%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM449+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:24:21 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 87 ( 18 unt; 5 def)
% Number of atoms : 674 ( 101 equ)
% Maximal formula atoms : 38 ( 7 avg)
% Number of connectives : 818 ( 231 ~; 218 |; 317 &)
% ( 14 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 3 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 158 ( 0 sgn 101 !; 57 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(f40,axiom,
! [X0] :
( ( aSet0(X0)
& isFinite0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( aSubsetOf0(X1,cS1395)
& isClosed0(X1) ) ) )
=> isClosed0(sbsmnsldt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mUnionSClosed) ).
fof(f41,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1)
& X1 != sz00 )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395)
& isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArSeqClosed) ).
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/sandbox2/benchmark/theBenchmark.p',m__2046) ).
fof(f44,axiom,
isFinite0(xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2117) ).
fof(f45,conjecture,
( ( 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,stldt0(sbsmnsldt0(xS)))
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS))) ) ) ) )
| isOpen0(stldt0(sbsmnsldt0(xS))) ) )
| isClosed0(sbsmnsldt0(xS)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f46,negated_conjecture,
~ ( ( 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,stldt0(sbsmnsldt0(xS)))
=> ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| sdteqdtlpzmzozddtrp0(X2,X0,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS))) ) ) ) )
| isOpen0(stldt0(sbsmnsldt0(xS))) ) )
| isClosed0(sbsmnsldt0(xS)) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f53,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(f55,plain,
~ ( ( aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) )
=> ( ( ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
=> ( ! [X3] :
( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
=> ? [X4] :
( aInteger0(X4)
& sz00 != X4
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& ! [X5] :
( ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) ) )
& ( ( aInteger0(X5)
& ( ? [X7] :
( aInteger0(X7)
& sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X7) )
| aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
| sdteqdtlpzmzozddtrp0(X5,X3,X4) ) )
=> aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) ) ) )
=> ( ! [X8] :
( aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> aElementOf0(X8,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS))) ) ) ) )
| isOpen0(stldt0(sbsmnsldt0(xS))) ) )
| isClosed0(sbsmnsldt0(xS)) ) ),
inference(rectify,[],[f46]) ).
fof(f108,plain,
! [X0] :
( isClosed0(sbsmnsldt0(X0))
| ~ aSet0(X0)
| ~ isFinite0(X0)
| ? [X1] :
( ( ~ aSubsetOf0(X1,cS1395)
| ~ isClosed0(X1) )
& aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f109,plain,
! [X0] :
( isClosed0(sbsmnsldt0(X0))
| ~ aSet0(X0)
| ~ isFinite0(X0)
| ? [X1] :
( ( ~ aSubsetOf0(X1,cS1395)
| ~ isClosed0(X1) )
& aElementOf0(X1,X0) ) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395)
& isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(ennf_transformation,[],[f41]) ).
fof(f111,plain,
! [X0,X1] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395)
& isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(flattening,[],[f110]) ).
fof(f112,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,[],[f53]) ).
fof(f113,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,[],[f112]) ).
fof(f114,plain,
( ? [X3] :
( ! [X4] :
( ~ aInteger0(X4)
| sz00 = X4
| ( ? [X8] :
( ~ aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& ! [X5] :
( ( ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ~ aInteger0(X5)
| ( ! [X7] :
( ~ aInteger0(X7)
| sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7) )
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ~ sdteqdtlpzmzozddtrp0(X5,X3,X4) ) ) ) ) )
& aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ~ isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f115,plain,
( ? [X3] :
( ! [X4] :
( ~ aInteger0(X4)
| sz00 = X4
| ( ? [X8] :
( ~ aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& ! [X5] :
( ( ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ~ aInteger0(X5)
| ( ! [X7] :
( ~ aInteger0(X7)
| sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7) )
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ~ sdteqdtlpzmzozddtrp0(X5,X3,X4) ) ) ) ) )
& aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ~ isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) ),
inference(flattening,[],[f114]) ).
