%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM455+6 : 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 08:17:03 AM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 100 ( 40 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 94 ( 23 ~; 30 |; 36 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 4 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2171,axiom,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(W0,stldt0(sbsmnsldt0(xS))) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) ) )
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( ( ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
| ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) )
& aInteger0(W0) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
& ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) )
& aInteger0(W0) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
file('theBenchmark.p',m__2171) ).
fof(m__2232,axiom,
( aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aInteger0(W0) )
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& ? [W0] :
( sdtasdt0(xp,W0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aInteger0(W0) ) ),
file('theBenchmark.p',m__2232) ).
fof(m__2258,axiom,
( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
file('theBenchmark.p',m__2258) ).
fof(m__,conjecture,
? [W0] :
( ~ ( aElementOf0(W0,cS2200)
& ( W0 = smndt0(sz10)
| W0 = sz10 ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
| ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) )
& aInteger0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( ~ ( aElementOf0(W0,cS2200)
& ( W0 = smndt0(sz10)
| W0 = sz10 ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ( sdteqdtlpzmzozddtrp0(W0,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(W0,smndt0(sz10)))
| ? [W1] :
( sdtasdt0(xp,W1) = sdtpldt0(W0,smndt0(sz10))
& aInteger0(W1) ) )
& aInteger0(W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_251,plain,
( aInteger0(A)
| ~ aElementOf0(A,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[m__2171]) ).
cnf(c_265,plain,
aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))),
inference(clausify,[status(thm)],[m__2232]) ).
cnf(c_267,plain,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(clausify,[status(thm)],[m__2232]) ).
cnf(c_270,plain,
aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))),
inference(clausify,[status(thm)],[m__2232]) ).
cnf(c_272,plain,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(clausify,[status(thm)],[m__2232]) ).
cnf(c_273,plain,
sdtpldt0(sz10,xp) != sz10,
inference(clausify,[status(thm)],[m__2258]) ).
cnf(c_274,plain,
sdtpldt0(sz10,smndt0(xp)) != sz10,
inference(clausify,[status(thm)],[m__2258]) ).
fof(m__2286,axiom,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
file('theBenchmark.p',m__2286) ).
cnf(c_275,plain,
( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10)
| sdtpldt0(sz10,xp) != smndt0(sz10) ),
inference(clausify,[status(thm)],[m__2286]) ).
cnf(c_278,negated_conjecture,
( smndt0(sz10) = A
| sz10 = A
| ~ aDivisorOf0(xp,sdtpldt0(A,smndt0(sz10)))
| ~ aInteger0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_730,plain,
aInteger0(sdtpldt0(sz10,xp)),
inference(resolve,[status(thm)],[c_267,c_251]) ).
cnf(c_817,plain,
aInteger0(sdtpldt0(sz10,smndt0(xp))),
inference(resolve,[status(thm)],[c_272,c_251]) ).
cnf(c_854,negated_conjecture,
( smndt0(sz10) = sdtpldt0(sz10,smndt0(xp))
| sz10 = sdtpldt0(sz10,smndt0(xp))
| ~ aInteger0(sdtpldt0(sz10,smndt0(xp))) ),
inference(resolve,[status(thm)],[c_278,c_270]) ).
cnf(c_855,negated_conjecture,
( smndt0(sz10) = sdtpldt0(sz10,smndt0(xp))
| sdtpldt0(sz10,smndt0(xp)) = sz10
| ~ aInteger0(sdtpldt0(sz10,smndt0(xp))) ),
inference(copy,[status(thm)],[c_854]) ).
cnf(c_856,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) = sz10
| ~ aInteger0(sdtpldt0(sz10,smndt0(xp))) ),
inference(copy,[status(thm)],[c_855]) ).
cnf(c_857,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(resolve,[status(thm)],[c_817,c_856]) ).
cnf(c_851,negated_conjecture,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(resolve,[status(thm)],[c_274,c_857]) ).
cnf(c_858,negated_conjecture,
( smndt0(sz10) = sdtpldt0(sz10,xp)
| sz10 = sdtpldt0(sz10,xp)
| ~ aInteger0(sdtpldt0(sz10,xp)) ),
inference(resolve,[status(thm)],[c_278,c_265]) ).
cnf(c_859,negated_conjecture,
( smndt0(sz10) = sdtpldt0(sz10,xp)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(sdtpldt0(sz10,xp)) ),
inference(copy,[status(thm)],[c_858]) ).
cnf(c_860,negated_conjecture,
( sdtpldt0(sz10,xp) = smndt0(sz10)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(sdtpldt0(sz10,xp)) ),
inference(copy,[status(thm)],[c_859]) ).
cnf(c_861,negated_conjecture,
( sdtpldt0(sz10,xp) = smndt0(sz10)
| sdtpldt0(sz10,xp) = sz10 ),
inference(resolve,[status(thm)],[c_730,c_860]) ).
cnf(c_852,negated_conjecture,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(resolve,[status(thm)],[c_273,c_861]) ).
cnf(c_862,plain,
sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10),
inference(resolve,[status(thm)],[c_852,c_275]) ).
cnf(c_853,plain,
$false,
inference(resolve,[status(thm)],[c_851,c_862]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM455+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n014.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 02:49:01 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1966582 was started by sandbox on n014,
% 0.10/0.36 % Sat Sep 26 02:49:01 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.45
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45
% 0.14/0.45 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.14/0.45 % Length of proof is 18.
% 0.14/0.45 % Level of proof is 4.
% 0.14/0.45 % Maximum clause weight is 31.000.
% 0.14/0.45 % Given clauses 192.
% 0.14/0.45
% 0.14/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------