TSTP Solution File: NUM449+6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM449+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 12:08:40 EDT 2023
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 10 unt; 0 def)
% Number of atoms : 704 ( 103 equ)
% Maximal formula atoms : 38 ( 11 avg)
% Number of connectives : 904 ( 263 ~; 220 |; 365 &)
% ( 10 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 187 (; 121 !; 66 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1367,plain,
$false,
inference(subsumption_resolution,[],[f1366,f214]) ).
fof(f214,plain,
aSet0(xS),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X3] :
( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
| ~ aInteger0(X3) ) )
| ~ aInteger0(X2) )
& ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,sK5(X1,X2))
& aInteger0(sK5(X1,X2))
& aInteger0(X2) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK6(X0)) = X0
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,sK6(X0)))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,sK6(X0))
& ~ aDivisorOf0(sK6(X0),sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(sK6(X0),X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X6) )
& ( ( sdteqdtlpzmzozddtrp0(X6,sz00,sK6(X0))
& aDivisorOf0(sK6(X0),sdtpldt0(X6,smndt0(sz00)))
& sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(sK6(X0),sK7(X0,X6))
& aInteger0(sK7(X0,X6))
& aInteger0(X6) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,sK6(X0))) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK6(X0)))
& isPrime0(sK6(X0))
& sz00 != sK6(X0)
& aInteger0(sK6(X0)) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f59,f128,f127,f126]) ).
fof(f126,plain,
! [X1,X2] :
( ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
=> ( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,sK5(X1,X2))
& aInteger0(sK5(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f127,plain,
! [X0] :
( ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X6) )
& ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
=> ( szAzrzSzezqlpdtcmdtrp0(sz00,sK6(X0)) = X0
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,sK6(X0)))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,sK6(X0))
& ~ aDivisorOf0(sK6(X0),sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(sK6(X0),X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X6) )
& ( ( sdteqdtlpzmzozddtrp0(X6,sz00,sK6(X0))
& aDivisorOf0(sK6(X0),sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(sK6(X0),X8)
& aInteger0(X8) )
& aInteger0(X6) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,sK6(X0))) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK6(X0)))
& isPrime0(sK6(X0))
& sz00 != sK6(X0)
& aInteger0(sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
! [X0,X6] :
( ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(sK6(X0),X8)
& aInteger0(X8) )
=> ( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(sK6(X0),sK7(X0,X6))
& aInteger0(sK7(X0,X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X3] :
( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
| ~ aInteger0(X3) ) )
| ~ aInteger0(X2) )
& ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
& aInteger0(X2) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X6) )
& ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X3] :
( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
| ~ aInteger0(X3) ) )
| ~ aInteger0(X2) )
& ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
& aInteger0(X2) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X6) )
& ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
( xS = cS2043
& ! [X0] :
( ( ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
& isPrime0(X1)
& sz00 != X1
& aInteger0(X1) )
=> aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
=> ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
| aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
| ? [X7] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X7)
& aInteger0(X7) ) )
& aInteger0(X6) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
=> ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) ) ) )
& aSet0(xS) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
( xS = cS2043
& ! [X0] :
( ( ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
& isPrime0(X1)
& sz00 != X1
& aInteger0(X1) )
=> aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
=> ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& sz00 != X1
& aInteger0(X1) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox/tmp/tmp.qXM7asOdtv/Vampire---4.8_32682',m__2046) ).
fof(f1366,plain,
~ aSet0(xS),
inference(subsumption_resolution,[],[f1365,f213]) ).
fof(f213,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
isFinite0(xS),
file('/export/starexec/sandbox/tmp/tmp.qXM7asOdtv/Vampire---4.8_32682',m__2117) ).
fof(f1365,plain,
( ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(subsumption_resolution,[],[f1364,f212]) ).
