TSTP Solution File: SEU505^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU505^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:18:00 EDT 2023
% Result : Theorem 41.18s 41.24s
% Output : Proof 41.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 248
% Syntax : Number of formulae : 337 ( 205 unt; 40 typ; 24 def)
% Number of atoms : 1041 ( 108 equ; 4 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 1788 ( 224 ~; 18 |; 18 &; 919 @)
% ( 39 <=>; 570 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 74 usr; 65 con; 0-2 aty)
% Number of variables : 450 ( 78 ^; 358 !; 14 ?; 450 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_exu,type,
exu: ( $i > $o ) > $o ).
thf(ty_descrp,type,
descrp: $o ).
thf(ty_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(ty_setadjoinAx,type,
setadjoinAx: $o ).
thf(ty_eigen__859,type,
eigen__859: $i > $o ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_emptysetAx,type,
emptysetAx: $o ).
thf(ty_eigen__860,type,
eigen__860: $i ).
thf(ty_emptysetE,type,
emptysetE: $o ).
thf(ty_eigen__858,type,
eigen__858: $i ).
thf(ty_dsetconstrI,type,
dsetconstrI: $o ).
thf(ty_prop2setE,type,
prop2setE: $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_eigen__857,type,
eigen__857: $i > $o ).
thf(ty_foundationAx,type,
foundationAx: $o ).
thf(ty_descr,type,
descr: ( $i > $o ) > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_omega0Ax,type,
omega0Ax: $o ).
thf(ty_powersetAx,type,
powersetAx: $o ).
thf(ty_setunionAx,type,
setunionAx: $o ).
thf(ty_prop2set,type,
prop2set: $o > $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_replAx,type,
replAx: $o ).
thf(ty_dsetconstrER,type,
dsetconstrER: $o ).
thf(ty_setextAx,type,
setextAx: $o ).
thf(ty_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_powerset,type,
powerset: $i > $i ).
thf(ty_omega,type,
omega: $i ).
thf(ty_eigen__861,type,
eigen__861: $i > $o ).
thf(ty_exuE3e,type,
exuE3e: $o ).
thf(ty_omegaIndAx,type,
omegaIndAx: $o ).
thf(ty_omegaSAx,type,
omegaSAx: $o ).
thf(ty_notinemptyset,type,
notinemptyset: $o ).
thf(ty_eigen__862,type,
eigen__862: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_exuE1,type,
exuE1: $o ).
thf(ty_wellorderingAx,type,
wellorderingAx: $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
( ( in @ X1 @ eigen__0 )
!= ( in @ X1 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> setunionAx ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> emptysetE ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> dsetconstrER ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> notinemptyset ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
= ( in @ X3 @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> setadjoinAx ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
= ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> emptysetimpfalse ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
= ( in @ X2 @ X1 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> omegaIndAx ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> omega0Ax ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> descrp ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( in @ eigen__5 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> exuE1 ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> dsetconstrEL ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( in @ eigen__5 @ eigen__0 )
= sP14 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> powersetAx ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP8
=> ( eigen__0 = eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> setextAx ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> replAx ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( in @ eigen__5 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> emptysetAx ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> prop2setE ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> dsetconstrI ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> foundationAx ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP14
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> wellorderingAx ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> exuE3e ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> omegaSAx ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP23
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(def_exu,definition,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 = X3 ) ) ) ) ) ).
thf(def_setextAx,definition,
( setextAx
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ( in @ X3 @ X1 )
<=> ( in @ X3 @ X2 ) )
@ ( X1 = X2 ) ) ) ) ).
thf(def_emptysetAx,definition,
( emptysetAx
= ( ! [X1: $i] : ( (~) @ ( in @ X1 @ emptyset ) ) ) ) ).
thf(def_setadjoinAx,definition,
( setadjoinAx
= ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
<=> ( ( X3 = X1 )
| ( in @ X3 @ X2 ) ) ) ) ) ).
thf(def_powersetAx,definition,
( powersetAx
= ( ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
<=> ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X2 )
@ ( in @ X3 @ X1 ) ) ) ) ) ).
