%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM542+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:24:44 PM UTC 2026
% Result : Theorem 2.34s 0.81s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 30
% Syntax : Number of formulae : 170 ( 17 unt; 21 def)
% Number of atoms : 717 ( 25 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 854 ( 307 ~; 311 |; 167 &)
% ( 42 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 20 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 126 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(f28,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> X0 != szszuzczcdt0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatNSucc) ).
fof(f33,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(f54,axiom,
( aElementOf0(xm,szNzAzT0)
& aElementOf0(xn,szNzAzT0) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f94,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f99,plain,
! [X0] :
( X0 != szszuzczcdt0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f104,plain,
! [X0] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f106,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f107,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f106]) ).
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(ennf_transformation,[],[f36]) ).
fof(f109,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f111,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f110]) ).
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(f141,definition,
( ! [X4] :
( aElementOf0(X4,slbdtrb0(xn))
<=> ( aElementOf0(X4,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X4),xn) ) )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f142,definition,
( ! [X3] :
( aElementOf0(X3,slbdtrb0(xm))
<=> ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),xm) ) )
| ~ sP5 ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f143,definition,
( ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
<=> ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) ) )
| ~ sP6 ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f144,definition,
( ! [X1] :
( aElementOf0(X1,slbdtrb0(xn))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),xn) ) )
| ~ sP7 ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f145,definition,
( ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(xn))
& aElementOf0(X2,slbdtrb0(xm)) )
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& sP7
& aSet0(slbdtrb0(xm))
& sP6
& sdtlseqdt0(xm,xn) )
| ~ sP8 ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f146,plain,
( sP8
| ( ~ sdtlseqdt0(xm,xn)
& aSet0(slbdtrb0(xm))
& sP5
& aSet0(slbdtrb0(xn))
& sP4
& ! [X5] :
( aElementOf0(X5,slbdtrb0(xn))
| ~ aElementOf0(X5,slbdtrb0(xm)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ),
inference(definition_folding,[],[f134,f145,f144,f143,f142,f141]) ).
fof(f180,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(f181,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,[],[f180]) ).
fof(f182,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,[],[f181]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ( ( ~ aElementOf0(sK17(X0,X1),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK17(X0,X1)),X0)
| ~ aElementOf0(sK17(X0,X1),X1) )
& ( ( aElementOf0(sK17(X0,X1),szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(sK17(X0,X1)),X0) )
| aElementOf0(sK17(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,[sK17]),skolemize(X2,sK17(X0,X1))],[f182]) ).
fof(f186,plain,
( ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(xn))
& aElementOf0(X2,slbdtrb0(xm)) )
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& sP7
& aSet0(slbdtrb0(xm))
& sP6
& sdtlseqdt0(xm,xn) )
| ~ sP8 ),
inference(nnf_transformation,[],[f145]) ).
fof(f187,plain,
( ( ? [X0] :
( ~ aElementOf0(X0,slbdtrb0(xn))
& aElementOf0(X0,slbdtrb0(xm)) )
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& sP7
& aSet0(slbdtrb0(xm))
& sP6
& sdtlseqdt0(xm,xn) )
| ~ sP8 ),
inference(rectify,[],[f186]) ).
fof(f188,plain,
( ( ~ aElementOf0(sK18,slbdtrb0(xn))
& aElementOf0(sK18,slbdtrb0(xm))
& ~ aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn))
& aSet0(slbdtrb0(xn))
& sP7
& aSet0(slbdtrb0(xm))
& sP6
& sdtlseqdt0(xm,xn) )
| ~ sP8 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X0,sK18)],[f187]) ).
fof(f192,plain,
( ! [X0] :
( ( aElementOf0(X0,slbdtrb0(xm))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm) )
& ( ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) )
| ~ aElementOf0(X0,slbdtrb0(xm)) ) )
| ~ sP6 ),
inference(nnf_transformation,[],[f143]) ).
