TSTP Solution File: SET024-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET024-7 : 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 : n025.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 14:27:59 EDT 2023
% Result : Unsatisfiable 0.18s 0.63s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET024-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n025.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 : Sat Aug 26 11:38:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.54 start to proof:theBenchmark
% 0.18/0.63 %-------------------------------------------
% 0.18/0.63 % File :CSE---1.6
% 0.18/0.63 % Problem :theBenchmark
% 0.18/0.63 % Transform :cnf
% 0.18/0.63 % Format :tptp:raw
% 0.18/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.63
% 0.18/0.63 % Result :Theorem 0.010000s
% 0.18/0.63 % Output :CNFRefutation 0.010000s
% 0.18/0.63 %-------------------------------------------
% 0.18/0.63 %--------------------------------------------------------------------------
% 0.18/0.63 % File : SET024-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.18/0.63 % Domain : Set Theory
% 0.18/0.63 % Problem : A set belongs to its singleton
% 0.18/0.63 % Version : [Qua92] axioms : Augmented.
% 0.18/0.63 % English :
% 0.18/0.63
% 0.18/0.63 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.18/0.63 % Source : [Quaife]
% 0.18/0.63 % Names : SS2 [Qua92]
% 0.18/0.63
% 0.18/0.63 % Status : Unsatisfiable
% 0.18/0.63 % Rating : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.20 v6.4.0, 0.13 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.00 v5.5.0, 0.10 v5.4.0, 0.15 v5.3.0, 0.06 v5.0.0, 0.14 v4.1.0, 0.15 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, 0.08 v2.6.0, 0.00 v2.5.0, 0.09 v2.4.0, 0.00 v2.1.0
% 0.18/0.63 % Syntax : Number of clauses : 123 ( 41 unt; 15 nHn; 82 RR)
% 0.18/0.63 % Number of literals : 242 ( 56 equ; 110 neg)
% 0.18/0.63 % Maximal clause size : 5 ( 1 avg)
% 0.18/0.63 % Maximal term depth : 6 ( 1 avg)
% 0.18/0.63 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.18/0.63 % Number of functors : 39 ( 39 usr; 9 con; 0-3 aty)
% 0.18/0.63 % Number of variables : 242 ( 46 sgn)
% 0.18/0.63 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.18/0.63
% 0.18/0.63 % Comments : Preceding lemmas are added.
% 0.18/0.63 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.18/0.63 %--------------------------------------------------------------------------
% 0.18/0.63 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.18/0.63 include('Axioms/SET004-0.ax').
% 0.18/0.63 %--------------------------------------------------------------------------
% 0.18/0.63 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.18/0.63 cnf(corollary_1_to_unordered_pair,axiom,
% 0.18/0.63 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.18/0.63 | member(X,unordered_pair(X,Y)) ) ).
% 0.18/0.63
% 0.18/0.63 cnf(corollary_2_to_unordered_pair,axiom,
% 0.18/0.63 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.18/0.63 | member(Y,unordered_pair(X,Y)) ) ).
% 0.18/0.63
% 0.18/0.63 %----Corollaries to Cartesian product axiom.
% 0.18/0.63 cnf(corollary_1_to_cartesian_product,axiom,
% 0.18/0.63 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.18/0.63 | member(U,universal_class) ) ).
% 0.18/0.63
% 0.18/0.63 cnf(corollary_2_to_cartesian_product,axiom,
% 0.18/0.63 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.18/0.63 | member(V,universal_class) ) ).
% 0.18/0.63
% 0.18/0.63 %---- PARTIAL ORDER.
% 0.18/0.63 %----(PO1): reflexive.
% 0.18/0.63 cnf(subclass_is_reflexive,axiom,
% 0.18/0.63 subclass(X,X) ).
% 0.18/0.63
% 0.18/0.63 %----(PO2): antisymmetry is part of A-3.
% 0.18/0.63 %----(x < y), (y < x) --> (x = y).
% 0.18/0.63
% 0.18/0.63 %----(PO3): transitivity.
% 0.18/0.63 cnf(transitivity_of_subclass,axiom,
% 0.18/0.63 ( ~ subclass(X,Y)
% 0.18/0.63 | ~ subclass(Y,Z)
% 0.18/0.63 | subclass(X,Z) ) ).
% 0.18/0.63
% 0.18/0.63 %---- EQUALITY.
% 0.18/0.63 %----(EQ1): equality axiom.
