%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM448+5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Tue Sep 29 12:15:13 PM UTC 2026
% Result : Theorem 8.21s 2.08s
% Output : Refutation 8.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 119 ( 11 unt; 8 def)
% Number of atoms : 866 ( 172 equ)
% Maximal formula atoms : 38 ( 7 avg)
% Number of connectives : 1096 ( 349 ~; 330 |; 358 &)
% ( 22 <=>; 34 =>; 0 <=; 3 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 6 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 207 ( 0 sgn 131 !; 76 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(f25,axiom,
! [X0] :
( aInteger0(X0)
=> ( ? [X1] :
( aDivisorOf0(X1,X0)
& isPrime0(X1) )
<=> ( X0 != sz10
& X0 != smndt0(sz10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimeDivisor) ).
fof(f42,axiom,
( aSet0(xS)
& ! [X0] :
( ( aElementOf0(X0,xS)
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 ) )
& ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) ) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 ) )
=> aElementOf0(X0,xS) ) )
& xS = cS2043 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2046) ).
fof(f43,conjecture,
( ! [X0] :
( aInteger0(X0)
=> ( ( ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) )
| aElementOf0(X0,sbsmnsldt0(xS)) )
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 )
& aDivisorOf0(X1,X0)
& isPrime0(X1) ) )
& ( ? [X1] :
( ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| aDivisorOf0(X1,X0) )
& isPrime0(X1) )
=> ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) )
& aElementOf0(X0,sbsmnsldt0(xS)) ) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) )
=> ( ( aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( X0 = sz10
| X0 = smndt0(sz10) ) )
| stldt0(sbsmnsldt0(xS)) = cS2076 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f44,negated_conjecture,
~ ( ! [X0] :
( aInteger0(X0)
=> ( ( ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) )
| aElementOf0(X0,sbsmnsldt0(xS)) )
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 )
& aDivisorOf0(X1,X0)
& isPrime0(X1) ) )
& ( ? [X1] :
( ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| aDivisorOf0(X1,X0) )
& isPrime0(X1) )
=> ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) )
& aElementOf0(X0,sbsmnsldt0(xS)) ) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) )
=> ( ( aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( X0 = sz10
| X0 = smndt0(sz10) ) )
| stldt0(sbsmnsldt0(xS)) = cS2076 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ ( ! [X0] :
( aInteger0(X0)
=> ( ( ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) )
| aElementOf0(X0,sbsmnsldt0(xS)) )
=> ? [X2] :
( aInteger0(X2)
& sz00 != X2
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X0 )
& aDivisorOf0(X2,X0)
& isPrime0(X2) ) )
& ( ? [X4] :
( ( ( aInteger0(X4)
& sz00 != X4
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(X4,X5) = X0 ) )
| aDivisorOf0(X4,X0) )
& isPrime0(X4) )
=> ( ? [X6] :
( aElementOf0(X6,xS)
& aElementOf0(X0,X6) )
& aElementOf0(X0,sbsmnsldt0(xS)) ) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X7] :
( aElementOf0(X7,sbsmnsldt0(xS))
<=> ( aInteger0(X7)
& ? [X8] :
( aElementOf0(X8,xS)
& aElementOf0(X7,X8) ) ) ) )
=> ( ( aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X9] :
( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X9)
& ~ aElementOf0(X9,sbsmnsldt0(xS)) ) ) )
=> ( ! [X10] :
( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
<=> ( sz10 = X10
| smndt0(sz10) = X10 ) )
| stldt0(sbsmnsldt0(xS)) = cS2076 ) ) ) ),
inference(rectify,[],[f44]) ).
fof(f47,plain,
( aSet0(xS)
& ! [X0] :
( ( aElementOf0(X0,xS)
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X4] :
( aInteger0(X4)
& sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 ) )
& ( ? [X5] :
( aInteger0(X5)
& sz00 != X5
& isPrime0(X5)
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
=> ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) )
& ( ( aInteger0(X6)
& ( ? [X8] :
( aInteger0(X8)
& sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8) )
| aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) ) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0 ) )
=> aElementOf0(X0,xS) ) )
& xS = cS2043 ),
inference(rectify,[],[f42]) ).
