TSTP Solution File: SET077-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET077-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n008.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 14:28:30 EDT 2023
% Result : Unsatisfiable 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET077-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 10:42:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.54 start to proof:theBenchmark
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % File :CSE---1.6
% 0.20/0.62 % Problem :theBenchmark
% 0.20/0.62 % Transform :cnf
% 0.20/0.62 % Format :tptp:raw
% 0.20/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.62
% 0.20/0.62 % Result :Theorem 0.000000s
% 0.20/0.62 % Output :CNFRefutation 0.000000s
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 %--------------------------------------------------------------------------
% 0.20/0.62 % File : SET077-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.20/0.62 % Domain : Set Theory
% 0.20/0.62 % Problem : Every singleton is a set
% 0.20/0.62 % Version : [Qua92] axioms : Augmented.
% 0.20/0.62 % English :
% 0.20/0.62
% 0.20/0.62 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.20/0.62 % Source : [Quaife]
% 0.20/0.62 % Names : SS1 [Qua92]
% 0.20/0.62
% 0.20/0.62 % Status : Unsatisfiable
% 0.20/0.62 % Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 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, 0.05 v5.3.0, 0.11 v5.2.0, 0.06 v5.0.0, 0.07 v4.1.0, 0.08 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
% 0.20/0.62 % Syntax : Number of clauses : 120 ( 38 unt; 15 nHn; 81 RR)
% 0.20/0.62 % Number of literals : 239 ( 56 equ; 110 neg)
% 0.20/0.62 % Maximal clause size : 5 ( 1 avg)
% 0.20/0.62 % Maximal term depth : 6 ( 1 avg)
% 0.20/0.62 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.20/0.62 % Number of functors : 39 ( 39 usr; 9 con; 0-3 aty)
% 0.20/0.62 % Number of variables : 239 ( 44 sgn)
% 0.20/0.62 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.20/0.62
% 0.20/0.62 % Comments : Preceding lemmas are added.
% 0.20/0.62 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.20/0.62 %--------------------------------------------------------------------------
% 0.20/0.62 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.20/0.62 include('Axioms/SET004-0.ax').
% 0.20/0.62 %--------------------------------------------------------------------------
% 0.20/0.62 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.20/0.62 cnf(corollary_1_to_unordered_pair,axiom,
% 0.20/0.62 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.62 | member(X,unordered_pair(X,Y)) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(corollary_2_to_unordered_pair,axiom,
% 0.20/0.62 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.62 | member(Y,unordered_pair(X,Y)) ) ).
% 0.20/0.62
% 0.20/0.62 %----Corollaries to Cartesian product axiom.
% 0.20/0.62 cnf(corollary_1_to_cartesian_product,axiom,
% 0.20/0.62 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.62 | member(U,universal_class) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(corollary_2_to_cartesian_product,axiom,
% 0.20/0.62 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.62 | member(V,universal_class) ) ).
% 0.20/0.62
% 0.20/0.62 %---- PARTIAL ORDER.
% 0.20/0.62 %----(PO1): reflexive.
% 0.20/0.62 cnf(subclass_is_reflexive,axiom,
% 0.20/0.62 subclass(X,X) ).
% 0.20/0.62
% 0.20/0.62 %----(PO2): antisymmetry is part of A-3.
% 0.20/0.62 %----(x < y), (y < x) --> (x = y).
% 0.20/0.62
% 0.20/0.62 %----(PO3): transitivity.
% 0.20/0.62 cnf(transitivity_of_subclass,axiom,
% 0.20/0.62 ( ~ subclass(X,Y)
% 0.20/0.62 | ~ subclass(Y,Z)
% 0.20/0.62 | subclass(X,Z) ) ).
% 0.20/0.62
% 0.20/0.62 %---- EQUALITY.
% 0.20/0.62 %----(EQ1): equality axiom.
% 0.20/0.62 %----a:x:(x = x).
% 0.20/0.62 %----This is always an axiom in the TPTP presentation
% 0.20/0.62
% 0.20/0.62 %----(EQ2): expanded equality definition.
% 0.20/0.62 cnf(equality1,axiom,
% 0.20/0.62 ( X = Y
% 0.20/0.62 | member(not_subclass_element(X,Y),X)
% 0.20/0.62 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(equality2,axiom,
% 0.20/0.62 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.62 | X = Y
% 0.20/0.62 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(equality3,axiom,
% 0.20/0.62 ( ~ member(not_subclass_element(Y,X),X)
% 0.20/0.62 | X = Y
% 0.20/0.62 | member(not_subclass_element(X,Y),X) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(equality4,axiom,
% 0.20/0.62 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.62 | ~ member(not_subclass_element(Y,X),X)
% 0.20/0.62 | X = Y ) ).
