%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE012+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 : n005.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 12:58:36 PM UTC 2026
% Result : Theorem 86.76s 18.27s
% Output : CNFRefutation 86.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 110 ( 63 unt; 0 def)
% Number of atoms : 190 ( 120 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 146 ( 66 ~; 63 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 150 ( 4 sgn 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> multiplication(X4,X5) = multiplication(X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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(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(c_0_14,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_15,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_16,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_17,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_20,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( ~ test(X1)
| multiplication(X1,esk1_1(X1)) = zero ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_24,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_25,negated_conjecture,
~ ! [X4,X5] :
( ( test(X4)
& test(X5) )
=> multiplication(X4,X5) = multiplication(X5,X4) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_26,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_27,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_28,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_29,plain,
( ~ test(X1)
| multiplication(X1,addition(X2,esk1_1(X1))) = multiplication(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_30,plain,
( ~ test(X1)
| addition(X1,esk1_1(X1)) = one ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_31,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,negated_conjecture,
( multiplication(esk2_0,esk3_0) != multiplication(esk3_0,esk2_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_25])])])]) ).
cnf(c_0_33,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( ~ test(X1)
| multiplication(esk1_1(X1),X1) = zero ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_35,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( ~ test(X1)
| multiplication(X1,X1) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_37,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_38,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_39,plain,
( ~ complement(X1,X2)
| test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_40,plain,
( addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_41,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_42,plain,
( ~ test(X1)
| multiplication(esk1_1(X1),multiplication(X1,X2)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_43,negated_conjecture,
multiplication(esk2_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
( multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one
| test(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,negated_conjecture,
multiplication(esk1_1(esk2_0),esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_37])]) ).
cnf(c_0_48,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_44]) ).
fof(c_0_49,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_50,plain,
( multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X2,X1) != one
| test(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
fof(c_0_51,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_52,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_53,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])])])]) ).
cnf(c_0_54,negated_conjecture,
multiplication(addition(esk1_1(esk2_0),X1),esk2_0) = multiplication(X1,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_55,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
( ~ test(X1)
| multiplication(esk1_1(X1),addition(X2,X1)) = multiplication(esk1_1(X1),X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_34]),c_0_22]) ).
cnf(c_0_57,plain,
( ~ test(X1)
| test(esk1_1(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_30]),c_0_34]),c_0_21]) ).
cnf(c_0_58,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,plain,
( ~ test(X1)
| ~ complement(X1,X2)
| c(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_61,negated_conjecture,
( ~ test(esk1_1(esk2_0))
| multiplication(esk1_1(esk1_1(esk2_0)),esk2_0) = esk2_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_30]),c_0_55]) ).
cnf(c_0_62,plain,
( ~ test(X1)
| multiplication(esk1_1(esk1_1(X1)),X1) = esk1_1(esk1_1(X1)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_30]),c_0_31]),c_0_57]) ).
cnf(c_0_63,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,plain,
( ~ test(X1)
| ~ test(esk1_1(X1))
| c(esk1_1(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_60,c_0_18]) ).
cnf(c_0_65,negated_conjecture,
( ~ test(esk1_1(esk2_0))
| esk1_1(esk1_1(esk2_0)) = esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_37])]) ).
cnf(c_0_66,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_31]),c_0_44]) ).
cnf(c_0_67,plain,
( ~ test(X1)
| addition(X1,one) = one ),
inference(spm,[status(thm)],[c_0_63,c_0_30]) ).
cnf(c_0_68,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_69,negated_conjecture,
( ~ test(esk1_1(esk2_0))
| esk1_1(esk2_0) = c(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_37])]) ).
cnf(c_0_70,plain,
( ~ test(X1)
| multiplication(esk1_1(X1),addition(X1,X2)) = multiplication(esk1_1(X1),X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_34]),c_0_48]) ).
cnf(c_0_71,negated_conjecture,
multiplication(esk2_0,addition(X1,one)) = multiplication(esk2_0,addition(X1,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_43]),c_0_44]),c_0_66]) ).
cnf(c_0_72,negated_conjecture,
addition(esk3_0,one) = one,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,negated_conjecture,
esk1_1(esk2_0) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_57]),c_0_37])]) ).
cnf(c_0_74,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_75,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_44]),c_0_58]) ).