fof(f53,plain,
( ? [X10] :
( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
<~> ( sz10 = X10
| smndt0(sz10) = X10 ) )
& stldt0(sbsmnsldt0(xS)) != cS2076
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X9] :
( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X9)
& ~ aElementOf0(X9,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X7] :
( aElementOf0(X7,sbsmnsldt0(xS))
<=> ( aInteger0(X7)
& ? [X8] :
( aElementOf0(X8,xS)
& aElementOf0(X7,X8) ) ) )
& ! [X0] :
( ( ( ? [X2] :
( aInteger0(X2)
& sz00 != X2
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X0 )
& aDivisorOf0(X2,X0)
& isPrime0(X2) )
| ( ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) )
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ( ( ? [X6] :
( aElementOf0(X6,xS)
& aElementOf0(X0,X6) )
& aElementOf0(X0,sbsmnsldt0(xS)) )
| ! [X4] :
( ( ( ~ aInteger0(X4)
| sz00 = X4
| ! [X5] :
( ~ aInteger0(X5)
| sdtasdt0(X4,X5) != X0 ) )
& ~ aDivisorOf0(X4,X0) )
| ~ isPrime0(X4) ) ) )
| ~ aInteger0(X0) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f54,plain,
( ? [X10] :
( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
<~> ( sz10 = X10
| smndt0(sz10) = X10 ) )
& stldt0(sbsmnsldt0(xS)) != cS2076
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X9] :
( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X9)
& ~ aElementOf0(X9,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X7] :
( aElementOf0(X7,sbsmnsldt0(xS))
<=> ( aInteger0(X7)
& ? [X8] :
( aElementOf0(X8,xS)
& aElementOf0(X7,X8) ) ) )
& ! [X0] :
( ( ( ? [X2] :
( aInteger0(X2)
& sz00 != X2
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X0 )
& aDivisorOf0(X2,X0)
& isPrime0(X2) )
| ( ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) )
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ( ( ? [X6] :
( aElementOf0(X6,xS)
& aElementOf0(X0,X6) )
& aElementOf0(X0,sbsmnsldt0(xS)) )
| ! [X4] :
( ( ( ~ aInteger0(X4)
| sz00 = X4
| ! [X5] :
( ~ aInteger0(X5)
| sdtasdt0(X4,X5) != X0 ) )
& ~ aDivisorOf0(X4,X0) )
| ~ isPrime0(X4) ) ) )
| ~ aInteger0(X0) ) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ( ? [X1] :
( aDivisorOf0(X1,X0)
& isPrime0(X1) )
<=> ( X0 != sz10
& X0 != smndt0(sz10) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f58,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4) )
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X5] :
( ~ aInteger0(X5)
| sz00 = X5
| ~ isPrime0(X5)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X6,sz00,X5) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8) )
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) ) ) ) ) ) )
& xS = cS2043 ),
inference(ennf_transformation,[],[f47]) ).
fof(f59,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& ! [X2] :
( ( ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4) )
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X5] :
( ~ aInteger0(X5)
| sz00 = X5
| ~ isPrime0(X5)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X6,sz00,X5) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8) )
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) ) ) ) ) ) )
& xS = cS2043 ),
inference(flattening,[],[f58]) ).
fof(f64,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f81,definition,
! [X0] :
( ? [X2] :
( aInteger0(X2)
& sz00 != X2
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X0 )
& aDivisorOf0(X2,X0)
& isPrime0(X2) )
| ~ sP0(X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f82,plain,
( ? [X10] :
( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
<~> ( sz10 = X10
| smndt0(sz10) = X10 ) )
& stldt0(sbsmnsldt0(xS)) != cS2076
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X9] :
( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X9)
& ~ aElementOf0(X9,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X7] :
( aElementOf0(X7,sbsmnsldt0(xS))
<=> ( aInteger0(X7)
& ? [X8] :
( aElementOf0(X8,xS)
& aElementOf0(X7,X8) ) ) )
& ! [X0] :
( ( ( sP0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) )
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ( ( ? [X6] :
( aElementOf0(X6,xS)
& aElementOf0(X0,X6) )
& aElementOf0(X0,sbsmnsldt0(xS)) )
| ! [X4] :
( ( ( ~ aInteger0(X4)
| sz00 = X4
| ! [X5] :
( ~ aInteger0(X5)
| sdtasdt0(X4,X5) != X0 ) )
& ~ aDivisorOf0(X4,X0) )
| ~ isPrime0(X4) ) ) )
| ~ aInteger0(X0) ) ),
inference(definition_folding,[],[f54,f81]) ).
fof(f83,definition,
! [X5] :
( ! [X6] :
( ( ( aInteger0(X6)
& ? [X7] :
( aInteger0(X7)
& sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00)) )
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X6,sz00,X5) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ~ aInteger0(X6)
| ( ! [X8] :
( ~ aInteger0(X8)
| sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X8) )
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5) ) ) )
| ~ sP1(X5) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f84,definition,
! [X1] :
( ! [X2] :
( ( ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X2,sz00,X1) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ aInteger0(X2)
| ( ! [X4] :
( ~ aInteger0(X4)
| sdtpldt0(X2,smndt0(sz00)) != sdtasdt0(X1,X4) )
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1) ) ) )
| ~ sP2(X1) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f85,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& sP2(X1)
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X5] :
( ~ aInteger0(X5)
| sz00 = X5
| ~ isPrime0(X5)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& sP1(X5) ) ) ) )
& xS = cS2043 ),
inference(definition_folding,[],[f59,f84,f83]) ).