fof(f125,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(f126,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(f127,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,[],[f113,f126,f125]) ).
fof(f128,definition,
! [X3,X4] :
( ! [X5] :
( ( ( aInteger0(X5)
& ? [X6] :
( aInteger0(X6)
& sdtasdt0(X4,X6) = sdtpldt0(X5,smndt0(X3)) )
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& sdteqdtlpzmzozddtrp0(X5,X3,X4) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ~ aInteger0(X5)
| ( ! [X7] :
( ~ aInteger0(X7)
| sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X7) )
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ~ sdteqdtlpzmzozddtrp0(X5,X3,X4) ) ) )
| ~ sP8(X3,X4) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f129,plain,
( ? [X3] :
( ! [X4] :
( ~ aInteger0(X4)
| sz00 = X4
| ( ? [X8] :
( ~ aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sP8(X3,X4) ) )
& aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
& ~ isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) ) ),
inference(definition_folding,[],[f115,f128]) ).
fof(f175,plain,
! [X0] :
( isClosed0(sbsmnsldt0(X0))
| ~ aSet0(X0)
| ~ isFinite0(X0)
| ( ( ~ aSubsetOf0(sK23(X0),cS1395)
| ~ isClosed0(sK23(X0)) )
& aElementOf0(sK23(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X1,sK23(X0))],[f109]) ).
fof(f182,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,[],[f127]) ).
fof(f183,plain,
( aSet0(xS)
& ! [X0] :
( ( ( aInteger0(sK26(X0))
& sz00 != sK26(X0)
& isPrime0(sK26(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK26(X0)))
& sP7(sK26(X0))
& szAzrzSzezqlpdtcmdtrp0(sz00,sK26(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,[sK26]),skolemize(X1,sK26(X0))],[f182]) ).
fof(f191,plain,
( ? [X3] :
( ! [X4] :
( ~ aInteger0(X4)
| sz00 = X4
| ( ? [X8] :
( ~ aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sP8(X3,X4) ) )
& aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ~ isOpen0(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))) ) )
& ~ isClosed0(sbsmnsldt0(xS))
& 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)) ) ) ),
inference(nnf_transformation,[],[f129]) ).
fof(f192,plain,
( ? [X3] :
( ! [X4] :
( ~ aInteger0(X4)
| sz00 = X4
| ( ? [X8] :
( ~ aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4))
& sP8(X3,X4) ) )
& aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ~ isOpen0(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))) ) )
& ~ isClosed0(sbsmnsldt0(xS))
& 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)) ) ) ),
inference(flattening,[],[f191]) ).
fof(f193,plain,
( ? [X0] :
( ! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| ( ? [X2] :
( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& sP8(X0,X1) ) )
& aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
& ~ isOpen0(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))) ) )
& ~ isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X4] :
( ( aElementOf0(X4,sbsmnsldt0(xS))
| ~ aInteger0(X4)
| ! [X5] :
( ~ aElementOf0(X5,xS)
| ~ aElementOf0(X4,X5) ) )
& ( ( aInteger0(X4)
& ? [X6] :
( aElementOf0(X6,xS)
& aElementOf0(X4,X6) ) )
| ~ aElementOf0(X4,sbsmnsldt0(xS)) ) ) ),
inference(rectify,[],[f192]) ).
fof(f194,plain,
( ! [X1] :
( ~ aInteger0(X1)
| sz00 = X1
| ( ~ aElementOf0(sK30(X1),stldt0(sbsmnsldt0(xS)))
& aElementOf0(sK30(X1),szAzrzSzezqlpdtcmdtrp0(sK29,X1))
& ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK29,X1),stldt0(sbsmnsldt0(xS)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK29,X1))
& sP8(sK29,X1) ) )
& aElementOf0(sK29,stldt0(sbsmnsldt0(xS)))
& ~ isOpen0(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))) ) )
& ~ isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [X4] :
( ( aElementOf0(X4,sbsmnsldt0(xS))
| ~ aInteger0(X4)
| ! [X5] :
( ~ aElementOf0(X5,xS)
| ~ aElementOf0(X4,X5) ) )
& ( ( aInteger0(X4)
& aElementOf0(sK31(X4),xS)
& aElementOf0(X4,sK31(X4)) )
| ~ aElementOf0(X4,sbsmnsldt0(xS)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29,sK30,sK31]),skolemize(X0,sK29),skolemize(X2,sK30(X1)),skolemize(X6,sK31(X4))],[f193]) ).
