%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM453+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 : n020.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 12:15:15 PM UTC 2026
% Result : Theorem 4.35s 1.59s
% Output : Refutation 5.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of formulae : 117 ( 16 unt; 5 def)
% Number of atoms : 543 ( 96 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 661 ( 235 ~; 212 |; 189 &)
% ( 13 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 84 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(f5,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f8,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f9,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(f46,axiom,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
& ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X0] :
( aElementOf0(X0,sbsmnsldt0(xS))
<=> ( aInteger0(X0)
& ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(X0,X1) ) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X0)
& ~ aElementOf0(X0,sbsmnsldt0(xS)) ) )
& ! [X0] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(f47,axiom,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xp,X0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ? [X0] :
( aInteger0(X0)
& sdtasdt0(xp,X0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2232) ).
fof(f48,conjecture,
( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f53,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
& ( ( aInteger0(X0)
& ( ? [X2] :
( aInteger0(X2)
& sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,X2) )
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
=> aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) ) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) ) )
& ! [X6] :
( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X6,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(rectify,[],[f46]) ).
fof(f54,plain,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xp,X0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(rectify,[],[f47]) ).
fof(f65,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) ) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) ) )
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(ennf_transformation,[],[f53]) ).
fof(f66,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( aElementOf0(X3,sbsmnsldt0(xS))
<=> ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) ) )
& ! [X5] :
( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) ) )
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
( sz10 = sdtpldt0(sz10,xp)
| sz10 = sdtpldt0(sz10,smndt0(xp)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f103,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f104,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f105,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f106,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f108,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f110,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f111,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f110]) ).
fof(f161,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) )
& ! [X5] :
( ( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X5)
| aElementOf0(X5,sbsmnsldt0(xS)) )
& ( ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) )
| ~ aElementOf0(X5,stldt0(sbsmnsldt0(xS))) ) )
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(nnf_transformation,[],[f66]) ).
fof(f162,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& ? [X4] :
( aElementOf0(X4,xS)
& aElementOf0(X3,X4) ) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) )
& ! [X5] :
( ( aElementOf0(X5,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X5)
| aElementOf0(X5,sbsmnsldt0(xS)) )
& ( ( aInteger0(X5)
& ~ aElementOf0(X5,sbsmnsldt0(xS)) )
| ~ aElementOf0(X5,stldt0(sbsmnsldt0(xS))) ) )
& ! [X6] :
( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(flattening,[],[f161]) ).
fof(f163,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& ? [X5] :
( aElementOf0(X5,xS)
& aElementOf0(X3,X5) ) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) )
& ! [X6] :
( ( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X6)
| aElementOf0(X6,sbsmnsldt0(xS)) )
& ( ( aInteger0(X6)
& ~ aElementOf0(X6,sbsmnsldt0(xS)) )
| ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X7] :
( aElementOf0(X7,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(rectify,[],[f162]) ).
fof(f164,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& aInteger0(sK20(X0))
& sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,sK20(X0))
& aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X0,sz10,xp) )
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X0)
| ( ! [X2] :
( ~ aInteger0(X2)
| sdtpldt0(X0,smndt0(sz10)) != sdtasdt0(xp,X2) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X3] :
( ( aElementOf0(X3,sbsmnsldt0(xS))
| ~ aInteger0(X3)
| ! [X4] :
( ~ aElementOf0(X4,xS)
| ~ aElementOf0(X3,X4) ) )
& ( ( aInteger0(X3)
& aElementOf0(sK21(X3),xS)
& aElementOf0(X3,sK21(X3)) )
| ~ aElementOf0(X3,sbsmnsldt0(xS)) ) )
& ! [X6] :
( ( aElementOf0(X6,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X6)
| aElementOf0(X6,sbsmnsldt0(xS)) )
& ( ( aInteger0(X6)
& ~ aElementOf0(X6,sbsmnsldt0(xS)) )
| ~ aElementOf0(X6,stldt0(sbsmnsldt0(xS))) ) )
& ! [X7] :
( aElementOf0(X7,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X7,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X1,sK20(X0)),skolemize(X5,sK21(X3))],[f163]) ).