thf(def_setunionAx,definition,
( setunionAx
= ( ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
<=> ? [X3: $i] :
( ( in @ X2 @ X3 )
& ( in @ X3 @ X1 ) ) ) ) ) ).
thf(def_omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ) ).
thf(def_omegaSAx,definition,
( omegaSAx
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( in @ X1 @ omega )
@ ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ) ) ).
thf(def_omegaIndAx,definition,
( omegaIndAx
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( ( in @ emptyset @ X1 )
& ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( ( in @ X2 @ omega )
& ( in @ X2 @ X1 ) )
@ ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
@ ! [X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ omega )
@ ( in @ X2 @ X1 ) ) ) ) ) ).
thf(def_replAx,definition,
( replAx
= ( ! [X1: $i > $i > $o,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X2 )
@ ( exu
@ ^ [X4: $i] : ( X1 @ X3 @ X4 ) ) )
@ ? [X3: $i] :
! [X4: $i] :
( ( in @ X4 @ X3 )
<=> ? [X5: $i] :
( ( in @ X5 @ X2 )
& ( X1 @ X5 @ X4 ) ) ) ) ) ) ).
thf(def_foundationAx,definition,
( foundationAx
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ? [X2: $i] : ( in @ X2 @ X1 )
@ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( (~)
@ ? [X3: $i] :
( ( in @ X3 @ X2 )
& ( in @ X3 @ X1 ) ) ) ) ) ) ) ).
thf(def_wellorderingAx,definition,
( wellorderingAx
= ( ! [X1: $i] :
? [X2: $i] :
( ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X2 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X3 )
@ ( in @ X4 @ X1 ) ) )
& ! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( in @ X3 @ X1 )
& ( in @ X4 @ X1 ) )
@ ( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( in @ X5 @ X2 )
@ ( ( in @ X3 @ X5 )
<=> ( in @ X4 @ X5 ) ) )
@ ( X3 = X4 ) ) )
& ! [X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( in @ X3 @ X2 )
& ( in @ X4 @ X2 ) )
@ ( ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( in @ X5 @ X3 )
@ ( in @ X5 @ X4 ) )
| ! [X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( in @ X5 @ X4 )
@ ( in @ X5 @ X3 ) ) ) )
& ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( in @ X4 @ X3 )
@ ( in @ X4 @ X1 ) )
& ? [X4: $i] : ( in @ X4 @ X3 ) )
@ ? [X4: $i,X5: $i] :
( ( in @ X4 @ X2 )
& ( in @ X5 @ X3 )
& ( (~)
@ ? [X6: $i] :
( ( in @ X6 @ X4 )
& ( in @ X6 @ X3 ) ) )
& ! [X6: $i] :
( ^ [X7: $o,X8: $o] :
( X7
=> X8 )
@ ( in @ X6 @ X2 )
@ ( ! [X7: $i] :
( ^ [X8: $o,X9: $o] :
( X8
=> X9 )
@ ( in @ X7 @ X6 )
@ ( in @ X7 @ X4 ) )
| ( in @ X5 @ X6 ) ) ) ) ) ) ) ) ).
thf(def_descrp,definition,
( descrp
= ( ! [X1: $i > $o] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_dsetconstrI,definition,
( dsetconstrI
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ).
thf(def_dsetconstrEL,definition,
( dsetconstrEL
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
@ ( in @ X3 @ X1 ) ) ) ) ).
thf(def_dsetconstrER,definition,
( dsetconstrER
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_exuE1,definition,
( exuE1
= ( ! [X1: $i > $o] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 = X3 ) ) ) ) ) ) ).
thf(def_prop2set,definition,
( prop2set
= ( ^ [X1: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X1 ) ) ) ).
thf(def_prop2setE,definition,
( prop2setE
= ( ! [X1: $o,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ( in @ X2 @ ( prop2set @ X1 ) )
@ X1 ) ) ) ).
thf(def_emptysetE,definition,
( emptysetE
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( in @ X1 @ emptyset )
@ ! [X2: $o] : X2 ) ) ) ).
thf(def_emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( in @ X1 @ emptyset )
@ $false ) ) ) ).
