%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LAT388+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 : Wed Oct 7 10:27:43 AM UTC 2026
% Result : Theorem 6.23s 1.36s
% Output : CNFRefutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 21
% Syntax : Number of formulae : 817 ( 253 unt; 0 typ; 0 def)
% Number of atoms : 9235 (2077 equ; 0 cnn)
% Maximal formula atoms : 37 ( 11 avg)
% Number of connectives : 23462 (6603 ~;4206 |; 214 &;12283 @)
% ( 0 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 8 con; 0-3 aty)
% Number of variables : 2052 ( 0 ^;2041 !; 11 ?;2052 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aCompleteLattice0,type,
aCompleteLattice0: $i > $o ).
thf(tp_aElement0,type,
aElement0: $i > $o ).
thf(tp_aElementOf0,type,
aElementOf0: $i > $i > $o ).
thf(tp_aFixedPointOf0,type,
aFixedPointOf0: $i > $i > $o ).
thf(tp_aFunction0,type,
aFunction0: $i > $o ).
thf(tp_aInfimumOfIn0,type,
aInfimumOfIn0: $i > $i > $i > $o ).
thf(tp_aLowerBoundOfIn0,type,
aLowerBoundOfIn0: $i > $i > $i > $o ).
thf(tp_aSet0,type,
aSet0: $i > $o ).
thf(tp_aSubsetOf0,type,
aSubsetOf0: $i > $i > $o ).
thf(tp_aSupremumOfIn0,type,
aSupremumOfIn0: $i > $i > $i > $o ).
thf(tp_aUpperBoundOfIn0,type,
aUpperBoundOfIn0: $i > $i > $i > $o ).
thf(tp_cS1142,type,
cS1142: $i > $i ).
thf(tp_cS1241,type,
cS1241: $i > $i > $i > $i ).
thf(tp_isEmpty0,type,
isEmpty0: $i > $o ).
thf(tp_isMonotone0,type,
isMonotone0: $i > $o ).
thf(tp_isOn0,type,
isOn0: $i > $i > $o ).
thf(tp_sK10_SY85,type,
sK10_SY85: $i > $i ).
thf(tp_sK11_SY89,type,
sK11_SY89: $i > $i ).
thf(tp_sK12_SY85,type,
sK12_SY85: $i > $i ).
thf(tp_sK13_SY89,type,
sK13_SY89: $i > $i ).
thf(tp_sK14_SY89,type,
sK14_SY89: $i > $i ).
thf(tp_sK15_SY117,type,
sK15_SY117: $i > $i > $i ).
thf(tp_sK16_SY124,type,
sK16_SY124: $i > $i > $i ).
thf(tp_sK17_SY125,type,
sK17_SY125: $i > $i > $i ).
thf(tp_sK18_SY126,type,
sK18_SY126: $i > $i > $i ).
thf(tp_sK19_SY127,type,
sK19_SY127: $i > $i > $i ).
thf(tp_sK1_SY68,type,
sK1_SY68: $i > $i ).
thf(tp_sK20_SY128,type,
sK20_SY128: $i > $i > $i ).
thf(tp_sK2_SY78,type,
sK2_SY78: $i > $i ).
thf(tp_sK3_SY79,type,
sK3_SY79: $i > $i ).
thf(tp_sK4_SY67,type,
sK4_SY67: $i > $i ).
thf(tp_sK5_SY68,type,
sK5_SY68: $i > $i ).
thf(tp_sK6_SY68,type,
sK6_SY68: $i > $i ).
thf(tp_sK7_SY75,type,
sK7_SY75: $i > $i ).
thf(tp_sK8_SY85,type,
sK8_SY85: $i > $i ).
thf(tp_sK9_SY84,type,
sK9_SY84: $i > $i ).
thf(tp_sdtlpdtrp0,type,
sdtlpdtrp0: $i > $i > $i ).
thf(tp_sdtlseqdt0,type,
sdtlseqdt0: $i > $i > $o ).
thf(tp_szDzozmdt0,type,
szDzozmdt0: $i > $i ).
thf(tp_szRzazndt0,type,
szRzazndt0: $i > $i ).
thf(tp_xP,type,
xP: $i ).
thf(tp_xS,type,
xS: $i ).
thf(tp_xT,type,
xT: $i ).
thf(tp_xU,type,
xU: $i ).
thf(tp_xf,type,
xf: $i ).
thf(tp_xp,type,
xp: $i ).
thf(1,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( szRzazndt0 @ W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgSort) ).
thf(2,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szRzazndt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mRanSort) ).
thf(3,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSort) ).
thf(4,axiom,
! [W0: $i] :
( ( aFunction0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConMap) ).
thf(5,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aInfimumOfIn0 @ W2 @ W1 @ W0 )
& ( aInfimumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mInfUn) ).
thf(6,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
& ( aSupremumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSupUn) ).
thf(7,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTrans) ).
thf(8,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mASymm) ).
thf(9,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mARefl) ).
thf(10,axiom,
! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessRel) ).
thf(11,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
thf(12,axiom,
! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSort) ).
thf(13,axiom,
! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSetSort) ).
thf(14,axiom,
( ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ xp )
= xp )
& ( aFixedPointOf0 @ xp @ xf )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xT )
=> ( sdtlseqdt0 @ W0 @ xp ) )
& ( aUpperBoundOfIn0 @ xp @ xT @ xS )
& ! [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ xS )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xS ) )
=> ( sdtlseqdt0 @ xp @ W0 ) )
& ( aSupremumOfIn0 @ xp @ xT @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1330) ).
thf(15,axiom,
( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ W0 ) )
& ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xT )
=> ( sdtlseqdt0 @ W0 @ ( sdtlpdtrp0 @ xf @ xp ) ) )
& ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1299) ).
thf(16,axiom,
( ( aElementOf0 @ xp @ xU )
& ( aElementOf0 @ xp @ xU )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( sdtlseqdt0 @ xp @ W0 ) )
& ( aLowerBoundOfIn0 @ xp @ xP @ xU )
& ! [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ xU )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xP )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) )
| ( aLowerBoundOfIn0 @ W0 @ xP @ xU ) )
=> ( sdtlseqdt0 @ W0 @ xp ) )
& ( aInfimumOfIn0 @ xp @ xP @ xU ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1261) ).
thf(17,axiom,
( ( aSet0 @ xP )
& ! [W0: $i] :
( ( ( aElementOf0 @ W0 @ xP )
=> ( ( aElementOf0 @ W0 @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ W0 ) @ W0 )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) )
& ( aUpperBoundOfIn0 @ W0 @ xT @ xU ) ) )
& ( ( ( aElementOf0 @ W0 @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ W0 ) @ W0 )
& ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xU ) ) )
=> ( aElementOf0 @ W0 @ xP ) ) )
& ( xP
= ( cS1241 @ xU @ xf @ xT ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1244) ).
thf(18,axiom,
( ( aSet0 @ xT )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xT )
=> ( aElementOf0 @ W0 @ xS ) )
& ( aSubsetOf0 @ xT @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1173) ).
thf(19,axiom,
( ( aSet0 @ xS )
& ! [W0: $i] :
( ( ( aElementOf0 @ W0 @ xS )
=> ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ W0 )
= W0 )
& ( aFixedPointOf0 @ W0 @ xf ) ) )
& ( ( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ W0 )
= W0 ) )
| ( aFixedPointOf0 @ W0 @ xf ) )
=> ( aElementOf0 @ W0 @ xS ) ) )
& ( xS
= ( cS1142 @ xf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1144) ).
thf(20,axiom,
( ( aSet0 @ xU )
& ! [W0: $i] :
( ( ( ( aSet0 @ W0 )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElementOf0 @ W1 @ xU ) ) )
| ( aSubsetOf0 @ W0 @ xU ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ xU )
& ( aElementOf0 @ W1 @ xU )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ W0 )
=> ( sdtlseqdt0 @ W1 @ W2 ) )
& ( aLowerBoundOfIn0 @ W1 @ W0 @ xU )
& ! [W2: $i] :
( ( ( ( aElementOf0 @ W2 @ xU )
& ! [W3: $i] :
( ( aElementOf0 @ W3 @ W0 )
=> ( sdtlseqdt0 @ W2 @ W3 ) ) )
| ( aLowerBoundOfIn0 @ W2 @ W0 @ xU ) )
=> ( sdtlseqdt0 @ W2 @ W1 ) )
& ( aInfimumOfIn0 @ W1 @ W0 @ xU )
& ? [W2: $i] :
( ( aElementOf0 @ W2 @ xU )
& ( aElementOf0 @ W2 @ xU )
& ! [W3: $i] :
( ( aElementOf0 @ W3 @ W0 )
=> ( sdtlseqdt0 @ W3 @ W2 ) )
& ( aUpperBoundOfIn0 @ W2 @ W0 @ xU )
& ! [W3: $i] :
( ( ( ( aElementOf0 @ W3 @ xU )
& ! [W4: $i] :
( ( aElementOf0 @ W4 @ W0 )
=> ( sdtlseqdt0 @ W4 @ W3 ) ) )
| ( aUpperBoundOfIn0 @ W3 @ W0 @ xU ) )
=> ( sdtlseqdt0 @ W2 @ W3 ) )
& ( aSupremumOfIn0 @ W2 @ W0 @ xU ) ) ) )
& ( aCompleteLattice0 @ xU )
& ( aFunction0 @ xf )
& ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xf ) )
& ( aElementOf0 @ W1 @ ( szDzozmdt0 @ xf ) ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ W0 ) @ ( sdtlpdtrp0 @ xf @ W1 ) ) ) )
& ( isMonotone0 @ xf )
& ( ( szDzozmdt0 @ xf )
= ( szRzazndt0 @ xf ) )
& ( ( szRzazndt0 @ xf )
= xU )
& ( isOn0 @ xf @ xU ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1123) ).
thf(21,conjecture,
? [W0: $i] :
( ( ( aElementOf0 @ W0 @ xS )
& ( ( ( aElementOf0 @ W0 @ xS )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xS ) )
& ! [W1: $i] :
( ( ( aElementOf0 @ W1 @ xS )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ xT )
=> ( sdtlseqdt0 @ W2 @ W1 ) )
& ( aUpperBoundOfIn0 @ W1 @ xT @ xS ) )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) )
| ( aSupremumOfIn0 @ W0 @ xT @ xS ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(22,negated_conjecture,
( ( ? [W0: $i] :
( ( ( aElementOf0 @ W0 @ xS )
& ( ( ( aElementOf0 @ W0 @ xS )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xS ) )
& ! [W1: $i] :
( ( ( aElementOf0 @ W1 @ xS )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ xT )
=> ( sdtlseqdt0 @ W2 @ W1 ) )
& ( aUpperBoundOfIn0 @ W1 @ xT @ xS ) )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) )
| ( aSupremumOfIn0 @ W0 @ xT @ xS ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,plain,
( ( ? [W0: $i] :
( ( ( aElementOf0 @ W0 @ xS )
& ( ( ( aElementOf0 @ W0 @ xS )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xS ) )
& ! [W1: $i] :
( ( ( aElementOf0 @ W1 @ xS )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ xT )
=> ( sdtlseqdt0 @ W2 @ W1 ) )
& ( aUpperBoundOfIn0 @ W1 @ xT @ xS ) )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) )
| ( aSupremumOfIn0 @ W0 @ xT @ xS ) ) )
= $false ),
inference(unfold_def,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( szRzazndt0 @ W0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(25,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szRzazndt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(26,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(28,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aInfimumOfIn0 @ W2 @ W1 @ W0 )
& ( aInfimumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(29,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
& ( aSupremumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(30,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(31,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(32,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(33,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(34,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(35,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(36,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(37,plain,
( ( ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ xp )
= xp )
& ( aFixedPointOf0 @ xp @ xf )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xT )
=> ( sdtlseqdt0 @ W0 @ xp ) )
& ( aUpperBoundOfIn0 @ xp @ xT @ xS )
& ! [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ xS )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xS ) )
=> ( sdtlseqdt0 @ xp @ W0 ) )
& ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(38,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ W0 ) )
& ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xT )
=> ( sdtlseqdt0 @ W0 @ ( sdtlpdtrp0 @ xf @ xp ) ) )
& ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(39,plain,
( ( ( aElementOf0 @ xp @ xU )
& ( aElementOf0 @ xp @ xU )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( sdtlseqdt0 @ xp @ W0 ) )
& ( aLowerBoundOfIn0 @ xp @ xP @ xU )
& ! [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ xU )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xP )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) )
| ( aLowerBoundOfIn0 @ W0 @ xP @ xU ) )
=> ( sdtlseqdt0 @ W0 @ xp ) )
& ( aInfimumOfIn0 @ xp @ xP @ xU ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(40,plain,
( ( ( aSet0 @ xP )
& ! [W0: $i] :
( ( ( aElementOf0 @ W0 @ xP )
=> ( ( aElementOf0 @ W0 @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ W0 ) @ W0 )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) )
& ( aUpperBoundOfIn0 @ W0 @ xT @ xU ) ) )
& ( ( ( aElementOf0 @ W0 @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ W0 ) @ W0 )
& ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xU ) ) )
=> ( aElementOf0 @ W0 @ xP ) ) )
& ( xP
= ( cS1241 @ xU @ xf @ xT ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(41,plain,
( ( ( aSet0 @ xT )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xT )
=> ( aElementOf0 @ W0 @ xS ) )
& ( aSubsetOf0 @ xT @ xS ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(42,plain,
( ( ( aSet0 @ xS )
& ! [W0: $i] :
( ( ( aElementOf0 @ W0 @ xS )
=> ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ W0 )
= W0 )
& ( aFixedPointOf0 @ W0 @ xf ) ) )
& ( ( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ W0 )
= W0 ) )
| ( aFixedPointOf0 @ W0 @ xf ) )
=> ( aElementOf0 @ W0 @ xS ) ) )
& ( xS
= ( cS1142 @ xf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(43,plain,
( ( ( aSet0 @ xU )
& ! [W0: $i] :
( ( ( ( aSet0 @ W0 )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElementOf0 @ W1 @ xU ) ) )
| ( aSubsetOf0 @ W0 @ xU ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ xU )
& ( aElementOf0 @ W1 @ xU )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ W0 )
=> ( sdtlseqdt0 @ W1 @ W2 ) )
& ( aLowerBoundOfIn0 @ W1 @ W0 @ xU )
& ! [W2: $i] :
( ( ( ( aElementOf0 @ W2 @ xU )
& ! [W3: $i] :
( ( aElementOf0 @ W3 @ W0 )
=> ( sdtlseqdt0 @ W2 @ W3 ) ) )
| ( aLowerBoundOfIn0 @ W2 @ W0 @ xU ) )
=> ( sdtlseqdt0 @ W2 @ W1 ) )
& ( aInfimumOfIn0 @ W1 @ W0 @ xU )
& ? [W2: $i] :
( ( aElementOf0 @ W2 @ xU )
& ( aElementOf0 @ W2 @ xU )
& ! [W3: $i] :
( ( aElementOf0 @ W3 @ W0 )
=> ( sdtlseqdt0 @ W3 @ W2 ) )
& ( aUpperBoundOfIn0 @ W2 @ W0 @ xU )
& ! [W3: $i] :
( ( ( ( aElementOf0 @ W3 @ xU )
& ! [W4: $i] :
( ( aElementOf0 @ W4 @ W0 )
=> ( sdtlseqdt0 @ W4 @ W3 ) ) )
| ( aUpperBoundOfIn0 @ W3 @ W0 @ xU ) )
=> ( sdtlseqdt0 @ W2 @ W3 ) )
& ( aSupremumOfIn0 @ W2 @ W0 @ xU ) ) ) )
& ( aCompleteLattice0 @ xU )
& ( aFunction0 @ xf )
& ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xf ) )
& ( aElementOf0 @ W1 @ ( szDzozmdt0 @ xf ) ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ W0 ) @ ( sdtlpdtrp0 @ xf @ W1 ) ) ) )
& ( isMonotone0 @ xf )
& ( ( szDzozmdt0 @ xf )
= ( szRzazndt0 @ xf ) )
& ( ( szRzazndt0 @ xf )
= xU )
& ( isOn0 @ xf @ xU ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(44,plain,
( ( ~ ? [W0: $i] :
( ( ( aElementOf0 @ W0 @ xS )
& ( ( ( aElementOf0 @ W0 @ xS )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xS ) )
& ! [W1: $i] :
( ( ( aElementOf0 @ W1 @ xS )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ xT )
=> ( sdtlseqdt0 @ W2 @ W1 ) )
& ( aUpperBoundOfIn0 @ W1 @ xT @ xS ) )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) )
| ( aSupremumOfIn0 @ W0 @ xT @ xS ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(45,plain,
( ( ( aSet0 @ xU )
& ! [W0: $i] :
( ( ( ( aSet0 @ W0 )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElementOf0 @ W1 @ xU ) ) )
| ( aSubsetOf0 @ W0 @ xU ) )
=> ? [W1: $i] :
( ( aElementOf0 @ W1 @ xU )
& ( aElementOf0 @ W1 @ xU )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ W0 )
=> ( sdtlseqdt0 @ W1 @ W2 ) )
& ( aLowerBoundOfIn0 @ W1 @ W0 @ xU )
& ! [W2: $i] :
( ( ( ( aElementOf0 @ W2 @ xU )
& ! [W3: $i] :
( ( aElementOf0 @ W3 @ W0 )
=> ( sdtlseqdt0 @ W2 @ W3 ) ) )
| ( aLowerBoundOfIn0 @ W2 @ W0 @ xU ) )
=> ( sdtlseqdt0 @ W2 @ W1 ) )
& ( aInfimumOfIn0 @ W1 @ W0 @ xU )
& ? [W2: $i] :
( ( aElementOf0 @ W2 @ xU )
& ( aElementOf0 @ W2 @ xU )
& ! [W3: $i] :
( ( aElementOf0 @ W3 @ W0 )
=> ( sdtlseqdt0 @ W3 @ W2 ) )
& ( aUpperBoundOfIn0 @ W2 @ W0 @ xU )
& ! [W3: $i] :
( ( ( ( aElementOf0 @ W3 @ xU )
& ! [W4: $i] :
( ( aElementOf0 @ W4 @ W0 )
=> ( sdtlseqdt0 @ W4 @ W3 ) ) )
| ( aUpperBoundOfIn0 @ W3 @ W0 @ xU ) )
=> ( sdtlseqdt0 @ W2 @ W3 ) )
& ( aSupremumOfIn0 @ W2 @ W0 @ xU ) ) ) )
& ( aCompleteLattice0 @ xU )
& ( aFunction0 @ xf )
& ! [W0: $i,W1: $i] :
( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xf ) )
& ( aElementOf0 @ W1 @ ( szDzozmdt0 @ xf ) ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ W0 ) @ ( sdtlpdtrp0 @ xf @ W1 ) ) ) )
& ( isMonotone0 @ xf )
& ( ( szDzozmdt0 @ xf )
= ( szRzazndt0 @ xf ) )
& ( ( szRzazndt0 @ xf )
= xU )
& ( isOn0 @ xf @ xU ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(46,plain,
( ( ( aSet0 @ xS )
& ! [W0: $i] :
( ( ( aElementOf0 @ W0 @ xS )
=> ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ W0 )
= W0 )
& ( aFixedPointOf0 @ W0 @ xf ) ) )
& ( ( ( ( aElementOf0 @ W0 @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ W0 )
= W0 ) )
| ( aFixedPointOf0 @ W0 @ xf ) )
=> ( aElementOf0 @ W0 @ xS ) ) )
& ( xS
= ( cS1142 @ xf ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(47,plain,
( ( ( aSet0 @ xT )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xT )
=> ( aElementOf0 @ W0 @ xS ) )
& ( aSubsetOf0 @ xT @ xS ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(48,plain,
( ( ( aSet0 @ xP )
& ! [W0: $i] :
( ( ( aElementOf0 @ W0 @ xP )
=> ( ( aElementOf0 @ W0 @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ W0 ) @ W0 )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) )
& ( aUpperBoundOfIn0 @ W0 @ xT @ xU ) ) )
& ( ( ( aElementOf0 @ W0 @ xU )
& ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ W0 ) @ W0 )
& ( ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xU ) ) )
=> ( aElementOf0 @ W0 @ xP ) ) )
& ( xP
= ( cS1241 @ xU @ xf @ xT ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(49,plain,
( ( ( aElementOf0 @ xp @ xU )
& ( aElementOf0 @ xp @ xU )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( sdtlseqdt0 @ xp @ W0 ) )
& ( aLowerBoundOfIn0 @ xp @ xP @ xU )
& ! [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ xU )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xP )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) )
| ( aLowerBoundOfIn0 @ W0 @ xP @ xU ) )
=> ( sdtlseqdt0 @ W0 @ xp ) )
& ( aInfimumOfIn0 @ xp @ xP @ xU ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(50,plain,
( ( ! [W0: $i] :
( ( aElementOf0 @ W0 @ xP )
=> ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ W0 ) )
& ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xT )
=> ( sdtlseqdt0 @ W0 @ ( sdtlpdtrp0 @ xf @ xp ) ) )
& ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(51,plain,
( ( ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
& ( ( sdtlpdtrp0 @ xf @ xp )
= xp )
& ( aFixedPointOf0 @ xp @ xf )
& ! [W0: $i] :
( ( aElementOf0 @ W0 @ xT )
=> ( sdtlseqdt0 @ W0 @ xp ) )
& ( aUpperBoundOfIn0 @ xp @ xT @ xS )
& ! [W0: $i] :
( ( ( ( aElementOf0 @ W0 @ xS )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xS ) )
=> ( sdtlseqdt0 @ xp @ W0 ) )
& ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(52,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> $true ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(53,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> $true ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(54,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ W0 )
