%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE033+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:35:33 PM UTC 2026
% Result : Theorem 27.53s 16.78s
% Output : CNFRefutation 27.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 132 ( 96 unt; 0 def)
% Number of atoms : 223 ( 107 equ)
% Maximal formula atoms : 20 ( 1 avg)
% Number of connectives : 149 ( 58 ~; 61 |; 22 &)
% ( 4 <=>; 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 : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 165 ( 7 sgn 69 !; 0 ?)
% 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] :
( ( test(X6)
& test(X5)
& ismeet(zero,X5,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)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
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)
<=> ( leq(X6,X4)
& leq(X6,X5)
& ! [X7] :
( ( leq(X7,X4)
& leq(X7,X5) )
=> leq(X7,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+3.ax',ismeet) ).
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_16,plain,
! [X76,X77] :
( ( c(X76) != X77
| complement(X76,X77)
| ~ test(X76) )
& ( ~ complement(X76,X77)
| c(X76) = X77
| ~ test(X76) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_17,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X6)
& test(X5)
& ismeet(zero,X5,X6) )
=> ismeet(zero,multiplication(X5,X4),multiplication(X6,X4)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_18,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,negated_conjecture,
( test(esk6_0)
& test(esk5_0)
& ismeet(zero,esk5_0,esk6_0)
& ~ ismeet(zero,multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_20,plain,
! [X74,X75] :
( ( multiplication(X74,X75) = zero
| ~ complement(X75,X74) )
& ( multiplication(X75,X74) = zero
| ~ complement(X75,X74) )
& ( addition(X74,X75) = one
| ~ complement(X75,X74) )
& ( multiplication(X74,X75) != zero
| multiplication(X75,X74) != zero
| addition(X74,X75) != one
| complement(X75,X74) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
cnf(c_0_21,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
test(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,plain,
! [X60,X61,X62] : multiplication(X60,addition(X61,X62)) = addition(multiplication(X60,X61),multiplication(X60,X62)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_24,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
complement(esk6_0,c(esk6_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
! [X53] : addition(X53,zero) = X53,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_27,plain,
! [X48,X49] : addition(X48,X49) = addition(X49,X48),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_28,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
multiplication(esk6_0,c(esk6_0)) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X58] : multiplication(X58,one) = X58,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_34,plain,
! [X63,X64,X65] : multiplication(addition(X63,X64),X65) = addition(multiplication(X63,X65),multiplication(X64,X65)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_35,plain,
! [X59] : multiplication(one,X59) = X59,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_36,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_37,plain,
! [X68,X69] :
( ( ~ leq(X68,X69)
| addition(X68,X69) = X69 )
& ( addition(X68,X69) != X69
| leq(X68,X69) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_38,negated_conjecture,
multiplication(esk6_0,addition(X1,c(esk6_0))) = multiplication(esk6_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_39,negated_conjecture,
addition(esk6_0,c(esk6_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_32]) ).
cnf(c_0_40,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,negated_conjecture,
complement(esk5_0,c(esk5_0)),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_44,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
multiplication(esk6_0,esk6_0) = esk6_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_46,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_32]) ).
cnf(c_0_47,negated_conjecture,
multiplication(esk5_0,c(esk5_0)) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_48,plain,
( leq(multiplication(X1,X2),multiplication(X3,X2))
| multiplication(addition(X1,X3),X2) != multiplication(X3,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_49,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_41,c_0_45]),c_0_46]) ).
fof(c_0_50,plain,
! [X55,X56,X57] : multiplication(X55,multiplication(X56,X57)) = multiplication(multiplication(X55,X56),X57),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_51,plain,
! [X50,X51,X52] : addition(X52,addition(X51,X50)) = addition(addition(X52,X51),X50),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_52,plain,
! [X54] : addition(X54,X54) = X54,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_53,negated_conjecture,
multiplication(esk5_0,addition(X1,c(esk5_0))) = multiplication(esk5_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_30]) ).
cnf(c_0_54,negated_conjecture,
addition(esk5_0,c(esk5_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_43]),c_0_32]) ).
cnf(c_0_55,negated_conjecture,
( leq(multiplication(X1,esk6_0),esk6_0)
| multiplication(addition(esk6_0,X1),esk6_0) != esk6_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_42]),c_0_42]) ).
cnf(c_0_56,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_58,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_59,negated_conjecture,
multiplication(esk5_0,esk5_0) = esk5_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_40]) ).
cnf(c_0_60,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_40]),c_0_32]) ).
