TSTP Solution File: SET081-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET081-7 : 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 : n031.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 14:28:32 EDT 2023
% Result : Unsatisfiable 0.65s 0.77s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET081-7 : 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
% 0.14/0.34 % Computer : n031.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 09:17:22 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 0.65/0.76 %-------------------------------------------
% 0.65/0.76 % File :CSE---1.6
% 0.65/0.76 % Problem :theBenchmark
% 0.65/0.76 % Transform :cnf
% 0.65/0.76 % Format :tptp:raw
% 0.65/0.76 % Command :java -jar mcs_scs.jar %d %s
% 0.65/0.76
% 0.65/0.76 % Result :Theorem 0.130000s
% 0.65/0.76 % Output :CNFRefutation 0.130000s
% 0.65/0.76 %-------------------------------------------
% 0.65/0.76 %--------------------------------------------------------------------------
% 0.65/0.76 % File : SET081-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.65/0.76 % Domain : Set Theory
% 0.65/0.76 % Problem : Only the element can belong to its singleton
% 0.65/0.76 % Version : [Qua92] axioms : Augmented.
% 0.65/0.76 % English :
% 0.65/0.76
% 0.65/0.76 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.65/0.76 % Source : [Quaife]
% 0.65/0.76 % Names : SS3 [Qua92]
% 0.65/0.76
% 0.65/0.76 % Status : Unsatisfiable
% 0.65/0.76 % Rating : 0.10 v8.1.0, 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, 0.00 v5.5.0, 0.15 v5.4.0, 0.20 v5.3.0, 0.11 v5.2.0, 0.12 v5.0.0, 0.14 v4.1.0, 0.15 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 v2.5.0, 0.09 v2.4.0, 0.12 v2.2.1, 0.00 v2.1.0
% 0.65/0.76 % Syntax : Number of clauses : 126 ( 42 unt; 15 nHn; 85 RR)
% 0.65/0.76 % Number of literals : 247 ( 58 equ; 113 neg)
% 0.65/0.76 % Maximal clause size : 5 ( 1 avg)
% 0.65/0.76 % Maximal term depth : 6 ( 1 avg)
% 0.65/0.76 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.65/0.76 % Number of functors : 40 ( 40 usr; 10 con; 0-3 aty)
% 0.65/0.76 % Number of variables : 244 ( 46 sgn)
% 0.65/0.76 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.65/0.76
% 0.65/0.76 % Comments : Preceding lemmas are added.
% 0.65/0.76 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.65/0.76 %--------------------------------------------------------------------------
% 0.65/0.76 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.65/0.76 include('Axioms/SET004-0.ax').
% 0.65/0.76 %--------------------------------------------------------------------------
% 0.65/0.76 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.65/0.76 cnf(corollary_1_to_unordered_pair,axiom,
% 0.65/0.76 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.65/0.76 | member(X,unordered_pair(X,Y)) ) ).
% 0.65/0.76
% 0.65/0.76 cnf(corollary_2_to_unordered_pair,axiom,
% 0.65/0.76 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.65/0.76 | member(Y,unordered_pair(X,Y)) ) ).
% 0.65/0.76
% 0.65/0.76 %----Corollaries to Cartesian product axiom.
% 0.65/0.76 cnf(corollary_1_to_cartesian_product,axiom,
% 0.65/0.76 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.65/0.76 | member(U,universal_class) ) ).
% 0.65/0.76
% 0.65/0.76 cnf(corollary_2_to_cartesian_product,axiom,
% 0.65/0.76 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.65/0.76 | member(V,universal_class) ) ).
% 0.65/0.76
% 0.65/0.76 %---- PARTIAL ORDER.
% 0.65/0.76 %----(PO1): reflexive.
% 0.65/0.76 cnf(subclass_is_reflexive,axiom,
% 0.65/0.76 subclass(X,X) ).
% 0.65/0.76
% 0.65/0.76 %----(PO2): antisymmetry is part of A-3.
% 0.65/0.76 %----(x < y), (y < x) --> (x = y).
% 0.65/0.76
% 0.65/0.76 %----(PO3): transitivity.
% 0.65/0.76 cnf(transitivity_of_subclass,axiom,
% 0.65/0.76 ( ~ subclass(X,Y)
% 0.65/0.76 | ~ subclass(Y,Z)
% 0.65/0.76 | subclass(X,Z) ) ).
% 0.65/0.76
% 0.65/0.76 %---- EQUALITY.
% 0.65/0.76 %----(EQ1): equality axiom.
% 0.65/0.76 %----a:x:(x = x).
% 0.65/0.76 %----This is always an axiom in the TPTP presentation.
% 0.65/0.76
% 0.65/0.76 %----(EQ2): expanded equality definition.
