /\ 1220 (!A C B. equal(A,B) ==> equal(greatest_lower_bound(C,A),greatest_lower_bound(C,B))) /\ 1221 (!A B C. equal(A,B) ==> equal(least_upper_bound(A,C),least_upper_bound(B,C))) /\ 1222 (!A C B. equal(A,B) ==> equal(least_upper_bound(C,A),least_upper_bound(C,B))) /\ 1223 (!A B C. equal(A,B) ==> equal(multiply(A,C),multiply(B,C))) /\ 1224 (!A C B. equal(A,B) ==> equal(multiply(C,A),multiply(C,B))) /\ 1225 (equal(least_upper_bound(a,b),b)) /\ 1226 (~equal(greatest_lower_bound(multiply(a,c),multiply(b,c)),multiply(a,c))) ==> F���; 1227 1228 1229val GRP168_1 = M "GRP168_1" $ 1230 ���(!X:'a. equal(X,X)) /\ 1231 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1232 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1233 (!X. equal(multiply(identity,X),X)) /\ 1234 (!X. equal(multiply(inverse(X),X),identity)) /\ 1235 (!X Y Z. equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z)))) /\ 1236 (!A B. equal(A,B) ==> equal(inverse(A),inverse(B))) /\ 1237 (!C D E. equal(C,D) ==> equal(multiply(C,E),multiply(D,E))) /\ 1238 (!F' H G. equal(F',G) ==> equal(multiply(H,F'),multiply(H,G))) /\ 1239 (!Y X. equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X))) /\ 1240 (!Y X. equal(least_upper_bound(X,Y),least_upper_bound(Y,X))) /\ 1241 (!X Y Z. equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z))) /\ 1242 (!X Y Z. equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z))) /\ 1243 (!X. equal(least_upper_bound(X,X),X)) /\ 1244 (!X. equal(greatest_lower_bound(X,X),X)) /\ 1245 (!Y X. equal(least_upper_bound(X,greatest_lower_bound(X,Y)),X)) /\ 1246 (!Y X. equal(greatest_lower_bound(X,least_upper_bound(X,Y)),X)) /\ 1247 (!Y X Z. equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z)))) /\ 1248 (!Y X Z. equal(multiply(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(multiply(X,Y),multiply(X,Z)))) /\ 1249 (!Y Z X. equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X)))) /\ 1250 (!Y Z X. equal(multiply(greatest_lower_bound(Y,Z),X),greatest_lower_bound(multiply(Y,X),multiply(Z,X)))) /\ 1251 (!A B C. equal(A,B) ==> equal(greatest_lower_bound(A,C),greatest_lower_bound(B,C))) /\ 1252 (!A C B. equal(A,B) ==> equal(greatest_lower_bound(C,A),greatest_lower_bound(C,B))) /\ 1253 (!A B C. equal(A,B) ==> equal(least_upper_bound(A,C),least_upper_bound(B,C))) /\ 1254 (!A C B. equal(A,B) ==> equal(least_upper_bound(C,A),least_upper_bound(C,B))) /\ 1255 (!A B C. equal(A,B) ==> equal(multiply(A,C),multiply(B,C))) /\ 1256 (!A C B. equal(A,B) ==> equal(multiply(C,A),multiply(C,B))) /\ 1257 (equal(least_upper_bound(a,b),b)) /\ 1258 (~equal(least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),multiply(inverse(c),multiply(b,c)))) ==> F���; 1259 1260 1261val HEN003_3 = M "HEN003_3" $ 1262 ���(!X:'a. equal(X,X)) /\ 1263 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1264 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1265 (!X Y. less_equal(X,Y) ==> equal(divide(X,Y),zero)) /\ 1266 (!X Y. equal(divide(X,Y),zero) ==> less_equal(X,Y)) /\ 1267 (!Y X. less_equal(divide(X,Y),X)) /\ 1268 (!X Y Z. less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z))) /\ 1269 (!X. less_equal(zero,X)) /\ 1270 (!X Y. less_equal(X,Y) /\ less_equal(Y,X) ==> equal(X,Y)) /\ 1271 (!X. less_equal(X,identity)) /\ 1272 (!A B C. equal(A,B) ==> equal(divide(A,C),divide(B,C))) /\ 1273 (!D F' E. equal(D,E) ==> equal(divide(F',D),divide(F',E))) /\ 1274 (!G H I'. equal(G,H) /\ less_equal(G,I') ==> less_equal(H,I')) /\ 1275 (!J L K'. equal(J,K') /\ less_equal(L,J) ==> less_equal(L,K')) /\ 1276 (~equal(divide(a,a),zero)) ==> F���; 1277 1278 1279val HEN007_2 = M "HEN007_2" $ 1280 ���(!X:'a. equal(X,X)) /\ 1281 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1282 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1283 (!X Y. less_equal(X,Y) ==> quotient(X,Y,zero)) /\ 1284 (!X Y. quotient(X,Y,zero) ==> less_equal(X,Y)) /\ 1285 (!Y Z X. quotient(X,Y,Z) ==> less_equal(Z,X)) /\ 1286 (!Y X V3 V2 V1 Z V4 V5. quotient(X,Y,V1) /\ quotient(Y,Z,V2) /\ quotient(X,Z,V3) /\ quotient(V3,V2,V4) /\ quotient(V1,Z,V5) ==> less_equal(V4,V5)) /\ 1287 (!X. less_equal(zero,X)) /\ 1288 (!X Y. less_equal(X,Y) /\ less_equal(Y,X) ==> equal(X,Y)) /\ 1289 (!X. less_equal(X,identity)) /\ 1290 (!X Y. quotient(X,Y,divide(X,Y))) /\ 1291 (!X Y Z W. quotient(X,Y,Z) /\ quotient(X,Y,W) ==> equal(Z,W)) /\ 1292 (!X Y W Z. equal(X,Y) /\ quotient(X,W,Z) ==> quotient(Y,W,Z)) /\ 1293 (!X W Y Z. equal(X,Y) /\ quotient(W,X,Z) ==> quotient(W,Y,Z)) /\ 1294 (!X W Z Y. equal(X,Y) /\ quotient(W,Z,X) ==> quotient(W,Z,Y)) /\ 1295 (!X Z Y. equal(X,Y) /\ less_equal(Z,X) ==> less_equal(Z,Y)) /\ 1296 (!X Y Z. equal(X,Y) /\ less_equal(X,Z) ==> less_equal(Y,Z)) /\ 1297 (!X Y W. equal(X,Y) ==> equal(divide(X,W),divide(Y,W))) /\ 1298 (!X W Y. equal(X,Y) ==> equal(divide(W,X),divide(W,Y))) /\ 1299 (!X. quotient(X,identity,zero)) /\ 1300 (!X. quotient(zero,X,zero)) /\ 1301 (!X. quotient(X,X,zero)) /\ 1302 (!X. quotient(X,zero,X)) /\ 1303 (!Y X Z. less_equal(X,Y) /\ less_equal(Y,Z) ==> less_equal(X,Z)) /\ 1304 (!W1 X Z W2 Y. quotient(X,Y,W1) /\ less_equal(W1,Z) /\ quotient(X,Z,W2) ==> less_equal(W2,Y)) /\ 1305 (less_equal(x,y)) /\ 1306 (quotient(z,y,zQy)) /\ 1307 (quotient(z,x,zQx)) /\ 1308 (~less_equal(zQy,zQx)) ==> F���; 1309 1310 1311val HEN008_4 = M "HEN008_4" $ 1312 ���(!X:'a. equal(X,X)) /\ 1313 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1314 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1315 (!X Y. less_equal(X,Y) ==> equal(divide(X,Y),zero)) /\ 1316 (!X Y. equal(divide(X,Y),zero) ==> less_equal(X,Y)) /\ 1317 (!Y X. less_equal(divide(X,Y),X)) /\ 1318 (!X Y Z. less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z))) /\ 1319 (!X. less_equal(zero,X)) /\ 1320 (!X Y. less_equal(X,Y) /\ less_equal(Y,X) ==> equal(X,Y)) /\ 1321 (!X. less_equal(X,identity)) /\ 1322 (!A B C. equal(A,B) ==> equal(divide(A,C),divide(B,C))) /\ 1323 (!D F' E. equal(D,E) ==> equal(divide(F',D),divide(F',E))) /\ 1324 (!G H I'. equal(G,H) /\ less_equal(G,I') ==> less_equal(H,I')) /\ 1325 (!J L K'. equal(J,K') /\ less_equal(L,J) ==> less_equal(L,K')) /\ 1326 (!X. equal(divide(X,identity),zero)) /\ 1327 (!X. equal(divide(zero,X),zero)) /\ 1328 (!X. equal(divide(X,X),zero)) /\ 1329 (equal(divide(a,zero),a)) /\ 1330 (!Y X Z. less_equal(X,Y) /\ less_equal(Y,Z) ==> less_equal(X,Z)) /\ 1331 (!X Z Y. less_equal(divide(X,Y),Z) ==> less_equal(divide(X,Z),Y)) /\ 1332 (!Y Z X. less_equal(X,Y) ==> less_equal(divide(Z,Y),divide(Z,X))) /\ 1333 (less_equal(a,b)) /\ 1334 (~less_equal(divide(a,c),divide(b,c))) ==> F���; 1335 1336 1337val HEN009_5 = M "HEN009_5" $ 1338 ���(!X:'a. equal(X,X)) /\ 1339 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1340 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1341 (!Y X. equal(divide(divide(X,Y),X),zero)) /\ 1342 (!X Y Z. equal(divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),zero)) /\ 1343 (!X. equal(divide(zero,X),zero)) /\ 1344 (!X Y. equal(divide(X,Y),zero) /\ equal(divide(Y,X),zero) ==> equal(X,Y)) /\ 1345 (!X. equal(divide(X,identity),zero)) /\ 1346 (!A B C. equal(A,B) ==> equal(divide(A,C),divide(B,C))) /\ 1347 (!D F' E. equal(D,E) ==> equal(divide(F',D),divide(F',E))) /\ 1348 (!Y X Z. equal(divide(X,Y),zero) /\ equal(divide(Y,Z),zero) ==> equal(divide(X,Z),zero)) /\ 1349 (!X Z Y. equal(divide(divide(X,Y),Z),zero) ==> equal(divide(divide(X,Z),Y),zero)) /\ 1350 (!Y Z X. equal(divide(X,Y),zero) ==> equal(divide(divide(Z,Y),divide(Z,X)),zero)) /\ 1351 (~equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a))))) /\ 1352 (equal(divide(identity,a),b)) /\ 1353 (equal(divide(identity,b),c)) /\ 1354 (equal(divide(identity,c),d)) /\ 1355 (~equal(b,d)) ==> F���; 1356 1357 1358val HEN012_3 = M "HEN012_3" $ 1359 ���(!X:'a. equal(X,X)) /\ 1360 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1361 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1362 (!X Y. less_equal(X,Y) ==> equal(divide(X,Y),zero)) /\ 1363 (!X Y. equal(divide(X,Y),zero) ==> less_equal(X,Y)) /\ 1364 (!Y X. less_equal(divide(X,Y),X)) /\ 1365 (!X Y Z. less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z))) /\ 1366 (!X. less_equal(zero,X)) /\ 1367 (!X Y. less_equal(X,Y) /\ less_equal(Y,X) ==> equal(X,Y)) /\ 1368 (!X. less_equal(X,identity)) /\ 1369 (!A B C. equal(A,B) ==> equal(divide(A,C),divide(B,C))) /\ 1370 (!D F' E. equal(D,E) ==> equal(divide(F',D),divide(F',E))) /\ 1371 (!G H I'. equal(G,H) /\ less_equal(G,I') ==> less_equal(H,I')) /\ 1372 (!J L K'. equal(J,K') /\ less_equal(L,J) ==> less_equal(L,K')) /\ 1373 (~less_equal(a,a)) ==> F���; 1374 1375 1376val LCL010_1 = M "LCL010_1" $ 1377 ���(!X Y:'a. is_a_theorem(equivalent(X,Y)) /\ is_a_theorem(X) ==> is_a_theorem(Y)) /\ 1378 (!X Z Y. is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(X,Z),equivalent(Z,Y))))) /\ 1379 (~is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,b),equivalent(a,c))))) ==> F���; 1380 1381 1382val LCL077_2 = M "LCL077_2" $ 1383 ���(!X Y:'a. is_a_theorem(implies(X,Y)) /\ is_a_theorem(X) ==> is_a_theorem(Y)) /\ 1384 (!Y X. is_a_theorem(implies(X,implies(Y,X)))) /\ 1385 (!Y X Z. is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z))))) /\ 1386 (!Y X. is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))) /\ 1387 (!X2 X1 X3. is_a_theorem(implies(X1,X2)) /\ is_a_theorem(implies(X2,X3)) ==> is_a_theorem(implies(X1,X3))) /\ 1388 (~is_a_theorem(implies(not(not(a)),a))) ==> F���; 1389 1390 1391val LCL082_1 = M "LCL082_1" $ 1392 ���(!X Y:'a. is_a_theorem(implies(X,Y)) /\ is_a_theorem(X) ==> is_a_theorem(Y)) /\ 1393 (!Y Z U X. is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X))))) /\ 1394 (~is_a_theorem(implies(a,implies(b,a)))) ==> F���; 1395 1396 1397val LCL111_1 = M "LCL111_1" $ 1398 ���(!X Y:'a. is_a_theorem(implies(X,Y)) /\ is_a_theorem(X) ==> is_a_theorem(Y)) /\ 1399 (!Y X. is_a_theorem(implies(X,implies(Y,X)))) /\ 1400 (!Y X Z. is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) /\ 1401 (!Y X. is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))) /\ 1402 (!Y X. is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))) /\ 1403 (~is_a_theorem(implies(implies(a,b),implies(implies(c,a),implies(c,b))))) ==> F���; 1404 1405 1406val LCL143_1 = M "LCL143_1" $ 1407 ���(!X:'a. equal(X,X)) /\ 1408 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1409 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1410 (!X. equal(implies(true,X),X)) /\ 1411 (!Y X Z. equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),true)) /\ 1412 (!Y X. equal(implies(implies(X,Y),Y),implies(implies(Y,X),X))) /\ 1413 (!Y X. equal(implies(implies(not(X),not(Y)),implies(Y,X)),true)) /\ 1414 (!A B C. equal(A,B) ==> equal(implies(A,C),implies(B,C))) /\ 1415 (!D F' E. equal(D,E) ==> equal(implies(F',D),implies(F',E))) /\ 1416 (!G H. equal(G,H) ==> equal(not(G),not(H))) /\ 1417 (!X Y. equal(big_V(X,Y),implies(implies(X,Y),Y))) /\ 1418 (!X Y. equal(big_hat(X,Y),not(big_V(not(X),not(Y))))) /\ 1419 (!X Y. ordered(X,Y) ==> equal(implies(X,Y),true)) /\ 1420 (!X Y. equal(implies(X,Y),true) ==> ordered(X,Y)) /\ 1421 (!A B C. equal(A,B) ==> equal(big_V(A,C),big_V(B,C))) /\ 1422 (!D F' E. equal(D,E) ==> equal(big_V(F',D),big_V(F',E))) /\ 1423 (!G H I'. equal(G,H) ==> equal(big_hat(G,I'),big_hat(H,I'))) /\ 1424 (!J L K'. equal(J,K') ==> equal(big_hat(L,J),big_hat(L,K'))) /\ 1425 (!M N O. equal(M,N) /\ ordered(M,O) ==> ordered(N,O)) /\ 1426 (!P R Q. equal(P,Q) /\ ordered(R,P) ==> ordered(R,Q)) /\ 1427 (ordered(x,y)) /\ 1428 (~ordered(implies(z,x),implies(z,y))) ==> F���; 1429 1430 1431val LCL182_1 = M "LCL182_1" $ 1432 ���(!A:'a. axiom(or(not(or(A,A)),A))) /\ 1433 (!B A. axiom(or(not(A),or(B,A)))) /\ 1434 (!B A. axiom(or(not(or(A,B)),or(B,A)))) /\ 1435 (!B A C. axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))) /\ 1436 (!A C B. axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))) /\ 1437 (!X. axiom(X) ==> theorem(X)) /\ 1438 (!X Y. axiom(or(not(Y),X)) /\ theorem(Y) ==> theorem(X)) /\ 1439 (!X Y Z. axiom(or(not(X),Y)) /\ theorem(or(not(Y),Z)) ==> theorem(or(not(X),Z))) /\ 1440 (~theorem(or(not(or(not(p),q)),or(not(not(q)),not(p))))) ==> F���; 1441 1442 1443val LCL200_1 = M "LCL200_1" $ 1444 ���(!A:'a. axiom(or(not(or(A,A)),A))) /\ 1445 (!B A. axiom(or(not(A),or(B,A)))) /\ 1446 (!B A. axiom(or(not(or(A,B)),or(B,A)))) /\ 1447 (!B A C. axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))) /\ 1448 (!A C B. axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))) /\ 1449 (!X. axiom(X) ==> theorem(X)) /\ 1450 (!X Y. axiom(or(not(Y),X)) /\ theorem(Y) ==> theorem(X)) /\ 1451 (!X Y Z. axiom(or(not(X),Y)) /\ theorem(or(not(Y),Z)) ==> theorem(or(not(X),Z))) /\ 1452 (~theorem(or(not(not(or(p,q))),not(q)))) ==> F���; 1453 1454 1455val LCL215_1 = M "LCL215_1" $ 1456 ���(!A:'a. axiom(or(not(or(A,A)),A))) /\ 1457 (!B A. axiom(or(not(A),or(B,A)))) /\ 1458 (!B A. axiom(or(not(or(A,B)),or(B,A)))) /\ 1459 (!B A C. axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))) /\ 1460 (!A C B. axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))) /\ 1461 (!X. axiom(X) ==> theorem(X)) /\ 1462 (!X Y. axiom(or(not(Y),X)) /\ theorem(Y) ==> theorem(X)) /\ 1463 (!X Y Z. axiom(or(not(X),Y)) /\ theorem(or(not(Y),Z)) ==> theorem(or(not(X),Z))) /\ 1464 (~theorem(or(not(or(not(p),q)),or(not(or(p,q)),q)))) ==> F���; 1465 1466 1467val LCL230_2 = M "LCL230_2" $ 1468 ���(q ==> p \/ r) /\ 1469 (~p) /\ 1470 (q) /\ 1471 (~r) ==> F���; 1472 1473 1474val LDA003_1 = M "LDA003_1" 1475 ���(!X:num. equal(X,X)) /\ 1476 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1477 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1478 (!Y X Z. equal(f(X,f(Y,Z)),f(f(X,Y),f(X,Z)))) /\ 1479 (!X Y. left(X,f(X,Y))) /\ 1480 (!Y X Z. left(X,Y) /\ left(Y,Z) ==> left(X,Z)) /\ 1481 (equal(n2,f(n1,n1))) /\ 1482 (equal(n3,f(n2,n1))) /\ 1483 (equal(u,f(n2,n2))) /\ 1484 (!A B C. equal(A,B) ==> equal(f(A,C),f(B,C))) /\ 1485 (!D F' E. equal(D,E) ==> equal(f(F',D),f(F',E))) /\ 1486 (!G H I'. equal(G,H) /\ left(G,I') ==> left(H,I')) /\ 1487 (!J L K'. equal(J,K') /\ left(L,J) ==> left(L,K')) /\ 1488 (~left(n3,u)) ==> F���; 1489 1490 1491val MSC002_1 = M "MSC002_1" $ 1492Lib.with_flag(Globals.guessing_tyvars,true) 1493 Term 1494`(at(something,here,now)) /\ 1495 (!Place Situation. hand_at(Place,Situation) ==> hand_at(Place,let_go(Situation))) /\ 1496 (!Place Another_place Situation. hand_at(Place,Situation) ==> hand_at(Another_place,go(Another_place,Situation))) /\ 1497 (!Thing Situation. ~held(Thing,let_go(Situation))) /\ 1498 (!Situation Thing. at(Thing,here,Situation) ==> red(Thing)) /\ 1499 (!Thing Place Situation. at(Thing,Place,Situation) ==> at(Thing,Place,let_go(Situation))) /\ 1500 (!Thing Place Situation. at(Thing,Place,Situation) ==> at(Thing,Place,pick_up(Situation))) /\ 1501 (!Thing Place Situation. at(Thing,Place,Situation) ==> grabbed(Thing,pick_up(go(Place,let_go(Situation))))) /\ 1502 (!Thing Situation. red(Thing) /\ put(Thing,there,Situation) ==> answer(Situation)) /\ 1503 (!Place Thing Another_place Situation. at(Thing,Place,Situation) /\ grabbed(Thing,Situation) ==> put(Thing,Another_place,go(Another_place,Situation))) /\ 1504 (!Thing Place Another_place Situation. at(Thing,Place,Situation) ==> held(Thing,Situation) \/ at(Thing,Place,go(Another_place,Situation))) /\ 1505 (!One_place Thing Place Situation. hand_at(One_place,Situation) /\ held(Thing,Situation) ==> at(Thing,Place,go(Place,Situation))) /\ 1506 (!Place Thing Situation. hand_at(Place,Situation) /\ at(Thing,Place,Situation) ==> held(Thing,pick_up(Situation))) /\ 1507 (!Situation. ~answer(Situation)) ==> F`; 1508 1509val MSC003_1 = M "MSC003_1" $ 1510Lib.with_flag(Globals.guessing_tyvars,true) 1511 Term 1512`(!Number_of_small_parts Small_part Big_part Number_of_mid_parts Mid_part. has_parts(Big_part,Number_of_mid_parts,Mid_part) ==> in'(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) \/ has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)) /\ 1513 (!Big_part Mid_part Number_of_mid_parts Number_of_small_parts Small_part. has_parts(Big_part,Number_of_mid_parts,Mid_part) /\ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ==> has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)) /\ 1514 (in'(john,boy)) /\ 1515 (!X. in'(X,boy) ==> in'(X,human)) /\ 1516 (!X. in'(X,hand) ==> has_parts(X,n5,fingers)) /\ 1517 (!X. in'(X,human) ==> has_parts(X,n2,arm)) /\ 1518 (!X. in'(X,arm) ==> has_parts(X,n1,hand)) /\ 1519 (~has_parts(john,times(n2,n1),hand)) ==> F`; 1520 1521 1522val MSC004_1 = M "MSC004_1" $ 1523Lib.with_flag(Globals.guessing_tyvars,true) 1524 Term 1525`(!Number_of_small_parts Small_part Big_part Number_of_mid_parts Mid_part. has_parts(Big_part,Number_of_mid_parts,Mid_part) ==> in'(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Mid_part) \/ has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)) /\ 1526 (!Big_part Mid_part Number_of_mid_parts Number_of_small_parts Small_part. has_parts(Big_part,Number_of_mid_parts,Mid_part) /\ has_parts(object_in(Big_part,Mid_part,Small_part,Number_of_mid_parts,Number_of_small_parts),Number_of_small_parts,Small_part) ==> has_parts(Big_part,times(Number_of_mid_parts,Number_of_small_parts),Small_part)) /\ 1527 (in'(john,boy)) /\ 1528 (!X. in'(X,boy) ==> in'(X,human)) /\ 1529 (!X. in'(X,hand) ==> has_parts(X,n5,fingers)) /\ 1530 (!X. in'(X,human) ==> has_parts(X,n2,arm)) /\ 1531 (!X. in'(X,arm) ==> has_parts(X,n1,hand)) /\ 1532 (~has_parts(john,times(times(n2,n1),n5),fingers)) ==> F`; 1533 1534 1535val MSC005_1 = M "MSC005_1" $ 1536Lib.with_flag(Globals.guessing_tyvars,true) 1537 Term 1538`(value(truth,truth)) /\ 1539 (value(falsity,falsity)) /\ 1540 (!X Y. value(X,truth) /\ value(Y,truth) ==> value(xor(X,Y),falsity)) /\ 1541 (!X Y. value(X,truth) /\ value(Y,falsity) ==> value(xor(X,Y),truth)) /\ 1542 (!X Y. value(X,falsity) /\ value(Y,truth) ==> value(xor(X,Y),truth)) /\ 1543 (!X Y. value(X,falsity) /\ value(Y,falsity) ==> value(xor(X,Y),falsity)) /\ 1544 (!Value. ~value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value)) 1545 ==> F`; 1546 1547 1548val MSC006_1 = M "MSC006_1" $ 1549 ���(!Y X Z:'a. p(X,Y) /\ p(Y,Z) ==> p(X,Z)) /\ 1550 (!Y X Z. q(X,Y) /\ q(Y,Z) ==> q(X,Z)) /\ 1551 (!Y X. q(X,Y) ==> q(Y,X)) /\ 1552 (!X Y. p(X,Y) \/ q(X,Y)) /\ 1553 (~p(a,b)) /\ 1554 (~q(c,d)) ==> F���; 1555 1556 1557val NUM001_1 = M "NUM001_1" 1558 ���(!A:'a. equal(A,A)) /\ 1559 (!B A C. equal(A,B) /\ equal(B,C) ==> equal(A,C)) /\ 1560 (!B A. equal(add(A,B),add(B,A))) /\ 1561 (!A B C. equal(add(A,add(B,C)),add(add(A,B),C))) /\ 1562 (!B A. equal(subtract(add(A,B),B),A)) /\ 1563 (!A B. equal(A,subtract(add(A,B),B))) /\ 1564 (!A C B. equal(add(subtract(A,B),C),subtract(add(A,C),B))) /\ 1565 (!A C B. equal(subtract(add(A,B),C),add(subtract(A,C),B))) /\ 1566 (!A C B D. equal(A,B) /\ equal(C,add(A,D)) ==> equal(C,add(B,D))) /\ 1567 (!A C D B. equal(A,B) /\ equal(C,add(D,A)) ==> equal(C,add(D,B))) /\ 1568 (!A C B D. equal(A,B) /\ equal(C,subtract(A,D)) ==> equal(C,subtract(B,D))) /\ 1569 (!A C D B. equal(A,B) /\ equal(C,subtract(D,A)) ==> equal(C,subtract(D,B))) /\ 1570 (~equal(add(add(a,b),c),add(a,add(b,c)))) ==> F���; 