%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM542+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:15:40 PM UTC 2026
% Result : Theorem 4.58s 1.68s
% Output : Refutation 6.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 142 ( 11 unt; 14 def)
% Number of atoms : 703 ( 23 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 858 ( 297 ~; 295 |; 198 &)
% ( 41 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 131 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f28,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> X0 != szszuzczcdt0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatNSucc) ).
fof(f33,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessSucc) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(f36,axiom,
! [X0,X1,X2] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTrans) ).
fof(f37,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSeg) ).
fof(f54,axiom,
( aElementOf0(xm,szNzAzT0)
& aElementOf0(xn,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1964) ).
fof(f55,conjecture,
( ( sdtlseqdt0(xm,xn)
=> ( ( aSet0(slbdtrb0(xm))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) ) ) )
=> ( ( aSet0(slbdtrb0(xn))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xn))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xn) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
=> aElementOf0(X0,slbdtrb0(xn)) )
| aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ) ) )
& ( ( aSet0(slbdtrb0(xm))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) ) )
& aSet0(slbdtrb0(xn))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xn))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xn) ) )
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
=> aElementOf0(X0,slbdtrb0(xn)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) )
=> sdtlseqdt0(xm,xn) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ ( ( sdtlseqdt0(xm,xn)
=> ( ( aSet0(slbdtrb0(xm))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) ) ) )
=> ( ( aSet0(slbdtrb0(xn))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xn))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xn) ) ) )
=> ( ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
=> aElementOf0(X0,slbdtrb0(xn)) )
| aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ) ) )
& ( ( aSet0(slbdtrb0(xm))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) ) )
& aSet0(slbdtrb0(xn))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xn))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xn) ) )
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
=> aElementOf0(X0,slbdtrb0(xn)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) )
=> sdtlseqdt0(xm,xn) ) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f63,plain,
~ ( ( sdtlseqdt0(xm,xn)
=> ( ( aSet0(slbdtrb0(xm))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) ) ) )
=> ( ( aSet0(slbdtrb0(xn))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(xn))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,slbdtrb0(xm))
=> aElementOf0(X2,slbdtrb0(xn)) )
| aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ) ) )
& ( ( aSet0(slbdtrb0(xm))
& ! [X3] :
( aElementOf0(X3,slbdtrb0(xm))
<=> ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),xm) ) )
& aSet0(slbdtrb0(xn))
& ! [X4] :
( aElementOf0(X4,slbdtrb0(xn))
<=> ( aElementOf0(X4,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X4),xn) ) )
& ! [X5] :
( aElementOf0(X5,slbdtrb0(xm))
=> aElementOf0(X5,slbdtrb0(xn)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) )
=> sdtlseqdt0(xm,xn) ) ),
inference(rectify,[],[f56]) ).
fof(f93,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f98,plain,
! [X0] :
( X0 != szszuzczcdt0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f103,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f106,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f108,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f110,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f109]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) ) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f133,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(xn))
& aElementOf0(X2,slbdtrb0(xm)) )
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(xn))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) ) )
& aSet0(slbdtrb0(xm))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) ) )
& sdtlseqdt0(xm,xn) )
| ( ~ sdtlseqdt0(xm,xn)
& aSet0(slbdtrb0(xm))
& ! [X3] :
( aElementOf0(X3,slbdtrb0(xm))
<=> ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),xm) ) )
& aSet0(slbdtrb0(xn))
& ! [X4] :
( aElementOf0(X4,slbdtrb0(xn))
<=> ( aElementOf0(X4,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X4),xn) ) )
& ! [X5] :
( aElementOf0(X5,slbdtrb0(xn))
| ~ aElementOf0(X5,slbdtrb0(xm)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ),
inference(ennf_transformation,[],[f63]) ).
fof(f134,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(xn))
& aElementOf0(X2,slbdtrb0(xm)) )
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(xn))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) ) )
& aSet0(slbdtrb0(xm))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) ) )
& sdtlseqdt0(xm,xn) )
| ( ~ sdtlseqdt0(xm,xn)
& aSet0(slbdtrb0(xm))
& ! [X3] :
( aElementOf0(X3,slbdtrb0(xm))
<=> ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),xm) ) )
& aSet0(slbdtrb0(xn))
& ! [X4] :
( aElementOf0(X4,slbdtrb0(xn))
<=> ( aElementOf0(X4,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X4),xn) ) )
& ! [X5] :
( aElementOf0(X5,slbdtrb0(xn))
| ~ aElementOf0(X5,slbdtrb0(xm)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ),
inference(flattening,[],[f133]) ).