% 0.65/0.76 cnf(equality1,axiom,
% 0.65/0.76 ( X = Y
% 0.65/0.76 | member(not_subclass_element(X,Y),X)
% 0.65/0.76 | member(not_subclass_element(Y,X),Y) ) ).
% 0.65/0.76
% 0.65/0.76 cnf(equality2,axiom,
% 0.65/0.76 ( ~ member(not_subclass_element(X,Y),Y)
% 0.65/0.76 | X = Y
% 0.65/0.76 | member(not_subclass_element(Y,X),Y) ) ).
% 0.65/0.76
% 0.65/0.76 cnf(equality3,axiom,
% 0.65/0.76 ( ~ member(not_subclass_element(Y,X),X)
% 0.65/0.76 | X = Y
% 0.65/0.76 | member(not_subclass_element(X,Y),X) ) ).
% 0.65/0.76
% 0.65/0.76 cnf(equality4,axiom,
% 0.65/0.76 ( ~ member(not_subclass_element(X,Y),Y)
% 0.65/0.76 | ~ member(not_subclass_element(Y,X),X)
% 0.65/0.76 | X = Y ) ).
% 0.65/0.76
% 0.65/0.76 %---- SPECIAL CLASSES.
% 0.65/0.76 %----(SP1): lemma.
% 0.65/0.76 cnf(special_classes_lemma,axiom,
% 0.65/0.76 ~ member(Y,intersection(complement(X),X)) ).
% 0.65/0.76
% 0.65/0.76 %----(SP2): Existence of O (null class).
% 0.65/0.76 %----e:x:a:z:(-(z e x)).
% 0.65/0.76 cnf(existence_of_null_class,axiom,
% 0.65/0.76 ~ member(Z,null_class) ).
% 0.65/0.76
% 0.65/0.76 %----(SP3): O is a subclass of every class.
% 0.65/0.76 cnf(null_class_is_subclass,axiom,
% 0.65/0.76 subclass(null_class,X) ).
% 0.65/0.76
% 0.65/0.76 %----corollary.
% 0.65/0.76 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.65/0.76 ( ~ subclass(X,null_class)
% 0.65/0.76 | X = null_class ) ).
% 0.65/0.76
% 0.65/0.76 %----(SP4): uniqueness of null class.
% 0.65/0.76 cnf(null_class_is_unique,axiom,
% 0.65/0.76 ( Z = null_class
% 0.65/0.76 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.65/0.76
% 0.65/0.76 %----(SP5): O is a set (follows from axiom of infinity).
% 0.65/0.76 cnf(null_class_is_a_set,axiom,
% 0.65/0.76 member(null_class,universal_class) ).
% 0.65/0.76
% 0.65/0.76 %---- UNORDERED PAIRS.
% 0.65/0.76 %----(UP1): unordered pair is commutative.
% 0.65/0.76 cnf(commutativity_of_unordered_pair,axiom,
% 0.65/0.76 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.65/0.76
% 0.65/0.76 %----(UP2): if one argument is a proper class, pair contains only the
% 0.65/0.76 %----other. In a slightly different form to the paper
% 0.65/0.76 cnf(singleton_in_unordered_pair1,axiom,
% 0.65/0.76 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.65/0.76
% 0.65/0.76 cnf(singleton_in_unordered_pair2,axiom,
% 0.65/0.76 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.65/0.76
% 0.65/0.76 cnf(unordered_pair_equals_singleton1,axiom,
% 0.65/0.76 ( member(Y,universal_class)
% 0.65/0.77 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.65/0.77
% 0.65/0.77 cnf(unordered_pair_equals_singleton2,axiom,
% 0.65/0.77 ( member(X,universal_class)
% 0.65/0.77 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.65/0.77
% 0.65/0.77 %----(UP3): if both arguments are proper classes, pair is null.
% 0.65/0.77 cnf(null_unordered_pair,axiom,
% 0.65/0.77 ( unordered_pair(X,Y) = null_class
% 0.65/0.77 | member(X,universal_class)
% 0.65/0.77 | member(Y,universal_class) ) ).
% 0.65/0.77
% 0.65/0.77 %----(UP4): left cancellation for unordered pairs.
% 0.65/0.77 cnf(left_cancellation,axiom,
% 0.65/0.77 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.65/0.77 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.65/0.77 | Y = Z ) ).
% 0.65/0.77
% 0.65/0.77 %----(UP5): right cancellation for unordered pairs.
% 0.65/0.77 cnf(right_cancellation,axiom,
% 0.65/0.77 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.65/0.77 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.65/0.77 | X = Y ) ).
% 0.65/0.77
% 0.65/0.77 %----(UP6): corollary to (A-4).
% 0.65/0.77 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.65/0.77 ( ~ member(X,universal_class)
% 0.65/0.77 | unordered_pair(X,Y) != null_class ) ).