fof(f89,plain,
! [X0] :
( ? [X2] :
( aInteger0(X2)
& sz00 != X2
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X0 )
& aDivisorOf0(X2,X0)
& isPrime0(X2) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f90,plain,
! [X0] :
( ? [X1] :
( aInteger0(X1)
& sz00 != X1
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 )
& aDivisorOf0(X1,X0)
& isPrime0(X1) )
| ~ sP0(X0) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ( aInteger0(sK5(X0))
& sz00 != sK5(X0)
& aInteger0(sK6(X0))
& sdtasdt0(sK5(X0),sK6(X0)) = X0
& aDivisorOf0(sK5(X0),X0)
& isPrime0(sK5(X0)) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f90]) ).
fof(f92,plain,
( ? [X10] :
( ( ( sz10 != X10
& smndt0(sz10) != X10 )
| ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS))) )
& ( sz10 = X10
| smndt0(sz10) = X10
| aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) != cS2076
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X9] :
( ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X9)
| aElementOf0(X9,sbsmnsldt0(xS)) )
& ( ( aInteger0(X9)
& ~ aElementOf0(X9,sbsmnsldt0(xS)) )
| ~ aElementOf0(X9,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X7] :
( ( aElementOf0(X7,sbsmnsldt0(xS))
| ~ aInteger0(X7)
| ! [X8] :
( ~ aElementOf0(X8,xS)
| ~ aElementOf0(X7,X8) ) )
& ( ( aInteger0(X7)
& ? [X8] :
( aElementOf0(X8,xS)
& aElementOf0(X7,X8) ) )
| ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
& ! [X0] :
( ( ( sP0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) )
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ( ( ? [X6] :
( aElementOf0(X6,xS)
& aElementOf0(X0,X6) )
& aElementOf0(X0,sbsmnsldt0(xS)) )
| ! [X4] :
( ( ( ~ aInteger0(X4)
| sz00 = X4
| ! [X5] :
( ~ aInteger0(X5)
| sdtasdt0(X4,X5) != X0 ) )
& ~ aDivisorOf0(X4,X0) )
| ~ isPrime0(X4) ) ) )
| ~ aInteger0(X0) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f93,plain,
( ? [X10] :
( ( ( sz10 != X10
& smndt0(sz10) != X10 )
| ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS))) )
& ( sz10 = X10
| smndt0(sz10) = X10
| aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) != cS2076
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X9] :
( ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X9)
| aElementOf0(X9,sbsmnsldt0(xS)) )
& ( ( aInteger0(X9)
& ~ aElementOf0(X9,sbsmnsldt0(xS)) )
| ~ aElementOf0(X9,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X7] :
( ( aElementOf0(X7,sbsmnsldt0(xS))
| ~ aInteger0(X7)
| ! [X8] :
( ~ aElementOf0(X8,xS)
| ~ aElementOf0(X7,X8) ) )
& ( ( aInteger0(X7)
& ? [X8] :
( aElementOf0(X8,xS)
& aElementOf0(X7,X8) ) )
| ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
& ! [X0] :
( ( ( sP0(X0)
| ( ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) )
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ( ( ? [X6] :
( aElementOf0(X6,xS)
& aElementOf0(X0,X6) )
& aElementOf0(X0,sbsmnsldt0(xS)) )
| ! [X4] :
( ( ( ~ aInteger0(X4)
| sz00 = X4
| ! [X5] :
( ~ aInteger0(X5)
| sdtasdt0(X4,X5) != X0 ) )
& ~ aDivisorOf0(X4,X0) )
| ~ isPrime0(X4) ) ) )
| ~ aInteger0(X0) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
( ? [X0] :
( ( ( sz10 != X0
& smndt0(sz10) != X0 )
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
& ( sz10 = X0
| smndt0(sz10) = X0
| aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) != cS2076
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X1)
| aElementOf0(X1,sbsmnsldt0(xS)) )
& ( ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) )
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X2] :
( ( aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2)
| ! [X3] :
( ~ aElementOf0(X3,xS)
| ~ aElementOf0(X2,X3) ) )
& ( ( aInteger0(X2)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X2,X4) ) )
| ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ! [X5] :
( ( ( sP0(X5)
| ( ! [X6] :
( ~ aElementOf0(X6,xS)
| ~ aElementOf0(X5,X6) )
& ~ aElementOf0(X5,sbsmnsldt0(xS)) ) )
& ( ( ? [X7] :
( aElementOf0(X7,xS)
& aElementOf0(X5,X7) )
& aElementOf0(X5,sbsmnsldt0(xS)) )
| ! [X8] :
( ( ( ~ aInteger0(X8)
| sz00 = X8
| ! [X9] :
( ~ aInteger0(X9)
| sdtasdt0(X8,X9) != X5 ) )
& ~ aDivisorOf0(X8,X5) )
| ~ isPrime0(X8) ) ) )
| ~ aInteger0(X5) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
( ( ( sz10 != sK7
& smndt0(sz10) != sK7 )
| ~ aElementOf0(sK7,stldt0(sbsmnsldt0(xS))) )
& ( sz10 = sK7
| smndt0(sz10) = sK7
| aElementOf0(sK7,stldt0(sbsmnsldt0(xS))) )
& stldt0(sbsmnsldt0(xS)) != cS2076
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X1)
| aElementOf0(X1,sbsmnsldt0(xS)) )
& ( ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) )
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X2] :
( ( aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2)
| ! [X3] :
( ~ aElementOf0(X3,xS)
| ~ aElementOf0(X2,X3) ) )
& ( ( aInteger0(X2)
& aElementOf0(sK8(X2),xS)
& aElementOf0(X2,sK8(X2)) )
| ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ! [X5] :
( ( ( sP0(X5)
| ( ! [X6] :
( ~ aElementOf0(X6,xS)
| ~ aElementOf0(X5,X6) )
& ~ aElementOf0(X5,sbsmnsldt0(xS)) ) )
& ( ( aElementOf0(sK9(X5),xS)
& aElementOf0(X5,sK9(X5))
& aElementOf0(X5,sbsmnsldt0(xS)) )
| ! [X8] :
( ( ( ~ aInteger0(X8)
| sz00 = X8
| ! [X9] :
( ~ aInteger0(X9)
| sdtasdt0(X8,X9) != X5 ) )
& ~ aDivisorOf0(X8,X5) )
| ~ isPrime0(X8) ) ) )
| ~ aInteger0(X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X4,sK8(X2)),skolemize(X7,sK9(X5))],[f94]) ).
fof(f96,plain,
! [X0] :
( ( ( ? [X1] :
( aDivisorOf0(X1,X0)
& isPrime0(X1) )
| sz10 = X0
| smndt0(sz10) = X0 )
& ( ( X0 != sz10
& X0 != smndt0(sz10) )
| ! [X1] :
( ~ aDivisorOf0(X1,X0)
| ~ isPrime0(X1) ) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f55]) ).
fof(f97,plain,
! [X0] :
( ( ( ? [X1] :
( aDivisorOf0(X1,X0)
& isPrime0(X1) )
| sz10 = X0
| smndt0(sz10) = X0 )
& ( ( X0 != sz10
& X0 != smndt0(sz10) )
| ! [X1] :
( ~ aDivisorOf0(X1,X0)
| ~ isPrime0(X1) ) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ( ( ? [X1] :
( aDivisorOf0(X1,X0)
& isPrime0(X1) )
| sz10 = X0
| smndt0(sz10) = X0 )
& ( ( X0 != sz10
& X0 != smndt0(sz10) )
| ! [X2] :
( ~ aDivisorOf0(X2,X0)
| ~ isPrime0(X2) ) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ( ( ( aDivisorOf0(sK10(X0),X0)
& isPrime0(sK10(X0)) )
| sz10 = X0
| smndt0(sz10) = X0 )
& ( ( X0 != sz10
& X0 != smndt0(sz10) )
| ! [X2] :
( ~ aDivisorOf0(X2,X0)
| ~ isPrime0(X2) ) ) )
| ~ aInteger0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f98]) ).
fof(f106,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& sP2(X1)
& szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ~ isPrime0(X2)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& sP1(X2) ) ) ) )
& xS = cS2043 ),
inference(rectify,[],[f85]) ).
fof(f107,plain,
( aSet0(xS)
& ! [X0] :
( ( ( aInteger0(sK13(X0))
& sz00 != sK13(X0)
& isPrime0(sK13(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK13(X0)))
& sP2(sK13(X0))
& szAzrzSzezqlpdtcmdtrp0(sz00,sK13(X0)) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ~ isPrime0(X2)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& sP1(X2) ) ) ) )
& xS = cS2043 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X1,sK13(X0))],[f106]) ).
fof(f130,plain,
! [X0] :
( isPrime0(sK5(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f131,plain,
! [X0] :
( aDivisorOf0(sK5(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f136,plain,
! [X8,X5] :
( aElementOf0(X5,sbsmnsldt0(xS))
| ~ aDivisorOf0(X8,X5)
| ~ isPrime0(X8)
| ~ aInteger0(X5) ),
inference(cnf_transformation,[],[f95]) ).
