TSTP Solution File: SYO544^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO544^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n012.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 : 600s
% DateTime : Thu Jul 21 19:33:20 EDT 2022
% Result : Theorem 0.89s 1.14s
% Output : Proof 9.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 795
% Syntax : Number of formulae : 831 ( 111 unt; 52 typ; 32 def)
% Number of atoms : 4640 (1745 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 5665 (2855 ~; 312 |; 0 &; 371 @)
% ( 441 <=>;1686 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 176 ( 174 usr; 170 con; 0-2 aty)
% Number of variables : 864 ( 744 ^ 120 !; 0 ?; 864 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__16,type,
eigen__16: $o ).
thf(ty_eps,type,
eps: ( $i > $o ) > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $o ).
thf(ty_eigen__5,type,
eigen__5: $o ).
thf(ty_eigen__11,type,
eigen__11: $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_f0,type,
f0: $o > $o ).
thf(ty_eigen__17,type,
eigen__17: $o ).
thf(ty_eigen__10,type,
eigen__10: $o ).
thf(ty_eigen__8,type,
eigen__8: $o ).
thf(ty_eigen__28,type,
eigen__28: $o ).
thf(ty_f3,type,
f3: $o > $o ).
thf(ty_f2,type,
f2: $o > $o ).
thf(ty_f1,type,
f1: $o > $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $o] :
( ( f1 @ X1 )
!= ( ~ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__0
@ ^ [X1: $o] :
( ( f2 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $o] :
( ( f0 @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $o] :
( ( f1 @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $o] :
( ( f1 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: $o] :
( ( f2 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $o] :
( ( f0 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__28,definition,
( eigen__28
= ( eps__0
@ ^ [X1: $o] :
( ( f3 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $o] :
( ( f0 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ( f3 @ $false )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( f3 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( f3 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ( ( f0
= ( ^ [X1: $o] : $false ) )
=> ( eigen__0 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__0 != eigen__1 ) ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__0 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__0 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( f0
= ( ^ [X1: $o] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( f0
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ~ $false )
= eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $o] :
( ( f1 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( f1 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $o] :
( ( f0 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ~ ( ( ( f3
= ( ^ [X1: $o] : $false ) )
=> ( eigen__3 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__3 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__3 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__3 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ~ $false )
= eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( ~ ( ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( eigen__1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__1 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $o] :
( ( f2 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( f1
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $o] :
( ( f0 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( $false = eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( f2 @ eigen__16 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ( sP5
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ ( sP7
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $o] :
( ( f3 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( f2 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__6 = $false ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__11 = eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( f0
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( f3
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__3 != eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( f3
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP2
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( f1 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( f1 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $o] :
( ( f2 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( f0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ ( ~ ( ( ( f2
= ( ^ [X1: $o] : $false ) )
=> ( eigen__2 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__2 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__2 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__2 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( ~ ( sP30
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( sP30
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( f2
= ( ^ [X1: $o] : X1 ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( f1
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( f1
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( $false = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( f1
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP40
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP7
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( f2
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $o] :
( ( f1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( sP5
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( eigen__5 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__6 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( f2
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $o] :
( ( f2 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: $o] :
( ( f0 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ( f0 @ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ( f0 @ ~ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP40
=> ( eigen__1 != eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP5
=> ~ sP26 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP52
=> ( eigen__2 != eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> eigen__5 ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( f1 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> eigen__16 ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ( ~ $false )
= eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( f1
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP27
=> ( eigen__10 = eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( sP10 = $false ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> eigen__4 ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP40
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ( f2 @ ~ $false )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ~ ( sP68
=> ~ ( sP40
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP40
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ sP43 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ( f2 @ eigen__17 )
= eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ( f2
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( ~ sP21
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( sP24
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( ( f1 @ eigen__11 )
= ( ~ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( sP35 = $false ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ! [X1: $o] :
( ( f1 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( f3
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ~ ( ~ ( ( ( f2
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ sP72 )
=> ~ sP39 )
=> ~ ( sP46
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( sP33 = $false ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ! [X1: $o] :
( ( f1 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( f3
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( eigen__11 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ! [X1: $o] :
( ( f0 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( f3
= ( ^ [X1: $o] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> eigen__17 ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> eigen__6 ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( ( f0 @ sP60 )
= sP60 ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP40
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X1 != eigen__3 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( eigen__10 = eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( f0 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> eigen__28 ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ! [X1: $o] :
( ( f3 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ( ~ ( ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( eigen__1 != eigen__0 ) )
=> ~ sP57 )
=> ~ ( sP64
=> ( eigen__1 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( sP32
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( sP30
=> ~ ( sP82
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP85
=> ( X1 != eigen__0 ) )
=> ~ ( sP82
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( ~ sP70
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( eigen__3 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( ~ ( sP58
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__0 != eigen__1 ) ) )
=> ~ ( sP7
=> ( eigen__0 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( sP82
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP85
=> ( X1 != eigen__0 ) )
=> ~ ( sP82
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( f3 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( f0 @ sP67 ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ( f1 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( sP58
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__0 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ( sP5
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> $false ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( sP85
=> ( X1 != eigen__0 ) )
=> ~ ( sP82
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ! [X1: $o] :
( ( f2 @ X1 )
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ sP109 ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( f0
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> eigen__10 ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( f0 @ ~ sP109 ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( f0 @ sP60 ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> eigen__8 ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( sP61
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( sP40
=> ~ sP89 ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( ( ( f2
= ( ^ [X1: $o] : sP109 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : sP109 ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ sP72 ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ! [X1: $o] :
( ( f3 @ X1 )
= sP109 ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ( f2
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ( f3
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( f2
= ( ^ [X1: $o] : sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( f2 @ sP86 ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ( sP86 = sP62 ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ! [X1: $o] :
( ( f3 @ X1 )
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ( f2 @ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ( sP3 = sP109 ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130,plain,
( sP130
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131,plain,
( sP131
<=> ( sP68
=> ~ sP119 ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132,plain,
( sP132
<=> ! [X1: $o] :
( ( eigen__11 = X1 )
=> ( X1 = eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133,plain,
( sP133
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP85
=> ( X1 != eigen__0 ) )
=> ~ ( sP82
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP123
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__3 ) ) ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134,plain,
( sP134
<=> ( sP78
=> ~ sP133 ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135,plain,
( sP135
<=> ( f1
= ( ^ [X1: $o] : sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136,plain,
( sP136
<=> ( f2 @ ~ sP109 ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137,plain,
( sP137
<=> eigen__11 ),
introduced(definition,[new_symbols(definition,[sP137])]) ).
