TSTP Solution File: SET079-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET079-7 : 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 : n027.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 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET079-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 08:53:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % File :CSE---1.6
% 0.20/0.65 % Problem :theBenchmark
% 0.20/0.65 % Transform :cnf
% 0.20/0.65 % Format :tptp:raw
% 0.20/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.65
% 0.20/0.65 % Result :Theorem 0.000000s
% 0.20/0.65 % Output :CNFRefutation 0.000000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 % File : SET079-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.20/0.65 % Domain : Set Theory
% 0.20/0.65 % Problem : Corollary to a set belongs to its singleton
% 0.20/0.65 % Version : [Qua92] axioms : Augmented.
% 0.20/0.65 % English :
% 0.20/0.65
% 0.20/0.65 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.20/0.65 % Source : [Quaife]
% 0.20/0.65 % Names : SS2 cor.1 [Qua92]
% 0.20/0.65
% 0.20/0.65 % Status : Unsatisfiable
% 0.20/0.65 % 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, 0.07 v6.0.0, 0.00 v5.5.0, 0.10 v5.4.0, 0.15 v5.3.0, 0.11 v5.2.0, 0.06 v5.1.0, 0.12 v5.0.0, 0.14 v4.1.0, 0.15 v4.0.1, 0.18 v4.0.0, 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, 0.00 v2.7.0, 0.08 v2.6.0, 0.00 v2.1.0
% 0.20/0.65 % Syntax : Number of clauses : 124 ( 41 unt; 15 nHn; 83 RR)
% 0.20/0.65 % Number of literals : 244 ( 57 equ; 110 neg)
% 0.20/0.65 % Maximal clause size : 5 ( 1 avg)
% 0.20/0.65 % Maximal term depth : 6 ( 1 avg)
% 0.20/0.65 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.20/0.65 % Number of functors : 39 ( 39 usr; 9 con; 0-3 aty)
% 0.20/0.65 % Number of variables : 243 ( 46 sgn)
% 0.20/0.65 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.20/0.65
% 0.20/0.65 % Comments : Preceding lemmas are added.
% 0.20/0.65 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.20/0.65 include('Axioms/SET004-0.ax').
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.20/0.65 cnf(corollary_1_to_unordered_pair,axiom,
% 0.20/0.65 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.65 | member(X,unordered_pair(X,Y)) ) ).
% 0.20/0.65
% 0.20/0.65 cnf(corollary_2_to_unordered_pair,axiom,
% 0.20/0.65 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.65 | member(Y,unordered_pair(X,Y)) ) ).
% 0.20/0.65
% 0.20/0.65 %----Corollaries to Cartesian product axiom.
% 0.20/0.65 cnf(corollary_1_to_cartesian_product,axiom,
% 0.20/0.65 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.65 | member(U,universal_class) ) ).
% 0.20/0.65
% 0.20/0.65 cnf(corollary_2_to_cartesian_product,axiom,
% 0.20/0.65 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.20/0.65 | member(V,universal_class) ) ).
% 0.20/0.65
% 0.20/0.65 %---- PARTIAL ORDER.
% 0.20/0.65 %----(PO1): reflexive.
% 0.20/0.65 cnf(subclass_is_reflexive,axiom,
% 0.20/0.65 subclass(X,X) ).
% 0.20/0.65
% 0.20/0.65 %----(PO2): antisymmetry is part of A-3.
% 0.20/0.65 %----(x < y), (y < x) --> (x = y).
% 0.20/0.65
% 0.20/0.65 %----(PO3): transitivity.
% 0.20/0.65 cnf(transitivity_of_subclass,axiom,
% 0.20/0.65 ( ~ subclass(X,Y)
% 0.20/0.65 | ~ subclass(Y,Z)
% 0.20/0.65 | subclass(X,Z) ) ).
% 0.20/0.65
% 0.20/0.65 %---- EQUALITY.
% 0.20/0.65 %----(EQ1): equality axiom.
% 0.20/0.65 %----a:x:(x = x).
% 0.20/0.65 %----This is always an axiom in the TPTP presentation.
% 0.20/0.65
% 0.20/0.65 %----(EQ2): expanded equality definition.
