%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM600+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:15:56 PM UTC 2026
% Result : Theorem 2.81s 6.33s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 13 unt; 0 def)
% Number of atoms : 321 ( 54 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 435 ( 187 ~; 166 |; 64 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 122 ( 105 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f67,axiom,
! [X0,X1] :
( ( aFunction0(X0)
& aElement0(X1) )
=> aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
fof(f68,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSImg) ).
fof(f73,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
fof(f91,axiom,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
fof(f92,axiom,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
=> sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
fof(f94,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4854) ).
fof(f95,axiom,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
fof(f97,conjecture,
! [X0] :
( aElementOf0(X0,xO)
=> ? [X1] :
( aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f98,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,xO)
=> ? [X1] :
( aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f97]) ).
fof(f126,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f127,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f92]) ).
fof(f128,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
? [X0] :
( ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X1) != X0 )
& aElementOf0(X0,xO) ),
inference(ennf_transformation,[],[f98]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = sdtlcdtrc0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 ) ) ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f191,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f192,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f191]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f226,plain,
( ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X1) != sK9 )
& aElementOf0(sK9,xO) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f129]) ).
fof(f227,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f139]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f227]) ).
fof(f229,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f228]) ).
fof(f230,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK10(X0,X1),X0)
& aElementOf0(sK10(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f229]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 ) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f234,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 ) )
& ( ? [X4] :
( aElementOf0(X4,X1)
& sdtlpdtrp0(X0,X4) = X3 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(flattening,[],[f233]) ).
fof(f235,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != X3 )
| ~ aElementOf0(X3,X2) )
& ( ? [X5] :
( aElementOf0(X5,X1)
& sdtlpdtrp0(X0,X5) = X3 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( ~ aElementOf0(X7,X1)
| sdtlpdtrp0(X0,X7) != X6 ) )
& ( ? [X8] :
( aElementOf0(X8,X1)
& sdtlpdtrp0(X0,X8) = X6 )
| ~ aElementOf0(X6,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = sdtlcdtrc0(X0,X1)
| ~ aSet0(X2)
| ( ( ! [X4] :
( ~ aElementOf0(X4,X1)
| sdtlpdtrp0(X0,X4) != sK14(X0,X1,X2) )
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( aElementOf0(sK15(X0,X1,X2),X1)
& sK14(X0,X1,X2) = sdtlpdtrp0(X0,sK15(X0,X1,X2)) )
| aElementOf0(sK14(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( ~ aElementOf0(X7,X1)
| sdtlpdtrp0(X0,X7) != X6 ) )
& ( ( aElementOf0(sK16(X0,X1,X6),X1)
& sdtlpdtrp0(X0,sK16(X0,X1,X6)) = X6 )
| ~ aElementOf0(X6,X2) ) ) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X3,sK14(X0,X1,X2)),skolemize(X5,sK15(X0,X1,X2)),skolemize(X8,sK16(X0,X1,X6))],[f235]) ).
fof(f271,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f310,plain,
szNzAzT0 = szDzozmdt0(xe),
inference(cnf_transformation,[],[f126]) ).
fof(f311,plain,
aFunction0(xe),
inference(cnf_transformation,[],[f126]) ).
fof(f313,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f128]) ).
fof(f314,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f128]) ).
fof(f317,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f94]) ).
fof(f318,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f95]) ).
fof(f322,plain,
aElementOf0(sK9,xO),
inference(cnf_transformation,[],[f226]) ).
fof(f323,plain,
! [X1] :
( sdtlpdtrp0(xe,X1) != sK9
| ~ aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f326,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f331,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f230]) ).
fof(f345,plain,
! [X2,X0,X1,X6] :
( sdtlpdtrp0(X0,sK16(X0,X1,X6)) = X6
| ~ aElementOf0(X6,X2)
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f346,plain,
! [X2,X0,X1,X6] :
( aElementOf0(sK16(X0,X1,X6),X1)
| ~ aElementOf0(X6,X2)
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f406,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f417,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f444,plain,
! [X0,X1,X6] :
( aElementOf0(sK16(X0,X1,X6),X1)
| ~ aElementOf0(X6,sdtlcdtrc0(X0,X1))
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f346]) ).
fof(f445,plain,
! [X0,X1,X6] :
( sdtlpdtrp0(X0,sK16(X0,X1,X6)) = X6
| ~ aElementOf0(X6,sdtlcdtrc0(X0,X1))
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f345]) ).
fof(f504,plain,
( aElement0(szDzizrdt0(xd))
| ~ aSet0(xT) ),
inference(resolution,[],[f417,f317]) ).