cnf(c_0_76,plain,
( ~ test(X1)
| addition(multiplication(esk1_1(X1),X2),multiplication(X3,addition(X1,X2))) = multiplication(addition(esk1_1(X1),X3),addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_46,c_0_70]) ).
cnf(c_0_77,negated_conjecture,
multiplication(esk2_0,addition(esk2_0,esk3_0)) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_31]),c_0_44]) ).
cnf(c_0_78,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_73]),c_0_37])]) ).
cnf(c_0_79,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_80,plain,
( ~ test(multiplication(X1,X2))
| multiplication(X1,multiplication(X2,esk1_1(multiplication(X1,X2)))) = zero ),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_81,plain,
( multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| addition(X2,X1) != one
| c(X1) = X2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_40]),c_0_50]) ).
cnf(c_0_82,plain,
addition(X1,addition(X2,multiplication(X1,X3))) = addition(X2,multiplication(X1,addition(X3,one))),
inference(spm,[status(thm)],[c_0_75,c_0_66]) ).
cnf(c_0_83,negated_conjecture,
addition(esk2_0,multiplication(c(esk2_0),esk3_0)) = addition(esk2_0,esk3_0),
inference(rw,[status(thm)],[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_76,c_0_77]),c_0_73]),c_0_44]),c_0_73]),c_0_78]),c_0_55]),c_0_37])]),c_0_44]) ).
cnf(c_0_84,plain,
( ~ test(X1)
| multiplication(c(X1),X1) = zero ),
inference(spm,[status(thm)],[c_0_17,c_0_79]) ).
cnf(c_0_85,plain,
( ~ test(X1)
| multiplication(X1,c(X1)) = zero ),
inference(spm,[status(thm)],[c_0_27,c_0_79]) ).
cnf(c_0_86,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,esk1_1(esk2_0))) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_43]),c_0_37])]) ).
cnf(c_0_87,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,X1),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_88,plain,
( multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| addition(X1,X2) != one
| c(X1) = X2 ),
inference(spm,[status(thm)],[c_0_81,c_0_44]) ).
cnf(c_0_89,negated_conjecture,
addition(esk2_0,addition(esk3_0,c(esk2_0))) = one,
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_82,c_0_83]),c_0_72]),c_0_31]),c_0_78]),c_0_44]),c_0_58]) ).
cnf(c_0_90,negated_conjecture,
test(c(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_73]),c_0_37])]) ).
cnf(c_0_91,plain,
( ~ test(X1)
| multiplication(c(X1),multiplication(X1,X2)) = zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_84]),c_0_35]) ).
cnf(c_0_92,plain,
( ~ test(X2)
| multiplication(addition(X1,X2),esk1_1(X2)) = multiplication(X1,esk1_1(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_21]),c_0_22]) ).
cnf(c_0_93,plain,
( ~ test(X1)
| multiplication(addition(X1,X2),c(X1)) = multiplication(X2,c(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_85]),c_0_48]) ).
cnf(c_0_94,negated_conjecture,
multiplication(esk2_0,esk1_1(esk2_0)) = zero,
inference(rw,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_95,plain,
( ~ test(X1)
| esk1_1(X1) = c(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_30]),c_0_34]),c_0_21]) ).
cnf(c_0_96,plain,
( ~ test(X3)
| addition(multiplication(X1,addition(X2,X3)),multiplication(esk1_1(X3),X2)) = multiplication(addition(X1,esk1_1(X3)),addition(X2,X3)) ),
inference(spm,[status(thm)],[c_0_46,c_0_56]) ).
cnf(c_0_97,negated_conjecture,
multiplication(c(esk2_0),addition(esk3_0,c(esk2_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(spm,[status(thm)],[c_0_70,c_0_89]),c_0_31]),c_0_73]),c_0_73]),c_0_37])]) ).
cnf(c_0_98,negated_conjecture,
esk1_1(c(esk2_0)) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_73]),c_0_73]),c_0_90])]) ).
cnf(c_0_99,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_43]),c_0_37])]) ).
cnf(c_0_100,plain,
( ~ test(X2)
| addition(multiplication(X1,esk1_1(X2)),multiplication(addition(X1,X2),X3)) = multiplication(addition(X1,X2),addition(esk1_1(X2),X3)) ),
inference(spm,[status(thm)],[c_0_20,c_0_92]) ).
