%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE108+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:58:52 PM UTC 2026
% Result : Theorem 50.71s 8.34s
% Output : CNFRefutation 50.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 22
% Syntax : Number of formulae : 140 ( 136 unt; 0 def)
% Number of atoms : 144 ( 143 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 2 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 189 ( 2 sgn 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( addition(backward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
<= addition(domain(X5),forward_box(X4,domain(X6))) = forward_box(X4,domain(X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(complement,axiom,
! [X4] : c(X4) = antidomain(domain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',complement) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(forward_box,axiom,
! [X4,X5] : forward_box(X4,X5) = c(forward_diamond(X4,c(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_box) ).
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/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
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/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(backward_diamond,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(c_0_22,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_23,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_24,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_25,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_26,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_29,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_30,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_31,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_36,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(backward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
<= addition(domain(X5),forward_box(X4,domain(X6))) = forward_box(X4,domain(X6)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_37,plain,
! [X39] : c(X39) = antidomain(domain(X39)),
inference(variable_rename,[status(thm)],[complement]) ).
fof(c_0_38,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_39,plain,
! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
fof(c_0_40,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_41,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_42,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_45,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_46,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_47,plain,
! [X37] : addition(coantidomain(coantidomain(X37)),coantidomain(X37)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_48,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(domain(X5),forward_box(X4,domain(X6))) = forward_box(X4,domain(X6))
=> addition(backward_diamond(X4,domain(X5)),domain(X6)) = domain(X6) ),
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_49,plain,
! [X46,X47] : forward_box(X46,X47) = c(forward_diamond(X46,c(X47))),
inference(variable_rename,[status(thm)],[forward_box]) ).
cnf(c_0_50,plain,
c(X1) = antidomain(domain(X1)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_51,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_52,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_53,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_27]) ).
cnf(c_0_56,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_57,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_58,negated_conjecture,
( addition(backward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != domain(esk3_0)
& addition(domain(esk2_0),forward_box(esk1_0,domain(esk3_0))) = forward_box(esk1_0,domain(esk3_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).
cnf(c_0_59,plain,
forward_box(X1,X2) = c(forward_diamond(X1,c(X2))),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,plain,
c(X1) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_61,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_51]),c_0_51]) ).
fof(c_0_62,plain,
! [X30,X31] : addition(antidomain(multiplication(X30,X31)),antidomain(multiplication(X30,antidomain(antidomain(X31))))) = antidomain(multiplication(X30,antidomain(antidomain(X31)))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(c_0_63,plain,
! [X34] : multiplication(X34,coantidomain(X34)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
cnf(c_0_64,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_43,c_0_32]) ).
cnf(c_0_65,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_66,plain,
multiplication(antidomain(antidomain(X1)),addition(X1,one)) = addition(X1,antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_27]) ).
cnf(c_0_67,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_57,c_0_27]) ).
cnf(c_0_68,negated_conjecture,
addition(domain(esk2_0),forward_box(esk1_0,domain(esk3_0))) = forward_box(esk1_0,domain(esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,plain,
forward_box(X1,X2) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(antidomain(X2))))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60]),c_0_61]) ).
cnf(c_0_70,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_26]) ).
cnf(c_0_71,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_62]) ).
cnf(c_0_72,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_64]),c_0_33]) ).
cnf(c_0_74,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_45]),c_0_27]) ).
cnf(c_0_75,plain,
multiplication(antidomain(antidomain(X1)),addition(one,X1)) = addition(X1,antidomain(antidomain(X1))),
inference(spm,[status(thm)],[c_0_66,c_0_27]) ).
cnf(c_0_76,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_67]),c_0_27]) ).
fof(c_0_77,plain,
! [X35,X36] : addition(coantidomain(multiplication(X35,X36)),coantidomain(multiplication(coantidomain(coantidomain(X35)),X36))) = coantidomain(multiplication(coantidomain(coantidomain(X35)),X36)),
inference(variable_rename,[status(thm)],[codomain2]) ).
fof(c_0_78,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_79,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0)))))))))))))) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk3_0))))))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_51]),c_0_51]),c_0_51]),c_0_69]),c_0_69]) ).
cnf(c_0_80,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_45]),c_0_43]),c_0_56]) ).
cnf(c_0_81,plain,
antidomain(multiplication(X1,antidomain(antidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74]) ).