thf(sP138,plain,
( sP138
<=> ( ~ sP120
=> ~ sP39 ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139,plain,
( sP139
<=> ( sP114
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140,plain,
( sP140
<=> ( sP124
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP124
=> ( X1 != eigen__0 ) )
=> ~ ( sP122
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141,plain,
( sP141
<=> ( f0
= ( ^ [X1: $o] : ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142,plain,
( sP142
<=> ( sP104
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143,plain,
( sP143
<=> ( ~ ( ( sP124
=> ( eigen__2 != eigen__0 ) )
=> ~ ( sP122
=> ( eigen__2 != eigen__1 ) ) )
=> ~ sP59 ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144,plain,
( sP144
<=> ( sP46
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP124
=> ( X1 != eigen__0 ) )
=> ~ ( sP122
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145,plain,
( sP145
<=> ( sP87 = sP60 ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146,plain,
( sP146
<=> ( ( sP135
=> ( eigen__1 != eigen__0 ) )
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP146])]) ).
thf(def_case,definition,
( case
= ( ^ [X1: $o > $o,X2: $i,X3: $i,X4: $i,X5: $i] :
( eps
@ ^ [X6: $i] :
( ~ ( ~ ( ( ( X1
= ( ^ [X7: $o] : sP109 ) )
=> ( X6 != X2 ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ X7 ) )
=> ( X6 != X3 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : X7 ) )
=> ( X6 != X4 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ sP109 ) )
=> ( X6 != X5 ) ) ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP5
=> ( X5 != X1 ) )
=> ~ ( sP113
=> ( X5 != X2 ) ) )
=> ~ ( sP7
=> ( X5 != X3 ) ) )
=> ~ ( sP141
=> ( X5 != X4 ) ) ) )
= X1 )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP135
=> ( X5 != X1 ) )
=> ~ ( sP40
=> ( X5 != X2 ) ) )
=> ~ ( sP64
=> ( X5 != X3 ) ) )
=> ~ ( sP41
=> ( X5 != X4 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP124
=> ( X5 != X1 ) )
=> ~ ( sP122
=> ( X5 != X2 ) ) )
=> ~ ( sP52
=> ( X5 != X3 ) ) )
=> ~ ( sP46
=> ( X5 != X4 ) ) ) )
!= X3 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP85
=> ( X5 != X1 ) )
=> ~ ( sP82
=> ( X5 != X2 ) ) )
=> ~ ( sP123
=> ( X5 != X3 ) ) )
=> ~ ( sP78
=> ( X5 != X4 ) ) ) )
!= X4 ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i,X4: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP5
=> ( X5 != X1 ) )
=> ~ ( sP113
=> ( X5 != X2 ) ) )
=> ~ ( sP7
=> ( X5 != X3 ) ) )
=> ~ ( sP141
=> ( X5 != X4 ) ) ) )
= X1 )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP135
=> ( X5 != X1 ) )
=> ~ ( sP40
=> ( X5 != X2 ) ) )
=> ~ ( sP64
=> ( X5 != X3 ) ) )
=> ~ ( sP41
=> ( X5 != X4 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP124
=> ( X5 != X1 ) )
=> ~ ( sP122
=> ( X5 != X2 ) ) )
=> ~ ( sP52
=> ( X5 != X3 ) ) )
=> ~ ( sP46
=> ( X5 != X4 ) ) ) )
!= X3 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP85
=> ( X5 != X1 ) )
=> ~ ( sP82
=> ( X5 != X2 ) ) )
=> ~ ( sP123
=> ( X5 != X3 ) ) )
=> ~ ( sP78
=> ( X5 != X4 ) ) ) )
!= X4 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP5
=> ( X4 != eigen__0 ) )
=> ~ ( sP113
=> ( X4 != X1 ) ) )
=> ~ ( sP7
=> ( X4 != X2 ) ) )
=> ~ ( sP141
=> ( X4 != X3 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP135
=> ( X4 != eigen__0 ) )
=> ~ ( sP40
=> ( X4 != X1 ) ) )
=> ~ ( sP64
=> ( X4 != X2 ) ) )
=> ~ ( sP41
=> ( X4 != X3 ) ) ) )
!= X1 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP124
=> ( X4 != eigen__0 ) )
=> ~ ( sP122
=> ( X4 != X1 ) ) )
=> ~ ( sP52
=> ( X4 != X2 ) ) )
=> ~ ( sP46
=> ( X4 != X3 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP85
=> ( X4 != eigen__0 ) )
=> ~ ( sP82
=> ( X4 != X1 ) ) )
=> ~ ( sP123
=> ( X4 != X2 ) ) )
=> ~ ( sP78
=> ( X4 != X3 ) ) ) )
!= X3 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i,X2: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP5
=> ( X3 != eigen__0 ) )
=> ~ ( sP113
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X3 != X1 ) ) )
=> ~ ( sP141
=> ( X3 != X2 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP135
=> ( X3 != eigen__0 ) )
=> ~ ( sP40
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X3 != X1 ) ) )
=> ~ ( sP41
=> ( X3 != X2 ) ) ) )
!= eigen__1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP124
=> ( X3 != eigen__0 ) )
=> ~ ( sP122
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X3 != X1 ) ) )
=> ~ ( sP46
=> ( X3 != X2 ) ) ) )
!= X1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP85
=> ( X3 != eigen__0 ) )
=> ~ ( sP82
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP123
=> ( X3 != X1 ) ) )
=> ~ ( sP78
=> ( X3 != X2 ) ) ) )
!= X2 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP5
=> ( X2 != eigen__0 ) )
=> ~ ( sP113
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP141
=> ( X2 != X1 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP135
=> ( X2 != eigen__0 ) )
=> ~ ( sP40
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X2 != X1 ) ) ) )
!= eigen__1 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP124
=> ( X2 != eigen__0 ) )
=> ~ ( sP122
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X2 != X1 ) ) ) )
!= eigen__2 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP85
=> ( X2 != eigen__0 ) )
=> ~ ( sP82
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP123
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X2 != X1 ) ) ) )
!= X1 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
( ~ ( ~ ( sP108
=> ~ sP89 )
=> ~ sP6 )
=> ~ sP133 ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ~ ( sP108
=> ~ sP89 )
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP133,
introduced(assumption,[]) ).
thf(h8,assumption,
( sP108
=> ~ sP89 ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h10,assumption,
~ sP108,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP89,
introduced(assumption,[]) ).
thf(h12,assumption,
sP91,
introduced(assumption,[]) ).
thf(h13,assumption,
sP109,
introduced(assumption,[]) ).
thf(h14,assumption,
~ sP91,
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP109,
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_false,[status(thm),assumptions([h12,h13,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13]) ).
thf(h16,assumption,
sP115,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP115,
introduced(assumption,[]) ).
thf(2,plain,
$false,
inference(tab_false,[status(thm),assumptions([h16,h13,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13]) ).
thf(h18,assumption,
sP10,
introduced(assumption,[]) ).
thf(h19,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h20,assumption,
sP61,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP61,
introduced(assumption,[]) ).