fof(f193,plain,
( ! [X0] :
( ( aElementOf0(X0,slbdtrb0(xm))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm) )
& ( ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) )
| ~ aElementOf0(X0,slbdtrb0(xm)) ) )
| ~ sP6 ),
inference(flattening,[],[f192]) ).
fof(f194,plain,
( ! [X3] :
( ( aElementOf0(X3,slbdtrb0(xm))
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),xm) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),xm) )
| ~ aElementOf0(X3,slbdtrb0(xm)) ) )
| ~ sP5 ),
inference(nnf_transformation,[],[f142]) ).
fof(f195,plain,
( ! [X3] :
( ( aElementOf0(X3,slbdtrb0(xm))
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),xm) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),xm) )
| ~ aElementOf0(X3,slbdtrb0(xm)) ) )
| ~ sP5 ),
inference(flattening,[],[f194]) ).
fof(f196,plain,
( ! [X0] :
( ( aElementOf0(X0,slbdtrb0(xm))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm) )
& ( ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xm) )
| ~ aElementOf0(X0,slbdtrb0(xm)) ) )
| ~ sP5 ),
inference(rectify,[],[f195]) ).
fof(f197,plain,
( ! [X4] :
( ( aElementOf0(X4,slbdtrb0(xn))
| ~ aElementOf0(X4,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X4),xn) )
& ( ( aElementOf0(X4,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X4),xn) )
| ~ aElementOf0(X4,slbdtrb0(xn)) ) )
| ~ sP4 ),
inference(nnf_transformation,[],[f141]) ).
fof(f198,plain,
( ! [X4] :
( ( aElementOf0(X4,slbdtrb0(xn))
| ~ aElementOf0(X4,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X4),xn) )
& ( ( aElementOf0(X4,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X4),xn) )
| ~ aElementOf0(X4,slbdtrb0(xn)) ) )
| ~ sP4 ),
inference(flattening,[],[f197]) ).
fof(f199,plain,
( ! [X0] :
( ( aElementOf0(X0,slbdtrb0(xn))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xn) )
& ( ( aElementOf0(X0,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X0),xn) )
| ~ aElementOf0(X0,slbdtrb0(xn)) ) )
| ~ sP4 ),
inference(rectify,[],[f198]) ).
fof(f200,plain,
( sP8
| ( ~ sdtlseqdt0(xm,xn)
& aSet0(slbdtrb0(xm))
& sP5
& aSet0(slbdtrb0(xn))
& sP4
& ! [X0] :
( aElementOf0(X0,slbdtrb0(xn))
| ~ aElementOf0(X0,slbdtrb0(xm)) )
& aSubsetOf0(slbdtrb0(xm),slbdtrb0(xn)) ) ),
inference(rectify,[],[f146]) ).
fof(f250,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f254,plain,
! [X0] :
( szszuzczcdt0(X0) != X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f259,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f261,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f262,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f263,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f285,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f295,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f54]) ).
fof(f296,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f54]) ).
fof(f297,plain,
( sdtlseqdt0(xm,xn)
| ~ sP8 ),
inference(cnf_transformation,[],[f188]) ).
fof(f298,plain,
( sP6
| ~ sP8 ),
inference(cnf_transformation,[],[f188]) ).
fof(f303,plain,
( aElementOf0(sK18,slbdtrb0(xm))
| ~ sP8 ),
inference(cnf_transformation,[],[f188]) ).
fof(f304,plain,
( ~ aElementOf0(sK18,slbdtrb0(xn))
| ~ sP8 ),
inference(cnf_transformation,[],[f188]) ).
fof(f308,plain,
! [X0] :
( sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,slbdtrb0(xm))
| ~ sP6 ),
inference(cnf_transformation,[],[f193]) ).
fof(f309,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm))
| ~ sP6 ),
inference(cnf_transformation,[],[f193]) ).
fof(f313,plain,
! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ sP5 ),
inference(cnf_transformation,[],[f196]) ).
