TSTP Solution File: SET082-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET082-7 : 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 : n009.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 14:28:33 EDT 2023
% Result : Unsatisfiable 0.59s 0.67s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET082-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 15:27:35 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 0.59/0.65 %-------------------------------------------
% 0.59/0.65 % File :CSE---1.6
% 0.59/0.65 % Problem :theBenchmark
% 0.59/0.65 % Transform :cnf
% 0.59/0.65 % Format :tptp:raw
% 0.59/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.59/0.66
% 0.59/0.66 % Result :Theorem 0.010000s
% 0.59/0.66 % Output :CNFRefutation 0.010000s
% 0.59/0.66 %-------------------------------------------
% 0.59/0.66 %--------------------------------------------------------------------------
% 0.59/0.66 % File : SET082-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.59/0.66 % Domain : Set Theory
% 0.59/0.66 % Problem : The singleton of a non-set is the null class
% 0.59/0.66 % Version : [Qua92] axioms : Augmented.
% 0.59/0.66 % English :
% 0.59/0.66
% 0.59/0.66 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.59/0.66 % Source : [Quaife]
% 0.59/0.66 % Names : SS4 [Qua92]
% 0.59/0.66
% 0.59/0.66 % Status : Unsatisfiable
% 0.59/0.66 % Rating : 0.10 v8.1.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.20 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.00 v5.5.0, 0.25 v5.4.0, 0.30 v5.3.0, 0.22 v5.2.0, 0.12 v5.0.0, 0.07 v4.1.0, 0.08 v4.0.1, 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 v2.1.0
% 0.59/0.66 % Syntax : Number of clauses : 127 ( 42 unt; 15 nHn; 86 RR)
% 0.59/0.66 % Number of literals : 249 ( 59 equ; 115 neg)
% 0.59/0.66 % Maximal clause size : 5 ( 1 avg)
% 0.59/0.66 % Maximal term depth : 6 ( 1 avg)
% 0.59/0.66 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.59/0.66 % Number of functors : 39 ( 39 usr; 9 con; 0-3 aty)
% 0.59/0.66 % Number of variables : 246 ( 46 sgn)
% 0.59/0.66 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.59/0.66
% 0.59/0.66 % Comments : Preceding lemmas are added.
% 0.59/0.66 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.59/0.66 %--------------------------------------------------------------------------
% 0.59/0.66 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.59/0.66 include('Axioms/SET004-0.ax').
% 0.59/0.66 %--------------------------------------------------------------------------
% 0.59/0.66 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.59/0.66 cnf(corollary_1_to_unordered_pair,axiom,
% 0.59/0.66 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.59/0.66 | member(X,unordered_pair(X,Y)) ) ).
% 0.59/0.66
% 0.59/0.66 cnf(corollary_2_to_unordered_pair,axiom,
% 0.59/0.66 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.59/0.66 | member(Y,unordered_pair(X,Y)) ) ).
% 0.59/0.66
% 0.59/0.66 %----Corollaries to Cartesian product axiom.
% 0.59/0.66 cnf(corollary_1_to_cartesian_product,axiom,
% 0.59/0.66 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.59/0.66 | member(U,universal_class) ) ).
% 0.59/0.66
% 0.59/0.66 cnf(corollary_2_to_cartesian_product,axiom,
% 0.59/0.66 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.59/0.66 | member(V,universal_class) ) ).
% 0.59/0.66
% 0.59/0.66 %---- PARTIAL ORDER.
% 0.59/0.66 %----(PO1): reflexive.
% 0.59/0.66 cnf(subclass_is_reflexive,axiom,
% 0.59/0.66 subclass(X,X) ).
% 0.59/0.66
% 0.59/0.66 %----(PO2): antisymmetry is part of A-3.
% 0.59/0.66 %----(x < y), (y < x) --> (x = y).
% 0.59/0.66
% 0.59/0.66 %----(PO3): transitivity.
% 0.59/0.66 cnf(transitivity_of_subclass,axiom,
% 0.59/0.66 ( ~ subclass(X,Y)
% 0.59/0.66 | ~ subclass(Y,Z)
% 0.59/0.66 | subclass(X,Z) ) ).
% 0.59/0.66
% 0.59/0.66 %---- EQUALITY.
% 0.59/0.66 %----(EQ1): equality axiom.
% 0.59/0.66 %----a:x:(x = x).
% 0.59/0.66 %----This is always an axiom in the TPTP presentation.
% 0.59/0.66
% 0.59/0.66 %----(EQ2): expanded equality definition.
