%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM573+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 : n016.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 02:26:04 PM UTC 2026
% Result : Theorem 10.55s 2.30s
% Output : CNFRefutation 10.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 128 ( 21 unt; 2 def)
% Number of atoms : 590 ( 52 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 728 ( 266 ~; 262 |; 159 &)
% ( 7 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 193 ( 0 sgn 178 !; 15 ?; 58 :)
% 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(f33,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessSucc) ).
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(f36,axiom,
! [X0,X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTrans) ).
fof(f37,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).
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,
! [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)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f83,axiom,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3786) ).
fof(f84,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( iLess0(X0,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f85,conjecture,
( ( ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) )
& sdtlseqdt0(xj,xi) )
=> ( sdtlseqdt0(xj,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,sdtlpdtrp0(xN,xj)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f86,negated_conjecture,
~ ( ( ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) )
& sdtlseqdt0(xj,xi) )
=> ( sdtlseqdt0(xj,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> aElementOf0(X0,sdtlpdtrp0(xN,xj)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f85]) ).
fof(f89,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(f90,plain,
~ ( ( ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) )
& sdtlseqdt0(xj,xi) )
=> ( sdtlseqdt0(xj,xi)
=> ( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,sdtlpdtrp0(xN,xj)) ) ) ) ),
inference(rectify,[],[f86]) ).
fof(f103,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,[],[f89]) ).
fof(f104,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,[],[f103]) ).
fof(f105,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)) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ iLess0(X0,xi)
| ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ),
inference(ennf_transformation,[],[f84]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ iLess0(X0,xi)
| ( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1)) ) ) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
( ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) )
& sdtlseqdt0(xj,xi)
& sdtlseqdt0(xj,xi)
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& ? [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
& ~ aElementOf0(X1,sdtlpdtrp0(xN,xj)) ) ),
inference(ennf_transformation,[],[f90]) ).
fof(f109,plain,
( ? [X0] :
( szszuzczcdt0(X0) = xi
& aElementOf0(X0,szNzAzT0) )
& sdtlseqdt0(xj,xi)
& sdtlseqdt0(xj,xi)
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& ? [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
& ~ aElementOf0(X1,sdtlpdtrp0(xN,xj)) ) ),
inference(flattening,[],[f108]) ).
fof(f121,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f147,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f153,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f154,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f173,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f174,plain,
! [X0,X1,X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f173]) ).
fof(f175,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f176,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f175]) ).
fof(f230,plain,
! [X0] :
( ~ sP5(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)))
& sP4(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,[],[f206]) ).
fof(f231,plain,
! [X0] :
( ~ sP5(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)))
& sP4(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,[],[f230]) ).
fof(f235,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( aElementOf0(sK20(X0),sdtlpdtrp0(xN,X0))
& ~ aElementOf0(sK20(X0),szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| sP5(X0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X1,sK20(X0))],[f207]) ).
fof(f236,plain,
( ? [X1] :
( szszuzczcdt0(X1) = xi
& aElementOf0(X1,szNzAzT0) )
& sdtlseqdt0(xj,xi)
& sdtlseqdt0(xj,xi)
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& ? [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
& ~ aElementOf0(X0,sdtlpdtrp0(xN,xj)) ) ),
inference(rectify,[],[f109]) ).
fof(f237,plain,
( xi = szszuzczcdt0(sK22)
& aElementOf0(sK22,szNzAzT0)
& sdtlseqdt0(xj,xi)
& sdtlseqdt0(xj,xi)
& ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
& aElementOf0(sK21,sdtlpdtrp0(xN,xi))
& ~ aElementOf0(sK21,sdtlpdtrp0(xN,xj)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X0,sK21),skolemize(X1,sK22)],[f236]) ).
fof(f238,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,[],[f121]) ).
fof(f239,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,[],[f238]) ).
fof(f240,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,[],[f239]) ).
fof(f241,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK23(X0,X1),X1)
& ~ aElementOf0(sK23(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X2,sK23(X0,X1))],[f240]) ).
fof(f343,plain,
! [X0] :
( ~ sP5(X0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f231]) ).
