%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM583+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 12:15:51 PM UTC 2026
% Result : Theorem 10.52s 2.62s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 41
% Syntax : Number of formulae : 261 ( 48 unt; 24 def)
% Number of atoms : 1075 ( 144 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1382 ( 568 ~; 591 |; 161 &)
% ( 49 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 25 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 8 con; 0-3 aty)
% Number of variables : 250 ( 0 sgn 231 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f9,axiom,
! [X0] :
( ( aSet0(X0)
& isCountable0(X0) )
=> X0 != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X0)
& aSet0(X1)
& aSet0(X2) )
=> ( ( aSubsetOf0(X0,X1)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
fof(f15,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(f16,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f47,axiom,
! [X0] :
( ( aSubsetOf0(X0,szNzAzT0)
& X0 != slcrc0 )
=> ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
fof(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f75,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
fof(f85,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989) ).
fof(f86,axiom,
aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989_02) ).
fof(f88,axiom,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4037) ).
fof(f89,conjecture,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f90,negated_conjecture,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f98,plain,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(flattening,[],[f90]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f100,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f103,plain,
! [X0] :
( X0 != slcrc0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f104,plain,
! [X0] :
( X0 != slcrc0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f111,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f112,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(flattening,[],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f114,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f116,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f115]) ).
fof(f158,plain,
! [X0] :
( ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(ennf_transformation,[],[f47]) ).
fof(f159,plain,
! [X0] :
( ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(flattening,[],[f158]) ).
fof(f173,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f174,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f173]) ).
fof(f202,plain,
! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f207,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f208,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f207]) ).
fof(f209,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f208]) ).
fof(f210,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK0(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f209]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f105]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f211]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f212]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK1(X0,X1),X0)
& aElementOf0(sK1(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f213]) ).
fof(f215,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtpldt0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ( ~ aElementOf0(X3,X0)
& X1 != X3 )
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ( ~ aElementOf0(X3,X0)
& X1 != X3 ) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) )
| ~ aElementOf0(X3,X2) ) ) )
| sdtpldt0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(nnf_transformation,[],[f114]) ).
fof(f216,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtpldt0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ( ~ aElementOf0(X3,X0)
& X1 != X3 )
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ( ~ aElementOf0(X3,X0)
& X1 != X3 ) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) )
| ~ aElementOf0(X3,X2) ) ) )
| sdtpldt0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f215]) ).
fof(f217,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtpldt0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ( ~ aElementOf0(X3,X0)
& X1 != X3 )
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElement0(X4)
| ( ~ aElementOf0(X4,X0)
& X1 != X4 ) )
& ( ( aElement0(X4)
& ( aElementOf0(X4,X0)
| X1 = X4 ) )
| ~ aElementOf0(X4,X2) ) ) )
| sdtpldt0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(rectify,[],[f216]) ).
fof(f218,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtpldt0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aElement0(sK2(X0,X1,X2))
| ( ~ aElementOf0(sK2(X0,X1,X2),X0)
& sK2(X0,X1,X2) != X1 )
| ~ aElementOf0(sK2(X0,X1,X2),X2) )
& ( ( aElement0(sK2(X0,X1,X2))
& ( aElementOf0(sK2(X0,X1,X2),X0)
| sK2(X0,X1,X2) = X1 ) )
| aElementOf0(sK2(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElement0(X4)
| ( ~ aElementOf0(X4,X0)
& X1 != X4 ) )
& ( ( aElement0(X4)
& ( aElementOf0(X4,X0)
| X1 = X4 ) )
| ~ aElementOf0(X4,X2) ) ) )
| sdtpldt0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(nnf_transformation,[],[f116]) ).
fof(f220,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f219]) ).
fof(f221,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X0)
| X1 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X0)
& X1 != X4 )
| ~ aElementOf0(X4,X2) ) ) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(rectify,[],[f220]) ).
fof(f222,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aElement0(sK3(X0,X1,X2))
| ~ aElementOf0(sK3(X0,X1,X2),X0)
| sK3(X0,X1,X2) = X1
| ~ aElementOf0(sK3(X0,X1,X2),X2) )
& ( ( aElement0(sK3(X0,X1,X2))
& aElementOf0(sK3(X0,X1,X2),X0)
& sK3(X0,X1,X2) != X1 )
| aElementOf0(sK3(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X0)
| X1 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X0)
& X1 != X4 )
| ~ aElementOf0(X4,X2) ) ) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f221]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(nnf_transformation,[],[f159]) ).
fof(f229,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(flattening,[],[f228]) ).
fof(f230,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(rectify,[],[f229]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ( ~ sdtlseqdt0(X1,sK6(X0,X1))
& aElementOf0(sK6(X0,X1),X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f230]) ).
fof(f244,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f174]) ).
fof(f245,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f244]) ).
fof(f246,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f245]) ).
fof(f247,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK10(X0,X1,X2),X0)
| sbrdtbr0(sK10(X0,X1,X2)) != X1
| ~ aElementOf0(sK10(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK10(X0,X1,X2),X0)
& sbrdtbr0(sK10(X0,X1,X2)) = X1 )
| aElementOf0(sK10(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X3,sK10(X0,X1,X2))],[f246]) ).
fof(f263,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f265,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f210]) ).
fof(f269,plain,
! [X0] :
( slcrc0 != X0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f270,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f214]) ).