% 0.59/0.66 cnf(equality1,axiom,
% 0.59/0.66 ( X = Y
% 0.59/0.66 | member(not_subclass_element(X,Y),X)
% 0.59/0.66 | member(not_subclass_element(Y,X),Y) ) ).
% 0.59/0.66
% 0.59/0.66 cnf(equality2,axiom,
% 0.59/0.66 ( ~ member(not_subclass_element(X,Y),Y)
% 0.59/0.66 | X = Y
% 0.59/0.66 | member(not_subclass_element(Y,X),Y) ) ).
% 0.59/0.66
% 0.59/0.66 cnf(equality3,axiom,
% 0.59/0.66 ( ~ member(not_subclass_element(Y,X),X)
% 0.59/0.66 | X = Y
% 0.59/0.66 | member(not_subclass_element(X,Y),X) ) ).
% 0.59/0.66
% 0.59/0.66 cnf(equality4,axiom,
% 0.59/0.66 ( ~ member(not_subclass_element(X,Y),Y)
% 0.59/0.66 | ~ member(not_subclass_element(Y,X),X)
% 0.59/0.66 | X = Y ) ).
% 0.59/0.66
% 0.59/0.66 %---- SPECIAL CLASSES.
% 0.59/0.66 %----(SP1): lemma.
% 0.59/0.66 cnf(special_classes_lemma,axiom,
% 0.59/0.66 ~ member(Y,intersection(complement(X),X)) ).
% 0.59/0.66
% 0.59/0.66 %----(SP2): Existence of O (null class).
% 0.59/0.66 %----e:x:a:z:(-(z e x)).
% 0.59/0.66 cnf(existence_of_null_class,axiom,
% 0.59/0.66 ~ member(Z,null_class) ).
% 0.59/0.66
% 0.59/0.66 %----(SP3): O is a subclass of every class.
% 0.59/0.66 cnf(null_class_is_subclass,axiom,
% 0.59/0.66 subclass(null_class,X) ).
% 0.59/0.66
% 0.59/0.66 %----corollary.
% 0.59/0.66 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.59/0.66 ( ~ subclass(X,null_class)
% 0.59/0.66 | X = null_class ) ).
% 0.59/0.66
% 0.59/0.66 %----(SP4): uniqueness of null class.
% 0.59/0.66 cnf(null_class_is_unique,axiom,
% 0.59/0.66 ( Z = null_class
% 0.59/0.66 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.59/0.66
% 0.59/0.66 %----(SP5): O is a set (follows from axiom of infinity).
% 0.59/0.66 cnf(null_class_is_a_set,axiom,
% 0.59/0.66 member(null_class,universal_class) ).
% 0.59/0.66
% 0.59/0.66 %---- UNORDERED PAIRS.
% 0.59/0.66 %----(UP1): unordered pair is commutative.
% 0.59/0.66 cnf(commutativity_of_unordered_pair,axiom,
% 0.59/0.66 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.59/0.66
% 0.59/0.66 %----(UP2): if one argument is a proper class, pair contains only the
% 0.59/0.66 %----other. In a slightly different form to the paper
% 0.59/0.66 cnf(singleton_in_unordered_pair1,axiom,
% 0.59/0.66 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.59/0.66
% 0.59/0.66 cnf(singleton_in_unordered_pair2,axiom,
% 0.59/0.66 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.59/0.66
% 0.59/0.66 cnf(unordered_pair_equals_singleton1,axiom,
% 0.59/0.66 ( member(Y,universal_class)
% 0.59/0.66 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.59/0.66
% 0.59/0.66 cnf(unordered_pair_equals_singleton2,axiom,
% 0.59/0.66 ( member(X,universal_class)
% 0.59/0.67 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.59/0.67
% 0.59/0.67 %----(UP3): if both arguments are proper classes, pair is null.
% 0.59/0.67 cnf(null_unordered_pair,axiom,
% 0.59/0.67 ( unordered_pair(X,Y) = null_class
% 0.59/0.67 | member(X,universal_class)
% 0.59/0.67 | member(Y,universal_class) ) ).
% 0.59/0.67
% 0.59/0.67 %----(UP4): left cancellation for unordered pairs.
% 0.59/0.67 cnf(left_cancellation,axiom,
% 0.59/0.67 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.59/0.67 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.59/0.67 | Y = Z ) ).
% 0.59/0.67
% 0.59/0.67 %----(UP5): right cancellation for unordered pairs.
