%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE033+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:58:41 PM UTC 2026
% Result : Theorem 38.63s 6.16s
% Output : CNFRefutation 38.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 17
% Syntax : Number of formulae : 149 ( 108 unt; 0 def)
% Number of atoms : 252 ( 124 equ)
% Maximal formula atoms : 20 ( 1 avg)
% Number of connectives : 171 ( 68 ~; 71 |; 23 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 177 ( 9 sgn 73 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( ismeet(zero,X5,X6)
& test(X5)
& test(X6) )
=> ismeet(zero,multiplication(X5,X4),multiplication(X6,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( addition(X4,X5) = one
& multiplication(X5,X4) = zero
& multiplication(X4,X5) = zero ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(ismeet,axiom,
! [X4,X5,X6] :
( ismeet(X6,X4,X5)
<=> ( ! [X7] :
( ( leq(X7,X5)
& leq(X7,X4) )
=> leq(X7,X6) )
& leq(X6,X5)
& leq(X6,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+3.ax',ismeet) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(c_0_17,plain,
! [X36,X37] :
( ( ~ test(X36)
| c(X36) = X37
| ~ complement(X36,X37) )
& ( ~ test(X36)
| complement(X36,X37)
| c(X36) != X37 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])])]) ).
fof(c_0_18,negated_conjecture,
~ ! [X4,X5,X6] :
( ( ismeet(zero,X5,X6)
& test(X5)
& test(X6) )
=> ismeet(zero,multiplication(X5,X4),multiplication(X6,X4)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_19,plain,
( ~ test(X1)
| c(X1) != X2
| complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,negated_conjecture,
( ~ ismeet(zero,multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0))
& ismeet(zero,esk5_0,esk6_0)
& test(esk5_0)
& test(esk6_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_21,plain,
! [X34,X35] :
( ( complement(X35,X34)
| addition(X34,X35) != one
| multiplication(X35,X34) != zero
| multiplication(X34,X35) != zero )
& ( ~ complement(X35,X34)
| addition(X34,X35) = one )
& ( ~ complement(X35,X34)
| multiplication(X35,X34) = zero )
& ( ~ complement(X35,X34)
| multiplication(X34,X35) = zero ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])])]) ).
cnf(c_0_22,plain,
( ~ test(X1)
| complement(X1,c(X1)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
test(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_24,plain,
! [X20,X21,X22] : multiplication(X20,addition(X21,X22)) = addition(multiplication(X20,X21),multiplication(X20,X22)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_25,plain,
( ~ complement(X1,X2)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
complement(esk6_0,c(esk6_0)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_27,plain,
! [X13] : addition(X13,zero) = X13,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_28,plain,
! [X8,X9] : addition(X8,X9) = addition(X9,X8),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_29,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
multiplication(esk6_0,c(esk6_0)) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
( ~ complement(X2,X1)
| addition(X1,X2) = one ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_34,plain,
! [X18] : multiplication(X18,one) = X18,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_35,plain,
! [X23,X24,X25] : multiplication(addition(X23,X24),X25) = addition(multiplication(X23,X25),multiplication(X24,X25)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_36,plain,
! [X19] : multiplication(one,X19) = X19,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_37,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_38,plain,
! [X28,X29] :
( ( leq(X28,X29)
| addition(X28,X29) != X29 )
& ( addition(X28,X29) = X29
| ~ leq(X28,X29) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_39,negated_conjecture,
multiplication(esk6_0,addition(X1,c(esk6_0))) = multiplication(esk6_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_40,negated_conjecture,
addition(esk6_0,c(esk6_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_33]) ).
cnf(c_0_41,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,negated_conjecture,
complement(esk5_0,c(esk5_0)),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_45,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,negated_conjecture,
multiplication(esk6_0,esk6_0) = esk6_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_47,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_33]) ).
cnf(c_0_48,negated_conjecture,
multiplication(esk5_0,c(esk5_0)) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_44]) ).
cnf(c_0_49,plain,
( multiplication(addition(X1,X3),X2) != multiplication(X3,X2)
| leq(multiplication(X1,X2),multiplication(X3,X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
multiplication(addition(X1,one),esk6_0) = multiplication(addition(esk6_0,X1),esk6_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_46]),c_0_47]) ).