fof(f515,plain,
aElement0(szDzizrdt0(xd)),
inference(forward_subsumption_resolution,[],[f504,f271]) ).
fof(f559,plain,
! [X0] :
( aSubsetOf0(sdtlbdtrb0(xd,X0),szNzAzT0)
| ~ aFunction0(xd)
| ~ aElement0(X0) ),
inference(superposition,[],[f406,f313]) ).
fof(f560,plain,
! [X0] :
( aSubsetOf0(sdtlbdtrb0(xd,X0),szNzAzT0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f559,f314]) ).
fof(f1581,plain,
! [X0,X1] :
( sK9 != X0
| ~ aElementOf0(sK16(xe,X1,X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(sK16(xe,X1,X0),szNzAzT0)
| ~ aElementOf0(X0,sdtlcdtrc0(xe,X1))
| ~ aSubsetOf0(X1,szDzozmdt0(xe))
| ~ aFunction0(xe) ),
inference(superposition,[],[f323,f445]) ).
fof(f1590,plain,
! [X0,X1] :
( sK9 != X0
| ~ aElementOf0(sK16(xe,X1,X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(sK16(xe,X1,X0),szNzAzT0)
| ~ aElementOf0(X0,sdtlcdtrc0(xe,X1))
| ~ aSubsetOf0(X1,szDzozmdt0(xe)) ),
inference(forward_subsumption_resolution,[],[f1581,f311]) ).
fof(f1612,plain,
! [X0,X1] :
( sK9 != X0
| ~ aSubsetOf0(X1,szNzAzT0)
| ~ aElementOf0(sK16(xe,X1,X0),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(sK16(xe,X1,X0),szNzAzT0)
| ~ aElementOf0(X0,sdtlcdtrc0(xe,X1)) ),
inference(forward_demodulation,[],[f1590,f310]) ).
fof(f1630,plain,
! [X0] :
( ~ aElementOf0(sK16(xe,X0,sK9),sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(sK16(xe,X0,sK9),szNzAzT0)
| ~ aElementOf0(sK9,sdtlcdtrc0(xe,X0)) ),
inference(equality_resolution,[],[f1612]) ).
fof(f1631,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK16(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),sK9),szNzAzT0)
| ~ aElementOf0(sK9,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aElementOf0(sK9,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ aFunction0(xe) ),
inference(resolution,[],[f1630,f444]) ).
fof(f1633,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK16(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),sK9),szNzAzT0)
| ~ aElementOf0(sK9,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ aFunction0(xe) ),
inference(duplicate_literal_removal,[],[f1631]) ).
fof(f1634,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK16(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),sK9),szNzAzT0)
| ~ aElementOf0(sK9,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(forward_subsumption_resolution,[],[f1633,f311]) ).
fof(f1635,plain,
( ~ aElementOf0(sK9,xO)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK16(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),sK9),szNzAzT0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(forward_demodulation,[],[f1634,f318]) ).
fof(f1636,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK16(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),sK9),szNzAzT0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(forward_subsumption_resolution,[],[f1635,f322]) ).
fof(f1637,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK16(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),sK9),szNzAzT0) ),
inference(forward_demodulation,[],[f1636,f310]) ).
fof(f1638,plain,
( ~ aElementOf0(sK16(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),sK9),szNzAzT0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
inference(duplicate_literal_removal,[],[f1637]) ).
fof(f1645,plain,
! [X0] :
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK16(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),sK9),X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f1638,f331]) ).
fof(f1646,plain,
! [X0] :
( ~ aElementOf0(sK16(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)),sK9),X0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1645,f326]) ).
fof(f1659,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK9,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ aFunction0(xe) ),
inference(resolution,[],[f1646,f444]) ).
fof(f1664,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK9,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ aFunction0(xe) ),
inference(duplicate_literal_removal,[],[f1659]) ).
fof(f1665,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aElementOf0(sK9,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(forward_subsumption_resolution,[],[f1664,f311]) ).
fof(f1666,plain,
( ~ aElementOf0(sK9,xO)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(forward_demodulation,[],[f1665,f318]) ).
fof(f1667,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(forward_subsumption_resolution,[],[f1666,f322]) ).
fof(f1668,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
inference(forward_demodulation,[],[f1667,f310]) ).
fof(f1669,plain,
~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),
inference(duplicate_literal_removal,[],[f1668]) ).
fof(f1670,plain,
~ aElement0(szDzizrdt0(xd)),
inference(resolution,[],[f1669,f560]) ).
fof(f1673,plain,
$false,
inference(forward_subsumption_resolution,[],[f1670,f515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM600+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.41 % Computer : n001.cluster.edu
% 0.12/5.41 % Model : x86_64 x86_64
% 0.12/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.41 % Memory : 8046.5625MB
% 0.12/5.41 % OS : Linux 6.8.0-71-generic
% 0.12/5.41 % CPULimit : 300
% 0.12/5.41 % WCLimit : 300
% 0.12/5.41 % DateTime : Sun Sep 27 20:47:37 UTC 2026
% 0.12/5.41 % CPUTime :
% 0.12/5.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.44 Running first-order theorem proving
% 0.12/5.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.81/6.33 % (3935319)Detected formulas, will run a generic FOF schedule.