thf(3,plain,
$false,
inference(tab_false,[status(thm),assumptions([h20,h13,h18,h15,h17,h15,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13]) ).
thf(h22,assumption,
sP24,
introduced(assumption,[]) ).
thf(h23,assumption,
~ sP24,
introduced(assumption,[]) ).
thf(4,plain,
$false,
inference(tab_false,[status(thm),assumptions([h22,h13,h21,h15,h18,h15,h17,h15,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13]) ).
thf(h24,assumption,
sP136,
introduced(assumption,[]) ).
thf(h25,assumption,
~ sP136,
introduced(assumption,[]) ).
thf(h26,assumption,
sP103,
introduced(assumption,[]) ).
thf(h27,assumption,
~ sP103,
introduced(assumption,[]) ).
thf(h28,assumption,
sP3,
introduced(assumption,[]) ).
thf(h29,assumption,
~ sP3,
introduced(assumption,[]) ).
thf(5,plain,
( sP25
| sP87
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP50
| ~ sP87
| ~ sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP145
| ~ sP87
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP49
| sP60
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP35
| sP91
| ~ sP25 ),
inference(mating_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP35
| sP104
| ~ sP50 ),
inference(mating_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP35
| sP116
| ~ sP145 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP116
| sP104
| ~ sP49 ),
inference(mating_rule,[status(thm)],]) ).
thf(13,plain,
~ sP109,
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP12
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP84
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP55
| sP91
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP56
| sP115
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP18
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( sP76
| sP35
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP54
| ~ sP76 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(21,plain,
( sP88
| ~ sP116
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP88
| sP116
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP84
| ~ sP88 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(24,plain,
( sP142
| ~ sP104
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP18
| ~ sP142 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(26,plain,
( ~ sP113
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP7
| sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP112
| sP113 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP107
| sP108 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP141
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP45
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP48
| ~ sP107
| ~ sP112 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP28
| sP141 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP21
| sP48
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP73
| sP21
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
sP26,
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP5
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP58
| ~ sP5
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP106
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP100
| ~ sP106 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP4
| ~ sP100 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP101
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
% SZS status Theorem
% Mode: mode515
% Inferences: 6541
% SZS output start Proof
thf(ty_eigen__6_001,type,
eigen__6: $o ).
thf(ty_eigen__2_002,type,
eigen__2: $i ).
thf(ty_eigen__16_003,type,
eigen__16: $o ).
thf(ty_eps_004,type,
eps: ( $i > $o ) > $i ).
thf(ty_eigen__1_005,type,
eigen__1: $i ).
thf(ty_eigen__0_006,type,
eigen__0: $i ).
thf(ty_eigen__4_007,type,
eigen__4: $o ).
thf(ty_eigen__5_008,type,
eigen__5: $o ).
thf(ty_eigen__11_009,type,
eigen__11: $o ).
thf(ty_eigen__3_010,type,
eigen__3: $i ).
thf(ty_f0_011,type,
f0: $o > $o ).
thf(ty_eigen__17_012,type,
eigen__17: $o ).
thf(ty_eigen__10_013,type,
eigen__10: $o ).
thf(ty_eigen__8_014,type,
eigen__8: $o ).
thf(ty_eigen__28_015,type,
eigen__28: $o ).
thf(ty_f3_016,type,
f3: $o > $o ).
thf(ty_f2_017,type,
f2: $o > $o ).
thf(ty_f1_018,type,
f1: $o > $o ).
thf(h0_019,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11_020,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $o] :
( ( f1 @ X1 )
!= ( ~ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__17_021,definition,
( eigen__17
= ( eps__0
@ ^ [X1: $o] :
( ( f2 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(eigendef_eigen__6_022,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $o] :
( ( f0 @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__10_023,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $o] :
( ( f1 @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__8_024,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $o] :
( ( f1 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__16_025,definition,
( eigen__16
= ( eps__0
@ ^ [X1: $o] :
( ( f2 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__4_026,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $o] :
( ( f0 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__28_027,definition,
( eigen__28
= ( eps__0
@ ^ [X1: $o] :
( ( f3 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(eigendef_eigen__5_028,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $o] :
( ( f0 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1_029,plain,
( sP1
<=> ( ( f3 @ $false )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2_030,plain,
( sP2
<=> ( f3 @ eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3_031,plain,
( sP3
<=> ( f3 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4_032,plain,
( sP4
<=> ( ~ ( ~ ( ( ( f0
= ( ^ [X1: $o] : $false ) )
=> ( eigen__0 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__0 != eigen__1 ) ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__0 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__0 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5_033,plain,
( sP5
<=> ( f0
= ( ^ [X1: $o] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6_034,plain,
( sP6
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7_035,plain,
( sP7
<=> ( f0
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8_036,plain,
( sP8
<=> ( ( ~ $false )
= eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9_037,plain,
( sP9
<=> ! [X1: $o] :
( ( f1 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10_038,plain,
( sP10
<=> ( f1 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11_039,plain,
( sP11
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12_040,plain,
( sP12
<=> ! [X1: $o] :
( ( f0 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13_041,plain,
( sP13
<=> ( ~ ( ~ ( ( ( f3
= ( ^ [X1: $o] : $false ) )
=> ( eigen__3 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__3 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__3 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__3 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14_042,plain,
( sP14
<=> ( ( ~ $false )
= eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15_043,plain,
( sP15
<=> ( ~ ( ~ ( ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( eigen__1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__1 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16_044,plain,
( sP16
<=> ! [X1: $o] :
( ( f2 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17_045,plain,
( sP17
<=> ( ( f1
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18_046,plain,
( sP18
<=> ! [X1: $o] :
( ( f0 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19_047,plain,
( sP19
<=> ( $false = eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20_048,plain,
( sP20
<=> ( ( f2 @ eigen__16 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21_049,plain,
( sP21
<=> ( ~ ( ( sP5
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ ( sP7
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22_050,plain,
( sP22
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23_051,plain,
( sP23
<=> ! [X1: $o] :
( ( f3 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24_052,plain,
( sP24
<=> ( f2 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25_053,plain,
( sP25
<=> ( eigen__6 = $false ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26_054,plain,
( sP26
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27_055,plain,
( sP27
<=> ( eigen__11 = eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28_056,plain,
( sP28
<=> ( ( f0
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29_057,plain,
( sP29
<=> ( ( f3
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__3 != eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30_058,plain,
( sP30
<=> ( ( f3
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31_059,plain,
( sP31
<=> ( sP2
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32_060,plain,
( sP32
<=> ( f1 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33_061,plain,
( sP33
<=> ( f1 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34_062,plain,
( sP34
<=> ! [X1: $o] :
( ( f2 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35_063,plain,
( sP35
<=> ( f0 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36_064,plain,
( sP36
<=> ( ~ ( ~ ( ( ( f2
= ( ^ [X1: $o] : $false ) )
=> ( eigen__2 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__2 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__2 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X1: $o] : ~ $false ) )
=> ( eigen__2 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37_065,plain,
( sP37
<=> ( ~ ( ~ ( sP30
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38_066,plain,
( sP38
<=> ( ~ ( sP30
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39_067,plain,
( sP39
<=> ( ( f2
= ( ^ [X1: $o] : X1 ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40_068,plain,
( sP40
<=> ( f1
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41_069,plain,
( sP41
<=> ( f1
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42_070,plain,
( sP42
<=> ( $false = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43_071,plain,
( sP43
<=> ( ( f1
