%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM590+1 : 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 : n004.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 01:49:41 PM UTC 2026
% Result : Theorem 24.80s 4.25s
% Output : CNFRefutation 24.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 28
% Syntax : Number of formulae : 145 ( 33 unt; 0 def)
% Number of atoms : 630 ( 117 equ)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 814 ( 329 ~; 345 |; 93 &)
% ( 14 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 13 con; 0-3 aty)
% Number of variables : 196 ( 0 sgn 104 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(mCardS,axiom,
! [X1] :
( aSet0(X1)
=> aElement0(sbrdtbr0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardS) ).
fof(mCardSeg,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> sbrdtbr0(slbdtrb0(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSeg) ).
fof(mDefSeg,axiom,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( X2 = slbdtrb0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlseqdt0(szszuzczcdt0(X3),X1)
& aElementOf0(X3,szNzAzT0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(mDefMin,axiom,
! [X1] :
( ( X1 != slcrc0
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aElementOf0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
fof(m__3623,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) )
=> ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ) ) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
fof(m__3671,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).
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(m__4448_02,hypothesis,
( xd = sdtlpdtrp0(xC,xi)
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448_02) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(mCountNFin,axiom,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
fof(mSubFSet,axiom,
! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aSubsetOf0(X2,X1)
=> isFinite0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
fof(m__4448,hypothesis,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( ~ ? [X2] : aElementOf0(X2,X1)
& aSet0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(mSelNSet,axiom,
! [X1] :
( ( ~ isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).
fof(m__4151,hypothesis,
( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
& aSet0(X2) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2) = sdtlpdtrp0(xc,sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& szDzozmdt0(sdtlpdtrp0(xC,X1)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)
& aFunction0(sdtlpdtrp0(xC,X1)) ) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aElementOf0(X2,szNzAzT0)
& aSet0(X1) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sbrdtbr0(X4) = X2
& aSubsetOf0(X4,X1) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
fof(m__3533,hypothesis,
( szszuzczcdt0(xk) = xK
& aElementOf0(xk,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3533) ).
fof(mDomSet,axiom,
! [X1] :
( aFunction0(X1)
=> aSet0(szDzozmdt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
fof(m__3965,hypothesis,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
& aSet0(X2) )
=> aElementOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),slbdtsldtrb0(xS,xK)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3965) ).
fof(m__3453,hypothesis,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(m__3435,hypothesis,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(m__3418,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
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/sandbox2/benchmark/theBenchmark.p',mDefCons) ).
fof(mSubTrans,axiom,
! [X1,X2,X3] :
( ( aSet0(X3)
& aSet0(X2)
& aSet0(X1) )
=> ( ( aSubsetOf0(X2,X3)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubTrans) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__,conjecture,
aSubsetOf0(xY,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_28,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_29,plain,
! [X105,X106,X107,X108,X109,X110] :
( ( ~ aElement0(X106)
| ~ aSet0(X105)
| X110 = sdtmndt0(X105,X106)
| ~ aSet0(X110)
| aElementOf0(esk12_3(X105,X106,X110),X110)
| esk12_3(X105,X106,X110) != X106 )
& ( ~ aElement0(X106)
| ~ aSet0(X105)
| X110 = sdtmndt0(X105,X106)
| ~ aSet0(X110)
| aElementOf0(esk12_3(X105,X106,X110),X110)
| aElementOf0(esk12_3(X105,X106,X110),X105) )
& ( ~ aElement0(X106)
| ~ aSet0(X105)
| X110 = sdtmndt0(X105,X106)
| ~ aSet0(X110)
| aElementOf0(esk12_3(X105,X106,X110),X110)
| aElement0(esk12_3(X105,X106,X110)) )
& ( ~ aElement0(X106)
| ~ aSet0(X105)
| X110 = sdtmndt0(X105,X106)
| ~ aSet0(X110)
| esk12_3(X105,X106,X110) = X106
| ~ aElementOf0(esk12_3(X105,X106,X110),X105)
| ~ aElement0(esk12_3(X105,X106,X110))
| ~ aElementOf0(esk12_3(X105,X106,X110),X110) )
& ( ~ aElement0(X106)
| ~ aSet0(X105)
| X107 != sdtmndt0(X105,X106)
| aElementOf0(X109,X107)
| X109 = X106
| ~ aElementOf0(X109,X105)
| ~ aElement0(X109) )
& ( ~ aElement0(X106)
| ~ aSet0(X105)
| X107 != sdtmndt0(X105,X106)
| ~ aElementOf0(X108,X107)
| X108 != X106 )
& ( ~ aElement0(X106)
| ~ aSet0(X105)
| X107 != sdtmndt0(X105,X106)
| ~ aElementOf0(X108,X107)
| aElementOf0(X108,X105) )
& ( ~ aElement0(X106)
| ~ aSet0(X105)
| X107 != sdtmndt0(X105,X106)
| ~ aElementOf0(X108,X107)
| aElement0(X108) )
& ( ~ aElement0(X106)
| ~ aSet0(X105)
| X107 != sdtmndt0(X105,X106)
| aSet0(X107) ) ),
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_28])])])])])])]) ).