% 0.18/0.63 %----a:x:(x = x).
% 0.18/0.63 %----This is always an axiom in the TPTP presentation.
% 0.18/0.63
% 0.18/0.63 %----(EQ2): expanded equality definition.
% 0.18/0.63 cnf(equality1,axiom,
% 0.18/0.63 ( X = Y
% 0.18/0.63 | member(not_subclass_element(X,Y),X)
% 0.18/0.63 | member(not_subclass_element(Y,X),Y) ) ).
% 0.18/0.63
% 0.18/0.63 cnf(equality2,axiom,
% 0.18/0.63 ( ~ member(not_subclass_element(X,Y),Y)
% 0.18/0.63 | X = Y
% 0.18/0.63 | member(not_subclass_element(Y,X),Y) ) ).
% 0.18/0.63
% 0.18/0.63 cnf(equality3,axiom,
% 0.18/0.63 ( ~ member(not_subclass_element(Y,X),X)
% 0.18/0.63 | X = Y
% 0.18/0.63 | member(not_subclass_element(X,Y),X) ) ).
% 0.18/0.63
% 0.18/0.63 cnf(equality4,axiom,
% 0.18/0.63 ( ~ member(not_subclass_element(X,Y),Y)
% 0.18/0.63 | ~ member(not_subclass_element(Y,X),X)
% 0.18/0.63 | X = Y ) ).
% 0.18/0.63
% 0.18/0.63 %---- SPECIAL CLASSES.
% 0.18/0.63 %----(SP1): lemma.
% 0.18/0.63 cnf(special_classes_lemma,axiom,
% 0.18/0.63 ~ member(Y,intersection(complement(X),X)) ).
% 0.18/0.63
% 0.18/0.63 %----(SP2): Existence of O (null class).
% 0.18/0.63 %----e:x:a:z:(-(z e x)).
% 0.18/0.63 cnf(existence_of_null_class,axiom,
% 0.18/0.63 ~ member(Z,null_class) ).
% 0.18/0.63
% 0.18/0.63 %----(SP3): O is a subclass of every class.
% 0.18/0.63 cnf(null_class_is_subclass,axiom,
% 0.18/0.63 subclass(null_class,X) ).
% 0.18/0.63
% 0.18/0.63 %----corollary.
% 0.18/0.63 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.18/0.63 ( ~ subclass(X,null_class)
% 0.18/0.63 | X = null_class ) ).
% 0.18/0.63
% 0.18/0.63 %----(SP4): uniqueness of null class.
% 0.18/0.63 cnf(null_class_is_unique,axiom,
% 0.18/0.63 ( Z = null_class
% 0.18/0.63 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.18/0.63
% 0.18/0.63 %----(SP5): O is a set (follows from axiom of infinity).
% 0.18/0.63 cnf(null_class_is_a_set,axiom,
% 0.18/0.63 member(null_class,universal_class) ).
% 0.18/0.63
% 0.18/0.63 %---- UNORDERED PAIRS.
% 0.18/0.63 %----(UP1): unordered pair is commutative.
% 0.18/0.63 cnf(commutativity_of_unordered_pair,axiom,
% 0.18/0.63 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.18/0.63
% 0.18/0.63 %----(UP2): if one argument is a proper class, pair contains only the
% 0.18/0.63 %----other. In a slightly different form to the paper
% 0.18/0.63 cnf(singleton_in_unordered_pair1,axiom,
% 0.18/0.63 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.18/0.63
% 0.18/0.63 cnf(singleton_in_unordered_pair2,axiom,
% 0.18/0.63 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.18/0.63
% 0.18/0.63 cnf(unordered_pair_equals_singleton1,axiom,
% 0.18/0.63 ( member(Y,universal_class)
% 0.18/0.63 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.18/0.63
% 0.18/0.63 cnf(unordered_pair_equals_singleton2,axiom,
% 0.18/0.63 ( member(X,universal_class)
% 0.18/0.63 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.18/0.63
% 0.18/0.63 %----(UP3): if both arguments are proper classes, pair is null.
% 0.18/0.63 cnf(null_unordered_pair,axiom,
% 0.18/0.63 ( unordered_pair(X,Y) = null_class
% 0.18/0.63 | member(X,universal_class)
% 0.18/0.63 | member(Y,universal_class) ) ).
% 0.18/0.63
% 0.18/0.63 %----(UP4): left cancellation for unordered pairs.