fof(c_0_61,plain,
! [X79,X80,X81,X82,X83,X84,X85] :
( ( leq(X81,X79)
| ~ ismeet(X81,X79,X80) )
& ( leq(X81,X80)
| ~ ismeet(X81,X79,X80) )
& ( ~ leq(X82,X79)
| ~ leq(X82,X80)
| leq(X82,X81)
| ~ ismeet(X81,X79,X80) )
& ( leq(esk2_3(X83,X84,X85),X83)
| ~ leq(X85,X83)
| ~ leq(X85,X84)
| ismeet(X85,X83,X84) )
& ( leq(esk2_3(X83,X84,X85),X84)
| ~ leq(X85,X83)
| ~ leq(X85,X84)
| ismeet(X85,X83,X84) )
& ( ~ leq(esk2_3(X83,X84,X85),X85)
| ~ leq(X85,X83)
| ~ leq(X85,X84)
| ismeet(X85,X83,X84) ) ),
inference(distribute,[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_62,negated_conjecture,
( leq(multiplication(X1,esk6_0),esk6_0)
| multiplication(addition(X1,one),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_55,c_0_46]),c_0_56]),c_0_45]),c_0_56]),c_0_45]) ).
cnf(c_0_63,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
( leq(multiplication(X1,X2),multiplication(X1,X3))
| multiplication(X1,addition(X2,X3)) != multiplication(X1,X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_28]) ).
cnf(c_0_65,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_28,c_0_59]),c_0_32]),c_0_60]) ).
cnf(c_0_66,plain,
( leq(X1,X4)
| ~ leq(X1,X2)
| ~ leq(X1,X3)
| ~ ismeet(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,negated_conjecture,
ismeet(zero,esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_68,negated_conjecture,
( leq(multiplication(X1,esk6_0),esk6_0)
| multiplication(addition(one,X1),esk6_0) != esk6_0 ),
inference(spm,[status(thm)],[c_0_62,c_0_32]) ).
cnf(c_0_69,negated_conjecture,
addition(one,esk5_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_54]),c_0_32]) ).
cnf(c_0_70,negated_conjecture,
( leq(multiplication(esk5_0,X1),esk5_0)
| multiplication(esk5_0,addition(X1,one)) != esk5_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_59]),c_0_59]) ).
cnf(c_0_71,negated_conjecture,
( leq(X1,zero)
| ~ leq(X1,esk6_0)
| ~ leq(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
leq(multiplication(esk5_0,esk6_0),esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_42])]) ).
cnf(c_0_73,negated_conjecture,
( leq(multiplication(esk5_0,X1),esk5_0)
| multiplication(esk5_0,addition(one,X1)) != esk5_0 ),
inference(spm,[status(thm)],[c_0_70,c_0_32]) ).
cnf(c_0_74,negated_conjecture,
addition(one,esk6_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_39]),c_0_32]) ).
cnf(c_0_75,negated_conjecture,
( leq(multiplication(esk5_0,esk6_0),zero)
| ~ leq(multiplication(esk5_0,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
leq(multiplication(esk5_0,esk6_0),esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_40])]) ).
cnf(c_0_77,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_78,negated_conjecture,
leq(multiplication(esk5_0,esk6_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]) ).
cnf(c_0_79,negated_conjecture,
multiplication(esk5_0,esk6_0) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_30]) ).
cnf(c_0_80,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_81,negated_conjecture,
multiplication(esk5_0,addition(esk6_0,X1)) = multiplication(esk5_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_79]),c_0_80]) ).
cnf(c_0_82,negated_conjecture,
multiplication(esk5_0,c(esk6_0)) = esk5_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_39]),c_0_40]) ).
cnf(c_0_83,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_46,c_0_82]),c_0_32]),c_0_69]),c_0_42]),c_0_32]) ).
cnf(c_0_84,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_85,plain,
! [X67] : multiplication(zero,X67) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_86,plain,
( leq(esk2_3(X1,X2,X3),X1)
| ismeet(X3,X1,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_87,plain,
leq(zero,X1),
inference(spm,[status(thm)],[c_0_44,c_0_80]) ).
cnf(c_0_88,plain,
( leq(esk2_3(X1,X2,X3),X2)
| ismeet(X3,X1,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_89,negated_conjecture,
multiplication(esk6_0,esk5_0) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_83]),c_0_29]) ).
cnf(c_0_90,negated_conjecture,
multiplication(c(esk5_0),esk5_0) = zero,
inference(spm,[status(thm)],[c_0_84,c_0_43]) ).
cnf(c_0_91,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_92,negated_conjecture,
~ ismeet(zero,multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_93,plain,
( ismeet(zero,X1,X2)
| leq(esk2_3(X1,X2,zero),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_87])]) ).
cnf(c_0_94,plain,
( ismeet(zero,X1,X2)
| leq(esk2_3(X1,X2,zero),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_87]),c_0_87])]) ).
