%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE028+4 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 11.03s 7.17s
% Output : CNFRefutation 11.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 54 unt; 0 def)
% Number of atoms : 169 ( 79 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 135 ( 60 ~; 52 |; 15 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 110 ( 1 sgn 56 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6,X7,X8,X9] :
( ( test(X8)
& test(X9) )
=> ( leq(addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7)))),addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7)))))
& leq(addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7)))),addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(test_3,axiom,
! [X4,X5] :
( test(X4)
=> ( c(X4) = X5
<=> complement(X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(test_2,axiom,
! [X4,X5] :
( complement(X5,X4)
<=> ( multiplication(X4,X5) = zero
& multiplication(X5,X4) = zero
& addition(X4,X5) = one ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(test_deMorgan1,axiom,
! [X4,X5] :
( ( test(X4)
& test(X5) )
=> c(addition(X4,X5)) = multiplication(c(X4),c(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+2.ax',test_deMorgan1) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(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(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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_11,negated_conjecture,
~ ! [X4,X5,X6,X7,X8,X9] :
( ( test(X8)
& test(X9) )
=> ( leq(addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7)))),addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7)))))
& leq(addition(multiplication(X9,addition(multiplication(X8,X4),multiplication(c(X8),X6))),multiplication(c(X9),addition(multiplication(X8,X5),multiplication(c(X8),X7)))),addition(multiplication(X8,addition(multiplication(X9,X4),multiplication(c(X9),X5))),multiplication(c(X8),addition(multiplication(X9,X6),multiplication(c(X9),X7))))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_12,plain,
! [X71,X73,X74] :
( ( ~ test(X71)
| complement(esk1_1(X71),X71) )
& ( ~ complement(X74,X73)
| test(X73) ) ),
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_13,negated_conjecture,
( test(esk6_0)
& test(esk7_0)
& ( ~ leq(addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))),addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))))
| ~ leq(addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))),addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0))))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_14,plain,
! [X77,X78] :
( ( c(X77) != X78
| complement(X77,X78)
| ~ test(X77) )
& ( ~ complement(X77,X78)
| c(X77) = X78
| ~ test(X77) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_15,plain,
! [X75,X76] :
( ( multiplication(X75,X76) = zero
| ~ complement(X76,X75) )
& ( multiplication(X76,X75) = zero
| ~ complement(X76,X75) )
& ( addition(X75,X76) = one
| ~ complement(X76,X75) )
& ( multiplication(X75,X76) != zero
| multiplication(X76,X75) != zero
| addition(X75,X76) != one
| complement(X76,X75) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_16,plain,
! [X49,X50] : addition(X49,X50) = addition(X50,X49),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_17,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
test(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
complement(esk1_1(esk7_0),esk7_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,plain,
( complement(X1,X2)
| addition(X1,X2) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
addition(esk7_0,esk1_1(esk7_0)) = one,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
multiplication(esk7_0,esk1_1(esk7_0)) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
multiplication(esk1_1(esk7_0),esk7_0) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_32,negated_conjecture,
test(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_33,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,negated_conjecture,
complement(esk7_0,c(esk7_0)),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_35,negated_conjecture,
( c(esk7_0) = X1
| ~ complement(esk7_0,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_36,negated_conjecture,
complement(esk7_0,esk1_1(esk7_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_37,plain,
( addition(X1,X2) = one
| ~ complement(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_38,negated_conjecture,
complement(esk1_1(esk6_0),esk6_0),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
test(c(esk7_0)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
esk1_1(esk7_0) = c(esk7_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
addition(esk6_0,esk1_1(esk6_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_21]) ).
cnf(c_0_42,negated_conjecture,
multiplication(esk6_0,esk1_1(esk6_0)) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
multiplication(esk1_1(esk6_0),esk6_0) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
fof(c_0_44,plain,
! [X80,X81] :
( ~ test(X80)
| ~ test(X81)
| c(addition(X80,X81)) = multiplication(c(X80),c(X81)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan1])]) ).
