%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM598+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 : 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 12:15:55 PM UTC 2026
% Result : Theorem 12.34s 2.96s
% Output : Refutation 14.45s
% 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(f96,conjecture,
isCountable0(xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f97,negated_conjecture,
~ isCountable0(xO),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f108,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(f114,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(f115,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(f116,plain,
~ isCountable0(xO),
inference(flattening,[],[f97]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f124]) ).
fof(f207,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f67]) ).
fof(f208,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f207]) ).
fof(f212,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(f213,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,[],[f212]) ).
fof(f214,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(f215,plain,
! [X0] :
( ( aElement0(szDzizrdt0(X0))
& isCountable0(sdtlbdtrb0(X0,szDzizrdt0(X0))) )
| ~ isCountable0(szDzozmdt0(X0))
| ~ isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aFunction0(X0) ),
inference(flattening,[],[f214]) ).
fof(f226,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,[],[f108]) ).
fof(f227,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,[],[f226]) ).
fof(f239,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(f240,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(f241,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,[],[f240]) ).
fof(f242,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,[],[f114]) ).
fof(f334,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))],[f213]) ).
fof(f357,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,[],[f227]) ).
fof(f358,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))],[f357]) ).
fof(f411,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))],[f241]) ).
fof(f412,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,[],[f242]) ).
fof(f413,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,[],[f412]) ).
fof(f414,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))],[f413]) ).
fof(f415,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(f416,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,[],[f415]) ).
fof(f417,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,[],[f115]) ).
fof(f418,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,[],[f417]) ).
fof(f419,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,[],[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 ) )
& ( ( 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))],[f419]) ).
fof(f421,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f432,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f466,plain,
isCountable0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f544,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f208]) ).
fof(f558,plain,
! [X0,X1] :
( sK42(X0) != sK43(X0)
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f559,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| aElementOf0(sK43(X0),szDzozmdt0(X0))
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f560,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| aElementOf0(sK42(X0),szDzozmdt0(X0))
| isCountable0(sdtlcdtrc0(X0,X1))
| ~ isCountable0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f561,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,[],[f334]) ).
fof(f562,plain,
! [X0] :
( ~ isFinite0(sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ isCountable0(szDzozmdt0(X0))
| isCountable0(sdtlbdtrb0(X0,szDzizrdt0(X0)))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f564,plain,
isFinite0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f565,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f647,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| X0 = X1 ),
inference(cnf_transformation,[],[f358]) ).
fof(f770,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f773,plain,
szNzAzT0 = szDzozmdt0(xe),
inference(cnf_transformation,[],[f239]) ).
fof(f774,plain,
aFunction0(xe),
inference(cnf_transformation,[],[f239]) ).
fof(f779,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(cnf_transformation,[],[f411]) ).
fof(f780,plain,
aFunction0(xd),
inference(cnf_transformation,[],[f411]) ).
fof(f781,plain,
aSubsetOf0(sdtlcdtrc0(xd,szDzozmdt0(xd)),xT),
inference(cnf_transformation,[],[f414]) ).
fof(f791,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f416]) ).
fof(f792,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(cnf_transformation,[],[f420]) ).
fof(f801,plain,
~ isCountable0(xO),
inference(cnf_transformation,[],[f116]) ).
fof(f892,plain,
( ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| ~ isCountable0(szNzAzT0)
| isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aFunction0(xd) ),
inference(superposition,[],[f562,f779]) ).
fof(f893,plain,
( ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aFunction0(xd) ),
inference(forward_subsumption_resolution,[],[f892,f466]) ).
fof(f894,plain,
( ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(forward_subsumption_resolution,[],[f893,f780]) ).
fof(f896,definition,
( spl70_7
<=> isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
introduced(definition,[new_symbols(definition,[spl70_7])],[avatar_definition]) ).
fof(f900,definition,
( spl70_8
<=> isFinite0(sdtlcdtrc0(xd,szNzAzT0)) ),
introduced(definition,[new_symbols(definition,[spl70_8])],[avatar_definition]) ).
