TSTP Solution File: NUM579+3 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : NUM579+3 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : n105.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 15:21:52 EST 2018
% Result : Theorem 13.41s
% Output : CNFRefutation 13.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 12
% Syntax : Number of formulae : 126 ( 26 unt; 0 def)
% Number of atoms : 953 ( 17 equ)
% Maximal formula atoms : 181 ( 7 avg)
% Number of connectives : 1253 ( 426 ~; 474 |; 307 &)
% ( 7 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 168 ( 0 sgn 138 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',mEOfElem) ).
fof(16,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',m__3671) ).
fof(19,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',mDefSub) ).
fof(46,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',mZeroNum) ).
fof(56,axiom,
( aElementOf0(xk,szNzAzT0)
& equal(szszuzczcdt0(xk),xK) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',m__3533) ).
fof(60,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',mZeroLess) ).
fof(62,axiom,
! [X1,X2] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X2,szNzAzT0) )
=> ( sdtlseqdt0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ) ) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',m__3754) ).
fof(63,axiom,
( aFunction0(xN)
& equal(szDzozmdt0(xN),szNzAzT0)
& equal(sdtlpdtrp0(xN,sz00),xS)
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X1)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X1))
& ~ equal(X2,szmzizndt0(sdtlpdtrp0(xN,X1))) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',m__3623) ).
fof(70,axiom,
( aSet0(xS)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',m__3435) ).
fof(78,axiom,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> equal(sbrdtbr0(sdtpldt0(X1,X2)),szszuzczcdt0(sbrdtbr0(X1))) ) ) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',mCardCons) ).
fof(81,conjecture,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aSet0(X2)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1))
& ~ equal(X3,szmzizndt0(sdtlpdtrp0(xN,X1))) ) )
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& equal(sbrdtbr0(X2),xk)
& aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) ) )
=> ( ( aSet0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X3)
& ( aElementOf0(X3,X2)
| equal(X3,szmzizndt0(sdtlpdtrp0(xN,X1))) ) ) ) )
=> ( ( ( ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
=> aElementOf0(X3,xS) )
| aSubsetOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),xS) )
& equal(sbrdtbr0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))),xK) )
| aElementOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),slbdtsldtrb0(xS,xK)) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',m__) ).
fof(83,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1',mCardNum) ).
fof(86,negated_conjecture,
~ ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aSet0(X2)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1))
& ~ equal(X3,szmzizndt0(sdtlpdtrp0(xN,X1))) ) )
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& equal(sbrdtbr0(X2),xk)
& aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) ) )
=> ( ( aSet0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X3)
& ( aElementOf0(X3,X2)
| equal(X3,szmzizndt0(sdtlpdtrp0(xN,X1))) ) ) ) )
=> ( ( ( ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
=> aElementOf0(X3,xS) )
| aSubsetOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),xS) )
& equal(sbrdtbr0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))),xK) )
| aElementOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),slbdtsldtrb0(xS,xK)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[81]) ).
fof(91,plain,
! [X1] :
( ( aSet0(X1)
& isFinite0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> equal(sbrdtbr0(sdtpldt0(X1,X2)),szszuzczcdt0(sbrdtbr0(X1))) ) ) ),
inference(fof_simplification,[status(thm)],[78,theory(equality)]) ).
fof(99,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ~ aElementOf0(X2,X1)
| aElement0(X2) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(100,plain,
! [X3] :
( ~ aSet0(X3)
| ! [X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4) ) ),
inference(variable_rename,[status(thm)],[99]) ).
fof(101,plain,
! [X3,X4] :
( ~ aElementOf0(X4,X3)
| aElement0(X4)
| ~ aSet0(X3) ),
inference(shift_quantors,[status(thm)],[100]) ).
cnf(102,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[101]) ).
fof(176,plain,
! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,X1))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| aElementOf0(X2,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X1)) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(177,plain,
! [X3] :
( ~ aElementOf0(X3,szNzAzT0)
| ( aSet0(sdtlpdtrp0(xN,X3))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,X3))
| aElementOf0(X4,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X3)) ) ),
inference(variable_rename,[status(thm)],[176]) ).
fof(178,plain,
! [X3,X4] :
( ( ( ~ aElementOf0(X4,sdtlpdtrp0(xN,X3))
| aElementOf0(X4,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X3))
& aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X3)) )
| ~ aElementOf0(X3,szNzAzT0) ),
inference(shift_quantors,[status(thm)],[177]) ).
fof(179,plain,
! [X3,X4] :
( ( ~ aElementOf0(X4,sdtlpdtrp0(xN,X3))
| aElementOf0(X4,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0) )
& ( aSet0(sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0) )
& ( isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X3,szNzAzT0) ) ),
inference(distribute,[status(thm)],[178]) ).
cnf(182,plain,
( aSet0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[179]) ).
