TSTP Solution File: SET074-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET074-7 : 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 : n002.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 14:28:28 EDT 2023
% Result : Unsatisfiable 0.72s 0.80s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET074-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 12:21:03 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.61 start to proof:theBenchmark
% 0.72/0.79 %-------------------------------------------
% 0.72/0.79 % File :CSE---1.6
% 0.72/0.79 % Problem :theBenchmark
% 0.72/0.79 % Transform :cnf
% 0.72/0.79 % Format :tptp:raw
% 0.72/0.79 % Command :java -jar mcs_scs.jar %d %s
% 0.72/0.79
% 0.72/0.79 % Result :Theorem 0.110000s
% 0.72/0.79 % Output :CNFRefutation 0.110000s
% 0.72/0.79 %-------------------------------------------
% 0.72/0.80 %--------------------------------------------------------------------------
% 0.72/0.80 % File : SET074-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.72/0.80 % Domain : Set Theory
% 0.72/0.80 % Problem : Corollary to unordered pair axiom
% 0.72/0.80 % Version : [Qua92] axioms : Augmented.
% 0.72/0.80 % English :
% 0.72/0.80
% 0.72/0.80 % Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.72/0.80 % Source : [Quaife]
% 0.72/0.80 % Names : UP6.2 [Qua92]
% 0.72/0.80
% 0.72/0.80 % Status : Unsatisfiable
% 0.72/0.80 % 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 v5.0.0, 0.07 v4.1.0, 0.08 v4.0.1, 0.18 v4.0.0, 0.27 v3.7.0, 0.30 v3.5.0, 0.27 v3.4.0, 0.17 v3.3.0, 0.14 v3.2.0, 0.00 v3.1.0, 0.09 v2.7.0, 0.08 v2.6.0, 0.00 v2.1.0
% 0.72/0.80 % Syntax : Number of clauses : 117 ( 39 unt; 15 nHn; 78 RR)
% 0.72/0.80 % Number of literals : 231 ( 54 equ; 101 neg)
% 0.72/0.80 % Maximal clause size : 5 ( 1 avg)
% 0.72/0.80 % Maximal term depth : 6 ( 1 avg)
% 0.72/0.80 % Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% 0.72/0.80 % Number of functors : 40 ( 40 usr; 10 con; 0-3 aty)
% 0.72/0.80 % Number of variables : 228 ( 40 sgn)
% 0.72/0.80 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.72/0.80
% 0.72/0.80 % Comments : Preceding lemmas are added.
% 0.72/0.80 % Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
% 0.72/0.80 %--------------------------------------------------------------------------
% 0.72/0.80 %----Include von Neuman-Bernays-Godel set theory axioms
% 0.72/0.80 include('Axioms/SET004-0.ax').
% 0.72/0.80 %--------------------------------------------------------------------------
% 0.72/0.80 %----Corollaries to Unordered pair axiom. Not in paper, but in email.
% 0.72/0.80 cnf(corollary_1_to_unordered_pair,axiom,
% 0.72/0.80 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.72/0.80 | member(X,unordered_pair(X,Y)) ) ).
% 0.72/0.80
% 0.72/0.80 cnf(corollary_2_to_unordered_pair,axiom,
% 0.72/0.80 ( ~ member(ordered_pair(X,Y),cross_product(U,V))
% 0.72/0.80 | member(Y,unordered_pair(X,Y)) ) ).
% 0.72/0.80
% 0.72/0.80 %----Corollaries to Cartesian product axiom.
% 0.72/0.80 cnf(corollary_1_to_cartesian_product,axiom,
% 0.72/0.80 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.72/0.80 | member(U,universal_class) ) ).
% 0.72/0.80
% 0.72/0.80 cnf(corollary_2_to_cartesian_product,axiom,
% 0.72/0.80 ( ~ member(ordered_pair(U,V),cross_product(X,Y))
% 0.72/0.80 | member(V,universal_class) ) ).
% 0.72/0.80
% 0.72/0.80 %---- PARTIAL ORDER.
% 0.72/0.80 %----(PO1): reflexive.
% 0.72/0.80 cnf(subclass_is_reflexive,axiom,
% 0.72/0.80 subclass(X,X) ).
% 0.72/0.80
% 0.72/0.80 %----(PO2): antisymmetry is part of A-3.
% 0.72/0.80 %----(x < y), (y < x) --> (x = y).
% 0.72/0.80
% 0.72/0.80 %----(PO3): transitivity.
% 0.72/0.80 cnf(transitivity_of_subclass,axiom,
% 0.72/0.80 ( ~ subclass(X,Y)
% 0.72/0.80 | ~ subclass(Y,Z)
% 0.72/0.80 | subclass(X,Z) ) ).