fof(f142,plain,
! [X5] :
( sP0(X5)
| ~ aElementOf0(X5,sbsmnsldt0(xS))
| ~ aInteger0(X5) ),
inference(cnf_transformation,[],[f95]) ).
fof(f149,plain,
! [X1] :
( ~ aElementOf0(X1,sbsmnsldt0(xS))
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f150,plain,
! [X1] :
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f151,plain,
! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X1)
| aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f154,plain,
( sz10 = sK7
| smndt0(sz10) = sK7
| aElementOf0(sK7,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f155,plain,
( smndt0(sz10) != sK7
| ~ aElementOf0(sK7,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f156,plain,
( sz10 != sK7
| ~ aElementOf0(sK7,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f95]) ).
fof(f158,plain,
! [X2,X0] :
( smndt0(sz10) != X0
| ~ aDivisorOf0(X2,X0)
| ~ isPrime0(X2)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f159,plain,
! [X2,X0] :
( sz10 != X0
| ~ aDivisorOf0(X2,X0)
| ~ isPrime0(X2)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f160,plain,
! [X0] :
( isPrime0(sK10(X0))
| sz10 = X0
| smndt0(sz10) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f161,plain,
! [X0] :
( aDivisorOf0(sK10(X0),X0)
| sz10 = X0
| smndt0(sz10) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f166,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f183,plain,
xS = cS2043,
inference(cnf_transformation,[],[f107]) ).
fof(f203,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f238,plain,
( sz10 != sK7
| ~ aElementOf0(sK7,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f156,f183]) ).
fof(f239,plain,
( smndt0(sz10) != sK7
| ~ aElementOf0(sK7,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f155,f183]) ).
fof(f240,plain,
( sz10 = sK7
| smndt0(sz10) = sK7
| aElementOf0(sK7,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f154,f183]) ).
fof(f243,plain,
! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(cS2043)))
| ~ aInteger0(X1)
| aElementOf0(X1,sbsmnsldt0(cS2043)) ),
inference(definition_unfolding,[],[f151,f183,f183]) ).
fof(f244,plain,
! [X1] :
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(cS2043)))
| aInteger0(X1) ),
inference(definition_unfolding,[],[f150,f183]) ).
fof(f245,plain,
! [X1] :
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X1,sbsmnsldt0(cS2043)) ),
inference(definition_unfolding,[],[f149,f183,f183]) ).
fof(f252,plain,
! [X5] :
( ~ aElementOf0(X5,sbsmnsldt0(cS2043))
| sP0(X5)
| ~ aInteger0(X5) ),
inference(definition_unfolding,[],[f142,f183]) ).
fof(f256,plain,
! [X8,X5] :
( ~ aDivisorOf0(X8,X5)
| aElementOf0(X5,sbsmnsldt0(cS2043))
| ~ isPrime0(X8)
| ~ aInteger0(X5) ),
inference(definition_unfolding,[],[f136,f183]) ).
fof(f270,plain,
! [X2] :
( ~ aDivisorOf0(X2,sz10)
| ~ isPrime0(X2)
| ~ aInteger0(sz10) ),
inference(equality_resolution,[],[f159]) ).
fof(f271,plain,
! [X2] :
( ~ aDivisorOf0(X2,smndt0(sz10))
| ~ isPrime0(X2)
| ~ aInteger0(smndt0(sz10)) ),
inference(equality_resolution,[],[f158]) ).
fof(f293,definition,
( spl22_4
<=> aInteger0(smndt0(sz10)) ),
introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition]) ).
fof(f294,plain,
( aInteger0(smndt0(sz10))
| ~ spl22_4 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f295,plain,
( ~ aInteger0(smndt0(sz10))
| spl22_4 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f297,definition,
( spl22_5
<=> ! [X2] :
( ~ aDivisorOf0(X2,smndt0(sz10))
| ~ isPrime0(X2) ) ),
introduced(definition,[new_symbols(definition,[spl22_5])],[avatar_definition]) ).
fof(f298,plain,
( ! [X2] :
( ~ aDivisorOf0(X2,smndt0(sz10))
| ~ isPrime0(X2) )
| ~ spl22_5 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( ~ spl22_4
| spl22_5 ),
inference(avatar_split_clause,[],[f271,f297,f293]) ).
fof(f300,plain,
! [X2] :
( ~ aDivisorOf0(X2,sz10)
| ~ isPrime0(X2) ),
inference(forward_subsumption_resolution,[],[f270,f166]) ).