fof(192,plain,
! [X1] :
( ~ aSet0(X1)
| ! [X2] :
( ( ~ aSubsetOf0(X2,X1)
| ( aSet0(X2)
& ! [X3] :
( ~ aElementOf0(X3,X2)
| aElementOf0(X3,X1) ) ) )
& ( ~ aSet0(X2)
| ? [X3] :
( aElementOf0(X3,X2)
& ~ aElementOf0(X3,X1) )
| aSubsetOf0(X2,X1) ) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(193,plain,
! [X4] :
( ~ aSet0(X4)
| ! [X5] :
( ( ~ aSubsetOf0(X5,X4)
| ( aSet0(X5)
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X4) ) ) )
& ( ~ aSet0(X5)
| ? [X7] :
( aElementOf0(X7,X5)
& ~ aElementOf0(X7,X4) )
| aSubsetOf0(X5,X4) ) ) ),
inference(variable_rename,[status(thm)],[192]) ).
fof(194,plain,
! [X4] :
( ~ aSet0(X4)
| ! [X5] :
( ( ~ aSubsetOf0(X5,X4)
| ( aSet0(X5)
& ! [X6] :
( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X4) ) ) )
& ( ~ aSet0(X5)
| ( aElementOf0(esk6_2(X4,X5),X5)
& ~ aElementOf0(esk6_2(X4,X5),X4) )
| aSubsetOf0(X5,X4) ) ) ),
inference(skolemize,[status(esa)],[193]) ).
fof(195,plain,
! [X4,X5,X6] :
( ( ( ( ( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X4) )
& aSet0(X5) )
| ~ aSubsetOf0(X5,X4) )
& ( ~ aSet0(X5)
| ( aElementOf0(esk6_2(X4,X5),X5)
& ~ aElementOf0(esk6_2(X4,X5),X4) )
| aSubsetOf0(X5,X4) ) )
| ~ aSet0(X4) ),
inference(shift_quantors,[status(thm)],[194]) ).
fof(196,plain,
! [X4,X5,X6] :
( ( ~ aElementOf0(X6,X5)
| aElementOf0(X6,X4)
| ~ aSubsetOf0(X5,X4)
| ~ aSet0(X4) )
& ( aSet0(X5)
| ~ aSubsetOf0(X5,X4)
| ~ aSet0(X4) )
& ( aElementOf0(esk6_2(X4,X5),X5)
| ~ aSet0(X5)
| aSubsetOf0(X5,X4)
| ~ aSet0(X4) )
& ( ~ aElementOf0(esk6_2(X4,X5),X4)
| ~ aSet0(X5)
| aSubsetOf0(X5,X4)
| ~ aSet0(X4) ) ),
inference(distribute,[status(thm)],[195]) ).
cnf(200,plain,
( aElementOf0(X3,X1)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X1)
| ~ aElementOf0(X3,X2) ),
inference(split_conjunct,[status(thm)],[196]) ).
cnf(4290,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[46]) ).
cnf(4339,plain,
szszuzczcdt0(xk) = xK,
inference(split_conjunct,[status(thm)],[56]) ).
cnf(4340,plain,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[56]) ).
fof(4363,plain,
! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(sz00,X1) ),
inference(fof_nnf,[status(thm)],[60]) ).
fof(4364,plain,
! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| sdtlseqdt0(sz00,X2) ),
inference(variable_rename,[status(thm)],[4363]) ).
cnf(4365,plain,
( sdtlseqdt0(sz00,X1)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[4364]) ).
fof(4369,plain,
! [X1,X2] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X2,X1)
| ( ! [X3] :
( ~ aElementOf0(X3,sdtlpdtrp0(xN,X1))
| aElementOf0(X3,sdtlpdtrp0(xN,X2)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ) ),
inference(fof_nnf,[status(thm)],[62]) ).
fof(4370,plain,
! [X4,X5] :
( ~ aElementOf0(X4,szNzAzT0)
| ~ aElementOf0(X5,szNzAzT0)
| ~ sdtlseqdt0(X5,X4)
| ( ! [X6] :
( ~ aElementOf0(X6,sdtlpdtrp0(xN,X4))
| aElementOf0(X6,sdtlpdtrp0(xN,X5)) )
& aSubsetOf0(sdtlpdtrp0(xN,X4),sdtlpdtrp0(xN,X5)) ) ),
inference(variable_rename,[status(thm)],[4369]) ).
fof(4371,plain,
! [X4,X5,X6] :
( ( ( ~ aElementOf0(X6,sdtlpdtrp0(xN,X4))
| aElementOf0(X6,sdtlpdtrp0(xN,X5)) )
& aSubsetOf0(sdtlpdtrp0(xN,X4),sdtlpdtrp0(xN,X5)) )
| ~ sdtlseqdt0(X5,X4)
| ~ aElementOf0(X4,szNzAzT0)
| ~ aElementOf0(X5,szNzAzT0) ),
inference(shift_quantors,[status(thm)],[4370]) ).
fof(4372,plain,
! [X4,X5,X6] :
( ( ~ aElementOf0(X6,sdtlpdtrp0(xN,X4))
| aElementOf0(X6,sdtlpdtrp0(xN,X5))
| ~ sdtlseqdt0(X5,X4)
| ~ aElementOf0(X4,szNzAzT0)
| ~ aElementOf0(X5,szNzAzT0) )
& ( aSubsetOf0(sdtlpdtrp0(xN,X4),sdtlpdtrp0(xN,X5))
| ~ sdtlseqdt0(X5,X4)
| ~ aElementOf0(X4,szNzAzT0)
| ~ aElementOf0(X5,szNzAzT0) ) ),
inference(distribute,[status(thm)],[4371]) ).