1571 1572 1573val NUM021_1 = M "NUM021_1" 1574 ���(!X. equal(X,X)) /\ 1575 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1576 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1577 (!A. equal(add(A,n0),A)) /\ 1578 (!A B. equal(add(A,successor(B)),successor(add(A,B)))) /\ 1579 (!A. equal(multiply(A,n0),n0)) /\ 1580 (!B A. equal(multiply(A,successor(B)),add(multiply(A,B),A))) /\ 1581 (!A B. equal(successor(A),successor(B)) ==> equal(A,B)) /\ 1582 (!A B. equal(A,B) ==> equal(successor(A),successor(B))) /\ 1583 (!A C B. less(A,B) /\ less(C,A) ==> less(C,B)) /\ 1584 (!A B C. equal(add(successor(A),B),C) ==> less(B,C)) /\ 1585 (!A B. less(A,B) ==> equal(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)) /\ 1586 (!A B. divides(A,B) ==> less(A,B) \/ equal(A,B)) /\ 1587 (!A B. less(A,B) ==> divides(A,B)) /\ 1588 (!A B. equal(A,B) ==> divides(A,B)) /\ 1589 (less(b,c)) /\ 1590 (~less(b,a)) /\ 1591 (divides(c,a)) /\ 1592 (!A. ~equal(successor(A),n0)) ==> F���; 1593 1594 1595val NUM024_1 = M "NUM024_1" $ 1596 ���(!X. equal(X,X)) /\ 1597 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1598 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1599 (!A. equal(add(A,n0),A)) /\ 1600 (!A B. equal(add(A,successor(B)),successor(add(A,B)))) /\ 1601 (!A. equal(multiply(A,n0),n0)) /\ 1602 (!B A. equal(multiply(A,successor(B)),add(multiply(A,B),A))) /\ 1603 (!A B. equal(successor(A),successor(B)) ==> equal(A,B)) /\ 1604 (!A B. equal(A,B) ==> equal(successor(A),successor(B))) /\ 1605 (!A C B. less(A,B) /\ less(C,A) ==> less(C,B)) /\ 1606 (!A B C. equal(add(successor(A),B),C) ==> less(B,C)) /\ 1607 (!A B. less(A,B) ==> equal(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)) /\ 1608 (!B A. equal(add(A,B),add(B,A))) /\ 1609 (!B A C. equal(add(A,B),add(C,B)) ==> equal(A,C)) /\ 1610 (less(a,a)) /\ 1611 (!A. ~equal(successor(A),n0)) ==> F���; 1612 1613val _ = hide "flip" 1614 1615val NUM180_1 = M "NUM180_1" $ 1616Lib.with_flag(Globals.guessing_tyvars,true) 1617 Term 1618`(!X:'a. equal(X,X)) /\ 1619 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1620 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1621 (!X U Y. subclass(X,Y) /\ member(U,X) ==> member(U,Y)) /\ 1622 (!X Y. member(not_subclass_element(X,Y),X) \/ subclass(X,Y)) /\ 1623 (!X Y. member(not_subclass_element(X,Y),Y) ==> subclass(X,Y)) /\ 1624 (!X. subclass(X,universal_class)) /\ 1625 (!X Y. equal(X,Y) ==> subclass(X,Y)) /\ 1626 (!Y X. equal(X,Y) ==> subclass(Y,X)) /\ 1627 (!X Y. subclass(X,Y) /\ subclass(Y,X) ==> equal(X,Y)) /\ 1628 (!X U Y. member(U,unordered_pair(X,Y)) ==> equal(U,X) \/ equal(U,Y)) /\ 1629 (!X Y. member(X,universal_class) ==> member(X,unordered_pair(X,Y))) /\ 1630 (!X Y. member(Y,universal_class) ==> member(Y,unordered_pair(X,Y))) /\ 1631 (!X Y. member(unordered_pair(X,Y),universal_class)) /\ 1632 (!X. equal(unordered_pair(X,X),singleton(X))) /\ 1633 (!X Y. equal(unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),ordered_pair(X,Y))) /\ 1634 (!V Y U X. member(ordered_pair(U,V),cross_product(X,Y)) ==> member(U,X)) /\ 1635 (!U X V Y. member(ordered_pair(U,V),cross_product(X,Y)) ==> member(V,Y)) /\ 1636 (!U V X Y. member(U,X) /\ member(V,Y) ==> member(ordered_pair(U,V),cross_product(X,Y))) /\ 1637 (!X Y Z. member(Z,cross_product(X,Y)) ==> equal(ordered_pair(first(Z),second(Z)),Z)) /\ 1638 (subclass(element_relation,cross_product(universal_class,universal_class))) /\ 1639 (!X Y. member(ordered_pair(X,Y),element_relation) ==> member(X,Y)) /\ 1640 (!X Y. member(ordered_pair(X,Y),cross_product(universal_class,universal_class)) /\ member(X,Y) ==> member(ordered_pair(X,Y),element_relation)) /\ 1641 (!Y Z X. member(Z,intersection(X,Y)) ==> member(Z,X)) /\ 1642 (!X Z Y. member(Z,intersection(X,Y)) ==> member(Z,Y)) /\ 1643 (!Z X Y. member(Z,X) /\ member(Z,Y) ==> member(Z,intersection(X,Y))) /\ 1644 (!Z X. ~(member(Z,complement(X)) /\ member(Z,X))) /\ 1645 (!Z X. member(Z,universal_class) ==> member(Z,complement(X)) \/ member(Z,X)) /\ 1646 (!X Y. equal(complement(intersection(complement(X),complement(Y))),union(X,Y))) /\ 1647 (!X Y. equal(intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y)))),difference(X,Y))) /\ 1648 (!Xr X Y. equal(intersection(Xr,cross_product(X,Y)),restrict(Xr,X,Y))) /\ 1649 (!Xr X Y. equal(intersection(cross_product(X,Y),Xr),restrict(Xr,X,Y))) /\ 1650 (!Z X. ~(equal(restrict(X,singleton(Z),universal_class),null_class) /\ member(Z,domain_of(X)))) /\ 1651 (!Z X. member(Z,universal_class) ==> equal(restrict(X,singleton(Z),universal_class),null_class) \/ member(Z,domain_of(X))) /\ 1652 (!X. subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) /\ 1653 (!V W U X. member(ordered_pair(ordered_pair(U,V),W),rotate(X)) ==> member(ordered_pair(ordered_pair(V,W),U),X)) /\ 1654 (!U V W X. member(ordered_pair(ordered_pair(V,W),U),X) /\ member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)) ==> member(ordered_pair(ordered_pair(U,V),W),rotate(X))) /\ 1655 (!X. subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) /\ 1656 (!V U W X. member(ordered_pair(ordered_pair(U,V),W),flip(X)) ==> member(ordered_pair(ordered_pair(V,U),W),X)) /\ 1657 (!U V W X. member(ordered_pair(ordered_pair(V,U),W),X) /\ member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)) ==> member(ordered_pair(ordered_pair(U,V),W),flip(X))) /\ 1658 (!Y. equal(domain_of(flip(cross_product(Y,universal_class))),inverse(Y))) /\ 1659 (!Z. equal(domain_of(inverse(Z)),range_of(Z))) /\ 1660 (!Z X Y. equal(first(not_subclass_element(restrict(Z,X,singleton(Y)),null_class)),domain(Z,X,Y))) /\ 1661 (!Z X Y. equal(second(not_subclass_element(restrict(Z,singleton(X),Y),null_class)),range(Z,X,Y))) /\ 1662 (!Xr X. equal(range_of(restrict(Xr,X,universal_class)),image(Xr,X))) /\ 1663 (!X. equal(union(X,singleton(X)),successor(X))) /\ 1664 (subclass(successor_relation,cross_product(universal_class,universal_class))) /\ 1665 (!X Y. member(ordered_pair(X,Y),successor_relation) ==> equal(successor(X),Y)) /\ 1666 (!X Y. equal(successor(X),Y) /\ member(ordered_pair(X,Y),cross_product(universal_class,universal_class)) ==> member(ordered_pair(X,Y),successor_relation)) /\ 1667 (!X. inductive(X) ==> member(null_class,X)) /\ 1668 (!X. inductive(X) ==> subclass(image(successor_relation,X),X)) /\ 1669 (!X. member(null_class,X) /\ subclass(image(successor_relation,X),X) ==> inductive(X)) /\ 1670 (inductive(omega)) /\ 1671 (!Y. inductive(Y) ==> subclass(omega,Y)) /\ 1672 (member(omega,universal_class)) /\ 1673 (!X. equal(domain_of(restrict(element_relation,universal_class,X)),sum_class(X))) /\ 1674 (!X. member(X,universal_class) ==> member(sum_class(X),universal_class)) /\ 1675 (!X. equal(complement(image(element_relation,complement(X))),power_class(X))) /\ 1676 (!U. member(U,universal_class) ==> member(power_class(U),universal_class)) /\ 1677 (!Yr Xr. subclass(compose(Yr,Xr),cross_product(universal_class,universal_class))) /\ 1678 (!Z Yr Xr Y. member(ordered_pair(Y,Z),compose(Yr,Xr)) ==> member(Z,image(Yr,image(Xr,singleton(Y))))) /\ 1679 (!Y Z Yr Xr. member(Z,image(Yr,image(Xr,singleton(Y)))) /\ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class)) ==> member(ordered_pair(Y,Z),compose(Yr,Xr))) /\ 1680 (!X. single_valued_class(X) ==> subclass(compose(X,inverse(X)),identity_relation)) /\ 1681 (!X. subclass(compose(X,inverse(X)),identity_relation) ==> single_valued_class(X)) /\ 1682 (!Xf. function(Xf) ==> subclass(Xf,cross_product(universal_class,universal_class))) /\ 1683 (!Xf. function(Xf) ==> subclass(compose(Xf,inverse(Xf)),identity_relation)) /\ 1684 (!Xf. subclass(Xf,cross_product(universal_class,universal_class)) /\ subclass(compose(Xf,inverse(Xf)),identity_relation) ==> function(Xf)) /\ 1685 (!Xf X. function(Xf) /\ member(X,universal_class) ==> member(image(Xf,X),universal_class)) /\ 1686 (!X. equal(X,null_class) \/ member(regular(X),X)) /\ 1687 (!X. equal(X,null_class) \/ equal(intersection(X,regular(X)),null_class)) /\ 1688 (!Xf Y. equal(sum_class(image(Xf,singleton(Y))),apply(Xf,Y))) /\ 1689 (function(choice)) /\ 1690 (!Y. member(Y,universal_class) ==> equal(Y,null_class) \/ member(apply(choice,Y),Y)) /\ 1691 (!Xf. one_to_one(Xf) ==> function(Xf)) /\ 1692 (!Xf. one_to_one(Xf) ==> function(inverse(Xf))) /\ 1693 (!Xf. function(inverse(Xf)) /\ function(Xf) ==> one_to_one(Xf)) /\ 1694 (equal(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),subset_relation)) /\ 1695 (equal(intersection(inverse(subset_relation),subset_relation),identity_relation)) /\ 1696 (!Xr. equal(complement(domain_of(intersection(Xr,identity_relation))),diagonalise(Xr))) /\ 1697 (!X. equal(intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))),cantor(X))) /\ 1698 (!Xf. operation(Xf) ==> function(Xf)) /\ 1699 (!Xf. operation(Xf) ==> equal(cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))),domain_of(Xf))) /\ 1700 (!Xf. operation(Xf) ==> subclass(range_of(Xf),domain_of(domain_of(Xf)))) /\ 1701 (!Xf. function(Xf) /\ equal(cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))),domain_of(Xf)) /\ subclass(range_of(Xf),domain_of(domain_of(Xf))) ==> operation(Xf)) /\ 1702 (!Xf1 Xf2 Xh. compatible(Xh,Xf1,Xf2) ==> function(Xh)) /\ 1703 (!Xf2 Xf1 Xh. compatible(Xh,Xf1,Xf2) ==> equal(domain_of(domain_of(Xf1)),domain_of(Xh))) /\ 1704 (!Xf1 Xh Xf2. compatible(Xh,Xf1,Xf2) ==> subclass(range_of(Xh),domain_of(domain_of(Xf2)))) /\ 1705 (!Xh Xh1 Xf1 Xf2. function(Xh) /\ equal(domain_of(domain_of(Xf1)),domain_of(Xh)) /\ subclass(range_of(Xh),domain_of(domain_of(Xf2))) ==> compatible(Xh1,Xf1,Xf2)) /\ 1706 (!Xh Xf2 Xf1. homomorphism(Xh,Xf1,Xf2) ==> operation(Xf1)) /\ 1707 (!Xh Xf1 Xf2. homomorphism(Xh,Xf1,Xf2) ==> operation(Xf2)) /\ 1708 (!Xh Xf1 Xf2. homomorphism(Xh,Xf1,Xf2) ==> compatible(Xh,Xf1,Xf2)) /\ 1709 (!Xf2 Xh Xf1 X Y. homomorphism(Xh,Xf1,Xf2) /\ member(ordered_pair(X,Y),domain_of(Xf1)) ==> equal(apply(Xf2,ordered_pair(apply(Xh,X),apply(Xh,Y))),apply(Xh,apply(Xf1,ordered_pair(X,Y))))) /\ 1710 (!Xh Xf1 Xf2. operation(Xf1) /\ operation(Xf2) /\ compatible(Xh,Xf1,Xf2) ==> member(ordered_pair(not_homomorphism1(Xh,Xf1,Xf2),not_homomorphism2(Xh,Xf1,Xf2)),domain_of(Xf1)) \/ homomorphism(Xh,Xf1,Xf2)) /\ 1711 (!Xh Xf1 Xf2. operation(Xf1) /\ operation(Xf2) /\ compatible(Xh,Xf1,Xf2) /\ equal(apply(Xf2,ordered_pair(apply(Xh,not_homomorphism1(Xh,Xf1,Xf2)),apply(Xh,not_homomorphism2(Xh,Xf1,Xf2)))),apply(Xh,apply(Xf1,ordered_pair(not_homomorphism1(Xh,Xf1,Xf2),not_homomorphism2(Xh,Xf1,Xf2))))) ==> homomorphism(Xh,Xf1,Xf2)) /\ 1712 (!D E F'. equal(D,E) ==> equal(apply(D,F'),apply(E,F'))) /\ 1713 (!G I' H. equal(G,H) ==> equal(apply(I',G),apply(I',H))) /\ 1714 (!J K'. equal(J,K') ==> equal(cantor(J),cantor(K'))) /\ 1715 (!L M. equal(L,M) ==> equal(complement(L),complement(M))) /\ 1716 (!N O P. equal(N,O) ==> equal(compose(N,P),compose(O,P))) /\ 1717 (!Q S' R. equal(Q,R) ==> equal(compose(S',Q),compose(S',R))) /\ 1718 (!T' U V. equal(T',U) ==> equal(cross_product(T',V),cross_product(U,V))) /\ 1719 (!W Y X. equal(W,X) ==> equal(cross_product(Y,W),cross_product(Y,X))) /\ 1720 (!Z A1. equal(Z,A1) ==> equal(diagonalise(Z),diagonalise(A1))) /\ 1721 (!B1 C1 D1. equal(B1,C1) ==> equal(difference(B1,D1),difference(C1,D1))) /\ 1722 (!E1 G1 F1. equal(E1,F1) ==> equal(difference(G1,E1),difference(G1,F1))) /\ 1723 (!H1 I1 J1 K1. equal(H1,I1) ==> equal(domain(H1,J1,K1),domain(I1,J1,K1))) /\ 1724 (!L1 N1 M1 O1. equal(L1,M1) ==> equal(domain(N1,L1,O1),domain(N1,M1,O1))) /\ 1725 (!P1 R1 S1 Q1. equal(P1,Q1) ==> equal(domain(R1,S1,P1),domain(R1,S1,Q1))) /\ 1726 (!T1 U1. equal(T1,U1) ==> equal(domain_of(T1),domain_of(U1))) /\ 1727 (!V1 W1. equal(V1,W1) ==> equal(first(V1),first(W1))) /\ 1728 (!X1 Y1. equal(X1,Y1) ==> equal(flip(X1),flip(Y1))) /\ 1729 (!Z1 A2 B2. equal(Z1,A2) ==> equal(image(Z1,B2),image(A2,B2))) /\ 1730 (!C2 E2 D2. equal(C2,D2) ==> equal(image(E2,C2),image(E2,D2))) /\ 1731 (!F2 G2 H2. equal(F2,G2) ==> equal(intersection(F2,H2),intersection(G2,H2))) /\ 1732 (!I2 K2 J2. equal(I2,J2) ==> equal(intersection(K2,I2),intersection(K2,J2))) /\ 1733 (!L2 M2. equal(L2,M2) ==> equal(inverse(L2),inverse(M2))) /\ 1734 (!N2 O2 P2 Q2. equal(N2,O2) ==> equal(not_homomorphism1(N2,P2,Q2),not_homomorphism1(O2,P2,Q2))) /\ 1735 (!R2 T2 S2 U2. equal(R2,S2) ==> equal(not_homomorphism1(T2,R2,U2),not_homomorphism1(T2,S2,U2))) /\ 1736 (!V2 X2 Y2 W2. equal(V2,W2) ==> equal(not_homomorphism1(X2,Y2,V2),not_homomorphism1(X2,Y2,W2))) /\ 1737 (!Z2 A3 B3 C3. equal(Z2,A3) ==> equal(not_homomorphism2(Z2,B3,C3),not_homomorphism2(A3,B3,C3))) /\ 1738 (!D3 F3 E3 G3. equal(D3,E3) ==> equal(not_homomorphism2(F3,D3,G3),not_homomorphism2(F3,E3,G3))) /\ 1739 (!H3 J3 K3 I3. equal(H3,I3) ==> equal(not_homomorphism2(J3,K3,H3),not_homomorphism2(J3,K3,I3))) /\ 1740 (!L3 M3 N3. equal(L3,M3) ==> equal(not_subclass_element(L3,N3),not_subclass_element(M3,N3))) /\ 1741 (!O3 Q3 P3. equal(O3,P3) ==> equal(not_subclass_element(Q3,O3),not_subclass_element(Q3,P3))) /\ 1742 (!R3 S3 T3. equal(R3,S3) ==> equal(ordered_pair(R3,T3),ordered_pair(S3,T3))) /\ 1743 (!U3 W3 V3. equal(U3,V3) ==> equal(ordered_pair(W3,U3),ordered_pair(W3,V3))) /\ 1744 (!X3 Y3. equal(X3,Y3) ==> equal(power_class(X3),power_class(Y3))) /\ 1745 (!Z3 A4 B4 C4. equal(Z3,A4) ==> equal(range(Z3,B4,C4),range(A4,B4,C4))) /\ 1746 (!D4 F4 E4 G4. equal(D4,E4) ==> equal(range(F4,D4,G4),range(F4,E4,G4))) /\ 1747 (!H4 J4 K4 I4. equal(H4,I4) ==> equal(range(J4,K4,H4),range(J4,K4,I4))) /\ 1748 (!L4 M4. equal(L4,M4) ==> equal(range_of(L4),range_of(M4))) /\ 1749 (!N4 O4. equal(N4,O4) ==> equal(regular(N4),regular(O4))) /\ 1750 (!P4 Q4 R4 S4. equal(P4,Q4) ==> equal(restrict(P4,R4,S4),restrict(Q4,R4,S4))) /\ 1751 (!T4 V4 U4 W4. equal(T4,U4) ==> equal(restrict(V4,T4,W4),restrict(V4,U4,W4))) /\ 1752 (!X4 Z4 A5 Y4. equal(X4,Y4) ==> equal(restrict(Z4,A5,X4),restrict(Z4,A5,Y4))) /\ 1753 (!B5 C5. equal(B5,C5) ==> equal(rotate(B5),rotate(C5))) /\ 1754 (!D5 E5. equal(D5,E5) ==> equal(second(D5),second(E5))) /\ 1755 (!F5 G5. equal(F5,G5) ==> equal(singleton(F5),singleton(G5))) /\ 1756 (!H5 I5. equal(H5,I5) ==> equal(successor(H5),successor(I5))) /\ 1757 (!J5 K5. equal(J5,K5) ==> equal(sum_class(J5),sum_class(K5))) /\ 1758 (!L5 M5 N5. equal(L5,M5) ==> equal(union(L5,N5),union(M5,N5))) /\ 1759 (!O5 Q5 P5. equal(O5,P5) ==> equal(union(Q5,O5),union(Q5,P5))) /\ 1760 (!R5 S5 T5. equal(R5,S5) ==> equal(unordered_pair(R5,T5),unordered_pair(S5,T5))) /\ 1761 (!U5 W5 V5. equal(U5,V5) ==> equal(unordered_pair(W5,U5),unordered_pair(W5,V5))) /\ 1762 (!X5 Y5 Z5 A6. equal(X5,Y5) /\ compatible(X5,Z5,A6) ==> compatible(Y5,Z5,A6)) /\ 1763 (!B6 D6 C6 E6. equal(B6,C6) /\ compatible(D6,B6,E6) ==> compatible(D6,C6,E6)) /\ 1764 (!F6 H6 I6 G6. equal(F6,G6) /\ compatible(H6,I6,F6) ==> compatible(H6,I6,G6)) /\ 1765 (!J6 K6. equal(J6,K6) /\ function(J6) ==> function(K6)) /\ 1766 (!L6 M6 N6 O6. equal(L6,M6) /\ homomorphism(L6,N6,O6) ==> homomorphism(M6,N6,O6)) /\ 1767 (!P6 R6 Q6 S6. equal(P6,Q6) /\ homomorphism(R6,P6,S6) ==> homomorphism(R6,Q6,S6)) /\ 1768 (!T6 V6 W6 U6. equal(T6,U6) /\ homomorphism(V6,W6,T6) ==> homomorphism(V6,W6,U6)) /\ 1769 (!X6 Y6. equal(X6,Y6) /\ inductive(X6) ==> inductive(Y6)) /\ 1770 (!Z6 A7 B7. equal(Z6,A7) /\ member(Z6,B7) ==> member(A7,B7)) /\ 1771 (!C7 E7 D7. equal(C7,D7) /\ member(E7,C7) ==> member(E7,D7)) /\ 1772 (!F7 G7. equal(F7,G7) /\ one_to_one(F7) ==> one_to_one(G7)) /\ 1773 (!H7 I7. equal(H7,I7) /\ operation(H7) ==> operation(I7)) /\ 1774 (!J7 K7. equal(J7,K7) /\ single_valued_class(J7) ==> single_valued_class(K7)) /\ 1775 (!L7 M7 N7. equal(L7,M7) /\ subclass(L7,N7) ==> subclass(M7,N7)) /\ 1776 (!O7 Q7 P7. equal(O7,P7) /\ subclass(Q7,O7) ==> subclass(Q7,P7)) /\ 1777 (!X. subclass(compose_class(X),cross_product(universal_class,universal_class))) /\ 1778 (!X Y Z. member(ordered_pair(Y,Z),compose_class(X)) ==> equal(compose(X,Y),Z)) /\ 1779 (!Y Z X. member(ordered_pair(Y,Z),cross_product(universal_class,universal_class)) /\ equal(compose(X,Y),Z) ==> member(ordered_pair(Y,Z),compose_class(X))) /\ 1780 (subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))) /\ 1781 (!X Y Z. member(ordered_pair(X,ordered_pair(Y,Z)),composition_function) ==> equal(compose(X,Y),Z)) /\ 1782 (!X Y. member(ordered_pair(X,Y),cross_product(universal_class,universal_class)) ==> member(ordered_pair(X,ordered_pair(Y,compose(X,Y))),composition_function)) /\ 1783 (subclass(domain_relation,cross_product(universal_class,universal_class))) /\ 1784 (!X Y. member(ordered_pair(X,Y),domain_relation) ==> equal(domain_of(X),Y)) /\ 1785 (!X. member(X,universal_class) ==> member(ordered_pair(X,domain_of(X)),domain_relation)) /\ 1786 (!X. equal(first(not_subclass_element(compose(X,inverse(X)),identity_relation)),single_valued1(X))) /\ 1787 (!X. equal(second(not_subclass_element(compose(X,inverse(X)),identity_relation)),single_valued2(X))) /\ 1788 (!X. equal(domain(X,image(inverse(X),singleton(single_valued1(X))),single_valued2(X)),single_valued3(X))) /\ 1789 (equal(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation)) /\ 1790 (subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))) /\ 1791 (!Z Y X. member(ordered_pair(X,ordered_pair(Y,Z)),application_function) ==> member(Y,domain_of(X))) /\ 1792 (!X Y Z. member(ordered_pair(X,ordered_pair(Y,Z)),application_function) ==> equal(apply(X,Y),Z)) /\ 1793 (!Z X Y. member(ordered_pair(X,ordered_pair(Y,Z)),cross_product(universal_class,cross_product(universal_class,universal_class))) /\ member(Y,domain_of(X)) ==> member(ordered_pair(X,ordered_pair(Y,apply(X,Y))),application_function)) /\ 1794 (!X Y Xf. maps(Xf,X,Y) ==> function(Xf)) /\ 1795 (!Y Xf X. maps(Xf,X,Y) ==> equal(domain_of(Xf),X)) /\ 1796 (!X Xf Y. maps(Xf,X,Y) ==> subclass(range_of(Xf),Y)) /\ 1797 (!Xf Y. function(Xf) /\ subclass(range_of(Xf),Y) ==> maps(Xf,domain_of(Xf),Y)) /\ 1798 (!L M. equal(L,M) ==> equal(compose_class(L),compose_class(M))) /\ 1799 (!N2 O2. equal(N2,O2) ==> equal(single_valued1(N2),single_valued1(O2))) /\ 1800 (!P2 Q2. equal(P2,Q2) ==> equal(single_valued2(P2),single_valued2(Q2))) /\ 1801 (!R2 S2. equal(R2,S2) ==> equal(single_valued3(R2),single_valued3(S2))) /\ 1802 (!X2 Y2 Z2 A3. equal(X2,Y2) /\ maps(X2,Z2,A3) ==> maps(Y2,Z2,A3)) /\ 1803 (!B3 D3 C3 E3. equal(B3,C3) /\ maps(D3,B3,E3) ==> maps(D3,C3,E3)) /\ 1804 (!F3 H3 I3 G3. equal(F3,G3) /\ maps(H3,I3,F3) ==> maps(H3,I3,G3)) /\ 1805 (!X. equal(union(X,inverse(X)),symmetrization_of(X))) /\ 1806 (!X Y. irreflexive(X,Y) ==> subclass(restrict(X,Y,Y),complement(identity_relation))) /\ 1807 (!X Y. subclass(restrict(X,Y,Y),complement(identity_relation)) ==> irreflexive(X,Y)) /\ 1808 (!Y X. connected(X,Y) ==> subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))) /\ 1809 (!X Y. subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X))) ==> connected(X,Y)) /\ 1810 (!Xr Y. transitive(Xr,Y) ==> subclass(compose(restrict(Xr,Y,Y),restrict(Xr,Y,Y)),restrict(Xr,Y,Y))) /\ 1811 (!Xr Y. subclass(compose(restrict(Xr,Y,Y),restrict(Xr,Y,Y)),restrict(Xr,Y,Y)) ==> transitive(Xr,Y)) /\ 1812 (!Xr Y. asymmetric(Xr,Y) ==> equal(restrict(intersection(Xr,inverse(Xr)),Y,Y),null_class)) /\ 1813 (!Xr