cnf(c_0_82,plain,
addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_53,c_0_67]) ).
cnf(c_0_83,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_43]) ).
cnf(c_0_84,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_72]),c_0_33]) ).
cnf(c_0_85,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_77]) ).
cnf(c_0_86,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_87,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_26]) ).
cnf(c_0_88,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(multiplication(esk1_0,antidomain(esk3_0)))) = antidomain(multiplication(esk1_0,antidomain(esk3_0))),
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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]) ).
cnf(c_0_89,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_46,c_0_72]) ).
cnf(c_0_90,plain,
multiplication(X1,antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_81]),c_0_46]) ).
cnf(c_0_91,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_74]) ).
cnf(c_0_92,plain,
multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_72]),c_0_26]) ).
cnf(c_0_93,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_67]),c_0_43]) ).
cnf(c_0_94,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_46]),c_0_27]) ).
cnf(c_0_95,plain,
addition(coantidomain(multiplication(X1,multiplication(X2,X3))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(X1,X2))),X3)),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_96,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),multiplication(esk1_0,antidomain(esk3_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_32]) ).
cnf(c_0_97,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_89]),c_0_33]) ).
cnf(c_0_98,plain,
multiplication(X1,addition(antidomain(antidomain(coantidomain(X1))),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_90]),c_0_33]) ).
cnf(c_0_99,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = antidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_91]),c_0_46]) ).
cnf(c_0_100,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_67]),c_0_46]),c_0_93]) ).
cnf(c_0_101,plain,
multiplication(addition(X1,one),coantidomain(coantidomain(X1))) = addition(X1,coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_93]),c_0_27]) ).
cnf(c_0_102,negated_conjecture,
coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(antidomain(esk2_0)),esk1_0))),antidomain(esk3_0))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_76]) ).
cnf(c_0_103,plain,
multiplication(X1,antidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_45]),c_0_43]),c_0_80]) ).
cnf(c_0_104,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
fof(c_0_105,plain,
! [X44,X45] : backward_diamond(X44,X45) = codomain(multiplication(codomain(X45),X44)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_106,plain,
! [X38] : codomain(X38) = coantidomain(coantidomain(X38)),
inference(variable_rename,[status(thm)],[codomain4]) ).
cnf(c_0_107,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(X1))),X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_32]),c_0_97]),c_0_76]) ).
cnf(c_0_108,plain,
multiplication(addition(one,X1),coantidomain(coantidomain(X1))) = addition(X1,coantidomain(coantidomain(X1))),
inference(spm,[status(thm)],[c_0_101,c_0_27]) ).
cnf(c_0_109,plain,
multiplication(X1,multiplication(X2,coantidomain(multiplication(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_72,c_0_86]) ).
cnf(c_0_110,negated_conjecture,
multiplication(coantidomain(coantidomain(multiplication(antidomain(antidomain(esk2_0)),esk1_0))),antidomain(esk3_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_102]),c_0_43]) ).
cnf(c_0_111,plain,
coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_100]),c_0_104]) ).
cnf(c_0_112,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_113,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_114,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_107]),c_0_43]) ).
cnf(c_0_115,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_53,c_0_45]) ).
cnf(c_0_116,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(X1)))) = coantidomain(coantidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_74]),c_0_46]) ).
cnf(c_0_117,plain,
multiplication(addition(X1,X2),multiplication(X3,coantidomain(multiplication(X2,X3)))) = multiplication(X1,multiplication(X3,coantidomain(multiplication(X2,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_109]),c_0_26]) ).
cnf(c_0_118,negated_conjecture,
multiplication(antidomain(coantidomain(multiplication(antidomain(antidomain(esk2_0)),esk1_0))),antidomain(esk3_0)) = zero,
inference(rw,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_119,negated_conjecture,
addition(backward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) != domain(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_120,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113]),c_0_113]) ).
cnf(c_0_121,plain,
multiplication(antidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[c_0_114,c_0_111]) ).
cnf(c_0_122,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_72]),c_0_26]) ).
cnf(c_0_123,plain,
addition(antidomain(X1),coantidomain(coantidomain(antidomain(antidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_76]) ).
cnf(c_0_124,negated_conjecture,
multiplication(addition(X1,antidomain(coantidomain(multiplication(antidomain(antidomain(esk2_0)),esk1_0)))),antidomain(esk3_0)) = multiplication(X1,antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_97]),c_0_43]),c_0_97]),c_0_43]) ).