% 0.72/0.80
% 0.72/0.80 %---- EQUALITY.
% 0.72/0.80 %----(EQ1): equality axiom.
% 0.72/0.80 %----a:x:(x = x).
% 0.72/0.80 %----This is always an axiom in the TPTP presentation.
% 0.72/0.80
% 0.72/0.80 %----(EQ2): expanded equality definition.
% 0.72/0.80 cnf(equality1,axiom,
% 0.72/0.80 ( X = Y
% 0.72/0.80 | member(not_subclass_element(X,Y),X)
% 0.72/0.80 | member(not_subclass_element(Y,X),Y) ) ).
% 0.72/0.80
% 0.72/0.80 cnf(equality2,axiom,
% 0.72/0.80 ( ~ member(not_subclass_element(X,Y),Y)
% 0.72/0.80 | X = Y
% 0.72/0.80 | member(not_subclass_element(Y,X),Y) ) ).
% 0.72/0.80
% 0.72/0.80 cnf(equality3,axiom,
% 0.72/0.80 ( ~ member(not_subclass_element(Y,X),X)
% 0.72/0.80 | X = Y
% 0.72/0.80 | member(not_subclass_element(X,Y),X) ) ).
% 0.72/0.80
% 0.72/0.80 cnf(equality4,axiom,
% 0.72/0.80 ( ~ member(not_subclass_element(X,Y),Y)
% 0.72/0.80 | ~ member(not_subclass_element(Y,X),X)
% 0.72/0.80 | X = Y ) ).
% 0.72/0.80
% 0.72/0.80 %---- SPECIAL CLASSES.
% 0.72/0.80 %----(SP1): lemma.
% 0.72/0.80 cnf(special_classes_lemma,axiom,
% 0.72/0.80 ~ member(Y,intersection(complement(X),X)) ).
% 0.72/0.80
% 0.72/0.80 %----(SP2): Existence of O (null class).
% 0.72/0.80 %----e:x:a:z:(-(z e x)).
% 0.72/0.80 cnf(existence_of_null_class,axiom,
% 0.72/0.80 ~ member(Z,null_class) ).
% 0.72/0.80
% 0.72/0.80 %----(SP3): O is a subclass of every class.
% 0.72/0.80 cnf(null_class_is_subclass,axiom,
% 0.72/0.80 subclass(null_class,X) ).
% 0.72/0.80
% 0.72/0.80 %----corollary.
% 0.72/0.80 cnf(corollary_of_null_class_is_subclass,axiom,
% 0.72/0.80 ( ~ subclass(X,null_class)
% 0.72/0.80 | X = null_class ) ).
% 0.72/0.80
% 0.72/0.80 %----(SP4): uniqueness of null class.
% 0.72/0.80 cnf(null_class_is_unique,axiom,
% 0.72/0.80 ( Z = null_class
% 0.72/0.80 | member(not_subclass_element(Z,null_class),Z) ) ).
% 0.72/0.80
% 0.72/0.80 %----(SP5): O is a set (follows from axiom of infinity).
% 0.72/0.80 cnf(null_class_is_a_set,axiom,
% 0.72/0.80 member(null_class,universal_class) ).
% 0.72/0.80
% 0.72/0.80 %---- UNORDERED PAIRS.
% 0.72/0.80 %----(UP1): unordered pair is commutative.
% 0.72/0.80 cnf(commutativity_of_unordered_pair,axiom,
% 0.72/0.80 unordered_pair(X,Y) = unordered_pair(Y,X) ).
% 0.72/0.80
% 0.72/0.80 %----(UP2): if one argument is a proper class, pair contains only the
% 0.72/0.80 %----other. In a slightly different form to the paper
% 0.72/0.80 cnf(singleton_in_unordered_pair1,axiom,
% 0.72/0.80 subclass(singleton(X),unordered_pair(X,Y)) ).
% 0.72/0.80
% 0.72/0.80 cnf(singleton_in_unordered_pair2,axiom,
% 0.72/0.80 subclass(singleton(Y),unordered_pair(X,Y)) ).
% 0.72/0.80
% 0.72/0.80 cnf(unordered_pair_equals_singleton1,axiom,
% 0.72/0.80 ( member(Y,universal_class)
% 0.72/0.80 | unordered_pair(X,Y) = singleton(X) ) ).
% 0.72/0.80
% 0.72/0.80 cnf(unordered_pair_equals_singleton2,axiom,
% 0.72/0.80 ( member(X,universal_class)
% 0.72/0.80 | unordered_pair(X,Y) = singleton(Y) ) ).
% 0.72/0.80
% 0.72/0.80 %----(UP3): if both arguments are proper classes, pair is null.