Y. equal(restrict(intersection(Xr,inverse(Xr)),Y,Y),null_class) ==> asymmetric(Xr,Y)) /\ 1814 (!Xr Y Z. equal(segment(Xr,Y,Z),domain_of(restrict(Xr,Y,singleton(Z))))) /\ 1815 (!X Y. well_ordering(X,Y) ==> connected(X,Y)) /\ 1816 (!Y Xr U. well_ordering(Xr,Y) /\ subclass(U,Y) ==> equal(U,null_class) \/ member(least(Xr,U),U)) /\ 1817 (!Y V Xr U. well_ordering(Xr,Y) /\ subclass(U,Y) /\ member(V,U) ==> member(least(Xr,U),U)) /\ 1818 (!Y Xr U. well_ordering(Xr,Y) /\ subclass(U,Y) ==> equal(segment(Xr,U,least(Xr,U)),null_class)) /\ 1819 (!Y V U Xr. ~(well_ordering(Xr,Y) /\ subclass(U,Y) /\ member(V,U) /\ member(ordered_pair(V,least(Xr,U)),Xr))) /\ 1820 (!Xr Y. connected(Xr,Y) /\ equal(not_well_ordering(Xr,Y),null_class) ==> well_ordering(Xr,Y)) /\ 1821 (!Xr Y. connected(Xr,Y) ==> subclass(not_well_ordering(Xr,Y),Y) \/ well_ordering(Xr,Y)) /\ 1822 (!V Xr Y. member(V,not_well_ordering(Xr,Y)) /\ equal(segment(Xr,not_well_ordering(Xr,Y),V),null_class) /\ connected(Xr,Y) ==> well_ordering(Xr,Y)) /\ 1823 (!Xr Y Z. section(Xr,Y,Z) ==> subclass(Y,Z)) /\ 1824 (!Xr Z Y. section(Xr,Y,Z) ==> subclass(domain_of(restrict(Xr,Z,Y)),Y)) /\ 1825 (!Xr Y Z. subclass(Y,Z) /\ subclass(domain_of(restrict(Xr,Z,Y)),Y) ==> section(Xr,Y,Z)) /\ 1826 (!X. member(X,ordinal_numbers) ==> well_ordering(element_relation,X)) /\ 1827 (!X. member(X,ordinal_numbers) ==> subclass(sum_class(X),X)) /\ 1828 (!X. well_ordering(element_relation,X) /\ subclass(sum_class(X),X) /\ member(X,universal_class) ==> member(X,ordinal_numbers)) /\ 1829 (!X. well_ordering(element_relation,X) /\ subclass(sum_class(X),X) ==> member(X,ordinal_numbers) \/ equal(X,ordinal_numbers)) /\ 1830 (equal(union(singleton(null_class),image(successor_relation,ordinal_numbers)),kind_1_ordinals)) /\ 1831 (equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals)) /\ 1832 (!X. subclass(rest_of(X),cross_product(universal_class,universal_class))) /\ 1833 (!V U X. member(ordered_pair(U,V),rest_of(X)) ==> member(U,domain_of(X))) /\ 1834 (!X U V. member(ordered_pair(U,V),rest_of(X)) ==> equal(restrict(X,U,universal_class),V)) /\ 1835 (!U V X. member(U,domain_of(X)) /\ equal(restrict(X,U,universal_class),V) ==> member(ordered_pair(U,V),rest_of(X))) /\ 1836 (subclass(rest_relation,cross_product(universal_class,universal_class))) /\ 1837 (!X Y. member(ordered_pair(X,Y),rest_relation) ==> equal(rest_of(X),Y)) /\ 1838 (!X. member(X,universal_class) ==> member(ordered_pair(X,rest_of(X)),rest_relation)) /\ 1839 (!X Z. member(X,recursion_equation_functions(Z)) ==> function(Z)) /\ 1840 (!Z X. member(X,recursion_equation_functions(Z)) ==> function(X)) /\ 1841 (!Z X. member(X,recursion_equation_functions(Z)) ==> member(domain_of(X),ordinal_numbers)) /\ 1842 (!Z X. member(X,recursion_equation_functions(Z)) ==> equal(compose(Z,rest_of(X)),X)) /\ 1843 (!X Z. function(Z) /\ function(X) /\ member(domain_of(X),ordinal_numbers) /\ equal(compose(Z,rest_of(X)),X) ==> member(X,recursion_equation_functions(Z))) /\ 1844 (subclass(union_of_range_map,cross_product(universal_class,universal_class))) /\ 1845 (!X Y. member(ordered_pair(X,Y),union_of_range_map) ==> equal(sum_class(range_of(X)),Y)) /\ 1846 (!X Y. member(ordered_pair(X,Y),cross_product(universal_class,universal_class)) /\ equal(sum_class(range_of(X)),Y) ==> member(ordered_pair(X,Y),union_of_range_map)) /\ 1847 (!X Y. equal(apply(recursion(X,successor_relation,union_of_range_map),Y),ordinal_add(X,Y))) /\ 1848 (!X Y. equal(recursion(null_class,apply(add_relation,X),union_of_range_map),ordinal_multiply(X,Y))) /\ 1849 (!X. member(X,omega) ==> equal(integer_of(X),X)) /\ 1850 (!X. member(X,omega) \/ equal(integer_of(X),null_class)) /\ 1851 (!D E. equal(D,E) ==> equal(integer_of(D),integer_of(E))) /\ 1852 (!F' G H. equal(F',G) ==> equal(least(F',H),least(G,H))) /\ 1853 (!I' K' J. equal(I',J) ==> equal(least(K',I'),least(K',J))) /\ 1854 (!L M N. equal(L,M) ==> equal(not_well_ordering(L,N),not_well_ordering(M,N))) /\ 1855 (!O Q P. equal(O,P) ==> equal(not_well_ordering(Q,O),not_well_ordering(Q,P))) /\ 1856 (!R S' T'. equal(R,S') ==> equal(ordinal_add(R,T'),ordinal_add(S',T'))) /\ 1857 (!U W V. equal(U,V) ==> equal(ordinal_add(W,U),ordinal_add(W,V))) /\ 1858 (!X Y Z. equal(X,Y) ==> equal(ordinal_multiply(X,Z),ordinal_multiply(Y,Z))) /\ 1859 (!A1 C1 B1. equal(A1,B1) ==> equal(ordinal_multiply(C1,A1),ordinal_multiply(C1,B1))) /\ 1860 (!F1 G1 H1 I1. equal(F1,G1) ==> equal(recursion(F1,H1,I1),recursion(G1,H1,I1))) /\ 1861 (!J1 L1 K1 M1. equal(J1,K1) ==> equal(recursion(L1,J1,M1),recursion(L1,K1,M1))) /\ 1862 (!N1 P1 Q1 O1. equal(N1,O1) ==> equal(recursion(P1,Q1,N1),recursion(P1,Q1,O1))) /\ 1863 (!R1 S1. equal(R1,S1) ==> equal(recursion_equation_functions(R1),recursion_equation_functions(S1))) /\ 1864 (!T1 U1. equal(T1,U1) ==> equal(rest_of(T1),rest_of(U1))) /\ 1865 (!V1 W1 X1 Y1. equal(V1,W1) ==> equal(segment(V1,X1,Y1),segment(W1,X1,Y1))) /\ 1866 (!Z1 B2 A2 C2. equal(Z1,A2) ==> equal(segment(B2,Z1,C2),segment(B2,A2,C2))) /\ 1867 (!D2 F2 G2 E2. equal(D2,E2) ==> equal(segment(F2,G2,D2),segment(F2,G2,E2))) /\ 1868 (!H2 I2. equal(H2,I2) ==> equal(symmetrization_of(H2),symmetrization_of(I2))) /\ 1869 (!J2 K2 L2. equal(J2,K2) /\ asymmetric(J2,L2) ==> asymmetric(K2,L2)) /\ 1870 (!M2 O2 N2. equal(M2,N2) /\ asymmetric(O2,M2) ==> asymmetric(O2,N2)) /\ 1871 (!P2 Q2 R2. equal(P2,Q2) /\ connected(P2,R2) ==> connected(Q2,R2)) /\ 1872 (!S2 U2 T2. equal(S2,T2) /\ connected(U2,S2) ==> connected(U2,T2)) /\ 1873 (!V2 W2 X2. equal(V2,W2) /\ irreflexive(V2,X2) ==> irreflexive(W2,X2)) /\ 1874 (!Y2 A3 Z2. equal(Y2,Z2) /\ irreflexive(A3,Y2) ==> irreflexive(A3,Z2)) /\ 1875 (!B3 C3 D3 E3. equal(B3,C3) /\ section(B3,D3,E3) ==> section(C3,D3,E3)) /\ 1876 (!F3 H3 G3 I3. equal(F3,G3) /\ section(H3,F3,I3) ==> section(H3,G3,I3)) /\ 1877 (!J3 L3 M3 K3. equal(J3,K3) /\ section(L3,M3,J3) ==> section(L3,M3,K3)) /\ 1878 (!N3 O3 P3. equal(N3,O3) /\ transitive(N3,P3) ==> transitive(O3,P3)) /\ 1879 (!Q3 S3 R3. equal(Q3,R3) /\ transitive(S3,Q3) ==> transitive(S3,R3)) /\ 1880 (!T3 U3 V3. equal(T3,U3) /\ well_ordering(T3,V3) ==> well_ordering(U3,V3)) /\ 1881 (!W3 Y3 X3. equal(W3,X3) /\ well_ordering(Y3,W3) ==> well_ordering(Y3,X3)) /\ 1882 (~subclass(limit_ordinals,ordinal_numbers)) ==> F`; 1883 1884 1885val NUM228_1 = M "NUM228_1" $ 1886Lib.with_flag(Globals.guessing_tyvars,false) 1887 Term 1888`(!X:'a. equal(X,X)) /\ 1889 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 1890 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 1891 (!X U Y. subclass(X,Y) /\ member(U,X) ==> member(U,Y)) /\ 1892 (!X Y. member(not_subclass_element(X,Y),X) \/ subclass(X,Y)) /\ 1893 (!X Y. member(not_subclass_element(X,Y),Y) ==> subclass(X,Y)) /\ 1894 (!X. subclass(X,universal_class)) /\ 1895 (!X Y. equal(X,Y) ==> subclass(X,Y)) /\ 1896 (!Y X. equal(X,Y) ==> subclass(Y,X)) /\ 1897 (!X Y. subclass(X,Y) /\ subclass(Y,X) ==> equal(X,Y)) /\ 1898 (!X U Y. member(U,unordered_pair(X,Y)) ==> equal(U,X) \/ equal(U,Y)) /\ 1899 (!X Y. member(X,universal_class) ==> member(X,unordered_pair(X,Y))) /\ 1900 (!X Y. member(Y,universal_class) ==> member(Y,unordered_pair(X,Y))) /\ 1901 (!X Y. member(unordered_pair(X,Y),universal_class)) /\ 1902 (!X. equal(unordered_pair(X,X),singleton(X))) /\ 1903 (!X Y. equal(unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),ordered_pair(X,Y))) /\ 1904 (!V Y U X. member(ordered_pair(U,V),cross_product(X,Y)) ==> member(U,X)) /\ 1905 (!U X V Y. member(ordered_pair(U,V),cross_product(X,Y)) ==> member(V,Y)) /\ 1906 (!U V X Y. member(U,X) /\ member(V,Y) ==> member(ordered_pair(U,V),cross_product(X,Y))) /\ 1907 (!X Y Z. member(Z,cross_product(X,Y)) ==> equal(ordered_pair(first(Z),second(Z)),Z)) /\ 1908 (subclass(element_relation,cross_product(universal_class,universal_class))) /\ 1909 (!X Y. member(ordered_pair(X,Y),element_relation) ==> member(X,Y)) /\ 1910 (!X Y. member(ordered_pair(X,Y),cross_product(universal_class,universal_class)) /\ member(X,Y) ==> member(ordered_pair(X,Y),element_relation)) /\ 1911 (!Y Z X. member(Z,intersection(X,Y)) ==> member(Z,X)) /\ 1912 (!X Z Y. member(Z,intersection(X,Y)) ==> member(Z,Y)) /\ 1913 (!Z X Y. member(Z,X) /\ member(Z,Y) ==> member(Z,intersection(X,Y))) /\ 1914 (!Z X. ~(member(Z,complement(X)) /\ member(Z,X))) /\ 1915 (!Z X. member(Z,universal_class) ==> member(Z,complement(X)) \/ member(Z,X)) /\ 1916 (!X Y. equal(complement(intersection(complement(X),complement(Y))),union(X,Y))) /\ 1917 (!X Y. equal(intersection(complement(intersection(X,Y)),complement(intersection(complement(X),complement(Y)))),difference(X,Y))) /\ 1918 (!Xr X Y. equal(intersection(Xr,cross_product(X,Y)),restrict(Xr,X,Y))) /\ 1919 (!Xr X Y. equal(intersection(cross_product(X,Y),Xr),restrict(Xr,X,Y))) /\ 1920 (!Z X. ~(equal(restrict(X,singleton(Z),universal_class),null_class) /\ member(Z,domain_of(X)))) /\ 1921 (!Z X. member(Z,universal_class) ==> equal(restrict(X,singleton(Z),universal_class),null_class) \/ member(Z,domain_of(X))) /\ 1922 (!X. subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) /\ 1923 (!V W U X. member(ordered_pair(ordered_pair(U,V),W),rotate(X)) ==> member(ordered_pair(ordered_pair(V,W),U),X)) /\ 1924 (!U V W X. member(ordered_pair(ordered_pair(V,W),U),X) /\ member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)) ==> member(ordered_pair(ordered_pair(U,V),W),rotate(X))) /\ 1925 (!X. subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) /\ 1926 (!V U W X. member(ordered_pair(ordered_pair(U,V),W),flip(X)) ==> member(ordered_pair(ordered_pair(V,U),W),X)) /\ 1927 (!U V W X. member(ordered_pair(ordered_pair(V,U),W),X) /\ member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)) ==> member(ordered_pair(ordered_pair(U,V),W),flip(X))) /\ 1928 (!Y. equal(domain_of(flip(cross_product(Y,universal_class))),inverse(Y))) /\ 1929 (!Z. equal(domain_of(inverse(Z)),range_of(Z))) /\ 1930 (!Z X Y. equal(first(not_subclass_element(restrict(Z,X,singleton(Y)),null_class)),domain(Z,X,Y))) /\ 1931 (!Z X Y. equal(second(not_subclass_element(restrict(Z,singleton(X),Y),null_class)),range(Z,X,Y))) /\ 1932 (!Xr X. equal(range_of(restrict(Xr,X,universal_class)),image(Xr,X))) /\ 1933 (!X. equal(union(X,singleton(X)),successor(X))) /\ 1934 (subclass(successor_relation,cross_product(universal_class,universal_class))) /\ 1935 (!X Y. member(ordered_pair(X,Y),successor_relation) ==> equal(successor(X),Y)) /\ 1936 (!X Y. equal(successor(X),Y) /\ member(ordered_pair(X,Y),cross_product(universal_class,universal_class)) ==> member(ordered_pair(X,Y),successor_relation)) /\ 1937 (!X. inductive(X) ==> member(null_class,X)) /\ 1938 (!X. inductive(X) ==> subclass(image(successor_relation,X),X)) /\ 1939 (!X. member(null_class,X) /\ subclass(image(successor_relation,X),X) ==> inductive(X)) /\ 1940 (inductive(omega)) /\ 1941 (!Y. inductive(Y) ==> subclass(omega,Y)) /\ 1942 (member(omega,universal_class)) /\ 1943 (!X. equal(domain_of(restrict(element_relation,universal_class,X)),sum_class(X))) /\ 1944 (!X. member(X,universal_class) ==> member(sum_class(X),universal_class)) /\ 1945 (!X. equal(complement(image(element_relation,complement(X))),power_class(X))) /\ 1946 (!U. member(U,universal_class) ==> member(power_class(U),universal_class)) /\ 1947 (!Yr Xr. subclass(compose(Yr,Xr),cross_product(universal_class,universal_class))) /\ 1948 (!Z Yr Xr Y. member(ordered_pair(Y,Z),compose(Yr,Xr)) ==> member(Z,image(Yr,image(Xr,singleton(Y))))) /\ 1949 (!Y Z Yr Xr. member(Z,image(Yr,image(Xr,singleton(Y)))) /\ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class)) ==> member(ordered_pair(Y,Z),compose(Yr,Xr))) /\ 1950 (!X. single_valued_class(X) ==> subclass(compose(X,inverse(X)),identity_relation)) /\ 1951 (!X. subclass(compose(X,inverse(X)),identity_relation) ==> single_valued_class(X)) /\ 1952 (!Xf. function(Xf) ==> subclass(Xf,cross_product(universal_class,universal_class))) /\ 1953 (!Xf. function(Xf) ==> subclass(compose(Xf,inverse(Xf)),identity_relation)) /\ 1954 (!Xf. subclass(Xf,cross_product(universal_class,universal_class)) /\ subclass(compose(Xf,inverse(Xf)),identity_relation) ==> function(Xf)) /\ 1955 (!Xf X. function(Xf) /\ member(X,universal_class) ==> member(image(Xf,X),universal_class)) /\ 1956 (!X. equal(X,null_class) \/ member(regular(X),X)) /\ 1957 (!X. equal(X,null_class) \/ equal(intersection(X,regular(X)),null_class)) /\ 1958 (!Xf Y. equal(sum_class(image(Xf,singleton(Y))),apply(Xf,Y))) /\ 1959 (function(choice)) /\ 1960 (!Y. member(Y,universal_class) ==> equal(Y,null_class) \/ member(apply(choice,Y),Y)) /\ 1961 (!Xf. one_to_one(Xf) ==> function(Xf)) /\ 1962 (!Xf. one_to_one(Xf) ==> function(inverse(Xf))) /\ 1963 (!Xf. function(inverse(Xf)) /\ function(Xf) ==> one_to_one(Xf)) /\ 1964 (equal(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),subset_relation)) /\ 1965 (equal(intersection(inverse(subset_relation),subset_relation),identity_relation)) /\ 1966 (!Xr. equal(complement(domain_of(intersection(Xr,identity_relation))),diagonalise(Xr))) /\ 1967 (!X. equal(intersection(domain_of(X),diagonalise(compose(inverse(element_relation),X))),cantor(X))) /\ 1968 (!Xf. operation(Xf) ==> function(Xf)) /\ 1969 (!Xf. operation(Xf) ==> equal(cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))),domain_of(Xf))) /\ 1970 (!Xf. operation(Xf) ==> subclass(range_of(Xf),domain_of(domain_of(Xf)))) /\ 1971 (!Xf. function(Xf) /\ equal(cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))),domain_of(Xf)) /\ subclass(range_of(Xf),domain_of(domain_of(Xf))) ==> operation(Xf)) /\ 1972 (!Xf1 Xf2 Xh. compatible(Xh,Xf1,Xf2) ==> function(Xh)) /\ 1973 (!Xf2 Xf1 Xh. compatible(Xh,Xf1,Xf2) ==> equal(domain_of(domain_of(Xf1)),domain_of(Xh))) /\ 1974 (!Xf1 Xh Xf2. compatible(Xh,Xf1,Xf2) ==> subclass(range_of(Xh),domain_of(domain_of(Xf2)))) /\ 1975 (!Xh Xh1 Xf1 Xf2. function(Xh) /\ equal(domain_of(domain_of(Xf1)),domain_of(Xh)) /\ subclass(range_of(Xh),domain_of(domain_of(Xf2))) ==> compatible(Xh1,Xf1,Xf2)) /\ 1976 (!Xh Xf2 Xf1. homomorphism(Xh,Xf1,Xf2) ==> operation(Xf1)) /\ 1977 (!Xh Xf1 Xf2. homomorphism(Xh,Xf1,Xf2) ==> operation(Xf2)) /\ 1978 (!Xh Xf1 Xf2. homomorphism(Xh,Xf1,Xf2) ==> compatible(Xh,Xf1,Xf2)) /\ 1979 (!Xf2 Xh Xf1 X Y. homomorphism(Xh,Xf1,Xf2) /\ member(ordered_pair(X,Y),domain_of(Xf1)) ==> equal(apply(Xf2,ordered_pair(apply(Xh,X),apply(Xh,Y))),apply(Xh,apply(Xf1,ordered_pair(X,Y))))) /\ 1980 (!Xh Xf1 Xf2. operation(Xf1) /\ operation(Xf2) /\ compatible(Xh,Xf1,Xf2) ==> member(ordered_pair(not_homomorphism1(Xh,Xf1,Xf2),not_homomorphism2(Xh,Xf1,Xf2)),domain_of(Xf1)) \/ homomorphism(Xh,Xf1,Xf2)) /\ 1981 (!Xh Xf1 Xf2. operation(Xf1) /\ operation(Xf2) /\ compatible(Xh,Xf1,Xf2) /\ equal(apply(Xf2,ordered_pair(apply(Xh,not_homomorphism1(Xh,Xf1,Xf2)),apply(Xh,not_homomorphism2(Xh,Xf1,Xf2)))),apply(Xh,apply(Xf1,ordered_pair(not_homomorphism1(Xh,Xf1,Xf2),not_homomorphism2(Xh,Xf1,Xf2))))) ==> homomorphism(Xh,Xf1,Xf2)) /\ 1982 (!D E F'. equal(D,E) ==> equal(apply(D,F'),apply(E,F'))) /\ 1983 (!G I' H. equal(G,H) ==> equal(apply(I',G),apply(I',H))) /\ 1984 (!J K'. equal(J,K') ==> equal(cantor(J),cantor(K'))) /\ 1985 (!L M. equal(L,M) ==> equal(complement(L),complement(M))) /\ 1986 (!N O P. equal(N,O) ==> equal(compose(N,P),compose(O,P))) /\ 1987 (!Q S' R. equal(Q,R) ==> equal(compose(S',Q),compose(S',R))) /\ 1988 (!T' U V. equal(T',U) ==> equal(cross_product(T',V),cross_product(U,V))) /\ 1989 (!W Y X. equal(W,X) ==> equal(cross_product(Y,W),cross_product(Y,X))) /\ 1990 (!Z A1. equal(Z,A1) ==> equal(diagonalise(Z),diagonalise(A1))) /\ 1991 (!B1 C1 D1. equal(B1,C1) ==> equal(difference(B1,D1),difference(C1,D1))) /\ 1992 (!E1 G1 F1. equal(E1,F1) ==> equal(difference(G1,E1),difference(G1,F1))) /\ 1993 (!H1 I1 J1 K1. equal(H1,I1) ==> equal(domain(H1,J1,K1),domain(I1,J1,K1))) /\ 1994 (!L1 N1 M1 O1. equal(L1,M1) ==> equal(domain(N1,L1,O1),domain(N1,M1,O1))) /\ 1995 (!P1 R1 S1 Q1. equal(P1,Q1) ==> equal(domain(R1,S1,P1),domain(R1,S1,Q1))) /\ 1996 (!T1 U1. equal(T1,U1) ==> equal(domain_of(T1),domain_of(U1))) /\ 1997 (!V1 W1. equal(V1,W1) ==> equal(first(V1),first(W1))) /\ 1998 (!X1 Y1. equal(X1,Y1) ==> equal(flip(X1),flip(Y1))) /\ 1999 (!Z1 A2 B2. equal(Z1,A2) ==> equal(image(Z1,B2),image(A2,B2))) /\ 2000 (!C2 E2 D2. equal(C2,D2) ==> equal(image(E2,C2),image(E2,D2))) /\ 2001 (!F2 G2 H2. equal(F2,G2) ==> equal(intersection(F2,H2),intersection(G2,H2))) /\ 2002 (!I2 K2 J2. equal(I2,J2) ==> equal(intersection(K2,I2),intersection(K2,J2))) /\ 2003 (!L2 M2. equal(L2,M2) ==> equal(inverse(L2),inverse(M2))) /\ 2004 (!N2 O2 P2 Q2. equal(N2,O2) ==> equal(not_homomorphism1(N2,P2,Q2),not_homomorphism1(O2,P2,Q2))) /\ 2005 (!R2 T2 S2 U2. equal(R2,S2) ==> equal(not_homomorphism1(T2,R2,U2),not_homomorphism1(T2,S2,U2))) /\ 2006 (!V2 X2 Y2 W2. equal(V2,W2) ==> equal(not_homomorphism1(X2,Y2,V2),not_homomorphism1(X2,Y2,W2))) /\ 2007 (!Z2 A3 B3 C3. equal(Z2,A3) ==> equal(not_homomorphism2(Z2,B3,C3),not_homomorphism2(A3,B3,C3))) /\ 2008 (!D3 F3 E3 G3. equal(D3,E3) ==> equal(not_homomorphism2(F3,D3,G3),not_homomorphism2(F3,E3,G3))) /\ 2009 (!H3 J3 K3 I3. equal(H3,I3) ==> equal(not_homomorphism2(J3,K3,H3),not_homomorphism2(J3,K3,I3))) /\ 2010 (!L3 M3 N3. equal(L3,M3) ==> equal(not_subclass_element(L3,N3),not_subclass_element(M3,N3))) /\ 2011 (!O3 Q3 P3. equal(O3,P3) ==> equal(not_subclass_element(Q3,O3),not_subclass_element(Q3,P3))) /\ 2012 (!R3 S3 T3. equal(R3,S3) ==> equal(ordered_pair(R3,T3),ordered_pair(S3,T3))) /\ 2013 (!U3 W3 V3. equal(U3,V3) ==> equal(ordered_pair(W3,U3),ordered_pair(W3,V3))) /\ 2014 (!X3 Y3. equal(X3,Y3) ==> equal(power_class(X3),power_class(Y3))) /\ 2015 (!Z3 A4 B4 C4. equal(Z3,A4) ==> equal(range(Z3,B4,C4),range(A4,B4,C4))) /\ 2016 (!D4 F4 E4 G4. equal(D4,E4) ==> equal(range(F4,D4,G4),range(F4,E4,G4))) /\ 2017 (!H4 J4 K4 I4. equal(H4,I4) ==> equal(range(J4,K4,H4),range(J4,K4,I4))) /\ 2018 (!L4 M4. equal(L4,M4) ==> equal(range_of(L4),range_of(M4))) /\ 2019 (!N4 O4. equal(N4,O4) ==> equal(regular(N4),regular(O4))) /\ 2020 (!P4 Q4 R4 S4. equal(P4,Q4) ==> equal(restrict(P4,R4,S4),restrict(Q4,R4,S4))) /\ 2021 (!T4 V4 U4 W4. equal(T4,U4) ==> equal(restrict(V4,T4,W4),restrict(V4,U4,W4))) /\ 2022 (!X4 Z4 A5 Y4. equal(X4,Y4) ==> equal(restrict(Z4,A5,X4),restrict(Z4,A5,Y4))) /\ 2023 (!B5 C5. equal(B5,C5) ==> equal(rotate(B5),rotate(C5))) /\ 2024 (!D5 E5. equal(D5,E5) ==> equal(second(D5),second(E5))) /\ 2025 (!F5 G5. equal(F5,G5) ==> equal(singleton(F5),singleton(G5))) /\ 2026 (!H5 I5. equal(H5,I5) ==> equal(successor(H5),successor(I5))) /\ 2027 (!J5 K5. equal(J5,K5) ==> equal(sum_class(J5),sum_class(K5))) /\ 2028 (!L5 M5 N5. equal(L5,M5) ==> equal(union(L5,N5),union(M5,N5))) /\ 2029 (!O5 Q5 P5. equal(O5,P5) ==> equal(union(Q5,O5),union(Q5,P5))) /\ 2030 (!R5 S5 T5. equal(R5,S5) ==> equal(unordered_pair(R5,T5),unordered_pair(S5,T5))) /\ 2031 (!U5 W5 V5. equal(U5,V5) ==> equal(unordered_pair(W5,U5),unordered_pair(W5,V5))) /\ 2032 (!X5 Y5 Z5 A6. equal(X5,Y5) /\ compatible(X5,Z5,A6) ==> compatible(Y5,Z5,A6)) /\ 2033 (!B6 D6 C6 E6. equal(B6,C6) /\ compatible(D6,B6,E6) ==> compatible(D6,C6,E6)) /\ 2034 (!F6 H6 I6 G6. equal(F6,G6) /\ compatible(H6,I6,F6) ==> compatible(H6,I6,G6)) /\ 2035 (!J6 