TSTP Solution File: KLE084+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : KLE084+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n003.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 : 600s
% DateTime : Sun Jul 17 01:55:46 EDT 2022
% Result : Theorem 0.25s 8.42s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 121 ( 121 unt; 0 def)
% Number of atoms : 121 ( 120 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 189 ( 22 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(codomain2,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(goals,conjecture,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(c_0_18,plain,
! [X5] : addition(antidomain(antidomain(X5)),antidomain(X5)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_19,plain,
! [X3,X4] : addition(X3,X4) = addition(X4,X3),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_20,plain,
! [X4,X5,X6] : addition(X6,addition(X5,X4)) = addition(addition(X6,X5),X4),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_21,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X6,X7] : addition(antidomain(multiplication(X6,X7)),antidomain(multiplication(X6,antidomain(antidomain(X7))))) = antidomain(multiplication(X6,antidomain(antidomain(X7)))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(c_0_24,plain,
! [X2] : multiplication(one,X2) = X2,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_25,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X2] : addition(X2,X2) = X2,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_30,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_32,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1))))) = addition(one,antidomain(antidomain(antidomain(antidomain(X1))))),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
addition(one,antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_32]),c_0_26]) ).
fof(c_0_35,plain,
! [X4,X5,X6] : multiplication(X4,addition(X5,X6)) = addition(multiplication(X4,X5),multiplication(X4,X6)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_36,plain,
! [X2] : multiplication(X2,one) = X2,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_37,plain,
! [X5] : addition(coantidomain(coantidomain(X5)),coantidomain(X5)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_38,plain,
! [X5] : multiplication(X5,coantidomain(X5)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_39,plain,
! [X2] : addition(X2,zero) = X2,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_40,plain,
! [X4,X5,X6] : multiplication(addition(X4,X5),X6) = addition(multiplication(X4,X6),multiplication(X5,X6)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_41,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(antidomain(X1))))) = one,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_44,plain,
! [X5] : multiplication(antidomain(X5),X5) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_45,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_48,plain,
! [X4,X5,X6] : multiplication(X4,multiplication(X5,X6)) = multiplication(multiplication(X4,X5),X6),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_49,plain,
! [X2] : multiplication(zero,X2) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_50,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_41]),c_0_34]),c_0_22]) ).
cnf(c_0_52,plain,
addition(multiplication(X1,antidomain(X2)),multiplication(X1,antidomain(antidomain(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_26]),c_0_43]) ).
cnf(c_0_53,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_54,plain,
! [X6,X7] : addition(coantidomain(multiplication(X6,X7)),coantidomain(multiplication(coantidomain(coantidomain(X6)),X7))) = coantidomain(multiplication(coantidomain(coantidomain(X6)),X7)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_55,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_56,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_46]) ).
cnf(c_0_57,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_22]) ).
cnf(c_0_58,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_59,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_60,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
addition(X1,multiplication(antidomain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_28]),c_0_28]) ).
cnf(c_0_62,plain,
multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_47]) ).
cnf(c_0_63,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_65,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_55]),c_0_22]) ).
cnf(c_0_66,plain,
addition(multiplication(X1,coantidomain(X2)),multiplication(X1,coantidomain(coantidomain(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_55]),c_0_43]) ).
cnf(c_0_67,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_53]),c_0_60]) ).
cnf(c_0_68,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_31]) ).
cnf(c_0_69,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_53,c_0_43]) ).
cnf(c_0_70,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_53]),c_0_64]),c_0_65]) ).
cnf(c_0_71,plain,
addition(multiplication(coantidomain(X1),X2),multiplication(coantidomain(coantidomain(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_55]),c_0_28]) ).
cnf(c_0_72,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_46]),c_0_57]) ).
cnf(c_0_73,plain,
multiplication(antidomain(X1),multiplication(antidomain(antidomain(X1)),X2)) = zero,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_69]),c_0_57]) ).
cnf(c_0_75,plain,
addition(multiplication(antidomain(addition(X1,X2)),X1),multiplication(antidomain(addition(X1,X2)),X2)) = zero,
inference(spm,[status(thm)],[c_0_53,c_0_42]) ).
cnf(c_0_76,plain,
addition(multiplication(X1,coantidomain(addition(X1,X2))),multiplication(X2,coantidomain(addition(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_46,c_0_50]) ).
cnf(c_0_77,plain,
addition(X1,multiplication(X1,antidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_51]),c_0_43]),c_0_43]) ).
cnf(c_0_78,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_70]),c_0_59]),c_0_43]) ).
cnf(c_0_79,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_46]),c_0_72]),c_0_47]) ).
