%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM851+2 : TPTP v9.2.1. Released v4.1.0.
% 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 : 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 04:58:44 PM UTC 2026
% Result : Theorem 1.61s 1.81s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('holds(conseq_conjunct2(conseq(302)), 475, 1)',conjecture,
vmul(vplus(vd471,vd473),vd469) = vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 1)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X7,X8] : vmul(X7,X8) = vmul(X8,X7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(281, 0), 0)',axiom,
! [X4,X5,X6] : vmul(X4,vplus(X5,X6)) = vplus(vmul(X4,X5),vmul(X4,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof('holds(conseq_conjunct1(conseq(302)), 474, 0)',axiom,
vd470 = vplus(vd471,vd473),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(302)), 474, 0)') ).
fof(c_0_4,negated_conjecture,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq_conjunct2(conseq(302)), 475, 1)'])]) ).
fof(c_0_5,plain,
! [X103,X104] : vmul(X103,X104) = vmul(X104,X103),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
fof(c_0_6,plain,
! [X100,X101,X102] : vmul(X100,vplus(X101,X102)) = vplus(vmul(X100,X101),vmul(X100,X102)),
inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).
cnf(c_0_7,negated_conjecture,
vmul(vplus(vd471,vd473),vd469) != vplus(vmul(vd471,vd469),vmul(vd473,vd469)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
vd470 = vplus(vd471,vd473),
inference(split_conjunct,[status(thm)],['holds(conseq_conjunct1(conseq(302)), 474, 0)']) ).
cnf(c_0_9,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
vplus(vmul(vd471,vd469),vmul(vd469,vd473)) != vmul(vd469,vd470),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_9]) ).
cnf(c_0_12,plain,
vplus(vmul(X1,X2),vmul(X2,X3)) = vmul(X2,vplus(X1,X3)),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_8])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM851+2 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % 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
% 0.16/0.32 % Computer : n015.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 01:16:32 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 1.61/1.81 % Version : CSE_E---1.7
% 1.61/1.81 % Problem : theBenchmark.p
% 1.61/1.81 % SZS status Theorem for theBenchmark.p
% 1.61/1.81 % SZS output start CNFRefutation
% See solution above
% 1.61/1.82 % Total time : 1.366s
%------------------------------------------------------------------------------