%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM456+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 : n013.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 2.70s 0.76s
% Output : CNFRefutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 88 ( 28 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 86 ( 17 ~; 13 |; 48 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 7 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2079,axiom,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( W0 = smndt0(sz10)
| W0 = sz10 ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(W0,sbsmnsldt0(xS))
& aInteger0(W0) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( ? [W1] :
( aElementOf0(W0,W1)
& aElementOf0(W1,xS) )
& aInteger0(W0) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('theBenchmark.p',m__2079) ).
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__2203,axiom,
? [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__2203) ).
cnf(c_212,plain,
( smndt0(sz10) = A
| sz10 = A
| ~ aElementOf0(A,stldt0(sbsmnsldt0(xS))) ),
inference(clausify,[status(thm)],[m__2079]) ).
cnf(c_215,plain,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(clausify,[status(thm)],[m__2079]) ).
cnf(c_300,plain,
( aElementOf0(A,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(A,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(clausify,[status(thm)],[m__2171]) ).
cnf(c_301,plain,
( aElementOf0(A,cS2076)
| ~ aElementOf0(A,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(paramod,[status(thm)],[c_215,c_300]) ).
fof(nnf_44,plain,
? [W0] :
( ~ aElementOf0(W0,cS2200)
& smndt0(sz10) != W0
& sz10 != W0
& 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(fof_nnf,[status(thm)],[m__2203]) ).
fof(sk_m__2203,plain,
( ~ aElementOf0(sK0,cS2200)
& smndt0(sz10) != sK0
& sz10 != sK0
& aElementOf0(sK0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sdteqdtlpzmzozddtrp0(sK0,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(sK0,smndt0(sz10)))
& sdtasdt0(xp,sK4) = sdtpldt0(sK0,smndt0(sz10))
& aInteger0(sK4)
& aInteger0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4]),skolemize(W0,sK0),skolemize(W1,sK4)],[nnf_44]) ).
cnf(c_311,plain,
aElementOf0(sK0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[sk_m__2203]) ).
cnf(c_312,plain,
sz10 != sK0,
inference(split_conjunct,[status(thm)],[sk_m__2203]) ).
cnf(c_313,plain,
sK0 != sz10,
inference(copy,[status(thm)],[c_312]) ).
cnf(c_314,plain,
smndt0(sz10) != sK0,
inference(split_conjunct,[status(thm)],[sk_m__2203]) ).
cnf(c_429,plain,
( smndt0(sz10) = A
| sz10 = A
| ~ aElementOf0(A,cS2076) ),
inference(paramod,[status(thm)],[c_215,c_212]) ).
cnf(c_1531,plain,
aElementOf0(sK0,cS2076),
inference(resolve,[status(thm)],[c_311,c_301]) ).
cnf(c_2562,plain,
( smndt0(sz10) = sK0
| sz10 = sK0 ),
inference(resolve,[status(thm)],[c_1531,c_429]) ).
cnf(c_2563,plain,
( smndt0(sz10) = sK0
| sK0 = sz10 ),
inference(copy,[status(thm)],[c_2562]) ).
cnf(c_2564,plain,
smndt0(sz10) = sK0,
inference(resolve,[status(thm)],[c_313,c_2563]) ).
cnf(c_2561,plain,
$false,
inference(resolve,[status(thm)],[c_314,c_2564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM456+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 02:48:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1786329 was started by sandbox on n013,
% 0.08/0.35 % Sat Sep 26 02:48:36 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 2.70/0.76
% 2.70/0.76 % SZS status Theorem for theBenchmark
% 2.70/0.76
% 2.70/0.76 % Proof 1 at 0.29 (+ 0.07) seconds.
% 2.70/0.76 % Length of proof is 14.
% 2.70/0.76 % Level of proof is 4.
% 2.70/0.76 % Maximum clause weight is 27.000.
% 2.70/0.76 % Given clauses 337.
% 2.70/0.76
% 2.70/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------