% 0.59/0.67 cnf(right_cancellation,axiom,
% 0.59/0.67 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.59/0.67 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.59/0.67 | X = Y ) ).
% 0.59/0.67
% 0.59/0.67 %----(UP6): corollary to (A-4).
% 0.59/0.67 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.59/0.67 ( ~ member(X,universal_class)
% 0.59/0.67 | unordered_pair(X,Y) != null_class ) ).
% 0.59/0.67
% 0.59/0.67 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.59/0.67 ( ~ member(Y,universal_class)
% 0.59/0.67 | unordered_pair(X,Y) != null_class ) ).
% 0.59/0.67
% 0.59/0.67 %----corollary to instantiate variables.
% 0.59/0.67 %----Not in the paper
% 0.59/0.67 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.59/0.67 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.59/0.67 | unordered_pair(X,Y) != null_class ) ).
% 0.59/0.67
% 0.59/0.67 %----(UP7): if both members of a pair belong to a set, the pair
% 0.59/0.67 %----is a subset.
% 0.59/0.67 cnf(unordered_pair_is_subset,axiom,
% 0.59/0.67 ( ~ member(X,Z)
% 0.59/0.67 | ~ member(Y,Z)
% 0.59/0.67 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.59/0.67
% 0.59/0.67 %---- SINGLETONS.
% 0.59/0.67 %----(SS1): every singleton is a set.
% 0.59/0.67 cnf(singletons_are_sets,axiom,
% 0.59/0.67 member(singleton(X),universal_class) ).
% 0.59/0.67
% 0.59/0.67 %----corollary, not in the paper.
% 0.59/0.67 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.59/0.67 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.59/0.67
% 0.59/0.67 %----(SS2): a set belongs to its singleton.
% 0.59/0.67 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.59/0.67 cnf(set_in_its_singleton,axiom,
% 0.59/0.67 ( ~ member(X,universal_class)
% 0.59/0.67 | member(X,singleton(X)) ) ).
% 0.59/0.67
% 0.59/0.67 %----corollary
% 0.59/0.67 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.59/0.67 ( ~ member(X,universal_class)
% 0.59/0.67 | singleton(X) != null_class ) ).
% 0.59/0.67
% 0.59/0.67 %----Not in the paper
% 0.59/0.67 cnf(null_class_in_its_singleton,axiom,
% 0.59/0.67 member(null_class,singleton(null_class)) ).
% 0.59/0.67
% 0.59/0.67 %----(SS3): only x can belong to {x}.
% 0.59/0.67 cnf(only_member_in_singleton,axiom,
% 0.59/0.67 ( ~ member(Y,singleton(X))
% 0.59/0.67 | Y = X ) ).
% 0.59/0.67
% 0.59/0.67 cnf(prove_singleton_is_null_class_1,negated_conjecture,
% 0.59/0.67 ~ member(x,universal_class) ).
% 0.59/0.67
% 0.59/0.67 cnf(prove_singleton_is_null_class_2,negated_conjecture,
% 0.59/0.67 singleton(x) != null_class ).
% 0.59/0.67
% 0.59/0.67 %--------------------------------------------------------------------------
% 0.59/0.67 %-------------------------------------------
% 0.59/0.67 % Proof found
% 0.59/0.67 % SZS status Theorem for theBenchmark
% 0.59/0.67 % SZS output start Proof
% 0.59/0.67 %ClaNum:154(EqnAxiom:42)
% 0.59/0.67 %VarNum:876(SingletonVarNum:215)
% 0.59/0.67 %MaxLitNum:5
% 0.59/0.67 %MaxfuncDepth:24
% 0.59/0.67 %SharedTerms:36
% 0.59/0.67 %goalClause: 66 67
