TSTP Solution File: SET065-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET065-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n020.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 : Thu Aug 31 14:28:22 EDT 2023
% Result : Unsatisfiable 0.14s 0.77s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET065-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.08/0.30 % Computer : n020.cluster.edu
% 0.08/0.30 % Model : x86_64 x86_64
% 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30 % Memory : 8042.1875MB
% 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Sat Aug 26 13:36:44 EDT 2023
% 0.08/0.30 % CPUTime :
% 0.14/0.51 start to proof:theBenchmark
% 0.14/0.76 %-------------------------------------------
% 0.14/0.76 % File :CSE---1.6
% 0.14/0.76 % Problem :theBenchmark
% 0.14/0.76 % Transform :cnf
% 0.14/0.76 % Format :tptp:raw
% 0.14/0.76 % Command :java -jar mcs_scs.jar %d %s
% 0.14/0.76
% 0.14/0.76 % Result :Theorem 0.160000s
% 0.14/0.76 % Output :CNFRefutation 0.160000s
% 0.14/0.76 %-------------------------------------------
% 0.14/0.76 %--------------------------------------------------------------------------
% 0.14/0.76 % File : SET065-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.76 % Domain : Set Theory
% 0.14/0.76 % Problem : The null class is a set
% 0.14/0.76 % Version : [Qua92] axioms : Augmented.
% 0.14/0.76 % English :
% 0.14/0.76
% 0.14/0.76 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.14/0.76 % Source : [Quaife]
% 0.14/0.76 % Names : SP5 [Qua92]
% 0.14/0.76
% 0.14/0.76 % Status : Unsatisfiable
% 0.14/0.76 % Rating : 0.05 v8.1.0, 0.11 v7.4.0, 0.18 v7.3.0, 0.08 v7.0.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.00 v5.5.0, 0.15 v5.3.0, 0.11 v5.2.0, 0.12 v5.0.0, 0.07 v4.1.0, 0.08 v4.0.1, 0.27 v3.7.0, 0.30 v3.5.0, 0.27 v3.4.0, 0.17 v3.3.0, 0.00 v2.1.0
% 0.14/0.76 % Syntax : Number of clauses : 107 ( 34 unt; 12 nHn; 74 RR)
% 0.14/0.76 % Number of literals : 213 ( 45 equ; 98 neg)
% 0.14/0.76 % Maximal clause size : 5 ( 1 avg)
% 0.14/0.76 % Maximal term depth : 6 ( 1 avg)
% 0.14/0.76 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.14/0.76 % Number of functors : 38 ( 38 usr; 8 con; 0-3 aty)
% 0.14/0.76 % Number of variables : 210 ( 38 sgn)
% 0.14/0.76 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.14/0.76
% 0.14/0.76 % Comments : Preceding lemmas are added.
% 0.14/0.76 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.14/0.76 %--------------------------------------------------------------------------
% 0.14/0.76 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.14/0.76 include('Axioms/SET004-0.ax').
% 0.14/0.76 %--------------------------------------------------------------------------
% 0.14/0.76 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.14/0.76 cnf(corollary_1_to_unordered_pair,axiom,
% 0.14/0.76 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.14/0.76 | member(X,unordered_pair(X,Y)) ) ).
% 0.14/0.76
% 0.14/0.76 cnf(corollary_2_to_unordered_pair,axiom,
% 0.14/0.76 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.14/0.76 | member(Y,unordered_pair(X,Y)) ) ).
% 0.14/0.76
% 0.14/0.76 %----Corollaries to Cartesian product axiom.
% 0.14/0.76 cnf(corollary_1_to_cartesian_product,axiom,
% 0.14/0.76 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.14/0.76 | member(U,universal_class) ) ).
% 0.14/0.76
% 0.14/0.76 cnf(corollary_2_to_cartesian_product,axiom,
% 0.14/0.76 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.14/0.76 | member(V,universal_class) ) ).
% 0.14/0.76
% 0.14/0.76 %---- PARTIAL ORDER.
% 0.14/0.76 %----(PO1): reflexive.
% 0.14/0.76 cnf(subclass_is_reflexive,axiom,
% 0.14/0.76 subclass(X,X) ).
% 0.14/0.76
% 0.14/0.76 %----(PO2): antisymmetry is part of A-3.
