TSTP Solution File: SET080-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET080-7 : 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 : n022.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 0.21s 0.64s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET080-7 : 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
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 09:30:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.55 start to proof:theBenchmark
% 0.21/0.63 %-------------------------------------------
% 0.21/0.63 % File :CSE---1.6
% 0.21/0.63 % Problem :theBenchmark
% 0.21/0.63 % Transform :cnf
% 0.21/0.63 % Format :tptp:raw
% 0.21/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.63
% 0.21/0.63 % Result :Theorem 0.000000s
% 0.21/0.63 % Output :CNFRefutation 0.000000s
% 0.21/0.63 %-------------------------------------------
% 0.21/0.63 %--------------------------------------------------------------------------
% 0.21/0.63 % File : SET080-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.21/0.63 % Domain : Set Theory
% 0.21/0.63 % Problem : Corollary to a set belongs to its singleton
% 0.21/0.63 % Version : [Qua92] axioms : Augmented.
% 0.21/0.63 % English :
% 0.21/0.63
% 0.21/0.63 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.21/0.63 % Source : [Quaife]
% 0.21/0.63 % Names : SS2 cor.2 [Quaife]
% 0.21/0.63
% 0.21/0.63 % Status : Unsatisfiable
% 0.21/0.63 % Rating : 0.05 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, 0.05 v5.3.0, 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 v2.1.0
% 0.21/0.63 % Syntax : Number of clauses : 124 ( 40 unt; 15 nHn; 83 RR)
% 0.21/0.63 % Number of literals : 245 ( 57 equ; 113 neg)
% 0.21/0.63 % Maximal clause size : 5 ( 1 avg)
% 0.21/0.63 % Maximal term depth : 6 ( 1 avg)
% 0.21/0.63 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.21/0.63 % Number of functors : 38 ( 38 usr; 8 con; 0-3 aty)
% 0.21/0.63 % Number of variables : 244 ( 46 sgn)
% 0.21/0.63 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.21/0.63
% 0.21/0.63 % Comments : Preceding lemmas are added.
% 0.21/0.63 % : Not in [Qua92].
% 0.21/0.63 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.21/0.63 %--------------------------------------------------------------------------
% 0.21/0.63 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.21/0.63 include('Axioms/SET004-0.ax').
% 0.21/0.63 %--------------------------------------------------------------------------
% 0.21/0.63 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.21/0.63 cnf(corollary_1_to_unordered_pair,axiom,
% 0.21/0.63 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.21/0.63 | member(X,unordered_pair(X,Y)) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(corollary_2_to_unordered_pair,axiom,
% 0.21/0.63 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.21/0.63 | member(Y,unordered_pair(X,Y)) ) ).
% 0.21/0.63
% 0.21/0.63 %----Corollaries to Cartesian product axiom.
% 0.21/0.63 cnf(corollary_1_to_cartesian_product,axiom,
% 0.21/0.63 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.21/0.63 | member(U,universal_class) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(corollary_2_to_cartesian_product,axiom,
% 0.21/0.63 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.21/0.63 | member(V,universal_class) ) ).
% 0.21/0.63
% 0.21/0.63 %---- PARTIAL ORDER.
% 0.21/0.63 %----(PO1): reflexive.
% 0.21/0.63 cnf(subclass_is_reflexive,axiom,
% 0.21/0.63 subclass(X,X) ).
% 0.21/0.63
% 0.21/0.63 %----(PO2): antisymmetry is part of A-3.
% 0.21/0.63 %----(x < y), (y < x) --> (x = y).
% 0.21/0.63
% 0.21/0.63 %----(PO3): transitivity.
% 0.21/0.63 cnf(transitivity_of_subclass,axiom,
% 0.21/0.63 ( ~ subclass(X,Y)
% 0.21/0.63 | ~ subclass(Y,Z)
% 0.21/0.63 | subclass(X,Z) ) ).
% 0.21/0.63
% 0.21/0.63 %---- EQUALITY.
% 0.21/0.63 %----(EQ1): equality axiom.