=> ( aElement0 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(55,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( sdtlseqdt0 @ W0 @ W1 )
=> $true ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(56,plain,
( ( ! [W0: $i] :
( ( aElement0 @ W0 )
=> ( sdtlseqdt0 @ W0 @ W0 ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(57,plain,
( ( ! [W0: $i,W1: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W0 ) )
=> ( W0 = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(58,plain,
( ( ! [W0: $i,W1: $i,W2: $i] :
( ( ( aElement0 @ W0 )
& ( aElement0 @ W1 )
& ( aElement0 @ W2 ) )
=> ( ( ( sdtlseqdt0 @ W0 @ W1 )
& ( sdtlseqdt0 @ W1 @ W2 ) )
=> ( sdtlseqdt0 @ W0 @ W2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(59,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aSupremumOfIn0 @ W2 @ W1 @ W0 )
& ( aSupremumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(60,plain,
( ( ! [W0: $i] :
( ( aSet0 @ W0 )
=> ! [W1: $i] :
( ( aSubsetOf0 @ W1 @ W0 )
=> ! [W2: $i,W3: $i] :
( ( ( aInfimumOfIn0 @ W2 @ W1 @ W0 )
& ( aInfimumOfIn0 @ W3 @ W1 @ W0 ) )
=> ( W2 = W3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(61,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> $true ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(62,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szDzozmdt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(63,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ( aSet0 @ ( szRzazndt0 @ W0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(64,plain,
( ( ! [W0: $i] :
( ( aFunction0 @ W0 )
=> ! [W1: $i] :
( ( aElementOf0 @ W1 @ ( szDzozmdt0 @ W0 ) )
=> ( aElementOf0 @ ( sdtlpdtrp0 @ W0 @ W1 ) @ ( szRzazndt0 @ W0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(65,plain,
( ( ~ ? [W0: $i] :
( ( ( aElementOf0 @ W0 @ xS )
& ( ( ( aElementOf0 @ W0 @ xS )
& ! [W1: $i] :
( ( aElementOf0 @ W1 @ xT )
=> ( sdtlseqdt0 @ W1 @ W0 ) ) )
| ( aUpperBoundOfIn0 @ W0 @ xT @ xS ) )
& ! [W1: $i] :
( ( ( aElementOf0 @ W1 @ xS )
& ! [W2: $i] :
( ( aElementOf0 @ W2 @ xT )
=> ( sdtlseqdt0 @ W2 @ W1 ) )
& ( aUpperBoundOfIn0 @ W1 @ xT @ xS ) )
=> ( sdtlseqdt0 @ W0 @ W1 ) ) )
| ( aSupremumOfIn0 @ W0 @ xT @ xS ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(66,plain,
( ( ~ ( ~ ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ~ ( aFixedPointOf0 @ SX0 @ xf ) ) )
| ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ( aFixedPointOf0 @ SX0 @ xf ) )
| ( aElementOf0 @ SX0 @ xS ) ) ) )
| ( xS
!= ( cS1142 @ xf ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(67,plain,
( ( ! [SX0: $i] :
( ~ ( aFunction0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ SX0 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SX0 @ SX1 ) @ ( szRzazndt0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(68,plain,
( ( ~ ( ~ ~ ( ~ ( aSet0 @ xT )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( aElementOf0 @ SX0 @ xS ) ) )
| ~ ( aSubsetOf0 @ xT @ xS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(69,plain,
( ( ~ ~ ! [SX0: $i] :
~ ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) ) )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX1 @ xT @ xS ) )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aSupremumOfIn0 @ SX0 @ xT @ xS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(70,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(71,plain,
( ( ~ ( ~ ~ ( ~ ( aSet0 @ xP )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ( ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ( aElementOf0 @ SX0 @ xP ) ) ) )
| ( xP
!= ( cS1241 @ xU @ xf @ xT ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ~ ( aElement0 @ SX2 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( sdtlseqdt0 @ SX1 @ SX2 ) )
| ( sdtlseqdt0 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(73,plain,
( ( ! [SX0: $i] :
( ~ ( aFunction0 @ SX0 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(74,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aSubsetOf0 @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SX2 @ SX1 @ SX0 )
| ~ ( aSupremumOfIn0 @ SX3 @ SX1 @ SX0 ) )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(75,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aSubsetOf0 @ SX1 @ SX0 )
| ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( aInfimumOfIn0 @ SX2 @ SX1 @ SX0 )
| ~ ( aInfimumOfIn0 @ SX3 @ SX1 @ SX0 ) )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(76,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(77,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ~ ( aFunction0 @ SX0 )
| ( aSet0 @ ( szRzazndt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElement0 @ SX0 )
| ~ ( aElement0 @ SX1 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ~ ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElement0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(81,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) )
| ( ( szDzozmdt0 @ xf )
!= ( szRzazndt0 @ xf ) ) )
| ( ( szRzazndt0 @ xf )
!= xU ) )
| ~ ( isOn0 @ xf @ xU ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ( aElement0 @ SX0 )
| ( sdtlseqdt0 @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(83,plain,
( ( ! [SX0: $i] :
( ~ ( aFunction0 @ SX0 )
| ( aSet0 @ ( szDzozmdt0 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(84,plain,
( ( ! [SX0: $i] :
( ~ ( aSet0 @ SX0 )
| $true ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(85,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aLowerBoundOfIn0 @ xp @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xP )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aLowerBoundOfIn0 @ SX0 @ xP @ xU ) )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aInfimumOfIn0 @ xp @ xP @ xU ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(86,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) )
| ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ ( sdtlpdtrp0 @ xf @ xp ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(87,plain,
( ( ~ ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ~ ( aFixedPointOf0 @ SX0 @ xf ) ) )
| ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ( aFixedPointOf0 @ SX0 @ xf ) )
| ( aElementOf0 @ SX0 @ xS ) ) ) )
| ( xS
!= ( cS1142 @ xf ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV1: $i] :
( ( ~ ( aFunction0 @ SV1 )
| ! [SY54: $i] :
( ~ ( aElementOf0 @ SY54 @ ( szDzozmdt0 @ SV1 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV1 @ SY54 ) @ ( szRzazndt0 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
( ( ~ ~ ( ~ ( aSet0 @ xT )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( aElementOf0 @ SX0 @ xS ) ) )
| ~ ( aSubsetOf0 @ xT @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(90,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) ) )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX1 @ xT @ xS ) )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aSupremumOfIn0 @ SX0 @ xT @ xS ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV2: $i] :
( ( ~ ( aElement0 @ SV2 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(92,plain,
( ( ~ ~ ( ~ ( aSet0 @ xP )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ( ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ( aElementOf0 @ SX0 @ xP ) ) ) )
| ( xP
!= ( cS1241 @ xU @ xf @ xT ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV3: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SY55 ) )
| ~ ( aElement0 @ SY56 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SY55 )
| ~ ( sdtlseqdt0 @ SY55 @ SY56 ) )
| ( sdtlseqdt0 @ SV3 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV4: $i] :
( ( ~ ( aFunction0 @ SV4 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV5: $i] :
( ( ~ ( aSet0 @ SV5 )
| ! [SY57: $i] :
( ~ ( aSubsetOf0 @ SY57 @ SV5 )
| ! [SY58: $i,SY59: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY58 @ SY57 @ SV5 )
| ~ ( aSupremumOfIn0 @ SY59 @ SY57 @ SV5 ) )
| ( SY58 = SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV6: $i] :
( ( ~ ( aSet0 @ SV6 )
| ! [SY60: $i] :
( ~ ( aSubsetOf0 @ SY60 @ SV6 )
| ! [SY61: $i,SY62: $i] :
( ~ ~ ( ~ ( aInfimumOfIn0 @ SY61 @ SY60 @ SV6 )
| ~ ( aInfimumOfIn0 @ SY62 @ SY60 @ SV6 ) )
| ( SY61 = SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV7: $i] :
( ( ! [SY63: $i] :
( ~ ~ ( ~ ( aElement0 @ SV7 )
| ~ ( aElement0 @ SY63 ) )
| ~ ( sdtlseqdt0 @ SV7 @ SY63 )
| $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(99,plain,
! [SV8: $i] :
( ( ~ ( aFunction0 @ SV8 )
| ( aSet0 @ ( szRzazndt0 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV9: $i] :
( ( ! [SY64: $i] :
( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SY64 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SY64 )
| ~ ( sdtlseqdt0 @ SY64 @ SV9 ) )
| ( SV9 = SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
! [SV10: $i] :
( ( ~ ( aSet0 @ SV10 )
| ! [SY65: $i] :
( ~ ( aElementOf0 @ SY65 @ SV10 )
| ( aElement0 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(102,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) )
| ( ( szDzozmdt0 @ xf )
!= ( szRzazndt0 @ xf ) ) )
| ( ( szRzazndt0 @ xf )
!= xU ) )
| ~ ( isOn0 @ xf @ xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV11: $i] :
( ( ~ ( aElement0 @ SV11 )
| ( sdtlseqdt0 @ SV11 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(104,plain,
! [SV12: $i] :
( ( ~ ( aFunction0 @ SV12 )
| ( aSet0 @ ( szDzozmdt0 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(105,plain,
! [SV13: $i] :
( ( ~ ( aSet0 @ SV13 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(106,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aLowerBoundOfIn0 @ xp @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xP )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aLowerBoundOfIn0 @ SX0 @ xP @ xU ) )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aInfimumOfIn0 @ xp @ xP @ xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(107,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) )
| ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ ( sdtlpdtrp0 @ xf @ xp ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(108,plain,
( ( ~ ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ~ ( aFixedPointOf0 @ SX0 @ xf ) ) )
| ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ( aFixedPointOf0 @ SX0 @ xf ) )
| ( aElementOf0 @ SX0 @ xS ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(109,plain,
( ( xS
!= ( cS1142 @ xf ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(110,plain,
! [SV1: $i] :
( ( ( ~ ( aFunction0 @ SV1 ) )
= $true )
| ( ( ! [SY54: $i] :
( ~ ( aElementOf0 @ SY54 @ ( szDzozmdt0 @ SV1 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV1 @ SY54 ) @ ( szRzazndt0 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(111,plain,
( ( ~ ~ ( ~ ( aSet0 @ xT )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( aElementOf0 @ SX0 @ xS ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(112,plain,
( ( ~ ( aSubsetOf0 @ xT @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(113,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) ) )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX1 @ xT @ xS ) )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aSupremumOfIn0 @ SX0 @ xT @ xS ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(114,plain,
! [SV2: $i] :
( ( ( ~ ( aElement0 @ SV2 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(115,plain,
( ( ~ ~ ( ~ ( aSet0 @ xP )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ( ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ( aElementOf0 @ SX0 @ xP ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(116,plain,
( ( xP
!= ( cS1241 @ xU @ xf @ xT ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(117,plain,
! [SV14: $i,SV3: $i] :
( ( ! [SY66: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 ) )
| ~ ( aElement0 @ SY66 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SY66 ) )
| ( sdtlseqdt0 @ SV3 @ SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(118,plain,
! [SV4: $i] :
( ( ( ~ ( aFunction0 @ SV4 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(119,plain,
! [SV5: $i] :
( ( ( ~ ( aSet0 @ SV5 ) )
= $true )
| ( ( ! [SY57: $i] :
( ~ ( aSubsetOf0 @ SY57 @ SV5 )
| ! [SY58: $i,SY59: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY58 @ SY57 @ SV5 )
| ~ ( aSupremumOfIn0 @ SY59 @ SY57 @ SV5 ) )
| ( SY58 = SY59 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(120,plain,
! [SV6: $i] :
( ( ( ~ ( aSet0 @ SV6 ) )
= $true )
| ( ( ! [SY60: $i] :
( ~ ( aSubsetOf0 @ SY60 @ SV6 )
| ! [SY61: $i,SY62: $i] :
( ~ ~ ( ~ ( aInfimumOfIn0 @ SY61 @ SY60 @ SV6 )
| ~ ( aInfimumOfIn0 @ SY62 @ SY60 @ SV6 ) )
| ( SY61 = SY62 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(121,plain,
! [SV15: $i,SV7: $i] :
( ( ~ ~ ( ~ ( aElement0 @ SV7 )
| ~ ( aElement0 @ SV15 ) )
| ~ ( sdtlseqdt0 @ SV7 @ SV15 )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(122,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) )
| ( sdtlseqdt0 @ xp @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(123,plain,
( ( ~ ( aSupremumOfIn0 @ xp @ xT @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(124,plain,
! [SV8: $i] :
( ( ( ~ ( aFunction0 @ SV8 ) )
= $true )
| ( ( aSet0 @ ( szRzazndt0 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(125,plain,
! [SV16: $i,SV9: $i] :
( ( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV16 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
| ( SV9 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(126,plain,
! [SV10: $i] :
( ( ( ~ ( aSet0 @ SV10 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( aElementOf0 @ SY65 @ SV10 )
| ( aElement0 @ SY65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(127,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) )
| ( ( szDzozmdt0 @ xf )
!= ( szRzazndt0 @ xf ) ) )
| ( ( szRzazndt0 @ xf )
!= xU ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(128,plain,
( ( ~ ( isOn0 @ xf @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(129,plain,
! [SV11: $i] :
( ( ( ~ ( aElement0 @ SV11 ) )
= $true )
| ( ( sdtlseqdt0 @ SV11 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(130,plain,
! [SV12: $i] :
( ( ( ~ ( aFunction0 @ SV12 ) )
= $true )
| ( ( aSet0 @ ( szDzozmdt0 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(131,plain,
! [SV13: $i] :
( ( ( ~ ( aSet0 @ SV13 ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(132,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aLowerBoundOfIn0 @ xp @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xP )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aLowerBoundOfIn0 @ SX0 @ xP @ xU ) )
| ( sdtlseqdt0 @ SX0 @ xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(133,plain,
( ( ~ ( aInfimumOfIn0 @ xp @ xP @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(134,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) )
| ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ ( sdtlpdtrp0 @ xf @ xp ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(135,plain,
( ( ~ ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(136,plain,
( ( ~ ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ~ ( aFixedPointOf0 @ SX0 @ xf ) ) )
| ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ( aFixedPointOf0 @ SX0 @ xf ) )
| ( aElementOf0 @ SX0 @ xS ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(137,plain,
( ( xS
= ( cS1142 @ xf ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(138,plain,
! [SV1: $i] :
( ( ( aFunction0 @ SV1 )
= $false )
| ( ( ! [SY54: $i] :
( ~ ( aElementOf0 @ SY54 @ ( szDzozmdt0 @ SV1 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV1 @ SY54 ) @ ( szRzazndt0 @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(139,plain,
( ( ~ ( ~ ( aSet0 @ xT )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( aElementOf0 @ SX0 @ xS ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(140,plain,
( ( aSubsetOf0 @ xT @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(141,plain,
! [SV17: $i] :
( ( ~ ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) ) )
| ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
| ( aSupremumOfIn0 @ SV17 @ xT @ xS ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(142,plain,
! [SV2: $i] :
( ( ( aElement0 @ SV2 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(143,plain,
( ( ~ ( ~ ( aSet0 @ xP )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ( ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ( aElementOf0 @ SX0 @ xP ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(144,plain,
( ( xP
= ( cS1241 @ xU @ xf @ xT ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(145,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 ) )
| ~ ( aElement0 @ SV18 ) )
| ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(146,plain,
! [SV4: $i] :
( ( ( aFunction0 @ SV4 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(147,plain,
! [SV5: $i] :
( ( ( aSet0 @ SV5 )
= $false )
| ( ( ! [SY57: $i] :
( ~ ( aSubsetOf0 @ SY57 @ SV5 )
| ! [SY58: $i,SY59: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY58 @ SY57 @ SV5 )
| ~ ( aSupremumOfIn0 @ SY59 @ SY57 @ SV5 ) )
| ( SY58 = SY59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(148,plain,
! [SV6: $i] :
( ( ( aSet0 @ SV6 )
= $false )
| ( ( ! [SY60: $i] :
( ~ ( aSubsetOf0 @ SY60 @ SV6 )
| ! [SY61: $i,SY62: $i] :
( ~ ~ ( ~ ( aInfimumOfIn0 @ SY61 @ SY60 @ SV6 )
| ~ ( aInfimumOfIn0 @ SY62 @ SY60 @ SV6 ) )
| ( SY61 = SY62 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(149,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV7 )
| ~ ( aElement0 @ SV15 ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV7 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(150,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) )
| ( sdtlseqdt0 @ xp @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(151,plain,
( ( aSupremumOfIn0 @ xp @ xT @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(152,plain,
! [SV8: $i] :
( ( ( aFunction0 @ SV8 )
= $false )
| ( ( aSet0 @ ( szRzazndt0 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(153,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV16 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
| ( SV9 = SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(154,plain,
! [SV10: $i] :
( ( ( aSet0 @ SV10 )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( aElementOf0 @ SY65 @ SV10 )
| ( aElement0 @ SY65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(155,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) )
| ( ( szDzozmdt0 @ xf )
!= ( szRzazndt0 @ xf ) ) )
| ( ( szRzazndt0 @ xf )
!= xU ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(156,plain,
( ( isOn0 @ xf @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(157,plain,
! [SV11: $i] :
( ( ( aElement0 @ SV11 )
= $false )
| ( ( sdtlseqdt0 @ SV11 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(158,plain,
! [SV12: $i] :