cnf(4373,plain,
( aSubsetOf0(sdtlpdtrp0(xN,X2),sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[4372]) ).
fof(4375,plain,
( aFunction0(xN)
& equal(szDzozmdt0(xN),szNzAzT0)
& equal(sdtlpdtrp0(xN,sz00),xS)
& ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X1))
| ? [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
& ~ aElementOf0(X2,szNzAzT0) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X1))
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( ( ~ aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X1))
& ~ equal(X2,szmzizndt0(sdtlpdtrp0(xN,X1))) ) )
& ( ~ aElement0(X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| equal(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ) ) ),
inference(fof_nnf,[status(thm)],[63]) ).
fof(4376,plain,
( aFunction0(xN)
& equal(szDzozmdt0(xN),szNzAzT0)
& equal(sdtlpdtrp0(xN,sz00),xS)
& ! [X3] :
( ~ aElementOf0(X3,szNzAzT0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X3))
| ? [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X3))
& ~ aElementOf0(X4,szNzAzT0) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X3)),sdtlpdtrp0(xN,X3))
& ! [X5] :
( ~ aElementOf0(X5,sdtlpdtrp0(xN,X3))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X3)),X5) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
& ! [X6] :
( ( ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ( aElement0(X6)
& aElementOf0(X6,sdtlpdtrp0(xN,X3))
& ~ equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3))) ) )
& ( ~ aElement0(X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X3))
| equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3)))
| aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3)))) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X3)))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X3)),sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X3))) ) ) ),
inference(variable_rename,[status(thm)],[4375]) ).
fof(4377,plain,
( aFunction0(xN)
& equal(szDzozmdt0(xN),szNzAzT0)
& equal(sdtlpdtrp0(xN,sz00),xS)
& ! [X3] :
( ~ aElementOf0(X3,szNzAzT0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X3))
| ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
& ~ aElementOf0(esk28_1(X3),szNzAzT0) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X3)),sdtlpdtrp0(xN,X3))
& ! [X5] :
( ~ aElementOf0(X5,sdtlpdtrp0(xN,X3))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X3)),X5) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
& ! [X6] :
( ( ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ( aElement0(X6)
& aElementOf0(X6,sdtlpdtrp0(xN,X3))
& ~ equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3))) ) )
& ( ~ aElement0(X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X3))
| equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3)))
| aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3)))) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X3)))
& ! [X7] :
( ~ aElementOf0(X7,sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X3)),sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X3))) ) ) ),
inference(skolemize,[status(esa)],[4376]) ).
fof(4378,plain,
! [X3,X5,X6,X7] :
( ( ( ( ~ aElementOf0(X7,sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3)))) )
& ( ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ( aElement0(X6)
& aElementOf0(X6,sdtlpdtrp0(xN,X3))
& ~ equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3))) ) )
& ( ~ aElement0(X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X3))
| equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3)))
| aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3)))) )
& ( ~ aElementOf0(X5,sdtlpdtrp0(xN,X3))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X3)),X5) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X3)),sdtlpdtrp0(xN,X3))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X3)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X3)),sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X3))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X3))
| ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
& ~ aElementOf0(esk28_1(X3),szNzAzT0) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X3,szNzAzT0) )
& aFunction0(xN)
& equal(szDzozmdt0(xN),szNzAzT0)
& equal(sdtlpdtrp0(xN,sz00),xS) ),
inference(shift_quantors,[status(thm)],[4377]) ).
fof(4379,plain,
! [X3,X5,X6,X7] :
( ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X7,sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X7,sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X7,sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aElement0(X6)
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aElementOf0(X6,sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aElementOf0(X6,sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aElementOf0(X6,sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3)))
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3)))
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3)))
| ~ aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X3))
| equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3)))
| aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X3))
| equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3)))
| aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElement0(X6)
| ~ aElementOf0(X6,sdtlpdtrp0(xN,X3))
| equal(X6,szmzizndt0(sdtlpdtrp0(xN,X3)))
| aElementOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X3))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X3)),X5)
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X3))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X3)),X5)
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X3))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X3)),X5)
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X3)),sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X3)),sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X3)),sdtlpdtrp0(xN,X3))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X3)),sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X3)),sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X3)),sdtmndt0(sdtlpdtrp0(xN,X3),szmzizndt0(sdtlpdtrp0(xN,X3))))
| ~ aElementOf0(X3,szNzAzT0) )
& ( aElementOf0(esk28_1(X3),sdtlpdtrp0(xN,X3))
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aElementOf0(esk28_1(X3),szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,X3))
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| ~ aElementOf0(X3,szNzAzT0) )
& ( ~ aSubsetOf0(sdtlpdtrp0(xN,X3),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X3))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X3)))
| ~ aElementOf0(X3,szNzAzT0) )
& aFunction0(xN)
& equal(szDzozmdt0(xN),szNzAzT0)
& equal(sdtlpdtrp0(xN,sz00),xS) ),
inference(distribute,[status(thm)],[4378]) ).