fof(c_0_30,plain,
! [X155] :
( aElement0(sbrdtbr0(X155))
| ~ aSet0(X155) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardS])])]) ).
fof(c_0_31,plain,
! [X162] :
( sbrdtbr0(slbdtrb0(X162)) = X162
| ~ aElementOf0(X162,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardSeg])])]) ).
fof(c_0_32,plain,
! [X163,X164,X165,X166,X167] :
( ( ~ aElementOf0(X163,szNzAzT0)
| X167 = slbdtrb0(X163)
| ~ aSet0(X167)
| aElementOf0(esk17_2(X163,X167),X167)
| sdtlseqdt0(szszuzczcdt0(esk17_2(X163,X167)),X163) )
& ( ~ aElementOf0(X163,szNzAzT0)
| X167 = slbdtrb0(X163)
| ~ aSet0(X167)
| aElementOf0(esk17_2(X163,X167),X167)
| aElementOf0(esk17_2(X163,X167),szNzAzT0) )
& ( ~ aElementOf0(X163,szNzAzT0)
| X167 = slbdtrb0(X163)
| ~ aSet0(X167)
| ~ sdtlseqdt0(szszuzczcdt0(esk17_2(X163,X167)),X163)
| ~ aElementOf0(esk17_2(X163,X167),szNzAzT0)
| ~ aElementOf0(esk17_2(X163,X167),X167) )
& ( ~ aElementOf0(X163,szNzAzT0)
| X164 != slbdtrb0(X163)
| aElementOf0(X166,X164)
| ~ sdtlseqdt0(szszuzczcdt0(X166),X163)
| ~ aElementOf0(X166,szNzAzT0) )
& ( ~ aElementOf0(X163,szNzAzT0)
| X164 != slbdtrb0(X163)
| ~ aElementOf0(X165,X164)
| sdtlseqdt0(szszuzczcdt0(X165),X163) )
& ( ~ aElementOf0(X163,szNzAzT0)
| X164 != slbdtrb0(X163)
| ~ aElementOf0(X165,X164)
| aElementOf0(X165,szNzAzT0) )
& ( ~ aElementOf0(X163,szNzAzT0)
| X164 != slbdtrb0(X163)
| aSet0(X164) ) ),
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)],[mDefSeg])])])])])])]) ).
fof(c_0_33,plain,
! [X1] :
( ( X1 != slcrc0
& aSubsetOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = szmzizndt0(X1)
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlseqdt0(X2,X3) )
& aElementOf0(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[mDefMin]) ).
fof(c_0_34,hypothesis,
! [X13] :
( ( ~ aElementOf0(X13,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X13))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X13),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X13))) )
& ( ~ aElementOf0(X13,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X13))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X13),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X13)),sdtmndt0(sdtlpdtrp0(xN,X13),szmzizndt0(sdtlpdtrp0(xN,X13)))) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
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__3623])])])])]) ).
fof(c_0_35,hypothesis,
! [X14] :
( ( ~ aElementOf0(X14,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X14)) )
& ( ~ aElementOf0(X14,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X14),szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])])]) ).
cnf(c_0_36,plain,
( ~ aElement0(X3)
| ~ aSet0(X2)
| X1 != sdtmndt0(X2,X3)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( ~ aSet0(X1)
| aElement0(sbrdtbr0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( ~ aElementOf0(X1,szNzAzT0)
| sbrdtbr0(slbdtrb0(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( ~ aElementOf0(X2,szNzAzT0)
| X1 != slbdtrb0(X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_40,plain,
! [X32,X33,X34,X35] :
( ( ~ aSet0(X32)
| aSubsetOf0(X35,X32)
| ~ aSet0(X35)
| ~ aElementOf0(esk3_2(X32,X35),X32) )
& ( ~ aSet0(X32)
| aSubsetOf0(X35,X32)
| ~ aSet0(X35)
| aElementOf0(esk3_2(X32,X35),X35) )
& ( ~ aSet0(X32)
| ~ aSubsetOf0(X33,X32)
| aElementOf0(X34,X32)
| ~ aElementOf0(X34,X33) )
& ( ~ aSet0(X32)
| ~ aSubsetOf0(X33,X32)
| aSet0(X33) ) ),
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])])])])])])]) ).
