%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM575+3 : 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 : n008.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 12:15:49 PM UTC 2026
% Result : Theorem 6.25s 1.97s
% Output : Refutation 8.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 147 ( 35 unt; 14 def)
% Number of atoms : 547 ( 56 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 633 ( 233 ~; 207 |; 152 &)
% ( 13 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 9 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 111 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
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(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(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& X1 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f84,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f85,negated_conjecture,
~ ! [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)) ) ),
inference(negated_conjecture,[status(cth)],[f84]) ).
fof(f95,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
inference(rectify,[],[f81]) ).
fof(f96,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,[],[f85]) ).
fof(f126,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f138,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f139,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f138]) ).
fof(f142,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f143,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f142]) ).
fof(f201,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f202,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f201]) ).
fof(f203,plain,
! [X0] :
( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f204,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f205,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f204]) ).
fof(f206,plain,
? [X0,X1] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& 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(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& X0 != X1 ),
inference(ennf_transformation,[],[f96]) ).
fof(f207,plain,
? [X0,X1] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& 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(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& X0 != X1 ),
inference(flattening,[],[f206]) ).
fof(f219,definition,
! [X0] :
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 ) )
| ~ sP8(X0) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f220,definition,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f221,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f202,f220,f219]) ).
fof(f297,plain,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f220]) ).
fof(f298,plain,
! [X0] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
inference(rectify,[],[f297]) ).
fof(f299,plain,
! [X0] :
( ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f219]) ).
fof(f300,plain,
! [X0] :
( ! [X3] :
( ( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP8(X0) ),
inference(flattening,[],[f299]) ).
fof(f301,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP8(X0) ),
inference(rectify,[],[f300]) ).
fof(f302,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK39(X0),szNzAzT0)
& aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f221]) ).
fof(f303,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK40)),sdtlpdtrp0(xN,sK40))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK40)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,sK40)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK40)),sdtlpdtrp0(xN,sK41))
& ! [X3] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK40)),X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,sK41)) )
& szmzizndt0(sdtlpdtrp0(xN,sK40)) = szmzizndt0(sdtlpdtrp0(xN,sK41))
& aElementOf0(sK40,szNzAzT0)
& aElementOf0(sK41,szNzAzT0)
& sK40 != sK41 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41]),skolemize(X0,sK40),skolemize(X1,sK41)],[f207]) ).
fof(f353,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f364,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f366,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f506,plain,
! [X2,X0] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f508,plain,
! [X0] :
( sP8(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f512,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f516,plain,
! [X0] :
( sP9(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f302]) ).
fof(f522,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f203]) ).
fof(f523,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f203]) ).
fof(f527,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f528,plain,
sK40 != sK41,
inference(cnf_transformation,[],[f303]) ).
fof(f529,plain,
aElementOf0(sK41,szNzAzT0),
inference(cnf_transformation,[],[f303]) ).
fof(f530,plain,
aElementOf0(sK40,szNzAzT0),
inference(cnf_transformation,[],[f303]) ).
fof(f531,plain,
szmzizndt0(sdtlpdtrp0(xN,sK40)) = szmzizndt0(sdtlpdtrp0(xN,sK41)),
inference(cnf_transformation,[],[f303]) ).
fof(f533,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK40)),sdtlpdtrp0(xN,sK41)),
inference(cnf_transformation,[],[f303]) ).
fof(f535,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK40)),sdtlpdtrp0(xN,sK40)),
inference(cnf_transformation,[],[f303]) ).
fof(f578,plain,
! [X0] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP8(X0) ),
inference(equality_resolution,[],[f512]) ).
fof(f579,definition,
sF42 = sdtlpdtrp0(xN,sK40),
introduced(definition,[new_symbols(definition,[sF42])],[function_definition]) ).
fof(f580,plain,
sdtlpdtrp0(xN,sK40) = sF42,
inference(reorient_equations,[],[f579]) ).
fof(f581,definition,
sF43 = szmzizndt0(sF42),
introduced(definition,[new_symbols(definition,[sF43])],[function_definition]) ).