fof(f305,definition,
( spl22_6
<=> aElementOf0(sK7,stldt0(sbsmnsldt0(cS2043))) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
fof(f306,plain,
( ~ aElementOf0(sK7,stldt0(sbsmnsldt0(cS2043)))
| spl22_6 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f307,plain,
( aElementOf0(sK7,stldt0(sbsmnsldt0(cS2043)))
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f309,definition,
( spl22_7
<=> smndt0(sz10) = sK7 ),
introduced(definition,[new_symbols(definition,[spl22_7])],[avatar_definition]) ).
fof(f310,plain,
( smndt0(sz10) != sK7
| spl22_7 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f311,plain,
( smndt0(sz10) = sK7
| ~ spl22_7 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f313,definition,
( spl22_8
<=> sz10 = sK7 ),
introduced(definition,[new_symbols(definition,[spl22_8])],[avatar_definition]) ).
fof(f314,plain,
( sz10 != sK7
| spl22_8 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f315,plain,
( sz10 = sK7
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f316,plain,
( spl22_6
| spl22_7
| spl22_8 ),
inference(avatar_split_clause,[],[f240,f313,f309,f305]) ).
fof(f317,plain,
( ~ spl22_6
| ~ spl22_7 ),
inference(avatar_split_clause,[],[f239,f309,f305]) ).
fof(f318,plain,
( ~ spl22_6
| ~ spl22_8 ),
inference(avatar_split_clause,[],[f238,f313,f305]) ).
fof(f319,plain,
( aInteger0(sK7)
| ~ spl22_6 ),
inference(unit_resulting_resolution,[],[f244,f307]) ).
fof(f320,plain,
( ~ aElementOf0(sK7,sbsmnsldt0(cS2043))
| ~ spl22_6 ),
inference(unit_resulting_resolution,[],[f245,f307]) ).
fof(f348,plain,
( ~ aInteger0(sz10)
| spl22_4 ),
inference(unit_resulting_resolution,[],[f203,f295]) ).
fof(f355,plain,
( $false
| spl22_4 ),
inference(forward_subsumption_resolution,[],[f348,f166]) ).
fof(f356,plain,
spl22_4,
inference(avatar_contradiction_clause,[],[f355]) ).
fof(f359,plain,
( aInteger0(sK7)
| ~ spl22_4
| ~ spl22_7 ),
inference(forward_demodulation,[],[f294,f311]) ).
fof(f360,plain,
( ! [X2] :
( ~ aDivisorOf0(X2,sK7)
| ~ isPrime0(X2) )
| ~ spl22_5
| ~ spl22_7 ),
inference(forward_demodulation,[],[f298,f311]) ).
fof(f364,plain,
( aElementOf0(sK7,sbsmnsldt0(cS2043))
| ~ spl22_4
| spl22_6
| ~ spl22_7 ),
inference(unit_resulting_resolution,[],[f243,f306,f359]) ).
fof(f402,plain,
( sP0(sK7)
| ~ spl22_4
| spl22_6
| ~ spl22_7 ),
inference(unit_resulting_resolution,[],[f252,f359,f364]) ).
fof(f407,plain,
( aDivisorOf0(sK5(sK7),sK7)
| ~ spl22_4
| spl22_6
| ~ spl22_7 ),
inference(unit_resulting_resolution,[],[f131,f402]) ).
fof(f410,plain,
( isPrime0(sK5(sK7))
| ~ spl22_4
| spl22_6
| ~ spl22_7 ),
inference(unit_resulting_resolution,[],[f130,f402]) ).
fof(f416,plain,
( ~ aDivisorOf0(sK5(sK7),sK7)
| ~ spl22_4
| ~ spl22_5
| spl22_6
| ~ spl22_7 ),
inference(unit_resulting_resolution,[],[f360,f410]) ).
fof(f417,plain,
( $false
| ~ spl22_4
| ~ spl22_5
| spl22_6
| ~ spl22_7 ),
inference(forward_subsumption_resolution,[],[f416,f407]) ).
fof(f418,plain,
( ~ spl22_4
| ~ spl22_5
| spl22_6
| ~ spl22_7 ),
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f419,plain,
( ~ aElementOf0(sz10,stldt0(sbsmnsldt0(cS2043)))
| spl22_6
| ~ spl22_8 ),
inference(superposition,[],[f306,f315]) ).
fof(f422,plain,
( aElementOf0(sz10,sbsmnsldt0(cS2043))
| spl22_6
| ~ spl22_8 ),
inference(unit_resulting_resolution,[],[f243,f166,f419]) ).
fof(f424,plain,
( sP0(sz10)
| spl22_6
| ~ spl22_8 ),
inference(unit_resulting_resolution,[],[f252,f166,f422]) ).