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP40
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44_072,plain,
( sP44
<=> ! [X1: $o,X2: $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45_073,plain,
( sP45
<=> ( sP7
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46_074,plain,
( sP46
<=> ( f2
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47_075,plain,
( sP47
<=> ! [X1: $o] :
( ( f1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48_076,plain,
( sP48
<=> ( ( sP5
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49_077,plain,
( sP49
<=> ( eigen__5 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50_078,plain,
( sP50
<=> ( eigen__6 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51_079,plain,
( sP51
<=> ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52_080,plain,
( sP52
<=> ( f2
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53_081,plain,
( sP53
<=> ! [X1: $o] :
( ( f2 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54_082,plain,
( sP54
<=> ! [X1: $o] :
( ( f0 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55_083,plain,
( sP55
<=> ( ( f0 @ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56_084,plain,
( sP56
<=> ( ( f0 @ ~ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57_085,plain,
( sP57
<=> ( sP40
=> ( eigen__1 != eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58_086,plain,
( sP58
<=> ( sP5
=> ~ sP26 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59_087,plain,
( sP59
<=> ( sP52
=> ( eigen__2 != eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60_088,plain,
( sP60
<=> eigen__5 ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61_089,plain,
( sP61
<=> ( f1 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62_090,plain,
( sP62
<=> eigen__16 ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63_091,plain,
( sP63
<=> ( ( ~ $false )
= eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64_092,plain,
( sP64
<=> ( f1
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65_093,plain,
( sP65
<=> ( sP27
=> ( eigen__10 = eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66_094,plain,
( sP66
<=> ( sP10 = $false ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67_095,plain,
( sP67
<=> eigen__4 ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68_096,plain,
( sP68
<=> ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP40
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69_097,plain,
( sP69
<=> ( ( f2 @ ~ $false )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70_098,plain,
( sP70
<=> ( ~ ( sP68
=> ~ ( sP40
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP40
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ sP43 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71_099,plain,
( sP71
<=> ( ( f2 @ eigen__17 )
= eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72_100,plain,
( sP72
<=> ( ( f2
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73_101,plain,
( sP73
<=> ( ~ sP21
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74_102,plain,
( sP74
<=> ( sP24
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75_103,plain,
( sP75
<=> ( ( f1 @ eigen__11 )
= ( ~ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76_104,plain,
( sP76
<=> ( sP35 = $false ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77_105,plain,
( sP77
<=> ! [X1: $o] :
( ( f1 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78_106,plain,
( sP78
<=> ( f3
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79_107,plain,
( sP79
<=> ( ~ ( ~ ( ( ( f2
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ sP72 )
=> ~ sP39 )
=> ~ ( sP46
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80_108,plain,
( sP80
<=> ( sP33 = $false ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81_109,plain,
( sP81
<=> ! [X1: $o] :
( ( f1 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82_110,plain,
( sP82
<=> ( f3
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83_111,plain,
( sP83
<=> ( eigen__11 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84_112,plain,
( sP84
<=> ! [X1: $o] :
( ( f0 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85_113,plain,
( sP85
<=> ( f3
= ( ^ [X1: $o] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86_114,plain,
( sP86
<=> eigen__17 ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87_115,plain,
( sP87
<=> eigen__6 ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88_116,plain,
( sP88
<=> ( ( f0 @ sP60 )
= sP60 ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89_117,plain,
( sP89
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP40
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X1 != eigen__3 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90_118,plain,
( sP90
<=> ( eigen__10 = eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91_119,plain,
( sP91
<=> ( f0 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92_120,plain,
( sP92
<=> eigen__28 ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93_121,plain,
( sP93
<=> ! [X1: $o] :
( ( f3 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94_122,plain,
( sP94
<=> ( ~ ( ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( eigen__1 != eigen__0 ) )
=> ~ sP57 )
=> ~ ( sP64
=> ( eigen__1 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95_123,plain,
( sP95
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96_124,plain,
( sP96
<=> ( sP32
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97_125,plain,
( sP97
<=> ( sP30
=> ~ ( sP82
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP85
=> ( X1 != eigen__0 ) )
=> ~ ( sP82
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98_126,plain,
( sP98
<=> ( ~ sP70
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99_127,plain,
( sP99
<=> ( eigen__3 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100_128,plain,
( sP100
<=> ( ~ ( sP58
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__0 != eigen__1 ) ) )
=> ~ ( sP7
=> ( eigen__0 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101_129,plain,
( sP101
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102_130,plain,
( sP102
<=> ( sP82
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP85
=> ( X1 != eigen__0 ) )
=> ~ ( sP82
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103_131,plain,
( sP103
<=> ( f3 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104_132,plain,
( sP104
<=> ( f0 @ sP67 ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105_133,plain,
( sP105
<=> ( f1 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106_134,plain,
( sP106
<=> ( sP58
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__0 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107_135,plain,
( sP107
<=> ( sP5
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108_136,plain,
( sP108
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109_137,plain,
( sP109
<=> $false ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110_138,plain,
( sP110
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( sP85
=> ( X1 != eigen__0 ) )
=> ~ ( sP82
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111_139,plain,
( sP111
<=> ! [X1: $o] :
( ( f2 @ X1 )
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112_140,plain,
( sP112
<=> ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP5
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ sP109 ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113_141,plain,
( sP113
<=> ( f0
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114_142,plain,
( sP114
<=> eigen__10 ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115_143,plain,
( sP115
<=> ( f0 @ ~ sP109 ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116_144,plain,
( sP116
<=> ( f0 @ sP60 ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117_145,plain,
( sP117
<=> eigen__8 ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118_146,plain,
( sP118
<=> ( sP61
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119_147,plain,
( sP119
<=> ( sP40
=> ~ sP89 ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120_148,plain,
( sP120
<=> ( ( ( f2
= ( ^ [X1: $o] : sP109 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : sP109 ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ sP72 ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121_149,plain,
( sP121
<=> ! [X1: $o] :
( ( f3 @ X1 )
= sP109 ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122_150,plain,
( sP122
<=> ( f2
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123_151,plain,
( sP123
<=> ( f3
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124_152,plain,
( sP124
<=> ( f2
= ( ^ [X1: $o] : sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125_153,plain,
( sP125
<=> ( f2 @ sP86 ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126_154,plain,
( sP126
<=> ( sP86 = sP62 ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127_155,plain,
( sP127
<=> ! [X1: $o] :
( ( f3 @ X1 )
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128_156,plain,
( sP128
<=> ( f2 @ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129_157,plain,
( sP129
<=> ( sP3 = sP109 ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130_158,plain,
( sP130
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131_159,plain,
( sP131
<=> ( sP68
=> ~ sP119 ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132_160,plain,
( sP132
<=> ! [X1: $o] :
( ( eigen__11 = X1 )
=> ( X1 = eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133_161,plain,
( sP133
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP85
=> ( X1 != eigen__0 ) )
=> ~ ( sP82
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP123
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__3 ) ) ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134_162,plain,
( sP134
<=> ( sP78
=> ~ sP133 ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135_163,plain,
( sP135
<=> ( f1
= ( ^ [X1: $o] : sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136_164,plain,
( sP136
<=> ( f2 @ ~ sP109 ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137_165,plain,
( sP137
<=> eigen__11 ),
introduced(definition,[new_symbols(definition,[sP137])]) ).