fof(c_0_51,plain,
! [X15,X16,X17] : multiplication(X15,multiplication(X16,X17)) = multiplication(multiplication(X15,X16),X17),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_52,plain,
! [X10,X11,X12] : addition(X12,addition(X11,X10)) = addition(addition(X12,X11),X10),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_53,plain,
! [X14] : addition(X14,X14) = X14,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_54,negated_conjecture,
multiplication(esk5_0,addition(X1,c(esk5_0))) = multiplication(esk5_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_48]),c_0_31]) ).
cnf(c_0_55,negated_conjecture,
addition(esk5_0,c(esk5_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_44]),c_0_33]) ).
cnf(c_0_56,negated_conjecture,
( multiplication(addition(esk6_0,X1),esk6_0) != esk6_0
| leq(multiplication(X1,esk6_0),esk6_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_43]),c_0_43]) ).
cnf(c_0_57,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,negated_conjecture,
multiplication(esk5_0,esk5_0) = esk5_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_41]) ).
cnf(c_0_61,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_33]) ).
fof(c_0_62,plain,
! [X39,X40,X41,X42,X43,X44,X45] :
( ( ismeet(X45,X43,X44)
| ~ leq(X45,X44)
| ~ leq(X45,X43)
| ~ leq(esk2_3(X43,X44,X45),X45) )
& ( ismeet(X45,X43,X44)
| ~ leq(X45,X44)
| ~ leq(X45,X43)
| leq(esk2_3(X43,X44,X45),X44) )
& ( ismeet(X45,X43,X44)
| ~ leq(X45,X44)
| ~ leq(X45,X43)
| leq(esk2_3(X43,X44,X45),X43) )
& ( ~ ismeet(X41,X39,X40)
| leq(X42,X41)
| ~ leq(X42,X40)
| ~ leq(X42,X39) )
& ( ~ ismeet(X41,X39,X40)
| leq(X41,X40) )
& ( ~ ismeet(X41,X39,X40)
| leq(X41,X39) ) ),
inference(distribute,[status(thm)],[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)],[ismeet])])])])])])]) ).
cnf(c_0_63,negated_conjecture,
( multiplication(addition(X1,one),esk6_0) != esk6_0
| leq(multiplication(X1,esk6_0),esk6_0) ),
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_47]),c_0_57]),c_0_46]),c_0_57]),c_0_46]) ).
cnf(c_0_64,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
( multiplication(X1,addition(X2,X3)) != multiplication(X1,X3)
| leq(multiplication(X1,X2),multiplication(X1,X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_29]) ).
cnf(c_0_66,negated_conjecture,
multiplication(esk5_0,addition(X1,esk5_0)) = multiplication(esk5_0,addition(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_60]),c_0_33]),c_0_61]) ).
cnf(c_0_67,plain,
( ~ ismeet(X4,X2,X3)
| ~ leq(X1,X3)
| ~ leq(X1,X2)
| leq(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_68,negated_conjecture,
ismeet(zero,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_69,negated_conjecture,
( multiplication(addition(one,X1),esk6_0) != esk6_0
| leq(multiplication(X1,esk6_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_33]) ).
cnf(c_0_70,negated_conjecture,
addition(one,esk5_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_55]),c_0_33]) ).
cnf(c_0_71,negated_conjecture,
( multiplication(esk5_0,addition(X1,one)) != esk5_0
| leq(multiplication(esk5_0,X1),esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_60]),c_0_60]) ).
cnf(c_0_72,negated_conjecture,
( ~ leq(X1,esk5_0)
| ~ leq(X1,esk6_0)
| leq(X1,zero) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,negated_conjecture,
leq(multiplication(esk5_0,esk6_0),esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_43])]) ).
cnf(c_0_74,negated_conjecture,
( multiplication(esk5_0,addition(one,X1)) != esk5_0
| leq(multiplication(esk5_0,X1),esk5_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_33]) ).
cnf(c_0_75,negated_conjecture,
addition(one,esk6_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_40]),c_0_33]) ).
