%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SET621+3 : TPTP v8.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 14:22:01 EDT 2024 % Result : Theorem 0.73s 0.81s % Output : CNFRefutation 0.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET621+3 : TPTP v8.2.0. Released v2.2.0. % 0.08/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n027.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Sun Jun 23 11:38:54 EDT 2024 % 0.12/0.34 % CPUTime : % 0.19/0.57 start to proof:theBenchmark % 0.73/0.80 %------------------------------------------- % 0.73/0.80 % File :CSE---1.7 % 0.73/0.80 % Problem :theBenchmark % 0.73/0.80 % Transform :cnf % 0.73/0.80 % Format :tptp:raw % 0.73/0.80 % Command :java -jar mcs_scs.jar %d %s % 0.73/0.80 % 0.73/0.80 % Result :Theorem 0.200000s % 0.73/0.80 % Output :CNFRefutation 0.200000s % 0.73/0.80 %------------------------------------------- % 0.73/0.80 %-------------------------------------------------------------------------- % 0.73/0.80 % File : SET621+3 : TPTP v8.2.0. Released v2.2.0. % 0.73/0.80 % Domain : Set Theory % 0.73/0.80 % Problem : (X sym\ Y) \ Z = (X \ (Y U Z)) U (Y \ (X U Z)) % 0.73/0.80 % Version : [Try90] axioms : Reduced > Incomplete. % 0.73/0.80 % English : The difference of (the symmetric difference of X and Y) and Z % 0.73/0.80 % is the union of (the difference of X and (the union of Y and Z)) % 0.73/0.80 % and (the difference of Y and (the union of X and Z)). % 0.73/0.80 % 0.73/0.80 % Refs : [ILF] The ILF Group (1998), The ILF System: A Tool for the Int % 0.73/0.80 % : [Try90] Trybulec (1990), Tarski Grothendieck Set Theory % 0.73/0.80 % : [TS89] Trybulec & Swieczkowska (1989), Boolean Properties of % 0.73/0.80 % Source : [ILF] % 0.73/0.80 % Names : BOOLE (97) [TS89] % 0.73/0.80 % 0.73/0.80 % Status : Theorem % 0.73/0.80 % Rating : 0.17 v7.5.0, 0.19 v7.4.0, 0.17 v7.3.0, 0.10 v7.1.0, 0.09 v7.0.0, 0.17 v6.4.0, 0.15 v6.3.0, 0.12 v6.2.0, 0.28 v6.1.0, 0.33 v6.0.0, 0.26 v5.5.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.37 v5.2.0, 0.20 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.30 v4.0.0, 0.33 v3.7.0, 0.30 v3.5.0, 0.32 v3.4.0, 0.26 v3.3.0, 0.21 v3.2.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.00 v2.2.1 % 0.73/0.80 % Syntax : Number of formulae : 12 ( 7 unt; 0 def) % 0.73/0.80 % Number of atoms : 22 ( 8 equ) % 0.73/0.80 % Maximal formula atoms : 3 ( 1 avg) % 0.73/0.80 % Number of connectives : 11 ( 1 ~; 1 |; 2 &) % 0.73/0.80 % ( 6 <=>; 1 =>; 0 <=; 0 <~>) % 0.73/0.80 % Maximal formula depth : 7 ( 4 avg) % 0.73/0.80 % Maximal term depth : 4 ( 1 avg) % 0.73/0.80 % Number of predicates : 3 ( 2 usr; 0 prp; 2-2 aty) % 0.73/0.80 % Number of functors : 3 ( 3 usr; 0 con; 2-2 aty) % 0.73/0.80 % Number of variables : 30 ( 30 !; 0 ?) % 0.73/0.80 % SPC : FOF_THM_RFO_SEQ % 0.73/0.80 % 0.73/0.80 % Comments : % 0.73/0.80 %-------------------------------------------------------------------------- % 0.73/0.80 %---- line(boole - df(7),1833089) % 0.73/0.80 fof(symmetric_difference_defn,axiom, % 0.73/0.80 ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ). % 0.73/0.80 % 0.73/0.80 %---- line(boole - th(88),1834157) % 0.73/0.80 fof(difference_difference_union,axiom, % 0.73/0.80 ! [B,C,D] : difference(difference(B,C),D) = difference(B,union(C,D)) ). % 0.73/0.80 % 0.73/0.80 %---- line(boole - th(89),1834187) % 0.73/0.81 fof(difference_distributes_over_union,axiom, % 0.73/0.81 ! [B,C,D] : difference(union(B,C),D) = union(difference(B,D),difference(C,D)) ). % 0.73/0.81 % 0.73/0.81 %---- line(boole - df(2),1833042) % 0.73/0.81 fof(union_defn,axiom, % 0.73/0.81 ! [B,C,D] : % 0.73/0.81 ( member(D,union(B,C)) % 0.73/0.81 <=> ( member(D,B) % 0.73/0.81 | member(D,C) ) ) ). % 0.73/0.81 % 0.73/0.81 %---- line(boole - df(4),1833078) % 0.73/0.81 fof(difference_defn,axiom, % 0.73/0.81 ! [B,C,D] : % 0.73/0.81 ( member(D,difference(B,C)) % 0.73/0.81 <=> ( member(D,B) % 0.73/0.81 & ~ member(D,C) ) ) ). % 0.73/0.81 % 0.73/0.81 %---- line(boole - df(8),1833103) % 0.73/0.81 fof(equal_defn,axiom, % 0.73/0.81 ! [B,C] : % 0.73/0.81 ( B = C % 0.73/0.81 <=> ( subset(B,C) % 0.73/0.81 & subset(C,B) ) ) ). % 0.73/0.81 % 0.73/0.81 %---- property(commutativity,op(union,2,function)) % 0.73/0.81 fof(commutativity_of_union,axiom, % 0.73/0.81 ! [B,C] : union(B,C) = union(C,B) ). % 0.73/0.81 % 0.73/0.81 %---- property(commutativity,op(symmetric_difference,2,function)) % 0.73/0.81 fof(commutativity_of_symmetric_difference,axiom, % 0.73/0.81 ! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B) ). % 0.73/0.81 % 0.73/0.81 %---- line(hidden - axiom179,1832615) % 0.73/0.81 fof(equal_member_defn,axiom, % 0.73/0.81 ! [B,C] : % 0.73/0.81 ( B = C % 0.73/0.81 <=> ! [D] : % 0.73/0.81 ( member(D,B) % 0.73/0.81 <=> member(D,C) ) ) ). % 0.73/0.81 % 0.73/0.81 %---- line(tarski - df(3),1832749) % 0.73/0.81 fof(subset_defn,axiom, % 0.73/0.81 ! [B,C] : % 0.73/0.81 ( subset(B,C) % 0.73/0.81 <=> ! [D] : % 0.73/0.81 ( member(D,B) % 0.73/0.81 => member(D,C) ) ) ). % 0.73/0.81 % 0.73/0.81 %---- property(reflexivity,op(subset,2,predicate)) % 0.73/0.81 fof(reflexivity_of_subset,axiom, % 0.73/0.81 ! [B] : subset(B,B) ). % 0.73/0.81 % 0.73/0.81 %---- line(boole - th(97),1834236) % 0.73/0.81 fof(prove_th97,conjecture, % 0.73/0.81 ! [B,C,D] : difference(symmetric_difference(B,C),D) = union(difference(B,union(C,D)),difference(C,union(B,D))) ). % 0.73/0.81 % 0.73/0.81 %-------------------------------------------------------------------------- % 0.73/0.81 %------------------------------------------- % 0.73/0.81 % Proof found % 0.73/0.81 % SZS status Theorem for theBenchmark % 0.73/0.81 % SZS output start Proof % 0.73/0.81 %ClaNum:35(EqnAxiom:15) % 