%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM434+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 : n006.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 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 5 unt; 0 def)
% Number of atoms : 30 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 28 ( 11 ~; 3 |; 14 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 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 : 7 ( 0 sgn 0 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1003,axiom,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& ? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) )
& sdtasdt0(xp,xq) != sz00 ),
file('theBenchmark.p',m__1003) ).
fof(m__,conjecture,
? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_22,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& ? [W0] :
( sdtasdt0(sdtasdt0(xp,xq),W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) )
& sdtasdt0(xp,xq) != sz00 ),
inference(fof_nnf,[status(thm)],[m__1003]) ).
fof(sk_m__1003,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
& aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
& sdtasdt0(sdtasdt0(xp,xq),sK0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(sK0)
& sdtasdt0(xp,xq) != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_22]) ).
cnf(c_73,plain,
aInteger0(sK0),
inference(split_conjunct,[status(thm)],[sk_m__1003]) ).
cnf(c_74,plain,
sdtasdt0(sdtasdt0(xp,xq),sK0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[sk_m__1003]) ).
cnf(c_75,plain,
sdtpldt0(xa,smndt0(xb)) = sdtasdt0(sdtasdt0(xp,xq),sK0),
inference(copy,[status(thm)],[c_74]) ).
cnf(c_79,negated_conjecture,
( sdtasdt0(sdtasdt0(xp,xq),A) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_483,negated_conjecture,
( sdtasdt0(sdtasdt0(xp,xq),A) != sdtasdt0(sdtasdt0(xp,xq),sK0)
| ~ aInteger0(A) ),
inference(paramod,[status(thm)],[c_75,c_79]) ).
cnf(c_80,negated_conjecture,
( sdtasdt0(sdtasdt0(xp,xq),sK0) != sdtasdt0(sdtasdt0(xp,xq),A)
| ~ aInteger0(A) ),
inference(copy,[status(thm)],[c_483]) ).
cnf(c_484,negated_conjecture,
sdtasdt0(sdtasdt0(xp,xq),sK0) != sdtasdt0(sdtasdt0(xp,xq),sK0),
inference(resolve,[status(thm)],[c_80,c_73]) ).
cnf(c_482,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_484]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM434+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 02:42:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 204813 was started by sandbox on n006,
% 0.09/0.36 % Sat Sep 26 02:42:58 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/0.41 % Length of proof is 8.
% 0.14/0.41 % Level of proof is 4.
% 0.14/0.41 % Maximum clause weight is 13.000.
% 0.14/0.41 % Given clauses 44.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------