% 0.20/0.65 cnf(equality1,axiom,
% 0.20/0.66 ( X = Y
% 0.20/0.66 | member(not_subclass_element(X,Y),X)
% 0.20/0.66 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(equality2,axiom,
% 0.20/0.66 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.66 | X = Y
% 0.20/0.66 | member(not_subclass_element(Y,X),Y) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(equality3,axiom,
% 0.20/0.66 ( ~ member(not_subclass_element(Y,X),X)
% 0.20/0.66 | X = Y
% 0.20/0.66 | member(not_subclass_element(X,Y),X) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(equality4,axiom,
% 0.20/0.66 ( ~ member(not_subclass_element(X,Y),Y)
% 0.20/0.66 | ~ member(not_subclass_element(Y,X),X)
% 0.20/0.66 | X = Y ) ).
% 0.20/0.66
% 0.20/0.66 %---- SPECIAL CLASSES.
% 0.20/0.66 %----(SP1): lemma.
% 0.20/0.66 cnf(special_classes_lemma,axiom,
% 0.20/0.66 ~ member(Y,intersection(complement(X),X)) ).
% 0.20/0.66
% 0.20/0.66 %----(SP2): Existence of O (null class).
% 0.20/0.66 %----e:x:a:z:(-(z e x)).
% 0.20/0.66 cnf(existence_of_null_class,axiom,
% 0.20/0.66 ~ member(Z,null_class) ).
% 0.20/0.66
% 0.20/0.66 %----(SP3): O is a subclass of every class.
% 0.20/0.66 cnf(null_class_is_subclass,axiom,
% 0.20/0.66 subclass(null_class,X) ).
% 0.20/0.66
% 0.20/0.66 %----corollary.
% 0.20/0.66 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.20/0.66 ( ~ subclass(X,null_class)
% 0.20/0.66 | X = null_class ) ).
% 0.20/0.66
% 0.20/0.66 %----(SP4): uniqueness of null class.
% 0.20/0.66 cnf(null_class_is_unique,axiom,
% 0.20/0.66 ( Z = null_class
% 0.20/0.66 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.20/0.66
% 0.20/0.66 %----(SP5): O is a set (follows from axiom of infinity).
% 0.20/0.66 cnf(null_class_is_a_set,axiom,
% 0.20/0.66 member(null_class,universal_class) ).
% 0.20/0.66
% 0.20/0.66 %---- UNORDERED PAIRS.
% 0.20/0.66 %----(UP1): unordered pair is commutative.
% 0.20/0.66 cnf(commutativity_of_unordered_pair,axiom,
% 0.20/0.66 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.20/0.66
% 0.20/0.66 %----(UP2): if one argument is a proper class, pair contains only the
% 0.20/0.66 %----other. In a slightly different form to the paper
% 0.20/0.66 cnf(singleton_in_unordered_pair1,axiom,
% 0.20/0.66 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.20/0.66
% 0.20/0.66 cnf(singleton_in_unordered_pair2,axiom,
% 0.20/0.66 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.20/0.66
% 0.20/0.66 cnf(unordered_pair_equals_singleton1,axiom,
% 0.20/0.66 ( member(Y,universal_class)
% 0.20/0.66 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(unordered_pair_equals_singleton2,axiom,
% 0.20/0.66 ( member(X,universal_class)
% 0.20/0.66 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.20/0.66
% 0.20/0.66 %----(UP3): if both arguments are proper classes, pair is null.
% 0.20/0.66 cnf(null_unordered_pair,axiom,
% 0.20/0.66 ( unordered_pair(X,Y) = null_class
% 0.20/0.66 | member(X,universal_class)
% 0.20/0.66 | member(Y,universal_class) ) ).
% 0.20/0.66
% 0.20/0.66 %----(UP4): left cancellation for unordered pairs.
% 0.20/0.66 cnf(left_cancellation,axiom,
% 0.20/0.66 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.20/0.66 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.20/0.66 | Y = Z ) ).
% 0.20/0.66
% 0.20/0.66 %----(UP5): right cancellation for unordered pairs.
% 0.20/0.66 cnf(right_cancellation,axiom,
% 0.20/0.66 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.20/0.66 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.20/0.66 | X = Y ) ).
% 0.20/0.66
% 0.20/0.66 %----(UP6): corollary to (A-4).
