%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE004+1 : 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 : n011.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 04:35:25 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 18 unt; 0 def)
% Number of atoms : 66 ( 37 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 62 ( 27 ~; 24 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 3 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(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_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(goals,conjecture,
c(zero) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(c_0_8,plain,
! [X63,X64] :
( ( c(X63) != X64
| complement(X63,X64)
| ~ test(X63) )
& ( ~ complement(X63,X64)
| c(X63) = X64
| ~ test(X63) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_3])])]) ).
fof(c_0_9,plain,
! [X40] : addition(X40,zero) = X40,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_10,plain,
! [X35,X36] : addition(X35,X36) = addition(X36,X35),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_11,plain,
! [X61,X62] :
( ( multiplication(X61,X62) = zero
| ~ complement(X62,X61) )
& ( multiplication(X62,X61) = zero
| ~ complement(X62,X61) )
& ( addition(X61,X62) = one
| ~ complement(X62,X61) )
& ( multiplication(X61,X62) != zero
| multiplication(X62,X61) != zero
| addition(X61,X62) != one
| complement(X62,X61) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[test_2])])]) ).
cnf(c_0_12,plain,
( complement(X1,X2)
| c(X1) != X2
| ~ test(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X57,X59,X60] :
( ( ~ test(X57)
| complement(esk1_1(X57),X57) )
& ( ~ complement(X60,X59)
| test(X59) ) ),
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_14,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( addition(X1,X2) = one
| ~ complement(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( complement(X1,c(X1))
| ~ test(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
fof(c_0_18,negated_conjecture,
c(zero) != one,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
cnf(c_0_19,plain,
( test(X2)
| ~ complement(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
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_11]) ).
fof(c_0_21,plain,
! [X53] : multiplication(X53,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(c_0_22,plain,
! [X54] : multiplication(zero,X54) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_23,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_24,plain,
( addition(X1,c(X1)) = one
| ~ test(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_15]) ).
cnf(c_0_25,negated_conjecture,
c(zero) != one,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( test(X1)
| addition(X1,X2) != one
| multiplication(X2,X1) != zero
| multiplication(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
~ test(zero),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_30,plain,
$false,
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_27]),c_0_28])]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE004+1 : 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
% 0.15/0.33 % Computer : n011.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 20:23:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------