% 0.20/0.62
% 0.20/0.62 %---- SPECIAL CLASSES.
% 0.20/0.62 %----(SP1): lemma.
% 0.20/0.62 cnf(special_classes_lemma,axiom,
% 0.20/0.62 ~ member(Y,intersection(complement(X),X)) ).
% 0.20/0.62
% 0.20/0.62 %----(SP2): Existence of O (null class).
% 0.20/0.62 %----e:x:a:z:(-(z e x)).
% 0.20/0.62 cnf(existence_of_null_class,axiom,
% 0.20/0.62 ~ member(Z,null_class) ).
% 0.20/0.62
% 0.20/0.62 %----(SP3): O is a subclass of every class.
% 0.20/0.62 cnf(null_class_is_subclass,axiom,
% 0.20/0.62 subclass(null_class,X) ).
% 0.20/0.62
% 0.20/0.62 %----corollary.
% 0.20/0.62 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.20/0.62 ( ~ subclass(X,null_class)
% 0.20/0.62 | X = null_class ) ).
% 0.20/0.62
% 0.20/0.62 %----(SP4): uniqueness of null class.
% 0.20/0.62 cnf(null_class_is_unique,axiom,
% 0.20/0.62 ( Z = null_class
% 0.20/0.62 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.20/0.62
% 0.20/0.62 %----(SP5): O is a set (follows from axiom of infinity).
% 0.20/0.62 cnf(null_class_is_a_set,axiom,
% 0.20/0.62 member(null_class,universal_class) ).
% 0.20/0.62
% 0.20/0.62 %---- UNORDERED PAIRS.
% 0.20/0.62 %----(UP1): unordered pair is commutative.
% 0.20/0.62 cnf(commutativity_of_unordered_pair,axiom,
% 0.20/0.62 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.20/0.63
% 0.20/0.63 %----(UP2): if one argument is a proper class, pair contains only the
% 0.20/0.63 %----other. In a slightly different form to the paper
% 0.20/0.63 cnf(singleton_in_unordered_pair1,axiom,
% 0.20/0.63 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.20/0.63
% 0.20/0.63 cnf(singleton_in_unordered_pair2,axiom,
% 0.20/0.63 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.20/0.63
% 0.20/0.63 cnf(unordered_pair_equals_singleton1,axiom,
% 0.20/0.63 ( member(Y,universal_class)
% 0.20/0.63 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.20/0.63
% 0.20/0.63 cnf(unordered_pair_equals_singleton2,axiom,
% 0.20/0.63 ( member(X,universal_class)
% 0.20/0.63 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.20/0.63
% 0.20/0.63 %----(UP3): if both arguments are proper classes, pair is null.
% 0.20/0.63 cnf(null_unordered_pair,axiom,
% 0.20/0.63 ( unordered_pair(X,Y) = null_class
% 0.20/0.63 | member(X,universal_class)
% 0.20/0.63 | member(Y,universal_class) ) ).
% 0.20/0.63
% 0.20/0.63 %----(UP4): left cancellation for unordered pairs.
% 0.20/0.63 cnf(left_cancellation,axiom,
% 0.20/0.63 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.20/0.63 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.20/0.63 | Y = Z ) ).
% 0.20/0.63
% 0.20/0.63 %----(UP5): right cancellation for unordered pairs.
% 0.20/0.63 cnf(right_cancellation,axiom,
% 0.20/0.63 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.20/0.63 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.20/0.63 | X = Y ) ).
% 0.20/0.63
% 0.20/0.63 %----(UP6): corollary to (A-4).
% 0.20/0.63 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.20/0.63 ( ~ member(X,universal_class)
% 0.20/0.63 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.63
% 0.20/0.63 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.20/0.63 ( ~ member(Y,universal_class)
% 0.20/0.63 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.63
% 0.20/0.63 %----corollary to instantiate variables.
% 0.20/0.63 %----Not in the paper
% 0.20/0.63 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.20/0.63 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.63 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.63
% 0.20/0.63 %----(UP7): if both members of a pair belong to a set, the pair
% 0.20/0.63 %----is a subset.