fof(f432,plain,
( aDivisorOf0(sK5(sz10),sz10)
| spl22_6
| ~ spl22_8 ),
inference(unit_resulting_resolution,[],[f131,f424]) ).
fof(f435,plain,
( isPrime0(sK5(sz10))
| spl22_6
| ~ spl22_8 ),
inference(unit_resulting_resolution,[],[f130,f424]) ).
fof(f453,plain,
( ~ aDivisorOf0(sK5(sz10),sz10)
| spl22_6
| ~ spl22_8 ),
inference(unit_resulting_resolution,[],[f300,f435]) ).
fof(f454,plain,
( $false
| spl22_6
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f453,f432]) ).
fof(f455,plain,
( spl22_6
| ~ spl22_8 ),
inference(avatar_contradiction_clause,[],[f454]) ).
fof(f2109,plain,
( isPrime0(sK10(sK7))
| ~ spl22_6
| spl22_7
| spl22_8 ),
inference(unit_resulting_resolution,[],[f160,f319,f314,f310]) ).
fof(f2110,plain,
( ~ aDivisorOf0(sK10(sK7),sK7)
| ~ spl22_6
| spl22_7
| spl22_8 ),
inference(unit_resulting_resolution,[],[f256,f319,f320,f2109]) ).
fof(f2414,plain,
( ~ aInteger0(sK7)
| ~ spl22_6
| spl22_7
| spl22_8 ),
inference(unit_resulting_resolution,[],[f161,f314,f310,f2110]) ).
fof(f2423,plain,
( $false
| ~ spl22_6
| spl22_7
| spl22_8 ),
inference(forward_subsumption_resolution,[],[f2414,f319]) ).
fof(f2424,plain,
( ~ spl22_6
| spl22_7
| spl22_8 ),
inference(avatar_contradiction_clause,[],[f2423]) ).
cnf(s3,plain,
( ~ spl22_4
| spl22_5 ),
inference(sat_conversion,[],[f299]) ).
cnf(s4,plain,
( spl22_6
| spl22_7
| spl22_8 ),
inference(sat_conversion,[],[f316]) ).
cnf(s5,plain,
( ~ spl22_6
| ~ spl22_7 ),
inference(sat_conversion,[],[f317]) ).
cnf(s6,plain,
( ~ spl22_6
| ~ spl22_8 ),
inference(sat_conversion,[],[f318]) ).
cnf(s10,plain,
spl22_4,
inference(sat_conversion,[],[f356]) ).
cnf(s13,plain,
( ~ spl22_4
| ~ spl22_5
| spl22_6
| ~ spl22_7 ),
inference(sat_conversion,[],[f418]) ).
cnf(s14,plain,
( spl22_6
| ~ spl22_8 ),
inference(sat_conversion,[],[f455]) ).
cnf(s35,plain,
( ~ spl22_6
| spl22_7
| spl22_8 ),
inference(sat_conversion,[],[f2424]) ).
cnf(s36,plain,
spl22_5,
inference(rat,[],[s3,s10]) ).
cnf(s39,plain,
spl22_6,
inference(rat,[],[s4,s13,s14,s10,s36]) ).
cnf(s40,plain,
~ spl22_8,
inference(rat,[],[s6,s39]) ).
cnf(s41,plain,
~ spl22_7,
inference(rat,[],[s5,s39]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s35,s39,s40,s41]) ).
fof(f2425,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM448+5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n004.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 19:58:06 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.47 Running first-order theorem proving
% 0.23/0.47 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.21/2.08 % (3840775)Detected formulas, will run a generic FOF schedule.
% 8.21/2.08 % (3840782)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3104604947:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.21/2.08 % (3840784)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3044318358:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.21/2.08 % (3840780)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=33499904:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.21/2.08 % (3840785)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3814147229:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.21/2.08 % (3840786)dis-21_1_sil=8000:lcm=predicate:random_seed=3370277534:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 8.21/2.08 % (3840781)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=602933611:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.21/2.08 % (3840783)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1684870339:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.21/2.08 % (3840786)Instruction limit reached!
% 8.21/2.08 % (3840786)------------------------------
% 8.21/2.08 % (3840786)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.21/2.08 % (3840786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.21/2.08 % (3840786)CaDiCaL version: 2.1.3
% 8.21/2.08 % (3840786)Termination reason: Instruction limit
% 8.21/2.08 % (3840786)Termination phase: Saturation
% 8.21/2.08 % (3840786)Time elapsed: 0.093 s
% 8.21/2.08 % (3840786)Peak memory usage: 88 MB
% 8.21/2.08 % (3840786)Instructions burned: 130 (million)
% 8.21/2.08 % (3840783)Instruction limit reached!
