%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM443+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:15:12 PM UTC 2026
% Result : Theorem 2.61s 1.29s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 12
% Syntax : Number of formulae : 102 ( 17 unt; 4 def)
% Number of atoms : 670 ( 113 equ)
% Maximal formula atoms : 34 ( 6 avg)
% Number of connectives : 846 ( 278 ~; 300 |; 232 &)
% ( 11 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 4 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 158 ( 0 sgn 126 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(f21,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
=> sdteqdtlpzmzozddtrp0(X1,X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModSym) ).
fof(f22,axiom,
! [X0,X1,X2,X3] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2)
& X2 != sz00
& aInteger0(X3) )
=> ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
& sdteqdtlpzmzozddtrp0(X1,X3,X2) )
=> sdteqdtlpzmzozddtrp0(X0,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModTrn) ).
fof(f34,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1)
& X1 != sz00 )
=> ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArSeq) ).
fof(f41,axiom,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1962) ).
fof(f42,axiom,
( aInteger0(xb)
& aInteger0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2010) ).
fof(f43,conjecture,
( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xc,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f44,negated_conjecture,
~ ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xc,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
& ( ( aInteger0(X0)
& ( ? [X2] :
( aInteger0(X2)
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,X2) )
| aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X0,xa,xq) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X3] :
( aInteger0(X3)
& sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,X3) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X4] :
( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(xq,X5) = sdtpldt0(X4,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X4,xa,xq) ) )
& ( ( aInteger0(X4)
& ( ? [X6] :
( aInteger0(X6)
& sdtpldt0(X4,smndt0(xa)) = sdtasdt0(xq,X6) )
| aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(X4,xa,xq) ) )
=> aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ),
inference(rectify,[],[f44]) ).
fof(f49,plain,
( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X4] :
( ( ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(xq,X5) = sdtpldt0(X4,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X4,xa,xq) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X4)
| ( ! [X6] :
( ~ aInteger0(X6)
| sdtpldt0(X4,smndt0(xa)) != sdtasdt0(xq,X6) )
& ~ aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X4,xa,xq) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2) )
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X0,xa,xq) ) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X3] :
( aInteger0(X3)
& sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,X3) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
inference(ennf_transformation,[],[f45]) ).
fof(f50,plain,
( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X4] :
( ( ( aInteger0(X4)
& ? [X5] :
( aInteger0(X5)
& sdtasdt0(xq,X5) = sdtpldt0(X4,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X4,xa,xq) )
| ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X4)
| ( ! [X6] :
( ~ aInteger0(X6)
| sdtpldt0(X4,smndt0(xa)) != sdtasdt0(xq,X6) )
& ~ aDivisorOf0(xq,sdtpldt0(X4,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X4,xa,xq) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2) )
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X0,xa,xq) ) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X3] :
( aInteger0(X3)
& sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,X3) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
inference(flattening,[],[f49]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( sdteqdtlpzmzozddtrp0(X0,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2
| ~ aInteger0(X3) ),
inference(ennf_transformation,[],[f22]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( sdteqdtlpzmzozddtrp0(X0,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2
| ~ aInteger0(X3) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(ennf_transformation,[],[f21]) ).
fof(f61,plain,
! [X0,X1,X2] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(flattening,[],[f60]) ).
fof(f80,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f81,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f80]) ).
fof(f86,plain,
! [X0,X1] :
( ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) ) ) ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(ennf_transformation,[],[f34]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) ) ) ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(X0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2) )
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X0,xa,xq) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( ( ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(xq,X4) = sdtpldt0(X3,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X3,xa,xq) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X3)
| ( ! [X5] :
( ~ aInteger0(X5)
| sdtasdt0(xq,X5) != sdtpldt0(X3,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X3,xa,xq) ) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [X6] :
( aInteger0(X6)
& sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,X6) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
inference(rectify,[],[f50]) ).