fof(f271,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f214]) ).
fof(f272,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| aElementOf0(sK1(X0,X1),X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f214]) ).
fof(f273,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK1(X0,X1),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f214]) ).
fof(f277,plain,
! [X2,X0,X1] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f278,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X0)
| X1 = X4
| ~ aElementOf0(X4,X2)
| sdtpldt0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f218]) ).
fof(f282,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtpldt0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f218]) ).
fof(f288,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| sdtmndt0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f291,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtmndt0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f303,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f332,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| szmzizndt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f231]) ).
fof(f358,plain,
! [X2,X0,X1,X4] :
( aSubsetOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f404,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f415,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f421,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f425,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f85]) ).
fof(f426,plain,
aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
inference(cnf_transformation,[],[f86]) ).
fof(f428,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(cnf_transformation,[],[f88]) ).
fof(f429,plain,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(cnf_transformation,[],[f98]) ).
fof(f430,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f265]) ).
fof(f432,plain,
( ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(equality_resolution,[],[f269]) ).
fof(f433,plain,
! [X0,X1] :
( aSet0(sdtpldt0(X0,X1))
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f282]) ).
fof(f438,plain,
! [X0,X1,X4] :
( aElementOf0(X4,X0)
| X1 = X4
| ~ aElementOf0(X4,sdtpldt0(X0,X1))
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f278]) ).
fof(f439,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f291]) ).
fof(f442,plain,
! [X0,X1,X4] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,sdtmndt0(X0,X1))
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f288]) ).
fof(f446,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(equality_resolution,[],[f332]) ).
fof(f458,plain,
! [X0,X1,X4] :
( aSubsetOf0(X4,X0)
| ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f358]) ).
fof(f482,definition,
( spl21_1
<=> aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
introduced(definition,[new_symbols(definition,[spl21_1])],[avatar_definition]) ).
fof(f484,plain,
( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| spl21_1 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f485,plain,
~ spl21_1,
inference(avatar_split_clause,[],[f429,f482]) ).
fof(f489,plain,
( ~ aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(xS)
| spl21_1 ),
inference(resolution,[],[f484,f272]) ).
fof(f490,plain,
( ~ aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xS)
| ~ aSet0(xS)
| spl21_1 ),
inference(resolution,[],[f484,f273]) ).
fof(f507,definition,
( spl21_2
<=> aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
introduced(definition,[new_symbols(definition,[spl21_2])],[avatar_definition]) ).
fof(f509,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),xS)
| ~ spl21_2 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f510,plain,
spl21_2,
inference(avatar_split_clause,[],[f428,f507]) ).
fof(f511,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| ~ aSet0(xS) )
| ~ spl21_2 ),
inference(resolution,[],[f509,f270]) ).
fof(f512,plain,
( aSet0(sdtlpdtrp0(xN,xi))
| ~ aSet0(xS)
| ~ spl21_2 ),
inference(resolution,[],[f509,f271]) ).
fof(f597,definition,
( spl21_5
<=> aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f599,plain,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f600,plain,
spl21_5,
inference(avatar_split_clause,[],[f426,f597]) ).
fof(f602,plain,
( aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(xk,szNzAzT0)
| ~ spl21_5 ),
inference(resolution,[],[f599,f458]) ).
fof(f638,plain,
( aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f602,f415]) ).
fof(f642,definition,
( spl21_6
<=> aSubsetOf0(xS,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl21_6])],[avatar_definition]) ).
fof(f644,plain,
( aSubsetOf0(xS,szNzAzT0)
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f645,plain,
spl21_6,
inference(avatar_split_clause,[],[f404,f642]) ).
fof(f659,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0)
| ~ spl21_6 ),
inference(resolution,[],[f644,f271]) ).
fof(f664,plain,
( ! [X0] :
( aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(X0)
| ~ aSet0(xS)
| ~ aSet0(szNzAzT0) )
| ~ spl21_6 ),
inference(resolution,[],[f644,f277]) ).
fof(f669,plain,
( ! [X0] :
( aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aSet0(szNzAzT0) )
| ~ spl21_6 ),
inference(forward_subsumption_resolution,[],[f664,f271]) ).
fof(f674,plain,
( aSet0(xS)
| ~ spl21_6 ),
inference(forward_subsumption_resolution,[],[f659,f303]) ).
fof(f676,plain,
( ! [X0] :
( aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(X0,xS)
| ~ aSet0(xS) )
| ~ spl21_6 ),
inference(forward_subsumption_resolution,[],[f669,f303]) ).
fof(f679,plain,
( ~ aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| spl21_1
| ~ spl21_6 ),
inference(backward_subsumption_resolution,[],[f489,f674]) ).
fof(f680,plain,
( ~ aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xS)
| spl21_1
| ~ spl21_6 ),
inference(backward_subsumption_resolution,[],[f490,f674]) ).
fof(f682,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
| ~ spl21_2
| ~ spl21_6 ),
inference(backward_subsumption_resolution,[],[f511,f674]) ).
fof(f683,plain,
( aSet0(sdtlpdtrp0(xN,xi))
| ~ spl21_2
| ~ spl21_6 ),
inference(backward_subsumption_resolution,[],[f512,f674]) ).
fof(f690,plain,
( ! [X0] :
( aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(X0,xS) )
| ~ spl21_6 ),
inference(forward_subsumption_resolution,[],[f676,f674]) ).
