TSTP Solution File: SET078-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET078-7 : 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 14:28:31 EDT 2023
% Result : Unsatisfiable 0.18s 0.64s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14 % Problem : SET078-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.35 % Computer : n031.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Aug 26 09:12:22 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.18/0.57 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 0.000000s
% 0.18/0.63 % Output :CNFRefutation 0.000000s
% 0.18/0.63 %-------------------------------------------
% 0.18/0.64 %--------------------------------------------------------------------------
% 0.18/0.64 % File : SET078-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.18/0.64 % Domain : Set Theory
% 0.18/0.64 % Problem : Corollary to every singleton is a set
% 0.18/0.64 % Version : [Qua92] axioms : Augmented.
% 0.18/0.64 % English :
% 0.18/0.64
% 0.18/0.64 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.18/0.64 % Source : [Quaife]
% 0.18/0.64 % Names : SS1 cor. [Quaife]
% 0.18/0.64
% 0.18/0.64 % Status : Unsatisfiable
% 0.18/0.64 % Rating : 0.05 v8.1.0, 0.11 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v5.5.0, 0.10 v5.4.0, 0.05 v5.3.0, 0.06 v5.1.0, 0.18 v5.0.0, 0.14 v4.1.0, 0.15 v4.0.1, 0.27 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
% 0.18/0.64 % Syntax : Number of clauses : 121 ( 39 unt; 15 nHn; 81 RR)
% 0.18/0.64 % Number of literals : 240 ( 56 equ; 110 neg)
% 0.18/0.64 % Maximal clause size : 5 ( 1 avg)
% 0.18/0.64 % Maximal term depth : 6 ( 1 avg)
% 0.18/0.64 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.18/0.64 % Number of functors : 40 ( 40 usr; 10 con; 0-3 aty)
% 0.18/0.64 % Number of variables : 240 ( 45 sgn)
% 0.18/0.64 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.18/0.64
% 0.18/0.64 % Comments : Preceding lemmas are added.
% 0.18/0.64 % : Not in [Qua92].
% 0.18/0.64 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.18/0.64 %--------------------------------------------------------------------------
% 0.18/0.64 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.18/0.64 include('Axioms/SET004-0.ax').
% 0.18/0.64 %--------------------------------------------------------------------------
% 0.18/0.64 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.18/0.64 cnf(corollary_1_to_unordered_pair,axiom,
% 0.18/0.64 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.18/0.64 | member(X,unordered_pair(X,Y)) ) ).
% 0.18/0.64
% 0.18/0.64 cnf(corollary_2_to_unordered_pair,axiom,
% 0.18/0.64 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.18/0.64 | member(Y,unordered_pair(X,Y)) ) ).
% 0.18/0.64
% 0.18/0.64 %----Corollaries to Cartesian product axiom.
% 0.18/0.64 cnf(corollary_1_to_cartesian_product,axiom,
% 0.18/0.64 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.18/0.64 | member(U,universal_class) ) ).
% 0.18/0.64
% 0.18/0.64 cnf(corollary_2_to_cartesian_product,axiom,
% 0.18/0.64 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.18/0.64 | member(V,universal_class) ) ).
% 0.18/0.64
% 0.18/0.64 %---- PARTIAL ORDER.
% 0.18/0.64 %----(PO1): reflexive.
% 0.18/0.64 cnf(subclass_is_reflexive,axiom,
% 0.18/0.64 subclass(X,X) ).
% 0.18/0.64
% 0.18/0.64 %----(PO2): antisymmetry is part of A-3.
% 0.18/0.64 %----(x < y), (y < x) --> (x = y).
% 0.18/0.64
% 0.18/0.64 %----(PO3): transitivity.
% 0.18/0.64 cnf(transitivity_of_subclass,axiom,
% 0.18/0.64 ( ~ subclass(X,Y)
% 0.18/0.64 | ~ subclass(Y,Z)
% 0.18/0.64 | subclass(X,Z) ) ).
% 0.18/0.64
% 0.18/0.64 %---- EQUALITY.
% 0.18/0.64 %----(EQ1): equality axiom.
% 0.18/0.64 %----a:x:(x = x).
% 0.18/0.64 %----This is always an axiom in the TPTP presentation.
% 0.18/0.64
% 0.18/0.64 %----(EQ2): expanded equality definition.