fof(f135,definition,
( ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(xn))
& aElementOf0(X2,slbdtrb0(xm)) )
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(xn))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) ) )
& aSet0(slbdtrb0(xm))
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) ) )
& sdtlseqdt0(xm,xn) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f136,plain,
( sP0
| ( ~ sdtlseqdt0(xm,xn)
& aSet0(slbdtrb0(xm))
& ! [X3] :
( aElementOf0(X3,slbdtrb0(xm))
<=> ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),xm) ) )
& aSet0(slbdtrb0(xn))
& ! [X4] :
( aElementOf0(X4,slbdtrb0(xn))
<=> ( aElementOf0(X4,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X4),xn) ) )
& ! [X5] :
( aElementOf0(X5,slbdtrb0(xn))
| ~ aElementOf0(X5,slbdtrb0(xm)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ),
inference(definition_folding,[],[f134,f135]) ).
fof(f166,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f129]) ).
fof(f167,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f166]) ).
fof(f168,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X0) )
| ~ aElementOf0(X3,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f167]) ).
fof(f169,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ( ( ~ aElementOf0(sK9(X0,X1),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK9(X0,X1)),X0)
| ~ aElementOf0(sK9(X0,X1),X1) )
& ( ( aElementOf0(sK9(X0,X1),szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(sK9(X0,X1)),X0) )
| aElementOf0(sK9(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X0) )
| ~ aElementOf0(X3,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f168]) ).
fof(f172,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(xn))
& aElementOf0(X2,slbdtrb0(xm)) )
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& ! [X1] :
( ( aElementOf0(X1,slbdtrb0(xn))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),xn) )
& ( ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) )
| ~ aElementOf0(X1,slbdtrb0(xn)) ) )
& aSet0(slbdtrb0(xm))
& ! [X0] :
( ( aElementOf0(X0,slbdtrb0(xm))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm) )
& ( ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) )
| ~ aElementOf0(X0,slbdtrb0(xm)) ) )
& sdtlseqdt0(xm,xn) )
| ~ sP0 ),
inference(nnf_transformation,[],[f135]) ).
fof(f173,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(xn))
& aElementOf0(X2,slbdtrb0(xm)) )
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& ! [X1] :
( ( aElementOf0(X1,slbdtrb0(xn))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),xn) )
& ( ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) )
| ~ aElementOf0(X1,slbdtrb0(xn)) ) )
& aSet0(slbdtrb0(xm))
& ! [X0] :
( ( aElementOf0(X0,slbdtrb0(xm))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm) )
& ( ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) )
| ~ aElementOf0(X0,slbdtrb0(xm)) ) )
& sdtlseqdt0(xm,xn) )
| ~ sP0 ),
inference(flattening,[],[f172]) ).
fof(f174,plain,
( ( ? [X0] :
( ~ aElementOf0(X0,slbdtrb0(xn))
& aElementOf0(X0,slbdtrb0(xm)) )
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& ! [X1] :
( ( aElementOf0(X1,slbdtrb0(xn))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),xn) )
& ( ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) )
| ~ aElementOf0(X1,slbdtrb0(xn)) ) )
& aSet0(slbdtrb0(xm))
& ! [X2] :
( ( aElementOf0(X2,slbdtrb0(xm))
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),xm) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),xm) )
| ~ aElementOf0(X2,slbdtrb0(xm)) ) )
& sdtlseqdt0(xm,xn) )
| ~ sP0 ),
inference(rectify,[],[f173]) ).
fof(f175,plain,
( ( ~ aElementOf0(sK10,slbdtrb0(xn))
& aElementOf0(sK10,slbdtrb0(xm))
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& ! [X1] :
( ( aElementOf0(X1,slbdtrb0(xn))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),xn) )
& ( ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) )
| ~ aElementOf0(X1,slbdtrb0(xn)) ) )
& aSet0(slbdtrb0(xm))
& ! [X2] :
( ( aElementOf0(X2,slbdtrb0(xm))
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),xm) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),xm) )
| ~ aElementOf0(X2,slbdtrb0(xm)) ) )
& sdtlseqdt0(xm,xn) )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f174]) ).