% 0.14/0.76 %----(x < y), (y < x) --> (x = y).
% 0.14/0.76
% 0.14/0.76 %----(PO3): transitivity.
% 0.14/0.76 cnf(transitivity_of_subclass,axiom,
% 0.14/0.76 ( ~ subclass(X,Y)
% 0.14/0.76 | ~ subclass(Y,Z)
% 0.14/0.76 | subclass(X,Z) ) ).
% 0.14/0.76
% 0.14/0.76 %---- EQUALITY.
% 0.14/0.76 %----(EQ1): equality axiom.
% 0.14/0.76 %----a:x:(x = x).
% 0.14/0.76 %----This is always an axiom in the TPTP presentation.
% 0.14/0.76
% 0.14/0.76 %----(EQ2): expanded equality definition.
% 0.14/0.77 cnf(equality1,axiom,
% 0.14/0.77 ( X = Y
% 0.14/0.77 | member(not_subclass_element(X,Y),X)
% 0.14/0.77 | member(not_subclass_element(Y,X),Y) ) ).
% 0.14/0.77
% 0.14/0.77 cnf(equality2,axiom,
% 0.14/0.77 ( ~ member(not_subclass_element(X,Y),Y)
% 0.14/0.77 | X = Y
% 0.14/0.77 | member(not_subclass_element(Y,X),Y) ) ).
% 0.14/0.77
% 0.14/0.77 cnf(equality3,axiom,
% 0.14/0.77 ( ~ member(not_subclass_element(Y,X),X)
% 0.14/0.77 | X = Y
% 0.14/0.77 | member(not_subclass_element(X,Y),X) ) ).
% 0.14/0.77
% 0.14/0.77 cnf(equality4,axiom,
% 0.14/0.77 ( ~ member(not_subclass_element(X,Y),Y)
% 0.14/0.77 | ~ member(not_subclass_element(Y,X),X)
% 0.14/0.77 | X = Y ) ).
% 0.14/0.77
% 0.14/0.77 %---- SPECIAL CLASSES.
% 0.14/0.77 %----(SP1): lemma.
% 0.14/0.77 cnf(special_classes_lemma,axiom,
% 0.14/0.77 ~ member(Y,intersection(complement(X),X)) ).
% 0.14/0.77
% 0.14/0.77 %----(SP2): Existence of O (null class).
% 0.14/0.77 %----e:x:a:z:(-(z e x)).
% 0.14/0.77 cnf(existence_of_null_class,axiom,
% 0.14/0.77 ~ member(Z,null_class) ).
% 0.14/0.77
% 0.14/0.77 %----(SP3): O is a subclass of every class.
% 0.14/0.77 cnf(null_class_is_subclass,axiom,
% 0.14/0.77 subclass(null_class,X) ).
% 0.14/0.77
% 0.14/0.77 %----corollary.
% 0.14/0.77 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.14/0.77 ( ~ subclass(X,null_class)
% 0.14/0.77 | X = null_class ) ).
% 0.14/0.77
% 0.14/0.77 %----(SP4): uniqueness of null class.
% 0.14/0.77 cnf(null_class_is_unique,axiom,
% 0.14/0.77 ( Z = null_class
% 0.14/0.77 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.14/0.77
% 0.14/0.77 cnf(prove_null_class_is_a_set_1,negated_conjecture,
% 0.14/0.77 ~ member(null_class,universal_class) ).