fof(f89,plain,
( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( aInteger0(X0)
& aInteger0(sK0(X0))
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK0(X0))
& aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X0,xa,xq) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(xa)) != sdtasdt0(xq,X2) )
& ~ aDivisorOf0(xq,sdtpldt0(X0,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X0,xa,xq) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X3] :
( ( ( aInteger0(X3)
& aInteger0(sK1(X3))
& sdtpldt0(X3,smndt0(xa)) = sdtasdt0(xq,sK1(X3))
& aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(X3,xa,xq) )
| ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X3)
| ( ! [X5] :
( ~ aInteger0(X5)
| sdtasdt0(xq,X5) != sdtpldt0(X3,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(X3,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(X3,xa,xq) ) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aInteger0(sK2)
& sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,sK2)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0(X0)),skolemize(X4,sK1(X3)),skolemize(X6,sK2)],[f88]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& aInteger0(sK3(X0,X1))
& sdtasdt0(X1,sK3(X0,X1)) = X0 )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f93]) ).
fof(f107,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| ~ aElementOf0(X3,X2) ) ) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(nnf_transformation,[],[f87]) ).
fof(f108,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| ~ aElementOf0(X3,X2) ) ) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,X0,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aInteger0(X3)
& sdteqdtlpzmzozddtrp0(X3,X0,X1) )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1) )
& ( ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X0,X1) )
| ~ aElementOf0(X4,X2) ) ) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(rectify,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = szAzrzSzezqlpdtcmdtrp0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aInteger0(sK8(X0,X1,X2))
| ~ sdteqdtlpzmzozddtrp0(sK8(X0,X1,X2),X0,X1)
| ~ aElementOf0(sK8(X0,X1,X2),X2) )
& ( ( aInteger0(sK8(X0,X1,X2))
& sdteqdtlpzmzozddtrp0(sK8(X0,X1,X2),X0,X1) )
| aElementOf0(sK8(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1) )
& ( ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X0,X1) )
| ~ aElementOf0(X4,X2) ) ) )
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2 ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f109]) ).
fof(f112,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f41]) ).
fof(f113,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f41]) ).
fof(f114,plain,
aInteger0(xc),
inference(cnf_transformation,[],[f42]) ).
fof(f115,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f42]) ).
fof(f116,plain,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(cnf_transformation,[],[f89]) ).
fof(f117,plain,
aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb))),
inference(cnf_transformation,[],[f89]) ).
fof(f118,plain,
sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,sK2),
inference(cnf_transformation,[],[f89]) ).
fof(f119,plain,
aInteger0(sK2),
inference(cnf_transformation,[],[f89]) ).
fof(f121,plain,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[],[f89]) ).
fof(f141,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[],[f89]) ).
fof(f147,plain,
! [X0,X1] :
( sz00 != X1
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X1,X3,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X0,X3,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2
| ~ aInteger0(X3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(cnf_transformation,[],[f61]) ).
fof(f170,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f189,plain,
! [X2,X0,X1,X4] :
( sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aElementOf0(X4,X2)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f110]) ).
fof(f191,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| szAzrzSzezqlpdtcmdtrp0(X0,X1) != X2
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f110]) ).
fof(f198,definition,
~ sP10(sz00),
introduced(definition,[new_symbols(definition,[sP10])],[inequality_splitting_name_introduction]) ).
fof(f199,plain,
! [X0,X1] :
( ~ aDivisorOf0(X1,X0)
| sP10(X1)
| ~ aInteger0(X0) ),
inference(inequality_splitting,[],[f147,f198]) ).
fof(f210,plain,
! [X0,X1,X4] :
( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(equality_resolution,[],[f191]) ).
fof(f212,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(X0,X1))
| sdteqdtlpzmzozddtrp0(X4,X0,X1)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sz00 = X1 ),
inference(equality_resolution,[],[f189]) ).
fof(f214,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| sdteqdtlpzmzozddtrp0(X0,xb,xq)
| ~ aInteger0(X0)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| sz00 = xq
| ~ aInteger0(xb) ),
inference(resolution,[],[f116,f155]) ).
fof(f215,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| sdteqdtlpzmzozddtrp0(X0,xb,xq)
| ~ aInteger0(X0)
| ~ aInteger0(xq)
| sz00 = xq
| ~ aInteger0(xb) ),
inference(forward_subsumption_resolution,[],[f214,f114]) ).
