%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n004.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 12:24:20 PM UTC 2026
% Result : Theorem 0.57s 0.59s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 15 unt; 2 def)
% Number of atoms : 411 ( 57 equ)
% Maximal formula atoms : 34 ( 6 avg)
% Number of connectives : 505 ( 155 ~; 149 |; 177 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 58 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f51,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(f80,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(f81,plain,
! [X0,X1,X2] :
( sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(flattening,[],[f80]) ).
fof(f82,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(f83,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,[],[f82]) ).
fof(f105,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,[],[f51]) ).
fof(f106,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,[],[f105]) ).
fof(f161,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,[],[f106]) ).
fof(f162,plain,
( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ~ aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [X0] :
( ( ( aInteger0(X0)
& aInteger0(sK20(X0))
& sdtpldt0(X0,smndt0(xa)) = sdtasdt0(xq,sK20(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(sK21(X3))
& sdtpldt0(X3,smndt0(xa)) = sdtasdt0(xq,sK21(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(sK22)
& sdtpldt0(xc,smndt0(xb)) = sdtasdt0(xq,sK22)
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22]),skolemize(X1,sK20(X0)),skolemize(X4,sK21(X3)),skolemize(X6,sK22)],[f161]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| sdteqdtlpzmzozddtrp0(X1,X0,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(cnf_transformation,[],[f81]) ).
fof(f194,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,[],[f83]) ).
fof(f267,plain,
sz00 != xq,
inference(cnf_transformation,[],[f41]) ).
fof(f268,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f41]) ).
fof(f269,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f41]) ).
fof(f271,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f42]) ).
fof(f272,plain,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(cnf_transformation,[],[f162]) ).
fof(f277,plain,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[],[f162]) ).
fof(f278,plain,
! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X3,xa,xq) ),
inference(cnf_transformation,[],[f162]) ).
fof(f281,plain,
! [X3] :
( ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| sdteqdtlpzmzozddtrp0(X3,xa,xq) ),
inference(cnf_transformation,[],[f162]) ).
fof(f285,plain,
! [X3] :
( ~ aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aInteger0(X3) ),
inference(cnf_transformation,[],[f162]) ).
fof(f297,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(cnf_transformation,[],[f162]) ).
fof(f330,plain,
aInteger0(xc),
inference(resolution,[],[f285,f297]) ).
fof(f334,plain,
sdteqdtlpzmzozddtrp0(xc,xa,xq),
inference(resolution,[],[f281,f297]) ).
fof(f335,plain,
( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(resolution,[],[f278,f277]) ).
fof(f341,definition,
( spl23_5
<=> sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
introduced(definition,[new_symbols(definition,[spl23_5])],[avatar_definition]) ).
fof(f343,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| spl23_5 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f345,definition,
( spl23_6
<=> aInteger0(xb) ),
introduced(definition,[new_symbols(definition,[spl23_6])],[avatar_definition]) ).
fof(f346,plain,
( aInteger0(xb)
| ~ spl23_6 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f348,plain,
( ~ spl23_5
| ~ spl23_6 ),
inference(avatar_split_clause,[],[f335,f345,f341]) ).
fof(f363,plain,
spl23_6,
inference(avatar_split_clause,[],[f271,f345]) ).
fof(f1492,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ~ aInteger0(xc)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(resolution,[],[f193,f334]) ).
fof(f1495,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f1492,f330]) ).
fof(f1497,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| ~ aInteger0(xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f1495,f269]) ).
fof(f1499,plain,
( sdteqdtlpzmzozddtrp0(xa,xc,xq)
| sz00 = xq ),
inference(forward_subsumption_resolution,[],[f1497,f268]) ).
fof(f1501,plain,
sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(forward_subsumption_resolution,[],[f1499,f267]) ).
fof(f1891,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| sdteqdtlpzmzozddtrp0(X0,xb,xq)
| ~ aInteger0(X0)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| sz00 = xq
| ~ aInteger0(xb) ),
inference(resolution,[],[f194,f272]) ).
fof(f1896,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| sdteqdtlpzmzozddtrp0(X0,xb,xq)
| ~ aInteger0(X0)
| ~ aInteger0(xq)
| sz00 = xq
| ~ aInteger0(xb) ),
inference(forward_subsumption_resolution,[],[f1891,f330]) ).
