%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE065+1 : 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 : n022.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 04:35:38 PM UTC 2026
% Result : Theorem 1.38s 1.77s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 18 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(domain2,axiom,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(goals,conjecture,
! [X4,X5] :
( multiplication(X4,X5) = zero
=> multiplication(X4,domain(X5)) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(domain4,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain4) ).
fof(c_0_6,plain,
! [X58] : addition(X58,multiplication(domain(X58),X58)) = multiplication(domain(X58),X58),
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_7,plain,
! [X59,X60] : domain(multiplication(X59,X60)) = domain(multiplication(X59,domain(X60))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(c_0_8,negated_conjecture,
~ ! [X4,X5] :
( multiplication(X4,X5) = zero
=> multiplication(X4,domain(X5)) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_9,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( multiplication(esk1_0,esk2_0) = zero
& multiplication(esk1_0,domain(esk2_0)) != zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X55] : multiplication(zero,X55) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_13,plain,
! [X41] : addition(X41,zero) = X41,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_14,plain,
addition(multiplication(X1,domain(X2)),multiplication(domain(multiplication(X1,X2)),multiplication(X1,domain(X2)))) = multiplication(domain(multiplication(X1,X2)),multiplication(X1,domain(X2))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
multiplication(esk1_0,esk2_0) = zero,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
domain(zero) = zero,
inference(split_conjunct,[status(thm)],[domain4]) ).
cnf(c_0_17,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
multiplication(esk1_0,domain(esk2_0)) != zero,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]),c_0_18]),c_0_16]),c_0_17]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE065+1 : 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
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 20:28:36 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.38/1.77 % Version : CSE_E---1.7
% 1.38/1.77 % Problem : theBenchmark.p
% 1.38/1.77 % SZS status Theorem for theBenchmark.p
% 1.38/1.77 % SZS output start CNFRefutation
% See solution above
% 1.38/1.77 % Total time : 1.375s
%------------------------------------------------------------------------------