%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET064-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 14:20:26 EDT 2024
% Result : Unsatisfiable 0.57s 0.65s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET064-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n023.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 12:59:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.57/0.64 %-------------------------------------------
% 0.57/0.64 % File :CSE---1.7
% 0.57/0.64 % Problem :theBenchmark
% 0.57/0.64 % Transform :cnf
% 0.57/0.64 % Format :tptp:raw
% 0.57/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.57/0.64
% 0.57/0.64 % Result :Theorem 0.010000s
% 0.57/0.64 % Output :CNFRefutation 0.010000s
% 0.57/0.64 %-------------------------------------------
% 0.57/0.65 %--------------------------------------------------------------------------
% 0.57/0.65 % File : SET064-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.57/0.65 % Domain : Set Theory
% 0.57/0.65 % Problem : The null class is unique
% 0.57/0.65 % Version : [Qua92] axioms : Augmented.
% 0.57/0.65 % English :
% 0.57/0.65
% 0.57/0.65 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.57/0.65 % Source : [Quaife]
% 0.57/0.65 % Names : SP4 [Qua92]
% 0.57/0.65
% 0.57/0.65 % Status : Unsatisfiable
% 0.57/0.65 % Rating : 0.10 v8.2.0, 0.14 v8.1.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v5.5.0, 0.10 v5.4.0, 0.15 v5.3.0, 0.06 v5.0.0, 0.07 v4.1.0, 0.08 v4.0.1, 0.09 v4.0.0, 0.18 v3.7.0, 0.20 v3.5.0, 0.18 v3.4.0, 0.08 v3.3.0, 0.07 v3.2.0, 0.08 v3.1.0, 0.09 v2.7.0, 0.17 v2.6.0, 0.11 v2.5.0, 0.09 v2.4.0, 0.00 v2.1.0
% 0.57/0.65 % Syntax : Number of clauses : 107 ( 35 unt; 11 nHn; 75 RR)
% 0.57/0.65 % Number of literals : 212 ( 45 equ; 99 neg)
% 0.57/0.65 % Maximal clause size : 5 ( 1 avg)
% 0.57/0.65 % Maximal term depth : 6 ( 1 avg)
% 0.57/0.65 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.57/0.65 % Number of functors : 39 ( 39 usr; 9 con; 0-3 aty)
% 0.57/0.65 % Number of variables : 209 ( 38 sgn)
% 0.57/0.65 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.57/0.65
% 0.57/0.65 % Comments : Preceding lemmas are added.
% 0.57/0.65 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.57/0.65 %--------------------------------------------------------------------------
% 0.57/0.65 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.57/0.65 include('Axioms/SET004-0.ax').
% 0.57/0.65 %--------------------------------------------------------------------------
% 0.57/0.65 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.57/0.65 cnf(corollary_1_to_unordered_pair,axiom,
% 0.57/0.65 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.57/0.65 | member(X,unordered_pair(X,Y)) ) ).
% 0.57/0.65
% 0.57/0.65 cnf(corollary_2_to_unordered_pair,axiom,
% 0.57/0.65 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.57/0.65 | member(Y,unordered_pair(X,Y)) ) ).
% 0.57/0.65
% 0.57/0.65 %----Corollaries to Cartesian product axiom.
% 0.57/0.65 cnf(corollary_1_to_cartesian_product,axiom,
% 0.57/0.65 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.57/0.65 | member(U,universal_class) ) ).
% 0.57/0.65
% 0.57/0.65 cnf(corollary_2_to_cartesian_product,axiom,
% 0.57/0.65 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.57/0.65 | member(V,universal_class) ) ).
% 0.57/0.65
% 0.57/0.65 %---- PARTIAL ORDER.
% 0.57/0.65 %----(PO1): reflexive.
% 0.57/0.65 cnf(subclass_is_reflexive,axiom,
% 0.57/0.65 subclass(X,X) ).
% 0.57/0.65
% 0.57/0.65 %----(PO2): antisymmetry is part of A-3.
% 0.57/0.65 %----(x < y), (y < x) --> (x = y).
% 0.57/0.65
% 0.57/0.65 %----(PO3): transitivity.
