%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM477+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 : n001.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 04:57:29 PM UTC 2026
% Result : Theorem 1.46s 1.75s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 51 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 47 ( 17 ~; 14 |; 13 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 7 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xn )
| sdtlseqdt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1494,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1494) ).
fof(m__1494_04,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xm,X1) )
& doDivides0(xm,xn)
& xn != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1494_04) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(c_0_5,plain,
! [X131,X132] :
( ~ aNaturalNumber0(X131)
| ~ aNaturalNumber0(X132)
| X131 = sz00
| sdtlseqdt0(X132,sdtasdt0(X132,X131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_6,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xn )
| sdtlseqdt0(xm,xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_7,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1494]) ).
fof(c_0_9,hypothesis,
( aNaturalNumber0(esk3_0)
& xn = sdtasdt0(xm,esk3_0)
& doDivides0(xm,xn)
& xn != sz00 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1494_04])]) ).
fof(c_0_10,negated_conjecture,
! [X152] :
( ( ~ aNaturalNumber0(X152)
| sdtpldt0(xm,X152) != xn )
& ~ sdtlseqdt0(xm,xn) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_11,hypothesis,
( X1 = sz00
| sdtlseqdt0(xm,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,hypothesis,
aNaturalNumber0(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
xn = sdtasdt0(xm,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
~ sdtlseqdt0(xm,xn),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X95] :
( ( sdtasdt0(X95,sz00) = sz00
| ~ aNaturalNumber0(X95) )
& ( sz00 = sdtasdt0(sz00,X95)
| ~ aNaturalNumber0(X95) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_16,hypothesis,
esk3_0 = sz00,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]) ).
cnf(c_0_17,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,hypothesis,
sdtasdt0(xm,sz00) = xn,
inference(rw,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_19,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_8])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM477+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
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 00:38:18 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.46/1.75 % Version : CSE_E---1.7
% 1.46/1.75 % Problem : theBenchmark.p
% 1.46/1.75 % SZS status Theorem for theBenchmark.p
% 1.46/1.75 % SZS output start CNFRefutation
% See solution above
% 1.46/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------