0.73/0.81 %VarNum:95(SingletonVarNum:42) % 0.73/0.81 %MaxLitNum:3 % 0.73/0.81 %MaxfuncDepth:3 % 0.73/0.81 %SharedTerms:12 % 0.73/0.81 %goalClause: 21 % 0.73/0.81 %singleGoalClaCount:1 % 0.73/0.81 [21]~E(f1(f2(a3,f1(a6,a7)),f2(a6,f1(a3,a7))),f2(f1(f2(a3,a6),f2(a6,a3)),a7)) % 0.73/0.81 [16]P1(x161,x161) % 0.73/0.81 [17]E(f1(x171,x172),f1(x172,x171)) % 0.73/0.81 [18]E(f2(f2(x181,x182),x183),f2(x181,f1(x182,x183))) % 0.73/0.81 [19]E(f1(f2(x191,x192),f2(x193,x192)),f2(f1(x191,x193),x192)) % 0.73/0.81 [23]~E(x231,x232)+P1(x231,x232) % 0.73/0.81 [25]P1(x251,x252)+P2(f4(x251,x252),x251) % 0.73/0.81 [31]P1(x311,x312)+~P2(f4(x311,x312),x312) % 0.73/0.81 [27]~P2(x271,x273)+P2(x271,f1(x272,x273)) % 0.73/0.81 [28]~P2(x281,x282)+P2(x281,f1(x282,x283)) % 0.73/0.81 [30]P2(x301,x302)+~P2(x301,f2(x302,x303)) % 0.73/0.81 [33]~P2(x331,x332)+~P2(x331,f2(x333,x332)) % 0.73/0.81 [24]~P1(x242,x241)+~P1(x241,x242)+E(x241,x242) % 0.73/0.81 [32]E(x321,x322)+P2(f5(x321,x322),x322)+P2(f5(x321,x322),x321) % 0.73/0.81 [35]E(x351,x352)+~P2(f5(x351,x352),x352)+~P2(f5(x351,x352),x351) % 0.73/0.81 [26]~P1(x263,x262)+P2(x261,x262)+~P2(x261,x263) % 0.73/0.81 [29]~P2(x291,x293)+P2(x291,x292)+P2(x291,f2(x293,x292)) % 0.73/0.81 [34]P2(x341,x342)+P2(x341,x343)+~P2(x341,f1(x343,x342)) % 0.73/0.81 %EqnAxiom % 0.73/0.81 [1]E(x11,x11) % 0.73/0.81 [2]E(x22,x21)+~E(x21,x22) % 0.73/0.81 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.73/0.81 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.73/0.81 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.73/0.81 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 0.73/0.81 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 0.73/0.81 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.73/0.81 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.73/0.81 [10]~E(x101,x102)+E(f4(x101,x103),f4(x102,x103)) % 0.73/0.81 [11]~E(x111,x112)+E(f4(x113,x111),f4(x113,x112)) % 0.73/0.81 [12]P1(x122,x123)+~E(x121,x122)+~P1(x121,x123) % 0.73/0.81 [13]P1(x133,x132)+~E(x131,x132)+~P1(x133,x131) % 0.73/0.81 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143) % 0.73/0.81 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151) % 0.73/0.81 % 0.73/0.81 %------------------------------------------- % 0.73/0.81 cnf(37,plain, % 0.73/0.81 (E(f2(f1(x371,x372),x373),f1(f2(x371,x373),f2(x372,x373)))), % 0.73/0.81 inference(scs_inference,[],[19,2])). % 0.73/0.81 cnf(38,plain, % 0.73/0.81 (~E(f1(f2(a3,f1(a6,a7)),f2(a6,f1(a3,a7))),f1(f2(f2(a3,a6),a7),f2(f2(a6,a3),a7)))), % 0.73/0.81 inference(scs_inference,[],[21,19,2,3])). % 0.73/0.81 cnf(40,plain, % 0.73/0.81 (P1(f1(x401,x402),f1(x402,x401))), % 0.73/0.81 inference(scs_inference,[],[21,16,17,19,2,3,12])). % 0.73/0.81 cnf(42,plain, % 0.73/0.81 (E(f2(x421,f1(x422,x423)),f2(f2(x421,x422),x423))), % 0.73/0.81 