%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM523+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 : n016.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 04:57:40 PM UTC 2026
% Result : Theorem 1.29s 1.72s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 82 ( 9 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 96 ( 40 ~; 36 |; 15 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 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 : 26 ( 0 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__,conjecture,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(mPDP,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( isPrime0(X3)
& doDivides0(X3,sdtasdt0(X1,X2)) )
=> ( doDivides0(X3,X1)
| doDivides0(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPDP) ).
fof(m__3025,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
fof(c_0_7,plain,
! [X148,X149,X151] :
( ( aNaturalNumber0(esk2_2(X148,X149))
| ~ doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) )
& ( X149 = sdtasdt0(X148,esk2_2(X148,X149))
| ~ doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) )
& ( ~ aNaturalNumber0(X151)
| X149 != sdtasdt0(X148,X151)
| doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_8,plain,
! [X94,X95] :
( ~ aNaturalNumber0(X94)
| ~ aNaturalNumber0(X95)
| aNaturalNumber0(sdtasdt0(X94,X95)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_9,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,negated_conjecture,
~ ( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_12,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_9]),c_0_10]) ).
cnf(c_0_13,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_14,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_15,negated_conjecture,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
cnf(c_0_16,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_18,plain,
! [X174,X175,X176] :
( ~ aNaturalNumber0(X174)
| ~ aNaturalNumber0(X175)
| ~ aNaturalNumber0(X176)
| ~ isPrime0(X176)
| ~ doDivides0(X176,sdtasdt0(X174,X175))
| doDivides0(X176,X174)
| doDivides0(X176,X175) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPDP])]) ).
cnf(c_0_19,negated_conjecture,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,hypothesis,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_10]),c_0_17])]) ).
cnf(c_0_21,plain,
( doDivides0(X3,X1)
| doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ isPrime0(X3)
| ~ doDivides0(X3,sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__3025]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_24,negated_conjecture,
~ doDivides0(xp,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_25,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]),c_0_14]),c_0_23])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM523+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n016.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:42:21 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.29/1.72 % Version : CSE_E---1.7
% 1.29/1.72 % Problem : theBenchmark.p
% 1.29/1.72 % SZS status Theorem for theBenchmark.p
% 1.29/1.72 % SZS output start CNFRefutation
% See solution above
% 1.29/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------