%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM456+6 : 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 : n008.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 12:15:16 PM UTC 2026
% Result : ContradictoryAxioms 1.03s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 15 unt; 6 def)
% Number of atoms : 684 ( 125 equ)
% Maximal formula atoms : 38 ( 10 avg)
% Number of connectives : 849 ( 231 ~; 190 |; 390 &)
% ( 18 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 4 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 155 ( 0 sgn 106 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
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,axiom,
( 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__2079) ).
fof(f46,axiom,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(f47,axiom,
? [X0] :
( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ~ ( X0 = sz10
| X0 = smndt0(sz10)
| aElementOf0(X0,cS2200) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).
fof(f56,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(f57,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ! [X3] :
( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
<=> ( sz10 = X3
| smndt0(sz10) = X3 ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(rectify,[],[f43]) ).
fof(f59,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
& ( ( aInteger0(X0)
& ( ? [X2] :
( aInteger0(X2)
& sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,X2) )
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) ) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) ) )
& ! [X6] :
( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(rectify,[],[f46]) ).
fof(f117,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,[],[f56]) ).
fof(f118,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,[],[f117]) ).
fof(f121,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) ) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) ) )
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(ennf_transformation,[],[f59]) ).
fof(f122,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) ) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) ) )
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
? [X0] :
( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sz10 != X0
& smndt0(sz10) != X0
& ~ aElementOf0(X0,cS2200) ),
inference(ennf_transformation,[],[f47]) ).
fof(f124,plain,
? [X0] :
( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp)
& aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sz10 != X0
& smndt0(sz10) != X0
& ~ aElementOf0(X0,cS2200) ),
inference(flattening,[],[f123]) ).
fof(f134,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) ) ) )
| ~ sP6(X5) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f135,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) ) ) )
| ~ sP7(X1) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f136,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& sP7(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))
& sP6(X5) ) ) ) )
& xS = cS2043 ),
inference(definition_folding,[],[f118,f135,f134]) ).
fof(f192,plain,
( aSet0(xS)
& ! [X0] :
( ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& isPrime0(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& sP7(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))
& sP6(X2) ) ) ) )
& xS = cS2043 ),
inference(rectify,[],[f136]) ).
fof(f193,plain,
( aSet0(xS)
& ! [X0] :
( ( ( aInteger0(sK27(X0))
& sz00 != sK27(X0)
& isPrime0(sK27(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)))
& sP7(sK27(X0))
& szAzrzSzezqlpdtcmdtrp0(sz00,sK27(X0)) = X0 )
| ~ aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
| ! [X2] :
( ~ aInteger0(X2)
| sz00 = X2
| ~ isPrime0(X2)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& sP6(X2) ) ) ) )
& xS = cS2043 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X1,sK27(X0))],[f192]) ).
fof(f194,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X2)
| aElementOf0(X2,sbsmnsldt0(xS)) )
& ( ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) )
| ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( sz10 != X3
& smndt0(sz10) != X3 ) )
& ( sz10 = X3
| smndt0(sz10) = X3
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(nnf_transformation,[],[f57]) ).
fof(f195,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X2)
| aElementOf0(X2,sbsmnsldt0(xS)) )
& ( ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) )
| ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ( sz10 != X3
& smndt0(sz10) != X3 ) )
& ( sz10 = X3
| smndt0(sz10) = X3
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(flattening,[],[f194]) ).
fof(f196,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X0,X2) ) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,sbsmnsldt0(xS)) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X4] :
( ( aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| ( sz10 != X4
& smndt0(sz10) != X4 ) )
& ( sz10 = X4
| smndt0(sz10) = X4
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(rectify,[],[f195]) ).
fof(f197,plain,
( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ~ aInteger0(X0)
| ! [X1] :
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X0,X1) ) )
& ( ( aInteger0(X0)
& aElementOf0(sK28(X0),xS)
& aElementOf0(X0,sK28(X0)) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X3] :
( ( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) )
& ( ( aInteger0(X3)
& ~ aElementOf0(X3,sbsmnsldt0(xS)) )
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ) )
& ! [X4] :
( ( aElementOf0(X4,stldt0(sbsmnsldt0(xS)))
| ( sz10 != X4
& smndt0(sz10) != X4 ) )
& ( sz10 = X4
| smndt0(sz10) = X4
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(X2,sK28(X0))],[f196]) ).
fof(f208,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) )
& ! [X5] :
( ( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X5)
| aElementOf0(X5,sbsmnsldt0(xS)) )
& ( ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) )
| ~ aElementOf0(X5,stldt0(sbsmnsldt0(xS))) ) )
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(nnf_transformation,[],[f122]) ).