fof(f582,plain,
szmzizndt0(sF42) = sF43,
inference(reorient_equations,[],[f581]) ).
fof(f583,plain,
aElementOf0(sF43,sF42),
inference(definition_folding,[],[f535,f580,f582,f580]) ).
fof(f585,definition,
sF44 = sdtlpdtrp0(xN,sK41),
introduced(definition,[new_symbols(definition,[sF44])],[function_definition]) ).
fof(f586,plain,
sdtlpdtrp0(xN,sK41) = sF44,
inference(reorient_equations,[],[f585]) ).
fof(f587,plain,
aElementOf0(sF43,sF44),
inference(definition_folding,[],[f533,f586,f582,f580]) ).
fof(f589,definition,
sF45 = szmzizndt0(sF44),
introduced(definition,[new_symbols(definition,[sF45])],[function_definition]) ).
fof(f590,plain,
szmzizndt0(sF44) = sF45,
inference(reorient_equations,[],[f589]) ).
fof(f591,plain,
sF43 = sF45,
inference(definition_folding,[],[f531,f590,f586,f582,f580]) ).
fof(f593,plain,
! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f516,f523]) ).
fof(f611,plain,
sF43 = szmzizndt0(sF44),
inference(forward_demodulation,[],[f590,f591]) ).
fof(f612,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP9(X0) ),
inference(forward_subsumption_resolution,[],[f593,f522]) ).
fof(f617,plain,
! [X0,X1] :
( ~ aElementOf0(X0,sF42)
| aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,sK40)
| ~ aElementOf0(sK40,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(superposition,[],[f527,f580]) ).
fof(f618,plain,
! [X0,X1] :
( ~ aElementOf0(X0,sF44)
| aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,sK41)
| ~ aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(superposition,[],[f527,f586]) ).
fof(f619,plain,
! [X0,X1] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,sF44)
| ~ sdtlseqdt0(X1,sK41)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f618,f529]) ).
fof(f620,plain,
! [X0,X1] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,sF42)
| ~ sdtlseqdt0(X1,sK40)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f617,f530]) ).
fof(f627,definition,
( spl46_4
<=> sdtlseqdt0(sK40,sK41) ),
introduced(definition,[new_symbols(definition,[spl46_4])],[avatar_definition]) ).
fof(f628,plain,
( sdtlseqdt0(sK40,sK41)
| ~ spl46_4 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f629,plain,
( ~ sdtlseqdt0(sK40,sK41)
| spl46_4 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f640,definition,
( spl46_6
<=> sdtlseqdt0(sK41,sK40) ),
introduced(definition,[new_symbols(definition,[spl46_6])],[avatar_definition]) ).
fof(f641,plain,
( sdtlseqdt0(sK41,sK40)
| ~ spl46_6 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f642,plain,
( ~ sdtlseqdt0(sK41,sK40)
| spl46_6 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f687,plain,
! [X0] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0)
| ~ sP8(X0) ),
inference(resolution,[],[f506,f578]) ).
fof(f692,plain,
! [X0] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(forward_subsumption_resolution,[],[f687,f508]) ).
fof(f695,definition,
( spl46_13
<=> sP9(sK41) ),
introduced(definition,[new_symbols(definition,[spl46_13])],[avatar_definition]) ).
fof(f696,plain,
( sP9(sK41)
| ~ spl46_13 ),
inference(avatar_component_clause,[],[f695]) ).
fof(f697,plain,
( ~ sP9(sK41)
| spl46_13 ),
inference(avatar_component_clause,[],[f695]) ).
fof(f703,definition,
( spl46_15
<=> sP9(sK40) ),
introduced(definition,[new_symbols(definition,[spl46_15])],[avatar_definition]) ).
fof(f704,plain,
( sP9(sK40)
| ~ spl46_15 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f705,plain,
( ~ sP9(sK40)
| spl46_15 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f712,plain,
( ~ aElementOf0(szmzizndt0(sF42),sdtlpdtrp0(xN,szszuzczcdt0(sK40)))
| ~ sP9(sK40) ),
inference(superposition,[],[f692,f580]) ).