thf(def_notinemptyset,definition,
( notinemptyset
= ( ! [X1: $i] : ( (~) @ ( in @ X1 @ emptyset ) ) ) ) ).
thf(def_exuE3e,definition,
( exuE3e
= ( ! [X1: $i > $o] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ? [X2: $i] : ( X1 @ X2 ) ) ) ) ).
thf(setext,conjecture,
( sP20
=> ( sP24
=> ( sP7
=> ( sP18
=> ( sP1
=> ( sP12
=> ( sP32
=> ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP20
=> ( sP24
=> ( sP7
=> ( sP18
=> ( sP1
=> ( sP12
=> ( sP32
=> ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setext]) ).
thf(h2,assumption,
sP20,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP24
=> ( sP7
=> ( sP18
=> ( sP1
=> ( sP12
=> ( sP32
=> ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP24,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP7
=> ( sP18
=> ( sP1
=> ( sP12
=> ( sP32
=> ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP7,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP18
=> ( sP1
=> ( sP12
=> ( sP32
=> ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP18,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP1
=> ( sP12
=> ( sP32
=> ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP12
=> ( sP32
=> ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP12,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( sP32
=> ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
sP32,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP11,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP21,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP28,
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
sP30,
introduced(assumption,[]) ).
thf(h23,assumption,
~ ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
sP13,
introduced(assumption,[]) ).
thf(h25,assumption,
~ ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
sP27,
introduced(assumption,[]) ).
thf(h27,assumption,
~ ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h28,assumption,
sP16,
introduced(assumption,[]) ).
thf(h29,assumption,
~ ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h30,assumption,
sP4,
introduced(assumption,[]) ).
thf(h31,assumption,
~ ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h32,assumption,
sP15,
introduced(assumption,[]) ).
thf(h33,assumption,
~ ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
sP26,
introduced(assumption,[]) ).
thf(h35,assumption,
~ ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h36,assumption,
sP3,
introduced(assumption,[]) ).
thf(h37,assumption,
~ ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
sP9,
introduced(assumption,[]) ).
thf(h39,assumption,
~ ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h40,assumption,
sP5,
introduced(assumption,[]) ).
thf(h41,assumption,
~ ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h42,assumption,
sP31,
introduced(assumption,[]) ).
thf(h43,assumption,
~ ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h44,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ eigen__0 ) )
=> ( eigen__0 = X1 ) ) ),
introduced(assumption,[]) ).
thf(h45,assumption,
~ ( sP22
=> ( sP2
=> sP25 ) ),
introduced(assumption,[]) ).
thf(h46,assumption,
sP22,
introduced(assumption,[]) ).
thf(h47,assumption,
~ ( sP2
=> sP25 ),
introduced(assumption,[]) ).
thf(h48,assumption,
sP2,
introduced(assumption,[]) ).
thf(h49,assumption,
~ sP25,
introduced(assumption,[]) ).
thf(h50,assumption,
sP6,
introduced(assumption,[]) ).
thf(h51,assumption,
~ sP20,
introduced(assumption,[]) ).
thf(h52,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h53,assumption,
! [X1: $i] :
~ ( in @ X1 @ emptyset ),
introduced(assumption,[]) ).
thf(h54,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(h55,assumption,
~ ! [X1: $i] :
~ ( in @ X1 @ emptyset ),
introduced(assumption,[]) ).
thf(h56,assumption,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
= ( ( X3 != X1 )
=> ( in @ X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h57,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h58,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
= ( ( X3 != X1 )
=> ( in @ X3 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h59,assumption,
! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
= ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h60,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h61,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
= ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h62,assumption,
! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
= ( ~ ! [X3: $i] :
( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h63,assumption,
~ sP1,
introduced(assumption,[]) ).
thf(h64,assumption,
~ ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
= ( ~ ! [X3: $i] :
( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h65,assumption,
in @ emptyset @ omega,
introduced(assumption,[]) ).
thf(h66,assumption,
~ sP12,
introduced(assumption,[]) ).
thf(h67,assumption,
~ ( in @ emptyset @ omega ),
introduced(assumption,[]) ).