fof(f195,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f299,plain,
! [X0] :
( aElementOf0(sK23(X0),X0)
| ~ aSet0(X0)
| ~ isFinite0(X0)
| isClosed0(sbsmnsldt0(X0)) ),
inference(cnf_transformation,[],[f175]) ).
fof(f300,plain,
! [X0] :
( ~ aSubsetOf0(sK23(X0),cS1395)
| ~ aSet0(X0)
| ~ isFinite0(X0)
| isClosed0(sbsmnsldt0(X0))
| ~ isClosed0(sK23(X0)) ),
inference(cnf_transformation,[],[f175]) ).
fof(f301,plain,
! [X0,X1] :
( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f111]) ).
fof(f302,plain,
! [X0,X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f111]) ).
fof(f319,plain,
xS = cS2043,
inference(cnf_transformation,[],[f183]) ).
fof(f323,plain,
! [X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,sK26(X0)) = X0
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f183]) ).
fof(f327,plain,
! [X0] :
( sz00 != sK26(X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f183]) ).
fof(f328,plain,
! [X0] :
( aInteger0(sK26(X0))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f183]) ).
fof(f329,plain,
aSet0(xS),
inference(cnf_transformation,[],[f183]) ).
fof(f343,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f44]) ).
fof(f357,plain,
~ isClosed0(sbsmnsldt0(xS)),
inference(cnf_transformation,[],[f194]) ).
fof(f368,plain,
aSet0(cS2043),
inference(definition_unfolding,[],[f329,f319]) ).
fof(f369,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| aInteger0(sK26(X0)) ),
inference(definition_unfolding,[],[f328,f319]) ).
fof(f370,plain,
! [X0] :
( sz00 != sK26(X0)
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f327,f319]) ).
fof(f374,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK26(X0)) = X0 ),
inference(definition_unfolding,[],[f323,f319]) ).
fof(f391,plain,
isFinite0(cS2043),
inference(definition_unfolding,[],[f343,f319]) ).
fof(f399,plain,
~ isClosed0(sbsmnsldt0(cS2043)),
inference(definition_unfolding,[],[f357,f319]) ).
fof(f1131,plain,
( ~ aSet0(cS2043)
| ~ isFinite0(cS2043)
| isClosed0(sbsmnsldt0(cS2043))
| sK23(cS2043) = szAzrzSzezqlpdtcmdtrp0(sz00,sK26(sK23(cS2043))) ),
inference(resolution,[],[f299,f374]) ).
fof(f1134,plain,
( ~ aSet0(cS2043)
| ~ isFinite0(cS2043)
| isClosed0(sbsmnsldt0(cS2043))
| aInteger0(sK26(sK23(cS2043))) ),
inference(resolution,[],[f299,f369]) ).
fof(f1142,plain,
( ~ isFinite0(cS2043)
| isClosed0(sbsmnsldt0(cS2043))
| aInteger0(sK26(sK23(cS2043))) ),
inference(forward_subsumption_resolution,[],[f1134,f368]) ).
fof(f1145,plain,
( ~ isFinite0(cS2043)
| isClosed0(sbsmnsldt0(cS2043))
| sK23(cS2043) = szAzrzSzezqlpdtcmdtrp0(sz00,sK26(sK23(cS2043))) ),
inference(forward_subsumption_resolution,[],[f1131,f368]) ).
fof(f1170,plain,
( isClosed0(sbsmnsldt0(cS2043))
| aInteger0(sK26(sK23(cS2043))) ),
inference(forward_subsumption_resolution,[],[f1142,f391]) ).
