%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM581+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 01:55:35 PM UTC 2026
% Result : Theorem 2.19s 1.87s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 16 unt; 0 def)
% Number of atoms : 538 ( 51 equ)
% Maximal formula atoms : 181 ( 9 avg)
% Number of connectives : 738 ( 258 ~; 275 |; 157 &)
% ( 12 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-3 aty)
% Number of variables : 101 ( 0 sgn 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__3989_02,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989_02) ).
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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/sandbox2/benchmark/theBenchmark.p',m__3671) ).
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/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__3989,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989) ).
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/sandbox2/benchmark/theBenchmark.p',m__3754) ).
fof(mZeroLess,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sdtlseqdt0(sz00,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(m__,conjecture,
( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__4007,hypothesis,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4007) ).
fof(c_0_14,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( X1 != szmzizndt0(sdtlpdtrp0(xN,xi))
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& aElement0(X1) ) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(fof_simplification,[status(thm)],[m__3989_02]) ).
fof(c_0_15,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]) ).
fof(c_0_16,hypothesis,
! [X42,X43] :
( ( ~ aElementOf0(X42,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X42)) )
& ( ~ aElementOf0(X42,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X42),szNzAzT0) )
& ( ~ aElementOf0(X42,szNzAzT0)
| aElementOf0(X43,szNzAzT0)
| ~ aElementOf0(X43,sdtlpdtrp0(xN,X42)) )
& ( ~ aElementOf0(X42,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X42)) ) ),
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,hypothesis,
! [X51,X52,X53] :
( aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElementOf0(X53,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X53,xQ) )
& aSet0(xQ)
& ( aElementOf0(X52,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| X52 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X52,sdtlpdtrp0(xN,xi))
| ~ aElement0(X52) )
& ( ~ aElementOf0(X52,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| X52 != szmzizndt0(sdtlpdtrp0(xN,xi)) )
& ( ~ aElementOf0(X52,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X52,sdtlpdtrp0(xN,xi)) )
& ( ~ aElementOf0(X52,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElement0(X52) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X51)
| ~ aElementOf0(X51,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])])]) ).
fof(c_0_18,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]) ).
fof(c_0_19,plain,
! [X142,X143,X144,X145,X146,X147] :
( ( ~ aElement0(X143)
| ~ aSet0(X142)
| X147 = sdtmndt0(X142,X143)
| ~ aSet0(X147)
| aElementOf0(esk25_3(X142,X143,X147),X147)
| esk25_3(X142,X143,X147) != X143 )
& ( ~ aElement0(X143)
| ~ aSet0(X142)
| X147 = sdtmndt0(X142,X143)
| ~ aSet0(X147)
| aElementOf0(esk25_3(X142,X143,X147),X147)
| aElementOf0(esk25_3(X142,X143,X147),X142) )
& ( ~ aElement0(X143)
| ~ aSet0(X142)
| X147 = sdtmndt0(X142,X143)
| ~ aSet0(X147)
| aElementOf0(esk25_3(X142,X143,X147),X147)
| aElement0(esk25_3(X142,X143,X147)) )
& ( ~ aElement0(X143)
| ~ aSet0(X142)
| X147 = sdtmndt0(X142,X143)
| ~ aSet0(X147)
| esk25_3(X142,X143,X147) = X143
| ~ aElementOf0(esk25_3(X142,X143,X147),X142)
| ~ aElement0(esk25_3(X142,X143,X147))
| ~ aElementOf0(esk25_3(X142,X143,X147),X147) )
& ( ~ aElement0(X143)
| ~ aSet0(X142)
| X144 != sdtmndt0(X142,X143)
| aElementOf0(X146,X144)
| X146 = X143
| ~ aElementOf0(X146,X142)
| ~ aElement0(X146) )
& ( ~ aElement0(X143)
| ~ aSet0(X142)
| X144 != sdtmndt0(X142,X143)
| ~ aElementOf0(X145,X144)
| X145 != X143 )
& ( ~ aElement0(X143)
| ~ aSet0(X142)
| X144 != sdtmndt0(X142,X143)
| ~ aElementOf0(X145,X144)
| aElementOf0(X145,X142) )
& ( ~ aElement0(X143)
| ~ aSet0(X142)
| X144 != sdtmndt0(X142,X143)
| ~ aElementOf0(X145,X144)
| aElement0(X145) )
& ( ~ aElement0(X143)
| ~ aSet0(X142)
| X144 != sdtmndt0(X142,X143)
| aSet0(X144) ) ),
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_15])])])])])])]) ).
