%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM599+3 : 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 8.26s 2.22s
% Output : Refutation 9.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 139 ( 28 unt; 7 def)
% Number of atoms : 591 ( 100 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 713 ( 261 ~; 258 |; 153 &)
% ( 15 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 8 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-2 aty)
% Number of variables : 149 ( 0 sgn 130 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f11,axiom,
! [X0] :
( ( aSet0(X0)
& isFinite0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
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(f71,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( ( aSubsetOf0(X1,szDzozmdt0(X0))
& isCountable0(X1) )
=> ( ! [X2,X3] :
( ( aElementOf0(X2,szDzozmdt0(X0))
& aElementOf0(X3,szDzozmdt0(X0))
& X2 != X3 )
=> sdtlpdtrp0(X0,X2) != sdtlpdtrp0(X0,X3) )
=> isCountable0(sdtlcdtrc0(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgCount) ).
fof(f72,axiom,
! [X0] :
( aFunction0(X0)
=> ( ( isCountable0(szDzozmdt0(X0))
& isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0))) )
=> ( aElement0(szDzizrdt0(X0))
& isCountable0(sdtlbdtrb0(X0,szDzizrdt0(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDirichlet) ).
fof(f73,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
fof(f84,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& X0 != X1 )
=> ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) ) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) ) )
| szmzizndt0(sdtlpdtrp0(xN,X0)) = szmzizndt0(sdtlpdtrp0(xN,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3821) ).
fof(f91,axiom,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& 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)
& ( ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& sbrdtbr0(X1) = xk )
| 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(f93,axiom,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> ? [X1] :
( aElementOf0(X1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X1) = X0 ) )
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
=> aElementOf0(X0,xT) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4758) ).
fof(f94,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4854) ).
fof(f95,axiom,
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) ) )
& ! [X0] :
( aElementOf0(X0,xO)
<=> ? [X1] :
( aElementOf0(X1,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X1) = X0 ) )
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
fof(f97,conjecture,
isCountable0(xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f98,negated_conjecture,
~ isCountable0(xO),
inference(negated_conjecture,[status(cth)],[f97]) ).
fof(f109,plain,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& X0 != X1 )
=> ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) ) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) ) )
| szmzizndt0(sdtlpdtrp0(xN,X0)) = szmzizndt0(sdtlpdtrp0(xN,X1)) ) ) ),
inference(rectify,[],[f84]) ).
fof(f115,plain,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> ? [X1] :
( aElementOf0(X1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X1) = X0 ) )
& ! [X2] :
( aElementOf0(X2,sdtlcdtrc0(xd,szDzozmdt0(xd)))
=> aElementOf0(X2,xT) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(rectify,[],[f93]) ).
fof(f116,plain,
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) ) )
& ! [X1] :
( aElementOf0(X1,xO)
<=> ? [X2] :
( aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X2) = X1 ) )
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(rectify,[],[f95]) ).
fof(f118,plain,
~ isCountable0(xO),
inference(flattening,[],[f98]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f126]) ).
fof(f209,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f210,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f209]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( isCountable0(sdtlcdtrc0(X0,X1))
| ? [X2,X3] :
( sdtlpdtrp0(X0,X3) = sdtlpdtrp0(X0,X2)
& aElementOf0(X2,szDzozmdt0(X0))
& aElementOf0(X3,szDzozmdt0(X0))
& X2 != X3 )
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ isCountable0(X1) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( isCountable0(sdtlcdtrc0(X0,X1))
| ? [X2,X3] :
( sdtlpdtrp0(X0,X3) = sdtlpdtrp0(X0,X2)
& aElementOf0(X2,szDzozmdt0(X0))
& aElementOf0(X3,szDzozmdt0(X0))
& X2 != X3 )
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ isCountable0(X1) )
| ~ aFunction0(X0) ),
inference(flattening,[],[f214]) ).