fof(f176,plain,
( sP0
| ( ~ sdtlseqdt0(xm,xn)
& aSet0(slbdtrb0(xm))
& ! [X3] :
( ( aElementOf0(X3,slbdtrb0(xm))
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),xm) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),xm) )
| ~ aElementOf0(X3,slbdtrb0(xm)) ) )
& aSet0(slbdtrb0(xn))
& ! [X4] :
( ( aElementOf0(X4,slbdtrb0(xn))
| ~ aElementOf0(X4,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X4),xn) )
& ( ( aElementOf0(X4,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X4),xn) )
| ~ aElementOf0(X4,slbdtrb0(xn)) ) )
& ! [X5] :
( aElementOf0(X5,slbdtrb0(xn))
| ~ aElementOf0(X5,slbdtrb0(xm)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ),
inference(nnf_transformation,[],[f136]) ).
fof(f177,plain,
( sP0
| ( ~ sdtlseqdt0(xm,xn)
& aSet0(slbdtrb0(xm))
& ! [X3] :
( ( aElementOf0(X3,slbdtrb0(xm))
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),xm) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),xm) )
| ~ aElementOf0(X3,slbdtrb0(xm)) ) )
& aSet0(slbdtrb0(xn))
& ! [X4] :
( ( aElementOf0(X4,slbdtrb0(xn))
| ~ aElementOf0(X4,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X4),xn) )
& ( ( aElementOf0(X4,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X4),xn) )
| ~ aElementOf0(X4,slbdtrb0(xn)) ) )
& ! [X5] :
( aElementOf0(X5,slbdtrb0(xn))
| ~ aElementOf0(X5,slbdtrb0(xm)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ),
inference(flattening,[],[f176]) ).
fof(f178,plain,
( sP0
| ( ~ sdtlseqdt0(xm,xn)
& aSet0(slbdtrb0(xm))
& ! [X0] :
( ( aElementOf0(X0,slbdtrb0(xm))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm) )
& ( ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) )
| ~ aElementOf0(X0,slbdtrb0(xm)) ) )
& aSet0(slbdtrb0(xn))
& ! [X1] :
( ( aElementOf0(X1,slbdtrb0(xn))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),xn) )
& ( ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) )
| ~ aElementOf0(X1,slbdtrb0(xn)) ) )
& ! [X2] :
( aElementOf0(X2,slbdtrb0(xn))
| ~ aElementOf0(X2,slbdtrb0(xm)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ),
inference(rectify,[],[f177]) ).
fof(f222,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f226,plain,
! [X0] :
( szszuzczcdt0(X0) != X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f231,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f233,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| X0 = X1 ),
inference(cnf_transformation,[],[f106]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f235,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f258,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f268,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f54]) ).
fof(f269,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f54]) ).
fof(f270,plain,
( sdtlseqdt0(xm,xn)
| ~ sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f271,plain,
! [X2] :
( sdtlseqdt0(szszuzczcdt0(X2),xm)
| ~ aElementOf0(X2,slbdtrb0(xm))
| ~ sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f272,plain,
! [X2] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X2,slbdtrb0(xm))
| ~ sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f280,plain,
( aElementOf0(sK10,slbdtrb0(xm))
| ~ sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f281,plain,
( ~ aElementOf0(sK10,slbdtrb0(xn))
| ~ sP0 ),
inference(cnf_transformation,[],[f175]) ).
fof(f283,plain,
! [X2] :
( sP0
| aElementOf0(X2,slbdtrb0(xn))
| ~ aElementOf0(X2,slbdtrb0(xm)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f284,plain,
! [X1] :
( sP0
| sdtlseqdt0(szszuzczcdt0(X1),xn)
| ~ aElementOf0(X1,slbdtrb0(xn)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f290,plain,
! [X0] :
( sP0
| aElementOf0(X0,slbdtrb0(xm))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm) ),
inference(cnf_transformation,[],[f178]) ).
fof(f292,plain,
( sP0
| ~ sdtlseqdt0(xm,xn) ),
inference(cnf_transformation,[],[f178]) ).
fof(f314,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| aElementOf0(X3,slbdtrb0(X0)) ),
inference(equality_resolution,[],[f258]) ).
fof(f324,definition,
( spl11_2
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f328,definition,
( spl11_3
<=> ! [X2] :
( aElementOf0(X2,slbdtrb0(xn))
| ~ aElementOf0(X2,slbdtrb0(xm)) ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f329,plain,
( ! [X2] :
( ~ aElementOf0(X2,slbdtrb0(xm))
| aElementOf0(X2,slbdtrb0(xn)) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f330,plain,
( spl11_3
| spl11_2 ),
inference(avatar_split_clause,[],[f283,f324,f328]) ).