% 0.18/0.63 cnf(left_cancellation,axiom,
% 0.18/0.63 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.18/0.63 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.18/0.63 | Y = Z ) ).
% 0.18/0.63
% 0.18/0.63 %----(UP5): right cancellation for unordered pairs.
% 0.18/0.63 cnf(right_cancellation,axiom,
% 0.18/0.63 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.18/0.63 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.18/0.63 | X = Y ) ).
% 0.18/0.63
% 0.18/0.63 %----(UP6): corollary to (A-4).
% 0.18/0.63 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.18/0.63 ( ~ member(X,universal_class)
% 0.18/0.63 | unordered_pair(X,Y) != null_class ) ).
% 0.18/0.63
% 0.18/0.63 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.18/0.63 ( ~ member(Y,universal_class)
% 0.18/0.63 | unordered_pair(X,Y) != null_class ) ).
% 0.18/0.63
% 0.18/0.63 %----corollary to instantiate variables.
% 0.18/0.63 %----Not in the paper
% 0.18/0.63 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.18/0.63 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.18/0.63 | unordered_pair(X,Y) != null_class ) ).
% 0.18/0.63
% 0.18/0.63 %----(UP7): if both members of a pair belong to a set, the pair
% 0.18/0.63 %----is a subset.
% 0.18/0.63 cnf(unordered_pair_is_subset,axiom,
% 0.18/0.63 ( ~ member(X,Z)
% 0.18/0.63 | ~ member(Y,Z)
% 0.18/0.63 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.18/0.63
% 0.18/0.63 %---- SINGLETONS.
% 0.18/0.63 %----(SS1): every singleton is a set.
% 0.18/0.63 cnf(singletons_are_sets,axiom,
% 0.18/0.63 member(singleton(X),universal_class) ).
% 0.18/0.63
% 0.18/0.63 %----corollary, not in the paper.
% 0.18/0.63 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.18/0.63 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.18/0.63
% 0.18/0.63 cnf(prove_set_in_its_singleton_1,negated_conjecture,
% 0.18/0.63 member(x,universal_class) ).
% 0.18/0.63
% 0.18/0.63 cnf(prove_set_in_its_singleton_2,negated_conjecture,
% 0.18/0.63 ~ member(x,singleton(x)) ).
% 0.18/0.63
% 0.18/0.63 %--------------------------------------------------------------------------
% 0.18/0.63 %-------------------------------------------
% 0.18/0.63 % Proof found
% 0.18/0.63 % SZS status Theorem for theBenchmark
% 0.18/0.63 % SZS output start Proof
% 0.18/0.63 %ClaNum:150(EqnAxiom:42)
% 0.18/0.63 %VarNum:871(SingletonVarNum:213)
% 0.18/0.63 %MaxLitNum:5
% 0.18/0.63 %MaxfuncDepth:24
% 0.18/0.63 %SharedTerms:34
% 0.18/0.63 %goalClause: 47 67
% 0.18/0.63 %singleGoalClaCount:2
% 0.18/0.63 [43]P1(a1)
% 0.18/0.63 [44]P2(a2)
% 0.18/0.63 [45]P5(a4,a17)
% 0.18/0.63 [46]P5(a1,a17)
% 0.18/0.63 [47]P5(a23,a17)
% 0.18/0.63 [52]P6(a5,f6(a17,a17))
% 0.18/0.63 [53]P6(a18,f6(a17,a17))
% 0.18/0.63 [67]~P5(a23,f24(a23,a23))
% 0.18/0.64 [62]E(f10(f9(f11(f6(a21,a17))),a21),a13)
% 0.18/0.64 [64]E(f10(f6(a17,a17),f10(f6(a17,a17),f8(f7(f8(a5),f9(f11(f6(a5,a17))))))),a21)
% 0.18/0.64 [48]P6(x481,a17)
% 0.18/0.64 [49]P6(a4,x491)
% 0.18/0.64 [50]P6(x501,x501)