fof(f1173,plain,
( isClosed0(sbsmnsldt0(cS2043))
| sK23(cS2043) = szAzrzSzezqlpdtcmdtrp0(sz00,sK26(sK23(cS2043))) ),
inference(forward_subsumption_resolution,[],[f1145,f391]) ).
fof(f1215,plain,
aInteger0(sK26(sK23(cS2043))),
inference(forward_subsumption_resolution,[],[f1170,f399]) ).
fof(f1218,plain,
sK23(cS2043) = szAzrzSzezqlpdtcmdtrp0(sz00,sK26(sK23(cS2043))),
inference(forward_subsumption_resolution,[],[f1173,f399]) ).
fof(f1253,definition,
( spl32_68
<=> sz00 = sK26(sK23(cS2043)) ),
introduced(definition,[new_symbols(definition,[spl32_68])],[avatar_definition]) ).
fof(f1254,plain,
( sz00 != sK26(sK23(cS2043))
| spl32_68 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f1255,plain,
( sz00 = sK26(sK23(cS2043))
| ~ spl32_68 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f1273,plain,
( sz00 != sz00
| ~ aElementOf0(sK23(cS2043),cS2043)
| ~ spl32_68 ),
inference(superposition,[],[f370,f1255]) ).
fof(f1274,plain,
( ~ aElementOf0(sK23(cS2043),cS2043)
| ~ spl32_68 ),
inference(trivial_inequality_removal,[],[f1273]) ).
fof(f1276,definition,
( spl32_70
<=> aElementOf0(sK23(cS2043),cS2043) ),
introduced(definition,[new_symbols(definition,[spl32_70])],[avatar_definition]) ).
fof(f1278,plain,
( ~ aElementOf0(sK23(cS2043),cS2043)
| spl32_70 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1286,plain,
( ~ spl32_70
| ~ spl32_68 ),
inference(avatar_split_clause,[],[f1274,f1253,f1276]) ).
fof(f1340,plain,
( ~ aSet0(cS2043)
| ~ isFinite0(cS2043)
| isClosed0(sbsmnsldt0(cS2043))
| spl32_70 ),
inference(resolution,[],[f1278,f299]) ).
fof(f1341,plain,
( ~ isFinite0(cS2043)
| isClosed0(sbsmnsldt0(cS2043))
| spl32_70 ),
inference(forward_subsumption_resolution,[],[f1340,f368]) ).
fof(f1342,plain,
( isClosed0(sbsmnsldt0(cS2043))
| spl32_70 ),
inference(forward_subsumption_resolution,[],[f1341,f391]) ).
fof(f1343,plain,
( $false
| spl32_70 ),
inference(forward_subsumption_resolution,[],[f1342,f399]) ).
fof(f1344,plain,
spl32_70,
inference(avatar_contradiction_clause,[],[f1343]) ).
fof(f1460,plain,
( isClosed0(sK23(cS2043))
| ~ aInteger0(sz00)
| ~ aInteger0(sK26(sK23(cS2043)))
| sz00 = sK26(sK23(cS2043)) ),
inference(superposition,[],[f301,f1218]) ).
fof(f1470,plain,
( isClosed0(sK23(cS2043))
| ~ aInteger0(sK26(sK23(cS2043)))
| sz00 = sK26(sK23(cS2043)) ),
inference(forward_subsumption_resolution,[],[f1460,f195]) ).
fof(f1480,plain,
( isClosed0(sK23(cS2043))
| sz00 = sK26(sK23(cS2043)) ),
inference(forward_subsumption_resolution,[],[f1470,f1215]) ).
fof(f1485,plain,
( isClosed0(sK23(cS2043))
| spl32_68 ),
inference(forward_subsumption_resolution,[],[f1480,f1254]) ).
fof(f1494,plain,
( aSubsetOf0(sK23(cS2043),cS1395)
| ~ aInteger0(sz00)
| ~ aInteger0(sK26(sK23(cS2043)))
| sz00 = sK26(sK23(cS2043)) ),
inference(superposition,[],[f302,f1218]) ).