% 0.72/0.80 cnf(null_unordered_pair,axiom,
% 0.72/0.80 ( unordered_pair(X,Y) = null_class
% 0.72/0.80 | member(X,universal_class)
% 0.72/0.80 | member(Y,universal_class) ) ).
% 0.72/0.80
% 0.72/0.80 %----(UP4): left cancellation for unordered pairs.
% 0.72/0.80 cnf(left_cancellation,axiom,
% 0.72/0.80 ( unordered_pair(X,Y) != unordered_pair(X,Z)
% 0.72/0.80 | ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
% 0.72/0.80 | Y = Z ) ).
% 0.72/0.80
% 0.72/0.80 %----(UP5): right cancellation for unordered pairs.
% 0.72/0.80 cnf(right_cancellation,axiom,
% 0.72/0.80 ( unordered_pair(X,Z) != unordered_pair(Y,Z)
% 0.72/0.80 | ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
% 0.72/0.80 | X = Y ) ).
% 0.72/0.80
% 0.72/0.80 cnf(prove_corollary_to_unordered_pair_axiom2_1,negated_conjecture,
% 0.72/0.80 member(y,universal_class) ).
% 0.72/0.80
% 0.72/0.80 cnf(prove_corollary_to_unordered_pair_axiom2_2,negated_conjecture,
% 0.72/0.80 unordered_pair(x,y) = null_class ).
% 0.72/0.80
% 0.72/0.80 %--------------------------------------------------------------------------
% 0.72/0.80 %-------------------------------------------
% 0.72/0.80 % Proof found
% 0.72/0.80 % SZS status Theorem for theBenchmark
% 0.72/0.80 % SZS output start Proof
% 0.72/0.80 %ClaNum:144(EqnAxiom:42)
% 0.72/0.80 %VarNum:844(SingletonVarNum:200)
% 0.72/0.80 %MaxLitNum:5
% 0.72/0.80 %MaxfuncDepth:24
% 0.72/0.80 %SharedTerms:35
% 0.72/0.80 %goalClause: 45 48
% 0.72/0.80 %singleGoalClaCount:2
% 0.72/0.80 [43]P1(a1)
% 0.72/0.80 [44]P2(a2)
% 0.72/0.80 [46]P5(a4,a19)
% 0.72/0.80 [47]P5(a1,a19)
% 0.72/0.80 [48]P5(a25,a19)
% 0.72/0.80 [45]E(f18(a17,a25),a4)
% 0.72/0.80 [53]P6(a5,f6(a19,a19))
% 0.72/0.80 [54]P6(a20,f6(a19,a19))
% 0.72/0.80 [62]E(f10(f9(f11(f6(a23,a19))),a23),a13)
% 0.72/0.80 [63]E(f10(f6(a19,a19),f10(f6(a19,a19),f8(f7(f8(a5),f9(f11(f6(a5,a19))))))),a23)
% 0.72/0.80 [49]P6(x491,a19)
% 0.72/0.80 [50]P6(a4,x501)
% 0.72/0.80 [51]P6(x511,x511)
% 0.72/0.80 [65]~P5(x651,a4)
% 0.72/0.80 [60]P6(f21(x601),f6(f6(a19,a19),a19))
% 0.72/0.80 [61]P6(f11(x611),f6(f6(a19,a19),a19))
% 0.72/0.80 [64]E(f10(f9(x641),f8(f9(f10(f7(f9(f11(f6(a5,a19))),x641),a13)))),f3(x641))
% 0.72/0.80 [52]E(f18(x521,x522),f18(x522,x521))
% 0.72/0.80 [55]P5(f18(x551,x552),a19)
% 0.72/0.80 [56]P6(f7(x561,x562),f6(a19,a19))
% 0.72/0.80 [57]P6(f18(x571,x571),f18(x572,x571))
% 0.72/0.80 [58]P6(f18(x581,x581),f18(x581,x582))
% 0.72/0.80 [66]~P5(x661,f10(f8(x662),x662))
% 0.72/0.80 [59]E(f10(f6(x591,x592),x593),f10(x593,f6(x591,x592)))
% 0.72/0.80 [67]~P7(x671)+P2(x671)
% 0.72/0.80 [68]~P8(x681)+P2(x681)
% 0.72/0.80 [71]~P1(x711)+P6(a1,x711)
% 0.72/0.80 [72]~P1(x721)+P5(a4,x721)
% 0.72/0.80 [73]~P6(x731,a4)+E(x731,a4)
% 0.72/0.80 [75]P5(f22(x751),x751)+E(x751,a4)
% 0.72/0.80 [76]E(x761,a4)+P5(f14(x761,a4),x761)
% 0.72/0.80 [80]~P2(x801)+P6(x801,f6(a19,a19))
% 0.72/0.80 [74]E(x741,a4)+E(f10(x741,f22(x741)),a4)
% 0.72/0.80 [89]~P8(x891)+E(f6(f9(f9(x891)),f9(f9(x891))),f9(x891))