cnf(c_0_76,negated_conjecture,
( ~ leq(multiplication(esk5_0,esk6_0),esk5_0)
| leq(multiplication(esk5_0,esk6_0),zero) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,negated_conjecture,
leq(multiplication(esk5_0,esk6_0),esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_41])]) ).
cnf(c_0_78,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_79,negated_conjecture,
leq(multiplication(esk5_0,esk6_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
fof(c_0_80,plain,
! [X30,X32,X33] :
( ( test(X32)
| ~ complement(X33,X32) )
& ( complement(esk1_1(X30),X30)
| ~ test(X30) ) ),
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])])])])])]) ).
cnf(c_0_81,negated_conjecture,
multiplication(esk5_0,esk6_0) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_31]) ).
cnf(c_0_82,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_83,plain,
( ~ test(X1)
| complement(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_84,negated_conjecture,
multiplication(esk5_0,addition(esk6_0,X1)) = multiplication(esk5_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_81]),c_0_82]) ).
cnf(c_0_85,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_86,negated_conjecture,
complement(esk1_1(esk5_0),esk5_0),
inference(spm,[status(thm)],[c_0_83,c_0_37]) ).
cnf(c_0_87,plain,
( ~ complement(X2,X1)
| multiplication(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_88,negated_conjecture,
multiplication(esk5_0,c(esk6_0)) = esk5_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_40]),c_0_41]) ).
fof(c_0_89,plain,
! [X27] : multiplication(zero,X27) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_90,plain,
( multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero
| addition(X1,X2) != one
| complement(X1,X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_33]) ).
cnf(c_0_91,negated_conjecture,
addition(esk5_0,esk1_1(esk5_0)) = one,
inference(spm,[status(thm)],[c_0_32,c_0_86]) ).
cnf(c_0_92,negated_conjecture,
multiplication(esk5_0,esk1_1(esk5_0)) = zero,
inference(spm,[status(thm)],[c_0_87,c_0_86]) ).
cnf(c_0_93,negated_conjecture,
multiplication(esk1_1(esk5_0),esk5_0) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_86]) ).
cnf(c_0_94,negated_conjecture,
complement(esk1_1(esk6_0),esk6_0),
inference(spm,[status(thm)],[c_0_83,c_0_23]) ).
cnf(c_0_95,negated_conjecture,
addition(esk5_0,c(esk6_0)) = c(esk6_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_88]),c_0_33]),c_0_70]),c_0_43]),c_0_33]) ).
cnf(c_0_96,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_97,plain,
( ~ test(X1)
| ~ complement(X1,X2)
| c(X1) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_98,negated_conjecture,
complement(esk5_0,esk1_1(esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_93])]) ).
cnf(c_0_99,plain,
( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ismeet(X3,X1,X2)
| leq(esk2_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_100,plain,
leq(zero,X1),
inference(spm,[status(thm)],[c_0_45,c_0_82]) ).
cnf(c_0_101,negated_conjecture,
addition(esk6_0,esk1_1(esk6_0)) = one,
inference(spm,[status(thm)],[c_0_32,c_0_94]) ).
cnf(c_0_102,negated_conjecture,
multiplication(esk6_0,esk1_1(esk6_0)) = zero,
inference(spm,[status(thm)],[c_0_87,c_0_94]) ).
cnf(c_0_103,negated_conjecture,
multiplication(esk1_1(esk6_0),esk6_0) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_94]) ).
cnf(c_0_104,negated_conjecture,
multiplication(esk6_0,esk5_0) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_95]),c_0_30]) ).
cnf(c_0_105,negated_conjecture,
multiplication(esk1_1(esk5_0),multiplication(esk5_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_93]),c_0_96]) ).
cnf(c_0_106,negated_conjecture,
esk1_1(esk5_0) = c(esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_37])]) ).
cnf(c_0_107,negated_conjecture,
~ ismeet(zero,multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_108,plain,
( leq(esk2_3(X1,X2,zero),X1)
| ismeet(zero,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_100])]) ).
cnf(c_0_109,negated_conjecture,
complement(esk6_0,esk1_1(esk6_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_101]),c_0_102]),c_0_103])]) ).
