TSTP Solution File: SET063-7 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET063-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n019.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 14:28:21 EDT 2023
% Result : Unsatisfiable 0.19s 0.67s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET063-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:35:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 % File :CSE---1.6
% 0.19/0.67 % Problem :theBenchmark
% 0.19/0.67 % Transform :cnf
% 0.19/0.67 % Format :tptp:raw
% 0.19/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.67
% 0.19/0.67 % Result :Theorem 0.010000s
% 0.19/0.67 % Output :CNFRefutation 0.010000s
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 %--------------------------------------------------------------------------
% 0.19/0.67 % File : SET063-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.19/0.67 % Domain : Set Theory
% 0.19/0.67 % Problem : If X is a subset of the empty set, then X is the empty set
% 0.19/0.67 % Version : [Qua92] axioms : Augmented.
% 0.19/0.67 % English :
% 0.19/0.67
% 0.19/0.67 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.19/0.67 % Source : [Quaife]
% 0.19/0.67 % Names : SP3 cor. [Qua92]
% 0.19/0.67
% 0.19/0.67 % Status : Unsatisfiable
% 0.19/0.67 % Rating : 0.14 v8.1.0, 0.16 v7.4.0, 0.18 v7.3.0, 0.08 v7.0.0, 0.07 v6.4.0, 0.13 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, 0.11 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.21 v4.1.0, 0.23 v4.0.1, 0.36 v3.7.0, 0.30 v3.5.0, 0.27 v3.4.0, 0.17 v3.3.0, 0.07 v3.2.0, 0.00 v2.1.0
% 0.19/0.67 % Syntax : Number of clauses : 106 ( 35 unt; 11 nHn; 74 RR)
% 0.19/0.67 % Number of literals : 210 ( 44 equ; 97 neg)
% 0.19/0.67 % Maximal clause size : 5 ( 1 avg)
% 0.19/0.67 % Maximal term depth : 6 ( 1 avg)
% 0.19/0.67 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.19/0.67 % Number of functors : 39 ( 39 usr; 9 con; 0-3 aty)
% 0.19/0.67 % Number of variables : 208 ( 38 sgn)
% 0.19/0.67 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.19/0.67
% 0.19/0.67 % Comments : Preceding lemmas are added.
% 0.19/0.67 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.19/0.67 %--------------------------------------------------------------------------
% 0.19/0.67 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.19/0.67 include('Axioms/SET004-0.ax').
% 0.19/0.67 %--------------------------------------------------------------------------
% 0.19/0.67 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.19/0.67 cnf(corollary_1_to_unordered_pair,axiom,
% 0.19/0.67 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.19/0.67 | member(X,unordered_pair(X,Y)) ) ).
% 0.19/0.67
% 0.19/0.67 cnf(corollary_2_to_unordered_pair,axiom,
% 0.19/0.67 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.19/0.67 | member(Y,unordered_pair(X,Y)) ) ).
% 0.19/0.67
% 0.19/0.67 %----Corollaries to Cartesian product axiom.
% 0.19/0.67 cnf(corollary_1_to_cartesian_product,axiom,
% 0.19/0.67 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.19/0.67 | member(U,universal_class) ) ).
% 0.19/0.67
% 0.19/0.67 cnf(corollary_2_to_cartesian_product,axiom,
% 0.19/0.67 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.19/0.67 | member(V,universal_class) ) ).
% 0.19/0.67
% 0.19/0.67 %---- PARTIAL ORDER.
% 0.19/0.67 %----(PO1): reflexive.
% 0.19/0.67 cnf(subclass_is_reflexive,axiom,
% 0.19/0.67 subclass(X,X) ).
% 0.19/0.67
% 0.19/0.67 %----(PO2): antisymmetry is part of A-3.
% 0.19/0.67 %----(x < y), (y < x) --> (x = y).
% 0.19/0.67
% 0.19/0.67 %----(PO3): transitivity.
% 0.19/0.67 cnf(transitivity_of_subclass,axiom,
% 0.19/0.67 ( ~ subclass(X,Y)
% 0.19/0.67 | ~ subclass(Y,Z)
% 0.19/0.67 | subclass(X,Z) ) ).
% 0.19/0.67
% 0.19/0.67 %---- EQUALITY.
% 0.19/0.67 %----(EQ1): equality axiom.
% 0.19/0.67 %----a:x:(x = x).