% 8.21/2.08 % (3840783)------------------------------
% 8.21/2.08 % (3840783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.21/2.08 % (3840783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.21/2.08 % (3840783)CaDiCaL version: 2.1.3
% 8.21/2.08 % (3840783)Termination reason: Instruction limit
% 8.21/2.08 % (3840783)Termination phase: Saturation
% 8.21/2.08 % (3840783)Time elapsed: 0.116 s
% 8.21/2.08 % (3840783)Peak memory usage: 89 MB
% 8.21/2.08 % (3840783)Instructions burned: 109 (million)
% 8.21/2.08 % (3840784)Instruction limit reached!
% 8.21/2.08 % (3840784)------------------------------
% 8.21/2.08 % (3840784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.21/2.08 % (3840784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.21/2.08 % (3840784)CaDiCaL version: 2.1.3
% 8.21/2.08 % (3840784)Termination reason: Instruction limit
% 8.21/2.08 % (3840784)Termination phase: Saturation
% 8.21/2.08 % (3840784)Time elapsed: 0.119 s
% 8.21/2.08 % (3840784)Peak memory usage: 88 MB
% 8.21/2.08 % (3840784)Instructions burned: 119 (million)
% 8.21/2.08 % (3840785)Instruction limit reached!
% 8.21/2.08 % (3840785)------------------------------
% 8.21/2.08 % (3840785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.21/2.08 % (3840785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.21/2.08 % (3840785)CaDiCaL version: 2.1.3
% 8.21/2.08 % (3840785)Termination reason: Instruction limit
% 8.21/2.08 % (3840785)Termination phase: Saturation
% 8.21/2.08 % (3840785)Time elapsed: 0.148 s
% 8.21/2.08 % (3840785)Peak memory usage: 90 MB
% 8.21/2.08 % (3840785)Instructions burned: 139 (million)
% 8.21/2.08 % (3840794)lrs+10_1_sil=8000:sp=occurrence:random_seed=1467850686:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 8.21/2.08 % (3840796)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1931308789:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 8.21/2.08 % (3840795)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3232893263:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 8.21/2.08 % (3840797)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2607292297:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 8.21/2.08 % (3840795)First to succeed.
% 8.21/2.08 % (3840795)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3840775"
% 8.21/2.08 % (3840794)Also succeeded, but the first one will report.
% 8.21/2.08 % (3840797)Instruction limit reached!
% 8.21/2.08 % (3840797)------------------------------
% 8.21/2.08 % (3840797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.21/2.08 % (3840797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.21/2.08 % (3840797)CaDiCaL version: 2.1.3
% 8.21/2.08 % (3840797)Termination reason: Instruction limit
% 8.21/2.08 % (3840797)Termination phase: Saturation
% 8.21/2.08 % (3840797)Time elapsed: 0.217 s
% 8.21/2.08 % (3840797)Peak memory usage: 93 MB
% 8.21/2.08 % (3840797)Instructions burned: 249 (million)
% 8.21/2.08 % (3840796)Instruction limit reached!
% 8.21/2.08 % (3840796)------------------------------
% 8.21/2.08 % (3840796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.21/2.08 % (3840796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.21/2.08 % (3840796)CaDiCaL version: 2.1.3
% 8.21/2.08 % (3840796)Termination reason: Instruction limit
% 8.21/2.08 % (3840796)Termination phase: Saturation
% 8.21/2.08 % (3840796)Time elapsed: 0.343 s
% 8.21/2.08 % (3840796)Peak memory usage: 92 MB
% 8.21/2.08 % (3840796)Instructions burned: 325 (million)
% 8.21/2.08 % (3840795)Refutation found. Thanks to Tanya!
% 8.21/2.08 % SZS status Theorem for theBenchmark
% 8.21/2.08 % SZS output start Proof for theBenchmark
% See solution above
% 8.76/2.39 % (3840795)------------------------------
% 8.76/2.39 % (3840795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.76/2.39 % (3840795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.76/2.39 % (3840795)CaDiCaL version: 2.1.3
% 8.76/2.39 % (3840795)Termination reason: Refutation
% 8.76/2.39 % (3840795)Time elapsed: 0.062 s
% 8.76/2.39 % (3840795)Peak memory usage: 90 MB
% 8.76/2.39 % (3840795)Instructions burned: 61 (million)
% 8.76/2.39 % (3840795)------------------------------
% 8.76/2.39 % (3840795)------------------------------
% 8.76/2.39 % (3840775)Success in time 1.129 s
% 8.76/2.39 % Vampire exiting
%------------------------------------------------------------------------------