%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM452+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 : n015.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 6.32s 1.85s
% Output : Refutation 7.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 115 ( 33 unt; 2 def)
% Number of atoms : 536 ( 119 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 620 ( 199 ~; 193 |; 201 &)
% ( 12 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 152 ( 0 sgn 125 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
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(f13,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(f16,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtasdt0(smndt0(sz10),X0) = smndt0(X0)
& smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
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,conjecture,
( ( ? [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__) ).
fof(f48,negated_conjecture,
~ ( ( ? [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)) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f58,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(f59,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,[],[f48]) ).
fof(f60,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f61,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f62,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f61]) ).
fof(f65,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(f66,plain,
! [X0,X1,X2] :
( sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f68,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f70,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f75,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f79,plain,
! [X0] :
( ( sdtasdt0(smndt0(sz10),X0) = smndt0(X0)
& smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f120,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,[],[f58]) ).
fof(f121,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,[],[f120]) ).
fof(f122,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(ennf_transformation,[],[f59]) ).
fof(f125,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,[],[f82]) ).
fof(f126,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,[],[f125]) ).
fof(f127,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,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& aInteger0(sK1(X0,X1))
& sdtasdt0(X1,sK1(X0,X1)) = X0 )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f127]) ).
fof(f174,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,[],[f121]) ).
fof(f175,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,[],[f174]) ).
fof(f176,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,[],[f175]) ).
fof(f177,plain,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X0] :
( ( ( aInteger0(X0)
& aInteger0(sK26(X0))
& sdtpldt0(X0,smndt0(sz10)) = sdtasdt0(xp,sK26(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(sK27(X3),xS)
& aElementOf0(X3,sK27(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,[sK26,sK27]),skolemize(X1,sK26(X0)),skolemize(X5,sK27(X3))],[f176]) ).
fof(f179,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f180,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f181,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ aInteger0(X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f184,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f185,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f69]) ).
fof(f186,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f69]) ).
fof(f187,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f192,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f75]) ).
fof(f197,plain,
! [X0] :
( ~ aInteger0(X0)
| smndt0(X0) = sdtasdt0(X0,smndt0(sz10)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f204,plain,
! [X2,X0,X1] :
( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f380,plain,
sz00 != xp,
inference(cnf_transformation,[],[f177]) ).
fof(f381,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f177]) ).
fof(f392,plain,
( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
| ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f490,plain,
! [X2,X1] :
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sz00 = X1
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f204]) ).
fof(f532,definition,
( spl28_4
<=> aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))) ),
introduced(definition,[new_symbols(definition,[spl28_4])],[avatar_definition]) ).
fof(f533,plain,
( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
| spl28_4 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f547,definition,
( spl28_7
<=> aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))) ),
introduced(definition,[new_symbols(definition,[spl28_7])],[avatar_definition]) ).
fof(f548,plain,
( ~ aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
| spl28_7 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f551,plain,
( ~ spl28_4
| ~ spl28_7 ),
inference(avatar_split_clause,[],[f392,f547,f532]) ).
fof(f625,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(sz10,X0) = sdtpldt0(X0,sz10) ),
inference(resolution,[],[f179,f184]) ).
fof(f629,plain,
xp = sdtasdt0(xp,sz10),
inference(resolution,[],[f192,f381]) ).
fof(f631,plain,
smndt0(xp) = sdtasdt0(xp,smndt0(sz10)),
inference(resolution,[],[f197,f381]) ).
fof(f634,plain,
sz00 = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[],[f187,f179]) ).
fof(f681,plain,
xp = sdtpldt0(sz00,xp),
inference(resolution,[],[f185,f381]) ).
fof(f686,plain,
aInteger0(smndt0(xp)),
inference(resolution,[],[f180,f381]) ).
fof(f687,plain,
aInteger0(smndt0(sz10)),
inference(resolution,[],[f180,f179]) ).
fof(f696,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(smndt0(xp),X0) = sdtpldt0(X0,smndt0(xp)) ),
inference(resolution,[],[f686,f184]) ).