cnf(4380,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[4379]) ).
fof(4442,plain,
( aSet0(xS)
& ! [X1] :
( ~ aElementOf0(X1,xS)
| aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(fof_nnf,[status(thm)],[70]) ).
fof(4443,plain,
( aSet0(xS)
& ! [X2] :
( ~ aElementOf0(X2,xS)
| aElementOf0(X2,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(variable_rename,[status(thm)],[4442]) ).
fof(4444,plain,
! [X2] :
( ( ~ aElementOf0(X2,xS)
| aElementOf0(X2,szNzAzT0) )
& aSet0(xS)
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(shift_quantors,[status(thm)],[4443]) ).
cnf(4447,plain,
aSet0(xS),
inference(split_conjunct,[status(thm)],[4444]) ).
fof(4481,plain,
! [X1] :
( ~ aSet0(X1)
| ~ isFinite0(X1)
| ! [X2] :
( ~ aElement0(X2)
| aElementOf0(X2,X1)
| equal(sbrdtbr0(sdtpldt0(X1,X2)),szszuzczcdt0(sbrdtbr0(X1))) ) ),
inference(fof_nnf,[status(thm)],[91]) ).
fof(4482,plain,
! [X3] :
( ~ aSet0(X3)
| ~ isFinite0(X3)
| ! [X4] :
( ~ aElement0(X4)
| aElementOf0(X4,X3)
| equal(sbrdtbr0(sdtpldt0(X3,X4)),szszuzczcdt0(sbrdtbr0(X3))) ) ),
inference(variable_rename,[status(thm)],[4481]) ).
fof(4483,plain,
! [X3,X4] :
( ~ aElement0(X4)
| aElementOf0(X4,X3)
| equal(sbrdtbr0(sdtpldt0(X3,X4)),szszuzczcdt0(sbrdtbr0(X3)))
| ~ aSet0(X3)
| ~ isFinite0(X3) ),
inference(shift_quantors,[status(thm)],[4482]) ).
cnf(4484,plain,
( sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| aElementOf0(X2,X1)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[4483]) ).
fof(4491,negated_conjecture,
? [X1] :
( aElementOf0(X1,szNzAzT0)
& ? [X2] :
( aSet0(X2)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X3] :
( ~ aElementOf0(X3,sdtlpdtrp0(xN,X1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( ( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1))
& ~ equal(X3,szmzizndt0(sdtlpdtrp0(xN,X1))) ) )
& ( ~ aElement0(X3)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X1))
| equal(X3,szmzizndt0(sdtlpdtrp0(xN,X1)))
| aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ) )
& ! [X3] :
( ~ aElementOf0(X3,X2)
| aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& equal(sbrdtbr0(X2),xk)
& aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X3] :
( ~ aElementOf0(X3,sdtlpdtrp0(xN,X1))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aSet0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( ( ~ aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
| ( aElement0(X3)
& ( aElementOf0(X3,X2)
| equal(X3,szmzizndt0(sdtlpdtrp0(xN,X1))) ) ) )
& ( ~ aElement0(X3)
| ( ~ aElementOf0(X3,X2)
& ~ equal(X3,szmzizndt0(sdtlpdtrp0(xN,X1))) )
| aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))) ) )
& ( ( ? [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
& ~ aElementOf0(X3,xS) )
& ~ aSubsetOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),xS) )
| ~ equal(sbrdtbr0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))),xK) )
& ~ aElementOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),slbdtsldtrb0(xS,xK)) ) ),
inference(fof_nnf,[status(thm)],[86]) ).
fof(4492,negated_conjecture,
? [X4] :
( aElementOf0(X4,szNzAzT0)
& ? [X5] :
( aSet0(X5)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X4)),sdtlpdtrp0(xN,X4))
& ! [X6] :
( ~ aElementOf0(X6,sdtlpdtrp0(xN,X4))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X4)),X6) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X4),szmzizndt0(sdtlpdtrp0(xN,X4))))
& ! [X7] :
( ( ~ aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X4),szmzizndt0(sdtlpdtrp0(xN,X4))))
| ( aElement0(X7)
& aElementOf0(X7,sdtlpdtrp0(xN,X4))
& ~ equal(X7,szmzizndt0(sdtlpdtrp0(xN,X4))) ) )
& ( ~ aElement0(X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X4))
| equal(X7,szmzizndt0(sdtlpdtrp0(xN,X4)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,X4),szmzizndt0(sdtlpdtrp0(xN,X4)))) ) )
& ! [X8] :
( ~ aElementOf0(X8,X5)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X4),szmzizndt0(sdtlpdtrp0(xN,X4)))) )
& aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X4),szmzizndt0(sdtlpdtrp0(xN,X4))))
& equal(sbrdtbr0(X5),xk)
& aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X4),szmzizndt0(sdtlpdtrp0(xN,X4))),xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X4)),sdtlpdtrp0(xN,X4))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,X4))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X4)),X9) )
& aSet0(sdtpldt0(X5,szmzizndt0(sdtlpdtrp0(xN,X4))))
& ! [X10] :
( ( ~ aElementOf0(X10,sdtpldt0(X5,szmzizndt0(sdtlpdtrp0(xN,X4))))
| ( aElement0(X10)
& ( aElementOf0(X10,X5)
| equal(X10,szmzizndt0(sdtlpdtrp0(xN,X4))) ) ) )
& ( ~ aElement0(X10)
| ( ~ aElementOf0(X10,X5)
& ~ equal(X10,szmzizndt0(sdtlpdtrp0(xN,X4))) )
| aElementOf0(X10,sdtpldt0(X5,szmzizndt0(sdtlpdtrp0(xN,X4)))) ) )
& ( ( ? [X11] :
( aElementOf0(X11,sdtpldt0(X5,szmzizndt0(sdtlpdtrp0(xN,X4))))
& ~ aElementOf0(X11,xS) )
& ~ aSubsetOf0(sdtpldt0(X5,szmzizndt0(sdtlpdtrp0(xN,X4))),xS) )
| ~ equal(sbrdtbr0(sdtpldt0(X5,szmzizndt0(sdtlpdtrp0(xN,X4)))),xK) )
& ~ aElementOf0(sdtpldt0(X5,szmzizndt0(sdtlpdtrp0(xN,X4))),slbdtsldtrb0(xS,xK)) ) ),
inference(variable_rename,[status(thm)],[4491]) ).