fof(f713,plain,
( ~ aElementOf0(szmzizndt0(sF44),sdtlpdtrp0(xN,szszuzczcdt0(sK41)))
| ~ sP9(sK41) ),
inference(superposition,[],[f692,f586]) ).
fof(f721,plain,
sP9(sK40),
inference(resolution,[],[f612,f530]) ).
fof(f722,plain,
sP9(sK41),
inference(resolution,[],[f612,f529]) ).
fof(f723,plain,
( $false
| spl46_13 ),
inference(forward_subsumption_resolution,[],[f722,f697]) ).
fof(f724,plain,
spl46_13,
inference(avatar_contradiction_clause,[],[f723]) ).
fof(f725,plain,
( $false
| spl46_15 ),
inference(forward_subsumption_resolution,[],[f721,f705]) ).
fof(f726,plain,
spl46_15,
inference(avatar_contradiction_clause,[],[f725]) ).
fof(f727,plain,
( ~ aElementOf0(szmzizndt0(sF42),sdtlpdtrp0(xN,szszuzczcdt0(sK40)))
| ~ spl46_15 ),
inference(forward_subsumption_resolution,[],[f712,f704]) ).
fof(f729,plain,
( ~ aElementOf0(szmzizndt0(sF44),sdtlpdtrp0(xN,szszuzczcdt0(sK41)))
| ~ spl46_13 ),
inference(forward_subsumption_resolution,[],[f713,f696]) ).
fof(f731,plain,
( ~ aElementOf0(sF43,sdtlpdtrp0(xN,szszuzczcdt0(sK40)))
| ~ spl46_15 ),
inference(forward_demodulation,[],[f727,f582]) ).
fof(f733,plain,
( ~ aElementOf0(sF43,sdtlpdtrp0(xN,szszuzczcdt0(sK41)))
| ~ spl46_13 ),
inference(forward_demodulation,[],[f729,f611]) ).
fof(f735,plain,
( ~ aElementOf0(sF43,sF42)
| ~ sdtlseqdt0(szszuzczcdt0(sK41),sK40)
| ~ aElementOf0(szszuzczcdt0(sK41),szNzAzT0)
| ~ spl46_13 ),
inference(resolution,[],[f733,f620]) ).
fof(f738,plain,
( ~ sdtlseqdt0(szszuzczcdt0(sK41),sK40)
| ~ aElementOf0(szszuzczcdt0(sK41),szNzAzT0)
| ~ spl46_13 ),
inference(forward_subsumption_resolution,[],[f735,f583]) ).
fof(f740,definition,
( spl46_17
<=> aElementOf0(szszuzczcdt0(sK41),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl46_17])],[avatar_definition]) ).
fof(f742,plain,
( ~ aElementOf0(szszuzczcdt0(sK41),szNzAzT0)
| spl46_17 ),
inference(avatar_component_clause,[],[f740]) ).
fof(f749,definition,
( spl46_19
<=> sdtlseqdt0(szszuzczcdt0(sK41),sK40) ),
introduced(definition,[new_symbols(definition,[spl46_19])],[avatar_definition]) ).
fof(f751,plain,
( ~ sdtlseqdt0(szszuzczcdt0(sK41),sK40)
| spl46_19 ),
inference(avatar_component_clause,[],[f749]) ).
fof(f752,plain,
( ~ spl46_17
| ~ spl46_19
| ~ spl46_13 ),
inference(avatar_split_clause,[],[f738,f695,f749,f740]) ).
fof(f754,plain,
( ~ aElementOf0(sF43,sF44)
| ~ sdtlseqdt0(szszuzczcdt0(sK40),sK41)
| ~ aElementOf0(szszuzczcdt0(sK40),szNzAzT0)
| ~ spl46_15 ),
inference(resolution,[],[f731,f619]) ).