% 0.65/0.77
% 0.65/0.77 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.65/0.77 ( ~ member(Y,universal_class)
% 0.65/0.77 | unordered_pair(X,Y) != null_class ) ).
% 0.65/0.77
% 0.65/0.77 %----corollary to instantiate variables.
% 0.65/0.77 %----Not in the paper
% 0.65/0.77 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.65/0.77 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.65/0.77 | unordered_pair(X,Y) != null_class ) ).
% 0.65/0.77
% 0.65/0.77 %----(UP7): if both members of a pair belong to a set, the pair
% 0.65/0.77 %----is a subset.
% 0.65/0.77 cnf(unordered_pair_is_subset,axiom,
% 0.65/0.77 ( ~ member(X,Z)
% 0.65/0.77 | ~ member(Y,Z)
% 0.65/0.77 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.65/0.77
% 0.65/0.77 %---- SINGLETONS.
% 0.65/0.77 %----(SS1): every singleton is a set.
% 0.65/0.77 cnf(singletons_are_sets,axiom,
% 0.65/0.77 member(singleton(X),universal_class) ).
% 0.65/0.77
% 0.65/0.77 %----corollary, not in the paper.
% 0.65/0.77 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.65/0.77 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.65/0.77
% 0.65/0.77 %----(SS2): a set belongs to its singleton.
% 0.65/0.77 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.65/0.77 cnf(set_in_its_singleton,axiom,
% 0.65/0.77 ( ~ member(X,universal_class)
% 0.65/0.77 | member(X,singleton(X)) ) ).
% 0.65/0.77
% 0.65/0.77 %----corollary
% 0.65/0.77 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.65/0.77 ( ~ member(X,universal_class)
% 0.65/0.77 | singleton(X) != null_class ) ).
% 0.65/0.77
% 0.65/0.77 %----Not in the paper
% 0.65/0.77 cnf(null_class_in_its_singleton,axiom,
% 0.65/0.77 member(null_class,singleton(null_class)) ).
% 0.65/0.77
% 0.65/0.77 cnf(prove_only_member_in_singleton_1,negated_conjecture,
% 0.65/0.77 member(y,singleton(x)) ).
% 0.65/0.77
% 0.65/0.77 cnf(prove_only_member_in_singleton_2,negated_conjecture,
% 0.65/0.77 y != x ).
% 0.65/0.77
% 0.65/0.77 %--------------------------------------------------------------------------
% 0.65/0.77 %-------------------------------------------
% 0.65/0.77 % Proof found
% 0.65/0.77 % SZS status Theorem for theBenchmark
% 0.65/0.77 % SZS output start Proof
% 0.65/0.77 %ClaNum:153(EqnAxiom:42)
% 0.65/0.77 %VarNum:871(SingletonVarNum:213)
% 0.65/0.77 %MaxLitNum:5
% 0.65/0.77 %MaxfuncDepth:24
% 0.65/0.77 %SharedTerms:37
% 0.65/0.77 %goalClause: 54 67
% 0.65/0.77 %singleGoalClaCount:2
% 0.65/0.77 [43]P1(a1)
% 0.65/0.77 [44]P2(a2)
% 0.65/0.77 [45]P5(a4,a17)
% 0.65/0.77 [46]P5(a1,a17)
% 0.65/0.77 [67]~E(a25,a24)
% 0.65/0.77 [51]P6(a5,f6(a17,a17))
% 0.65/0.77 [52]P6(a18,f6(a17,a17))
% 0.65/0.77 [53]P5(a4,f23(a4,a4))
% 0.65/0.77 [54]P5(a24,f23(a25,a25))
% 0.65/0.77 [63]E(f10(f9(f11(f6(a21,a17))),a21),a13)
% 0.65/0.77 [65]E(f10(f6(a17,a17),f10(f6(a17,a17),f8(f7(f8(a5),f9(f11(f6(a5,a17))))))),a21)
% 0.65/0.77 [47]P6(x471,a17)
% 0.65/0.77 [48]P6(a4,x481)
% 0.65/0.77 [49]P6(x491,x491)
% 0.65/0.77 [68]~P5(x681,a4)
% 0.65/0.77 [61]P6(f19(x611),f6(f6(a17,a17),a17))
% 0.65/0.77 [62]P6(f11(x621),f6(f6(a17,a17),a17))
% 0.65/0.77 [66]E(f10(f9(x661),f8(f9(f10(f7(f9(f11(f6(a5,a17))),x661),a13)))),f3(x661))
% 0.65/0.77 [50]E(f23(x501,x502),f23(x502,x501))
% 0.65/0.77 [55]P5(f23(x551,x552),a17)
% 0.65/0.77 [57]P6(f7(x571,x572),f6(a17,a17))