fof(c_0_20,plain,
! [X167,X168] :
( aElement0(X168)
| ~ aElementOf0(X168,X167)
| ~ aSet0(X167) ),
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(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X2))
| aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3989]) ).
fof(c_0_24,hypothesis,
! [X44,X45,X46] :
( ( ~ aElementOf0(X45,szNzAzT0)
| ~ aElementOf0(X44,szNzAzT0)
| ~ sdtlseqdt0(X45,X44)
| aSubsetOf0(sdtlpdtrp0(xN,X44),sdtlpdtrp0(xN,X45)) )
& ( ~ aElementOf0(X45,szNzAzT0)
| ~ aElementOf0(X44,szNzAzT0)
| ~ sdtlseqdt0(X45,X44)
| aElementOf0(X46,sdtlpdtrp0(xN,X45))
| ~ aElementOf0(X46,sdtlpdtrp0(xN,X44)) ) ),
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])])])])]) ).
fof(c_0_25,hypothesis,
! [X36,X38,X39,X40,X41] :
( ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X36)),sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aElementOf0(X41,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| ~ aElementOf0(X41,sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aElementOf0(X40,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X40 = szmzizndt0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X40,sdtlpdtrp0(xN,X36))
| ~ aElement0(X40) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X39 != szmzizndt0(sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElementOf0(X39,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElement0(X39) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X36)),X38)
| ~ aElementOf0(X38,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X36),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X36)),sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X36)),sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aElementOf0(X41,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| ~ aElementOf0(X41,sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aElementOf0(X40,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X40 = szmzizndt0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X40,sdtlpdtrp0(xN,X36))
| ~ aElement0(X40) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X39 != szmzizndt0(sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElementOf0(X39,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElement0(X39) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X36)),X38)
| ~ aElementOf0(X38,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(esk12_1(X36),szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X36)),sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X36)),sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aElementOf0(X41,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| ~ aElementOf0(X41,sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X36))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aElementOf0(X40,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X40 = szmzizndt0(sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X40,sdtlpdtrp0(xN,X36))
| ~ aElement0(X40) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| X39 != szmzizndt0(sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElementOf0(X39,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| ~ aElementOf0(X39,sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36))))
| aElement0(X39) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X36),szmzizndt0(sdtlpdtrp0(xN,X36)))) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X36)),X38)
| ~ aElementOf0(X38,sdtlpdtrp0(xN,X36)) )
& ( ~ aElementOf0(X36,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X36))
| ~ aSet0(sdtlpdtrp0(xN,X36))
| aElementOf0(esk12_1(X36),sdtlpdtrp0(xN,X36))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X36)),sdtlpdtrp0(xN,X36)) )
& 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_18])])])])])])]) ).
fof(c_0_26,plain,
! [X132] :
( sdtlseqdt0(sz00,X132)
| ~ aElementOf0(X132,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroLess])])]) ).
cnf(c_0_27,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_30,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_31,plain,
! [X74,X75,X76,X77] :
( ( ~ aSet0(X74)
| aSubsetOf0(X77,X74)
| ~ aSet0(X77)
| ~ aElementOf0(esk16_2(X74,X77),X74) )
& ( ~ aSet0(X74)
| aSubsetOf0(X77,X74)
| ~ aSet0(X77)
| aElementOf0(esk16_2(X74,X77),X77) )
& ( ~ aSet0(X74)
| ~ aSubsetOf0(X75,X74)
| aElementOf0(X76,X74)
| ~ aElementOf0(X76,X75) )
& ( ~ aSet0(X74)
| ~ aSubsetOf0(X75,X74)
| aSet0(X75) ) ),
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_32,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X2,X1)
| aSubsetOf0(sdtlpdtrp0(xN,X1),sdtlpdtrp0(xN,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,hypothesis,
sdtlpdtrp0(xN,sz00) = xS,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,plain,
aElementOf0(sz00,szNzAzT0),
inference(split_conjunct,[status(thm)],[mZeroNum]) ).