fof(f722,definition,
( spl21_8
<=> ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
introduced(definition,[new_symbols(definition,[spl21_8])],[avatar_definition]) ).
fof(f723,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
| aElementOf0(X0,xS) )
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f724,plain,
( spl21_8
| ~ spl21_2
| ~ spl21_6 ),
inference(avatar_split_clause,[],[f682,f642,f507,f722]) ).
fof(f727,plain,
( ! [X0,X1] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),X1))
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X1) )
| ~ spl21_8 ),
inference(resolution,[],[f723,f442]) ).
fof(f730,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| slcrc0 = sdtlpdtrp0(xN,xi)
| ~ spl21_8 ),
inference(resolution,[],[f723,f446]) ).
fof(f774,plain,
( ! [X0,X1] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),X1))
| ~ aElement0(X1) )
| ~ spl21_2
| ~ spl21_6
| ~ spl21_8 ),
inference(forward_subsumption_resolution,[],[f727,f683]) ).
fof(f779,definition,
( spl21_9
<=> aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
introduced(definition,[new_symbols(definition,[spl21_9])],[avatar_definition]) ).
fof(f780,plain,
( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl21_9 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f781,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| spl21_9 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f783,definition,
( spl21_10
<=> aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
introduced(definition,[new_symbols(definition,[spl21_10])],[avatar_definition]) ).
fof(f785,plain,
( aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl21_10 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f786,plain,
( ~ spl21_9
| spl21_10
| ~ spl21_5 ),
inference(avatar_split_clause,[],[f638,f597,f783,f779]) ).
fof(f787,plain,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| spl21_9 ),
inference(resolution,[],[f781,f439]) ).
fof(f807,plain,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ spl21_2
| ~ spl21_6
| spl21_9 ),
inference(forward_subsumption_resolution,[],[f787,f683]) ).
fof(f816,definition,
( spl21_12
<=> aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xS) ),
introduced(definition,[new_symbols(definition,[spl21_12])],[avatar_definition]) ).
fof(f818,plain,
( ~ aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xS)
| spl21_12 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f820,definition,
( spl21_13
<=> aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
introduced(definition,[new_symbols(definition,[spl21_13])],[avatar_definition]) ).
fof(f821,plain,
( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl21_13 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f822,plain,
( ~ aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| spl21_13 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f823,plain,
( ~ spl21_12
| ~ spl21_13
| spl21_1
| ~ spl21_6 ),
inference(avatar_split_clause,[],[f680,f642,f482,f820,f816]) ).
fof(f862,definition,
( spl21_15
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[spl21_15])],[avatar_definition]) ).
fof(f864,plain,
( aSet0(xS)
| ~ spl21_15 ),
inference(avatar_component_clause,[],[f862]) ).
fof(f865,plain,
( spl21_15
| ~ spl21_6 ),
inference(avatar_split_clause,[],[f674,f642,f862]) ).
fof(f949,plain,
( ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| spl21_13 ),
inference(resolution,[],[f822,f433]) ).
fof(f970,definition,
( spl21_18
<=> aElementOf0(xi,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl21_18])],[avatar_definition]) ).
fof(f972,plain,
( aElementOf0(xi,szNzAzT0)
| ~ spl21_18 ),
inference(avatar_component_clause,[],[f970]) ).
fof(f973,plain,
spl21_18,
inference(avatar_split_clause,[],[f425,f970]) ).
fof(f1125,definition,
( spl21_23
<=> aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
introduced(definition,[new_symbols(definition,[spl21_23])],[avatar_definition]) ).
fof(f1127,plain,
( aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl21_23 ),
inference(avatar_component_clause,[],[f1125]) ).
fof(f1128,plain,
( spl21_23
| ~ spl21_13
| spl21_1
| ~ spl21_6 ),
inference(avatar_split_clause,[],[f679,f642,f482,f820,f1125]) ).
fof(f1130,definition,
( spl21_24
<=> aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
introduced(definition,[new_symbols(definition,[spl21_24])],[avatar_definition]) ).
fof(f1131,plain,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ spl21_24 ),
inference(avatar_component_clause,[],[f1130]) ).
fof(f1132,plain,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| spl21_24 ),
inference(avatar_component_clause,[],[f1130]) ).
fof(f1133,plain,
( ~ spl21_24
| ~ spl21_2
| ~ spl21_6
| spl21_9 ),
inference(avatar_split_clause,[],[f807,f779,f642,f507,f1130]) ).
fof(f1521,definition,
( spl21_34
<=> ! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
introduced(definition,[new_symbols(definition,[spl21_34])],[avatar_definition]) ).
fof(f1522,plain,
( ! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) )
| ~ spl21_34 ),
inference(avatar_component_clause,[],[f1521]) ).
fof(f1523,plain,
spl21_34,
inference(avatar_split_clause,[],[f421,f1521]) ).
fof(f2800,plain,
~ isCountable0(slcrc0),
inference(forward_subsumption_resolution,[],[f432,f430]) ).
fof(f2802,definition,
( spl21_60
<=> isCountable0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl21_60])],[avatar_definition]) ).
fof(f2804,plain,
( ~ isCountable0(slcrc0)
| spl21_60 ),
inference(avatar_component_clause,[],[f2802]) ).