( ( ( aFunction0 @ SV12 )
= $false )
| ( ( aSet0 @ ( szDzozmdt0 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(159,plain,
! [SV13: $i] :
( ( ( aSet0 @ SV13 )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(160,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aLowerBoundOfIn0 @ xp @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xP )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aLowerBoundOfIn0 @ SX0 @ xP @ xU ) )
| ( sdtlseqdt0 @ SX0 @ xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(161,plain,
( ( aInfimumOfIn0 @ xp @ xP @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(162,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) )
| ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ ( sdtlpdtrp0 @ xf @ xp ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(163,plain,
( ( aUpperBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xT @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(164,plain,
( ( ~ ( aSet0 @ xS )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ~ ( aFixedPointOf0 @ SX0 @ xf ) ) )
| ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ( aFixedPointOf0 @ SX0 @ xf ) )
| ( aElementOf0 @ SX0 @ xS ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(165,plain,
! [SV1: $i,SV19: $i] :
( ( ( ~ ( aElementOf0 @ SV19 @ ( szDzozmdt0 @ SV1 ) )
| ( aElementOf0 @ ( sdtlpdtrp0 @ SV1 @ SV19 ) @ ( szRzazndt0 @ SV1 ) ) )
= $true )
| ( ( aFunction0 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(166,plain,
( ( ~ ( aSet0 @ xT )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(167,plain,
! [SV17: $i] :
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) ) )
| ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
| ( aSupremumOfIn0 @ SV17 @ xT @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(168,plain,
( ( ~ ( aSet0 @ xP )
| ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ( ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ( aElementOf0 @ SX0 @ xP ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(169,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 ) )
| ~ ( aElement0 @ SV18 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(170,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ( aSubsetOf0 @ SV20 @ SV5 )
| ! [SY70: $i,SY71: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY70 @ SV20 @ SV5 )
| ~ ( aSupremumOfIn0 @ SY71 @ SV20 @ SV5 ) )
| ( SY70 = SY71 ) ) )
= $true )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(171,plain,
! [SV6: $i,SV21: $i] :
( ( ( ~ ( aSubsetOf0 @ SV21 @ SV6 )
| ! [SY72: $i,SY73: $i] :
( ~ ~ ( ~ ( aInfimumOfIn0 @ SY72 @ SV21 @ SV6 )
| ~ ( aInfimumOfIn0 @ SY73 @ SV21 @ SV6 ) )
| ( SY72 = SY73 ) ) )
= $true )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(172,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV7 )
| ~ ( aElement0 @ SV15 ) ) )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV7 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(173,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(174,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV16 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
| ( SV9 = SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(175,plain,
! [SV10: $i,SV22: $i] :
( ( ( ~ ( aElementOf0 @ SV22 @ SV10 )
| ( aElement0 @ SV22 ) )
= $true )
| ( ( aSet0 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(176,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) )
| ( ( szDzozmdt0 @ xf )
!= ( szRzazndt0 @ xf ) ) )
| ( ( szRzazndt0 @ xf )
!= xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(177,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aLowerBoundOfIn0 @ xp @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xP )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aLowerBoundOfIn0 @ SX0 @ xP @ xU ) )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(178,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) )
| ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ ( sdtlpdtrp0 @ xf @ xp ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(179,plain,
( ( ~ ( aSet0 @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(180,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ~ ( aFixedPointOf0 @ SX0 @ xf ) ) )
| ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ( aFixedPointOf0 @ SX0 @ xf ) )
| ( aElementOf0 @ SX0 @ xS ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(181,plain,
! [SV1: $i,SV19: $i] :
( ( ( ~ ( aElementOf0 @ SV19 @ ( szDzozmdt0 @ SV1 ) ) )
= $true )
| ( ( aElementOf0 @ ( sdtlpdtrp0 @ SV1 @ SV19 ) @ ( szRzazndt0 @ SV1 ) )
= $true )
| ( ( aFunction0 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(182,plain,
( ( ~ ( aSet0 @ xT ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(183,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(184,plain,
! [SV17: $i] :
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) ) )
| ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(185,plain,
! [SV17: $i] :
( ( aSupremumOfIn0 @ SV17 @ xT @ xS )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(186,plain,
( ( ~ ( aSet0 @ xP ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(187,plain,
( ( ~ ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ( ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ( aElementOf0 @ SX0 @ xP ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(188,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 ) )
| ~ ( aElement0 @ SV18 ) ) )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(189,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ( aSubsetOf0 @ SV20 @ SV5 ) )
= $true )
| ( ( ! [SY70: $i,SY71: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY70 @ SV20 @ SV5 )
| ~ ( aSupremumOfIn0 @ SY71 @ SV20 @ SV5 ) )
| ( SY70 = SY71 ) ) )
= $true )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(190,plain,
! [SV6: $i,SV21: $i] :
( ( ( ~ ( aSubsetOf0 @ SV21 @ SV6 ) )
= $true )
| ( ( ! [SY72: $i,SY73: $i] :
( ~ ~ ( ~ ( aInfimumOfIn0 @ SY72 @ SV21 @ SV6 )
| ~ ( aInfimumOfIn0 @ SY73 @ SV21 @ SV6 ) )
| ( SY72 = SY73 ) ) )
= $true )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(191,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ( aElement0 @ SV7 )
| ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV7 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(192,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(193,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(194,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( aElement0 @ SV9 )
| ~ ( aElement0 @ SV16 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
| ( SV9 = SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(195,plain,
! [SV10: $i,SV22: $i] :
( ( ( ~ ( aElementOf0 @ SV22 @ SV10 ) )
= $true )
| ( ( aElement0 @ SV22 )
= $true )
| ( ( aSet0 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(196,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) )
| ( ( szDzozmdt0 @ xf )
!= ( szRzazndt0 @ xf ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(197,plain,
( ( ( szRzazndt0 @ xf )
!= xU )
= $false ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(198,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aLowerBoundOfIn0 @ xp @ xP @ xU ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(199,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xP )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aLowerBoundOfIn0 @ SX0 @ xP @ xU ) )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(200,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) )
| ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(201,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ ( sdtlpdtrp0 @ xf @ xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(202,plain,
( ( aSet0 @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(203,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ~ ( aFixedPointOf0 @ SX0 @ xf ) ) )
| ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SX0 )
!= SX0 ) )
| ( aFixedPointOf0 @ SX0 @ xf ) )
| ( aElementOf0 @ SX0 @ xS ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(204,plain,
! [SV1: $i,SV19: $i] :
( ( ( aElementOf0 @ SV19 @ ( szDzozmdt0 @ SV1 ) )
= $false )
| ( ( aElementOf0 @ ( sdtlpdtrp0 @ SV1 @ SV19 ) @ ( szRzazndt0 @ SV1 ) )
= $true )
| ( ( aFunction0 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(205,plain,
( ( aSet0 @ xT )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(206,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( aElementOf0 @ SX0 @ xS ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(207,plain,
! [SV17: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) ) )
| ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(208,plain,
( ( aSet0 @ xP )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(209,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ SX0 ) )
| ~ ( ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xU ) ) )
| ( aElementOf0 @ SX0 @ xP ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(210,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 ) )
| ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(211,plain,
! [SV5: $i,SV20: $i] :
( ( ( aSubsetOf0 @ SV20 @ SV5 )
= $false )
| ( ( ! [SY70: $i,SY71: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SY70 @ SV20 @ SV5 )
| ~ ( aSupremumOfIn0 @ SY71 @ SV20 @ SV5 ) )
| ( SY70 = SY71 ) ) )
= $true )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(212,plain,
! [SV6: $i,SV21: $i] :
( ( ( aSubsetOf0 @ SV21 @ SV6 )
= $false )
| ( ( ! [SY72: $i,SY73: $i] :
( ~ ~ ( ~ ( aInfimumOfIn0 @ SY72 @ SV21 @ SV6 )
| ~ ( aInfimumOfIn0 @ SY73 @ SV21 @ SV6 ) )
| ( SY72 = SY73 ) ) )
= $true )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(213,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ( aElement0 @ SV7 ) )
= $true )
| ( ( ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV7 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(214,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(215,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xS )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xT )
| ( sdtlseqdt0 @ SX1 @ SX0 ) ) )
| ( aUpperBoundOfIn0 @ SX0 @ xT @ xS ) )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(216,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( aElement0 @ SV9 ) )
= $true )
| ( ( ~ ( aElement0 @ SV16 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
| ( SV9 = SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(217,plain,
! [SV10: $i,SV22: $i] :
( ( ( aElementOf0 @ SV22 @ SV10 )
= $false )
| ( ( aElement0 @ SV22 )
= $true )
| ( ( aSet0 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(218,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) )
| ( ( szDzozmdt0 @ xf )
!= ( szRzazndt0 @ xf ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(219,plain,
( ( ( szRzazndt0 @ xf )
= xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(220,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aLowerBoundOfIn0 @ xp @ xP @ xU ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(221,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX0 @ xU )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ xP )
| ( sdtlseqdt0 @ SX0 @ SX1 ) ) )
| ( aLowerBoundOfIn0 @ SX0 @ xP @ xU ) )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(222,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) )
| ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(223,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ ( sdtlpdtrp0 @ xf @ xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(224,plain,
! [SV23: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV23 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ~ ( aFixedPointOf0 @ SV23 @ xf ) ) )
| ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ( aFixedPointOf0 @ SV23 @ xf ) )
| ( aElementOf0 @ SV23 @ xS ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(225,plain,
! [SV24: $i] :
( ( ~ ( aElementOf0 @ SV24 @ xT )
| ( aElementOf0 @ SV24 @ xS ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(226,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) ) ) )
= $true )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(227,plain,
! [SV25: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV25 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
| ~ ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
| ( aElementOf0 @ SV25 @ xP ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(228,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 ) ) )
= $true )
| ( ( ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(229,plain,
! [SV5: $i,SV20: $i,SV26: $i] :
( ( ( ! [SY76: $i] :
( ~ ~ ( ~ ( aSupremumOfIn0 @ SV26 @ SV20 @ SV5 )
| ~ ( aSupremumOfIn0 @ SY76 @ SV20 @ SV5 ) )
| ( SV26 = SY76 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV5 )
= $false )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(230,plain,
! [SV6: $i,SV21: $i,SV27: $i] :
( ( ( ! [SY77: $i] :
( ~ ~ ( ~ ( aInfimumOfIn0 @ SV27 @ SV21 @ SV6 )
| ~ ( aInfimumOfIn0 @ SY77 @ SV21 @ SV6 ) )
| ( SV27 = SY77 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV21 @ SV6 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(231,plain,
! [SV15: $i,SV7: $i] :
( ( ( aElement0 @ SV7 )
= $false )
| ( ( ~ ( aElement0 @ SV15 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV7 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(232,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
| ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(233,plain,
! [SV28: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV28 @ xS )
| ~ ! [SY78: $i] :
( ~ ( aElementOf0 @ SY78 @ xT )
| ( sdtlseqdt0 @ SY78 @ SV28 ) ) )
| ( aUpperBoundOfIn0 @ SV28 @ xT @ xS ) )
| ( sdtlseqdt0 @ xp @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(234,plain,
! [SV16: $i,SV9: $i] :
( ( ( aElement0 @ SV9 )
= $false )
| ( ( ~ ( aElement0 @ SV16 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
| ( SV9 = SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(235,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) )
| ( ( szDzozmdt0 @ xf )
!= ( szRzazndt0 @ xf ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(236,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
| ~ ( aLowerBoundOfIn0 @ xp @ xP @ xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(237,plain,
! [SV29: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV29 @ xU )
| ~ ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ xP )
| ( sdtlseqdt0 @ SV29 @ SY79 ) ) )
| ( aLowerBoundOfIn0 @ SV29 @ xP @ xU ) )
| ( sdtlseqdt0 @ SV29 @ xp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(238,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) )
| ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(239,plain,
! [SV30: $i] :
( ( ~ ( aElementOf0 @ SV30 @ xT )
| ( sdtlseqdt0 @ SV30 @ ( sdtlpdtrp0 @ xf @ xp ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(240,plain,
! [SV23: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV23 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ~ ( aFixedPointOf0 @ SV23 @ xf ) ) )
| ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ( aFixedPointOf0 @ SV23 @ xf ) )
| ( aElementOf0 @ SV23 @ xS ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(241,plain,
! [SV24: $i] :
( ( ( ~ ( aElementOf0 @ SV24 @ xT ) )
= $true )
| ( ( aElementOf0 @ SV24 @ xS )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(242,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) ) ) )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(243,plain,
! [SV25: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV25 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
| ~ ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
| ( aElementOf0 @ SV25 @ xP ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(244,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 ) ) )
= $false )
| ( ( ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(245,plain,
! [SV31: $i,SV5: $i,SV20: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( aSupremumOfIn0 @ SV26 @ SV20 @ SV5 )
| ~ ( aSupremumOfIn0 @ SV31 @ SV20 @ SV5 ) )
| ( SV26 = SV31 ) )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV5 )
= $false )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(246,plain,
! [SV32: $i,SV6: $i,SV21: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( aInfimumOfIn0 @ SV27 @ SV21 @ SV6 )
| ~ ( aInfimumOfIn0 @ SV32 @ SV21 @ SV6 ) )
| ( SV27 = SV32 ) )
= $true )
| ( ( aSubsetOf0 @ SV21 @ SV6 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(247,plain,
! [SV7: $i,SV15: $i] :
( ( ( aElement0 @ SV15 )
= $false )
| ( ( aElement0 @ SV7 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV7 @ SV15 )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(248,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(249,plain,
( ( ~ ( aUpperBoundOfIn0 @ xp @ xT @ xS ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(250,plain,
! [SV28: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV28 @ xS )
| ~ ! [SY78: $i] :
( ~ ( aElementOf0 @ SY78 @ xT )
| ( sdtlseqdt0 @ SY78 @ SV28 ) ) )
| ( aUpperBoundOfIn0 @ SV28 @ xT @ xS ) ) )
= $true )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(251,plain,
! [SV9: $i,SV16: $i] :
( ( ( aElement0 @ SV16 )
= $false )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
| ( SV9 = SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(252,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(253,plain,
( ( ( szDzozmdt0 @ xf )
!= ( szRzazndt0 @ xf ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(254,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(255,plain,
( ( ~ ( aLowerBoundOfIn0 @ xp @ xP @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(256,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV29 @ xU )
| ~ ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ xP )
| ( sdtlseqdt0 @ SV29 @ SY79 ) ) )
| ( aLowerBoundOfIn0 @ SV29 @ xP @ xU ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(257,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(258,plain,
( ( ~ ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(259,plain,
! [SV30: $i] :
( ( ( ~ ( aElementOf0 @ SV30 @ xT ) )
= $true )
| ( ( sdtlseqdt0 @ SV30 @ ( sdtlpdtrp0 @ xf @ xp ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(260,plain,
! [SV23: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV23 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ~ ( aFixedPointOf0 @ SV23 @ xf ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(261,plain,
! [SV23: $i] :
( ( ~ ( ~ ( ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ( aFixedPointOf0 @ SV23 @ xf ) )
| ( aElementOf0 @ SV23 @ xS ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(262,plain,
! [SV24: $i] :
( ( ( aElementOf0 @ SV24 @ xT )
= $false )
| ( ( aElementOf0 @ SV24 @ xS )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(263,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) ) )