fof(f902,plain,
( ~ isFinite0(sdtlcdtrc0(xd,szNzAzT0))
| spl70_8 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f903,plain,
( spl70_7
| ~ spl70_8 ),
inference(avatar_split_clause,[],[f894,f900,f896]) ).
fof(f936,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK42(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aFunction0(xe) ),
inference(superposition,[],[f560,f773]) ).
fof(f939,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK42(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[],[f936,f774]) ).
fof(f951,definition,
( spl70_15
<=> aElementOf0(sK42(xe),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl70_15])],[avatar_definition]) ).
fof(f953,plain,
( aElementOf0(sK42(xe),szNzAzT0)
| ~ spl70_15 ),
inference(avatar_component_clause,[],[f951]) ).
fof(f955,definition,
( spl70_16
<=> ! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| ~ isCountable0(X0)
| isCountable0(sdtlcdtrc0(xe,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl70_16])],[avatar_definition]) ).
fof(f956,plain,
( ! [X0] :
( isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aSubsetOf0(X0,szNzAzT0) )
| ~ spl70_16 ),
inference(avatar_component_clause,[],[f955]) ).
fof(f957,plain,
( spl70_15
| spl70_16 ),
inference(avatar_split_clause,[],[f939,f955,f951]) ).
fof(f971,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| sdtlpdtrp0(xe,sK43(xe)) = sdtlpdtrp0(xe,sK42(xe))
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aFunction0(xe) ),
inference(superposition,[],[f561,f773]) ).
fof(f974,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| sdtlpdtrp0(xe,sK43(xe)) = sdtlpdtrp0(xe,sK42(xe))
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[],[f971,f774]) ).
fof(f983,definition,
( spl70_20
<=> sdtlpdtrp0(xe,sK43(xe)) = sdtlpdtrp0(xe,sK42(xe)) ),
introduced(definition,[new_symbols(definition,[spl70_20])],[avatar_definition]) ).
fof(f985,plain,
( sdtlpdtrp0(xe,sK43(xe)) = sdtlpdtrp0(xe,sK42(xe))
| ~ spl70_20 ),
inference(avatar_component_clause,[],[f983]) ).
fof(f986,plain,
( spl70_20
| spl70_16 ),
inference(avatar_split_clause,[],[f974,f955,f983]) ).
fof(f992,plain,
( isCountable0(xO)
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ spl70_16 ),
inference(superposition,[],[f956,f792]) ).
fof(f993,plain,
( ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| ~ spl70_16 ),
inference(forward_subsumption_resolution,[],[f992,f801]) ).
fof(f995,definition,
( spl70_22
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl70_22])],[avatar_definition]) ).
fof(f997,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
| spl70_22 ),
inference(avatar_component_clause,[],[f995]) ).
fof(f998,plain,
( ~ spl70_22
| ~ spl70_7
| ~ spl70_16 ),
inference(avatar_split_clause,[],[f993,f955,f896,f995]) ).
fof(f1005,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK43(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0)
| ~ aFunction0(xe) ),
inference(superposition,[],[f559,f773]) ).
fof(f1099,plain,
! [X0] :
( aSubsetOf0(sdtlbdtrb0(xd,X0),szNzAzT0)
| ~ aFunction0(xd)
| ~ aElement0(X0) ),
inference(superposition,[],[f544,f779]) ).
fof(f1103,plain,
! [X0] :
( aSubsetOf0(sdtlbdtrb0(xd,X0),szNzAzT0)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[],[f1099,f780]) ).
fof(f1108,plain,
( aElement0(szDzizrdt0(xd))
| ~ aSet0(xT) ),
inference(resolution,[],[f421,f791]) ).
fof(f1113,plain,
aElement0(szDzizrdt0(xd)),
inference(forward_subsumption_resolution,[],[f1108,f565]) ).
fof(f1280,plain,
( isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ aSet0(xT)
| ~ isFinite0(xT) ),
inference(resolution,[],[f781,f432]) ).