K6. equal(J6,K6) /\ function(J6) ==> function(K6)) /\ 2036 (!L6 M6 N6 O6. equal(L6,M6) /\ homomorphism(L6,N6,O6) ==> homomorphism(M6,N6,O6)) /\ 2037 (!P6 R6 Q6 S6. equal(P6,Q6) /\ homomorphism(R6,P6,S6) ==> homomorphism(R6,Q6,S6)) /\ 2038 (!T6 V6 W6 U6. equal(T6,U6) /\ homomorphism(V6,W6,T6) ==> homomorphism(V6,W6,U6)) /\ 2039 (!X6 Y6. equal(X6,Y6) /\ inductive(X6) ==> inductive(Y6)) /\ 2040 (!Z6 A7 B7. equal(Z6,A7) /\ member(Z6,B7) ==> member(A7,B7)) /\ 2041 (!C7 E7 D7. equal(C7,D7) /\ member(E7,C7) ==> member(E7,D7)) /\ 2042 (!F7 G7. equal(F7,G7) /\ one_to_one(F7) ==> one_to_one(G7)) /\ 2043 (!H7 I7. equal(H7,I7) /\ operation(H7) ==> operation(I7)) /\ 2044 (!J7 K7. equal(J7,K7) /\ single_valued_class(J7) ==> single_valued_class(K7)) /\ 2045 (!L7 M7 N7. equal(L7,M7) /\ subclass(L7,N7) ==> subclass(M7,N7)) /\ 2046 (!O7 Q7 P7. equal(O7,P7) /\ subclass(Q7,O7) ==> subclass(Q7,P7)) /\ 2047 (!X. subclass(compose_class(X),cross_product(universal_class,universal_class))) /\ 2048 (!X Y Z. member(ordered_pair(Y,Z),compose_class(X)) ==> equal(compose(X,Y),Z)) /\ 2049 (!Y Z X. member(ordered_pair(Y,Z),cross_product(universal_class,universal_class)) /\ equal(compose(X,Y),Z) ==> member(ordered_pair(Y,Z),compose_class(X))) /\ 2050 (subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))) /\ 2051 (!X Y Z. member(ordered_pair(X,ordered_pair(Y,Z)),composition_function) ==> equal(compose(X,Y),Z)) /\ 2052 (!X Y. member(ordered_pair(X,Y),cross_product(universal_class,universal_class)) ==> member(ordered_pair(X,ordered_pair(Y,compose(X,Y))),composition_function)) /\ 2053 (subclass(domain_relation,cross_product(universal_class,universal_class))) /\ 2054 (!X Y. member(ordered_pair(X,Y),domain_relation) ==> equal(domain_of(X),Y)) /\ 2055 (!X. member(X,universal_class) ==> member(ordered_pair(X,domain_of(X)),domain_relation)) /\ 2056 (!X. equal(first(not_subclass_element(compose(X,inverse(X)),identity_relation)),single_valued1(X))) /\ 2057 (!X. equal(second(not_subclass_element(compose(X,inverse(X)),identity_relation)),single_valued2(X))) /\ 2058 (!X. equal(domain(X,image(inverse(X),singleton(single_valued1(X))),single_valued2(X)),single_valued3(X))) /\ 2059 (equal(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation)) /\ 2060 (subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))) /\ 2061 (!Z Y X. member(ordered_pair(X,ordered_pair(Y,Z)),application_function) ==> member(Y,domain_of(X))) /\ 2062 (!X Y Z. member(ordered_pair(X,ordered_pair(Y,Z)),application_function) ==> equal(apply(X,Y),Z)) /\ 2063 (!Z X Y. member(ordered_pair(X,ordered_pair(Y,Z)),cross_product(universal_class,cross_product(universal_class,universal_class))) /\ member(Y,domain_of(X)) ==> member(ordered_pair(X,ordered_pair(Y,apply(X,Y))),application_function)) /\ 2064 (!X Y Xf. maps(Xf,X,Y) ==> function(Xf)) /\ 2065 (!Y Xf X. maps(Xf,X,Y) ==> equal(domain_of(Xf),X)) /\ 2066 (!X Xf Y. maps(Xf,X,Y) ==> subclass(range_of(Xf),Y)) /\ 2067 (!Xf Y. function(Xf) /\ subclass(range_of(Xf),Y) ==> maps(Xf,domain_of(Xf),Y)) /\ 2068 (!L M. equal(L,M) ==> equal(compose_class(L),compose_class(M))) /\ 2069 (!N2 O2. equal(N2,O2) ==> equal(single_valued1(N2),single_valued1(O2))) /\ 2070 (!P2 Q2. equal(P2,Q2) ==> equal(single_valued2(P2),single_valued2(Q2))) /\ 2071 (!R2 S2. equal(R2,S2) ==> equal(single_valued3(R2),single_valued3(S2))) /\ 2072 (!X2 Y2 Z2 A3. equal(X2,Y2) /\ maps(X2,Z2,A3) ==> maps(Y2,Z2,A3)) /\ 2073 (!B3 D3 C3 E3. equal(B3,C3) /\ maps(D3,B3,E3) ==> maps(D3,C3,E3)) /\ 2074 (!F3 H3 I3 G3. equal(F3,G3) /\ maps(H3,I3,F3) ==> maps(H3,I3,G3)) /\ 2075 (!X. equal(union(X,inverse(X)),symmetrization_of(X))) /\ 2076 (!X Y. irreflexive(X,Y) ==> subclass(restrict(X,Y,Y),complement(identity_relation))) /\ 2077 (!X Y. subclass(restrict(X,Y,Y),complement(identity_relation)) ==> irreflexive(X,Y)) /\ 2078 (!Y X. connected(X,Y) ==> subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))) /\ 2079 (!X Y. subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X))) ==> connected(X,Y)) /\ 2080 (!Xr Y. transitive(Xr,Y) ==> subclass(compose(restrict(Xr,Y,Y),restrict(Xr,Y,Y)),restrict(Xr,Y,Y))) /\ 2081 (!Xr Y. subclass(compose(restrict(Xr,Y,Y),restrict(Xr,Y,Y)),restrict(Xr,Y,Y)) ==> transitive(Xr,Y)) /\ 2082 (!Xr Y. asymmetric(Xr,Y) ==> equal(restrict(intersection(Xr,inverse(Xr)),Y,Y),null_class)) /\ 2083 (!Xr Y. equal(restrict(intersection(Xr,inverse(Xr)),Y,Y),null_class) ==> asymmetric(Xr,Y)) /\ 2084 (!Xr Y Z. equal(segment(Xr,Y,Z),domain_of(restrict(Xr,Y,singleton(Z))))) /\ 2085 (!X Y. well_ordering(X,Y) ==> connected(X,Y)) /\ 2086 (!Y Xr U. well_ordering(Xr,Y) /\ subclass(U,Y) ==> equal(U,null_class) \/ member(least(Xr,U),U)) /\ 2087 (!Y V Xr U. well_ordering(Xr,Y) /\ subclass(U,Y) /\ member(V,U) ==> member(least(Xr,U),U)) /\ 2088 (!Y Xr U. well_ordering(Xr,Y) /\ subclass(U,Y) ==> equal(segment(Xr,U,least(Xr,U)),null_class)) /\ 2089 (!Y V U Xr. ~(well_ordering(Xr,Y) /\ subclass(U,Y) /\ member(V,U) /\ member(ordered_pair(V,least(Xr,U)),Xr))) /\ 2090 (!Xr Y. connected(Xr,Y) /\ equal(not_well_ordering(Xr,Y),null_class) ==> well_ordering(Xr,Y)) /\ 2091 (!Xr Y. connected(Xr,Y) ==> subclass(not_well_ordering(Xr,Y),Y) \/ well_ordering(Xr,Y)) /\ 2092 (!V Xr Y. member(V,not_well_ordering(Xr,Y)) /\ equal(segment(Xr,not_well_ordering(Xr,Y),V),null_class) /\ connected(Xr,Y) ==> well_ordering(Xr,Y)) /\ 2093 (!Xr Y Z. section(Xr,Y,Z) ==> subclass(Y,Z)) /\ 2094 (!Xr Z Y. section(Xr,Y,Z) ==> subclass(domain_of(restrict(Xr,Z,Y)),Y)) /\ 2095 (!Xr Y Z. subclass(Y,Z) /\ subclass(domain_of(restrict(Xr,Z,Y)),Y) ==> section(Xr,Y,Z)) /\ 2096 (!X. member(X,ordinal_numbers) ==> well_ordering(element_relation,X)) /\ 2097 (!X. member(X,ordinal_numbers) ==> subclass(sum_class(X),X)) /\ 2098 (!X. well_ordering(element_relation,X) /\ subclass(sum_class(X),X) /\ member(X,universal_class) ==> member(X,ordinal_numbers)) /\ 2099 (!X. well_ordering(element_relation,X) /\ subclass(sum_class(X),X) ==> member(X,ordinal_numbers) \/ equal(X,ordinal_numbers)) /\ 2100 (equal(union(singleton(null_class),image(successor_relation,ordinal_numbers)),kind_1_ordinals)) /\ 2101 (equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals)) /\ 2102 (!X. subclass(rest_of(X),cross_product(universal_class,universal_class))) /\ 2103 (!V U X. member(ordered_pair(U,V),rest_of(X)) ==> member(U,domain_of(X))) /\ 2104 (!X U V. member(ordered_pair(U,V),rest_of(X)) ==> equal(restrict(X,U,universal_class),V)) /\ 2105 (!U V X. member(U,domain_of(X)) /\ equal(restrict(X,U,universal_class),V) ==> member(ordered_pair(U,V),rest_of(X))) /\ 2106 (subclass(rest_relation,cross_product(universal_class,universal_class))) /\ 2107 (!X Y. member(ordered_pair(X,Y),rest_relation) ==> equal(rest_of(X),Y)) /\ 2108 (!X. member(X,universal_class) ==> member(ordered_pair(X,rest_of(X)),rest_relation)) /\ 2109 (!X Z. member(X,recursion_equation_functions(Z)) ==> function(Z)) /\ 2110 (!Z X. member(X,recursion_equation_functions(Z)) ==> function(X)) /\ 2111 (!Z X. member(X,recursion_equation_functions(Z)) ==> member(domain_of(X),ordinal_numbers)) /\ 2112 (!Z X. member(X,recursion_equation_functions(Z)) ==> equal(compose(Z,rest_of(X)),X)) /\ 2113 (!X Z. function(Z) /\ function(X) /\ member(domain_of(X),ordinal_numbers) /\ equal(compose(Z,rest_of(X)),X) ==> member(X,recursion_equation_functions(Z))) /\ 2114 (subclass(union_of_range_map,cross_product(universal_class,universal_class))) /\ 2115 (!X Y. member(ordered_pair(X,Y),union_of_range_map) ==> equal(sum_class(range_of(X)),Y)) /\ 2116 (!X Y. member(ordered_pair(X,Y),cross_product(universal_class,universal_class)) /\ equal(sum_class(range_of(X)),Y) ==> member(ordered_pair(X,Y),union_of_range_map)) /\ 2117 (!X Y. equal(apply(recursion(X,successor_relation,union_of_range_map),Y),ordinal_add(X,Y))) /\ 2118 (!X Y. equal(recursion(null_class,apply(add_relation,X),union_of_range_map),ordinal_multiply(X,Y))) /\ 2119 (!X. member(X,omega) ==> equal(integer_of(X),X)) /\ 2120 (!X. member(X,omega) \/ equal(integer_of(X),null_class)) /\ 2121 (!D E. equal(D,E) ==> equal(integer_of(D),integer_of(E))) /\ 2122 (!F' G H. equal(F',G) ==> equal(least(F',H),least(G,H))) /\ 2123 (!I' K' J. equal(I',J) ==> equal(least(K',I'),least(K',J))) /\ 2124 (!L M N. equal(L,M) ==> equal(not_well_ordering(L,N),not_well_ordering(M,N))) /\ 2125 (!O Q P. equal(O,P) ==> equal(not_well_ordering(Q,O),not_well_ordering(Q,P))) /\ 2126 (!R S' T'. equal(R,S') ==> equal(ordinal_add(R,T'),ordinal_add(S',T'))) /\ 2127 (!U W V. equal(U,V) ==> equal(ordinal_add(W,U),ordinal_add(W,V))) /\ 2128 (!X Y Z. equal(X,Y) ==> equal(ordinal_multiply(X,Z),ordinal_multiply(Y,Z))) /\ 2129 (!A1 C1 B1. equal(A1,B1) ==> equal(ordinal_multiply(C1,A1),ordinal_multiply(C1,B1))) /\ 2130 (!F1 G1 H1 I1. equal(F1,G1) ==> equal(recursion(F1,H1,I1),recursion(G1,H1,I1))) /\ 2131 (!J1 L1 K1 M1. equal(J1,K1) ==> equal(recursion(L1,J1,M1),recursion(L1,K1,M1))) /\ 2132 (!N1 P1 Q1 O1. equal(N1,O1) ==> equal(recursion(P1,Q1,N1),recursion(P1,Q1,O1))) /\ 2133 (!R1 S1. equal(R1,S1) ==> equal(recursion_equation_functions(R1),recursion_equation_functions(S1))) /\ 2134 (!T1 U1. equal(T1,U1) ==> equal(rest_of(T1),rest_of(U1))) /\ 2135 (!V1 W1 X1 Y1. equal(V1,W1) ==> equal(segment(V1,X1,Y1),segment(W1,X1,Y1))) /\ 2136 (!Z1 B2 A2 C2. equal(Z1,A2) ==> equal(segment(B2,Z1,C2),segment(B2,A2,C2))) /\ 2137 (!D2 F2 G2 E2. equal(D2,E2) ==> equal(segment(F2,G2,D2),segment(F2,G2,E2))) /\ 2138 (!H2 I2. equal(H2,I2) ==> equal(symmetrization_of(H2),symmetrization_of(I2))) /\ 2139 (!J2 K2 L2. equal(J2,K2) /\ asymmetric(J2,L2) ==> asymmetric(K2,L2)) /\ 2140 (!M2 O2 N2. equal(M2,N2) /\ asymmetric(O2,M2) ==> asymmetric(O2,N2)) /\ 2141 (!P2 Q2 R2. equal(P2,Q2) /\ connected(P2,R2) ==> connected(Q2,R2)) /\ 2142 (!S2 U2 T2. equal(S2,T2) /\ connected(U2,S2) ==> connected(U2,T2)) /\ 2143 (!V2 W2 X2. equal(V2,W2) /\ irreflexive(V2,X2) ==> irreflexive(W2,X2)) /\ 2144 (!Y2 A3 Z2. equal(Y2,Z2) /\ irreflexive(A3,Y2) ==> irreflexive(A3,Z2)) /\ 2145 (!B3 C3 D3 E3. equal(B3,C3) /\ section(B3,D3,E3) ==> section(C3,D3,E3)) /\ 2146 (!F3 H3 G3 I3. equal(F3,G3) /\ section(H3,F3,I3) ==> section(H3,G3,I3)) /\ 2147 (!J3 L3 M3 K3. equal(J3,K3) /\ section(L3,M3,J3) ==> section(L3,M3,K3)) /\ 2148 (!N3 O3 P3. equal(N3,O3) /\ transitive(N3,P3) ==> transitive(O3,P3)) /\ 2149 (!Q3 S3 R3. equal(Q3,R3) /\ transitive(S3,Q3) ==> transitive(S3,R3)) /\ 2150 (!T3 U3 V3. equal(T3,U3) /\ well_ordering(T3,V3) ==> well_ordering(U3,V3)) /\ 2151 (!W3 Y3 X3. equal(W3,X3) /\ well_ordering(Y3,W3) ==> well_ordering(Y3,X3)) /\ 2152 (~function(z)) /\ 2153 (~equal(recursion_equation_functions(z),null_class)) ==> F`; 2154 2155 2156val PLA002_1 = M "PLA002_1" 2157 ���(!Situation1 Situation2. warm(Situation1) \/ cold(Situation2)) /\ 2158 (!Situation. at(a:'a,Situation) ==> at(b,walk(b,Situation))) /\ 2159 (!Situation. at(a,Situation) ==> at(b,drive(b,Situation))) /\ 2160 (!Situation. at(b,Situation) ==> at(a,walk(a,Situation))) /\ 2161 (!Situation. at(b,Situation) ==> at(a,drive(a,Situation))) /\ 2162 (!Situation. cold(Situation) /\ at(b,Situation) ==> at(c,skate(c,Situation))) /\ 2163 (!Situation. cold(Situation) /\ at(c,Situation) ==> at(b,skate(b,Situation))) /\ 2164 (!Situation. warm(Situation) /\ at(b,Situation) ==> at(d,climb(d,Situation))) /\ 2165 (!Situation. warm(Situation) /\ at(d,Situation) ==> at(b,climb(b,Situation))) /\ 2166 (!Situation. at(c,Situation) ==> at(d,go(d,Situation))) /\ 2167 (!Situation. at(d,Situation) ==> at(c,go(c,Situation))) /\ 2168 (!Situation. at(c,Situation) ==> at(e,go(e,Situation))) /\ 2169 (!Situation. at(e,Situation) ==> at(c,go(c,Situation))) /\ 2170 (!Situation. at(d,Situation) ==> at(f,go(f,Situation))) /\ 2171 (!Situation:'a. at(f,Situation) ==> at(d,go(d,Situation))) /\ 2172 (at(f,s0)) /\ 2173 (!S'. ~at(a,S')) ==> F���; 2174 2175 2176val PLA006_1 = M "PLA006_1" $ 2177Lib.with_flag(Globals.guessing_tyvars,true) 2178 Term 2179`(!X Y State. holds(X,State) /\ holds(Y,State) ==> holds(and'(X,Y),State)) /\ 2180 (!State X. holds(empty,State) /\ holds(clear(X),State) /\ differ(X,table) ==> holds(holding(X),do(pickup(X),State))) /\ 2181 (!Y X State. holds(on(X,Y),State) /\ holds(clear(X),State) /\ holds(empty,State) ==> holds(clear(Y),do(pickup(X),State))) /\ 2182 (!Y State X Z. holds(on(X,Y),State) /\ differ(X,Z) ==> holds(on(X,Y),do(pickup(Z),State))) /\ 2183 (!State X Z. holds(clear(X),State) /\ differ(X,Z) ==> holds(clear(X),do(pickup(Z),State))) /\ 2184 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(empty,do(putdown(X,Y),State))) /\ 2185 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(on(X,Y),do(putdown(X,Y),State))) /\ 2186 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(clear(X),do(putdown(X,Y),State))) /\ 2187 (!Z W X Y State. holds(on(X,Y),State) ==> holds(on(X,Y),do(putdown(Z,W),State))) /\ 2188 (!X State Z Y. holds(clear(Z),State) /\ differ(Z,Y) ==> holds(clear(Z),do(putdown(X,Y),State))) /\ 2189 (!Y X. differ(Y,X) ==> differ(X,Y)) /\ 2190 (differ(a,b)) /\ 2191 (differ(a,c)) /\ 2192 (differ(a,d)) /\ 2193 (differ(a,table)) /\ 2194 (differ(b,c)) /\ 2195 (differ(b,d)) /\ 2196 (differ(b,table)) /\ 2197 (differ(c,d)) /\ 2198 (differ(c,table)) /\ 2199 (differ(d,table)) /\ 2200 (holds(on(a,table),s0)) /\ 2201 (holds(on(b,table),s0)) /\ 2202 (holds(on(c,d),s0)) /\ 2203 (holds(on(d,table),s0)) /\ 2204 (holds(clear(a),s0)) /\ 2205 (holds(clear(b),s0)) /\ 2206 (holds(clear(c),s0)) /\ 2207 (holds(empty,s0)) /\ 2208 (!State. holds(clear(table),State)) /\ 2209 (!State. ~holds(on(c,table),State)) ==> F`; 2210 2211 2212val PLA017_1 = M "PLA017_1" $ 2213Lib.with_flag(Globals.guessing_tyvars,true) 2214 Term 2215`(!X Y State. holds(X,State) /\ holds(Y,State) ==> holds(and'(X,Y),State)) /\ 2216 (!State X. holds(empty,State) /\ holds(clear(X),State) /\ differ(X,table) ==> holds(holding(X),do(pickup(X),State))) /\ 2217 (!Y X State. holds(on(X,Y),State) /\ holds(clear(X),State) /\ holds(empty,State) ==> holds(clear(Y),do(pickup(X),State))) /\ 2218 (!Y State X Z. holds(on(X,Y),State) /\ differ(X,Z) ==> holds(on(X,Y),do(pickup(Z),State))) /\ 2219 (!State X Z. holds(clear(X),State) /\ differ(X,Z) ==> holds(clear(X),do(pickup(Z),State))) /\ 2220 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(empty,do(putdown(X,Y),State))) /\ 2221 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(on(X,Y),do(putdown(X,Y),State))) /\ 2222 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(clear(X),do(putdown(X,Y),State))) /\ 2223 (!Z W X Y State. holds(on(X,Y),State) ==> holds(on(X,Y),do(putdown(Z,W),State))) /\ 2224 (!X State Z Y. holds(clear(Z),State) /\ differ(Z,Y) ==> holds(clear(Z),do(putdown(X,Y),State))) /\ 2225 (!Y X. differ(Y,X) ==> differ(X,Y)) /\ 2226 (differ(a,b)) /\ 2227 (differ(a,c)) /\ 2228 (differ(a,d)) /\ 2229 (differ(a,table)) /\ 2230 (differ(b,c)) /\ 2231 (differ(b,d)) /\ 2232 (differ(b,table)) /\ 2233 (differ(c,d)) /\ 2234 (differ(c,table)) /\ 2235 (differ(d,table)) /\ 2236 (holds(on(a,table),s0)) /\ 2237 (holds(on(b,table),s0)) /\ 2238 (holds(on(c,d),s0)) /\ 2239 (holds(on(d,table),s0)) /\ 2240 (holds(clear(a),s0)) /\ 2241 (holds(clear(b),s0)) /\ 2242 (holds(clear(c),s0)) /\ 2243 (holds(empty,s0)) /\ 2244 (!State. holds(clear(table),State)) /\ 2245 (!State. ~holds(on(a,c),State)) ==> F`; 2246 2247 2248val PLA022_1 = M "PLA022_1" $ 2249Lib.with_flag(Globals.guessing_tyvars,true) 2250 Term 2251`(!X Y State. holds(X,State) /\ holds(Y,State) ==> holds(and'(X,Y),State)) /\ 2252 (!State X. holds(empty,State) /\ holds(clear(X),State) /\ differ(X,table) ==> holds(holding(X),do(pickup(X),State))) /\ 2253 (!Y X State. holds(on(X,Y),State) /\ holds(clear(X),State) /\ holds(empty,State) ==> holds(clear(Y),do(pickup(X),State))) /\ 2254 (!Y State X Z. holds(on(X,Y),State) /\ differ(X,Z) ==> holds(on(X,Y),do(pickup(Z),State))) /\ 2255 (!State X Z. holds(clear(X),State) /\ differ(X,Z) ==> holds(clear(X),do(pickup(Z),State))) /\ 2256 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(empty,do(putdown(X,Y),State))) /\ 2257 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(on(X,Y),do(putdown(X,Y),State))) /\ 2258 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(clear(X),do(putdown(X,Y),State))) /\ 2259 (!Z W X Y State. holds(on(X,Y),State) ==> holds(on(X,Y),do(putdown(Z,W),State))) /\ 2260 (!X State Z Y. holds(clear(Z),State) /\ differ(Z,Y) ==> holds(clear(Z),do(putdown(X,Y),State))) /\ 2261 (!Y X. differ(Y,X) ==> differ(X,Y)) /\ 2262 (differ(a,b)) /\ 2263 (differ(a,c)) /\ 2264 (differ(a,d)) /\ 2265 (differ(a,table)) /\ 2266 (differ(b,c)) /\ 2267 (differ(b,d)) /\ 2268 (differ(b,table)) /\ 2269 (differ(c,d)) /\ 2270 (differ(c,table)) /\ 2271 (differ(d,table)) /\ 2272 (holds(on(a,table),s0)) /\ 2273 (holds(on(b,table),s0)) /\ 2274 (holds(on(c,d),s0)) /\ 2275 (holds(on(d,table),s0)) /\ 2276 (holds(clear(a),s0)) /\ 2277 (holds(clear(b),s0)) /\ 2278 (holds(clear(c),s0)) /\ 2279 (holds(empty,s0)) /\ 2280 (!State. holds(clear(table),State)) /\ 2281 (!State. ~holds(and'(on(c,d),on(a,c)),State)) ==> F`; 2282 2283 2284val PLA022_2 = M "PLA022_2" $ 2285Lib.with_flag(Globals.guessing_tyvars,true) 2286 Term 2287`(!X Y State. holds(X,State) /\ holds(Y,State) ==> holds(and'(X,Y),State)) /\ 2288 (!State X. holds(empty,State) /\ holds(clear(X),State) /\ differ(X,table) ==> holds(holding(X),do(pickup(X),State))) /\ 2289 (!Y X State. holds(on(X,Y),State) /\ holds(clear(X),State) /\ holds(empty,State) ==> holds(clear(Y),do(pickup(X),State))) /\ 2290 (!Y State X Z. holds(on(X,Y),State) /\ differ(X,Z) ==> holds(on(X,Y),do(pickup(Z),State))) /\ 2291 (!State X Z. holds(clear(X),State) /\ differ(X,Z) ==> holds(clear(X),do(pickup(Z),State))) /\ 2292 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(empty,do(putdown(X,Y),State))) /\ 2293 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(on(X,Y),do(putdown(X,Y),State))) /\ 2294 (!X Y State. holds(holding(X),State) /\ holds(clear(Y),State) ==> holds(clear(X),do(putdown(X,Y),State))) /\ 2295 (!Z W X Y State. holds(on(X,Y),State) ==> holds(on(X,Y),do(putdown(Z,W),State))) /\ 2296 (!X State Z Y. holds(clear(Z),State) /\ differ(Z,Y) ==> holds(clear(Z),do(putdown(X,Y),State))) /\ 2297 (!Y X. differ(Y,X) ==> differ(X,Y)) /\ 2298 (differ(a,b)) /\ 2299 (differ(a,c)) /\ 2300 (differ(a,d)) /\ 2301 (differ(a,table)) /\ 2302 (differ(b,c)) /\ 2303 (differ(b,d)) /\ 2304 (differ(b,table)) /\ 2305 (differ(c,d)) /\ 2306 (differ(c,table)) /\ 2307 (differ(d,table)) /\ 2308 (holds(on(a,table),s0)) /\ 2309 (holds(on(b,table),s0)) /\ 2310 (holds(on(c,d),s0)) /\ 2311 (holds(on(d,table),s0)) /\ 2312 (holds(clear(a),s0)) /\ 2313 (holds(clear(b),s0)) /\ 2314 (holds(clear(c),s0)) /\ 2315 (holds(empty,s0)) /\ 2316 (!State. holds(clear(table),State)) /\ 2317 (!State. ~holds(and'(on(a,c),on(c,d)),State)) ==> F`; 2318 2319 2320val PRV001_1 = M "PRV001_1" $ 2321Lib.with_flag(Globals.guessing_tyvars,true) 2322 Term 2323`(!X Y Z. q1(X,Y,Z) /\ less_or_equal(X,Y) ==> q2(X,Y,Z)) /\ 2324 (!X Y Z. q1(X,Y,Z) ==> less_or_equal(X,Y) \/ q3(X,Y,Z)) /\ 2325 (!Z X Y. q2(X,Y,Z) ==> q4(X,Y,Y)) /\ 2326 (!Z Y X. q3(X,Y,Z) ==> q4(X,Y,X)) /\ 2327 (!X. less_or_equal(X,X)) /\ 2328 (!X