%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM579+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 : Thu Sep 24 01:55:34 PM UTC 2026
% Result : Theorem 27.32s 9.27s
% Output : CNFRefutation 27.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 24 unt; 0 def)
% Number of atoms : 673 ( 84 equ)
% Maximal formula atoms : 181 ( 8 avg)
% Number of connectives : 911 ( 316 ~; 346 |; 178 &)
% ( 16 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 130 ( 0 sgn 101 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
& sbrdtbr0(X2) = xk
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( X3 != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(X3,sdtlpdtrp0(xN,X1))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& aSet0(X2) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( ( X3 = szmzizndt0(sdtlpdtrp0(xN,X1))
| aElementOf0(X3,X2) )
& aElement0(X3) ) )
& aSet0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))) )
=> ( aElementOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))) = xK
& ( aSubsetOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),xS)
| ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
=> aElementOf0(X3,xS) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(mCardCons,axiom,
! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
fof(mCardNum,axiom,
! [X1] :
( aSet0(X1)
=> ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
<=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefCons,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtpldt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( ( X4 = X2
| aElementOf0(X4,X1) )
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
fof(m__3533,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
fof(m__3623,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X1))
& ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( X2 != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(X2,sdtlpdtrp0(xN,X1))
& aElement0(X2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(m__3754,hypothesis,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X2,X1)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> aElementOf0(X3,sdtlpdtrp0(xN,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(c_0_14,negated_conjecture,
~ ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
& sbrdtbr0(X2) = xk
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( X3 != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(X3,sdtlpdtrp0(xN,X1))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& aSet0(X2) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( ( X3 = szmzizndt0(sdtlpdtrp0(xN,X1))
| aElementOf0(X3,X2) )
& aElement0(X3) ) )
& aSet0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))) )
=> ( aElementOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))) = xK
& ( aSubsetOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),xS)
| ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
=> aElementOf0(X3,xS) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
& sbrdtbr0(X2) = xk
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( X3 != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(X3,sdtlpdtrp0(xN,X1))
& aElement0(X3) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& aSet0(X2) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) )
=> ( ( ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( ( X3 = szmzizndt0(sdtlpdtrp0(xN,X1))
| aElementOf0(X3,X2) )
& aElement0(X3) ) )
& aSet0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))) )
=> ( aElementOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),slbdtsldtrb0(xS,xK))
| ( sbrdtbr0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))) = xK
& ( aSubsetOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),xS)
| ! [X3] :
( aElementOf0(X3,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))))
=> aElementOf0(X3,xS) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_16,hypothesis,
! [X212,X213] :
( ( ~ aElementOf0(X212,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X212)) )
& ( ~ aElementOf0(X212,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X212),szNzAzT0) )
& ( ~ aElementOf0(X212,szNzAzT0)
| aElementOf0(X213,szNzAzT0)
| ~ aElementOf0(X213,sdtlpdtrp0(xN,X212)) )
& ( ~ aElementOf0(X212,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X212)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])])])]) ).
fof(c_0_17,negated_conjecture,
! [X223,X224,X225,X226,X227] :
( ~ aElementOf0(sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0))),slbdtsldtrb0(xS,xK))
& ( sbrdtbr0(sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0)))) != xK
| ~ aSubsetOf0(sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0))),xS) )
& ( sbrdtbr0(sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0)))) != xK
| ~ aElementOf0(esk35_0,xS) )
& ( sbrdtbr0(sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0)))) != xK
| aElementOf0(esk35_0,sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0)))) )
& ( aElementOf0(X227,sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| ~ aElement0(X227)
| X227 != szmzizndt0(sdtlpdtrp0(xN,esk33_0)) )
& ( aElementOf0(X227,sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| ~ aElement0(X227)
| ~ aElementOf0(X227,esk34_0) )
& ( ~ aElementOf0(X227,sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| X227 = szmzizndt0(sdtlpdtrp0(xN,esk33_0))
| aElementOf0(X227,esk34_0) )
& ( ~ aElementOf0(X227,sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| aElement0(X227) )
& aSet0(sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),X226)
| ~ aElementOf0(X226,sdtlpdtrp0(xN,esk33_0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),sdtlpdtrp0(xN,esk33_0))
& aElementOf0(esk34_0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0))),xk))
& sbrdtbr0(esk34_0) = xk
& aSubsetOf0(esk34_0,sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
& ( aElementOf0(X225,sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| ~ aElementOf0(X225,esk34_0) )
& ( aElementOf0(X224,sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| X224 = szmzizndt0(sdtlpdtrp0(xN,esk33_0))
| ~ aElementOf0(X224,sdtlpdtrp0(xN,esk33_0))
| ~ aElement0(X224) )
& ( ~ aElementOf0(X224,sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| X224 != szmzizndt0(sdtlpdtrp0(xN,esk33_0)) )
& ( ~ aElementOf0(X224,sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| aElementOf0(X224,sdtlpdtrp0(xN,esk33_0)) )
& ( ~ aElementOf0(X224,sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| aElement0(X224) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),X223)
| ~ aElementOf0(X223,sdtlpdtrp0(xN,esk33_0)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),sdtlpdtrp0(xN,esk33_0))
& aSet0(esk34_0)
& aElementOf0(esk33_0,szNzAzT0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])])]) ).
