%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM427+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 : 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 08:16:58 AM UTC 2026
% Result : Theorem 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 8 unt; 0 def)
% Number of atoms : 24 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 15 ( 5 ~; 6 |; 3 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 1 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntNeg,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('theBenchmark.p',mIntNeg) ).
fof(m__747,axiom,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('theBenchmark.p',m__747) ).
fof(m__,conjecture,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa))
& aInteger0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa))
& aInteger0(W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_25,plain,
( aInteger0(smndt0(A))
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[mIntNeg]) ).
cnf(c_70,plain,
aInteger0(xn),
inference(clausify,[status(thm)],[m__747]) ).
fof(m__767,axiom,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('theBenchmark.p',m__767) ).
cnf(c_73,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(clausify,[status(thm)],[m__767]) ).
cnf(c_74,plain,
sdtpldt0(xb,smndt0(xa)) = sdtasdt0(xq,smndt0(xn)),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_75,negated_conjecture,
( sdtasdt0(xq,A) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_450,plain,
aInteger0(smndt0(xn)),
inference(resolve,[status(thm)],[c_70,c_25]) ).
cnf(c_479,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(copy,[status(thm)],[c_74]) ).
cnf(c_480,negated_conjecture,
~ aInteger0(smndt0(xn)),
inference(resolve,[status(thm)],[c_75,c_479]) ).
cnf(c_478,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_450,c_480]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM427+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.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 02:41:02 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 1961113 was started by sandbox on n014,
% 0.10/0.37 % Sat Sep 26 02:41:02 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).
% 0.10/0.42
% 0.10/0.42 % SZS status Theorem for theBenchmark
% 0.10/0.42
% 0.10/0.42 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.10/0.42 % Length of proof is 10.
% 0.10/0.42 % Level of proof is 3.
% 0.10/0.42 % Maximum clause weight is 25.000.
% 0.10/0.42 % Given clauses 42.
% 0.10/0.42
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------