% 0.59/0.67 %singleGoalClaCount:2
% 0.59/0.67 [43]P1(a1)
% 0.59/0.67 [44]P2(a2)
% 0.59/0.67 [45]P5(a4,a17)
% 0.59/0.67 [46]P5(a1,a17)
% 0.59/0.67 [67]~P5(a24,a17)
% 0.59/0.67 [51]P6(a5,f6(a17,a17))
% 0.59/0.67 [52]P6(a18,f6(a17,a17))
% 0.59/0.67 [53]P5(a4,f23(a4,a4))
% 0.59/0.67 [66]~E(f23(a24,a24),a4)
% 0.59/0.67 [62]E(f10(f9(f11(f6(a21,a17))),a21),a13)
% 0.59/0.67 [64]E(f10(f6(a17,a17),f10(f6(a17,a17),f8(f7(f8(a5),f9(f11(f6(a5,a17))))))),a21)
% 0.59/0.67 [47]P6(x471,a17)
% 0.59/0.67 [48]P6(a4,x481)
% 0.59/0.67 [49]P6(x491,x491)
% 0.59/0.67 [68]~P5(x681,a4)
% 0.59/0.67 [60]P6(f19(x601),f6(f6(a17,a17),a17))
% 0.59/0.67 [61]P6(f11(x611),f6(f6(a17,a17),a17))
% 0.59/0.67 [65]E(f10(f9(x651),f8(f9(f10(f7(f9(f11(f6(a5,a17))),x651),a13)))),f3(x651))
% 0.59/0.67 [50]E(f23(x501,x502),f23(x502,x501))
% 0.59/0.67 [54]P5(f23(x541,x542),a17)
% 0.59/0.67 [56]P6(f7(x561,x562),f6(a17,a17))
% 0.59/0.67 [57]P6(f23(x571,x571),f23(x572,x571))
% 0.59/0.67 [58]P6(f23(x581,x581),f23(x581,x582))
% 0.59/0.67 [63]P5(f23(x631,x631),f23(x632,f23(x631,x631)))
% 0.59/0.67 [69]~P5(x691,f10(f8(x692),x692))
% 0.59/0.67 [59]E(f10(f6(x591,x592),x593),f10(x593,f6(x591,x592)))
% 0.59/0.67 [70]~P7(x701)+P2(x701)
% 0.59/0.67 [71]~P8(x711)+P2(x711)
% 0.59/0.67 [74]~P1(x741)+P6(a1,x741)
% 0.59/0.67 [75]~P1(x751)+P5(a4,x751)
% 0.59/0.67 [76]~P6(x761,a4)+E(x761,a4)
% 0.59/0.67 [78]P5(f20(x781),x781)+E(x781,a4)
% 0.59/0.67 [79]E(x791,a4)+P5(f14(x791,a4),x791)
% 0.59/0.67 [83]~P2(x831)+P6(x831,f6(a17,a17))
% 0.59/0.67 [77]E(x771,a4)+E(f10(x771,f20(x771)),a4)
% 0.59/0.67 [96]~P8(x961)+E(f6(f9(f9(x961)),f9(f9(x961))),f9(x961))
% 0.59/0.67 [111]~P7(x1111)+P2(f9(f11(f6(x1111,a17))))
% 0.59/0.67 [116]~P5(x1161,a17)+P5(f9(f10(a5,f6(a17,x1161))),a17)
% 0.59/0.67 [118]~P9(x1181)+P6(f7(x1181,f9(f11(f6(x1181,a17)))),a13)
% 0.59/0.67 [119]~P2(x1191)+P6(f7(x1191,f9(f11(f6(x1191,a17)))),a13)
% 0.59/0.67 [120]~P8(x1201)+P6(f9(f9(f11(f6(x1201,a17)))),f9(f9(x1201)))
% 0.59/0.67 [125]P9(x1251)+~P6(f7(x1251,f9(f11(f6(x1251,a17)))),a13)
% 0.59/0.67 [141]~P1(x1411)+P6(f9(f9(f11(f6(f10(a18,f6(x1411,a17)),a17)))),x1411)
% 0.59/0.67 [145]~P5(x1451,a17)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1451),a17)),a17))))),a17)
% 0.59/0.67 [72]~E(x722,x721)+P6(x721,x722)
% 0.59/0.67 [73]~E(x731,x732)+P6(x731,x732)
% 0.59/0.67 [81]P5(x812,a17)+E(f23(x811,x812),f23(x811,x811))
% 0.59/0.67 [82]P5(x821,a17)+E(f23(x821,x822),f23(x822,x822))
% 0.59/0.67 [84]~P5(x842,a17)+~E(f23(x841,x842),a4)
% 0.59/0.67 [85]~P5(x851,a17)+~E(f23(x851,x852),a4)
% 0.59/0.67 [88]P6(x881,x882)+P5(f14(x881,x882),x881)
% 0.59/0.67 [89]~P5(x891,x892)+~P5(x891,f8(x892))
% 0.59/0.67 [93]~P5(x931,a17)+P5(x931,f23(x932,x931))
% 0.59/0.67 [94]~P5(x941,a17)+P5(x941,f23(x941,x942))
% 0.59/0.67 [97]E(x971,x972)+~P5(x971,f23(x972,x972))
% 0.59/0.67 [101]P6(x1011,x1012)+~P5(f14(x1011,x1012),x1012)
% 0.59/0.67 [115]~P5(x1152,f9(x1151))+~E(f10(x1151,f6(f23(x1152,x1152),a17)),a4)
% 0.59/0.67 [124]P5(x1241,x1242)+~P5(f23(f23(x1241,x1241),f23(x1241,f23(x1242,x1242))),a5)