inference(scs_inference,[],[18,2])). % 0.73/0.81 cnf(43,plain, % 0.73/0.81 (P1(f2(f1(x431,x432),x433),f1(f2(x431,x433),f2(x432,x433)))), % 0.73/0.81 inference(scs_inference,[],[37,18,16,2,13])). % 0.73/0.81 cnf(44,plain, % 0.73/0.81 (P1(x441,x441)), % 0.73/0.81 inference(rename_variables,[],[16])). % 0.73/0.81 cnf(45,plain, % 0.73/0.81 (P1(f1(f2(x451,x452),f2(x453,x452)),f2(f1(x451,x453),x452))), % 0.73/0.81 inference(scs_inference,[],[37,18,16,44,2,13,12])). % 0.73/0.81 cnf(47,plain, % 0.73/0.81 (~E(f1(f2(a3,f1(a6,a7)),f2(a6,f1(a3,a7))),f1(f2(f2(a6,a3),a7),f2(f2(a3,a6),a7)))), % 0.73/0.81 inference(scs_inference,[],[37,38,18,16,44,17,2,13,12,3])). % 0.73/0.81 cnf(49,plain, % 0.73/0.81 (P1(f2(f1(x491,x492),x493),f1(f2(x492,x493),f2(x491,x493)))), % 0.73/0.81 inference(scs_inference,[],[43,17,13])). % 0.73/0.81 cnf(51,plain, % 0.73/0.81 (P1(f2(f2(f1(x511,x512),x513),x514),f1(f2(x511,f1(x513,x514)),f2(x512,f1(x513,x514))))), % 0.73/0.81 inference(scs_inference,[],[42,43,17,13,12])). % 0.73/0.81 cnf(63,plain, % 0.73/0.81 (P1(f2(f1(x631,x632),x633),f1(f2(x632,x633),f2(x631,x633)))), % 0.73/0.81 inference(rename_variables,[],[49])). % 0.73/0.81 cnf(65,plain, % 0.73/0.81 (E(f1(f2(x651,x652),f2(x653,x652)),f2(f1(x653,x651),x652))), % 0.73/0.81 inference(scs_inference,[],[42,19,40,49,63,13,12,24])). % 0.73/0.81 cnf(68,plain, % 0.73/0.81 (P1(f2(f2(f1(x681,x682),x683),x684),f2(f1(x682,x681),f1(x683,x684)))), % 0.73/0.81 inference(scs_inference,[],[65,51,13])). % 0.73/0.81 cnf(70,plain, % 0.73/0.81 (E(f1(f2(x701,x702),f2(x703,x702)),f2(f1(x703,x701),x702))), % 0.73/0.81 inference(rename_variables,[],[65])). % 0.73/0.81 cnf(71,plain, % 0.73/0.81 (E(f1(f2(x711,f1(x712,x713)),f2(x714,f1(x712,x713))),f2(f2(f1(x714,x711),x712),x713))), % 0.73/0.81 inference(scs_inference,[],[65,70,42,51,13,3])). % 0.73/0.81 cnf(73,plain, % 0.73/0.81 (E(f1(f2(x731,x732),f2(x733,x732)),f2(f1(x733,x731),x732))), % 0.73/0.81 inference(rename_variables,[],[65])). % 0.73/0.81 cnf(76,plain, % 0.73/0.81 (E(f2(f2(f1(x761,x762),x763),x764),f1(f2(x762,f1(x763,x764)),f2(x761,f1(x763,x764))))), % 0.73/0.81 inference(scs_inference,[],[65,70,73,42,51,45,13,3,12,2])). % 0.73/0.81 cnf(79,plain, % 0.73/0.81 (P1(f2(f2(f1(x791,x792),x793),x794),f2(f2(f1(x792,x791),x793),x794))), % 0.73/0.81 inference(scs_inference,[],[71,51,13])). % 0.73/0.81 cnf(88,plain, % 0.73/0.81 (E(f1(f2(x881,f1(x882,x883)),f2(x884,f1(x882,x883))),f2(f2(f1(x881,x884),x882),x883))), % 0.73/0.81 inference(scs_inference,[],[76,51,79,12,24,2])). % 0.73/0.81 cnf(98,plain, % 0.73/0.81 (P1(f2(f1(x981,x982),f1(x983,x984)),f2(f2(f1(x982,x981),x983),x984))), % 0.73/0.81 inference(scs_inference,[],[88,49,13])). % 0.73/0.81 cnf(103,plain, % 0.73/0.81 (P1(f2(f2(x1031,x1032),x1033),f2(x1031,f1(x1032,x1033)))), % 0.73/0.81 inference(scs_inference,[],[18,16,13])). % 0.73/0.81 cnf(104,plain, % 