%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM523+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:17:16 AM UTC 2026
% Result : Theorem 3.35s 1.35s
% Output : CNFRefutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 86 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 92 ( 38 ~; 36 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 7 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mDefDiv,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefDiv) ).
fof(mPDP,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W2,sdtasdt0(W0,W1))
& isPrime0(W2) )
=> ( doDivides0(W2,W1)
| doDivides0(W2,W0) ) ) ),
file('theBenchmark.p',mPDP) ).
fof(m__2987,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__2987) ).
fof(m__,conjecture,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_50,plain,
( doDivides0(C,B)
| doDivides0(C,A)
| ~ doDivides0(C,sdtasdt0(A,B))
| ~ isPrime0(C)
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mPDP]) ).
fof(m__3025,axiom,
isPrime0(xp),
file('theBenchmark.p',m__3025) ).
cnf(c_52,plain,
isPrime0(xp),
inference(clausify,[status(thm)],[m__3025]) ).
cnf(c_59,plain,
( doDivides0(xp,B)
| doDivides0(xp,A)
| ~ doDivides0(xp,sdtasdt0(A,B))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_52,c_50]) ).
cnf(c_95,negated_conjecture,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__3014,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('theBenchmark.p',m__3014) ).
cnf(c_96,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(clausify,[status(thm)],[m__3014]) ).
cnf(c_100,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_101,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_102,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_114,plain,
( sdtasdt0(A,C) != B
| ~ aNaturalNumber0(C)
| doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiv]) ).
cnf(c_162,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_1822,plain,
( doDivides0(xp,A)
| doDivides0(xp,A)
| ~ doDivides0(xp,sdtasdt0(A,A))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(A) ),
inference(factor,[status(thm)],[c_59]) ).
cnf(c_1823,plain,
( doDivides0(xp,A)
| ~ doDivides0(xp,sdtasdt0(A,A))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_1822]) ).
cnf(c_167,plain,
( doDivides0(xp,A)
| ~ doDivides0(xp,sdtasdt0(A,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_100,c_1823]) ).
cnf(c_287,plain,
( aNaturalNumber0(sdtasdt0(A,A))
| ~ aNaturalNumber0(A) ),
inference(factor,[status(thm)],[c_162]) ).
cnf(c_1824,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_114,c_96]) ).
cnf(c_709,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_100,c_1824]) ).
cnf(c_1440,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_167,c_102]) ).
cnf(c_1809,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(resolve,[status(thm)],[c_287,c_102]) ).
cnf(c_1810,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(resolve,[status(thm)],[c_287,c_101]) ).
cnf(c_1825,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_1809,c_709]) ).
cnf(c_1813,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(resolve,[status(thm)],[c_1810,c_1825]) ).
cnf(c_1820,plain,
doDivides0(xp,xn),
inference(resolve,[status(thm)],[c_1813,c_1440]) ).
cnf(c_1826,negated_conjecture,
~ doDivides0(xp,xn),
inference(resolve,[status(thm)],[c_1813,c_95]) ).
cnf(c_1821,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1820,c_1826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM523+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 03:05:34 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2002558 was started by sandbox on n014,
% 0.08/0.35 % Sat Sep 26 03:05:34 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 3.35/1.35
% 3.35/1.35 % SZS status Theorem for theBenchmark
% 3.35/1.35
% 3.35/1.35 % Proof 1 at 0.40 (+ 0.04) seconds.
% 3.35/1.35 % Length of proof is 24.
% 3.35/1.35 % Level of proof is 6.
% 3.35/1.35 % Maximum clause weight is 27.000.
% 3.35/1.35 % Given clauses 191.
% 3.35/1.35
% 3.35/1.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------