thf(h68,assumption,
! [X1: $i] :
( ( in @ X1 @ omega )
=> ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ),
introduced(assumption,[]) ).
thf(h69,assumption,
~ sP32,
introduced(assumption,[]) ).
thf(h70,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ),
introduced(assumption,[]) ).
thf(h71,assumption,
! [X1: $i] :
( ~ ( ( in @ emptyset @ X1 )
=> ~ ! [X2: $i] :
( ~ ( ( in @ X2 @ omega )
=> ~ ( in @ X2 @ X1 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h72,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h73,assumption,
~ ! [X1: $i] :
( ~ ( ( in @ emptyset @ X1 )
=> ~ ! [X2: $i] :
( ~ ( ( in @ X2 @ omega )
=> ~ ( in @ X2 @ X1 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h74,assumption,
! [X1: $i > $i > $o,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( exu @ ( X1 @ X3 ) ) )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ~ ( X1 @ X5 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h75,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(h76,assumption,
~ ! [X1: $i > $i > $o,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( exu @ ( X1 @ X3 ) ) )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ~ ( X1 @ X5 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h77,assumption,
! [X1: $i] :
( ~ ! [X2: $i] :
~ ( in @ X2 @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h78,assumption,
~ sP28,
introduced(assumption,[]) ).
thf(h79,assumption,
~ ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( in @ X2 @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h80,assumption,
! [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( in @ X4 @ X1 ) ) )
=> ~ ! [X3: $i,X4: $i] :
( ~ ( ( in @ X3 @ X1 )
=> ~ ( in @ X4 @ X1 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ X3 @ X5 )
= ( in @ X4 @ X5 ) ) )
=> ( X3 = X4 ) ) ) )
=> ~ ! [X3: $i,X4: $i] :
( ~ ( ( in @ X3 @ X2 )
=> ~ ( in @ X4 @ X2 ) )
=> ( ~ ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( in @ X5 @ X4 ) )
=> ! [X5: $i] :
( ( in @ X5 @ X4 )
=> ( in @ X5 @ X3 ) ) ) ) )
=> ~ ! [X3: $i] :
( ~ ( ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( in @ X4 @ X1 ) )
=> ! [X4: $i] :
~ ( in @ X4 @ X3 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( in @ X4 @ X2 )
=> ~ ( in @ X5 @ X3 ) )
=> ~ ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ~ ( in @ X6 @ X3 ) ) )
=> ~ ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ~ ! [X7: $i] :
( ( in @ X7 @ X6 )
=> ( in @ X7 @ X4 ) )
=> ( in @ X5 @ X6 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h81,assumption,
~ sP30,
introduced(assumption,[]) ).
thf(h82,assumption,
~ ! [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( in @ X4 @ X1 ) ) )
=> ~ ! [X3: $i,X4: $i] :
( ~ ( ( in @ X3 @ X1 )
=> ~ ( in @ X4 @ X1 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ X3 @ X5 )
= ( in @ X4 @ X5 ) ) )
=> ( X3 = X4 ) ) ) )
=> ~ ! [X3: $i,X4: $i] :
( ~ ( ( in @ X3 @ X2 )
=> ~ ( in @ X4 @ X2 ) )
=> ( ~ ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( in @ X5 @ X4 ) )
=> ! [X5: $i] :
( ( in @ X5 @ X4 )
=> ( in @ X5 @ X3 ) ) ) ) )
=> ~ ! [X3: $i] :
( ~ ( ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( in @ X4 @ X1 ) )
=> ! [X4: $i] :
~ ( in @ X4 @ X3 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( in @ X4 @ X2 )
=> ~ ( in @ X5 @ X3 ) )
=> ~ ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ~ ( in @ X6 @ X3 ) ) )
=> ~ ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ~ ! [X7: $i] :
( ( in @ X7 @ X6 )
=> ( in @ X7 @ X4 ) )
=> ( in @ X5 @ X6 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h83,assumption,
! [X1: $i > $o] :
( ( exu @ X1 )
=> ( X1 @ ( descr @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h84,assumption,
~ sP13,
introduced(assumption,[]) ).