fof(f165,plain,
( aInteger0(sK22)
& sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) = sdtasdt0(xp,sK22)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& aInteger0(sK23)
& sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) = sdtasdt0(xp,sK23)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23]),skolemize(X0,sK22),skolemize(X1,sK23)],[f54]) ).
fof(f318,plain,
sz00 != xp,
inference(cnf_transformation,[],[f164]) ).
fof(f319,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f164]) ).
fof(f328,plain,
sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) = sdtasdt0(xp,sK22),
inference(cnf_transformation,[],[f165]) ).
fof(f330,plain,
( sz10 = sdtpldt0(sz10,xp)
| sz10 = sdtpldt0(sz10,smndt0(xp)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f416,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f417,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f419,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f420,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f421,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f422,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f423,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f424,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f434,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f523,definition,
( spl39_1
<=> aInteger0(smndt0(sz10)) ),
introduced(definition,[new_symbols(definition,[spl39_1])],[avatar_definition]) ).
fof(f524,plain,
( aInteger0(smndt0(sz10))
| ~ spl39_1 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f525,plain,
( ~ aInteger0(smndt0(sz10))
| spl39_1 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f532,definition,
( spl39_3
<=> sz10 = sdtpldt0(sz10,smndt0(xp)) ),
introduced(definition,[new_symbols(definition,[spl39_3])],[avatar_definition]) ).
fof(f534,plain,
( sz10 = sdtpldt0(sz10,smndt0(xp))
| ~ spl39_3 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f536,definition,
( spl39_4
<=> sz10 = sdtpldt0(sz10,xp) ),
introduced(definition,[new_symbols(definition,[spl39_4])],[avatar_definition]) ).
fof(f537,plain,
( sz10 != sdtpldt0(sz10,xp)
| spl39_4 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f538,plain,
( sz10 = sdtpldt0(sz10,xp)
| ~ spl39_4 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f539,plain,
( spl39_3
| spl39_4 ),
inference(avatar_split_clause,[],[f330,f536,f532]) ).
fof(f556,plain,
( ~ aInteger0(sz10)
| spl39_1 ),
inference(resolution,[],[f423,f525]) ).
fof(f557,plain,
( $false
| spl39_1 ),
inference(forward_subsumption_resolution,[],[f556,f434]) ).
fof(f558,plain,
spl39_1,
inference(avatar_contradiction_clause,[],[f557]) ).
fof(f715,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(sz10,X0) = sdtpldt0(X0,sz10) ),
inference(resolution,[],[f420,f434]) ).
fof(f1119,plain,
( sdtasdt0(xp,sK22) = sdtpldt0(sz10,smndt0(sz10))
| ~ spl39_4 ),
inference(superposition,[],[f328,f538]) ).
fof(f1201,plain,
( sz00 = sdtasdt0(xp,sK22)
| ~ aInteger0(sz10)
| ~ spl39_4 ),
inference(superposition,[],[f417,f1119]) ).
fof(f1203,plain,
( sz00 = sdtasdt0(xp,sK22)
| ~ spl39_4 ),
inference(forward_subsumption_resolution,[],[f1201,f434]) ).
fof(f1245,plain,
( sdtasdt0(xp,sK22) = sdtpldt0(sz10,smndt0(sz10))
| ~ spl39_4 ),
inference(superposition,[],[f328,f538]) ).
fof(f1251,plain,
( sz00 = sdtpldt0(sz10,smndt0(sz10))
| ~ spl39_4 ),
inference(forward_demodulation,[],[f1245,f1203]) ).
fof(f1740,plain,
( sdtasdt0(xp,sK22) = sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10)))
| ~ aInteger0(sz10)
| ~ aInteger0(xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(superposition,[],[f328,f421]) ).
fof(f1773,plain,
( sdtasdt0(xp,sK22) = sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10)))
| ~ aInteger0(xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(forward_subsumption_resolution,[],[f1740,f434]) ).
fof(f1801,plain,
( sdtasdt0(xp,sK22) = sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10)))
| ~ aInteger0(smndt0(sz10)) ),
inference(forward_subsumption_resolution,[],[f1773,f319]) ).