fof(f216,plain,
! [X0] :
( ( aElement0(szDzizrdt0(X0))
& isCountable0(sdtlbdtrb0(X0,szDzizrdt0(X0))) )
| ~ isCountable0(szDzozmdt0(X0))
| ~ isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f72]) ).
fof(f217,plain,
! [X0] :
( ( aElement0(szDzizrdt0(X0))
& isCountable0(sdtlbdtrb0(X0,szDzizrdt0(X0))) )
| ~ isCountable0(szDzozmdt0(X0))
| ~ isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aFunction0(X0) ),
inference(flattening,[],[f216]) ).
fof(f228,plain,
! [X0,X1] :
( ( ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1))
| ? [X3] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1)) ) )
& szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(ennf_transformation,[],[f109]) ).
fof(f229,plain,
! [X0,X1] :
( ( ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1))
| ? [X3] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1)) ) )
& szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(flattening,[],[f228]) ).
fof(f241,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f242,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f92]) ).
fof(f243,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f242]) ).
fof(f244,plain,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
<=> ? [X1] :
( aElementOf0(X1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X1) = X0 ) )
& ! [X2] :
( aElementOf0(X2,xT)
| ~ aElementOf0(X2,sdtlcdtrc0(xd,szDzozmdt0(xd))) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(ennf_transformation,[],[f115]) ).
fof(f337,plain,
! [X0] :
( ! [X1] :
( isCountable0(sdtlcdtrc0(X0,X1))
| ( sdtlpdtrp0(X0,sK43(X0)) = sdtlpdtrp0(X0,sK42(X0))
& aElementOf0(sK42(X0),szDzozmdt0(X0))
& aElementOf0(sK43(X0),szDzozmdt0(X0))
& sK42(X0) != sK43(X0) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ isCountable0(X1) )
| ~ aFunction0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42,sK43]),skolemize(X2,sK42(X0)),skolemize(X3,sK43(X0))],[f215]) ).
fof(f360,plain,
! [X0,X1] :
( ( ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1))
| ? [X2] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) )
& szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(rectify,[],[f229]) ).
fof(f361,plain,
! [X0,X1] :
( ( ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X1))
| ( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),sK55(X0,X1))
& aElementOf0(sK55(X0,X1),sdtlpdtrp0(xN,X1)) ) )
& szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0)) ) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(X2,sK55(X0,X1))],[f360]) ).
fof(f414,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ( ( ( ~ aElementOf0(sK67(X0,X1),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aElementOf0(sK67(X0,X1),X1)
& ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(X2,sK67(X0,X1))],[f243]) ).
fof(f415,plain,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X1) != X0 ) )
& ( ? [X1] :
( aElementOf0(X1,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X1) = X0 )
| ~ aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd))) ) )
& ! [X2] :
( aElementOf0(X2,xT)
| ~ aElementOf0(X2,sdtlcdtrc0(xd,szDzozmdt0(xd))) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(nnf_transformation,[],[f244]) ).
fof(f416,plain,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X1) != X0 ) )
& ( ? [X2] :
( aElementOf0(X2,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X2) = X0 )
| ~ aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd))) ) )
& ! [X3] :
( aElementOf0(X3,xT)
| ~ aElementOf0(X3,sdtlcdtrc0(xd,szDzozmdt0(xd))) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(rectify,[],[f415]) ).
fof(f417,plain,
( aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ! [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X1) != X0 ) )
& ( ( aElementOf0(sK68(X0),szDzozmdt0(xd))
& sdtlpdtrp0(xd,sK68(X0)) = X0 )
| ~ aElementOf0(X0,sdtlcdtrc0(xd,szDzozmdt0(xd))) ) )
& ! [X3] :
( aElementOf0(X3,xT)
| ~ aElementOf0(X3,sdtlcdtrc0(xd,szDzozmdt0(xd))) )
& aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(X2,sK68(X0))],[f416]) ).
fof(f418,plain,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd) )
& ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f419,plain,
( aElementOf0(szDzizrdt0(xd),xT)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd) )
& ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ) ),
inference(flattening,[],[f418]) ).