% 0.14/0.77
% 0.14/0.77 %--------------------------------------------------------------------------
% 0.14/0.77 %-------------------------------------------
% 0.14/0.77 % Proof found
% 0.14/0.77 % SZS status Theorem for theBenchmark
% 0.14/0.77 % SZS output start Proof
% 0.14/0.77 %ClaNum:134(EqnAxiom:42)
% 0.14/0.77 %VarNum:796(SingletonVarNum:182)
% 0.14/0.77 %MaxLitNum:5
% 0.14/0.77 %MaxfuncDepth:24
% 0.14/0.77 %SharedTerms:30
% 0.14/0.77 %goalClause: 59
% 0.14/0.77 %singleGoalClaCount:1
% 0.14/0.77 [43]P1(a1)
% 0.14/0.77 [44]P2(a2)
% 0.14/0.77 [45]P5(a1,a17)
% 0.14/0.77 [59]~P5(a4,a17)
% 0.14/0.77 [49]P6(a5,f6(a17,a17))
% 0.14/0.77 [50]P6(a18,f6(a17,a17))
% 0.14/0.77 [56]E(f10(f9(f11(f6(a21,a17))),a21),a13)
% 0.14/0.77 [57]E(f10(f6(a17,a17),f10(f6(a17,a17),f8(f7(f8(a5),f9(f11(f6(a5,a17))))))),a21)
% 0.14/0.77 [46]P6(x461,a17)
% 0.14/0.77 [47]P6(a4,x471)
% 0.14/0.77 [48]P6(x481,x481)
% 0.14/0.77 [60]~P5(x601,a4)
% 0.14/0.77 [54]P6(f19(x541),f6(f6(a17,a17),a17))
% 0.14/0.77 [55]P6(f11(x551),f6(f6(a17,a17),a17))
% 0.14/0.77 [58]E(f10(f9(x581),f8(f9(f10(f7(f9(f11(f6(a5,a17))),x581),a13)))),f3(x581))
% 0.14/0.77 [51]P5(f23(x511,x512),a17)
% 0.14/0.77 [52]P6(f7(x521,x522),f6(a17,a17))
% 0.14/0.77 [61]~P5(x611,f10(f8(x612),x612))
% 0.14/0.77 [53]E(f10(f6(x531,x532),x533),f10(x533,f6(x531,x532)))
% 0.14/0.77 [62]~P7(x621)+P2(x621)
% 0.14/0.77 [63]~P8(x631)+P2(x631)
% 0.14/0.77 [66]~P1(x661)+P6(a1,x661)
% 0.14/0.77 [67]~P1(x671)+P5(a4,x671)
% 0.14/0.77 [68]~P6(x681,a4)+E(x681,a4)
% 0.14/0.77 [70]P5(f20(x701),x701)+E(x701,a4)
% 0.14/0.77 [71]E(x711,a4)+P5(f14(x711,a4),x711)
% 0.14/0.77 [72]~P2(x721)+P6(x721,f6(a17,a17))
% 0.14/0.77 [69]E(x691,a4)+E(f10(x691,f20(x691)),a4)
% 0.14/0.77 [81]~P8(x811)+E(f6(f9(f9(x811)),f9(f9(x811))),f9(x811))
% 0.14/0.77 [94]~P7(x941)+P2(f9(f11(f6(x941,a17))))
% 0.14/0.77 [99]~P5(x991,a17)+P5(f9(f10(a5,f6(a17,x991))),a17)
% 0.14/0.77 [101]~P9(x1011)+P6(f7(x1011,f9(f11(f6(x1011,a17)))),a13)
% 0.14/0.77 [102]~P2(x1021)+P6(f7(x1021,f9(f11(f6(x1021,a17)))),a13)
% 0.14/0.77 [103]~P8(x1031)+P6(f9(f9(f11(f6(x1031,a17)))),f9(f9(x1031)))
% 0.14/0.77 [108]P9(x1081)+~P6(f7(x1081,f9(f11(f6(x1081,a17)))),a13)
% 0.14/0.77 [121]~P1(x1211)+P6(f9(f9(f11(f6(f10(a18,f6(x1211,a17)),a17)))),x1211)
% 0.14/0.77 [125]~P5(x1251,a17)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1251),a17)),a17))))),a17)
% 0.14/0.77 [64]~E(x642,x641)+P6(x641,x642)
% 0.14/0.77 [65]~E(x651,x652)+P6(x651,x652)
% 0.14/0.77 [74]P6(x741,x742)+P5(f14(x741,x742),x741)
% 0.14/0.77 [75]~P5(x751,x752)+~P5(x751,f8(x752))
% 0.14/0.77 [79]~P5(x791,a17)+P5(x791,f23(x792,x791))
% 0.14/0.77 [80]~P5(x801,a17)+P5(x801,f23(x801,x802))
% 0.14/0.77 [85]P6(x851,x852)+~P5(f14(x851,x852),x852)
% 0.14/0.77 [98]~P5(x982,f9(x981))+~E(f10(x981,f6(f23(x982,x982),a17)),a4)
% 0.14/0.77 [107]P5(x1071,x1072)+~P5(f23(f23(x1071,x1071),f23(x1071,f23(x1072,x1072))),a5)
% 0.14/0.77 [118]~P5(f23(f23(x1181,x1181),f23(x1181,f23(x1182,x1182))),a18)+E(f8(f10(f8(x1181),f8(f23(x1181,x1181)))),x1182)
% 0.14/0.77 [88]P2(x881)+~P3(x881,x882,x883)