thf(h85,assumption,
~ ! [X1: $i > $o] :
( ( exu @ X1 )
=> ( X1 @ ( descr @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h86,assumption,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h87,assumption,
~ sP27,
introduced(assumption,[]) ).
thf(h88,assumption,
~ ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h89,assumption,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ),
introduced(assumption,[]) ).
thf(h90,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(h91,assumption,
~ ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ),
introduced(assumption,[]) ).
thf(h92,assumption,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ),
introduced(assumption,[]) ).
thf(h93,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h94,assumption,
~ ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ),
introduced(assumption,[]) ).
thf(h95,assumption,
! [X1: $i > $o] :
( ( exu @ X1 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h96,assumption,
~ sP15,
introduced(assumption,[]) ).
thf(h97,assumption,
~ ! [X1: $i > $o] :
( ( exu @ X1 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h98,assumption,
! [X1: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X1 ) )
=> X1 ),
introduced(assumption,[]) ).
thf(h99,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(h100,assumption,
~ ! [X1: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X1 ) )
=> X1 ),
introduced(assumption,[]) ).
thf(h101,assumption,
! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $o] : X2 ),
introduced(assumption,[]) ).
thf(h102,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(h103,assumption,
~ ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $o] : X2 ),
introduced(assumption,[]) ).
thf(h104,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(h105,assumption,
~ sP5,
introduced(assumption,[]) ).
thf(h106,assumption,
! [X1: $i > $o] :
( ( exu @ X1 )
=> ~ ! [X2: $i] :
~ ( X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(h107,assumption,
~ sP31,
introduced(assumption,[]) ).
thf(h108,assumption,
~ ! [X1: $i > $o] :
( ( exu @ X1 )
=> ~ ! [X2: $i] :
~ ( X1 @ X2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP29
| ~ sP14
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP33
| ~ sP23
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP22
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP17
| ~ sP23
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP17
| sP23
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP8
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(8,plain,
( ~ sP19
| ~ sP8
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP10
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h42,h106,h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h50,h46,h48,h49]) ).
thf(h109,assumption,
~ ( ( exu @ eigen__857 )
=> ~ ! [X1: $i] :
~ ( eigen__857 @ X1 ) ),
introduced(assumption,[]) ).
thf(h110,assumption,
exu @ eigen__857,
introduced(assumption,[]) ).
thf(h111,assumption,
! [X1: $i] :
~ ( eigen__857 @ X1 ),
introduced(assumption,[]) ).
thf(12,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h110,h111,h109,h107,h108,h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h42,h107]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h109,h107,h108,h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h110,h111])],[h109,12,h110,h111]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h107,h108,h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h109]),tab_negall(eigenvar,eigen__857)],[h108,13,h109]) ).
thf(exuE3e,axiom,
( sP31
= ( ! [X1: $i > $o] :
( ( exu @ X1 )
=> ~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ) ).
thf(15,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h42,h106]),tab_bq(discharge,[h107,h108])],[exuE3e,11,14,h42,h106,h107,h108]) ).
thf(h112,assumption,
in @ eigen__858 @ emptyset,
introduced(assumption,[]) ).
thf(16,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h42,h106,h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h40,h105]) ).
thf(h113,assumption,
~ ( ( exu @ eigen__859 )
=> ~ ! [X1: $i] :
~ ( eigen__859 @ X1 ) ),
introduced(assumption,[]) ).
thf(h114,assumption,
exu @ eigen__859,
introduced(assumption,[]) ).
thf(h115,assumption,
! [X1: $i] :
~ ( eigen__859 @ X1 ),
introduced(assumption,[]) ).
thf(17,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h114,h115,h113,h107,h108,h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h42,h107]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h113,h107,h108,h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h114,h115])],[h113,17,h114,h115]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h107,h108,h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h113]),tab_negall(eigenvar,eigen__859)],[h108,18,h113]) ).
thf(20,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h42,h106]),tab_bq(discharge,[h107,h108])],[exuE3e,16,19,h42,h106,h107,h108]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h112]),tab_negall(eigenvar,eigen__858)],[h55,20,h112]) ).
thf(notinemptyset,axiom,
( sP5
= ( ! [X1: $i] :
~ ( in @ X1 @ emptyset ) ) ) ).