% 0.20/0.63 cnf(unordered_pair_is_subset,axiom,
% 0.20/0.63 ( ~ member(X,Z)
% 0.20/0.63 | ~ member(Y,Z)
% 0.20/0.63 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.20/0.63
% 0.20/0.63 cnf(prove_singletons_are_sets_1,negated_conjecture,
% 0.20/0.63 ~ member(singleton(x),universal_class) ).
% 0.20/0.63
% 0.20/0.63 %--------------------------------------------------------------------------
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 %ClaNum:147(EqnAxiom:42)
% 0.20/0.63 %VarNum:866(SingletonVarNum:211)
% 0.20/0.63 %MaxLitNum:5
% 0.20/0.63 %MaxfuncDepth:24
% 0.20/0.63 %SharedTerms:33
% 0.20/0.63 %goalClause: 64
% 0.20/0.63 %singleGoalClaCount:1
% 0.20/0.63 [43]P1(a1)
% 0.20/0.63 [44]P2(a2)
% 0.20/0.63 [45]P5(a4,a17)
% 0.20/0.63 [46]P5(a1,a17)
% 0.20/0.63 [51]P6(a5,f6(a17,a17))
% 0.20/0.63 [52]P6(a18,f6(a17,a17))
% 0.20/0.63 [64]~P5(f23(a24,a24),a17)
% 0.20/0.63 [60]E(f10(f9(f11(f6(a21,a17))),a21),a13)
% 0.20/0.63 [61]E(f10(f6(a17,a17),f10(f6(a17,a17),f8(f7(f8(a5),f9(f11(f6(a5,a17))))))),a21)
% 0.20/0.63 [47]P6(x471,a17)
% 0.20/0.63 [48]P6(a4,x481)
% 0.20/0.63 [49]P6(x491,x491)
% 0.20/0.63 [63]~P5(x631,a4)
% 0.20/0.63 [58]P6(f19(x581),f6(f6(a17,a17),a17))
% 0.20/0.63 [59]P6(f11(x591),f6(f6(a17,a17),a17))
% 0.20/0.63 [62]E(f10(f9(x621),f8(f9(f10(f7(f9(f11(f6(a5,a17))),x621),a13)))),f3(x621))
% 0.20/0.63 [50]E(f23(x501,x502),f23(x502,x501))
% 0.20/0.63 [53]P5(f23(x531,x532),a17)
% 0.20/0.63 [54]P6(f7(x541,x542),f6(a17,a17))
% 0.20/0.63 [55]P6(f23(x551,x551),f23(x552,x551))
% 0.20/0.63 [56]P6(f23(x561,x561),f23(x561,x562))
% 0.20/0.63 [65]~P5(x651,f10(f8(x652),x652))
% 0.20/0.63 [57]E(f10(f6(x571,x572),x573),f10(x573,f6(x571,x572)))
% 0.20/0.63 [66]~P7(x661)+P2(x661)
% 0.20/0.63 [67]~P8(x671)+P2(x671)
% 0.20/0.63 [70]~P1(x701)+P6(a1,x701)
% 0.20/0.63 [71]~P1(x711)+P5(a4,x711)
% 0.20/0.63 [72]~P6(x721,a4)+E(x721,a4)
% 0.20/0.63 [74]P5(f20(x741),x741)+E(x741,a4)
% 0.20/0.63 [75]E(x751,a4)+P5(f14(x751,a4),x751)
% 0.20/0.63 [79]~P2(x791)+P6(x791,f6(a17,a17))
% 0.20/0.63 [73]E(x731,a4)+E(f10(x731,f20(x731)),a4)
% 0.20/0.63 [90]~P8(x901)+E(f6(f9(f9(x901)),f9(f9(x901))),f9(x901))
% 0.20/0.63 [104]~P7(x1041)+P2(f9(f11(f6(x1041,a17))))
% 0.20/0.63 [109]~P5(x1091,a17)+P5(f9(f10(a5,f6(a17,x1091))),a17)
% 0.20/0.63 [111]~P9(x1111)+P6(f7(x1111,f9(f11(f6(x1111,a17)))),a13)
% 0.20/0.63 [112]~P2(x1121)+P6(f7(x1121,f9(f11(f6(x1121,a17)))),a13)
% 0.20/0.63 [113]~P8(x1131)+P6(f9(f9(f11(f6(x1131,a17)))),f9(f9(x1131)))
% 0.20/0.63 [118]P9(x1181)+~P6(f7(x1181,f9(f11(f6(x1181,a17)))),a13)
% 0.20/0.63 [134]~P1(x1341)+P6(f9(f9(f11(f6(f10(a18,f6(x1341,a17)),a17)))),x1341)
% 0.20/0.63 [138]~P5(x1381,a17)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1381),a17)),a17))))),a17)
% 0.20/0.63 [68]~E(x682,x681)+P6(x681,x682)
% 0.20/0.63 [69]~E(x691,x692)+P6(x691,x692)
% 0.20/0.63 [77]P5(x772,a17)+E(f23(x771,x772),f23(x771,x771))
% 0.20/0.63 [78]P5(x781,a17)+E(f23(x781,x782),f23(x782,x782))