% 0.21/0.63 %----a:x:(x = x).
% 0.21/0.63 %----This is always an axiom in the TPTP presentation.
% 0.21/0.63
% 0.21/0.63 %----(EQ2): expanded equality definition.
% 0.21/0.63 cnf(equality1,axiom,
% 0.21/0.63 ( X = Y
% 0.21/0.63 | member(not_subclass_element(X,Y),X)
% 0.21/0.63 | member(not_subclass_element(Y,X),Y) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(equality2,axiom,
% 0.21/0.63 ( ~ member(not_subclass_element(X,Y),Y)
% 0.21/0.63 | X = Y
% 0.21/0.63 | member(not_subclass_element(Y,X),Y) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(equality3,axiom,
% 0.21/0.63 ( ~ member(not_subclass_element(Y,X),X)
% 0.21/0.63 | X = Y
% 0.21/0.63 | member(not_subclass_element(X,Y),X) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(equality4,axiom,
% 0.21/0.63 ( ~ member(not_subclass_element(X,Y),Y)
% 0.21/0.63 | ~ member(not_subclass_element(Y,X),X)
% 0.21/0.63 | X = Y ) ).
% 0.21/0.63
% 0.21/0.63 %---- SPECIAL CLASSES.
% 0.21/0.63 %----(SP1): lemma.
% 0.21/0.63 cnf(special_classes_lemma,axiom,
% 0.21/0.63 ~ member(Y,intersection(complement(X),X)) ).
% 0.21/0.63
% 0.21/0.63 %----(SP2): Existence of O (null class).
% 0.21/0.63 %----e:x:a:z:(-(z e x)).
% 0.21/0.63 cnf(existence_of_null_class,axiom,
% 0.21/0.63 ~ member(Z,null_class) ).
% 0.21/0.63
% 0.21/0.63 %----(SP3): O is a subclass of every class.
% 0.21/0.63 cnf(null_class_is_subclass,axiom,
% 0.21/0.63 subclass(null_class,X) ).
% 0.21/0.63
% 0.21/0.63 %----corollary.
% 0.21/0.63 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.21/0.63 ( ~ subclass(X,null_class)
% 0.21/0.63 | X = null_class ) ).
% 0.21/0.63
% 0.21/0.63 %----(SP4): uniqueness of null class.
% 0.21/0.63 cnf(null_class_is_unique,axiom,
% 0.21/0.63 ( Z = null_class
% 0.21/0.63 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.21/0.63
% 0.21/0.63 %----(SP5): O is a set (follows from axiom of infinity).
% 0.21/0.63 cnf(null_class_is_a_set,axiom,
% 0.21/0.63 member(null_class,universal_class) ).
% 0.21/0.63
% 0.21/0.63 %---- UNORDERED PAIRS.
% 0.21/0.63 %----(UP1): unordered pair is commutative.
% 0.21/0.63 cnf(commutativity_of_unordered_pair,axiom,
% 0.21/0.63 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.21/0.63
% 0.21/0.63 %----(UP2): if one argument is a proper class, pair contains only the
% 0.21/0.63 %----other. In a slightly different form to the paper
% 0.21/0.63 cnf(singleton_in_unordered_pair1,axiom,
% 0.21/0.63 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.21/0.63
% 0.21/0.63 cnf(singleton_in_unordered_pair2,axiom,
% 0.21/0.63 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.21/0.63
% 0.21/0.63 cnf(unordered_pair_equals_singleton1,axiom,
% 0.21/0.63 ( member(Y,universal_class)
% 0.21/0.63 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.21/0.63
% 0.21/0.63 cnf(unordered_pair_equals_singleton2,axiom,
% 0.21/0.63 ( member(X,universal_class)
% 0.21/0.63 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.21/0.64
% 0.21/0.64 %----(UP3): if both arguments are proper classes, pair is null.
% 0.21/0.64 cnf(null_unordered_pair,axiom,
% 0.21/0.64 ( unordered_pair(X,Y) = null_class
% 0.21/0.64 | member(X,universal_class)
% 0.21/0.64 | member(Y,universal_class) ) ).
