%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE084+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:58:48 PM UTC 2026
% Result : Theorem 18.80s 3.00s
% Output : CNFRefutation 18.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 113 ( 113 unt; 0 def)
% Number of atoms : 113 ( 112 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 206 ( 23 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
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(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
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(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(goals,conjecture,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(c_0_15,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_16,plain,
! [X28] : multiplication(antidomain(X28),X28) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_17,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_18,plain,
! [X29,X30] : addition(antidomain(multiplication(X29,X30)),antidomain(multiplication(X29,antidomain(antidomain(X30))))) = antidomain(multiplication(X29,antidomain(antidomain(X30)))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(c_0_19,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_20,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,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_18]) ).
cnf(c_0_24,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X31] : addition(antidomain(antidomain(X31)),antidomain(X31)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_26,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_27,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_28,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_29,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_30,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_31,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_32,plain,
addition(antidomain(X1),antidomain(antidomain(antidomain(X1)))) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
fof(c_0_33,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_34,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
multiplication(antidomain(X1),antidomain(antidomain(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_21]) ).
cnf(c_0_41,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_44,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_45,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
multiplication(antidomain(X1),multiplication(antidomain(antidomain(X1)),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_47,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_42]),c_0_35]) ).
fof(c_0_49,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_50,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_23,c_0_46]),c_0_47]),c_0_48]) ).
cnf(c_0_51,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_52,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_44]) ).
cnf(c_0_53,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_50]),c_0_24]) ).
cnf(c_0_54,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_21]),c_0_22]) ).
cnf(c_0_55,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_42]),c_0_24]) ).
cnf(c_0_56,plain,
multiplication(addition(X1,antidomain(X2)),antidomain(antidomain(multiplication(antidomain(antidomain(X2)),X3)))) = multiplication(X1,antidomain(antidomain(multiplication(antidomain(antidomain(X2)),X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_53]),c_0_22]) ).
cnf(c_0_57,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_42]),c_0_36]),c_0_55]) ).
cnf(c_0_58,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_36]),c_0_35]) ).
cnf(c_0_59,plain,
multiplication(antidomain(X1),antidomain(antidomain(multiplication(antidomain(X1),X2)))) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_42]),c_0_57]),c_0_24]),c_0_57]) ).
cnf(c_0_60,plain,
multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_55]) ).
cnf(c_0_61,plain,
addition(X1,addition(antidomain(X2),multiplication(X1,X2))) = multiplication(addition(X1,antidomain(X2)),addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_31]),c_0_37]) ).
cnf(c_0_62,plain,
multiplication(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(X1,X2)))) = antidomain(antidomain(multiplication(X1,X2))),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_21]),c_0_41]) ).
cnf(c_0_64,plain,
addition(antidomain(antidomain(X1)),antidomain(multiplication(X1,X2))) = one,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_57]),c_0_42]),c_0_35]),c_0_48]),c_0_57]),c_0_35]),c_0_48]),c_0_36]) ).
cnf(c_0_65,plain,
multiplication(addition(antidomain(X1),X2),multiplication(X1,X3)) = multiplication(X2,multiplication(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_63]),c_0_44]) ).
cnf(c_0_66,plain,
addition(antidomain(X1),antidomain(multiplication(antidomain(X1),X2))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_59]),c_0_57]),c_0_57]) ).
cnf(c_0_67,plain,
multiplication(antidomain(addition(X1,X2)),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_45]),c_0_21]) ).
cnf(c_0_68,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X3,X1),X2)) = multiplication(antidomain(multiplication(X1,X2)),multiplication(X3,X2)),
inference(spm,[status(thm)],[c_0_54,c_0_20]) ).
cnf(c_0_69,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),multiplication(X1,X3)) = multiplication(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_24]) ).
cnf(c_0_70,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,antidomain(antidomain(X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_21]) ).
cnf(c_0_71,plain,
multiplication(antidomain(multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) = zero,
inference(spm,[status(thm)],[c_0_67,c_0_20]) ).