% 0.19/0.67 %----This is always an axiom in the TPTP presentation.
% 0.19/0.67
% 0.19/0.67 %----(EQ2): expanded equality definition.
% 0.19/0.67 cnf(equality1,axiom,
% 0.19/0.67 ( X = Y
% 0.19/0.67 | member(not_subclass_element(X,Y),X)
% 0.19/0.67 | member(not_subclass_element(Y,X),Y) ) ).
% 0.19/0.67
% 0.19/0.67 cnf(equality2,axiom,
% 0.19/0.67 ( ~ member(not_subclass_element(X,Y),Y)
% 0.19/0.67 | X = Y
% 0.19/0.67 | member(not_subclass_element(Y,X),Y) ) ).
% 0.19/0.67
% 0.19/0.67 cnf(equality3,axiom,
% 0.19/0.67 ( ~ member(not_subclass_element(Y,X),X)
% 0.19/0.67 | X = Y
% 0.19/0.67 | member(not_subclass_element(X,Y),X) ) ).
% 0.19/0.67
% 0.19/0.67 cnf(equality4,axiom,
% 0.19/0.67 ( ~ member(not_subclass_element(X,Y),Y)
% 0.19/0.67 | ~ member(not_subclass_element(Y,X),X)
% 0.19/0.67 | X = Y ) ).
% 0.19/0.67
% 0.19/0.67 %---- SPECIAL CLASSES.
% 0.19/0.67 %----(SP1): lemma.
% 0.19/0.67 cnf(special_classes_lemma,axiom,
% 0.19/0.67 ~ member(Y,intersection(complement(X),X)) ).
% 0.19/0.67
% 0.19/0.67 %----(SP2): Existence of O (null class).
% 0.19/0.67 %----e:x:a:z:(-(z e x)).
% 0.19/0.67 cnf(existence_of_null_class,axiom,
% 0.19/0.67 ~ member(Z,null_class) ).
% 0.19/0.67
% 0.19/0.67 %----(SP3): O is a subclass of every class.
% 0.19/0.67 cnf(null_class_is_subclass,axiom,
% 0.19/0.67 subclass(null_class,X) ).
% 0.19/0.67
% 0.19/0.67 cnf(prove_corollary_of_null_class_is_subclass_1,negated_conjecture,
% 0.19/0.67 subclass(x,null_class) ).
% 0.19/0.67
% 0.19/0.67 cnf(prove_corollary_of_null_class_is_subclass_2,negated_conjecture,
% 0.19/0.67 x != null_class ).
% 0.19/0.67
% 0.19/0.67 %--------------------------------------------------------------------------
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 % Proof found
% 0.19/0.67 % SZS status Theorem for theBenchmark
% 0.19/0.67 % SZS output start Proof
% 0.19/0.67 %ClaNum:133(EqnAxiom:42)
% 0.19/0.67 %VarNum:791(SingletonVarNum:180)
% 0.19/0.67 %MaxLitNum:5
% 0.19/0.67 %MaxfuncDepth:24
% 0.19/0.67 %SharedTerms:32
% 0.19/0.67 %goalClause: 45 60
% 0.19/0.67 %singleGoalClaCount:2
% 0.19/0.67 [43]P1(a1)
% 0.19/0.67 [44]P2(a2)
% 0.19/0.67 [45]P5(a17,a4)
% 0.19/0.67 [46]P6(a1,a18)
% 0.19/0.67 [60]~E(a17,a4)
% 0.19/0.67 [50]P5(a5,f6(a18,a18))
% 0.19/0.67 [51]P5(a19,f6(a18,a18))
% 0.19/0.67 [57]E(f10(f9(f11(f6(a22,a18))),a22),a13)
% 0.19/0.67 [58]E(f10(f6(a18,a18),f10(f6(a18,a18),f8(f7(f8(a5),f9(f11(f6(a5,a18))))))),a22)
% 0.19/0.67 [47]P5(x471,a18)
% 0.19/0.67 [48]P5(a4,x481)
% 0.19/0.67 [49]P5(x491,x491)
% 0.19/0.67 [61]~P6(x611,a4)
% 0.19/0.67 [55]P5(f20(x551),f6(f6(a18,a18),a18))
% 0.19/0.67 [56]P5(f11(x561),f6(f6(a18,a18),a18))
% 0.19/0.67 [59]E(f10(f9(x591),f8(f9(f10(f7(f9(f11(f6(a5,a18))),x591),a13)))),f3(x591))
% 0.19/0.67 [52]P6(f24(x521,x522),a18)
% 0.19/0.67 [53]P5(f7(x531,x532),f6(a18,a18))