% 0.65/0.77 [58]P6(f23(x581,x581),f23(x582,x581))
% 0.65/0.77 [59]P6(f23(x591,x591),f23(x591,x592))
% 0.65/0.77 [64]P5(f23(x641,x641),f23(x642,f23(x641,x641)))
% 0.65/0.77 [69]~P5(x691,f10(f8(x692),x692))
% 0.65/0.77 [60]E(f10(f6(x601,x602),x603),f10(x603,f6(x601,x602)))
% 0.65/0.77 [70]~P7(x701)+P2(x701)
% 0.65/0.77 [71]~P8(x711)+P2(x711)
% 0.65/0.77 [74]~P1(x741)+P6(a1,x741)
% 0.65/0.77 [75]~P1(x751)+P5(a4,x751)
% 0.65/0.77 [76]~P6(x761,a4)+E(x761,a4)
% 0.65/0.77 [78]P5(f20(x781),x781)+E(x781,a4)
% 0.65/0.77 [79]E(x791,a4)+P5(f14(x791,a4),x791)
% 0.65/0.77 [83]~P2(x831)+P6(x831,f6(a17,a17))
% 0.65/0.77 [77]E(x771,a4)+E(f10(x771,f20(x771)),a4)
% 0.65/0.77 [96]~P8(x961)+E(f6(f9(f9(x961)),f9(f9(x961))),f9(x961))
% 0.65/0.77 [110]~P7(x1101)+P2(f9(f11(f6(x1101,a17))))
% 0.65/0.77 [115]~P5(x1151,a17)+P5(f9(f10(a5,f6(a17,x1151))),a17)
% 0.65/0.77 [117]~P9(x1171)+P6(f7(x1171,f9(f11(f6(x1171,a17)))),a13)
% 0.65/0.77 [118]~P2(x1181)+P6(f7(x1181,f9(f11(f6(x1181,a17)))),a13)
% 0.65/0.77 [119]~P8(x1191)+P6(f9(f9(f11(f6(x1191,a17)))),f9(f9(x1191)))
% 0.65/0.77 [124]P9(x1241)+~P6(f7(x1241,f9(f11(f6(x1241,a17)))),a13)
% 0.65/0.77 [140]~P1(x1401)+P6(f9(f9(f11(f6(f10(a18,f6(x1401,a17)),a17)))),x1401)
% 0.65/0.77 [144]~P5(x1441,a17)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1441),a17)),a17))))),a17)
% 0.65/0.77 [72]~E(x722,x721)+P6(x721,x722)
% 0.65/0.77 [73]~E(x731,x732)+P6(x731,x732)
% 0.65/0.77 [81]P5(x812,a17)+E(f23(x811,x812),f23(x811,x811))
% 0.65/0.77 [82]P5(x821,a17)+E(f23(x821,x822),f23(x822,x822))
% 0.65/0.77 [84]~P5(x842,a17)+~E(f23(x841,x842),a4)
% 0.65/0.77 [85]~P5(x851,a17)+~E(f23(x851,x852),a4)
% 0.65/0.77 [88]P6(x881,x882)+P5(f14(x881,x882),x881)
% 0.65/0.77 [89]~P5(x891,x892)+~P5(x891,f8(x892))
% 0.65/0.77 [93]~P5(x931,a17)+P5(x931,f23(x932,x931))
% 0.65/0.77 [94]~P5(x941,a17)+P5(x941,f23(x941,x942))
% 0.65/0.77 [100]P6(x1001,x1002)+~P5(f14(x1001,x1002),x1002)
% 0.65/0.77 [114]~P5(x1142,f9(x1141))+~E(f10(x1141,f6(f23(x1142,x1142),a17)),a4)
% 0.65/0.77 [123]P5(x1231,x1232)+~P5(f23(f23(x1231,x1231),f23(x1231,f23(x1232,x1232))),a5)
% 0.65/0.77 [137]~P5(f23(f23(x1371,x1371),f23(x1371,f23(x1372,x1372))),a18)+E(f8(f10(f8(x1371),f8(f23(x1371,x1371)))),x1372)
% 0.65/0.77 [104]P2(x1041)+~P3(x1041,x1042,x1043)
% 0.65/0.77 [105]P8(x1051)+~P4(x1052,x1053,x1051)
% 0.65/0.77 [106]P8(x1061)+~P4(x1062,x1061,x1063)
% 0.65/0.77 [113]~P4(x1131,x1132,x1133)+P3(x1131,x1132,x1133)
% 0.65/0.77 [98]P5(x981,x982)+~P5(x981,f10(x983,x982))
% 0.65/0.77 [99]P5(x991,x992)+~P5(x991,f10(x992,x993))
% 0.65/0.77 [107]~P3(x1072,x1071,x1073)+E(f9(f9(x1071)),f9(x1072))
% 0.65/0.77 [120]~P5(x1201,f6(x1202,x1203))+E(f23(f23(f12(x1201),f12(x1201)),f23(f12(x1201),f23(f22(x1201),f22(x1201)))),x1201)
% 0.65/0.77 [122]~P3(x1221,x1223,x1222)+P6(f9(f9(f11(f6(x1221,a17)))),f9(f9(x1222)))
% 0.65/0.77 [125]P5(x1251,a17)+~P5(f23(f23(x1252,x1252),f23(x1252,f23(x1251,x1251))),f6(x1253,x1254))
% 0.65/0.77 [126]P5(x1261,a17)+~P5(f23(f23(x1261,x1261),f23(x1261,f23(x1262,x1262))),f6(x1263,x1264))
% 0.65/0.77 [127]P5(x1271,x1272)+~P5(f23(f23(x1273,x1273),f23(x1273,f23(x1271,x1271))),f6(x1274,x1272))
% 0.65/0.77 [128]P5(x1281,x1282)+~P5(f23(f23(x1281,x1281),f23(x1281,f23(x1283,x1283))),f6(x1282,x1284))
% 0.65/0.77 [129]~E(f23(x1291,x1292),a4)+~P5(f23(f23(x1291,x1291),f23(x1291,f23(x1292,x1292))),f6(x1293,x1294))
