%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE034+2 : 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 : n025.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 2.11s 1.99s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 37 unt; 0 def)
% Number of atoms : 97 ( 48 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 68 ( 23 ~; 19 |; 20 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 72 ( 2 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X6)
& test(X8)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X7,X5),c(X8)),zero) )
=> leq(multiplication(multiplication(multiplication(X6,X4),X5),c(X8)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
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(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(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(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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_11,negated_conjecture,
~ ! [X4,X5,X6,X7,X8] :
( ( test(X7)
& test(X6)
& test(X8)
& leq(multiplication(multiplication(X6,X4),c(X7)),zero)
& leq(multiplication(multiplication(X7,X5),c(X8)),zero) )
=> leq(multiplication(multiplication(multiplication(X6,X4),X5),c(X8)),zero) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_12,negated_conjecture,
( test(esk5_0)
& test(esk4_0)
& test(esk6_0)
& leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero)
& leq(multiplication(multiplication(esk5_0,esk3_0),c(esk6_0)),zero)
& ~ leq(multiplication(multiplication(multiplication(esk4_0,esk2_0),esk3_0),c(esk6_0)),zero) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_13,plain,
! [X54,X55,X56] : multiplication(X54,multiplication(X55,X56)) = multiplication(multiplication(X54,X55),X56),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_14,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_15,negated_conjecture,
leq(multiplication(multiplication(esk5_0,esk3_0),c(esk6_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X52] : addition(X52,zero) = X52,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_18,plain,
! [X47,X48] : addition(X47,X48) = addition(X48,X47),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_19,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])])]) ).
cnf(c_0_20,negated_conjecture,
leq(multiplication(multiplication(esk4_0,esk2_0),c(esk5_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,plain,
! [X62,X63,X64] : multiplication(addition(X62,X63),X64) = addition(multiplication(X62,X64),multiplication(X63,X64)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_22,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
leq(multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))),zero),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_26,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])])]) ).
cnf(c_0_27,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
leq(multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))),zero),
inference(rw,[status(thm)],[c_0_20,c_0_16]) ).
fof(c_0_29,plain,
! [X66] : multiplication(zero,X66) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_30,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
multiplication(esk5_0,multiplication(esk3_0,c(esk6_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_32,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X58] : multiplication(one,X58) = X58,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_36,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,c(esk5_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_24]) ).
cnf(c_0_37,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,negated_conjecture,
multiplication(addition(esk5_0,X1),multiplication(esk3_0,c(esk6_0))) = multiplication(X1,multiplication(esk3_0,c(esk6_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_39,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_25]) ).
cnf(c_0_40,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,negated_conjecture,
test(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_42,plain,
! [X53] : addition(X53,X53) = X53,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_43,negated_conjecture,
~ leq(multiplication(multiplication(multiplication(esk4_0,esk2_0),esk3_0),c(esk6_0)),zero),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_44,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,multiplication(c(esk5_0),X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_36]),c_0_37]),c_0_16]) ).
cnf(c_0_45,negated_conjecture,
multiplication(c(esk5_0),multiplication(esk3_0,c(esk6_0))) = multiplication(esk3_0,c(esk6_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_46,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_47,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,negated_conjecture,
~ leq(multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))),zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_16]),c_0_16]) ).
cnf(c_0_49,negated_conjecture,
multiplication(esk4_0,multiplication(esk2_0,multiplication(esk3_0,c(esk6_0)))) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE034+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:26:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.11/1.99 % Version : CSE_E---1.7
% 2.11/1.99 % Problem : theBenchmark.p
% 2.11/1.99 % SZS status Theorem for theBenchmark.p
% 2.11/1.99 % SZS output start CNFRefutation
% See solution above
% 2.11/2.00 % Total time : 1.369s
%------------------------------------------------------------------------------