% 0.20/0.63 [80]~P5(x802,a17)+~E(f23(x801,x802),a4)
% 0.20/0.63 [81]~P5(x811,a17)+~E(f23(x811,x812),a4)
% 0.20/0.63 [83]P6(x831,x832)+P5(f14(x831,x832),x831)
% 0.20/0.63 [84]~P5(x841,x842)+~P5(x841,f8(x842))
% 0.20/0.63 [88]~P5(x881,a17)+P5(x881,f23(x882,x881))
% 0.20/0.63 [89]~P5(x891,a17)+P5(x891,f23(x891,x892))
% 0.20/0.63 [94]P6(x941,x942)+~P5(f14(x941,x942),x942)
% 0.20/0.63 [108]~P5(x1082,f9(x1081))+~E(f10(x1081,f6(f23(x1082,x1082),a17)),a4)
% 0.20/0.63 [117]P5(x1171,x1172)+~P5(f23(f23(x1171,x1171),f23(x1171,f23(x1172,x1172))),a5)
% 0.20/0.63 [131]~P5(f23(f23(x1311,x1311),f23(x1311,f23(x1312,x1312))),a18)+E(f8(f10(f8(x1311),f8(f23(x1311,x1311)))),x1312)
% 0.20/0.63 [98]P2(x981)+~P3(x981,x982,x983)
% 0.20/0.63 [99]P8(x991)+~P4(x992,x993,x991)
% 0.20/0.63 [100]P8(x1001)+~P4(x1002,x1001,x1003)
% 0.20/0.63 [107]~P4(x1071,x1072,x1073)+P3(x1071,x1072,x1073)
% 0.20/0.63 [92]P5(x921,x922)+~P5(x921,f10(x923,x922))
% 0.20/0.63 [93]P5(x931,x932)+~P5(x931,f10(x932,x933))
% 0.20/0.63 [101]~P3(x1012,x1011,x1013)+E(f9(f9(x1011)),f9(x1012))
% 0.20/0.63 [114]~P5(x1141,f6(x1142,x1143))+E(f23(f23(f12(x1141),f12(x1141)),f23(f12(x1141),f23(f22(x1141),f22(x1141)))),x1141)
% 0.20/0.63 [116]~P3(x1161,x1163,x1162)+P6(f9(f9(f11(f6(x1161,a17)))),f9(f9(x1162)))
% 0.20/0.63 [119]P5(x1191,a17)+~P5(f23(f23(x1192,x1192),f23(x1192,f23(x1191,x1191))),f6(x1193,x1194))
% 0.20/0.63 [120]P5(x1201,a17)+~P5(f23(f23(x1201,x1201),f23(x1201,f23(x1202,x1202))),f6(x1203,x1204))
% 0.20/0.63 [121]P5(x1211,x1212)+~P5(f23(f23(x1213,x1213),f23(x1213,f23(x1211,x1211))),f6(x1214,x1212))
% 0.20/0.63 [122]P5(x1221,x1222)+~P5(f23(f23(x1221,x1221),f23(x1221,f23(x1223,x1223))),f6(x1222,x1224))
% 0.20/0.63 [123]~E(f23(x1231,x1232),a4)+~P5(f23(f23(x1231,x1231),f23(x1231,f23(x1232,x1232))),f6(x1233,x1234))
% 0.20/0.63 [127]P5(x1271,f23(x1272,x1271))+~P5(f23(f23(x1272,x1272),f23(x1272,f23(x1271,x1271))),f6(x1273,x1274))
% 0.20/0.63 [128]P5(x1281,f23(x1281,x1282))+~P5(f23(f23(x1281,x1281),f23(x1281,f23(x1282,x1282))),f6(x1283,x1284))
% 0.20/0.63 [139]~P5(f23(f23(f23(f23(x1393,x1393),f23(x1393,f23(x1391,x1391))),f23(f23(x1393,x1393),f23(x1393,f23(x1391,x1391)))),f23(f23(f23(x1393,x1393),f23(x1393,f23(x1391,x1391))),f23(x1392,x1392))),f19(x1394))+P5(f23(f23(f23(f23(x1391,x1391),f23(x1391,f23(x1392,x1392))),f23(f23(x1391,x1391),f23(x1391,f23(x1392,x1392)))),f23(f23(f23(x1391,x1391),f23(x1391,f23(x1392,x1392))),f23(x1393,x1393))),x1394)
% 0.20/0.63 [140]~P5(f23(f23(f23(f23(x1402,x1402),f23(x1402,f23(x1401,x1401))),f23(f23(x1402,x1402),f23(x1402,f23(x1401,x1401)))),f23(f23(f23(x1402,x1402),f23(x1402,f23(x1401,x1401))),f23(x1403,x1403))),f11(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)
% 0.20/0.63 [144]~P5(f23(f23(x1444,x1444),f23(x1444,f23(x1441,x1441))),f7(x1442,x1443))+P5(x1441,f9(f9(f11(f6(f10(x1442,f6(f9(f9(f11(f6(f10(x1443,f6(f23(x1444,x1444),a17)),a17)))),a17)),a17)))))
% 0.20/0.63 [110]~P2(x1101)+P7(x1101)+~P2(f9(f11(f6(x1101,a17))))