cnf(c_0_80,plain,
antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_73]),c_0_74]),c_0_51]) ).
cnf(c_0_81,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_61]),c_0_53]),c_0_57]) ).
cnf(c_0_82,plain,
multiplication(X1,multiplication(antidomain(X2),coantidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_46]),c_0_59]),c_0_57]) ).
cnf(c_0_83,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_78]),c_0_79]),c_0_57]) ).
cnf(c_0_84,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_80]),c_0_28]) ).
cnf(c_0_85,plain,
addition(multiplication(antidomain(X1),X2),multiplication(antidomain(antidomain(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_26]),c_0_28]) ).
cnf(c_0_86,plain,
antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X2),X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_81]),c_0_74]),c_0_51]) ).
cnf(c_0_87,plain,
addition(multiplication(antidomain(multiplication(X1,X2)),X3),multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X3)) = multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X3),
inference(spm,[status(thm)],[c_0_50,c_0_27]) ).
cnf(c_0_88,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(X1)) = zero,
inference(spm,[status(thm)],[c_0_82,c_0_72]) ).
cnf(c_0_89,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_83,c_0_68]) ).
cnf(c_0_90,plain,
multiplication(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(antidomain(X1),X2)))) = zero,
inference(spm,[status(thm)],[c_0_84,c_0_68]) ).
cnf(c_0_91,plain,
multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_67]),c_0_57]) ).
cnf(c_0_92,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X2),X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_86]),c_0_28]) ).
cnf(c_0_93,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_53]),c_0_47]) ).
cnf(c_0_94,plain,
antidomain(antidomain(X1)) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_88]),c_0_89]),c_0_57]) ).
cnf(c_0_95,plain,
coantidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_88]),c_0_83]),c_0_47]) ).
fof(c_0_96,negated_conjecture,
~ ! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_97,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_68]) ).
cnf(c_0_98,plain,
multiplication(antidomain(X1),antidomain(multiplication(antidomain(X2),X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_92]),c_0_68]),c_0_57]) ).
cnf(c_0_99,plain,
addition(multiplication(X1,multiplication(X2,coantidomain(X3))),multiplication(X1,multiplication(X2,coantidomain(coantidomain(X3))))) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_66]) ).
cnf(c_0_100,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,coantidomain(antidomain(X2)))) = zero,
inference(rw,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_101,plain,
coantidomain(coantidomain(antidomain(X1))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_79,c_0_95]) ).
cnf(c_0_102,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),antidomain(antidomain(X1)))) = zero,
inference(spm,[status(thm)],[c_0_81,c_0_68]) ).
fof(c_0_103,negated_conjecture,
domain(multiplication(esk1_0,esk2_0)) != domain(multiplication(esk1_0,domain(esk2_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])]) ).
fof(c_0_104,plain,
! [X5] : domain(X5) = antidomain(antidomain(X5)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_105,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_97]),c_0_68]),c_0_57]) ).
cnf(c_0_106,plain,
multiplication(antidomain(X1),multiplication(antidomain(multiplication(antidomain(X2),X1)),X3)) = multiplication(antidomain(X1),X3),
inference(spm,[status(thm)],[c_0_59,c_0_98]) ).
cnf(c_0_107,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(X2))) = multiplication(antidomain(multiplication(X1,X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),c_0_57]) ).
cnf(c_0_108,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),antidomain(X1))) = multiplication(antidomain(X2),antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_102]),c_0_68]),c_0_47]),c_0_68]) ).
cnf(c_0_109,negated_conjecture,
domain(multiplication(esk1_0,esk2_0)) != domain(multiplication(esk1_0,domain(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_110,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_111,plain,
addition(antidomain(X1),antidomain(multiplication(antidomain(X2),X1))) = antidomain(multiplication(antidomain(X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_98]),c_0_22]) ).
cnf(c_0_112,plain,
multiplication(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,multiplication(X2,X3)))) = antidomain(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_105,c_0_59]) ).
cnf(c_0_113,plain,
multiplication(antidomain(X1),antidomain(X2)) = multiplication(antidomain(X2),antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_106]),c_0_108]) ).
cnf(c_0_114,negated_conjecture,
antidomain(antidomain(multiplication(esk1_0,esk2_0))) != antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_110]),c_0_110]) ).
cnf(c_0_115,plain,
addition(coantidomain(antidomain(X1)),coantidomain(antidomain(multiplication(X1,X2)))) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_105]),c_0_94]),c_0_94]),c_0_94]),c_0_22]) ).