% 0.18/0.64 [66]~P5(x661,a4)
% 0.18/0.64 [60]P6(f19(x601),f6(f6(a17,a17),a17))
% 0.18/0.64 [61]P6(f11(x611),f6(f6(a17,a17),a17))
% 0.18/0.64 [65]E(f10(f9(x651),f8(f9(f10(f7(f9(f11(f6(a5,a17))),x651),a13)))),f3(x651))
% 0.18/0.64 [51]E(f24(x511,x512),f24(x512,x511))
% 0.18/0.64 [54]P5(f24(x541,x542),a17)
% 0.18/0.64 [56]P6(f7(x561,x562),f6(a17,a17))
% 0.18/0.64 [57]P6(f24(x571,x571),f24(x572,x571))
% 0.18/0.64 [58]P6(f24(x581,x581),f24(x581,x582))
% 0.18/0.64 [63]P5(f24(x631,x631),f24(x632,f24(x631,x631)))
% 0.18/0.64 [68]~P5(x681,f10(f8(x682),x682))
% 0.18/0.64 [59]E(f10(f6(x591,x592),x593),f10(x593,f6(x591,x592)))
% 0.18/0.64 [69]~P7(x691)+P2(x691)
% 0.18/0.64 [70]~P8(x701)+P2(x701)
% 0.18/0.64 [73]~P1(x731)+P6(a1,x731)
% 0.18/0.64 [74]~P1(x741)+P5(a4,x741)
% 0.18/0.64 [75]~P6(x751,a4)+E(x751,a4)
% 0.18/0.64 [77]P5(f20(x771),x771)+E(x771,a4)
% 0.18/0.64 [78]E(x781,a4)+P5(f14(x781,a4),x781)
% 0.18/0.64 [82]~P2(x821)+P6(x821,f6(a17,a17))
% 0.18/0.64 [76]E(x761,a4)+E(f10(x761,f20(x761)),a4)
% 0.18/0.64 [93]~P8(x931)+E(f6(f9(f9(x931)),f9(f9(x931))),f9(x931))
% 0.18/0.64 [107]~P7(x1071)+P2(f9(f11(f6(x1071,a17))))
% 0.18/0.64 [112]~P5(x1121,a17)+P5(f9(f10(a5,f6(a17,x1121))),a17)
% 0.18/0.64 [114]~P9(x1141)+P6(f7(x1141,f9(f11(f6(x1141,a17)))),a13)
% 0.18/0.64 [115]~P2(x1151)+P6(f7(x1151,f9(f11(f6(x1151,a17)))),a13)
% 0.18/0.64 [116]~P8(x1161)+P6(f9(f9(f11(f6(x1161,a17)))),f9(f9(x1161)))
% 0.18/0.64 [121]P9(x1211)+~P6(f7(x1211,f9(f11(f6(x1211,a17)))),a13)
% 0.18/0.64 [137]~P1(x1371)+P6(f9(f9(f11(f6(f10(a18,f6(x1371,a17)),a17)))),x1371)
% 0.18/0.64 [141]~P5(x1411,a17)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1411),a17)),a17))))),a17)
% 0.18/0.64 [71]~E(x712,x711)+P6(x711,x712)
% 0.18/0.64 [72]~E(x721,x722)+P6(x721,x722)
% 0.18/0.64 [80]P5(x802,a17)+E(f24(x801,x802),f24(x801,x801))
% 0.18/0.64 [81]P5(x811,a17)+E(f24(x811,x812),f24(x812,x812))
% 0.18/0.64 [83]~P5(x832,a17)+~E(f24(x831,x832),a4)
% 0.18/0.64 [84]~P5(x841,a17)+~E(f24(x841,x842),a4)
% 0.18/0.64 [86]P6(x861,x862)+P5(f14(x861,x862),x861)
% 0.18/0.64 [87]~P5(x871,x872)+~P5(x871,f8(x872))
% 0.18/0.64 [91]~P5(x911,a17)+P5(x911,f24(x912,x911))
% 0.18/0.64 [92]~P5(x921,a17)+P5(x921,f24(x921,x922))
% 0.18/0.64 [97]P6(x971,x972)+~P5(f14(x971,x972),x972)
% 0.18/0.64 [111]~P5(x1112,f9(x1111))+~E(f10(x1111,f6(f24(x1112,x1112),a17)),a4)
% 0.18/0.64 [120]P5(x1201,x1202)+~P5(f24(f24(x1201,x1201),f24(x1201,f24(x1202,x1202))),a5)
% 0.18/0.64 [134]~P5(f24(f24(x1341,x1341),f24(x1341,f24(x1342,x1342))),a18)+E(f8(f10(f8(x1341),f8(f24(x1341,x1341)))),x1342)
% 0.18/0.64 [101]P2(x1011)+~P3(x1011,x1012,x1013)
% 0.18/0.64 [102]P8(x1021)+~P4(x1022,x1023,x1021)
% 0.18/0.64 [103]P8(x1031)+~P4(x1032,x1031,x1033)
% 0.18/0.64 [110]~P4(x1101,x1102,x1103)+P3(x1101,x1102,x1103)
% 0.18/0.64 [95]P5(x951,x952)+~P5(x951,f10(x953,x952))
% 0.18/0.64 [96]P5(x961,x962)+~P5(x961,f10(x962,x963))
% 0.18/0.64 [104]~P3(x1042,x1041,x1043)+E(f9(f9(x1041)),f9(x1042))