% 0.18/0.64 cnf(equality1,axiom,
% 0.18/0.64 ( X = Y
% 0.18/0.64 | member(not_subclass_element(X,Y),X)
% 0.18/0.64 | member(not_subclass_element(Y,X),Y) ) ).
% 0.18/0.64
% 0.18/0.64 cnf(equality2,axiom,
% 0.18/0.64 ( ~ member(not_subclass_element(X,Y),Y)
% 0.18/0.64 | X = Y
% 0.18/0.64 | member(not_subclass_element(Y,X),Y) ) ).
% 0.18/0.64
% 0.18/0.64 cnf(equality3,axiom,
% 0.18/0.64 ( ~ member(not_subclass_element(Y,X),X)
% 0.18/0.64 | X = Y
% 0.18/0.64 | member(not_subclass_element(X,Y),X) ) ).
% 0.18/0.64
% 0.18/0.64 cnf(equality4,axiom,
% 0.18/0.64 ( ~ member(not_subclass_element(X,Y),Y)
% 0.18/0.64 | ~ member(not_subclass_element(Y,X),X)
% 0.18/0.64 | X = Y ) ).
% 0.18/0.64
% 0.18/0.64 %---- SPECIAL CLASSES.
% 0.18/0.64 %----(SP1): lemma.
% 0.18/0.64 cnf(special_classes_lemma,axiom,
% 0.18/0.64 ~ member(Y,intersection(complement(X),X)) ).
% 0.18/0.64
% 0.18/0.64 %----(SP2): Existence of O (null class).
% 0.18/0.64 %----e:x:a:z:(-(z e x)).
% 0.18/0.64 cnf(existence_of_null_class,axiom,
% 0.18/0.64 ~ member(Z,null_class) ).
% 0.18/0.64
% 0.18/0.64 %----(SP3): O is a subclass of every class.
% 0.18/0.64 cnf(null_class_is_subclass,axiom,
% 0.18/0.64 subclass(null_class,X) ).
% 0.18/0.64
% 0.18/0.64 %----corollary.
% 0.18/0.64 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.18/0.64 ( ~ subclass(X,null_class)
% 0.18/0.64 | X = null_class ) ).
% 0.18/0.64
% 0.18/0.64 %----(SP4): uniqueness of null class.
% 0.18/0.64 cnf(null_class_is_unique,axiom,
% 0.18/0.64 ( Z = null_class
% 0.18/0.64 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.18/0.64
% 0.18/0.64 %----(SP5): O is a set (follows from axiom of infinity).
% 0.18/0.64 cnf(null_class_is_a_set,axiom,
% 0.18/0.64 member(null_class,universal_class) ).
% 0.18/0.64
% 0.18/0.64 %---- UNORDERED PAIRS.
% 0.18/0.64 %----(UP1): unordered pair is commutative.
% 0.18/0.64 cnf(commutativity_of_unordered_pair,axiom,
% 0.18/0.64 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.18/0.64
% 0.18/0.64 %----(UP2): if one argument is a proper class, pair contains only the
% 0.18/0.64 %----other. In a slightly different form to the paper
% 0.18/0.64 cnf(singleton_in_unordered_pair1,axiom,
% 0.18/0.64 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.18/0.64
% 0.18/0.64 cnf(singleton_in_unordered_pair2,axiom,
% 0.18/0.64 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.18/0.64
% 0.18/0.64 cnf(unordered_pair_equals_singleton1,axiom,
% 0.18/0.64 ( member(Y,universal_class)
% 0.18/0.64 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.18/0.64
% 0.18/0.64 cnf(unordered_pair_equals_singleton2,axiom,
% 0.18/0.64 ( member(X,universal_class)
% 0.18/0.64 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.18/0.64
% 0.18/0.64 %----(UP3): if both arguments are proper classes, pair is null.
% 0.18/0.64 cnf(null_unordered_pair,axiom,
% 0.18/0.64 ( unordered_pair(X,Y) = null_class
% 0.18/0.64 | member(X,universal_class)
% 0.18/0.64 | member(Y,universal_class) ) ).
% 0.18/0.64
% 0.18/0.64 %----(UP4): left cancellation for unordered pairs.
% 0.18/0.64 cnf(left_cancellation,axiom,
% 0.18/0.64 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.18/0.64 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.18/0.64 | Y = Z ) ).