cnf(c_0_45,negated_conjecture,
( c(c(esk7_0)) = X1
| ~ complement(c(esk7_0),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
complement(c(esk7_0),esk7_0),
inference(rw,[status(thm)],[c_0_23,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
complement(esk6_0,c(esk6_0)),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_48,negated_conjecture,
( c(esk6_0) = X1
| ~ complement(esk6_0,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_49,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_28,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_50,plain,
( c(addition(X1,X2)) = multiplication(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,negated_conjecture,
c(c(esk7_0)) = esk7_0,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
test(c(esk6_0)),
inference(spm,[status(thm)],[c_0_33,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
esk1_1(esk6_0) = c(esk6_0),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( c(addition(X1,c(esk7_0))) = multiplication(c(X1),esk7_0)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_39]),c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( c(c(esk6_0)) = X1
| ~ complement(c(esk6_0),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
complement(c(esk6_0),esk6_0),
inference(rw,[status(thm)],[c_0_38,c_0_53]) ).
fof(c_0_57,plain,
! [X61,X62,X63] : multiplication(X61,addition(X62,X63)) = addition(multiplication(X61,X62),multiplication(X61,X63)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_58,plain,
! [X51,X52,X53] : addition(X53,addition(X52,X51)) = addition(addition(X53,X52),X51),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_59,negated_conjecture,
c(addition(c(esk6_0),c(esk7_0))) = multiplication(c(c(esk6_0)),esk7_0),
inference(spm,[status(thm)],[c_0_54,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
c(c(esk6_0)) = esk6_0,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
( ~ leq(addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0)))),addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))))
| ~ leq(addition(multiplication(esk7_0,addition(multiplication(esk6_0,esk2_0),multiplication(c(esk6_0),esk4_0))),multiplication(c(esk7_0),addition(multiplication(esk6_0,esk3_0),multiplication(c(esk6_0),esk5_0)))),addition(multiplication(esk6_0,addition(multiplication(esk7_0,esk2_0),multiplication(c(esk7_0),esk3_0))),multiplication(c(esk6_0),addition(multiplication(esk7_0,esk4_0),multiplication(c(esk7_0),esk5_0))))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_62,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
fof(c_0_64,plain,
! [X56,X57,X58] : multiplication(X56,multiplication(X57,X58)) = multiplication(multiplication(X56,X57),X58),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_65,plain,
( c(addition(X1,X2)) = multiplication(c(X2),c(X1))
| ~ test(X1)
| ~ test(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_21]) ).
cnf(c_0_66,negated_conjecture,
c(addition(c(esk6_0),c(esk7_0))) = multiplication(esk6_0,esk7_0),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,negated_conjecture,
( c(addition(X1,esk6_0)) = multiplication(c(X1),c(esk6_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_32]) ).
cnf(c_0_68,negated_conjecture,
( ~ leq(addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))),addition(multiplication(esk7_0,multiplication(esk6_0,esk2_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))))
| ~ leq(addition(multiplication(esk7_0,multiplication(esk6_0,esk2_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))),addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),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(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_61,c_0_62]),c_0_62]),c_0_63]),c_0_62]),c_0_62]),c_0_63]),c_0_62]),c_0_62]),c_0_63]),c_0_62]),c_0_62]),c_0_63]) ).
cnf(c_0_69,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_21]),c_0_63]) ).
cnf(c_0_70,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_71,negated_conjecture,
multiplication(esk7_0,esk6_0) = multiplication(esk6_0,esk7_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_65,c_0_66]),c_0_51]),c_0_60]),c_0_52]),c_0_39])]) ).
cnf(c_0_72,negated_conjecture,
c(addition(esk6_0,c(esk7_0))) = multiplication(esk7_0,c(esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_39]),c_0_21]),c_0_51]) ).
cnf(c_0_73,negated_conjecture,
( c(addition(X1,esk7_0)) = multiplication(c(X1),c(esk7_0))
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_18]) ).