fof(4493,negated_conjecture,
( aElementOf0(esk31_0,szNzAzT0)
& aSet0(esk32_0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtlpdtrp0(xN,esk31_0))
& ! [X6] :
( ~ aElementOf0(X6,sdtlpdtrp0(xN,esk31_0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),X6) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& ! [X7] :
( ( ~ aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| ( aElement0(X7)
& aElementOf0(X7,sdtlpdtrp0(xN,esk31_0))
& ~ equal(X7,szmzizndt0(sdtlpdtrp0(xN,esk31_0))) ) )
& ( ~ aElement0(X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,esk31_0))
| equal(X7,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) ) )
& ! [X8] :
( ~ aElementOf0(X8,esk32_0)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& aSubsetOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& equal(sbrdtbr0(esk32_0),xk)
& aElementOf0(esk32_0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))),xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtlpdtrp0(xN,esk31_0))
& ! [X9] :
( ~ aElementOf0(X9,sdtlpdtrp0(xN,esk31_0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),X9) )
& aSet0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& ! [X10] :
( ( ~ aElementOf0(X10,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| ( aElement0(X10)
& ( aElementOf0(X10,esk32_0)
| equal(X10,szmzizndt0(sdtlpdtrp0(xN,esk31_0))) ) ) )
& ( ~ aElement0(X10)
| ( ~ aElementOf0(X10,esk32_0)
& ~ equal(X10,szmzizndt0(sdtlpdtrp0(xN,esk31_0))) )
| aElementOf0(X10,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) ) )
& ( ( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& ~ aElementOf0(esk33_0,xS)
& ~ aSubsetOf0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))),xS) )
| ~ equal(sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))),xK) )
& ~ aElementOf0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))),slbdtsldtrb0(xS,xK)) ),
inference(skolemize,[status(esa)],[4492]) ).
fof(4494,negated_conjecture,
! [X6,X7,X8,X9,X10] :
( ( ~ aElementOf0(X10,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| ( aElement0(X10)
& ( aElementOf0(X10,esk32_0)
| equal(X10,szmzizndt0(sdtlpdtrp0(xN,esk31_0))) ) ) )
& ( ~ aElement0(X10)
| ( ~ aElementOf0(X10,esk32_0)
& ~ equal(X10,szmzizndt0(sdtlpdtrp0(xN,esk31_0))) )
| aElementOf0(X10,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& aSet0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& ( ( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& ~ aElementOf0(esk33_0,xS)
& ~ aSubsetOf0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))),xS) )
| ~ equal(sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))),xK) )
& ~ aElementOf0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))),slbdtsldtrb0(xS,xK))
& ( ~ aElementOf0(X9,sdtlpdtrp0(xN,esk31_0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),X9) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtlpdtrp0(xN,esk31_0))
& ( ~ aElementOf0(X8,esk32_0)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( ~ aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| ( aElement0(X7)
& aElementOf0(X7,sdtlpdtrp0(xN,esk31_0))
& ~ equal(X7,szmzizndt0(sdtlpdtrp0(xN,esk31_0))) ) )
& ( ~ aElement0(X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,esk31_0))
| equal(X7,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( ~ aElementOf0(X6,sdtlpdtrp0(xN,esk31_0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),X6) )
& aSet0(esk32_0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtlpdtrp0(xN,esk31_0))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& aSubsetOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& equal(sbrdtbr0(esk32_0),xk)
& aElementOf0(esk32_0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))),xk))
& aElementOf0(esk31_0,szNzAzT0) ),
inference(shift_quantors,[status(thm)],[4493]) ).