fof(f1814,definition,
( spl39_46
<=> aInteger0(smndt0(xp)) ),
introduced(definition,[new_symbols(definition,[spl39_46])],[avatar_definition]) ).
fof(f1815,plain,
( aInteger0(smndt0(xp))
| ~ spl39_46 ),
inference(avatar_component_clause,[],[f1814]) ).
fof(f1816,plain,
( ~ aInteger0(smndt0(xp))
| spl39_46 ),
inference(avatar_component_clause,[],[f1814]) ).
fof(f1828,plain,
( sdtasdt0(xp,sK22) = sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10)))
| ~ spl39_1 ),
inference(forward_subsumption_resolution,[],[f1801,f524]) ).
fof(f1832,plain,
( sz00 = sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10)))
| ~ spl39_1
| ~ spl39_4 ),
inference(forward_demodulation,[],[f1828,f1203]) ).
fof(f2053,definition,
( spl39_53
<=> aInteger0(sdtpldt0(xp,smndt0(sz10))) ),
introduced(definition,[new_symbols(definition,[spl39_53])],[avatar_definition]) ).
fof(f2054,plain,
( aInteger0(sdtpldt0(xp,smndt0(sz10)))
| ~ spl39_53 ),
inference(avatar_component_clause,[],[f2053]) ).
fof(f2055,plain,
( ~ aInteger0(sdtpldt0(xp,smndt0(sz10)))
| spl39_53 ),
inference(avatar_component_clause,[],[f2053]) ).
fof(f2109,plain,
( ~ aInteger0(xp)
| ~ aInteger0(smndt0(sz10))
| spl39_53 ),
inference(resolution,[],[f2055,f424]) ).
fof(f2120,plain,
( ~ aInteger0(smndt0(sz10))
| spl39_53 ),
inference(forward_subsumption_resolution,[],[f2109,f319]) ).
fof(f2121,plain,
( $false
| ~ spl39_1
| spl39_53 ),
inference(forward_subsumption_resolution,[],[f2120,f524]) ).
fof(f2122,plain,
( ~ spl39_1
| spl39_53 ),
inference(avatar_contradiction_clause,[],[f2121]) ).
fof(f2321,plain,
( ~ aInteger0(xp)
| spl39_46 ),
inference(resolution,[],[f1816,f423]) ).
fof(f2332,plain,
( $false
| spl39_46 ),
inference(forward_subsumption_resolution,[],[f2321,f319]) ).
fof(f2333,plain,
spl39_46,
inference(avatar_contradiction_clause,[],[f2332]) ).
fof(f2352,plain,
( ! [X0] :
( sdtpldt0(sz10,X0) = sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0))
| ~ aInteger0(sz10)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0) )
| ~ spl39_3 ),
inference(superposition,[],[f421,f534]) ).
fof(f2354,plain,
( ! [X0] :
( sdtpldt0(sz10,X0) = sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0))
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(X0) )
| ~ spl39_3 ),
inference(forward_subsumption_resolution,[],[f2352,f434]) ).
fof(f2356,plain,
( ! [X0] :
( sdtpldt0(sz10,X0) = sdtpldt0(sz10,sdtpldt0(smndt0(xp),X0))
| ~ aInteger0(X0) )
| ~ spl39_3
| ~ spl39_46 ),
inference(forward_subsumption_resolution,[],[f2354,f1815]) ).
fof(f2372,plain,
( sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| ~ aInteger0(xp)
| ~ aInteger0(xp)
| ~ spl39_3
| ~ spl39_46 ),
inference(superposition,[],[f2356,f416]) ).
fof(f2373,plain,
( sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,sz00)
| ~ aInteger0(sz00)
| ~ aInteger0(smndt0(xp))
| ~ spl39_3
| ~ spl39_46 ),
inference(superposition,[],[f2356,f419]) ).
fof(f2378,plain,
( sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| ~ aInteger0(xp)
| ~ spl39_3
| ~ spl39_46 ),
inference(duplicate_literal_removal,[],[f2372]) ).