% 0.20/0.66 cnf(corollary_to_unordered_pair_axiom1,axiom,
% 0.20/0.66 ( ~ member(X,universal_class)
% 0.20/0.66 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.66
% 0.20/0.66 cnf(corollary_to_unordered_pair_axiom2,axiom,
% 0.20/0.66 ( ~ member(Y,universal_class)
% 0.20/0.66 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.66
% 0.20/0.66 %----corollary to instantiate variables.
% 0.20/0.66 %----Not in the paper
% 0.20/0.66 cnf(corollary_to_unordered_pair_axiom3,axiom,
% 0.20/0.66 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.20/0.66 | unordered_pair(X,Y) != null_class ) ).
% 0.20/0.66
% 0.20/0.66 %----(UP7): if both members of a pair belong to a set, the pair
% 0.20/0.66 %----is a subset.
% 0.20/0.66 cnf(unordered_pair_is_subset,axiom,
% 0.20/0.66 ( ~ member(X,Z)
% 0.20/0.66 | ~ member(Y,Z)
% 0.20/0.66 | subclass(unordered_pair(X,Y),Z) ) ).
% 0.20/0.66
% 0.20/0.66 %---- SINGLETONS.
% 0.20/0.66 %----(SS1): every singleton is a set.
% 0.20/0.66 cnf(singletons_are_sets,axiom,
% 0.20/0.66 member(singleton(X),universal_class) ).
% 0.20/0.66
% 0.20/0.66 %----corollary, not in the paper.
% 0.20/0.66 cnf(corollary_1_to_singletons_are_sets,axiom,
% 0.20/0.66 member(singleton(Y),unordered_pair(X,singleton(Y))) ).
% 0.20/0.66
% 0.20/0.66 %----(SS2): a set belongs to its singleton.
% 0.20/0.66 %----(u = x), (u e universal_class) --> (u e {x}).
% 0.20/0.66 cnf(set_in_its_singleton,axiom,
% 0.20/0.66 ( ~ member(X,universal_class)
% 0.20/0.66 | member(X,singleton(X)) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(prove_corollary_to_set_in_its_singleton_1,negated_conjecture,
% 0.20/0.66 member(x,universal_class) ).
% 0.20/0.66
% 0.20/0.66 cnf(prove_corollary_to_set_in_its_singleton_2,negated_conjecture,
% 0.20/0.66 singleton(x) = null_class ).
% 0.20/0.66
% 0.20/0.66 %--------------------------------------------------------------------------
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % Proof found
% 0.20/0.66 % SZS status Theorem for theBenchmark
% 0.20/0.66 % SZS output start Proof
% 0.20/0.66 %ClaNum:151(EqnAxiom:42)
% 0.20/0.66 %VarNum:871(SingletonVarNum:213)
% 0.20/0.66 %MaxLitNum:5
% 0.20/0.66 %MaxfuncDepth:24
% 0.20/0.66 %SharedTerms:34
% 0.20/0.66 %goalClause: 45 48
% 0.20/0.66 %singleGoalClaCount:2
% 0.20/0.66 [43]P1(a1)
% 0.20/0.66 [44]P2(a2)
% 0.20/0.66 [46]P5(a4,a19)
% 0.20/0.66 [47]P5(a1,a19)
% 0.20/0.66 [48]P5(a17,a19)
% 0.20/0.66 [45]E(f18(a17,a17),a4)
% 0.20/0.66 [53]P6(a5,f6(a19,a19))
% 0.20/0.66 [54]P6(a20,f6(a19,a19))
% 0.20/0.66 [63]E(f10(f9(f11(f6(a23,a19))),a23),a13)
% 0.20/0.66 [65]E(f10(f6(a19,a19),f10(f6(a19,a19),f8(f7(f8(a5),f9(f11(f6(a5,a19))))))),a23)
% 0.20/0.66 [49]P6(x491,a19)
% 0.20/0.66 [50]P6(a4,x501)
% 0.20/0.66 [51]P6(x511,x511)
% 0.20/0.66 [67]~P5(x671,a4)
% 0.20/0.66 [61]P6(f21(x611),f6(f6(a19,a19),a19))
% 0.20/0.66 [62]P6(f11(x621),f6(f6(a19,a19),a19))