% 0.19/0.67 [62]~P6(x621,f10(f8(x622),x622))
% 0.19/0.67 [54]E(f10(f6(x541,x542),x543),f10(x543,f6(x541,x542)))
% 0.19/0.67 [63]~P7(x631)+P2(x631)
% 0.19/0.67 [64]~P8(x641)+P2(x641)
% 0.19/0.67 [67]~P1(x671)+P5(a1,x671)
% 0.19/0.67 [68]~P1(x681)+P6(a4,x681)
% 0.19/0.67 [70]P6(f21(x701),x701)+E(x701,a4)
% 0.19/0.67 [71]~P2(x711)+P5(x711,f6(a18,a18))
% 0.19/0.67 [69]E(x691,a4)+E(f10(x691,f21(x691)),a4)
% 0.19/0.67 [80]~P8(x801)+E(f6(f9(f9(x801)),f9(f9(x801))),f9(x801))
% 0.19/0.67 [93]~P7(x931)+P2(f9(f11(f6(x931,a18))))
% 0.19/0.67 [98]~P6(x981,a18)+P6(f9(f10(a5,f6(a18,x981))),a18)
% 0.19/0.67 [100]~P9(x1001)+P5(f7(x1001,f9(f11(f6(x1001,a18)))),a13)
% 0.19/0.67 [101]~P2(x1011)+P5(f7(x1011,f9(f11(f6(x1011,a18)))),a13)
% 0.19/0.67 [102]~P8(x1021)+P5(f9(f9(f11(f6(x1021,a18)))),f9(f9(x1021)))
% 0.19/0.67 [107]P9(x1071)+~P5(f7(x1071,f9(f11(f6(x1071,a18)))),a13)
% 0.19/0.67 [120]~P1(x1201)+P5(f9(f9(f11(f6(f10(a19,f6(x1201,a18)),a18)))),x1201)
% 0.19/0.67 [124]~P6(x1241,a18)+P6(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1241),a18)),a18))))),a18)
% 0.19/0.67 [65]~E(x652,x651)+P5(x651,x652)
% 0.19/0.67 [66]~E(x661,x662)+P5(x661,x662)
% 0.19/0.67 [73]P5(x731,x732)+P6(f14(x731,x732),x731)
% 0.19/0.67 [74]~P6(x741,x742)+~P6(x741,f8(x742))
% 0.19/0.67 [78]~P6(x781,a18)+P6(x781,f24(x782,x781))
% 0.19/0.67 [79]~P6(x791,a18)+P6(x791,f24(x791,x792))
% 0.19/0.67 [84]P5(x841,x842)+~P6(f14(x841,x842),x842)
% 0.19/0.67 [97]~P6(x972,f9(x971))+~E(f10(x971,f6(f24(x972,x972),a18)),a4)
% 0.19/0.67 [106]P6(x1061,x1062)+~P6(f24(f24(x1061,x1061),f24(x1061,f24(x1062,x1062))),a5)
% 0.19/0.67 [117]~P6(f24(f24(x1171,x1171),f24(x1171,f24(x1172,x1172))),a19)+E(f8(f10(f8(x1171),f8(f24(x1171,x1171)))),x1172)
% 0.19/0.67 [87]P2(x871)+~P3(x871,x872,x873)
% 0.19/0.67 [88]P8(x881)+~P4(x882,x883,x881)
% 0.19/0.67 [89]P8(x891)+~P4(x892,x891,x893)
% 0.19/0.67 [96]~P4(x961,x962,x963)+P3(x961,x962,x963)
% 0.19/0.67 [82]P6(x821,x822)+~P6(x821,f10(x823,x822))
% 0.19/0.67 [83]P6(x831,x832)+~P6(x831,f10(x832,x833))
% 0.19/0.67 [90]~P3(x902,x901,x903)+E(f9(f9(x901)),f9(x902))
% 0.19/0.67 [103]~P6(x1031,f6(x1032,x1033))+E(f24(f24(f12(x1031),f12(x1031)),f24(f12(x1031),f24(f23(x1031),f23(x1031)))),x1031)
% 0.19/0.67 [105]~P3(x1051,x1053,x1052)+P5(f9(f9(f11(f6(x1051,a18)))),f9(f9(x1052)))
% 0.19/0.67 [108]P6(x1081,a18)+~P6(f24(f24(x1082,x1082),f24(x1082,f24(x1081,x1081))),f6(x1083,x1084))
% 0.19/0.67 [109]P6(x1091,a18)+~P6(f24(f24(x1091,x1091),f24(x1091,f24(x1092,x1092))),f6(x1093,x1094))
% 0.19/0.67 [110]P6(x1101,x1102)+~P6(f24(f24(x1103,x1103),f24(x1103,f24(x1101,x1101))),f6(x1104,x1102))
% 0.19/0.67 [111]P6(x1111,x1112)+~P6(f24(f24(x1111,x1111),f24(x1111,f24(x1113,x1113))),f6(x1112,x1114))
% 0.19/0.67 [113]P6(x1131,f24(x1132,x1131))+~P6(f24(f24(x1132,x1132),f24(x1132,f24(x1131,x1131))),f6(x1133,x1134))