fof(c_0_41,plain,
! [X120,X121,X122,X123] :
( ( X120 = slcrc0
| ~ aSubsetOf0(X120,szNzAzT0)
| X123 = szmzizndt0(X120)
| ~ aElementOf0(X123,X120)
| ~ sdtlseqdt0(X123,esk13_2(X120,X123)) )
& ( X120 = slcrc0
| ~ aSubsetOf0(X120,szNzAzT0)
| X123 = szmzizndt0(X120)
| ~ aElementOf0(X123,X120)
| aElementOf0(esk13_2(X120,X123),X120) )
& ( X120 = slcrc0
| ~ aSubsetOf0(X120,szNzAzT0)
| X121 != szmzizndt0(X120)
| sdtlseqdt0(X121,X122)
| ~ aElementOf0(X122,X120) )
& ( X120 = slcrc0
| ~ aSubsetOf0(X120,szNzAzT0)
| X121 != szmzizndt0(X120)
| aElementOf0(X121,X120) ) ),
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_33])])])])])])]) ).
cnf(c_0_42,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X1))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSet0(sdtmndt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_36]) ).
cnf(c_0_46,hypothesis,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(split_conjunct,[status(thm)],[m__4448_02]) ).
cnf(c_0_47,plain,
( ~ aSet0(slbdtrb0(X1))
| ~ aElementOf0(X1,szNzAzT0)
| aElement0(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_48,plain,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(slbdtrb0(X1)) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
( ~ aSet0(X3)
| ~ aSubsetOf0(X2,X3)
| ~ aElementOf0(X1,X2)
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
cnf(c_0_51,plain,
( ~ aSubsetOf0(X2,szNzAzT0)
| X1 != szmzizndt0(X2)
| X2 = slcrc0
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_52,plain,
! [X1] :
( ( isCountable0(X1)
& aSet0(X1) )
=> ~ isFinite0(X1) ),
inference(fof_simplification,[status(thm)],[mCountNFin]) ).
fof(c_0_53,plain,
! [X29,X30] :
( isFinite0(X30)
| ~ aSubsetOf0(X30,X29)
| ~ isFinite0(X29)
| ~ aSet0(X29) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubFSet])])])]) ).
cnf(c_0_54,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_55,hypothesis,
aElementOf0(xi,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__4448]) ).
cnf(c_0_56,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| aSet0(xY) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_57,plain,
( ~ aElementOf0(X1,szNzAzT0)
| aElement0(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X2))
| aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_50])]) ).
cnf(c_0_59,plain,
( ~ aSubsetOf0(X1,szNzAzT0)
| aElementOf0(szmzizndt0(X1),X1)
| X1 = slcrc0 ),
inference(er,[status(thm)],[c_0_51]) ).
fof(c_0_60,plain,
! [X148,X149,X150] :
( ( X150 = slcrc0
| aElementOf0(esk15_1(X150),X150)
| ~ aSet0(X150) )
& ( X148 != slcrc0
| ~ aElementOf0(X149,X148) )
& ( X148 != slcrc0
| aSet0(X148) ) ),
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)],[mDefEmp])])])])])])]) ).
fof(c_0_61,plain,
! [X28] :
( ~ isFinite0(X28)
| ~ isCountable0(X28)
| ~ aSet0(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
cnf(c_0_62,plain,
( ~ aSubsetOf0(X2,X1)
| ~ isFinite0(X1)
| ~ aSet0(X1)
| isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,hypothesis,
aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xi)),xY),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_46]),c_0_55])]) ).
cnf(c_0_64,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_65,plain,
! [X1] :
( ( ~ isFinite0(X1)
& aSet0(X1) )
=> ! [X2] :
( aElementOf0(X2,szNzAzT0)
=> slbdtsldtrb0(X1,X2) != slcrc0 ) ),
inference(fof_simplification,[status(thm)],[mSelNSet]) ).
