%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE024+2 : 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 : n015.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 4.42s 3.34s
% Output : CNFRefutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 24 unt; 0 def)
% Number of atoms : 94 ( 52 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 78 ( 31 ~; 27 |; 12 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 71 ( 4 sgn 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(test_1,axiom,
! [X4] :
( test(X4)
<=> ? [X5] : complement(X5,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
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_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4)
=> multiplication(multiplication(X5,X4),c(X6)) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(c_0_9,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_10,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_11,plain,
! [X55,X56,X57] : multiplication(X55,addition(X56,X57)) = addition(multiplication(X55,X56),multiplication(X55,X57)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_12,plain,
( multiplication(X1,X2) = zero
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( complement(esk1_1(X1),X1)
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X48] : addition(X48,zero) = X48,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_15,plain,
! [X71,X72] :
( ( c(X71) != X72
| complement(X71,X72)
| ~ test(X71) )
& ( ~ complement(X71,X72)
| c(X71) = X72
| ~ test(X71) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
cnf(c_0_16,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( multiplication(X1,esk1_1(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_20,plain,
! [X53] : multiplication(X53,one) = X53,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_21,negated_conjecture,
~ ! [X4,X5,X6] :
( ( test(X5)
& test(X6) )
=> ( addition(multiplication(X4,c(X6)),multiplication(c(X5),X4)) = multiplication(c(X5),X4)
=> multiplication(multiplication(X5,X4),c(X6)) = zero ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_22,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( multiplication(X1,addition(X2,esk1_1(X1))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_24,plain,
( addition(X1,esk1_1(X1)) = one
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_25,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,negated_conjecture,
( test(esk3_0)
& test(esk4_0)
& addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),esk2_0)
& multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) != zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_27,plain,
! [X50,X51,X52] : multiplication(X50,multiplication(X51,X52)) = multiplication(multiplication(X50,X51),X52),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_28,plain,
( multiplication(X1,X2) = zero
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( multiplication(X1,X1) = X1
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_31,negated_conjecture,
test(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X62] : multiplication(zero,X62) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_33,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( multiplication(X1,c(X1)) = zero
| ~ test(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
multiplication(esk3_0,esk3_0) = esk3_0,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( multiplication(X1,multiplication(X2,c(multiplication(X1,X2)))) = zero
| ~ test(multiplication(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
multiplication(esk3_0,multiplication(esk3_0,X1)) = multiplication(esk3_0,X1),
inference(spm,[status(thm)],[c_0_33,c_0_35]) ).
cnf(c_0_39,plain,
( multiplication(X1,multiplication(c(X1),X2)) = zero
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
multiplication(esk3_0,c(esk3_0)) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_35]),c_0_38]),c_0_31])]) ).
cnf(c_0_41,negated_conjecture,
multiplication(multiplication(esk3_0,esk2_0),c(esk4_0)) != zero,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_42,plain,
( multiplication(X1,addition(X2,multiplication(c(X1),X3))) = multiplication(X1,X2)
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_39]),c_0_18]) ).
cnf(c_0_43,negated_conjecture,
addition(multiplication(esk2_0,c(esk4_0)),multiplication(c(esk3_0),esk2_0)) = multiplication(c(esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_44,negated_conjecture,
multiplication(esk3_0,multiplication(c(esk3_0),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_36]) ).
cnf(c_0_45,negated_conjecture,
multiplication(esk3_0,multiplication(esk2_0,c(esk4_0))) != zero,
inference(rw,[status(thm)],[c_0_41,c_0_33]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_31])]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE024+2 : 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
% 0.16/0.33 % Computer : n015.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 20:27:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.42/3.34 % Version : CSE_E---1.7
% 4.42/3.34 % Problem : theBenchmark.p
% 4.42/3.34 % SZS status Theorem for theBenchmark.p
% 4.42/3.34 % SZS output start CNFRefutation
% See solution above
% 4.42/3.35 % Total time : 2.373s
%------------------------------------------------------------------------------