fof(f314,plain,
! [X0] :
( sdtlseqdt0(szszuzczcdt0(X0),xn)
| ~ aElementOf0(X0,slbdtrb0(xn))
| ~ sP4 ),
inference(cnf_transformation,[],[f199]) ).
fof(f318,plain,
! [X0] :
( sP8
| aElementOf0(X0,slbdtrb0(xn))
| ~ aElementOf0(X0,slbdtrb0(xm)) ),
inference(cnf_transformation,[],[f200]) ).
fof(f319,plain,
( sP8
| sP4 ),
inference(cnf_transformation,[],[f200]) ).
fof(f321,plain,
( sP8
| sP5 ),
inference(cnf_transformation,[],[f200]) ).
fof(f323,plain,
( sP8
| ~ sdtlseqdt0(xm,xn) ),
inference(cnf_transformation,[],[f200]) ).
fof(f337,plain,
! [X3,X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f285]) ).
fof(f341,definition,
sF19 = slbdtrb0(xm),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f342,plain,
slbdtrb0(xm) = sF19,
inference(reorient_equations,[],[f341]) ).
fof(f344,definition,
sF20 = slbdtrb0(xn),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f345,plain,
slbdtrb0(xn) = sF20,
inference(reorient_equations,[],[f344]) ).
fof(f347,plain,
! [X0] :
( sP8
| aElementOf0(X0,sF20)
| ~ aElementOf0(X0,sF19) ),
inference(definition_folding,[],[f318,f342,f345]) ).
fof(f355,definition,
( spl21_2
<=> sP8 ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f360,definition,
( spl21_3
<=> ! [X0] :
( aElementOf0(X0,sF20)
| ~ aElementOf0(X0,sF19) ) ),
introduced(definition,[new_symbols(definition,[spl21_3])],[avatar_definition]) ).
fof(f361,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF19)
| aElementOf0(X0,sF20) )
| ~ spl21_3 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f362,plain,
( spl21_3
| spl21_2 ),
inference(avatar_split_clause,[],[f347,f355,f360]) ).
fof(f364,definition,
( spl21_4
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
fof(f367,plain,
( spl21_4
| spl21_2 ),
inference(avatar_split_clause,[],[f319,f355,f364]) ).
fof(f374,definition,
( spl21_6
<=> sP5 ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
fof(f377,plain,
( spl21_6
| spl21_2 ),
inference(avatar_split_clause,[],[f321,f355,f374]) ).
fof(f384,definition,
( spl21_8
<=> sdtlseqdt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition]) ).
fof(f385,plain,
( sdtlseqdt0(xm,xn)
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f386,plain,
( ~ sdtlseqdt0(xm,xn)
| spl21_8 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f387,plain,
( ~ spl21_8
| spl21_2 ),
inference(avatar_split_clause,[],[f323,f355,f384]) ).
fof(f389,definition,
( spl21_9
<=> ! [X0] :
( sdtlseqdt0(szszuzczcdt0(X0),xn)
| ~ aElementOf0(X0,slbdtrb0(xn)) ) ),
introduced(definition,[new_symbols(definition,[spl21_9])],[avatar_definition]) ).
fof(f390,plain,
( ! [X0] :
( sdtlseqdt0(szszuzczcdt0(X0),xn)
| ~ aElementOf0(X0,slbdtrb0(xn)) )
| ~ spl21_9 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f391,plain,
( ~ spl21_4
| spl21_9 ),
inference(avatar_split_clause,[],[f314,f389,f364]) ).
fof(f401,definition,
( spl21_12
<=> ! [X0] :
( sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,slbdtrb0(xm)) ) ),
introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition]) ).
fof(f402,plain,
( ! [X0] :
( sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,slbdtrb0(xm)) )
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f405,definition,
( spl21_13
<=> ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) ) ),
introduced(definition,[new_symbols(definition,[spl21_13])],[avatar_definition]) ).
fof(f406,plain,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(xm)) )
| ~ spl21_13 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f409,definition,
( spl21_14
<=> ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[spl21_14])],[avatar_definition]) ).
