%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM570+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p 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 : Fri Sep 25 02:26:03 PM UTC 2026
% Result : Theorem 116.01s 16.72s
% Output : CNFRefutation 116.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 137 ( 17 unt; 2 def)
% Number of atoms : 599 ( 94 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 761 ( 299 ~; 284 |; 145 &)
% ( 7 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 171 ( 0 sgn 158 !; 13 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtra) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(f39,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH) ).
fof(f81,axiom,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,X0))
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f82,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3702) ).
fof(f83,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( iLess0(X0,xi)
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f84,conjecture,
( xi != sz00
=> ( isCountable0(sdtlpdtrp0(xN,xi))
& ( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,xi)) ) )
& ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f85,negated_conjecture,
~ ( xi != sz00
=> ( isCountable0(sdtlpdtrp0(xN,xi))
& ( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,xi)) ) )
& ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) ) ) ),
inference(negated_conjecture,[status(cth)],[f84]) ).
fof(f95,plain,
( ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(rectify,[],[f81]) ).
fof(f96,plain,
~ ( xi != sz00
=> ( isCountable0(sdtlpdtrp0(xN,xi))
& ( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,xi)) ) )
& ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) ) ) ),
inference(rectify,[],[f85]) ).
fof(f103,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f129,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(ennf_transformation,[],[f27]) ).
fof(f130,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(flattening,[],[f129]) ).
fof(f132,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f138,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f139,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f138]) ).
fof(f144,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f201,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
& ~ aElementOf0(X1,szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(ennf_transformation,[],[f95]) ).
fof(f202,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
& ~ aElementOf0(X1,szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(flattening,[],[f201]) ).
fof(f203,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,xi)
| ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f204,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,xi)
| ( isCountable0(sdtlpdtrp0(xN,X0))
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ),
inference(flattening,[],[f203]) ).
fof(f205,plain,
( xi != sz00
& ( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& ( ? [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
& ~ aElementOf0(X1,szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,xi)) ) )
| ! [X0] :
( szszuzczcdt0(X0) != xi
| ~ aElementOf0(X0,szNzAzT0) ) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f224,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f225,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f224]) ).
fof(f226,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f225]) ).
fof(f227,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK11(X0,X1),X1)
& ~ aElementOf0(sK11(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f226]) ).
fof(f240,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(sK14(X0)) = X0
& aElementOf0(sK14(X0),szNzAzT0) )
| X0 = sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f130]) ).
fof(f295,plain,
! [X0] :
( ~ sP9(X0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ),
inference(nnf_transformation,[],[f218]) ).
fof(f296,plain,
! [X0] :
( ~ sP9(X0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ),
inference(rectify,[],[f295]) ).
fof(f300,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0))
& ~ aElementOf0(sK39(X0),szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| sP9(X0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f219]) ).
fof(f301,plain,
( xi != sz00
& ( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& ( ( aElementOf0(sK40,sdtlpdtrp0(xN,xi))
& ~ aElementOf0(sK40,szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,xi)) ) )
| ! [X0] :
( szszuzczcdt0(X0) != xi
| ~ aElementOf0(X0,szNzAzT0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(X1,sK40)],[f205]) ).
fof(f309,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f227]) ).
fof(f310,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| aSet0(X1) ),
inference(cnf_transformation,[],[f227]) ).
fof(f349,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f353,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(sK14(X0)) = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f240]) ).
fof(f354,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sK14(X0),szNzAzT0)
| sz00 = X0 ),
inference(cnf_transformation,[],[f240]) ).
fof(f356,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f362,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f365,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f144]) ).
fof(f502,plain,
! [X0] :
( ~ sP9(X0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
! [X0] :
( ~ sP9(X0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
! [X0] :
( ~ sP9(X0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
! [X0] :
( ~ sP9(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
! [X0] :
( ~ sP9(X0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f296]) ).
fof(f514,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| sP9(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f520,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f82]) ).
fof(f521,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,xi)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f204]) ).
fof(f522,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,xi)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f523,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ iLess0(X0,xi)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f525,plain,
sz00 != xi,
inference(cnf_transformation,[],[f301]) ).
fof(f526,plain,
! [X0] :
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| szszuzczcdt0(X0) != xi
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f527,plain,
! [X0] :
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| aElementOf0(sK40,sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtlpdtrp0(xN,xi))
| szszuzczcdt0(X0) != xi
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f528,plain,
! [X0] :
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(sK40,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,xi))
| szszuzczcdt0(X0) != xi
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f301]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X0,X1) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_96,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f349]) ).
tcf(c_100,plain,
! [X0: $i] :
( aElementOf0(sK14(X0),szNzAzT0)
| ( X0 = sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f354]) ).
tcf(c_101,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( szszuzczcdt0(sK14(X0)) = X0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f353]) ).
tcf(c_103,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f356]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f362]) ).