thf(22,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h40,h53]),tab_bq(discharge,[h105,h55])],[notinemptyset,15,21,h40,h53,h105,h55]) ).
thf(h116,assumption,
in @ eigen__860 @ emptyset,
introduced(assumption,[]) ).
thf(23,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h42,h106,h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h38,h104]) ).
thf(h117,assumption,
~ ( ( exu @ eigen__861 )
=> ~ ! [X1: $i] :
~ ( eigen__861 @ X1 ) ),
introduced(assumption,[]) ).
thf(h118,assumption,
exu @ eigen__861,
introduced(assumption,[]) ).
thf(h119,assumption,
! [X1: $i] :
~ ( eigen__861 @ X1 ),
introduced(assumption,[]) ).
thf(24,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h118,h119,h117,h107,h108,h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h42,h107]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h117,h107,h108,h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h118,h119])],[h117,24,h118,h119]) ).
thf(26,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h107,h108,h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h117]),tab_negall(eigenvar,eigen__861)],[h108,25,h117]) ).
thf(27,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h42,h106]),tab_bq(discharge,[h107,h108])],[exuE3e,23,26,h42,h106,h107,h108]) ).
thf(h120,assumption,
in @ eigen__862 @ emptyset,
introduced(assumption,[]) ).
thf(28,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h42,h106,h120,h105,h55,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h40,h105]) ).
thf(29,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h107,h108,h120,h105,h55,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h42,h107]) ).
thf(30,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h120,h105,h55,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h42,h106]),tab_bq(discharge,[h107,h108])],[exuE3e,28,29,h42,h106,h107,h108]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h105,h55,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h120]),tab_negall(eigenvar,eigen__862)],[h55,30,h120]) ).
thf(32,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h40,h53]),tab_bq(discharge,[h105,h55])],[notinemptyset,27,31,h40,h53,h105,h55]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h116]),tab_negall(eigenvar,eigen__860)],[h55,32,h116]) ).
thf(emptysetimpfalse,axiom,
( sP9
= ( ! [X1: $i] :
~ ( in @ X1 @ emptyset ) ) ) ).
thf(34,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h38,h53]),tab_bq(discharge,[h104,h55])],[emptysetimpfalse,22,33,h38,h53,h104,h55]) ).
thf(35,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h102,h103,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h36,h102]) ).
thf(emptysetE,axiom,
( sP3
= ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X2: $o] : X2 ) ) ) ).
thf(36,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h36,h101]),tab_bq(discharge,[h102,h103])],[emptysetE,34,35,h36,h101,h102,h103]) ).
thf(37,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h99,h100,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h34,h99]) ).
thf(prop2setE,axiom,
( sP26
= ( ! [X1: $o,X2: $i] :
( ( in @ X2 @ ( prop2set @ X1 ) )
=> X1 ) ) ) ).
thf(38,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h34,h98]),tab_bq(discharge,[h99,h100])],[prop2setE,36,37,h34,h98,h99,h100]) ).
thf(39,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h96,h97,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h32,h96]) ).
thf(exuE1,axiom,
( sP15
= ( ! [X1: $i > $o] :
( ( exu @ X1 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ).
thf(40,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h32,h95]),tab_bq(discharge,[h96,h97])],[exuE1,38,39,h32,h95,h96,h97]) ).
thf(41,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h93,h94,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h30,h93]) ).
thf(dsetconstrER,axiom,
( sP4
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ) ) ) ).
thf(42,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h30,h92]),tab_bq(discharge,[h93,h94])],[dsetconstrER,40,41,h30,h92,h93,h94]) ).
thf(43,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h90,h91,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h28,h90]) ).
thf(dsetconstrEL,axiom,
( sP16
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ) ) ).
thf(44,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h28,h89]),tab_bq(discharge,[h90,h91])],[dsetconstrEL,42,43,h28,h89,h90,h91]) ).
thf(45,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h87,h88,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h26,h87]) ).
thf(dsetconstrI,axiom,
( sP27
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ) ) ) ).