fof(f212,plain,
~ isClosed0(sbsmnsldt0(xS)),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
( ~ isClosed0(sbsmnsldt0(xS))
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK1,X1),stldt0(sbsmnsldt0(xS)))
& ~ aElementOf0(sK2(X1),stldt0(sbsmnsldt0(xS)))
& aElementOf0(sK2(X1),szAzrzSzezqlpdtcmdtrp0(sK1,X1))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sK1,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,sK1,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(sK1)))
& ! [X4] :
( sdtasdt0(X1,X4) != sdtpldt0(X3,smndt0(sK1))
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,sK1,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(sK1)))
& sdtpldt0(X3,smndt0(sK1)) = sdtasdt0(X1,sK3(X1,X3))
& aInteger0(sK3(X1,X3))
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sK1,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK1,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(sK1,stldt0(sbsmnsldt0(xS)))
& ! [X6] :
( ( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X6,sbsmnsldt0(xS))
| ~ aInteger0(X6) )
& ( ( ~ aElementOf0(X6,sbsmnsldt0(xS))
& aInteger0(X6) )
| ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X7] :
( ( aElementOf0(X7,sbsmnsldt0(xS))
| ! [X8] :
( ~ aElementOf0(X7,X8)
| ~ aElementOf0(X8,xS) )
| ~ aInteger0(X7) )
& ( ( aElementOf0(X7,sK4(X7))
& aElementOf0(sK4(X7),xS)
& aInteger0(X7) )
| ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f120,f124,f123,f122,f121]) ).
fof(f121,plain,
( ? [X0] :
( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS)))
& ? [X2] :
( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtasdt0(X1,X4) != sdtpldt0(X3,smndt0(X0))
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
=> ( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK1,X1),stldt0(sbsmnsldt0(xS)))
& ? [X2] :
( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sK1,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sK1,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,sK1,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(sK1)))
& ! [X4] :
( sdtasdt0(X1,X4) != sdtpldt0(X3,smndt0(sK1))
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,sK1,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(sK1)))
& ? [X5] :
( sdtasdt0(X1,X5) = sdtpldt0(X3,smndt0(sK1))
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sK1,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sK1,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(sK1,stldt0(sbsmnsldt0(xS))) ) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
! [X1] :
( ? [X2] :
( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sK1,X1)) )
=> ( ~ aElementOf0(sK2(X1),stldt0(sbsmnsldt0(xS)))
& aElementOf0(sK2(X1),szAzrzSzezqlpdtcmdtrp0(sK1,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X1,X3] :
( ? [X5] :
( sdtasdt0(X1,X5) = sdtpldt0(X3,smndt0(sK1))
& aInteger0(X5) )
=> ( sdtpldt0(X3,smndt0(sK1)) = sdtasdt0(X1,sK3(X1,X3))
& aInteger0(sK3(X1,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
! [X7] :
( ? [X9] :
( aElementOf0(X7,X9)
& aElementOf0(X9,xS) )
=> ( aElementOf0(X7,sK4(X7))
& aElementOf0(sK4(X7),xS) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
( ~ isClosed0(sbsmnsldt0(xS))
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ? [X0] :
( ! [X1] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS)))
& ? [X2] :
( ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ! [X4] :
( sdtasdt0(X1,X4) != sdtpldt0(X3,smndt0(X0))
| ~ aInteger0(X4) ) )
| ~ aInteger0(X3) )
& ( ( sdteqdtlpzmzozddtrp0(X3,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X3,smndt0(X0)))
& ? [X5] :
( sdtpldt0(X3,smndt0(X0)) = sdtasdt0(X1,X5)
& aInteger0(X5) )
& aInteger0(X3) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X0,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
| sz00 = X1
| ~ aInteger0(X1) )
& aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
& ! [X6] :
( ( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X6,sbsmnsldt0(xS))
| ~ aInteger0(X6) )
& ( ( ~ aElementOf0(X6,sbsmnsldt0(xS))
& aInteger0(X6) )
| ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X7] :
( ( aElementOf0(X7,sbsmnsldt0(xS))
| ! [X8] :
( ~ aElementOf0(X7,X8)
| ~ aElementOf0(X8,xS) )
| ~ aInteger0(X7) )
& ( ( ? [X9] :
( aElementOf0(X7,X9)
& aElementOf0(X9,xS) )
& aInteger0(X7) )
| ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(rectify,[],[f119]) ).