fof(f1282,plain,
( isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd)))
| ~ isFinite0(xT) ),
inference(forward_subsumption_resolution,[],[f1280,f565]) ).
fof(f1285,plain,
isFinite0(sdtlcdtrc0(xd,szDzozmdt0(xd))),
inference(forward_subsumption_resolution,[],[f1282,f564]) ).
fof(f1288,plain,
isFinite0(sdtlcdtrc0(xd,szNzAzT0)),
inference(forward_demodulation,[],[f1285,f779]) ).
fof(f1291,plain,
( $false
| spl70_8 ),
inference(forward_subsumption_resolution,[],[f1288,f902]) ).
fof(f1292,plain,
spl70_8,
inference(avatar_contradiction_clause,[],[f1291]) ).
fof(f1304,plain,
( ~ aElement0(szDzizrdt0(xd))
| spl70_22 ),
inference(resolution,[],[f997,f1103]) ).
fof(f1305,plain,
( $false
| spl70_22 ),
inference(forward_subsumption_resolution,[],[f1304,f1113]) ).
fof(f1306,plain,
spl70_22,
inference(avatar_contradiction_clause,[],[f1305]) ).
fof(f1308,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(sK43(xe),szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) ),
inference(forward_subsumption_resolution,[],[f1005,f774]) ).
fof(f1310,definition,
( spl70_41
<=> aElementOf0(sK43(xe),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl70_41])],[avatar_definition]) ).
fof(f1312,plain,
( aElementOf0(sK43(xe),szNzAzT0)
| ~ spl70_41 ),
inference(avatar_component_clause,[],[f1310]) ).
fof(f1313,plain,
( spl70_41
| spl70_16 ),
inference(avatar_split_clause,[],[f1308,f955,f1310]) ).
fof(f1339,plain,
( sdtlpdtrp0(xe,sK42(xe)) = szmzizndt0(sdtlpdtrp0(xN,sK42(xe)))
| ~ spl70_15 ),
inference(resolution,[],[f953,f770]) ).
fof(f1353,plain,
( sdtlpdtrp0(xe,sK43(xe)) = szmzizndt0(sdtlpdtrp0(xN,sK43(xe)))
| ~ spl70_41 ),
inference(resolution,[],[f1312,f770]) ).
fof(f1357,plain,
( sdtlpdtrp0(xe,sK42(xe)) = szmzizndt0(sdtlpdtrp0(xN,sK43(xe)))
| ~ spl70_20
| ~ spl70_41 ),
inference(forward_demodulation,[],[f1353,f985]) ).
fof(f1727,plain,
( ! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != sdtlpdtrp0(xe,sK42(xe))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK42(xe),szNzAzT0)
| sK42(xe) = X0 )
| ~ spl70_15 ),
inference(superposition,[],[f647,f1339]) ).
fof(f1730,plain,
( ! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != sdtlpdtrp0(xe,sK42(xe))
| ~ aElementOf0(X0,szNzAzT0)
| sK42(xe) = X0 )
| ~ spl70_15 ),
inference(forward_subsumption_resolution,[],[f1727,f953]) ).
fof(f1808,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,[],[f1730,f1357]) ).
fof(f1809,plain,
( ~ aElementOf0(sK43(xe),szNzAzT0)
| sK42(xe) = sK43(xe)
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(trivial_inequality_removal,[],[f1808]) ).
fof(f1810,plain,
( sK42(xe) = sK43(xe)
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(forward_subsumption_resolution,[],[f1809,f1312]) ).
fof(f1817,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,[],[f558,f1810]) ).
fof(f1818,plain,
( ! [X0] :
( isCountable0(sdtlcdtrc0(xe,X0))
| ~ aSubsetOf0(X0,szDzozmdt0(xe))
| ~ isCountable0(X0)
| ~ aFunction0(xe) )
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(trivial_inequality_removal,[],[f1817]) ).