cnf(c_0_125,plain,
addition(coantidomain(X1),antidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_67,c_0_111]) ).
cnf(c_0_126,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk2_0)))),esk1_0))),antidomain(antidomain(esk3_0))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_51]),c_0_51]),c_0_51]),c_0_120]) ).
cnf(c_0_127,plain,
multiplication(addition(X1,antidomain(coantidomain(antidomain(X2)))),X2) = 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_117,c_0_121]),c_0_97]),c_0_43]),c_0_97]),c_0_43]) ).
cnf(c_0_128,plain,
multiplication(coantidomain(antidomain(antidomain(X1))),antidomain(X1)) = coantidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_43]) ).
cnf(c_0_129,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_55,c_0_87]),c_0_53]) ).
cnf(c_0_130,negated_conjecture,
multiplication(coantidomain(multiplication(antidomain(antidomain(esk2_0)),esk1_0)),antidomain(esk3_0)) = antidomain(esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_46]) ).
cnf(c_0_131,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk2_0)))),esk1_0)))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[c_0_126,c_0_27]) ).
cnf(c_0_132,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_125]),c_0_46]) ).
cnf(c_0_133,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_128,c_0_80]) ).
cnf(c_0_134,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),coantidomain(multiplication(antidomain(antidomain(esk2_0)),esk1_0))) = 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_129,c_0_130]),c_0_27]),c_0_45]),c_0_27]),c_0_74]),c_0_43]),c_0_27]),c_0_27]),c_0_76]) ).
cnf(c_0_135,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(esk2_0)))),esk1_0)))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_111]),c_0_111]) ).
cnf(c_0_136,plain,
coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_80]),c_0_133]) ).
cnf(c_0_137,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),antidomain(coantidomain(multiplication(antidomain(antidomain(esk2_0)),esk1_0)))) = antidomain(coantidomain(multiplication(antidomain(antidomain(esk2_0)),esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_134]),c_0_111]),c_0_46]),c_0_111]) ).
cnf(c_0_138,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(coantidomain(multiplication(antidomain(antidomain(esk2_0)),esk1_0)))) != antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_80]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_137]),c_0_27]),c_0_74]),c_0_43]),c_0_138]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE108+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n018.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 20 22:46:15 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 50.71/8.34 % Version: 3.5.1
% 50.71/8.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 50.71/8.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.71/8.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 50.71/8.34 % Starting new_bool_3 with 300s (1) cores
% 50.71/8.34 % Starting new_bool_1 with 300s (1) cores
% 50.71/8.34 % Starting sh5l with 300s (1) cores
% 50.71/8.34 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 360657 completed with status 0
% 50.71/8.34 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 50.71/8.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 50.71/8.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.71/8.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 50.71/8.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 50.71/8.34 % No SInE strategy applied
% 50.71/8.34 % Search class: FHUSM-FFMF21-DFFFFFNN
% 50.71/8.34 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 50.71/8.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 50.71/8.34 % Starting SubtermCWHack with 136s (1) cores
% 50.71/8.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 50.71/8.34 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 50.71/8.34 % Starting H----_042_B03_F1_AE_Q4_SP_S2S with 136s (1) cores
% 50.71/8.34 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 50.71/8.34 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 360668 completed with status 0
% 50.71/8.34 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 50.71/8.34 % Preprocessing class: FSMSSMSSSSSNFFN.
% 50.71/8.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 50.71/8.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 50.71/8.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 50.71/8.34 % No SInE strategy applied
% 50.71/8.34 % Search class: FHUSM-FFMF21-DFFFFFNN
% 50.71/8.34 % partial match(1): FHUSM-FFMF21-MFFFFFNN
% 50.71/8.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 50.71/8.34 % Starting SubtermCWHack with 136s (1) cores
% 50.71/8.34 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 50.71/8.34 % Starting G-E--_100_C18_F1_PI_AE_Q4_CS_SP_S0Y with 212s (1) cores
% 50.71/8.34 % Starting H----_042_B03_F1_AE_Q4_SP_S2S with 136s (1) cores
% 50.71/8.34 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 50.71/8.34 % Preprocessing time : 0.001 s
% 50.71/8.34 % Presaturation interreduction done
% 50.71/8.34
% 50.71/8.34 % Proof found!
