%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE011+4 : 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 : n009.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 12:58:35 PM UTC 2026
% Result : Theorem 2.57s 0.82s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 144 ( 95 unt; 0 def)
% Number of atoms : 231 ( 125 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 152 ( 65 ~; 60 |; 16 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 152 ( 4 sgn 71 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> ( leq(addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5))),one)
& leq(one,addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(test_deMorgan1,axiom,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> c(addition(X4,X5)) = multiplication(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan1) ).
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_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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(test_4,axiom,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_4) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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(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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(test_deMorgan2,axiom,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> c(multiplication(X4,X5)) = addition(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan2) ).
fof(c_0_19,negated_conjecture,
~ ! [X4,X5] :
( ( test(X4)
& test(X5) )
=> ( leq(addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5))),one)
& leq(one,addition(addition(multiplication(addition(X5,c(X5)),X4),multiplication(addition(X4,c(X4)),X5)),multiplication(c(X4),c(X5)))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_20,plain,
! [X34,X35] :
( ( ~ test(X34)
| c(X34) = X35
| ~ complement(X34,X35) )
& ( ~ test(X34)
| complement(X34,X35)
| c(X34) != X35 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_21,plain,
! [X32,X33] :
( ( complement(X33,X32)
| addition(X32,X33) != one
| multiplication(X33,X32) != zero
| multiplication(X32,X33) != zero )
& ( ~ complement(X33,X32)
| addition(X32,X33) = one )
& ( ~ complement(X33,X32)
| multiplication(X33,X32) = zero )
& ( ~ complement(X33,X32)
| multiplication(X32,X33) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])]) ).
fof(c_0_22,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_23,plain,
! [X28,X30,X31] :
( ( test(X30)
| ~ complement(X31,X30) )
& ( complement(esk1_1(X28),X28)
| ~ test(X28) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[test_1])])])])])]) ).
fof(c_0_24,negated_conjecture,
( ( ~ leq(addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one)
| ~ leq(one,addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk3_0)),multiplication(c(esk2_0),c(esk3_0)))) )
& test(esk2_0)
& test(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])]) ).
cnf(c_0_25,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X37,X38] :
( c(addition(X37,X38)) = multiplication(c(X37),c(X38))
| ~ test(X38)
| ~ test(X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan1])])]) ).
cnf(c_0_31,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
( ~ complement(X1,X2)
| addition(X1,X2) = one ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
complement(esk1_1(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_36,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_37,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,plain,
( ~ test(X2)
| ~ test(X1)
| c(addition(X1,X2)) = multiplication(c(X1),c(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
( ~ complement(X1,X2)
| test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_40,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_41,plain,
( ~ test(X1)
| ~ complement(X1,X2)
| c(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_42,plain,
( multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| addition(X1,X2) != one
| complement(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_43,negated_conjecture,
addition(esk2_0,esk1_1(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27]) ).
cnf(c_0_44,negated_conjecture,
multiplication(esk2_0,esk1_1(esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_45,negated_conjecture,
multiplication(esk1_1(esk2_0),esk2_0) = zero,
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
fof(c_0_46,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_47,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
fof(c_0_48,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_49,negated_conjecture,
( ~ test(X1)
| c(addition(X1,esk3_0)) = multiplication(c(X1),c(esk3_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_50,negated_conjecture,
test(c(esk2_0)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_51,negated_conjecture,
( ~ complement(esk2_0,X1)
| c(esk2_0) = X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_29]) ).
cnf(c_0_52,negated_conjecture,
complement(esk2_0,esk1_1(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]) ).
cnf(c_0_53,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_47]),c_0_27]) ).
cnf(c_0_55,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_56,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_57,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_58,plain,
! [X24] : multiplication(X24,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_59,negated_conjecture,
c(addition(esk3_0,c(esk2_0))) = multiplication(c(c(esk2_0)),c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_27]) ).
cnf(c_0_60,negated_conjecture,
esk1_1(esk2_0) = c(esk2_0),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_39,c_0_47]) ).
cnf(c_0_62,negated_conjecture,
addition(multiplication(X1,esk3_0),multiplication(X1,c(esk3_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_63,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,negated_conjecture,
multiplication(c(esk3_0),esk3_0) = zero,
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_66,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_36,c_0_47]) ).