fof(f1819,plain,
( ! [X0] :
( isCountable0(sdtlcdtrc0(xe,X0))
| ~ aSubsetOf0(X0,szDzozmdt0(xe))
| ~ isCountable0(X0) )
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(forward_subsumption_resolution,[],[f1818,f774]) ).
fof(f1820,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| isCountable0(sdtlcdtrc0(xe,X0))
| ~ isCountable0(X0) )
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(forward_demodulation,[],[f1819,f773]) ).
fof(f1821,plain,
( spl70_16
| ~ spl70_15
| ~ spl70_20
| ~ spl70_41 ),
inference(avatar_split_clause,[],[f1820,f1310,f983,f951,f955]) ).
cnf(s6,plain,
( spl70_7
| ~ spl70_8 ),
inference(sat_conversion,[],[f903]) ).
cnf(s10,plain,
( spl70_15
| spl70_16 ),
inference(sat_conversion,[],[f957]) ).
cnf(s13,plain,
( spl70_16
| spl70_20 ),
inference(sat_conversion,[],[f986]) ).
cnf(s15,plain,
( ~ spl70_7
| ~ spl70_16
| ~ spl70_22 ),
inference(sat_conversion,[],[f998]) ).
cnf(s25,plain,
spl70_8,
inference(sat_conversion,[],[f1292]) ).
cnf(s27,plain,
spl70_22,
inference(sat_conversion,[],[f1306]) ).
cnf(s28,plain,
( spl70_16
| spl70_41 ),
inference(sat_conversion,[],[f1313]) ).
cnf(s56,plain,
( ~ spl70_15
| spl70_16
| ~ spl70_20
| ~ spl70_41 ),
inference(sat_conversion,[],[f1821]) ).
cnf(s57,plain,
( ~ spl70_7
| ~ spl70_16 ),
inference(rat,[],[s15,s27]) ).
cnf(s58,plain,
spl70_7,
inference(rat,[],[s6,s25]) ).
cnf(s59,plain,
~ spl70_16,
inference(rat,[],[s57,s58]) ).
cnf(s60,plain,
spl70_41,
inference(rat,[],[s28,s59]) ).
cnf(s61,plain,
spl70_20,
inference(rat,[],[s13,s59]) ).
cnf(s62,plain,
spl70_15,
inference(rat,[],[s10,s59]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s56,s60,s59,s61,s62]) ).
fof(f1822,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM598+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n004.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 20:40:37 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 Running first-order theorem proving
% 0.16/0.45 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
% 12.34/2.96 % (3859280)Detected formulas, will run a generic FOF schedule.
% 12.34/2.96 % (3859295)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1154364428:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.34/2.96 % (3859297)dis-21_1_sil=8000:lcm=predicate:random_seed=286076606: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)
% 12.34/2.96 % (3859293)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=640179731:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.34/2.96 % (3859294)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=974746190:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.34/2.96 % (3859292)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=1570263870:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.34/2.96 % (3859291)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=2342755982:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.34/2.96 % (3859295)Instruction limit reached!
% 12.34/2.96 % (3859295)------------------------------
% 12.34/2.96 % (3859295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859295)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859295)Termination reason: Instruction limit
% 12.34/2.96 % (3859295)Termination phase: Saturation
% 12.34/2.96 % (3859295)Time elapsed: 0.064 s
% 12.34/2.96 % (3859295)Peak memory usage: 89 MB
% 12.34/2.96 % (3859295)Instructions burned: 121 (million)
% 12.34/2.96 % (3859296)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1487246336:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.34/2.96 % (3859297)Instruction limit reached!
% 12.34/2.96 % (3859297)------------------------------
% 12.34/2.96 % (3859297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859297)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859297)Termination reason: Instruction limit
% 12.34/2.96 % (3859297)Termination phase: Saturation
% 12.34/2.96 % (3859297)Time elapsed: 0.115 s
% 12.34/2.96 % (3859297)Peak memory usage: 90 MB
% 12.34/2.96 % (3859297)Instructions burned: 130 (million)
% 12.34/2.96 % (3859294)Instruction limit reached!