Y. less_or_equal(X,Y) /\ less_or_equal(Y,X) ==> equal(X,Y)) /\ 2329 (!Y X Z. less_or_equal(X,Y) /\ less_or_equal(Y,Z) ==> less_or_equal(X,Z)) /\ 2330 (!Y X. less_or_equal(X,Y) \/ less_or_equal(Y,X)) /\ 2331 (!X Y. equal(X,Y) ==> less_or_equal(X,Y)) /\ 2332 (!X Y Z. equal(X,Y) /\ less_or_equal(X,Z) ==> less_or_equal(Y,Z)) /\ 2333 (!X Z Y. equal(X,Y) /\ less_or_equal(Z,X) ==> less_or_equal(Z,Y)) /\ 2334 (q1(a,b,c)) /\ 2335 (!W. ~(q4(a,b,W) /\ less_or_equal(a,W) /\ less_or_equal(b,W) /\ less_or_equal(W,a))) /\ 2336 (!W. ~(q4(a,b,W) /\ less_or_equal(a,W) /\ less_or_equal(b,W) /\ 2337 less_or_equal(W,b))) 2338 ==> F`; 2339 2340 2341val PRV003_1 = M"PRV003_1" 2342 ���(!X:'a. equal(X,X)) /\ 2343 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2344 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2345 (!X. equal(predecessor(successor(X)),X)) /\ 2346 (!X. equal(successor(predecessor(X)),X)) /\ 2347 (!X Y. equal(predecessor(X),predecessor(Y)) ==> equal(X,Y)) /\ 2348 (!X Y. equal(successor(X),successor(Y)) ==> equal(X,Y)) /\ 2349 (!X. less_than(predecessor(X),X)) /\ 2350 (!X. less_than(X,successor(X))) /\ 2351 (!X Y Z. less_than(X,Y) /\ less_than(Y,Z) ==> less_than(X,Z)) /\ 2352 (!X Y. less_than(X,Y) \/ less_than(Y,X) \/ equal(X,Y)) /\ 2353 (!X. ~less_than(X,X)) /\ 2354 (!Y X. ~(less_than(X,Y) /\ less_than(Y,X))) /\ 2355 (!Y X Z. equal(X,Y) /\ less_than(X,Z) ==> less_than(Y,Z)) /\ 2356 (!Y Z X. equal(X,Y) /\ less_than(Z,X) ==> less_than(Z,Y)) /\ 2357 (!X Y. equal(X,Y) ==> equal(predecessor(X),predecessor(Y))) /\ 2358 (!X Y. equal(X,Y) ==> equal(successor(X),successor(Y))) /\ 2359 (!X Y. equal(X,Y) ==> equal(a(X),a(Y))) /\ 2360 (~less_than(n,j)) /\ 2361 (less_than(k,j)) /\ 2362 (~less_than(k,i)) /\ 2363 (less_than(i,n)) /\ 2364 (less_than(a(j),a(k))) /\ 2365 (!X. less_than(X,j) /\ less_than(a(X),a(k)) ==> less_than(X,i)) /\ 2366 (!X. less_than(one,i) /\ less_than(a(X),a(predecessor(i))) ==> less_than(X,i) \/ less_than(n,X)) /\ 2367 (!X. ~(less_than(one,X) /\ less_than(X,i) /\ less_than(a(X),a(predecessor(X))))) /\ 2368 (less_than(j,i)) ==> F���; 2369 2370 2371val PRV005_1 =M "PRV005_1" 2372 ���(!X:'a. equal(X,X)) /\ 2373 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2374 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2375 (!X. equal(predecessor(successor(X)),X)) /\ 2376 (!X. equal(successor(predecessor(X)),X)) /\ 2377 (!X Y. equal(predecessor(X),predecessor(Y)) ==> equal(X,Y)) /\ 2378 (!X Y. equal(successor(X),successor(Y)) ==> equal(X,Y)) /\ 2379 (!X. less_than(predecessor(X),X)) /\ 2380 (!X. less_than(X,successor(X))) /\ 2381 (!X Y Z. less_than(X,Y) /\ less_than(Y,Z) ==> less_than(X,Z)) /\ 2382 (!X Y. less_than(X,Y) \/ less_than(Y,X) \/ equal(X,Y)) /\ 2383 (!X. ~less_than(X,X)) /\ 2384 (!Y X. ~(less_than(X,Y) /\ less_than(Y,X))) /\ 2385 (!Y X Z. equal(X,Y) /\ less_than(X,Z) ==> less_than(Y,Z)) /\ 2386 (!Y Z X. equal(X,Y) /\ less_than(Z,X) ==> less_than(Z,Y)) /\ 2387 (!X Y. equal(X,Y) ==> equal(predecessor(X),predecessor(Y))) /\ 2388 (!X Y. equal(X,Y) ==> equal(successor(X),successor(Y))) /\ 2389 (!X Y. equal(X,Y) ==> equal(a(X),a(Y))) /\ 2390 (~less_than(n,k)) /\ 2391 (~less_than(k,l)) /\ 2392 (~less_than(k,i)) /\ 2393 (less_than(l,n)) /\ 2394 (less_than(one,l)) /\ 2395 (less_than(a(k),a(predecessor(l)))) /\ 2396 (!X. less_than(X,successor(n)) /\ less_than(a(X),a(k)) ==> less_than(X,l)) /\ 2397 (!X. less_than(one,l) /\ less_than(a(X),a(predecessor(l))) ==> less_than(X,l) \/ less_than(n,X)) /\ 2398 (!X. ~(less_than(one,X) /\ less_than(X,l) /\ less_than(a(X),a(predecessor(X))))) ==> F���; 2399 2400 2401val PRV006_1 = M "PRV006_1" 2402 ���(!X:'a. equal(X,X)) /\ 2403 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2404 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2405 (!X. equal(predecessor(successor(X)),X)) /\ 2406 (!X. equal(successor(predecessor(X)),X)) /\ 2407 (!X Y. equal(predecessor(X),predecessor(Y)) ==> equal(X,Y)) /\ 2408 (!X Y. equal(successor(X),successor(Y)) ==> equal(X,Y)) /\ 2409 (!X. less_than(predecessor(X),X)) /\ 2410 (!X. less_than(X,successor(X))) /\ 2411 (!X Y Z. less_than(X,Y) /\ less_than(Y,Z) ==> less_than(X,Z)) /\ 2412 (!X Y. less_than(X,Y) \/ less_than(Y,X) \/ equal(X,Y)) /\ 2413 (!X. ~less_than(X,X)) /\ 2414 (!Y X. ~(less_than(X,Y) /\ less_than(Y,X))) /\ 2415 (!Y X Z. equal(X,Y) /\ less_than(X,Z) ==> less_than(Y,Z)) /\ 2416 (!Y Z X. equal(X,Y) /\ less_than(Z,X) ==> less_than(Z,Y)) /\ 2417 (!X Y. equal(X,Y) ==> equal(predecessor(X),predecessor(Y))) /\ 2418 (!X Y. equal(X,Y) ==> equal(successor(X),successor(Y))) /\ 2419 (!X Y. equal(X,Y) ==> equal(a(X),a(Y))) /\ 2420 (~less_than(n,m)) /\ 2421 (less_than(i,m)) /\ 2422 (less_than(i,n)) /\ 2423 (~less_than(i,one)) /\ 2424 (less_than(a(i),a(m))) /\ 2425 (!X. less_than(X,successor(n)) /\ less_than(a(X),a(m)) ==> less_than(X,i)) /\ 2426 (!X. less_than(one,i) /\ less_than(a(X),a(predecessor(i))) ==> less_than(X,i) \/ less_than(n,X)) /\ 2427 (!X. ~(less_than(one,X) /\ less_than(X,i) /\ less_than(a(X),a(predecessor(X))))) ==> F���; 2428 2429 2430val PRV009_1 = M"PRV009_1" $ 2431Lib.with_flag(Globals.guessing_tyvars,true) 2432 Term 2433`(!Y X. less_or_equal(X,Y) \/ less(Y,X)) /\ 2434 (less(j,i)) /\ 2435 (less_or_equal(m,p)) /\ 2436 (less_or_equal(p,q)) /\ 2437 (less_or_equal(q,n)) /\ 2438 (!X Y. less_or_equal(m,X) /\ less(X,i) /\ less(j,Y) /\ less_or_equal(Y,n) ==> less_or_equal(a(X),a(Y))) /\ 2439 (!X Y. less_or_equal(m,X) /\ less_or_equal(X,Y) /\ less_or_equal(Y,j) ==> less_or_equal(a(X),a(Y))) /\ 2440 (!X Y. less_or_equal(i,X) /\ less_or_equal(X,Y) /\ less_or_equal(Y,n) ==> less_or_equal(a(X),a(Y))) /\ 2441 (~less_or_equal(a(p),a(q))) ==> F`; 2442 2443 2444val PUZ012_1 = M"PUZ012_1" $ 2445Lib.with_flag(Globals.guessing_tyvars,true) 2446 Term 2447`(!X. equal_fruits(X,X)) /\ 2448 (!X. equal_boxes(X,X)) /\ 2449 (!X Y. ~(label(X,Y) /\ contains(X,Y))) /\ 2450 (!X. contains(boxa,X) \/ contains(boxb,X) \/ contains(boxc,X)) /\ 2451 (!X. contains(X,apples) \/ contains(X,bananas) \/ contains(X,oranges)) /\ 2452 (!X Y Z. contains(X,Y) /\ contains(X,Z) ==> equal_fruits(Y,Z)) /\ 2453 (!Y X Z. contains(X,Y) /\ contains(Z,Y) ==> equal_boxes(X,Z)) /\ 2454 (~equal_boxes(boxa,boxb)) /\ 2455 (~equal_boxes(boxb,boxc)) /\ 2456 (~equal_boxes(boxa,boxc)) /\ 2457 (~equal_fruits(apples,bananas)) /\ 2458 (~equal_fruits(bananas,oranges)) /\ 2459 (~equal_fruits(apples,oranges)) /\ 2460 (label(boxa,apples)) /\ 2461 (label(boxb,oranges)) /\ 2462 (label(boxc,bananas)) /\ 2463 (contains(boxb,apples)) /\ 2464 (~(contains(boxa,bananas) /\ contains(boxc,oranges))) ==> F`; 2465 2466 2467val PUZ020_1 = M "PUZ020_1" $ 2468Term`(!X:'a. equal(X,X)) /\ 2469 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2470 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2471 (!A B. equal(A,B) ==> equal(statement_by(A),statement_by(B))) /\ 2472 (!X. person(X) ==> knight(X) \/ knave(X)) /\ 2473 (!X. ~(person(X) /\ knight(X) /\ knave(X))) /\ 2474 (!X Y. says(X,Y) /\ a_truth(Y) ==> a_truth(Y)) /\ 2475 (!X Y. ~(says(X,Y) /\ equal(X,Y))) /\ 2476 (!Y X. says(X,Y) ==> equal(Y,statement_by(X))) /\ 2477 (!X Y. ~(person(X) /\ equal(X,statement_by(Y)))) /\ 2478 (!X. person(X) /\ a_truth(statement_by(X)) ==> knight(X)) /\ 2479 (!X. person(X) ==> a_truth(statement_by(X)) \/ knave(X)) /\ 2480 (!X Y. equal(X,Y) /\ knight(X) ==> knight(Y)) /\ 2481 (!X Y. equal(X,Y) /\ knave(X) ==> knave(Y)) /\ 2482 (!X Y. equal(X,Y) /\ person(X) ==> person(Y)) /\ 2483 (!X Y Z. equal(X,Y) /\ says(X,Z) ==> says(Y,Z)) /\ 2484 (!X Z Y. equal(X,Y) /\ says(Z,X) ==> says(Z,Y)) /\ 2485 (!X Y. equal(X,Y) /\ a_truth(X) ==> a_truth(Y)) /\ 2486 (!X Y. knight(X) /\ says(X,Y) ==> a_truth(Y)) /\ 2487 (!X Y. ~(knave(X) /\ says(X,Y) /\ a_truth(Y))) /\ 2488 (person(husband)) /\ 2489 (person(wife)) /\ 2490 (~equal(husband,wife)) /\ 2491 (says(husband,statement_by(husband))) /\ 2492 (a_truth(statement_by(husband)) /\ knight(husband) ==> knight(wife)) /\ 2493 (knight(husband) ==> a_truth(statement_by(husband))) /\ 2494 (a_truth(statement_by(husband)) \/ knight(wife)) /\ 2495 (knight(wife) ==> a_truth(statement_by(husband))) /\ 2496 (~knight(husband)) ==> F`; 2497 2498 2499val PUZ025_1 = M "PUZ025_1" $ 2500Lib.with_flag(Globals.guessing_tyvars,true) 2501 Term 2502`(!X. a_truth(truthteller(X)) \/ a_truth(liar(X))) /\ 2503 (!X. ~(a_truth(truthteller(X)) /\ a_truth(liar(X)))) /\ 2504 (!Truthteller Statement. a_truth(truthteller(Truthteller)) /\ a_truth(says(Truthteller,Statement)) ==> a_truth(Statement)) /\ 2505 (!Liar Statement. ~(a_truth(liar(Liar)) /\ a_truth(says(Liar,Statement)) /\ a_truth(Statement))) /\ 2506 (!Statement Truthteller. a_truth(Statement) /\ a_truth(says(Truthteller,Statement)) ==> a_truth(truthteller(Truthteller))) /\ 2507 (!Statement Liar. a_truth(says(Liar,Statement)) ==> a_truth(Statement) \/ a_truth(liar(Liar))) /\ 2508 (!Z X Y. people(X,Y,Z) /\ a_truth(liar(X)) /\ a_truth(liar(Y)) ==> a_truth(equal_type(X,Y))) /\ 2509 (!Z X Y. people(X,Y,Z) /\ a_truth(truthteller(X)) /\ a_truth(truthteller(Y)) ==> a_truth(equal_type(X,Y))) /\ 2510 (!X Y. a_truth(equal_type(X,Y)) /\ a_truth(truthteller(X)) ==> a_truth(truthteller(Y))) /\ 2511 (!X Y. a_truth(equal_type(X,Y)) /\ a_truth(liar(X)) ==> a_truth(liar(Y))) /\ 2512 (!X Y. a_truth(truthteller(X)) ==> a_truth(equal_type(X,Y)) \/ a_truth(liar(Y))) /\ 2513 (!X Y. a_truth(liar(X)) ==> a_truth(equal_type(X,Y)) \/ a_truth(truthteller(Y))) /\ 2514 (!Y X. a_truth(equal_type(X,Y)) ==> a_truth(equal_type(Y,X))) /\ 2515 (!X Y. ask_1_if_2(X,Y) /\ a_truth(truthteller(X)) /\ a_truth(Y) ==> answer(yes)) /\ 2516 (!X Y. ask_1_if_2(X,Y) /\ a_truth(truthteller(X)) ==> a_truth(Y) \/ answer(no)) /\ 2517 (!X Y. ask_1_if_2(X,Y) /\ a_truth(liar(X)) /\ a_truth(Y) ==> answer(no)) /\ 2518 (!X Y. ask_1_if_2(X,Y) /\ a_truth(liar(X)) ==> a_truth(Y) \/ answer(yes)) /\ 2519 (people(b,c,a)) /\ 2520 (people(a,b,a)) /\ 2521 (people(a,c,b)) /\ 2522 (people(c,b,a)) /\ 2523 (a_truth(says(a,equal_type(b,c)))) /\ 2524 (ask_1_if_2(c,equal_type(a,b))) /\ 2525 (!Answer. ~answer(Answer)) ==> F`; 2526 2527 2528val PUZ029_1 = M "PUZ029_1" 2529 ���(!X:'a. dances_on_tightropes(X) \/ eats_pennybuns(X) \/ old(X)) /\ 2530 (!X. pig(X) /\ liable_to_giddiness(X) ==> treated_with_respect(X)) /\ 2531 (!X. wise(X) /\ balloonist(X) ==> has_umbrella(X)) /\ 2532 (!X. ~(looks_ridiculous(X) /\ eats_pennybuns(X) /\ eats_lunch_in_public(X))) /\ 2533 (!X. balloonist(X) /\ young(X) ==> liable_to_giddiness(X)) /\ 2534 (!X. fat(X) /\ looks_ridiculous(X) ==> dances_on_tightropes(X) \/ eats_lunch_in_public(X)) /\ 2535 (!X. ~(liable_to_giddiness(X) /\ wise(X) /\ dances_on_tightropes(X))) /\ 2536 (!X. pig(X) /\ has_umbrella(X) ==> looks_ridiculous(X)) /\ 2537 (!X. treated_with_respect(X) ==> dances_on_tightropes(X) \/ fat(X)) /\ 2538 (!X. young(X) \/ old(X)) /\ 2539 (!X. ~(young(X) /\ old(X))) /\ 2540 (wise(piggy)) /\ 2541 (young(piggy)) /\ 2542 (pig(piggy)) /\ 2543 (balloonist(piggy)) ==> F���; 2544 2545 2546val RNG001_3 = M "RNG001_3" $ 2547Lib.with_flag(Globals.guessing_tyvars,true) 2548 Term 2549`(!X. sum(additive_identity,X,X)) /\ 2550 (!X. sum(additive_inverse(X),X,additive_identity)) /\ 2551 (!Y U Z X V W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(U,Z,W) ==> sum(X,V,W)) /\ 2552 (!Y X V U Z W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(X,V,W) ==> sum(U,Z,W)) /\ 2553 (!X Y. product(X,Y,multiply(X,Y))) /\ 2554 (!Y Z X V3 V1 V2 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ product(X,V3,V4) ==> sum(V1,V2,V4)) /\ 2555 (!Y Z V1 V2 X V3 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(X,V3,V4)) /\ 2556 (~product(a,additive_identity,additive_identity)) ==> F`; 2557 2558 2559val RNG001_5 = M "RNG001_5" $ 2560 ���(!X:'a. equal(X,X)) /\ 2561 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2562 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2563 (!X. sum(additive_identity,X,X)) /\ 2564 (!X. sum(X,additive_identity,X)) /\ 2565 (!X Y. product(X,Y,multiply(X,Y))) /\ 2566 (!X Y. sum(X,Y,add(X,Y))) /\ 2567 (!X. sum(additive_inverse(X),X,additive_identity)) /\ 2568 (!X. sum(X,additive_inverse(X),additive_identity)) /\ 2569 (!Y U Z X V W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(U,Z,W) ==> sum(X,V,W)) /\ 2570 (!Y X V U Z W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(X,V,W) ==> sum(U,Z,W)) /\ 2571 (!Y X Z. sum(X,Y,Z) ==> sum(Y,X,Z)) /\ 2572 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 2573 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 2574 (!Y Z X V3 V1 V2 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ product(X,V3,V4) ==> sum(V1,V2,V4)) /\ 2575 (!Y Z V1 V2 X V3 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(X,V3,V4)) /\ 2576 (!Y Z V3 X V1 V2 V4. product(Y,X,V1) /\ product(Z,X,V2) /\ sum(Y,Z,V3) /\ product(V3,X,V4) ==> sum(V1,V2,V4)) /\ 2577 (!Y Z V1 V2 V3 X V4. product(Y,X,V1) /\ product(Z,X,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(V3,X,V4)) /\ 2578 (!X Y U V. sum(X,Y,U) /\ sum(X,Y,V) ==> equal(U,V)) /\ 2579 (!X Y U V. product(X,Y,U) /\ product(X,Y,V) ==> equal(U,V)) /\ 2580 (!X Y. equal(X,Y) ==> equal(additive_inverse(X),additive_inverse(Y))) /\ 2581 (!X Y W. equal(X,Y) ==> equal(add(X,W),add(Y,W))) /\ 2582 (!X Y W Z. equal(X,Y) /\ sum(X,W,Z) ==> sum(Y,W,Z)) /\ 2583 (!X W Y Z. equal(X,Y) /\ sum(W,X,Z) ==> sum(W,Y,Z)) /\ 2584 (!X W Z Y. equal(X,Y) /\ sum(W,Z,X) ==> sum(W,Z,Y)) /\ 2585 (!X Y W. equal(X,Y) ==> equal(multiply(X,W),multiply(Y,W))) /\ 2586 (!X Y W Z. equal(X,Y) /\ product(X,W,Z) ==> product(Y,W,Z)) /\ 2587 (!X W Y Z. equal(X,Y) /\ product(W,X,Z) ==> product(W,Y,Z)) /\ 2588 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 2589 (~product(a,additive_identity,additive_identity)) ==> F���; 2590 2591 2592val RNG011_5 = M "RNG011_5" $ 2593 ���(!X:'a. equal(X,X)) /\ 2594 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2595 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2596 (!A B C. equal(A,B) ==> equal(add(A,C),add(B,C))) /\ 2597 (!D F' E. equal(D,E) ==> equal(add(F',D),add(F',E))) /\ 2598 (!G H. equal(G,H) ==> equal(additive_inverse(G),additive_inverse(H))) /\ 2599 (!I' J K'. equal(I',J) ==> equal(multiply(I',K'),multiply(J,K'))) /\ 2600 (!L N M. equal(L,M) ==> equal(multiply(N,L),multiply(N,M))) /\ 2601 (!A B C D. equal(A,B) ==> equal(associator(A,C,D),associator(B,C,D))) /\ 2602 (!E G F' H. equal(E,F') ==> equal(associator(G,E,H),associator(G,F',H))) /\ 2603 (!I' K' L J. equal(I',J) ==> equal(associator(K',L,I'),associator(K',L,J))) /\ 2604 (!M N O. equal(M,N) ==> equal(commutator(M,O),commutator(N,O))) /\ 2605 (!P R Q. equal(P,Q) ==> equal(commutator(R,P),commutator(R,Q))) /\ 2606 (!Y X. equal(add(X,Y),add(Y,X))) /\ 2607 (!X Y Z. equal(add(add(X,Y),Z),add(X,add(Y,Z)))) /\ 2608 (!X. equal(add(X,additive_identity),X)) /\ 2609 (!X. equal(add(additive_identity,X),X)) /\ 2610 (!X. equal(add(X,additive_inverse(X)),additive_identity)) /\ 2611 (!X. equal(add(additive_inverse(X),X),additive_identity)) /\ 2612 (equal(additive_inverse(additive_identity),additive_identity)) /\ 2613 (!X Y. equal(add(X,add(additive_inverse(X),Y)),Y)) /\ 2614 (!X Y. equal(additive_inverse(add(X,Y)),add(additive_inverse(X),additive_inverse(Y)))) /\ 2615 (!X. equal(additive_inverse(additive_inverse(X)),X)) /\ 2616 (!X. equal(multiply(X,additive_identity),additive_identity)) /\ 2617 (!X. equal(multiply(additive_identity,X),additive_identity)) /\ 2618 (!X Y. equal(multiply(additive_inverse(X),additive_inverse(Y)),multiply(X,Y))) /\ 2619 (!X Y. equal(multiply(X,additive_inverse(Y)),additive_inverse(multiply(X,Y)))) /\ 2620 (!X Y. equal(multiply(additive_inverse(X),Y),additive_inverse(multiply(X,Y)))) /\ 2621 (!Y X Z. equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z)))) /\ 2622 (!X Y Z. equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z)))) /\ 2623 (!X Y. equal(multiply(multiply(X,Y),Y),multiply(X,multiply(Y,Y)))) /\ 2624 (!X Y Z. equal(associator(X,Y,Z),add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))))) /\ 2625 (!X Y. equal(commutator(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y))))) /\ 2626 (!X Y. equal(multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)),additive_identity)) /\ 2627 (~equal(multiply(multiply(associator(a,a,b),a),associator(a,a,b)),additive_identity)) ==> F���; 2628 2629 2630val RNG023_6 = M "RNG023_6" $ 2631 ���(!X:'a. equal(X,X)) /\ 2632 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2633 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2634 (!Y X. equal(add(X,Y),add(Y,X))) /\ 2635 (!X Y Z. equal(add(X,add(Y,Z)),add(add(X,Y),Z))) /\ 2636 (!X. equal(add(additive_identity,X),X)) /\ 2637 (!X. equal(add(X,additive_identity),X)) /\ 2638 (!X. equal(multiply(additive_identity,X),additive_identity)) /\ 2639 (!X. equal(multiply(X,additive_identity),additive_identity)) /\ 2640 (!X. equal(add(additive_inverse(X),X),additive_identity)) /\ 2641 (!X. equal(add(X,additive_inverse(X)),additive_identity)) /\ 2642 (!Y X Z. equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z)))) /\ 2643 (!X Y Z. equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z)))) /\ 2644 (!X. equal(additive_inverse(additive_inverse(X)),X)) /\ 2645 (!X Y. equal(multiply(multiply(X,Y),Y),multiply(X,multiply(Y,Y)))) /\ 2646 (!X Y. equal(multiply(multiply(X,X),Y),multiply(X,multiply(X,Y)))) /\ 2647 (!X Y Z. equal(associator(X,Y,Z),add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))))) /\ 2648 (!X Y. equal(commutator(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y))))) /\ 2649 (!D E F'. equal(D,E) ==> equal(add(D,F'),add(E,F'))) /\ 2650 (!G I' H. equal(G,H) ==> equal(add(I',G),add(I',H))) /\ 2651 (!J K'. equal(J,K') ==> equal(additive_inverse(J),additive_inverse(K'))) /\ 2652 (!L M N O. equal(L,M) ==> equal(associator(L,N,O),associator(M,N,O))) /\ 2653 (!P R Q S'. equal(P,Q) ==> equal(associator(R,P,S'),associator(R,Q,S'))) /\ 2654 (!T' V W U. equal(T',U) ==> equal(associator(V,W,T'),associator(V,W,U))) /\ 2655 (!X Y Z. equal(X,Y) ==> equal(commutator(X,Z),commutator(Y,Z))) /\ 2656 (!A1 C1 B1. equal(A1,B1) ==> equal(commutator(C1,A1),commutator(C1,B1))) /\ 2657 (!D1 E1 F1. equal(D1,E1) ==> equal(multiply(D1,F1),multiply(E1,F1))) /\ 2658 (!G1 I1 H1. equal(G1,H1) ==> equal(multiply(I1,G1),multiply(I1,H1))) /\ 2659 (~equal(associator(x,x,y),additive_identity)) ==> F���; 2660 2661 2662val RNG028_2 = M "RNG028_2" $ 2663 ���(!X:'a. equal(X,X)) /\ 2664 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2665 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2666 (!X. equal(add(additive_identity,X),X)) /\ 2667 (!X. equal(multiply(additive_identity,X),additive_identity)) /\ 2668 (!X. equal(multiply(X,additive_identity),additive_identity)) /\ 2669 (!X. equal(add(additive_inverse(X),X),additive_identity)) /\ 2670 (!X Y. equal(additive_inverse(add(X,Y)),add(additive_inverse(X),additive_inverse(Y)))) /\ 2671 (!X. equal(additive_inverse(additive_inverse(X)),X)) /\ 2672 (!Y X Z. equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z)))) /\ 2673 (!X Y Z. equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z)))) /\ 2674 (!X Y. equal(multiply(multiply(X,Y),Y),multiply(X,multiply(Y,Y)))) /\ 