% 0.20/0.63 [124]P2(x1241)+~P6(x1241,f6(a17,a17))+~P6(f7(x1241,f9(f11(f6(x1241,a17)))),a13)
% 0.20/0.63 [136]P1(x1361)+~P5(a4,x1361)+~P6(f9(f9(f11(f6(f10(a18,f6(x1361,a17)),a17)))),x1361)
% 0.20/0.63 [143]~P5(x1431,a17)+E(x1431,a4)+P5(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(a2,f6(f23(x1431,x1431),a17)),a17))))))),x1431)
% 0.20/0.63 [82]~P6(x822,x821)+~P6(x821,x822)+E(x821,x822)
% 0.20/0.63 [76]P5(x762,a17)+P5(x761,a17)+E(f23(x761,x762),a4)
% 0.20/0.63 [85]P5(x851,x852)+P5(x851,f8(x852))+~P5(x851,a17)
% 0.20/0.63 [95]E(x951,x952)+P5(f14(x952,x951),x952)+P5(f14(x951,x952),x951)
% 0.20/0.63 [103]E(x1031,x1032)+P5(f14(x1032,x1031),x1032)+~P5(f14(x1031,x1032),x1032)
% 0.20/0.63 [105]E(x1051,x1052)+~P5(f14(x1052,x1051),x1051)+~P5(f14(x1051,x1052),x1052)
% 0.20/0.63 [106]P5(x1062,f9(x1061))+~P5(x1062,a17)+E(f10(x1061,f6(f23(x1062,x1062),a17)),a4)
% 0.20/0.63 [132]~P5(x1321,x1322)+~P5(f23(f23(x1321,x1321),f23(x1321,f23(x1322,x1322))),f6(a17,a17))+P5(f23(f23(x1321,x1321),f23(x1321,f23(x1322,x1322))),a5)
% 0.20/0.63 [133]~P5(f23(f23(x1331,x1331),f23(x1331,f23(x1332,x1332))),f6(a17,a17))+~E(f8(f10(f8(x1331),f8(f23(x1331,x1331)))),x1332)+P5(f23(f23(x1331,x1331),f23(x1331,f23(x1332,x1332))),a18)
% 0.20/0.63 [135]~P2(x1351)+~P5(x1352,a17)+P5(f9(f9(f11(f6(f10(x1351,f6(x1352,a17)),a17)))),a17)
% 0.20/0.63 [86]~P6(x861,x863)+P6(x861,x862)+~P6(x863,x862)
% 0.20/0.63 [87]~P5(x871,x873)+P5(x871,x872)+~P6(x873,x872)
% 0.20/0.63 [91]E(x911,x912)+E(x911,x913)+~P5(x911,f23(x913,x912))
% 0.20/0.63 [96]~P5(x961,x963)+~P5(x961,x962)+P5(x961,f10(x962,x963))
% 0.20/0.63 [97]~P5(x972,x973)+~P5(x971,x973)+P6(f23(x971,x972),x973)
% 0.20/0.63 [125]E(x1251,x1252)+~E(f23(x1253,x1251),f23(x1253,x1252))+~P5(f23(f23(x1251,x1251),f23(x1251,f23(x1252,x1252))),f6(a17,a17))
% 0.20/0.63 [126]E(x1261,x1262)+~E(f23(x1261,x1263),f23(x1262,x1263))+~P5(f23(f23(x1261,x1261),f23(x1261,f23(x1262,x1262))),f6(a17,a17))
% 0.20/0.63 [115]~P5(x1152,x1154)+~P5(x1151,x1153)+P5(f23(f23(x1151,x1151),f23(x1151,f23(x1152,x1152))),f6(x1153,x1154))
% 0.20/0.63 [141]~P5(f23(f23(f23(f23(x1412,x1412),f23(x1412,f23(x1413,x1413))),f23(f23(x1412,x1412),f23(x1412,f23(x1413,x1413)))),f23(f23(f23(x1412,x1412),f23(x1412,f23(x1413,x1413))),f23(x1411,x1411))),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))),f19(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))),f6(f6(a17,a17),a17))
% 0.20/0.63 [142]~P5(f23(f23(f23(f23(x1422,x1422),f23(x1422,f23(x1421,x1421))),f23(f23(x1422,x1422),f23(x1422,f23(x1421,x1421)))),f23(f23(f23(x1422,x1422),f23(x1422,f23(x1421,x1421))),f23(x1423,x1423))),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))),f11(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))
% 0.20/0.63 [145]P5(f23(f23(x1451,x1451),f23(x1451,f23(x1452,x1452))),f7(x1453,x1454))+~P5(f23(f23(x1451,x1451),f23(x1451,f23(x1452,x1452))),f6(a17,a17))+~P5(x1452,f9(f9(f11(f6(f10(x1453,f6(f9(f9(f11(f6(f10(x1454,f6(f23(x1451,x1451),a17)),a17)))),a17)),a17)))))