fof(f705,plain,
sdtpldt0(sz10,smndt0(xp)) = sdtpldt0(smndt0(xp),sz10),
inference(resolution,[],[f686,f625]) ).
fof(f708,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(sz10)) = sdtpldt0(smndt0(sz10),X0) ),
inference(resolution,[],[f687,f184]) ).
fof(f726,plain,
sdtpldt0(smndt0(xp),smndt0(sz10)) = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(resolution,[],[f696,f687]) ).
fof(f730,plain,
smndt0(xp) = sdtpldt0(smndt0(xp),sz00),
inference(resolution,[],[f186,f686]) ).
fof(f733,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(X1,xp)) = sdtpldt0(sdtpldt0(X0,X1),xp) ),
inference(resolution,[],[f183,f381]) ).
fof(f734,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(X1,sz10)) = sdtpldt0(sdtpldt0(X0,X1),sz10) ),
inference(resolution,[],[f183,f179]) ).
fof(f744,plain,
! [X0] :
( ~ aInteger0(sdtasdt0(X0,sz10))
| sz00 = X0
| aDivisorOf0(X0,sdtasdt0(X0,sz10))
| ~ aInteger0(X0) ),
inference(resolution,[],[f490,f179]) ).
fof(f746,plain,
! [X0] :
( ~ aInteger0(sdtasdt0(X0,smndt0(sz10)))
| sz00 = X0
| aDivisorOf0(X0,sdtasdt0(X0,smndt0(sz10)))
| ~ aInteger0(X0) ),
inference(resolution,[],[f490,f687]) ).
fof(f1075,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(sz10,xp)) = sdtpldt0(sdtpldt0(X0,sz10),xp) ),
inference(resolution,[],[f733,f179]) ).
fof(f1455,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(smndt0(xp),sz10)) = sdtpldt0(sdtpldt0(X0,smndt0(xp)),sz10) ),
inference(resolution,[],[f734,f686]) ).
fof(f1456,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(smndt0(sz10),sz10)) = sdtpldt0(sdtpldt0(X0,smndt0(sz10)),sz10) ),
inference(resolution,[],[f734,f687]) ).
fof(f1464,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(sz10,smndt0(xp))) = sdtpldt0(sdtpldt0(X0,smndt0(xp)),sz10) ),
inference(forward_demodulation,[],[f1455,f705]) ).
fof(f1476,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(sdtpldt0(X0,sz10)) ),
inference(resolution,[],[f181,f179]) ).
fof(f1480,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(sdtpldt0(X0,xp)) ),
inference(resolution,[],[f181,f381]) ).
fof(f1486,plain,
aInteger0(sdtpldt0(sz10,xp)),
inference(resolution,[],[f1480,f179]) ).
fof(f1626,plain,
aInteger0(sdtpldt0(smndt0(xp),sz10)),
inference(resolution,[],[f1476,f686]) ).
fof(f1639,plain,
aInteger0(sdtpldt0(sz10,smndt0(xp))),
inference(forward_demodulation,[],[f1626,f705]) ).
fof(f1811,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = sdtpldt0(sdtpldt0(X0,smndt0(sz10)),sz10) ),
inference(forward_demodulation,[],[f1456,f634]) ).
fof(f2101,plain,
sdtpldt0(smndt0(xp),sz00) = sdtpldt0(sdtpldt0(smndt0(xp),smndt0(sz10)),sz10),
inference(resolution,[],[f1811,f686]) ).
fof(f2118,plain,
sdtpldt0(smndt0(xp),sz00) = sdtpldt0(sdtpldt0(smndt0(sz10),smndt0(xp)),sz10),
inference(forward_demodulation,[],[f2101,f726]) ).
fof(f2332,plain,
smndt0(xp) = sdtpldt0(sdtpldt0(smndt0(sz10),smndt0(xp)),sz10),
inference(forward_demodulation,[],[f2118,f730]) ).