fof(f346,plain,
! [X0] :
( ~ sP5(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f347,plain,
! [X0] :
( ~ sP5(X0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f231]) ).
fof(f354,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| sP5(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f355,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| aElementOf0(sK20(X0),sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f360,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f361,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f364,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f83]) ).
fof(f365,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[],[f83]) ).
fof(f367,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ iLess0(X0,xi)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f368,plain,
xi = szszuzczcdt0(sK22),
inference(cnf_transformation,[],[f237]) ).
fof(f369,plain,
aElementOf0(sK22,szNzAzT0),
inference(cnf_transformation,[],[f237]) ).
fof(f370,plain,
sdtlseqdt0(xj,xi),
inference(cnf_transformation,[],[f237]) ).
fof(f373,plain,
aElementOf0(sK21,sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[],[f237]) ).
fof(f374,plain,
~ aElementOf0(sK21,sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f237]) ).
fof(f383,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f423,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f147]) ).
fof(f431,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f432,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f455,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f174]) ).
fof(f456,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_108,plain,
! [X0: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f347]) ).
tcf(c_109,plain,
! [X0: $i] :
( sP4(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f346]) ).
tcf(c_112,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f343]) ).
tcf(c_122,plain,
! [X0: $i] :
( sP5(X0)
| aElementOf0(sK20(X0),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f355]) ).
tcf(c_123,plain,
! [X0: $i] :
( sP5(X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f354]) ).
tcf(c_126,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f361]) ).
tcf(c_127,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f360]) ).
tcf(c_128,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[],[f365]) ).
tcf(c_129,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f364]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X2))
| ~ iLess0(X1,xi)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X2,X1)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,X1)) ),
inference(cnf_transformation,[],[f367]) ).
tcf(c_132,negated_conjecture,
~ aElementOf0(sK21,sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f374]) ).
tcf(c_133,negated_conjecture,
aElementOf0(sK21,sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[],[f373]) ).
tcf(c_136,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(cnf_transformation,[],[f370]) ).
tcf(c_137,negated_conjecture,
aElementOf0(sK22,szNzAzT0),
inference(cnf_transformation,[],[f369]) ).
tcf(c_138,negated_conjecture,
szszuzczcdt0(sK22) = xi,
inference(cnf_transformation,[],[f368]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f383]) ).
tcf(c_187,plain,
! [X0: $i] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f423]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f431]) ).
tcf(c_196,plain,
! [X0: $i] :
( sdtlseqdt0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f432]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X0,X2)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f455]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f456]) ).
tcf(c_429,plain,
! [X0: $i] :
( sP5(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_122,c_127,c_126,c_123]) ).
tcf(c_3239,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_429,c_112]) ).
tcf(c_3240,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(unflattening,[status(thm)],[c_3239]) ).
tcf(c_3257,plain,
! [X0: $i,X1: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_429,c_108]) ).
tcf(c_3258,plain,
! [X0: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(unflattening,[status(thm)],[c_3257]) ).
tcf(c_3562,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X2,sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X3,X0)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| ( X0 != X1 )
| ( szszuzczcdt0(X1) != xi ) ),
inference(resolution_lifted,[status(thm)],[c_130,c_187]) ).
tcf(c_3563,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X1,sdtlpdtrp0(xN,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X2,X0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ( szszuzczcdt0(X0) != xi ) ),
inference(unflattening,[status(thm)],[c_3562]) ).
tcf(c_22655,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aElementOf0(sK22,szNzAzT0) ),
inference(superposition,[status(thm)],[c_138,c_3240]) ).
tcf(c_22659,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))),
inference(forward_subsumption_resolution,[status(thm)],[c_22655,c_137]) ).
tcf(c_22739,plain,
( sdtlseqdt0(sK22,xi)
| ~ aElementOf0(sK22,szNzAzT0) ),
inference(superposition,[status(thm)],[c_138,c_196]) ).
tcf(c_22740,plain,
sdtlseqdt0(sK22,xi),
inference(forward_subsumption_resolution,[status(thm)],[c_22739,c_137]) ).
tcf(c_25277,plain,
( aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aElementOf0(sK22,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_3258]) ).