cnf(c_0_110,plain,
( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ismeet(X3,X1,X2)
| leq(esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_111,negated_conjecture,
multiplication(esk6_0,addition(esk5_0,X1)) = multiplication(esk6_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_104]),c_0_82]) ).
cnf(c_0_112,negated_conjecture,
multiplication(c(esk5_0),multiplication(esk5_0,X1)) = zero,
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_113,negated_conjecture,
leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),multiplication(esk5_0,esk4_0)),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_114,negated_conjecture,
multiplication(esk1_1(esk6_0),multiplication(esk6_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_103]),c_0_96]) ).
cnf(c_0_115,negated_conjecture,
esk1_1(esk6_0) = c(esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_109]),c_0_23])]) ).
cnf(c_0_116,plain,
( leq(esk2_3(X1,X2,zero),X2)
| ismeet(zero,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_100]),c_0_100])]) ).
cnf(c_0_117,negated_conjecture,
multiplication(esk6_0,c(esk5_0)) = esk6_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_55]),c_0_41]) ).
cnf(c_0_118,negated_conjecture,
multiplication(c(esk5_0),addition(multiplication(esk5_0,X1),X2)) = multiplication(c(esk5_0),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_112]),c_0_82]) ).
cnf(c_0_119,negated_conjecture,
addition(multiplication(esk5_0,esk4_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)) = multiplication(esk5_0,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_113]),c_0_33]) ).
fof(c_0_120,plain,
! [X26] : multiplication(X26,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_121,negated_conjecture,
multiplication(c(esk6_0),multiplication(esk6_0,X1)) = zero,
inference(rw,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_122,negated_conjecture,
leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),multiplication(esk6_0,esk4_0)),
inference(spm,[status(thm)],[c_0_107,c_0_116]) ).
cnf(c_0_123,negated_conjecture,
multiplication(c(esk6_0),esk6_0) = zero,
inference(spm,[status(thm)],[c_0_87,c_0_26]) ).
cnf(c_0_124,negated_conjecture,
multiplication(esk6_0,multiplication(c(esk5_0),X1)) = multiplication(esk6_0,X1),
inference(spm,[status(thm)],[c_0_57,c_0_117]) ).
cnf(c_0_125,negated_conjecture,
multiplication(c(esk5_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_112]) ).
cnf(c_0_126,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_127,negated_conjecture,
multiplication(c(esk6_0),addition(multiplication(esk6_0,X1),X2)) = multiplication(c(esk6_0),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_121]),c_0_82]) ).
cnf(c_0_128,negated_conjecture,
addition(multiplication(esk6_0,esk4_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)) = multiplication(esk6_0,esk4_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_122]),c_0_33]) ).
cnf(c_0_129,negated_conjecture,
multiplication(c(esk6_0),addition(esk6_0,X1)) = multiplication(c(esk6_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_123]),c_0_82]) ).
cnf(c_0_130,negated_conjecture,
multiplication(esk6_0,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]) ).
cnf(c_0_131,negated_conjecture,
multiplication(c(esk5_0),esk5_0) = zero,
inference(spm,[status(thm)],[c_0_87,c_0_44]) ).
cnf(c_0_132,negated_conjecture,
multiplication(esk5_0,multiplication(c(esk6_0),X1)) = multiplication(esk5_0,X1),
inference(spm,[status(thm)],[c_0_57,c_0_88]) ).
cnf(c_0_133,negated_conjecture,
multiplication(c(esk6_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_121]) ).
cnf(c_0_134,negated_conjecture,
addition(multiplication(c(esk6_0),X1),multiplication(X2,addition(esk6_0,X1))) = multiplication(addition(c(esk6_0),X2),addition(esk6_0,X1)),
inference(spm,[status(thm)],[c_0_42,c_0_129]) ).
cnf(c_0_135,negated_conjecture,
multiplication(esk6_0,addition(X1,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero))) = multiplication(esk6_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_130]),c_0_31]) ).
cnf(c_0_136,negated_conjecture,
multiplication(c(esk5_0),addition(esk5_0,X1)) = multiplication(c(esk5_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_131]),c_0_82]) ).