cnf(c_0_68,negated_conjecture,
multiplication(c(c(esk2_0)),c(esk3_0)) = multiplication(c(esk3_0),c(c(esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_59]),c_0_50]),c_0_37])]) ).
cnf(c_0_69,negated_conjecture,
( ~ complement(c(esk2_0),X1)
| c(c(esk2_0)) = X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_50]) ).
cnf(c_0_70,negated_conjecture,
complement(c(esk2_0),esk2_0),
inference(rw,[status(thm)],[c_0_34,c_0_60]) ).
cnf(c_0_71,negated_conjecture,
( ~ complement(c(esk3_0),X1)
| c(c(esk3_0)) = X1 ),
inference(spm,[status(thm)],[c_0_41,c_0_61]) ).
cnf(c_0_72,negated_conjecture,
complement(c(esk3_0),esk3_0),
inference(cn,[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(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_62]),c_0_63]),c_0_63])]),c_0_64]),c_0_64]),c_0_64]),c_0_65]),c_0_66]),c_0_64]),c_0_67]),c_0_66])]) ).
fof(c_0_73,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_74,plain,
! [X4] :
( ~ test(X4)
=> c(X4) = zero ),
inference(fof_simplification,[status(thm)],[test_4]) ).
cnf(c_0_75,negated_conjecture,
c(addition(esk3_0,c(esk2_0))) = multiplication(c(esk3_0),c(c(esk2_0))),
inference(rw,[status(thm)],[c_0_59,c_0_68]) ).
cnf(c_0_76,negated_conjecture,
c(c(esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_77,negated_conjecture,
c(c(esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
fof(c_0_79,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_80,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_81,plain,
! [X36] :
( c(X36) = zero
| test(X36) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])]) ).
cnf(c_0_82,negated_conjecture,
c(addition(esk3_0,c(esk2_0))) = multiplication(c(esk3_0),esk2_0),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
multiplication(c(esk3_0),esk2_0) = multiplication(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_76]),c_0_76]) ).
fof(c_0_84,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_85,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_86,negated_conjecture,
( ~ test(X1)
| c(addition(X1,c(esk3_0))) = multiplication(c(X1),esk3_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_61]),c_0_77]) ).
cnf(c_0_87,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_78,c_0_27]) ).
cnf(c_0_88,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_89,negated_conjecture,
( ~ leq(addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one)
| ~ leq(one,addition(addition(multiplication(addition(esk3_0,c(esk3_0)),esk2_0),multiplication(addition(esk2_0,c(esk2_0)),esk3_0)),multiplication(c(esk2_0),c(esk3_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_90,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_91,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_40]),c_0_27]) ).
cnf(c_0_92,plain,
( c(X1) = zero
| test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_93,negated_conjecture,
c(addition(esk3_0,c(esk2_0))) = multiplication(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_94,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_95,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_96,plain,
! [X26,X27] :
( ( leq(X26,X27)
| addition(X26,X27) != X27 )
& ( addition(X26,X27) = X27
| ~ leq(X26,X27) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_97,negated_conjecture,
( ~ test(X1)
| c(addition(X1,c(esk2_0))) = multiplication(c(X1),c(c(esk2_0))) ),
inference(spm,[status(thm)],[c_0_38,c_0_50]) ).
cnf(c_0_98,negated_conjecture,
c(addition(c(esk2_0),c(esk3_0))) = multiplication(c(c(esk2_0)),esk3_0),
inference(spm,[status(thm)],[c_0_86,c_0_50]) ).
cnf(c_0_99,plain,
complement(one,zero),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_87]),c_0_66]),c_0_88])])]) ).
fof(c_0_100,plain,
! [X39,X40] :
( c(multiplication(X39,X40)) = addition(c(X39),c(X40))
| ~ test(X40)
| ~ test(X39) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan2])])]) ).
cnf(c_0_101,negated_conjecture,
( ~ leq(addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0))),one)
| ~ leq(one,addition(multiplication(c(esk2_0),c(esk3_0)),addition(multiplication(addition(esk2_0,c(esk2_0)),esk3_0),multiplication(addition(esk3_0,c(esk3_0)),esk2_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_102,negated_conjecture,
addition(multiplication(esk2_0,X1),multiplication(c(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_64]) ).