fof(f332,definition,
( spl11_4
<=> ! [X1] :
( sdtlseqdt0(szszuzczcdt0(X1),xn)
| ~ aElementOf0(X1,slbdtrb0(xn)) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
fof(f333,plain,
( ! [X1] :
( ~ aElementOf0(X1,slbdtrb0(xn))
| sdtlseqdt0(szszuzczcdt0(X1),xn) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f334,plain,
( spl11_4
| spl11_2 ),
inference(avatar_split_clause,[],[f284,f324,f332]) ).
fof(f348,definition,
( spl11_8
<=> ! [X0] :
( sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,slbdtrb0(xm)) ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
fof(f349,plain,
( ! [X0] :
( ~ aElementOf0(X0,slbdtrb0(xm))
| sdtlseqdt0(szszuzczcdt0(X0),xm) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f352,definition,
( spl11_9
<=> ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
fof(f353,plain,
( ! [X0] :
( ~ aElementOf0(X0,slbdtrb0(xm))
| aElementOf0(X0,szNzAzT0) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f356,definition,
( spl11_10
<=> ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
fof(f357,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm)
| aElementOf0(X0,slbdtrb0(xm)) )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f358,plain,
( spl11_10
| spl11_2 ),
inference(avatar_split_clause,[],[f290,f324,f356]) ).
fof(f364,definition,
( spl11_12
<=> sdtlseqdt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
fof(f365,plain,
( ~ sdtlseqdt0(xm,xn)
| spl11_12 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f366,plain,
( ~ spl11_12
| spl11_2 ),
inference(avatar_split_clause,[],[f292,f324,f364]) ).
fof(f368,plain,
( sdtlseqdt0(xm,xn)
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f369,plain,
( ~ spl11_2
| spl11_12 ),
inference(avatar_split_clause,[],[f270,f364,f324]) ).
fof(f370,plain,
( ~ spl11_2
| spl11_8 ),
inference(avatar_split_clause,[],[f271,f348,f324]) ).
fof(f371,plain,
( ~ spl11_2
| spl11_9 ),
inference(avatar_split_clause,[],[f272,f352,f324]) ).
fof(f381,definition,
( spl11_13
<=> aElementOf0(sK10,slbdtrb0(xm)) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
fof(f382,plain,
( aElementOf0(sK10,slbdtrb0(xm))
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f383,plain,
( ~ spl11_2
| spl11_13 ),
inference(avatar_split_clause,[],[f280,f381,f324]) ).
fof(f385,definition,
( spl11_14
<=> aElementOf0(sK10,slbdtrb0(xn)) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
fof(f386,plain,
( ~ aElementOf0(sK10,slbdtrb0(xn))
| spl11_14 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f387,plain,
( ~ spl11_2
| ~ spl11_14 ),
inference(avatar_split_clause,[],[f281,f385,f324]) ).
fof(f401,plain,
( sdtlseqdt0(szszuzczcdt0(sK10),xm)
| ~ spl11_8
| ~ spl11_13 ),
inference(resolution,[],[f349,f382]) ).
fof(f402,plain,
( aElementOf0(sK10,szNzAzT0)
| ~ spl11_9
| ~ spl11_13 ),
inference(resolution,[],[f353,f382]) ).
fof(f436,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| aElementOf0(xn,slbdtrb0(xm))
| ~ spl11_10 ),
inference(resolution,[],[f268,f357]) ).
fof(f437,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X1,xn)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,xn) ),
inference(resolution,[],[f268,f234]) ).
fof(f438,plain,
! [X0] :
( sdtlseqdt0(szszuzczcdt0(xn),X0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,xn) ),
inference(resolution,[],[f268,f235]) ).
fof(f440,definition,
( spl11_22
<=> aElementOf0(xn,slbdtrb0(xm)) ),
introduced(definition,[new_symbols(definition,[spl11_22])],[avatar_definition]) ).
fof(f441,plain,
( aElementOf0(xn,slbdtrb0(xm))
| ~ spl11_22 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f443,definition,
( spl11_23
<=> sdtlseqdt0(szszuzczcdt0(xn),xm) ),
introduced(definition,[new_symbols(definition,[spl11_23])],[avatar_definition]) ).