fof(f2805,plain,
~ spl21_60,
inference(avatar_split_clause,[],[f2800,f2802]) ).
fof(f6024,definition,
( spl21_127
<=> ! [X0] :
( aSubsetOf0(X0,szNzAzT0)
| ~ aSubsetOf0(X0,xS) ) ),
introduced(definition,[new_symbols(definition,[spl21_127])],[avatar_definition]) ).
fof(f6025,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,xS)
| aSubsetOf0(X0,szNzAzT0) )
| ~ spl21_127 ),
inference(avatar_component_clause,[],[f6024]) ).
fof(f6026,plain,
( spl21_127
| ~ spl21_6 ),
inference(avatar_split_clause,[],[f690,f642,f6024]) ).
fof(f6033,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ~ spl21_2
| ~ spl21_127 ),
inference(resolution,[],[f6025,f509]) ).
fof(f6049,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS)
| slcrc0 = sdtlpdtrp0(xN,xi)
| ~ spl21_2
| ~ spl21_8
| ~ spl21_127 ),
inference(backward_subsumption_resolution,[],[f730,f6033]) ).
fof(f6129,definition,
( spl21_129
<=> slcrc0 = sdtlpdtrp0(xN,xi) ),
introduced(definition,[new_symbols(definition,[spl21_129])],[avatar_definition]) ).
fof(f6130,plain,
( slcrc0 != sdtlpdtrp0(xN,xi)
| spl21_129 ),
inference(avatar_component_clause,[],[f6129]) ).
fof(f6131,plain,
( slcrc0 = sdtlpdtrp0(xN,xi)
| ~ spl21_129 ),
inference(avatar_component_clause,[],[f6129]) ).
fof(f6166,plain,
( isCountable0(slcrc0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ spl21_34
| ~ spl21_129 ),
inference(superposition,[],[f1522,f6131]) ).
fof(f6197,plain,
( ~ aElementOf0(xi,szNzAzT0)
| ~ spl21_34
| spl21_60
| ~ spl21_129 ),
inference(forward_subsumption_resolution,[],[f6166,f2804]) ).
fof(f6207,plain,
( $false
| ~ spl21_18
| ~ spl21_34
| spl21_60
| ~ spl21_129 ),
inference(forward_subsumption_resolution,[],[f6197,f972]) ).
fof(f6208,plain,
( ~ spl21_18
| ~ spl21_34
| spl21_60
| ~ spl21_129 ),
inference(avatar_contradiction_clause,[],[f6207]) ).
fof(f6226,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS)
| ~ spl21_2
| ~ spl21_8
| ~ spl21_127
| spl21_129 ),
inference(backward_subsumption_resolution,[],[f6049,f6130]) ).
fof(f6291,definition,
( spl21_131
<=> aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS) ),
introduced(definition,[new_symbols(definition,[spl21_131])],[avatar_definition]) ).
fof(f6293,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS)
| ~ spl21_131 ),
inference(avatar_component_clause,[],[f6291]) ).
fof(f6294,plain,
( spl21_131
| ~ spl21_2
| ~ spl21_8
| ~ spl21_127
| spl21_129 ),
inference(avatar_split_clause,[],[f6226,f6129,f6024,f722,f507,f6291]) ).
fof(f6298,plain,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(xS)
| ~ spl21_131 ),
inference(resolution,[],[f6293,f263]) ).
fof(f6326,plain,
( ~ aSet0(xS)
| spl21_24
| ~ spl21_131 ),
inference(forward_subsumption_resolution,[],[f6298,f1132]) ).
fof(f6332,plain,
( $false
| ~ spl21_15
| spl21_24
| ~ spl21_131 ),
inference(forward_subsumption_resolution,[],[f6326,f864]) ).
fof(f6333,plain,
( ~ spl21_15
| spl21_24
| ~ spl21_131 ),
inference(avatar_contradiction_clause,[],[f6332]) ).
fof(f6387,plain,
( ~ aSet0(xQ)
| spl21_13
| ~ spl21_24 ),
inference(forward_subsumption_resolution,[],[f949,f1131]) ).
fof(f6476,definition,
( spl21_132
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl21_132])],[avatar_definition]) ).
fof(f6477,plain,
( aSet0(xQ)
| ~ spl21_132 ),
inference(avatar_component_clause,[],[f6476]) ).
fof(f6478,plain,
( ~ aSet0(xQ)
| spl21_132 ),
inference(avatar_component_clause,[],[f6476]) ).
fof(f6479,plain,
( ~ spl21_132
| spl21_13
| ~ spl21_24 ),
inference(avatar_split_clause,[],[f6387,f1130,f820,f6476]) ).
fof(f6480,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X0,xQ)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| ~ spl21_10 ),
inference(resolution,[],[f785,f270]) ).
fof(f6481,plain,
( aSet0(xQ)
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl21_10 ),
inference(resolution,[],[f785,f271]) ).
fof(f6512,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl21_10
| spl21_132 ),
inference(forward_subsumption_resolution,[],[f6481,f6478]) ).
fof(f6513,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X0,xQ) )
| ~ spl21_9
| ~ spl21_10 ),
inference(forward_subsumption_resolution,[],[f6480,f780]) ).
fof(f6524,plain,
( $false
| ~ spl21_9
| ~ spl21_10
| spl21_132 ),
inference(forward_subsumption_resolution,[],[f6512,f780]) ).
