%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM432+3 : 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 : n001.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 08:16:59 AM UTC 2026
% Result : Theorem 0.83s 0.53s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 29 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 8 ~; 8 |; 5 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 2 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntPlus,axiom,
! [W0,W1] :
( ( aInteger0(W1)
& aInteger0(W0) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mIntPlus) ).
fof(m__876,axiom,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('theBenchmark.p',m__876) ).
fof(m__899,axiom,
( sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc))
& aInteger0(xm) ),
file('theBenchmark.p',m__899) ).
fof(m__,conjecture,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc))
& aInteger0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xc))
& aInteger0(W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_28,plain,
( aInteger0(sdtpldt0(A,B))
| ~ aInteger0(B)
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mIntPlus]) ).
cnf(c_80,plain,
aInteger0(xn),
inference(clausify,[status(thm)],[m__876]) ).
cnf(c_83,plain,
aInteger0(xm),
inference(clausify,[status(thm)],[m__899]) ).
fof(m__924,axiom,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('theBenchmark.p',m__924) ).
cnf(c_86,plain,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(clausify,[status(thm)],[m__924]) ).
cnf(c_87,negated_conjecture,
( sdtasdt0(xq,A) != sdtpldt0(xa,smndt0(xc))
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_656,negated_conjecture,
~ aInteger0(sdtpldt0(xn,xm)),
inference(resolve,[status(thm)],[c_87,c_86]) ).
cnf(c_1148,plain,
( aInteger0(sdtpldt0(A,xm))
| ~ aInteger0(A) ),
inference(resolve,[status(thm)],[c_28,c_83]) ).
cnf(c_1149,plain,
~ aInteger0(xn),
inference(resolve,[status(thm)],[c_1148,c_656]) ).
cnf(c_1147,plain,
$false,
inference(resolve,[status(thm)],[c_80,c_1149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM432+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 02:48:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 737888 was started by sandbox on n001,
% 0.10/0.37 % Sat Sep 26 02:48:43 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.83/0.53
% 0.83/0.53 % SZS status Theorem for theBenchmark
% 0.83/0.53
% 0.83/0.53 % Proof 1 at 0.11 (+ 0.03) seconds.
% 0.83/0.53 % Length of proof is 11.
% 0.83/0.53 % Level of proof is 3.
% 0.83/0.53 % Maximum clause weight is 25.000.
% 0.83/0.53 % Given clauses 114.
% 0.83/0.53
% 0.83/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------