% 0.20/0.66 [66]E(f10(f9(x661),f8(f9(f10(f7(f9(f11(f6(a5,a19))),x661),a13)))),f3(x661))
% 0.20/0.66 [52]E(f18(x521,x522),f18(x522,x521))
% 0.20/0.66 [55]P5(f18(x551,x552),a19)
% 0.20/0.66 [57]P6(f7(x571,x572),f6(a19,a19))
% 0.20/0.66 [58]P6(f18(x581,x581),f18(x582,x581))
% 0.20/0.66 [59]P6(f18(x591,x591),f18(x591,x592))
% 0.20/0.66 [64]P5(f18(x641,x641),f18(x642,f18(x641,x641)))
% 0.20/0.66 [68]~P5(x681,f10(f8(x682),x682))
% 0.20/0.66 [60]E(f10(f6(x601,x602),x603),f10(x603,f6(x601,x602)))
% 0.20/0.66 [69]~P7(x691)+P2(x691)
% 0.20/0.66 [70]~P8(x701)+P2(x701)
% 0.20/0.66 [73]~P1(x731)+P6(a1,x731)
% 0.20/0.66 [74]~P1(x741)+P5(a4,x741)
% 0.20/0.66 [75]~P6(x751,a4)+E(x751,a4)
% 0.20/0.66 [77]P5(f22(x771),x771)+E(x771,a4)
% 0.20/0.66 [78]E(x781,a4)+P5(f14(x781,a4),x781)
% 0.20/0.66 [82]~P2(x821)+P6(x821,f6(a19,a19))
% 0.20/0.66 [76]E(x761,a4)+E(f10(x761,f22(x761)),a4)
% 0.20/0.66 [94]~P8(x941)+E(f6(f9(f9(x941)),f9(f9(x941))),f9(x941))
% 0.20/0.66 [108]~P7(x1081)+P2(f9(f11(f6(x1081,a19))))
% 0.20/0.66 [113]~P5(x1131,a19)+P5(f9(f10(a5,f6(a19,x1131))),a19)
% 0.20/0.66 [115]~P9(x1151)+P6(f7(x1151,f9(f11(f6(x1151,a19)))),a13)
% 0.20/0.66 [116]~P2(x1161)+P6(f7(x1161,f9(f11(f6(x1161,a19)))),a13)
% 0.20/0.66 [117]~P8(x1171)+P6(f9(f9(f11(f6(x1171,a19)))),f9(f9(x1171)))
% 0.20/0.66 [122]P9(x1221)+~P6(f7(x1221,f9(f11(f6(x1221,a19)))),a13)
% 0.20/0.66 [138]~P1(x1381)+P6(f9(f9(f11(f6(f10(a20,f6(x1381,a19)),a19)))),x1381)
% 0.20/0.66 [142]~P5(x1421,a19)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1421),a19)),a19))))),a19)
% 0.20/0.66 [71]~E(x712,x711)+P6(x711,x712)
% 0.20/0.66 [72]~E(x721,x722)+P6(x721,x722)
% 0.20/0.66 [80]P5(x802,a19)+E(f18(x801,x802),f18(x801,x801))
% 0.20/0.66 [81]P5(x811,a19)+E(f18(x811,x812),f18(x812,x812))
% 0.20/0.66 [83]~P5(x832,a19)+~E(f18(x831,x832),a4)
% 0.20/0.66 [84]~P5(x841,a19)+~E(f18(x841,x842),a4)
% 0.20/0.66 [86]P6(x861,x862)+P5(f14(x861,x862),x861)
% 0.20/0.66 [87]~P5(x871,x872)+~P5(x871,f8(x872))
% 0.20/0.66 [91]~P5(x911,a19)+P5(x911,f18(x912,x911))
% 0.20/0.66 [92]~P5(x921,a19)+P5(x921,f18(x921,x922))
% 0.20/0.66 [98]P6(x981,x982)+~P5(f14(x981,x982),x982)
% 0.20/0.66 [112]~P5(x1122,f9(x1121))+~E(f10(x1121,f6(f18(x1122,x1122),a19)),a4)
% 0.20/0.66 [121]P5(x1211,x1212)+~P5(f18(f18(x1211,x1211),f18(x1211,f18(x1212,x1212))),a5)
% 0.20/0.66 [135]~P5(f18(f18(x1351,x1351),f18(x1351,f18(x1352,x1352))),a20)+E(f8(f10(f8(x1351),f8(f18(x1351,x1351)))),x1352)
% 0.20/0.66 [102]P2(x1021)+~P3(x1021,x1022,x1023)
% 0.20/0.66 [103]P8(x1031)+~P4(x1032,x1033,x1031)
% 0.20/0.66 [104]P8(x1041)+~P4(x1042,x1041,x1043)
% 0.20/0.66 [111]~P4(x1111,x1112,x1113)+P3(x1111,x1112,x1113)
% 0.20/0.66 [96]P5(x961,x962)+~P5(x961,f10(x963,x962))
% 0.20/0.66 [97]P5(x971,x972)+~P5(x971,f10(x972,x973))
% 0.20/0.66 [105]~P3(x1052,x1051,x1053)+E(f9(f9(x1051)),f9(x1052))