thf(sP138_166,plain,
( sP138
<=> ( ~ sP120
=> ~ sP39 ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139_167,plain,
( sP139
<=> ( sP114
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140_168,plain,
( sP140
<=> ( sP124
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP124
=> ( X1 != eigen__0 ) )
=> ~ ( sP122
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141_169,plain,
( sP141
<=> ( f0
= ( ^ [X1: $o] : ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142_170,plain,
( sP142
<=> ( sP104
= ( ~ sP109 ) ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143_171,plain,
( sP143
<=> ( ~ ( ( sP124
=> ( eigen__2 != eigen__0 ) )
=> ~ ( sP122
=> ( eigen__2 != eigen__1 ) ) )
=> ~ sP59 ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144_172,plain,
( sP144
<=> ( sP46
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP124
=> ( X1 != eigen__0 ) )
=> ~ ( sP122
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145_173,plain,
( sP145
<=> ( sP87 = sP60 ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146_174,plain,
( sP146
<=> ( ( sP135
=> ( eigen__1 != eigen__0 ) )
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP146])]) ).
thf(def_case_175,definition,
( case
= ( ^ [X1: $o > $o,X2: $i,X3: $i,X4: $i,X5: $i] :
( eps
@ ^ [X6: $i] :
( ~ ( ~ ( ( ( X1
= ( ^ [X7: $o] : sP109 ) )
=> ( X6 != X2 ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ X7 ) )
=> ( X6 != X3 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : X7 ) )
=> ( X6 != X4 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ sP109 ) )
=> ( X6 != X5 ) ) ) ) ) ) ).
thf(conj_176,conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP5
=> ( X5 != X1 ) )
=> ~ ( sP113
=> ( X5 != X2 ) ) )
=> ~ ( sP7
=> ( X5 != X3 ) ) )
=> ~ ( sP141
=> ( X5 != X4 ) ) ) )
= X1 )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP135
=> ( X5 != X1 ) )
=> ~ ( sP40
=> ( X5 != X2 ) ) )
=> ~ ( sP64
=> ( X5 != X3 ) ) )
=> ~ ( sP41
=> ( X5 != X4 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP124
=> ( X5 != X1 ) )
=> ~ ( sP122
=> ( X5 != X2 ) ) )
=> ~ ( sP52
=> ( X5 != X3 ) ) )
=> ~ ( sP46
=> ( X5 != X4 ) ) ) )
!= X3 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP85
=> ( X5 != X1 ) )
=> ~ ( sP82
=> ( X5 != X2 ) ) )
=> ~ ( sP123
=> ( X5 != X3 ) ) )
=> ~ ( sP78
=> ( X5 != X4 ) ) ) )
!= X4 ) ) ).
thf(h1_177,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i,X4: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP5
=> ( X5 != X1 ) )
=> ~ ( sP113
=> ( X5 != X2 ) ) )
=> ~ ( sP7
=> ( X5 != X3 ) ) )
=> ~ ( sP141
=> ( X5 != X4 ) ) ) )
= X1 )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP135
=> ( X5 != X1 ) )
=> ~ ( sP40
=> ( X5 != X2 ) ) )
=> ~ ( sP64
=> ( X5 != X3 ) ) )
=> ~ ( sP41
=> ( X5 != X4 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP124
=> ( X5 != X1 ) )
=> ~ ( sP122
=> ( X5 != X2 ) ) )
=> ~ ( sP52
=> ( X5 != X3 ) ) )
=> ~ ( sP46
=> ( X5 != X4 ) ) ) )
!= X3 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP85
=> ( X5 != X1 ) )
=> ~ ( sP82
=> ( X5 != X2 ) ) )
=> ~ ( sP123
=> ( X5 != X3 ) ) )
=> ~ ( sP78
=> ( X5 != X4 ) ) ) )
!= X4 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h2_178,assumption,
~ ! [X1: $i,X2: $i,X3: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP5
=> ( X4 != eigen__0 ) )
=> ~ ( sP113
=> ( X4 != X1 ) ) )
=> ~ ( sP7
=> ( X4 != X2 ) ) )
=> ~ ( sP141
=> ( X4 != X3 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP135
=> ( X4 != eigen__0 ) )
=> ~ ( sP40
=> ( X4 != X1 ) ) )
=> ~ ( sP64
=> ( X4 != X2 ) ) )
=> ~ ( sP41
=> ( X4 != X3 ) ) ) )
!= X1 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP124
=> ( X4 != eigen__0 ) )
=> ~ ( sP122
=> ( X4 != X1 ) ) )
=> ~ ( sP52
=> ( X4 != X2 ) ) )
=> ~ ( sP46
=> ( X4 != X3 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( sP85
=> ( X4 != eigen__0 ) )
=> ~ ( sP82
=> ( X4 != X1 ) ) )
=> ~ ( sP123
=> ( X4 != X2 ) ) )
=> ~ ( sP78
=> ( X4 != X3 ) ) ) )
!= X3 ) ),
introduced(assumption,[]) ).
thf(h3_179,assumption,
~ ! [X1: $i,X2: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP5
=> ( X3 != eigen__0 ) )
=> ~ ( sP113
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X3 != X1 ) ) )
=> ~ ( sP141
=> ( X3 != X2 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP135
=> ( X3 != eigen__0 ) )
=> ~ ( sP40
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X3 != X1 ) ) )
=> ~ ( sP41
=> ( X3 != X2 ) ) ) )
!= eigen__1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP124
=> ( X3 != eigen__0 ) )
=> ~ ( sP122
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X3 != X1 ) ) )
=> ~ ( sP46
=> ( X3 != X2 ) ) ) )
!= X1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP85
=> ( X3 != eigen__0 ) )
=> ~ ( sP82
=> ( X3 != eigen__1 ) ) )
=> ~ ( sP123
=> ( X3 != X1 ) ) )
=> ~ ( sP78
=> ( X3 != X2 ) ) ) )
!= X2 ) ),
introduced(assumption,[]) ).