% 0.57/0.65 cnf(transitivity_of_subclass,axiom,
% 0.57/0.65 ( ~ subclass(X,Y)
% 0.57/0.65 | ~ subclass(Y,Z)
% 0.57/0.65 | subclass(X,Z) ) ).
% 0.57/0.65
% 0.57/0.65 %---- EQUALITY.
% 0.57/0.65 %----(EQ1): equality axiom.
% 0.57/0.65 %----a:x:(x = x).
% 0.57/0.65 %----This is always an axiom in the TPTP presentation
% 0.57/0.65
% 0.57/0.65 %----(EQ2): expanded equality definition.
% 0.57/0.65 cnf(equality1,axiom,
% 0.57/0.65 ( X = Y
% 0.57/0.65 | member(not_subclass_element(X,Y),X)
% 0.57/0.65 | member(not_subclass_element(Y,X),Y) ) ).
% 0.57/0.65
% 0.57/0.65 cnf(equality2,axiom,
% 0.57/0.65 ( ~ member(not_subclass_element(X,Y),Y)
% 0.57/0.65 | X = Y
% 0.57/0.65 | member(not_subclass_element(Y,X),Y) ) ).
% 0.57/0.65
% 0.57/0.65 cnf(equality3,axiom,
% 0.57/0.65 ( ~ member(not_subclass_element(Y,X),X)
% 0.57/0.65 | X = Y
% 0.57/0.65 | member(not_subclass_element(X,Y),X) ) ).
% 0.57/0.65
% 0.57/0.65 cnf(equality4,axiom,
% 0.57/0.65 ( ~ member(not_subclass_element(X,Y),Y)
% 0.57/0.65 | ~ member(not_subclass_element(Y,X),X)
% 0.57/0.65 | X = Y ) ).
% 0.57/0.65
% 0.57/0.65 %---- SPECIAL CLASSES.
% 0.57/0.65 %----(SP1): lemma.
% 0.57/0.65 cnf(special_classes_lemma,axiom,
% 0.57/0.65 ~ member(Y,intersection(complement(X),X)) ).
% 0.57/0.65
% 0.57/0.65 %----(SP2): Existence of O (null class).
% 0.57/0.65 %----e:x:a:z:(-(z e x)).
% 0.57/0.65 cnf(existence_of_null_class,axiom,
% 0.57/0.65 ~ member(Z,null_class) ).
% 0.57/0.65
% 0.57/0.65 %----(SP3): O is a subclass of every class.
% 0.57/0.65 cnf(null_class_is_subclass,axiom,
% 0.57/0.65 subclass(null_class,X) ).
% 0.57/0.65
% 0.57/0.65 %----corollary.
% 0.57/0.65 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.57/0.65 ( ~ subclass(X,null_class)
% 0.57/0.65 | X = null_class ) ).
% 0.57/0.65
% 0.57/0.65 cnf(prove_null_class_is_unique_1,negated_conjecture,
% 0.57/0.65 z != null_class ).
% 0.57/0.65
% 0.57/0.65 cnf(prove_null_class_is_unique_2,negated_conjecture,
% 0.57/0.65 ~ member(not_subclass_element(z,null_class),z) ).