% 0.72/0.80 [102]~P7(x1021)+P2(f9(f11(f6(x1021,a19))))
% 0.72/0.80 [107]~P5(x1071,a19)+P5(f9(f10(a5,f6(a19,x1071))),a19)
% 0.72/0.80 [109]~P9(x1091)+P6(f7(x1091,f9(f11(f6(x1091,a19)))),a13)
% 0.72/0.80 [110]~P2(x1101)+P6(f7(x1101,f9(f11(f6(x1101,a19)))),a13)
% 0.72/0.80 [111]~P8(x1111)+P6(f9(f9(f11(f6(x1111,a19)))),f9(f9(x1111)))
% 0.72/0.80 [116]P9(x1161)+~P6(f7(x1161,f9(f11(f6(x1161,a19)))),a13)
% 0.72/0.80 [131]~P1(x1311)+P6(f9(f9(f11(f6(f10(a20,f6(x1311,a19)),a19)))),x1311)
% 0.72/0.80 [135]~P5(x1351,a19)+P5(f8(f9(f9(f11(f6(f10(a5,f6(f8(x1351),a19)),a19))))),a19)
% 0.72/0.80 [69]~E(x692,x691)+P6(x691,x692)
% 0.72/0.80 [70]~E(x701,x702)+P6(x701,x702)
% 0.72/0.80 [78]P5(x782,a19)+E(f18(x781,x782),f18(x781,x781))
% 0.72/0.80 [79]P5(x791,a19)+E(f18(x791,x792),f18(x792,x792))
% 0.72/0.80 [82]P6(x821,x822)+P5(f14(x821,x822),x821)
% 0.72/0.80 [83]~P5(x831,x832)+~P5(x831,f8(x832))
% 0.72/0.80 [87]~P5(x871,a19)+P5(x871,f18(x872,x871))
% 0.72/0.80 [88]~P5(x881,a19)+P5(x881,f18(x881,x882))
% 0.72/0.80 [93]P6(x931,x932)+~P5(f14(x931,x932),x932)
% 0.72/0.80 [106]~P5(x1062,f9(x1061))+~E(f10(x1061,f6(f18(x1062,x1062),a19)),a4)
% 0.72/0.80 [115]P5(x1151,x1152)+~P5(f18(f18(x1151,x1151),f18(x1151,f18(x1152,x1152))),a5)
% 0.72/0.80 [128]~P5(f18(f18(x1281,x1281),f18(x1281,f18(x1282,x1282))),a20)+E(f8(f10(f8(x1281),f8(f18(x1281,x1281)))),x1282)
% 0.72/0.80 [96]P2(x961)+~P3(x961,x962,x963)
% 0.72/0.80 [97]P8(x971)+~P4(x972,x973,x971)
% 0.72/0.80 [98]P8(x981)+~P4(x982,x981,x983)
% 0.72/0.80 [105]~P4(x1051,x1052,x1053)+P3(x1051,x1052,x1053)
% 0.72/0.80 [91]P5(x911,x912)+~P5(x911,f10(x913,x912))
% 0.72/0.80 [92]P5(x921,x922)+~P5(x921,f10(x922,x923))
% 0.72/0.80 [99]~P3(x992,x991,x993)+E(f9(f9(x991)),f9(x992))
% 0.72/0.80 [112]~P5(x1121,f6(x1122,x1123))+E(f18(f18(f12(x1121),f12(x1121)),f18(f12(x1121),f18(f24(x1121),f24(x1121)))),x1121)
% 0.72/0.80 [114]~P3(x1141,x1143,x1142)+P6(f9(f9(f11(f6(x1141,a19)))),f9(f9(x1142)))
% 0.72/0.80 [117]P5(x1171,a19)+~P5(f18(f18(x1172,x1172),f18(x1172,f18(x1171,x1171))),f6(x1173,x1174))
% 0.72/0.80 [118]P5(x1181,a19)+~P5(f18(f18(x1181,x1181),f18(x1181,f18(x1182,x1182))),f6(x1183,x1184))
% 0.72/0.80 [119]P5(x1191,x1192)+~P5(f18(f18(x1193,x1193),f18(x1193,f18(x1191,x1191))),f6(x1194,x1192))
% 0.72/0.80 [120]P5(x1201,x1202)+~P5(f18(f18(x1201,x1201),f18(x1201,f18(x1203,x1203))),f6(x1202,x1204))
% 0.72/0.80 [124]P5(x1241,f18(x1242,x1241))+~P5(f18(f18(x1242,x1242),f18(x1242,f18(x1241,x1241))),f6(x1243,x1244))
% 0.72/0.80 [125]P5(x1251,f18(x1251,x1252))+~P5(f18(f18(x1251,x1251),f18(x1251,f18(x1252,x1252))),f6(x1253,x1254))
% 0.72/0.80 [136]~P5(f18(f18(f18(f18(x1363,x1363),f18(x1363,f18(x1361,x1361))),f18(f18(x1363,x1363),f18(x1363,f18(x1361,x1361)))),f18(f18(f18(x1363,x1363),f18(x1363,f18(x1361,x1361))),f18(x1362,x1362))),f21(x1364))+P5(f18(f18(f18(f18(x1361,x1361),f18(x1361,f18(x1362,x1362))),f18(f18(x1361,x1361),f18(x1361,f18(x1362,x1362)))),f18(f18(f18(x1361,x1361),f18(x1361,f18(x1362,x1362))),f18(x1363,x1363))),x1364)