fof(c_0_18,plain,
! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ( ~ aElementOf0(X2,X1)
=> sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1)) ) ) ),
inference(fof_simplification,[status(thm)],[mCardCons]) ).
fof(c_0_19,plain,
! [X84] :
( ( ~ aSet0(X84)
| aElementOf0(sbrdtbr0(X84),szNzAzT0)
| ~ isFinite0(X84) )
& ( ~ aSet0(X84)
| isFinite0(X84)
| ~ aElementOf0(sbrdtbr0(X84),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])])]) ).
fof(c_0_20,plain,
! [X10,X11] :
( aElement0(X11)
| ~ aElementOf0(X11,X10)
| ~ aSet0(X10) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_21,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
aElementOf0(esk33_0,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X33,X34,X35,X36,X37,X38] :
( ( ~ aElement0(X34)
| ~ aSet0(X33)
| X38 = sdtpldt0(X33,X34)
| ~ aSet0(X38)
| aElementOf0(esk3_3(X33,X34,X38),X38)
| esk3_3(X33,X34,X38) = X34
| aElementOf0(esk3_3(X33,X34,X38),X33) )
& ( ~ aElement0(X34)
| ~ aSet0(X33)
| X38 = sdtpldt0(X33,X34)
| ~ aSet0(X38)
| aElementOf0(esk3_3(X33,X34,X38),X38)
| aElement0(esk3_3(X33,X34,X38)) )
& ( ~ aElement0(X34)
| ~ aSet0(X33)
| X38 = sdtpldt0(X33,X34)
| ~ aSet0(X38)
| ~ aElementOf0(esk3_3(X33,X34,X38),X38)
| ~ aElement0(esk3_3(X33,X34,X38))
| esk3_3(X33,X34,X38) != X34 )
& ( ~ aElement0(X34)
| ~ aSet0(X33)
| X38 = sdtpldt0(X33,X34)
| ~ aSet0(X38)
| ~ aElementOf0(esk3_3(X33,X34,X38),X38)
| ~ aElement0(esk3_3(X33,X34,X38))
| ~ aElementOf0(esk3_3(X33,X34,X38),X33) )
& ( ~ aElement0(X34)
| ~ aSet0(X33)
| X35 != sdtpldt0(X33,X34)
| aElementOf0(X37,X35)
| ~ aElement0(X37)
| X37 != X34 )
& ( ~ aElement0(X34)
| ~ aSet0(X33)
| X35 != sdtpldt0(X33,X34)
| aElementOf0(X37,X35)
| ~ aElement0(X37)
| ~ aElementOf0(X37,X33) )
& ( ~ aElement0(X34)
| ~ aSet0(X33)
| X35 != sdtpldt0(X33,X34)
| ~ aElementOf0(X36,X35)
| X36 = X34
| aElementOf0(X36,X33) )
& ( ~ aElement0(X34)
| ~ aSet0(X33)
| X35 != sdtpldt0(X33,X34)
| ~ aElementOf0(X36,X35)
| aElement0(X36) )
& ( ~ aElement0(X34)
| ~ aSet0(X33)
| X35 != sdtpldt0(X33,X34)
| aSet0(X35) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefCons])])])])])])]) ).