% 0.57/0.65
% 0.57/0.65 %--------------------------------------------------------------------------
% 0.57/0.65 %-------------------------------------------
% 0.57/0.65 % Proof found
% 0.57/0.65 % SZS status Theorem for theBenchmark
% 0.57/0.65 % SZS output start Proof
% 0.57/0.65 %ClaNum:134(EqnAxiom:42)
% 0.57/0.65 %VarNum:793(SingletonVarNum:181)
% 0.57/0.65 %MaxLitNum:5
% 0.57/0.65 %MaxfuncDepth:24
% 0.57/0.65 %SharedTerms:33
% 0.57/0.65 %goalClause: 59 61
% 0.57/0.65 %singleGoalClaCount:2
% 0.57/0.65 [43]P1(a1)
% 0.57/0.65 [44]P2(a2)
% 0.57/0.65 [45]P5(a1,a17)
% 0.57/0.65 [59]~E(a24,a4)
% 0.57/0.65 [49]P6(a5,f6(a17,a17))
% 0.57/0.65 [50]P6(a18,f6(a17,a17))
% 0.57/0.65 [61]~P5(f14(a24,a4),a24)
% 0.57/0.65 [56]E(f10(f9(f11(f6(a21,a17))),a21),a13)
% 0.57/0.65 [57]E(f10(f6(a17,a17),f10(f6(a17,a17),f8(f7(f8(a5),f9(f11(f6(a5,a17))))))),a21)
% 0.57/0.65 [46]P6(x461,a17)
% 0.57/0.65 [47]P6(a4,x471)
% 0.57/0.65 [48]P6(x481,x481)
% 0.57/0.65 [60]~P5(x601,a4)
% 0.57/0.65 [54]P6(f19(x541),f6(f6(a17,a17),a17))
% 0.57/0.65 [55]P6(f11(x551),f6(f6(a17,a17),a17))
% 0.57/0.65 [58]E(f10(f9(x581),f8(f9(f10(f7(f9(f11(f6(a5,a17))),x581),a13)))),f3(x581))
% 0.57/0.65 [51]P5(f23(x511,x512),a17)
% 0.57/0.65 [52]P6(f7(x521,x522),f6(a17,a17))
% 0.57/0.65 [62]~P5(x621,f10(f8(x622),x622))
% 0.57/0.65 [53]E(f10(f6(x531,x532),x533),f10(x533,f6(x531,x532)))
% 0.57/0.65 [63]~P7(x631)+P2(x631)
% 0.57/0.65 [64]~P8(x641)+P2(x641)
% 0.57/0.65 [67]~P1(x671)+P6(a1,x671)
% 0.57/0.65 [68]~P1(x681)+P5(a4,x681)
% 0.57/0.65 [69]~P6(x691,a4)+E(x691,a4)
% 0.57/0.65 [71]P5(f20(x711),x711)+E(x711,a4)
% 0.57/0.65 [72]~P2(x721)+P6(x721,f6(a17,a17))
% 0.57/0.65 [70]E(x701,a4)+E(f10(x701,f20(x701)),a4)
% 0.57/0.65 [81]~P8(x811)+E(f6(f9(f9(x811)),f9(f9(x811))),f9(x811))
% 0.57/0.65 [94]~P7(x941)+P2(f9(f11(f6(x941,a17))))
% 0.57/0.65 [99]~P5(x991,a17)+P5(f9(f10(a5,f6(a17,x991))),a17)
% 0.57/0.65 [101]~P9(x1011)+P6(f7(x1011,f9(f11(f6(x1011,a17)))),a13)
% 0.57/0.65 [102]~P2(x1021)+P6(f7(x1021,f9(f11(f6(x1021,a17)))),a13)
% 0.57/0.65 [103]~P8(x1031)+P6(f9(f9(f11(f6(x1031,a17)))),f9(f9(x1031)))
% 0.57/0.65 [108]P9(x1081)+~P6(f7(x1081,f9(f11(f6(x1081,a17)))),a13)
% 0.57/0.65 [121]~P1(x1211)+P6(f9(f9(f11(f6(f10(a18,f6(x1211,a17)),a17)))),x1211)
% 0.57/0.65 [125]~P5(x1251,a17)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1251),a17)),a17))))),a17)
% 0.57/0.65 [65]~E(x652,x651)+P6(x651,x652)
% 0.57/0.65 [66]~E(x661,x662)+P6(x661,x662)
% 0.57/0.65 [74]P6(x741,x742)+P5(f14(x741,x742),x741)
% 0.57/0.65 [75]~P5(x751,x752)+~P5(x751,f8(x752))
% 0.57/0.65 [79]~P5(x791,a17)+P5(x791,f23(x792,x791))
% 0.57/0.65 [80]~P5(x801,a17)+P5(x801,f23(x801,x802))
% 0.57/0.65 [85]P6(x851,x852)+~P5(f14(x851,x852),x852)
% 0.57/0.65 [98]~P5(x982,f9(x981))+~E(f10(x981,f6(f23(x982,x982),a17)),a4)
% 0.57/0.65 [107]P5(x1071,x1072)+~P5(f23(f23(x1071,x1071),f23(x1071,f23(x1072,x1072))),a5)