% 0.72/0.80 [137]~P5(f18(f18(f18(f18(x1372,x1372),f18(x1372,f18(x1371,x1371))),f18(f18(x1372,x1372),f18(x1372,f18(x1371,x1371)))),f18(f18(f18(x1372,x1372),f18(x1372,f18(x1371,x1371))),f18(x1373,x1373))),f11(x1374))+P5(f18(f18(f18(f18(x1371,x1371),f18(x1371,f18(x1372,x1372))),f18(f18(x1371,x1371),f18(x1371,f18(x1372,x1372)))),f18(f18(f18(x1371,x1371),f18(x1371,f18(x1372,x1372))),f18(x1373,x1373))),x1374)
% 0.72/0.80 [141]~P5(f18(f18(x1414,x1414),f18(x1414,f18(x1411,x1411))),f7(x1412,x1413))+P5(x1411,f9(f9(f11(f6(f10(x1412,f6(f9(f9(f11(f6(f10(x1413,f6(f18(x1414,x1414),a19)),a19)))),a19)),a19)))))
% 0.72/0.80 [108]~P2(x1081)+P7(x1081)+~P2(f9(f11(f6(x1081,a19))))
% 0.72/0.80 [121]P2(x1211)+~P6(x1211,f6(a19,a19))+~P6(f7(x1211,f9(f11(f6(x1211,a19)))),a13)
% 0.72/0.80 [133]P1(x1331)+~P5(a4,x1331)+~P6(f9(f9(f11(f6(f10(a20,f6(x1331,a19)),a19)))),x1331)
% 0.72/0.80 [140]~P5(x1401,a19)+E(x1401,a4)+P5(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(a2,f6(f18(x1401,x1401),a19)),a19))))))),x1401)
% 0.72/0.80 [81]~P6(x812,x811)+~P6(x811,x812)+E(x811,x812)
% 0.72/0.80 [77]P5(x772,a19)+P5(x771,a19)+E(f18(x771,x772),a4)
% 0.72/0.80 [84]P5(x841,x842)+P5(x841,f8(x842))+~P5(x841,a19)
% 0.72/0.80 [94]E(x941,x942)+P5(f14(x942,x941),x942)+P5(f14(x941,x942),x941)
% 0.72/0.80 [101]E(x1011,x1012)+P5(f14(x1012,x1011),x1012)+~P5(f14(x1011,x1012),x1012)
% 0.72/0.80 [103]E(x1031,x1032)+~P5(f14(x1032,x1031),x1031)+~P5(f14(x1031,x1032),x1032)
% 0.72/0.80 [104]P5(x1042,f9(x1041))+~P5(x1042,a19)+E(f10(x1041,f6(f18(x1042,x1042),a19)),a4)
% 0.72/0.80 [129]~P5(x1291,x1292)+~P5(f18(f18(x1291,x1291),f18(x1291,f18(x1292,x1292))),f6(a19,a19))+P5(f18(f18(x1291,x1291),f18(x1291,f18(x1292,x1292))),a5)
% 0.72/0.80 [130]~P5(f18(f18(x1301,x1301),f18(x1301,f18(x1302,x1302))),f6(a19,a19))+~E(f8(f10(f8(x1301),f8(f18(x1301,x1301)))),x1302)+P5(f18(f18(x1301,x1301),f18(x1301,f18(x1302,x1302))),a20)
% 0.72/0.80 [132]~P2(x1321)+~P5(x1322,a19)+P5(f9(f9(f11(f6(f10(x1321,f6(x1322,a19)),a19)))),a19)
% 0.72/0.80 [85]~P6(x851,x853)+P6(x851,x852)+~P6(x853,x852)
% 0.72/0.80 [86]~P5(x861,x863)+P5(x861,x862)+~P6(x863,x862)
% 0.72/0.80 [90]E(x901,x902)+E(x901,x903)+~P5(x901,f18(x903,x902))
% 0.72/0.80 [95]~P5(x951,x953)+~P5(x951,x952)+P5(x951,f10(x952,x953))
% 0.72/0.80 [122]E(x1221,x1222)+~E(f18(x1223,x1221),f18(x1223,x1222))+~P5(f18(f18(x1221,x1221),f18(x1221,f18(x1222,x1222))),f6(a19,a19))
% 0.72/0.80 [123]E(x1231,x1232)+~E(f18(x1231,x1233),f18(x1232,x1233))+~P5(f18(f18(x1231,x1231),f18(x1231,f18(x1232,x1232))),f6(a19,a19))
% 0.72/0.80 [113]~P5(x1132,x1134)+~P5(x1131,x1133)+P5(f18(f18(x1131,x1131),f18(x1131,f18(x1132,x1132))),f6(x1133,x1134))