% 0.18/0.64 [117]~P5(x1171,f6(x1172,x1173))+E(f24(f24(f12(x1171),f12(x1171)),f24(f12(x1171),f24(f22(x1171),f22(x1171)))),x1171)
% 0.18/0.64 [119]~P3(x1191,x1193,x1192)+P6(f9(f9(f11(f6(x1191,a17)))),f9(f9(x1192)))
% 0.18/0.64 [122]P5(x1221,a17)+~P5(f24(f24(x1222,x1222),f24(x1222,f24(x1221,x1221))),f6(x1223,x1224))
% 0.18/0.64 [123]P5(x1231,a17)+~P5(f24(f24(x1231,x1231),f24(x1231,f24(x1232,x1232))),f6(x1233,x1234))
% 0.18/0.64 [124]P5(x1241,x1242)+~P5(f24(f24(x1243,x1243),f24(x1243,f24(x1241,x1241))),f6(x1244,x1242))
% 0.18/0.64 [125]P5(x1251,x1252)+~P5(f24(f24(x1251,x1251),f24(x1251,f24(x1253,x1253))),f6(x1252,x1254))
% 0.18/0.64 [126]~E(f24(x1261,x1262),a4)+~P5(f24(f24(x1261,x1261),f24(x1261,f24(x1262,x1262))),f6(x1263,x1264))
% 0.18/0.64 [130]P5(x1301,f24(x1302,x1301))+~P5(f24(f24(x1302,x1302),f24(x1302,f24(x1301,x1301))),f6(x1303,x1304))
% 0.18/0.64 [131]P5(x1311,f24(x1311,x1312))+~P5(f24(f24(x1311,x1311),f24(x1311,f24(x1312,x1312))),f6(x1313,x1314))
% 0.18/0.64 [142]~P5(f24(f24(f24(f24(x1423,x1423),f24(x1423,f24(x1421,x1421))),f24(f24(x1423,x1423),f24(x1423,f24(x1421,x1421)))),f24(f24(f24(x1423,x1423),f24(x1423,f24(x1421,x1421))),f24(x1422,x1422))),f19(x1424))+P5(f24(f24(f24(f24(x1421,x1421),f24(x1421,f24(x1422,x1422))),f24(f24(x1421,x1421),f24(x1421,f24(x1422,x1422)))),f24(f24(f24(x1421,x1421),f24(x1421,f24(x1422,x1422))),f24(x1423,x1423))),x1424)
% 0.18/0.64 [143]~P5(f24(f24(f24(f24(x1432,x1432),f24(x1432,f24(x1431,x1431))),f24(f24(x1432,x1432),f24(x1432,f24(x1431,x1431)))),f24(f24(f24(x1432,x1432),f24(x1432,f24(x1431,x1431))),f24(x1433,x1433))),f11(x1434))+P5(f24(f24(f24(f24(x1431,x1431),f24(x1431,f24(x1432,x1432))),f24(f24(x1431,x1431),f24(x1431,f24(x1432,x1432)))),f24(f24(f24(x1431,x1431),f24(x1431,f24(x1432,x1432))),f24(x1433,x1433))),x1434)
% 0.18/0.64 [147]~P5(f24(f24(x1474,x1474),f24(x1474,f24(x1471,x1471))),f7(x1472,x1473))+P5(x1471,f9(f9(f11(f6(f10(x1472,f6(f9(f9(f11(f6(f10(x1473,f6(f24(x1474,x1474),a17)),a17)))),a17)),a17)))))
% 0.18/0.64 [113]~P2(x1131)+P7(x1131)+~P2(f9(f11(f6(x1131,a17))))
% 0.18/0.64 [127]P2(x1271)+~P6(x1271,f6(a17,a17))+~P6(f7(x1271,f9(f11(f6(x1271,a17)))),a13)
% 0.18/0.64 [139]P1(x1391)+~P5(a4,x1391)+~P6(f9(f9(f11(f6(f10(a18,f6(x1391,a17)),a17)))),x1391)
% 0.18/0.64 [146]~P5(x1461,a17)+E(x1461,a4)+P5(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(a2,f6(f24(x1461,x1461),a17)),a17))))))),x1461)
% 0.18/0.64 [85]~P6(x852,x851)+~P6(x851,x852)+E(x851,x852)
% 0.18/0.64 [79]P5(x792,a17)+P5(x791,a17)+E(f24(x791,x792),a4)
% 0.18/0.64 [88]P5(x881,x882)+P5(x881,f8(x882))+~P5(x881,a17)
% 0.18/0.64 [98]E(x981,x982)+P5(f14(x982,x981),x982)+P5(f14(x981,x982),x981)
% 0.18/0.64 [106]E(x1061,x1062)+P5(f14(x1062,x1061),x1062)+~P5(f14(x1061,x1062),x1062)
% 0.18/0.64 [108]E(x1081,x1082)+~P5(f14(x1082,x1081),x1081)+~P5(f14(x1081,x1082),x1082)
% 0.18/0.64 [109]P5(x1092,f9(x1091))+~P5(x1092,a17)+E(f10(x1091,f6(f24(x1092,x1092),a17)),a4)