cnf(c_0_103,negated_conjecture,
( test(addition(esk3_0,c(esk2_0)))
| multiplication(esk2_0,c(esk3_0)) = zero ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_104,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_105,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_106,negated_conjecture,
multiplication(c(c(esk2_0)),esk3_0) = multiplication(esk3_0,c(c(esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_61]),c_0_27]),c_0_98]),c_0_77]) ).
cnf(c_0_107,plain,
test(zero),
inference(spm,[status(thm)],[c_0_39,c_0_99]) ).
cnf(c_0_108,plain,
( ~ test(X2)
| ~ test(X1)
| c(multiplication(X1,X2)) = addition(c(X1),c(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_109,negated_conjecture,
( ~ leq(addition(esk2_0,addition(esk3_0,multiplication(c(esk2_0),c(esk3_0)))),one)
| ~ leq(one,addition(esk2_0,addition(esk3_0,multiplication(c(esk2_0),c(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_91]),c_0_64]),c_0_54]),c_0_64]),c_0_27]),c_0_27]),c_0_94]),c_0_64]),c_0_54]),c_0_64]),c_0_27]),c_0_27]),c_0_94]) ).
cnf(c_0_110,negated_conjecture,
( test(addition(esk3_0,c(esk2_0)))
| multiplication(c(esk2_0),c(esk3_0)) = c(esk3_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_87]) ).
cnf(c_0_111,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_43]),c_0_27]) ).
cnf(c_0_112,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_105,c_0_95]) ).
cnf(c_0_113,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk3_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_65]),c_0_88]) ).
cnf(c_0_114,negated_conjecture,
multiplication(esk3_0,esk2_0) = multiplication(esk2_0,esk3_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_76]),c_0_76]) ).
cnf(c_0_115,plain,
complement(zero,c(zero)),
inference(spm,[status(thm)],[c_0_31,c_0_107]) ).
cnf(c_0_116,negated_conjecture,
( ~ test(X1)
| c(multiplication(X1,c(esk3_0))) = addition(esk3_0,c(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_61]),c_0_77]),c_0_27]) ).
cnf(c_0_117,negated_conjecture,
test(addition(esk3_0,c(esk2_0))),
inference(cn,[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(spm,[status(thm)],[c_0_109,c_0_110]),c_0_54]),c_0_27]),c_0_111]),c_0_112]),c_0_54]),c_0_27]),c_0_111]),c_0_112])]) ).
cnf(c_0_118,plain,
( ~ test(X3)
| ~ test(multiplication(X1,X2))
| c(multiplication(X1,multiplication(X2,X3))) = addition(c(multiplication(X1,X2)),c(X3)) ),
inference(spm,[status(thm)],[c_0_108,c_0_63]) ).
cnf(c_0_119,negated_conjecture,
multiplication(c(esk3_0),multiplication(esk2_0,esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_120,plain,
c(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_115]),c_0_87]) ).
cnf(c_0_121,negated_conjecture,
c(multiplication(esk2_0,c(esk3_0))) = addition(esk3_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_116,c_0_29]) ).
cnf(c_0_122,negated_conjecture,
complement(addition(esk3_0,c(esk2_0)),multiplication(esk2_0,c(esk3_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_117]),c_0_75]),c_0_76]),c_0_83]) ).
cnf(c_0_123,negated_conjecture,
( ~ test(multiplication(esk2_0,c(esk3_0)))
| addition(esk3_0,addition(c(esk2_0),c(esk3_0))) = one ),
inference(cn,[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_118,c_0_119]),c_0_120]),c_0_83]),c_0_121]),c_0_94]),c_0_83]),c_0_37])]) ).
cnf(c_0_124,negated_conjecture,
test(multiplication(esk2_0,c(esk3_0))),
inference(spm,[status(thm)],[c_0_39,c_0_122]) ).
cnf(c_0_125,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_94]) ).
cnf(c_0_126,negated_conjecture,
addition(esk3_0,addition(c(esk2_0),c(esk3_0))) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_127,negated_conjecture,
addition(esk3_0,addition(c(esk3_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_94,c_0_54]) ).
cnf(c_0_128,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_27]),c_0_94]) ).