fof(f410,plain,
( ! [X0] :
( aElementOf0(X0,slbdtrb0(xm))
| ~ sdtlseqdt0(szszuzczcdt0(X0),xm)
| ~ aElementOf0(X0,szNzAzT0) )
| ~ spl21_14 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f411,plain,
( ~ spl21_6
| spl21_14 ),
inference(avatar_split_clause,[],[f313,f409,f374]) ).
fof(f413,definition,
( spl21_15
<=> sP6 ),
introduced(definition,[new_symbols(definition,[spl21_15])],[avatar_definition]) ).
fof(f416,plain,
( ~ spl21_15
| spl21_12 ),
inference(avatar_split_clause,[],[f308,f401,f413]) ).
fof(f417,plain,
( ~ spl21_15
| spl21_13 ),
inference(avatar_split_clause,[],[f309,f405,f413]) ).
fof(f426,plain,
( ~ spl21_2
| spl21_8 ),
inference(avatar_split_clause,[],[f297,f384,f355]) ).
fof(f427,plain,
( ~ spl21_2
| spl21_15 ),
inference(avatar_split_clause,[],[f298,f413,f355]) ).
fof(f445,definition,
( spl21_20
<=> aElementOf0(sK18,slbdtrb0(xm)) ),
introduced(definition,[new_symbols(definition,[spl21_20])],[avatar_definition]) ).
fof(f447,plain,
( aElementOf0(sK18,slbdtrb0(xm))
| ~ spl21_20 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f448,plain,
( ~ spl21_2
| spl21_20 ),
inference(avatar_split_clause,[],[f303,f445,f355]) ).
fof(f450,definition,
( spl21_21
<=> aElementOf0(sK18,slbdtrb0(xn)) ),
introduced(definition,[new_symbols(definition,[spl21_21])],[avatar_definition]) ).
fof(f452,plain,
( ~ aElementOf0(sK18,slbdtrb0(xn))
| spl21_21 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f453,plain,
( ~ spl21_2
| ~ spl21_21 ),
inference(avatar_split_clause,[],[f304,f450,f355]) ).
fof(f469,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF20)
| sdtlseqdt0(szszuzczcdt0(X0),xn) )
| ~ spl21_9 ),
inference(forward_demodulation,[],[f390,f345]) ).
fof(f472,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF19)
| sdtlseqdt0(szszuzczcdt0(X0),xm) )
| ~ spl21_12 ),
inference(forward_demodulation,[],[f402,f342]) ).
fof(f473,plain,
( ! [X0] :
( ~ aElementOf0(X0,sF19)
| aElementOf0(X0,szNzAzT0) )
| ~ spl21_13 ),
inference(forward_demodulation,[],[f406,f342]) ).
fof(f474,plain,
( ! [X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),xm)
| aElementOf0(X0,sF19)
| ~ aElementOf0(X0,szNzAzT0) )
| ~ spl21_14 ),
inference(forward_demodulation,[],[f410,f342]) ).
fof(f478,plain,
( aElementOf0(sK18,sF19)
| ~ spl21_20 ),
inference(forward_demodulation,[],[f447,f342]) ).
fof(f479,plain,
( ~ aElementOf0(sK18,sF20)
| spl21_21 ),
inference(forward_demodulation,[],[f452,f345]) ).
fof(f525,plain,
( aElementOf0(sK18,szNzAzT0)
| ~ spl21_13
| ~ spl21_20 ),
inference(resolution,[],[f473,f478]) ).
fof(f569,plain,
sdtlseqdt0(xn,szszuzczcdt0(xn)),
inference(resolution,[],[f259,f295]) ).
fof(f571,plain,
( sdtlseqdt0(szszuzczcdt0(sK18),xm)
| ~ spl21_12
| ~ spl21_20 ),
inference(resolution,[],[f472,f478]) ).
fof(f1067,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(xn),X0)
| sdtlseqdt0(X0,xn) ),
inference(resolution,[],[f263,f295]) ).