thf(h4_180,assumption,
~ ! [X1: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP5
=> ( X2 != eigen__0 ) )
=> ~ ( sP113
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP7
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP141
=> ( X2 != X1 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP135
=> ( X2 != eigen__0 ) )
=> ~ ( sP40
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP64
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP41
=> ( X2 != X1 ) ) ) )
!= eigen__1 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP124
=> ( X2 != eigen__0 ) )
=> ~ ( sP122
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP52
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP46
=> ( X2 != X1 ) ) ) )
!= eigen__2 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP85
=> ( X2 != eigen__0 ) )
=> ~ ( sP82
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP123
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP78
=> ( X2 != X1 ) ) ) )
!= X1 ) ),
introduced(assumption,[]) ).
thf(h5_181,assumption,
( ~ ( ~ ( sP108
=> ~ sP89 )
=> ~ sP6 )
=> ~ sP133 ),
introduced(assumption,[]) ).
thf(h6_182,assumption,
( ~ ( sP108
=> ~ sP89 )
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h7_183,assumption,
~ sP133,
introduced(assumption,[]) ).
thf(h8_184,assumption,
( sP108
=> ~ sP89 ),
introduced(assumption,[]) ).
thf(h9_185,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h10_186,assumption,
~ sP108,
introduced(assumption,[]) ).
thf(h11_187,assumption,
~ sP89,
introduced(assumption,[]) ).
thf(h12_188,assumption,
sP91,
introduced(assumption,[]) ).
thf(h13_189,assumption,
sP109,
introduced(assumption,[]) ).
thf(h14_190,assumption,
~ sP91,
introduced(assumption,[]) ).
thf(h15_191,assumption,
~ sP109,
introduced(assumption,[]) ).
thf('1_192',plain,
$false,
inference(tab_false,[status(thm),assumptions([h12,h13,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13]) ).
thf(h16_193,assumption,
sP115,
introduced(assumption,[]) ).
thf(h17_194,assumption,
~ sP115,
introduced(assumption,[]) ).
thf('2_195',plain,
$false,
inference(tab_false,[status(thm),assumptions([h16,h13,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13]) ).
thf(h18_196,assumption,
sP10,
introduced(assumption,[]) ).
thf(h19_197,assumption,
~ sP10,
introduced(assumption,[]) ).
thf(h20_198,assumption,
sP61,
introduced(assumption,[]) ).
thf(h21_199,assumption,
~ sP61,
introduced(assumption,[]) ).
thf('3_200',plain,
$false,
inference(tab_false,[status(thm),assumptions([h20,h13,h18,h15,h17,h15,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13]) ).
thf(h22_201,assumption,
sP24,
introduced(assumption,[]) ).
thf(h23_202,assumption,
~ sP24,
introduced(assumption,[]) ).
thf('4_203',plain,
$false,
inference(tab_false,[status(thm),assumptions([h22,h13,h21,h15,h18,h15,h17,h15,h14,h15,h10,h8,h6,h5,h4,h3,h2,h1,h0])],[h13]) ).
thf(h24_204,assumption,
sP136,
introduced(assumption,[]) ).
thf(h25_205,assumption,
~ sP136,
introduced(assumption,[]) ).
thf(h26_206,assumption,
sP103,
introduced(assumption,[]) ).
thf(h27_207,assumption,
~ sP103,
introduced(assumption,[]) ).
thf(h28_208,assumption,
sP3,
introduced(assumption,[]) ).
thf(h29_209,assumption,
~ sP3,
introduced(assumption,[]) ).
thf('5_210',plain,
( sP25
| sP87
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf('6_211',plain,
( sP50
| ~ sP87
| ~ sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf('7_212',plain,
( sP145
| ~ sP87
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf('8_213',plain,
( sP49
| sP60
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf('9_214',plain,
( ~ sP35
| sP91
| ~ sP25 ),
inference(mating_rule,[status(thm)],]) ).
thf('10_215',plain,
( ~ sP35
| sP104
| ~ sP50 ),
inference(mating_rule,[status(thm)],]) ).
thf('11_216',plain,
( ~ sP35
| sP116
| ~ sP145 ),
inference(mating_rule,[status(thm)],]) ).
thf('12_217',plain,
( ~ sP116
| sP104
| ~ sP49 ),
inference(mating_rule,[status(thm)],]) ).
thf('13_218',plain,
~ sP109,
inference(prop_rule,[status(thm)],]) ).
thf('14_219',plain,
( ~ sP12
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf('15_220',plain,
( ~ sP84
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf('16_221',plain,
( ~ sP55
| sP91
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf('17_222',plain,
( ~ sP56
| sP115
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf('18_223',plain,
( ~ sP18
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf('19_224',plain,
( sP76
| sP35
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf('20_225',plain,
( sP54
| ~ sP76 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf('21_226',plain,
( sP88
| ~ sP116
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf('22_227',plain,
( sP88
| sP116
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf('23_228',plain,
( sP84
| ~ sP88 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf('24_229',plain,
( sP142
| ~ sP104
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf('25_230',plain,
( sP18
| ~ sP142 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf('26_231',plain,
( ~ sP113
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf('27_232',plain,
( ~ sP7
| sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf('28_233',plain,
( sP112
| sP113 ),
inference(prop_rule,[status(thm)],]) ).
thf('29_234',plain,
( sP107
| sP108 ),
inference(prop_rule,[status(thm)],]) ).
thf('30_235',plain,
( ~ sP141
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf('31_236',plain,
( sP45
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf('32_237',plain,
( ~ sP48
| ~ sP107
| ~ sP112 ),
inference(prop_rule,[status(thm)],]) ).
thf('33_238',plain,
( sP28
| sP141 ),
inference(prop_rule,[status(thm)],]) ).
thf('34_239',plain,
( ~ sP21
| sP48
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf('35_240',plain,
( ~ sP73
| sP21
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf('36_241',plain,
sP26,
inference(prop_rule,[status(thm)],]) ).
thf('37_242',plain,
( sP5
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf('38_243',plain,
( ~ sP58
| ~ sP5
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf('39_244',plain,
( sP106
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf('40_245',plain,
( sP100
| ~ sP106 ),
inference(prop_rule,[status(thm)],]) ).
thf('41_246',plain,
( sP4
| ~ sP100 ),
inference(prop_rule,[status(thm)],]) ).
