%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE009+3 : 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 : n012.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 04:35:27 PM UTC 2026
% Result : Theorem 9.43s 6.28s
% Output : CNFRefutation 9.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 103 ( 74 unt; 0 def)
% Number of atoms : 163 ( 90 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 105 ( 45 ~; 39 |; 14 &)
% ( 4 <=>; 3 =>; 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 : 129 ( 5 sgn 58 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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(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(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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(c_0_15,negated_conjecture,
~ ! [X4,X5] :
( ( test(X5)
& test(X4) )
=> ( leq(one,addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))))
& leq(addition(addition(addition(multiplication(X4,X5),multiplication(X4,c(X5))),multiplication(c(X4),X5)),multiplication(c(X4),c(X5))),one) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_16,plain,
! [X39,X40,X41] : addition(X41,addition(X40,X39)) = addition(addition(X41,X40),X39),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_17,plain,
! [X43] : addition(X43,X43) = X43,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_18,plain,
! [X65,X66] :
( ( c(X65) != X66
| complement(X65,X66)
| ~ test(X65) )
& ( ~ complement(X65,X66)
| c(X65) = X66
| ~ test(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_19,plain,
! [X59,X61,X62] :
( ( ~ test(X59)
| complement(esk1_1(X59),X59) )
& ( ~ complement(X62,X61)
| test(X61) ) ),
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_20,negated_conjecture,
( test(esk3_0)
& test(esk2_0)
& ( ~ leq(one,addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_21,plain,
! [X57,X58] :
( ( ~ leq(X57,X58)
| addition(X57,X58) = X58 )
& ( addition(X57,X58) != X58
| leq(X57,X58) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_22,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X63,X64] :
( ( multiplication(X63,X64) = zero
| ~ complement(X64,X63) )
& ( multiplication(X64,X63) = zero
| ~ complement(X64,X63) )
& ( addition(X63,X64) = one
| ~ complement(X64,X63) )
& ( multiplication(X63,X64) != zero
| multiplication(X64,X63) != zero
| addition(X63,X64) != one
| complement(X64,X63) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_26,plain,
! [X37,X38] : addition(X37,X38) = addition(X38,X37),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_27,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_32,negated_conjecture,
test(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,negated_conjecture,
complement(esk1_1(esk3_0),esk3_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_39,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,negated_conjecture,
complement(esk2_0,c(esk2_0)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
complement(esk1_1(esk2_0),esk2_0),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_42,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,plain,
( complement(X1,X2)
| addition(X1,X2) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,negated_conjecture,
addition(esk3_0,esk1_1(esk3_0)) = one,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,negated_conjecture,
multiplication(esk3_0,esk1_1(esk3_0)) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_46,negated_conjecture,
multiplication(esk1_1(esk3_0),esk3_0) = zero,
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
fof(c_0_47,plain,
! [X49,X50,X51] : multiplication(X49,addition(X50,X51)) = addition(multiplication(X49,X50),multiplication(X49,X51)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_48,negated_conjecture,
complement(esk3_0,c(esk3_0)),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
fof(c_0_49,plain,
! [X47] : multiplication(X47,one) = X47,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_50,plain,
leq(X1,addition(X2,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_34]) ).
cnf(c_0_51,negated_conjecture,
addition(esk2_0,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_40]),c_0_34]) ).
fof(c_0_52,plain,
! [X52,X53,X54] : multiplication(addition(X52,X53),X54) = addition(multiplication(X52,X54),multiplication(X53,X54)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_53,negated_conjecture,
addition(esk2_0,esk1_1(esk2_0)) = one,
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
fof(c_0_54,plain,
! [X48] : multiplication(one,X48) = X48,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_55,negated_conjecture,
( c(esk3_0) = X1
| ~ complement(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_28]) ).
cnf(c_0_56,negated_conjecture,
complement(esk3_0,esk1_1(esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]) ).
fof(c_0_57,plain,
! [X44,X45,X46] : multiplication(X44,multiplication(X45,X46)) = multiplication(multiplication(X44,X45),X46),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_58,plain,
! [X56] : multiplication(zero,X56) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_59,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_60,negated_conjecture,
( ~ leq(one,addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))))
| ~ leq(addition(addition(addition(multiplication(esk2_0,esk3_0),multiplication(esk2_0,c(esk3_0))),multiplication(c(esk2_0),esk3_0)),multiplication(c(esk2_0),c(esk3_0))),one) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_61,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_62,negated_conjecture,
addition(esk3_0,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_48]),c_0_34]) ).
cnf(c_0_63,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_64,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_65,negated_conjecture,
leq(c(esk2_0),one),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_66,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_67,negated_conjecture,
addition(one,esk2_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_53]),c_0_34]) ).
cnf(c_0_68,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_69,negated_conjecture,
addition(esk3_0,addition(esk1_1(esk3_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_22,c_0_44]) ).