fof(c_0_24,plain,
! [X86,X87] :
( sbrdtbr0(sdtpldt0(X86,X87)) = szszuzczcdt0(sbrdtbr0(X86))
| aElementOf0(X87,X86)
| ~ aElement0(X87)
| ~ isFinite0(X86)
| ~ aSet0(X86) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
cnf(c_0_25,plain,
( ~ aSet0(X1)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
sbrdtbr0(esk34_0) = xk,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_28,negated_conjecture,
aSet0(esk34_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_29,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),sdtlpdtrp0(xN,esk33_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,negated_conjecture,
aSet0(sdtlpdtrp0(xN,esk33_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_32,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X4 != sdtpldt0(X2,X3)
| ~ aElementOf0(X1,X4)
| X1 = X3
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,negated_conjecture,
( sbrdtbr0(sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0)))) != xK
| aElementOf0(esk35_0,sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_34,plain,
( ~ aElement0(X2)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| sbrdtbr0(sdtpldt0(X1,X2)) = szszuzczcdt0(sbrdtbr0(X1))
| aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_35,hypothesis,
szszuzczcdt0(xk) = xK,
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_36,negated_conjecture,
isFinite0(esk34_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_37,negated_conjecture,
aElement0(szmzizndt0(sdtlpdtrp0(xN,esk33_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
fof(c_0_38,plain,
! [X67] :
( sdtlseqdt0(sz00,X67)
| ~ aElementOf0(X67,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])])]) ).
fof(c_0_39,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X1))
& ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( X2 != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(X2,sdtlpdtrp0(xN,X1))
& aElement0(X2) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1)) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(fof_simplification,[status(thm)],[m__3623]) ).
cnf(c_0_40,plain,
( ~ aSet0(X3)
| ~ aElement0(X2)
| ~ aElementOf0(X1,sdtpldt0(X3,X2))
| aElementOf0(X1,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),esk34_0)
| aElementOf0(esk35_0,sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_26]),c_0_35]),c_0_36]),c_0_37]),c_0_28])]) ).
cnf(c_0_42,negated_conjecture,
( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0))))
| X1 != szmzizndt0(sdtlpdtrp0(xN,esk33_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_43,hypothesis,
! [X214,X215,X216] :
( ( ~ aElementOf0(X215,szNzAzT0)
| ~ aElementOf0(X214,szNzAzT0)
| ~ sdtlseqdt0(X215,X214)
| aSubsetOf0(sdtlpdtrp0(xN,X214),sdtlpdtrp0(xN,X215)) )
& ( ~ aElementOf0(X215,szNzAzT0)
| ~ aElementOf0(X214,szNzAzT0)
| ~ sdtlseqdt0(X215,X214)
| aElementOf0(X216,sdtlpdtrp0(xN,X215))
| ~ aElementOf0(X216,sdtlpdtrp0(xN,X214)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3754])])])])]) ).
cnf(c_0_44,plain,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_45,hypothesis,
! [X206,X208,X209,X210,X211] :
( ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X206)),sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aElementOf0(X211,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| ~ aElementOf0(X211,sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aElementOf0(X210,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X210 = szmzizndt0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X210,sdtlpdtrp0(xN,X206))
| ~ aElement0(X210) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X209 != szmzizndt0(sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElementOf0(X209,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElement0(X209) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X206)),X208)
| ~ aElementOf0(X208,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X206),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X206)),sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X206)),sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aElementOf0(X211,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| ~ aElementOf0(X211,sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aElementOf0(X210,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X210 = szmzizndt0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X210,sdtlpdtrp0(xN,X206))
| ~ aElement0(X210) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X209 != szmzizndt0(sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElementOf0(X209,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElement0(X209) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X206)),X208)
| ~ aElementOf0(X208,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(esk31_1(X206),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X206)),sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X206)),sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aElementOf0(X211,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| ~ aElementOf0(X211,sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X206))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aElementOf0(X210,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X210 = szmzizndt0(sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X210,sdtlpdtrp0(xN,X206))
| ~ aElement0(X210) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| X209 != szmzizndt0(sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElementOf0(X209,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| ~ aElementOf0(X209,sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206))))
| aElement0(X209) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X206),szmzizndt0(sdtlpdtrp0(xN,X206)))) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X206)),X208)
| ~ aElementOf0(X208,sdtlpdtrp0(xN,X206)) )
& ( ~ aElementOf0(X206,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X206))
| ~ aSet0(sdtlpdtrp0(xN,X206))
| aElementOf0(esk31_1(X206),sdtlpdtrp0(xN,X206))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X206)),sdtlpdtrp0(xN,X206)) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])])])])]) ).