fof(4495,negated_conjecture,
! [X6,X7,X8,X9,X10] :
( ( aElement0(X10)
| ~ aElementOf0(X10,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( aElementOf0(X10,esk32_0)
| equal(X10,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ aElementOf0(X10,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( ~ aElementOf0(X10,esk32_0)
| ~ aElement0(X10)
| aElementOf0(X10,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( ~ equal(X10,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ aElement0(X10)
| aElementOf0(X10,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& aSet0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& ( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| ~ equal(sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))),xK) )
& ( ~ aElementOf0(esk33_0,xS)
| ~ equal(sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))),xK) )
& ( ~ aSubsetOf0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))),xS)
| ~ equal(sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))),xK) )
& ~ aElementOf0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))),slbdtsldtrb0(xS,xK))
& ( ~ aElementOf0(X9,sdtlpdtrp0(xN,esk31_0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),X9) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtlpdtrp0(xN,esk31_0))
& ( ~ aElementOf0(X8,esk32_0)
| aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( aElement0(X7)
| ~ aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( aElementOf0(X7,sdtlpdtrp0(xN,esk31_0))
| ~ aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( ~ equal(X7,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( ~ aElement0(X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,esk31_0))
| equal(X7,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| aElementOf0(X7,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) )
& ( ~ aElementOf0(X6,sdtlpdtrp0(xN,esk31_0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),X6) )
& aSet0(esk32_0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtlpdtrp0(xN,esk31_0))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& aSubsetOf0(esk32_0,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
& equal(sbrdtbr0(esk32_0),xk)
& aElementOf0(esk32_0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))),xk))
& aElementOf0(esk31_0,szNzAzT0) ),
inference(distribute,[status(thm)],[4494]) ).
cnf(4496,negated_conjecture,
aElementOf0(esk31_0,szNzAzT0),
inference(split_conjunct,[status(thm)],[4495]) ).
cnf(4498,negated_conjecture,
sbrdtbr0(esk32_0) = xk,
inference(split_conjunct,[status(thm)],[4495]) ).
cnf(4501,negated_conjecture,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtlpdtrp0(xN,esk31_0)),
inference(split_conjunct,[status(thm)],[4495]) ).
cnf(4502,negated_conjecture,
aSet0(esk32_0),
inference(split_conjunct,[status(thm)],[4495]) ).
cnf(4505,negated_conjecture,
( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| X1 != szmzizndt0(sdtlpdtrp0(xN,esk31_0)) ),
inference(split_conjunct,[status(thm)],[4495]) ).
cnf(4506,negated_conjecture,
( aElementOf0(X1,sdtlpdtrp0(xN,esk31_0))
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) ),
inference(split_conjunct,[status(thm)],[4495]) ).
cnf(4508,negated_conjecture,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| ~ aElementOf0(X1,esk32_0) ),
inference(split_conjunct,[status(thm)],[4495]) ).
cnf(4513,negated_conjecture,
( sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) != xK
| ~ aElementOf0(esk33_0,xS) ),
inference(split_conjunct,[status(thm)],[4495]) ).
cnf(4514,negated_conjecture,
( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) != xK ),
inference(split_conjunct,[status(thm)],[4495]) ).
cnf(4518,negated_conjecture,
( X1 = szmzizndt0(sdtlpdtrp0(xN,esk31_0))
| aElementOf0(X1,esk32_0)
| ~ aElementOf0(X1,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) ),
inference(split_conjunct,[status(thm)],[4495]) ).
fof(4523,plain,
! [X1] :
( ~ aSet0(X1)
| ( ( ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| isFinite0(X1) )
& ( ~ isFinite0(X1)
| aElementOf0(sbrdtbr0(X1),szNzAzT0) ) ) ),
inference(fof_nnf,[status(thm)],[83]) ).
fof(4524,plain,
! [X2] :
( ~ aSet0(X2)
| ( ( ~ aElementOf0(sbrdtbr0(X2),szNzAzT0)
| isFinite0(X2) )
& ( ~ isFinite0(X2)
| aElementOf0(sbrdtbr0(X2),szNzAzT0) ) ) ),
inference(variable_rename,[status(thm)],[4523]) ).
fof(4525,plain,
! [X2] :
( ( ~ aElementOf0(sbrdtbr0(X2),szNzAzT0)
| isFinite0(X2)
| ~ aSet0(X2) )
& ( ~ isFinite0(X2)
| aElementOf0(sbrdtbr0(X2),szNzAzT0)
| ~ aSet0(X2) ) ),
inference(distribute,[status(thm)],[4524]) ).
cnf(4527,plain,
( isFinite0(X1)
| ~ aSet0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[4525]) ).
cnf(4567,negated_conjecture,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ aSet0(sdtlpdtrp0(xN,esk31_0)) ),
inference(spm,[status(thm)],[102,4501,theory(equality)]) ).
cnf(4571,negated_conjecture,
sdtlseqdt0(sz00,esk31_0),
inference(spm,[status(thm)],[4365,4496,theory(equality)]) ).
cnf(4581,negated_conjecture,
aSet0(sdtlpdtrp0(xN,esk31_0)),
inference(spm,[status(thm)],[182,4496,theory(equality)]) ).