fof(f755,plain,
( ~ sdtlseqdt0(szszuzczcdt0(sK40),sK41)
| ~ aElementOf0(szszuzczcdt0(sK40),szNzAzT0)
| ~ spl46_15 ),
inference(forward_subsumption_resolution,[],[f754,f587]) ).
fof(f758,definition,
( spl46_20
<=> aElementOf0(szszuzczcdt0(sK40),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl46_20])],[avatar_definition]) ).
fof(f760,plain,
( ~ aElementOf0(szszuzczcdt0(sK40),szNzAzT0)
| spl46_20 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f762,definition,
( spl46_21
<=> sdtlseqdt0(szszuzczcdt0(sK40),sK41) ),
introduced(definition,[new_symbols(definition,[spl46_21])],[avatar_definition]) ).
fof(f764,plain,
( ~ sdtlseqdt0(szszuzczcdt0(sK40),sK41)
| spl46_21 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f765,plain,
( ~ spl46_20
| ~ spl46_21
| ~ spl46_15 ),
inference(avatar_split_clause,[],[f755,f703,f762,f758]) ).
fof(f1199,plain,
( ~ aElementOf0(sK41,szNzAzT0)
| spl46_17 ),
inference(resolution,[],[f353,f742]) ).
fof(f1200,plain,
( ~ aElementOf0(sK40,szNzAzT0)
| spl46_20 ),
inference(resolution,[],[f353,f760]) ).
fof(f1203,plain,
( $false
| spl46_20 ),
inference(forward_subsumption_resolution,[],[f1200,f530]) ).
fof(f1204,plain,
spl46_20,
inference(avatar_contradiction_clause,[],[f1203]) ).
fof(f1205,plain,
( $false
| spl46_17 ),
inference(forward_subsumption_resolution,[],[f1199,f529]) ).
fof(f1206,plain,
spl46_17,
inference(avatar_contradiction_clause,[],[f1205]) ).
fof(f1217,plain,
( sdtlseqdt0(sK41,sK40)
| ~ aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(sK40,szNzAzT0)
| spl46_21 ),
inference(resolution,[],[f764,f366]) ).
fof(f1218,plain,
( ~ aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(sK40,szNzAzT0)
| spl46_6
| spl46_21 ),
inference(forward_subsumption_resolution,[],[f1217,f642]) ).
fof(f1219,plain,
( ~ aElementOf0(sK40,szNzAzT0)
| spl46_6
| spl46_21 ),
inference(forward_subsumption_resolution,[],[f1218,f529]) ).
fof(f1220,plain,
( $false
| spl46_6
| spl46_21 ),
inference(forward_subsumption_resolution,[],[f1219,f530]) ).
fof(f1221,plain,
( spl46_6
| spl46_21 ),
inference(avatar_contradiction_clause,[],[f1220]) ).
fof(f1242,plain,
( sdtlseqdt0(sK40,sK41)
| ~ aElementOf0(sK40,szNzAzT0)
| ~ aElementOf0(sK41,szNzAzT0)
| spl46_19 ),
inference(resolution,[],[f751,f366]) ).
fof(f1243,plain,
( ~ aElementOf0(sK40,szNzAzT0)
| ~ aElementOf0(sK41,szNzAzT0)
| spl46_4
| spl46_19 ),
inference(forward_subsumption_resolution,[],[f1242,f629]) ).
fof(f1244,plain,
( ~ aElementOf0(sK41,szNzAzT0)
| spl46_4
| spl46_19 ),
inference(forward_subsumption_resolution,[],[f1243,f530]) ).
fof(f1245,plain,
( $false
| spl46_4
| spl46_19 ),
inference(forward_subsumption_resolution,[],[f1244,f529]) ).
fof(f1246,plain,
( spl46_4
| spl46_19 ),
inference(avatar_contradiction_clause,[],[f1245]) ).
fof(f1263,plain,
( ~ sdtlseqdt0(sK41,sK40)
| sK40 = sK41
| ~ aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(sK40,szNzAzT0)
| ~ spl46_4 ),
inference(resolution,[],[f628,f364]) ).