% 0.57/0.65 [118]~P5(f23(f23(x1181,x1181),f23(x1181,f23(x1182,x1182))),a18)+E(f8(f10(f8(x1181),f8(f23(x1181,x1181)))),x1182)
% 0.57/0.65 [88]P2(x881)+~P3(x881,x882,x883)
% 0.57/0.65 [89]P8(x891)+~P4(x892,x893,x891)
% 0.57/0.65 [90]P8(x901)+~P4(x902,x901,x903)
% 0.57/0.65 [97]~P4(x971,x972,x973)+P3(x971,x972,x973)
% 0.57/0.65 [83]P5(x831,x832)+~P5(x831,f10(x833,x832))
% 0.57/0.65 [84]P5(x841,x842)+~P5(x841,f10(x842,x843))
% 0.57/0.65 [91]~P3(x912,x911,x913)+E(f9(f9(x911)),f9(x912))
% 0.57/0.65 [104]~P5(x1041,f6(x1042,x1043))+E(f23(f23(f12(x1041),f12(x1041)),f23(f12(x1041),f23(f22(x1041),f22(x1041)))),x1041)
% 0.57/0.65 [106]~P3(x1061,x1063,x1062)+P6(f9(f9(f11(f6(x1061,a17)))),f9(f9(x1062)))
% 0.57/0.65 [109]P5(x1091,a17)+~P5(f23(f23(x1092,x1092),f23(x1092,f23(x1091,x1091))),f6(x1093,x1094))
% 0.57/0.65 [110]P5(x1101,a17)+~P5(f23(f23(x1101,x1101),f23(x1101,f23(x1102,x1102))),f6(x1103,x1104))
% 0.57/0.65 [111]P5(x1111,x1112)+~P5(f23(f23(x1113,x1113),f23(x1113,f23(x1111,x1111))),f6(x1114,x1112))
% 0.57/0.65 [112]P5(x1121,x1122)+~P5(f23(f23(x1121,x1121),f23(x1121,f23(x1123,x1123))),f6(x1122,x1124))
% 0.57/0.65 [114]P5(x1141,f23(x1142,x1141))+~P5(f23(f23(x1142,x1142),f23(x1142,f23(x1141,x1141))),f6(x1143,x1144))
% 0.57/0.65 [115]P5(x1151,f23(x1151,x1152))+~P5(f23(f23(x1151,x1151),f23(x1151,f23(x1152,x1152))),f6(x1153,x1154))
% 0.57/0.65 [126]~P5(f23(f23(f23(f23(x1263,x1263),f23(x1263,f23(x1261,x1261))),f23(f23(x1263,x1263),f23(x1263,f23(x1261,x1261)))),f23(f23(f23(x1263,x1263),f23(x1263,f23(x1261,x1261))),f23(x1262,x1262))),f19(x1264))+P5(f23(f23(f23(f23(x1261,x1261),f23(x1261,f23(x1262,x1262))),f23(f23(x1261,x1261),f23(x1261,f23(x1262,x1262)))),f23(f23(f23(x1261,x1261),f23(x1261,f23(x1262,x1262))),f23(x1263,x1263))),x1264)
% 0.57/0.65 [127]~P5(f23(f23(f23(f23(x1272,x1272),f23(x1272,f23(x1271,x1271))),f23(f23(x1272,x1272),f23(x1272,f23(x1271,x1271)))),f23(f23(f23(x1272,x1272),f23(x1272,f23(x1271,x1271))),f23(x1273,x1273))),f11(x1274))+P5(f23(f23(f23(f23(x1271,x1271),f23(x1271,f23(x1272,x1272))),f23(f23(x1271,x1271),f23(x1271,f23(x1272,x1272)))),f23(f23(f23(x1271,x1271),f23(x1271,f23(x1272,x1272))),f23(x1273,x1273))),x1274)
% 0.57/0.65 [131]~P5(f23(f23(x1314,x1314),f23(x1314,f23(x1311,x1311))),f7(x1312,x1313))+P5(x1311,f9(f9(f11(f6(f10(x1312,f6(f9(f9(f11(f6(f10(x1313,f6(f23(x1314,x1314),a17)),a17)))),a17)),a17)))))
% 0.57/0.65 [100]~P2(x1001)+P7(x1001)+~P2(f9(f11(f6(x1001,a17))))
% 0.57/0.65 [113]P2(x1131)+~P6(x1131,f6(a17,a17))+~P6(f7(x1131,f9(f11(f6(x1131,a17)))),a13)
% 0.57/0.65 [123]P1(x1231)+~P5(a4,x1231)+~P6(f9(f9(f11(f6(f10(a18,f6(x1231,a17)),a17)))),x1231)
% 0.57/0.65 [130]~P5(x1301,a17)+E(x1301,a4)+P5(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(a2,f6(f23(x1301,x1301),a17)),a17))))))),x1301)
% 0.57/0.65 [73]~P6(x732,x731)+~P6(x731,x732)+E(x731,x732)
% 0.57/0.65 [76]P5(x761,x762)+P5(x761,f8(x762))+~P5(x761,a17)