% 0.18/0.64 [135]~P5(x1351,x1352)+~P5(f24(f24(x1351,x1351),f24(x1351,f24(x1352,x1352))),f6(a17,a17))+P5(f24(f24(x1351,x1351),f24(x1351,f24(x1352,x1352))),a5)
% 0.18/0.64 [136]~P5(f24(f24(x1361,x1361),f24(x1361,f24(x1362,x1362))),f6(a17,a17))+~E(f8(f10(f8(x1361),f8(f24(x1361,x1361)))),x1362)+P5(f24(f24(x1361,x1361),f24(x1361,f24(x1362,x1362))),a18)
% 0.18/0.64 [138]~P2(x1381)+~P5(x1382,a17)+P5(f9(f9(f11(f6(f10(x1381,f6(x1382,a17)),a17)))),a17)
% 0.18/0.64 [89]~P6(x891,x893)+P6(x891,x892)+~P6(x893,x892)
% 0.18/0.64 [90]~P5(x901,x903)+P5(x901,x902)+~P6(x903,x902)
% 0.18/0.64 [94]E(x941,x942)+E(x941,x943)+~P5(x941,f24(x943,x942))
% 0.18/0.64 [99]~P5(x991,x993)+~P5(x991,x992)+P5(x991,f10(x992,x993))
% 0.18/0.64 [100]~P5(x1002,x1003)+~P5(x1001,x1003)+P6(f24(x1001,x1002),x1003)
% 0.18/0.64 [128]E(x1281,x1282)+~E(f24(x1283,x1281),f24(x1283,x1282))+~P5(f24(f24(x1281,x1281),f24(x1281,f24(x1282,x1282))),f6(a17,a17))
% 0.18/0.64 [129]E(x1291,x1292)+~E(f24(x1291,x1293),f24(x1292,x1293))+~P5(f24(f24(x1291,x1291),f24(x1291,f24(x1292,x1292))),f6(a17,a17))
% 0.18/0.64 [118]~P5(x1182,x1184)+~P5(x1181,x1183)+P5(f24(f24(x1181,x1181),f24(x1181,f24(x1182,x1182))),f6(x1183,x1184))
% 0.18/0.64 [144]~P5(f24(f24(f24(f24(x1442,x1442),f24(x1442,f24(x1443,x1443))),f24(f24(x1442,x1442),f24(x1442,f24(x1443,x1443)))),f24(f24(f24(x1442,x1442),f24(x1442,f24(x1443,x1443))),f24(x1441,x1441))),x1444)+P5(f24(f24(f24(f24(x1441,x1441),f24(x1441,f24(x1442,x1442))),f24(f24(x1441,x1441),f24(x1441,f24(x1442,x1442)))),f24(f24(f24(x1441,x1441),f24(x1441,f24(x1442,x1442))),f24(x1443,x1443))),f19(x1444))+~P5(f24(f24(f24(f24(x1441,x1441),f24(x1441,f24(x1442,x1442))),f24(f24(x1441,x1441),f24(x1441,f24(x1442,x1442)))),f24(f24(f24(x1441,x1441),f24(x1441,f24(x1442,x1442))),f24(x1443,x1443))),f6(f6(a17,a17),a17))
% 0.18/0.64 [145]~P5(f24(f24(f24(f24(x1452,x1452),f24(x1452,f24(x1451,x1451))),f24(f24(x1452,x1452),f24(x1452,f24(x1451,x1451)))),f24(f24(f24(x1452,x1452),f24(x1452,f24(x1451,x1451))),f24(x1453,x1453))),x1454)+P5(f24(f24(f24(f24(x1451,x1451),f24(x1451,f24(x1452,x1452))),f24(f24(x1451,x1451),f24(x1451,f24(x1452,x1452)))),f24(f24(f24(x1451,x1451),f24(x1451,f24(x1452,x1452))),f24(x1453,x1453))),f11(x1454))+~P5(f24(f24(f24(f24(x1451,x1451),f24(x1451,f24(x1452,x1452))),f24(f24(x1451,x1451),f24(x1451,f24(x1452,x1452)))),f24(f24(f24(x1451,x1451),f24(x1451,f24(x1452,x1452))),f24(x1453,x1453))),f6(f6(a17,a17),a17))
% 0.18/0.64 [148]P5(f24(f24(x1481,x1481),f24(x1481,f24(x1482,x1482))),f7(x1483,x1484))+~P5(f24(f24(x1481,x1481),f24(x1481,f24(x1482,x1482))),f6(a17,a17))+~P5(x1482,f9(f9(f11(f6(f10(x1483,f6(f9(f9(f11(f6(f10(x1484,f6(f24(x1481,x1481),a17)),a17)))),a17)),a17)))))