fof(f3167,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| xn = szszuzczcdt0(xn)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f569,f261]) ).
fof(f3169,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f3167,f254]) ).
fof(f3171,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f3169,f250]) ).
fof(f3173,plain,
~ sdtlseqdt0(szszuzczcdt0(xn),xn),
inference(forward_subsumption_resolution,[],[f3171,f295]) ).
fof(f5115,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xm)
| sdtlseqdt0(xm,xn) ),
inference(resolution,[],[f1067,f296]) ).
fof(f5166,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xm)
| spl21_8 ),
inference(forward_subsumption_resolution,[],[f5115,f386]) ).
fof(f5252,plain,
( aElementOf0(xn,sF19)
| ~ aElementOf0(xn,szNzAzT0)
| spl21_8
| ~ spl21_14 ),
inference(resolution,[],[f5166,f474]) ).
fof(f5258,plain,
( aElementOf0(xn,sF19)
| spl21_8
| ~ spl21_14 ),
inference(forward_subsumption_resolution,[],[f5252,f295]) ).
fof(f5806,plain,
( aElementOf0(xn,sF20)
| ~ spl21_3
| spl21_8
| ~ spl21_14 ),
inference(resolution,[],[f5258,f361]) ).
fof(f5878,plain,
( sdtlseqdt0(szszuzczcdt0(xn),xn)
| ~ spl21_3
| spl21_8
| ~ spl21_9
| ~ spl21_14 ),
inference(resolution,[],[f5806,f469]) ).
fof(f5885,plain,
( $false
| ~ spl21_3
| spl21_8
| ~ spl21_9
| ~ spl21_14 ),
inference(forward_subsumption_resolution,[],[f5878,f3173]) ).
fof(f5886,plain,
( ~ spl21_3
| spl21_8
| ~ spl21_9
| ~ spl21_14 ),
inference(avatar_contradiction_clause,[],[f5885]) ).
fof(f5916,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xm)
| sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) )
| ~ spl21_8 ),
inference(resolution,[],[f385,f262]) ).
fof(f5921,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xm)
| sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) )
| ~ spl21_8 ),
inference(forward_subsumption_resolution,[],[f5916,f296]) ).
fof(f5924,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xm)
| sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0) )
| ~ spl21_8 ),
inference(forward_subsumption_resolution,[],[f5921,f295]) ).
fof(f7820,plain,
( sdtlseqdt0(szszuzczcdt0(sK18),xn)
| ~ aElementOf0(szszuzczcdt0(sK18),szNzAzT0)
| ~ spl21_8
| ~ spl21_12
| ~ spl21_20 ),
inference(resolution,[],[f571,f5924]) ).
fof(f7828,definition,
( spl21_439
<=> aElementOf0(szszuzczcdt0(sK18),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl21_439])],[avatar_definition]) ).
fof(f7830,plain,
( ~ aElementOf0(szszuzczcdt0(sK18),szNzAzT0)
| spl21_439 ),
inference(avatar_component_clause,[],[f7828]) ).
fof(f7832,definition,
( spl21_440
<=> sdtlseqdt0(szszuzczcdt0(sK18),xn) ),
introduced(definition,[new_symbols(definition,[spl21_440])],[avatar_definition]) ).
fof(f7834,plain,
( sdtlseqdt0(szszuzczcdt0(sK18),xn)
| ~ spl21_440 ),
inference(avatar_component_clause,[],[f7832]) ).
fof(f7835,plain,
( ~ spl21_439
| spl21_440
| ~ spl21_8
| ~ spl21_12
| ~ spl21_20 ),
inference(avatar_split_clause,[],[f7820,f445,f401,f384,f7832,f7828]) ).
fof(f9605,plain,
( ~ aElementOf0(sK18,szNzAzT0)
| spl21_439 ),
inference(resolution,[],[f7830,f250]) ).