fof(f1264,plain,
( sK40 = sK41
| ~ aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(sK40,szNzAzT0)
| ~ spl46_4
| ~ spl46_6 ),
inference(forward_subsumption_resolution,[],[f1263,f641]) ).
fof(f1265,plain,
( ~ aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(sK40,szNzAzT0)
| ~ spl46_4
| ~ spl46_6 ),
inference(forward_subsumption_resolution,[],[f1264,f528]) ).
fof(f1266,plain,
( ~ aElementOf0(sK40,szNzAzT0)
| ~ spl46_4
| ~ spl46_6 ),
inference(forward_subsumption_resolution,[],[f1265,f529]) ).
fof(f1267,plain,
( $false
| ~ spl46_4
| ~ spl46_6 ),
inference(forward_subsumption_resolution,[],[f1266,f530]) ).
fof(f1268,plain,
( ~ spl46_4
| ~ spl46_6 ),
inference(avatar_contradiction_clause,[],[f1267]) ).
cnf(s11,plain,
spl46_13,
inference(sat_conversion,[],[f724]) ).
cnf(s12,plain,
spl46_15,
inference(sat_conversion,[],[f726]) ).
cnf(s14,plain,
( ~ spl46_13
| ~ spl46_17
| ~ spl46_19 ),
inference(sat_conversion,[],[f752]) ).
cnf(s15,plain,
( ~ spl46_15
| ~ spl46_20
| ~ spl46_21 ),
inference(sat_conversion,[],[f765]) ).
cnf(s46,plain,
spl46_20,
inference(sat_conversion,[],[f1204]) ).
cnf(s47,plain,
spl46_17,
inference(sat_conversion,[],[f1206]) ).
cnf(s50,plain,
( spl46_6
| spl46_21 ),
inference(sat_conversion,[],[f1221]) ).
cnf(s51,plain,
( spl46_4
| spl46_19 ),
inference(sat_conversion,[],[f1246]) ).
cnf(s52,plain,
( ~ spl46_4
| ~ spl46_6 ),
inference(sat_conversion,[],[f1268]) ).
cnf(s65,plain,
( ~ spl46_15
| ~ spl46_21 ),
inference(rat,[],[s15,s46]) ).
cnf(s66,plain,
( ~ spl46_13
| ~ spl46_19 ),
inference(rat,[],[s14,s47]) ).
cnf(s69,plain,
~ spl46_21,
inference(rat,[],[s65,s12]) ).
cnf(s70,plain,
spl46_6,
inference(rat,[],[s50,s69]) ).
cnf(s71,plain,
~ spl46_4,
inference(rat,[],[s52,s70]) ).
cnf(s72,plain,
spl46_19,
inference(rat,[],[s51,s71]) ).
cnf(s73,plain,
~ spl46_13,
inference(rat,[],[s66,s72]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s11,s73]) ).
fof(f1269,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM575+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 20:34:55 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 6.25/1.97 % (1579227)Detected formulas, will run a generic FOF schedule.
% 6.25/1.97 % (1579236)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2628735856:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.25/1.97 % (1579236)Instruction limit reached!
% 6.25/1.97 % (1579236)------------------------------
% 6.25/1.97 % (1579236)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579236)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579236)Termination reason: Instruction limit
% 6.25/1.97 % (1579236)Termination phase: Saturation
% 6.25/1.97 % (1579236)Time elapsed: 0.040 s
% 6.25/1.97 % (1579232)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=3958823007:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.25/1.97 % (1579236)Peak memory usage: 89 MB
% 6.25/1.97 % (1579233)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=3006426681:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.25/1.97 % (1579235)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=92834497:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.25/1.97 % (1579234)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=3279581657:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.25/1.97 % (1579236)Instructions burned: 120 (million)
% 6.25/1.97 % (1579237)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2787170660:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.25/1.97 % (1579238)dis-21_1_sil=8000:lcm=predicate:random_seed=2116660387: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)
% 6.25/1.97 % (1579238)Instruction limit reached!