% 0.18/0.64
% 0.18/0.64 %----(UP5): right cancellation for unordered pairs.
% 0.18/0.64 cnf(right_cancellation,axiom,
% 0.18/0.64 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.18/0.64 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.18/0.64 | X = Y ) ).
% 0.18/0.64
% 0.18/0.64 %----(UP6): corollary to (A-4).
% 0.18/0.64 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.18/0.64 ( ~ member(X,universal_class)
% 0.18/0.64 | unordered_pair(X,Y) != null_class ) ).
% 0.18/0.64
% 0.18/0.64 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.18/0.64 ( ~ member(Y,universal_class)
% 0.18/0.64 | unordered_pair(X,Y) != null_class ) ).
% 0.18/0.64
% 0.18/0.64 %----corollary to instantiate variables.
% 0.18/0.64 %----Not in the paper
% 0.18/0.64 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.18/0.64 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.18/0.64 | unordered_pair(X,Y) != null_class ) ).
% 0.18/0.64
% 0.18/0.64 %----(UP7): if both members of a pair belong to a set, the pair
% 0.18/0.64 %----is a subset.
% 0.18/0.64 cnf(unordered_pair_is_subset,axiom,
% 0.18/0.64 ( ~ member(X,Z)
% 0.18/0.64 | ~ member(Y,Z)
% 0.18/0.64 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.18/0.64
% 0.18/0.64 %---- SINGLETONS.
% 0.18/0.64 %----(SS1): every singleton is a set.
% 0.18/0.64 cnf(singletons_are_sets,axiom,
% 0.18/0.64 member(singleton(X),universal_class) ).
% 0.18/0.64
% 0.18/0.64 cnf(prove_corollary_1_to_singletons_are_sets_1,negated_conjecture,
% 0.18/0.64 ~ member(singleton(y),unordered_pair(x,singleton(y))) ).
% 0.18/0.64
% 0.18/0.64 %--------------------------------------------------------------------------
% 0.18/0.64 %-------------------------------------------
% 0.18/0.64 % Proof found
% 0.18/0.64 % SZS status Theorem for theBenchmark
% 0.18/0.64 % SZS output start Proof
% 0.18/0.65 %ClaNum:148(EqnAxiom:42)
% 0.18/0.65 %VarNum:866(SingletonVarNum:211)
% 0.18/0.65 %MaxLitNum:5
% 0.18/0.65 %MaxfuncDepth:24
% 0.18/0.65 %SharedTerms:35
% 0.18/0.65 %goalClause: 66
% 0.18/0.65 %singleGoalClaCount:1
% 0.18/0.65 [43]P1(a1)
% 0.18/0.65 [44]P2(a2)
% 0.18/0.65 [45]P5(a4,a17)
% 0.18/0.65 [46]P5(a1,a17)
% 0.18/0.65 [51]P6(a5,f6(a17,a17))
% 0.18/0.65 [52]P6(a18,f6(a17,a17))
% 0.18/0.65 [66]~P5(f23(a24,a24),f23(a25,f23(a24,a24)))
% 0.18/0.65 [61]E(f10(f9(f11(f6(a21,a17))),a21),a13)
% 0.18/0.65 [62]E(f10(f6(a17,a17),f10(f6(a17,a17),f8(f7(f8(a5),f9(f11(f6(a5,a17))))))),a21)
% 0.18/0.65 [47]P6(x471,a17)
% 0.18/0.65 [48]P6(a4,x481)
% 0.18/0.65 [49]P6(x491,x491)
% 0.18/0.65 [64]~P5(x641,a4)
% 0.18/0.65 [59]P6(f19(x591),f6(f6(a17,a17),a17))
% 0.18/0.65 [60]P6(f11(x601),f6(f6(a17,a17),a17))
% 0.18/0.65 [63]E(f10(f9(x631),f8(f9(f10(f7(f9(f11(f6(a5,a17))),x631),a13)))),f3(x631))
% 0.18/0.65 [50]E(f23(x501,x502),f23(x502,x501))