cnf(c_0_101,negated_conjecture,
multiplication(addition(esk3_0,c(esk2_0)),c(esk2_0)) = c(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_89]),c_0_55]),c_0_37])]) ).
cnf(c_0_102,negated_conjecture,
multiplication(esk2_0,c(esk2_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_37])]) ).
cnf(c_0_103,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),c(esk2_0)) = addition(esk3_0,c(esk2_0)),
inference(rw,[status(thm)],[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_96,c_0_97]),c_0_98]),c_0_98]),c_0_44]),c_0_78]),c_0_55]),c_0_90])]),c_0_44]) ).
cnf(c_0_104,negated_conjecture,
multiplication(addition(X1,c(esk2_0)),esk2_0) = multiplication(X1,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_99]),c_0_22]) ).
cnf(c_0_105,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),c(esk2_0)) = 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(spm,[status(thm)],[c_0_100,c_0_101]),c_0_98]),c_0_98]),c_0_78]),c_0_31]),c_0_90])]) ).
cnf(c_0_106,negated_conjecture,
multiplication(esk2_0,addition(X1,c(esk2_0))) = multiplication(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_102]),c_0_22]) ).
cnf(c_0_107,negated_conjecture,
multiplication(esk2_0,multiplication(esk3_0,esk2_0)) = multiplication(esk3_0,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(spm,[status(thm)],[c_0_92,c_0_103]),c_0_98]),c_0_104]),c_0_98]),c_0_33]),c_0_90])]) ).
cnf(c_0_108,negated_conjecture,
multiplication(esk2_0,esk3_0) != multiplication(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_109,negated_conjecture,
$false,
inference(sr,[status(thm)],[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(spm,[status(thm)],[c_0_56,c_0_105]),c_0_98]),c_0_106]),c_0_98]),c_0_107]),c_0_90])]),c_0_108]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE012+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.39 % Computer : n005.cluster.edu
% 0.14/5.39 % Model : x86_64 x86_64
% 0.14/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.39 % Memory : 8046.5625MB
% 0.14/5.39 % OS : Linux 6.8.0-71-generic
% 0.14/5.39 % CPULimit : 300
% 0.14/5.39 % WCLimit : 300
% 0.14/5.39 % DateTime : Sun Sep 20 22:38:23 UTC 2026
% 0.14/5.40 % CPUTime :
% 0.18/5.40 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/5.47 Running first-order theorem proving
% 0.18/5.47 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
% 86.76/18.27 % Version: 3.5.1
% 86.76/18.27 % Preprocessing class: FSMSSMSSSSSNFFN.
% 86.76/18.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 86.76/18.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 86.76/18.27 % Starting new_bool_3 with 300s (1) cores
% 86.76/18.27 % Starting new_bool_1 with 300s (1) cores
% 86.76/18.27 % Starting sh5l with 300s (1) cores
% 86.76/18.27 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1909424 completed with status 0
% 86.76/18.27 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 86.76/18.27 % Preprocessing class: FSMSSMSSSSSNFFN.
% 86.76/18.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 86.76/18.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 86.76/18.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 86.76/18.27 % No SInE strategy applied
% 86.76/18.27 % Search class: FGUSM-FFSF21-SFFFFFNN
% 86.76/18.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 86.76/18.27 % Starting SubtermCWHack with 136s (1) cores
% 86.76/18.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 86.76/18.27 % Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 86.76/18.27 % Starting new_bool_3 with 136s (1) cores
% 86.76/18.27 % Starting new_bool_1 with 136s (1) cores
% 86.76/18.27 % G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1909432 completed with status 0
% 86.76/18.27 % Result found by G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 86.76/18.27 % Preprocessing class: FSMSSMSSSSSNFFN.
% 86.76/18.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 86.76/18.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 86.76/18.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 86.76/18.27 % No SInE strategy applied
% 86.76/18.27 % Search class: FGUSM-FFSF21-SFFFFFNN
% 86.76/18.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 86.76/18.27 % Starting SubtermCWHack with 136s (1) cores
% 86.76/18.27 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 86.76/18.27 % Starting G-E--_208_C18AMC_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 86.76/18.27 % Preprocessing time : 0.002 s
% 86.76/18.27 % Presaturation interreduction done
% 86.76/18.27
% 86.76/18.27 % Proof found!