% 0.65/0.77 [133]P5(x1331,f23(x1332,x1331))+~P5(f23(f23(x1332,x1332),f23(x1332,f23(x1331,x1331))),f6(x1333,x1334))
% 0.65/0.77 [134]P5(x1341,f23(x1341,x1342))+~P5(f23(f23(x1341,x1341),f23(x1341,f23(x1342,x1342))),f6(x1343,x1344))
% 0.65/0.77 [145]~P5(f23(f23(f23(f23(x1453,x1453),f23(x1453,f23(x1451,x1451))),f23(f23(x1453,x1453),f23(x1453,f23(x1451,x1451)))),f23(f23(f23(x1453,x1453),f23(x1453,f23(x1451,x1451))),f23(x1452,x1452))),f19(x1454))+P5(f23(f23(f23(f23(x1451,x1451),f23(x1451,f23(x1452,x1452))),f23(f23(x1451,x1451),f23(x1451,f23(x1452,x1452)))),f23(f23(f23(x1451,x1451),f23(x1451,f23(x1452,x1452))),f23(x1453,x1453))),x1454)
% 0.65/0.77 [146]~P5(f23(f23(f23(f23(x1462,x1462),f23(x1462,f23(x1461,x1461))),f23(f23(x1462,x1462),f23(x1462,f23(x1461,x1461)))),f23(f23(f23(x1462,x1462),f23(x1462,f23(x1461,x1461))),f23(x1463,x1463))),f11(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)
% 0.65/0.77 [150]~P5(f23(f23(x1504,x1504),f23(x1504,f23(x1501,x1501))),f7(x1502,x1503))+P5(x1501,f9(f9(f11(f6(f10(x1502,f6(f9(f9(f11(f6(f10(x1503,f6(f23(x1504,x1504),a17)),a17)))),a17)),a17)))))
% 0.65/0.77 [116]~P2(x1161)+P7(x1161)+~P2(f9(f11(f6(x1161,a17))))
% 0.65/0.77 [130]P2(x1301)+~P6(x1301,f6(a17,a17))+~P6(f7(x1301,f9(f11(f6(x1301,a17)))),a13)
% 0.65/0.77 [142]P1(x1421)+~P5(a4,x1421)+~P6(f9(f9(f11(f6(f10(a18,f6(x1421,a17)),a17)))),x1421)
% 0.65/0.77 [149]~P5(x1491,a17)+E(x1491,a4)+P5(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(a2,f6(f23(x1491,x1491),a17)),a17))))))),x1491)
% 0.65/0.77 [87]~P6(x872,x871)+~P6(x871,x872)+E(x871,x872)
% 0.65/0.77 [80]P5(x802,a17)+P5(x801,a17)+E(f23(x801,x802),a4)
% 0.65/0.77 [90]P5(x901,x902)+P5(x901,f8(x902))+~P5(x901,a17)
% 0.65/0.77 [101]E(x1011,x1012)+P5(f14(x1012,x1011),x1012)+P5(f14(x1011,x1012),x1011)
% 0.65/0.77 [109]E(x1091,x1092)+P5(f14(x1092,x1091),x1092)+~P5(f14(x1091,x1092),x1092)
% 0.65/0.77 [111]E(x1111,x1112)+~P5(f14(x1112,x1111),x1111)+~P5(f14(x1111,x1112),x1112)
% 0.65/0.77 [112]P5(x1122,f9(x1121))+~P5(x1122,a17)+E(f10(x1121,f6(f23(x1122,x1122),a17)),a4)
% 0.65/0.77 [138]~P5(x1381,x1382)+~P5(f23(f23(x1381,x1381),f23(x1381,f23(x1382,x1382))),f6(a17,a17))+P5(f23(f23(x1381,x1381),f23(x1381,f23(x1382,x1382))),a5)
% 0.65/0.77 [139]~P5(f23(f23(x1391,x1391),f23(x1391,f23(x1392,x1392))),f6(a17,a17))+~E(f8(f10(f8(x1391),f8(f23(x1391,x1391)))),x1392)+P5(f23(f23(x1391,x1391),f23(x1391,f23(x1392,x1392))),a18)
% 0.65/0.77 [141]~P2(x1411)+~P5(x1412,a17)+P5(f9(f9(f11(f6(f10(x1411,f6(x1412,a17)),a17)))),a17)
% 0.65/0.77 [91]~P6(x911,x913)+P6(x911,x912)+~P6(x913,x912)
% 0.65/0.77 [92]~P5(x921,x923)+P5(x921,x922)+~P6(x923,x922)
% 0.65/0.77 [97]E(x971,x972)+E(x971,x973)+~P5(x971,f23(x973,x972))
% 0.65/0.77 [102]~P5(x1021,x1023)+~P5(x1021,x1022)+P5(x1021,f10(x1022,x1023))
% 0.65/0.77 [103]~P5(x1032,x1033)+~P5(x1031,x1033)+P6(f23(x1031,x1032),x1033)
% 0.65/0.77 [131]E(x1311,x1312)+~E(f23(x1313,x1311),f23(x1313,x1312))+~P5(f23(f23(x1311,x1311),f23(x1311,f23(x1312,x1312))),f6(a17,a17))
% 0.65/0.77 [132]E(x1321,x1322)+~E(f23(x1321,x1323),f23(x1322,x1323))+~P5(f23(f23(x1321,x1321),f23(x1321,f23(x1322,x1322))),f6(a17,a17))
% 0.65/0.77 [121]~P5(x1212,x1214)+~P5(x1211,x1213)+P5(f23(f23(x1211,x1211),f23(x1211,f23(x1212,x1212))),f6(x1213,x1214))