tcf(c_25294,plain,
! [X0: $i] :
( sdtlseqdt0(xi,X0)
| sdtlseqdt0(X0,sK22)
| ~ aElementOf0(sK22,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_138,c_195]) ).
tcf(c_25297,plain,
! [X0: $i] :
( sdtlseqdt0(xi,X0)
| sdtlseqdt0(X0,sK22)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25294,c_137]) ).
tcf(c_25563,plain,
( sdtlseqdt0(xi,xj)
| sdtlseqdt0(xj,sK22) ),
inference(superposition,[status(thm)],[c_128,c_25297]) ).
tcf(c_27562,plain,
! [X0: $i] :
( aElementOf0(sK21,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sK21,sdtlpdtrp0(xN,xi))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),X0) ),
inference(instantiation,[status(thm)],[c_150]) ).
tcf(c_29907,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(sK22,szNzAzT0)
| ~ sdtlseqdt0(X1,sK22)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,sK22))
| ( szszuzczcdt0(sK22) != xi ) ),
inference(instantiation,[status(thm)],[c_3563]) ).
tcf(c_30618,plain,
( ( xj = xi )
| ~ sdtlseqdt0(xi,xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(superposition,[status(thm)],[c_136,c_220]) ).
tcf(c_30663,plain,
( sdtlseqdt0(xi,xj)
| ( xj = sK22 )
| ~ sdtlseqdt0(sK22,xj)
| ~ aElementOf0(sK22,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(superposition,[status(thm)],[c_25563,c_220]) ).
tcf(c_30693,plain,
( ( xj = xi )
| ~ sdtlseqdt0(xi,xj) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30618,c_129,c_128]) ).
tcf(c_30707,plain,
( sdtlseqdt0(xi,xj)
| ( xj = sK22 )
| ~ sdtlseqdt0(sK22,xj) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30663,c_137,c_128]) ).
tcf(c_33374,plain,
( aElementOf0(sK21,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aElementOf0(sK21,sdtlpdtrp0(xN,xi))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22))))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ),
inference(instantiation,[status(thm)],[c_27562]) ).
tcf(c_34892,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sK22,X1)
| ~ sdtlseqdt0(sK22,X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(superposition,[status(thm)],[c_137,c_219]) ).
tcf(c_35569,plain,
( aElementOf0(sK21,sdtlpdtrp0(xN,xj))
| ~ sdtlseqdt0(xj,sK22)
| ~ aElementOf0(sK22,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(sK21,sdtlpdtrp0(xN,sK22))
| ( szszuzczcdt0(sK22) != xi ) ),
inference(instantiation,[status(thm)],[c_29907]) ).
tcf(c_35939,plain,
! [X0: $i] :
( sdtlseqdt0(sK22,X0)
| ~ sdtlseqdt0(sK22,xi)
| ~ sdtlseqdt0(xi,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_129,c_34892]) ).
tcf(c_35971,plain,
! [X0: $i] :
( sdtlseqdt0(sK22,X0)
| ~ sdtlseqdt0(xi,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35939,c_22740]) ).
tcf(c_36213,plain,
( sdtlseqdt0(sK22,xj)
| ~ sdtlseqdt0(xi,xj) ),
inference(superposition,[status(thm)],[c_128,c_35971]) ).
fof(f205,definition,
! [X0] :
( ~ sP4(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,[sP4])],[predicate_definition_introduction]) ).
fof(f206,definition,
! [X0] :
( ~ sP5(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)))
& sP4(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,[sP5])],[predicate_definition_introduction]) ).
fof(f207,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)) ) )
| sP5(X0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(definition_folding,[],[f104,f206,f205]) ).
fof(f232,plain,
! [X0] :
( ~ sP4(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,[],[f205]) ).
fof(f233,plain,
! [X0] :
( ~ sP4(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,[],[f232]) ).
fof(f234,plain,
! [X0] :
( ~ sP4(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,[],[f233]) ).
fof(f351,plain,
! [X0,X1] :
( ~ sP4(X0)
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X1,sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sP4(X1)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(cnf_transformation,[],[f351]) ).
tcf(c_3166,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ sP5(X0)
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_109,c_116]) ).