% 0.19/0.67 [114]P6(x1141,f24(x1141,x1142))+~P6(f24(f24(x1141,x1141),f24(x1141,f24(x1142,x1142))),f6(x1143,x1144))
% 0.19/0.67 [125]~P6(f24(f24(f24(f24(x1253,x1253),f24(x1253,f24(x1251,x1251))),f24(f24(x1253,x1253),f24(x1253,f24(x1251,x1251)))),f24(f24(f24(x1253,x1253),f24(x1253,f24(x1251,x1251))),f24(x1252,x1252))),f20(x1254))+P6(f24(f24(f24(f24(x1251,x1251),f24(x1251,f24(x1252,x1252))),f24(f24(x1251,x1251),f24(x1251,f24(x1252,x1252)))),f24(f24(f24(x1251,x1251),f24(x1251,f24(x1252,x1252))),f24(x1253,x1253))),x1254)
% 0.19/0.67 [126]~P6(f24(f24(f24(f24(x1262,x1262),f24(x1262,f24(x1261,x1261))),f24(f24(x1262,x1262),f24(x1262,f24(x1261,x1261)))),f24(f24(f24(x1262,x1262),f24(x1262,f24(x1261,x1261))),f24(x1263,x1263))),f11(x1264))+P6(f24(f24(f24(f24(x1261,x1261),f24(x1261,f24(x1262,x1262))),f24(f24(x1261,x1261),f24(x1261,f24(x1262,x1262)))),f24(f24(f24(x1261,x1261),f24(x1261,f24(x1262,x1262))),f24(x1263,x1263))),x1264)
% 0.19/0.67 [130]~P6(f24(f24(x1304,x1304),f24(x1304,f24(x1301,x1301))),f7(x1302,x1303))+P6(x1301,f9(f9(f11(f6(f10(x1302,f6(f9(f9(f11(f6(f10(x1303,f6(f24(x1304,x1304),a18)),a18)))),a18)),a18)))))
% 0.19/0.68 [99]~P2(x991)+P7(x991)+~P2(f9(f11(f6(x991,a18))))
% 0.19/0.68 [112]P2(x1121)+~P5(x1121,f6(a18,a18))+~P5(f7(x1121,f9(f11(f6(x1121,a18)))),a13)
% 0.19/0.68 [122]P1(x1221)+~P6(a4,x1221)+~P5(f9(f9(f11(f6(f10(a19,f6(x1221,a18)),a18)))),x1221)
% 0.19/0.68 [129]~P6(x1291,a18)+E(x1291,a4)+P6(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(a2,f6(f24(x1291,x1291),a18)),a18))))))),x1291)
% 0.19/0.68 [72]~P5(x722,x721)+~P5(x721,x722)+E(x721,x722)
% 0.19/0.68 [75]P6(x751,x752)+P6(x751,f8(x752))+~P6(x751,a18)
% 0.19/0.68 [85]E(x851,x852)+P6(f14(x852,x851),x852)+P6(f14(x851,x852),x851)
% 0.19/0.68 [92]E(x921,x922)+P6(f14(x922,x921),x922)+~P6(f14(x921,x922),x922)
% 0.19/0.68 [94]E(x941,x942)+~P6(f14(x942,x941),x941)+~P6(f14(x941,x942),x942)
% 0.19/0.68 [95]P6(x952,f9(x951))+~P6(x952,a18)+E(f10(x951,f6(f24(x952,x952),a18)),a4)
% 0.19/0.68 [118]~P6(x1181,x1182)+~P6(f24(f24(x1181,x1181),f24(x1181,f24(x1182,x1182))),f6(a18,a18))+P6(f24(f24(x1181,x1181),f24(x1181,f24(x1182,x1182))),a5)
% 0.19/0.68 [119]~P6(f24(f24(x1191,x1191),f24(x1191,f24(x1192,x1192))),f6(a18,a18))+~E(f8(f10(f8(x1191),f8(f24(x1191,x1191)))),x1192)+P6(f24(f24(x1191,x1191),f24(x1191,f24(x1192,x1192))),a19)
% 0.19/0.68 [121]~P2(x1211)+~P6(x1212,a18)+P6(f9(f9(f11(f6(f10(x1211,f6(x1212,a18)),a18)))),a18)
% 0.19/0.68 [76]~P5(x761,x763)+P5(x761,x762)+~P5(x763,x762)
% 0.19/0.68 [77]~P6(x771,x773)+P6(x771,x772)+~P5(x773,x772)
% 0.19/0.68 [81]E(x811,x812)+E(x811,x813)+~P6(x811,f24(x813,x812))
% 0.19/0.68 [86]~P6(x861,x863)+~P6(x861,x862)+P6(x861,f10(x862,x863))
% 0.19/0.68 [104]~P6(x1042,x1044)+~P6(x1041,x1043)+P6(f24(f24(x1041,x1041),f24(x1041,f24(x1042,x1042))),f6(x1043,x1044))