% 0.21/0.64
% 0.21/0.64 %----(UP4): left cancellation for unordered pairs.
% 0.21/0.64 cnf(left_cancellation,axiom,
% 0.21/0.64 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.21/0.64 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.21/0.64 | Y = Z ) ).
% 0.21/0.64
% 0.21/0.64 %----(UP5): right cancellation for unordered pairs.
% 0.21/0.64 cnf(right_cancellation,axiom,
% 0.21/0.64 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.21/0.64 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.21/0.64 | X = Y ) ).
% 0.21/0.64
% 0.21/0.64 %----(UP6): corollary to (A-4).
% 0.21/0.64 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.21/0.64 ( ~ member(X,universal_class)
% 0.21/0.64 | unordered_pair(X,Y) != null_class ) ).
% 0.21/0.64
% 0.21/0.64 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.21/0.64 ( ~ member(Y,universal_class)
% 0.21/0.64 | unordered_pair(X,Y) != null_class ) ).
% 0.21/0.64
% 0.21/0.64 %----corollary to instantiate variables.
% 0.21/0.64 %----Not in the paper
% 0.21/0.64 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.21/0.64 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.21/0.64 | unordered_pair(X,Y) != null_class ) ).
% 0.21/0.64
% 0.21/0.64 %----(UP7): if both members of a pair belong to a set, the pair
% 0.21/0.64 %----is a subset.
% 0.21/0.64 cnf(unordered_pair_is_subset,axiom,
% 0.21/0.64 ( ~ member(X,Z)
% 0.21/0.64 | ~ member(Y,Z)
% 0.21/0.64 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.21/0.64
% 0.21/0.64 %---- SINGLETONS.
% 0.21/0.64 %----(SS1): every singleton is a set.
% 0.21/0.64 cnf(singletons_are_sets,axiom,
% 0.21/0.64 member(singleton(X),universal_class) ).
% 0.21/0.64
% 0.21/0.64 %----corollary, not in the paper.
% 0.21/0.64 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.21/0.64 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.21/0.64
% 0.21/0.64 %----(SS2): a set belongs to its singleton.
% 0.21/0.64 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.21/0.64 cnf(set_in_its_singleton,axiom,
% 0.21/0.64 ( ~ member(X,universal_class)
% 0.21/0.64 | member(X,singleton(X)) ) ).
% 0.21/0.64
% 0.21/0.64 %----corollary
% 0.21/0.64 cnf(corollary_to_set_in_its_singleton,axiom,
% 0.21/0.64 ( ~ member(X,universal_class)
% 0.21/0.64 | singleton(X) != null_class ) ).
% 0.21/0.64
% 0.21/0.64 cnf(prove_null_class_in_its_singleton_1,negated_conjecture,
% 0.21/0.64 ~ member(null_class,singleton(null_class)) ).
