%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE026+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 : n010.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 04:35:31 PM UTC 2026
% Result : Theorem 1.36s 1.79s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 27 unt; 0 def)
% Number of atoms : 75 ( 43 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 53 ( 19 ~; 15 |; 12 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 44 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
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_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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
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_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(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(c_0_10,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( multiplication(X5,X4) = multiplication(multiplication(X5,X4),X6)
=> leq(multiplication(X5,X4),multiplication(X4,X6)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_11,plain,
! [X45,X46,X47] : addition(X47,addition(X46,X45)) = addition(addition(X47,X46),X45),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_12,plain,
! [X49] : addition(X49,X49) = X49,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_13,plain,
! [X69,X70] :
( ( multiplication(X69,X70) = zero
| ~ complement(X70,X69) )
& ( multiplication(X70,X69) = zero
| ~ complement(X70,X69) )
& ( addition(X69,X70) = one
| ~ complement(X70,X69) )
& ( multiplication(X69,X70) != zero
| multiplication(X70,X69) != zero
| addition(X69,X70) != one
| complement(X70,X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
fof(c_0_14,plain,
! [X65,X67,X68] :
( ( ~ test(X65)
| complement(esk1_1(X65),X65) )
& ( ~ complement(X68,X67)
| test(X67) ) ),
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_15,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0)
& ~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_16,plain,
! [X50,X51,X52] : multiplication(X50,multiplication(X51,X52)) = multiplication(multiplication(X50,X51),X52),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_17,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X58,X59,X60] : multiplication(addition(X58,X59),X60) = addition(multiplication(X58,X60),multiplication(X59,X60)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_22,negated_conjecture,
multiplication(esk3_0,esk2_0) = multiplication(multiplication(esk3_0,esk2_0),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_24,plain,
! [X43,X44] : addition(X43,X44) = addition(X44,X43),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_25,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_27,plain,
! [X63,X64] :
( ( ~ leq(X63,X64)
| addition(X63,X64) = X64 )
& ( addition(X63,X64) != X64
| leq(X63,X64) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_28,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,esk4_0)) = multiplication(esk3_0,esk2_0),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X54] : multiplication(one,X54) = X54,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_32,plain,
( addition(X1,one) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_34,negated_conjecture,
~ leq(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_35,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(X1,multiplication(esk2_0,esk4_0))) = multiplication(addition(X1,esk3_0),multiplication(esk2_0,esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_37,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,negated_conjecture,
addition(one,esk3_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30]) ).
cnf(c_0_39,negated_conjecture,
addition(multiplication(esk3_0,esk2_0),multiplication(esk2_0,esk4_0)) != multiplication(esk2_0,esk4_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_37]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KLE026+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % 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
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 4 20:27:21 EDT 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % start to proof: theBenchmark
% 1.36/1.79 % Version : CSE_E---1.7
% 1.36/1.79 % Problem : theBenchmark.p
% 1.36/1.79 % SZS status Theorem for theBenchmark.p
% 1.36/1.79 % SZS output start CNFRefutation
% See solution above
% 1.36/1.79 % Total time : 1.376s
%------------------------------------------------------------------------------