= $true )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(264,plain,
! [SV25: $i] :
( ( ~ ( ~ ( aElementOf0 @ SV25 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
| ~ ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(265,plain,
! [SV25: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
| ( aElementOf0 @ SV25 @ xP ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(266,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( aElement0 @ SV3 )
| ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(267,plain,
! [SV31: $i,SV5: $i,SV20: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( aSupremumOfIn0 @ SV26 @ SV20 @ SV5 )
| ~ ( aSupremumOfIn0 @ SV31 @ SV20 @ SV5 ) ) )
= $true )
| ( ( SV26 = SV31 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV5 )
= $false )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(268,plain,
! [SV32: $i,SV6: $i,SV21: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( aInfimumOfIn0 @ SV27 @ SV21 @ SV6 )
| ~ ( aInfimumOfIn0 @ SV32 @ SV21 @ SV6 ) ) )
= $true )
| ( ( SV27 = SV32 )
= $true )
| ( ( aSubsetOf0 @ SV21 @ SV6 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(269,plain,
! [SV15: $i,SV7: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV7 @ SV15 ) )
= $true )
| ( $true = $true )
| ( ( aElement0 @ SV7 )
= $false )
| ( ( aElement0 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(270,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(271,plain,
( ( aUpperBoundOfIn0 @ xp @ xT @ xS )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(272,plain,
! [SV28: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV28 @ xS )
| ~ ! [SY78: $i] :
( ~ ( aElementOf0 @ SY78 @ xT )
| ( sdtlseqdt0 @ SY78 @ SV28 ) ) )
| ( aUpperBoundOfIn0 @ SV28 @ xT @ xS ) )
= $false )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(273,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) ) )
= $true )
| ( ( SV9 = SV16 )
= $true )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(274,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(275,plain,
( ( ( szDzozmdt0 @ xf )
= ( szRzazndt0 @ xf ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(276,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(277,plain,
( ( aLowerBoundOfIn0 @ xp @ xP @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(278,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV29 @ xU )
| ~ ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ xP )
| ( sdtlseqdt0 @ SV29 @ SY79 ) ) )
| ( aLowerBoundOfIn0 @ SV29 @ xP @ xU ) )
= $false )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(279,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(280,plain,
( ( aLowerBoundOfIn0 @ ( sdtlpdtrp0 @ xf @ xp ) @ xP @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(281,plain,
! [SV30: $i] :
( ( ( aElementOf0 @ SV30 @ xT )
= $false )
| ( ( sdtlseqdt0 @ SV30 @ ( sdtlpdtrp0 @ xf @ xp ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(282,plain,
! [SV23: $i] :
( ( ~ ( aElementOf0 @ SV23 @ xS )
| ~ ( ~ ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ~ ( aFixedPointOf0 @ SV23 @ xf ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(283,plain,
! [SV23: $i] :
( ( ~ ( ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ( aFixedPointOf0 @ SV23 @ xf ) )
| ( aElementOf0 @ SV23 @ xS ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(284,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ SV17 @ xS ) )
= $true )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) ) )
= $true )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(285,plain,
! [SV25: $i] :
( ( ~ ( aElementOf0 @ SV25 @ xP )
| ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
| ~ ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(286,plain,
! [SV25: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
| ( aElementOf0 @ SV25 @ xP ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(287,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( aElement0 @ SV3 ) )
= $true )
| ( ( ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(288,plain,
! [SV31: $i,SV5: $i,SV20: $i,SV26: $i] :
( ( ( ~ ( ~ ( aSupremumOfIn0 @ SV26 @ SV20 @ SV5 )
| ~ ( aSupremumOfIn0 @ SV31 @ SV20 @ SV5 ) ) )
= $false )
| ( ( SV26 = SV31 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV5 )
= $false )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(289,plain,
! [SV32: $i,SV6: $i,SV21: $i,SV27: $i] :
( ( ( ~ ( ~ ( aInfimumOfIn0 @ SV27 @ SV21 @ SV6 )
| ~ ( aInfimumOfIn0 @ SV32 @ SV21 @ SV6 ) ) )
= $false )
| ( ( SV27 = SV32 )
= $true )
| ( ( aSubsetOf0 @ SV21 @ SV6 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(290,plain,
! [SV15: $i,SV7: $i] :
( ( ( sdtlseqdt0 @ SV7 @ SV15 )
= $false )
| ( $true = $true )
| ( ( aElement0 @ SV7 )
= $false )
| ( ( aElement0 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(291,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(292,plain,
! [SV28: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV28 @ xS )
| ~ ! [SY78: $i] :
( ~ ( aElementOf0 @ SY78 @ xT )
| ( sdtlseqdt0 @ SY78 @ SV28 ) ) ) )
= $false )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(293,plain,
! [SV28: $i] :
( ( ( aUpperBoundOfIn0 @ SV28 @ xT @ xS )
= $false )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(294,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) ) )
= $false )
| ( ( SV9 = SV16 )
= $true )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(295,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
| ~ ( isMonotone0 @ xf ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(296,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
| ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(297,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV29 @ xU )
| ~ ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ xP )
| ( sdtlseqdt0 @ SV29 @ SY79 ) ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(298,plain,
! [SV29: $i] :
( ( ( aLowerBoundOfIn0 @ SV29 @ xP @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(299,plain,
! [SV33: $i] :
( ( ~ ( aElementOf0 @ SV33 @ xP )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(300,plain,
! [SV23: $i] :
( ( ( ~ ( aElementOf0 @ SV23 @ xS ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ~ ( aFixedPointOf0 @ SV23 @ xf ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(301,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ( aFixedPointOf0 @ SV23 @ xf ) ) )
= $true )
| ( ( aElementOf0 @ SV23 @ xS )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(302,plain,
! [SV17: $i] :
( ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) ) )
= $true )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(303,plain,
! [SV25: $i] :
( ( ( ~ ( aElementOf0 @ SV25 @ xP ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
| ~ ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(304,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(305,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( aElement0 @ SV3 )
= $false )
| ( ( ~ ( aElement0 @ SV14 ) )
= $true )
| ( ( ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(306,plain,
! [SV31: $i,SV5: $i,SV20: $i,SV26: $i] :
( ( ( ~ ( aSupremumOfIn0 @ SV26 @ SV20 @ SV5 )
| ~ ( aSupremumOfIn0 @ SV31 @ SV20 @ SV5 ) )
= $true )
| ( ( SV26 = SV31 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV5 )
= $false )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(307,plain,
! [SV32: $i,SV6: $i,SV21: $i,SV27: $i] :
( ( ( ~ ( aInfimumOfIn0 @ SV27 @ SV21 @ SV6 )
| ~ ( aInfimumOfIn0 @ SV32 @ SV21 @ SV6 ) )
= $true )
| ( ( SV27 = SV32 )
= $true )
| ( ( aSubsetOf0 @ SV21 @ SV6 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(308,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(309,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(310,plain,
! [SV28: $i] :
( ( ( ~ ( aElementOf0 @ SV28 @ xS )
| ~ ! [SY78: $i] :
( ~ ( aElementOf0 @ SY78 @ xT )
| ( sdtlseqdt0 @ SY78 @ SV28 ) ) )
= $true )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(311,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV9 @ SV16 )
| ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
= $true )
| ( ( SV9 = SV16 )
= $true )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(312,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(313,plain,
( ( ~ ( isMonotone0 @ xf ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(314,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(315,plain,
( ( ~ ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(316,plain,
! [SV29: $i] :
( ( ( ~ ( aElementOf0 @ SV29 @ xU )
| ~ ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ xP )
| ( sdtlseqdt0 @ SV29 @ SY79 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(317,plain,
! [SV33: $i] :
( ( ( ~ ( aElementOf0 @ SV33 @ xP ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(318,plain,
! [SV23: $i] :
( ( ( aElementOf0 @ SV23 @ xS )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ~ ( aFixedPointOf0 @ SV23 @ xf ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(319,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ( aFixedPointOf0 @ SV23 @ xf ) )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(320,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
| ( aUpperBoundOfIn0 @ SV17 @ xT @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(321,plain,
! [SV25: $i] :
( ( ( aElementOf0 @ SV25 @ xP )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
| ~ ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(322,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(323,plain,
! [SV18: $i,SV3: $i,SV14: $i] :
( ( ( aElement0 @ SV14 )
= $false )
| ( ( aElement0 @ SV3 )
= $false )
| ( ( ~ ( aElement0 @ SV18 ) )
= $true )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(324,plain,
! [SV31: $i,SV5: $i,SV20: $i,SV26: $i] :
( ( ( ~ ( aSupremumOfIn0 @ SV26 @ SV20 @ SV5 ) )
= $true )
| ( ( ~ ( aSupremumOfIn0 @ SV31 @ SV20 @ SV5 ) )
= $true )
| ( ( SV26 = SV31 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV5 )
= $false )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(325,plain,
! [SV32: $i,SV6: $i,SV21: $i,SV27: $i] :
( ( ( ~ ( aInfimumOfIn0 @ SV27 @ SV21 @ SV6 ) )
= $true )
| ( ( ~ ( aInfimumOfIn0 @ SV32 @ SV21 @ SV6 ) )
= $true )
| ( ( SV27 = SV32 )
= $true )
| ( ( aSubsetOf0 @ SV21 @ SV6 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(326,plain,
( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(327,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xT )
| ( sdtlseqdt0 @ SX0 @ xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(328,plain,
! [SV28: $i] :
( ( ( ~ ( aElementOf0 @ SV28 @ xS ) )
= $true )
| ( ( ~ ! [SY78: $i] :
( ~ ( aElementOf0 @ SY78 @ xT )
| ( sdtlseqdt0 @ SY78 @ SV28 ) ) )
= $true )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(329,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV9 @ SV16 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
= $true )
| ( ( SV9 = SV16 )
= $true )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(330,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(331,plain,
( ( isMonotone0 @ xf )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(332,plain,
( ( ~ ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(333,plain,
( ( ! [SX0: $i] :
( ~ ( aElementOf0 @ SX0 @ xP )
| ( sdtlseqdt0 @ xp @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(334,plain,
! [SV29: $i] :
( ( ( ~ ( aElementOf0 @ SV29 @ xU ) )
= $true )
| ( ( ~ ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ xP )
| ( sdtlseqdt0 @ SV29 @ SY79 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(335,plain,
! [SV33: $i] :
( ( ( aElementOf0 @ SV33 @ xP )
= $false )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ xp ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(336,plain,
! [SV23: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
| ~ ( aFixedPointOf0 @ SV23 @ xf ) )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(337,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) ) )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(338,plain,
! [SV23: $i] :
( ( ( aFixedPointOf0 @ SV23 @ xf )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(339,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(340,plain,
! [SV17: $i] :
( ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(341,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
| ~ ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(342,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(343,plain,
! [SV14: $i,SV3: $i,SV18: $i] :
( ( ( aElement0 @ SV18 )
= $false )
| ( ( aElement0 @ SV3 )
= $false )
| ( ( aElement0 @ SV14 )
= $false )
| ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
| ( sdtlseqdt0 @ SV3 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(344,plain,
! [SV31: $i,SV5: $i,SV20: $i,SV26: $i] :
( ( ( aSupremumOfIn0 @ SV26 @ SV20 @ SV5 )
= $false )
| ( ( ~ ( aSupremumOfIn0 @ SV31 @ SV20 @ SV5 ) )
= $true )
| ( ( SV26 = SV31 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV5 )
= $false )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(345,plain,
! [SV32: $i,SV6: $i,SV21: $i,SV27: $i] :
( ( ( aInfimumOfIn0 @ SV27 @ SV21 @ SV6 )
= $false )
| ( ( ~ ( aInfimumOfIn0 @ SV32 @ SV21 @ SV6 ) )
= $true )
| ( ( SV27 = SV32 )
= $true )
| ( ( aSubsetOf0 @ SV21 @ SV6 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(346,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
| ~ ( aFixedPointOf0 @ xp @ xf ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(347,plain,
! [SV34: $i] :
( ( ~ ( aElementOf0 @ SV34 @ xT )
| ( sdtlseqdt0 @ SV34 @ xp ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(348,plain,
! [SV28: $i] :
( ( ( aElementOf0 @ SV28 @ xS )
= $false )
| ( ( ~ ! [SY78: $i] :
( ~ ( aElementOf0 @ SY78 @ xT )
| ( sdtlseqdt0 @ SY78 @ SV28 ) ) )
= $true )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(349,plain,
! [SV16: $i,SV9: $i] :
( ( ( sdtlseqdt0 @ SV9 @ SV16 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV16 @ SV9 ) )
= $true )
| ( ( SV9 = SV16 )
= $true )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(350,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(351,plain,
( ( ~ ( aElementOf0 @ xp @ xU )
| ~ ( aElementOf0 @ xp @ xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(352,plain,
! [SV35: $i] :
( ( ~ ( aElementOf0 @ SV35 @ xP )
| ( sdtlseqdt0 @ xp @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(353,plain,
! [SV29: $i] :
( ( ( aElementOf0 @ SV29 @ xU )
= $false )
| ( ( ~ ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ xP )
| ( sdtlseqdt0 @ SV29 @ SY79 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(354,plain,
! [SV23: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) ) )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(355,plain,
! [SV23: $i] :
( ( ( ~ ( aFixedPointOf0 @ SV23 @ xf ) )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(356,plain,
! [SV23: $i] :
( ( ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
= $true )
| ( ( aElementOf0 @ SV23 @ xS )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(357,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ SV17 @ xS )
| ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(358,plain,
! [SV17: $i] :
( ( ( ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(359,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(360,plain,
! [SV25: $i] :
( ( ( ~ ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(361,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) ) )
= $true )
| ( ( ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(362,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV3 @ SV18 )
= $true )
| ( ( aElement0 @ SV14 )
= $false )
| ( ( aElement0 @ SV3 )
= $false )
| ( ( aElement0 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(363,plain,
! [SV26: $i,SV5: $i,SV20: $i,SV31: $i] :
( ( ( aSupremumOfIn0 @ SV31 @ SV20 @ SV5 )
= $false )
| ( ( aSupremumOfIn0 @ SV26 @ SV20 @ SV5 )
= $false )
| ( ( SV26 = SV31 )
= $true )
| ( ( aSubsetOf0 @ SV20 @ SV5 )
= $false )
| ( ( aSet0 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(364,plain,
! [SV27: $i,SV6: $i,SV21: $i,SV32: $i] :
( ( ( aInfimumOfIn0 @ SV32 @ SV21 @ SV6 )
= $false )
| ( ( aInfimumOfIn0 @ SV27 @ SV21 @ SV6 )
= $false )
| ( ( SV27 = SV32 )
= $true )
| ( ( aSubsetOf0 @ SV21 @ SV6 )
= $false )
| ( ( aSet0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(365,plain,
( ( ~ ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(366,plain,
( ( ~ ( aFixedPointOf0 @ xp @ xf ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(367,plain,
! [SV34: $i] :
( ( ( ~ ( aElementOf0 @ SV34 @ xT ) )
= $true )
| ( ( sdtlseqdt0 @ SV34 @ xp )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(368,plain,
! [SV28: $i] :
( ( ( ! [SY78: $i] :
( ~ ( aElementOf0 @ SY78 @ xT )
| ( sdtlseqdt0 @ SY78 @ SV28 ) ) )
= $false )
| ( ( aElementOf0 @ SV28 @ xS )
= $false )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(369,plain,
! [SV9: $i,SV16: $i] :
( ( ( sdtlseqdt0 @ SV16 @ SV9 )
= $false )
| ( ( sdtlseqdt0 @ SV9 @ SV16 )
= $false )
| ( ( SV9 = SV16 )
= $true )
| ( ( aElement0 @ SV9 )
= $false )
| ( ( aElement0 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(370,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(371,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(372,plain,
( ( ~ ( aElementOf0 @ xp @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(373,plain,
( ( ~ ( aElementOf0 @ xp @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(374,plain,
! [SV35: $i] :
( ( ( ~ ( aElementOf0 @ SV35 @ xP ) )
= $true )
| ( ( sdtlseqdt0 @ xp @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(375,plain,
! [SV29: $i] :
( ( ( ! [SY79: $i] :
( ~ ( aElementOf0 @ SY79 @ xP )
| ( sdtlseqdt0 @ SV29 @ SY79 ) ) )
= $false )
| ( ( aElementOf0 @ SV29 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(376,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) ) )
= $true )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(377,plain,
! [SV23: $i] :
( ( ( aFixedPointOf0 @ SV23 @ xf )
= $true )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(378,plain,
! [SV23: $i] :
( ( ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) ) )
= $true )
| ( ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 )
= $true )
| ( ( aElementOf0 @ SV23 @ xS )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(379,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ SV17 @ xS ) )
= $true )
| ( ( ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(380,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY68 @ SV17 ) @ xS )
| ~ ! [SY80: $i] :
( ~ ( aElementOf0 @ SY80 @ xT )
| ( sdtlseqdt0 @ SY80 @ ( sK1_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK1_SY68 @ SV17 ) @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ ( sK1_SY68 @ SV17 ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[358]) ).