fof(f420,plain,
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd) )
& ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ! [X1] :
( ( aElementOf0(X1,xO)
| ! [X2] :
( ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X2) != X1 ) )
& ( ? [X2] :
( aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X2) = X1 )
| ~ aElementOf0(X1,xO) ) )
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(nnf_transformation,[],[f116]) ).
fof(f421,plain,
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd) )
& ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ! [X1] :
( ( aElementOf0(X1,xO)
| ! [X2] :
( ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X2) != X1 ) )
& ( ? [X2] :
( aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X2) = X1 )
| ~ aElementOf0(X1,xO) ) )
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(flattening,[],[f420]) ).
fof(f422,plain,
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd) )
& ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ! [X1] :
( ( aElementOf0(X1,xO)
| ! [X2] :
( ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X2) != X1 ) )
& ( ? [X3] :
( aElementOf0(X3,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X3) = X1 )
| ~ aElementOf0(X1,xO) ) )
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(rectify,[],[f421]) ).
fof(f423,plain,
( aSet0(xO)
& aSet0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aElementOf0(X0,szDzozmdt0(xd))
| sdtlpdtrp0(xd,X0) != szDzizrdt0(xd) )
& ( ( aElementOf0(X0,szDzozmdt0(xd))
& sdtlpdtrp0(xd,X0) = szDzizrdt0(xd) )
| ~ aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) )
& ! [X1] :
( ( aElementOf0(X1,xO)
| ! [X2] :
( ~ aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| sdtlpdtrp0(xe,X2) != X1 ) )
& ( ( aElementOf0(sK69(X1),sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,sK69(X1)) = X1 )
| ~ aElementOf0(X1,xO) ) )
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(X3,sK69(X1))],[f422]) ).
fof(f426,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f437,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f471,plain,
isCountable0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f549,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f210]) ).
fof(f563,plain,
! [X0,X1] :
( sK42(X0) != sK43(X0)
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f564,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| aElementOf0(sK43(X0),szDzozmdt0(X0))
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f565,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| aElementOf0(sK42(X0),szDzozmdt0(X0))
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f566,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| sdtlpdtrp0(X0,sK43(X0)) = sdtlpdtrp0(X0,sK42(X0))
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f567,plain,
! [X0] :
( ~ isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ isCountable0(szDzozmdt0(X0))
| isCountable0(sdtlbdtrb0(X0,szDzizrdt0(X0)))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f569,plain,
isFinite0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f570,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f652,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(cnf_transformation,[],[f361]) ).
fof(f775,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f778,plain,
szNzAzT0 = szDzozmdt0(xe),
inference(cnf_transformation,[],[f241]) ).
fof(f779,plain,
aFunction0(xe),
inference(cnf_transformation,[],[f241]) ).
fof(f784,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f414]) ).
fof(f785,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f414]) ).
fof(f786,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(cnf_transformation,[],[f417]) ).
fof(f796,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f419]) ).
fof(f797,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f423]) ).
fof(f814,plain,
~ isCountable0(xO),
inference(cnf_transformation,[],[f118]) ).
fof(f905,plain,
( ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| ~ isCountable0(szNzAzT0)
| isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aFunction0(xd) ),
inference(superposition,[],[f567,f784]) ).
fof(f906,plain,
( ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aFunction0(xd) ),
inference(forward_subsumption_resolution,[],[f905,f471]) ).
fof(f907,plain,
( ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(forward_subsumption_resolution,[],[f906,f785]) ).
fof(f909,definition,
( spl70_7
<=> isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
introduced(definition,[new_symbols(definition,[spl70_7])],[avatar_definition]) ).
fof(f913,definition,
( spl70_8
<=> isFinite0(sdtlcdtrc0(xd,szNzAzT0)) ),
introduced(definition,[new_symbols(definition,[spl70_8])],[avatar_definition]) ).