% 0.20/0.63 [146]~P4(x1462,x1465,x1461)+~P5(f23(f23(x1463,x1463),f23(x1463,f23(x1464,x1464))),f9(x1465))+E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1461,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1463,x1463),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1463,x1463),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1463,x1463),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1464,x1464),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1464,x1464),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1463,x1463),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1463,x1463),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1463,x1463),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1464,x1464),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(x1464,x1464),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1462,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1465,f6(f23(f23(f23(x1463,x1463),f23(x1463,f23(x1464,x1464))),f23(f23(x1463,x1463),f23(x1463,f23(x1464,x1464)))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1465,f6(f23(f23(f23(x1463,x1463),f23(x1463,f23(x1464,x1464))),f23(f23(x1463,x1463),f23(x1463,f23(x1464,x1464)))),a17)),a17)))))))),a17)),a17))))))))
% 0.20/0.63 [130]~P2(x1301)+P8(x1301)+~E(f6(f9(f9(x1301)),f9(f9(x1301))),f9(x1301))+~P6(f9(f9(f11(f6(x1301,a17)))),f9(f9(x1301)))
% 0.20/0.63 [129]~P2(x1291)+P3(x1291,x1292,x1293)+~E(f9(f9(x1292)),f9(x1291))+~P6(f9(f9(f11(f6(x1291,a17)))),f9(f9(x1293)))
% 0.20/0.63 [137]~P8(x1373)+~P8(x1372)+~P3(x1371,x1372,x1373)+P4(x1371,x1372,x1373)+P5(f23(f23(f15(x1371,x1372,x1373),f15(x1371,x1372,x1373)),f23(f15(x1371,x1372,x1373),f23(f16(x1371,x1372,x1373),f16(x1371,x1372,x1373)))),f9(x1372))
% 0.20/0.63 [147]~P8(x1473)+~P8(x1472)+~P3(x1471,x1472,x1473)+P4(x1471,x1472,x1473)+~E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1473,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f16(x1471,x1472,x1473),f16(x1471,x1472,x1473)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f16(x1471,x1472,x1473),f16(x1471,x1472,x1473)),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f16(x1471,x1472,x1473),f16(x1471,x1472,x1473)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f16(x1471,x1472,x1473),f16(x1471,x1472,x1473)),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1471,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(f23(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),f23(f15(x1471,x1472,x1473),f23(f16(x1471,x1472,x1473),f16(x1471,x1472,x1473)))),f23(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),f23(f15(x1471,x1472,x1473),f23(f16(x1471,x1472,x1473),f16(x1471,x1472,x1473))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1472,f6(f23(f23(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),f23(f15(x1471,x1472,x1473),f23(f16(x1471,x1472,x1473),f16(x1471,x1472,x1473)))),f23(f23(f15(x1471,x1472,x1473),f15(x1471,x1472,x1473)),f23(f15(x1471,x1472,x1473),f23(f16(x1471,x1472,x1473),f16(x1471,x1472,x1473))))),a17)),a17)))))))),a17)),a17))))))))