cnf(c_0_116,plain,
multiplication(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,coantidomain(antidomain(X2))))) = antidomain(multiplication(X1,coantidomain(antidomain(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_83]),c_0_113]) ).
cnf(c_0_117,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,coantidomain(antidomain(X2))))) = antidomain(multiplication(X1,coantidomain(antidomain(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_94]),c_0_94]) ).
cnf(c_0_118,negated_conjecture,
coantidomain(antidomain(multiplication(esk1_0,coantidomain(antidomain(esk2_0))))) != coantidomain(antidomain(multiplication(esk1_0,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_94]),c_0_94]),c_0_94]) ).
cnf(c_0_119,plain,
antidomain(multiplication(X1,coantidomain(antidomain(X2)))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_94]),c_0_101]),c_0_94]),c_0_101]),c_0_117]),c_0_94]),c_0_101]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE084+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : run_ET %s %d
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jun 16 12:39:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.25/8.42 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.25/8.42 # Preprocessing time : 0.014 s
% 0.25/8.42
% 0.25/8.42 # Proof found!
% 0.25/8.42 # SZS status Theorem
% 0.25/8.42 # SZS output start CNFRefutation
% See solution above
% 0.25/8.42 # Proof object total steps : 121
% 0.25/8.42 # Proof object clause steps : 84
% 0.25/8.42 # Proof object formula steps : 37
% 0.25/8.42 # Proof object conjectures : 7
% 0.25/8.42 # Proof object clause conjectures : 4
% 0.25/8.42 # Proof object formula conjectures : 3
% 0.25/8.42 # Proof object initial clauses used : 18
% 0.25/8.42 # Proof object initial formulas used : 18
% 0.25/8.42 # Proof object generating inferences : 58
% 0.25/8.42 # Proof object simplifying inferences : 83
% 0.25/8.42 # Training examples: 0 positive, 0 negative
% 0.25/8.42 # Parsed axioms : 21
% 0.25/8.42 # Removed by relevancy pruning/SinE : 0
% 0.25/8.42 # Initial clauses : 22
% 0.25/8.42 # Removed in clause preprocessing : 2
% 0.25/8.42 # Initial clauses in saturation : 20
% 0.25/8.42 # Processed clauses : 5709
% 0.25/8.42 # ...of these trivial : 2108
% 0.25/8.42 # ...subsumed : 2595
% 0.25/8.42 # ...remaining for further processing : 1006
% 0.25/8.42 # Other redundant clauses eliminated : 0
% 0.25/8.42 # Clauses deleted for lack of memory : 134814
% 0.25/8.42 # Backward-subsumed : 0
% 0.25/8.42 # Backward-rewritten : 355
% 0.25/8.42 # Generated clauses : 609059
% 0.25/8.42 # ...of the previous two non-trivial : 269848
% 0.25/8.42 # Contextual simplify-reflections : 0
% 0.25/8.42 # Paramodulations : 609059
% 0.25/8.42 # Factorizations : 0
% 0.25/8.42 # Equation resolutions : 0
% 0.25/8.42 # Current number of processed clauses : 651
% 0.25/8.42 # Positive orientable unit clauses : 622
% 0.25/8.42 # Positive unorientable unit clauses: 27
% 0.25/8.42 # Negative unit clauses : 0
% 0.25/8.42 # Non-unit-clauses : 2
% 0.25/8.42 # Current number of unprocessed clauses: 83868
% 0.25/8.42 # ...number of literals in the above : 83868
% 0.25/8.42 # Current number of archived formulas : 0
% 0.25/8.42 # Current number of archived clauses : 357
% 0.25/8.42 # Clause-clause subsumption calls (NU) : 0
% 0.25/8.42 # Rec. Clause-clause subsumption calls : 0
% 0.25/8.42 # Non-unit clause-clause subsumptions : 0
% 0.25/8.42 # Unit Clause-clause subsumption calls : 188
% 0.25/8.42 # Rewrite failures with RHS unbound : 576
% 0.25/8.42 # BW rewrite match attempts : 13255
% 0.25/8.42 # BW rewrite match successes : 796
% 0.25/8.42 # Condensation attempts : 0
% 0.25/8.42 # Condensation successes : 0
% 0.25/8.42 # Termbank termtop insertions : 12391207
% 0.25/8.42
% 0.25/8.42 # -------------------------------------------------
% 0.25/8.42 # User time : 7.234 s
% 0.25/8.42 # System time : 0.093 s
% 0.25/8.42 # Total time : 7.327 s
% 0.25/8.42 # Maximum resident set size: 147584 pages
%------------------------------------------------------------------------------