% 0.65/0.77 [147]~P5(f23(f23(f23(f23(x1472,x1472),f23(x1472,f23(x1473,x1473))),f23(f23(x1472,x1472),f23(x1472,f23(x1473,x1473)))),f23(f23(f23(x1472,x1472),f23(x1472,f23(x1473,x1473))),f23(x1471,x1471))),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))),f19(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))),f6(f6(a17,a17),a17))
% 0.65/0.77 [148]~P5(f23(f23(f23(f23(x1482,x1482),f23(x1482,f23(x1481,x1481))),f23(f23(x1482,x1482),f23(x1482,f23(x1481,x1481)))),f23(f23(f23(x1482,x1482),f23(x1482,f23(x1481,x1481))),f23(x1483,x1483))),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))),f11(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))
% 0.65/0.77 [151]P5(f23(f23(x1511,x1511),f23(x1511,f23(x1512,x1512))),f7(x1513,x1514))+~P5(f23(f23(x1511,x1511),f23(x1511,f23(x1512,x1512))),f6(a17,a17))+~P5(x1512,f9(f9(f11(f6(f10(x1513,f6(f9(f9(f11(f6(f10(x1514,f6(f23(x1511,x1511),a17)),a17)))),a17)),a17)))))
% 0.65/0.77 [152]~P4(x1522,x1525,x1521)+~P5(f23(f23(x1523,x1523),f23(x1523,f23(x1524,x1524))),f9(x1525))+E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1521,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1523,x1523),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1523,x1523),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1523,x1523),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1524,x1524),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1524,x1524),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1523,x1523),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1523,x1523),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1523,x1523),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1524,x1524),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(x1524,x1524),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1522,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1525,f6(f23(f23(f23(x1523,x1523),f23(x1523,f23(x1524,x1524))),f23(f23(x1523,x1523),f23(x1523,f23(x1524,x1524)))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1525,f6(f23(f23(f23(x1523,x1523),f23(x1523,f23(x1524,x1524))),f23(f23(x1523,x1523),f23(x1523,f23(x1524,x1524)))),a17)),a17)))))))),a17)),a17))))))))
% 0.65/0.77 [136]~P2(x1361)+P8(x1361)+~E(f6(f9(f9(x1361)),f9(f9(x1361))),f9(x1361))+~P6(f9(f9(f11(f6(x1361,a17)))),f9(f9(x1361)))
% 0.65/0.77 [135]~P2(x1351)+P3(x1351,x1352,x1353)+~E(f9(f9(x1352)),f9(x1351))+~P6(f9(f9(f11(f6(x1351,a17)))),f9(f9(x1353)))
% 0.65/0.77 [143]~P8(x1433)+~P8(x1432)+~P3(x1431,x1432,x1433)+P4(x1431,x1432,x1433)+P5(f23(f23(f15(x1431,x1432,x1433),f15(x1431,x1432,x1433)),f23(f15(x1431,x1432,x1433),f23(f16(x1431,x1432,x1433),f16(x1431,x1432,x1433)))),f9(x1432))
% 0.65/0.77 [153]~P8(x1533)+~P8(x1532)+~P3(x1531,x1532,x1533)+P4(x1531,x1532,x1533)+~E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1533,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f16(x1531,x1532,x1533),f16(x1531,x1532,x1533)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f16(x1531,x1532,x1533),f16(x1531,x1532,x1533)),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f16(x1531,x1532,x1533),f16(x1531,x1532,x1533)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f16(x1531,x1532,x1533),f16(x1531,x1532,x1533)),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1531,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(f23(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),f