% 0.21/0.64
% 0.21/0.64 %--------------------------------------------------------------------------
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 % Proof found
% 0.21/0.64 % SZS status Theorem for theBenchmark
% 0.21/0.64 % SZS output start Proof
% 0.21/0.64 %ClaNum:151(EqnAxiom:42)
% 0.21/0.64 %VarNum:871(SingletonVarNum:213)
% 0.21/0.64 %MaxLitNum:5
% 0.21/0.64 %MaxfuncDepth:24
% 0.21/0.64 %SharedTerms:32
% 0.21/0.64 %goalClause: 66
% 0.21/0.64 %singleGoalClaCount:1
% 0.21/0.64 [43]P1(a1)
% 0.21/0.64 [44]P2(a2)
% 0.21/0.64 [45]P5(a4,a17)
% 0.21/0.64 [46]P5(a1,a17)
% 0.21/0.64 [51]P6(a5,f6(a17,a17))
% 0.21/0.64 [52]P6(a18,f6(a17,a17))
% 0.21/0.64 [66]~P5(a4,f23(a4,a4))
% 0.21/0.64 [61]E(f10(f9(f11(f6(a21,a17))),a21),a13)
% 0.21/0.64 [63]E(f10(f6(a17,a17),f10(f6(a17,a17),f8(f7(f8(a5),f9(f11(f6(a5,a17))))))),a21)
% 0.21/0.64 [47]P6(x471,a17)
% 0.21/0.64 [48]P6(a4,x481)
% 0.21/0.64 [49]P6(x491,x491)
% 0.21/0.64 [65]~P5(x651,a4)
% 0.21/0.64 [59]P6(f19(x591),f6(f6(a17,a17),a17))
% 0.21/0.64 [60]P6(f11(x601),f6(f6(a17,a17),a17))
% 0.21/0.64 [64]E(f10(f9(x641),f8(f9(f10(f7(f9(f11(f6(a5,a17))),x641),a13)))),f3(x641))
% 0.21/0.64 [50]E(f23(x501,x502),f23(x502,x501))
% 0.21/0.64 [53]P5(f23(x531,x532),a17)
% 0.21/0.64 [55]P6(f7(x551,x552),f6(a17,a17))
% 0.21/0.64 [56]P6(f23(x561,x561),f23(x562,x561))
% 0.21/0.64 [57]P6(f23(x571,x571),f23(x571,x572))
% 0.21/0.64 [62]P5(f23(x621,x621),f23(x622,f23(x621,x621)))
% 0.21/0.64 [67]~P5(x671,f10(f8(x672),x672))
% 0.21/0.64 [58]E(f10(f6(x581,x582),x583),f10(x583,f6(x581,x582)))
% 0.21/0.64 [68]~P7(x681)+P2(x681)
% 0.21/0.64 [69]~P8(x691)+P2(x691)
% 0.21/0.64 [72]~P1(x721)+P6(a1,x721)
% 0.21/0.64 [73]~P1(x731)+P5(a4,x731)
% 0.21/0.64 [74]~P6(x741,a4)+E(x741,a4)
% 0.21/0.64 [76]P5(f20(x761),x761)+E(x761,a4)
% 0.21/0.64 [77]E(x771,a4)+P5(f14(x771,a4),x771)
% 0.21/0.64 [81]~P2(x811)+P6(x811,f6(a17,a17))
% 0.21/0.64 [75]E(x751,a4)+E(f10(x751,f20(x751)),a4)
% 0.21/0.64 [94]~P8(x941)+E(f6(f9(f9(x941)),f9(f9(x941))),f9(x941))
% 0.21/0.64 [108]~P7(x1081)+P2(f9(f11(f6(x1081,a17))))
% 0.21/0.64 [113]~P5(x1131,a17)+P5(f9(f10(a5,f6(a17,x1131))),a17)
% 0.21/0.64 [115]~P9(x1151)+P6(f7(x1151,f9(f11(f6(x1151,a17)))),a13)
% 0.21/0.64 [116]~P2(x1161)+P6(f7(x1161,f9(f11(f6(x1161,a17)))),a13)
% 0.21/0.64 [117]~P8(x1171)+P6(f9(f9(f11(f6(x1171,a17)))),f9(f9(x1171)))
% 0.21/0.64 [122]P9(x1221)+~P6(f7(x1221,f9(f11(f6(x1221,a17)))),a13)
% 0.21/0.64 [138]~P1(x1381)+P6(f9(f9(f11(f6(f10(a18,f6(x1381,a17)),a17)))),x1381)
% 0.21/0.64 [142]~P5(x1421,a17)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1421),a17)),a17))))),a17)
% 0.21/0.64 [70]~E(x702,x701)+P6(x701,x702)
% 0.21/0.64 [71]~E(x711,x712)+P6(x711,x712)
% 0.21/0.64 [79]P5(x792,a17)+E(f23(x791,x792),f23(x791,x791))
% 0.21/0.64 [80]P5(x801,a17)+E(f23(x801,x802),f23(x802,x802))
% 0.21/0.64 [82]~P5(x822,a17)+~E(f23(x821,x822),a4)
% 0.21/0.64 [83]~P5(x831,a17)+~E(f23(x831,x832),a4)