fof(f1495,plain,
( aSubsetOf0(sK23(cS2043),cS1395)
| ~ aInteger0(sK26(sK23(cS2043)))
| sz00 = sK26(sK23(cS2043)) ),
inference(forward_subsumption_resolution,[],[f1494,f195]) ).
fof(f1505,plain,
( aSubsetOf0(sK23(cS2043),cS1395)
| sz00 = sK26(sK23(cS2043)) ),
inference(forward_subsumption_resolution,[],[f1495,f1215]) ).
fof(f1506,plain,
( aSubsetOf0(sK23(cS2043),cS1395)
| spl32_68 ),
inference(forward_subsumption_resolution,[],[f1505,f1254]) ).
fof(f1729,plain,
( ~ aSet0(cS2043)
| ~ isFinite0(cS2043)
| isClosed0(sbsmnsldt0(cS2043))
| ~ isClosed0(sK23(cS2043))
| spl32_68 ),
inference(resolution,[],[f300,f1506]) ).
fof(f1730,plain,
( ~ isFinite0(cS2043)
| isClosed0(sbsmnsldt0(cS2043))
| ~ isClosed0(sK23(cS2043))
| spl32_68 ),
inference(forward_subsumption_resolution,[],[f1729,f368]) ).
fof(f1731,plain,
( isClosed0(sbsmnsldt0(cS2043))
| ~ isClosed0(sK23(cS2043))
| spl32_68 ),
inference(forward_subsumption_resolution,[],[f1730,f391]) ).
fof(f1732,plain,
( ~ isClosed0(sK23(cS2043))
| spl32_68 ),
inference(forward_subsumption_resolution,[],[f1731,f399]) ).
fof(f1733,plain,
( $false
| spl32_68 ),
inference(forward_subsumption_resolution,[],[f1732,f1485]) ).
fof(f1734,plain,
spl32_68,
inference(avatar_contradiction_clause,[],[f1733]) ).
cnf(s60,plain,
( ~ spl32_68
| ~ spl32_70 ),
inference(sat_conversion,[],[f1286]) ).
cnf(s65,plain,
spl32_70,
inference(sat_conversion,[],[f1344]) ).
cnf(s78,plain,
spl32_68,
inference(sat_conversion,[],[f1734]) ).
cnf(s79,plain,
$false,
inference(rat,[],[s60,s65,s78]) ).
fof(f1735,plain,
$false,
inference(avatar_sat_refutation,[],[s79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM449+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 19:58:34 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 Running first-order model finding
% 0.13/0.37 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45 % (3371053)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (3371060)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3408485020:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.45 % (3371059)% WARNING: option uhcvi not known.
% 0.13/0.45 % (3371058)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2045919226_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.45 % (3371059)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3802640410:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.45 % (3371061)dis+10_1_sil=32000:sp=arity:random_seed=3745178868:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.45 % (3371062)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3822700968:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.45 % (3371063)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3202960628:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.45 % (3371064)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=381880491:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.45 % TRYING [1]
% 0.13/0.45 % TRYING [2]
% 0.13/0.45 % TRYING [3]
% 0.13/0.45 % (3371061) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3371053-3371061"...
% 0.13/0.45 % (3371061)...printing done.
% 0.13/0.45 % (3371061)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.45 % (3371061)------------------------------
% 0.13/0.45 % (3371061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.45 % (3371061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.45 % (3371061)CaDiCaL version: 2.1.3
% 0.13/0.45 % (3371061)Termination reason: Refutation
% 0.13/0.45 % (3371061)Time elapsed: 0.032 s
% 0.13/0.45 % (3371061)Peak memory usage: 13 MB
% 0.13/0.45 % (3371061)Instructions burned: 49 (million)
% 0.13/0.45 % (3371053)Success in time 0.068 s
% 0.13/0.45 % Vampire exiting
%------------------------------------------------------------------------------