cnf(c_0_70,negated_conjecture,
esk1_1(esk3_0) = c(esk3_0),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_71,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_72,negated_conjecture,
multiplication(c(esk2_0),esk2_0) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_73,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_74,plain,
! [X42] : addition(X42,zero) = X42,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_75,negated_conjecture,
test(c(esk3_0)),
inference(spm,[status(thm)],[c_0_59,c_0_48]) ).
cnf(c_0_76,negated_conjecture,
( ~ leq(one,addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),c(esk3_0))))))
| ~ leq(addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),c(esk3_0))))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_34]),c_0_34]),c_0_22]),c_0_22]),c_0_22]),c_0_22]) ).
cnf(c_0_77,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_34]),c_0_22]) ).
cnf(c_0_78,negated_conjecture,
addition(multiplication(X1,esk3_0),multiplication(X1,c(esk3_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_79,negated_conjecture,
addition(one,c(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_34]) ).
cnf(c_0_80,negated_conjecture,
addition(X1,multiplication(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_68]) ).
cnf(c_0_81,negated_conjecture,
addition(esk3_0,addition(c(esk3_0),X1)) = addition(one,X1),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_82,negated_conjecture,
addition(multiplication(esk2_0,X1),multiplication(c(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_51]),c_0_68]) ).
cnf(c_0_83,negated_conjecture,
multiplication(c(esk2_0),multiplication(esk2_0,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_84,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_85,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_44]),c_0_34]) ).
cnf(c_0_86,plain,
( addition(X1,X2) = one
| ~ complement(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_87,negated_conjecture,
complement(c(esk3_0),c(c(esk3_0))),
inference(spm,[status(thm)],[c_0_31,c_0_75]) ).
cnf(c_0_88,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),c(esk3_0))))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),addition(multiplication(esk2_0,c(esk3_0)),multiplication(c(esk2_0),c(esk3_0))))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77]),c_0_77]) ).
cnf(c_0_89,negated_conjecture,
addition(multiplication(X1,esk3_0),addition(X2,multiplication(X1,c(esk3_0)))) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_90,negated_conjecture,
addition(X1,multiplication(c(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_79]),c_0_68]),c_0_68]) ).
cnf(c_0_91,negated_conjecture,
addition(X1,addition(X2,addition(multiplication(esk2_0,X1),multiplication(esk2_0,X2)))) = addition(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_80]),c_0_61]) ).
cnf(c_0_92,negated_conjecture,
addition(multiplication(X1,esk3_0),addition(multiplication(X1,c(esk3_0)),multiplication(X1,X2))) = addition(X1,multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_81]),c_0_61]),c_0_63]),c_0_61]) ).
cnf(c_0_93,negated_conjecture,
multiplication(esk2_0,multiplication(esk2_0,X1)) = multiplication(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
cnf(c_0_94,negated_conjecture,
addition(X1,multiplication(X1,esk3_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_85]),c_0_63]),c_0_63]) ).
cnf(c_0_95,negated_conjecture,
addition(c(esk3_0),c(c(esk3_0))) = one,
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_96,negated_conjecture,
( ~ leq(one,addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),c(esk3_0))))
| ~ leq(addition(multiplication(esk2_0,esk3_0),addition(multiplication(c(esk2_0),esk3_0),c(esk3_0))),one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_82]),c_0_82]) ).
cnf(c_0_97,negated_conjecture,
addition(multiplication(c(esk2_0),esk3_0),c(esk3_0)) = addition(c(esk2_0),c(esk3_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_34]) ).
cnf(c_0_98,negated_conjecture,
addition(multiplication(esk2_0,esk3_0),c(esk3_0)) = addition(esk2_0,c(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94]),c_0_34]),c_0_34]) ).
cnf(c_0_99,negated_conjecture,
addition(esk2_0,addition(c(esk2_0),X1)) = addition(one,X1),
inference(spm,[status(thm)],[c_0_22,c_0_51]) ).
cnf(c_0_100,negated_conjecture,
addition(one,c(esk3_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_95]),c_0_34]) ).
cnf(c_0_101,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_102,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_77]),c_0_98]),c_0_77]),c_0_99]),c_0_100]),c_0_101]),c_0_97]),c_0_77]),c_0_98]),c_0_77]),c_0_99]),c_0_100]),c_0_101])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : KLE009+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.06/0.25 % Computer : n012.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Mon May 4 20:25:16 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.26 % start to proof: theBenchmark
% 9.43/6.28 % Version : CSE_E---1.7
% 9.43/6.28 % Problem : theBenchmark.p
% 9.43/6.28 % SZS status Theorem for theBenchmark.p
% 9.43/6.28 % SZS output start CNFRefutation
% See solution above
% 9.54/6.32 % Total time : 4.369s
%------------------------------------------------------------------------------