% 0.57/0.65 [86]E(x861,x862)+P5(f14(x862,x861),x862)+P5(f14(x861,x862),x861)
% 0.57/0.65 [93]E(x931,x932)+P5(f14(x932,x931),x932)+~P5(f14(x931,x932),x932)
% 0.57/0.65 [95]E(x951,x952)+~P5(f14(x952,x951),x951)+~P5(f14(x951,x952),x952)
% 0.57/0.65 [96]P5(x962,f9(x961))+~P5(x962,a17)+E(f10(x961,f6(f23(x962,x962),a17)),a4)
% 0.57/0.65 [119]~P5(x1191,x1192)+~P5(f23(f23(x1191,x1191),f23(x1191,f23(x1192,x1192))),f6(a17,a17))+P5(f23(f23(x1191,x1191),f23(x1191,f23(x1192,x1192))),a5)
% 0.57/0.65 [120]~P5(f23(f23(x1201,x1201),f23(x1201,f23(x1202,x1202))),f6(a17,a17))+~E(f8(f10(f8(x1201),f8(f23(x1201,x1201)))),x1202)+P5(f23(f23(x1201,x1201),f23(x1201,f23(x1202,x1202))),a18)
% 0.57/0.65 [122]~P2(x1221)+~P5(x1222,a17)+P5(f9(f9(f11(f6(f10(x1221,f6(x1222,a17)),a17)))),a17)
% 0.57/0.65 [77]~P6(x771,x773)+P6(x771,x772)+~P6(x773,x772)
% 0.57/0.65 [78]~P5(x781,x783)+P5(x781,x782)+~P6(x783,x782)
% 0.57/0.65 [82]E(x821,x822)+E(x821,x823)+~P5(x821,f23(x823,x822))
% 0.57/0.65 [87]~P5(x871,x873)+~P5(x871,x872)+P5(x871,f10(x872,x873))
% 0.57/0.65 [105]~P5(x1052,x1054)+~P5(x1051,x1053)+P5(f23(f23(x1051,x1051),f23(x1051,f23(x1052,x1052))),f6(x1053,x1054))
% 0.57/0.65 [128]~P5(f23(f23(f23(f23(x1282,x1282),f23(x1282,f23(x1283,x1283))),f23(f23(x1282,x1282),f23(x1282,f23(x1283,x1283)))),f23(f23(f23(x1282,x1282),f23(x1282,f23(x1283,x1283))),f23(x1281,x1281))),x1284)+P5(f23(f23(f23(f23(x1281,x1281),f23(x1281,f23(x1282,x1282))),f23(f23(x1281,x1281),f23(x1281,f23(x1282,x1282)))),f23(f23(f23(x1281,x1281),f23(x1281,f23(x1282,x1282))),f23(x1283,x1283))),f19(x1284))+~P5(f23(f23(f23(f23(x1281,x1281),f23(x1281,f23(x1282,x1282))),f23(f23(x1281,x1281),f23(x1281,f23(x1282,x1282)))),f23(f23(f23(x1281,x1281),f23(x1281,f23(x1282,x1282))),f23(x1283,x1283))),f6(f6(a17,a17),a17))
% 0.57/0.65 [129]~P5(f23(f23(f23(f23(x1292,x1292),f23(x1292,f23(x1291,x1291))),f23(f23(x1292,x1292),f23(x1292,f23(x1291,x1291)))),f23(f23(f23(x1292,x1292),f23(x1292,f23(x1291,x1291))),f23(x1293,x1293))),x1294)+P5(f23(f23(f23(f23(x1291,x1291),f23(x1291,f23(x1292,x1292))),f23(f23(x1291,x1291),f23(x1291,f23(x1292,x1292)))),f23(f23(f23(x1291,x1291),f23(x1291,f23(x1292,x1292))),f23(x1293,x1293))),f11(x1294))+~P5(f23(f23(f23(f23(x1291,x1291),f23(x1291,f23(x1292,x1292))),f23(f23(x1291,x1291),f23(x1291,f23(x1292,x1292)))),f23(f23(f23(x1291,x1291),f23(x1291,f23(x1292,x1292))),f23(x1293,x1293))),f6(f6(a17,a17),a17))
% 0.57/0.65 [132]P5(f23(f23(x1321,x1321),f23(x1321,f23(x1322,x1322))),f7(x1323,x1324))+~P5(f23(f23(x1321,x1321),f23(x1321,f23(x1322,x1322))),f6(a17,a17))+~P5(x1322,f9(f9(f11(f6(f10(x1323,f6(f9(f9(f11(f6(f10(x1324,f6(f23(x1321,x1321),a17)),a17)))),a17)),a17)))))