% 50.71/8.34 % SZS status Theorem
% 50.71/8.34 % SZS output start CNFRefutation
% See solution above
% 50.71/8.34 % Parsed axioms : 27
% 50.71/8.34 % Removed by relevancy pruning/SinE : 0
% 50.71/8.34 % Initial clauses : 29
% 50.71/8.34 % Removed in clause preprocessing : 8
% 50.71/8.34 % Initial clauses in saturation : 21
% 50.71/8.34 % Processed clauses : 7334
% 50.71/8.34 % ...of these trivial : 4100
% 50.71/8.34 % ...subsumed : 1589
% 50.71/8.34 % ...remaining for further processing : 1645
% 50.71/8.34 % Other redundant clauses eliminated : 0
% 50.71/8.34 % Clauses deleted for lack of memory : 0
% 50.71/8.34 % Backward-subsumed : 0
% 50.71/8.34 % Backward-rewritten : 536
% 50.71/8.34 % Generated clauses : 352276
% 50.71/8.34 % ...of the previous two non-redundant : 151379
% 50.71/8.34 % ...aggressively subsumed : 0
% 50.71/8.34 % Contextual simplify-reflections : 0
% 50.71/8.34 % Paramodulations : 352276
% 50.71/8.34 % Factorizations : 0
% 50.71/8.34 % NegExts : 0
% 50.71/8.34 % Equation resolutions : 0
% 50.71/8.34 % Disequality decompositions : 0
% 50.71/8.34 % Total rewrite steps : 798274
% 50.71/8.34 % ...of those cached : 704061
% 50.71/8.34 % Propositional unsat checks : 0
% 50.71/8.34 % Propositional check models : 0
% 50.71/8.34 % Propositional check unsatisfiable : 0
% 50.71/8.34 % Propositional clauses : 0
% 50.71/8.34 % Propositional clauses after purity: 0
% 50.71/8.34 % Propositional unsat core size : 0
% 50.71/8.34 % Propositional preprocessing time : 0.000
% 50.71/8.34 % Propositional encoding time : 0.000
% 50.71/8.34 % Propositional solver time : 0.000
% 50.71/8.34 % Success case prop preproc time : 0.000
% 50.71/8.34 % Success case prop encoding time : 0.000
% 50.71/8.34 % Success case prop solver time : 0.000
% 50.71/8.34 % Current number of processed clauses : 1088
% 50.71/8.34 % Positive orientable unit clauses : 1074
% 50.71/8.34 % Positive unorientable unit clauses: 10
% 50.71/8.34 % Negative unit clauses : 2
% 50.71/8.34 % Non-unit-clauses : 2
% 50.71/8.34 % Current number of unprocessed clauses: 142377
% 50.71/8.34 % ...number of literals in the above : 142377
% 50.71/8.34 % Current number of archived formulas : 0
% 50.71/8.34 % Current number of archived clauses : 565
% 50.71/8.34 % Clause-clause subsumption calls (NU) : 0
% 50.71/8.34 % Rec. Clause-clause subsumption calls : 0
% 50.71/8.34 % Non-unit clause-clause subsumptions : 0
% 50.71/8.34 % Unit Clause-clause subsumption calls : 171
% 50.71/8.34 % Rewrite failures with RHS unbound : 0
% 50.71/8.34 % BW rewrite match attempts : 9625
% 50.71/8.34 % BW rewrite match successes : 472
% 50.71/8.34 % Condensation attempts : 0
% 50.71/8.34 % Condensation successes : 0
% 50.71/8.34 % Termbank termtop insertions : 5923078
% 50.71/8.34 % Search garbage collected termcells : 55
% 50.71/8.34
% 50.71/8.34 % -------------------------------------------------
% 50.71/8.34 % User time : 5.905 s
% 50.71/8.34 % System time : 0.243 s
% 50.71/8.34 % Total time : 6.148 s
% 50.71/8.34 % Maximum resident set size: 3660 pages
% 50.71/8.34
% 50.71/8.34 % -------------------------------------------------
% 50.71/8.34 % User time : 33.534 s
% 50.71/8.34 % System time : 1.322 s
% 50.71/8.34 % Total time : 34.856 s
% 50.71/8.34 % Maximum resident set size: 4864 pages
% 50.71/8.34 % E exiting
%------------------------------------------------------------------------------