cnf(c_0_72,plain,
multiplication(antidomain(multiplication(antidomain(antidomain(X1)),X2)),X2) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_42]),c_0_24]),c_0_69]) ).
cnf(c_0_73,plain,
multiplication(addition(antidomain(addition(X1,X2)),X3),X1) = multiplication(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_67]),c_0_44]) ).
cnf(c_0_74,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,multiplication(antidomain(antidomain(X2)),X3))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_70]),c_0_41]),c_0_39]) ).
cnf(c_0_75,plain,
multiplication(antidomain(X1),multiplication(antidomain(X2),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_42]),c_0_24]) ).
cnf(c_0_76,plain,
multiplication(antidomain(multiplication(antidomain(X1),X2)),X2) = multiplication(antidomain(antidomain(X1)),X2),
inference(spm,[status(thm)],[c_0_72,c_0_57]) ).
cnf(c_0_77,plain,
multiplication(antidomain(antidomain(addition(X1,X2))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_42]),c_0_24]) ).
cnf(c_0_78,plain,
multiplication(antidomain(X1),addition(antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))),X3)) = multiplication(antidomain(X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_53]),c_0_44]) ).
cnf(c_0_79,plain,
multiplication(antidomain(X1),multiplication(antidomain(antidomain(multiplication(antidomain(X2),X1))),X3)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_47]),c_0_24]) ).
cnf(c_0_80,plain,
multiplication(antidomain(antidomain(X1)),multiplication(antidomain(X2),X1)) = multiplication(antidomain(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_47]),c_0_24]) ).
cnf(c_0_81,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_23]),c_0_57]) ).
cnf(c_0_82,plain,
multiplication(antidomain(antidomain(multiplication(X1,X2))),antidomain(antidomain(X1))) = antidomain(antidomain(multiplication(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_64]),c_0_36]) ).
cnf(c_0_83,plain,
multiplication(antidomain(X1),antidomain(multiplication(antidomain(antidomain(X1)),X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_42]),c_0_36]),c_0_57]) ).
cnf(c_0_84,plain,
multiplication(antidomain(antidomain(multiplication(antidomain(X1),antidomain(X2)))),X2) = zero,
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
antidomain(multiplication(antidomain(antidomain(multiplication(X1,X2))),X1)) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_57]),c_0_83]) ).
cnf(c_0_86,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(spm,[status(thm)],[c_0_83,c_0_60]) ).
cnf(c_0_87,plain,
multiplication(antidomain(multiplication(antidomain(X1),antidomain(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_84]),c_0_47]),c_0_24]),c_0_57]) ).
cnf(c_0_88,plain,
multiplication(antidomain(antidomain(multiplication(antidomain(X1),X2))),X2) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_76]),c_0_76]),c_0_57]) ).
cnf(c_0_89,plain,
antidomain(multiplication(antidomain(antidomain(multiplication(antidomain(antidomain(X1)),X2))),X1)) = antidomain(multiplication(antidomain(antidomain(X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_85]),c_0_83]) ).
cnf(c_0_90,plain,
antidomain(antidomain(multiplication(antidomain(X1),antidomain(X2)))) = multiplication(antidomain(X1),antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_91,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,multiplication(X2,X3))) = zero,
inference(spm,[status(thm)],[c_0_63,c_0_39]) ).
cnf(c_0_92,plain,
antidomain(multiplication(antidomain(antidomain(X1)),antidomain(X2))) = antidomain(multiplication(antidomain(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_39]),c_0_80]) ).
cnf(c_0_93,plain,
multiplication(antidomain(antidomain(multiplication(antidomain(X1),X2))),antidomain(X1)) = antidomain(antidomain(multiplication(antidomain(X1),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_66]),c_0_36]) ).
cnf(c_0_94,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
fof(c_0_95,negated_conjecture,
~ ! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_96,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),multiplication(X1,X2)) = zero,
inference(spm,[status(thm)],[c_0_91,c_0_55]) ).