% 0.18/0.65 [53]P5(f23(x531,x532),a17)
% 0.18/0.65 [55]P6(f7(x551,x552),f6(a17,a17))
% 0.18/0.65 [56]P6(f23(x561,x561),f23(x562,x561))
% 0.18/0.65 [57]P6(f23(x571,x571),f23(x571,x572))
% 0.18/0.65 [65]~P5(x651,f10(f8(x652),x652))
% 0.18/0.65 [58]E(f10(f6(x581,x582),x583),f10(x583,f6(x581,x582)))
% 0.18/0.65 [67]~P7(x671)+P2(x671)
% 0.18/0.65 [68]~P8(x681)+P2(x681)
% 0.18/0.65 [71]~P1(x711)+P6(a1,x711)
% 0.18/0.65 [72]~P1(x721)+P5(a4,x721)
% 0.18/0.65 [73]~P6(x731,a4)+E(x731,a4)
% 0.18/0.65 [75]P5(f20(x751),x751)+E(x751,a4)
% 0.18/0.65 [76]E(x761,a4)+P5(f14(x761,a4),x761)
% 0.18/0.65 [80]~P2(x801)+P6(x801,f6(a17,a17))
% 0.18/0.65 [74]E(x741,a4)+E(f10(x741,f20(x741)),a4)
% 0.18/0.65 [91]~P8(x911)+E(f6(f9(f9(x911)),f9(f9(x911))),f9(x911))
% 0.18/0.65 [105]~P7(x1051)+P2(f9(f11(f6(x1051,a17))))
% 0.18/0.65 [110]~P5(x1101,a17)+P5(f9(f10(a5,f6(a17,x1101))),a17)
% 0.18/0.65 [112]~P9(x1121)+P6(f7(x1121,f9(f11(f6(x1121,a17)))),a13)
% 0.18/0.65 [113]~P2(x1131)+P6(f7(x1131,f9(f11(f6(x1131,a17)))),a13)
% 0.18/0.65 [114]~P8(x1141)+P6(f9(f9(f11(f6(x1141,a17)))),f9(f9(x1141)))
% 0.18/0.65 [119]P9(x1191)+~P6(f7(x1191,f9(f11(f6(x1191,a17)))),a13)
% 0.18/0.65 [135]~P1(x1351)+P6(f9(f9(f11(f6(f10(a18,f6(x1351,a17)),a17)))),x1351)
% 0.18/0.65 [139]~P5(x1391,a17)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1391),a17)),a17))))),a17)
% 0.18/0.65 [69]~E(x692,x691)+P6(x691,x692)
% 0.18/0.65 [70]~E(x701,x702)+P6(x701,x702)
% 0.18/0.65 [78]P5(x782,a17)+E(f23(x781,x782),f23(x781,x781))
% 0.18/0.65 [79]P5(x791,a17)+E(f23(x791,x792),f23(x792,x792))
% 0.18/0.65 [81]~P5(x812,a17)+~E(f23(x811,x812),a4)
% 0.18/0.65 [82]~P5(x821,a17)+~E(f23(x821,x822),a4)
% 0.18/0.65 [84]P6(x841,x842)+P5(f14(x841,x842),x841)
% 0.18/0.65 [85]~P5(x851,x852)+~P5(x851,f8(x852))
% 0.18/0.65 [89]~P5(x891,a17)+P5(x891,f23(x892,x891))
% 0.18/0.65 [90]~P5(x901,a17)+P5(x901,f23(x901,x902))
% 0.18/0.65 [95]P6(x951,x952)+~P5(f14(x951,x952),x952)
% 0.18/0.65 [109]~P5(x1092,f9(x1091))+~E(f10(x1091,f6(f23(x1092,x1092),a17)),a4)
% 0.18/0.65 [118]P5(x1181,x1182)+~P5(f23(f23(x1181,x1181),f23(x1181,f23(x1182,x1182))),a5)
% 0.18/0.65 [132]~P5(f23(f23(x1321,x1321),f23(x1321,f23(x1322,x1322))),a18)+E(f8(f10(f8(x1321),f8(f23(x1321,x1321)))),x1322)
% 0.18/0.65 [99]P2(x991)+~P3(x991,x992,x993)
% 0.18/0.65 [100]P8(x1001)+~P4(x1002,x1003,x1001)
% 0.18/0.65 [101]P8(x1011)+~P4(x1012,x1011,x1013)
% 0.18/0.65 [108]~P4(x1081,x1082,x1083)+P3(x1081,x1082,x1083)
% 0.18/0.65 [93]P5(x931,x932)+~P5(x931,f10(x933,x932))
% 0.18/0.65 [94]P5(x941,x942)+~P5(x941,f10(x942,x943))
% 0.18/0.65 [102]~P3(x1022,x1021,x1023)+E(f9(f9(x1021)),f9(x1022))
% 0.18/0.65 [115]~P5(x1151,f6(x1152,x1153))+E(f23(f23(f12(x1151),f12(x1151)),f23(f12(x1151),f23(f22(x1151),f22(x1151)))),x1151)
% 0.18/0.65 [117]~P3(x1171,x1173,x1172)+P6(f9(f9(f11(f6(x1171,a17)))),f9(f9(x1172)))