% 12.34/2.96 % (3859294)------------------------------
% 12.34/2.96 % (3859294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859294)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859294)Termination reason: Instruction limit
% 12.34/2.96 % (3859294)Termination phase: Saturation
% 12.34/2.96 % (3859294)Time elapsed: 0.107 s
% 12.34/2.96 % (3859294)Peak memory usage: 90 MB
% 12.34/2.96 % (3859294)Instructions burned: 109 (million)
% 12.34/2.96 % (3859306)lrs+10_1_sil=8000:sp=occurrence:random_seed=922382109:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.34/2.96 % (3859296)Instruction limit reached!
% 12.34/2.96 % (3859296)------------------------------
% 12.34/2.96 % (3859296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859296)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859296)Termination reason: Instruction limit
% 12.34/2.96 % (3859296)Termination phase: Saturation
% 12.34/2.96 % (3859296)Time elapsed: 0.155 s
% 12.34/2.96 % (3859296)Peak memory usage: 90 MB
% 12.34/2.96 % (3859296)Instructions burned: 139 (million)
% 12.34/2.96 % (3859310)lrs+10_1_sil=32000:urr=on:br=off:random_seed=196698143:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 12.34/2.96 % (3859310)Refutation not found, incomplete strategy
% 12.34/2.96 % (3859310)------------------------------
% 12.34/2.96 % (3859310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859310)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859310)Termination reason: Refutation not found, incomplete strategy
% 12.34/2.96 % (3859310)Time elapsed: 0.003 s
% 12.34/2.96 % (3859310)Peak memory usage: 89 MB
% 12.34/2.96 % (3859310)Instructions burned: 3 (million)
% 12.34/2.96 % (3859306)Instruction limit reached!
% 12.34/2.96 % (3859306)------------------------------
% 12.34/2.96 % (3859306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859306)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859306)Termination reason: Instruction limit
% 12.34/2.96 % (3859306)Termination phase: Saturation
% 12.34/2.96 % (3859306)Time elapsed: 0.146 s
% 12.34/2.96 % (3859306)Peak memory usage: 92 MB
% 12.34/2.96 % (3859306)Instructions burned: 286 (million)
% 12.34/2.96 % (3859311)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3014355964:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 12.34/2.96 % (3859313)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=718501893:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 12.34/2.96 % (3859315)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1595254845:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 12.34/2.96 % (3859315)Instruction limit reached!
% 12.34/2.96 % (3859315)------------------------------
% 12.34/2.96 % (3859315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859315)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859315)Termination reason: Instruction limit
% 12.34/2.96 % (3859315)Termination phase: Saturation
% 12.34/2.96 % (3859315)Time elapsed: 0.158 s
% 12.34/2.96 % (3859315)Peak memory usage: 90 MB
% 12.34/2.96 % (3859315)Instructions burned: 296 (million)
% 12.34/2.96 % (3859310)------------------------------
% 12.34/2.96 % (3859310)------------------------------
% 12.34/2.96 % (3859313)Instruction limit reached!
% 12.34/2.96 % (3859313)------------------------------
% 12.34/2.96 % (3859313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859313)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859313)Termination reason: Instruction limit
% 12.34/2.96 % (3859313)Termination phase: Saturation
% 12.34/2.96 % (3859313)Time elapsed: 0.243 s
% 12.34/2.96 % (3859313)Peak memory usage: 92 MB
% 12.34/2.96 % (3859313)Instructions burned: 248 (million)
% 12.34/2.96 % (3859311)Instruction limit reached!
% 12.34/2.96 % (3859311)------------------------------
% 12.34/2.96 % (3859311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859311)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859311)Termination reason: Instruction limit
% 12.34/2.96 % (3859311)Termination phase: Saturation
% 12.34/2.96 % (3859311)Time elapsed: 0.354 s
% 12.34/2.96 % (3859311)Peak memory usage: 92 MB
% 12.34/2.96 % (3859311)Instructions burned: 325 (million)
% 12.34/2.96 % (3859319)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=898298969:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 12.34/2.96 % (3859320)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4136186341:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 12.34/2.96 % (3859321)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2458350720:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 12.34/2.96 % (3859322)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3524752704:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 12.34/2.96 % (3859321)Instruction limit reached!