cnf(4693,negated_conjecture,
( isFinite0(esk32_0)
| ~ aElementOf0(xk,szNzAzT0)
| ~ aSet0(esk32_0) ),
inference(spm,[status(thm)],[4527,4498,theory(equality)]) ).
cnf(4694,negated_conjecture,
( isFinite0(esk32_0)
| $false
| ~ aSet0(esk32_0) ),
inference(rw,[status(thm)],[4693,4340,theory(equality)]) ).
cnf(4695,negated_conjecture,
( isFinite0(esk32_0)
| $false
| $false ),
inference(rw,[status(thm)],[4694,4502,theory(equality)]) ).
cnf(4696,negated_conjecture,
isFinite0(esk32_0),
inference(cn,[status(thm)],[4695,theory(equality)]) ).
cnf(4965,negated_conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,esk31_0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,esk31_0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(spm,[status(thm)],[4373,4496,theory(equality)]) ).
cnf(5118,negated_conjecture,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))),
inference(er,[status(thm)],[4505,theory(equality)]) ).
cnf(5237,negated_conjecture,
( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| szszuzczcdt0(sbrdtbr0(esk32_0)) != xK
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ isFinite0(esk32_0)
| ~ aSet0(esk32_0) ),
inference(spm,[status(thm)],[4514,4484,theory(equality)]) ).
cnf(5243,negated_conjecture,
( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ isFinite0(esk32_0)
| ~ aSet0(esk32_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[5237,4498,theory(equality)]),4339,theory(equality)]) ).
cnf(5244,negated_conjecture,
( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ isFinite0(esk32_0)
| $false ),
inference(rw,[status(thm)],[5243,4502,theory(equality)]) ).
cnf(5245,negated_conjecture,
( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ isFinite0(esk32_0) ),
inference(cn,[status(thm)],[5244,theory(equality)]) ).
cnf(15108,negated_conjecture,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| $false ),
inference(rw,[status(thm)],[4567,4581,theory(equality)]) ).
cnf(15109,negated_conjecture,
aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0))),
inference(cn,[status(thm)],[15108,theory(equality)]) ).
cnf(66367,negated_conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,esk31_0),sdtlpdtrp0(xN,sz00))
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(spm,[status(thm)],[4965,4571,theory(equality)]) ).
cnf(66377,negated_conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,esk31_0),xS)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(rw,[status(thm)],[66367,4380,theory(equality)]) ).
cnf(66378,negated_conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,esk31_0),xS)
| $false ),
inference(rw,[status(thm)],[66377,4290,theory(equality)]) ).
cnf(66379,negated_conjecture,
aSubsetOf0(sdtlpdtrp0(xN,esk31_0),xS),
inference(cn,[status(thm)],[66378,theory(equality)]) ).
cnf(66426,negated_conjecture,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,esk31_0))
| ~ aSet0(xS) ),
inference(spm,[status(thm)],[200,66379,theory(equality)]) ).
cnf(66435,negated_conjecture,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,esk31_0))
| $false ),
inference(rw,[status(thm)],[66426,4447,theory(equality)]) ).
cnf(66436,negated_conjecture,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,esk31_0)) ),
inference(cn,[status(thm)],[66435,theory(equality)]) ).
cnf(67170,negated_conjecture,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),xS),
inference(spm,[status(thm)],[66436,4501,theory(equality)]) ).
cnf(111281,negated_conjecture,
( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| ~ isFinite0(esk32_0) ),
inference(rw,[status(thm)],[5245,15109,theory(equality)]) ).
cnf(111282,negated_conjecture,
( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| $false ),
inference(rw,[status(thm)],[111281,4696,theory(equality)]) ).
cnf(111283,negated_conjecture,
( aElementOf0(esk33_0,sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0) ),
inference(cn,[status(thm)],[111282,theory(equality)]) ).
cnf(111287,negated_conjecture,
( szmzizndt0(sdtlpdtrp0(xN,esk31_0)) = esk33_0
| aElementOf0(esk33_0,esk32_0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0) ),
inference(spm,[status(thm)],[4518,111283,theory(equality)]) ).
cnf(111704,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| szmzizndt0(sdtlpdtrp0(xN,esk31_0)) = esk33_0
| aElementOf0(esk33_0,esk32_0) ),
inference(spm,[status(thm)],[4508,111287,theory(equality)]) ).
cnf(111713,negated_conjecture,
( szmzizndt0(sdtlpdtrp0(xN,esk31_0)) = esk33_0
| aElementOf0(esk33_0,esk32_0) ),
inference(sr,[status(thm)],[111704,5118,theory(equality)]) ).
cnf(111757,negated_conjecture,
( aElementOf0(esk33_0,xS)
| aElementOf0(esk33_0,esk32_0) ),
inference(spm,[status(thm)],[67170,111713,theory(equality)]) ).
cnf(111981,negated_conjecture,
( aElementOf0(esk33_0,esk32_0)
| sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) != xK ),
inference(spm,[status(thm)],[4513,111757,theory(equality)]) ).