23(f15(x1531,x1532,x1533),f23(f16(x1531,x1532,x1533),f16(x1531,x1532,x1533)))),f23(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),f23(f15(x1531,x1532,x1533),f23(f16(x1531,x1532,x1533),f16(x1531,x1532,x1533))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1532,f6(f23(f23(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),f23(f15(x1531,x1532,x1533),f23(f16(x1531,x1532,x1533),f16(x1531,x1532,x1533)))),f23(f23(f15(x1531,x1532,x1533),f15(x1531,x1532,x1533)),f23(f15(x1531,x1532,x1533),f23(f16(x1531,x1532,x1533),f16(x1531,x1532,x1533))))),a17)),a17)))))))),a17)),a17))))))))
% 0.65/0.77 %EqnAxiom
% 0.65/0.77 [1]E(x11,x11)
% 0.65/0.77 [2]E(x22,x21)+~E(x21,x22)
% 0.65/0.77 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.65/0.77 [4]~E(x41,x42)+E(f23(x41,x43),f23(x42,x43))
% 0.65/0.77 [5]~E(x51,x52)+E(f23(x53,x51),f23(x53,x52))
% 0.65/0.77 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.65/0.77 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.65/0.77 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.65/0.77 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.65/0.77 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.65/0.77 [11]~E(x111,x112)+E(f11(x111),f11(x112))
% 0.65/0.77 [12]~E(x121,x122)+E(f8(x121),f8(x122))
% 0.65/0.77 [13]~E(x131,x132)+E(f16(x131,x133,x134),f16(x132,x133,x134))
% 0.65/0.77 [14]~E(x141,x142)+E(f16(x143,x141,x144),f16(x143,x142,x144))
% 0.65/0.77 [15]~E(x151,x152)+E(f16(x153,x154,x151),f16(x153,x154,x152))
% 0.65/0.77 [16]~E(x161,x162)+E(f14(x161,x163),f14(x162,x163))
% 0.65/0.77 [17]~E(x171,x172)+E(f14(x173,x171),f14(x173,x172))
% 0.65/0.77 [18]~E(x181,x182)+E(f7(x181,x183),f7(x182,x183))
% 0.65/0.77 [19]~E(x191,x192)+E(f7(x193,x191),f7(x193,x192))
% 0.65/0.77 [20]~E(x201,x202)+E(f15(x201,x203,x204),f15(x202,x203,x204))
% 0.65/0.77 [21]~E(x211,x212)+E(f15(x213,x211,x214),f15(x213,x212,x214))
% 0.65/0.77 [22]~E(x221,x222)+E(f15(x223,x224,x221),f15(x223,x224,x222))
% 0.65/0.77 [23]~E(x231,x232)+E(f20(x231),f20(x232))
% 0.65/0.77 [24]~E(x241,x242)+E(f19(x241),f19(x242))
% 0.65/0.77 [25]~E(x251,x252)+E(f3(x251),f3(x252))
% 0.65/0.77 [26]~E(x261,x262)+E(f22(x261),f22(x262))
% 0.65/0.77 [27]~E(x271,x272)+E(f12(x271),f12(x272))
% 0.65/0.77 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.65/0.77 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.65/0.77 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.65/0.77 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.65/0.77 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.65/0.77 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.65/0.77 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.65/0.77 [35]P6(x352,x353)+~E(x351,x352)+~P6(x351,x353)
% 0.65/0.77 [36]P6(x363,x362)+~E(x361,x362)+~P6(x363,x361)
% 0.65/0.77 [37]~P8(x371)+P8(x372)+~E(x371,x372)
% 0.65/0.77 [38]P4(x382,x383,x384)+~E(x381,x382)+~P4(x381,x383,x384)
% 0.65/0.77 [39]P4(x393,x392,x394)+~E(x391,x392)+~P4(x393,x391,x394)
% 0.65/0.77 [40]P4(x403,x404,x402)+~E(x401,x402)+~P4(x403,x404,x401)
% 0.65/0.77 [41]~P9(x411)+P9(x412)+~E(x411,x412)
% 0.65/0.77 [42]~P7(x421)+P7(x422)+~E(x421,x422)
% 0.65/0.77
% 0.65/0.77 %-------------------------------------------
% 0.65/0.77 cnf(156,plain,
% 0.65/0.77 (~P5(x1561,a4)),
% 0.65/0.77 inference(rename_variables,[],[68])).