fof(f209,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) )
& ! [X5] :
( ( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X5)
| aElementOf0(X5,sbsmnsldt0(xS)) )
& ( ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) )
| ~ aElementOf0(X5,stldt0(sbsmnsldt0(xS))) ) )
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(flattening,[],[f208]) ).
fof(f210,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& ? [X5] :
( aElementOf0(X5,xS)
& aElementOf0(X3,X5) ) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) )
& ! [X6] :
( ( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X6)
| aElementOf0(X6,sbsmnsldt0(xS)) )
& ( ( aInteger0(X6)
& ~ aElementOf0(X6,sbsmnsldt0(xS)) )
| ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X7] :
( aElementOf0(X7,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(rectify,[],[f209]) ).
fof(f211,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& aInteger0(sK35(X0))
& sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,sK35(X0))
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& aElementOf0(sK36(X3),xS)
& aElementOf0(X3,sK36(X3)) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) )
& ! [X6] :
( ( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X6)
| aElementOf0(X6,sbsmnsldt0(xS)) )
& ( ( aInteger0(X6)
& ~ aElementOf0(X6,sbsmnsldt0(xS)) )
| ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X7] :
( aElementOf0(X7,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35,sK36]),skolemize(X1,sK35(X0)),skolemize(X5,sK36(X3))],[f210]) ).
fof(f212,plain,
( aInteger0(sK37)
& aInteger0(sK38)
& sdtasdt0(xp,sK38) = sdtpldt0(sK37,smndt0(sz10))
& aDivisorOf0(xp,sdtpldt0(sK37,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sK37,sz10,xp)
& aElementOf0(sK37,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& sz10 != sK37
& smndt0(sz10) != sK37
& ~ aElementOf0(sK37,cS2200) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38]),skolemize(X0,sK37),skolemize(X1,sK38)],[f124]) ).
fof(f337,plain,
xS = cS2043,
inference(cnf_transformation,[],[f193]) ).
fof(f349,plain,
! [X4] :
( sz10 = X4
| smndt0(sz10) = X4
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f197]) ).
fof(f352,plain,
! [X3] :
( ~ aElementOf0(X3,sbsmnsldt0(xS))
| ~ aElementOf0(X3,stldt0(sbsmnsldt0(xS))) ),
inference(cnf_transformation,[],[f197]) ).
fof(f354,plain,
! [X3] :
( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X3)
| aElementOf0(X3,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f197]) ).
fof(f409,plain,
! [X7] :
( aElementOf0(X7,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cnf_transformation,[],[f211]) ).
fof(f430,plain,
smndt0(sz10) != sK37,
inference(cnf_transformation,[],[f212]) ).
fof(f431,plain,
sz10 != sK37,
inference(cnf_transformation,[],[f212]) ).
fof(f432,plain,
aElementOf0(sK37,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f212]) ).
fof(f437,plain,
aInteger0(sK37),
inference(cnf_transformation,[],[f212]) ).
fof(f454,plain,
! [X3] :
( ~ aInteger0(X3)
| aElementOf0(X3,stldt0(sbsmnsldt0(cS2043)))
| aElementOf0(X3,sbsmnsldt0(cS2043)) ),
inference(definition_unfolding,[],[f354,f337,f337]) ).
fof(f456,plain,
! [X3] :
( ~ aElementOf0(X3,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X3,sbsmnsldt0(cS2043)) ),
inference(definition_unfolding,[],[f352,f337,f337]) ).
fof(f459,plain,
! [X4] :
( sz10 = X4
| smndt0(sz10) = X4
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043))) ),
inference(definition_unfolding,[],[f349,f337]) ).
fof(f500,plain,
! [X7] :
( aElementOf0(X7,stldt0(sbsmnsldt0(cS2043)))
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(definition_unfolding,[],[f409,f337]) ).
fof(f520,definition,
! [X0,X1] :
( sQ39_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ39_eqProxy])],[equality_proxy_definition]) ).
fof(f575,plain,
! [X4] :
( sQ39_eqProxy(smndt0(sz10),X4)
| sQ39_eqProxy(sz10,X4)
| ~ aElementOf0(X4,stldt0(sbsmnsldt0(cS2043))) ),
inference(equality_proxy_replacement,[],[f459,f520,f520]) ).
fof(f587,plain,
~ sQ39_eqProxy(sz10,sK37),
inference(equality_proxy_replacement,[],[f431,f520]) ).
fof(f588,plain,
~ sQ39_eqProxy(smndt0(sz10),sK37),
inference(equality_proxy_replacement,[],[f430,f520]) ).
fof(f667,plain,
! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
inference(resolution,[],[f500,f456]) ).