% 0.59/0.67 [138]~P5(f23(f23(x1381,x1381),f23(x1381,f23(x1382,x1382))),a18)+E(f8(f10(f8(x1381),f8(f23(x1381,x1381)))),x1382)
% 0.59/0.67 [105]P2(x1051)+~P3(x1051,x1052,x1053)
% 0.59/0.67 [106]P8(x1061)+~P4(x1062,x1063,x1061)
% 0.59/0.67 [107]P8(x1071)+~P4(x1072,x1071,x1073)
% 0.59/0.67 [114]~P4(x1141,x1142,x1143)+P3(x1141,x1142,x1143)
% 0.59/0.67 [99]P5(x991,x992)+~P5(x991,f10(x993,x992))
% 0.59/0.67 [100]P5(x1001,x1002)+~P5(x1001,f10(x1002,x1003))
% 0.59/0.67 [108]~P3(x1082,x1081,x1083)+E(f9(f9(x1081)),f9(x1082))
% 0.59/0.67 [121]~P5(x1211,f6(x1212,x1213))+E(f23(f23(f12(x1211),f12(x1211)),f23(f12(x1211),f23(f22(x1211),f22(x1211)))),x1211)
% 0.59/0.67 [123]~P3(x1231,x1233,x1232)+P6(f9(f9(f11(f6(x1231,a17)))),f9(f9(x1232)))
% 0.59/0.67 [126]P5(x1261,a17)+~P5(f23(f23(x1262,x1262),f23(x1262,f23(x1261,x1261))),f6(x1263,x1264))
% 0.59/0.67 [127]P5(x1271,a17)+~P5(f23(f23(x1271,x1271),f23(x1271,f23(x1272,x1272))),f6(x1273,x1274))
% 0.59/0.67 [128]P5(x1281,x1282)+~P5(f23(f23(x1283,x1283),f23(x1283,f23(x1281,x1281))),f6(x1284,x1282))
% 0.59/0.67 [129]P5(x1291,x1292)+~P5(f23(f23(x1291,x1291),f23(x1291,f23(x1293,x1293))),f6(x1292,x1294))
% 0.59/0.67 [130]~E(f23(x1301,x1302),a4)+~P5(f23(f23(x1301,x1301),f23(x1301,f23(x1302,x1302))),f6(x1303,x1304))
% 0.59/0.67 [134]P5(x1341,f23(x1342,x1341))+~P5(f23(f23(x1342,x1342),f23(x1342,f23(x1341,x1341))),f6(x1343,x1344))
% 0.59/0.67 [135]P5(x1351,f23(x1351,x1352))+~P5(f23(f23(x1351,x1351),f23(x1351,f23(x1352,x1352))),f6(x1353,x1354))
% 0.59/0.67 [146]~P5(f23(f23(f23(f23(x1463,x1463),f23(x1463,f23(x1461,x1461))),f23(f23(x1463,x1463),f23(x1463,f23(x1461,x1461)))),f23(f23(f23(x1463,x1463),f23(x1463,f23(x1461,x1461))),f23(x1462,x1462))),f19(x1464))+P5(f23(f23(f23(f23(x1461,x1461),f23(x1461,f23(x1462,x1462))),f23(f23(x1461,x1461),f23(x1461,f23(x1462,x1462)))),f23(f23(f23(x1461,x1461),f23(x1461,f23(x1462,x1462))),f23(x1463,x1463))),x1464)
% 0.59/0.67 [147]~P5(f23(f23(f23(f23(x1472,x1472),f23(x1472,f23(x1471,x1471))),f23(f23(x1472,x1472),f23(x1472,f23(x1471,x1471)))),f23(f23(f23(x1472,x1472),f23(x1472,f23(x1471,x1471))),f23(x1473,x1473))),f11(x1474))+P5(f23(f23(f23(f23(x1471,x1471),f23(x1471,f23(x1472,x1472))),f23(f23(x1471,x1471),f23(x1471,f23(x1472,x1472)))),f23(f23(f23(x1471,x1471),f23(x1471,f23(x1472,x1472))),f23(x1473,x1473))),x1474)
% 0.59/0.67 [151]~P5(f23(f23(x1514,x1514),f23(x1514,f23(x1511,x1511))),f7(x1512,x1513))+P5(x1511,f9(f9(f11(f6(f10(x1512,f6(f9(f9(f11(f6(f10(x1513,f6(f23(x1514,x1514),a17)),a17)))),a17)),a17)))))
% 0.59/0.67 [117]~P2(x1171)+P7(x1171)+~P2(f9(f11(f6(x1171,a17))))
% 0.59/0.67 [131]P2(x1311)+~P6(x1311,f6(a17,a17))+~P6(f7(x1311,f9(f11(f6(x1311,a17)))),a13)
% 0.59/0.67 [143]P1(x1431)+~P5(a4,x1431)+~P6(f9(f9(f11(f6(f10(a18,f6(x1431,a17)),a17)))),x1431)
% 0.59/0.67 [150]~P5(x1501,a17)+E(x1501,a4)+P5(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(a2,f6(f23(x1501,x1501),a17)),a17))))))),x1501)
% 0.59/0.67 [87]~P6(x872,x871)+~P6(x871,x872)+E(x871,x872)