0.73/0.81 (P1(x1041,x1041)), % 0.73/0.81 inference(rename_variables,[],[16])). % 0.73/0.81 cnf(105,plain, % 0.73/0.81 (P1(f2(x1051,f1(x1052,x1053)),f2(f2(x1051,x1052),x1053))), % 0.73/0.81 inference(scs_inference,[],[18,16,104,13,12])). % 0.73/0.81 cnf(110,plain, % 0.73/0.81 (E(f2(f2(x1101,x1102),x1103),f2(x1101,f1(x1102,x1103)))), % 0.73/0.81 inference(rename_variables,[],[18])). % 0.73/0.81 cnf(116,plain, % 0.73/0.81 (E(f2(x1161,f1(x1162,f1(x1163,x1164))),f2(f2(f2(x1161,x1162),x1163),x1164))), % 0.73/0.81 inference(scs_inference,[],[18,110,103,105,13,12,24,2])). % 0.73/0.81 cnf(117,plain, % 0.73/0.81 (E(f1(f2(x1171,f1(x1172,x1173)),x1174),f1(f2(f2(x1171,x1172),x1173),x1174))), % 0.73/0.81 inference(scs_inference,[],[18,4,2])). % 0.73/0.81 cnf(118,plain, % 0.73/0.81 (E(f1(f2(f2(x1181,x1182),x1183),x1184),f1(f2(x1181,f1(x1182,x1183)),x1184))), % 0.73/0.81 inference(scs_inference,[],[117,2])). % 0.73/0.81 cnf(121,plain, % 0.73/0.81 (P1(f2(f2(f1(x1211,x1212),x1213),f1(x1214,x1215)),f2(f2(f2(f1(x1212,x1211),x1213),x1214),x1215))), % 0.73/0.81 inference(scs_inference,[],[116,68,117,47,2,3,13])). % 0.73/0.81 cnf(123,plain, % 0.73/0.81 (E(f2(x1231,f1(x1232,f1(x1233,x1234))),f2(f2(f2(x1231,x1232),x1233),x1234))), % 0.73/0.81 inference(rename_variables,[],[116])). % 0.73/0.81 cnf(124,plain, % 0.73/0.81 (P1(f2(f2(f2(f1(x1241,x1242),x1243),x1244),x1245),f2(f2(f1(x1242,x1241),x1243),f1(x1244,x1245)))), % 0.73/0.81 inference(scs_inference,[],[116,123,68,98,117,47,2,3,13,12])). % 0.73/0.81 cnf(131,plain, % 0.73/0.81 (E(f1(f2(f2(x1311,x1312),x1313),f2(x1314,f1(x1312,x1313))),f2(f2(f1(x1311,x1314),x1312),x1313))), % 0.73/0.81 inference(scs_inference,[],[118,88,124,121,24,3])). % 0.73/0.81 cnf(133,plain, % 0.73/0.81 (E(f1(f2(f2(x1331,x1332),x1333),x1334),f1(f2(x1331,f1(x1332,x1333)),x1334))), % 0.73/0.81 inference(rename_variables,[],[118])). % 0.73/0.81 cnf(134,plain, % 0.73/0.81 (P1(f1(x1341,f2(f2(x1342,x1343),x1344)),f1(f2(x1342,f1(x1343,x1344)),x1341))), % 0.73/0.81 inference(scs_inference,[],[118,133,88,124,121,40,24,3,13])). % 0.73/0.81 cnf(135,plain, % 0.73/0.81 (P1(f1(x1351,x1352),f1(x1352,x1351))), % 0.73/0.81 inference(rename_variables,[],[40])). % 0.73/0.81 cnf(136,plain, % 0.73/0.81 (P1(f1(f2(x1361,f1(x1362,x1363)),x1364),f1(x1364,f2(f2(x1361,x1362),x1363)))), % 0.73/0.81 inference(scs_inference,[],[118,133,88,124,121,40,135,24,3,13,12])). % 0.73/0.81 cnf(147,plain, % 0.73/0.81 (P1(f1(x1471,x1472),f1(x1472,x1471))), % 0.73/0.81 inference(rename_variables,[],[40])). % 0.73/0.81 cnf(150,plain, % 0.73/0.81 ($false), % 0.73/0.81 inference(scs_inference,[],[131,42,134,136,38,40,147,117,2,24,3,13,12,5]), % 0.73/0.81 ['proof']). % 0.73/0.81 % SZS output end Proof % 0.73/0.81 % Total time :0.200000s %------------------------------------------------------------------------------