fof(f915,plain,
( ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| spl70_8 ),
inference(avatar_component_clause,[],[f913]) ).
fof(f916,plain,
( spl70_7
| ~ spl70_8 ),
inference(avatar_split_clause,[],[f907,f913,f909]) ).
fof(f949,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK42(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aFunction0(xe) ),
inference(superposition,[],[f565,f778]) ).
fof(f952,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK42(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[],[f949,f779]) ).
fof(f964,definition,
( spl70_15
<=> aElementOf0(sK42(xe),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl70_15])],[avatar_definition]) ).
fof(f966,plain,
( aElementOf0(sK42(xe),szNzAzT0)
| ~ spl70_15 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f968,definition,
( spl70_16
<=> ! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| ~ isCountable0(X0)
| isCountable0(sdtlcdtrc0(xe,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl70_16])],[avatar_definition]) ).
fof(f969,plain,
( ! [X0] :
( isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aSubsetOf0(X0,szNzAzT0) )
| ~ spl70_16 ),
inference(avatar_component_clause,[],[f968]) ).
fof(f970,plain,
( spl70_15
| spl70_16 ),
inference(avatar_split_clause,[],[f952,f968,f964]) ).
fof(f984,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| sdtlpdtrp0(xe,sK43(xe)) = sdtlpdtrp0(xe,sK42(xe))
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aFunction0(xe) ),
inference(superposition,[],[f566,f778]) ).
fof(f987,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| sdtlpdtrp0(xe,sK43(xe)) = sdtlpdtrp0(xe,sK42(xe))
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[],[f984,f779]) ).
fof(f996,definition,
( spl70_20
<=> sdtlpdtrp0(xe,sK43(xe)) = sdtlpdtrp0(xe,sK42(xe)) ),
introduced(definition,[new_symbols(definition,[spl70_20])],[avatar_definition]) ).
fof(f998,plain,
( sdtlpdtrp0(xe,sK43(xe)) = sdtlpdtrp0(xe,sK42(xe))
| ~ spl70_20 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f999,plain,
( spl70_20
| spl70_16 ),
inference(avatar_split_clause,[],[f987,f968,f996]) ).
fof(f1005,plain,
( isCountable0(xO)
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ spl70_16 ),
inference(superposition,[],[f969,f797]) ).
fof(f1006,plain,
( ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ spl70_16 ),
inference(forward_subsumption_resolution,[],[f1005,f814]) ).
fof(f1008,definition,
( spl70_22
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl70_22])],[avatar_definition]) ).
fof(f1010,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| spl70_22 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f1011,plain,
( ~ spl70_22
| ~ spl70_7
| ~ spl70_16 ),
inference(avatar_split_clause,[],[f1006,f968,f909,f1008]) ).
fof(f1020,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK43(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aFunction0(xe) ),
inference(superposition,[],[f564,f778]) ).
fof(f1106,plain,
! [X0] :
( aSubsetOf0(sdtlbdtrb0(xd,X0),szNzAzT0)
| ~ aFunction0(xd)
| ~ aElement0(X0) ),
inference(superposition,[],[f549,f784]) ).
fof(f1110,plain,
! [X0] :
( aSubsetOf0(sdtlbdtrb0(xd,X0),szNzAzT0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f1106,f785]) ).
fof(f1119,plain,
( aElement0(szDzizrdt0(xd))
| ~ aSet0(xT) ),
inference(resolution,[],[f426,f796]) ).
fof(f1124,plain,
aElement0(szDzizrdt0(xd)),
inference(forward_subsumption_resolution,[],[f1119,f570]) ).
fof(f1296,plain,
( isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aSet0(xT)
| ~ isFinite0(xT) ),
inference(resolution,[],[f786,f437]) ).
fof(f1298,plain,
( isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ isFinite0(xT) ),
inference(forward_subsumption_resolution,[],[f1296,f570]) ).
fof(f1301,plain,
isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(forward_subsumption_resolution,[],[f1298,f569]) ).