thf(46,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h26,h86]),tab_bq(discharge,[h87,h88])],[dsetconstrI,44,45,h26,h86,h87,h88]) ).
thf(47,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h84,h85,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h24,h84]) ).
thf(descrp,axiom,
( sP13
= ( ! [X1: $i > $o] :
( ( exu @ X1 )
=> ( X1 @ ( descr @ X1 ) ) ) ) ) ).
thf(48,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h24,h83]),tab_bq(discharge,[h84,h85])],[descrp,46,47,h24,h83,h84,h85]) ).
thf(49,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h81,h82,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h22,h81]) ).
thf(wellorderingAx,axiom,
( sP30
= ( ! [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( in @ X4 @ X1 ) ) )
=> ~ ! [X3: $i,X4: $i] :
( ~ ( ( in @ X3 @ X1 )
=> ~ ( in @ X4 @ X1 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ X3 @ X5 )
= ( in @ X4 @ X5 ) ) )
=> ( X3 = X4 ) ) ) )
=> ~ ! [X3: $i,X4: $i] :
( ~ ( ( in @ X3 @ X2 )
=> ~ ( in @ X4 @ X2 ) )
=> ( ~ ! [X5: $i] :
( ( in @ X5 @ X3 )
=> ( in @ X5 @ X4 ) )
=> ! [X5: $i] :
( ( in @ X5 @ X4 )
=> ( in @ X5 @ X3 ) ) ) ) )
=> ~ ! [X3: $i] :
( ~ ( ! [X4: $i] :
( ( in @ X4 @ X3 )
=> ( in @ X4 @ X1 ) )
=> ! [X4: $i] :
~ ( in @ X4 @ X3 ) )
=> ~ ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( in @ X4 @ X2 )
=> ~ ( in @ X5 @ X3 ) )
=> ~ ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ~ ( in @ X6 @ X3 ) ) )
=> ~ ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ~ ! [X7: $i] :
( ( in @ X7 @ X6 )
=> ( in @ X7 @ X4 ) )
=> ( in @ X5 @ X6 ) ) ) ) ) ) ) ) ).
thf(50,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h22,h80]),tab_bq(discharge,[h81,h82])],[wellorderingAx,48,49,h22,h80,h81,h82]) ).
thf(51,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h78,h79,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h20,h78]) ).
thf(foundationAx,axiom,
( sP28
= ( ! [X1: $i] :
( ~ ! [X2: $i] :
~ ( in @ X2 @ X1 )
=> ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ).
thf(52,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h20,h77]),tab_bq(discharge,[h78,h79])],[foundationAx,50,51,h20,h77,h78,h79]) ).
thf(53,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h75,h76,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h18,h75]) ).
thf(replAx,axiom,
( sP21
= ( ! [X1: $i > $i > $o,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( exu @ ( X1 @ X3 ) ) )
=> ~ ! [X3: $i] :
~ ! [X4: $i] :
( ( in @ X4 @ X3 )
= ( ~ ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ~ ( X1 @ X5 @ X4 ) ) ) ) ) ) ) ).
thf(54,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h18,h74]),tab_bq(discharge,[h75,h76])],[replAx,52,53,h18,h74,h75,h76]) ).
thf(55,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h72,h73,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h16,h72]) ).
thf(omegaIndAx,axiom,
( sP11
= ( ! [X1: $i] :
( ~ ( ( in @ emptyset @ X1 )
=> ~ ! [X2: $i] :
( ~ ( ( in @ X2 @ omega )
=> ~ ( in @ X2 @ X1 ) )
=> ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( in @ X2 @ X1 ) ) ) ) ) ).
thf(56,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h16,h71]),tab_bq(discharge,[h72,h73])],[omegaIndAx,54,55,h16,h71,h72,h73]) ).
thf(57,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h69,h70,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h14,h69]) ).
thf(omegaSAx,axiom,
( sP32
= ( ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ) ) ).
thf(58,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h14,h68]),tab_bq(discharge,[h69,h70])],[omegaSAx,56,57,h14,h68,h69,h70]) ).
thf(59,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h66,h67,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h12,h66]) ).
thf(omega0Ax,axiom,
( sP12
= ( in @ emptyset @ omega ) ) ).