% 0.65/0.77 cnf(159,plain,
% 0.65/0.77 (~P5(x1591,f10(f8(x1592),x1592))),
% 0.65/0.77 inference(rename_variables,[],[69])).
% 0.65/0.77 cnf(162,plain,
% 0.65/0.77 (~P5(x1621,f10(f8(x1622),x1622))),
% 0.65/0.77 inference(rename_variables,[],[69])).
% 0.65/0.77 cnf(167,plain,
% 0.65/0.77 (~P5(x1671,a4)),
% 0.65/0.77 inference(rename_variables,[],[68])).
% 0.65/0.77 cnf(170,plain,
% 0.65/0.77 (~P5(x1701,a4)),
% 0.65/0.77 inference(rename_variables,[],[68])).
% 0.65/0.77 cnf(173,plain,
% 0.65/0.77 (P6(x1731,x1731)),
% 0.65/0.77 inference(rename_variables,[],[49])).
% 0.65/0.77 cnf(177,plain,
% 0.65/0.77 (~P5(x1771,a4)),
% 0.65/0.77 inference(rename_variables,[],[68])).
% 0.65/0.77 cnf(183,plain,
% 0.65/0.77 (~P5(x1831,f10(f8(x1832),x1832))),
% 0.65/0.77 inference(rename_variables,[],[69])).
% 0.65/0.77 cnf(185,plain,
% 0.65/0.77 (E(a24,a25)),
% 0.65/0.77 inference(scs_inference,[],[54,49,173,47,68,156,167,170,63,69,159,162,2,75,79,88,114,146,145,36,35,31,28,3,92,102,97])).
% 0.65/0.77 cnf(191,plain,
% 0.65/0.77 (~P5(x1911,a4)),
% 0.65/0.77 inference(rename_variables,[],[68])).
% 0.65/0.77 cnf(250,plain,
% 0.65/0.77 (~P5(x2501,a4)),
% 0.65/0.77 inference(rename_variables,[],[68])).
% 0.65/0.77 cnf(258,plain,
% 0.65/0.77 (~P6(f23(a25,a25),a4)),
% 0.65/0.77 inference(scs_inference,[],[54,49,173,47,48,68,156,167,170,177,191,250,43,44,45,63,65,69,159,162,183,2,75,79,88,114,146,145,36,35,31,28,3,92,102,97,80,101,73,72,83,144,140,115,99,98,94,93,89,85,84,78,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,118,77,127,128,123,30,29,87])).
% 0.65/0.77 cnf(271,plain,
% 0.65/0.77 (P5(f23(f23(a24,a24),f23(a24,f23(a24,a24))),f6(f23(a25,a25),f23(a25,a25)))),
% 0.65/0.77 inference(scs_inference,[],[54,49,173,47,48,68,156,167,170,177,191,250,43,44,45,63,65,55,69,159,162,183,2,75,79,88,114,146,145,36,35,31,28,3,92,102,97,80,101,73,72,83,144,140,115,99,98,94,93,89,85,84,78,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,118,77,127,128,123,30,29,87,90,141,103,149,121])).
% 0.65/0.77 cnf(279,plain,
% 0.65/0.77 (~E(f23(a24,a24),a4)),
% 0.65/0.77 inference(scs_inference,[],[54,49,173,47,48,68,156,167,170,177,191,250,43,44,45,63,65,55,69,159,162,183,2,75,79,88,114,146,145,36,35,31,28,3,92,102,97,80,101,73,72,83,144,140,115,99,98,94,93,89,85,84,78,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,118,77,127,128,123,30,29,87,90,141,103,149,121,76,124,134,129])).
% 0.65/0.77 cnf(324,plain,
% 0.65/0.77 ($false),
% 0.65/0.77 inference(scs_inference,[],[54,46,68,55,47,67,44,45,271,258,279,185,120,142,79,141,102,149,92,72,2]),
% 0.65/0.77 ['proof']).
% 0.65/0.77 % SZS output end Proof
% 0.65/0.77 % Total time :0.130000s
%------------------------------------------------------------------------------