% 6.25/1.97 % (1579238)------------------------------
% 6.25/1.97 % (1579238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579238)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579238)Termination reason: Instruction limit
% 6.25/1.97 % (1579238)Termination phase: Saturation
% 6.25/1.97 % (1579238)Time elapsed: 0.042 s
% 6.25/1.97 % (1579238)Peak memory usage: 90 MB
% 6.25/1.97 % (1579238)Instructions burned: 131 (million)
% 6.25/1.97 % (1579235)Instruction limit reached!
% 6.25/1.97 % (1579235)------------------------------
% 6.25/1.97 % (1579235)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579235)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579235)Termination reason: Instruction limit
% 6.25/1.97 % (1579235)Termination phase: Saturation
% 6.25/1.97 % (1579235)Time elapsed: 0.068 s
% 6.25/1.97 % (1579235)Peak memory usage: 89 MB
% 6.25/1.97 % (1579235)Instructions burned: 109 (million)
% 6.25/1.97 % (1579237)Instruction limit reached!
% 6.25/1.97 % (1579237)------------------------------
% 6.25/1.97 % (1579237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579237)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579237)Termination reason: Instruction limit
% 6.25/1.97 % (1579237)Termination phase: Saturation
% 6.25/1.97 % (1579237)Time elapsed: 0.102 s
% 6.25/1.97 % (1579237)Peak memory usage: 90 MB
% 6.25/1.97 % (1579237)Instructions burned: 139 (million)
% 6.25/1.97 % (1579247)lrs+10_1_sil=32000:urr=on:br=off:random_seed=621457617:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.25/1.97 % (1579245)lrs+10_1_sil=8000:sp=occurrence:random_seed=3840193902:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.25/1.97 % (1579247)Instruction limit reached!
% 6.25/1.97 % (1579247)------------------------------
% 6.25/1.97 % (1579247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579247)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579247)Termination reason: Instruction limit
% 6.25/1.97 % (1579247)Termination phase: Saturation
% 6.25/1.97 % (1579247)Time elapsed: 0.043 s
% 6.25/1.97 % (1579247)Peak memory usage: 89 MB
% 6.25/1.97 % (1579247)Instructions burned: 157 (million)
% 6.25/1.97 % (1579248)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3150485234:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.25/1.97 % (1579249)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=1114060798:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.25/1.97 % (1579252)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1463628077:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.25/1.97 % (1579245)Instruction limit reached!
% 6.25/1.97 % (1579245)------------------------------
% 6.25/1.97 % (1579245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579245)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579245)Termination reason: Instruction limit
% 6.25/1.97 % (1579245)Termination phase: Saturation
% 6.25/1.97 % (1579245)Time elapsed: 0.184 s
% 6.25/1.97 % (1579245)Peak memory usage: 92 MB
% 6.25/1.97 % (1579245)Instructions burned: 285 (million)
% 6.25/1.97 % (1579252)Instruction limit reached!
% 6.25/1.97 % (1579252)------------------------------
% 6.25/1.97 % (1579252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579252)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579252)Termination reason: Instruction limit
% 6.25/1.97 % (1579252)Termination phase: Saturation
% 6.25/1.97 % (1579252)Time elapsed: 0.098 s
% 6.25/1.97 % (1579252)Peak memory usage: 90 MB
% 6.25/1.97 % (1579252)Instructions burned: 297 (million)
% 6.25/1.97 % (1579249)Instruction limit reached!
% 6.25/1.97 % (1579249)------------------------------
% 6.25/1.97 % (1579249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579249)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579249)Termination reason: Instruction limit
% 6.25/1.97 % (1579249)Termination phase: Saturation
% 6.25/1.97 % (1579249)Time elapsed: 0.149 s
% 6.25/1.97 % (1579249)Peak memory usage: 92 MB
% 6.25/1.97 % (1579249)Instructions burned: 249 (million)
% 6.25/1.97 % (1579248)Instruction limit reached!