fof(c_0_66,hypothesis,
! [X21,X22] :
( ( ~ aElementOf0(X21,szNzAzT0)
| sdtlpdtrp0(sdtlpdtrp0(xC,X21),X22) = sdtlpdtrp0(xc,sdtpldt0(X22,szmzizndt0(sdtlpdtrp0(xN,X21))))
| ~ aElementOf0(X22,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X21),szmzizndt0(sdtlpdtrp0(xN,X21))),xk))
| ~ aSet0(X22) )
& ( ~ aElementOf0(X21,szNzAzT0)
| szDzozmdt0(sdtlpdtrp0(xC,X21)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X21),szmzizndt0(sdtlpdtrp0(xN,X21))),xk) )
& ( ~ aElementOf0(X21,szNzAzT0)
| aFunction0(sdtlpdtrp0(xC,X21)) )
& szDzozmdt0(xC) = szNzAzT0
& aFunction0(xC) ),
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__4151])])])])]) ).
fof(c_0_67,plain,
! [X69,X70,X71,X72,X73,X74] :
( ( ~ aElementOf0(X70,szNzAzT0)
| ~ aSet0(X69)
| X74 = slbdtsldtrb0(X69,X70)
| ~ aSet0(X74)
| aElementOf0(esk9_3(X69,X70,X74),X74)
| sbrdtbr0(esk9_3(X69,X70,X74)) = X70 )
& ( ~ aElementOf0(X70,szNzAzT0)
| ~ aSet0(X69)
| X74 = slbdtsldtrb0(X69,X70)
| ~ aSet0(X74)
| aElementOf0(esk9_3(X69,X70,X74),X74)
| aSubsetOf0(esk9_3(X69,X70,X74),X69) )
& ( ~ aElementOf0(X70,szNzAzT0)
| ~ aSet0(X69)
| X74 = slbdtsldtrb0(X69,X70)
| ~ aSet0(X74)
| sbrdtbr0(esk9_3(X69,X70,X74)) != X70
| ~ aSubsetOf0(esk9_3(X69,X70,X74),X69)
| ~ aElementOf0(esk9_3(X69,X70,X74),X74) )
& ( ~ aElementOf0(X70,szNzAzT0)
| ~ aSet0(X69)
| X71 != slbdtsldtrb0(X69,X70)
| aElementOf0(X73,X71)
| sbrdtbr0(X73) != X70
| ~ aSubsetOf0(X73,X69) )
& ( ~ aElementOf0(X70,szNzAzT0)
| ~ aSet0(X69)
| X71 != slbdtsldtrb0(X69,X70)
| ~ aElementOf0(X72,X71)
| sbrdtbr0(X72) = X70 )
& ( ~ aElementOf0(X70,szNzAzT0)
| ~ aSet0(X69)
| X71 != slbdtsldtrb0(X69,X70)
| ~ aElementOf0(X72,X71)
| aSubsetOf0(X72,X69) )
& ( ~ aElementOf0(X70,szNzAzT0)
| ~ aSet0(X69)
| X71 != slbdtsldtrb0(X69,X70)
| aSet0(X71) ) ),
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)],[mDefSel])])])])])])]) ).
cnf(c_0_68,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),szNzAzT0)
| aSet0(xY) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_69,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),szNzAzT0)
| sdtlpdtrp0(xN,X1) = slcrc0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_44]) ).
cnf(c_0_70,plain,
( X1 != slcrc0
| aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,plain,
( ~ isFinite0(X1)
| ~ isCountable0(X1)
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,hypothesis,
( ~ aSet0(xY)
| ~ isFinite0(xY)
| isFinite0(sdtlpdtrp0(xN,szszuzczcdt0(xi))) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_73,hypothesis,
( ~ aSet0(xY)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xi))) ),
inference(spm,[status(thm)],[c_0_64,c_0_63]) ).
cnf(c_0_74,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X1))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_75,plain,
! [X78,X79] :
( slbdtsldtrb0(X78,X79) != slcrc0
| ~ aElementOf0(X79,szNzAzT0)
| isFinite0(X78)
| ~ aSet0(X78) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])]) ).
cnf(c_0_76,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| szDzozmdt0(sdtlpdtrp0(xC,X1)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_77,hypothesis,
xd = sdtlpdtrp0(xC,xi),
inference(split_conjunct,[status(thm)],[m__4448_02]) ).
cnf(c_0_78,plain,
( ~ aElementOf0(X4,szNzAzT0)
| ~ aSet0(X2)
| X3 != slbdtsldtrb0(X2,X4)
| ~ aElementOf0(X1,X3)
| aSubsetOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_79,hypothesis,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| aSet0(xY)
| sdtlpdtrp0(xN,xi) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_55])]) ).
cnf(c_0_80,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_44]),c_0_50])]) ).
cnf(c_0_81,plain,
isFinite0(slcrc0),
inference(split_conjunct,[status(thm)],[mEmpFin]) ).
cnf(c_0_82,plain,
aSet0(slcrc0),
inference(er,[status(thm)],[c_0_70]) ).