% 0.18/0.64 [149]~P4(x1492,x1495,x1491)+~P5(f24(f24(x1493,x1493),f24(x1493,f24(x1494,x1494))),f9(x1495))+E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1491,f6(f24(f24(f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1493,x1493),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1493,x1493),a17)),a17)))))))),f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1493,x1493),a17)),a17))))))),f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1494,x1494),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1494,x1494),a17)),a17)))))))))),f24(f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1493,x1493),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1493,x1493),a17)),a17)))))))),f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1493,x1493),a17)),a17))))))),f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1494,x1494),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(x1494,x1494),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1492,f6(f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1495,f6(f24(f24(f24(x1493,x1493),f24(x1493,f24(x1494,x1494))),f24(f24(x1493,x1493),f24(x1493,f24(x1494,x1494)))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1495,f6(f24(f24(f24(x1493,x1493),f24(x1493,f24(x1494,x1494))),f24(f24(x1493,x1493),f24(x1493,f24(x1494,x1494)))),a17)),a17)))))))),a17)),a17))))))))
% 0.18/0.64 [133]~P2(x1331)+P8(x1331)+~E(f6(f9(f9(x1331)),f9(f9(x1331))),f9(x1331))+~P6(f9(f9(f11(f6(x1331,a17)))),f9(f9(x1331)))
% 0.18/0.64 [132]~P2(x1321)+P3(x1321,x1322,x1323)+~E(f9(f9(x1322)),f9(x1321))+~P6(f9(f9(f11(f6(x1321,a17)))),f9(f9(x1323)))
% 0.18/0.64 [140]~P8(x1403)+~P8(x1402)+~P3(x1401,x1402,x1403)+P4(x1401,x1402,x1403)+P5(f24(f24(f15(x1401,x1402,x1403),f15(x1401,x1402,x1403)),f24(f15(x1401,x1402,x1403),f24(f16(x1401,x1402,x1403),f16(x1401,x1402,x1403)))),f9(x1402))
% 0.18/0.64 [150]~P8(x1503)+~P8(x1502)+~P3(x1501,x1502,x1503)+P4(x1501,x1502,x1503)+~E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1503,f6(f24(f24(f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),a17)),a17)))))))),f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),a17)),a17))))))),f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f16(x1501,x1502,x1503),f16(x1501,x1502,x1503)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f16(x1501,x1502,x1503),f16(x1501,x1502,x1503)),a17)),a17)))))))))),f24(f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),a17)),a17)))))))),f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),a17)),a17))))))),f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f16(x1501,x1502,x1503),f16(x1501,x1502,x1503)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f16(x1501,x1502,x1503),f16(x1501,x1502,x1503)),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f24(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f24(f24(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),f24(f15(x1501,x1502,x1503),f24(f16(x1501,x1502,x1503),f16(x1501,x1502,x1503)))),f24(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),f24(f15(x1501,x1502,x1503),f24(f16(x1501,x1502,x1503),f16(x1501,x1502,x1503))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f24(f24(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),f24(f15(x1501,x1502,x1503),f24(f16(x1501,x1502,x1503),f16(x1501,x1502,x1503)))),f24(f24(f15(x1501,x1502,x1503),f15(x1501,x1502,x1503)),f24(f15(x1501,x1502,x1503),f24(f16(x1501,x1502,x1503),f16(x1501,x1502,x1503))))),a17)),a17)))))))),a17)),a17))))))))