fof(f6525,plain,
( ~ spl21_9
| ~ spl21_10
| spl21_132 ),
inference(avatar_contradiction_clause,[],[f6524]) ).
fof(f6590,plain,
( aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ spl21_23 ),
inference(resolution,[],[f1127,f438]) ).
fof(f6636,plain,
( aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ spl21_23
| ~ spl21_132 ),
inference(forward_subsumption_resolution,[],[f6590,f6477]) ).
fof(f6652,plain,
( aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl21_23
| ~ spl21_24
| ~ spl21_132 ),
inference(forward_subsumption_resolution,[],[f6636,f1131]) ).
fof(f7333,definition,
( spl21_134
<=> ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X0,xQ) ) ),
introduced(definition,[new_symbols(definition,[spl21_134])],[avatar_definition]) ).
fof(f7334,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X0,xQ) )
| ~ spl21_134 ),
inference(avatar_component_clause,[],[f7333]) ).
fof(f7335,plain,
( spl21_134
| ~ spl21_9
| ~ spl21_10 ),
inference(avatar_split_clause,[],[f6513,f783,f779,f7333]) ).
fof(f7880,definition,
( spl21_141
<=> szmzizndt0(sdtlpdtrp0(xN,xi)) = sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
introduced(definition,[new_symbols(definition,[spl21_141])],[avatar_definition]) ).
fof(f7882,plain,
( szmzizndt0(sdtlpdtrp0(xN,xi)) = sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl21_141 ),
inference(avatar_component_clause,[],[f7880]) ).
fof(f7884,definition,
( spl21_142
<=> aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xQ) ),
introduced(definition,[new_symbols(definition,[spl21_142])],[avatar_definition]) ).
fof(f7886,plain,
( aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xQ)
| ~ spl21_142 ),
inference(avatar_component_clause,[],[f7884]) ).
fof(f7887,plain,
( spl21_141
| spl21_142
| ~ spl21_23
| ~ spl21_24
| ~ spl21_132 ),
inference(avatar_split_clause,[],[f6652,f6476,f1130,f1125,f7884,f7880]) ).
fof(f8537,definition,
( spl21_152
<=> ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) ) ),
introduced(definition,[new_symbols(definition,[spl21_152])],[avatar_definition]) ).
fof(f8538,plain,
( ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,xS) )
| ~ spl21_152 ),
inference(avatar_component_clause,[],[f8537]) ).
fof(f8804,plain,
( aElementOf0(sK1(xS,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),xS)
| ~ spl21_142
| ~ spl21_152 ),
inference(resolution,[],[f7886,f8538]) ).
fof(f8847,plain,
( $false
| spl21_12
| ~ spl21_142
| ~ spl21_152 ),
inference(forward_subsumption_resolution,[],[f8804,f818]) ).
fof(f8848,plain,
( spl21_12
| ~ spl21_142
| ~ spl21_152 ),
inference(avatar_contradiction_clause,[],[f8847]) ).
fof(f9295,plain,
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS)
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ~ aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(xS)
| ~ spl21_141 ),
inference(superposition,[],[f273,f7882]) ).
fof(f9296,plain,
( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ~ aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(xS)
| ~ spl21_131
| ~ spl21_141 ),
inference(forward_subsumption_resolution,[],[f9295,f6293]) ).
fof(f9311,plain,
( ~ aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(xS)
| spl21_1
| ~ spl21_131
| ~ spl21_141 ),
inference(forward_subsumption_resolution,[],[f9296,f484]) ).
fof(f9321,plain,
( ~ aSet0(xS)
| spl21_1
| ~ spl21_13
| ~ spl21_131
| ~ spl21_141 ),
inference(forward_subsumption_resolution,[],[f9311,f821]) ).
fof(f9327,plain,
( $false
| spl21_1
| ~ spl21_13
| ~ spl21_15
| ~ spl21_131
| ~ spl21_141 ),
inference(forward_subsumption_resolution,[],[f9321,f864]) ).
fof(f9328,plain,
( spl21_1
| ~ spl21_13
| ~ spl21_15
| ~ spl21_131
| ~ spl21_141 ),
inference(avatar_contradiction_clause,[],[f9327]) ).
fof(f12002,definition,
( spl21_201
<=> ! [X0,X1] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),X1))
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl21_201])],[avatar_definition]) ).
fof(f12003,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),X1))
| aElementOf0(X0,xS)
| ~ aElement0(X1) )
| ~ spl21_201 ),
inference(avatar_component_clause,[],[f12002]) ).
fof(f12004,plain,
( spl21_201
| ~ spl21_2
| ~ spl21_6
| ~ spl21_8 ),
inference(avatar_split_clause,[],[f774,f722,f642,f507,f12002]) ).
fof(f12005,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aElementOf0(X0,xQ) )
| ~ spl21_134
| ~ spl21_201 ),
inference(resolution,[],[f12003,f7334]) ).
fof(f12080,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xQ) )
| ~ spl21_24
| ~ spl21_134
| ~ spl21_201 ),
inference(forward_subsumption_resolution,[],[f12005,f1131]) ).
fof(f12087,plain,
( spl21_152
| ~ spl21_24
| ~ spl21_134
| ~ spl21_201 ),
inference(avatar_split_clause,[],[f12080,f12002,f7333,f1130,f8537]) ).