cnf(c_0_46,negated_conjecture,
( ~ aElementOf0(X1,esk34_0)
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_47,negated_conjecture,
( aElementOf0(esk35_0,esk34_0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),esk34_0)
| szmzizndt0(sdtlpdtrp0(xN,esk33_0)) = esk35_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_37]),c_0_28])]) ).
cnf(c_0_48,negated_conjecture,
~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0)))),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_49,negated_conjecture,
aSet0(sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0)))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_50,plain,
! [X20,X21,X22,X23] :
( ( ~ aSet0(X20)
| aSubsetOf0(X23,X20)
| ~ aSet0(X23)
| ~ aElementOf0(esk2_2(X20,X23),X20) )
& ( ~ aSet0(X20)
| aSubsetOf0(X23,X20)
| ~ aSet0(X23)
| aElementOf0(esk2_2(X20,X23),X23) )
& ( ~ aSet0(X20)
| ~ aSubsetOf0(X21,X20)
| aElementOf0(X22,X20)
| ~ aElementOf0(X22,X21) )
& ( ~ aSet0(X20)
| ~ aSubsetOf0(X21,X20)
| aSet0(X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSub])])])])])])]) ).
cnf(c_0_51,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X2,X1)
| aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,negated_conjecture,
sdtlseqdt0(sz00,esk33_0),
inference(spm,[status(thm)],[c_0_44,c_0_22]) ).
cnf(c_0_53,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
fof(c_0_55,hypothesis,
! [X178] :
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ( aElementOf0(X178,szNzAzT0)
| ~ aElementOf0(X178,xS) )
& aSet0(xS) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3435])])])]) ).
cnf(c_0_56,negated_conjecture,
( sbrdtbr0(sdtpldt0(esk34_0,szmzizndt0(sdtlpdtrp0(xN,esk33_0)))) != xK
| ~ aElementOf0(esk35_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_57,negated_conjecture,
( aElementOf0(esk35_0,esk34_0)
| szmzizndt0(sdtlpdtrp0(xN,esk33_0)) = esk35_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_58,negated_conjecture,
( aElement0(esk35_0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),esk34_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_49])]) ).
fof(c_0_59,plain,
! [X1,X2] :
( ( aElement0(X2)
& aSet0(X1) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( X4 != X2
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mDefDiff]) ).
cnf(c_0_60,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_61,negated_conjecture,
aSubsetOf0(sdtlpdtrp0(xN,esk33_0),xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54]),c_0_22])]) ).
cnf(c_0_62,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( ~ aElementOf0(esk35_0,xS)
| sbrdtbr0(sdtpldt0(esk34_0,esk35_0)) != xK
| aElementOf0(esk35_0,esk34_0) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
aElement0(esk35_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_58]),c_0_48]) ).
fof(c_0_65,plain,
! [X40,X41,X42,X43,X44,X45] :
( ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| aElementOf0(esk4_3(X40,X41,X45),X45)
| esk4_3(X40,X41,X45) != X41 )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| aElementOf0(esk4_3(X40,X41,X45),X45)
| aElementOf0(esk4_3(X40,X41,X45),X40) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| aElementOf0(esk4_3(X40,X41,X45),X45)
| aElement0(esk4_3(X40,X41,X45)) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X45 = sdtmndt0(X40,X41)
| ~ aSet0(X45)
| esk4_3(X40,X41,X45) = X41
| ~ aElementOf0(esk4_3(X40,X41,X45),X40)
| ~ aElement0(esk4_3(X40,X41,X45))
| ~ aElementOf0(esk4_3(X40,X41,X45),X45) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| aElementOf0(X44,X42)
| X44 = X41
| ~ aElementOf0(X44,X40)
| ~ aElement0(X44) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| ~ aElementOf0(X43,X42)
| X43 != X41 )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| ~ aElementOf0(X43,X42)
| aElementOf0(X43,X40) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| ~ aElementOf0(X43,X42)
| aElement0(X43) )
& ( ~ aElement0(X41)
| ~ aSet0(X40)
| X42 != sdtmndt0(X40,X41)
| aSet0(X42) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])])])])]) ).