% 0.18/0.65 [120]P5(x1201,a17)+~P5(f23(f23(x1202,x1202),f23(x1202,f23(x1201,x1201))),f6(x1203,x1204))
% 0.18/0.65 [121]P5(x1211,a17)+~P5(f23(f23(x1211,x1211),f23(x1211,f23(x1212,x1212))),f6(x1213,x1214))
% 0.18/0.65 [122]P5(x1221,x1222)+~P5(f23(f23(x1223,x1223),f23(x1223,f23(x1221,x1221))),f6(x1224,x1222))
% 0.18/0.65 [123]P5(x1231,x1232)+~P5(f23(f23(x1231,x1231),f23(x1231,f23(x1233,x1233))),f6(x1232,x1234))
% 0.18/0.65 [124]~E(f23(x1241,x1242),a4)+~P5(f23(f23(x1241,x1241),f23(x1241,f23(x1242,x1242))),f6(x1243,x1244))
% 0.18/0.65 [128]P5(x1281,f23(x1282,x1281))+~P5(f23(f23(x1282,x1282),f23(x1282,f23(x1281,x1281))),f6(x1283,x1284))
% 0.18/0.65 [129]P5(x1291,f23(x1291,x1292))+~P5(f23(f23(x1291,x1291),f23(x1291,f23(x1292,x1292))),f6(x1293,x1294))
% 0.18/0.65 [140]~P5(f23(f23(f23(f23(x1403,x1403),f23(x1403,f23(x1401,x1401))),f23(f23(x1403,x1403),f23(x1403,f23(x1401,x1401)))),f23(f23(f23(x1403,x1403),f23(x1403,f23(x1401,x1401))),f23(x1402,x1402))),f19(x1404))+P5(f23(f23(f23(f23(x1401,x1401),f23(x1401,f23(x1402,x1402))),f23(f23(x1401,x1401),f23(x1401,f23(x1402,x1402)))),f23(f23(f23(x1401,x1401),f23(x1401,f23(x1402,x1402))),f23(x1403,x1403))),x1404)
% 0.18/0.65 [141]~P5(f23(f23(f23(f23(x1412,x1412),f23(x1412,f23(x1411,x1411))),f23(f23(x1412,x1412),f23(x1412,f23(x1411,x1411)))),f23(f23(f23(x1412,x1412),f23(x1412,f23(x1411,x1411))),f23(x1413,x1413))),f11(x1414))+P5(f23(f23(f23(f23(x1411,x1411),f23(x1411,f23(x1412,x1412))),f23(f23(x1411,x1411),f23(x1411,f23(x1412,x1412)))),f23(f23(f23(x1411,x1411),f23(x1411,f23(x1412,x1412))),f23(x1413,x1413))),x1414)
% 0.18/0.65 [145]~P5(f23(f23(x1454,x1454),f23(x1454,f23(x1451,x1451))),f7(x1452,x1453))+P5(x1451,f9(f9(f11(f6(f10(x1452,f6(f9(f9(f11(f6(f10(x1453,f6(f23(x1454,x1454),a17)),a17)))),a17)),a17)))))
% 0.18/0.65 [111]~P2(x1111)+P7(x1111)+~P2(f9(f11(f6(x1111,a17))))
% 0.18/0.65 [125]P2(x1251)+~P6(x1251,f6(a17,a17))+~P6(f7(x1251,f9(f11(f6(x1251,a17)))),a13)
% 0.18/0.65 [137]P1(x1371)+~P5(a4,x1371)+~P6(f9(f9(f11(f6(f10(a18,f6(x1371,a17)),a17)))),x1371)
% 0.18/0.65 [144]~P5(x1441,a17)+E(x1441,a4)+P5(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(a2,f6(f23(x1441,x1441),a17)),a17))))))),x1441)
% 0.18/0.65 [83]~P6(x832,x831)+~P6(x831,x832)+E(x831,x832)
% 0.18/0.65 [77]P5(x772,a17)+P5(x771,a17)+E(f23(x771,x772),a4)
% 0.18/0.65 [86]P5(x861,x862)+P5(x861,f8(x862))+~P5(x861,a17)
% 0.18/0.65 [96]E(x961,x962)+P5(f14(x962,x961),x962)+P5(f14(x961,x962),x961)
% 0.18/0.65 [104]E(x1041,x1042)+P5(f14(x1042,x1041),x1042)+~P5(f14(x1041,x1042),x1042)
% 0.18/0.65 [106]E(x1061,x1062)+~P5(f14(x1062,x1061),x1061)+~P5(f14(x1061,x1062),x1062)
% 0.18/0.65 [107]P5(x1072,f9(x1071))+~P5(x1072,a17)+E(f10(x1071,f6(f23(x1072,x1072),a17)),a4)