fof(f217,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| sdteqdtlpzmzozddtrp0(X0,xb,xq)
| ~ aInteger0(X0)
| sz00 = xq
| ~ aInteger0(xb) ),
inference(forward_subsumption_resolution,[],[f215,f112]) ).
fof(f219,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| sdteqdtlpzmzozddtrp0(X0,xb,xq)
| ~ aInteger0(X0)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f217,f115]) ).
fof(f222,definition,
( spl13_1
<=> sz00 = xq ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f223,plain,
( sz00 != xq
| spl13_1 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( sz00 = xq
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f226,definition,
( spl13_2
<=> ! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| ~ aInteger0(X0)
| sdteqdtlpzmzozddtrp0(X0,xb,xq) ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f227,plain,
( ! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| ~ aInteger0(X0)
| sdteqdtlpzmzozddtrp0(X0,xb,xq) )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f228,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f219,f226,f222]) ).
fof(f234,plain,
( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(resolution,[],[f121,f210]) ).
fof(f235,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f234,f115]) ).
fof(f236,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f235,f113]) ).
fof(f237,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f236,f112]) ).
fof(f239,definition,
( spl13_4
<=> sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f241,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| spl13_4 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f242,plain,
( spl13_1
| ~ spl13_4 ),
inference(avatar_split_clause,[],[f237,f239,f222]) ).
fof(f252,plain,
( sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(resolution,[],[f141,f212]) ).
fof(f260,plain,
( sP10(xq)
| ~ aInteger0(sdtpldt0(xc,smndt0(xb))) ),
inference(resolution,[],[f117,f199]) ).
fof(f267,plain,
( sP10(sz00)
| ~ aInteger0(sdtpldt0(xc,smndt0(xb)))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f260,f224]) ).
fof(f270,plain,
( ~ aInteger0(sdtpldt0(xc,smndt0(xb)))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f267,f198]) ).
fof(f330,plain,
( aInteger0(sdtpldt0(xc,smndt0(xb)))
| ~ aInteger0(xq)
| ~ aInteger0(sK2) ),
inference(superposition,[],[f170,f118]) ).
fof(f333,plain,
( ~ aInteger0(xq)
| ~ aInteger0(sK2)
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f330,f270]) ).
fof(f335,plain,
( ~ aInteger0(sK2)
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f333,f112]) ).
fof(f337,plain,
( $false
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f335,f119]) ).
fof(f338,plain,
~ spl13_1,
inference(avatar_contradiction_clause,[],[f337]) ).
fof(f340,plain,
( sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f252,f113]) ).
fof(f369,plain,
( sdteqdtlpzmzozddtrp0(xc,xa,xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f340,f112]) ).
fof(f374,plain,
( sdteqdtlpzmzozddtrp0(xc,xa,xq)
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f369,f223]) ).
fof(f667,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ~ aInteger0(xc)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq
| spl13_1 ),
inference(resolution,[],[f374,f156]) ).
fof(f670,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f667,f114]) ).
fof(f672,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ~ aInteger0(xq)
| sz00 = xq
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f670,f113]) ).
fof(f674,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| sz00 = xq
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f672,f112]) ).
fof(f676,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f674,f223]) ).
fof(f874,plain,
( ~ aInteger0(xa)
| sdteqdtlpzmzozddtrp0(xa,xb,xq)
| spl13_1
| ~ spl13_2 ),
inference(resolution,[],[f227,f676]) ).
fof(f879,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| spl13_1
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f874,f113]) ).
fof(f899,plain,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| sz00 = xq
| spl13_1
| ~ spl13_2 ),
inference(resolution,[],[f879,f156]) ).
fof(f902,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| sz00 = xq
| spl13_1
| ~ spl13_2
| spl13_4 ),
inference(forward_subsumption_resolution,[],[f899,f241]) ).
fof(f904,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xq)
| sz00 = xq
| spl13_1
| ~ spl13_2
| spl13_4 ),
inference(forward_subsumption_resolution,[],[f902,f113]) ).
fof(f906,plain,
( ~ aInteger0(xq)
| sz00 = xq
| spl13_1
| ~ spl13_2
| spl13_4 ),
inference(forward_subsumption_resolution,[],[f904,f115]) ).