% 0.20/0.66 [118]~P5(x1181,f6(x1182,x1183))+E(f18(f18(f12(x1181),f12(x1181)),f18(f12(x1181),f18(f24(x1181),f24(x1181)))),x1181)
% 0.20/0.66 [120]~P3(x1201,x1203,x1202)+P6(f9(f9(f11(f6(x1201,a19)))),f9(f9(x1202)))
% 0.20/0.66 [123]P5(x1231,a19)+~P5(f18(f18(x1232,x1232),f18(x1232,f18(x1231,x1231))),f6(x1233,x1234))
% 0.20/0.66 [124]P5(x1241,a19)+~P5(f18(f18(x1241,x1241),f18(x1241,f18(x1242,x1242))),f6(x1243,x1244))
% 0.20/0.66 [125]P5(x1251,x1252)+~P5(f18(f18(x1253,x1253),f18(x1253,f18(x1251,x1251))),f6(x1254,x1252))
% 0.20/0.66 [126]P5(x1261,x1262)+~P5(f18(f18(x1261,x1261),f18(x1261,f18(x1263,x1263))),f6(x1262,x1264))
% 0.20/0.66 [127]~E(f18(x1271,x1272),a4)+~P5(f18(f18(x1271,x1271),f18(x1271,f18(x1272,x1272))),f6(x1273,x1274))
% 0.20/0.66 [131]P5(x1311,f18(x1312,x1311))+~P5(f18(f18(x1312,x1312),f18(x1312,f18(x1311,x1311))),f6(x1313,x1314))
% 0.20/0.66 [132]P5(x1321,f18(x1321,x1322))+~P5(f18(f18(x1321,x1321),f18(x1321,f18(x1322,x1322))),f6(x1323,x1324))
% 0.20/0.66 [143]~P5(f18(f18(f18(f18(x1433,x1433),f18(x1433,f18(x1431,x1431))),f18(f18(x1433,x1433),f18(x1433,f18(x1431,x1431)))),f18(f18(f18(x1433,x1433),f18(x1433,f18(x1431,x1431))),f18(x1432,x1432))),f21(x1434))+P5(f18(f18(f18(f18(x1431,x1431),f18(x1431,f18(x1432,x1432))),f18(f18(x1431,x1431),f18(x1431,f18(x1432,x1432)))),f18(f18(f18(x1431,x1431),f18(x1431,f18(x1432,x1432))),f18(x1433,x1433))),x1434)
% 0.20/0.66 [144]~P5(f18(f18(f18(f18(x1442,x1442),f18(x1442,f18(x1441,x1441))),f18(f18(x1442,x1442),f18(x1442,f18(x1441,x1441)))),f18(f18(f18(x1442,x1442),f18(x1442,f18(x1441,x1441))),f18(x1443,x1443))),f11(x1444))+P5(f18(f18(f18(f18(x1441,x1441),f18(x1441,f18(x1442,x1442))),f18(f18(x1441,x1441),f18(x1441,f18(x1442,x1442)))),f18(f18(f18(x1441,x1441),f18(x1441,f18(x1442,x1442))),f18(x1443,x1443))),x1444)
% 0.20/0.66 [148]~P5(f18(f18(x1484,x1484),f18(x1484,f18(x1481,x1481))),f7(x1482,x1483))+P5(x1481,f9(f9(f11(f6(f10(x1482,f6(f9(f9(f11(f6(f10(x1483,f6(f18(x1484,x1484),a19)),a19)))),a19)),a19)))))
% 0.20/0.66 [114]~P2(x1141)+P7(x1141)+~P2(f9(f11(f6(x1141,a19))))
% 0.20/0.66 [128]P2(x1281)+~P6(x1281,f6(a19,a19))+~P6(f7(x1281,f9(f11(f6(x1281,a19)))),a13)
% 0.20/0.66 [140]P1(x1401)+~P5(a4,x1401)+~P6(f9(f9(f11(f6(f10(a20,f6(x1401,a19)),a19)))),x1401)
% 0.20/0.66 [147]~P5(x1471,a19)+E(x1471,a4)+P5(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(a2,f6(f18(x1471,x1471),a19)),a19))))))),x1471)
% 0.20/0.66 [85]~P6(x852,x851)+~P6(x851,x852)+E(x851,x852)
% 0.20/0.66 [79]P5(x792,a19)+P5(x791,a19)+E(f18(x791,x792),a4)
% 0.20/0.66 [88]P5(x881,x882)+P5(x881,f8(x882))+~P5(x881,a19)
% 0.20/0.66 [99]E(x991,x992)+P5(f14(x992,x991),x992)+P5(f14(x991,x992),x991)
% 0.20/0.66 [107]E(x1071,x1072)+P5(f14(x1072,x1071),x1072)+~P5(f14(x1071,x1072),x1072)
% 0.20/0.66 [109]E(x1091,x1092)+~P5(f14(x1092,x1091),x1091)+~P5(f14(x1091,x1092),x1092)
% 0.20/0.66 [110]P5(x1102,f9(x1101))+~P5(x1102,a19)+E(f10(x1101,f6(f18(x1102,x1102),a19)),a4)
