%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM491+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 : n010.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 08:17:10 AM UTC 2026
% Result : Theorem 0.68s 0.52s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 38 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 40 ( 19 ~; 13 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 4 !; 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(m__1837,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__1837) ).
fof(m__,conjecture,
doDivides0(xp,sdtasdt0(xp,xm)),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_83,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_96,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_97,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_110,plain,
( sdtasdt0(A,C) != B
| ~ aNaturalNumber0(C)
| doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiv]) ).
cnf(c_156,plain,
( aNaturalNumber0(sdtasdt0(A,B))
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mSortsB_02]) ).
cnf(c_948,plain,
( sdtasdt0(xp,B) != A
| ~ aNaturalNumber0(B)
| doDivides0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_110,c_96]) ).
cnf(c_949,negated_conjecture,
( sdtasdt0(xp,A) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(A)
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolve,[status(thm)],[c_948,c_83]) ).
cnf(c_950,negated_conjecture,
( sdtasdt0(xp,xm) != sdtasdt0(xp,xm)
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(resolve,[status(thm)],[c_949,c_97]) ).
cnf(c_340,plain,
~ aNaturalNumber0(sdtasdt0(xp,xm)),
inference(xxres,[status(thm)],[c_950]) ).
cnf(c_951,plain,
( aNaturalNumber0(sdtasdt0(A,xm))
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_156,c_97]) ).
cnf(c_952,plain,
~ aNaturalNumber0(xp),
inference(resolve,[status(thm)],[c_951,c_340]) ).
cnf(c_947,plain,
$false,
inference(resolve,[status(thm)],[c_96,c_952]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM491+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 02:58:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 2325870 was started by sandbox on n010,
% 0.11/0.38 % Sat Sep 26 02:58:30 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.68/0.52
% 0.68/0.52 % SZS status Theorem for theBenchmark
% 0.68/0.52
% 0.68/0.52 % Proof 1 at 0.11 (+ 0.01) seconds.
% 0.68/0.52 % Length of proof is 11.
% 0.68/0.52 % Level of proof is 3.
% 0.68/0.52 % Maximum clause weight is 24.000.
% 0.68/0.52 % Given clauses 191.
% 0.68/0.52
% 0.68/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------