fof(f3276,plain,
( ~ aInteger0(xp)
| sz00 = xp
| aDivisorOf0(xp,xp)
| ~ aInteger0(xp) ),
inference(superposition,[],[f744,f629]) ).
fof(f3283,plain,
( ~ aInteger0(xp)
| sz00 = xp
| aDivisorOf0(xp,xp) ),
inference(duplicate_literal_removal,[],[f3276]) ).
fof(f3287,plain,
( sz00 = xp
| aDivisorOf0(xp,xp) ),
inference(forward_subsumption_resolution,[],[f3283,f381]) ).
fof(f3294,plain,
aDivisorOf0(xp,xp),
inference(forward_subsumption_resolution,[],[f3287,f380]) ).
fof(f3405,plain,
sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) = sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)),
inference(resolution,[],[f708,f1486]) ).
fof(f3406,plain,
sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) = sdtpldt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))),
inference(resolution,[],[f708,f1639]) ).
fof(f4924,plain,
sdtpldt0(sdtpldt0(smndt0(sz10),smndt0(xp)),sz10) = sdtpldt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))),
inference(resolution,[],[f1464,f687]) ).
fof(f5408,plain,
smndt0(xp) = sdtpldt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))),
inference(forward_demodulation,[],[f4924,f2332]) ).
fof(f6694,plain,
( ~ aDivisorOf0(xp,sdtpldt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))))
| spl28_4 ),
inference(forward_demodulation,[],[f533,f3406]) ).
fof(f6709,plain,
( ~ aDivisorOf0(xp,smndt0(xp))
| spl28_4 ),
inference(forward_demodulation,[],[f6694,f5408]) ).
fof(f7360,plain,
sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)) = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp),
inference(resolution,[],[f1075,f687]) ).
fof(f7389,plain,
sdtpldt0(sz00,xp) = sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)),
inference(forward_demodulation,[],[f7360,f634]) ).
fof(f7401,plain,
xp = sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)),
inference(forward_demodulation,[],[f7389,f681]) ).
fof(f8326,plain,
( ~ aInteger0(smndt0(xp))
| sz00 = xp
| aDivisorOf0(xp,smndt0(xp))
| ~ aInteger0(xp) ),
inference(superposition,[],[f746,f631]) ).
fof(f8333,plain,
( sz00 = xp
| aDivisorOf0(xp,smndt0(xp))
| ~ aInteger0(xp) ),
inference(forward_subsumption_resolution,[],[f8326,f180]) ).
fof(f8337,plain,
( aDivisorOf0(xp,smndt0(xp))
| ~ aInteger0(xp) ),
inference(forward_subsumption_resolution,[],[f8333,f380]) ).
fof(f8341,plain,
( ~ aInteger0(xp)
| spl28_4 ),
inference(forward_subsumption_resolution,[],[f8337,f6709]) ).
fof(f8343,plain,
( $false
| spl28_4 ),
inference(forward_subsumption_resolution,[],[f8341,f381]) ).
fof(f8344,plain,
spl28_4,
inference(avatar_contradiction_clause,[],[f8343]) ).
fof(f8345,plain,
( ~ aDivisorOf0(xp,sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)))
| spl28_7 ),
inference(forward_demodulation,[],[f548,f3405]) ).
fof(f8348,plain,
( ~ aDivisorOf0(xp,xp)
| spl28_7 ),
inference(forward_demodulation,[],[f8345,f7401]) ).
fof(f8351,plain,
( $false
| spl28_7 ),
inference(forward_subsumption_resolution,[],[f8348,f3294]) ).
fof(f8352,plain,
spl28_7,
inference(avatar_contradiction_clause,[],[f8351]) ).
cnf(s11,plain,
( ~ spl28_4
| ~ spl28_7 ),
inference(sat_conversion,[],[f551]) ).
cnf(s384,plain,
spl28_4,
inference(sat_conversion,[],[f8344]) ).
cnf(s386,plain,
spl28_7,
inference(sat_conversion,[],[f8352]) ).
cnf(s423,plain,
$false,
inference(rat,[],[s11,s386,s384]) ).
fof(f8353,plain,
$false,
inference(avatar_sat_refutation,[],[s423]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM452+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:03:31 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 6.32/1.85 % (1978585)Detected formulas, will run a generic FOF schedule.