thf(381,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(382,plain,
! [SV25: $i] :
( ( ( aUpperBoundOfIn0 @ SV25 @ xT @ xU )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(383,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) ) )
= $false )
| ( ( ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(384,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV3 @ SV18 )
= $true )
| ( ( aElement0 @ SV14 )
= $false )
| ( ( aElement0 @ SV3 )
= $false )
| ( ( aElement0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(385,plain,
( ( ~ ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(386,plain,
( ( aFixedPointOf0 @ xp @ xf )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(387,plain,
! [SV34: $i] :
( ( ( aElementOf0 @ SV34 @ xT )
= $false )
| ( ( sdtlseqdt0 @ SV34 @ xp )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(388,plain,
! [SV28: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_SY78 @ SV28 ) @ xT )
| ( sdtlseqdt0 @ ( sK2_SY78 @ SV28 ) @ SV28 ) )
= $false )
| ( ( aElementOf0 @ SV28 @ xS )
= $false )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[368]) ).
thf(389,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(390,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SX0 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SX1 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SX0 @ SX1 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SX0 ) @ ( sdtlpdtrp0 @ xf @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(391,plain,
( ( aElementOf0 @ xp @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(392,plain,
( ( aElementOf0 @ xp @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(393,plain,
! [SV35: $i] :
( ( ( aElementOf0 @ SV35 @ xP )
= $false )
| ( ( sdtlseqdt0 @ xp @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(394,plain,
! [SV29: $i] :
( ( ( ~ ( aElementOf0 @ ( sK3_SY79 @ SV29 ) @ xP )
| ( sdtlseqdt0 @ SV29 @ ( sK3_SY79 @ SV29 ) ) )
= $false )
| ( ( aElementOf0 @ SV29 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[375]) ).
thf(395,plain,
! [SV23: $i] :
( ( ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 ) )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(396,plain,
! [SV23: $i] :
( ( ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
= $false )
| ( ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 )
= $true )
| ( ( aElementOf0 @ SV23 @ xS )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(397,plain,
! [SV17: $i] :
( ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(398,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY68 @ SV17 ) @ xS )
| ~ ! [SY80: $i] :
( ~ ( aElementOf0 @ SY80 @ xT )
| ( sdtlseqdt0 @ SY80 @ ( sK1_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK1_SY68 @ SV17 ) @ xT @ xS ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(399,plain,
! [SV17: $i] :
( ( ( sdtlseqdt0 @ SV17 @ ( sK1_SY68 @ SV17 ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(400,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
| ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(401,plain,
! [SV25: $i] :
( ( ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
= $true )
| ( ( ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(402,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV3 @ SV14 )
| ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
= $true )
| ( ( sdtlseqdt0 @ SV3 @ SV18 )
= $true )
| ( ( aElement0 @ SV14 )
= $false )
| ( ( aElement0 @ SV3 )
= $false )
| ( ( aElement0 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(403,plain,
( ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
| ( ( sdtlpdtrp0 @ xf @ xp )
!= xp ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(404,plain,
! [SV28: $i] :
( ( ( ~ ( aElementOf0 @ ( sK2_SY78 @ SV28 ) @ xT ) )
= $false )
| ( ( aElementOf0 @ SV28 @ xS )
= $false )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(405,plain,
! [SV28: $i] :
( ( ( sdtlseqdt0 @ ( sK2_SY78 @ SV28 ) @ SV28 )
= $false )
| ( ( aElementOf0 @ SV28 @ xS )
= $false )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(406,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
| ~ ( aFunction0 @ xf ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(407,plain,
! [SV36: $i] :
( ( ! [SY81: $i] :
( ~ ~ ( ~ ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SY81 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SV36 @ SY81 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(408,plain,
! [SV29: $i] :
( ( ( ~ ( aElementOf0 @ ( sK3_SY79 @ SV29 ) @ xP ) )
= $false )
| ( ( aElementOf0 @ SV29 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(409,plain,
! [SV29: $i] :
( ( ( sdtlseqdt0 @ SV29 @ ( sK3_SY79 @ SV29 ) )
= $false )
| ( ( aElementOf0 @ SV29 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(410,plain,
! [SV23: $i] :
( ( ( ~ ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) ) )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(411,plain,
! [SV23: $i] :
( ( ( ( sdtlpdtrp0 @ xf @ SV23 )
!= SV23 )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(412,plain,
! [SV23: $i] :
( ( ( ( sdtlpdtrp0 @ xf @ SV23 )
= SV23 )
= $false )
| ( ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
= $false )
| ( ( aElementOf0 @ SV23 @ xS )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(413,plain,
! [SV17: $i] :
( ( ( ! [SY67: $i] :
( ~ ( aElementOf0 @ SY67 @ xT )
| ( sdtlseqdt0 @ SY67 @ SV17 ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(414,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY68 @ SV17 ) @ xS )
| ~ ! [SY80: $i] :
( ~ ( aElementOf0 @ SY80 @ xT )
| ( sdtlseqdt0 @ SY80 @ ( sK1_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK1_SY68 @ SV17 ) @ xT @ xS ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(415,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(416,plain,
! [SV25: $i] :
( ( ( ~ ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(417,plain,
! [SV25: $i] :
( ( ( ~ ( aElementOf0 @ SV25 @ xU ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
= $true )
| ( ( ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(418,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV3 @ SV14 ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
= $true )
| ( ( sdtlseqdt0 @ SV3 @ SV18 )
= $true )
| ( ( aElement0 @ SV14 )
= $false )
| ( ( aElement0 @ SV3 )
= $false )
| ( ( aElement0 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(419,plain,
( ( ~ ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(420,plain,
( ( ( sdtlpdtrp0 @ xf @ xp )
!= xp )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(421,plain,
! [SV28: $i] :
( ( ( aElementOf0 @ ( sK2_SY78 @ SV28 ) @ xT )
= $true )
| ( ( aElementOf0 @ SV28 @ xS )
= $false )
| ( ( sdtlseqdt0 @ xp @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(422,plain,
( ( ~ ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(423,plain,
( ( ~ ( aFunction0 @ xf ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(424,plain,
! [SV37: $i,SV36: $i] :
( ( ~ ~ ( ~ ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SV37 @ ( szDzozmdt0 @ xf ) ) )
| ~ ( sdtlseqdt0 @ SV36 @ SV37 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(425,plain,
! [SV29: $i] :
( ( ( aElementOf0 @ ( sK3_SY79 @ SV29 ) @ xP )
= $true )
| ( ( aElementOf0 @ SV29 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV29 @ xp )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(426,plain,
! [SV23: $i] :
( ( ( aElementOf0 @ SV23 @ ( szDzozmdt0 @ xf ) )
= $true )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(427,plain,
! [SV23: $i] :
( ( ( ( sdtlpdtrp0 @ xf @ SV23 )
= SV23 )
= $true )
| ( ( aElementOf0 @ SV23 @ xS )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(428,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
| ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[413]) ).
thf(429,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY68 @ SV17 ) @ xS )
| ~ ! [SY80: $i] :
( ~ ( aElementOf0 @ SY80 @ xT )
| ( sdtlseqdt0 @ SY80 @ ( sK1_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK1_SY68 @ SV17 ) @ xT @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(430,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(431,plain,
! [SV25: $i] :
( ( ( ! [SY74: $i] :
( ~ ( aElementOf0 @ SY74 @ xT )
| ( sdtlseqdt0 @ SY74 @ SV25 ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(432,plain,
! [SV25: $i] :
( ( ( aElementOf0 @ SV25 @ xU )
= $false )
| ( ( ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
= $true )
| ( ( ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(433,plain,
! [SV18: $i,SV14: $i,SV3: $i] :
( ( ( sdtlseqdt0 @ SV3 @ SV14 )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV14 @ SV18 ) )
= $true )
| ( ( sdtlseqdt0 @ SV3 @ SV18 )
= $true )
| ( ( aElement0 @ SV14 )
= $false )
| ( ( aElement0 @ SV3 )
= $false )
| ( ( aElement0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(434,plain,
( ( aElementOf0 @ xp @ ( szDzozmdt0 @ xf ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(435,plain,
( ( ( sdtlpdtrp0 @ xf @ xp )
= xp )
= $true ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(436,plain,
( ( ~ ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(437,plain,
( ( aFunction0 @ xf )
= $true ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(438,plain,
! [SV37: $i,SV36: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SV37 @ ( szDzozmdt0 @ xf ) ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV37 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(439,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(440,plain,
! [SV17: $i] :
( ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(441,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK1_SY68 @ SV17 ) @ xS )
| ~ ! [SY80: $i] :
( ~ ( aElementOf0 @ SY80 @ xT )
| ( sdtlseqdt0 @ SY80 @ ( sK1_SY68 @ SV17 ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(442,plain,
! [SV17: $i] :
( ( ( ~ ( aUpperBoundOfIn0 @ ( sK1_SY68 @ SV17 ) @ xT @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(443,plain,
! [SV25: $i] :
( ( ( ~ ( aElementOf0 @ SV25 @ xU )
| ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(444,plain,
! [SV25: $i,SV38: $i] :
( ( ( ~ ( aElementOf0 @ SV38 @ xT )
| ( sdtlseqdt0 @ SV38 @ SV25 ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(445,plain,
! [SV25: $i] :
( ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 )
= $false )
| ( ( aElementOf0 @ SV25 @ xU )
= $false )
| ( ( ~ ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) ) )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(446,plain,
! [SV3: $i,SV18: $i,SV14: $i] :
( ( ( sdtlseqdt0 @ SV14 @ SV18 )
= $false )
| ( ( sdtlseqdt0 @ SV3 @ SV14 )
= $false )
| ( ( sdtlseqdt0 @ SV3 @ SV18 )
= $true )
| ( ( aElement0 @ SV14 )
= $false )
| ( ( aElement0 @ SV3 )
= $false )
| ( ( aElement0 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(447,plain,
( ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
| ~ ( aCompleteLattice0 @ xU ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(448,plain,
! [SV37: $i,SV36: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SV37 @ ( szDzozmdt0 @ xf ) ) ) )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV37 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(449,plain,
! [SV17: $i] :
( ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( ~ ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(450,plain,
! [SV17: $i] :
( ( ( ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(451,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK1_SY68 @ SV17 ) @ xS )
| ~ ! [SY80: $i] :
( ~ ( aElementOf0 @ SY80 @ xT )
| ( sdtlseqdt0 @ SY80 @ ( sK1_SY68 @ SV17 ) ) ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(452,plain,
! [SV17: $i] :
( ( ( aUpperBoundOfIn0 @ ( sK1_SY68 @ SV17 ) @ xT @ xS )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(453,plain,
! [SV25: $i] :
( ( ( ~ ( aElementOf0 @ SV25 @ xU ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(454,plain,
! [SV25: $i] :
( ( ( ~ ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(455,plain,
! [SV25: $i,SV38: $i] :
( ( ( ~ ( aElementOf0 @ SV38 @ xT ) )
= $true )
| ( ( sdtlseqdt0 @ SV38 @ SV25 )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(456,plain,
! [SV25: $i] :
( ( ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) )
| ( aUpperBoundOfIn0 @ SV25 @ xT @ xU ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(457,plain,
( ( ~ ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(458,plain,
( ( ~ ( aCompleteLattice0 @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(459,plain,
! [SV37: $i,SV36: $i] :
( ( ( ~ ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) )
| ~ ( aElementOf0 @ SV37 @ ( szDzozmdt0 @ xf ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV37 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(460,plain,
! [SV17: $i] :
( ( ( ! [SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY68 @ xS )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ xT )
| ( sdtlseqdt0 @ SX2 @ SY68 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY68 @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ SY68 ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(461,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK5_SY68 @ SV17 ) @ xS )
| ~ ! [SY82: $i] :
( ~ ( aElementOf0 @ SY82 @ xT )
| ( sdtlseqdt0 @ SY82 @ ( sK5_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK5_SY68 @ SV17 ) @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ ( sK5_SY68 @ SV17 ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[450]) ).
thf(462,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_SY68 @ SV17 ) @ xS )
| ~ ! [SY80: $i] :
( ~ ( aElementOf0 @ SY80 @ xT )
| ( sdtlseqdt0 @ SY80 @ ( sK1_SY68 @ SV17 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(463,plain,
! [SV25: $i] :
( ( ( aElementOf0 @ SV25 @ xU )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(464,plain,
! [SV25: $i] :
( ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(465,plain,
! [SV25: $i,SV38: $i] :
( ( ( aElementOf0 @ SV38 @ xT )
= $false )
| ( ( sdtlseqdt0 @ SV38 @ SV25 )
= $true )
| ( ( aElementOf0 @ SV25 @ xP )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(466,plain,
! [SV25: $i] :
( ( ( ! [SY75: $i] :
( ~ ( aElementOf0 @ SY75 @ xT )
| ( sdtlseqdt0 @ SY75 @ SV25 ) ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(467,plain,
! [SV25: $i] :
( ( ( aUpperBoundOfIn0 @ SV25 @ xT @ xU )
= $false )
| ( ( aElementOf0 @ SV25 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(468,plain,
( ( ~ ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(469,plain,
( ( aCompleteLattice0 @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(470,plain,
! [SV37: $i,SV36: $i] :
( ( ( ~ ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) ) )
= $true )
| ( ( ~ ( aElementOf0 @ SV37 @ ( szDzozmdt0 @ xf ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV37 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(471,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK6_SY68 @ SV17 ) @ xS )
| ~ ! [SY83: $i] :
( ~ ( aElementOf0 @ SY83 @ xT )
| ( sdtlseqdt0 @ SY83 @ ( sK6_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK6_SY68 @ SV17 ) @ xT @ xS ) )
| ( sdtlseqdt0 @ SV17 @ ( sK6_SY68 @ SV17 ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[460]) ).
thf(472,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK5_SY68 @ SV17 ) @ xS )
| ~ ! [SY82: $i] :
( ~ ( aElementOf0 @ SY82 @ xT )
| ( sdtlseqdt0 @ SY82 @ ( sK5_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK5_SY68 @ SV17 ) @ xT @ xS ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(473,plain,
! [SV17: $i] :
( ( ( sdtlseqdt0 @ SV17 @ ( sK5_SY68 @ SV17 ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(474,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ ( sK1_SY68 @ SV17 ) @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(475,plain,
! [SV17: $i] :
( ( ( ~ ! [SY80: $i] :
( ~ ( aElementOf0 @ SY80 @ xT )
| ( sdtlseqdt0 @ SY80 @ ( sK1_SY68 @ SV17 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(476,plain,
! [SV25: $i] :
( ( ( ~ ( aElementOf0 @ ( sK7_SY75 @ SV25 ) @ xT )
| ( sdtlseqdt0 @ ( sK7_SY75 @ SV25 ) @ SV25 ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[466]) ).