fof(f908,plain,
( sz00 = xq
| spl13_1
| ~ spl13_2
| spl13_4 ),
inference(forward_subsumption_resolution,[],[f906,f112]) ).
fof(f909,plain,
( $false
| spl13_1
| ~ spl13_2
| spl13_4 ),
inference(forward_subsumption_resolution,[],[f908,f223]) ).
fof(f910,plain,
( spl13_1
| ~ spl13_2
| spl13_4 ),
inference(avatar_contradiction_clause,[],[f909]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f228]) ).
cnf(s3,plain,
( spl13_1
| ~ spl13_4 ),
inference(sat_conversion,[],[f242]) ).
cnf(s9,plain,
~ spl13_1,
inference(sat_conversion,[],[f338]) ).
cnf(s34,plain,
( spl13_1
| ~ spl13_2
| spl13_4 ),
inference(sat_conversion,[],[f910]) ).
cnf(s47,plain,
~ spl13_4,
inference(rat,[],[s3,s9]) ).
cnf(s48,plain,
~ spl13_2,
inference(rat,[],[s34,s9,s47]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s1,s48,s9]) ).
fof(f911,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM443+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:00:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.61/1.29 % (3172992)Detected formulas, will run a generic FOF schedule.
% 2.61/1.29 % (3172999)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=1422175564:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.61/1.29 % (3172997)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=3209269281:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.61/1.29 % (3172998)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=2738242149:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.61/1.29 % (3173002)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4093726640:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.61/1.29 % (3173001)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1134986759:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.61/1.29 % (3173000)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4194741439:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.61/1.29 % (3173003)dis-21_1_sil=8000:lcm=predicate:random_seed=479629450: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)
% 2.61/1.29 % (3173000)First to succeed.
% 2.61/1.29 % (3173000)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3172992"
% 2.61/1.29 % (3173001)Also succeeded, but the first one will report.
% 2.61/1.29 % (3173002)Instruction limit reached!
% 2.61/1.29 % (3173002)------------------------------
% 2.61/1.29 % (3173002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.29 % (3173002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.29 % (3173002)CaDiCaL version: 2.1.3
% 2.61/1.29 % (3173002)Termination reason: Instruction limit
% 2.61/1.29 % (3173002)Termination phase: Saturation
% 2.61/1.29 % (3173002)Time elapsed: 0.093 s
% 2.61/1.29 % (3173002)Peak memory usage: 90 MB
% 2.61/1.29 % (3173002)Instructions burned: 140 (million)
% 2.61/1.29 % (3173003)Instruction limit reached!
% 2.61/1.29 % (3173003)------------------------------
% 2.61/1.29 % (3173003)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.29 % (3173003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.29 % (3173003)CaDiCaL version: 2.1.3
% 2.61/1.29 % (3173003)Termination reason: Instruction limit
% 2.61/1.29 % (3173003)Termination phase: Saturation
% 2.61/1.29 % (3173003)Time elapsed: 0.084 s
% 2.61/1.29 % (3173003)Peak memory usage: 89 MB
% 2.61/1.29 % (3173003)Instructions burned: 131 (million)
% 2.61/1.29 % (3173011)lrs+10_1_sil=8000:sp=occurrence:random_seed=2083386026:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.61/1.29 % (3173012)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1149551109:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.61/1.29 % (3173000)Refutation found. Thanks to Tanya!
% 2.61/1.29 % SZS status Theorem for theBenchmark
% 2.61/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.48 % (3173000)------------------------------
% 3.55/1.48 % (3173000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.48 % (3173000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.48 % (3173000)CaDiCaL version: 2.1.3
% 3.55/1.48 % (3173000)Termination reason: Refutation
% 3.55/1.48 % (3173000)Time elapsed: 0.020 s
% 3.55/1.48 % (3173000)Peak memory usage: 90 MB
% 3.55/1.48 % (3173000)Instructions burned: 30 (million)
% 3.55/1.48 % (3173000)------------------------------
% 3.55/1.48 % (3173000)------------------------------
% 3.55/1.48 % (3172992)Success in time 0.426 s
% 3.55/1.48 % Vampire exiting
%------------------------------------------------------------------------------