cnf(c_0_83,hypothesis,
( ~ aSet0(xY)
| ~ isFinite0(xY)
| ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xi))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_84,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_74,c_0_43]),c_0_44]) ).
cnf(c_0_85,plain,
( slbdtsldtrb0(X1,X2) != slcrc0
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1)
| isFinite0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_86,hypothesis,
slbdtsldtrb0(xY,xk) = szDzozmdt0(xd),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_46]),c_0_77]),c_0_55])]) ).
cnf(c_0_87,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3533]) ).
cnf(c_0_88,plain,
( ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
| aSubsetOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_78]) ).
cnf(c_0_89,hypothesis,
( aSet0(xY)
| sdtlpdtrp0(xN,xi) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_55])]) ).
cnf(c_0_90,plain,
~ isCountable0(slcrc0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_81]),c_0_82])]) ).
fof(c_0_91,plain,
! [X66] :
( aSet0(szDzozmdt0(X66))
| ~ aFunction0(X66) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDomSet])])]) ).
cnf(c_0_92,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aFunction0(sdtlpdtrp0(xC,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_93,hypothesis,
( ~ aSet0(xY)
| ~ isFinite0(xY) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_55])]) ).
cnf(c_0_94,hypothesis,
( ~ aSet0(xY)
| szDzozmdt0(xd) != slcrc0
| isFinite0(xY) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
fof(c_0_95,hypothesis,
! [X19,X20] :
( aElementOf0(sdtpldt0(X20,szmzizndt0(sdtlpdtrp0(xN,X19))),slbdtsldtrb0(xS,xK))
| ~ aElementOf0(X20,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X19),szmzizndt0(sdtlpdtrp0(xN,X19))),xk))
| ~ aSet0(X20)
| ~ aElementOf0(X19,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3965])])])]) ).
cnf(c_0_96,hypothesis,
( ~ aSet0(xY)
| ~ aElementOf0(X1,szDzozmdt0(xd))
| aSubsetOf0(X1,xY) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_86]),c_0_87])]) ).
cnf(c_0_97,hypothesis,
aSet0(xY),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_89]),c_0_55])]),c_0_90]) ).
cnf(c_0_98,plain,
( ~ aFunction0(X1)
| aSet0(szDzozmdt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_99,hypothesis,
aFunction0(xd),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_77]),c_0_55])]) ).
cnf(c_0_100,hypothesis,
( ~ aSet0(xY)
| szDzozmdt0(xd) != slcrc0 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_101,hypothesis,
( ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
| ~ aSet0(X2)
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(sdtpldt0(X2,szmzizndt0(sdtlpdtrp0(xN,X1))),slbdtsldtrb0(xS,xK)) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_102,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_103,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xd))
| aSubsetOf0(X1,xY) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97])]) ).
cnf(c_0_104,plain,
( ~ aSet0(X1)
| X1 = slcrc0
| aElementOf0(esk15_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_105,hypothesis,
aSet0(szDzozmdt0(xd)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,hypothesis,
szDzozmdt0(xd) != slcrc0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_97])]) ).
cnf(c_0_107,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_108,hypothesis,
( ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X2),szmzizndt0(sdtlpdtrp0(xN,X2))),xk))
| aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X2))),szDzozmdt0(xc)) ),
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_109,hypothesis,
aSubsetOf0(esk15_1(szDzozmdt0(xd)),xY),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105])]),c_0_106]) ).
cnf(c_0_110,hypothesis,
aElementOf0(xK,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3418]) ).
cnf(c_0_111,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_107]),c_0_50])]) ).
cnf(c_0_112,hypothesis,
( ~ aSet0(slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk))
| ~ aSet0(esk15_1(slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)))
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(sdtpldt0(esk15_1(slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)),szmzizndt0(sdtlpdtrp0(xN,X1))),szDzozmdt0(xc))
| slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk) = slcrc0 ),
inference(spm,[status(thm)],[c_0_108,c_0_104]) ).
cnf(c_0_113,hypothesis,
aSet0(esk15_1(szDzozmdt0(xd))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_109]),c_0_97])]) ).
cnf(c_0_114,hypothesis,
( ~ aElementOf0(X1,szDzozmdt0(xc))
| aSubsetOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_102]),c_0_110]),c_0_111])]) ).
cnf(c_0_115,hypothesis,
aElementOf0(sdtpldt0(esk15_1(szDzozmdt0(xd)),szmzizndt0(sdtlpdtrp0(xN,xi))),szDzozmdt0(xc)),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_46]),c_0_86]),c_0_86]),c_0_55]),c_0_86]),c_0_113]),c_0_86]),c_0_105])]),c_0_106]) ).