cnf(c_0_35,plain,
( ~ aElementOf0(X1,szNzAzT0)
| sdtlseqdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_36,hypothesis,
! [X8] :
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ( aElementOf0(X8,szNzAzT0)
| ~ aElementOf0(X8,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_37,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_38,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_39,hypothesis,
aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
fof(c_0_40,negated_conjecture,
~ ( ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) )
=> ( ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( ( X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) )
& aElement0(X1) ) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
=> ( aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_41,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),xS) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),c_0_35]) ).
cnf(c_0_43,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,xQ)
| aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_45,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_46,negated_conjecture,
! [X56,X57] :
( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
& ~ aElementOf0(esk14_0,xS)
& aElementOf0(esk14_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElementOf0(X57,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X57)
| X57 != szmzizndt0(sdtlpdtrp0(xN,xi)) )
& ( aElementOf0(X57,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X57)
| ~ aElementOf0(X57,xQ) )
& ( ~ aElementOf0(X57,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| X57 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X57,xQ) )
& ( ~ aElementOf0(X57,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElement0(X57) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X56)
| ~ aElementOf0(X56,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
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_40])])])])])]) ).
cnf(c_0_47,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X2))
| aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_48,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_23])]) ).
fof(c_0_49,hypothesis,
! [X54,X55] :
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK
& ( aElementOf0(X55,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X55)
| X55 != szmzizndt0(sdtlpdtrp0(xN,xi)) )
& ( aElementOf0(X55,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X55)
| ~ aElementOf0(X55,xQ) )
& ( ~ aElementOf0(X55,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| X55 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X55,xQ) )
& ( ~ aElementOf0(X55,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElement0(X55) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X54)
| ~ aElementOf0(X54,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
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__4007])])])])]) ).
cnf(c_0_50,negated_conjecture,
~ aElementOf0(esk14_0,xS),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,hypothesis,
( ~ aElementOf0(X1,xQ)
| aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_23])]) ).
cnf(c_0_52,hypothesis,
( ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
aElementOf0(esk14_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,negated_conjecture,
~ aElementOf0(esk14_0,xQ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_22]),c_0_23])]) ).
cnf(c_0_56,negated_conjecture,
szmzizndt0(sdtlpdtrp0(xN,xi)) = esk14_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_57,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM581+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.69 % Computer : n014.cluster.edu
% 0.20/0.69 % Model : x86_64 x86_64
% 0.20/0.69 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.69 % Memory : 8046.5625MB
% 0.20/0.69 % OS : Linux 6.8.0-71-generic
% 0.20/0.69 % CPULimit : 300
% 0.20/0.69 % WCLimit : 300
% 0.20/0.69 % DateTime : Mon Sep 21 02:42:05 UTC 2026
% 0.20/0.70 % CPUTime :
% 0.20/0.70 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.77 Running first-order theorem proving
% 0.24/0.77 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 2.19/1.87 % Version: 3.5.1
% 2.19/1.87 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.19/1.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.19/1.87 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.19/1.87 % Starting new_bool_3 with 300s (1) cores
% 2.19/1.87 % Starting new_bool_1 with 300s (1) cores
% 2.19/1.87 % Starting sh5l with 300s (1) cores
% 2.19/1.87 % new_bool_3 with pid 2973849 completed with status 0
% 2.19/1.87 % Result found by new_bool_3
% 2.19/1.87 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.19/1.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.19/1.87 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.19/1.87 % Starting new_bool_3 with 300s (1) cores
% 2.19/1.87 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.19/1.87 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.19/1.87 % Search class: FGHSF-SMLM32-MFFFFFNN
% 2.19/1.87 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.19/1.87 % Starting SubtermCWHack with 31s (1) cores
% 2.19/1.87 % SubtermCWHack with pid 2973853 completed with status 0
% 2.19/1.87 % Result found by SubtermCWHack
% 2.19/1.87 % Preprocessing class: FSLSSMSMSSSNFFN.
% 2.19/1.87 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.19/1.87 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 2.19/1.87 % Starting new_bool_3 with 300s (1) cores
% 2.19/1.87 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.19/1.87 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.19/1.87 % Search class: FGHSF-SMLM32-MFFFFFNN
% 2.19/1.87 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.19/1.87 % Starting SubtermCWHack with 31s (1) cores
% 2.19/1.87 % Preprocessing time : 0.170 s
% 2.19/1.87
% 2.19/1.87 % Proof found!