fof(f119,plain,
( ~ isClosed0(sbsmnsldt0(xS))
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ? [X3] :
( ! [X4] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ? [X8] :
( ~ aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ! [X5] :
( ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ( ~ sdteqdtlpzmzozddtrp0(X5,X3,X4)
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ! [X6] :
( sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X5) )
& ( ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X7] :
( sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X7)
& aInteger0(X7) )
& aInteger0(X5) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
| sz00 = X4
| ~ aInteger0(X4) )
& aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ! [X2] :
( ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2) )
& ( ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) )
| ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0) )
& ( ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
( ~ isClosed0(sbsmnsldt0(xS))
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ? [X3] :
( ! [X4] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ? [X8] :
( ~ aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ! [X5] :
( ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ( ~ sdteqdtlpzmzozddtrp0(X5,X3,X4)
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ! [X6] :
( sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X5) )
& ( ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X7] :
( sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X7)
& aInteger0(X7) )
& aInteger0(X5) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
| sz00 = X4
| ~ aInteger0(X4) )
& aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ! [X2] :
( ( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X2,sbsmnsldt0(xS))
| ~ aInteger0(X2) )
& ( ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) )
| ~ aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) )
& ! [X0] :
( ( aElementOf0(X0,sbsmnsldt0(xS))
| ! [X1] :
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,xS) )
| ~ aInteger0(X0) )
& ( ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) )
| ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
( ~ isClosed0(sbsmnsldt0(xS))
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ? [X3] :
( ! [X4] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ? [X8] :
( ~ aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ! [X5] :
( ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ( ~ sdteqdtlpzmzozddtrp0(X5,X3,X4)
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ! [X6] :
( sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X5) )
& ( ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X7] :
( sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X7)
& aInteger0(X7) )
& aInteger0(X5) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
| sz00 = X4
| ~ aInteger0(X4) )
& aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
( ~ isClosed0(sbsmnsldt0(xS))
& ~ isOpen0(stldt0(sbsmnsldt0(xS)))
& ? [X3] :
( ! [X4] :
( ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
& ? [X8] :
( ~ aElementOf0(X8,stldt0(sbsmnsldt0(xS)))
& aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ! [X5] :
( ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
| ( ~ sdteqdtlpzmzozddtrp0(X5,X3,X4)
& ~ aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ! [X6] :
( sdtpldt0(X5,smndt0(X3)) != sdtasdt0(X4,X6)
| ~ aInteger0(X6) ) )
| ~ aInteger0(X5) )
& ( ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X7] :
( sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X7)
& aInteger0(X7) )
& aInteger0(X5) )
| ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
| sz00 = X4
| ~ aInteger0(X4) )
& aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isClosed0(sbsmnsldt0(xS))
| ( ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X2,sbsmnsldt0(xS))
& aInteger0(X2) ) )
=> ( isOpen0(stldt0(sbsmnsldt0(xS)))
| ! [X3] :
( aElementOf0(X3,stldt0(sbsmnsldt0(xS)))
=> ? [X4] :
( ( ( ! [X5] :
( ( ( ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
| aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
| ? [X6] :
( sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X6)
& aInteger0(X6) ) )
& aInteger0(X5) )
=> aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
& ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> ( sdteqdtlpzmzozddtrp0(X5,X3,X4)
& aDivisorOf0(X4,sdtpldt0(X5,smndt0(X3)))
& ? [X7] :
( sdtpldt0(X5,smndt0(X3)) = sdtasdt0(X4,X7)
& aInteger0(X7) )
& aInteger0(X5) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X3,X4)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),stldt0(sbsmnsldt0(xS)))
| ! [X8] :
( aElementOf0(X8,szAzrzSzezqlpdtcmdtrp0(X3,X4))
=> aElementOf0(X8,stldt0(sbsmnsldt0(xS))) ) ) )
& sz00 != X4
& aInteger0(X4) ) ) ) ) ) ),
inference(rectify,[],[f46]) ).