% 0.21/0.64 [86]P6(x861,x862)+P5(f14(x861,x862),x861)
% 0.21/0.64 [87]~P5(x871,x872)+~P5(x871,f8(x872))
% 0.21/0.64 [91]~P5(x911,a17)+P5(x911,f23(x912,x911))
% 0.21/0.64 [92]~P5(x921,a17)+P5(x921,f23(x921,x922))
% 0.21/0.64 [98]P6(x981,x982)+~P5(f14(x981,x982),x982)
% 0.21/0.64 [112]~P5(x1122,f9(x1121))+~E(f10(x1121,f6(f23(x1122,x1122),a17)),a4)
% 0.21/0.64 [121]P5(x1211,x1212)+~P5(f23(f23(x1211,x1211),f23(x1211,f23(x1212,x1212))),a5)
% 0.21/0.64 [135]~P5(f23(f23(x1351,x1351),f23(x1351,f23(x1352,x1352))),a18)+E(f8(f10(f8(x1351),f8(f23(x1351,x1351)))),x1352)
% 0.21/0.64 [102]P2(x1021)+~P3(x1021,x1022,x1023)
% 0.21/0.64 [103]P8(x1031)+~P4(x1032,x1033,x1031)
% 0.21/0.64 [104]P8(x1041)+~P4(x1042,x1041,x1043)
% 0.21/0.64 [111]~P4(x1111,x1112,x1113)+P3(x1111,x1112,x1113)
% 0.21/0.64 [96]P5(x961,x962)+~P5(x961,f10(x963,x962))
% 0.21/0.64 [97]P5(x971,x972)+~P5(x971,f10(x972,x973))
% 0.21/0.64 [105]~P3(x1052,x1051,x1053)+E(f9(f9(x1051)),f9(x1052))
% 0.21/0.64 [118]~P5(x1181,f6(x1182,x1183))+E(f23(f23(f12(x1181),f12(x1181)),f23(f12(x1181),f23(f22(x1181),f22(x1181)))),x1181)
% 0.21/0.64 [120]~P3(x1201,x1203,x1202)+P6(f9(f9(f11(f6(x1201,a17)))),f9(f9(x1202)))
% 0.21/0.64 [123]P5(x1231,a17)+~P5(f23(f23(x1232,x1232),f23(x1232,f23(x1231,x1231))),f6(x1233,x1234))
% 0.21/0.64 [124]P5(x1241,a17)+~P5(f23(f23(x1241,x1241),f23(x1241,f23(x1242,x1242))),f6(x1243,x1244))
% 0.21/0.64 [125]P5(x1251,x1252)+~P5(f23(f23(x1253,x1253),f23(x1253,f23(x1251,x1251))),f6(x1254,x1252))
% 0.21/0.64 [126]P5(x1261,x1262)+~P5(f23(f23(x1261,x1261),f23(x1261,f23(x1263,x1263))),f6(x1262,x1264))
% 0.21/0.64 [127]~E(f23(x1271,x1272),a4)+~P5(f23(f23(x1271,x1271),f23(x1271,f23(x1272,x1272))),f6(x1273,x1274))
% 0.21/0.64 [131]P5(x1311,f23(x1312,x1311))+~P5(f23(f23(x1312,x1312),f23(x1312,f23(x1311,x1311))),f6(x1313,x1314))
% 0.21/0.64 [132]P5(x1321,f23(x1321,x1322))+~P5(f23(f23(x1321,x1321),f23(x1321,f23(x1322,x1322))),f6(x1323,x1324))
% 0.21/0.64 [143]~P5(f23(f23(f23(f23(x1433,x1433),f23(x1433,f23(x1431,x1431))),f23(f23(x1433,x1433),f23(x1433,f23(x1431,x1431)))),f23(f23(f23(x1433,x1433),f23(x1433,f23(x1431,x1431))),f23(x1432,x1432))),f19(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))),x1434)
% 0.21/0.64 [144]~P5(f23(f23(f23(f23(x1442,x1442),f23(x1442,f23(x1441,x1441))),f23(f23(x1442,x1442),f23(x1442,f23(x1441,x1441)))),f23(f23(f23(x1442,x1442),f23(x1442,f23(x1441,x1441))),f23(x1443,x1443))),f11(x1444))+P5(f23(f23(f23(f23(x1441,x1441),f23(x1441,f23(x1442,x1442))),f23(f23(x1441,x1441),f23(x1441,f23(x1442,x1442)))),f23(f23(f23(x1441,x1441),f23(x1441,f23(x1442,x1442))),f23(x1443,x1443))),x1444)
% 0.21/0.64 [148]~P5(f23(f23(x1484,x1484),f23(x1484,f23(x1481,x1481))),f7(x1482,x1483))+P5(x1481,f9(f9(f11(f6(f10(x1482,f6(f9(f9(f11(f6(f10(x1483,f6(f23(x1484,x1484),a17)),a17)))),a17)),a17)))))
% 0.21/0.64 [114]~P2(x1141)+P7(x1141)+~P2(f9(f11(f6(x1141,a17))))