cnf(c_0_97,plain,
antidomain(antidomain(multiplication(antidomain(X1),X2))) = multiplication(antidomain(antidomain(X2)),antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_92]),c_0_93]) ).
cnf(c_0_98,plain,
addition(antidomain(multiplication(X1,X2)),addition(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X3)) = addition(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X3),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_99,plain,
addition(antidomain(X1),addition(X2,antidomain(antidomain(X1)))) = addition(one,X2),
inference(spm,[status(thm)],[c_0_94,c_0_35]) ).
fof(c_0_100,negated_conjecture,
domain(multiplication(esk1_0,esk2_0)) != domain(multiplication(esk1_0,domain(esk2_0))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])])]) ).
fof(c_0_101,plain,
! [X32] : domain(X32) = antidomain(antidomain(X32)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_102,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),antidomain(antidomain(multiplication(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_96]),c_0_47]),c_0_24]) ).
cnf(c_0_103,plain,
multiplication(antidomain(X1),antidomain(X2)) = multiplication(antidomain(X2),antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_97]),c_0_57]) ).
cnf(c_0_104,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_21]),c_0_44]) ).
cnf(c_0_105,plain,
addition(antidomain(antidomain(multiplication(X1,X2))),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_48]),c_0_35]) ).
cnf(c_0_106,negated_conjecture,
domain(multiplication(esk1_0,esk2_0)) != domain(multiplication(esk1_0,domain(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_107,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_108,plain,
multiplication(antidomain(antidomain(multiplication(X1,X2))),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = zero,
inference(rw,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,plain,
multiplication(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_57]),c_0_36]),c_0_57]) ).
cnf(c_0_110,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_106,c_0_107]),c_0_107]),c_0_107]) ).
cnf(c_0_111,plain,
antidomain(multiplication(X1,antidomain(antidomain(X2)))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_108]),c_0_47]),c_0_24]),c_0_57]),c_0_109]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE084+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n002.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 20 22:44:48 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.53 Running first-order theorem proving
% 0.24/0.53 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.80/3.00 % Version: 3.5.1
% 18.80/3.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 18.80/3.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.80/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 18.80/3.00 % Starting new_bool_3 with 300s (1) cores
% 18.80/3.00 % Starting new_bool_1 with 300s (1) cores
% 18.80/3.00 % Starting sh5l with 300s (1) cores
% 18.80/3.00 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1865190 completed with status 0
% 18.80/3.00 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 18.80/3.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 18.80/3.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.80/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 18.80/3.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.80/3.00 % No SInE strategy applied
% 18.80/3.00 % Search class: FHUSM-FFSF21-MFFFFFNN
% 18.80/3.00 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 18.80/3.00 % Starting SubtermCWHack with 136s (1) cores
% 18.80/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 18.80/3.00 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 18.80/3.00 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 18.80/3.00 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 18.80/3.00 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1865198 completed with status 0
% 18.80/3.00 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 18.80/3.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 18.80/3.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 18.80/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 18.80/3.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 18.80/3.00 % No SInE strategy applied
% 18.80/3.00 % Search class: FHUSM-FFSF21-MFFFFFNN
% 18.80/3.00 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 18.80/3.00 % Starting SubtermCWHack with 136s (1) cores
% 18.80/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 18.80/3.00 % Preprocessing time : 0.002 s
% 18.80/3.00 % Presaturation interreduction done
% 18.80/3.00
% 18.80/3.00 % Proof found!