% 0.59/0.67 [80]P5(x802,a17)+P5(x801,a17)+E(f23(x801,x802),a4)
% 0.59/0.67 [90]P5(x901,x902)+P5(x901,f8(x902))+~P5(x901,a17)
% 0.59/0.67 [102]E(x1021,x1022)+P5(f14(x1022,x1021),x1022)+P5(f14(x1021,x1022),x1021)
% 0.59/0.67 [110]E(x1101,x1102)+P5(f14(x1102,x1101),x1102)+~P5(f14(x1101,x1102),x1102)
% 0.59/0.67 [112]E(x1121,x1122)+~P5(f14(x1122,x1121),x1121)+~P5(f14(x1121,x1122),x1122)
% 0.59/0.67 [113]P5(x1132,f9(x1131))+~P5(x1132,a17)+E(f10(x1131,f6(f23(x1132,x1132),a17)),a4)
% 0.59/0.67 [139]~P5(x1391,x1392)+~P5(f23(f23(x1391,x1391),f23(x1391,f23(x1392,x1392))),f6(a17,a17))+P5(f23(f23(x1391,x1391),f23(x1391,f23(x1392,x1392))),a5)
% 0.59/0.67 [140]~P5(f23(f23(x1401,x1401),f23(x1401,f23(x1402,x1402))),f6(a17,a17))+~E(f8(f10(f8(x1401),f8(f23(x1401,x1401)))),x1402)+P5(f23(f23(x1401,x1401),f23(x1401,f23(x1402,x1402))),a18)
% 0.59/0.67 [142]~P2(x1421)+~P5(x1422,a17)+P5(f9(f9(f11(f6(f10(x1421,f6(x1422,a17)),a17)))),a17)
% 0.59/0.67 [91]~P6(x911,x913)+P6(x911,x912)+~P6(x913,x912)
% 0.59/0.67 [92]~P5(x921,x923)+P5(x921,x922)+~P6(x923,x922)
% 0.59/0.67 [98]E(x981,x982)+E(x981,x983)+~P5(x981,f23(x983,x982))
% 0.59/0.67 [103]~P5(x1031,x1033)+~P5(x1031,x1032)+P5(x1031,f10(x1032,x1033))
% 0.59/0.67 [104]~P5(x1042,x1043)+~P5(x1041,x1043)+P6(f23(x1041,x1042),x1043)
% 0.59/0.67 [132]E(x1321,x1322)+~E(f23(x1323,x1321),f23(x1323,x1322))+~P5(f23(f23(x1321,x1321),f23(x1321,f23(x1322,x1322))),f6(a17,a17))
% 0.59/0.67 [133]E(x1331,x1332)+~E(f23(x1331,x1333),f23(x1332,x1333))+~P5(f23(f23(x1331,x1331),f23(x1331,f23(x1332,x1332))),f6(a17,a17))
% 0.59/0.67 [122]~P5(x1222,x1224)+~P5(x1221,x1223)+P5(f23(f23(x1221,x1221),f23(x1221,f23(x1222,x1222))),f6(x1223,x1224))
% 0.59/0.67 [148]~P5(f23(f23(f23(f23(x1482,x1482),f23(x1482,f23(x1483,x1483))),f23(f23(x1482,x1482),f23(x1482,f23(x1483,x1483)))),f23(f23(f23(x1482,x1482),f23(x1482,f23(x1483,x1483))),f23(x1481,x1481))),x1484)+P5(f23(f23(f23(f23(x1481,x1481),f23(x1481,f23(x1482,x1482))),f23(f23(x1481,x1481),f23(x1481,f23(x1482,x1482)))),f23(f23(f23(x1481,x1481),f23(x1481,f23(x1482,x1482))),f23(x1483,x1483))),f19(x1484))+~P5(f23(f23(f23(f23(x1481,x1481),f23(x1481,f23(x1482,x1482))),f23(f23(x1481,x1481),f23(x1481,f23(x1482,x1482)))),f23(f23(f23(x1481,x1481),f23(x1481,f23(x1482,x1482))),f23(x1483,x1483))),f6(f6(a17,a17),a17))
% 0.59/0.67 [149]~P5(f23(f23(f23(f23(x1492,x1492),f23(x1492,f23(x1491,x1491))),f23(f23(x1492,x1492),f23(x1492,f23(x1491,x1491)))),f23(f23(f23(x1492,x1492),f23(x1492,f23(x1491,x1491))),f23(x1493,x1493))),x1494)+P5(f23(f23(f23(f23(x1491,x1491),f23(x1491,f23(x1492,x1492))),f23(f23(x1491,x1491),f23(x1491,f23(x1492,x1492)))),f23(f23(f23(x1491,x1491),f23(x1491,f23(x1492,x1492))),f23(x1493,x1493))),f11(x1494))+~P5(f23(f23(f23(f23(x1491,x1491),f23(x1491,f23(x1492,x1492))),f23(f23(x1491,x1491),f23(x1491,f23(x1492,x1492)))),f23(f23(f23(x1491,x1491),f23(x1491,f23(x1492,x1492))),f23(x1493,x1493))),f6(f6(a17,a17),a17))