% 0.20/0.63 %EqnAxiom
% 0.20/0.63 [1]E(x11,x11)
% 0.20/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.63 [4]~E(x41,x42)+E(f23(x41,x43),f23(x42,x43))
% 0.20/0.63 [5]~E(x51,x52)+E(f23(x53,x51),f23(x53,x52))
% 0.20/0.63 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.20/0.63 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.20/0.63 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.20/0.63 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.20/0.63 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.20/0.63 [11]~E(x111,x112)+E(f8(x111),f8(x112))
% 0.20/0.63 [12]~E(x121,x122)+E(f7(x121,x123),f7(x122,x123))
% 0.20/0.63 [13]~E(x131,x132)+E(f7(x133,x131),f7(x133,x132))
% 0.20/0.63 [14]~E(x141,x142)+E(f11(x141),f11(x142))
% 0.20/0.63 [15]~E(x151,x152)+E(f19(x151),f19(x152))
% 0.20/0.63 [16]~E(x161,x162)+E(f15(x161,x163,x164),f15(x162,x163,x164))
% 0.20/0.63 [17]~E(x171,x172)+E(f15(x173,x171,x174),f15(x173,x172,x174))
% 0.20/0.63 [18]~E(x181,x182)+E(f15(x183,x184,x181),f15(x183,x184,x182))
% 0.20/0.63 [19]~E(x191,x192)+E(f14(x191,x193),f14(x192,x193))
% 0.20/0.63 [20]~E(x201,x202)+E(f14(x203,x201),f14(x203,x202))
% 0.20/0.63 [21]~E(x211,x212)+E(f22(x211),f22(x212))
% 0.20/0.63 [22]~E(x221,x222)+E(f16(x221,x223,x224),f16(x222,x223,x224))
% 0.20/0.63 [23]~E(x231,x232)+E(f16(x233,x231,x234),f16(x233,x232,x234))
% 0.20/0.63 [24]~E(x241,x242)+E(f16(x243,x244,x241),f16(x243,x244,x242))
% 0.20/0.63 [25]~E(x251,x252)+E(f12(x251),f12(x252))
% 0.20/0.63 [26]~E(x261,x262)+E(f20(x261),f20(x262))
% 0.20/0.63 [27]~E(x271,x272)+E(f3(x271),f3(x272))
% 0.20/0.63 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.20/0.63 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.20/0.63 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.20/0.63 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.20/0.63 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.20/0.63 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.20/0.63 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.20/0.63 [35]P6(x352,x353)+~E(x351,x352)+~P6(x351,x353)
% 0.20/0.63 [36]P6(x363,x362)+~E(x361,x362)+~P6(x363,x361)
% 0.20/0.63 [37]P4(x372,x373,x374)+~E(x371,x372)+~P4(x371,x373,x374)
% 0.20/0.63 [38]P4(x383,x382,x384)+~E(x381,x382)+~P4(x383,x381,x384)
% 0.20/0.63 [39]P4(x393,x394,x392)+~E(x391,x392)+~P4(x393,x394,x391)
% 0.20/0.63 [40]~P8(x401)+P8(x402)+~E(x401,x402)
% 0.20/0.63 [41]~P7(x411)+P7(x412)+~E(x411,x412)
% 0.20/0.63 [42]~P9(x421)+P9(x422)+~E(x421,x422)
% 0.20/0.63
% 0.20/0.63 %-------------------------------------------
% 0.20/0.64 cnf(148,plain,
% 0.20/0.64 ($false),
% 0.20/0.64 inference(scs_inference,[],[64,53]),
% 0.20/0.64 ['proof']).
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time :0.000000s
%------------------------------------------------------------------------------