thf('42_247',plain,
( ~ sP101
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
% SZS status Theorem
% Mode: mode454
% Inferences: 1505
% SZS output start Proof
thf(ty_eigen__14,type,
eigen__14: $o ).
thf(ty_eigen__2_248,type,
eigen__2: $i ).
thf(ty_eigen__16_249,type,
eigen__16: $o ).
thf(ty_eps_250,type,
eps: ( $i > $o ) > $i ).
thf(ty_eigen__1_251,type,
eigen__1: $i ).
thf(ty_eigen__0_252,type,
eigen__0: $i ).
thf(ty_eigen__4_253,type,
eigen__4: $o ).
thf(ty_eigen__19,type,
eigen__19: $o ).
thf(ty_f0_254,type,
f0: $o > $o ).
thf(ty_eigen__3_255,type,
eigen__3: $i ).
thf(ty_eigen__8_256,type,
eigen__8: $o ).
thf(ty_eigen__9,type,
eigen__9: $o ).
thf(ty_f3_257,type,
f3: $o > $o ).
thf(ty_eigen__18,type,
eigen__18: $o ).
thf(ty_f2_258,type,
f2: $o > $o ).
thf(ty_f1_259,type,
f1: $o > $o ).
thf(h0_260,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ~ ( ~ ( ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( ( f0
= ( ^ [X3: $o] : $false ) )
=> ( X2 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X3: $o] : ~ X3 ) )
=> ( X2 != eigen__1 ) ) )
=> ~ ( ( f0
= ( ^ [X3: $o] : X3 ) )
=> ( X2 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X3: $o] : ~ $false ) )
=> ( X2 != X1 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X3: $o] : $false ) )
=> ( X2 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X3: $o] : ~ X3 ) )
=> ( X2 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X3: $o] : X3 ) )
=> ( X2 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X3: $o] : ~ $false ) )
=> ( X2 != X1 ) ) ) )
!= eigen__1 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X3: $o] : $false ) )
=> ( X2 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X3: $o] : ~ X3 ) )
=> ( X2 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X3: $o] : X3 ) )
=> ( X2 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X3: $o] : ~ $false ) )
=> ( X2 != X1 ) ) ) )
!= eigen__2 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X3: $o] : $false ) )
=> ( X2 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X3: $o] : ~ X3 ) )
=> ( X2 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X3: $o] : X3 ) )
=> ( X2 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X3: $o] : ~ $false ) )
=> ( X2 != X1 ) ) ) )
!= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( ( f0
= ( ^ [X5: $o] : $false ) )
=> ( X4 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X5: $o] : ~ X5 ) )
=> ( X4 != X1 ) ) )
=> ~ ( ( f0
= ( ^ [X5: $o] : X5 ) )
=> ( X4 != X2 ) ) )
=> ~ ( ( f0
= ( ^ [X5: $o] : ~ $false ) )
=> ( X4 != X3 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X5: $o] : $false ) )
=> ( X4 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X5: $o] : ~ X5 ) )
=> ( X4 != X1 ) ) )
=> ~ ( ( f1
= ( ^ [X5: $o] : X5 ) )
=> ( X4 != X2 ) ) )
=> ~ ( ( f1
= ( ^ [X5: $o] : ~ $false ) )
=> ( X4 != X3 ) ) ) )
!= X1 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X5: $o] : $false ) )
=> ( X4 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X5: $o] : ~ X5 ) )
=> ( X4 != X1 ) ) )
=> ~ ( ( f2
= ( ^ [X5: $o] : X5 ) )
=> ( X4 != X2 ) ) )
=> ~ ( ( f2
= ( ^ [X5: $o] : ~ $false ) )
=> ( X4 != X3 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X5: $o] : $false ) )
=> ( X4 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X5: $o] : ~ X5 ) )
=> ( X4 != X1 ) ) )
=> ~ ( ( f3
= ( ^ [X5: $o] : X5 ) )
=> ( X4 != X2 ) ) )
=> ~ ( ( f3
= ( ^ [X5: $o] : ~ $false ) )
=> ( X4 != X3 ) ) ) )
!= X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1_261,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__1
@ ^ [X1: $o] :
( ( f0 @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i,X4: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( ( f0
= ( ^ [X6: $o] : $false ) )
=> ( X5 != X1 ) )
=> ~ ( ( f0
= ( ^ [X6: $o] : ~ X6 ) )
=> ( X5 != X2 ) ) )
=> ~ ( ( f0
= ( ^ [X6: $o] : X6 ) )
=> ( X5 != X3 ) ) )
=> ~ ( ( f0
= ( ^ [X6: $o] : ~ $false ) )
=> ( X5 != X4 ) ) ) )
= X1 )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X6: $o] : $false ) )
=> ( X5 != X1 ) )
=> ~ ( ( f1
= ( ^ [X6: $o] : ~ X6 ) )
=> ( X5 != X2 ) ) )
=> ~ ( ( f1
= ( ^ [X6: $o] : X6 ) )
=> ( X5 != X3 ) ) )
=> ~ ( ( f1
= ( ^ [X6: $o] : ~ $false ) )
=> ( X5 != X4 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X6: $o] : $false ) )
=> ( X5 != X1 ) )
=> ~ ( ( f2
= ( ^ [X6: $o] : ~ X6 ) )
=> ( X5 != X2 ) ) )
=> ~ ( ( f2
= ( ^ [X6: $o] : X6 ) )
=> ( X5 != X3 ) ) )
=> ~ ( ( f2
= ( ^ [X6: $o] : ~ $false ) )
=> ( X5 != X4 ) ) ) )
!= X3 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X6: $o] : $false ) )
=> ( X5 != X1 ) )
=> ~ ( ( f3
= ( ^ [X6: $o] : ~ X6 ) )
=> ( X5 != X2 ) ) )
=> ~ ( ( f3
= ( ^ [X6: $o] : X6 ) )
=> ( X5 != X3 ) ) )
=> ~ ( ( f3
= ( ^ [X6: $o] : ~ $false ) )
=> ( X5 != X4 ) ) ) )
!= X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__1
@ ^ [X1: $o] :
( ( f1 @ X1 )
!= $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).