fof(f1304,plain,
isFinite0(sdtlcdtrc0(xd,szNzAzT0)),
inference(forward_demodulation,[],[f1301,f784]) ).
fof(f1307,plain,
( $false
| spl70_8 ),
inference(forward_subsumption_resolution,[],[f1304,f915]) ).
fof(f1308,plain,
spl70_8,
inference(avatar_contradiction_clause,[],[f1307]) ).
fof(f1320,plain,
( ~ aElement0(szDzizrdt0(xd))
| spl70_22 ),
inference(resolution,[],[f1010,f1110]) ).
fof(f1321,plain,
( $false
| spl70_22 ),
inference(forward_subsumption_resolution,[],[f1320,f1124]) ).
fof(f1322,plain,
spl70_22,
inference(avatar_contradiction_clause,[],[f1321]) ).
fof(f1324,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK43(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[],[f1020,f779]) ).
fof(f1326,definition,
( spl70_41
<=> aElementOf0(sK43(xe),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl70_41])],[avatar_definition]) ).
fof(f1328,plain,
( aElementOf0(sK43(xe),szNzAzT0)
| ~ spl70_41 ),
inference(avatar_component_clause,[],[f1326]) ).
fof(f1329,plain,
( spl70_41
| spl70_16 ),
inference(avatar_split_clause,[],[f1324,f968,f1326]) ).
fof(f1354,plain,
( sdtlpdtrp0(xe,sK42(xe)) = szmzizndt0(sdtlpdtrp0(xN,sK42(xe)))
| ~ spl70_15 ),
inference(resolution,[],[f966,f775]) ).
fof(f1369,plain,
( sdtlpdtrp0(xe,sK43(xe)) = szmzizndt0(sdtlpdtrp0(xN,sK43(xe)))
| ~ spl70_41 ),
inference(resolution,[],[f1328,f775]) ).
fof(f1373,plain,
( sdtlpdtrp0(xe,sK42(xe)) = szmzizndt0(sdtlpdtrp0(xN,sK43(xe)))
| ~ spl70_20
| ~ spl70_41 ),
inference(forward_demodulation,[],[f1369,f998]) ).
fof(f3071,plain,
( ! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != sdtlpdtrp0(xe,sK42(xe))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK42(xe),szNzAzT0)
| sK42(xe) = X0 )
| ~ spl70_15 ),
inference(superposition,[],[f652,f1354]) ).
fof(f3093,plain,
( ! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != sdtlpdtrp0(xe,sK42(xe))
| ~ aElementOf0(X0,szNzAzT0)
| sK42(xe) = X0 )
| ~ spl70_15 ),
inference(forward_subsumption_resolution,[],[f3071,f966]) ).
fof(f3105,plain,
( sdtlpdtrp0(xe,sK42(xe)) != sdtlpdtrp0(xe,sK42(xe))
| ~ aElementOf0(sK43(xe),szNzAzT0)
| sK42(xe) = sK43(xe)
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(superposition,[],[f3093,f1373]) ).
fof(f3106,plain,
( ~ aElementOf0(sK43(xe),szNzAzT0)
| sK42(xe) = sK43(xe)
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(trivial_inequality_removal,[],[f3105]) ).
fof(f3107,plain,
( sK42(xe) = sK43(xe)
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(forward_subsumption_resolution,[],[f3106,f1328]) ).
fof(f3120,plain,
( ! [X0] :
( sK42(xe) != sK42(xe)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ aSubsetOf0(X0,szDzozmdt0(xe))
| ~ isCountable0(X0)
| ~ aFunction0(xe) )
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(superposition,[],[f563,f3107]) ).
fof(f3121,plain,
( ! [X0] :
( isCountable0(sdtlcdtrc0(xe,X0))
| ~ aSubsetOf0(X0,szDzozmdt0(xe))
| ~ isCountable0(X0)
| ~ aFunction0(xe) )
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(trivial_inequality_removal,[],[f3120]) ).