% 12.34/2.96 % (3859321)------------------------------
% 12.34/2.96 % (3859321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859321)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859321)Termination reason: Instruction limit
% 12.34/2.96 % (3859321)Termination phase: Saturation
% 12.34/2.96 % (3859321)Time elapsed: 0.115 s
% 12.34/2.96 % (3859321)Peak memory usage: 89 MB
% 12.34/2.96 % (3859321)Instructions burned: 128 (million)
% 12.34/2.96 % (3859320)Instruction limit reached!
% 12.34/2.96 % (3859320)------------------------------
% 12.34/2.96 % (3859320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859320)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859320)Termination reason: Instruction limit
% 12.34/2.96 % (3859320)Termination phase: Saturation
% 12.34/2.96 % (3859320)Time elapsed: 0.117 s
% 12.34/2.96 % (3859320)Peak memory usage: 91 MB
% 12.34/2.96 % (3859320)Instructions burned: 114 (million)
% 12.34/2.96 % (3859322)Instruction limit reached!
% 12.34/2.96 % (3859322)------------------------------
% 12.34/2.96 % (3859322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859322)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859322)Termination reason: Instruction limit
% 12.34/2.96 % (3859322)Termination phase: Saturation
% 12.34/2.96 % (3859322)Time elapsed: 0.119 s
% 12.34/2.96 % (3859322)Peak memory usage: 89 MB
% 12.34/2.96 % (3859322)Instructions burned: 114 (million)
% 12.34/2.96 % (3859329)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=290893092:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 12.34/2.96 % (3859328)lrs+10_1_sil=8000:sp=occurrence:random_seed=1134914668:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 12.34/2.96 % (3859330)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2925187067:i=5202:ss=axioms:sgt=16_2987 on theBenchmark for (2987ds/5202Mi)
% 12.34/2.96 % (3859291)First to succeed.
% 12.34/2.96 % (3859291)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3859280"
% 12.34/2.96 % (3859292)Also succeeded, but the first one will report.
% 12.34/2.96 % (3859329)Instruction limit reached!
% 12.34/2.96 % (3859329)------------------------------
% 12.34/2.96 % (3859329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.34/2.96 % (3859329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.34/2.96 % (3859329)CaDiCaL version: 2.1.3
% 12.34/2.96 % (3859329)Termination reason: Instruction limit
% 12.34/2.96 % (3859329)Termination phase: Saturation
% 12.34/2.96 % (3859329)Time elapsed: 0.409 s
% 12.34/2.96 % (3859329)Peak memory usage: 93 MB
% 12.34/2.96 % (3859329)Instructions burned: 437 (million)
% 12.34/2.96 % (3859319)Also succeeded, but the first one will report.
% 12.34/2.96 % (3859334)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4260900094:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2982 on theBenchmark for (2982ds/134Mi)
% 12.34/2.96 % (3859291)Refutation found. Thanks to Tanya!
% 12.34/2.96 % SZS status Theorem for theBenchmark
% 12.34/2.96 % SZS output start Proof for theBenchmark
% See solution above
% 14.45/3.26 % (3859291)------------------------------
% 14.45/3.26 % (3859291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.45/3.26 % (3859291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.45/3.26 % (3859291)CaDiCaL version: 2.1.3
% 14.45/3.26 % (3859291)Termination reason: Refutation
% 14.45/3.26 % (3859291)Time elapsed: 1.285 s
% 14.45/3.26 % (3859291)Peak memory usage: 134 MB
% 14.45/3.26 % (3859291)Instructions burned: 1175 (million)
% 14.45/3.26 % (3859291)------------------------------
% 14.45/3.26 % (3859291)------------------------------
% 14.45/3.26 % (3859280)Success in time 1.934 s
% 14.45/3.26 % Vampire exiting
%------------------------------------------------------------------------------