cnf(c_0_95,negated_conjecture,
multiplication(esk6_0,addition(esk5_0,X1)) = multiplication(esk6_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_89]),c_0_80]) ).
cnf(c_0_96,negated_conjecture,
multiplication(c(esk5_0),multiplication(esk5_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_90]),c_0_91]) ).
cnf(c_0_97,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_92,c_0_93]) ).
cnf(c_0_98,plain,
( leq(X1,X2)
| addition(X2,X1) != X2 ),
inference(spm,[status(thm)],[c_0_44,c_0_32]) ).
cnf(c_0_99,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_92,c_0_94]) ).
cnf(c_0_100,negated_conjecture,
multiplication(esk6_0,c(esk5_0)) = esk6_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_54]),c_0_40]) ).
cnf(c_0_101,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_28,c_0_96]),c_0_80]) ).
cnf(c_0_102,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_77,c_0_97]),c_0_32]) ).
fof(c_0_103,plain,
! [X66] : multiplication(X66,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_104,plain,
( leq(multiplication(X1,X2),multiplication(X1,X3))
| multiplication(X1,addition(X3,X2)) != multiplication(X1,X3) ),
inference(spm,[status(thm)],[c_0_98,c_0_28]) ).
cnf(c_0_105,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_77,c_0_99]),c_0_32]) ).
cnf(c_0_106,negated_conjecture,
multiplication(c(esk6_0),esk6_0) = zero,
inference(spm,[status(thm)],[c_0_84,c_0_25]) ).
cnf(c_0_107,negated_conjecture,
multiplication(esk6_0,multiplication(c(esk5_0),X1)) = multiplication(esk6_0,X1),
inference(spm,[status(thm)],[c_0_56,c_0_100]) ).
cnf(c_0_108,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_101,c_0_102]),c_0_96]) ).
cnf(c_0_109,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_110,negated_conjecture,
leq(multiplication(X1,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)),multiplication(X1,multiplication(esk6_0,esk4_0))),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
multiplication(c(esk6_0),multiplication(esk6_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_106]),c_0_91]) ).
cnf(c_0_112,negated_conjecture,
multiplication(esk5_0,multiplication(esk6_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_79]),c_0_91]) ).
cnf(c_0_113,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_28,c_0_106]),c_0_80]) ).
cnf(c_0_114,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_107,c_0_108]),c_0_109]) ).
cnf(c_0_115,negated_conjecture,
leq(multiplication(c(esk6_0),esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)),zero),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
leq(multiplication(esk5_0,esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero)),zero),
inference(spm,[status(thm)],[c_0_110,c_0_112]) ).
cnf(c_0_117,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_41,c_0_113]) ).
cnf(c_0_118,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_28,c_0_114]),c_0_30]) ).
cnf(c_0_119,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_77,c_0_115]),c_0_30]) ).
cnf(c_0_120,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_28,c_0_90]),c_0_80]) ).
cnf(c_0_121,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_77,c_0_116]),c_0_30]) ).
cnf(c_0_122,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_117,c_0_118]),c_0_119]),c_0_45]),c_0_80]),c_0_32]),c_0_39]),c_0_42]) ).
cnf(c_0_123,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_41,c_0_120]) ).
cnf(c_0_124,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_28,c_0_121]),c_0_30]) ).
cnf(c_0_125,negated_conjecture,
leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),esk6_0),
inference(spm,[status(thm)],[c_0_98,c_0_122]) ).
cnf(c_0_126,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_123,c_0_124]),c_0_108]),c_0_59]),c_0_80]),c_0_32]),c_0_54]),c_0_42]) ).
cnf(c_0_127,negated_conjecture,
( leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),zero)
| ~ leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),esk5_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_125]) ).
cnf(c_0_128,negated_conjecture,
leq(esk2_3(multiplication(esk5_0,esk4_0),multiplication(esk6_0,esk4_0),zero),esk5_0),
inference(spm,[status(thm)],[c_0_98,c_0_126]) ).
cnf(c_0_129,plain,
( ismeet(X3,X1,X2)
| ~ leq(esk2_3(X1,X2,X3),X3)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_130,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_127,c_0_128])]) ).
cnf(c_0_131,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_129,c_0_130]),c_0_87]),c_0_87])]),c_0_92]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE033+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n011.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 20:26:02 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 27.53/16.78 % Version : CSE_E---1.7
% 27.53/16.78 % Problem : theBenchmark.p
% 27.53/16.78 % SZS status Theorem for theBenchmark.p
% 27.53/16.78 % SZS output start CNFRefutation
% See solution above
% 27.63/16.89 % Total time : 12.395s
%------------------------------------------------------------------------------