fof(f3122,plain,
( ! [X0] :
( isCountable0(sdtlcdtrc0(xe,X0))
| ~ aSubsetOf0(X0,szDzozmdt0(xe))
| ~ isCountable0(X0) )
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(forward_subsumption_resolution,[],[f3121,f779]) ).
fof(f3123,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) )
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(forward_demodulation,[],[f3122,f778]) ).
fof(f3124,plain,
( spl70_16
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(avatar_split_clause,[],[f3123,f1326,f996,f964,f968]) ).
cnf(s6,plain,
( spl70_7
| ~ spl70_8 ),
inference(sat_conversion,[],[f916]) ).
cnf(s10,plain,
( spl70_15
| spl70_16 ),
inference(sat_conversion,[],[f970]) ).
cnf(s13,plain,
( spl70_16
| spl70_20 ),
inference(sat_conversion,[],[f999]) ).
cnf(s15,plain,
( ~ spl70_7
| ~ spl70_16
| ~ spl70_22 ),
inference(sat_conversion,[],[f1011]) ).
cnf(s25,plain,
spl70_8,
inference(sat_conversion,[],[f1308]) ).
cnf(s27,plain,
spl70_22,
inference(sat_conversion,[],[f1322]) ).
cnf(s28,plain,
( spl70_16
| spl70_41 ),
inference(sat_conversion,[],[f1329]) ).
cnf(s131,plain,
( ~ spl70_15
| spl70_16
| ~ spl70_20
| ~ spl70_41 ),
inference(sat_conversion,[],[f3124]) ).
cnf(s134,plain,
( ~ spl70_7
| ~ spl70_16 ),
inference(rat,[],[s15,s27]) ).
cnf(s135,plain,
spl70_7,
inference(rat,[],[s6,s25]) ).
cnf(s136,plain,
~ spl70_16,
inference(rat,[],[s134,s135]) ).
cnf(s137,plain,
spl70_41,
inference(rat,[],[s28,s136]) ).
cnf(s138,plain,
spl70_20,
inference(rat,[],[s13,s136]) ).
cnf(s139,plain,
spl70_15,
inference(rat,[],[s10,s136]) ).
cnf(s140,plain,
$false,
inference(rat,[],[s131,s137,s136,s138,s139]) ).
fof(f3125,plain,
$false,
inference(avatar_sat_refutation,[],[s140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM599+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n001.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Sun Sep 27 20:47:02 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 8.26/2.22 % (3934877)Detected formulas, will run a generic FOF schedule.
% 8.26/2.22 % (3934886)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4155220652:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.26/2.22 % (3934886)Instruction limit reached!
% 8.26/2.22 % (3934886)------------------------------
% 8.26/2.22 % (3934886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934886)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934886)Termination reason: Instruction limit
% 8.26/2.22 % (3934886)Termination phase: Saturation
% 8.26/2.22 % (3934886)Time elapsed: 0.041 s
% 8.26/2.22 % (3934886)Peak memory usage: 89 MB
% 8.26/2.22 % (3934886)Instructions burned: 119 (million)
% 8.26/2.22 % (3934887)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=705065444:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.26/2.22 % (3934882)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=1175828314:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.26/2.22 % (3934885)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=284242576:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.26/2.22 % (3934888)dis-21_1_sil=8000:lcm=predicate:random_seed=414486524: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)
% 8.26/2.22 % (3934883)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=2777200335:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.26/2.22 % (3934884)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=1669718653:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.26/2.22 % (3934885)Instruction limit reached!
% 8.26/2.22 % (3934885)------------------------------
% 8.26/2.22 % (3934885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934885)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934885)Termination reason: Instruction limit
% 8.26/2.22 % (3934885)Termination phase: Saturation
% 8.26/2.22 % (3934885)Time elapsed: 0.068 s
% 8.26/2.22 % (3934885)Peak memory usage: 90 MB
% 8.26/2.22 % (3934885)Instructions burned: 109 (million)
% 8.26/2.22 % (3934888)Instruction limit reached!