% 0.18/0.64 %EqnAxiom
% 0.18/0.64 [1]E(x11,x11)
% 0.18/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.64 [4]~E(x41,x42)+E(f24(x41,x43),f24(x42,x43))
% 0.18/0.64 [5]~E(x51,x52)+E(f24(x53,x51),f24(x53,x52))
% 0.18/0.64 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.18/0.64 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.18/0.64 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.18/0.64 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.18/0.64 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.18/0.64 [11]~E(x111,x112)+E(f8(x111),f8(x112))
% 0.18/0.64 [12]~E(x121,x122)+E(f11(x121),f11(x122))
% 0.18/0.64 [13]~E(x131,x132)+E(f7(x131,x133),f7(x132,x133))
% 0.18/0.64 [14]~E(x141,x142)+E(f7(x143,x141),f7(x143,x142))
% 0.18/0.64 [15]~E(x151,x152)+E(f19(x151),f19(x152))
% 0.18/0.64 [16]~E(x161,x162)+E(f16(x161,x163,x164),f16(x162,x163,x164))
% 0.18/0.64 [17]~E(x171,x172)+E(f16(x173,x171,x174),f16(x173,x172,x174))
% 0.18/0.64 [18]~E(x181,x182)+E(f16(x183,x184,x181),f16(x183,x184,x182))
% 0.18/0.64 [19]~E(x191,x192)+E(f15(x191,x193,x194),f15(x192,x193,x194))
% 0.18/0.64 [20]~E(x201,x202)+E(f15(x203,x201,x204),f15(x203,x202,x204))
% 0.18/0.64 [21]~E(x211,x212)+E(f15(x213,x214,x211),f15(x213,x214,x212))
% 0.18/0.64 [22]~E(x221,x222)+E(f20(x221),f20(x222))
% 0.18/0.64 [23]~E(x231,x232)+E(f14(x231,x233),f14(x232,x233))
% 0.18/0.64 [24]~E(x241,x242)+E(f14(x243,x241),f14(x243,x242))
% 0.18/0.64 [25]~E(x251,x252)+E(f22(x251),f22(x252))
% 0.18/0.64 [26]~E(x261,x262)+E(f12(x261),f12(x262))
% 0.18/0.64 [27]~E(x271,x272)+E(f3(x271),f3(x272))
% 0.18/0.64 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.18/0.64 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.18/0.64 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.18/0.64 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.18/0.64 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.18/0.64 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.18/0.64 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.18/0.64 [35]~P8(x351)+P8(x352)+~E(x351,x352)
% 0.18/0.64 [36]P6(x362,x363)+~E(x361,x362)+~P6(x361,x363)
% 0.18/0.64 [37]P6(x373,x372)+~E(x371,x372)+~P6(x373,x371)
% 0.18/0.64 [38]P4(x382,x383,x384)+~E(x381,x382)+~P4(x381,x383,x384)
% 0.18/0.64 [39]P4(x393,x392,x394)+~E(x391,x392)+~P4(x393,x391,x394)
% 0.18/0.64 [40]P4(x403,x404,x402)+~E(x401,x402)+~P4(x403,x404,x401)
% 0.18/0.64 [41]~P7(x411)+P7(x412)+~E(x411,x412)
% 0.18/0.64 [42]~P9(x421)+P9(x422)+~E(x421,x422)
% 0.18/0.64
% 0.18/0.64 %-------------------------------------------
% 0.18/0.64 cnf(151,plain,
% 0.18/0.64 ($false),
% 0.18/0.64 inference(scs_inference,[],[47,67,91]),
% 0.18/0.64 ['proof']).
% 0.18/0.64 % SZS output end Proof
% 0.18/0.64 % Total time :0.010000s
%------------------------------------------------------------------------------