tcf(c_112,plain,
! [X0: $i] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f365]) ).
tcf(c_251,plain,
! [X0: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_252,plain,
! [X0: $i] :
( sP8(X0)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_253,plain,
! [X0: $i] :
( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_255,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_256,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_266,plain,
! [X0: $i] :
( sP9(X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_267,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f520]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ iLess0(X1,xi)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,X1)) ),
inference(cnf_transformation,[],[f523]) ).
tcf(c_270,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ iLess0(X0,xi)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f522]) ).
tcf(c_271,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ iLess0(X0,xi)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f521]) ).
tcf(c_272,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(sK40,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ( szszuzczcdt0(X0) != xi ) ),
inference(cnf_transformation,[],[f528]) ).
tcf(c_273,negated_conjecture,
! [X0: $i] :
( aElementOf0(sK40,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ( szszuzczcdt0(X0) != xi ) ),
inference(cnf_transformation,[],[f527]) ).
tcf(c_274,negated_conjecture,
! [X0: $i] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ( szszuzczcdt0(X0) != xi ) ),
inference(cnf_transformation,[],[f526]) ).
tcf(c_275,negated_conjecture,
sz00 != xi,
inference(cnf_transformation,[],[f525]) ).
tcf(c_3835,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ( X0 != X1 )
| ( szszuzczcdt0(X0) != xi ) ),
inference(resolution_lifted,[status(thm)],[c_112,c_269]) ).
tcf(c_3836,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ( szszuzczcdt0(X0) != xi ) ),
inference(unflattening,[status(thm)],[c_3835]) ).
tcf(c_3849,plain,
! [X0: $i,X1: $i] :
( isCountable0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 )
| ( szszuzczcdt0(X0) != xi ) ),
inference(resolution_lifted,[status(thm)],[c_112,c_271]) ).
tcf(c_3850,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != xi ) ),
inference(unflattening,[status(thm)],[c_3849]) ).
tcf(c_3861,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 )
| ( szszuzczcdt0(X0) != xi ) ),
inference(resolution_lifted,[status(thm)],[c_112,c_270]) ).
tcf(c_3862,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != xi ) ),
inference(unflattening,[status(thm)],[c_3861]) ).
tcf(c_26905,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( szszuzczcdt0(X0) != xi )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_274]) ).
tcf(c_26907,negated_conjecture,
( iPr_def_10
| aElementOf0(sK40,sdtlpdtrp0(xN,xi))
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_273]) ).
tcf(c_26908,negated_conjecture,
( iPr_def_10
| ~ aElementOf0(sK40,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_272]) ).
tcf(c_26911,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_30335,plain,
( sdtlseqdt0(sz00,sz00)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_30353,plain,
( aElementOf0(sK14(xi),szNzAzT0)
| ( xi = sz00 )
| ~ aElementOf0(xi,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_30385,plain,
( ( xi = sz00 )
| ( szszuzczcdt0(sK14(xi)) = xi )
| ~ aElementOf0(xi,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_30592,plain,
! [X0: $i] :
( ( sz00 = xi )
| ( xi != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_26911]) ).
tcf(c_31557,plain,
( ( sz00 = sz00 )
| ~ sdtlseqdt0(sz00,sz00)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_32899,plain,
! [X0: $i] :
( iPr_def_10
| aElementOf0(sK40,X0)
| ~ aSet0(X0)
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),X0) ),
inference(superposition,[status(thm)],[c_26907,c_59]) ).
tcf(c_32948,plain,
( ( sz00 = xi )
| ( xi != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_30592]) ).
tcf(c_33181,plain,
! [X0: $i] :
( iPr_def_10
| aElementOf0(sK40,X0)
| ~ aSet0(X0)
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32899,c_58]) ).
tcf(c_33291,plain,
( ( sz00 = xi )
| ( szszuzczcdt0(sK14(xi)) = xi ) ),
inference(superposition,[status(thm)],[c_267,c_101]) ).
tcf(c_33296,plain,
szszuzczcdt0(sK14(xi)) = xi,
inference(forward_subsumption_resolution,[status(thm)],[c_33291,c_275]) ).
tcf(c_33583,plain,
( isCountable0(sdtlpdtrp0(xN,xi))
| ~ sP9(sK14(xi)) ),
inference(superposition,[status(thm)],[c_33296,c_256]) ).
tcf(c_33584,plain,
( aSet0(sdtlpdtrp0(xN,xi))
| ~ sP9(sK14(xi)) ),
inference(superposition,[status(thm)],[c_33296,c_253]) ).
tcf(c_33587,plain,
( ~ iPr_def_10
| ~ aElementOf0(sK14(xi),szNzAzT0) ),
inference(superposition,[status(thm)],[c_33296,c_26905]) ).