fof(f444,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| spl11_23 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f445,plain,
( spl11_22
| ~ spl11_23
| ~ spl11_10 ),
inference(avatar_split_clause,[],[f436,f356,f443,f440]) ).
fof(f466,plain,
( ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(xm,xn)
| spl11_23 ),
inference(resolution,[],[f444,f438]) ).
fof(f468,plain,
! [X0] :
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,xm)
| sdtlseqdt0(X0,xn) ),
inference(resolution,[],[f437,f269]) ).
fof(f505,plain,
( sdtlseqdt0(xm,xn)
| spl11_23 ),
inference(forward_subsumption_resolution,[],[f466,f269]) ).
fof(f506,plain,
( $false
| spl11_12
| spl11_23 ),
inference(forward_subsumption_resolution,[],[f505,f365]) ).
fof(f507,plain,
( spl11_12
| spl11_23 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f508,plain,
( aElementOf0(xn,slbdtrb0(xn))
| ~ spl11_3
| ~ spl11_22 ),
inference(resolution,[],[f441,f329]) ).
fof(f514,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ spl11_3
| ~ spl11_4
| ~ spl11_22 ),
inference(resolution,[],[f508,f333]) ).
fof(f571,plain,
! [X0] :
( ~ sdtlseqdt0(xn,X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0)
| xn = X0 ),
inference(resolution,[],[f233,f268]) ).
fof(f860,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| xn = szszuzczcdt0(xn)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f571,f231]) ).
fof(f861,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| xn = szszuzczcdt0(xn)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f860,f222]) ).
fof(f862,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f861,f226]) ).
fof(f863,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ spl11_3
| ~ spl11_4
| ~ spl11_22 ),
inference(forward_subsumption_resolution,[],[f862,f514]) ).
fof(f864,plain,
( $false
| ~ spl11_3
| ~ spl11_4
| ~ spl11_22 ),
inference(forward_subsumption_resolution,[],[f863,f268]) ).
fof(f865,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_22 ),
inference(avatar_contradiction_clause,[],[f864]) ).
fof(f881,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xm)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,xn) )
| ~ spl11_12 ),
inference(forward_subsumption_resolution,[],[f468,f368]) ).
fof(f980,plain,
( ~ aElementOf0(szszuzczcdt0(sK10),szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(sK10),xn)
| ~ spl11_8
| ~ spl11_12
| ~ spl11_13 ),
inference(resolution,[],[f401,f881]) ).
fof(f982,definition,
( spl11_80
<=> sdtlseqdt0(szszuzczcdt0(sK10),xn) ),
introduced(definition,[new_symbols(definition,[spl11_80])],[avatar_definition]) ).
fof(f983,plain,
( sdtlseqdt0(szszuzczcdt0(sK10),xn)
| ~ spl11_80 ),
inference(avatar_component_clause,[],[f982]) ).
fof(f985,definition,
( spl11_81
<=> aElementOf0(szszuzczcdt0(sK10),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl11_81])],[avatar_definition]) ).
fof(f986,plain,
( ~ aElementOf0(szszuzczcdt0(sK10),szNzAzT0)
| spl11_81 ),
inference(avatar_component_clause,[],[f985]) ).
fof(f987,plain,
( spl11_80
| ~ spl11_81
| ~ spl11_8
| ~ spl11_12
| ~ spl11_13 ),
inference(avatar_split_clause,[],[f980,f381,f364,f348,f985,f982]) ).
fof(f989,plain,
( aElementOf0(szszuzczcdt0(sK10),szNzAzT0)
| ~ spl11_9
| ~ spl11_13 ),
inference(resolution,[],[f402,f222]) ).
fof(f1011,plain,
( $false
| ~ spl11_9
| ~ spl11_13
| spl11_81 ),
inference(forward_subsumption_resolution,[],[f989,f986]) ).
fof(f1012,plain,
( ~ spl11_9
| ~ spl11_13
| spl11_81 ),
inference(avatar_contradiction_clause,[],[f1011]) ).
fof(f1014,plain,
( $false
| ~ spl11_9
| ~ spl11_13
| spl11_14
| ~ spl11_80 ),
inference(unit_resulting_resolution,[],[f314,f402,f268,f386,f983]) ).
fof(f1017,plain,
( ~ spl11_9
| ~ spl11_13
| spl11_14
| ~ spl11_80 ),
inference(avatar_contradiction_clause,[],[f1014]) ).