tcf(c_3167,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ sP5(X1)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(unflattening,[status(thm)],[c_3166]) ).
tcf(c_3305,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_429,c_3167]) ).
tcf(c_3306,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(unflattening,[status(thm)],[c_3305]) ).
tcf(c_27270,plain,
! [X0: $i] :
( aElementOf0(X0,sdtlpdtrp0(xN,sK22))
| ~ aElementOf0(sK22,szNzAzT0)
| ~ aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ),
inference(instantiation,[status(thm)],[c_3306]) ).
tcf(c_33375,plain,
( aElementOf0(sK21,sdtlpdtrp0(xN,sK22))
| ~ aElementOf0(sK22,szNzAzT0)
| ~ aElementOf0(sK21,sdtmndt0(sdtlpdtrp0(xN,sK22),szmzizndt0(sdtlpdtrp0(xN,sK22)))) ),
inference(instantiation,[status(thm)],[c_27270]) ).
tcf(c_40313,plain,
sdtlseqdt0(sK22,xj),
inference(global_subsumption_just,[status(thm)],[c_36213,c_137,c_128,c_138,c_133,c_132,c_22659,c_25277,c_25563,c_33374,c_33375,c_35569,c_36213]) ).
tcf(c_40315,plain,
( sdtlseqdt0(xi,xj)
| ( xj = sK22 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_30707,c_40313]) ).
tcf(c_40352,plain,
sdtlseqdt0(xi,xj),
inference(global_subsumption_just,[status(thm)],[c_40315,c_137,c_128,c_138,c_133,c_132,c_22659,c_25277,c_25563,c_33374,c_33375,c_35569]) ).
tcf(c_40354,plain,
xj = xi,
inference(backward_subsumption_resolution,[status(thm)],[c_30693,c_40352]) ).
tcf(c_40375,plain,
~ aElementOf0(sK21,sdtlpdtrp0(xN,xi)),
inference(demodulation,[status(thm)],[c_132,c_40354]) ).
tcf(c_40377,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_40375,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM573+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 04:46:57 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 10.55/2.30 % SZS status Started for theBenchmark.p
% 10.55/2.30 % SZS status Theorem for theBenchmark.p
% 10.55/2.30
% 10.55/2.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.55/2.30
% 10.55/2.30 % ------ iProver source info
% 10.55/2.30
% 10.55/2.30 % git: date: 2026-07-19 20:42:38 +0200
% 10.55/2.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.55/2.30 % git: non_committed_changes: false
% 10.55/2.30
% 10.55/2.30 % ------ Parsing...
% 10.55/2.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.55/2.30
% 10.55/2.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 10.55/2.30
% 10.55/2.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.55/2.30
% 10.55/2.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.55/2.30 % ------ Proving...
% 10.55/2.30 % ------ Problem Properties
% 10.55/2.30
% 10.55/2.30 %
% 10.55/2.30 % clauses 222
% 10.55/2.30 % conjectures 6
% 10.55/2.30 % EPR 45
% 10.55/2.30 % Horn 168
% 10.55/2.30 % unary 33
% 10.55/2.30 % binary 50
% 10.55/2.30 % lits 728
% 10.55/2.30 % lits eq 103
% 10.55/2.30 % fd_pure 0
% 10.55/2.30 % fd_pseudo 0
% 10.55/2.30 % fd_cond 8
% 10.55/2.30 % fd_pseudo_cond 28
% 10.55/2.30 % AC symbols 0
% 10.55/2.30
% 10.55/2.30 % ------ Schedule dynamic 5 is on
% 10.55/2.30
% 10.55/2.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.55/2.30
% 10.55/2.30
% 10.55/2.30 % ------
% 10.55/2.30 % Current options:
% 10.55/2.30 % ------
% 10.55/2.30
% 10.55/2.30
% 10.55/2.30 %
% 10.55/2.30
% 10.55/2.30 % ------ Proving...
% 10.55/2.30 %
% 10.55/2.30
% 10.55/2.30 % SZS status Theorem for theBenchmark.p
% 10.55/2.30
% 10.55/2.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.59/2.30
% 10.59/2.30
%------------------------------------------------------------------------------