% 2.81/6.33 % (3935325)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=663977988:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.81/6.33 % (3935328)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=10007459:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.81/6.33 % (3935324)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=1924511071:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.81/6.33 % (3935326)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=1169007505:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.81/6.33 % (3935327)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3752287813:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.81/6.33 % (3935329)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=975215211:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.81/6.33 % (3935330)dis-21_1_sil=8000:lcm=predicate:random_seed=3119236920:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.81/6.33 % (3935328)First to succeed.
% 2.81/6.33 % (3935328)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3935319"
% 2.81/6.33 % (3935327)Instruction limit reached!
% 2.81/6.33 % (3935327)------------------------------
% 2.81/6.33 % (3935327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/6.33 % (3935327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/6.33 % (3935327)CaDiCaL version: 2.1.3
% 2.81/6.33 % (3935327)Termination reason: Instruction limit
% 2.81/6.33 % (3935327)Termination phase: Saturation
% 2.81/6.33 % (3935327)Time elapsed: 0.064 s
% 2.81/6.33 % (3935327)Peak memory usage: 89 MB
% 2.81/6.33 % (3935327)Instructions burned: 109 (million)
% 2.81/6.33 % (3935330)Instruction limit reached!
% 2.81/6.33 % (3935330)------------------------------
% 2.81/6.33 % (3935330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/6.33 % (3935330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/6.33 % (3935330)CaDiCaL version: 2.1.3
% 2.81/6.33 % (3935330)Termination reason: Instruction limit
% 2.81/6.33 % (3935330)Termination phase: Saturation
% 2.81/6.33 % (3935330)Time elapsed: 0.071 s
% 2.81/6.33 % (3935330)Peak memory usage: 91 MB
% 2.81/6.33 % (3935330)Instructions burned: 129 (million)
% 2.81/6.33 % (3935329)Instruction limit reached!
% 2.81/6.33 % (3935329)------------------------------
% 2.81/6.33 % (3935329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/6.33 % (3935329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/6.33 % (3935329)CaDiCaL version: 2.1.3
% 2.81/6.33 % (3935329)Termination reason: Instruction limit
% 2.81/6.33 % (3935329)Termination phase: Saturation
% 2.81/6.33 % (3935329)Time elapsed: 0.101 s
% 2.81/6.33 % (3935329)Peak memory usage: 90 MB
% 2.81/6.33 % (3935329)Instructions burned: 139 (million)
% 2.81/6.33 % (3935338)lrs+10_1_sil=8000:sp=occurrence:random_seed=113216081:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.81/6.33 % (3935339)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3943392370:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.81/6.33 % (3935339)Refutation not found, incomplete strategy
% 2.81/6.33 % (3935339)------------------------------
% 2.81/6.33 % (3935339)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.81/6.33 % (3935339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.81/6.33 % (3935339)CaDiCaL version: 2.1.3
% 2.81/6.33 % (3935339)Termination reason: Refutation not found, incomplete strategy
% 2.81/6.33 % (3935339)Time elapsed: 0.002 s
% 2.81/6.33 % (3935339)Peak memory usage: 89 MB
% 2.81/6.33 % (3935339)Instructions burned: 2 (million)
% 2.81/6.33 % (3935340)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2359053678:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.81/6.33 % (3935328)Refutation found. Thanks to Tanya!
% 2.81/6.33 % SZS status Theorem for theBenchmark
% 2.81/6.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/6.51 % (3935328)------------------------------
% 3.71/6.51 % (3935328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/6.51 % (3935328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/6.51 % (3935328)CaDiCaL version: 2.1.3
% 3.71/6.51 % (3935328)Termination reason: Refutation
% 3.71/6.51 % (3935328)Time elapsed: 0.038 s
% 3.71/6.51 % (3935328)Peak memory usage: 89 MB
% 3.71/6.51 % (3935328)Instructions burned: 57 (million)
% 3.71/6.51 % (3935328)------------------------------
% 3.71/6.51 % (3935328)------------------------------
% 3.71/6.51 % (3935319)Success in time 0.436 s
% 3.71/6.51 % Vampire exiting
%------------------------------------------------------------------------------