% 0.20/0.66 [136]~P5(x1361,x1362)+~P5(f18(f18(x1361,x1361),f18(x1361,f18(x1362,x1362))),f6(a19,a19))+P5(f18(f18(x1361,x1361),f18(x1361,f18(x1362,x1362))),a5)
% 0.20/0.66 [137]~P5(f18(f18(x1371,x1371),f18(x1371,f18(x1372,x1372))),f6(a19,a19))+~E(f8(f10(f8(x1371),f8(f18(x1371,x1371)))),x1372)+P5(f18(f18(x1371,x1371),f18(x1371,f18(x1372,x1372))),a20)
% 0.20/0.66 [139]~P2(x1391)+~P5(x1392,a19)+P5(f9(f9(f11(f6(f10(x1391,f6(x1392,a19)),a19)))),a19)
% 0.20/0.66 [89]~P6(x891,x893)+P6(x891,x892)+~P6(x893,x892)
% 0.20/0.66 [90]~P5(x901,x903)+P5(x901,x902)+~P6(x903,x902)
% 0.20/0.66 [95]E(x951,x952)+E(x951,x953)+~P5(x951,f18(x953,x952))
% 0.20/0.66 [100]~P5(x1001,x1003)+~P5(x1001,x1002)+P5(x1001,f10(x1002,x1003))
% 0.20/0.66 [101]~P5(x1012,x1013)+~P5(x1011,x1013)+P6(f18(x1011,x1012),x1013)
% 0.20/0.66 [129]E(x1291,x1292)+~E(f18(x1293,x1291),f18(x1293,x1292))+~P5(f18(f18(x1291,x1291),f18(x1291,f18(x1292,x1292))),f6(a19,a19))
% 0.20/0.66 [130]E(x1301,x1302)+~E(f18(x1301,x1303),f18(x1302,x1303))+~P5(f18(f18(x1301,x1301),f18(x1301,f18(x1302,x1302))),f6(a19,a19))
% 0.20/0.66 [119]~P5(x1192,x1194)+~P5(x1191,x1193)+P5(f18(f18(x1191,x1191),f18(x1191,f18(x1192,x1192))),f6(x1193,x1194))
% 0.20/0.66 [145]~P5(f18(f18(f18(f18(x1452,x1452),f18(x1452,f18(x1453,x1453))),f18(f18(x1452,x1452),f18(x1452,f18(x1453,x1453)))),f18(f18(f18(x1452,x1452),f18(x1452,f18(x1453,x1453))),f18(x1451,x1451))),x1454)+P5(f18(f18(f18(f18(x1451,x1451),f18(x1451,f18(x1452,x1452))),f18(f18(x1451,x1451),f18(x1451,f18(x1452,x1452)))),f18(f18(f18(x1451,x1451),f18(x1451,f18(x1452,x1452))),f18(x1453,x1453))),f21(x1454))+~P5(f18(f18(f18(f18(x1451,x1451),f18(x1451,f18(x1452,x1452))),f18(f18(x1451,x1451),f18(x1451,f18(x1452,x1452)))),f18(f18(f18(x1451,x1451),f18(x1451,f18(x1452,x1452))),f18(x1453,x1453))),f6(f6(a19,a19),a19))
% 0.20/0.66 [146]~P5(f18(f18(f18(f18(x1462,x1462),f18(x1462,f18(x1461,x1461))),f18(f18(x1462,x1462),f18(x1462,f18(x1461,x1461)))),f18(f18(f18(x1462,x1462),f18(x1462,f18(x1461,x1461))),f18(x1463,x1463))),x1464)+P5(f18(f18(f18(f18(x1461,x1461),f18(x1461,f18(x1462,x1462))),f18(f18(x1461,x1461),f18(x1461,f18(x1462,x1462)))),f18(f18(f18(x1461,x1461),f18(x1461,f18(x1462,x1462))),f18(x1463,x1463))),f11(x1464))+~P5(f18(f18(f18(f18(x1461,x1461),f18(x1461,f18(x1462,x1462))),f18(f18(x1461,x1461),f18(x1461,f18(x1462,x1462)))),f18(f18(f18(x1461,x1461),f18(x1461,f18(x1462,x1462))),f18(x1463,x1463))),f6(f6(a19,a19),a19))
% 0.20/0.66 [149]P5(f18(f18(x1491,x1491),f18(x1491,f18(x1492,x1492))),f7(x1493,x1494))+~P5(f18(f18(x1491,x1491),f18(x1491,f18(x1492,x1492))),f6(a19,a19))+~P5(x1492,f9(f9(f11(f6(f10(x1493,f6(f9(f9(f11(f6(f10(x1494,f6(f18(x1491,x1491),a19)),a19)))),a19)),a19)))))