fof(f2382,plain,
( sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,sz00)
| ~ aInteger0(smndt0(xp))
| ~ spl39_3
| ~ spl39_46 ),
inference(forward_subsumption_resolution,[],[f2373,f422]) ).
fof(f2383,plain,
( sdtpldt0(sz10,xp) = sdtpldt0(sz10,sz00)
| ~ spl39_3
| ~ spl39_46 ),
inference(forward_subsumption_resolution,[],[f2378,f319]) ).
fof(f2386,plain,
( sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(sz10,sz00)
| ~ spl39_3
| ~ spl39_46 ),
inference(forward_subsumption_resolution,[],[f2382,f1815]) ).
fof(f2974,plain,
( sdtpldt0(sz10,smndt0(sz10)) = sdtpldt0(smndt0(sz10),sz10)
| ~ spl39_1 ),
inference(resolution,[],[f715,f524]) ).
fof(f2985,plain,
( sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))) = sdtpldt0(sdtpldt0(xp,smndt0(sz10)),sz10)
| ~ spl39_53 ),
inference(resolution,[],[f715,f2054]) ).
fof(f3025,plain,
( sz00 = sdtpldt0(sdtpldt0(xp,smndt0(sz10)),sz10)
| ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(forward_demodulation,[],[f2985,f1832]) ).
fof(f3031,plain,
( sz00 = sdtpldt0(smndt0(sz10),sz10)
| ~ spl39_1
| ~ spl39_4 ),
inference(forward_demodulation,[],[f2974,f1251]) ).
fof(f3093,plain,
( sz00 = sdtpldt0(xp,sdtpldt0(smndt0(sz10),sz10))
| ~ aInteger0(xp)
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sz10)
| ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(superposition,[],[f421,f3025]) ).
fof(f3097,plain,
( sz00 = sdtpldt0(xp,sdtpldt0(smndt0(sz10),sz10))
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sz10)
| ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(forward_subsumption_resolution,[],[f3093,f319]) ).
fof(f3100,plain,
( sz00 = sdtpldt0(xp,sdtpldt0(smndt0(sz10),sz10))
| ~ aInteger0(sz10)
| ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(forward_subsumption_resolution,[],[f3097,f423]) ).
fof(f3102,plain,
( sz00 = sdtpldt0(xp,sdtpldt0(smndt0(sz10),sz10))
| ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(forward_subsumption_resolution,[],[f3100,f434]) ).
fof(f3104,plain,
( sz00 = sdtpldt0(xp,sz00)
| ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(forward_demodulation,[],[f3102,f3031]) ).
fof(f3126,plain,
( sz00 = xp
| ~ aInteger0(xp)
| ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(superposition,[],[f3104,f419]) ).
fof(f3134,plain,
( ~ aInteger0(xp)
| ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(forward_subsumption_resolution,[],[f3126,f318]) ).
fof(f3139,plain,
( $false
| ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(forward_subsumption_resolution,[],[f3134,f319]) ).
fof(f3140,plain,
( ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(avatar_contradiction_clause,[],[f3139]) ).
fof(f3150,plain,
( sz10 = sdtpldt0(sz10,sz00)
| ~ spl39_3
| ~ spl39_46 ),
inference(forward_demodulation,[],[f2386,f534]) ).
fof(f4441,plain,
( sz10 != sdtpldt0(sz10,sz00)
| ~ spl39_3
| spl39_4
| ~ spl39_46 ),
inference(superposition,[],[f537,f2383]) ).
fof(f4450,plain,
( $false
| ~ spl39_3
| spl39_4
| ~ spl39_46 ),
inference(forward_subsumption_resolution,[],[f4441,f3150]) ).
fof(f4451,plain,
( ~ spl39_3
| spl39_4
| ~ spl39_46 ),
inference(avatar_contradiction_clause,[],[f4450]) ).
cnf(s2,plain,
( spl39_3
| spl39_4 ),
inference(sat_conversion,[],[f539]) ).
cnf(s5,plain,
spl39_1,
inference(sat_conversion,[],[f558]) ).