fof(f668,plain,
~ aElementOf0(sK37,sbsmnsldt0(cS2043)),
inference(resolution,[],[f667,f432]) ).
fof(f691,plain,
( aElementOf0(sK37,stldt0(sbsmnsldt0(cS2043)))
| aElementOf0(sK37,sbsmnsldt0(cS2043)) ),
inference(resolution,[],[f454,f437]) ).
fof(f701,definition,
( spl40_13
<=> aElementOf0(sK37,sbsmnsldt0(cS2043)) ),
introduced(definition,[new_symbols(definition,[spl40_13])],[avatar_definition]) ).
fof(f702,plain,
( aElementOf0(sK37,sbsmnsldt0(cS2043))
| ~ spl40_13 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f704,definition,
( spl40_14
<=> aElementOf0(sK37,stldt0(sbsmnsldt0(cS2043))) ),
introduced(definition,[new_symbols(definition,[spl40_14])],[avatar_definition]) ).
fof(f706,plain,
( spl40_13
| spl40_14 ),
inference(avatar_split_clause,[],[f691,f704,f701]) ).
fof(f730,plain,
( $false
| ~ spl40_13 ),
inference(resolution,[],[f702,f668]) ).
fof(f731,plain,
~ spl40_13,
inference(avatar_contradiction_clause,[],[f730]) ).
fof(f999,plain,
( sQ39_eqProxy(sz10,sK37)
| ~ aElementOf0(sK37,stldt0(sbsmnsldt0(cS2043))) ),
inference(resolution,[],[f575,f588]) ).
fof(f1002,definition,
( spl40_34
<=> sQ39_eqProxy(sz10,sK37) ),
introduced(definition,[new_symbols(definition,[spl40_34])],[avatar_definition]) ).
fof(f1003,plain,
( sQ39_eqProxy(sz10,sK37)
| ~ spl40_34 ),
inference(avatar_component_clause,[],[f1002]) ).
fof(f1004,plain,
( ~ spl40_14
| spl40_34 ),
inference(avatar_split_clause,[],[f999,f1002,f704]) ).
fof(f1005,plain,
( $false
| ~ spl40_34 ),
inference(resolution,[],[f1003,f587]) ).
fof(f1006,plain,
~ spl40_34,
inference(avatar_contradiction_clause,[],[f1005]) ).
cnf(s11,plain,
( spl40_13
| spl40_14 ),
inference(sat_conversion,[],[f706]) ).
cnf(s15,plain,
~ spl40_13,
inference(sat_conversion,[],[f731]) ).
cnf(s29,plain,
( ~ spl40_14
| spl40_34 ),
inference(sat_conversion,[],[f1004]) ).
cnf(s30,plain,
~ spl40_34,
inference(sat_conversion,[],[f1006]) ).
cnf(s31,plain,
~ spl40_14,
inference(rat,[],[s29,s30]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s11,s31,s15]) ).
fof(f1007,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM456+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 19:59:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 1.03/1.31 % (1566356)Detected formulas, will run a generic FOF schedule.
% 1.03/1.31 % (1566363)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=3802012100:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.03/1.31 % (1566361)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=1864480743:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.03/1.31 % (1566365)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3807948857:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.03/1.31 % (1566362)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=300185998:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.03/1.31 % (1566364)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3502862774:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.03/1.31 % (1566367)dis-21_1_sil=8000:lcm=predicate:random_seed=388346728: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)
% 1.03/1.31 % (1566366)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1456144659:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.03/1.31 % (1566367)First to succeed.
% 1.03/1.31 % (1566367)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1566356"
% 1.03/1.31 % (1566364)Also succeeded, but the first one will report.
% 1.03/1.31 % (1566365)Also succeeded, but the first one will report.
% 1.03/1.31 % (1566366)Also succeeded, but the first one will report.
% 1.03/1.31 % (1566367)Refutation found. Thanks to Tanya!
% 1.03/1.31 % SZS status ContradictoryAxioms for theBenchmark
% 1.03/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.41 % (1566367)------------------------------
% 0.17/1.41 % (1566367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.41 % (1566367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.41 % (1566367)CaDiCaL version: 2.1.3
% 0.17/1.41 % (1566367)Termination reason: Refutation
% 0.17/1.41 % (1566367)Time elapsed: 0.017 s
% 0.17/1.41 % (1566367)Peak memory usage: 89 MB
% 0.17/1.41 % (1566367)Instructions burned: 26 (million)
% 0.17/1.41 % (1566367)------------------------------
% 0.17/1.41 % (1566367)------------------------------
% 0.17/1.41 % (1566356)Success in time 0.452 s
% 0.17/1.41 % Vampire exiting
%------------------------------------------------------------------------------