% 6.25/1.97 % (1579248)------------------------------
% 6.25/1.97 % (1579248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579248)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579248)Termination reason: Instruction limit
% 6.25/1.97 % (1579248)Termination phase: Saturation
% 6.25/1.97 % (1579248)Time elapsed: 0.226 s
% 6.25/1.97 % (1579248)Peak memory usage: 92 MB
% 6.25/1.97 % (1579248)Instructions burned: 326 (million)
% 6.25/1.97 % (1579256)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4129079036:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.25/1.97 % (1579258)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=619618317:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.25/1.97 % (1579257)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2855670108:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.25/1.97 % (1579258)Instruction limit reached!
% 6.25/1.97 % (1579258)------------------------------
% 6.25/1.97 % (1579258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579258)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579258)Termination reason: Instruction limit
% 6.25/1.97 % (1579258)Termination phase: Saturation
% 6.25/1.97 % (1579258)Time elapsed: 0.037 s
% 6.25/1.97 % (1579258)Peak memory usage: 89 MB
% 6.25/1.97 % (1579258)Instructions burned: 129 (million)
% 6.25/1.97 % (1579259)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3473516394:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 6.25/1.97 % (1579257)Instruction limit reached!
% 6.25/1.97 % (1579257)------------------------------
% 6.25/1.97 % (1579257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579257)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579257)Termination reason: Instruction limit
% 6.25/1.97 % (1579257)Termination phase: Saturation
% 6.25/1.97 % (1579257)Time elapsed: 0.076 s
% 6.25/1.97 % (1579257)Peak memory usage: 91 MB
% 6.25/1.97 % (1579257)Instructions burned: 113 (million)
% 6.25/1.97 % (1579263)lrs+10_1_sil=8000:sp=occurrence:random_seed=2720322477:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 6.25/1.97 % (1579259)Instruction limit reached!
% 6.25/1.97 % (1579259)------------------------------
% 6.25/1.97 % (1579259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579259)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579259)Termination reason: Instruction limit
% 6.25/1.97 % (1579259)Termination phase: Saturation
% 6.25/1.97 % (1579259)Time elapsed: 0.069 s
% 6.25/1.97 % (1579259)Peak memory usage: 89 MB
% 6.25/1.97 % (1579259)Instructions burned: 114 (million)
% 6.25/1.97 % (1579265)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=620212255:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.25/1.97 % (1579232)First to succeed.
% 6.25/1.97 % (1579232)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1579227"
% 6.25/1.97 % (1579267)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=605618528:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 6.25/1.97 % (1579263)Instruction limit reached!
% 6.25/1.97 % (1579263)------------------------------
% 6.25/1.97 % (1579263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.25/1.97 % (1579263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.25/1.97 % (1579263)CaDiCaL version: 2.1.3
% 6.25/1.97 % (1579263)Termination reason: Instruction limit
% 6.25/1.97 % (1579263)Termination phase: Saturation
% 6.25/1.97 % (1579263)Time elapsed: 0.306 s
% 6.25/1.97 % (1579263)Peak memory usage: 98 MB
% 6.25/1.97 % (1579263)Instructions burned: 907 (million)
% 6.25/1.97 % (1579232)Refutation found. Thanks to Tanya!
% 6.25/1.97 % SZS status Theorem for theBenchmark
% 6.25/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 8.37/2.08 % (1579232)------------------------------
% 8.37/2.08 % (1579232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.37/2.08 % (1579232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.37/2.08 % (1579232)CaDiCaL version: 2.1.3
% 8.37/2.08 % (1579232)Termination reason: Refutation
% 8.37/2.08 % (1579232)Time elapsed: 0.713 s
% 8.37/2.08 % (1579232)Peak memory usage: 132 MB
% 8.37/2.08 % (1579232)Instructions burned: 1068 (million)
% 8.37/2.08 % (1579232)------------------------------
% 8.37/2.08 % (1579232)------------------------------
% 8.37/2.08 % (1579227)Success in time 1.116 s
% 8.37/2.08 % Vampire exiting
%------------------------------------------------------------------------------