cnf(c_0_137,negated_conjecture,
multiplication(esk5_0,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_126]) ).
cnf(c_0_138,plain,
( addition(X2,X1) != X2
| leq(X1,X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_33]) ).
cnf(c_0_139,negated_conjecture,
addition(esk6_0,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)) = esk6_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(spm,[status(thm)],[c_0_134,c_0_135]),c_0_133]),c_0_46]),c_0_82]),c_0_33]),c_0_40]),c_0_43]) ).
cnf(c_0_140,negated_conjecture,
addition(multiplication(c(esk5_0),X1),multiplication(X2,addition(esk5_0,X1))) = multiplication(addition(c(esk5_0),X2),addition(esk5_0,X1)),
inference(spm,[status(thm)],[c_0_42,c_0_136]) ).
cnf(c_0_141,negated_conjecture,
multiplication(esk5_0,addition(X1,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero))) = multiplication(esk5_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_137]),c_0_31]) ).
cnf(c_0_142,negated_conjecture,
leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),esk6_0),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_143,negated_conjecture,
addition(esk5_0,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)) = esk5_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(spm,[status(thm)],[c_0_140,c_0_141]),c_0_125]),c_0_60]),c_0_82]),c_0_33]),c_0_55]),c_0_43]) ).
cnf(c_0_144,negated_conjecture,
( ~ leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),esk5_0)
| leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),zero) ),
inference(spm,[status(thm)],[c_0_72,c_0_142]) ).
cnf(c_0_145,negated_conjecture,
leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),esk5_0),
inference(spm,[status(thm)],[c_0_138,c_0_143]) ).
cnf(c_0_146,plain,
( ~ leq(X3,X2)
| ~ leq(X3,X1)
| ~ leq(esk2_3(X1,X2,X3),X3)
| ismeet(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_147,negated_conjecture,
leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_145])]) ).
cnf(c_0_148,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_100]),c_0_100])]),c_0_107]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE033+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:40:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.45 Running first-order theorem proving
% 0.10/0.45 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.63/6.16 % Version: 3.5.1
% 38.63/6.16 % Preprocessing class: FSMSSMSSSSSNFFN.
% 38.63/6.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 38.63/6.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 38.63/6.16 % Starting new_bool_3 with 300s (1) cores
% 38.63/6.16 % Starting new_bool_1 with 300s (1) cores
% 38.63/6.16 % Starting sh5l with 300s (1) cores
% 38.63/6.16 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1383605 completed with status 0
% 38.63/6.16 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 38.63/6.16 % Preprocessing class: FSMSSMSSSSSNFFN.
% 38.63/6.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 38.63/6.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 38.63/6.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 38.63/6.16 % No SInE strategy applied
% 38.63/6.16 % Search class: FGUSM-FFMS32-SFFFFFNN
% 38.63/6.16 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 38.63/6.16 % Starting SubtermCWHack with 136s (1) cores
% 38.63/6.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 38.63/6.16 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 38.63/6.16 % Starting new_bool_3 with 136s (1) cores
% 38.63/6.16 % Starting new_bool_1 with 136s (1) cores
% 38.63/6.16 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with pid 1383613 completed with status 0
% 38.63/6.16 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI
% 38.63/6.16 % Preprocessing class: FSMSSMSSSSSNFFN.
% 38.63/6.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 38.63/6.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 38.63/6.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 38.63/6.16 % No SInE strategy applied
% 38.63/6.16 % Search class: FGUSM-FFMS32-SFFFFFNN
% 38.63/6.16 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 38.63/6.16 % Starting SubtermCWHack with 136s (1) cores
% 38.63/6.16 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 38.63/6.16 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2SI with 136s (1) cores
% 38.63/6.16 % Preprocessing time : 0.002 s
% 38.63/6.16 % Presaturation interreduction done
% 38.63/6.16
% 38.63/6.16 % Proof found!