2675 (!X Y. equal(multiply(multiply(X,X),Y),multiply(X,multiply(X,Y)))) /\ 2676 (!X Y. equal(multiply(additive_inverse(X),Y),additive_inverse(multiply(X,Y)))) /\ 2677 (!X Y. equal(multiply(X,additive_inverse(Y)),additive_inverse(multiply(X,Y)))) /\ 2678 (equal(additive_inverse(additive_identity),additive_identity)) /\ 2679 (!Y X. equal(add(X,Y),add(Y,X))) /\ 2680 (!X Y Z. equal(add(X,add(Y,Z)),add(add(X,Y),Z))) /\ 2681 (!Z X Y. equal(add(X,Z),add(Y,Z)) ==> equal(X,Y)) /\ 2682 (!Z X Y. equal(add(Z,X),add(Z,Y)) ==> equal(X,Y)) /\ 2683 (!D E F'. equal(D,E) ==> equal(add(D,F'),add(E,F'))) /\ 2684 (!G I' H. equal(G,H) ==> equal(add(I',G),add(I',H))) /\ 2685 (!J K'. equal(J,K') ==> equal(additive_inverse(J),additive_inverse(K'))) /\ 2686 (!D1 E1 F1. equal(D1,E1) ==> equal(multiply(D1,F1),multiply(E1,F1))) /\ 2687 (!G1 I1 H1. equal(G1,H1) ==> equal(multiply(I1,G1),multiply(I1,H1))) /\ 2688 (!X Y Z. equal(associator(X,Y,Z),add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))))) /\ 2689 (!L M N O. equal(L,M) ==> equal(associator(L,N,O),associator(M,N,O))) /\ 2690 (!P R Q S'. equal(P,Q) ==> equal(associator(R,P,S'),associator(R,Q,S'))) /\ 2691 (!T' V W U. equal(T',U) ==> equal(associator(V,W,T'),associator(V,W,U))) /\ 2692 (!X Y. ~equal(multiply(multiply(Y,X),Y),multiply(Y,multiply(X,Y)))) /\ 2693 (!X Y Z. ~equal(associator(Y,X,Z),additive_inverse(associator(X,Y,Z)))) /\ 2694 (!X Y Z. ~equal(associator(Z,Y,X),additive_inverse(associator(X,Y,Z)))) /\ 2695 (~equal(multiply(multiply(cx,multiply(cy,cx)),cz),multiply(cx,multiply(cy,multiply(cx,cz))))) ==> F���; 2696 2697 2698val RNG038_2 = M "RNG038_2" $ 2699 Term 2700`(!X:'a. sum(X,additive_identity,X)) /\ 2701 (!X Y. product(X,Y,multiply(X,Y))) /\ 2702 (!X Y. sum(X,Y,add(X,Y))) /\ 2703 (!X. sum(X,additive_inverse(X),additive_identity)) /\ 2704 (!Y U Z X V W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(U,Z,W) ==> sum(X,V,W)) /\ 2705 (!Y X V U Z W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(X,V,W) ==> sum(U,Z,W)) /\ 2706 (!Y X Z. sum(X,Y,Z) ==> sum(Y,X,Z)) /\ 2707 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 2708 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 2709 (!Y Z X V3 V1 V2 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ product(X,V3,V4) ==> sum(V1,V2,V4)) /\ 2710 (!Y Z V1 V2 X V3 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(X,V3,V4)) /\ 2711 (!Y Z V3 X V1 V2 V4. product(Y,X,V1) /\ product(Z,X,V2) /\ sum(Y,Z,V3) /\ product(V3,X,V4) ==> sum(V1,V2,V4)) /\ 2712 (!Y Z V1 V2 V3 X V4. product(Y,X,V1) /\ product(Z,X,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(V3,X,V4)) /\ 2713 (!X Y U V. sum(X,Y,U) /\ sum(X,Y,V) ==> equal(U,V)) /\ 2714 (!X Y U V. product(X,Y,U) /\ product(X,Y,V) ==> equal(U,V)) /\ 2715 (!X Y. equal(X,Y) ==> equal(additive_inverse(X),additive_inverse(Y))) /\ 2716 (!X Y W. equal(X,Y) ==> equal(add(X,W),add(Y,W))) /\ 2717 (!X Y W Z. equal(X,Y) /\ sum(X,W,Z) ==> sum(Y,W,Z)) /\ 2718 (!X W Y Z. equal(X,Y) /\ sum(W,X,Z) ==> sum(W,Y,Z)) /\ 2719 (!X W Z Y. equal(X,Y) /\ sum(W,Z,X) ==> sum(W,Z,Y)) /\ 2720 (!X Y W. equal(X,Y) ==> equal(multiply(X,W),multiply(Y,W))) /\ 2721 (!X Y W Z. equal(X,Y) /\ product(X,W,Z) ==> product(Y,W,Z)) /\ 2722 (!X W Y Z. equal(X,Y) /\ product(W,X,Z) ==> product(W,Y,Z)) /\ 2723 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 2724 (!X. product(additive_identity,X,additive_identity)) /\ 2725 (!X. product(X,additive_identity,additive_identity)) /\ 2726 (!X Y. equal(X,additive_identity) ==> product(X,h(X,Y),Y)) /\ 2727 (product(a,b,additive_identity)) /\ 2728 (~equal(a,additive_identity)) /\ 2729 (~equal(b,additive_identity)) ==> F`; 2730 2731 2732val RNG040_2 = M "RNG040_2" $ 2733 ���(!X:'a. equal(X,X)) /\ 2734 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2735 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2736 (!X Y. equal(X,Y) ==> equal(additive_inverse(X),additive_inverse(Y))) /\ 2737 (!X Y W. equal(X,Y) ==> equal(add(X,W),add(Y,W))) /\ 2738 (!X W Y. equal(X,Y) ==> equal(add(W,X),add(W,Y))) /\ 2739 (!X Y W Z. equal(X,Y) /\ sum(X,W,Z) ==> sum(Y,W,Z)) /\ 2740 (!X W Y Z. equal(X,Y) /\ sum(W,X,Z) ==> sum(W,Y,Z)) /\ 2741 (!X W Z Y. equal(X,Y) /\ sum(W,Z,X) ==> sum(W,Z,Y)) /\ 2742 (!X Y W. equal(X,Y) ==> equal(multiply(X,W),multiply(Y,W))) /\ 2743 (!X W Y. equal(X,Y) ==> equal(multiply(W,X),multiply(W,Y))) /\ 2744 (!X Y W Z. equal(X,Y) /\ product(X,W,Z) ==> product(Y,W,Z)) /\ 2745 (!X W Y Z. equal(X,Y) /\ product(W,X,Z) ==> product(W,Y,Z)) /\ 2746 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 2747 (!X. sum(additive_identity,X,X)) /\ 2748 (!X. sum(X,additive_identity,X)) /\ 2749 (!X Y. product(X,Y,multiply(X,Y))) /\ 2750 (!X Y. sum(X,Y,add(X,Y))) /\ 2751 (!X. sum(additive_inverse(X),X,additive_identity)) /\ 2752 (!X. sum(X,additive_inverse(X),additive_identity)) /\ 2753 (!Y U Z X V W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(U,Z,W) ==> sum(X,V,W)) /\ 2754 (!Y X V U Z W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(X,V,W) ==> sum(U,Z,W)) /\ 2755 (!Y X Z. sum(X,Y,Z) ==> sum(Y,X,Z)) /\ 2756 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 2757 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 2758 (!Y Z X V3 V1 V2 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ product(X,V3,V4) ==> sum(V1,V2,V4)) /\ 2759 (!Y Z V1 V2 X V3 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(X,V3,V4)) /\ 2760 (!X Y U V. sum(X,Y,U) /\ sum(X,Y,V) ==> equal(U,V)) /\ 2761 (!X Y U V. product(X,Y,U) /\ product(X,Y,V) ==> equal(U,V)) /\ 2762 (!A. product(A,multiplicative_identity,A)) /\ 2763 (!A. product(multiplicative_identity,A,A)) /\ 2764 (!A. product(A,h(A),multiplicative_identity) \/ equal(A,additive_identity)) /\ 2765 (!A. product(h(A),A,multiplicative_identity) \/ equal(A,additive_identity)) /\ 2766 (!B A C. product(A,B,C) ==> product(B,A,C)) /\ 2767 (!A B. equal(A,B) ==> equal(h(A),h(B))) /\ 2768 (sum(b,c,d)) /\ 2769 (product(d,a,additive_identity)) /\ 2770 (product(b,a,l)) /\ 2771 (product(c,a,n)) /\ 2772 (~sum(l,n,additive_identity)) ==> F���; 2773 2774 2775val RNG041_1 = M "RNG041_1" $ 2776 ���(!X:'a. equal(X,X)) /\ 2777 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2778 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2779 (!X. sum(additive_identity,X,X)) /\ 2780 (!X. sum(X,additive_identity,X)) /\ 2781 (!X Y. product(X,Y,multiply(X,Y))) /\ 2782 (!X Y. sum(X,Y,add(X,Y))) /\ 2783 (!X. sum(additive_inverse(X),X,additive_identity)) /\ 2784 (!X. sum(X,additive_inverse(X),additive_identity)) /\ 2785 (!Y U Z X V W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(U,Z,W) ==> sum(X,V,W)) /\ 2786 (!Y X V U Z W. sum(X,Y,U) /\ sum(Y,Z,V) /\ sum(X,V,W) ==> sum(U,Z,W)) /\ 2787 (!Y X Z. sum(X,Y,Z) ==> sum(Y,X,Z)) /\ 2788 (!Y U Z X V W. product(X,Y,U) /\ product(Y,Z,V) /\ product(U,Z,W) ==> product(X,V,W)) /\ 2789 (!Y X V U Z W. product(X,Y,U) /\ product(Y,Z,V) /\ product(X,V,W) ==> product(U,Z,W)) /\ 2790 (!Y Z X V3 V1 V2 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ product(X,V3,V4) ==> sum(V1,V2,V4)) /\ 2791 (!Y Z V1 V2 X V3 V4. product(X,Y,V1) /\ product(X,Z,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(X,V3,V4)) /\ 2792 (!Y Z V3 X V1 V2 V4. product(Y,X,V1) /\ product(Z,X,V2) /\ sum(Y,Z,V3) /\ product(V3,X,V4) ==> sum(V1,V2,V4)) /\ 2793 (!Y Z V1 V2 V3 X V4. product(Y,X,V1) /\ product(Z,X,V2) /\ sum(Y,Z,V3) /\ sum(V1,V2,V4) ==> product(V3,X,V4)) /\ 2794 (!X Y U V. sum(X,Y,U) /\ sum(X,Y,V) ==> equal(U,V)) /\ 2795 (!X Y U V. product(X,Y,U) /\ product(X,Y,V) ==> equal(U,V)) /\ 2796 (!X Y. equal(X,Y) ==> equal(additive_inverse(X),additive_inverse(Y))) /\ 2797 (!X Y W. equal(X,Y) ==> equal(add(X,W),add(Y,W))) /\ 2798 (!X W Y. equal(X,Y) ==> equal(add(W,X),add(W,Y))) /\ 2799 (!X Y W Z. equal(X,Y) /\ sum(X,W,Z) ==> sum(Y,W,Z)) /\ 2800 (!X W Y Z. equal(X,Y) /\ sum(W,X,Z) ==> sum(W,Y,Z)) /\ 2801 (!X W Z Y. equal(X,Y) /\ sum(W,Z,X) ==> sum(W,Z,Y)) /\ 2802 (!X Y W. equal(X,Y) ==> equal(multiply(X,W),multiply(Y,W))) /\ 2803 (!X W Y. equal(X,Y) ==> equal(multiply(W,X),multiply(W,Y))) /\ 2804 (!X Y W Z. equal(X,Y) /\ product(X,W,Z) ==> product(Y,W,Z)) /\ 2805 (!X W Y Z. equal(X,Y) /\ product(W,X,Z) ==> product(W,Y,Z)) /\ 2806 (!X W Z Y. equal(X,Y) /\ product(W,Z,X) ==> product(W,Z,Y)) /\ 2807 (!A B. equal(A,B) ==> equal(h(A),h(B))) /\ 2808 (!A. product(additive_identity,A,additive_identity)) /\ 2809 (!A. product(A,additive_identity,additive_identity)) /\ 2810 (!A. product(A,multiplicative_identity,A)) /\ 2811 (!A. product(multiplicative_identity,A,A)) /\ 2812 (!A. product(A,h(A),multiplicative_identity) \/ equal(A,additive_identity)) /\ 2813 (!A. product(h(A),A,multiplicative_identity) \/ equal(A,additive_identity)) /\ 2814 (product(a,b,additive_identity)) /\ 2815 (~equal(a,additive_identity)) /\ 2816 (~equal(b,additive_identity)) ==> F���; 2817 2818 2819val ROB010_1 = M "ROB010_1" $ 2820 ���(!X:'a. equal(X,X)) /\ 2821 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2822 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2823 (!Y X. equal(add(X,Y),add(Y,X))) /\ 2824 (!X Y Z. equal(add(add(X,Y),Z),add(X,add(Y,Z)))) /\ 2825 (!Y X. equal(negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))),X)) /\ 2826 (!A B C. equal(A,B) ==> equal(add(A,C),add(B,C))) /\ 2827 (!D F' E. equal(D,E) ==> equal(add(F',D),add(F',E))) /\ 2828 (!G H. equal(G,H) ==> equal(negate(G),negate(H))) /\ 2829 (equal(negate(add(a,negate(b))),c)) /\ 2830 (~equal(negate(add(c,negate(add(b,a)))),a)) ==> F���; 2831 2832 2833val ROB013_1 = M "ROB013_1" $ 2834 ���(!X:'a. equal(X,X)) /\ 2835 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2836 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2837 (!Y X. equal(add(X,Y),add(Y,X))) /\ 2838 (!X Y Z. equal(add(add(X,Y),Z),add(X,add(Y,Z)))) /\ 2839 (!Y X. equal(negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))),X)) /\ 2840 (!A B C. equal(A,B) ==> equal(add(A,C),add(B,C))) /\ 2841 (!D F' E. equal(D,E) ==> equal(add(F',D),add(F',E))) /\ 2842 (!G H. equal(G,H) ==> equal(negate(G),negate(H))) /\ 2843 (equal(negate(add(a,b)),c)) /\ 2844 (~equal(negate(add(c,negate(add(negate(b),a)))),a)) ==> F���; 2845 2846 2847val ROB016_1 = M "ROB016_1" $ 2848 ���(!X:'a. equal(X,X)) /\ 2849 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2850 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2851 (!Y X. equal(add(X,Y),add(Y,X))) /\ 2852 (!X Y Z. equal(add(add(X,Y),Z),add(X,add(Y,Z)))) /\ 2853 (!Y X. equal(negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))),X)) /\ 2854 (!A B C. equal(A,B) ==> equal(add(A,C),add(B,C))) /\ 2855 (!D F' E. equal(D,E) ==> equal(add(F',D),add(F',E))) /\ 2856 (!G H. equal(G,H) ==> equal(negate(G),negate(H))) /\ 2857 (!J K' L. equal(J,K') ==> equal(multiply(J,L),multiply(K',L))) /\ 2858 (!M O N. equal(M,N) ==> equal(multiply(O,M),multiply(O,N))) /\ 2859 (!P Q. equal(P,Q) ==> equal(successor(P),successor(Q))) /\ 2860 (!R S'. equal(R,S') /\ positive_integer(R) ==> positive_integer(S')) /\ 2861 (!X. equal(multiply(one:'a,X),X)) /\ 2862 (!V X. positive_integer(X) ==> equal(multiply(successor(V),X),add(X,multiply(V,X)))) /\ 2863 (positive_integer(one)) /\ 2864 (!X. positive_integer(X) ==> positive_integer(successor(X))) /\ 2865 (equal(negate(add(d,e)),negate(e))) /\ 2866 (positive_integer(k)) /\ 2867 (!Vk X Y. equal(negate(add(negate(Y),negate(add(X,negate(Y))))),X) /\ positive_integer(Vk) ==> equal(negate(add(Y,multiply(Vk,add(X,negate(add(X,negate(Y))))))),negate(Y))) /\ 2868 (~equal(negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),negate(e))) ==> F���; 2869 2870 2871val ROB021_1 = M "ROB021_1" $ 2872 ���(!X:'a. equal(X,X)) /\ 2873 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2874 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2875 (!Y X. equal(add(X,Y),add(Y,X))) /\ 2876 (!X Y Z. equal(add(add(X,Y),Z),add(X,add(Y,Z)))) /\ 2877 (!Y X. equal(negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))),X)) /\ 2878 (!A B C. equal(A,B) ==> equal(add(A,C),add(B,C))) /\ 2879 (!D F' E. equal(D,E) ==> equal(add(F',D),add(F',E))) /\ 2880 (!G H. equal(G,H) ==> equal(negate(G),negate(H))) /\ 2881 (!X Y. equal(negate(X),negate(Y)) ==> equal(X,Y)) /\ 2882 (~equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b)) ==> F���; 2883 2884 2885val SET005_1 = Mfail "SET005_1" $ 2886Lib.with_flag(Globals.guessing_tyvars,true) 2887 Term 2888`(!Subset Element Superset. member(Element,Subset) /\ subset(Subset,Superset) ==> member(Element,Superset)) /\ 2889 (!Superset Subset. subset(Subset,Superset) \/ member(member_of_1_not_of_2(Subset,Superset),Subset)) /\ 2890 (!Subset Superset. member(member_of_1_not_of_2(Subset,Superset),Superset) ==> subset(Subset,Superset)) /\ 2891 (!Subset Superset. equal_sets(Subset,Superset) ==> subset(Subset,Superset)) /\ 2892 (!Subset Superset. equal_sets(Superset,Subset) ==> subset(Subset,Superset)) /\ 2893 (!Set2 Set1. subset(Set1,Set2) /\ subset(Set2,Set1) ==> equal_sets(Set2,Set1)) /\ 2894 (!Set2 Intersection Element Set1. intersection(Set1,Set2,Intersection) /\ member(Element,Intersection) ==> member(Element,Set1)) /\ 2895 (!Set1 Intersection Element Set2. intersection(Set1,Set2,Intersection) /\ member(Element,Intersection) ==> member(Element,Set2)) /\ 2896 (!Set2 Set1 Element Intersection. intersection(Set1,Set2,Intersection) /\ member(Element,Set2) /\ member(Element,Set1) ==> member(Element,Intersection)) /\ 2897 (!Set2 Intersection Set1. member(h(Set1,Set2,Intersection),Intersection) \/ intersection(Set1,Set2,Intersection) \/ member(h(Set1,Set2,Intersection),Set1)) /\ 2898 (!Set1 Intersection Set2. member(h(Set1,Set2,Intersection),Intersection) \/ intersection(Set1,Set2,Intersection) \/ member(h(Set1,Set2,Intersection),Set2)) /\ 2899 (!Set1 Set2 Intersection. member(h(Set1,Set2,Intersection),Intersection) /\ member(h(Set1,Set2,Intersection),Set2) /\ member(h(Set1,Set2,Intersection),Set1) ==> intersection(Set1,Set2,Intersection)) /\ 2900 (intersection(a,b,aIb)) /\ 2901 (intersection(b,c,bIc)) /\ 2902 (intersection(a,bIc,aIbIc)) /\ 2903 (~intersection(aIb,c,aIbIc)) ==> F`; 2904 2905 2906val SET009_1 = M "SET009_1" $ 2907Lib.with_flag(Globals.guessing_tyvars,true) 2908 Term 2909`(!Subset Element Superset. member(Element,Subset) /\ subset(Subset,Superset) ==> member(Element,Superset)) /\ 2910 (!Superset Subset. subset(Subset,Superset) \/ member(member_of_1_not_of_2(Subset,Superset),Subset)) /\ 2911 (!Subset Superset. member(member_of_1_not_of_2(Subset,Superset),Superset) ==> subset(Subset,Superset)) /\ 2912 (!Subset Superset. equal_sets(Subset,Superset) ==> subset(Subset,Superset)) /\ 2913 (!Subset Superset. equal_sets(Superset,Subset) ==> subset(Subset,Superset)) /\ 2914 (!Set2 Set1. subset(Set1,Set2) /\ subset(Set2,Set1) ==> equal_sets(Set2,Set1)) /\ 2915 (!Set2 Difference Element Set1. difference(Set1,Set2,Difference) /\ member(Element,Difference) ==> member(Element,Set1)) /\ 2916 (!Element A_set Set1 Set2. ~(member(Element,Set1) /\ member(Element,Set2) /\ difference(A_set,Set1,Set2))) /\ 2917 (!Set1 Difference Element Set2. member(Element,Set1) /\ difference(Set1,Set2,Difference) ==> member(Element,Difference) \/ member(Element,Set2)) /\ 2918 (!Set1 Set2 Difference. difference(Set1,Set2,Difference) \/ member(k(Set1,Set2,Difference),Set1) \/ member(k(Set1,Set2,Difference),Difference)) /\ 2919 (!Set1 Set2 Difference. member(k(Set1,Set2,Difference),Set2) ==> member(k(Set1,Set2,Difference),Difference) \/ difference(Set1,Set2,Difference)) /\ 2920 (!Set1 Set2 Difference. member(k(Set1,Set2,Difference),Difference) /\ member(k(Set1,Set2,Difference),Set1) ==> member(k(Set1,Set2,Difference),Set2) \/ difference(Set1,Set2,Difference)) /\ 2921 (subset(d,a)) /\ 2922 (difference(b,a,bDa)) /\ 2923 (difference(b,d,bDd)) /\ 2924 (~subset(bDa,bDd)) ==> F`; 2925 2926 2927val SET025_4 = M "SET025_4" $ 2928 ���(!X:'a. equal(X,X)) /\ 2929 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 2930 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 2931 (!Y X. member(X,Y) ==> little_set(X)) /\ 2932 (!X Y. little_set(f1(X,Y)) \/ equal(X,Y)) /\ 2933 (!X Y. member(f1(X,Y),X) \/ member(f1(X,Y),Y) \/ equal(X,Y)) /\ 2934 (!X Y. member(f1(X,Y),X) /\ member(f1(X,Y),Y) ==> equal(X,Y)) /\ 2935 (!X U Y. member(U,non_ordered_pair(X,Y)) ==> equal(U,X) \/ equal(U,Y)) /\ 2936 (!Y U X. little_set(U) /\ equal(U,X) ==> member(U,non_ordered_pair(X,Y))) /\ 2937 (!X U Y. little_set(U) /\ equal(U,Y) ==> member(U,non_ordered_pair(X,Y))) /\ 2938 (!X Y. little_set(non_ordered_pair(X,Y))) /\ 2939 (!X. equal(singleton_set(X),non_ordered_pair(X,X))) /\ 2940 (!X Y. equal(ordered_pair(X,Y),non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)))) /\ 2941 (!X. ordered_pair_predicate(X) ==> little_set(f2(X))) /\ 2942 (!X. ordered_pair_predicate(X) ==> little_set(f3(X))) /\ 2943 (!X. ordered_pair_predicate(X) ==> equal(X,ordered_pair(f2(X),f3(X)))) /\ 2944 (!X Y Z. little_set(Y) /\ little_set(Z) /\ equal(X,ordered_pair(Y,Z)) ==> ordered_pair_predicate(X)) /\ 2945 (!Z X. member(Z,first(X)) ==> little_set(f4(Z,X))) /\ 2946 (!Z X. member(Z,first(X)) ==> little_set(f5(Z,X))) /\ 2947 (!Z X. member(Z,first(X)) ==> equal(X,ordered_pair(f4(Z,X),f5(Z,X)))) /\ 2948 (!Z X. member(Z,first(X)) ==> member(Z,f4(Z,X))) /\ 2949 (!X V Z U. little_set(U) /\ little_set(V) /\ equal(X,ordered_pair(U,V)) /\ member(Z,U) ==> member(Z,first(X))) /\ 2950 (!Z X. member(Z,second(X)) ==> little_set(f6(Z,X))) /\ 2951 (!Z X. member(Z,second(X)) ==> little_set(f7(Z,X))) /\ 2952 (!Z X. member(Z,second(X)) ==> equal(X,ordered_pair(f6(Z,X),f7(Z,X)))) /\ 2953 (!Z X. member(Z,second(X)) ==> member(Z,f7(Z,X))) /\ 2954 (!X U Z V. little_set(U) /\ little_set(V) /\ equal(X,ordered_pair(U,V)) /\ member(Z,V) ==> member(Z,second(X))) /\ 2955 (!Z. member(Z,estin) ==> ordered_pair_predicate(Z)) /\ 2956 (!Z. member(Z,estin) ==> member(first(Z),second(Z))) /\ 2957 (!Z. little_set(Z) /\ ordered_pair_predicate(Z) /\ member(first(Z),second(Z)) ==> member(Z,estin)) /\ 2958 (!Y Z X. member(Z,intersection(X,Y)) ==> member(Z,X)) /\ 2959 (!X Z Y. member(Z,intersection(X,Y)) ==> member(Z,Y)) /\ 2960 (!X Z Y. member(Z,X) /\ member(Z,Y) ==> member(Z,intersection(X,Y))) /\ 2961 (!Z X. ~(member(Z,complement(X)) /\ member(Z,X))) /\ 2962 (!Z X. little_set(Z) ==> member(Z,complement(X)) \/ member(Z,X)) /\ 2963 (!X Y. equal(union(X,Y),complement(intersection(complement(X),complement(Y))))) /\ 2964 (!Z X. member(Z,domain_of(X)) ==> ordered_pair_predicate(f8(Z,X))) /\ 2965 (!Z X. member(Z,domain_of(X)) ==> member(f8(Z,X),X)) /\ 2966 (!Z X. member(Z,domain_of(X)) ==> equal(Z,first(f8(Z,X)))) /\ 2967 (!X Z Xp. little_set(Z) /\ ordered_pair_predicate(Xp) /\ member(Xp,X) /\ equal(Z,first(Xp)) ==> member(Z,domain_of(X))) /\ 2968 (!X Y Z. member(Z,cross_product(X,Y)) ==> ordered_pair_predicate(Z)) /\ 2969 (!Y Z X. member(Z,cross_product(X,Y)) ==> member(first(Z),X)) /\ 2970 (!X Z Y. member(Z,cross_product(X,Y)) ==> member(second(Z),Y)) /\ 2971 (!X Z Y. little_set(Z) /\ ordered_pair_predicate(Z) /\ member(first(Z),X) /\ member(second(Z),Y) ==> member(Z,cross_product(X,Y))) /\ 2972 (!X