% 0.20/0.67 [150]~P4(x1502,x1505,x1501)+~P5(f18(f18(x1503,x1503),f18(x1503,f18(x1504,x1504))),f9(x1505))+E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1501,f6(f18(f18(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1503,x1503),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1503,x1503),a19)),a19)))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1503,x1503),a19)),a19))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1504,x1504),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1504,x1504),a19)),a19)))))))))),f18(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1503,x1503),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1503,x1503),a19)),a19)))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1503,x1503),a19)),a19))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1504,x1504),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(x1504,x1504),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1502,f6(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1505,f6(f18(f18(f18(x1503,x1503),f18(x1503,f18(x1504,x1504))),f18(f18(x1503,x1503),f18(x1503,f18(x1504,x1504)))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1505,f6(f18(f18(f18(x1503,x1503),f18(x1503,f18(x1504,x1504))),f18(f18(x1503,x1503),f18(x1503,f18(x1504,x1504)))),a19)),a19)))))))),a19)),a19))))))))
% 0.20/0.67 [134]~P2(x1341)+P8(x1341)+~E(f6(f9(f9(x1341)),f9(f9(x1341))),f9(x1341))+~P6(f9(f9(f11(f6(x1341,a19)))),f9(f9(x1341)))
% 0.20/0.67 [133]~P2(x1331)+P3(x1331,x1332,x1333)+~E(f9(f9(x1332)),f9(x1331))+~P6(f9(f9(f11(f6(x1331,a19)))),f9(f9(x1333)))
% 0.20/0.67 [141]~P8(x1413)+~P8(x1412)+~P3(x1411,x1412,x1413)+P4(x1411,x1412,x1413)+P5(f18(f18(f15(x1411,x1412,x1413),f15(x1411,x1412,x1413)),f18(f15(x1411,x1412,x1413),f18(f16(x1411,x1412,x1413),f16(x1411,x1412,x1413)))),f9(x1412))
% 0.20/0.67 [151]~P8(x1513)+~P8(x1512)+~P3(x1511,x1512,x1513)+P4(x1511,x1512,x1513)+~E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1513,f6(f18(f18(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a19)),a19)))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a19)),a19))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)),a19)),a19)))))))))),f18(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a19)),a19)))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),a19)),a19))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1511,f6(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1512,f6(f18(f18(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),f18(f15(x1511,x1512,x1513),f18(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)))),f18(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),f18(f15(x1511,x1512,x1513),f18(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1512,f6(f18(f18(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),f18(f15(x1511,x1512,x1513),f18(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513)))),f18(f18(f15(x1511,x1512,x1513),f15(x1511,x1512,x1513)),f18(f15(x1511,x1512,x1513),f18(f16(x1511,x1512,x1513),f16(x1511,x1512,x1513))))),a19)),a19)))))))),a19)),a19))))))))