fof(f1899,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| sdteqdtlpzmzozddtrp0(X0,xb,xq)
| ~ aInteger0(X0)
| sz00 = xq
| ~ aInteger0(xb) ),
inference(forward_subsumption_resolution,[],[f1896,f268]) ).
fof(f1902,plain,
! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| sdteqdtlpzmzozddtrp0(X0,xb,xq)
| ~ aInteger0(X0)
| ~ aInteger0(xb) ),
inference(forward_subsumption_resolution,[],[f1899,f267]) ).
fof(f1905,plain,
( ! [X0] :
( ~ sdteqdtlpzmzozddtrp0(X0,xc,xq)
| sdteqdtlpzmzozddtrp0(X0,xb,xq)
| ~ aInteger0(X0) )
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f1902,f346]) ).
fof(f2765,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ aInteger0(xa)
| ~ spl23_6 ),
inference(resolution,[],[f1905,f1501]) ).
fof(f2771,plain,
( sdteqdtlpzmzozddtrp0(xa,xb,xq)
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f2765,f269]) ).
fof(f2911,plain,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| sz00 = xq
| ~ spl23_6 ),
inference(resolution,[],[f2771,f193]) ).
fof(f2912,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(xq)
| sz00 = xq
| spl23_5
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f2911,f343]) ).
fof(f2914,plain,
( ~ aInteger0(xb)
| ~ aInteger0(xq)
| sz00 = xq
| spl23_5
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f2912,f269]) ).
fof(f2916,plain,
( ~ aInteger0(xq)
| sz00 = xq
| spl23_5
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f2914,f346]) ).
fof(f2918,plain,
( sz00 = xq
| spl23_5
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f2916,f268]) ).
fof(f2920,plain,
( $false
| spl23_5
| ~ spl23_6 ),
inference(forward_subsumption_resolution,[],[f2918,f267]) ).
fof(f2921,plain,
( spl23_5
| ~ spl23_6 ),
inference(avatar_contradiction_clause,[],[f2920]) ).
cnf(s4,plain,
( ~ spl23_5
| ~ spl23_6 ),
inference(sat_conversion,[],[f348]) ).
cnf(s5,plain,
spl23_6,
inference(sat_conversion,[],[f363]) ).
cnf(s102,plain,
( spl23_5
| ~ spl23_6 ),
inference(sat_conversion,[],[f2921]) ).
cnf(s103,plain,
spl23_5,
inference(rat,[],[s102,s5]) ).
cnf(s106,plain,
$false,
inference(rat,[],[s4,s5,s103]) ).
fof(f2922,plain,
$false,
inference(avatar_sat_refutation,[],[s106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM443+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.19/0.45 % Computer : n004.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 19:57:22 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.50 Running first-order model finding
% 0.24/0.50 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.59 % (3839043)Will run a generic schedule for satisfiability detection.
% 0.57/0.59 % (3839051)dis+10_1_sil=32000:sp=arity:random_seed=2578485404:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.57/0.59 % (3839049)% WARNING: option uhcvi not known.
% 0.57/0.59 % (3839048)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2090550701_2999 on theBenchmark for (2999ds/0Mi)
% 0.57/0.59 % (3839050)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2029787485:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.57/0.59 % (3839052)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2233373807:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.57/0.59 % (3839054)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=272107207:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.57/0.59 % (3839049)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=688116871:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.57/0.59 % (3839053)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3582421953:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.57/0.59 % TRYING [1]
% 0.57/0.59 % TRYING [2]
% 0.57/0.59 % TRYING [3]
% 0.57/0.59 % (3839051) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3839043-3839051"...
% 0.57/0.59 % (3839051)...printing done.
% 0.57/0.59 % (3839051)Refutation found. Thanks to Tanya!
% 0.57/0.59 % SZS status Theorem for theBenchmark
% 0.57/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.57/0.59 % (3839051)------------------------------
% 0.57/0.59 % (3839051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.59 % (3839051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.59 % (3839051)CaDiCaL version: 2.1.3
% 0.57/0.59 % (3839051)Termination reason: Refutation
% 0.57/0.59 % (3839051)Time elapsed: 0.053 s
% 0.57/0.59 % (3839051)Peak memory usage: 14 MB
% 0.57/0.59 % (3839051)Instructions burned: 96 (million)
% 0.57/0.59 % (3839043)Success in time 0.08 s
% 0.57/0.60 % Vampire exiting
%------------------------------------------------------------------------------