% 38.63/6.16 % SZS status Theorem
% 38.63/6.16 % SZS output start CNFRefutation
% See solution above
% 38.63/6.16 % Parsed axioms : 19
% 38.63/6.16 % Removed by relevancy pruning/SinE : 0
% 38.63/6.16 % Initial clauses : 38
% 38.63/6.16 % Removed in clause preprocessing : 0
% 38.63/6.16 % Initial clauses in saturation : 38
% 38.63/6.16 % Processed clauses : 16055
% 38.63/6.16 % ...of these trivial : 717
% 38.63/6.16 % ...subsumed : 12869
% 38.63/6.16 % ...remaining for further processing : 2469
% 38.63/6.16 % Other redundant clauses eliminated : 766
% 38.63/6.16 % Clauses deleted for lack of memory : 0
% 38.63/6.16 % Backward-subsumed : 43
% 38.63/6.16 % Backward-rewritten : 287
% 38.63/6.16 % Generated clauses : 294646
% 38.63/6.16 % ...of the previous two non-redundant : 239798
% 38.63/6.16 % ...aggressively subsumed : 0
% 38.63/6.16 % Contextual simplify-reflections : 67
% 38.63/6.16 % Paramodulations : 293814
% 38.63/6.16 % Factorizations : 66
% 38.63/6.16 % NegExts : 0
% 38.63/6.16 % Equation resolutions : 766
% 38.63/6.16 % Disequality decompositions : 0
% 38.63/6.16 % Total rewrite steps : 478827
% 38.63/6.16 % ...of those cached : 414643
% 38.63/6.16 % Propositional unsat checks : 0
% 38.63/6.16 % Propositional check models : 0
% 38.63/6.16 % Propositional check unsatisfiable : 0
% 38.63/6.16 % Propositional clauses : 0
% 38.63/6.16 % Propositional clauses after purity: 0
% 38.63/6.16 % Propositional unsat core size : 0
% 38.63/6.16 % Propositional preprocessing time : 0.000
% 38.63/6.16 % Propositional encoding time : 0.000
% 38.63/6.16 % Propositional solver time : 0.000
% 38.63/6.16 % Success case prop preproc time : 0.000
% 38.63/6.16 % Success case prop encoding time : 0.000
% 38.63/6.16 % Success case prop solver time : 0.000
% 38.63/6.16 % Current number of processed clauses : 2100
% 38.63/6.16 % Positive orientable unit clauses : 572
% 38.63/6.16 % Positive unorientable unit clauses: 24
% 38.63/6.16 % Negative unit clauses : 1
% 38.63/6.16 % Non-unit-clauses : 1503
% 38.63/6.16 % Current number of unprocessed clauses: 223028
% 38.63/6.16 % ...number of literals in the above : 521058
% 38.63/6.16 % Current number of archived formulas : 0
% 38.63/6.16 % Current number of archived clauses : 368
% 38.63/6.16 % Clause-clause subsumption calls (NU) : 623834
% 38.63/6.16 % Rec. Clause-clause subsumption calls : 529363
% 38.63/6.16 % Non-unit clause-clause subsumptions : 12702
% 38.63/6.16 % Unit Clause-clause subsumption calls : 21760
% 38.63/6.16 % Rewrite failures with RHS unbound : 0
% 38.63/6.16 % BW rewrite match attempts : 1981
% 38.63/6.16 % BW rewrite match successes : 499
% 38.63/6.16 % Condensation attempts : 0
% 38.63/6.16 % Condensation successes : 0
% 38.63/6.16 % Termbank termtop insertions : 6216690
% 38.63/6.16 % Search garbage collected termcells : 480
% 38.63/6.16
% 38.63/6.16 % -------------------------------------------------
% 38.63/6.16 % User time : 5.236 s
% 38.63/6.16 % System time : 0.233 s
% 38.63/6.16 % Total time : 5.469 s
% 38.63/6.16 % Maximum resident set size: 3396 pages
% 38.63/6.16
% 38.63/6.16 % -------------------------------------------------
% 38.63/6.16 % User time : 26.142 s
% 38.63/6.16 % System time : 1.039 s
% 38.63/6.16 % Total time : 27.181 s
% 38.63/6.16 % Maximum resident set size: 4608 pages
% 38.63/6.16 % E exiting
%------------------------------------------------------------------------------