% 0.18/0.65 [133]~P5(x1331,x1332)+~P5(f23(f23(x1331,x1331),f23(x1331,f23(x1332,x1332))),f6(a17,a17))+P5(f23(f23(x1331,x1331),f23(x1331,f23(x1332,x1332))),a5)
% 0.18/0.65 [134]~P5(f23(f23(x1341,x1341),f23(x1341,f23(x1342,x1342))),f6(a17,a17))+~E(f8(f10(f8(x1341),f8(f23(x1341,x1341)))),x1342)+P5(f23(f23(x1341,x1341),f23(x1341,f23(x1342,x1342))),a18)
% 0.18/0.65 [136]~P2(x1361)+~P5(x1362,a17)+P5(f9(f9(f11(f6(f10(x1361,f6(x1362,a17)),a17)))),a17)
% 0.18/0.65 [87]~P6(x871,x873)+P6(x871,x872)+~P6(x873,x872)
% 0.18/0.65 [88]~P5(x881,x883)+P5(x881,x882)+~P6(x883,x882)
% 0.18/0.65 [92]E(x921,x922)+E(x921,x923)+~P5(x921,f23(x923,x922))
% 0.18/0.65 [97]~P5(x971,x973)+~P5(x971,x972)+P5(x971,f10(x972,x973))
% 0.18/0.65 [98]~P5(x982,x983)+~P5(x981,x983)+P6(f23(x981,x982),x983)
% 0.18/0.65 [126]E(x1261,x1262)+~E(f23(x1263,x1261),f23(x1263,x1262))+~P5(f23(f23(x1261,x1261),f23(x1261,f23(x1262,x1262))),f6(a17,a17))
% 0.18/0.65 [127]E(x1271,x1272)+~E(f23(x1271,x1273),f23(x1272,x1273))+~P5(f23(f23(x1271,x1271),f23(x1271,f23(x1272,x1272))),f6(a17,a17))
% 0.18/0.65 [116]~P5(x1162,x1164)+~P5(x1161,x1163)+P5(f23(f23(x1161,x1161),f23(x1161,f23(x1162,x1162))),f6(x1163,x1164))
% 0.18/0.65 [142]~P5(f23(f23(f23(f23(x1422,x1422),f23(x1422,f23(x1423,x1423))),f23(f23(x1422,x1422),f23(x1422,f23(x1423,x1423)))),f23(f23(f23(x1422,x1422),f23(x1422,f23(x1423,x1423))),f23(x1421,x1421))),x1424)+P5(f23(f23(f23(f23(x1421,x1421),f23(x1421,f23(x1422,x1422))),f23(f23(x1421,x1421),f23(x1421,f23(x1422,x1422)))),f23(f23(f23(x1421,x1421),f23(x1421,f23(x1422,x1422))),f23(x1423,x1423))),f19(x1424))+~P5(f23(f23(f23(f23(x1421,x1421),f23(x1421,f23(x1422,x1422))),f23(f23(x1421,x1421),f23(x1421,f23(x1422,x1422)))),f23(f23(f23(x1421,x1421),f23(x1421,f23(x1422,x1422))),f23(x1423,x1423))),f6(f6(a17,a17),a17))
% 0.18/0.65 [143]~P5(f23(f23(f23(f23(x1432,x1432),f23(x1432,f23(x1431,x1431))),f23(f23(x1432,x1432),f23(x1432,f23(x1431,x1431)))),f23(f23(f23(x1432,x1432),f23(x1432,f23(x1431,x1431))),f23(x1433,x1433))),x1434)+P5(f23(f23(f23(f23(x1431,x1431),f23(x1431,f23(x1432,x1432))),f23(f23(x1431,x1431),f23(x1431,f23(x1432,x1432)))),f23(f23(f23(x1431,x1431),f23(x1431,f23(x1432,x1432))),f23(x1433,x1433))),f11(x1434))+~P5(f23(f23(f23(f23(x1431,x1431),f23(x1431,f23(x1432,x1432))),f23(f23(x1431,x1431),f23(x1431,f23(x1432,x1432)))),f23(f23(f23(x1431,x1431),f23(x1431,f23(x1432,x1432))),f23(x1433,x1433))),f6(f6(a17,a17),a17))
% 0.18/0.65 [146]P5(f23(f23(x1461,x1461),f23(x1461,f23(x1462,x1462))),f7(x1463,x1464))+~P5(f23(f23(x1461,x1461),f23(x1461,f23(x1462,x1462))),f6(a17,a17))+~P5(x1462,f9(f9(f11(f6(f10(x1463,f6(f9(f9(f11(f6(f10(x1464,f6(f23(x1461,x1461),a17)),a17)))),a17)),a17)))))
