%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM449+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 : n018.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 12:15:14 PM UTC 2026
% Result : Theorem 3.24s 1.30s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 84 ( 16 unt; 7 def)
% Number of atoms : 668 ( 93 equ)
% Maximal formula atoms : 38 ( 7 avg)
% Number of connectives : 821 ( 237 ~; 213 |; 317 &)
% ( 16 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 5 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn 99 !; 57 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',m__2046) ).
fof(f44,axiom,
isFinite0(xS),
file('/export/starexec/sandbox/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/sandbox/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] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| isClosed0(sbsmnsldt0(X0))
| aElementOf0(sK23(X0),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] :
( ~ aInteger0(X0)
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f111]) ).
fof(f323,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK26(X0)) = X0 ),
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(f563,plain,
( ~ aSet0(xS)
| isClosed0(sbsmnsldt0(xS))
| aElementOf0(sK23(xS),xS) ),
inference(resolution,[],[f299,f343]) ).
fof(f564,plain,
( isClosed0(sbsmnsldt0(xS))
| aElementOf0(sK23(xS),xS) ),
inference(forward_subsumption_resolution,[],[f563,f329]) ).
fof(f565,plain,
aElementOf0(sK23(xS),xS),
inference(forward_subsumption_resolution,[],[f564,f357]) ).
fof(f566,plain,
sK23(xS) = szAzrzSzezqlpdtcmdtrp0(sz00,sK26(sK23(xS))),
inference(resolution,[],[f565,f323]) ).
fof(f577,plain,
( isClosed0(sK23(xS))
| ~ aInteger0(sz00)
| ~ aInteger0(sK26(sK23(xS)))
| sz00 = sK26(sK23(xS)) ),
inference(superposition,[],[f301,f566]) ).
fof(f578,plain,
( isClosed0(sK23(xS))
| ~ aInteger0(sK26(sK23(xS)))
| sz00 = sK26(sK23(xS)) ),
inference(forward_subsumption_resolution,[],[f577,f195]) ).
fof(f581,definition,
( spl32_13
<=> sz00 = sK26(sK23(xS)) ),
introduced(definition,[new_symbols(definition,[spl32_13])],[avatar_definition]) ).
fof(f582,plain,
( sz00 != sK26(sK23(xS))
| spl32_13 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f583,plain,
( sz00 = sK26(sK23(xS))
| ~ spl32_13 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f589,definition,
( spl32_15
<=> aInteger0(sK26(sK23(xS))) ),
introduced(definition,[new_symbols(definition,[spl32_15])],[avatar_definition]) ).
fof(f590,plain,
( aInteger0(sK26(sK23(xS)))
| ~ spl32_15 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f591,plain,
( ~ aInteger0(sK26(sK23(xS)))
| spl32_15 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f599,definition,
( spl32_17
<=> isClosed0(sK23(xS)) ),
introduced(definition,[new_symbols(definition,[spl32_17])],[avatar_definition]) ).
fof(f601,plain,
( isClosed0(sK23(xS))
| ~ spl32_17 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f602,plain,
( spl32_13
| ~ spl32_15
| spl32_17 ),
inference(avatar_split_clause,[],[f578,f599,f589,f581]) ).
fof(f637,plain,
( ~ aElementOf0(sK23(xS),xS)
| spl32_15 ),
inference(resolution,[],[f591,f328]) ).
fof(f640,plain,
( $false
| spl32_15 ),
inference(forward_subsumption_resolution,[],[f637,f565]) ).
fof(f641,plain,
spl32_15,
inference(avatar_contradiction_clause,[],[f640]) ).
fof(f672,plain,
( sz00 != sz00
| ~ aElementOf0(sK23(xS),xS)
| ~ spl32_13 ),
inference(superposition,[],[f327,f583]) ).
fof(f676,plain,
( ~ aElementOf0(sK23(xS),xS)
| ~ spl32_13 ),
inference(trivial_inequality_removal,[],[f672]) ).
fof(f679,plain,
( $false
| ~ spl32_13 ),
inference(forward_subsumption_resolution,[],[f676,f565]) ).
fof(f680,plain,
~ spl32_13,
inference(avatar_contradiction_clause,[],[f679]) ).
fof(f694,definition,
( spl32_20
<=> aSubsetOf0(sK23(xS),cS1395) ),
introduced(definition,[new_symbols(definition,[spl32_20])],[avatar_definition]) ).
fof(f695,plain,
( aSubsetOf0(sK23(xS),cS1395)
| ~ spl32_20 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f703,plain,
! [X0] :
( ~ aInteger0(X0)
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X0),cS1395)
| sz00 = X0 ),
inference(resolution,[],[f302,f195]) ).
fof(f1504,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz00,sK26(sK23(xS))),cS1395)
| sz00 = sK26(sK23(xS))
| ~ spl32_15 ),
inference(resolution,[],[f703,f590]) ).
fof(f1508,plain,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz00,sK26(sK23(xS))),cS1395)
| spl32_13
| ~ spl32_15 ),
inference(forward_subsumption_resolution,[],[f1504,f582]) ).
fof(f1513,plain,
( aSubsetOf0(sK23(xS),cS1395)
| spl32_13
| ~ spl32_15 ),
inference(forward_demodulation,[],[f1508,f566]) ).
fof(f1517,plain,
( spl32_20
| spl32_13
| ~ spl32_15 ),
inference(avatar_split_clause,[],[f1513,f589,f581,f694]) ).