cnf(c_0_66,negated_conjecture,
( ~ aElementOf0(X1,sdtlpdtrp0(xN,esk33_0))
| aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62])]) ).
cnf(c_0_67,negated_conjecture,
( aElementOf0(esk35_0,esk34_0)
| aElementOf0(esk35_0,sdtlpdtrp0(xN,esk33_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_57]) ).
cnf(c_0_68,negated_conjecture,
( ~ aElementOf0(esk35_0,xS)
| aElementOf0(esk35_0,esk34_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_34]),c_0_26]),c_0_35]),c_0_36]),c_0_64]),c_0_28])]) ).
cnf(c_0_69,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_70,negated_conjecture,
aElementOf0(esk35_0,esk34_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_71,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_72,negated_conjecture,
aElementOf0(esk35_0,sdtmndt0(sdtlpdtrp0(xN,esk33_0),szmzizndt0(sdtlpdtrp0(xN,esk33_0)))),
inference(spm,[status(thm)],[c_0_46,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
aElementOf0(esk35_0,sdtlpdtrp0(xN,esk33_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_37]),c_0_31])]) ).
cnf(c_0_74,negated_conjecture,
( ~ aElementOf0(esk35_0,xS)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),esk34_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_34]),c_0_26]),c_0_35]),c_0_36]),c_0_37]),c_0_28])]) ).
cnf(c_0_75,negated_conjecture,
aElementOf0(esk35_0,xS),
inference(spm,[status(thm)],[c_0_66,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk33_0)),esk34_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_76]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM579+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.58 % Computer : n003.cluster.edu
% 0.12/5.58 % Model : x86_64 x86_64
% 0.12/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.58 % Memory : 8046.5625MB
% 0.12/5.58 % OS : Linux 6.8.0-71-generic
% 0.12/5.58 % CPULimit : 300
% 0.12/5.58 % WCLimit : 300
% 0.12/5.58 % DateTime : Mon Sep 21 02:43:06 UTC 2026
% 0.12/5.58 % CPUTime :
% 0.12/5.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/5.63 Running first-order theorem proving
% 0.16/5.63 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.32/9.27 % Version: 3.5.1
% 27.32/9.27 % Preprocessing class: FSLSSMSMSSSNFFN.
% 27.32/9.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.32/9.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 27.32/9.27 % Starting new_bool_3 with 300s (1) cores
% 27.32/9.27 % Starting new_bool_1 with 300s (1) cores
% 27.32/9.27 % Starting sh5l with 300s (1) cores
% 27.32/9.27 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 3233659 completed with status 0
% 27.32/9.27 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 27.32/9.27 % Preprocessing class: FSLSSMSMSSSNFFN.
% 27.32/9.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.32/9.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 27.32/9.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.32/9.27 % No SInE strategy applied
% 27.32/9.27 % Search class: FGHSF-SMLM32-MFFFFFNN
% 27.32/9.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 27.32/9.27 % Starting SubtermCWHack with 136s (1) cores
% 27.32/9.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 27.32/9.27 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 27.32/9.27 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 27.32/9.27 % Starting new_bool_3 with 136s (1) cores
% 27.32/9.27 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 3233712 completed with status 0
% 27.32/9.27 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 27.32/9.27 % Preprocessing class: FSLSSMSMSSSNFFN.
% 27.32/9.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.32/9.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 27.32/9.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.32/9.27 % No SInE strategy applied
% 27.32/9.27 % Search class: FGHSF-SMLM32-MFFFFFNN
% 27.32/9.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 27.32/9.27 % Starting SubtermCWHack with 136s (1) cores
% 27.32/9.27 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 27.32/9.27 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 27.32/9.27 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 27.32/9.27 % Preprocessing time : 0.086 s
% 27.32/9.27 % Presaturation interreduction done
% 27.32/9.27
% 27.32/9.27 % Proof found!