cnf(s1,plain,
~ spl21_1,
inference(sat_conversion,[],[f485]) ).
cnf(s2,plain,
spl21_2,
inference(sat_conversion,[],[f510]) ).
cnf(s5,plain,
spl21_5,
inference(sat_conversion,[],[f600]) ).
cnf(s6,plain,
spl21_6,
inference(sat_conversion,[],[f645]) ).
cnf(s8,plain,
( ~ spl21_2
| ~ spl21_6
| spl21_8 ),
inference(sat_conversion,[],[f724]) ).
cnf(s9,plain,
( ~ spl21_5
| ~ spl21_9
| spl21_10 ),
inference(sat_conversion,[],[f786]) ).
cnf(s11,plain,
( spl21_1
| ~ spl21_6
| ~ spl21_12
| ~ spl21_13 ),
inference(sat_conversion,[],[f823]) ).
cnf(s13,plain,
( ~ spl21_6
| spl21_15 ),
inference(sat_conversion,[],[f865]) ).
cnf(s16,plain,
spl21_18,
inference(sat_conversion,[],[f973]) ).
cnf(s21,plain,
( spl21_1
| ~ spl21_6
| ~ spl21_13
| spl21_23 ),
inference(sat_conversion,[],[f1128]) ).
cnf(s22,plain,
( ~ spl21_2
| ~ spl21_6
| spl21_9
| ~ spl21_24 ),
inference(sat_conversion,[],[f1133]) ).
cnf(s32,plain,
spl21_34,
inference(sat_conversion,[],[f1523]) ).
cnf(s55,plain,
~ spl21_60,
inference(sat_conversion,[],[f2805]) ).
cnf(s121,plain,
( ~ spl21_6
| spl21_127 ),
inference(sat_conversion,[],[f6026]) ).
cnf(s125,plain,
( ~ spl21_18
| ~ spl21_34
| spl21_60
| ~ spl21_129 ),
inference(sat_conversion,[],[f6208]) ).
cnf(s126,plain,
( ~ spl21_2
| ~ spl21_8
| ~ spl21_127
| spl21_129
| spl21_131 ),
inference(sat_conversion,[],[f6294]) ).
cnf(s127,plain,
( ~ spl21_15
| spl21_24
| ~ spl21_131 ),
inference(sat_conversion,[],[f6333]) ).
cnf(s128,plain,
( spl21_13
| ~ spl21_24
| ~ spl21_132 ),
inference(sat_conversion,[],[f6479]) ).
cnf(s129,plain,
( ~ spl21_9
| ~ spl21_10
| spl21_132 ),
inference(sat_conversion,[],[f6525]) ).
cnf(s131,plain,
( ~ spl21_9
| ~ spl21_10
| spl21_134 ),
inference(sat_conversion,[],[f7335]) ).
cnf(s139,plain,
( ~ spl21_23
| ~ spl21_24
| ~ spl21_132
| spl21_141
| spl21_142 ),
inference(sat_conversion,[],[f7887]) ).
cnf(s168,plain,
( spl21_12
| ~ spl21_142
| ~ spl21_152 ),
inference(sat_conversion,[],[f8848]) ).
cnf(s174,plain,
( spl21_1
| ~ spl21_13
| ~ spl21_15
| ~ spl21_131
| ~ spl21_141 ),
inference(sat_conversion,[],[f9328]) ).
cnf(s229,plain,
( ~ spl21_2
| ~ spl21_6
| ~ spl21_8
| spl21_201 ),
inference(sat_conversion,[],[f12004]) ).
cnf(s230,plain,
( ~ spl21_24
| ~ spl21_134
| spl21_152
| ~ spl21_201 ),
inference(sat_conversion,[],[f12087]) ).
cnf(s250,plain,
~ spl21_129,
inference(rat,[],[s125,s32,s55,s16]) ).
cnf(s259,plain,
spl21_127,
inference(rat,[],[s121,s6]) ).
cnf(s266,plain,
spl21_15,
inference(rat,[],[s13,s6]) ).
cnf(s308,plain,
spl21_8,
inference(rat,[],[s8,s6,s2]) ).
cnf(s314,plain,
spl21_131,
inference(rat,[],[s126,s2,s250,s259,s308]) ).
cnf(s315,plain,
spl21_201,
inference(rat,[],[s229,s2,s6,s308]) ).
cnf(s323,plain,
spl21_24,
inference(rat,[],[s127,s266,s314]) ).
cnf(s325,plain,
spl21_9,
inference(rat,[],[s22,s2,s6,s323]) ).
cnf(s329,plain,
spl21_10,
inference(rat,[],[s9,s5,s325]) ).
cnf(s332,plain,
spl21_134,
inference(rat,[],[s131,s325,s329]) ).
cnf(s333,plain,
spl21_132,
inference(rat,[],[s129,s325,s329]) ).
cnf(s334,plain,
spl21_152,
inference(rat,[],[s230,s315,s323,s332]) ).
cnf(s341,plain,
spl21_13,
inference(rat,[],[s128,s323,s333]) ).
cnf(s356,plain,
~ spl21_141,
inference(rat,[],[s174,s341,s314,s266,s1]) ).
cnf(s362,plain,
spl21_23,
inference(rat,[],[s21,s341,s6,s1]) ).
cnf(s363,plain,
~ spl21_12,
inference(rat,[],[s11,s341,s6,s1]) ).
cnf(s368,plain,
spl21_142,
inference(rat,[],[s139,s356,s333,s323,s362]) ).
cnf(s371,plain,
$false,
inference(rat,[],[s168,s334,s368,s363]) ).
fof(f12088,plain,
$false,
inference(avatar_sat_refutation,[],[s371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM583+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:36:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.52/2.62 % (1580864)Detected formulas, will run a generic FOF schedule.