thf(477,plain,
( ( ~ ( aSet0 @ xU )
| ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(478,plain,
! [SV37: $i,SV36: $i] :
( ( ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) )
= $false )
| ( ( ~ ( aElementOf0 @ SV37 @ ( szDzozmdt0 @ xf ) ) )
= $true )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV37 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(479,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK6_SY68 @ SV17 ) @ xS )
| ~ ! [SY83: $i] :
( ~ ( aElementOf0 @ SY83 @ xT )
| ( sdtlseqdt0 @ SY83 @ ( sK6_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK6_SY68 @ SV17 ) @ xT @ xS ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(480,plain,
! [SV17: $i] :
( ( ( sdtlseqdt0 @ SV17 @ ( sK6_SY68 @ SV17 ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(481,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK5_SY68 @ SV17 ) @ xS )
| ~ ! [SY82: $i] :
( ~ ( aElementOf0 @ SY82 @ xT )
| ( sdtlseqdt0 @ SY82 @ ( sK5_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK5_SY68 @ SV17 ) @ xT @ xS ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(482,plain,
! [SV17: $i] :
( ( ( aElementOf0 @ ( sK1_SY68 @ SV17 ) @ xS )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(483,plain,
! [SV17: $i] :
( ( ( ! [SY80: $i] :
( ~ ( aElementOf0 @ SY80 @ xT )
| ( sdtlseqdt0 @ SY80 @ ( sK1_SY68 @ SV17 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(484,plain,
! [SV25: $i] :
( ( ( ~ ( aElementOf0 @ ( sK7_SY75 @ SV25 ) @ xT ) )
= $false )
| ( ( aElementOf0 @ SV25 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(485,plain,
! [SV25: $i] :
( ( ( sdtlseqdt0 @ ( sK7_SY75 @ SV25 ) @ SV25 )
= $false )
| ( ( aElementOf0 @ SV25 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(486,plain,
( ( ~ ( aSet0 @ xU ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(487,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(488,plain,
! [SV36: $i,SV37: $i] :
( ( ( aElementOf0 @ SV37 @ ( szDzozmdt0 @ xf ) )
= $false )
| ( ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) )
= $false )
| ( ( ~ ( sdtlseqdt0 @ SV36 @ SV37 )
| ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(489,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK6_SY68 @ SV17 ) @ xS )
| ~ ! [SY83: $i] :
( ~ ( aElementOf0 @ SY83 @ xT )
| ( sdtlseqdt0 @ SY83 @ ( sK6_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK6_SY68 @ SV17 ) @ xT @ xS ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(490,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK5_SY68 @ SV17 ) @ xS )
| ~ ! [SY82: $i] :
( ~ ( aElementOf0 @ SY82 @ xT )
| ( sdtlseqdt0 @ SY82 @ ( sK5_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK5_SY68 @ SV17 ) @ xT @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(491,plain,
! [SV17: $i,SV39: $i] :
( ( ( ~ ( aElementOf0 @ SV39 @ xT )
| ( sdtlseqdt0 @ SV39 @ ( sK1_SY68 @ SV17 ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(492,plain,
! [SV25: $i] :
( ( ( aElementOf0 @ ( sK7_SY75 @ SV25 ) @ xT )
= $true )
| ( ( aElementOf0 @ SV25 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV25 ) @ SV25 )
= $false )
| ( ( aElementOf0 @ SV25 @ xP )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(493,plain,
( ( aSet0 @ xU )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(494,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( ~ ( aSet0 @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( aElementOf0 @ SX1 @ SX0 )
| ( aElementOf0 @ SX1 @ xU ) ) )
| ( aSubsetOf0 @ SX0 @ xU ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX1 @ xU )
| ~ ( aElementOf0 @ SX1 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( aElementOf0 @ SX2 @ SX0 )
| ( sdtlseqdt0 @ SX1 @ SX2 ) ) )
| ~ ( aLowerBoundOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ! [SX2: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ( aLowerBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX1 ) ) )
| ~ ( aInfimumOfIn0 @ SX1 @ SX0 @ xU ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SX2 @ xU )
| ~ ( aElementOf0 @ SX2 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( aElementOf0 @ SX3 @ SX0 )
| ( sdtlseqdt0 @ SX3 @ SX2 ) ) )
| ~ ( aUpperBoundOfIn0 @ SX2 @ SX0 @ xU ) )
| ~ ! [SX3: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SX3 @ xU )
| ~ ! [SX4: $i] :
( ~ ( aElementOf0 @ SX4 @ SX0 )
| ( sdtlseqdt0 @ SX4 @ SX3 ) ) )
| ( aUpperBoundOfIn0 @ SX3 @ SX0 @ xU ) )
| ( sdtlseqdt0 @ SX2 @ SX3 ) ) )
| ~ ( aSupremumOfIn0 @ SX2 @ SX0 @ xU ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(495,plain,
! [SV37: $i,SV36: $i] :
( ( ( ~ ( sdtlseqdt0 @ SV36 @ SV37 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SV37 ) )
= $true )
| ( ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) )
= $false )
| ( ( aElementOf0 @ SV37 @ ( szDzozmdt0 @ xf ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(496,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK6_SY68 @ SV17 ) @ xS )
| ~ ! [SY83: $i] :
( ~ ( aElementOf0 @ SY83 @ xT )
| ( sdtlseqdt0 @ SY83 @ ( sK6_SY68 @ SV17 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK6_SY68 @ SV17 ) @ xT @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(497,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK5_SY68 @ SV17 ) @ xS )
| ~ ! [SY82: $i] :
( ~ ( aElementOf0 @ SY82 @ xT )
| ( sdtlseqdt0 @ SY82 @ ( sK5_SY68 @ SV17 ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(498,plain,
! [SV17: $i] :
( ( ( ~ ( aUpperBoundOfIn0 @ ( sK5_SY68 @ SV17 ) @ xT @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(499,plain,
! [SV17: $i,SV39: $i] :
( ( ( ~ ( aElementOf0 @ SV39 @ xT ) )
= $true )
| ( ( sdtlseqdt0 @ SV39 @ ( sK1_SY68 @ SV17 ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(500,plain,
! [SV40: $i] :
( ( ~ ( ~ ( ~ ( aSet0 @ SV40 )
| ~ ! [SY84: $i] :
( ~ ( aElementOf0 @ SY84 @ SV40 )
| ( aElementOf0 @ SY84 @ xU ) ) )
| ( aSubsetOf0 @ SV40 @ xU ) )
| ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(501,plain,
! [SV37: $i,SV36: $i] :
( ( ( sdtlseqdt0 @ SV36 @ SV37 )
= $false )
| ( ( sdtlseqdt0 @ ( sdtlpdtrp0 @ xf @ SV36 ) @ ( sdtlpdtrp0 @ xf @ SV37 ) )
= $true )
| ( ( aElementOf0 @ SV36 @ ( szDzozmdt0 @ xf ) )
= $false )
| ( ( aElementOf0 @ SV37 @ ( szDzozmdt0 @ xf ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(502,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK6_SY68 @ SV17 ) @ xS )
| ~ ! [SY83: $i] :
( ~ ( aElementOf0 @ SY83 @ xT )
| ( sdtlseqdt0 @ SY83 @ ( sK6_SY68 @ SV17 ) ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(503,plain,
! [SV17: $i] :
( ( ( ~ ( aUpperBoundOfIn0 @ ( sK6_SY68 @ SV17 ) @ xT @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(504,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK5_SY68 @ SV17 ) @ xS )
| ~ ! [SY82: $i] :
( ~ ( aElementOf0 @ SY82 @ xT )
| ( sdtlseqdt0 @ SY82 @ ( sK5_SY68 @ SV17 ) ) ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(505,plain,
! [SV17: $i] :
( ( ( aUpperBoundOfIn0 @ ( sK5_SY68 @ SV17 ) @ xT @ xS )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(506,plain,
! [SV17: $i,SV39: $i] :
( ( ( aElementOf0 @ SV39 @ xT )
= $false )
| ( ( sdtlseqdt0 @ SV39 @ ( sK1_SY68 @ SV17 ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aUpperBoundOfIn0 @ SV17 @ xT @ xS )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(507,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( ~ ( aSet0 @ SV40 )
| ~ ! [SY84: $i] :
( ~ ( aElementOf0 @ SY84 @ SV40 )
| ( aElementOf0 @ SY84 @ xU ) ) )
| ( aSubsetOf0 @ SV40 @ xU ) ) )
= $true )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(508,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK6_SY68 @ SV17 ) @ xS )
| ~ ! [SY83: $i] :
( ~ ( aElementOf0 @ SY83 @ xT )
| ( sdtlseqdt0 @ SY83 @ ( sK6_SY68 @ SV17 ) ) ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(509,plain,
! [SV17: $i] :
( ( ( aUpperBoundOfIn0 @ ( sK6_SY68 @ SV17 ) @ xT @ xS )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(510,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ ( sK5_SY68 @ SV17 ) @ xS )
| ~ ! [SY82: $i] :
( ~ ( aElementOf0 @ SY82 @ xT )
| ( sdtlseqdt0 @ SY82 @ ( sK5_SY68 @ SV17 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(511,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( aSet0 @ SV40 )
| ~ ! [SY84: $i] :
( ~ ( aElementOf0 @ SY84 @ SV40 )
| ( aElementOf0 @ SY84 @ xU ) ) )
| ( aSubsetOf0 @ SV40 @ xU ) )
= $false )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(512,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ ( sK6_SY68 @ SV17 ) @ xS )
| ~ ! [SY83: $i] :
( ~ ( aElementOf0 @ SY83 @ xT )
| ( sdtlseqdt0 @ SY83 @ ( sK6_SY68 @ SV17 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(513,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ ( sK5_SY68 @ SV17 ) @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(514,plain,
! [SV17: $i] :
( ( ( ~ ! [SY82: $i] :
( ~ ( aElementOf0 @ SY82 @ xT )
| ( sdtlseqdt0 @ SY82 @ ( sK5_SY68 @ SV17 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(515,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( aSet0 @ SV40 )
| ~ ! [SY84: $i] :
( ~ ( aElementOf0 @ SY84 @ SV40 )
| ( aElementOf0 @ SY84 @ xU ) ) ) )
= $false )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(516,plain,
! [SV40: $i] :
( ( ( aSubsetOf0 @ SV40 @ xU )
= $false )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(517,plain,
! [SV17: $i] :
( ( ( ~ ( aElementOf0 @ ( sK6_SY68 @ SV17 ) @ xS ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(518,plain,
! [SV17: $i] :
( ( ( ~ ! [SY83: $i] :
( ~ ( aElementOf0 @ SY83 @ xT )
| ( sdtlseqdt0 @ SY83 @ ( sK6_SY68 @ SV17 ) ) ) )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[512]) ).
thf(519,plain,
! [SV17: $i] :
( ( ( aElementOf0 @ ( sK5_SY68 @ SV17 ) @ xS )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(520,plain,
! [SV17: $i] :
( ( ( ! [SY82: $i] :
( ~ ( aElementOf0 @ SY82 @ xT )
| ( sdtlseqdt0 @ SY82 @ ( sK5_SY68 @ SV17 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(521,plain,
! [SV40: $i] :
( ( ( ~ ( aSet0 @ SV40 )
| ~ ! [SY84: $i] :
( ~ ( aElementOf0 @ SY84 @ SV40 )
| ( aElementOf0 @ SY84 @ xU ) ) )
= $true )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(522,plain,
! [SV40: $i] :
( ( ( ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(523,plain,
! [SV17: $i] :
( ( ( aElementOf0 @ ( sK6_SY68 @ SV17 ) @ xS )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(524,plain,
! [SV17: $i] :
( ( ( ! [SY83: $i] :
( ~ ( aElementOf0 @ SY83 @ xT )
| ( sdtlseqdt0 @ SY83 @ ( sK6_SY68 @ SV17 ) ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(525,plain,
! [SV17: $i,SV41: $i] :
( ( ( ~ ( aElementOf0 @ SV41 @ xT )
| ( sdtlseqdt0 @ SV41 @ ( sK5_SY68 @ SV17 ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(526,plain,
! [SV40: $i] :
( ( ( ~ ( aSet0 @ SV40 ) )
= $true )
| ( ( ~ ! [SY84: $i] :
( ~ ( aElementOf0 @ SY84 @ SV40 )
| ( aElementOf0 @ SY84 @ xU ) ) )
= $true )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(527,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[522]) ).
thf(528,plain,
! [SV17: $i,SV42: $i] :
( ( ( ~ ( aElementOf0 @ SV42 @ xT )
| ( sdtlseqdt0 @ SV42 @ ( sK6_SY68 @ SV17 ) ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(529,plain,
! [SV17: $i,SV41: $i] :
( ( ( ~ ( aElementOf0 @ SV41 @ xT ) )
= $true )
| ( ( sdtlseqdt0 @ SV41 @ ( sK5_SY68 @ SV17 ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(530,plain,
! [SV40: $i] :
( ( ( aSet0 @ SV40 )
= $false )
| ( ( ~ ! [SY84: $i] :
( ~ ( aElementOf0 @ SY84 @ SV40 )
| ( aElementOf0 @ SY84 @ xU ) ) )
= $true )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(531,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(532,plain,
! [SV17: $i,SV42: $i] :
( ( ( ~ ( aElementOf0 @ SV42 @ xT ) )
= $true )
| ( ( sdtlseqdt0 @ SV42 @ ( sK6_SY68 @ SV17 ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(533,plain,
! [SV17: $i,SV41: $i] :
( ( ( aElementOf0 @ SV41 @ xT )
= $false )
| ( ( sdtlseqdt0 @ SV41 @ ( sK5_SY68 @ SV17 ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( sdtlseqdt0 @ ( sK4_SY67 @ SV17 ) @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(534,plain,
! [SV40: $i] :
( ( ( ! [SY84: $i] :
( ~ ( aElementOf0 @ SY84 @ SV40 )
| ( aElementOf0 @ SY84 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(535,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(536,plain,
! [SV17: $i,SV42: $i] :
( ( ( aElementOf0 @ SV42 @ xT )
= $false )
| ( ( sdtlseqdt0 @ SV42 @ ( sK6_SY68 @ SV17 ) )
= $true )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ SV17 @ xS )
= $false )
| ( ( aElementOf0 @ ( sK4_SY67 @ SV17 ) @ xT )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(537,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
| ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[534]) ).
thf(538,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(539,plain,
! [SV40: $i] :
( ( ( ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(540,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(541,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(542,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(543,plain,
! [SV40: $i] :
( ( ( ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(544,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(545,plain,
! [SV40: $i] :
( ( ( ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(546,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(547,plain,
! [SV40: $i] :
( ( ( ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(548,plain,
! [SV40: $i] :
( ( ( ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY85 @ xU )
| ~ ( aElementOf0 @ SY85 @ xU ) )
| ~ ! [SY86: $i] :
( ~ ( aElementOf0 @ SY86 @ SV40 )
| ( sdtlseqdt0 @ SY85 @ SY86 ) ) )
| ~ ( aLowerBoundOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ! [SY87: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY87 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY87 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY87 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY87 @ SY85 ) ) )
| ~ ( aInfimumOfIn0 @ SY85 @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(549,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[545]) ).
thf(550,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(551,plain,
! [SV40: $i] :
( ( ( ~ ( aInfimumOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(552,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY108: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY108 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY108 ) ) )
| ( aUpperBoundOfIn0 @ SY108 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SY108 ) ) )
| ~ ( aSupremumOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[547]) ).
thf(553,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[548]) ).
thf(554,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(555,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(556,plain,
! [SV40: $i] :
( ( ( aInfimumOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(557,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY108: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY108 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY108 ) ) )
| ( aUpperBoundOfIn0 @ SY108 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SY108 ) ) )
| ~ ( aSupremumOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(558,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(559,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(560,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(561,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY108: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY108 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY108 ) ) )
| ( aUpperBoundOfIn0 @ SY108 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SY108 ) ) )
| ~ ( aSupremumOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(562,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(563,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(564,plain,
! [SV40: $i] :
( ( ( ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(565,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(566,plain,
! [SV40: $i] :
( ( ( ~ ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(567,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY108: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY108 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY108 ) ) )
| ( aUpperBoundOfIn0 @ SY108 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SY108 ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(568,plain,
! [SV40: $i] :
( ( ( ~ ( aSupremumOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(569,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(570,plain,
! [SV40: $i] :
( ( ( ~ ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(571,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(572,plain,
! [SV40: $i] :
( ( ( ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(573,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(574,plain,
! [SV40: $i] :
( ( ( ! [SY94: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY94 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY94 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY94 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY94 @ ( sK8_SY85 @ SV40 ) ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(575,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY108: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY108 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY108 ) ) )
| ( aUpperBoundOfIn0 @ SY108 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SY108 ) ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(576,plain,
! [SV40: $i] :
( ( ( aSupremumOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(577,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(578,plain,
! [SV40: $i] :
( ( ( ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(579,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(580,plain,
! [SV40: $i] :
( ( ( ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(581,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(582,plain,
! [SV40: $i,SV43: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV43 @ xU )
| ~ ! [SY117: $i] :
( ~ ( aElementOf0 @ SY117 @ SV40 )
| ( sdtlseqdt0 @ SV43 @ SY117 ) ) )
| ( aLowerBoundOfIn0 @ SV43 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(583,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY108: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY108 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY108 ) ) )
| ( aUpperBoundOfIn0 @ SY108 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SY108 ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(584,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) )
| ~ ( aInfimumOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(585,plain,
! [SV40: $i] :
( ( ( ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ SY89 @ xU )
| ~ ( aElementOf0 @ SY89 @ xU ) )
| ~ ! [SY90: $i] :
( ~ ( aElementOf0 @ SY90 @ SV40 )
| ( sdtlseqdt0 @ SY90 @ SY89 ) ) )
| ~ ( aUpperBoundOfIn0 @ SY89 @ SV40 @ xU ) )
| ~ ! [SY91: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY91 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY91 ) ) )
| ( aUpperBoundOfIn0 @ SY91 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY89 @ SY91 ) ) )
| ~ ( aSupremumOfIn0 @ SY89 @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(586,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(587,plain,
! [SV40: $i] :
( ( ( ~ ( aInfimumOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(588,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY119: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY119 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY119 ) ) )
| ( aUpperBoundOfIn0 @ SY119 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SY119 ) ) )
| ~ ( aSupremumOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[580]) ).