cnf(c_0_129,negated_conjecture,
complement(esk1_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_130,negated_conjecture,
addition(X1,one) = addition(one,addition(c(esk2_0),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_94]),c_0_125]),c_0_127]),c_0_128]) ).
cnf(c_0_131,negated_conjecture,
addition(esk3_0,esk1_1(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_129]),c_0_27]) ).
cnf(c_0_132,negated_conjecture,
addition(one,addition(c(esk2_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_27,c_0_130]) ).
cnf(c_0_133,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_131]),c_0_27]) ).
cnf(c_0_134,negated_conjecture,
( ~ leq(addition(esk2_0,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),multiplication(c(esk2_0),c(esk3_0))))),one)
| ~ leq(one,addition(esk2_0,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),multiplication(c(esk2_0),c(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_54]),c_0_64]),c_0_27]),c_0_27]),c_0_94]),c_0_64]),c_0_27]),c_0_27]),c_0_94]),c_0_90]),c_0_94]),c_0_90]),c_0_94]) ).
cnf(c_0_135,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_94,c_0_91]) ).
cnf(c_0_136,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_125,c_0_95]) ).
cnf(c_0_137,negated_conjecture,
addition(one,addition(X1,c(esk2_0))) = addition(one,X1),
inference(spm,[status(thm)],[c_0_132,c_0_27]) ).
cnf(c_0_138,negated_conjecture,
addition(one,addition(esk3_0,X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_94,c_0_133]) ).
cnf(c_0_139,negated_conjecture,
addition(X1,multiplication(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_111]),c_0_64]),c_0_64]) ).
cnf(c_0_140,negated_conjecture,
( ~ leq(addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0))),one)
| ~ leq(one,addition(esk2_0,addition(multiplication(esk2_0,esk3_0),c(esk2_0)))) ),
inference(spm,[status(thm)],[c_0_134,c_0_62]) ).
cnf(c_0_141,negated_conjecture,
addition(esk2_0,addition(X1,c(esk2_0))) = addition(one,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]) ).
cnf(c_0_142,negated_conjecture,
addition(one,multiplication(esk2_0,esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_133]) ).
cnf(c_0_143,negated_conjecture,
$false,
inference(cn,[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_140,c_0_141]),c_0_142]),c_0_112]),c_0_141]),c_0_142]),c_0_112])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE011+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n009.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 20 22:38:12 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 2.57/0.82 % Version: 3.5.1
% 2.57/0.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.57/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.57/0.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.57/0.82 % Starting new_bool_3 with 300s (1) cores
% 2.57/0.82 % Starting new_bool_1 with 300s (1) cores
% 2.57/0.82 % Starting sh5l with 300s (1) cores
% 2.57/0.82 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 200618 completed with status 0
% 2.57/0.82 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.57/0.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.57/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.57/0.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.57/0.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.57/0.82 % No SInE strategy applied
% 2.57/0.82 % Search class: FGHSM-FFMF21-MFFFFFNN
% 2.57/0.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.57/0.82 % Starting SubtermCWHack with 136s (1) cores
% 2.57/0.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.57/0.82 % Starting U----_210g_02_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.57/0.82 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S00EN with 136s (1) cores
% 2.57/0.82 % Starting new_bool_3 with 136s (1) cores
% 2.57/0.82 % G-E--_208_B00_00_F1_SE_CS_SP_PS_S00EN with pid 200626 completed with status 0
% 2.57/0.82 % Result found by G-E--_208_B00_00_F1_SE_CS_SP_PS_S00EN
% 2.57/0.82 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.57/0.82 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.57/0.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.57/0.82 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.57/0.82 % No SInE strategy applied
% 2.57/0.82 % Search class: FGHSM-FFMF21-MFFFFFNN
% 2.57/0.82 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.57/0.82 % Starting SubtermCWHack with 136s (1) cores
% 2.57/0.82 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.57/0.82 % Starting U----_210g_02_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.57/0.82 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S00EN with 136s (1) cores
% 2.57/0.82 % Preprocessing time : 0.001 s
% 2.57/0.82 % Presaturation interreduction done
% 2.57/0.82
% 2.57/0.82 % Proof found!