fof(f1518,plain,
( ~ aSet0(xS)
| ~ isFinite0(xS)
| isClosed0(sbsmnsldt0(xS))
| ~ isClosed0(sK23(xS))
| ~ spl32_20 ),
inference(resolution,[],[f695,f300]) ).
fof(f1559,plain,
( ~ isFinite0(xS)
| isClosed0(sbsmnsldt0(xS))
| ~ isClosed0(sK23(xS))
| ~ spl32_20 ),
inference(forward_subsumption_resolution,[],[f1518,f329]) ).
fof(f1560,plain,
( isClosed0(sbsmnsldt0(xS))
| ~ isClosed0(sK23(xS))
| ~ spl32_20 ),
inference(forward_subsumption_resolution,[],[f1559,f343]) ).
fof(f1561,plain,
( ~ isClosed0(sK23(xS))
| ~ spl32_20 ),
inference(forward_subsumption_resolution,[],[f1560,f357]) ).
fof(f1562,plain,
( $false
| ~ spl32_17
| ~ spl32_20 ),
inference(forward_subsumption_resolution,[],[f1561,f601]) ).
fof(f1563,plain,
( ~ spl32_17
| ~ spl32_20 ),
inference(avatar_contradiction_clause,[],[f1562]) ).
cnf(s13,plain,
( spl32_13
| ~ spl32_15
| spl32_17 ),
inference(sat_conversion,[],[f602]) ).
cnf(s17,plain,
spl32_15,
inference(sat_conversion,[],[f641]) ).
cnf(s18,plain,
~ spl32_13,
inference(sat_conversion,[],[f680]) ).
cnf(s63,plain,
( spl32_13
| ~ spl32_15
| spl32_20 ),
inference(sat_conversion,[],[f1517]) ).
cnf(s68,plain,
( ~ spl32_17
| ~ spl32_20 ),
inference(sat_conversion,[],[f1563]) ).
cnf(s70,plain,
spl32_20,
inference(rat,[],[s63,s18,s17]) ).
cnf(s71,plain,
~ spl32_17,
inference(rat,[],[s68,s70]) ).
cnf(s72,plain,
$false,
inference(rat,[],[s13,s71,s17,s18]) ).
fof(f1564,plain,
$false,
inference(avatar_sat_refutation,[],[s72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM449+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 20:00:38 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 3.24/1.30 % (2689957)Detected formulas, will run a generic FOF schedule.
% 3.24/1.30 % (2690093)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=1740318492:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.24/1.30 % (2690097)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=862995806:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.24/1.30 % (2690096)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2552248148:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.24/1.30 % (2690098)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3337962217:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.24/1.30 % (2690100)dis-21_1_sil=8000:lcm=predicate:random_seed=3790385517: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)
% 3.24/1.30 % (2690095)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=744509319:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.24/1.30 % (2690094)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=4270480775:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.24/1.30 % (2690098)First to succeed.
% 3.24/1.30 % (2690098)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2689957"
% 3.24/1.30 % (2690100)Instruction limit reached!
% 3.24/1.30 % (2690100)------------------------------
% 3.24/1.30 % (2690100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.30 % (2690100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.30 % (2690100)CaDiCaL version: 2.1.3
% 3.24/1.30 % (2690100)Termination reason: Instruction limit
% 3.24/1.30 % (2690100)Termination phase: Saturation
% 3.24/1.30 % (2690100)Time elapsed: 0.054 s
% 3.24/1.30 % (2690100)Peak memory usage: 88 MB
% 3.24/1.30 % (2690100)Instructions burned: 131 (million)
% 3.24/1.30 % (2690096)Also succeeded, but the first one will report.
% 3.24/1.30 % (2690097)Instruction limit reached!
% 3.24/1.30 % (2690097)------------------------------
% 3.24/1.30 % (2690097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.24/1.30 % (2690097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.24/1.30 % (2690097)CaDiCaL version: 2.1.3
% 3.24/1.30 % (2690097)Termination reason: Instruction limit
% 3.24/1.30 % (2690097)Termination phase: Saturation
% 3.24/1.30 % (2690097)Time elapsed: 0.073 s
% 3.24/1.30 % (2690097)Peak memory usage: 88 MB
% 3.24/1.30 % (2690097)Instructions burned: 120 (million)
% 3.24/1.30 % (2690146)lrs+10_1_sil=8000:sp=occurrence:random_seed=275878293:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.24/1.30 % (2690147)lrs+10_1_sil=32000:urr=on:br=off:random_seed=202757187:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.24/1.30 % (2690098)Refutation found. Thanks to Tanya!
% 3.24/1.30 % SZS status Theorem for theBenchmark
% 3.24/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.40 % (2690098)------------------------------
% 0.15/1.40 % (2690098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.40 % (2690098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.40 % (2690098)CaDiCaL version: 2.1.3
% 0.15/1.40 % (2690098)Termination reason: Refutation
% 0.15/1.40 % (2690098)Time elapsed: 0.046 s
% 0.15/1.40 % (2690098)Peak memory usage: 90 MB
% 0.15/1.40 % (2690098)Instructions burned: 57 (million)
% 0.15/1.40 % (2690098)------------------------------
% 0.15/1.40 % (2690098)------------------------------
% 0.15/1.40 % (2689957)Success in time 0.471 s
% 0.15/1.40 % Vampire exiting
%------------------------------------------------------------------------------