fof(c_0_116,plain,
! [X135,X136,X137,X138,X139,X140] :
( ( ~ aElement0(X136)
| ~ aSet0(X135)
| X140 = sdtpldt0(X135,X136)
| ~ aSet0(X140)
| aElementOf0(esk14_3(X135,X136,X140),X140)
| esk14_3(X135,X136,X140) = X136
| aElementOf0(esk14_3(X135,X136,X140),X135) )
& ( ~ aElement0(X136)
| ~ aSet0(X135)
| X140 = sdtpldt0(X135,X136)
| ~ aSet0(X140)
| aElementOf0(esk14_3(X135,X136,X140),X140)
| aElement0(esk14_3(X135,X136,X140)) )
& ( ~ aElement0(X136)
| ~ aSet0(X135)
| X140 = sdtpldt0(X135,X136)
| ~ aSet0(X140)
| ~ aElementOf0(esk14_3(X135,X136,X140),X140)
| ~ aElement0(esk14_3(X135,X136,X140))
| esk14_3(X135,X136,X140) != X136 )
& ( ~ aElement0(X136)
| ~ aSet0(X135)
| X140 = sdtpldt0(X135,X136)
| ~ aSet0(X140)
| ~ aElementOf0(esk14_3(X135,X136,X140),X140)
| ~ aElement0(esk14_3(X135,X136,X140))
| ~ aElementOf0(esk14_3(X135,X136,X140),X135) )
& ( ~ aElement0(X136)
| ~ aSet0(X135)
| X137 != sdtpldt0(X135,X136)
| aElementOf0(X139,X137)
| ~ aElement0(X139)
| X139 != X136 )
& ( ~ aElement0(X136)
| ~ aSet0(X135)
| X137 != sdtpldt0(X135,X136)
| aElementOf0(X139,X137)
| ~ aElement0(X139)
| ~ aElementOf0(X139,X135) )
& ( ~ aElement0(X136)
| ~ aSet0(X135)
| X137 != sdtpldt0(X135,X136)
| ~ aElementOf0(X138,X137)
| X138 = X136
| aElementOf0(X138,X135) )
& ( ~ aElement0(X136)
| ~ aSet0(X135)
| X137 != sdtpldt0(X135,X136)
| ~ aElementOf0(X138,X137)
| aElement0(X138) )
& ( ~ aElement0(X136)
| ~ aSet0(X135)
| X137 != sdtpldt0(X135,X136)
| aSet0(X137) ) ),
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_117,plain,
! [X40,X41,X42] :
( aSubsetOf0(X40,X42)
| ~ aSubsetOf0(X41,X42)
| ~ aSubsetOf0(X40,X41)
| ~ aSet0(X42)
| ~ aSet0(X41)
| ~ aSet0(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubTrans])])]) ).
cnf(c_0_118,plain,
( ~ aElement0(X4)
| ~ aSet0(X2)
| X3 != sdtmndt0(X2,X4)
| ~ aElementOf0(X1,X3)
| aElementOf0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_119,hypothesis,
aSubsetOf0(sdtpldt0(esk15_1(szDzozmdt0(xd)),szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_120,plain,
( ~ aElement0(X2)
| ~ aSet0(X4)
| X3 != sdtpldt0(X4,X2)
| ~ aElement0(X1)
| X1 != X2
| aElementOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
fof(c_0_121,plain,
! [X153,X154] :
( aElement0(X154)
| ~ aElementOf0(X154,X153)
| ~ aSet0(X153) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).
cnf(c_0_122,plain,
( ~ aSubsetOf0(X2,X3)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X3)
| ~ aSet0(X2)
| ~ aSet0(X1)
| aSubsetOf0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_123,plain,
( ~ aSet0(X2)
| ~ aElement0(X3)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| aElementOf0(X1,X2) ),
inference(er,[status(thm)],[c_0_118]) ).
cnf(c_0_124,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| aSubsetOf0(X2,X1)
| aElementOf0(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_125,negated_conjecture,
~ aSubsetOf0(xY,szNzAzT0),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_126,hypothesis,
( ~ aElementOf0(X1,sdtpldt0(esk15_1(szDzozmdt0(xd)),szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_119]),c_0_111])]) ).
cnf(c_0_127,plain,
( ~ aSet0(X2)
| ~ aElement0(X1)
| aElementOf0(X1,sdtpldt0(X2,X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_120])]) ).