% 2.19/1.87 % SZS status Theorem
% 2.19/1.87 % SZS output start CNFRefutation
% See solution above
% 2.19/1.87 % Parsed axioms : 88
% 2.19/1.87 % Removed by relevancy pruning/SinE : 5
% 2.19/1.87 % Initial clauses : 4198
% 2.19/1.87 % Removed in clause preprocessing : 7
% 2.19/1.87 % Initial clauses in saturation : 4191
% 2.19/1.87 % Processed clauses : 892
% 2.19/1.87 % ...of these trivial : 6
% 2.19/1.87 % ...subsumed : 342
% 2.19/1.87 % ...remaining for further processing : 544
% 2.19/1.87 % Other redundant clauses eliminated : 39
% 2.19/1.87 % Clauses deleted for lack of memory : 0
% 2.19/1.87 % Backward-subsumed : 38
% 2.19/1.87 % Backward-rewritten : 21
% 2.19/1.87 % Generated clauses : 2043
% 2.19/1.87 % ...of the previous two non-redundant : 1669
% 2.19/1.87 % ...aggressively subsumed : 0
% 2.19/1.87 % Contextual simplify-reflections : 29
% 2.19/1.87 % Paramodulations : 2003
% 2.19/1.87 % Factorizations : 0
% 2.19/1.87 % NegExts : 0
% 2.19/1.87 % Equation resolutions : 41
% 2.19/1.87 % Disequality decompositions : 0
% 2.19/1.87 % Total rewrite steps : 1540
% 2.19/1.87 % ...of those cached : 1476
% 2.19/1.87 % Propositional unsat checks : 0
% 2.19/1.87 % Propositional check models : 0
% 2.19/1.87 % Propositional check unsatisfiable : 0
% 2.19/1.87 % Propositional clauses : 0
% 2.19/1.87 % Propositional clauses after purity: 0
% 2.19/1.87 % Propositional unsat core size : 0
% 2.19/1.87 % Propositional preprocessing time : 0.000
% 2.19/1.87 % Propositional encoding time : 0.000
% 2.19/1.87 % Propositional solver time : 0.000
% 2.19/1.87 % Success case prop preproc time : 0.000
% 2.19/1.87 % Success case prop encoding time : 0.000
% 2.19/1.87 % Success case prop solver time : 0.000
% 2.19/1.87 % Current number of processed clauses : 452
% 2.19/1.87 % Positive orientable unit clauses : 73
% 2.19/1.87 % Positive unorientable unit clauses: 0
% 2.19/1.87 % Negative unit clauses : 23
% 2.19/1.87 % Non-unit-clauses : 356
% 2.19/1.87 % Current number of unprocessed clauses: 4939
% 2.19/1.87 % ...number of literals in the above : 55109
% 2.19/1.87 % Current number of archived formulas : 0
% 2.19/1.87 % Current number of archived clauses : 62
% 2.19/1.87 % Clause-clause subsumption calls (NU) : 18769
% 2.19/1.87 % Rec. Clause-clause subsumption calls : 11234
% 2.19/1.87 % Non-unit clause-clause subsumptions : 310
% 2.19/1.87 % Unit Clause-clause subsumption calls : 2015
% 2.19/1.87 % Rewrite failures with RHS unbound : 0
% 2.19/1.87 % BW rewrite match attempts : 16
% 2.19/1.87 % BW rewrite match successes : 16
% 2.19/1.87 % Condensation attempts : 0
% 2.19/1.87 % Condensation successes : 0
% 2.19/1.87 % Termbank termtop insertions : 365846
% 2.19/1.87 % Search garbage collected termcells : 26673
% 2.19/1.87
% 2.19/1.87 % -------------------------------------------------
% 2.19/1.87 % User time : 0.708 s
% 2.19/1.87 % System time : 0.053 s
% 2.19/1.87 % Total time : 0.760 s
% 2.19/1.87 % Maximum resident set size: 15036 pages
% 2.19/1.87
% 2.19/1.87 % -------------------------------------------------
% 2.19/1.87 % User time : 0.716 s
% 2.19/1.87 % System time : 0.060 s
% 2.19/1.87 % Total time : 0.777 s
% 2.19/1.87 % Maximum resident set size: 4864 pages
% 2.19/1.87 % E exiting
%------------------------------------------------------------------------------