tcf(c_33589,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_33587,c_267,c_96,c_275,c_30335,c_30353,c_31557,c_32948,c_33587]) ).
tcf(c_33592,plain,
! [X0: $i] :
( aElementOf0(sK40,X0)
| ~ aSet0(X0)
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_33181,c_33589]) ).
tcf(c_33594,plain,
( ~ aElementOf0(sK40,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_26908,c_33589]) ).
tcf(c_33620,plain,
( ~ sP9(sK14(xi))
| ~ aElementOf0(sK40,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(superposition,[status(thm)],[c_33584,c_33594]) ).
tcf(c_33885,plain,
( ~ sP9(sK14(xi))
| ~ aElementOf0(sK40,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_33620,c_33583,c_33620]) ).
tcf(c_35101,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi)))))
| ~ sP9(sK14(xi)) ),
inference(superposition,[status(thm)],[c_33296,c_255]) ).
tcf(c_35359,plain,
( aElementOf0(sK40,sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi)))))
| ~ sP9(sK14(xi))
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi))))) ),
inference(superposition,[status(thm)],[c_35101,c_33592]) ).
tcf(c_35375,plain,
( aElementOf0(sK40,sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi)))))
| ~ sP9(sK14(xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi))))) ),
inference(global_subsumption_just,[status(thm)],[c_35359,c_33583,c_35359]) ).
tcf(c_39493,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK14(xi)),szNzAzT0)
| ~ aElementOf0(sK14(xi),szNzAzT0)
| ( szszuzczcdt0(sK14(xi)) != xi ) ),
inference(instantiation,[status(thm)],[c_3862]) ).
tcf(c_39494,plain,
( isCountable0(sdtlpdtrp0(xN,sK14(xi)))
| ~ aElementOf0(sK14(xi),szNzAzT0)
| ( szszuzczcdt0(sK14(xi)) != xi ) ),
inference(instantiation,[status(thm)],[c_3850]) ).
tcf(c_98593,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK14(xi),szNzAzT0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(xi)))
| ( szszuzczcdt0(sK14(xi)) != xi ) ),
inference(instantiation,[status(thm)],[c_3836]) ).
tcf(c_102105,plain,
( aElementOf0(sK40,szNzAzT0)
| ~ aElementOf0(sK14(xi),szNzAzT0)
| ~ aElementOf0(sK40,sdtlpdtrp0(xN,sK14(xi)))
| ( szszuzczcdt0(sK14(xi)) != xi ) ),
inference(instantiation,[status(thm)],[c_98593]) ).
tcf(c_107133,plain,
( sP9(sK14(xi))
| ~ aElementOf0(sK14(xi),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK14(xi)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK14(xi)),szNzAzT0) ),
inference(instantiation,[status(thm)],[c_266]) ).
tcf(c_142145,negated_conjecture,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_26905,c_267,c_96,c_275,c_30335,c_30353,c_31557,c_32948,c_33587]) ).
tcf(c_142148,plain,
( aElementOf0(sK40,sdtlpdtrp0(xN,xi))
| ~ isCountable0(sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_26907,c_142145]) ).
tcf(c_142154,plain,
aElementOf0(sK40,sdtlpdtrp0(xN,xi)),
inference(global_subsumption_just,[status(thm)],[c_142148,c_267,c_96,c_275,c_26907,c_30335,c_30353,c_30385,c_31557,c_32948,c_33587,c_33584,c_33583,c_39494,c_39493,c_107133]) ).
tcf(c_143117,plain,
! [X0: $i] :
( aElementOf0(sK40,X0)
| ~ aSet0(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),X0) ),
inference(superposition,[status(thm)],[c_142154,c_59]) ).
tcf(c_143184,plain,
( ( sz00 = xi )
| ( szszuzczcdt0(sK14(xi)) = xi ) ),
inference(superposition,[status(thm)],[c_267,c_101]) ).
tcf(c_143188,plain,
szszuzczcdt0(sK14(xi)) = xi,
inference(forward_subsumption_resolution,[status(thm)],[c_143184,c_275]) ).
tcf(c_143888,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi)))))
| ~ sP9(sK14(xi)) ),
inference(superposition,[status(thm)],[c_143188,c_255]) ).
tcf(c_143903,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi))))),
inference(global_subsumption_just,[status(thm)],[c_143888,c_267,c_96,c_275,c_30335,c_30353,c_30385,c_31557,c_32948,c_35101,c_39494,c_39493,c_107133]) ).
tcf(c_143907,plain,
( aElementOf0(sK40,sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi)))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi))))) ),
inference(superposition,[status(thm)],[c_143903,c_143117]) ).
fof(f217,definition,
! [X0] :
( ~ sP8(X0)
| ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f218,definition,
! [X0] :
( ~ sP9(X0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f219,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
& ~ aElementOf0(X1,szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| sP9(X0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(definition_folding,[],[f202,f218,f217]) ).