cnf(s78,plain,
( ~ spl39_1
| spl39_53 ),
inference(sat_conversion,[],[f2122]) ).
cnf(s85,plain,
spl39_46,
inference(sat_conversion,[],[f2333]) ).
cnf(s101,plain,
( ~ spl39_1
| ~ spl39_4
| ~ spl39_53 ),
inference(sat_conversion,[],[f3140]) ).
cnf(s136,plain,
( ~ spl39_3
| spl39_4
| ~ spl39_46 ),
inference(sat_conversion,[],[f4451]) ).
cnf(s156,plain,
spl39_53,
inference(rat,[],[s78,s5]) ).
cnf(s161,plain,
~ spl39_4,
inference(rat,[],[s101,s5,s156]) ).
cnf(s163,plain,
~ spl39_3,
inference(rat,[],[s136,s85,s161]) ).
cnf(s166,plain,
$false,
inference(rat,[],[s2,s161,s163]) ).
fof(f4469,plain,
$false,
inference(avatar_sat_refutation,[],[s166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM453+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.36 % Computer : n020.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8046.5625MB
% 0.13/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun Sep 27 20:00:49 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 4.35/1.59 % (3708207)Detected formulas, will run a generic FOF schedule.
% 4.35/1.59 % (3708216)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2889629912:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.35/1.59 % (3708216)Instruction limit reached!
% 4.35/1.59 % (3708216)------------------------------
% 4.35/1.59 % (3708216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.59 % (3708216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.59 % (3708216)CaDiCaL version: 2.1.3
% 4.35/1.59 % (3708216)Termination reason: Instruction limit
% 4.35/1.59 % (3708216)Termination phase: Saturation
% 4.35/1.59 % (3708216)Time elapsed: 0.041 s
% 4.35/1.59 % (3708216)Peak memory usage: 89 MB
% 4.35/1.59 % (3708216)Instructions burned: 128 (million)
% 4.35/1.59 % (3708218)dis-21_1_sil=8000:lcm=predicate:random_seed=3171183883: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)
% 4.35/1.59 % (3708213)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=102487113:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.35/1.59 % (3708215)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1716321492:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.35/1.59 % (3708214)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=963410994:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.35/1.59 % (3708212)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=1690996692:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.35/1.59 % (3708217)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3203516441:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.35/1.59 % (3708217)Instruction limit reached!
% 4.35/1.59 % (3708217)------------------------------
% 4.35/1.59 % (3708217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.59 % (3708217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.59 % (3708217)CaDiCaL version: 2.1.3
% 4.35/1.59 % (3708217)Termination reason: Instruction limit
% 4.35/1.59 % (3708217)Termination phase: Saturation
% 4.35/1.59 % (3708217)Time elapsed: 0.049 s
% 4.35/1.59 % (3708217)Peak memory usage: 90 MB
% 4.35/1.59 % (3708217)Instructions burned: 140 (million)
% 4.35/1.59 % (3708215)Instruction limit reached!
% 4.35/1.59 % (3708215)------------------------------
% 4.35/1.59 % (3708215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.59 % (3708215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.59 % (3708215)CaDiCaL version: 2.1.3
% 4.35/1.59 % (3708215)Termination reason: Instruction limit
% 4.35/1.59 % (3708215)Termination phase: Saturation
% 4.35/1.59 % (3708215)Time elapsed: 0.069 s
% 4.35/1.59 % (3708215)Peak memory usage: 89 MB
% 4.35/1.59 % (3708215)Instructions burned: 110 (million)
% 4.35/1.59 % (3708218)Instruction limit reached!
% 4.35/1.59 % (3708218)------------------------------
% 4.35/1.59 % (3708218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.59 % (3708218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.59 % (3708218)CaDiCaL version: 2.1.3
% 4.35/1.59 % (3708218)Termination reason: Instruction limit
% 4.35/1.59 % (3708218)Termination phase: Saturation
% 4.35/1.59 % (3708218)Time elapsed: 0.075 s
% 4.35/1.59 % (3708218)Peak memory usage: 90 MB
% 4.35/1.59 % (3708218)Instructions burned: 130 (million)
% 4.35/1.59 % (3708226)lrs+10_1_sil=8000:sp=occurrence:random_seed=3023180146:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.35/1.59 % (3708227)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1264973106:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.35/1.59 % (3708228)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3790044994:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.35/1.59 % (3708227)Instruction limit reached!