% 18.80/3.00 % SZS status Theorem
% 18.80/3.00 % SZS output start CNFRefutation
% See solution above
% 18.80/3.00 % Parsed axioms : 21
% 18.80/3.00 % Removed by relevancy pruning/SinE : 0
% 18.80/3.00 % Initial clauses : 22
% 18.80/3.00 % Removed in clause preprocessing : 2
% 18.80/3.00 % Initial clauses in saturation : 20
% 18.80/3.00 % Processed clauses : 4027
% 18.80/3.00 % ...of these trivial : 2116
% 18.80/3.00 % ...subsumed : 1175
% 18.80/3.00 % ...remaining for further processing : 736
% 18.80/3.00 % Other redundant clauses eliminated : 0
% 18.80/3.00 % Clauses deleted for lack of memory : 0
% 18.80/3.00 % Backward-subsumed : 0
% 18.80/3.00 % Backward-rewritten : 232
% 18.80/3.00 % Generated clauses : 192960
% 18.80/3.00 % ...of the previous two non-redundant : 68947
% 18.80/3.00 % ...aggressively subsumed : 0
% 18.80/3.00 % Contextual simplify-reflections : 0
% 18.80/3.00 % Paramodulations : 192960
% 18.80/3.00 % Factorizations : 0
% 18.80/3.00 % NegExts : 0
% 18.80/3.00 % Equation resolutions : 0
% 18.80/3.00 % Disequality decompositions : 0
% 18.80/3.00 % Total rewrite steps : 464568
% 18.80/3.00 % ...of those cached : 425102
% 18.80/3.00 % Propositional unsat checks : 0
% 18.80/3.00 % Propositional check models : 0
% 18.80/3.00 % Propositional check unsatisfiable : 0
% 18.80/3.00 % Propositional clauses : 0
% 18.80/3.00 % Propositional clauses after purity: 0
% 18.80/3.00 % Propositional unsat core size : 0
% 18.80/3.00 % Propositional preprocessing time : 0.000
% 18.80/3.00 % Propositional encoding time : 0.000
% 18.80/3.00 % Propositional solver time : 0.000
% 18.80/3.00 % Success case prop preproc time : 0.000
% 18.80/3.00 % Success case prop encoding time : 0.000
% 18.80/3.00 % Success case prop solver time : 0.000
% 18.80/3.00 % Current number of processed clauses : 484
% 18.80/3.00 % Positive orientable unit clauses : 468
% 18.80/3.00 % Positive unorientable unit clauses: 14
% 18.80/3.00 % Negative unit clauses : 0
% 18.80/3.00 % Non-unit-clauses : 2
% 18.80/3.00 % Current number of unprocessed clauses: 64257
% 18.80/3.00 % ...number of literals in the above : 64257
% 18.80/3.00 % Current number of archived formulas : 0
% 18.80/3.00 % Current number of archived clauses : 254
% 18.80/3.00 % Clause-clause subsumption calls (NU) : 0
% 18.80/3.00 % Rec. Clause-clause subsumption calls : 0
% 18.80/3.00 % Non-unit clause-clause subsumptions : 0
% 18.80/3.00 % Unit Clause-clause subsumption calls : 114
% 18.80/3.00 % Rewrite failures with RHS unbound : 0
% 18.80/3.00 % BW rewrite match attempts : 4917
% 18.80/3.00 % BW rewrite match successes : 387
% 18.80/3.00 % Condensation attempts : 0
% 18.80/3.00 % Condensation successes : 0
% 18.80/3.00 % Termbank termtop insertions : 2535317
% 18.80/3.00 % Search garbage collected termcells : 38
% 18.80/3.00
% 18.80/3.00 % -------------------------------------------------
% 18.80/3.00 % User time : 2.288 s
% 18.80/3.00 % System time : 0.102 s
% 18.80/3.00 % Total time : 2.390 s
% 18.80/3.00 % Maximum resident set size: 3652 pages
% 18.80/3.00
% 18.80/3.00 % -------------------------------------------------
% 18.80/3.00 % User time : 11.474 s
% 18.80/3.00 % System time : 0.514 s
% 18.80/3.00 % Total time : 11.988 s
% 18.80/3.00 % Maximum resident set size: 4608 pages
% 18.80/3.00 % E exiting
%------------------------------------------------------------------------------