thf(60,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h12,h65]),tab_bq(discharge,[h66,h67])],[omega0Ax,58,59,h12,h65,h66,h67]) ).
thf(61,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h63,h64,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h10,h63]) ).
thf(setunionAx,axiom,
( sP1
= ( ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
= ( ~ ! [X3: $i] :
( ( in @ X2 @ X3 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ).
thf(62,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h10,h62]),tab_bq(discharge,[h63,h64])],[setunionAx,60,61,h10,h62,h63,h64]) ).
thf(63,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h60,h61,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h8,h60]) ).
thf(powersetAx,axiom,
( sP18
= ( ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
= ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) ) ) ) ) ) ).
thf(64,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h8,h59]),tab_bq(discharge,[h60,h61])],[powersetAx,62,63,h8,h59,h60,h61]) ).
thf(65,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h57,h58,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h6,h57]) ).
thf(setadjoinAx,axiom,
( sP7
= ( ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
= ( ( X3 != X1 )
=> ( in @ X3 @ X2 ) ) ) ) ) ).
thf(66,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h6,h56]),tab_bq(discharge,[h57,h58])],[setadjoinAx,64,65,h6,h56,h57,h58]) ).
thf(67,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h54,h55,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h4,h54]) ).
thf(emptysetAx,axiom,
( sP24
= ( ! [X1: $i] :
~ ( in @ X1 @ emptyset ) ) ) ).
thf(68,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h4,h53]),tab_bq(discharge,[h54,h55])],[emptysetAx,66,67,h4,h53,h54,h55]) ).
thf(69,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h51,h52,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h2,h51]) ).
thf(setextAx,axiom,
sP20 = sP6 ).
thf(70,plain,
$false,
inference(tab_bq,[status(thm),assumptions([h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h2,h50]),tab_bq(discharge,[h51,h52])],[setextAx,68,69,h2,h50,h51,h52]) ).
thf(71,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h48,h49])],[h47,70,h48,h49]) ).
thf(72,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h46,h47])],[h45,71,h46,h47]) ).
thf(73,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__1)],[h44,72,h45]) ).
thf(74,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h44]),tab_negall(eigenvar,eigen__0)],[h43,73,h44]) ).
thf(75,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h42,h43])],[h41,74,h42,h43]) ).
thf(76,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h40,h41])],[h39,75,h40,h41]) ).
thf(77,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h38,h39])],[h37,76,h38,h39]) ).
thf(78,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h36,h37])],[h35,77,h36,h37]) ).
thf(79,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,78,h34,h35]) ).
thf(80,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h32,h33])],[h31,79,h32,h33]) ).
thf(81,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h30,h31])],[h29,80,h30,h31]) ).
thf(82,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,81,h28,h29]) ).
thf(83,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,82,h26,h27]) ).
thf(84,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,83,h24,h25]) ).
thf(85,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,84,h22,h23]) ).
thf(86,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,85,h20,h21]) ).
thf(87,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,86,h18,h19]) ).
thf(88,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,87,h16,h17]) ).
thf(89,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,88,h14,h15]) ).
thf(90,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,89,h12,h13]) ).
thf(91,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,90,h10,h11]) ).
thf(92,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,91,h8,h9]) ).
thf(93,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,92,h6,h7]) ).
thf(94,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,93,h4,h5]) ).
thf(95,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,94,h2,h3]) ).
thf(96,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[95,h0]) ).
thf(0,theorem,
( sP20
=> ( sP24
=> ( sP7
=> ( sP18
=> ( sP1
=> ( sP12
=> ( sP32
=> ( sP11
=> ( sP21
=> ( sP28
=> ( sP30
=> ( sP13
=> ( sP27
=> ( sP16
=> ( sP4
=> ( sP15
=> ( sP26
=> ( sP3
=> ( sP9
=> ( sP5
=> ( sP31
=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[95,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU505^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 19:30:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 41.18/41.24 % SZS status Theorem
% 41.18/41.24 % Mode: cade22grackle2x6987
% 41.18/41.24 % Steps: 22891
% 41.18/41.24 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------