% 0.14/0.77 [89]P8(x891)+~P4(x892,x893,x891)
% 0.14/0.77 [90]P8(x901)+~P4(x902,x901,x903)
% 0.14/0.77 [97]~P4(x971,x972,x973)+P3(x971,x972,x973)
% 0.14/0.77 [83]P5(x831,x832)+~P5(x831,f10(x833,x832))
% 0.14/0.77 [84]P5(x841,x842)+~P5(x841,f10(x842,x843))
% 0.14/0.77 [91]~P3(x912,x911,x913)+E(f9(f9(x911)),f9(x912))
% 0.14/0.77 [104]~P5(x1041,f6(x1042,x1043))+E(f23(f23(f12(x1041),f12(x1041)),f23(f12(x1041),f23(f22(x1041),f22(x1041)))),x1041)
% 0.14/0.77 [106]~P3(x1061,x1063,x1062)+P6(f9(f9(f11(f6(x1061,a17)))),f9(f9(x1062)))
% 0.14/0.77 [109]P5(x1091,a17)+~P5(f23(f23(x1092,x1092),f23(x1092,f23(x1091,x1091))),f6(x1093,x1094))
% 0.14/0.77 [110]P5(x1101,a17)+~P5(f23(f23(x1101,x1101),f23(x1101,f23(x1102,x1102))),f6(x1103,x1104))
% 0.14/0.77 [111]P5(x1111,x1112)+~P5(f23(f23(x1113,x1113),f23(x1113,f23(x1111,x1111))),f6(x1114,x1112))
% 0.14/0.77 [112]P5(x1121,x1122)+~P5(f23(f23(x1121,x1121),f23(x1121,f23(x1123,x1123))),f6(x1122,x1124))
% 0.14/0.77 [114]P5(x1141,f23(x1142,x1141))+~P5(f23(f23(x1142,x1142),f23(x1142,f23(x1141,x1141))),f6(x1143,x1144))
% 0.14/0.77 [115]P5(x1151,f23(x1151,x1152))+~P5(f23(f23(x1151,x1151),f23(x1151,f23(x1152,x1152))),f6(x1153,x1154))
% 0.14/0.77 [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)
% 0.14/0.77 [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)
% 0.14/0.77 [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)))))
% 0.14/0.77 [100]~P2(x1001)+P7(x1001)+~P2(f9(f11(f6(x1001,a17))))
% 0.14/0.77 [113]P2(x1131)+~P6(x1131,f6(a17,a17))+~P6(f7(x1131,f9(f11(f6(x1131,a17)))),a13)
% 0.14/0.77 [123]P1(x1231)+~P5(a4,x1231)+~P6(f9(f9(f11(f6(f10(a18,f6(x1231,a17)),a17)))),x1231)
% 0.14/0.77 [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)
% 0.14/0.77 [73]~P6(x732,x731)+~P6(x731,x732)+E(x731,x732)
% 0.14/0.77 [76]P5(x761,x762)+P5(x761,f8(x762))+~P5(x761,a17)
% 0.14/0.77 [86]E(x861,x862)+P5(f14(x862,x861),x862)+P5(f14(x861,x862),x861)
% 0.14/0.77 [93]E(x931,x932)+P5(f14(x932,x931),x932)+~P5(f14(x931,x932),x932)
% 0.14/0.77 [95]E(x951,x952)+~P5(f14(x952,x951),x951)+~P5(f14(x951,x952),x952)
% 0.14/0.77 [96]P5(x962,f9(x961))+~P5(x962,a17)+E(f10(x961,f6(f23(x962,x962),a17)),a4)
% 0.14/0.77 [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)
% 0.14/0.77 [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)
% 0.14/0.77 [122]~P2(x1221)+~P5(x1222,a17)+P5(f9(f9(f11(f6(f10(x1221,f6(x1222,a17)),a17)))),a17)
% 0.14/0.77 [77]~P6(x771,x773)+P6(x771,x772)+~P6(x773,x772)
% 0.14/0.77 [78]~P5(x781,x783)+P5(x781,x782)+~P6(x783,x782)
% 0.14/0.77 [82]E(x821,x822)+E(x821,x823)+~P5(x821,f23(x823,x822))
% 0.64/0.77 [87]~P5(x871,x873)+~P5(x871,x872)+P5(x871,f10(x872,x873))
% 0.64/0.77 [105]~P5(x1052,x1054)+~P5(x1051,x1053)+P5(f23(f23(x1051,x1051),f23(x1051,f23(x1052,x1052))),f6(x1053,x1054))
% 0.64/0.77 [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))
% 0.64/0.77 [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))
% 0.64/0.77 [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)))))
% 0.64/0.77 [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))))))))