% 8.26/2.22 % (3934888)------------------------------
% 8.26/2.22 % (3934888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934888)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934888)Termination reason: Instruction limit
% 8.26/2.22 % (3934888)Termination phase: Saturation
% 8.26/2.22 % (3934888)Time elapsed: 0.068 s
% 8.26/2.22 % (3934888)Peak memory usage: 90 MB
% 8.26/2.22 % (3934888)Instructions burned: 132 (million)
% 8.26/2.22 % (3934896)lrs+10_1_sil=8000:sp=occurrence:random_seed=3928000295:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.26/2.22 % (3934887)Instruction limit reached!
% 8.26/2.22 % (3934887)------------------------------
% 8.26/2.22 % (3934887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934887)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934887)Termination reason: Instruction limit
% 8.26/2.22 % (3934887)Termination phase: Saturation
% 8.26/2.22 % (3934887)Time elapsed: 0.100 s
% 8.26/2.22 % (3934887)Peak memory usage: 90 MB
% 8.26/2.22 % (3934887)Instructions burned: 139 (million)
% 8.26/2.22 % (3934896)Instruction limit reached!
% 8.26/2.22 % (3934896)------------------------------
% 8.26/2.22 % (3934896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934896)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934896)Termination reason: Instruction limit
% 8.26/2.22 % (3934896)Termination phase: Saturation
% 8.26/2.22 % (3934896)Time elapsed: 0.095 s
% 8.26/2.22 % (3934896)Peak memory usage: 92 MB
% 8.26/2.22 % (3934896)Instructions burned: 287 (million)
% 8.26/2.22 % (3934898)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2798801607:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.26/2.22 % (3934897)lrs+10_1_sil=32000:urr=on:br=off:random_seed=9589642:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.26/2.22 % (3934897)Refutation not found, incomplete strategy
% 8.26/2.22 % (3934897)------------------------------
% 8.26/2.22 % (3934897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934897)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934897)Termination reason: Refutation not found, incomplete strategy
% 8.26/2.22 % (3934897)Time elapsed: 0.003 s
% 8.26/2.22 % (3934897)Peak memory usage: 89 MB
% 8.26/2.22 % (3934897)Instructions burned: 3 (million)
% 8.26/2.22 % (3934900)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=3803470201:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.26/2.22 % (3934901)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2101247042:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 8.26/2.22 % (3934901)Instruction limit reached!
% 8.26/2.22 % (3934901)------------------------------
% 8.26/2.22 % (3934901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934901)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934901)Termination reason: Instruction limit
% 8.26/2.22 % (3934901)Termination phase: Saturation
% 8.26/2.22 % (3934901)Time elapsed: 0.091 s
% 8.26/2.22 % (3934901)Peak memory usage: 90 MB
% 8.26/2.22 % (3934901)Instructions burned: 294 (million)
% 8.26/2.22 % (3934900)Instruction limit reached!
% 8.26/2.22 % (3934900)------------------------------
% 8.26/2.22 % (3934900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934900)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934900)Termination reason: Instruction limit
% 8.26/2.22 % (3934900)Termination phase: Saturation
% 8.26/2.22 % (3934900)Time elapsed: 0.151 s
% 8.26/2.22 % (3934900)Peak memory usage: 92 MB
% 8.26/2.22 % (3934900)Instructions burned: 249 (million)
% 8.26/2.22 % (3934898)Instruction limit reached!
% 8.26/2.22 % (3934898)------------------------------
% 8.26/2.22 % (3934898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934898)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934898)Termination reason: Instruction limit
% 8.26/2.22 % (3934898)Termination phase: Saturation
% 8.26/2.22 % (3934898)Time elapsed: 0.229 s
% 8.26/2.22 % (3934898)Peak memory usage: 92 MB
% 8.26/2.22 % (3934898)Instructions burned: 326 (million)
% 8.26/2.22 % (3934906)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2067937378:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.26/2.22 % (3934897)------------------------------
% 8.26/2.22 % (3934897)------------------------------
% 8.26/2.22 % (3934907)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4906789:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.26/2.22 % (3934908)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2377401233:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 8.26/2.22 % (3934907)Instruction limit reached!