% 6.32/1.85 % (1978591)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=1444162656:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.32/1.85 % (1978596)dis-21_1_sil=8000:lcm=predicate:random_seed=1007745677: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)
% 6.32/1.85 % (1978593)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1973716581:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.32/1.85 % (1978594)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4113239158:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.32/1.85 % (1978592)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=1886560145:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.32/1.85 % (1978595)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2845949048:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.32/1.85 % (1978590)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=3794895512:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.32/1.85 % (1978593)Instruction limit reached!
% 6.32/1.85 % (1978593)------------------------------
% 6.32/1.85 % (1978593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978593)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978593)Termination reason: Instruction limit
% 6.32/1.85 % (1978593)Termination phase: Saturation
% 6.32/1.85 % (1978593)Time elapsed: 0.070 s
% 6.32/1.85 % (1978593)Peak memory usage: 89 MB
% 6.32/1.85 % (1978593)Instructions burned: 109 (million)
% 6.32/1.85 % (1978594)Instruction limit reached!
% 6.32/1.85 % (1978594)------------------------------
% 6.32/1.85 % (1978594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978594)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978594)Termination reason: Instruction limit
% 6.32/1.85 % (1978594)Termination phase: Saturation
% 6.32/1.85 % (1978594)Time elapsed: 0.071 s
% 6.32/1.85 % (1978594)Peak memory usage: 89 MB
% 6.32/1.85 % (1978594)Instructions burned: 120 (million)
% 6.32/1.85 % (1978596)Instruction limit reached!
% 6.32/1.85 % (1978596)------------------------------
% 6.32/1.85 % (1978596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978596)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978596)Termination reason: Instruction limit
% 6.32/1.85 % (1978596)Termination phase: Saturation
% 6.32/1.85 % (1978596)Time elapsed: 0.073 s
% 6.32/1.85 % (1978596)Peak memory usage: 89 MB
% 6.32/1.85 % (1978596)Instructions burned: 130 (million)
% 6.32/1.85 % (1978595)Instruction limit reached!
% 6.32/1.85 % (1978595)------------------------------
% 6.32/1.85 % (1978595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978595)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978595)Termination reason: Instruction limit
% 6.32/1.85 % (1978595)Termination phase: Saturation
% 6.32/1.85 % (1978595)Time elapsed: 0.091 s
% 6.32/1.85 % (1978595)Peak memory usage: 90 MB
% 6.32/1.85 % (1978595)Instructions burned: 140 (million)
% 6.32/1.85 % (1978606)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2280368330:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.32/1.85 % (1978604)lrs+10_1_sil=8000:sp=occurrence:random_seed=1140794800:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.32/1.85 % (1978605)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1521189628:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.32/1.85 % (1978607)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=2989951261:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.32/1.85 % (1978605)Instruction limit reached!
% 6.32/1.85 % (1978605)------------------------------
% 6.32/1.85 % (1978605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978605)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978605)Termination reason: Instruction limit
% 6.32/1.85 % (1978605)Termination phase: Saturation
% 6.32/1.85 % (1978605)Time elapsed: 0.085 s
% 6.32/1.85 % (1978605)Peak memory usage: 91 MB
% 6.32/1.85 % (1978605)Instructions burned: 158 (million)
% 6.32/1.85 % (1978607)Instruction limit reached!
% 6.32/1.85 % (1978607)------------------------------
% 6.32/1.85 % (1978607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978607)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978607)Termination reason: Instruction limit
% 6.32/1.85 % (1978607)Termination phase: Saturation
% 6.32/1.85 % (1978607)Time elapsed: 0.122 s
% 6.32/1.85 % (1978607)Peak memory usage: 95 MB
% 6.32/1.85 % (1978607)Instructions burned: 250 (million)
% 6.32/1.85 % (1978604)Instruction limit reached!