Z. member(Z,converse(X)) ==> ordered_pair_predicate(Z)) /\ 2973 (!Z X. member(Z,converse(X)) ==> member(ordered_pair(second(Z),first(Z)),X)) /\ 2974 (!Z X. little_set(Z) /\ ordered_pair_predicate(Z) /\ member(ordered_pair(second(Z),first(Z)),X) ==> member(Z,converse(X))) /\ 2975 (!Z X. member(Z,rotate_right(X)) ==> little_set(f9(Z,X))) /\ 2976 (!Z X. member(Z,rotate_right(X)) ==> little_set(f10(Z,X))) /\ 2977 (!Z X. member(Z,rotate_right(X)) ==> little_set(f11(Z,X))) /\ 2978 (!Z X. member(Z,rotate_right(X)) ==> equal(Z,ordered_pair(f9(Z,X),ordered_pair(f10(Z,X),f11(Z,X))))) /\ 2979 (!Z X. member(Z,rotate_right(X)) ==> member(ordered_pair(f10(Z,X),ordered_pair(f11(Z,X),f9(Z,X))),X)) /\ 2980 (!Z V W U X. little_set(Z) /\ little_set(U) /\ little_set(V) /\ little_set(W) /\ equal(Z,ordered_pair(U,ordered_pair(V,W))) /\ member(ordered_pair(V,ordered_pair(W,U)),X) ==> member(Z,rotate_right(X))) /\ 2981 (!Z X. member(Z,flip_range_of(X)) ==> little_set(f12(Z,X))) /\ 2982 (!Z X. member(Z,flip_range_of(X)) ==> little_set(f13(Z,X))) /\ 2983 (!Z X. member(Z,flip_range_of(X)) ==> little_set(f14(Z,X))) /\ 2984 (!Z X. member(Z,flip_range_of(X)) ==> equal(Z,ordered_pair(f12(Z,X),ordered_pair(f13(Z,X),f14(Z,X))))) /\ 2985 (!Z X. member(Z,flip_range_of(X)) ==> member(ordered_pair(f12(Z,X),ordered_pair(f14(Z,X),f13(Z,X))),X)) /\ 2986 (!Z U W V X. little_set(Z) /\ little_set(U) /\ little_set(V) /\ little_set(W) /\ equal(Z,ordered_pair(U,ordered_pair(V,W))) /\ member(ordered_pair(U,ordered_pair(W,V)),X) ==> member(Z,flip_range_of(X))) /\ 2987 (!X. equal(successor(X),union(X,singleton_set(X)))) /\ 2988 (!Z. ~member(Z,empty_set)) /\ 2989 (!Z. little_set(Z) ==> member(Z,universal_set)) /\ 2990 (little_set(infinity)) /\ 2991 (member(empty_set,infinity)) /\ 2992 (!X. member(X,infinity) ==> member(successor(X),infinity)) /\ 2993 (!Z X. member(Z,sigma(X)) ==> member(f16(Z,X),X)) /\ 2994 (!Z X. member(Z,sigma(X)) ==> member(Z,f16(Z,X))) /\ 2995 (!X Z Y. member(Y,X) /\ member(Z,Y) ==> member(Z,sigma(X))) /\ 2996 (!U. little_set(U) ==> little_set(sigma(U))) /\ 2997 (!X U Y. subset(X,Y) /\ member(U,X) ==> member(U,Y)) /\ 2998 (!Y X. subset(X,Y) \/ member(f17(X,Y),X)) /\ 2999 (!X Y. member(f17(X,Y),Y) ==> subset(X,Y)) /\ 3000 (!X Y. proper_subset(X,Y) ==> subset(X,Y)) /\ 3001 (!X Y. ~(proper_subset(X,Y) /\ equal(X,Y))) /\ 3002 (!X Y. subset(X,Y) ==> proper_subset(X,Y) \/ equal(X,Y)) /\ 3003 (!Z X. member(Z,powerset(X)) ==> subset(Z,X)) /\ 3004 (!Z X. little_set(Z) /\ subset(Z,X) ==> member(Z,powerset(X))) /\ 3005 (!U. little_set(U) ==> little_set(powerset(U))) /\ 3006 (!Z X. relation(Z) /\ member(X,Z) ==> ordered_pair_predicate(X)) /\ 3007 (!Z. relation(Z) \/ member(f18(Z),Z)) /\ 3008 (!Z. ordered_pair_predicate(f18(Z)) ==> relation(Z)) /\ 3009 (!U X V W. single_valued_set(X) /\ little_set(U) /\ little_set(V) /\ little_set(W) /\ member(ordered_pair(U,V),X) /\ member(ordered_pair(U,W),X) ==> equal(V,W)) /\ 3010 (!X. single_valued_set(X) \/ little_set(f19(X))) /\ 3011 (!X. single_valued_set(X) \/ little_set(f20(X))) /\ 3012 (!X. single_valued_set(X) \/ little_set(f21(X))) /\ 3013 (!X. single_valued_set(X) \/ member(ordered_pair(f19(X),f20(X)),X)) /\ 3014 (!X. single_valued_set(X) \/ member(ordered_pair(f19(X),f21(X)),X)) /\ 3015 (!X. equal(f20(X),f21(X)) ==> single_valued_set(X)) /\ 3016 (!Xf. function(Xf) ==> relation(Xf)) /\ 3017 (!Xf. function(Xf) ==> single_valued_set(Xf)) /\ 3018 (!Xf. relation(Xf) /\ single_valued_set(Xf) ==> function(Xf)) /\ 3019 (!Z X Xf. member(Z,image(X,Xf)) ==> ordered_pair_predicate(f22(Z,X,Xf))) /\ 3020 (!Z X Xf. member(Z,image(X,Xf)) ==> member(f22(Z,X,Xf),Xf)) /\ 3021 (!Z Xf X. member(Z,image(X,Xf)) ==> member(first(f22(Z,X,Xf)),X)) /\ 3022 (!X Xf Z. member(Z,image(X,Xf)) ==> equal(second(f22(Z,X,Xf)),Z)) /\ 3023 (!Xf X Y Z. little_set(Z) /\ ordered_pair_predicate(Y) /\ member(Y,Xf) /\ member(first(Y),X) /\ equal(second(Y),Z) ==> member(Z,image(X,Xf))) /\ 3024 (!X Xf. little_set(X) /\ function(Xf) ==> little_set(image(X,Xf))) /\ 3025 (!X U Y. ~(disjoint(X,Y) /\ member(U,X) /\ member(U,Y))) /\ 3026 (!Y X. disjoint(X,Y) \/ member(f23(X,Y),X)) /\ 3027 (!X Y. disjoint(X,Y) \/ member(f23(X,Y),Y)) /\ 3028 (!X. equal(X,empty_set) \/ member(f24(X),X)) /\ 3029 (!X. equal(X,empty_set) \/ disjoint(f24(X),X)) /\ 3030 (function(f25)) /\ 3031 (!X. little_set(X) ==> equal(X,empty_set) \/ member(f26(X),X)) /\ 3032 (!X. little_set(X) ==> equal(X,empty_set) \/ member(ordered_pair(X,f26(X)),f25)) /\ 3033 (!Z X. member(Z,range_of(X)) ==> ordered_pair_predicate(f27(Z,X))) /\ 3034 (!Z X. member(Z,range_of(X)) ==> member(f27(Z,X),X)) /\ 3035 (!Z X. member(Z,range_of(X)) ==> equal(Z,second(f27(Z,X)))) /\ 3036 (!X Z Xp. little_set(Z) /\ ordered_pair_predicate(Xp) /\ member(Xp,X) /\ equal(Z,second(Xp)) ==> member(Z,range_of(X))) /\ 3037 (!Z. member(Z,identity_relation) ==> ordered_pair_predicate(Z)) /\ 3038 (!Z. member(Z,identity_relation) ==> equal(first(Z),second(Z))) /\ 3039 (!Z. little_set(Z) /\ ordered_pair_predicate(Z) /\ equal(first(Z),second(Z)) ==> member(Z,identity_relation)) /\ 3040 (!X Y. equal(restrict(X,Y),intersection(X,cross_product(Y,universal_set)))) /\ 3041 (!Xf. one_to_one_function(Xf) ==> function(Xf)) /\ 3042 (!Xf. one_to_one_function(Xf) ==> function(converse(Xf))) /\ 3043 (!Xf. function(Xf) /\ function(converse(Xf)) ==> one_to_one_function(Xf)) /\ 3044 (!Z Xf Y. member(Z,apply(Xf,Y)) ==> ordered_pair_predicate(f28(Z,Xf,Y))) /\ 3045 (!Z Y Xf. member(Z,apply(Xf,Y)) ==> member(f28(Z,Xf,Y),Xf)) /\ 3046 (!Z Xf Y. member(Z,apply(Xf,Y)) ==> equal(first(f28(Z,Xf,Y)),Y)) /\ 3047 (!Z Xf Y. member(Z,apply(Xf,Y)) ==> member(Z,second(f28(Z,Xf,Y)))) /\ 3048 (!Xf Y Z W. ordered_pair_predicate(W) /\ member(W,Xf) /\ equal(first(W),Y) /\ member(Z,second(W)) ==> member(Z,apply(Xf,Y))) /\ 3049 (!Xf X Y. equal(apply_to_two_arguments(Xf,X,Y),apply(Xf,ordered_pair(X,Y)))) /\ 3050 (!X Y Xf. maps(Xf,X,Y) ==> function(Xf)) /\ 3051 (!Y Xf X. maps(Xf,X,Y) ==> equal(domain_of(Xf),X)) /\ 3052 (!X Xf Y. maps(Xf,X,Y) ==> subset(range_of(Xf),Y)) /\ 3053 (!X Xf Y. function(Xf) /\ equal(domain_of(Xf),X) /\ subset(range_of(Xf),Y) ==> maps(Xf,X,Y)) /\ 3054 (!Xf Xs. closed(Xs,Xf) ==> little_set(Xs)) /\ 3055 (!Xs Xf. closed(Xs,Xf) ==> little_set(Xf)) /\ 3056 (!Xf Xs. closed(Xs,Xf) ==> maps(Xf,cross_product(Xs,Xs),Xs)) /\ 3057 (!Xf Xs. little_set(Xs) /\ little_set(Xf) /\ maps(Xf,cross_product(Xs,Xs),Xs) ==> closed(Xs,Xf)) /\ 3058 (!Z Xf Xg. member(Z,composition(Xf,Xg)) ==> little_set(f29(Z,Xf,Xg))) /\ 3059 (!Z Xf Xg. member(Z,composition(Xf,Xg)) ==> little_set(f30(Z,Xf,Xg))) /\ 3060 (!Z Xf Xg. member(Z,composition(Xf,Xg)) ==> little_set(f31(Z,Xf,Xg))) /\ 3061 (!Z Xf Xg. member(Z,composition(Xf,Xg)) ==> equal(Z,ordered_pair(f29(Z,Xf,Xg),f30(Z,Xf,Xg)))) /\ 3062 (!Z Xg Xf. member(Z,composition(Xf,Xg)) ==> member(ordered_pair(f29(Z,Xf,Xg),f31(Z,Xf,Xg)),Xf)) /\ 3063 (!Z Xf Xg. member(Z,composition(Xf,Xg)) ==> member(ordered_pair(f31(Z,Xf,Xg),f30(Z,Xf,Xg)),Xg)) /\ 3064 (!Z X Xf W Y Xg. little_set(Z) /\ little_set(X) /\ little_set(Y) /\ little_set(W) /\ equal(Z,ordered_pair(X,Y)) /\ member(ordered_pair(X,W),Xf) /\ member(ordered_pair(W,Y),Xg) ==> member(Z,composition(Xf,Xg))) /\ 3065 (!Xh Xs2 Xf2 Xs1 Xf1. homomorphism(Xh,Xs1,Xf1,Xs2,Xf2) ==> closed(Xs1,Xf1)) /\ 3066 (!Xh Xs1 Xf1 Xs2 Xf2. homomorphism(Xh,Xs1,Xf1,Xs2,Xf2) ==> closed(Xs2,Xf2)) /\ 3067 (!Xf1 Xf2 Xh Xs1 Xs2. homomorphism(Xh,Xs1,Xf1,Xs2,Xf2) ==> maps(Xh,Xs1,Xs2)) /\ 3068 (!Xs2 Xs1 Xf1 Xf2 X Xh Y. homomorphism(Xh,Xs1,Xf1,Xs2,Xf2) /\ member(X,Xs1) /\ member(Y,Xs1) ==> equal(apply(Xh,apply_to_two_arguments(Xf1,X,Y)),apply_to_two_arguments(Xf2,apply(Xh,X),apply(Xh,Y)))) /\ 3069 (!Xh Xf1 Xs2 Xf2 Xs1. closed(Xs1,Xf1) /\ closed(Xs2,Xf2) /\ maps(Xh,Xs1,Xs2) ==> homomorphism(Xh,Xs1,Xf1,Xs2,Xf2) \/ member(f32(Xh,Xs1,Xf1,Xs2,Xf2),Xs1)) /\ 3070 (!Xh Xf1 Xs2 Xf2 Xs1. closed(Xs1,Xf1) /\ closed(Xs2,Xf2) /\ maps(Xh,Xs1,Xs2) ==> homomorphism(Xh,Xs1,Xf1,Xs2,Xf2) \/ member(f33(Xh,Xs1,Xf1,Xs2,Xf2),Xs1)) /\ 3071 (!Xh Xs1 Xf1 Xs2 Xf2. closed(Xs1,Xf1) /\ closed(Xs2,Xf2) /\ maps(Xh,Xs1,Xs2) /\ equal(apply(Xh,apply_to_two_arguments(Xf1,f32(Xh,Xs1,Xf1,Xs2,Xf2),f33(Xh,Xs1,Xf1,Xs2,Xf2))),apply_to_two_arguments(Xf2,apply(Xh,f32(Xh,Xs1,Xf1,Xs2,Xf2)),apply(Xh,f33(Xh,Xs1,Xf1,Xs2,Xf2)))) ==> homomorphism(Xh,Xs1,Xf1,Xs2,Xf2)) /\ 3072 (!A B C. equal(A,B) ==> equal(f1(A,C),f1(B,C))) /\ 3073 (!D F' E. equal(D,E) ==> equal(f1(F',D),f1(F',E))) /\ 3074 (!A2 B2. equal(A2,B2) ==> equal(f2(A2),f2(B2))) /\ 3075 (!G4 H4. equal(G4,H4) ==> equal(f3(G4),f3(H4))) /\ 3076 (!O7 P7 Q7. equal(O7,P7) ==> equal(f4(O7,Q7),f4(P7,Q7))) /\ 3077 (!R7 T7 S7. equal(R7,S7) ==> equal(f4(T7,R7),f4(T7,S7))) /\ 3078 (!U7 V7 W7. equal(U7,V7) ==> equal(f5(U7,W7),f5(V7,W7))) /\ 3079 (!X7 Z7 Y7. equal(X7,Y7) ==> equal(f5(Z7,X7),f5(Z7,Y7))) /\ 3080 (!A8 B8 C8. equal(A8,B8) ==> equal(f6(A8,C8),f6(B8,C8))) /\ 3081 (!D8 F8 E8. equal(D8,E8) ==> equal(f6(F8,D8),f6(F8,E8))) /\ 3082 (!G8 H8 I8. equal(G8,H8) ==> equal(f7(G8,I8),f7(H8,I8))) /\ 3083 (!J8 L8 K8. equal(J8,K8) ==> equal(f7(L8,J8),f7(L8,K8))) /\ 3084 (!M8 N8 O8. equal(M8,N8) ==> equal(f8(M8,O8),f8(N8,O8))) /\ 3085 (!P8 R8 Q8. equal(P8,Q8) ==> equal(f8(R8,P8),f8(R8,Q8))) /\ 3086 (!S8 T8 U8. equal(S8,T8) ==> equal(f9(S8,U8),f9(T8,U8))) /\ 3087 (!V8 X8 W8. equal(V8,W8) ==> equal(f9(X8,V8),f9(X8,W8))) /\ 3088 (!G H I'. equal(G,H) ==> equal(f10(G,I'),f10(H,I'))) /\ 3089 (!J L K'. equal(J,K') ==> equal(f10(L,J),f10(L,K'))) /\ 3090 (!M N O. equal(M,N) ==> equal(f11(M,O),f11(N,O))) /\ 3091 (!P R Q. equal(P,Q) ==> equal(f11(R,P),f11(R,Q))) /\ 3092 (!S' T' U. equal(S',T') ==> equal(f12(S',U),f12(T',U))) /\ 3093 (!V X W. equal(V,W) ==> equal(f12(X,V),f12(X,W))) /\ 3094 (!Y Z A1. equal(Y,Z) ==> equal(f13(Y,A1),f13(Z,A1))) /\ 3095 (!B1 D1 C1. equal(B1,C1) ==> equal(f13(D1,B1),f13(D1,C1))) /\ 3096 (!E1 F1 G1. equal(E1,F1) ==> equal(f14(E1,G1),f14(F1,G1))) /\ 3097 (!H1 J1 I1. equal(H1,I1) ==> equal(f14(J1,H1),f14(J1,I1))) /\ 3098 (!K1 L1 M1. equal(K1,L1) ==> equal(f16(K1,M1),f16(L1,M1))) /\ 3099 (!N1 P1 O1. equal(N1,O1) ==> equal(f16(P1,N1),f16(P1,O1))) /\ 3100 (!Q1 R1 S1. equal(Q1,R1) ==> equal(f17(Q1,S1),f17(R1,S1))) /\ 3101 (!T1 V1 U1. equal(T1,U1) ==> equal(f17(V1,T1),f17(V1,U1))) /\ 3102 (!W1 X1. equal(W1,X1) ==> equal(f18(W1),f18(X1))) /\ 3103 (!Y1 Z1. equal(Y1,Z1) ==> equal(f19(Y1),f19(Z1))) /\ 3104 (!C2 D2. equal(C2,D2) ==> equal(f20(C2),f20(D2))) /\ 3105 (!E2 F2. equal(E2,F2) ==> equal(f21(E2),f21(F2))) /\ 3106 (!G2 H2 I2 J2. equal(G2,H2) ==> equal(f22(G2,I2,J2),f22(H2,I2,J2))) /\ 3107 (!K2 M2 L2 N2. equal(K2,L2) ==> equal(f22(M2,K2,N2),f22(M2,L2,N2))) /\ 3108 (!O2 Q2 R2 P2. equal(O2,P2) ==> equal(f22(Q2,R2,O2),f22(Q2,R2,P2))) /\ 3109 (!S2 T2 U2. equal(S2,T2) ==> equal(f23(S2,U2),f23(T2,U2))) /\ 3110 (!V2 X2 W2. equal(V2,W2) ==> equal(f23(X2,V2),f23(X2,W2))) /\ 3111 (!Y2 Z2. equal(Y2,Z2) ==> equal(f24(Y2),f24(Z2))) /\ 3112 (!A3 B3. equal(A3,B3) ==> equal(f26(A3),f26(B3))) /\ 3113 (!C3 D3 E3. equal(C3,D3) ==> equal(f27(C3,E3),f27(D3,E3))) /\ 3114 (!F3 H3 G3. equal(F3,G3) ==> equal(f27(H3,F3),f27(H3,G3))) /\ 3115 (!I3 J3 K3 L3. equal(I3,J3) ==> equal(f28(I3,K3,L3),f28(J3,K3,L3))) /\ 3116 (!M3 O3 N3 P3. equal(M3,N3) ==> equal(f28(O3,M3,P3),f28(O3,N3,P3))) /\ 3117 (!Q3 S3 T3 R3. equal(Q3,R3) ==> equal(f28(S3,T3,Q3),f28(S3,T3,R3))) /\ 3118 (!U3 V3 W3 X3. equal(U3,V3) ==> equal(f29(U3,W3,X3),f29(V3,W3,X3))) /\ 3119 (!Y3 A4 Z3 B4. equal(Y3,Z3) ==> equal(f29(A4,Y3,B4),f29(A4,Z3,B4))) /\ 3120 (!C4 E4 F4 D4. equal(C4,D4) ==> equal(f29(E4,F4,C4),f29(E4,F4,D4))) /\ 3121 (!I4 J4 K4 L4. equal(I4,J4) ==> equal(f30(I4,K4,L4),f30(J4,K4,L4))) /\ 3122 (!M4 O4 N4 P4. equal(M4,N4) ==> equal(f30(O4,M4,P4),f30(O4,N4,P4))) /\ 3123 (!Q4 S4 T4 R4. equal(Q4,R4) ==> equal(f30(S4,T4,Q4),f30(S4,T4,R4))) /\ 3124 (!U4 V4 W4 X4. equal(U4,V4) ==> equal(f31(U4,W4,X4),f31(V4,W4,X4))) /\ 3125 (!Y4 A5 Z4 B5. equal(Y4,Z4) ==> equal(f31(A5,Y4,B5),f31(A5,Z4,B5))) /\ 3126 (!C5 E5 F5 D5. equal(C5,D5) ==> equal(f31(E5,F5,C5),f31(E5,F5,D5))) /\ 3127 (!G5 H5 I5 J5 K5 L5. equal(G5,H5) ==> equal(f32(G5,I5,J5,K5,L5),f32(H5,I5,J5,K5,L5))) /\ 3128 (!M5 O5 N5 P5 Q5 R5. equal(M5,N5) ==> equal(f32(O5,M5,P5,Q5,R5),f32(O5,N5,P5,Q5,R5))) /\ 3129 (!S5 U5 V5 T5 W5 X5. equal(S5,T5) ==> equal(f32(U5,V5,S5,W5,X5),f32(U5,V5,T5,W5,X5))) /\ 3130 (!Y5 A6 B6 C6 Z5 D6. equal(Y5,Z5) ==> equal(f32(A6,B6,C6,Y5,D6),f32(A6,B6,C6,Z5,D6))) /\ 3131 (!E6 G6 H6 I6 J6 F6. equal(E6,F6) ==> equal(f32(G6,H6,I6,J6,E6),f32(G6,H6,I6,J6,F6))) /\ 3132 (!K6 L6 M6 N6 O6 P6. equal(K6,L6) ==> equal(f33(K6,M6,N6,O6,P6),f33(L6,M6,N6,O6,P6))) /\ 3133 (!Q6 S6 R6 T6 U6 V6. equal(Q6,R6) ==> equal(f33(S6,Q6,T6,U6,V6),f33(S6,R6,T6,U6,V6))) /\ 3134 (!W6 Y6 Z6 X6 A7 B7. equal(W6,X6) ==> equal(f33(Y6,Z6,W6,A7,B7),f33(Y6,Z6,X6,A7,B7))) /\ 3135 (!C7 E7 F7 G7 D7 H7. equal(C7,D7) ==> equal(f33(E7,F7,G7,C7,H7),f33(E7,F7,G7,D7,H7))) /\ 3136 (!I7 K7 L7 M7 N7 J7. equal(I7,J7) ==> equal(f33(K7,L7,M7,N7,I7),f33(K7,L7,M7,N7,J7))) /\ 3137 (!A B C. equal(A,B) ==> equal(apply(A,C),apply(B,C))) /\ 3138 (!D F' E. equal(D,E) ==> equal(apply(F',D),apply(F',E))) /\ 3139 (!G H I' J. equal(G,H) ==> equal(apply_to_two_arguments(G,I',J),apply_to_two_arguments(H,I',J))) /\ 3140 (!K' M L N. equal(K',L) ==> equal(apply_to_two_arguments(M,K',N),apply_to_two_arguments(M,L,N))) /\ 3141 (!O Q R P. equal(O,P) ==> equal(apply_to_two_arguments(Q,R,O),apply_to_two_arguments(Q,R,P))) /\ 3142 (!S' T'. equal(S',T') ==> equal(complement(S'),complement(T'))) /\ 3143 (!U V W. equal(U,V) ==> equal(composition(U,W),composition(V,W))) /\ 3144 (!X Z Y. equal(X,Y) ==> equal(composition(Z,X),composition(Z,Y))) /\ 3145 (!A1 B1. equal(A1,B1) ==> equal(converse(A1),converse(B1))) /\ 3146 (!C1 D1 E1. equal(C1,D1) ==> equal(cross_product(C1,E1),cross_product(D1,E1))) /\ 3147 (!F1 H1 G1. equal(F1,G1) ==> equal(cross_product(H1,F1),cross_product(H1,G1))) /\ 3148 (!I1 J1. equal(I1,J1) ==> equal(domain_of(I1),domain_of(J1))) /\ 3149 (!I10 J10. equal(I10,J10) ==> equal(first(I10),first(J10))) /\ 3150 (!Q10 R10. equal(Q10,R10) ==> equal(flip_range_of(Q10),flip_range_of(R10))) /\ 3151 (!S10 T10 U10. equal(S10,T10) ==> equal(image(S10,U10),image(T10,U10))) /\ 3152 (!V10 X10 W10. equal(V10,W10) ==> equal(image(X10,V10),image(X10,W10))) /\ 3153 (!Y10 Z10 A11. equal(Y10,Z10) ==> equal(intersection(Y10,A11),intersection(Z10,A11))) /\ 3154 (!B11 D11 C11. equal(B11,C11) ==> equal(intersection(D11,B11),intersection(D11,C11))) /\ 3155 (!E11 F11 G11. equal(E11,F11) ==> equal(non_ordered_pair(E11,G11),non_ordered_pair(F11,G11))) /\ 3156 (!H11 J11 I11. equal(H11,I11) ==> equal(non_ordered_pair(J11,H11),non_ordered_pair(J11,I11))) /\ 3157 (!K11 L11 M11. equal(K11,L11) ==> equal(ordered_pair(K11,M11),ordered_pair(L11,M11))) /\ 3158 (!N11 P11 O11. equal(N11,O11) ==> equal(ordered_pair(P11,N11),ordered_pair(P11,O11))) /\ 3159 (!Q11 R11. equal(Q11,R11) ==> equal(powerset(Q11),powerset(R11))) /\ 3160 (!S11 T11. equal(S11,T11) ==> equal(range_of(S11),range_of(T11))) /\ 3161 (!U11 V11 W11. equal(U11,V11) ==> equal(restrict(U11,W11),restrict(V11,W11))) /\ 3162 (!X11 Z11 Y11. equal(X11,Y11) ==> equal(restrict(Z11,X11),restrict(Z11,Y11))) /\ 3163 (!A12 B12. equal(A12,B12) ==> equal(rotate_right(A12),rotate_right(B12))) /\ 3164 (!C12 D12. equal(C12,D12) ==> equal(second(C12),second(D12))) /\ 3165 (!K12 L12. equal(K12,L12) ==> equal(sigma(K12),sigma(L12))) /\ 3166 (!M12 N12. equal(M12,N12) ==> equal(singleton_set(M12),singleton_set(N12))) /\ 3167 (!O12 P12. equal(O12,P12) ==> equal(successor(O12),successor(P12))) /\ 3168 (!Q12 R12 S12. equal(Q12,R12) ==> equal(union(Q12,S12),union(R12,S12))) /\ 3169 (!T12 V12 U12. equal(T12,U12) ==> equal(union(V12,T12),union(V12,U12))) /\ 3170 (!W12 X12 Y12. equal(W12,X12) /\ closed(W12,Y12) ==> closed(X12,Y12)) /\ 3171 (!Z12 B13 A13. equal(Z12,A13) /\ closed(B13,Z12) ==> closed(B13,A13)) /\ 3172 (!C13 D13 E13. equal(C13,D13) /\ disjoint(C13,E13) ==> disjoint(D13,E13)) /\ 3173 (!F13 H13 G13. equal(F13,G13) /\ disjoint(H13,F13) ==> disjoint(H13,G13)) /\ 3174 (!I13 J13. equal(I13,J13) /\ function(I13) ==> function(J13)) /\ 3175 (!K13 L13 M13 N13 O13 P13. equal(K13,L13) /\ homomorphism(K13,M13,N13,O13,P13) ==> homomorphism(L13,M13,N13,O13,P13)) /\ 3176 (!Q13 S13 R13 T13 U13 V13. equal(Q13,R13) /\ homomorphism(S13,Q13,T13,U13,V13) ==> homomorphism(S13,R13,T13,U13,V13)) /\ 3177 (!W13 Y13 Z13 X13 A14 B14. equal(W13,X13) /\ homomorphism(Y13,Z13,W13,A14,B14) ==> homomorphism(Y13,Z13,X13,A14,B14)) /\ 3178 (!C14 E14 F14 G14 D14 H14. equal(C14,D14) /\ homomorphism(E14,F14,G14,C14,H14) ==> homomorphism(E14,F14,G14,D14,H14)) /\ 3179 (!I14 K14 L14 M14 N14 J14. equal(I14,J14) /\ homomorphism(K14,L14,M14,N14,I14) ==> homomorphism(K14,L14,M14,N14,J14)) /\ 3180 (!O14 P14. equal(O14,P14) /\ little_set(O14) ==> little_set(P14)) /\ 3181 (!Q14 R14 S14 T14. equal(Q14,R14) /\ maps(Q14,S14,T14) ==> maps(R14,S14,T14)) /\ 3182 (!U14 W14 V14 X14. equal(U14,V14) /\ maps(W14,U14,X14) ==> maps(W14,V14,X14)) /\ 3183 (!Y14 A15 B15 Z14. equal(Y14,Z14) /\ maps(A15,B15,Y14) ==> maps(A15,B15,Z14)) /\ 3184 (!C15 D15 E15. equal(C15,D15) /\ member(C15,E15) ==> member(D15,E15)) /\ 3185 (!F15 H15 G15. equal(F15,G15) /\ member(H15,F15) ==> member(H15,G15)) /\ 3186 (!I15 J15. equal(I15,J15) /\ one_to_one_function(I15) ==> one_to_one_function(J15)) /\ 3187 (!K15 L15. equal(K15,L15) /\ ordered_pair_predicate(K15) ==> ordered_pair_predicate(L15)) /\ 3188 (!M15 N15 O15. equal(M15,N15) /\ proper_subset(M15,O15) ==> proper_subset(N15,O15)) /\ 3189 (!P15 R15 Q15. equal(P15,Q15) /\ proper_subset(R15,P15) ==> proper_subset(R15,Q15)) /\ 3190 (!S15 T15. equal(S15,T15) /\ relation(S15) ==> relation(T15)) /\ 3191 (!U15 V15. equal(U15,V15) /\ single_valued_set(U15) ==> single_valued_set(V15)) /\ 3192 (!W15 X15 Y15. equal(W15,X15) /\ subset(W15,Y15) ==> subset(X15,Y15)) /\ 3193 (!Z15 B16 A16. equal(Z15,A16) /\ subset(B16,Z15) ==> subset(B16,A16)) /\ 3194 (~little_set(ordered_pair(a,b))) ==> F���; 3195 3196 3197val SET046_5 = M "SET046_5" $ 3198 Term 3199`(!Y X. ~(element(X,a) /\ element(X,Y) /\ element(Y,X))) /\ 3200 (!X:'a. element(X,f(X)) \/ element(X,a)) /\ 3201 (!X. element(f(X),X) \/ element(X,a)) ==> F`; 3202 3203 3204val SET047_5 = M "SET047_5" $ 3205Lib.with_flag(Globals.guessing_tyvars,true) 3206 Term 3207`(!X Z Y. set_equal(X,Y) /\ element(Z,X) ==> element(Z,Y)) /\ 3208 (!Y Z X. set_equal(X,Y) /\ element(Z,Y) ==> element(Z,X)) /\ 3209 (!X Y. element(f(X,Y),X) \/ element(f(X,Y),Y) \/ set_equal(X,Y)) /\ 3210 (!X Y. element(f(X,Y),Y) /\ element(f(X,Y),X) ==> set_equal(X,Y)) /\ 3211 (set_equal(a,b) \/ set_equal(b,a)) /\ 3212 (~(set_equal(b,a) /\ set_equal(a,b))) ==> F`; 3213 3214 3215val SYN034_1 = M "SYN034_1" $ 3216 ���(!A:'a. p(A,a) \/ p(A,f(A))) /\ 3217 (!A. p(A,a) \/ p(f(A),A)) /\ 3218 (!A B. ~(p(A,B) /\ p(B,A) /\ p(B,a))) ==> F���; 3219 3220 3221val SYN071_1 = M "SYN071_1" $ 3222 ���(!X:'a. equal(X,X)) /\ 3223 (!Y X. equal(X,Y) ==> equal(Y,X)) /\ 3224 (!Y X Z. equal(X,Y) /\ equal(Y,Z) ==> equal(X,Z)) /\ 3225 (equal(a,b) \/ equal(c,d)) /\ 3226 (equal(a,c) \/ equal(b,d)) /\ 3227 (~equal(a,d)) /\ 3228 (~equal(b,c)) ==> F���; 3229 3230 3231val SYN349_1 = Mfail "SYN349_1" $ 3232 ���(!X Y. f(w(X),g(X,Y)) ==> f(X,g(X,Y))) /\ 3233 (!X Y:'a. f(X,g(X,Y)) ==> f(w(X),g(X,Y))) /\ 3234 (!Y X. f(X,g(X,Y)) /\ f(Y,g(X,Y)) ==> f(g(X,Y),Y) \/ f(g(X,Y),w(X))) /\ 3235 (!Y X. f(g(X,Y),Y) /\ f(Y,g(X,Y)) ==> f(X,g(X,Y)) \/ f(g(X,Y),w(X))) /\ 3236 (!Y X. f(X,g(X,Y)) \/ f(g(X,Y),Y) \/ f(Y,g(X,Y)) \/ f(g(X,Y),w(X))) /\ 3237 (!Y X. f(X,g(X,Y)) /\ f(g(X,Y),Y) ==> f(Y,g(X,Y)) \/ f(g(X,Y),w(X))) /\ 3238 (!Y X. f(X,g(X,Y)) /\ f(g(X,Y),w(X)) ==> f(g(X,Y),Y) \/ f(Y,g(X,Y))) /\ 3239 (!Y X. f(g(X,Y),Y) /\ f(g(X,Y),w(X)) ==> f(X,g(X,Y)) \/ f(Y,g(X,Y))) /\ 3240 (!Y X. f(Y,g(X,Y)) /\ f(g(X,Y),w(X)) ==> f(X,g(X,Y)) \/ f(g(X,Y),Y)) /\ 3241 (!Y X. ~(f(X,g(X,Y)) /\ f(g(X,Y),Y) /\ f(Y,g(X,Y)) /\ f(g(X,Y),w(X)))) ==> F���; 3242 3243 3244val SYN352_1 = M "SYN352_1" $ 3245 ���(f(a,b)) /\ 3246 (!X Y:'a. f(X,Y) ==> f(b,z(X,Y)) \/ f(Y,z(X,Y))) /\ 3247 (!X Y. f(X,Y) \/ f(z(X,Y),z(X,Y))) /\ 3248 (!X Y. f(b,z(X,Y)) \/ f(X,z(X,Y)) \/ f(z(X,Y),z(X,Y))) /\ 3249 (!X Y. f(b,z(X,Y)) /\ f(X,z(X,Y)) ==> f(z(X,Y),z(X,Y))) /\ 3250 (!X Y. ~(f(X,Y) /\ f(X,z(X,Y)) /\ f(Y,z(X,Y)))) /\ 3251 (!X Y. f(X,Y) ==> f(X,z(X,Y)) \/ f(Y,z(X,Y))) ==> F���; 3252 3253 3254val TOP001_2 = M "TOP001_2" $ 3255Lib.with_flag(Globals.guessing_tyvars,true) 3256 Term 3257`(!Vf U. element_of_set(U,union_of_members(Vf)) ==> element_of_set(U,f1(Vf,U))) /\ 3258 (!U Vf. element_of_set(U,union_of_members(Vf)) ==> element_of_collection(f1(Vf,U),Vf)) /\ 3259 (!U Uu1 Vf. element_of_set(U,Uu1) /\ element_of_collection(Uu1,Vf) ==> element_of_set(U,union_of_members(Vf))) /\ 3260 (!Vf X. basis(X,Vf) ==> equal_sets(union_of_members(Vf),X)) /\ 3261 (!Vf U X. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> element_of_set(X,f10(Vf,U,X))) /\ 3262 (!U X Vf. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> element_of_collection(f10(Vf,U,X),Vf)) /\ 3263 (!X. subset_sets(X,X)) /\ 3264 (!X U Y. subset_sets(X,Y) /\ element_of_set(U,X) ==> element_of_set(U,Y)) /\ 3265 (!X Y. equal_sets(X,Y) ==> subset_sets(X,Y)) /\ 3266 (!Y X. subset_sets(X,Y) \/ element_of_set(in_1st_set(X,Y),X)) /\ 3267 (!X Y. element_of_set(in_1st_set(X,Y),Y) ==> subset_sets(X,Y)) /\ 3268 (basis(cx,f)) /\ 3269 (~subset_sets(union_of_members(top_of_basis(f)),cx)) ==> F`; 3270 3271 3272val TOP002_2 = M "TOP002_2" $ 3273Lib.with_flag(Globals.guessing_tyvars,true) 3274 Term 3275`(!Vf U. element_of_collection(U,top_of_basis(Vf)) \/ element_of_set(f11(Vf,U),U)) /\ 3276 (!X. ~element_of_set(X,empty_set)) /\ 3277 (~element_of_collection(empty_set,top_of_basis(f))) ==> F`; 3278 3279 3280val TOP004_1 = M "TOP004_1" $ 3281 Term 3282`(!(Vf:'a) (U:'b). element_of_set(U,union_of_members(Vf)) ==> element_of_set(U,f1(Vf,U))) /\ 3283 (!U Vf. element_of_set(U,union_of_members(Vf)) ==> element_of_collection(f1(Vf,U),Vf)) /\ 3284 (!U (Uu1:'c) Vf. element_of_set(U,Uu1) /\ element_of_collection(Uu1,Vf) ==> element_of_set(U,union_of_members(Vf))) /\ 3285 (!Vf U Va. element_of_set(U,intersection_of_members(Vf)) /\ element_of_collection(Va,Vf) ==> element_of_set(U,Va)) /\ 3286 (!U Vf. element_of_set(U,intersection_of_members(Vf)) \/ element_of_collection(f2(Vf,U),Vf)) /\ 3287 (!Vf U. element_of_set(U,f2(Vf,U)) ==> element_of_set(U,intersection_of_members(Vf))) /\ 3288 (!Vt X. topological_space(X,Vt) ==> equal_sets(union_of_members(Vt),X)) /\ 3289 (!X Vt. topological_space(X,Vt) ==> element_of_collection(empty_set,Vt)) /\ 3290 (!X Vt. topological_space(X,Vt) ==> element_of_collection(X,Vt)) /\ 3291 (!X Y Z Vt. topological_space(X,Vt) /\ element_of_collection(Y,Vt) /\ element_of_collection(Z,Vt) ==> element_of_collection(intersection_of_sets(Y,Z),Vt)) /\ 3292 (!X Vf Vt. topological_space(X,Vt) /\ subset_collections(Vf,Vt) ==> element_of_collection(union_of_members(Vf),Vt)) /\ 3293 (!X Vt. equal_sets(union_of_members(Vt),X) /\ element_of_collection(empty_set,Vt) /\ element_of_collection(X,Vt) ==> topological_space(X,Vt) \/ element_of_collection(f3(X,Vt),Vt) \/ subset_collections(f5(X,Vt),Vt)) /\ 3294 (!X Vt. equal_sets(union_of_members(Vt),X) /\ element_of_collection(empty_set,Vt) /\ element_of_collection(X,Vt) /\ element_of_collection(union_of_members(f5(X,Vt)),Vt) ==> topological_space(X,Vt) \/ element_of_collection(f3(X,Vt),Vt)) /\ 3295 (!X Vt. equal_sets(union_of_members(Vt),X) /\ element_of_collection(empty_set,Vt) /\ element_of_collection(X,Vt) ==> topological_space(X,Vt) \/ element_of_collection(f4(X,Vt),Vt) \/ subset_collections(f5(X,Vt),Vt)) /\ 3296 (!X Vt. equal_sets(union_of_members(Vt),X) /\ element_of_collection(empty_set,Vt) /\ element_of_collection(X,Vt) /\ element_of_collection(union_of_members(f5(X,Vt)),Vt) ==> topological_space(X,Vt) \/ element_of_collection(f4(X,Vt),Vt)) /\ 3297 (!X Vt. equal_sets(union_of_members(Vt),X) /\ element_of_collection(empty_set,Vt) /\ element_of_collection(X,Vt) /\ element_of_collection(intersection_of_sets(f3(X,Vt),f4(X,Vt)),Vt) ==> topological_space(X,Vt) \/ subset_collections(f5(X,Vt),Vt)) /\ 3298 (!X Vt. equal_sets(union_of_members(Vt),X) /\ element_of_collection(empty_set,Vt) /\ element_of_collection(X,Vt) /\ element_of_collection(intersection_of_sets(f3(X,Vt),f4(X,Vt)),Vt) /\ element_of_collection(union_of_members(f5(X,Vt)),Vt) ==> topological_space(X,Vt)) /\ 3299 (!U X Vt. open(U,X,Vt) ==> topological_space(X,Vt)) /\ 3300 (!X U Vt. open(U,X,Vt) ==> element_of_collection(U,Vt)) /\ 3301 (!X U Vt. topological_space(X,Vt) /\ element_of_collection(U,Vt) ==> open(U,X,Vt)) /\ 3302 (!U X Vt. closed(U,X,Vt) ==> topological_space(X,Vt)) /\ 3303 (!U X Vt. closed(U,X,Vt) ==> open(relative_complement_sets(U,X),X,Vt)) /\ 3304 (!U X Vt. topological_space(X,Vt) /\ open(relative_complement_sets(U,X),X,Vt) ==> closed(U,X,Vt)) /\ 3305 (!Vs X Vt. finer(Vt,Vs,X) ==> topological_space(X,Vt)) /\ 3306 (!Vt X Vs. finer(Vt,Vs,X) ==> topological_space(X,Vs)) /\ 3307 (!X Vs Vt. finer(Vt,Vs,X) ==> subset_collections(Vs,Vt)) /\ 3308 (!X Vs Vt. topological_space(X,Vt) /\ topological_space(X,Vs) /\ subset_collections(Vs,Vt) ==> finer(Vt,Vs,X)) /\ 3309 (!Vf X. basis(X,Vf) ==> equal_sets(union_of_members(Vf),X)) /\ 3310 (!X Vf Y Vb1 Vb2. basis(X,Vf) /\ element_of_set(Y,X) /\ element_of_collection(Vb1,Vf) /\ element_of_collection(Vb2,Vf) /\ element_of_set(Y,intersection_of_sets(Vb1,Vb2)) ==> element_of_set(Y,f6(X,Vf,Y,Vb1,Vb2))) /\ 3311 (!X Y Vb1 Vb2 Vf. basis(X,Vf) /\ element_of_set(Y,X) /\ element_of_collection(Vb1,Vf) /\ element_of_collection(Vb2,Vf) /\ element_of_set(Y,intersection_of_sets(Vb1,Vb2)) ==> element_of_collection(f6(X,Vf,Y,Vb1,Vb2),Vf)) /\ 3312 (!X Vf Y Vb1 Vb2. basis(X,Vf) /\ element_of_set(Y,X) /\ element_of_collection(Vb1,Vf) /\ element_of_collection(Vb2,Vf) /\ element_of_set(Y,intersection_of_sets(Vb1,Vb2)) ==> subset_sets(f6(X,Vf,Y,Vb1,Vb2),intersection_of_sets(Vb1,Vb2))) /\ 3313 (!Vf X. equal_sets(union_of_members(Vf),X) ==> basis(X,Vf) \/ element_of_set(f7(X,Vf),X)) /\ 3314 (!X Vf. equal_sets(union_of_members(Vf),X) ==> basis(X,Vf) \/ element_of_collection(f8(X,Vf),Vf)) /\ 3315 (!X Vf. equal_sets(union_of_members(Vf),X) ==> basis(X,Vf) \/ element_of_collection(f9(X,Vf),Vf)) /\ 3316 (!X Vf. equal_sets(union_of_members(Vf),X) ==> basis(X,Vf) \/ element_of_set(f7(X,Vf),intersection_of_sets(f8(X,Vf),f9(X,Vf)))) /\ 3317 (!Uu9 X Vf. equal_sets(union_of_members(Vf),X) /\ element_of_set(f7(X,Vf),Uu9) /\ element_of_collection(Uu9,Vf) /\ subset_sets(Uu9,intersection_of_sets(f8(X,Vf),f9(X,Vf))) ==> basis(X,Vf)) /\ 3318 (!Vf U X. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> element_of_set(X,f10(Vf,U,X))) /\ 3319 (!U X Vf. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> element_of_collection(f10(Vf,U,X),Vf)) /\ 3320 (!Vf X U. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> subset_sets(f10(Vf,U,X),U)) /\ 3321 (!Vf U. element_of_collection(U,top_of_basis(Vf)) \/ element_of_set(f11(Vf,U),U)) /\ 3322 (!Vf Uu11 U. element_of_set(f11(Vf,U),Uu11) /\ element_of_collection(Uu11,Vf) /\ subset_sets(Uu11,U) ==> element_of_collection(U,top_of_basis(Vf))) /\ 3323 (!U Y X Vt. element_of_collection(U,subspace_topology(X,Vt,Y)) ==> topological_space(X,Vt)) /\ 3324 (!U Vt Y X. element_of_collection(U,subspace_topology(X,Vt,Y)) ==> subset_sets(Y,X)) /\ 3325 (!X Y U Vt. element_of_collection(U,subspace_topology(X,Vt,Y)) ==> element_of_collection(f12(X,Vt,Y,U),Vt)) /\ 3326 (!X Vt Y U. element_of_collection(U,subspace_topology(X,Vt,Y)) ==> equal_sets(U,intersection_of_sets(Y,f12(X,Vt,Y,U)))) /\ 3327 (!X Vt U Y Uu12. topological_space(X,Vt) /\ subset_sets(Y,X) /\ element_of_collection(Uu12,Vt) /\ equal_sets(U,intersection_of_sets(Y,Uu12)) ==> element_of_collection(U,subspace_topology(X,Vt,Y))) /\ 3328 (!U Y X Vt. element_of_set(U,interior(Y,X,Vt)) ==> topological_space(X,Vt)) /\ 3329 (!U Vt Y X. element_of_set(U,interior(Y,X,Vt)) ==> subset_sets(Y,X)) /\ 3330 (!Y X Vt U. element_of_set(U,interior(Y,X,Vt)) ==> element_of_set(U,f13(Y,X,Vt,U))) /\ 3331 (!X Vt U Y. element_of_set(U,interior(Y,X,Vt)) ==> subset_sets(f13(Y,X,Vt,U),Y)) /\ 3332 (!Y U X Vt. element_of_set(U,interior(Y,X,Vt)) ==> open(f13(Y,X,Vt,U),X,Vt)) /\ 3333 (!U Y Uu13 X Vt. topological_space(X,Vt) /\ subset_sets(Y,X) /\ element_of_set(U,Uu13) /\ subset_sets(Uu13,Y) /\ open(Uu13,X,Vt) ==> element_of_set(U,interior(Y,X,Vt))) /\ 3334 (!U Y X Vt. element_of_set(U,closure(Y,X,Vt)) ==> topological_space(X,Vt)) /\ 3335 (!U Vt Y X. element_of_set(U,closure(Y,X,Vt)) ==> subset_sets(Y,X)) /\ 3336 (!Y X Vt U V. element_of_set(U,closure(Y,X,Vt)) /\ subset_sets(Y,V) /\ closed(V,X,Vt) ==> element_of_set(U,V)) /\ 3337 (!Y X Vt U. topological_space(X,Vt) /\ subset_sets(Y,X) ==> element_of_set(U,closure(Y,X,Vt)) \/ subset_sets(Y,f14(Y,X,Vt,U))) /\ 3338 (!Y U X Vt. topological_space(X,Vt) /\ subset_sets(Y,X) ==> element_of_set(U,closure(Y,X,Vt)) \/ closed(f14(Y,X,Vt,U),X,Vt)) /\ 3339 (!Y X Vt U. topological_space(X,Vt) /\ subset_sets(Y,X) /\ element_of_set(U,f14(Y,X,Vt,U)) ==> element_of_set(U,closure(Y,X,Vt))) /\ 3340 (!U Y X Vt. neighborhood(U,Y,X,Vt) ==> topological_space(X,Vt)) /\ 3341 (!Y U X Vt. neighborhood(U,Y,X,Vt) ==> open(U,X,Vt)) /\ 3342 (!X Vt Y U. neighborhood(U,Y,X,Vt) ==> element_of_set(Y,U)) /\ 3343 (!X Vt Y U. topological_space(X,Vt) /\ open(U,X,Vt) /\ element_of_set(Y,U) ==> neighborhood(U,Y,X,Vt)) /\ 3344 (!Z Y X Vt. limit_point(Z,Y,X,Vt) ==> topological_space(X,Vt)) /\ 3345 (!Z Vt Y X. limit_point(Z,Y,X,Vt) ==> subset_sets(Y,X)) /\ 3346 (!Z X Vt U Y. limit_point(Z,Y,X,Vt) /\ neighborhood(U,Z,X,Vt) ==> element_of_set(f15(Z,Y,X,Vt,U),intersection_of_sets(U,Y))) /\ 3347 (!Y X Vt U Z. ~(limit_point(Z,Y,X,Vt) /\ neighborhood(U,Z,X,Vt) /\ eq_p(f15(Z,Y,X,Vt,U),Z))) /\ 3348 (!Y Z X Vt. topological_space(X,Vt) /\ subset_sets(Y,X) ==> limit_point(Z,Y,X,Vt) \/ neighborhood(f16(Z,Y,X,Vt),Z,X,Vt)) /\ 3349 (!X Vt Y Uu16 Z. topological_space(X,Vt) /\ subset_sets(Y,X) /\ element_of_set(Uu16,intersection_of_sets(f16(Z,Y,X,Vt),Y)) ==> limit_point(Z,Y,X,Vt) \/ eq_p(Uu16,Z)) /\ 3350 (!U Y X Vt. element_of_set(U,boundary(Y,X,Vt)) ==> topological_space(X,Vt)) /\ 3351 (!U Y X Vt. element_of_set(U,boundary(Y,X,Vt)) ==> element_of_set(U,closure(Y,X,Vt))) /\ 3352 (!U Y X Vt. element_of_set(U,boundary(Y,X,Vt)) ==> element_of_set(U,closure(relative_complement_sets(Y,X),X,Vt))) /\ 3353 (!U Y X Vt. topological_space(X,Vt) /\ element_of_set(U,closure(Y,X,Vt)) /\ element_of_set(U,closure(relative_complement_sets(Y,X),X,Vt)) ==> element_of_set(U,boundary(Y,X,Vt))) /\ 3354 (!X Vt. hausdorff(X,Vt) ==> topological_space(X,Vt)) /\ 3355 (!X_2 X_1 X Vt. hausdorff(X,Vt) /\ element_of_set(X_1,X) /\ element_of_set(X_2,X) ==> eq_p(X_1,X_2) \/ neighborhood(f17(X,Vt,X_1,X_2),X_1,X,Vt)) /\ 3356 (!X_1 X_2 X Vt. hausdorff(X,Vt) /\ element_of_set(X_1,X) /\ element_of_set(X_2,X) ==> eq_p(X_1,X_2) \/ neighborhood(f18(X,Vt,X_1,X_2),X_2,X,Vt)) /\ 3357 (!X Vt X_1 X_2. hausdorff(X,Vt) /\ element_of_set(X_1,X) /\ element_of_set(X_2,X) ==> eq_p(X_1,X_2) \/ disjoint_s(f17(X,Vt,X_1,X_2),f18(X,Vt,X_1,X_2))) /\ 3358 (!Vt X. topological_space(X,Vt) ==> hausdorff(X,Vt) \/ element_of_set(f19(X,Vt),X)) /\ 3359 (!Vt X. topological_space(X,Vt) ==> hausdorff(X,Vt) \/ element_of_set(f20(X,Vt),X)) /\ 3360 (!X Vt. topological_space(X,Vt) /\ eq_p(f19(X,Vt),f20(X,Vt)) ==> hausdorff(X,Vt)) /\ 3361 (!X Vt Uu19 Uu20. topological_space(X,Vt) /\ neighborhood(Uu19,f19(X,Vt),X,Vt) /\ neighborhood(Uu20,f20(X,Vt),X,Vt) /\ disjoint_s(Uu19,Uu20) ==> hausdorff(X,Vt)) /\ 3362 (!Va1 Va2 X Vt. separation(Va1,Va2,X,Vt) ==> topological_space(X,Vt)) /\ 3363 (!Va2 X Vt Va1. ~(separation(Va1,Va2,X,Vt) /\ equal_sets(Va1,empty_set))) /\ 3364 (!Va1 X Vt Va2. ~(separation(Va1,Va2,X,Vt) /\ equal_sets(Va2,empty_set))) /\ 3365 (!Va2 X Va1 Vt. separation(Va1,Va2,X,Vt) ==> element_of_collection(Va1,Vt)) /\ 3366 (!Va1 X Va2 Vt. separation(Va1,Va2,X,Vt) ==> element_of_collection(Va2,Vt)) /\ 3367 (!Vt Va1 Va2 X. separation(Va1,Va2,X,Vt) ==> equal_sets(union_of_sets(Va1,Va2),X)) /\ 3368 (!X Vt Va1 Va2. separation(Va1,Va2,X,Vt) ==> disjoint_s(Va1,Va2)) /\ 3369 (!Vt X Va1 Va2. topological_space(X,Vt) /\ element_of_collection(Va1,Vt) /\ element_of_collection(Va2,Vt) /\ equal_sets(union_of_sets(Va1,Va2),X) /\ disjoint_s(Va1,Va2) ==> separation(Va1,Va2,X,Vt) \/ equal_sets(Va1,empty_set) \/ equal_sets(Va2,empty_set)) /\ 3370 (!X Vt. connected_space(X,Vt) ==> topological_space(X,Vt)) /\ 3371 (!Va1 Va2 X Vt. ~(connected_space(X,Vt) /\ separation(Va1,Va2,X,Vt))) /\ 3372 (!X Vt. topological_space(X,Vt) ==> connected_space(X,Vt) \/ separation(f21(X,Vt),f22(X,Vt),X,Vt)) /\ 3373 (!Va X Vt. connected_set(Va,X,Vt) ==> topological_space(X,Vt)) /\ 3374 (!Vt Va X. connected_set(Va,X,Vt) ==> subset_sets(Va,X)) /\ 3375 (!X Vt Va. connected_set(Va,X,Vt) ==> connected_space(Va,subspace_topology(X,Vt,Va))) /\ 3376 (!X Vt Va. topological_space(X,Vt) /\ subset_sets(Va,X) /\ connected_space(Va,subspace_topology(X,Vt,Va)) ==> connected_set(Va,X,Vt)) /\ 3377 (!Vf X Vt. open_covering(Vf,X,Vt) ==> topological_space(X,Vt)) /\ 3378 (!X Vf Vt. open_covering(Vf,X,Vt) ==> subset_collections(Vf,Vt)) /\ 3379 (!Vt Vf X. open_covering(Vf,X,Vt) ==> equal_sets(union_of_members(Vf),X)) /\ 3380 (!Vt Vf X. topological_space(X,Vt) /\ subset_collections(Vf,Vt) /\ equal_sets(union_of_members(Vf),X) ==> open_covering(Vf,X,Vt)) /\ 3381 (!X Vt. compact_space(X,Vt) ==> topological_space(X,Vt)) /\ 3382 (!X Vt Vf1. compact_space(X,Vt) /\ open_covering(Vf1,X,Vt) ==> finite(f23(X,Vt,Vf1))) /\ 3383 (!X Vt Vf1. compact_space(X,Vt) /\ open_covering(Vf1,X,Vt) ==> subset_collections(f23(X,Vt,Vf1),Vf1)) /\ 3384 (!Vf1 X Vt. compact_space(X,Vt) /\ open_covering(Vf1,X,Vt) ==> open_covering(f23(X,Vt,Vf1),X,Vt)) /\ 3385 (!X Vt. topological_space(X,Vt) ==> compact_space(X,Vt) \/ open_covering(f24(X,Vt),X,Vt)) /\ 3386 (!Uu24 X Vt. topological_space(X,Vt) /\ finite(Uu24) /\ subset_collections(Uu24,f24(X,Vt)) /\ open_covering(Uu24,X,Vt) ==> compact_space(X,Vt)) /\ 3387 (!Va X Vt. compact_set(Va,X,Vt) ==> topological_space(X,Vt)) /\ 3388 (!Vt Va X. compact_set(Va,X,Vt) ==> subset_sets(Va,X)) /\ 3389 (!X Vt Va. compact_set(Va,X,Vt) ==> compact_space(Va,subspace_topology(X,Vt,Va))) /\ 3390 (!X Vt Va. topological_space(X,Vt) /\ subset_sets(Va,X) /\ compact_space(Va,subspace_topology(X,Vt,Va)) ==> compact_set(Va,X,Vt)) /\ 3391 (basis(cx,f)) /\ 3392 (!U. element_of_collection(U,top_of_basis(f))) /\ 3393 (!V. element_of_collection(V,top_of_basis(f))) /\ 3394 (!U V. ~element_of_collection(intersection_of_sets(U,V),top_of_basis(f))) 3395 ==> F`; 3396 3397 3398val TOP004_2 = M "TOP004_2" $ 3399Lib.with_flag(Globals.guessing_tyvars,true) 3400 Term 3401`(!U Uu1 Vf. element_of_set(U,Uu1) /\ element_of_collection(Uu1,Vf) ==> element_of_set(U,union_of_members(Vf))) /\ 3402 (!Vf X. basis(X,Vf) ==> equal_sets(union_of_members(Vf),X)) /\ 3403 (!X Vf Y Vb1 Vb2. basis(X,Vf) /\ element_of_set(Y,X) /\ element_of_collection(Vb1,Vf) /\ element_of_collection(Vb2,Vf) /\ element_of_set(Y,intersection_of_sets(Vb1,Vb2)) ==> element_of_set(Y,f6(X,Vf,Y,Vb1,Vb2))) /\ 3404 (!X Y Vb1 Vb2 Vf. basis(X,Vf) /\ element_of_set(Y,X) /\ element_of_collection(Vb1,Vf) /\ element_of_collection(Vb2,Vf) /\ element_of_set(Y,intersection_of_sets(Vb1,Vb2)) ==> element_of_collection(f6(X,Vf,Y,Vb1,Vb2),Vf)) /\ 3405 (!X Vf Y Vb1 Vb2. basis(X,Vf) /\ element_of_set(Y,X) /\ element_of_collection(Vb1,Vf) /\ element_of_collection(Vb2,Vf) /\ element_of_set(Y,intersection_of_sets(Vb1,Vb2)) ==> subset_sets(f6(X,Vf,Y,Vb1,Vb2),intersection_of_sets(Vb1,Vb2))) /\ 3406 (!Vf U X. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> element_of_set(X,f10(Vf,U,X))) /\ 3407 (!U X Vf. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> element_of_collection(f10(Vf,U,X),Vf)) /\ 3408 (!Vf X U. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> subset_sets(f10(Vf,U,X),U)) /\ 3409 (!Vf U. element_of_collection(U,top_of_basis(Vf)) \/ element_of_set(f11(Vf,U),U)) /\ 3410 (!Vf Uu11 U. element_of_set(f11(Vf,U),Uu11) /\ element_of_collection(Uu11,Vf) /\ subset_sets(Uu11,U) ==> element_of_collection(U,top_of_basis(Vf))) /\ 3411 (!Y X Z. subset_sets(X,Y) /\ subset_sets(Y,Z) ==> subset_sets(X,Z)) /\ 3412 (!Y Z X. element_of_set(Z,intersection_of_sets(X,Y)) ==> element_of_set(Z,X)) /\ 3413 (!X Z Y. element_of_set(Z,intersection_of_sets(X,Y)) ==> element_of_set(Z,Y)) /\ 3414 (!X Z Y. element_of_set(Z,X) /\ element_of_set(Z,Y) ==> element_of_set(Z,intersection_of_sets(X,Y))) /\ 3415 (!X U Y V. subset_sets(X,Y) /\ subset_sets(U,V) ==> subset_sets(intersection_of_sets(X,U),intersection_of_sets(Y,V))) /\ 3416 (!X Z Y. equal_sets(X,Y) /\ element_of_set(Z,X) ==> element_of_set(Z,Y)) /\ 3417 (!Y X. equal_sets(intersection_of_sets(X,Y),intersection_of_sets(Y,X))) /\ 3418 (basis(cx,f)) /\ 3419 (!U. element_of_collection(U,top_of_basis(f))) /\ 3420 (!V. element_of_collection(V,top_of_basis(f))) /\ 3421 (!U V. ~element_of_collection(intersection_of_sets(U,V),top_of_basis(f))) 3422 ==> F`; 3423 3424 3425val TOP005_2 = Mfail "TOP005_2" $ 3426Lib.with_flag(Globals.guessing_tyvars,true) 3427 Term 3428`(!Vf U. element_of_set(U,union_of_members(Vf)) ==> element_of_set(U,f1(Vf,U))) /\ 3429 (!U Vf. element_of_set(U,union_of_members(Vf)) ==> element_of_collection(f1(Vf,U),Vf)) /\ 3430 (!Vf U X. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> element_of_set(X,f10(Vf,U,X))) /\ 3431 (!U X Vf. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> element_of_collection(f10(Vf,U,X),Vf)) /\ 3432 (!Vf X U. element_of_collection(U,top_of_basis(Vf)) /\ element_of_set(X,U) ==> subset_sets(f10(Vf,U,X),U)) /\ 3433 (!Vf U. element_of_collection(U,top_of_basis(Vf)) \/ element_of_set(f11(Vf,U),U)) /\ 3434 (!Vf Uu11 U. element_of_set(f11(Vf,U),Uu11) /\ element_of_collection(Uu11,Vf) /\ subset_sets(Uu11,U) ==> element_of_collection(U,top_of_basis(Vf))) /\ 3435 (!X U Y. element_of_set(U,X) ==> subset_sets(X,Y) \/ element_of_set(U,Y)) /\ 3436 (!Y X Z. subset_sets(X,Y) /\ element_of_collection(Y,Z) ==> subset_sets(X,union_of_members(Z))) /\ 3437 (!X U Y. subset_collections(X,Y) /\ element_of_collection(U,X) ==> element_of_collection(U,Y)) /\ 3438 (subset_collections(g,top_of_basis(f))) /\ 3439 (~element_of_collection(union_of_members(g),top_of_basis(f))) ==> F`; 3440