% 0.18/0.65 [147]~P4(x1472,x1475,x1471)+~P5(f23(f23(x1473,x1473),f23(x1473,f23(x1474,x1474))),f9(x1475))+E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1473,x1473),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1473,x1473),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1473,x1473),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1474,x1474),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1474,x1474),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1473,x1473),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1473,x1473),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1473,x1473),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1474,x1474),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(x1474,x1474),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1475,f6(f23(f23(f23(x1473,x1473),f23(x1473,f23(x1474,x1474))),f23(f23(x1473,x1473),f23(x1473,f23(x1474,x1474)))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1475,f6(f23(f23(f23(x1473,x1473),f23(x1473,f23(x1474,x1474))),f23(f23(x1473,x1473),f23(x1473,f23(x1474,x1474)))),a17)),a17)))))))),a17)),a17))))))))
% 0.18/0.65 [131]~P2(x1311)+P8(x1311)+~E(f6(f9(f9(x1311)),f9(f9(x1311))),f9(x1311))+~P6(f9(f9(f11(f6(x1311,a17)))),f9(f9(x1311)))
% 0.18/0.65 [130]~P2(x1301)+P3(x1301,x1302,x1303)+~E(f9(f9(x1302)),f9(x1301))+~P6(f9(f9(f11(f6(x1301,a17)))),f9(f9(x1303)))
% 0.18/0.65 [138]~P8(x1383)+~P8(x1382)+~P3(x1381,x1382,x1383)+P4(x1381,x1382,x1383)+P5(f23(f23(f15(x1381,x1382,x1383),f15(x1381,x1382,x1383)),f23(f15(x1381,x1382,x1383),f23(f16(x1381,x1382,x1383),f16(x1381,x1382,x1383)))),f9(x1382))
% 0.18/0.65 [148]~P8(x1483)+~P8(x1482)+~P3(x1481,x1482,x1483)+P4(x1481,x1482,x1483)+~E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1483,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f16(x1481,x1482,x1483),f16(x1481,x1482,x1483)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f16(x1481,x1482,x1483),f16(x1481,x1482,x1483)),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f16(x1481,x1482,x1483),f16(x1481,x1482,x1483)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f16(x1481,x1482,x1483),f16(x1481,x1482,x1483)),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1481,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1482,f6(f23(f23(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),f23(f15(x1481,x1482,x1483),f23(f16(x1481,x1482,x1483),f16(x1481,x1482,x1483)))),f23(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),f23(f15(x1481,x1482,x1483),f23(f16(x1481,x1482,x1483),f16(x1481,x1482,x1483))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1482,f6(f23(f23(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),f23(f15(x1481,x1482,x1483),f23(f16(x1481,x1482,x1483),f16(x1481,x1482,x1483)))),f23(f23(f15(x1481,x1482,x1483),f15(x1481,x1482,x1483)),f23(f15(x1481,x1482,x1483),f23(f16(x1481,x1482,x1483),f16(x1481,x1482,x1483))))),a17)),a17)))))))),a17)),a17))))))))
% 0.18/0.65 %EqnAxiom
% 0.18/0.65 [1]E(x11,x11)