cnf(144945,negated_conjecture,
( aElementOf0(esk33_0,esk32_0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| szszuzczcdt0(sbrdtbr0(esk32_0)) != xK
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ isFinite0(esk32_0)
| ~ aSet0(esk32_0) ),
inference(spm,[status(thm)],[111981,4484,theory(equality)]) ).
cnf(144947,negated_conjecture,
( aElementOf0(esk33_0,esk32_0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ isFinite0(esk32_0)
| ~ aSet0(esk32_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[144945,4498,theory(equality)]),4339,theory(equality)]) ).
cnf(144948,negated_conjecture,
( aElementOf0(esk33_0,esk32_0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| $false
| ~ isFinite0(esk32_0)
| ~ aSet0(esk32_0) ),
inference(rw,[status(thm)],[144947,15109,theory(equality)]) ).
cnf(144949,negated_conjecture,
( aElementOf0(esk33_0,esk32_0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| $false
| $false
| ~ aSet0(esk32_0) ),
inference(rw,[status(thm)],[144948,4696,theory(equality)]) ).
cnf(144950,negated_conjecture,
( aElementOf0(esk33_0,esk32_0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[144949,4502,theory(equality)]) ).
cnf(144951,negated_conjecture,
( aElementOf0(esk33_0,esk32_0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0) ),
inference(cn,[status(thm)],[144950,theory(equality)]) ).
cnf(144953,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0))))
| aElementOf0(esk33_0,esk32_0) ),
inference(spm,[status(thm)],[4508,144951,theory(equality)]) ).
cnf(144963,negated_conjecture,
aElementOf0(esk33_0,esk32_0),
inference(sr,[status(thm)],[144953,5118,theory(equality)]) ).
cnf(144978,negated_conjecture,
aElementOf0(esk33_0,sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))),
inference(spm,[status(thm)],[4508,144963,theory(equality)]) ).
cnf(145177,negated_conjecture,
aElementOf0(esk33_0,sdtlpdtrp0(xN,esk31_0)),
inference(spm,[status(thm)],[4506,144978,theory(equality)]) ).
cnf(145209,negated_conjecture,
aElementOf0(esk33_0,xS),
inference(spm,[status(thm)],[66436,145177,theory(equality)]) ).
cnf(145238,negated_conjecture,
( sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) != xK
| $false ),
inference(rw,[status(thm)],[4513,145209,theory(equality)]) ).
cnf(145239,negated_conjecture,
sbrdtbr0(sdtpldt0(esk32_0,szmzizndt0(sdtlpdtrp0(xN,esk31_0)))) != xK,
inference(cn,[status(thm)],[145238,theory(equality)]) ).
cnf(145253,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| szszuzczcdt0(sbrdtbr0(esk32_0)) != xK
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ isFinite0(esk32_0)
| ~ aSet0(esk32_0) ),
inference(spm,[status(thm)],[145239,4484,theory(equality)]) ).
cnf(145254,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)))
| ~ isFinite0(esk32_0)
| ~ aSet0(esk32_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[145253,4498,theory(equality)]),4339,theory(equality)]) ).
cnf(145255,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| $false
| ~ isFinite0(esk32_0)
| ~ aSet0(esk32_0) ),
inference(rw,[status(thm)],[145254,15109,theory(equality)]) ).
cnf(145256,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| $false
| $false
| ~ aSet0(esk32_0) ),
inference(rw,[status(thm)],[145255,4696,theory(equality)]) ).
cnf(145257,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0)
| $false
| $false
| $false
| $false ),
inference(rw,[status(thm)],[145256,4502,theory(equality)]) ).
cnf(145258,negated_conjecture,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),esk32_0),
inference(cn,[status(thm)],[145257,theory(equality)]) ).
cnf(145285,negated_conjecture,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk31_0)),sdtmndt0(sdtlpdtrp0(xN,esk31_0),szmzizndt0(sdtlpdtrp0(xN,esk31_0)))),
inference(spm,[status(thm)],[4508,145258,theory(equality)]) ).
cnf(145295,negated_conjecture,
$false,
inference(sr,[status(thm)],[145285,5118,theory(equality)]) ).
cnf(145296,negated_conjecture,
$false,
145295,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM579+3 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04 % Command : Source/sine.py -e eprover -t %d %s
% 0.03/0.23 % Computer : n105.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.625MB
% 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Fri Jan 5 09:32:44 CST 2018
% 0.03/0.23 % CPUTime :
% 0.03/0.27 % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.27 --creating new selector for []
% 13.41/13.65 -running prover on /export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1 with time limit 29
% 13.41/13.65 -running prover with command ['/export/starexec/sandbox/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox/tmp/tmpBKea3D/sel_theBenchmark.p_1']
% 13.41/13.65 -prover status Theorem
% 13.41/13.65 Problem theBenchmark.p solved in phase 0.
% 13.41/13.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.41/13.65 % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.41/13.65 Solved 1 out of 1.
% 13.41/13.65 # Problem is unsatisfiable (or provable), constructing proof object
% 13.41/13.65 # SZS status Theorem
% 13.41/13.65 # SZS output start CNFRefutation.
% See solution above
% 13.41/13.65 # SZS output end CNFRefutation
%------------------------------------------------------------------------------