thf(589,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[581]) ).
thf(590,plain,
! [SV40: $i] :
( ( ( ~ ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[581]) ).
thf(591,plain,
! [SV40: $i,SV43: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV43 @ xU )
| ~ ! [SY117: $i] :
( ~ ( aElementOf0 @ SY117 @ SV40 )
| ( sdtlseqdt0 @ SV43 @ SY117 ) ) )
| ( aLowerBoundOfIn0 @ SV43 @ SV40 @ xU ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(592,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(593,plain,
! [SV40: $i] :
( ( ( ~ ! [SY108: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY108 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY108 ) ) )
| ( aUpperBoundOfIn0 @ SY108 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SY108 ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(594,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(595,plain,
! [SV40: $i] :
( ( ( ~ ( aInfimumOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[584]) ).
thf(596,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY122: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY122 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY122 ) ) )
| ( aUpperBoundOfIn0 @ SY122 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SY122 ) ) )
| ~ ( aSupremumOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[585]) ).
thf(597,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(598,plain,
! [SV40: $i] :
( ( ( aInfimumOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(599,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY119: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY119 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY119 ) ) )
| ( aUpperBoundOfIn0 @ SY119 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SY119 ) ) )
| ~ ( aSupremumOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(600,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(601,plain,
! [SV40: $i] :
( ( ( aLowerBoundOfIn0 @ ( sK8_SY85 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(602,plain,
! [SV40: $i,SV43: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV43 @ xU )
| ~ ! [SY117: $i] :
( ~ ( aElementOf0 @ SY117 @ SV40 )
| ( sdtlseqdt0 @ SV43 @ SY117 ) ) )
| ( aLowerBoundOfIn0 @ SV43 @ SV40 @ xU ) )
= $false )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(603,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(604,plain,
! [SV40: $i] :
( ( ( ! [SY108: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY108 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY108 ) ) )
| ( aUpperBoundOfIn0 @ SY108 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SY108 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(605,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(606,plain,
! [SV40: $i] :
( ( ( aInfimumOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(607,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY122: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY122 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY122 ) ) )
| ( aUpperBoundOfIn0 @ SY122 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SY122 ) ) )
| ~ ( aSupremumOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(608,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(609,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY119: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY119 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY119 ) ) )
| ( aUpperBoundOfIn0 @ SY119 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SY119 ) ) )
| ~ ( aSupremumOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(610,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(611,plain,
! [SV40: $i,SV43: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV43 @ xU )
| ~ ! [SY117: $i] :
( ~ ( aElementOf0 @ SY117 @ SV40 )
| ( sdtlseqdt0 @ SV43 @ SY117 ) ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(612,plain,
! [SV40: $i,SV43: $i] :
( ( ( aLowerBoundOfIn0 @ SV43 @ SV40 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[602]) ).
thf(613,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(614,plain,
! [SV40: $i,SV44: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV44 @ xU )
| ~ ! [SY124: $i] :
( ~ ( aElementOf0 @ SY124 @ SV40 )
| ( sdtlseqdt0 @ SY124 @ SV44 ) ) )
| ( aUpperBoundOfIn0 @ SV44 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(615,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(616,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY122: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY122 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY122 ) ) )
| ( aUpperBoundOfIn0 @ SY122 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SY122 ) ) )
| ~ ( aSupremumOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(617,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(618,plain,
! [SV40: $i] :
( ( ( ~ ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(619,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY119: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY119 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY119 ) ) )
| ( aUpperBoundOfIn0 @ SY119 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SY119 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(620,plain,
! [SV40: $i] :
( ( ( ~ ( aSupremumOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(621,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(622,plain,
! [SV40: $i] :
( ( ( ~ ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(623,plain,
! [SV40: $i,SV43: $i] :
( ( ( ~ ( aElementOf0 @ SV43 @ xU )
| ~ ! [SY117: $i] :
( ~ ( aElementOf0 @ SY117 @ SV40 )
| ( sdtlseqdt0 @ SV43 @ SY117 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(624,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(625,plain,
! [SV40: $i] :
( ( ( ~ ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(626,plain,
! [SV40: $i,SV44: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV44 @ xU )
| ~ ! [SY124: $i] :
( ~ ( aElementOf0 @ SY124 @ SV40 )
| ( sdtlseqdt0 @ SY124 @ SV44 ) ) )
| ( aUpperBoundOfIn0 @ SV44 @ SV40 @ xU ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(627,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(628,plain,
! [SV40: $i] :
( ( ( ~ ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(629,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY122: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY122 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY122 ) ) )
| ( aUpperBoundOfIn0 @ SY122 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SY122 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(630,plain,
! [SV40: $i] :
( ( ( ~ ( aSupremumOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(631,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(632,plain,
! [SV40: $i] :
( ( ( ! [SY101: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY101 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY101 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY101 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY101 @ ( sK10_SY85 @ SV40 ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(633,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY119: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY119 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY119 ) ) )
| ( aUpperBoundOfIn0 @ SY119 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SY119 ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(634,plain,
! [SV40: $i] :
( ( ( aSupremumOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(635,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(636,plain,
! [SV40: $i] :
( ( ( ! [SY93: $i] :
( ~ ( aElementOf0 @ SY93 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SY93 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(637,plain,
! [SV40: $i,SV43: $i] :
( ( ( ~ ( aElementOf0 @ SV43 @ xU ) )
= $true )
| ( ( ~ ! [SY117: $i] :
( ~ ( aElementOf0 @ SY117 @ SV40 )
| ( sdtlseqdt0 @ SV43 @ SY117 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(638,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(639,plain,
! [SV40: $i] :
( ( ( aUpperBoundOfIn0 @ ( sK11_SY89 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(640,plain,
! [SV40: $i,SV44: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV44 @ xU )
| ~ ! [SY124: $i] :
( ~ ( aElementOf0 @ SY124 @ SV40 )
| ( sdtlseqdt0 @ SY124 @ SV44 ) ) )
| ( aUpperBoundOfIn0 @ SV44 @ SV40 @ xU ) )
= $false )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(641,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(642,plain,
! [SV40: $i] :
( ( ( ! [SY111: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY111 @ xU )
| ~ ! [SY88: $i] :
( ~ ( aElementOf0 @ SY88 @ SV40 )
| ( sdtlseqdt0 @ SY111 @ SY88 ) ) )
| ( aLowerBoundOfIn0 @ SY111 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SY111 @ ( sK12_SY85 @ SV40 ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(643,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY122: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY122 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY122 ) ) )
| ( aUpperBoundOfIn0 @ SY122 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SY122 ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(644,plain,
! [SV40: $i] :
( ( ( aSupremumOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(645,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(646,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV45 @ xU )
| ~ ! [SY125: $i] :
( ~ ( aElementOf0 @ SY125 @ SV40 )
| ( sdtlseqdt0 @ SV45 @ SY125 ) ) )
| ( aLowerBoundOfIn0 @ SV45 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(647,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY119: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY119 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY119 ) ) )
| ( aUpperBoundOfIn0 @ SY119 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SY119 ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(648,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(649,plain,
! [SV40: $i,SV46: $i] :
( ( ( ~ ( aElementOf0 @ SV46 @ SV40 )
| ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SV46 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(650,plain,
! [SV40: $i,SV43: $i] :
( ( ( aElementOf0 @ SV43 @ xU )
= $false )
| ( ( ~ ! [SY117: $i] :
( ~ ( aElementOf0 @ SY117 @ SV40 )
| ( sdtlseqdt0 @ SV43 @ SY117 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(651,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(652,plain,
! [SV40: $i,SV44: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV44 @ xU )
| ~ ! [SY124: $i] :
( ~ ( aElementOf0 @ SY124 @ SV40 )
| ( sdtlseqdt0 @ SY124 @ SV44 ) ) ) )
= $false )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(653,plain,
! [SV40: $i,SV44: $i] :
( ( ( aUpperBoundOfIn0 @ SV44 @ SV40 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(654,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
| ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(655,plain,
! [SV40: $i,SV47: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV47 @ xU )
| ~ ! [SY126: $i] :
( ~ ( aElementOf0 @ SY126 @ SV40 )
| ( sdtlseqdt0 @ SV47 @ SY126 ) ) )
| ( aLowerBoundOfIn0 @ SV47 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(656,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
| ~ ! [SY122: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY122 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY122 ) ) )
| ( aUpperBoundOfIn0 @ SY122 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SY122 ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(657,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(658,plain,
! [SV40: $i] :
( ( ( ~ ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(659,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV45 @ xU )
| ~ ! [SY125: $i] :
( ~ ( aElementOf0 @ SY125 @ SV40 )
| ( sdtlseqdt0 @ SV45 @ SY125 ) ) )
| ( aLowerBoundOfIn0 @ SV45 @ SV40 @ xU ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(660,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(661,plain,
! [SV40: $i] :
( ( ( ~ ! [SY119: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY119 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY119 ) ) )
| ( aUpperBoundOfIn0 @ SY119 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SY119 ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[647]) ).
thf(662,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(663,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(664,plain,
! [SV40: $i,SV46: $i] :
( ( ( ~ ( aElementOf0 @ SV46 @ SV40 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SV46 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(665,plain,
! [SV43: $i,SV40: $i] :
( ( ( ! [SY117: $i] :
( ~ ( aElementOf0 @ SY117 @ SV40 )
| ( sdtlseqdt0 @ SV43 @ SY117 ) ) )
= $false )
| ( ( aElementOf0 @ SV43 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(666,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(667,plain,
! [SV40: $i] :
( ( ( ~ ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(668,plain,
! [SV40: $i,SV44: $i] :
( ( ( ~ ( aElementOf0 @ SV44 @ xU )
| ~ ! [SY124: $i] :
( ~ ( aElementOf0 @ SY124 @ SV40 )
| ( sdtlseqdt0 @ SY124 @ SV44 ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(669,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(670,plain,
! [SV40: $i] :
( ( ( ~ ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[654]) ).
thf(671,plain,
! [SV40: $i,SV47: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV47 @ xU )
| ~ ! [SY126: $i] :
( ~ ( aElementOf0 @ SY126 @ SV40 )
| ( sdtlseqdt0 @ SV47 @ SY126 ) ) )
| ( aLowerBoundOfIn0 @ SV47 @ SV40 @ xU ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(672,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(673,plain,
! [SV40: $i] :
( ( ( ~ ! [SY122: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY122 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY122 ) ) )
| ( aUpperBoundOfIn0 @ SY122 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SY122 ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(674,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[657]) ).
thf(675,plain,
! [SV40: $i] :
( ( ( aLowerBoundOfIn0 @ ( sK10_SY85 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[658]) ).
thf(676,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV45 @ xU )
| ~ ! [SY125: $i] :
( ~ ( aElementOf0 @ SY125 @ SV40 )
| ( sdtlseqdt0 @ SV45 @ SY125 ) ) )
| ( aLowerBoundOfIn0 @ SV45 @ SV40 @ xU ) )
= $false )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(677,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(678,plain,
! [SV40: $i] :
( ( ( ! [SY119: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY119 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY119 ) ) )
| ( aUpperBoundOfIn0 @ SY119 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SY119 ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(679,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(680,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK8_SY85 @ SV40 ) @ xU )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(681,plain,
! [SV40: $i,SV46: $i] :
( ( ( aElementOf0 @ SV46 @ SV40 )
= $false )
| ( ( sdtlseqdt0 @ ( sK8_SY85 @ SV40 ) @ SV46 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(682,plain,
! [SV40: $i,SV43: $i] :
( ( ( ~ ( aElementOf0 @ ( sK15_SY117 @ SV43 @ SV40 ) @ SV40 )
| ( sdtlseqdt0 @ SV43 @ ( sK15_SY117 @ SV43 @ SV40 ) ) )
= $false )
| ( ( aElementOf0 @ SV43 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[665]) ).
thf(683,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[666]) ).
thf(684,plain,
! [SV40: $i] :
( ( ( ! [SY107: $i] :
( ~ ( aElementOf0 @ SY107 @ SV40 )
| ( sdtlseqdt0 @ SY107 @ ( sK11_SY89 @ SV40 ) ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(685,plain,
! [SV40: $i,SV44: $i] :
( ( ( ~ ( aElementOf0 @ SV44 @ xU ) )
= $true )
| ( ( ~ ! [SY124: $i] :
( ~ ( aElementOf0 @ SY124 @ SV40 )
| ( sdtlseqdt0 @ SY124 @ SV44 ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(686,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(687,plain,
! [SV40: $i] :
( ( ( aLowerBoundOfIn0 @ ( sK12_SY85 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(688,plain,
! [SV40: $i,SV47: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV47 @ xU )
| ~ ! [SY126: $i] :
( ~ ( aElementOf0 @ SY126 @ SV40 )
| ( sdtlseqdt0 @ SV47 @ SY126 ) ) )
| ( aLowerBoundOfIn0 @ SV47 @ SV40 @ xU ) )
= $false )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(689,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[672]) ).
thf(690,plain,
! [SV40: $i] :
( ( ( ! [SY122: $i] :
( ~ ( ~ ( ~ ( aElementOf0 @ SY122 @ xU )
| ~ ! [SY92: $i] :
( ~ ( aElementOf0 @ SY92 @ SV40 )
| ( sdtlseqdt0 @ SY92 @ SY122 ) ) )
| ( aUpperBoundOfIn0 @ SY122 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SY122 ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[673]) ).
thf(691,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(692,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV45 @ xU )
| ~ ! [SY125: $i] :
( ~ ( aElementOf0 @ SY125 @ SV40 )
| ( sdtlseqdt0 @ SV45 @ SY125 ) ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(693,plain,
! [SV40: $i,SV45: $i] :
( ( ( aLowerBoundOfIn0 @ SV45 @ SV40 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(694,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(695,plain,
! [SV40: $i,SV48: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV48 @ xU )
| ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV40 )
| ( sdtlseqdt0 @ SY127 @ SV48 ) ) )
| ( aUpperBoundOfIn0 @ SV48 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(696,plain,
! [SV40: $i,SV43: $i] :
( ( ( ~ ( aElementOf0 @ ( sK15_SY117 @ SV43 @ SV40 ) @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV43 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(697,plain,
! [SV40: $i,SV43: $i] :
( ( ( sdtlseqdt0 @ SV43 @ ( sK15_SY117 @ SV43 @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV43 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(698,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(699,plain,
! [SV40: $i,SV49: $i] :
( ( ( ~ ( aElementOf0 @ SV49 @ SV40 )
| ( sdtlseqdt0 @ SV49 @ ( sK11_SY89 @ SV40 ) ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(700,plain,
! [SV40: $i,SV44: $i] :
( ( ( aElementOf0 @ SV44 @ xU )
= $false )
| ( ( ~ ! [SY124: $i] :
( ~ ( aElementOf0 @ SY124 @ SV40 )
| ( sdtlseqdt0 @ SY124 @ SV44 ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(701,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
| ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(702,plain,
! [SV40: $i,SV47: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV47 @ xU )
| ~ ! [SY126: $i] :
( ~ ( aElementOf0 @ SY126 @ SV40 )
| ( sdtlseqdt0 @ SV47 @ SY126 ) ) ) )
= $false )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(703,plain,
! [SV40: $i,SV47: $i] :
( ( ( aLowerBoundOfIn0 @ SV47 @ SV40 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(704,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
| ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(705,plain,
! [SV40: $i,SV50: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV50 @ xU )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV40 )
| ( sdtlseqdt0 @ SY128 @ SV50 ) ) )
| ( aUpperBoundOfIn0 @ SV50 @ SV40 @ xU ) )
| ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(706,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(707,plain,
! [SV40: $i] :
( ( ( ~ ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(708,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( aElementOf0 @ SV45 @ xU )
| ~ ! [SY125: $i] :
( ~ ( aElementOf0 @ SY125 @ SV40 )
| ( sdtlseqdt0 @ SV45 @ SY125 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(709,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(710,plain,
! [SV40: $i] :
( ( ( ~ ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(711,plain,
! [SV40: $i,SV48: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV48 @ xU )
| ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV40 )
| ( sdtlseqdt0 @ SY127 @ SV48 ) ) )
| ( aUpperBoundOfIn0 @ SV48 @ SV40 @ xU ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(712,plain,
! [SV40: $i,SV43: $i] :
( ( ( aElementOf0 @ ( sK15_SY117 @ SV43 @ SV40 ) @ SV40 )
= $true )
| ( ( aElementOf0 @ SV43 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV43 @ ( sK8_SY85 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[696]) ).
thf(713,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(714,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU ) )
= $false )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(715,plain,
! [SV40: $i,SV49: $i] :
( ( ( ~ ( aElementOf0 @ SV49 @ SV40 ) )
= $true )
| ( ( sdtlseqdt0 @ SV49 @ ( sK11_SY89 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(716,plain,
! [SV44: $i,SV40: $i] :
( ( ( ! [SY124: $i] :
( ~ ( aElementOf0 @ SY124 @ SV40 )
| ( sdtlseqdt0 @ SY124 @ SV44 ) ) )
= $false )
| ( ( aElementOf0 @ SV44 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(717,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(718,plain,
! [SV40: $i] :
( ( ( ~ ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(719,plain,
! [SV40: $i,SV47: $i] :
( ( ( ~ ( aElementOf0 @ SV47 @ xU )
| ~ ! [SY126: $i] :
( ~ ( aElementOf0 @ SY126 @ SV40 )
| ( sdtlseqdt0 @ SV47 @ SY126 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(720,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(721,plain,
! [SV40: $i] :
( ( ( ~ ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[704]) ).