cnf(c_0_128,plain,
( ~ aElementOf0(X2,X1)
| ~ aSet0(X1)
| aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_129,plain,
( ~ aSet0(X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSubsetOf0(X3,X2)
| aSubsetOf0(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_122,c_0_64]),c_0_64]) ).
cnf(c_0_130,plain,
( ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aElementOf0(esk3_2(X1,X2),X1)
| aSubsetOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_131,plain,
( ~ aSet0(X3)
| ~ aSet0(X1)
| ~ aElement0(X2)
| aElementOf0(esk3_2(X3,sdtmndt0(X1,X2)),X1)
| aSubsetOf0(sdtmndt0(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_45]) ).
fof(c_0_132,negated_conjecture,
~ aSubsetOf0(xY,szNzAzT0),
inference(fof_simplification,[status(thm)],[c_0_125]) ).
cnf(c_0_133,hypothesis,
( ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_113])]) ).
cnf(c_0_134,hypothesis,
( ~ aElementOf0(X1,szNzAzT0)
| aElement0(szmzizndt0(sdtlpdtrp0(xN,X1)))
| sdtlpdtrp0(xN,X1) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_69]),c_0_50])]) ).
cnf(c_0_135,hypothesis,
( ~ aElementOf0(X2,szNzAzT0)
| ~ aSubsetOf0(X1,sdtlpdtrp0(xN,X2))
| aSubsetOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_44]),c_0_50])]) ).
cnf(c_0_136,plain,
( ~ aSet0(X1)
| ~ aElement0(X2)
| aSubsetOf0(sdtmndt0(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_45]) ).
fof(c_0_137,negated_conjecture,
~ aSubsetOf0(xY,szNzAzT0),
inference(fof_nnf,[status(thm)],[c_0_132]) ).
cnf(c_0_138,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS)
| sdtlpdtrp0(xN,xi) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_55])]) ).
cnf(c_0_139,hypothesis,
( ~ aElement0(X2)
| ~ aElementOf0(X1,szNzAzT0)
| aSubsetOf0(sdtmndt0(sdtlpdtrp0(xN,X1),X2),szNzAzT0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_80]) ).
cnf(c_0_140,negated_conjecture,
~ aSubsetOf0(xY,szNzAzT0),
inference(split_conjunct,[status(thm)],[c_0_137]) ).
cnf(c_0_141,hypothesis,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| sdtlpdtrp0(xN,xi) = slcrc0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_138]),c_0_111])]) ).
cnf(c_0_142,hypothesis,
~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_46]),c_0_55])]),c_0_140]) ).
cnf(c_0_143,hypothesis,
sdtlpdtrp0(xN,xi) = slcrc0,
inference(sr,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_144,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_143]),c_0_55])]),c_0_90]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM590+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.58 % Computer : n004.cluster.edu
% 0.12/0.58 % Model : x86_64 x86_64
% 0.12/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.58 % Memory : 8046.5625MB
% 0.12/0.58 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Mon Sep 21 02:42:36 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.62 Running first-order theorem proving
% 0.12/0.62 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
% 24.80/4.25 % Version: 3.5.1
% 24.80/4.25 % Preprocessing class: FSLSSMSMSSSNFFN.
% 24.80/4.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.80/4.25 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 24.80/4.25 % Starting new_bool_3 with 300s (1) cores
% 24.80/4.25 % Starting new_bool_1 with 300s (1) cores
% 24.80/4.25 % Starting sh5l with 300s (1) cores
% 24.80/4.25 % new_bool_1 with pid 2080743 completed with status 0
% 24.80/4.25 % Result found by new_bool_1
% 24.80/4.25 % Preprocessing class: FSLSSMSMSSSNFFN.
% 24.80/4.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.80/4.25 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 24.80/4.25 % Starting new_bool_3 with 300s (1) cores
% 24.80/4.25 % Starting new_bool_1 with 300s (1) cores
% 24.80/4.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 24.80/4.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 24.80/4.25 % Search class: FGHSF-FSLM32-MFFFFFNN
% 24.80/4.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 24.80/4.25 % Starting SubtermCWHack with 28s (1) cores
% 24.80/4.25 % SubtermCWHack with pid 2080751 completed with status 0
% 24.80/4.25 % Result found by SubtermCWHack
% 24.80/4.25 % Preprocessing class: FSLSSMSMSSSNFFN.
% 24.80/4.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.80/4.25 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 24.80/4.25 % Starting new_bool_3 with 300s (1) cores
% 24.80/4.25 % Starting new_bool_1 with 300s (1) cores
% 24.80/4.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 24.80/4.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 24.80/4.25 % Search class: FGHSF-FSLM32-MFFFFFNN
% 24.80/4.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 24.80/4.25 % Starting SubtermCWHack with 28s (1) cores
% 24.80/4.25 % Preprocessing time : 0.003 s
% 24.80/4.25
% 24.80/4.25 % Proof found!