fof(f46,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isClosed0(sbsmnsldt0(xS))
| ( ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
=> ( isOpen0(stldt0(sbsmnsldt0(xS)))
| ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) ) )
& sz00 != X1
& aInteger0(X1) ) ) ) ) ) ),
inference(negated_conjecture,[],[f45]) ).
fof(f45,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( ? [X1] :
( aElementOf0(X0,X1)
& aElementOf0(X1,xS) )
& aInteger0(X0) ) )
& aSet0(sbsmnsldt0(xS)) )
=> ( isClosed0(sbsmnsldt0(xS))
| ( ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
& aInteger0(X0) ) )
=> ( isOpen0(stldt0(sbsmnsldt0(xS)))
| ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sbsmnsldt0(xS)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) ) ) )
& sz00 != X1
& aInteger0(X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qXM7asOdtv/Vampire---4.8_32682',m__) ).
fof(f1364,plain,
( isClosed0(sbsmnsldt0(xS))
| ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(subsumption_resolution,[],[f1359,f1219]) ).
fof(f1219,plain,
isClosed0(sK15(xS)),
inference(subsumption_resolution,[],[f1218,f214]) ).
fof(f1218,plain,
( isClosed0(sK15(xS))
| ~ aSet0(xS) ),
inference(subsumption_resolution,[],[f1217,f213]) ).
fof(f1217,plain,
( isClosed0(sK15(xS))
| ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(subsumption_resolution,[],[f1203,f212]) ).
fof(f1203,plain,
( isClosed0(sK15(xS))
| isClosed0(sbsmnsldt0(xS))
| ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(resolution,[],[f1061,f292]) ).
fof(f292,plain,
! [X0] :
( aElementOf0(sK15(X0),X0)
| isClosed0(sbsmnsldt0(X0))
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0] :
( isClosed0(sbsmnsldt0(X0))
| ( ( ~ isClosed0(sK15(X0))
| ~ aSubsetOf0(sK15(X0),cS1395) )
& aElementOf0(sK15(X0),X0) )
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f73,f161]) ).
fof(f161,plain,
! [X0] :
( ? [X1] :
( ( ~ isClosed0(X1)
| ~ aSubsetOf0(X1,cS1395) )
& aElementOf0(X1,X0) )
=> ( ( ~ isClosed0(sK15(X0))
| ~ aSubsetOf0(sK15(X0),cS1395) )
& aElementOf0(sK15(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( isClosed0(sbsmnsldt0(X0))
| ? [X1] :
( ( ~ isClosed0(X1)
| ~ aSubsetOf0(X1,cS1395) )
& aElementOf0(X1,X0) )
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0] :
( isClosed0(sbsmnsldt0(X0))
| ? [X1] :
( ( ~ isClosed0(X1)
| ~ aSubsetOf0(X1,cS1395) )
& aElementOf0(X1,X0) )
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ( ! [X1] :
( aElementOf0(X1,X0)
=> ( isClosed0(X1)
& aSubsetOf0(X1,cS1395) ) )
& isFinite0(X0)
& aSet0(X0) )
=> isClosed0(sbsmnsldt0(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.qXM7asOdtv/Vampire---4.8_32682',mUnionSClosed) ).
fof(f1061,plain,
! [X9] :
( ~ aElementOf0(X9,xS)
| isClosed0(X9) ),
inference(subsumption_resolution,[],[f1060,f215]) ).
fof(f215,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aInteger0(sK6(X0)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f1060,plain,
! [X9] :
( isClosed0(X9)
| ~ aInteger0(sK6(X9))
| ~ aElementOf0(X9,xS) ),
inference(subsumption_resolution,[],[f1059,f216]) ).
fof(f216,plain,
! [X0] :
( sz00 != sK6(X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f129]) ).
fof(f1059,plain,
! [X9] :
( isClosed0(X9)
| sz00 = sK6(X9)
| ~ aInteger0(sK6(X9))
| ~ aElementOf0(X9,xS) ),
inference(subsumption_resolution,[],[f999,f253]) ).