% 10.52/2.62 % (1580874)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3160539640:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.52/2.62 % (1580871)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=262895764:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.52/2.62 % (1580872)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=609885717:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.52/2.62 % (1580870)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=809881447:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.52/2.62 % (1580869)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=1686725085:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.52/2.62 % (1580873)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1024846933:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.52/2.62 % (1580874)Instruction limit reached!
% 10.52/2.62 % (1580874)------------------------------
% 10.52/2.62 % (1580874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580874)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580874)Termination reason: Instruction limit
% 10.52/2.62 % (1580874)Termination phase: Saturation
% 10.52/2.62 % (1580874)Time elapsed: 0.054 s
% 10.52/2.62 % (1580874)Peak memory usage: 90 MB
% 10.52/2.62 % (1580874)Instructions burned: 142 (million)
% 10.52/2.62 % (1580875)dis-21_1_sil=8000:lcm=predicate:random_seed=3712446487: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)
% 10.52/2.62 % (1580873)Instruction limit reached!
% 10.52/2.62 % (1580873)------------------------------
% 10.52/2.62 % (1580873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580873)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580873)Termination reason: Instruction limit
% 10.52/2.62 % (1580873)Termination phase: Saturation
% 10.52/2.62 % (1580873)Time elapsed: 0.057 s
% 10.52/2.62 % (1580873)Peak memory usage: 88 MB
% 10.52/2.62 % (1580873)Instructions burned: 120 (million)
% 10.52/2.62 % (1580872)Instruction limit reached!
% 10.52/2.62 % (1580872)------------------------------
% 10.52/2.62 % (1580872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580872)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580872)Termination reason: Instruction limit
% 10.52/2.62 % (1580872)Termination phase: Saturation
% 10.52/2.62 % (1580872)Time elapsed: 0.070 s
% 10.52/2.62 % (1580872)Peak memory usage: 89 MB
% 10.52/2.62 % (1580872)Instructions burned: 109 (million)
% 10.52/2.62 % (1580875)Instruction limit reached!
% 10.52/2.62 % (1580875)------------------------------
% 10.52/2.62 % (1580875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580875)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580875)Termination reason: Instruction limit
% 10.52/2.62 % (1580875)Termination phase: Saturation
% 10.52/2.62 % (1580875)Time elapsed: 0.062 s
% 10.52/2.62 % (1580875)Peak memory usage: 88 MB
% 10.52/2.62 % (1580875)Instructions burned: 129 (million)
% 10.52/2.62 % (1580882)lrs+10_1_sil=8000:sp=occurrence:random_seed=3879757732:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.52/2.62 % (1580884)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1370954983:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.52/2.62 % (1580884)Refutation not found, incomplete strategy
% 10.52/2.62 % (1580884)------------------------------
% 10.52/2.62 % (1580884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580884)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580884)Termination reason: Refutation not found, incomplete strategy
% 10.52/2.62 % (1580884)Time elapsed: 0.006 s
% 10.52/2.62 % (1580884)Peak memory usage: 89 MB
% 10.52/2.62 % (1580884)Instructions burned: 6 (million)
% 10.52/2.62 % (1580885)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4233637824:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.52/2.62 % (1580886)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=1507384226:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 10.52/2.62 % (1580882)Instruction limit reached!
% 10.52/2.62 % (1580882)------------------------------
% 10.52/2.62 % (1580882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580882)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580882)Termination reason: Instruction limit
% 10.52/2.62 % (1580882)Termination phase: Saturation
% 10.52/2.62 % (1580882)Time elapsed: 0.102 s
% 10.52/2.62 % (1580882)Peak memory usage: 92 MB
% 10.52/2.62 % (1580882)Instructions burned: 287 (million)
% 10.52/2.62 % (1580891)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3587724175:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 10.52/2.62 % (1580886)Instruction limit reached!
% 10.52/2.62 % (1580886)------------------------------
% 10.52/2.62 % (1580886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580886)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580886)Termination reason: Instruction limit
% 10.52/2.62 % (1580886)Termination phase: Saturation
% 10.52/2.62 % (1580886)Time elapsed: 0.145 s
% 10.52/2.62 % (1580886)Peak memory usage: 91 MB
% 10.52/2.62 % (1580886)Instructions burned: 248 (million)
% 10.52/2.62 % (1580885)Instruction limit reached!
% 10.52/2.62 % (1580885)------------------------------
% 10.52/2.62 % (1580885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580885)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580885)Termination reason: Instruction limit
% 10.52/2.62 % (1580885)Termination phase: Saturation
% 10.52/2.62 % (1580885)Time elapsed: 0.208 s
% 10.52/2.62 % (1580885)Peak memory usage: 91 MB
% 10.52/2.62 % (1580885)Instructions burned: 325 (million)
% 10.52/2.62 % (1580884)------------------------------
% 10.52/2.62 % (1580884)------------------------------
% 10.52/2.62 % (1580891)Instruction limit reached!