fof(f9617,plain,
( $false
| ~ spl21_13
| ~ spl21_20
| spl21_439 ),
inference(forward_subsumption_resolution,[],[f9605,f525]) ).
fof(f9618,plain,
( ~ spl21_13
| ~ spl21_20
| spl21_439 ),
inference(avatar_contradiction_clause,[],[f9617]) ).
fof(f9733,plain,
( ~ aElementOf0(sK18,szNzAzT0)
| aElementOf0(sK18,slbdtrb0(xn))
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl21_440 ),
inference(resolution,[],[f7834,f337]) ).
fof(f9740,plain,
( aElementOf0(sK18,slbdtrb0(xn))
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl21_13
| ~ spl21_20
| ~ spl21_440 ),
inference(forward_subsumption_resolution,[],[f9733,f525]) ).
fof(f9745,plain,
( aElementOf0(sK18,slbdtrb0(xn))
| ~ spl21_13
| ~ spl21_20
| ~ spl21_440 ),
inference(forward_subsumption_resolution,[],[f9740,f295]) ).
fof(f9757,plain,
( aElementOf0(sK18,sF20)
| ~ spl21_13
| ~ spl21_20
| ~ spl21_440 ),
inference(forward_demodulation,[],[f9745,f345]) ).
fof(f9758,plain,
( $false
| ~ spl21_13
| ~ spl21_20
| spl21_21
| ~ spl21_440 ),
inference(forward_subsumption_resolution,[],[f9757,f479]) ).
fof(f9759,plain,
( ~ spl21_13
| ~ spl21_20
| spl21_21
| ~ spl21_440 ),
inference(avatar_contradiction_clause,[],[f9758]) ).
cnf(s2,plain,
( spl21_2
| spl21_3 ),
inference(sat_conversion,[],[f362]) ).
cnf(s3,plain,
( spl21_2
| spl21_4 ),
inference(sat_conversion,[],[f367]) ).
cnf(s5,plain,
( spl21_2
| spl21_6 ),
inference(sat_conversion,[],[f377]) ).
cnf(s7,plain,
( spl21_2
| ~ spl21_8 ),
inference(sat_conversion,[],[f387]) ).
cnf(s8,plain,
( ~ spl21_4
| spl21_9 ),
inference(sat_conversion,[],[f391]) ).
cnf(s13,plain,
( ~ spl21_6
| spl21_14 ),
inference(sat_conversion,[],[f411]) ).
cnf(s14,plain,
( spl21_12
| ~ spl21_15 ),
inference(sat_conversion,[],[f416]) ).
cnf(s15,plain,
( spl21_13
| ~ spl21_15 ),
inference(sat_conversion,[],[f417]) ).
cnf(s20,plain,
( ~ spl21_2
| spl21_8 ),
inference(sat_conversion,[],[f426]) ).
cnf(s21,plain,
( ~ spl21_2
| spl21_15 ),
inference(sat_conversion,[],[f427]) ).
cnf(s26,plain,
( ~ spl21_2
| spl21_20 ),
inference(sat_conversion,[],[f448]) ).
cnf(s27,plain,
( ~ spl21_2
| ~ spl21_21 ),
inference(sat_conversion,[],[f453]) ).
cnf(s270,plain,
( ~ spl21_3
| spl21_8
| ~ spl21_9
| ~ spl21_14 ),
inference(sat_conversion,[],[f5886]) ).
cnf(s368,plain,
( ~ spl21_8
| ~ spl21_12
| ~ spl21_20
| ~ spl21_439
| spl21_440 ),
inference(sat_conversion,[],[f7835]) ).
cnf(s483,plain,
( ~ spl21_13
| ~ spl21_20
| spl21_439 ),
inference(sat_conversion,[],[f9618]) ).
cnf(s490,plain,
( ~ spl21_13
| ~ spl21_20
| spl21_21
| ~ spl21_440 ),
inference(sat_conversion,[],[f9759]) ).
cnf(s495,plain,
~ spl21_2,
inference(rat,[],[s368,s483,s490,s14,s15,s20,s21,s26,s27]) ).
