%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE027+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 : n006.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 04:35:32 PM UTC 2026
% Result : Theorem 1.58s 1.83s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 73 ( 40 unt; 0 def)
% Number of atoms : 140 ( 62 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 117 ( 50 ~; 44 |; 15 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 94 ( 3 sgn 52 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(goals,conjecture,
! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X8) )
=> ( leq(addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6)),addition(multiplication(X7,X4),multiplication(c(X7),X6)))
& leq(addition(multiplication(X7,X4),multiplication(c(X7),X6)),addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6))) ) ),
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_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(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
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(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(c_0_12,plain,
! [X75,X76] :
( ( c(X75) != X76
| complement(X75,X76)
| ~ test(X75) )
& ( ~ complement(X75,X76)
| c(X75) = X76
| ~ test(X75) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X8) )
=> ( leq(addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6)),addition(multiplication(X7,X4),multiplication(c(X7),X6)))
& leq(addition(multiplication(X7,X4),multiplication(c(X7),X6)),addition(multiplication(X7,addition(multiplication(X7,X4),multiplication(c(X7),X5))),multiplication(c(X7),X6))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_14,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,negated_conjecture,
( test(esk5_0)
& test(esk6_0)
& ( ~ leq(addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)))
| ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X69,X71,X72] :
( ( ~ test(X69)
| complement(esk1_1(X69),X69) )
& ( ~ complement(X72,X71)
| test(X71) ) ),
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_17,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X73,X74] :
( ( multiplication(X73,X74) = zero
| ~ complement(X74,X73) )
& ( multiplication(X74,X73) = zero
| ~ complement(X74,X73) )
& ( addition(X73,X74) = one
| ~ complement(X74,X73) )
& ( multiplication(X73,X74) != zero
| multiplication(X74,X73) != zero
| addition(X73,X74) != one
| complement(X74,X73) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_20,plain,
! [X47,X48] : addition(X47,X48) = addition(X48,X47),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_21,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
complement(esk5_0,c(esk5_0)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
test(c(esk5_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( complement(X2,X1)
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero
| addition(X1,X2) != one ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( addition(X1,X2) = one
| ~ complement(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
complement(esk1_1(esk5_0),esk5_0),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,negated_conjecture,
complement(c(esk5_0),c(c(esk5_0))),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_33,plain,
( c(X1) = X2
| ~ complement(X1,X2)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,plain,
( complement(X1,X2)
| addition(X1,X2) != one
| multiplication(X1,X2) != zero
| multiplication(X2,X1) != zero ),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_35,negated_conjecture,
addition(esk5_0,esk1_1(esk5_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24]) ).
cnf(c_0_36,negated_conjecture,
multiplication(esk5_0,esk1_1(esk5_0)) = zero,
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
multiplication(esk1_1(esk5_0),esk5_0) = zero,
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
fof(c_0_38,plain,
! [X78,X79] :
( ~ test(X78)
| ~ test(X79)
| c(addition(X78,X79)) = multiplication(c(X78),c(X79)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_deMorgan1])]) ).
fof(c_0_39,plain,
! [X53] : addition(X53,X53) = X53,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_40,negated_conjecture,
test(c(c(esk5_0))),
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( c(esk5_0) = X1
| ~ complement(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_42,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_34,c_0_35]),c_0_36]),c_0_37])]) ).
cnf(c_0_43,plain,
( c(addition(X1,X2)) = multiplication(c(X1),c(X2))
| ~ test(X1)
| ~ test(X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,negated_conjecture,
complement(c(c(esk5_0)),c(c(c(esk5_0)))),
inference(spm,[status(thm)],[c_0_17,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
esk1_1(esk5_0) = c(esk5_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( ~ leq(addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)))
| ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0))),multiplication(c(esk5_0),esk4_0))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_48,plain,
! [X59,X60,X61] : multiplication(X59,addition(X60,X61)) = addition(multiplication(X59,X60),multiplication(X59,X61)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_49,plain,
! [X54,X55,X56] : multiplication(X54,multiplication(X55,X56)) = multiplication(multiplication(X54,X55),X56),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_50,plain,
! [X66] : multiplication(zero,X66) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_51,plain,
( multiplication(c(X1),c(X1)) = c(X1)
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
test(c(c(c(esk5_0)))),
inference(spm,[status(thm)],[c_0_21,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( c(c(esk5_0)) = X1
| ~ complement(c(esk5_0),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_54,negated_conjecture,
complement(c(esk5_0),esk5_0),
inference(rw,[status(thm)],[c_0_29,c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(c(esk5_0),esk4_0),multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0)))))
| ~ leq(addition(multiplication(c(esk5_0),esk4_0),multiplication(esk5_0,addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk3_0)))),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_24]),c_0_24]) ).
cnf(c_0_56,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,negated_conjecture,
multiplication(esk5_0,c(esk5_0)) = zero,
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_59,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_60,plain,
! [X52] : addition(X52,zero) = X52,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_61,negated_conjecture,
multiplication(c(c(c(c(esk5_0)))),c(c(c(c(esk5_0))))) = c(c(c(c(esk5_0)))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_62,negated_conjecture,
c(c(esk5_0)) = esk5_0,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_63,plain,
! [X67,X68] :
( ( ~ leq(X67,X68)
| addition(X67,X68) = X68 )
& ( addition(X67,X68) != X68
| leq(X67,X68) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_64,negated_conjecture,
( ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(c(esk5_0),esk4_0),addition(multiplication(esk5_0,multiplication(esk5_0,esk2_0)),multiplication(esk5_0,multiplication(c(esk5_0),esk3_0)))))
| ~ leq(addition(multiplication(c(esk5_0),esk4_0),addition(multiplication(esk5_0,multiplication(esk5_0,esk2_0)),multiplication(esk5_0,multiplication(c(esk5_0),esk3_0)))),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56]) ).
cnf(c_0_65,negated_conjecture,
multiplication(esk5_0,multiplication(c(esk5_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_66,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_67,negated_conjecture,
multiplication(esk5_0,esk5_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)],[c_0_61,c_0_62]),c_0_62]),c_0_62]),c_0_62]),c_0_62]),c_0_62]) ).
cnf(c_0_68,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( ~ leq(addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,multiplication(esk5_0,esk2_0)),multiplication(c(esk5_0),esk4_0)))
| ~ leq(addition(multiplication(esk5_0,multiplication(esk5_0,esk2_0)),multiplication(c(esk5_0),esk4_0)),addition(multiplication(esk5_0,esk2_0),multiplication(c(esk5_0),esk4_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)],[c_0_64,c_0_65]),c_0_66]),c_0_24]),c_0_65]),c_0_66]),c_0_24]) ).
cnf(c_0_70,negated_conjecture,
multiplication(esk5_0,multiplication(esk5_0,X1)) = multiplication(esk5_0,X1),
inference(spm,[status(thm)],[c_0_57,c_0_67]) ).
cnf(c_0_71,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_68,c_0_44]) ).
cnf(c_0_72,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_69,c_0_70]),c_0_71]),c_0_70]),c_0_71])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE027+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n006.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 20:26:31 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.58/1.83 % Version : CSE_E---1.7
% 1.58/1.83 % Problem : theBenchmark.p
% 1.58/1.83 % SZS status Theorem for theBenchmark.p
% 1.58/1.83 % SZS output start CNFRefutation
% See solution above
% 1.58/1.84 % Total time : 1.370s
%------------------------------------------------------------------------------