% 0.19/0.68 [127]~P6(f24(f24(f24(f24(x1272,x1272),f24(x1272,f24(x1273,x1273))),f24(f24(x1272,x1272),f24(x1272,f24(x1273,x1273)))),f24(f24(f24(x1272,x1272),f24(x1272,f24(x1273,x1273))),f24(x1271,x1271))),x1274)+P6(f24(f24(f24(f24(x1271,x1271),f24(x1271,f24(x1272,x1272))),f24(f24(x1271,x1271),f24(x1271,f24(x1272,x1272)))),f24(f24(f24(x1271,x1271),f24(x1271,f24(x1272,x1272))),f24(x1273,x1273))),f20(x1274))+~P6(f24(f24(f24(f24(x1271,x1271),f24(x1271,f24(x1272,x1272))),f24(f24(x1271,x1271),f24(x1271,f24(x1272,x1272)))),f24(f24(f24(x1271,x1271),f24(x1271,f24(x1272,x1272))),f24(x1273,x1273))),f6(f6(a18,a18),a18))
% 0.19/0.68 [128]~P6(f24(f24(f24(f24(x1282,x1282),f24(x1282,f24(x1281,x1281))),f24(f24(x1282,x1282),f24(x1282,f24(x1281,x1281)))),f24(f24(f24(x1282,x1282),f24(x1282,f24(x1281,x1281))),f24(x1283,x1283))),x1284)+P6(f24(f24(f24(f24(x1281,x1281),f24(x1281,f24(x1282,x1282))),f24(f24(x1281,x1281),f24(x1281,f24(x1282,x1282)))),f24(f24(f24(x1281,x1281),f24(x1281,f24(x1282,x1282))),f24(x1283,x1283))),f11(x1284))+~P6(f24(f24(f24(f24(x1281,x1281),f24(x1281,f24(x1282,x1282))),f24(f24(x1281,x1281),f24(x1281,f24(x1282,x1282)))),f24(f24(f24(x1281,x1281),f24(x1281,f24(x1282,x1282))),f24(x1283,x1283))),f6(f6(a18,a18),a18))
% 0.19/0.68 [131]P6(f24(f24(x1311,x1311),f24(x1311,f24(x1312,x1312))),f7(x1313,x1314))+~P6(f24(f24(x1311,x1311),f24(x1311,f24(x1312,x1312))),f6(a18,a18))+~P6(x1312,f9(f9(f11(f6(f10(x1313,f6(f9(f9(f11(f6(f10(x1314,f6(f24(x1311,x1311),a18)),a18)))),a18)),a18)))))
% 0.19/0.68 [132]~P4(x1322,x1325,x1321)+~P6(f24(f24(x1323,x1323),f24(x1323,f24(x1324,x1324))),f9(x1325))+E(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1321,f6(f24(f24(f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1323,x1323),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1323,x1323),a18)),a18)))))))),f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1323,x1323),a18)),a18))))))),f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1324,x1324),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1324,x1324),a18)),a18)))))))))),f24(f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1323,x1323),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1323,x1323),a18)),a18)))))))),f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1323,x1323),a18)),a18))))))),f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1324,x1324),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(x1324,x1324),a18)),a18))))))))))),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1322,f6(f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1325,f6(f24(f24(f24(x1323,x1323),f24(x1323,f24(x1324,x1324))),f24(f24(x1323,x1323),f24(x1323,f24(x1324,x1324)))),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1325,f6(f24(f24(f24(x1323,x1323),f24(x1323,f24(x1324,x1324))),f24(f24(x1323,x1323),f24(x1323,f24(x1324,x1324)))),a18)),a18)))))))),a18)),a18))))))))