% 0.21/0.64 [128]P2(x1281)+~P6(x1281,f6(a17,a17))+~P6(f7(x1281,f9(f11(f6(x1281,a17)))),a13)
% 0.21/0.64 [140]P1(x1401)+~P5(a4,x1401)+~P6(f9(f9(f11(f6(f10(a18,f6(x1401,a17)),a17)))),x1401)
% 0.21/0.64 [147]~P5(x1471,a17)+E(x1471,a4)+P5(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(a2,f6(f23(x1471,x1471),a17)),a17))))))),x1471)
% 0.21/0.64 [85]~P6(x852,x851)+~P6(x851,x852)+E(x851,x852)
% 0.21/0.64 [78]P5(x782,a17)+P5(x781,a17)+E(f23(x781,x782),a4)
% 0.21/0.64 [88]P5(x881,x882)+P5(x881,f8(x882))+~P5(x881,a17)
% 0.21/0.64 [99]E(x991,x992)+P5(f14(x992,x991),x992)+P5(f14(x991,x992),x991)
% 0.21/0.64 [107]E(x1071,x1072)+P5(f14(x1072,x1071),x1072)+~P5(f14(x1071,x1072),x1072)
% 0.21/0.64 [109]E(x1091,x1092)+~P5(f14(x1092,x1091),x1091)+~P5(f14(x1091,x1092),x1092)
% 0.21/0.64 [110]P5(x1102,f9(x1101))+~P5(x1102,a17)+E(f10(x1101,f6(f23(x1102,x1102),a17)),a4)
% 0.21/0.64 [136]~P5(x1361,x1362)+~P5(f23(f23(x1361,x1361),f23(x1361,f23(x1362,x1362))),f6(a17,a17))+P5(f23(f23(x1361,x1361),f23(x1361,f23(x1362,x1362))),a5)
% 0.21/0.64 [137]~P5(f23(f23(x1371,x1371),f23(x1371,f23(x1372,x1372))),f6(a17,a17))+~E(f8(f10(f8(x1371),f8(f23(x1371,x1371)))),x1372)+P5(f23(f23(x1371,x1371),f23(x1371,f23(x1372,x1372))),a18)
% 0.21/0.64 [139]~P2(x1391)+~P5(x1392,a17)+P5(f9(f9(f11(f6(f10(x1391,f6(x1392,a17)),a17)))),a17)
% 0.21/0.64 [89]~P6(x891,x893)+P6(x891,x892)+~P6(x893,x892)
% 0.21/0.64 [90]~P5(x901,x903)+P5(x901,x902)+~P6(x903,x902)
% 0.21/0.64 [95]E(x951,x952)+E(x951,x953)+~P5(x951,f23(x953,x952))
% 0.21/0.64 [100]~P5(x1001,x1003)+~P5(x1001,x1002)+P5(x1001,f10(x1002,x1003))
% 0.21/0.64 [101]~P5(x1012,x1013)+~P5(x1011,x1013)+P6(f23(x1011,x1012),x1013)
% 0.21/0.64 [129]E(x1291,x1292)+~E(f23(x1293,x1291),f23(x1293,x1292))+~P5(f23(f23(x1291,x1291),f23(x1291,f23(x1292,x1292))),f6(a17,a17))
% 0.21/0.64 [130]E(x1301,x1302)+~E(f23(x1301,x1303),f23(x1302,x1303))+~P5(f23(f23(x1301,x1301),f23(x1301,f23(x1302,x1302))),f6(a17,a17))
% 0.21/0.64 [119]~P5(x1192,x1194)+~P5(x1191,x1193)+P5(f23(f23(x1191,x1191),f23(x1191,f23(x1192,x1192))),f6(x1193,x1194))
% 0.21/0.64 [145]~P5(f23(f23(f23(f23(x1452,x1452),f23(x1452,f23(x1453,x1453))),f23(f23(x1452,x1452),f23(x1452,f23(x1453,x1453)))),f23(f23(f23(x1452,x1452),f23(x1452,f23(x1453,x1453))),f23(x1451,x1451))),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))),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))),f6(f6(a17,a17),a17))
% 0.21/0.64 [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))),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))),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))),f6(f6(a17,a17),a17))
% 0.21/0.64 [149]P5(f23(f23(x1491,x1491),f23(x1491,f23(x1492,x1492))),f7(x1493,x1494))+~P5(f23(f23(x1491,x1491),f23(x1491,f23(x1492,x1492))),f6(a17,a17))+~P5(x1492,f9(f9(f11(f6(f10(x1493,f6(f9(f9(f11(f6(f10(x1494,f6(f23(x1491,x1491),a17)),a17)))),a17)),a17)))))