% 0.72/0.80 [138]~P5(f18(f18(f18(f18(x1382,x1382),f18(x1382,f18(x1383,x1383))),f18(f18(x1382,x1382),f18(x1382,f18(x1383,x1383)))),f18(f18(f18(x1382,x1382),f18(x1382,f18(x1383,x1383))),f18(x1381,x1381))),x1384)+P5(f18(f18(f18(f18(x1381,x1381),f18(x1381,f18(x1382,x1382))),f18(f18(x1381,x1381),f18(x1381,f18(x1382,x1382)))),f18(f18(f18(x1381,x1381),f18(x1381,f18(x1382,x1382))),f18(x1383,x1383))),f21(x1384))+~P5(f18(f18(f18(f18(x1381,x1381),f18(x1381,f18(x1382,x1382))),f18(f18(x1381,x1381),f18(x1381,f18(x1382,x1382)))),f18(f18(f18(x1381,x1381),f18(x1381,f18(x1382,x1382))),f18(x1383,x1383))),f6(f6(a19,a19),a19))
% 0.72/0.80 [139]~P5(f18(f18(f18(f18(x1392,x1392),f18(x1392,f18(x1391,x1391))),f18(f18(x1392,x1392),f18(x1392,f18(x1391,x1391)))),f18(f18(f18(x1392,x1392),f18(x1392,f18(x1391,x1391))),f18(x1393,x1393))),x1394)+P5(f18(f18(f18(f18(x1391,x1391),f18(x1391,f18(x1392,x1392))),f18(f18(x1391,x1391),f18(x1391,f18(x1392,x1392)))),f18(f18(f18(x1391,x1391),f18(x1391,f18(x1392,x1392))),f18(x1393,x1393))),f11(x1394))+~P5(f18(f18(f18(f18(x1391,x1391),f18(x1391,f18(x1392,x1392))),f18(f18(x1391,x1391),f18(x1391,f18(x1392,x1392)))),f18(f18(f18(x1391,x1391),f18(x1391,f18(x1392,x1392))),f18(x1393,x1393))),f6(f6(a19,a19),a19))
% 0.72/0.80 [142]P5(f18(f18(x1421,x1421),f18(x1421,f18(x1422,x1422))),f7(x1423,x1424))+~P5(f18(f18(x1421,x1421),f18(x1421,f18(x1422,x1422))),f6(a19,a19))+~P5(x1422,f9(f9(f11(f6(f10(x1423,f6(f9(f9(f11(f6(f10(x1424,f6(f18(x1421,x1421),a19)),a19)))),a19)),a19)))))
% 0.72/0.80 [143]~P4(x1432,x1435,x1431)+~P5(f18(f18(x1433,x1433),f18(x1433,f18(x1434,x1434))),f9(x1435))+E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1431,f6(f18(f18(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1433,x1433),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1433,x1433),a19)),a19)))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1433,x1433),a19)),a19))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1434,x1434),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1434,x1434),a19)),a19)))))))))),f18(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1433,x1433),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1433,x1433),a19)),a19)))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1433,x1433),a19)),a19))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1434,x1434),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(x1434,x1434),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1432,f6(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1435,f6(f18(f18(f18(x1433,x1433),f18(x1433,f18(x1434,x1434))),f18(f18(x1433,x1433),f18(x1433,f18(x1434,x1434)))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1435,f6(f18(f18(f18(x1433,x1433),f18(x1433,f18(x1434,x1434))),f18(f18(x1433,x1433),f18(x1433,f18(x1434,x1434)))),a19)),a19)))))))),a19)),a19))))))))
% 0.72/0.80 [127]~P2(x1271)+P8(x1271)+~E(f6(f9(f9(x1271)),f9(f9(x1271))),f9(x1271))+~P6(f9(f9(f11(f6(x1271,a19)))),f9(f9(x1271)))
% 0.72/0.80 [126]~P2(x1261)+P3(x1261,x1262,x1263)+~E(f9(f9(x1262)),f9(x1261))+~P6(f9(f9(f11(f6(x1261,a19)))),f9(f9(x1263)))
% 0.72/0.80 [134]~P8(x1343)+~P8(x1342)+~P3(x1341,x1342,x1343)+P4(x1341,x1342,x1343)+P5(f18(f18(f15(x1341,x1342,x1343),f15(x1341,x1342,x1343)),f18(f15(x1341,x1342,x1343),f18(f16(x1341,x1342,x1343),f16(x1341,x1342,x1343)))),f9(x1342))