cnf(c_0_74,negated_conjecture,
( ~ leq(addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))),addition(multiplication(esk7_0,multiplication(esk6_0,esk2_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))))
| ~ leq(addition(multiplication(esk7_0,multiplication(esk6_0,esk2_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))),addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_69]) ).
cnf(c_0_75,negated_conjecture,
multiplication(esk7_0,multiplication(esk6_0,X1)) = multiplication(esk6_0,multiplication(esk7_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_70]) ).
cnf(c_0_76,negated_conjecture,
multiplication(esk7_0,c(esk6_0)) = multiplication(c(esk6_0),esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_72]),c_0_51]),c_0_39]),c_0_32])]) ).
cnf(c_0_77,negated_conjecture,
c(addition(esk6_0,esk7_0)) = multiplication(c(esk6_0),c(esk7_0)),
inference(spm,[status(thm)],[c_0_73,c_0_32]) ).
cnf(c_0_78,negated_conjecture,
c(addition(c(esk6_0),esk7_0)) = multiplication(c(c(esk6_0)),c(esk7_0)),
inference(spm,[status(thm)],[c_0_73,c_0_52]) ).
cnf(c_0_79,negated_conjecture,
( ~ leq(addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))),addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))))
| ~ leq(addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(esk7_0,multiplication(c(esk6_0),esk4_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))),addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75]),c_0_75]) ).
cnf(c_0_80,negated_conjecture,
multiplication(esk7_0,multiplication(c(esk6_0),X1)) = multiplication(c(esk6_0),multiplication(esk7_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_76]),c_0_70]) ).
cnf(c_0_81,negated_conjecture,
multiplication(c(esk7_0),c(esk6_0)) = multiplication(c(esk6_0),c(esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_18]),c_0_21]),c_0_77]) ).
cnf(c_0_82,negated_conjecture,
c(addition(c(esk6_0),esk7_0)) = multiplication(esk6_0,c(esk7_0)),
inference(rw,[status(thm)],[c_0_78,c_0_60]) ).
fof(c_0_83,plain,
! [X69,X70] :
( ( ~ leq(X69,X70)
| addition(X69,X70) = X70 )
& ( addition(X69,X70) != X70
| leq(X69,X70) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_84,plain,
! [X55] : addition(X55,X55) = X55,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_85,negated_conjecture,
( ~ leq(addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))),addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))))
| ~ leq(addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk7_0),multiplication(c(esk6_0),esk5_0))))),addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_80]) ).
cnf(c_0_86,negated_conjecture,
multiplication(c(esk7_0),multiplication(c(esk6_0),X1)) = multiplication(c(esk6_0),multiplication(c(esk7_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_81]),c_0_70]) ).
cnf(c_0_87,negated_conjecture,
multiplication(c(esk7_0),esk6_0) = multiplication(esk6_0,c(esk7_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_82]),c_0_60]),c_0_52]),c_0_18])]) ).
cnf(c_0_88,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_89,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_90,negated_conjecture,
( ~ leq(addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))),addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))))
| ~ leq(addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(c(esk7_0),multiplication(esk6_0,esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0))))),addition(multiplication(esk6_0,multiplication(esk7_0,esk2_0)),addition(multiplication(esk6_0,multiplication(c(esk7_0),esk3_0)),addition(multiplication(c(esk6_0),multiplication(esk7_0,esk4_0)),multiplication(c(esk6_0),multiplication(c(esk7_0),esk5_0)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86]),c_0_86]) ).
cnf(c_0_91,negated_conjecture,
multiplication(c(esk7_0),multiplication(esk6_0,X1)) = multiplication(esk6_0,multiplication(c(esk7_0),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_87]),c_0_70]) ).
cnf(c_0_92,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_91]),c_0_92])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE028+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:26:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 11.03/7.17 % Version : CSE_E---1.7
% 11.03/7.17 % Problem : theBenchmark.p
% 11.03/7.17 % SZS status Theorem for theBenchmark.p
% 11.03/7.17 % SZS output start CNFRefutation
% See solution above
% 11.10/7.22 % Total time : 5.375s
%------------------------------------------------------------------------------