% 27.32/9.27 % SZS status Theorem
% 27.32/9.27 % SZS output start CNFRefutation
% See solution above
% 27.32/9.27 % Parsed axioms : 85
% 27.32/9.27 % Removed by relevancy pruning/SinE : 0
% 27.32/9.27 % Initial clauses : 4210
% 27.32/9.27 % Removed in clause preprocessing : 7
% 27.32/9.27 % Initial clauses in saturation : 4203
% 27.32/9.27 % Processed clauses : 7340
% 27.32/9.27 % ...of these trivial : 52
% 27.32/9.27 % ...subsumed : 814
% 27.32/9.27 % ...remaining for further processing : 6474
% 27.32/9.27 % Other redundant clauses eliminated : 1942
% 27.32/9.27 % Clauses deleted for lack of memory : 0
% 27.32/9.27 % Backward-subsumed : 36
% 27.32/9.27 % Backward-rewritten : 61
% 27.32/9.27 % Generated clauses : 7503
% 27.32/9.27 % ...of the previous two non-redundant : 6888
% 27.32/9.27 % ...aggressively subsumed : 0
% 27.32/9.27 % Contextual simplify-reflections : 70
% 27.32/9.27 % Paramodulations : 5746
% 27.32/9.27 % Factorizations : 6
% 27.32/9.27 % NegExts : 0
% 27.32/9.27 % Equation resolutions : 1945
% 27.32/9.27 % Disequality decompositions : 0
% 27.32/9.27 % Total rewrite steps : 4300
% 27.32/9.27 % ...of those cached : 4054
% 27.32/9.27 % Propositional unsat checks : 2
% 27.32/9.27 % Propositional check models : 2
% 27.32/9.27 % Propositional check unsatisfiable : 0
% 27.32/9.27 % Propositional clauses : 0
% 27.32/9.27 % Propositional clauses after purity: 0
% 27.32/9.27 % Propositional unsat core size : 0
% 27.32/9.27 % Propositional preprocessing time : 0.000
% 27.32/9.27 % Propositional encoding time : 0.025
% 27.32/9.27 % Propositional solver time : 0.001
% 27.32/9.27 % Success case prop preproc time : 0.000
% 27.32/9.27 % Success case prop encoding time : 0.000
% 27.32/9.27 % Success case prop solver time : 0.000
% 27.32/9.27 % Current number of processed clauses : 1021
% 27.32/9.27 % Positive orientable unit clauses : 395
% 27.32/9.27 % Positive unorientable unit clauses: 0
% 27.32/9.27 % Negative unit clauses : 47
% 27.32/9.27 % Non-unit-clauses : 579
% 27.32/9.27 % Current number of unprocessed clauses: 7302
% 27.32/9.27 % ...number of literals in the above : 54819
% 27.32/9.27 % Current number of archived formulas : 0
% 27.32/9.27 % Current number of archived clauses : 3706
% 27.32/9.27 % Clause-clause subsumption calls (NU) : 6695061
% 27.32/9.27 % Rec. Clause-clause subsumption calls : 82653
% 27.32/9.27 % Non-unit clause-clause subsumptions : 817
% 27.32/9.27 % Unit Clause-clause subsumption calls : 21614
% 27.32/9.27 % Rewrite failures with RHS unbound : 0
% 27.32/9.27 % BW rewrite match attempts : 586
% 27.32/9.27 % BW rewrite match successes : 34
% 27.32/9.27 % Condensation attempts : 0
% 27.32/9.27 % Condensation successes : 0
% 27.32/9.27 % Termbank termtop insertions : 886740
% 27.32/9.27 % Search garbage collected termcells : 27369
% 27.32/9.27
% 27.32/9.27 % -------------------------------------------------
% 27.32/9.27 % User time : 3.556 s
% 27.32/9.27 % System time : 0.033 s
% 27.32/9.27 % Total time : 3.589 s
% 27.32/9.27 % Maximum resident set size: 15292 pages
% 27.32/9.27
% 27.32/9.27 % -------------------------------------------------
% 27.32/9.27 % User time : 16.638 s
% 27.32/9.27 % System time : 0.187 s
% 27.32/9.27 % Total time : 16.825 s
% 27.32/9.27 % Maximum resident set size: 4864 pages
% 27.32/9.27 % E exiting
%------------------------------------------------------------------------------