% 0.20/0.67 %EqnAxiom
% 0.20/0.67 [1]E(x11,x11)
% 0.20/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.67 [4]~E(x41,x42)+E(f18(x41,x43),f18(x42,x43))
% 0.20/0.67 [5]~E(x51,x52)+E(f18(x53,x51),f18(x53,x52))
% 0.20/0.67 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.20/0.67 [7]~E(x71,x72)+E(f10(x71,x73),f10(x72,x73))
% 0.20/0.67 [8]~E(x81,x82)+E(f10(x83,x81),f10(x83,x82))
% 0.20/0.67 [9]~E(x91,x92)+E(f6(x91,x93),f6(x92,x93))
% 0.20/0.67 [10]~E(x101,x102)+E(f6(x103,x101),f6(x103,x102))
% 0.20/0.67 [11]~E(x111,x112)+E(f11(x111),f11(x112))
% 0.20/0.67 [12]~E(x121,x122)+E(f8(x121),f8(x122))
% 0.20/0.67 [13]~E(x131,x132)+E(f14(x131,x133),f14(x132,x133))
% 0.20/0.67 [14]~E(x141,x142)+E(f14(x143,x141),f14(x143,x142))
% 0.20/0.67 [15]~E(x151,x152)+E(f7(x151,x153),f7(x152,x153))
% 0.20/0.67 [16]~E(x161,x162)+E(f7(x163,x161),f7(x163,x162))
% 0.20/0.67 [17]~E(x171,x172)+E(f15(x171,x173,x174),f15(x172,x173,x174))
% 0.20/0.67 [18]~E(x181,x182)+E(f15(x183,x181,x184),f15(x183,x182,x184))
% 0.20/0.67 [19]~E(x191,x192)+E(f15(x193,x194,x191),f15(x193,x194,x192))
% 0.20/0.67 [20]~E(x201,x202)+E(f16(x201,x203,x204),f16(x202,x203,x204))
% 0.20/0.67 [21]~E(x211,x212)+E(f16(x213,x211,x214),f16(x213,x212,x214))
% 0.20/0.67 [22]~E(x221,x222)+E(f16(x223,x224,x221),f16(x223,x224,x222))
% 0.20/0.67 [23]~E(x231,x232)+E(f24(x231),f24(x232))
% 0.20/0.67 [24]~E(x241,x242)+E(f12(x241),f12(x242))
% 0.20/0.67 [25]~E(x251,x252)+E(f22(x251),f22(x252))
% 0.20/0.67 [26]~E(x261,x262)+E(f21(x261),f21(x262))
% 0.20/0.67 [27]~E(x271,x272)+E(f3(x271),f3(x272))
% 0.20/0.67 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.20/0.67 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.20/0.67 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.20/0.67 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.20/0.67 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.20/0.67 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.20/0.67 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.20/0.67 [35]~P8(x351)+P8(x352)+~E(x351,x352)
% 0.20/0.67 [36]P6(x362,x363)+~E(x361,x362)+~P6(x361,x363)
% 0.20/0.67 [37]P6(x373,x372)+~E(x371,x372)+~P6(x373,x371)
% 0.20/0.67 [38]~P7(x381)+P7(x382)+~E(x381,x382)
% 0.20/0.67 [39]~P9(x391)+P9(x392)+~E(x391,x392)
% 0.20/0.67 [40]P4(x402,x403,x404)+~E(x401,x402)+~P4(x401,x403,x404)
% 0.20/0.67 [41]P4(x413,x412,x414)+~E(x411,x412)+~P4(x413,x411,x414)
% 0.20/0.67 [42]P4(x423,x424,x422)+~E(x421,x422)+~P4(x423,x424,x421)
% 0.20/0.67
% 0.20/0.67 %-------------------------------------------
% 0.20/0.67 cnf(152,plain,
% 0.20/0.67 ($false),
% 0.20/0.67 inference(scs_inference,[],[48,45,83]),
% 0.20/0.67 ['proof']).
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67 % Total time :0.000000s
%------------------------------------------------------------------------------