% 0.21/0.64 [150]~P4(x1502,x1505,x1501)+~P5(f23(f23(x1503,x1503),f23(x1503,f23(x1504,x1504))),f9(x1505))+E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1501,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1503,x1503),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1503,x1503),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1503,x1503),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1504,x1504),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1504,x1504),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1503,x1503),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1503,x1503),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1503,x1503),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1504,x1504),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(x1504,x1504),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1502,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1505,f6(f23(f23(f23(x1503,x1503),f23(x1503,f23(x1504,x1504))),f23(f23(x1503,x1503),f23(x1503,f23(x1504,x1504)))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1505,f6(f23(f23(f23(x1503,x1503),f23(x1503,f23(x1504,x1504))),f23(f23(x1503,x1503),f23(x1503,f23(x1504,x1504)))),a17)),a17)))))))),a17)),a17))))))))
% 0.21/0.64 [134]~P2(x1341)+P8(x1341)+~E(f6(f9(f9(x1341)),f9(f9(x1341))),f9(x1341))+~P6(f9(f9(f11(f6(x1341,a17)))),f9(f9(x1341)))
% 0.21/0.64 [133]~P2(x1331)+P3(x1331,x1332,x1333)+~E(f9(f9(x1332)),f9(x1331))+~P6(f9(f9(f11(f6(x1331,a17)))),f9(f9(x1333)))
% 0.21/0.64 [141]~P8(x1413)+~P8(x1412)+~P3(x1411,x1412,x1413)+P4(x1411,x1412,x1413)+P5(f23(f23(f15(x1411,x1412,x1413),f15(x1411,x1412,x1413)),f23(f15(x1411,x1412,x1413),f23(f16(x1411,x1412,x1413),f16(x1411,x1412,x1413)))),f9(x1412))
% 0.21/0.64 [151]~P8(x1513)+~P8(x1512)+~P3(x1511,x1512,x1513)+P4(x1511,x1512,x1513)+~E(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1513,f6(f23(f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)),a17)),a17)))))))))),f23(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a17)),a17)))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a17)),a17))))))),f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)),a17)),a17))))))))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1511,f6(f23(f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1512,f6(f23(f23(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),f23(f15(x1511,x1512,x1513),f23(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)))),f23(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),f23(f15(x1511,x1512,x1513),f23(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513))))),a17)),a17))))))),f9(f10(a5,f6(a17,f9(f9(f11(f6(f10(x1512,f6(f23(f23(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),f23(f15(x1511,x1512,x1513),f23(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)))),f23(f23(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),f23(f15(x1511,x1512,x1513),f23(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513))))),a17)),a17)))))))),a17)),a17))))))))