fof(f297,plain,
! [X0] :
( ~ sP8(X0)
| ! [X3] :
( ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3)
| aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ),
inference(nnf_transformation,[],[f217]) ).
fof(f298,plain,
! [X0] :
( ~ sP8(X0)
| ! [X3] :
( ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X3
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& aElement0(X3) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X3
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X0))
| ~ aElement0(X3)
| aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ),
inference(flattening,[],[f297]) ).
fof(f299,plain,
! [X0] :
( ~ sP8(X0)
| ! [X1] :
( ( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& aElement0(X1) ) )
& ( szmzizndt0(sdtlpdtrp0(xN,X0)) = X1
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ~ aElement0(X1)
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ),
inference(rectify,[],[f298]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sP8(X0)
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X1,sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f299]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sP8(X1)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_3606,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
| ~ sP9(X1)
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_259,c_252]) ).
tcf(c_3607,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sP9(X1)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(unflattening,[status(thm)],[c_3606]) ).
tcf(c_103055,plain,
( aElementOf0(sK40,sdtlpdtrp0(xN,sK14(xi)))
| ~ sP9(sK14(xi))
| ~ aElementOf0(sK40,sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi))))) ),
inference(instantiation,[status(thm)],[c_3607]) ).
tcf(c_143909,plain,
~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(xi)),szmzizndt0(sdtlpdtrp0(xN,sK14(xi))))),
inference(global_subsumption_just,[status(thm)],[c_143907,c_267,c_96,c_275,c_30335,c_30353,c_30385,c_31557,c_32948,c_33885,c_35375,c_39494,c_39493,c_102105,c_103055,c_107133]) ).
tcf(c_143911,plain,
~ sP9(sK14(xi)),
inference(superposition,[status(thm)],[c_251,c_143909]) ).
tcf(c_143913,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_143911,c_107133,c_39493,c_39494,c_32948,c_31557,c_30385,c_30353,c_30335,c_275,c_96,c_267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM570+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.60 % Computer : n008.cluster.edu
% 0.12/0.60 % Model : x86_64 x86_64
% 0.12/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.60 % Memory : 8046.5625MB
% 0.12/0.60 % OS : Linux 6.8.0-71-generic
% 0.12/0.60 % CPULimit : 300
% 0.12/0.60 % WCLimit : 300
% 0.12/0.60 % DateTime : Thu Sep 24 04:41:54 UTC 2026
% 0.12/0.60 % CPUTime :
% 0.12/0.60 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.64 Running first-order theorem proving
% 0.16/0.64 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.65
% 0.16/0.65 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.65
% 0.16/0.65 % Detected problem language: tptp
% 0.16/0.67 % Proving...
% 116.01/16.72 % SZS status Started for theBenchmark.p
% 116.01/16.72 % SZS status Theorem for theBenchmark.p
% 116.01/16.72
% 116.01/16.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 116.01/16.72
% 116.01/16.72 % ------ iProver source info
% 116.01/16.72
% 116.01/16.72 % git: date: 2026-07-19 20:42:38 +0200
% 116.01/16.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 116.01/16.72 % git: non_committed_changes: false
% 116.01/16.72
% 116.01/16.72 % ------ Parsing...
% 116.01/16.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 116.01/16.72
% 116.01/16.72 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 116.01/16.72
% 116.01/16.72 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 116.01/16.72
% 116.01/16.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 116.01/16.72 % ------ Proving...
% 116.01/16.72 % ------ Problem Properties
% 116.01/16.72
% 116.01/16.72 %
% 116.01/16.72 % clauses 223
% 116.01/16.72 % conjectures 5
% 116.01/16.72 % EPR 45
% 116.01/16.72 % Horn 171
% 116.01/16.72 % unary 27
% 116.01/16.72 % binary 43
% 116.01/16.72 % lits 765
% 116.01/16.72 % lits eq 109
% 116.01/16.72 % fd_pure 0
% 116.01/16.72 % fd_pseudo 0
% 116.01/16.72 % fd_cond 10
% 116.01/16.72 % fd_pseudo_cond 30
% 116.01/16.72 % AC symbols 0
% 116.01/16.72
% 116.01/16.72 % ------ Input Options Time Limit: Unbounded
% 116.01/16.72
% 116.01/16.72
% 116.01/16.72 % ------
% 116.01/16.72 % Current options:
% 116.01/16.72 % ------
% 116.01/16.72
% 116.01/16.72
% 116.01/16.72 %
% 116.01/16.72
% 116.01/16.72 % ------ Proving...
% 116.01/16.72 %
% 116.01/16.72
% 116.01/16.72 % SZS status Theorem for theBenchmark.p
% 116.01/16.72
% 116.01/16.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 116.01/16.72
% 116.01/16.72
%------------------------------------------------------------------------------