cnf(s496,plain,
~ spl21_8,
inference(rat,[],[s7,s495]) ).
cnf(s498,plain,
spl21_6,
inference(rat,[],[s5,s495]) ).
cnf(s500,plain,
spl21_4,
inference(rat,[],[s3,s495]) ).
cnf(s501,plain,
spl21_3,
inference(rat,[],[s2,s495]) ).
cnf(s505,plain,
spl21_14,
inference(rat,[],[s13,s498]) ).
cnf(s513,plain,
spl21_9,
inference(rat,[],[s8,s500]) ).
cnf(s514,plain,
$false,
inference(rat,[],[s270,s505,s496,s513,s501]) ).
fof(f9760,plain,
$false,
inference(avatar_sat_refutation,[],[s514]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 20:25:02 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.34/0.81 % (137206)Will run a generic schedule for satisfiability detection.
% 2.34/0.81 % (137217)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3437328624:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.34/0.81 % (137212)% WARNING: option uhcvi not known.
% 2.34/0.81 % (137211)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4129145149_2999 on theBenchmark for (2999ds/0Mi)
% 2.34/0.81 % (137213)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2936284024:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.34/0.81 % (137214)dis+10_1_sil=32000:sp=arity:random_seed=291594995:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.34/0.81 % (137215)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2865415126:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.34/0.81 % (137216)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2298350355:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.34/0.81 % (137212)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2113044292:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.34/0.81 % TRYING [1]
% 2.34/0.81 % TRYING [2]
% 2.34/0.81 % TRYING [3]
% 2.34/0.81 % TRYING [4]
% 2.34/0.81 % TRYING [5]
% 2.34/0.81 % (137217)Instruction limit reached!
% 2.34/0.81 % (137217)------------------------------
% 2.34/0.81 % (137217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.81 % (137217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.81 % (137217)CaDiCaL version: 2.1.3
% 2.34/0.81 % (137217)Termination reason: Instruction limit
% 2.34/0.81 % (137217)Termination phase: Saturation
% 2.34/0.81 % (137217)Time elapsed: 0.056 s
% 2.34/0.81 % (137217)Peak memory usage: 15 MB
% 2.34/0.81 % (137217)Instructions burned: 162 (million)
% 2.34/0.81 % (137214)Instruction limit reached!
% 2.34/0.81 % (137214)------------------------------
% 2.34/0.81 % (137214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.81 % (137225)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4110228214:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.34/0.81 % (137214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.81 % (137214)CaDiCaL version: 2.1.3
% 2.34/0.81 % (137214)Termination reason: Instruction limit
% 2.34/0.81 % (137214)Termination phase: Saturation
% 2.34/0.81 % (137214)Time elapsed: 0.069 s
% 2.34/0.81 % (137214)Peak memory usage: 13 MB
% 2.34/0.81 % (137214)Instructions burned: 103 (million)
% 2.34/0.81 % TRYING [6]
% 2.34/0.81 % (137215)Instruction limit reached!
% 2.34/0.81 % (137215)------------------------------
% 2.34/0.81 % (137215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.81 % (137215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.81 % (137215)CaDiCaL version: 2.1.3
% 2.34/0.81 % (137215)Termination reason: Instruction limit
% 2.34/0.81 % (137215)Termination phase: Saturation
% 2.34/0.81 % (137215)Time elapsed: 0.076 s
% 2.34/0.81 % (137215)Peak memory usage: 13 MB
% 2.34/0.81 % (137215)Instructions burned: 116 (million)
% 2.34/0.81 % TRYING [1]
% 2.34/0.81 % (137216)Instruction limit reached!