% 0.59/0.67 [152]P5(f23(f23(x1521,x1521),f23(x1521,f23(x1522,x1522))),f7(x1523,x1524))+~P5(f23(f23(x1521,x1521),f23(x1521,f23(x1522,x1522))),f6(a17,a17))+~P5(x1522,f9(f9(f11(f6(f10(x1523,f6(f9(f9(f11(f6(f10(x1524,f6(f23(x1521,x1521),a17)),a17)))),a17)),a17)))))
% 0.59/0.67 [153]~P4(x1532,x1535,x1531)+~P5(f23(f23(x1533,x1533),f23(x1533,f23(x1534,x1534))),f9(x1535))+E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1533,x1533),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1533,x1533),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1533,x1533),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1534,x1534),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1534,x1534),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1533,x1533),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1533,x1533),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1533,x1533),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1534,x1534),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(x1534,x1534),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1535,f6(f23(f23(f23(x1533,x1533),f23(x1533,f23(x1534,x1534))),f23(f23(x1533,x1533),f23(x1533,f23(x1534,x1534)))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1535,f6(f23(f23(f23(x1533,x1533),f23(x1533,f23(x1534,x1534))),f23(f23(x1533,x1533),f23(x1533,f23(x1534,x1534)))),a17)),a17)))))))),a17)),a17))))))))
% 0.59/0.67 [137]~P2(x1371)+P8(x1371)+~E(f6(f9(f9(x1371)),f9(f9(x1371))),f9(x1371))+~P6(f9(f9(f11(f6(x1371,a17)))),f9(f9(x1371)))
% 0.59/0.67 [136]~P2(x1361)+P3(x1361,x1362,x1363)+~E(f9(f9(x1362)),f9(x1361))+~P6(f9(f9(f11(f6(x1361,a17)))),f9(f9(x1363)))
% 0.59/0.67 [144]~P8(x1443)+~P8(x1442)+~P3(x1441,x1442,x1443)+P4(x1441,x1442,x1443)+P5(f23(f23(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),f23(f15(x1441,x1442,x1443),f23(f16(x1441,x1442,x1443),f16(x1441,x1442,x1443)))),f9(x1442))
% 0.59/0.67 [154]~P8(x1543)+~P8(x1542)+~P3(x1541,x1542,x1543)+P4(x1541,x1542,x1543)+~E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1543,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f16(x1541,x1542,x1543),f16(x1541,x1542,x1543)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f16(x1541,x1542,x1543),f16(x1541,x1542,x1543)),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f16(x1541,x1542,x1543),f16(x1541,x1542,x1543)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f16(x1541,x1542,x1543),f16(x1541,x1542,x1543)),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1541,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1542,f6(f23(f23(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),f23(f15(x1541,x1542,x1543),f23(f16(x1541,x1542,x1543),f16(x1541,x1542,x1543)))),f23(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),f23(f15(x1541,x1542,x1543),f23(f16(x1541,x1542,x1543),f16(x1541,x1542,x1543))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1542,f6(f23(f23(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),f23(f15(x1541,x1542,x1543),f23(f16(x1541,x1542,x1543),f16(x1541,x1542,x1543)))),f23(f23(f15(x1541,x1542,x1543),f15(x1541,x1542,x1543)),f23(f15(x1541,x1542,x1543),f23(f16(x1541,x1542,x1543),f16(x1541,x1542,x1543))))),a17)),a17)))))))),a17)),a17))))))))