% 6.32/1.85 % (1978604)------------------------------
% 6.32/1.85 % (1978604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978604)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978604)Termination reason: Instruction limit
% 6.32/1.85 % (1978604)Termination phase: Saturation
% 6.32/1.85 % (1978604)Time elapsed: 0.168 s
% 6.32/1.85 % (1978604)Peak memory usage: 92 MB
% 6.32/1.85 % (1978604)Instructions burned: 285 (million)
% 6.32/1.85 % (1978606)Instruction limit reached!
% 6.32/1.85 % (1978606)------------------------------
% 6.32/1.85 % (1978606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978606)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978606)Termination reason: Instruction limit
% 6.32/1.85 % (1978606)Termination phase: Saturation
% 6.32/1.85 % (1978606)Time elapsed: 0.210 s
% 6.32/1.85 % (1978606)Peak memory usage: 92 MB
% 6.32/1.85 % (1978606)Instructions burned: 325 (million)
% 6.32/1.85 % (1978612)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=404184191:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.32/1.85 % (1978613)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2434705603:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.32/1.85 % (1978614)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2139370176:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.32/1.85 % (1978615)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=348318259:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.32/1.85 % (1978614)Instruction limit reached!
% 6.32/1.85 % (1978614)------------------------------
% 6.32/1.85 % (1978614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978614)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978614)Termination reason: Instruction limit
% 6.32/1.85 % (1978614)Termination phase: Saturation
% 6.32/1.85 % (1978614)Time elapsed: 0.072 s
% 6.32/1.85 % (1978614)Peak memory usage: 91 MB
% 6.32/1.85 % (1978614)Instructions burned: 113 (million)
% 6.32/1.85 % (1978591)First to succeed.
% 6.32/1.85 % (1978591)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1978585"
% 6.32/1.85 % (1978612)Instruction limit reached!
% 6.32/1.85 % (1978612)------------------------------
% 6.32/1.85 % (1978612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978612)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978612)Termination reason: Instruction limit
% 6.32/1.85 % (1978612)Termination phase: Saturation
% 6.32/1.85 % (1978612)Time elapsed: 0.180 s
% 6.32/1.85 % (1978612)Peak memory usage: 90 MB
% 6.32/1.85 % (1978612)Instructions burned: 294 (million)
% 6.32/1.85 % (1978615)Instruction limit reached!
% 6.32/1.85 % (1978615)------------------------------
% 6.32/1.85 % (1978615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.85 % (1978615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.85 % (1978615)CaDiCaL version: 2.1.3
% 6.32/1.85 % (1978615)Termination reason: Instruction limit
% 6.32/1.85 % (1978615)Termination phase: Saturation
% 6.32/1.85 % (1978615)Time elapsed: 0.067 s
% 6.32/1.85 % (1978615)Peak memory usage: 89 MB
% 6.32/1.85 % (1978615)Instructions burned: 129 (million)
% 6.32/1.85 % (1978620)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2710491963:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 6.32/1.85 % (1978621)lrs+10_1_sil=8000:sp=occurrence:random_seed=3425033847:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.32/1.85 % (1978591)Refutation found. Thanks to Tanya!
% 6.32/1.85 % SZS status Theorem for theBenchmark
% 6.32/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 7.58/2.04 % (1978591)------------------------------
% 7.58/2.04 % (1978591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.58/2.04 % (1978591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.58/2.04 % (1978591)CaDiCaL version: 2.1.3
% 7.58/2.04 % (1978591)Termination reason: Refutation
% 7.58/2.04 % (1978591)Time elapsed: 0.677 s
% 7.58/2.04 % (1978591)Peak memory usage: 139 MB
% 7.58/2.04 % (1978591)Instructions burned: 1834 (million)
% 7.58/2.04 % (1978591)------------------------------
% 7.58/2.04 % (1978591)------------------------------
% 7.58/2.04 % (1978585)Success in time 0.987 s
% 7.58/2.04 % Vampire exiting
%------------------------------------------------------------------------------