% 10.52/2.62 % (1580891)------------------------------
% 10.52/2.62 % (1580891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580891)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580891)Termination reason: Instruction limit
% 10.52/2.62 % (1580891)Termination phase: Saturation
% 10.52/2.62 % (1580891)Time elapsed: 0.094 s
% 10.52/2.62 % (1580891)Peak memory usage: 90 MB
% 10.52/2.62 % (1580891)Instructions burned: 296 (million)
% 10.52/2.62 % (1580893)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2312060383:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 10.52/2.62 % (1580895)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3037150338:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 10.52/2.62 % (1580894)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2829989910:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 10.52/2.62 % (1580896)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3569110197:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 10.52/2.62 % (1580895)Instruction limit reached!
% 10.52/2.62 % (1580895)------------------------------
% 10.52/2.62 % (1580895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580895)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580895)Termination reason: Instruction limit
% 10.52/2.62 % (1580895)Termination phase: Saturation
% 10.52/2.62 % (1580895)Time elapsed: 0.065 s
% 10.52/2.62 % (1580895)Peak memory usage: 88 MB
% 10.52/2.62 % (1580895)Instructions burned: 127 (million)
% 10.52/2.62 % (1580894)Instruction limit reached!
% 10.52/2.62 % (1580894)------------------------------
% 10.52/2.62 % (1580894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580894)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580894)Termination reason: Instruction limit
% 10.52/2.62 % (1580894)Termination phase: Saturation
% 10.52/2.62 % (1580894)Time elapsed: 0.074 s
% 10.52/2.62 % (1580894)Peak memory usage: 91 MB
% 10.52/2.62 % (1580894)Instructions burned: 113 (million)
% 10.52/2.62 % (1580896)Instruction limit reached!
% 10.52/2.62 % (1580896)------------------------------
% 10.52/2.62 % (1580896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580896)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580896)Termination reason: Instruction limit
% 10.52/2.62 % (1580896)Termination phase: Saturation
% 10.52/2.62 % (1580896)Time elapsed: 0.066 s
% 10.52/2.62 % (1580896)Peak memory usage: 89 MB
% 10.52/2.62 % (1580896)Instructions burned: 114 (million)
% 10.52/2.62 % (1580901)lrs+10_1_sil=8000:sp=occurrence:random_seed=3912565853:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 10.52/2.62 % (1580902)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1552892235:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 10.52/2.62 % (1580903)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3946928841:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 10.52/2.62 % (1580902)Instruction limit reached!
% 10.52/2.62 % (1580902)------------------------------
% 10.52/2.62 % (1580902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580902)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580902)Termination reason: Instruction limit
% 10.52/2.62 % (1580902)Termination phase: Saturation
% 10.52/2.62 % (1580902)Time elapsed: 0.275 s
% 10.52/2.62 % (1580902)Peak memory usage: 92 MB
% 10.52/2.62 % (1580902)Instructions burned: 437 (million)
% 10.52/2.62 % (1580907)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2421399313:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 10.52/2.62 % (1580907)Instruction limit reached!
% 10.52/2.62 % (1580907)------------------------------
% 10.52/2.62 % (1580907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580907)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580907)Termination reason: Instruction limit
% 10.52/2.62 % (1580907)Termination phase: Saturation
% 10.52/2.62 % (1580907)Time elapsed: 0.079 s
% 10.52/2.62 % (1580907)Peak memory usage: 91 MB
% 10.52/2.62 % (1580907)Instructions burned: 135 (million)
% 10.52/2.62 % (1580901)Instruction limit reached!
% 10.52/2.62 % (1580901)------------------------------
% 10.52/2.62 % (1580901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.52/2.62 % (1580901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.52/2.62 % (1580901)CaDiCaL version: 2.1.3
% 10.52/2.62 % (1580901)Termination reason: Instruction limit
% 10.52/2.62 % (1580901)Termination phase: Saturation
% 10.52/2.62 % (1580901)Time elapsed: 0.553 s
% 10.52/2.62 % (1580901)Peak memory usage: 98 MB
% 10.52/2.62 % (1580901)Instructions burned: 908 (million)
% 10.52/2.62 % (1580871)First to succeed.
% 10.52/2.62 % (1580871)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1580864"
% 10.52/2.62 % (1580909)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3393621819:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 10.52/2.62 % (1580910)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4091355306:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 10.52/2.62 % (1580871)Refutation found. Thanks to Tanya!
% 10.52/2.62 % SZS status Theorem for theBenchmark
% 10.52/2.62 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/2.81 % (1580871)------------------------------
% 0.14/2.81 % (1580871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/2.81 % (1580871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/2.81 % (1580871)CaDiCaL version: 2.1.3
% 0.14/2.81 % (1580871)Termination reason: Refutation
% 0.14/2.81 % (1580871)Time elapsed: 1.424 s
% 0.14/2.81 % (1580871)Peak memory usage: 151 MB
% 0.14/2.81 % (1580871)Instructions burned: 3433 (million)
% 0.14/2.81 % (1580871)------------------------------
% 0.14/2.81 % (1580871)------------------------------
% 0.14/2.81 % (1580864)Success in time 1.761 s
% 0.14/2.81 % Vampire exiting
%------------------------------------------------------------------------------