% 0.57/0.65 [133]~P4(x1332,x1335,x1331)+~P5(f23(f23(x1333,x1333),f23(x1333,f23(x1334,x1334))),f9(x1335))+E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1331,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1333,x1333),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1333,x1333),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1333,x1333),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1334,x1334),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1334,x1334),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1333,x1333),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1333,x1333),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1333,x1333),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1334,x1334),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(x1334,x1334),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1332,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1335,f6(f23(f23(f23(x1333,x1333),f23(x1333,f23(x1334,x1334))),f23(f23(x1333,x1333),f23(x1333,f23(x1334,x1334)))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1335,f6(f23(f23(f23(x1333,x1333),f23(x1333,f23(x1334,x1334))),f23(f23(x1333,x1333),f23(x1333,f23(x1334,x1334)))),a17)),a17)))))))),a17)),a17))))))))
% 0.57/0.65 [117]~P2(x1171)+P8(x1171)+~E(f6(f9(f9(x1171)),f9(f9(x1171))),f9(x1171))+~P6(f9(f9(f11(f6(x1171,a17)))),f9(f9(x1171)))
% 0.57/0.65 [116]~P2(x1161)+P3(x1161,x1162,x1163)+~E(f9(f9(x1162)),f9(x1161))+~P6(f9(f9(f11(f6(x1161,a17)))),f9(f9(x1163)))
% 0.57/0.65 [124]~P8(x1243)+~P8(x1242)+~P3(x1241,x1242,x1243)+P4(x1241,x1242,x1243)+P5(f23(f23(f15(x1241,x1242,x1243),f15(x1241,x1242,x1243)),f23(f15(x1241,x1242,x1243),f23(f16(x1241,x1242,x1243),f16(x1241,x1242,x1243)))),f9(x1242))
% 0.57/0.65 [134]~P8(x1343)+~P8(x1342)+~P3(x1341,x1342,x1343)+P4(x1341,x1342,x1343)+~E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1343,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f16(x1341,x1342,x1343),f16(x1341,x1342,x1343)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f16(x1341,x1342,x1343),f16(x1341,x1342,x1343)),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f16(x1341,x1342,x1343),f16(x1341,x1342,x1343)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f16(x1341,x1342,x1343),f16(x1341,x1342,x1343)),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1341,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1342,f6(f23(f23(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),f23(f15(x1341,x1342,x1343),f23(f16(x1341,x1342,x1343),f16(x1341,x1342,x1343)))),f23(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),f23(f15(x1341,x1342,x1343),f23(f16(x1341,x1342,x1343),f16(x1341,x1342,x1343))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1342,f6(f23(f23(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),f23(f15(x1341,x1342,x1343),f23(f16(x1341,x1342,x1343),f16(x1341,x1342,x1343)))),f23(f23(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),f23(f15(x1341,x1342,x1343),f23(f16(x1341,x1342,x1343),f16(x1341,x1342,x1343))))),a17)),a17)))))))),a17)),a17))))))))
% 0.57/0.65 %EqnAxiom
% 0.57/0.65 [1]E(x11,x11)