% 24.80/4.25 % SZS status Theorem
% 24.80/4.25 % SZS output start CNFRefutation
% See solution above
% 24.80/4.25 % Parsed axioms : 92
% 24.80/4.25 % Removed by relevancy pruning/SinE : 5
% 24.80/4.25 % Initial clauses : 163
% 24.80/4.25 % Removed in clause preprocessing : 7
% 24.80/4.25 % Initial clauses in saturation : 156
% 24.80/4.25 % Processed clauses : 19384
% 24.80/4.25 % ...of these trivial : 97
% 24.80/4.25 % ...subsumed : 14836
% 24.80/4.25 % ...remaining for further processing : 4451
% 24.80/4.25 % Other redundant clauses eliminated : 81
% 24.80/4.25 % Clauses deleted for lack of memory : 0
% 24.80/4.25 % Backward-subsumed : 507
% 24.80/4.25 % Backward-rewritten : 224
% 24.80/4.25 % Generated clauses : 121047
% 24.80/4.25 % ...of the previous two non-redundant : 104075
% 24.80/4.25 % ...aggressively subsumed : 0
% 24.80/4.25 % Contextual simplify-reflections : 592
% 24.80/4.25 % Paramodulations : 120964
% 24.80/4.25 % Factorizations : 0
% 24.80/4.25 % NegExts : 0
% 24.80/4.25 % Equation resolutions : 84
% 24.80/4.25 % Disequality decompositions : 0
% 24.80/4.25 % Total rewrite steps : 95849
% 24.80/4.25 % ...of those cached : 95717
% 24.80/4.25 % Propositional unsat checks : 0
% 24.80/4.25 % Propositional check models : 0
% 24.80/4.25 % Propositional check unsatisfiable : 0
% 24.80/4.25 % Propositional clauses : 0
% 24.80/4.25 % Propositional clauses after purity: 0
% 24.80/4.25 % Propositional unsat core size : 0
% 24.80/4.25 % Propositional preprocessing time : 0.000
% 24.80/4.25 % Propositional encoding time : 0.000
% 24.80/4.25 % Propositional solver time : 0.000
% 24.80/4.25 % Success case prop preproc time : 0.000
% 24.80/4.25 % Success case prop encoding time : 0.000
% 24.80/4.25 % Success case prop solver time : 0.000
% 24.80/4.25 % Current number of processed clauses : 3688
% 24.80/4.25 % Positive orientable unit clauses : 145
% 24.80/4.25 % Positive unorientable unit clauses: 0
% 24.80/4.25 % Negative unit clauses : 55
% 24.80/4.25 % Non-unit-clauses : 3488
% 24.80/4.25 % Current number of unprocessed clauses: 83201
% 24.80/4.25 % ...number of literals in the above : 528528
% 24.80/4.25 % Current number of archived formulas : 0
% 24.80/4.25 % Current number of archived clauses : 734
% 24.80/4.25 % Clause-clause subsumption calls (NU) : 2025782
% 24.80/4.25 % Rec. Clause-clause subsumption calls : 644517
% 24.80/4.25 % Non-unit clause-clause subsumptions : 11813
% 24.80/4.25 % Unit Clause-clause subsumption calls : 40738
% 24.80/4.25 % Rewrite failures with RHS unbound : 0
% 24.80/4.25 % BW rewrite match attempts : 55
% 24.80/4.25 % BW rewrite match successes : 29
% 24.80/4.25 % Condensation attempts : 0
% 24.80/4.25 % Condensation successes : 0
% 24.80/4.25 % Termbank termtop insertions : 2837876
% 24.80/4.25 % Search garbage collected termcells : 3176
% 24.80/4.25
% 24.80/4.25 % -------------------------------------------------
% 24.80/4.25 % User time : 3.454 s
% 24.80/4.25 % System time : 0.097 s
% 24.80/4.25 % Total time : 3.551 s
% 24.80/4.25 % Maximum resident set size: 4264 pages
% 24.80/4.25
% 24.80/4.25 % -------------------------------------------------
% 24.80/4.25 % User time : 3.457 s
% 24.80/4.25 % System time : 0.103 s
% 24.80/4.25 % Total time : 3.560 s
% 24.80/4.25 % Maximum resident set size: 4864 pages
% 24.80/4.25 % E exiting
%------------------------------------------------------------------------------