% 0.72/0.80 [144]~P8(x1443)+~P8(x1442)+~P3(x1441,x1442,x1443)+P4(x1441,x1442,x1443)+~E(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1443,f6(f18(f18(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),a19)),a19)))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),a19)),a19))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f16(x1441,x1442,x1443),f16(x1441,x1442,x1443)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f16(x1441,x1442,x1443),f16(x1441,x1442,x1443)),a19)),a19)))))))))),f18(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),a19)),a19)))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),a19)),a19))))))),f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f16(x1441,x1442,x1443),f16(x1441,x1442,x1443)),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f16(x1441,x1442,x1443),f16(x1441,x1442,x1443)),a19)),a19))))))))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1441,f6(f18(f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1442,f6(f18(f18(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),f18(f15(x1441,x1442,x1443),f18(f16(x1441,x1442,x1443),f16(x1441,x1442,x1443)))),f18(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),f18(f15(x1441,x1442,x1443),f18(f16(x1441,x1442,x1443),f16(x1441,x1442,x1443))))),a19)),a19))))))),f9(f10(a5,f6(a19,f9(f9(f11(f6(f10(x1442,f6(f18(f18(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),f18(f15(x1441,x1442,x1443),f18(f16(x1441,x1442,x1443),f16(x1441,x1442,x1443)))),f18(f18(f15(x1441,x1442,x1443),f15(x1441,x1442,x1443)),f18(f15(x1441,x1442,x1443),f18(f16(x1441,x1442,x1443),f16(x1441,x1442,x1443))))),a19)),a19)))))))),a19)),a19))))))))
% 0.72/0.80 %EqnAxiom
% 0.72/0.80 [1]E(x11,x11)
% 0.72/0.80 [2]E(x22,x21)+~E(x21,x22)
% 0.72/0.80 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.72/0.80 [4]~E(x41,x42)+E(f18(x41,x43),f18(x42,x43))
% 0.72/0.80 [5]~E(x51,x52)+E(f18(x53,x51),f18(x53,x52))
% 0.72/0.80 [6]~E(x61,x62)+E(f9(x61),f9(x62))
% 0.72/0.80 [7]~E(x71,x72)+E(f10(x71,x73),f10(x72,x73))
% 0.72/0.80 [8]~E(x81,x82)+E(f10(x83,x81),f10(x83,x82))
% 0.72/0.80 [9]~E(x91,x92)+E(f6(x91,x93),f6(x92,x93))
% 0.72/0.80 [10]~E(x101,x102)+E(f6(x103,x101),f6(x103,x102))
% 0.72/0.80 [11]~E(x111,x112)+E(f11(x111),f11(x112))
% 0.72/0.80 [12]~E(x121,x122)+E(f15(x121,x123,x124),f15(x122,x123,x124))
% 0.72/0.80 [13]~E(x131,x132)+E(f15(x133,x131,x134),f15(x133,x132,x134))
% 0.72/0.81 [14]~E(x141,x142)+E(f15(x143,x144,x141),f15(x143,x144,x142))
% 0.72/0.81 [15]~E(x151,x152)+E(f7(x151,x153),f7(x152,x153))
% 0.72/0.81 [16]~E(x161,x162)+E(f7(x163,x161),f7(x163,x162))
% 0.72/0.81 [17]~E(x171,x172)+E(f16(x171,x173,x174),f16(x172,x173,x174))
% 0.72/0.81 [18]~E(x181,x182)+E(f16(x183,x181,x184),f16(x183,x182,x184))
% 0.72/0.81 [19]~E(x191,x192)+E(f16(x193,x194,x191),f16(x193,x194,x192))
% 0.72/0.81 [20]~E(x201,x202)+E(f8(x201),f8(x202))