% 0.21/0.64 %EqnAxiom
% 0.21/0.64 [1]E(x11,x11)
% 0.21/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.64 [4]~E(x41,x42)+E(f23(x41,x43),f23(x42,x43))
% 0.21/0.64 [5]~E(x51,x52)+E(f23(x53,x51),f23(x53,x52))
% 0.21/0.64 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.21/0.64 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.21/0.64 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.21/0.64 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.21/0.64 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.21/0.64 [11]~E(x111,x112)+E(f11(x111),f11(x112))
% 0.21/0.64 [12]~E(x121,x122)+E(f8(x121),f8(x122))
% 0.21/0.64 [13]~E(x131,x132)+E(f7(x131,x133),f7(x132,x133))
% 0.21/0.64 [14]~E(x141,x142)+E(f7(x143,x141),f7(x143,x142))
% 0.21/0.64 [15]~E(x151,x152)+E(f16(x151,x153,x154),f16(x152,x153,x154))
% 0.21/0.64 [16]~E(x161,x162)+E(f16(x163,x161,x164),f16(x163,x162,x164))
% 0.21/0.64 [17]~E(x171,x172)+E(f16(x173,x174,x171),f16(x173,x174,x172))
% 0.21/0.64 [18]~E(x181,x182)+E(f19(x181),f19(x182))
% 0.21/0.64 [19]~E(x191,x192)+E(f14(x191,x193),f14(x192,x193))
% 0.21/0.64 [20]~E(x201,x202)+E(f14(x203,x201),f14(x203,x202))
% 0.21/0.64 [21]~E(x211,x212)+E(f20(x211),f20(x212))
% 0.21/0.64 [22]~E(x221,x222)+E(f15(x221,x223,x224),f15(x222,x223,x224))
% 0.21/0.64 [23]~E(x231,x232)+E(f15(x233,x231,x234),f15(x233,x232,x234))
% 0.21/0.64 [24]~E(x241,x242)+E(f15(x243,x244,x241),f15(x243,x244,x242))
% 0.21/0.64 [25]~E(x251,x252)+E(f3(x251),f3(x252))
% 0.21/0.64 [26]~E(x261,x262)+E(f12(x261),f12(x262))
% 0.21/0.64 [27]~E(x271,x272)+E(f22(x271),f22(x272))
% 0.21/0.64 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.21/0.64 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.21/0.64 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.21/0.64 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.21/0.64 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.21/0.64 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.21/0.64 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.21/0.64 [35]P6(x352,x353)+~E(x351,x352)+~P6(x351,x353)
% 0.21/0.64 [36]P6(x363,x362)+~E(x361,x362)+~P6(x363,x361)
% 0.21/0.64 [37]~P8(x371)+P8(x372)+~E(x371,x372)
% 0.21/0.64 [38]P4(x382,x383,x384)+~E(x381,x382)+~P4(x381,x383,x384)
% 0.21/0.64 [39]P4(x393,x392,x394)+~E(x391,x392)+~P4(x393,x391,x394)
% 0.21/0.64 [40]P4(x403,x404,x402)+~E(x401,x402)+~P4(x403,x404,x401)
% 0.21/0.64 [41]~P9(x411)+P9(x412)+~E(x411,x412)
% 0.21/0.64 [42]~P7(x421)+P7(x422)+~E(x421,x422)
% 0.21/0.64
% 0.21/0.64 %-------------------------------------------
% 0.21/0.65 cnf(152,plain,
% 0.21/0.65 ($false),
% 0.21/0.65 inference(scs_inference,[],[45,66,91]),
% 0.21/0.65 ['proof']).
% 0.21/0.65 % SZS output end Proof
% 0.21/0.65 % Total time :0.000000s
%------------------------------------------------------------------------------