fof(f253,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/tmp/tmp.qXM7asOdtv/Vampire---4.8_32682',mIntZero) ).
fof(f999,plain,
! [X9] :
( isClosed0(X9)
| sz00 = sK6(X9)
| ~ aInteger0(sK6(X9))
| ~ aInteger0(sz00)
| ~ aElementOf0(X9,xS) ),
inference(superposition,[],[f309,f227]) ).
fof(f227,plain,
! [X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,sK6(X0)) = X0
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f129]) ).
fof(f309,plain,
! [X0,X1] :
( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395) )
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395) )
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
( ( sz00 != X1
& aInteger0(X1)
& aInteger0(X0) )
=> ( isClosed0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395) ) ),
file('/export/starexec/sandbox/tmp/tmp.qXM7asOdtv/Vampire---4.8_32682',mArSeqClosed) ).
fof(f1359,plain,
( ~ isClosed0(sK15(xS))
| isClosed0(sbsmnsldt0(xS))
| ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(resolution,[],[f1349,f293]) ).
fof(f293,plain,
! [X0] :
( ~ aSubsetOf0(sK15(X0),cS1395)
| ~ isClosed0(sK15(X0))
| isClosed0(sbsmnsldt0(X0))
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f1349,plain,
aSubsetOf0(sK15(xS),cS1395),
inference(subsumption_resolution,[],[f1348,f214]) ).
fof(f1348,plain,
( aSubsetOf0(sK15(xS),cS1395)
| ~ aSet0(xS) ),
inference(subsumption_resolution,[],[f1347,f213]) ).
fof(f1347,plain,
( aSubsetOf0(sK15(xS),cS1395)
| ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(subsumption_resolution,[],[f1333,f212]) ).
fof(f1333,plain,
( aSubsetOf0(sK15(xS),cS1395)
| isClosed0(sbsmnsldt0(xS))
| ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(resolution,[],[f1064,f292]) ).
fof(f1064,plain,
! [X8] :
( ~ aElementOf0(X8,xS)
| aSubsetOf0(X8,cS1395) ),
inference(subsumption_resolution,[],[f1063,f215]) ).
fof(f1063,plain,
! [X8] :
( aSubsetOf0(X8,cS1395)
| ~ aInteger0(sK6(X8))
| ~ aElementOf0(X8,xS) ),
inference(subsumption_resolution,[],[f1062,f216]) ).
fof(f1062,plain,
! [X8] :
( aSubsetOf0(X8,cS1395)
| sz00 = sK6(X8)
| ~ aInteger0(sK6(X8))
| ~ aElementOf0(X8,xS) ),
inference(subsumption_resolution,[],[f998,f253]) ).
fof(f998,plain,
! [X8] :
( aSubsetOf0(X8,cS1395)
| sz00 = sK6(X8)
| ~ aInteger0(sK6(X8))
| ~ aInteger0(sz00)
| ~ aElementOf0(X8,xS) ),
inference(superposition,[],[f308,f227]) ).
fof(f308,plain,
! [X0,X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),cS1395)
| sz00 = X1
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM449+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 18:17:49 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.qXM7asOdtv/Vampire---4.8_32682
% 0.15/0.37 % (321)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (328)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.22/0.43 % (323)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.22/0.43 % (325)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.22/0.43 % (322)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.22/0.43 % (326)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.22/0.43 % (327)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.22/0.43 % (324)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.22/0.45 % (328)First to succeed.
% 0.22/0.45 % (328)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for Vampire---4
% 0.22/0.45 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.45 % (328)------------------------------
% 0.22/0.45 % (328)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45 % (328)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45 % (328)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (328)Memory used [KB]: 6268
% 0.22/0.45 % (328)Time elapsed: 0.027 s
% 0.22/0.45 % (328)------------------------------
% 0.22/0.45 % (328)------------------------------
% 0.22/0.45 % (321)Success in time 0.082 s
% 0.22/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------