%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM523+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 2.23s 0.72s
% Output : CNFRefutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 104 ( 16 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 113 ( 42 ~; 44 |; 21 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 5 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 8 !; 6 ?)
% 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__3025,axiom,
( isPrime0(xp)
& ! [W0] :
( ( ( doDivides0(W0,xp)
| ? [W1] :
( xp = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xp
| W0 = sz10 ) )
& xp != sz10 ),
file('theBenchmark.p',m__3025) ).
fof(m__,conjecture,
( ( doDivides0(xp,xn)
| ? [W0] :
( xn = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) )
& ( doDivides0(xp,sdtasdt0(xn,xn))
| ? [W0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( doDivides0(xp,xn)
| ? [W0] :
( xn = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) )
& ( doDivides0(xp,sdtasdt0(xn,xn))
| ? [W0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_51,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]) ).
cnf(c_53,plain,
isPrime0(xp),
inference(clausify,[status(thm)],[m__3025]) ).
cnf(c_60,plain,
( doDivides0(xp,B)
| doDivides0(xp,A)
| ~ doDivides0(xp,sdtasdt0(A,B))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_53,c_51]) ).
cnf(c_98,negated_conjecture,
( ~ doDivides0(xp,xn)
| sdtasdt0(xp,A) != sdtasdt0(xn,xn)
| ~ aNaturalNumber0(A) ),
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_103,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(clausify,[status(thm)],[m__3014]) ).
cnf(c_119,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_120,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_121,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_133,plain,
( sdtasdt0(A,C) != B
| ~ aNaturalNumber0(C)
| doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiv]) ).
cnf(c_181,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_2075,plain,
( doDivides0(xp,A)
| doDivides0(xp,A)
| ~ doDivides0(xp,sdtasdt0(A,A))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(A) ),
inference(factor,[status(thm)],[c_60]) ).
cnf(c_2076,plain,
( doDivides0(xp,A)
| ~ doDivides0(xp,sdtasdt0(A,A))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_2075]) ).
cnf(c_186,plain,
( doDivides0(xp,A)
| ~ doDivides0(xp,sdtasdt0(A,A))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_119,c_2076]) ).
cnf(c_324,plain,
( aNaturalNumber0(sdtasdt0(A,A))
| ~ aNaturalNumber0(A) ),
inference(factor,[status(thm)],[c_181]) ).
cnf(c_360,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(resolve,[status(thm)],[c_103,c_98]) ).
cnf(c_2077,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_133,c_103]) ).
cnf(c_906,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_119,c_2077]) ).
cnf(c_1618,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_186,c_121]) ).
cnf(c_2039,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(resolve,[status(thm)],[c_324,c_121]) ).
cnf(c_2040,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(resolve,[status(thm)],[c_324,c_120]) ).
cnf(c_2078,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(resolve,[status(thm)],[c_2039,c_906]) ).
cnf(c_2043,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(resolve,[status(thm)],[c_2040,c_2078]) ).
cnf(c_2068,plain,
~ doDivides0(xp,xn),
inference(resolve,[status(thm)],[c_2040,c_360]) ).
cnf(c_2079,plain,
doDivides0(xp,xn),
inference(resolve,[status(thm)],[c_2043,c_1618]) ).
cnf(c_2074,plain,
$false,
inference(resolve,[status(thm)],[c_2068,c_2079]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM523+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 03:01:32 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 3843536 was started by sandbox2 on n017,
% 0.11/0.39 % Sat Sep 26 03:01:32 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 2.23/0.72
% 2.23/0.72 % SZS status Theorem for theBenchmark
% 2.23/0.72
% 2.23/0.72 % Proof 1 at 0.22 (+ 0.07) seconds.
% 2.23/0.72 % Length of proof is 26.
% 2.23/0.72 % Level of proof is 5.
% 2.23/0.72 % Maximum clause weight is 29.000.
% 2.23/0.72 % Given clauses 221.
% 2.23/0.72
% 2.23/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------