% 0.18/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.65 [4]~E(x41,x42)+E(f23(x41,x43),f23(x42,x43))
% 0.18/0.65 [5]~E(x51,x52)+E(f23(x53,x51),f23(x53,x52))
% 0.18/0.65 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.18/0.65 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.18/0.65 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.18/0.65 [9]~E(x91,x92)+E(f19(x91),f19(x92))
% 0.18/0.65 [10]~E(x101,x102)+E(f10(x101,x103),f10(x102,x103))
% 0.18/0.65 [11]~E(x111,x112)+E(f10(x113,x111),f10(x113,x112))
% 0.18/0.65 [12]~E(x121,x122)+E(f11(x121),f11(x122))
% 0.18/0.65 [13]~E(x131,x132)+E(f7(x131,x133),f7(x132,x133))
% 0.18/0.65 [14]~E(x141,x142)+E(f7(x143,x141),f7(x143,x142))
% 0.18/0.65 [15]~E(x151,x152)+E(f8(x151),f8(x152))
% 0.18/0.65 [16]~E(x161,x162)+E(f15(x161,x163,x164),f15(x162,x163,x164))
% 0.18/0.65 [17]~E(x171,x172)+E(f15(x173,x171,x174),f15(x173,x172,x174))
% 0.18/0.65 [18]~E(x181,x182)+E(f15(x183,x184,x181),f15(x183,x184,x182))
% 0.18/0.65 [19]~E(x191,x192)+E(f16(x191,x193,x194),f16(x192,x193,x194))
% 0.18/0.65 [20]~E(x201,x202)+E(f16(x203,x201,x204),f16(x203,x202,x204))
% 0.18/0.65 [21]~E(x211,x212)+E(f16(x213,x214,x211),f16(x213,x214,x212))
% 0.18/0.65 [22]~E(x221,x222)+E(f3(x221),f3(x222))
% 0.18/0.65 [23]~E(x231,x232)+E(f14(x231,x233),f14(x232,x233))
% 0.18/0.65 [24]~E(x241,x242)+E(f14(x243,x241),f14(x243,x242))
% 0.18/0.65 [25]~E(x251,x252)+E(f20(x251),f20(x252))
% 0.18/0.65 [26]~E(x261,x262)+E(f12(x261),f12(x262))
% 0.18/0.65 [27]~E(x271,x272)+E(f22(x271),f22(x272))
% 0.18/0.65 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.18/0.65 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.18/0.65 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.18/0.65 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.18/0.65 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.18/0.65 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.18/0.65 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.18/0.65 [35]P6(x352,x353)+~E(x351,x352)+~P6(x351,x353)
% 0.18/0.65 [36]P6(x363,x362)+~E(x361,x362)+~P6(x363,x361)
% 0.18/0.65 [37]~P8(x371)+P8(x372)+~E(x371,x372)
% 0.18/0.65 [38]P4(x382,x383,x384)+~E(x381,x382)+~P4(x381,x383,x384)
% 0.18/0.65 [39]P4(x393,x392,x394)+~E(x391,x392)+~P4(x393,x391,x394)
% 0.18/0.65 [40]P4(x403,x404,x402)+~E(x401,x402)+~P4(x403,x404,x401)
% 0.18/0.65 [41]~P9(x411)+P9(x412)+~E(x411,x412)
% 0.18/0.65 [42]~P7(x421)+P7(x422)+~E(x421,x422)
% 0.18/0.65
% 0.18/0.65 %-------------------------------------------
% 0.18/0.66 cnf(153,plain,
% 0.18/0.66 ($false),
% 0.18/0.66 inference(scs_inference,[],[66,64,61,53,2,72,89]),
% 0.18/0.66 ['proof']).
% 0.18/0.66 % SZS output end Proof
% 0.18/0.66 % Total time :0.000000s
%------------------------------------------------------------------------------