% 0.64/0.77 [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)))
% 0.64/0.77 [116]~P2(x1161)+P3(x1161,x1162,x1163)+~E(f9(f9(x1162)),f9(x1161))+~P6(f9(f9(f11(f6(x1161,a17)))),f9(f9(x1163)))
% 0.64/0.77 [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))
% 0.64/0.77 [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))))))))
% 0.64/0.77 %EqnAxiom
% 0.64/0.77 [1]E(x11,x11)
% 0.64/0.77 [2]E(x22,x21)+~E(x21,x22)
% 0.64/0.77 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.64/0.77 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.64/0.77 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.64/0.77 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.64/0.77 [7]~E(x71,x72)+E(f23(x71,x73),f23(x72,x73))
% 0.64/0.77 [8]~E(x81,x82)+E(f23(x83,x81),f23(x83,x82))
% 0.64/0.77 [9]~E(x91,x92)+E(f7(x91,x93),f7(x92,x93))
% 0.64/0.77 [10]~E(x101,x102)+E(f7(x103,x101),f7(x103,x102))
% 0.64/0.77 [11]~E(x111,x112)+E(f10(x111,x113),f10(x112,x113))
% 0.64/0.77 [12]~E(x121,x122)+E(f10(x123,x121),f10(x123,x122))
% 0.64/0.77 [13]~E(x131,x132)+E(f11(x131),f11(x132))
% 0.64/0.77 [14]~E(x141,x142)+E(f16(x141,x143,x144),f16(x142,x143,x144))
% 0.64/0.77 [15]~E(x151,x152)+E(f16(x153,x151,x154),f16(x153,x152,x154))
% 0.64/0.77 [16]~E(x161,x162)+E(f16(x163,x164,x161),f16(x163,x164,x162))
% 0.64/0.77 [17]~E(x171,x172)+E(f15(x171,x173,x174),f15(x172,x173,x174))
% 0.64/0.77 [18]~E(x181,x182)+E(f15(x183,x181,x184),f15(x183,x182,x184))
% 0.64/0.77 [19]~E(x191,x192)+E(f15(x193,x194,x191),f15(x193,x194,x192))
% 0.64/0.77 [20]~E(x201,x202)+E(f8(x201),f8(x202))
% 0.64/0.77 [21]~E(x211,x212)+E(f19(x211),f19(x212))
% 0.64/0.77 [22]~E(x221,x222)+E(f14(x221,x223),f14(x222,x223))
% 0.64/0.77 [23]~E(x231,x232)+E(f14(x233,x231),f14(x233,x232))
% 0.64/0.77 [24]~E(x241,x242)+E(f20(x241),f20(x242))
% 0.64/0.77 [25]~E(x251,x252)+E(f22(x251),f22(x252))
% 0.64/0.77 [26]~E(x261,x262)+E(f3(x261),f3(x262))
% 0.64/0.77 [27]~E(x271,x272)+E(f12(x271),f12(x272))
% 0.64/0.77 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.64/0.77 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.64/0.77 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.64/0.77 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.64/0.77 [32]P6(x322,x323)+~E(x321,x322)+~P6(x321,x323)
% 0.64/0.77 [33]P6(x333,x332)+~E(x331,x332)+~P6(x333,x331)
% 0.64/0.77 [34]P3(x342,x343,x344)+~E(x341,x342)+~P3(x341,x343,x344)
% 0.64/0.77 [35]P3(x353,x352,x354)+~E(x351,x352)+~P3(x353,x351,x354)
% 0.64/0.77 [36]P3(x363,x364,x362)+~E(x361,x362)+~P3(x363,x364,x361)
% 0.64/0.77 [37]~P8(x371)+P8(x372)+~E(x371,x372)
% 0.64/0.77 [38]P4(x382,x383,x384)+~E(x381,x382)+~P4(x381,x383,x384)
% 0.64/0.77 [39]P4(x393,x392,x394)+~E(x391,x392)+~P4(x393,x391,x394)
% 0.64/0.77 [40]P4(x403,x404,x402)+~E(x401,x402)+~P4(x403,x404,x401)
% 0.64/0.77 [41]~P7(x411)+P7(x412)+~E(x411,x412)
% 0.64/0.77 [42]~P9(x421)+P9(x422)+~E(x421,x422)
% 0.64/0.77
% 0.64/0.77 %-------------------------------------------
% 0.64/0.77 cnf(139,plain,
% 0.64/0.77 (~P5(x1391,f10(f8(x1392),x1392))),
% 0.64/0.78 inference(rename_variables,[],[61])).