thf(722,plain,
! [SV40: $i,SV50: $i] :
( ( ( ~ ( ~ ( ~ ( aElementOf0 @ SV50 @ xU )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV40 )
| ( sdtlseqdt0 @ SY128 @ SV50 ) ) )
| ( aUpperBoundOfIn0 @ SV50 @ SV40 @ xU ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(723,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(724,plain,
! [SV40: $i] :
( ( ( ! [SY100: $i] :
( ~ ( aElementOf0 @ SY100 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SY100 ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(725,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( aElementOf0 @ SV45 @ xU ) )
= $true )
| ( ( ~ ! [SY125: $i] :
( ~ ( aElementOf0 @ SY125 @ SV40 )
| ( sdtlseqdt0 @ SV45 @ SY125 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(726,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(727,plain,
! [SV40: $i] :
( ( ( aUpperBoundOfIn0 @ ( sK13_SY89 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(728,plain,
! [SV40: $i,SV48: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV48 @ xU )
| ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV40 )
| ( sdtlseqdt0 @ SY127 @ SV48 ) ) )
| ( aUpperBoundOfIn0 @ SV48 @ SV40 @ xU ) )
= $false )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(729,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(730,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK11_SY89 @ SV40 ) @ xU )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(731,plain,
! [SV40: $i,SV49: $i] :
( ( ( aElementOf0 @ SV49 @ SV40 )
= $false )
| ( ( sdtlseqdt0 @ SV49 @ ( sK11_SY89 @ SV40 ) )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(732,plain,
! [SV40: $i,SV44: $i] :
( ( ( ~ ( aElementOf0 @ ( sK16_SY124 @ SV44 @ SV40 ) @ SV40 )
| ( sdtlseqdt0 @ ( sK16_SY124 @ SV44 @ SV40 ) @ SV44 ) )
= $false )
| ( ( aElementOf0 @ SV44 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[716]) ).
thf(733,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(734,plain,
! [SV40: $i] :
( ( ( ! [SY110: $i] :
( ~ ( aElementOf0 @ SY110 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SY110 ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(735,plain,
! [SV40: $i,SV47: $i] :
( ( ( ~ ( aElementOf0 @ SV47 @ xU ) )
= $true )
| ( ( ~ ! [SY126: $i] :
( ~ ( aElementOf0 @ SY126 @ SV40 )
| ( sdtlseqdt0 @ SV47 @ SY126 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(736,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(737,plain,
! [SV40: $i] :
( ( ( aUpperBoundOfIn0 @ ( sK14_SY89 @ SV40 ) @ SV40 @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(738,plain,
! [SV40: $i,SV50: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV50 @ xU )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV40 )
| ( sdtlseqdt0 @ SY128 @ SV50 ) ) )
| ( aUpperBoundOfIn0 @ SV50 @ SV40 @ xU ) )
= $false )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(739,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(740,plain,
! [SV40: $i,SV51: $i] :
( ( ( ~ ( aElementOf0 @ SV51 @ SV40 )
| ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SV51 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(741,plain,
! [SV40: $i,SV45: $i] :
( ( ( aElementOf0 @ SV45 @ xU )
= $false )
| ( ( ~ ! [SY125: $i] :
( ~ ( aElementOf0 @ SY125 @ SV40 )
| ( sdtlseqdt0 @ SV45 @ SY125 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(742,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(743,plain,
! [SV40: $i,SV48: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV48 @ xU )
| ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV40 )
| ( sdtlseqdt0 @ SY127 @ SV48 ) ) ) )
= $false )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(744,plain,
! [SV40: $i,SV48: $i] :
( ( ( aUpperBoundOfIn0 @ SV48 @ SV40 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(745,plain,
! [SV40: $i,SV44: $i] :
( ( ( ~ ( aElementOf0 @ ( sK16_SY124 @ SV44 @ SV40 ) @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV44 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(746,plain,
! [SV40: $i,SV44: $i] :
( ( ( sdtlseqdt0 @ ( sK16_SY124 @ SV44 @ SV40 ) @ SV44 )
= $false )
| ( ( aElementOf0 @ SV44 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(747,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(748,plain,
! [SV40: $i,SV52: $i] :
( ( ( ~ ( aElementOf0 @ SV52 @ SV40 )
| ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SV52 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(749,plain,
! [SV40: $i,SV47: $i] :
( ( ( aElementOf0 @ SV47 @ xU )
= $false )
| ( ( ~ ! [SY126: $i] :
( ~ ( aElementOf0 @ SY126 @ SV40 )
| ( sdtlseqdt0 @ SV47 @ SY126 ) ) )
= $true )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(750,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
| ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(751,plain,
! [SV40: $i,SV50: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ SV50 @ xU )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV40 )
| ( sdtlseqdt0 @ SY128 @ SV50 ) ) ) )
= $false )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(752,plain,
! [SV40: $i,SV50: $i] :
( ( ( aUpperBoundOfIn0 @ SV50 @ SV40 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(753,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(754,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(755,plain,
! [SV40: $i,SV51: $i] :
( ( ( ~ ( aElementOf0 @ SV51 @ SV40 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SV51 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(756,plain,
! [SV45: $i,SV40: $i] :
( ( ( ! [SY125: $i] :
( ~ ( aElementOf0 @ SY125 @ SV40 )
| ( sdtlseqdt0 @ SV45 @ SY125 ) ) )
= $false )
| ( ( aElementOf0 @ SV45 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(757,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(758,plain,
! [SV40: $i] :
( ( ( ~ ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[742]) ).
thf(759,plain,
! [SV40: $i,SV48: $i] :
( ( ( ~ ( aElementOf0 @ SV48 @ xU )
| ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV40 )
| ( sdtlseqdt0 @ SY127 @ SV48 ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(760,plain,
! [SV40: $i,SV44: $i] :
( ( ( aElementOf0 @ ( sK16_SY124 @ SV44 @ SV40 ) @ SV40 )
= $true )
| ( ( aElementOf0 @ SV44 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK11_SY89 @ SV40 ) @ SV44 )
= $true )
| ( ( aSubsetOf0 @ SV40 @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(761,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(762,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(763,plain,
! [SV40: $i,SV52: $i] :
( ( ( ~ ( aElementOf0 @ SV52 @ SV40 ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SV52 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(764,plain,
! [SV47: $i,SV40: $i] :
( ( ( ! [SY126: $i] :
( ~ ( aElementOf0 @ SY126 @ SV40 )
| ( sdtlseqdt0 @ SV47 @ SY126 ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(765,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(766,plain,
! [SV40: $i] :
( ( ( ~ ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(767,plain,
! [SV40: $i,SV50: $i] :
( ( ( ~ ( aElementOf0 @ SV50 @ xU )
| ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV40 )
| ( sdtlseqdt0 @ SY128 @ SV50 ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(768,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(769,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK10_SY85 @ SV40 ) @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[754]) ).
thf(770,plain,
! [SV40: $i,SV51: $i] :
( ( ( aElementOf0 @ SV51 @ SV40 )
= $false )
| ( ( sdtlseqdt0 @ ( sK10_SY85 @ SV40 ) @ SV51 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(771,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( aElementOf0 @ ( sK17_SY125 @ SV45 @ SV40 ) @ SV40 )
| ( sdtlseqdt0 @ SV45 @ ( sK17_SY125 @ SV45 @ SV40 ) ) )
= $false )
| ( ( aElementOf0 @ SV45 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[756]) ).
thf(772,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(773,plain,
! [SV40: $i] :
( ( ( ! [SY118: $i] :
( ~ ( aElementOf0 @ SY118 @ SV40 )
| ( sdtlseqdt0 @ SY118 @ ( sK13_SY89 @ SV40 ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(774,plain,
! [SV40: $i,SV48: $i] :
( ( ( ~ ( aElementOf0 @ SV48 @ xU ) )
= $true )
| ( ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV40 )
| ( sdtlseqdt0 @ SY127 @ SV48 ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(775,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(776,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK12_SY85 @ SV40 ) @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(777,plain,
! [SV40: $i,SV52: $i] :
( ( ( aElementOf0 @ SV52 @ SV40 )
= $false )
| ( ( sdtlseqdt0 @ ( sK12_SY85 @ SV40 ) @ SV52 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(778,plain,
! [SV40: $i,SV47: $i] :
( ( ( ~ ( aElementOf0 @ ( sK18_SY126 @ SV47 @ SV40 ) @ SV40 )
| ( sdtlseqdt0 @ SV47 @ ( sK18_SY126 @ SV47 @ SV40 ) ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[764]) ).
thf(779,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(780,plain,
! [SV40: $i] :
( ( ( ! [SY121: $i] :
( ~ ( aElementOf0 @ SY121 @ SV40 )
| ( sdtlseqdt0 @ SY121 @ ( sK14_SY89 @ SV40 ) ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(781,plain,
! [SV40: $i,SV50: $i] :
( ( ( ~ ( aElementOf0 @ SV50 @ xU ) )
= $true )
| ( ( ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV40 )
| ( sdtlseqdt0 @ SY128 @ SV50 ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(782,plain,
! [SV40: $i,SV45: $i] :
( ( ( ~ ( aElementOf0 @ ( sK17_SY125 @ SV45 @ SV40 ) @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV45 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[771]) ).
thf(783,plain,
! [SV40: $i,SV45: $i] :
( ( ( sdtlseqdt0 @ SV45 @ ( sK17_SY125 @ SV45 @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV45 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[771]) ).
thf(784,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(785,plain,
! [SV40: $i,SV53: $i] :
( ( ( ~ ( aElementOf0 @ SV53 @ SV40 )
| ( sdtlseqdt0 @ SV53 @ ( sK13_SY89 @ SV40 ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(786,plain,
! [SV40: $i,SV48: $i] :
( ( ( aElementOf0 @ SV48 @ xU )
= $false )
| ( ( ~ ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV40 )
| ( sdtlseqdt0 @ SY127 @ SV48 ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(787,plain,
! [SV40: $i,SV47: $i] :
( ( ( ~ ( aElementOf0 @ ( sK18_SY126 @ SV47 @ SV40 ) @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(788,plain,
! [SV40: $i,SV47: $i] :
( ( ( sdtlseqdt0 @ SV47 @ ( sK18_SY126 @ SV47 @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV47 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[778]) ).
thf(789,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
| ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(790,plain,
! [SV40: $i,SV54: $i] :
( ( ( ~ ( aElementOf0 @ SV54 @ SV40 )
| ( sdtlseqdt0 @ SV54 @ ( sK14_SY89 @ SV40 ) ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(791,plain,
! [SV40: $i,SV50: $i] :
( ( ( aElementOf0 @ SV50 @ xU )
= $false )
| ( ( ~ ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV40 )
| ( sdtlseqdt0 @ SY128 @ SV50 ) ) )
= $true )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(792,plain,
! [SV40: $i,SV45: $i] :
( ( ( aElementOf0 @ ( sK17_SY125 @ SV45 @ SV40 ) @ SV40 )
= $true )
| ( ( aElementOf0 @ SV45 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV45 @ ( sK10_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(793,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(794,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(795,plain,
! [SV40: $i,SV53: $i] :
( ( ( ~ ( aElementOf0 @ SV53 @ SV40 ) )
= $true )
| ( ( sdtlseqdt0 @ SV53 @ ( sK13_SY89 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(796,plain,
! [SV48: $i,SV40: $i] :
( ( ( ! [SY127: $i] :
( ~ ( aElementOf0 @ SY127 @ SV40 )
| ( sdtlseqdt0 @ SY127 @ SV48 ) ) )
= $false )
| ( ( aElementOf0 @ SV48 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(797,plain,
! [SV40: $i,SV47: $i] :
( ( ( aElementOf0 @ ( sK18_SY126 @ SV47 @ SV40 ) @ SV40 )
= $true )
| ( ( aElementOf0 @ SV47 @ xU )
= $false )
| ( ( sdtlseqdt0 @ SV47 @ ( sK12_SY85 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[787]) ).
thf(798,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(799,plain,
! [SV40: $i] :
( ( ( ~ ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU ) )
= $false )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(800,plain,
! [SV40: $i,SV54: $i] :
( ( ( ~ ( aElementOf0 @ SV54 @ SV40 ) )
= $true )
| ( ( sdtlseqdt0 @ SV54 @ ( sK14_SY89 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(801,plain,
! [SV50: $i,SV40: $i] :
( ( ( ! [SY128: $i] :
( ~ ( aElementOf0 @ SY128 @ SV40 )
| ( sdtlseqdt0 @ SY128 @ SV50 ) ) )
= $false )
| ( ( aElementOf0 @ SV50 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(802,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(803,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK13_SY89 @ SV40 ) @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(804,plain,
! [SV40: $i,SV53: $i] :
( ( ( aElementOf0 @ SV53 @ SV40 )
= $false )
| ( ( sdtlseqdt0 @ SV53 @ ( sK13_SY89 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(805,plain,
! [SV40: $i,SV48: $i] :
( ( ( ~ ( aElementOf0 @ ( sK19_SY127 @ SV48 @ SV40 ) @ SV40 )
| ( sdtlseqdt0 @ ( sK19_SY127 @ SV48 @ SV40 ) @ SV48 ) )
= $false )
| ( ( aElementOf0 @ SV48 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[796]) ).
thf(806,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(807,plain,
! [SV40: $i] :
( ( ( aElementOf0 @ ( sK14_SY89 @ SV40 ) @ xU )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(808,plain,
! [SV40: $i,SV54: $i] :
( ( ( aElementOf0 @ SV54 @ SV40 )
= $false )
| ( ( sdtlseqdt0 @ SV54 @ ( sK14_SY89 @ SV40 ) )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(809,plain,
! [SV40: $i,SV50: $i] :
( ( ( ~ ( aElementOf0 @ ( sK20_SY128 @ SV50 @ SV40 ) @ SV40 )
| ( sdtlseqdt0 @ ( sK20_SY128 @ SV50 @ SV40 ) @ SV50 ) )
= $false )
| ( ( aElementOf0 @ SV50 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[801]) ).
thf(810,plain,
! [SV40: $i,SV48: $i] :
( ( ( ~ ( aElementOf0 @ ( sK19_SY127 @ SV48 @ SV40 ) @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV48 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(811,plain,
! [SV40: $i,SV48: $i] :
( ( ( sdtlseqdt0 @ ( sK19_SY127 @ SV48 @ SV40 ) @ SV48 )
= $false )
| ( ( aElementOf0 @ SV48 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[805]) ).
thf(812,plain,
! [SV40: $i,SV50: $i] :
( ( ( ~ ( aElementOf0 @ ( sK20_SY128 @ SV50 @ SV40 ) @ SV40 ) )
= $false )
| ( ( aElementOf0 @ SV50 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(813,plain,
! [SV40: $i,SV50: $i] :
( ( ( sdtlseqdt0 @ ( sK20_SY128 @ SV50 @ SV40 ) @ SV50 )
= $false )
| ( ( aElementOf0 @ SV50 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(814,plain,
! [SV40: $i,SV48: $i] :
( ( ( aElementOf0 @ ( sK19_SY127 @ SV48 @ SV40 ) @ SV40 )
= $true )
| ( ( aElementOf0 @ SV48 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK13_SY89 @ SV40 ) @ SV48 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ xU )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(815,plain,
! [SV40: $i,SV50: $i] :
( ( ( aElementOf0 @ ( sK20_SY128 @ SV50 @ SV40 ) @ SV40 )
= $true )
| ( ( aElementOf0 @ SV50 @ xU )
= $false )
| ( ( sdtlseqdt0 @ ( sK14_SY89 @ SV40 ) @ SV50 )
= $true )
| ( ( aSet0 @ SV40 )
= $false )
| ( ( aElementOf0 @ ( sK9_SY84 @ SV40 ) @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(816,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[137,815,814,813,811,808,807,806,804,803,802,797,792,788,783,777,776,775,770,769,768,760,752,746,744,737,731,730,729,727,712,703,697,693,687,681,680,679,675,653,644,639,634,612,606,601,598,576,556,536,533,523,519,509,506,505,501,493,492,485,482,480,473,469,467,465,464,463,452,446,437,435,434,427,426,425,421,412,409,405,399,393,392,391,387,386,382,377,369,364,363,338,335,331,298,293,290,281,280,277,275,271,262,219,217,208,205,204,202,185,163,161,159,158,157,156,152,151,146,144,142,140]) ).
thf(817,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[816]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT388+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n026.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 12:08:01 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.23/1.36
% 6.23/1.36 No.of.Axioms: 20
% 6.23/1.36
% 6.23/1.36 Length.of.Defs: 0
% 6.23/1.36
% 6.23/1.36 Contains.Choice.Funs: false
% 6.23/1.36 ............................
% 6.23/1.36
% 6.23/1.36 ********************************
% 6.23/1.36 * All subproblems solved! *
% 6.23/1.36 ********************************
% 6.23/1.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:20,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:816,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.23/1.36
% 6.23/1.36 %**** Beginning of derivation protocol ****
% 6.23/1.36 % SZS output start CNFRefutation
% See solution above
% 6.23/1.37
% 6.23/1.37 %**** End of derivation protocol ****
% 6.23/1.37 %**** no. of clauses in derivation: 817 ****
% 6.23/1.37 %**** clause counter: 816 ****
% 6.23/1.37
% 6.23/1.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:20,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:816,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------