% 8.26/2.22 % (3934907)------------------------------
% 8.26/2.22 % (3934907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934907)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934907)Termination reason: Instruction limit
% 8.26/2.22 % (3934907)Termination phase: Saturation
% 8.26/2.22 % (3934907)Time elapsed: 0.075 s
% 8.26/2.22 % (3934907)Peak memory usage: 91 MB
% 8.26/2.22 % (3934907)Instructions burned: 114 (million)
% 8.26/2.22 % (3934910)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1951502051:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 8.26/2.22 % (3934908)Instruction limit reached!
% 8.26/2.22 % (3934908)------------------------------
% 8.26/2.22 % (3934908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934908)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934908)Termination reason: Instruction limit
% 8.26/2.22 % (3934908)Termination phase: Saturation
% 8.26/2.22 % (3934908)Time elapsed: 0.067 s
% 8.26/2.22 % (3934908)Peak memory usage: 89 MB
% 8.26/2.22 % (3934908)Instructions burned: 127 (million)
% 8.26/2.22 % (3934910)Instruction limit reached!
% 8.26/2.22 % (3934910)------------------------------
% 8.26/2.22 % (3934910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934910)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934910)Termination reason: Instruction limit
% 8.26/2.22 % (3934910)Termination phase: Saturation
% 8.26/2.22 % (3934910)Time elapsed: 0.074 s
% 8.26/2.22 % (3934910)Peak memory usage: 89 MB
% 8.26/2.22 % (3934910)Instructions burned: 115 (million)
% 8.26/2.22 % (3934913)lrs+10_1_sil=8000:sp=occurrence:random_seed=4045926740:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.26/2.22 % (3934915)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=964398410:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 8.26/2.22 % (3934916)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=445610939:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 8.26/2.22 % (3934882)First to succeed.
% 8.26/2.22 % (3934882)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3934877"
% 8.26/2.22 % (3934906)Also succeeded, but the first one will report.
% 8.26/2.22 % (3934915)Instruction limit reached!
% 8.26/2.22 % (3934915)------------------------------
% 8.26/2.22 % (3934915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.22 % (3934915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.22 % (3934915)CaDiCaL version: 2.1.3
% 8.26/2.22 % (3934915)Termination reason: Instruction limit
% 8.26/2.22 % (3934915)Termination phase: Saturation
% 8.26/2.22 % (3934915)Time elapsed: 0.277 s
% 8.26/2.22 % (3934915)Peak memory usage: 93 MB
% 8.26/2.22 % (3934915)Instructions burned: 437 (million)
% 8.26/2.22 % (3934883)Also succeeded, but the first one will report.
% 8.26/2.22 % (3934882)Refutation found. Thanks to Tanya!
% 8.26/2.22 % SZS status Theorem for theBenchmark
% 8.26/2.22 % SZS output start Proof for theBenchmark
% See solution above
% 9.88/2.31 % (3934882)------------------------------
% 9.88/2.31 % (3934882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.88/2.31 % (3934882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.88/2.31 % (3934882)CaDiCaL version: 2.1.3
% 9.88/2.31 % (3934882)Termination reason: Refutation
% 9.88/2.31 % (3934882)Time elapsed: 0.912 s
% 9.88/2.31 % (3934882)Peak memory usage: 135 MB
% 9.88/2.31 % (3934882)Instructions burned: 1367 (million)
% 9.88/2.31 % (3934882)------------------------------
% 9.88/2.31 % (3934882)------------------------------
% 9.88/2.31 % (3934877)Success in time 1.324 s
% 9.88/2.31 % Vampire exiting
%------------------------------------------------------------------------------