cnf(s2,plain,
( spl11_2
| spl11_3 ),
inference(sat_conversion,[],[f330]) ).
cnf(s3,plain,
( spl11_2
| spl11_4 ),
inference(sat_conversion,[],[f334]) ).
cnf(s9,plain,
( spl11_2
| spl11_10 ),
inference(sat_conversion,[],[f358]) ).
cnf(s11,plain,
( spl11_2
| ~ spl11_12 ),
inference(sat_conversion,[],[f366]) ).
cnf(s12,plain,
( ~ spl11_2
| spl11_12 ),
inference(sat_conversion,[],[f369]) ).
cnf(s13,plain,
( ~ spl11_2
| spl11_8 ),
inference(sat_conversion,[],[f370]) ).
cnf(s14,plain,
( ~ spl11_2
| spl11_9 ),
inference(sat_conversion,[],[f371]) ).
cnf(s22,plain,
( ~ spl11_2
| spl11_13 ),
inference(sat_conversion,[],[f383]) ).
cnf(s23,plain,
( ~ spl11_2
| ~ spl11_14 ),
inference(sat_conversion,[],[f387]) ).
cnf(s29,plain,
( ~ spl11_10
| spl11_22
| ~ spl11_23 ),
inference(sat_conversion,[],[f445]) ).
cnf(s36,plain,
( spl11_12
| spl11_23 ),
inference(sat_conversion,[],[f507]) ).
cnf(s76,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_22 ),
inference(sat_conversion,[],[f865]) ).
cnf(s93,plain,
( ~ spl11_8
| ~ spl11_12
| ~ spl11_13
| spl11_80
| ~ spl11_81 ),
inference(sat_conversion,[],[f987]) ).
cnf(s95,plain,
( ~ spl11_9
| ~ spl11_13
| spl11_81 ),
inference(sat_conversion,[],[f1012]) ).
cnf(s97,plain,
( ~ spl11_9
| ~ spl11_13
| spl11_14
| ~ spl11_80 ),
inference(sat_conversion,[],[f1017]) ).
cnf(s104,plain,
~ spl11_2,
inference(rat,[],[s93,s95,s97,s12,s13,s14,s22,s23]) ).
cnf(s105,plain,
~ spl11_12,
inference(rat,[],[s11,s104]) ).
cnf(s107,plain,
spl11_10,
inference(rat,[],[s9,s104]) ).
cnf(s113,plain,
spl11_4,
inference(rat,[],[s3,s104]) ).
cnf(s114,plain,
spl11_3,
inference(rat,[],[s2,s104]) ).
cnf(s118,plain,
spl11_23,
inference(rat,[],[s36,s105]) ).
cnf(s121,plain,
~ spl11_22,
inference(rat,[],[s76,s113,s114]) ).
cnf(s124,plain,
$false,
inference(rat,[],[s29,s107,s118,s121]) ).
fof(f1021,plain,
$false,
inference(avatar_sat_refutation,[],[s124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM542+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:26:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.58/1.68 % (3720730)Detected formulas, will run a generic FOF schedule.
% 4.58/1.68 % (3720749)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=3768865333:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.58/1.68 % (3720751)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3926262299:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.58/1.68 % (3720751)Refutation not found, incomplete strategy
% 4.58/1.68 % (3720751)------------------------------
% 4.58/1.68 % (3720751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.68 % (3720751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.68 % (3720751)CaDiCaL version: 2.1.3
% 4.58/1.68 % (3720751)Termination reason: Refutation not found, incomplete strategy
% 4.58/1.68 % (3720751)Time elapsed: 0.004 s
% 4.58/1.68 % (3720751)Peak memory usage: 88 MB
% 4.58/1.68 % (3720751)Instructions burned: 4 (million)
% 4.58/1.68 % (3720748)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=455587717:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.58/1.68 % (3720750)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=703268763:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.58/1.68 % (3720752)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3531504135:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.58/1.68 % (3720756)dis-21_1_sil=8000:lcm=predicate:random_seed=1571878441: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)
% 4.58/1.68 % (3720755)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=380690266:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.58/1.68 % (3720756)Instruction limit reached!