% 0.59/0.67 %EqnAxiom
% 0.59/0.67 [1]E(x11,x11)
% 0.59/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.59/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.59/0.67 [4]~E(x41,x42)+E(f23(x41,x43),f23(x42,x43))
% 0.59/0.67 [5]~E(x51,x52)+E(f23(x53,x51),f23(x53,x52))
% 0.59/0.67 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.59/0.67 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.59/0.67 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.59/0.67 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.59/0.67 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.59/0.67 [11]~E(x111,x112)+E(f11(x111),f11(x112))
% 0.59/0.67 [12]~E(x121,x122)+E(f8(x121),f8(x122))
% 0.59/0.67 [13]~E(x131,x132)+E(f16(x131,x133,x134),f16(x132,x133,x134))
% 0.59/0.67 [14]~E(x141,x142)+E(f16(x143,x141,x144),f16(x143,x142,x144))
% 0.59/0.67 [15]~E(x151,x152)+E(f16(x153,x154,x151),f16(x153,x154,x152))
% 0.59/0.67 [16]~E(x161,x162)+E(f7(x161,x163),f7(x162,x163))
% 0.59/0.67 [17]~E(x171,x172)+E(f7(x173,x171),f7(x173,x172))
% 0.59/0.67 [18]~E(x181,x182)+E(f15(x181,x183,x184),f15(x182,x183,x184))
% 0.59/0.67 [19]~E(x191,x192)+E(f15(x193,x191,x194),f15(x193,x192,x194))
% 0.59/0.67 [20]~E(x201,x202)+E(f15(x203,x204,x201),f15(x203,x204,x202))
% 0.59/0.67 [21]~E(x211,x212)+E(f14(x211,x213),f14(x212,x213))
% 0.59/0.67 [22]~E(x221,x222)+E(f14(x223,x221),f14(x223,x222))
% 0.59/0.67 [23]~E(x231,x232)+E(f19(x231),f19(x232))
% 0.59/0.67 [24]~E(x241,x242)+E(f12(x241),f12(x242))
% 0.59/0.67 [25]~E(x251,x252)+E(f22(x251),f22(x252))
% 0.59/0.67 [26]~E(x261,x262)+E(f20(x261),f20(x262))
% 0.59/0.67 [27]~E(x271,x272)+E(f3(x271),f3(x272))
% 0.59/0.67 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.59/0.67 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.59/0.67 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.59/0.67 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.59/0.67 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.59/0.67 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.59/0.67 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.59/0.67 [35]P6(x352,x353)+~E(x351,x352)+~P6(x351,x353)
% 0.59/0.67 [36]P6(x363,x362)+~E(x361,x362)+~P6(x363,x361)
% 0.59/0.67 [37]~P8(x371)+P8(x372)+~E(x371,x372)
% 0.59/0.67 [38]P4(x382,x383,x384)+~E(x381,x382)+~P4(x381,x383,x384)
% 0.59/0.67 [39]P4(x393,x392,x394)+~E(x391,x392)+~P4(x393,x391,x394)
% 0.59/0.67 [40]P4(x403,x404,x402)+~E(x401,x402)+~P4(x403,x404,x401)
% 0.59/0.67 [41]~P9(x411)+P9(x412)+~E(x411,x412)
% 0.59/0.67 [42]~P7(x421)+P7(x422)+~E(x421,x422)
% 0.59/0.67
% 0.59/0.67 %-------------------------------------------
% 0.59/0.67 cnf(155,plain,
% 0.59/0.67 ($false),
% 0.59/0.67 inference(scs_inference,[],[67,66,80]),
% 0.59/0.67 ['proof']).
% 0.59/0.67 % SZS output end Proof
% 0.59/0.67 % Total time :0.010000s
%------------------------------------------------------------------------------