% 0.64/0.78 cnf(142,plain,
% 0.64/0.78 (~P5(x1421,f10(f8(x1422),x1422))),
% 0.64/0.78 inference(rename_variables,[],[61])).
% 0.64/0.78 cnf(147,plain,
% 0.64/0.78 (~P5(x1471,a4)),
% 0.64/0.78 inference(rename_variables,[],[60])).
% 0.64/0.78 cnf(150,plain,
% 0.64/0.78 (~P5(x1501,a4)),
% 0.64/0.78 inference(rename_variables,[],[60])).
% 0.64/0.78 cnf(153,plain,
% 0.64/0.78 (P6(x1531,x1531)),
% 0.64/0.78 inference(rename_variables,[],[48])).
% 0.64/0.78 cnf(157,plain,
% 0.64/0.78 (~P5(x1571,a4)),
% 0.64/0.78 inference(rename_variables,[],[60])).
% 0.64/0.78 cnf(159,plain,
% 0.64/0.78 (~E(a17,f10(f8(f6(f23(x1591,x1591),a17)),f6(f23(x1591,x1591),a17)))),
% 0.64/0.78 inference(scs_inference,[],[59,48,153,60,147,150,45,56,61,139,2,67,71,74,98,127,126,33,32,31,30,3])).
% 0.64/0.78 cnf(161,plain,
% 0.64/0.78 (~P5(x1611,f10(f8(x1612),x1612))),
% 0.64/0.78 inference(rename_variables,[],[61])).
% 0.64/0.78 cnf(165,plain,
% 0.64/0.78 (~P5(x1651,a4)),
% 0.64/0.78 inference(rename_variables,[],[60])).
% 0.64/0.78 cnf(213,plain,
% 0.64/0.78 (~P5(f23(f23(x2131,x2131),f23(x2131,f23(a4,a4))),f6(x2132,x2133))),
% 0.64/0.78 inference(scs_inference,[],[59,48,153,60,147,150,157,43,44,45,56,57,51,61,139,142,161,2,67,71,74,98,127,126,33,32,31,30,3,87,86,65,64,72,125,121,99,84,83,80,79,75,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,109])).
% 0.64/0.78 cnf(230,plain,
% 0.64/0.78 (~P5(x2301,a4)),
% 0.64/0.78 inference(rename_variables,[],[60])).
% 0.64/0.78 cnf(244,plain,
% 0.64/0.78 (P5(f23(f23(a1,a1),f23(a1,f23(a1,a1))),f6(a17,a17))),
% 0.64/0.78 inference(scs_inference,[],[59,48,153,47,60,147,150,157,165,230,43,44,45,56,57,51,61,139,142,161,2,67,71,74,98,127,126,33,32,31,30,3,87,86,65,64,72,125,121,99,84,83,80,79,75,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,109,102,69,111,110,112,107,29,28,78,73,76,122,82,130,105])).
% 0.64/0.78 cnf(290,plain,
% 0.64/0.78 ($false),
% 0.64/0.78 inference(scs_inference,[],[60,43,51,213,244,159,104,76,87,82,105,67]),
% 0.64/0.78 ['proof']).
% 0.64/0.78 % SZS output end Proof
% 0.64/0.78 % Total time :0.160000s
%------------------------------------------------------------------------------