% 4.58/1.68 % (3720756)------------------------------
% 4.58/1.68 % (3720756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.68 % (3720756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.68 % (3720756)CaDiCaL version: 2.1.3
% 4.58/1.68 % (3720756)Termination reason: Instruction limit
% 4.58/1.68 % (3720756)Termination phase: Saturation
% 4.58/1.68 % (3720756)Time elapsed: 0.073 s
% 4.58/1.68 % (3720756)Peak memory usage: 88 MB
% 4.58/1.68 % (3720756)Instructions burned: 129 (million)
% 4.58/1.68 % (3720752)Instruction limit reached!
% 4.58/1.68 % (3720752)------------------------------
% 4.58/1.68 % (3720752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.68 % (3720752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.68 % (3720752)CaDiCaL version: 2.1.3
% 4.58/1.68 % (3720752)Termination reason: Instruction limit
% 4.58/1.68 % (3720752)Termination phase: Saturation
% 4.58/1.68 % (3720752)Time elapsed: 0.096 s
% 4.58/1.68 % (3720752)Peak memory usage: 88 MB
% 4.58/1.68 % (3720752)Instructions burned: 119 (million)
% 4.58/1.68 % (3720755)Instruction limit reached!
% 4.58/1.68 % (3720755)------------------------------
% 4.58/1.68 % (3720755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.68 % (3720755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.68 % (3720755)CaDiCaL version: 2.1.3
% 4.58/1.68 % (3720755)Termination reason: Instruction limit
% 4.58/1.68 % (3720755)Termination phase: Saturation
% 4.58/1.68 % (3720755)Time elapsed: 0.165 s
% 4.58/1.68 % (3720755)Peak memory usage: 90 MB
% 4.58/1.68 % (3720755)Instructions burned: 140 (million)
% 4.58/1.68 % (3720774)lrs+10_1_sil=8000:sp=occurrence:random_seed=2244905519:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.58/1.68 % (3720751)------------------------------
% 4.58/1.68 % (3720751)------------------------------
% 4.58/1.68 % (3720775)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4223912093:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.58/1.68 % (3720775)Refutation not found, incomplete strategy
% 4.58/1.68 % (3720775)------------------------------
% 4.58/1.68 % (3720775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.68 % (3720775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.68 % (3720782)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1785556398:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 4.58/1.68 % (3720775)CaDiCaL version: 2.1.3
% 4.58/1.68 % (3720775)Termination reason: Refutation not found, incomplete strategy
% 4.58/1.68 % (3720775)Time elapsed: 0.019 s
% 4.58/1.68 % (3720775)Peak memory usage: 89 MB
% 4.58/1.68 % (3720775)Instructions burned: 17 (million)
% 4.58/1.68 % (3720749)First to succeed.
% 4.58/1.68 % (3720749)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3720730"
% 4.58/1.68 % (3720782)Also succeeded, but the first one will report.
% 4.58/1.68 % (3720784)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=1581189846:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.58/1.68 % (3720774)Instruction limit reached!
% 4.58/1.68 % (3720774)------------------------------
% 4.58/1.68 % (3720774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.58/1.68 % (3720774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.58/1.68 % (3720774)CaDiCaL version: 2.1.3
% 4.58/1.68 % (3720774)Termination reason: Instruction limit
% 4.58/1.68 % (3720774)Termination phase: Saturation
% 4.58/1.68 % (3720774)Time elapsed: 0.225 s
% 4.58/1.68 % (3720774)Peak memory usage: 91 MB
% 4.58/1.68 % (3720774)Instructions burned: 285 (million)
% 4.58/1.68 % (3720784)Also succeeded, but the first one will report.
% 4.58/1.68 % (3720775)------------------------------
% 4.58/1.68 % (3720775)------------------------------
% 4.58/1.68 % (3720749)Refutation found. Thanks to Tanya!
% 4.58/1.68 % SZS status Theorem for theBenchmark
% 4.58/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 6.40/1.87 % (3720749)------------------------------
% 6.40/1.87 % (3720749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.40/1.87 % (3720749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.40/1.87 % (3720749)CaDiCaL version: 2.1.3
% 6.40/1.87 % (3720749)Termination reason: Refutation
% 6.40/1.87 % (3720749)Time elapsed: 0.555 s
% 6.40/1.87 % (3720749)Peak memory usage: 131 MB
% 6.40/1.87 % (3720749)Instructions burned: 1016 (million)
% 6.40/1.87 % (3720749)------------------------------
% 6.40/1.87 % (3720749)------------------------------
% 6.40/1.87 % (3720730)Success in time 0.842 s
% 6.40/1.87 % Vampire exiting
%------------------------------------------------------------------------------