% 2.34/0.81 % (137216)------------------------------
% 2.34/0.81 % (137216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.81 % (137216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.81 % (137216)CaDiCaL version: 2.1.3
% 2.34/0.81 % (137216)Termination reason: Instruction limit
% 2.34/0.81 % (137216)Termination phase: Saturation
% 2.34/0.81 % (137216)Time elapsed: 0.084 s
% 2.34/0.81 % (137216)Peak memory usage: 13 MB
% 2.34/0.81 % (137216)Instructions burned: 132 (million)
% 2.34/0.81 % TRYING [2]
% 2.34/0.81 % (137227)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=757090656:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.34/0.81 % TRYING [3]
% 2.34/0.81 % (137228)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=358110000:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.34/0.81 % TRYING [4]
% 2.34/0.81 % (137229)ott-21_1_sil=16000:fs=off:random_seed=2543945542:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.34/0.81 % TRYING [5]
% 2.34/0.81 % TRYING [6]
% 2.34/0.81 % TRYING [7]
% 2.34/0.81 % (137227)Instruction limit reached!
% 2.34/0.81 % (137227)------------------------------
% 2.34/0.81 % (137227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.81 % (137227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.81 % (137227)CaDiCaL version: 2.1.3
% 2.34/0.81 % (137227)Termination reason: Instruction limit
% 2.34/0.81 % (137227)Termination phase: Saturation
% 2.34/0.81 % (137227)Time elapsed: 0.084 s
% 2.34/0.81 % (137227)Peak memory usage: 13 MB
% 2.34/0.81 % (137227)Instructions burned: 131 (million)
% 2.34/0.81 % (137233)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1237165044:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 2.34/0.81 % (137229)Instruction limit reached!
% 2.34/0.81 % (137229)------------------------------
% 2.34/0.81 % (137229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.81 % (137229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.81 % (137229)CaDiCaL version: 2.1.3
% 2.34/0.81 % (137229)Termination reason: Instruction limit
% 2.34/0.81 % (137229)Termination phase: Saturation
% 2.34/0.81 % (137229)Time elapsed: 0.100 s
% 2.34/0.81 % (137229)Peak memory usage: 13 MB
% 2.34/0.81 % (137229)Instructions burned: 180 (million)
% 2.34/0.81 % TRYING [7]
% 2.34/0.81 % (137235)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=109040116:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.34/0.81 % TRYING [1]
% 2.34/0.81 % TRYING [2]
% 2.34/0.81 % TRYING [3]
% 2.34/0.81 % (137225)Instruction limit reached!
% 2.34/0.81 % (137225)------------------------------
% 2.34/0.81 % (137225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.81 % (137225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.81 % (137225)CaDiCaL version: 2.1.3
% 2.34/0.81 % (137225)Termination reason: Instruction limit
% 2.34/0.81 % (137225)Termination phase: Finite model building constraint generation
% 2.34/0.81 % (137225)Time elapsed: 0.181 s
% 2.34/0.81 % (137225)Peak memory usage: 24 MB
% 2.34/0.81 % (137225)Instructions burned: 715 (million)
% 2.34/0.81 % TRYING [4]
% 2.34/0.81 % (137237)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4125438125:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.34/0.81 % TRYING [8]
% 2.34/0.81 % TRYING [5]
% 2.34/0.81 % (137237) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-137206-137237"...
% 2.34/0.81 % (137237)...printing done.
% 2.34/0.81 % (137237)Refutation found. Thanks to Tanya!
% 2.34/0.81 % SZS status Theorem for theBenchmark
% 2.34/0.81 % SZS output start Proof for theBenchmark
% See solution above
% 2.34/0.82 % (137237)------------------------------
% 2.34/0.82 % (137237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.82 % (137237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.82 % (137237)CaDiCaL version: 2.1.3
% 2.34/0.82 % (137237)Termination reason: Refutation
% 2.34/0.82 % (137237)Time elapsed: 0.108 s
% 2.34/0.82 % (137237)Peak memory usage: 17 MB
% 2.34/0.82 % (137237)Instructions burned: 314 (million)
% 2.34/0.82 % (137206)Success in time 0.41 s
% 2.34/0.82 % Vampire exiting
%------------------------------------------------------------------------------