% 0.19/0.68 [116]~P2(x1161)+P8(x1161)+~E(f6(f9(f9(x1161)),f9(f9(x1161))),f9(x1161))+~P5(f9(f9(f11(f6(x1161,a18)))),f9(f9(x1161)))
% 0.19/0.68 [115]~P2(x1151)+P3(x1151,x1152,x1153)+~E(f9(f9(x1152)),f9(x1151))+~P5(f9(f9(f11(f6(x1151,a18)))),f9(f9(x1153)))
% 0.19/0.68 [123]~P8(x1233)+~P8(x1232)+~P3(x1231,x1232,x1233)+P4(x1231,x1232,x1233)+P6(f24(f24(f15(x1231,x1232,x1233),f15(x1231,x1232,x1233)),f24(f15(x1231,x1232,x1233),f24(f16(x1231,x1232,x1233),f16(x1231,x1232,x1233)))),f9(x1232))
% 0.19/0.68 [133]~P8(x1333)+~P8(x1332)+~P3(x1331,x1332,x1333)+P4(x1331,x1332,x1333)+~E(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1333,f6(f24(f24(f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),a18)),a18)))))))),f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),a18)),a18))))))),f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f16(x1331,x1332,x1333),f16(x1331,x1332,x1333)),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f16(x1331,x1332,x1333),f16(x1331,x1332,x1333)),a18)),a18)))))))))),f24(f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),a18)),a18)))))))),f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),a18)),a18))))))),f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f16(x1331,x1332,x1333),f16(x1331,x1332,x1333)),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f16(x1331,x1332,x1333),f16(x1331,x1332,x1333)),a18)),a18))))))))))),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1331,f6(f24(f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1332,f6(f24(f24(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),f24(f15(x1331,x1332,x1333),f24(f16(x1331,x1332,x1333),f16(x1331,x1332,x1333)))),f24(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),f24(f15(x1331,x1332,x1333),f24(f16(x1331,x1332,x1333),f16(x1331,x1332,x1333))))),a18)),a18))))))),f9(f10(a5,f6(a18,f9(f9(f11(f6(f10(x1332,f6(f24(f24(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),f24(f15(x1331,x1332,x1333),f24(f16(x1331,x1332,x1333),f16(x1331,x1332,x1333)))),f24(f24(f15(x1331,x1332,x1333),f15(x1331,x1332,x1333)),f24(f15(x1331,x1332,x1333),f24(f16(x1331,x1332,x1333),f16(x1331,x1332,x1333))))),a18)),a18)))))))),a18)),a18))))))))
% 0.19/0.68 %EqnAxiom
% 0.19/0.68 [1]E(x11,x11)
% 0.19/0.68 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.68 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.19/0.68 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.19/0.68 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.19/0.68 [7]~E(x71,x72)+E(f24(x71,x73),f24(x72,x73))
% 0.19/0.68 [8]~E(x81,x82)+E(f24(x83,x81),f24(x83,x82))
% 0.19/0.68 [9]~E(x91,x92)+E(f7(x91,x93),f7(x92,x93))
% 0.19/0.68 [10]~E(x101,x102)+E(f7(x103,x101),f7(x103,x102))
% 0.19/0.68 [11]~E(x111,x112)+E(f10(x111,x113),f10(x112,x113))
% 0.19/0.68 [12]~E(x121,x122)+E(f10(x123,x121),f10(x123,x122))