% 86.76/18.27 % SZS status Theorem
% 86.76/18.27 % SZS output start CNFRefutation
% See solution above
% 86.76/18.27 % Parsed axioms : 17
% 86.76/18.27 % Removed by relevancy pruning/SinE : 0
% 86.76/18.27 % Initial clauses : 25
% 86.76/18.27 % Removed in clause preprocessing : 0
% 86.76/18.27 % Initial clauses in saturation : 25
% 86.76/18.27 % Processed clauses : 12745
% 86.76/18.27 % ...of these trivial : 597
% 86.76/18.27 % ...subsumed : 10511
% 86.76/18.27 % ...remaining for further processing : 1637
% 86.76/18.27 % Other redundant clauses eliminated : 607
% 86.76/18.27 % Clauses deleted for lack of memory : 0
% 86.76/18.27 % Backward-subsumed : 241
% 86.76/18.27 % Backward-rewritten : 207
% 86.76/18.27 % Generated clauses : 384208
% 86.76/18.27 % ...of the previous two non-redundant : 333358
% 86.76/18.27 % ...aggressively subsumed : 0
% 86.76/18.27 % Contextual simplify-reflections : 85
% 86.76/18.27 % Paramodulations : 383601
% 86.76/18.27 % Factorizations : 0
% 86.76/18.27 % NegExts : 0
% 86.76/18.27 % Equation resolutions : 607
% 86.76/18.27 % Disequality decompositions : 0
% 86.76/18.27 % Total rewrite steps : 528266
% 86.76/18.27 % ...of those cached : 461002
% 86.76/18.27 % Propositional unsat checks : 0
% 86.76/18.27 % Propositional check models : 0
% 86.76/18.27 % Propositional check unsatisfiable : 0
% 86.76/18.27 % Propositional clauses : 0
% 86.76/18.27 % Propositional clauses after purity: 0
% 86.76/18.27 % Propositional unsat core size : 0
% 86.76/18.27 % Propositional preprocessing time : 0.000
% 86.76/18.27 % Propositional encoding time : 0.000
% 86.76/18.27 % Propositional solver time : 0.000
% 86.76/18.27 % Success case prop preproc time : 0.000
% 86.76/18.27 % Success case prop encoding time : 0.000
% 86.76/18.27 % Success case prop solver time : 0.000
% 86.76/18.27 % Current number of processed clauses : 1163
% 86.76/18.27 % Positive orientable unit clauses : 298
% 86.76/18.27 % Positive unorientable unit clauses: 19
% 86.76/18.27 % Negative unit clauses : 19
% 86.76/18.27 % Non-unit-clauses : 827
% 86.76/18.27 % Current number of unprocessed clauses: 318685
% 86.76/18.27 % ...number of literals in the above : 850593
% 86.76/18.27 % Current number of archived formulas : 0
% 86.76/18.27 % Current number of archived clauses : 473
% 86.76/18.27 % Clause-clause subsumption calls (NU) : 107429
% 86.76/18.27 % Rec. Clause-clause subsumption calls : 80729
% 86.76/18.27 % Non-unit clause-clause subsumptions : 5670
% 86.76/18.27 % Unit Clause-clause subsumption calls : 5497
% 86.76/18.27 % Rewrite failures with RHS unbound : 0
% 86.76/18.27 % BW rewrite match attempts : 1091
% 86.76/18.27 % BW rewrite match successes : 246
% 86.76/18.27 % Condensation attempts : 0
% 86.76/18.27 % Condensation successes : 0
% 86.76/18.27 % Termbank termtop insertions : 7834646
% 86.76/18.27 % Search garbage collected termcells : 171
% 86.76/18.27
% 86.76/18.27 % -------------------------------------------------
% 86.76/18.27 % User time : 11.849 s
% 86.76/18.27 % System time : 0.469 s
% 86.76/18.27 % Total time : 12.318 s
% 86.76/18.27 % Maximum resident set size: 3648 pages
% 86.76/18.27
% 86.76/18.27 % -------------------------------------------------
% 86.76/18.27 % User time : 58.882 s
% 86.76/18.27 % System time : 2.392 s
% 86.76/18.27 % Total time : 61.274 s
% 86.76/18.27 % Maximum resident set size: 4608 pages
% 86.76/18.27 % E exiting
%------------------------------------------------------------------------------