% 0.72/0.81 [21]~E(x211,x212)+E(f12(x211),f12(x212))
% 0.72/0.81 [22]~E(x221,x222)+E(f14(x221,x223),f14(x222,x223))
% 0.72/0.81 [23]~E(x231,x232)+E(f14(x233,x231),f14(x233,x232))
% 0.72/0.81 [24]~E(x241,x242)+E(f21(x241),f21(x242))
% 0.72/0.81 [25]~E(x251,x252)+E(f22(x251),f22(x252))
% 0.72/0.81 [26]~E(x261,x262)+E(f24(x261),f24(x262))
% 0.72/0.81 [27]~E(x271,x272)+E(f3(x271),f3(x272))
% 0.72/0.81 [28]~P1(x281)+P1(x282)+~E(x281,x282)
% 0.72/0.81 [29]~P2(x291)+P2(x292)+~E(x291,x292)
% 0.72/0.81 [30]P5(x302,x303)+~E(x301,x302)+~P5(x301,x303)
% 0.72/0.81 [31]P5(x313,x312)+~E(x311,x312)+~P5(x313,x311)
% 0.72/0.81 [32]P3(x322,x323,x324)+~E(x321,x322)+~P3(x321,x323,x324)
% 0.72/0.81 [33]P3(x333,x332,x334)+~E(x331,x332)+~P3(x333,x331,x334)
% 0.72/0.81 [34]P3(x343,x344,x342)+~E(x341,x342)+~P3(x343,x344,x341)
% 0.72/0.81 [35]~P8(x351)+P8(x352)+~E(x351,x352)
% 0.72/0.81 [36]P6(x362,x363)+~E(x361,x362)+~P6(x361,x363)
% 0.72/0.81 [37]P6(x373,x372)+~E(x371,x372)+~P6(x373,x371)
% 0.72/0.81 [38]P4(x382,x383,x384)+~E(x381,x382)+~P4(x381,x383,x384)
% 0.72/0.81 [39]P4(x393,x392,x394)+~E(x391,x392)+~P4(x393,x391,x394)
% 0.72/0.81 [40]P4(x403,x404,x402)+~E(x401,x402)+~P4(x403,x404,x401)
% 0.72/0.81 [41]~P9(x411)+P9(x412)+~E(x411,x412)
% 0.72/0.81 [42]~P7(x421)+P7(x422)+~E(x421,x422)
% 0.72/0.81
% 0.72/0.81 %-------------------------------------------
% 0.72/0.81 cnf(147,plain,
% 0.72/0.81 (~P5(x1471,a4)),
% 0.72/0.81 inference(rename_variables,[],[65])).
% 0.72/0.81 cnf(150,plain,
% 0.72/0.81 (~P5(x1501,f10(f8(x1502),x1502))),
% 0.72/0.81 inference(rename_variables,[],[66])).
% 0.72/0.81 cnf(153,plain,
% 0.72/0.81 (~P5(x1531,f10(f8(x1532),x1532))),
% 0.72/0.81 inference(rename_variables,[],[66])).
% 0.72/0.81 cnf(158,plain,
% 0.72/0.81 (~P5(x1581,a4)),
% 0.72/0.81 inference(rename_variables,[],[65])).
% 0.72/0.81 cnf(161,plain,
% 0.72/0.81 (~P5(x1611,a4)),
% 0.72/0.81 inference(rename_variables,[],[65])).
% 0.72/0.81 cnf(167,plain,
% 0.72/0.81 (~P5(x1671,a4)),
% 0.72/0.81 inference(rename_variables,[],[65])).
% 0.72/0.81 cnf(170,plain,
% 0.72/0.81 (~P5(x1701,f18(a17,a25))),
% 0.72/0.81 inference(scs_inference,[],[45,51,50,65,147,158,161,167,48,66,150,2,72,76,82,106,137,136,37,36,31,28,3,86])).
% 0.72/0.81 cnf(176,plain,
% 0.72/0.81 (~P5(x1761,f10(f8(x1762),x1762))),
% 0.72/0.81 inference(rename_variables,[],[66])).
% 0.72/0.81 cnf(180,plain,
% 0.72/0.81 (~P5(x1801,a4)),
% 0.72/0.81 inference(rename_variables,[],[65])).
% 0.72/0.81 cnf(200,plain,
% 0.72/0.81 (P5(a25,f18(x2001,a25))),
% 0.72/0.81 inference(scs_inference,[],[45,51,49,50,65,147,158,161,167,180,48,43,44,46,62,66,150,153,176,2,72,76,82,106,137,136,37,36,31,28,3,86,133,95,94,70,69,80,135,131,107,92,91,88,87])).
% 0.72/0.81 cnf(285,plain,
% 0.72/0.81 ($false),
% 0.72/0.81 inference(scs_inference,[],[170,200]),
% 0.72/0.81 ['proof']).
% 0.72/0.81 % SZS output end Proof
% 0.72/0.81 % Total time :0.110000s
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