% 0.19/0.68 [13]~E(x131,x132)+E(f11(x131),f11(x132))
% 0.19/0.68 [14]~E(x141,x142)+E(f16(x141,x143,x144),f16(x142,x143,x144))
% 0.19/0.68 [15]~E(x151,x152)+E(f16(x153,x151,x154),f16(x153,x152,x154))
% 0.19/0.68 [16]~E(x161,x162)+E(f16(x163,x164,x161),f16(x163,x164,x162))
% 0.19/0.68 [17]~E(x171,x172)+E(f15(x171,x173,x174),f15(x172,x173,x174))
% 0.19/0.68 [18]~E(x181,x182)+E(f15(x183,x181,x184),f15(x183,x182,x184))
% 0.19/0.68 [19]~E(x191,x192)+E(f15(x193,x194,x191),f15(x193,x194,x192))
% 0.19/0.68 [20]~E(x201,x202)+E(f8(x201),f8(x202))
% 0.19/0.68 [21]~E(x211,x212)+E(f20(x211),f20(x212))
% 0.19/0.68 [22]~E(x221,x222)+E(f14(x221,x223),f14(x222,x223))
% 0.19/0.68 [23]~E(x231,x232)+E(f14(x233,x231),f14(x233,x232))
% 0.19/0.68 [24]~E(x241,x242)+E(f23(x241),f23(x242))
% 0.19/0.68 [25]~E(x251,x252)+E(f12(x251),f12(x252))
% 0.19/0.68 [26]~E(x261,x262)+E(f3(x261),f3(x262))
% 0.19/0.68 [27]~E(x271,x272)+E(f21(x271),f21(x272))
% 0.19/0.68 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.19/0.68 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.19/0.68 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.19/0.68 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.19/0.68 [32]P6(x322,x323)+~E(x321,x322)+~P6(x321,x323)
% 0.19/0.68 [33]P6(x333,x332)+~E(x331,x332)+~P6(x333,x331)
% 0.19/0.68 [34]~P8(x341)+P8(x342)+~E(x341,x342)
% 0.19/0.68 [35]P3(x352,x353,x354)+~E(x351,x352)+~P3(x351,x353,x354)
% 0.19/0.68 [36]P3(x363,x362,x364)+~E(x361,x362)+~P3(x363,x361,x364)
% 0.19/0.68 [37]P3(x373,x374,x372)+~E(x371,x372)+~P3(x373,x374,x371)
% 0.19/0.68 [38]~P9(x381)+P9(x382)+~E(x381,x382)
% 0.19/0.68 [39]P4(x392,x393,x394)+~E(x391,x392)+~P4(x391,x393,x394)
% 0.19/0.68 [40]P4(x403,x402,x404)+~E(x401,x402)+~P4(x403,x401,x404)
% 0.19/0.68 [41]P4(x413,x414,x412)+~E(x411,x412)+~P4(x413,x414,x411)
% 0.19/0.68 [42]~P7(x421)+P7(x422)+~E(x421,x422)
% 0.19/0.68
% 0.19/0.68 %-------------------------------------------
% 0.19/0.68 cnf(136,plain,
% 0.19/0.68 (~P6(x1361,a4)),
% 0.19/0.68 inference(rename_variables,[],[61])).
% 0.19/0.68 cnf(144,plain,
% 0.19/0.68 (~P6(x1441,a4)),
% 0.19/0.68 inference(rename_variables,[],[61])).
% 0.19/0.68 cnf(147,plain,
% 0.19/0.68 (~P6(x1471,a4)),
% 0.19/0.68 inference(rename_variables,[],[61])).
% 0.19/0.68 cnf(150,plain,
% 0.19/0.68 (~P6(x1501,a4)),
% 0.19/0.68 inference(rename_variables,[],[61])).
% 0.19/0.68 cnf(152,plain,
% 0.19/0.68 (P5(x1521,x1521)),
% 0.19/0.68 inference(rename_variables,[],[49])).
% 0.19/0.68 cnf(155,plain,
% 0.19/0.68 ($false),
% 0.19/0.68 inference(scs_inference,[],[45,49,152,61,136,144,147,150,60,46,57,62,2,68,70,73,126,125,33,31,30,77]),
% 0.19/0.68 ['proof']).
% 0.19/0.68 % SZS output end Proof
% 0.19/0.68 % Total time :0.010000s
%------------------------------------------------------------------------------