% 2.57/0.82 % SZS status Theorem
% 2.57/0.82 % SZS output start CNFRefutation
% See solution above
% 2.57/0.82 % Parsed axioms : 19
% 2.57/0.82 % Removed by relevancy pruning/SinE : 0
% 2.57/0.82 % Initial clauses : 27
% 2.57/0.82 % Removed in clause preprocessing : 0
% 2.57/0.82 % Initial clauses in saturation : 27
% 2.57/0.82 % Processed clauses : 1673
% 2.57/0.82 % ...of these trivial : 155
% 2.57/0.82 % ...subsumed : 796
% 2.57/0.82 % ...remaining for further processing : 722
% 2.57/0.82 % Other redundant clauses eliminated : 78
% 2.57/0.82 % Clauses deleted for lack of memory : 0
% 2.57/0.82 % Backward-subsumed : 30
% 2.57/0.82 % Backward-rewritten : 227
% 2.57/0.82 % Generated clauses : 11998
% 2.57/0.82 % ...of the previous two non-redundant : 8333
% 2.57/0.82 % ...aggressively subsumed : 0
% 2.57/0.82 % Contextual simplify-reflections : 0
% 2.57/0.82 % Paramodulations : 11920
% 2.57/0.82 % Factorizations : 0
% 2.57/0.82 % NegExts : 0
% 2.57/0.82 % Equation resolutions : 78
% 2.57/0.82 % Disequality decompositions : 0
% 2.57/0.82 % Total rewrite steps : 22688
% 2.57/0.82 % ...of those cached : 20582
% 2.57/0.82 % Propositional unsat checks : 0
% 2.57/0.82 % Propositional check models : 0
% 2.57/0.82 % Propositional check unsatisfiable : 0
% 2.57/0.82 % Propositional clauses : 0
% 2.57/0.82 % Propositional clauses after purity: 0
% 2.57/0.82 % Propositional unsat core size : 0
% 2.57/0.82 % Propositional preprocessing time : 0.000
% 2.57/0.82 % Propositional encoding time : 0.000
% 2.57/0.82 % Propositional solver time : 0.000
% 2.57/0.82 % Success case prop preproc time : 0.000
% 2.57/0.82 % Success case prop encoding time : 0.000
% 2.57/0.82 % Success case prop solver time : 0.000
% 2.57/0.82 % Current number of processed clauses : 437
% 2.57/0.82 % Positive orientable unit clauses : 186
% 2.57/0.82 % Positive unorientable unit clauses: 4
% 2.57/0.82 % Negative unit clauses : 0
% 2.57/0.82 % Non-unit-clauses : 247
% 2.57/0.82 % Current number of unprocessed clauses: 6452
% 2.57/0.82 % ...number of literals in the above : 13866
% 2.57/0.82 % Current number of archived formulas : 0
% 2.57/0.82 % Current number of archived clauses : 284
% 2.57/0.82 % Clause-clause subsumption calls (NU) : 10496
% 2.57/0.82 % Rec. Clause-clause subsumption calls : 10352
% 2.57/0.82 % Non-unit clause-clause subsumptions : 725
% 2.57/0.82 % Unit Clause-clause subsumption calls : 1774
% 2.57/0.82 % Rewrite failures with RHS unbound : 0
% 2.57/0.82 % BW rewrite match attempts : 391
% 2.57/0.82 % BW rewrite match successes : 193
% 2.57/0.82 % Condensation attempts : 0
% 2.57/0.82 % Condensation successes : 0
% 2.57/0.82 % Termbank termtop insertions : 164812
% 2.57/0.82 % Search garbage collected termcells : 215
% 2.57/0.82
% 2.57/0.82 % -------------------------------------------------
% 2.57/0.82 % User time : 0.247 s
% 2.57/0.82 % System time : 0.016 s
% 2.57/0.82 % Total time : 0.263 s
% 2.57/0.82 % Maximum resident set size: 3652 pages
% 2.57/0.82
% 2.57/0.82 % -------------------------------------------------
% 2.57/0.82 % User time : 1.587 s
% 2.57/0.82 % System time : 0.088 s
% 2.57/0.82 % Total time : 1.675 s
% 2.57/0.82 % Maximum resident set size: 4864 pages
% 2.57/0.82 % E exiting
%------------------------------------------------------------------------------