% 0.57/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.57/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.57/0.65 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.57/0.65 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.57/0.65 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.57/0.65 [7]~E(x71,x72)+E(f23(x71,x73),f23(x72,x73))
% 0.57/0.65 [8]~E(x81,x82)+E(f23(x83,x81),f23(x83,x82))
% 0.57/0.65 [9]~E(x91,x92)+E(f7(x91,x93),f7(x92,x93))
% 0.57/0.65 [10]~E(x101,x102)+E(f7(x103,x101),f7(x103,x102))
% 0.57/0.65 [11]~E(x111,x112)+E(f10(x111,x113),f10(x112,x113))
% 0.57/0.65 [12]~E(x121,x122)+E(f10(x123,x121),f10(x123,x122))
% 0.57/0.65 [13]~E(x131,x132)+E(f11(x131),f11(x132))
% 0.57/0.65 [14]~E(x141,x142)+E(f16(x141,x143,x144),f16(x142,x143,x144))
% 0.57/0.65 [15]~E(x151,x152)+E(f16(x153,x151,x154),f16(x153,x152,x154))
% 0.57/0.65 [16]~E(x161,x162)+E(f16(x163,x164,x161),f16(x163,x164,x162))
% 0.57/0.65 [17]~E(x171,x172)+E(f15(x171,x173,x174),f15(x172,x173,x174))
% 0.57/0.65 [18]~E(x181,x182)+E(f15(x183,x181,x184),f15(x183,x182,x184))
% 0.57/0.65 [19]~E(x191,x192)+E(f15(x193,x194,x191),f15(x193,x194,x192))
% 0.57/0.65 [20]~E(x201,x202)+E(f8(x201),f8(x202))
% 0.57/0.65 [21]~E(x211,x212)+E(f19(x211),f19(x212))
% 0.57/0.65 [22]~E(x221,x222)+E(f14(x221,x223),f14(x222,x223))
% 0.57/0.65 [23]~E(x231,x232)+E(f14(x233,x231),f14(x233,x232))
% 0.57/0.65 [24]~E(x241,x242)+E(f22(x241),f22(x242))
% 0.57/0.65 [25]~E(x251,x252)+E(f3(x251),f3(x252))
% 0.57/0.65 [26]~E(x261,x262)+E(f12(x261),f12(x262))
% 0.57/0.65 [27]~E(x271,x272)+E(f20(x271),f20(x272))
% 0.57/0.65 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.57/0.65 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.57/0.65 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.57/0.65 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.57/0.65 [32]P6(x322,x323)+~E(x321,x322)+~P6(x321,x323)
% 0.57/0.65 [33]P6(x333,x332)+~E(x331,x332)+~P6(x333,x331)
% 0.57/0.65 [34]P3(x342,x343,x344)+~E(x341,x342)+~P3(x341,x343,x344)
% 0.57/0.65 [35]P3(x353,x352,x354)+~E(x351,x352)+~P3(x353,x351,x354)
% 0.57/0.65 [36]P3(x363,x364,x362)+~E(x361,x362)+~P3(x363,x364,x361)
% 0.57/0.65 [37]~P8(x371)+P8(x372)+~E(x371,x372)
% 0.57/0.65 [38]P4(x382,x383,x384)+~E(x381,x382)+~P4(x381,x383,x384)
% 0.57/0.65 [39]P4(x393,x392,x394)+~E(x391,x392)+~P4(x393,x391,x394)
% 0.57/0.65 [40]P4(x403,x404,x402)+~E(x401,x402)+~P4(x403,x404,x401)
% 0.57/0.65 [41]~P7(x411)+P7(x412)+~E(x411,x412)
% 0.57/0.65 [42]~P9(x421)+P9(x422)+~E(x421,x422)
% 0.57/0.65
% 0.57/0.65 %-------------------------------------------
% 0.57/0.65 cnf(139,plain,
% 0.57/0.65 ($false),
% 0.57/0.66 inference(scs_inference,[],[59,60,61,86]),
% 0.57/0.66 ['proof']).
% 0.57/0.66 % SZS output end Proof
% 0.57/0.66 % Total time :0.010000s
%------------------------------------------------------------------------------