% 4.35/1.59 % (3708227)------------------------------
% 4.35/1.59 % (3708227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.59 % (3708227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.59 % (3708227)CaDiCaL version: 2.1.3
% 4.35/1.59 % (3708227)Termination reason: Instruction limit
% 4.35/1.59 % (3708227)Termination phase: Saturation
% 4.35/1.59 % (3708227)Time elapsed: 0.045 s
% 4.35/1.59 % (3708227)Peak memory usage: 94 MB
% 4.35/1.59 % (3708227)Instructions burned: 157 (million)
% 4.35/1.59 % (3708229)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=70998542:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.35/1.59 % (3708228)First to succeed.
% 4.35/1.59 % (3708226)Instruction limit reached!
% 4.35/1.59 % (3708226)------------------------------
% 4.35/1.59 % (3708226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.59 % (3708226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.59 % (3708226)CaDiCaL version: 2.1.3
% 4.35/1.59 % (3708226)Termination reason: Instruction limit
% 4.35/1.59 % (3708226)Termination phase: Saturation
% 4.35/1.59 % (3708226)Time elapsed: 0.171 s
% 4.35/1.59 % (3708226)Peak memory usage: 92 MB
% 4.35/1.59 % (3708226)Instructions burned: 287 (million)
% 4.35/1.59 % (3708228)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3708207"
% 4.35/1.59 % (3708233)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1862686438:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.35/1.59 % (3708229)Instruction limit reached!
% 4.35/1.59 % (3708229)------------------------------
% 4.35/1.59 % (3708229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.59 % (3708229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.59 % (3708229)CaDiCaL version: 2.1.3
% 4.35/1.59 % (3708229)Termination reason: Instruction limit
% 4.35/1.59 % (3708229)Termination phase: Saturation
% 4.35/1.59 % (3708229)Time elapsed: 0.126 s
% 4.35/1.59 % (3708229)Peak memory usage: 94 MB
% 4.35/1.59 % (3708229)Instructions burned: 249 (million)
% 4.35/1.59 % (3708233)Instruction limit reached!
% 4.35/1.59 % (3708233)------------------------------
% 4.35/1.59 % (3708233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.35/1.59 % (3708233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.35/1.59 % (3708233)CaDiCaL version: 2.1.3
% 4.35/1.59 % (3708233)Termination reason: Instruction limit
% 4.35/1.59 % (3708233)Termination phase: Saturation
% 4.35/1.59 % (3708233)Time elapsed: 0.098 s
% 4.35/1.59 % (3708233)Peak memory usage: 91 MB
% 4.35/1.59 % (3708233)Instructions burned: 294 (million)
% 4.35/1.59 % (3708235)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=902387252:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.35/1.59 % (3708237)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1286190141:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.35/1.59 % (3708238)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=577848400:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 4.35/1.59 % (3708228)Refutation found. Thanks to Tanya!
% 4.35/1.59 % SZS status Theorem for theBenchmark
% 4.35/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 5.87/1.79 % (3708228)------------------------------
% 5.87/1.79 % (3708228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.79 % (3708228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.79 % (3708228)CaDiCaL version: 2.1.3
% 5.87/1.79 % (3708228)Termination reason: Refutation
% 5.87/1.79 % (3708228)Time elapsed: 0.115 s
% 5.87/1.79 % (3708228)Peak memory usage: 92 MB
% 5.87/1.79 % (3708228)Instructions burned: 168 (million)
% 5.87/1.79 % (3708228)------------------------------
% 5.87/1.79 % (3708228)------------------------------
% 5.87/1.79 % (3708207)Success in time 0.753 s
% 5.87/1.79 % Vampire exiting
%------------------------------------------------------------------------------