thf(eigendef_eigen__8_262,definition,
( eigen__8
= ( eps__1
@ ^ [X1: $o] :
( ( f2 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( ( f0
= ( ^ [X4: $o] : $false ) )
=> ( X3 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X4: $o] : ~ X4 ) )
=> ( X3 != eigen__1 ) ) )
=> ~ ( ( f0
= ( ^ [X4: $o] : X4 ) )
=> ( X3 != X1 ) ) )
=> ~ ( ( f0
= ( ^ [X4: $o] : ~ $false ) )
=> ( X3 != X2 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X4: $o] : $false ) )
=> ( X3 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X4: $o] : ~ X4 ) )
=> ( X3 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X4: $o] : X4 ) )
=> ( X3 != X1 ) ) )
=> ~ ( ( f1
= ( ^ [X4: $o] : ~ $false ) )
=> ( X3 != X2 ) ) ) )
!= eigen__1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X4: $o] : $false ) )
=> ( X3 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X4: $o] : ~ X4 ) )
=> ( X3 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X4: $o] : X4 ) )
=> ( X3 != X1 ) ) )
=> ~ ( ( f2
= ( ^ [X4: $o] : ~ $false ) )
=> ( X3 != X2 ) ) ) )
!= X1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X4: $o] : $false ) )
=> ( X3 != eigen__0 ) )
=> ~ ( ( f3
= ( ^ [X4: $o] : ~ X4 ) )
=> ( X3 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X4: $o] : X4 ) )
=> ( X3 != X1 ) ) )
=> ~ ( ( f3
= ( ^ [X4: $o] : ~ $false ) )
=> ( X3 != X2 ) ) ) )
!= X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4_263,definition,
( eigen__4
= ( eps__1
@ ^ [X1: $o] :
( ( f3 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__16_264,definition,
( eigen__16
= ( eps__1
@ ^ [X1: $o] :
( ( f1 @ X1 )
!= ( ~ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__1
@ ^ [X1: $o] :
( ( f2 @ X1 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__19,definition,
( eigen__19
= ( eps__1
@ ^ [X1: $o] :
( ( f1 @ X1 )
!= ( ~ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__19])]) ).
thf(sP1_265,plain,
( sP1
<=> ( ( f3 @ ~ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2_266,plain,
( sP2
<=> ( ( f0 @ eigen__14 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3_267,plain,
( sP3
<=> ( f3
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4_268,plain,
( sP4
<=> ( ( f0 @ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5_269,plain,
( sP5
<=> ( ( f1
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6_270,plain,
( sP6
<=> ( $false = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7_271,plain,
( sP7
<=> ( eigen__9 = eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8_272,plain,
( sP8
<=> eigen__14 ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9_273,plain,
( sP9
<=> ( ( f1 @ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10_274,plain,
( sP10
<=> eigen__19 ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11_275,plain,
( sP11
<=> ( ( f0
= ( ^ [X1: $o] : $false ) )
=> ( eigen__0 != eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12_276,plain,
( sP12
<=> ( f1 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13_277,plain,
( sP13
<=> ! [X1: $o] :
( ( f1 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14_278,plain,
( sP14
<=> ( ( f2
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__2 != eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15_279,plain,
( sP15
<=> ( sP11
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( eigen__0 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16_280,plain,
( sP16
<=> ( ( f0
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f0
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17_281,plain,
( sP17
<=> ! [X1: $i,X2: $i,X3: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( ( f0
= ( ^ [X5: $o] : $false ) )
=> ( X4 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X5: $o] : ~ X5 ) )
=> ( X4 != X1 ) ) )
=> ~ ( ( f0
= ( ^ [X5: $o] : X5 ) )
=> ( X4 != X2 ) ) )
=> ~ ( ( f0
= ( ^ [X5: $o] : ~ $false ) )
=> ( X4 != X3 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X5: $o] : $false ) )
=> ( X4 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X5: $o] : ~ X5 ) )
=> ( X4 != X1 ) ) )
=> ~ ( ( f1
= ( ^ [X5: $o] : X5 ) )
=> ( X4 != X2 ) ) )
=> ~ ( ( f1
= ( ^ [X5: $o] : ~ $false ) )
=> ( X4 != X3 ) ) ) )
!= X1 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X5: $o] : $false ) )
=> ( X4 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X5: $o] : ~ X5 ) )
=> ( X4 != X1 ) ) )
=> ~ ( ( f2
= ( ^ [X5: $o] : X5 ) )
=> ( X4 != X2 ) ) )
=> ~ ( ( f2
= ( ^ [X5: $o] : ~ $false ) )
=> ( X4 != X3 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X4: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X5: $o] : $false ) )
=> ( X4 != eigen__0 ) )
=> ~ ( sP3
=> ( X4 != X1 ) ) )
=> ~ ( ( f3
= ( ^ [X5: $o] : X5 ) )
=> ( X4 != X2 ) ) )
=> ~ ( ( f3
= ( ^ [X5: $o] : ~ $false ) )
=> ( X4 != X3 ) ) ) )
!= X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18_282,plain,
( sP18
<=> ( eigen__3 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19_283,plain,
( sP19
<=> ! [X1: $o] :
( ( f0 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20_284,plain,
( sP20
<=> ! [X1: $o] :
( ( f1 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21_285,plain,
( sP21
<=> ( f0
= ( ^ [X1: $o] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22_286,plain,
( sP22
<=> ( ( ~ $false )
= eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23_287,plain,
( sP23
<=> ( ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP21
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24_288,plain,
( sP24
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25_289,plain,
( sP25
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26_290,plain,
( sP26
<=> ( ( f2 @ $false )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27_291,plain,
( sP27
<=> ( f1
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28_292,plain,
( sP28
<=> ( f1 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29_293,plain,
( sP29
<=> ( ~ ( ~ ( ( ( f3
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( sP3
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30_294,plain,
( sP30
<=> ( ~ ( ~ ( ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP27
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X1: $o] : ~ X1 ) )
=> ~ sP25 ) )
=> ~ sP5 )
=> ~ ( sP27
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP27
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31_295,plain,
( sP31
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32_296,plain,
( sP32
<=> ( ( f0
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP21
=> ( X1 != eigen__0 ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33_297,plain,
( sP33
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP27
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34_298,plain,
( sP34
<=> ( f2 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35_299,plain,
( sP35
<=> ( sP28 = $false ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36_300,plain,
( sP36
<=> ! [X1: $o] :
( ( f2 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37_301,plain,
( sP37
<=> ( f1
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38_302,plain,
( sP38
<=> ( ( f2 @ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39_303,plain,
( sP39
<=> ( ~ sP15
=> ~ ( ( f0
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__0 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40_304,plain,
( sP40
<=> ( sP10 = eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41_305,plain,
( sP41
<=> ( ~ ( ( ( f3
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( sP3
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f3
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42_306,plain,
( sP42
<=> ( ~ ( ~ ( ( ( f3
= ( ^ [X1: $o] : $false ) )
=> ( eigen__3 != eigen__0 ) )
=> ~ ( sP3
=> ( eigen__3 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__3 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X1: $o] : ~ $false ) )
=> ~ sP18 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43_307,plain,
( sP43
<=> ( ~ ( ( ( f2
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X1: $o] : ~ X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X1: $o] : X1 ) )
=> ~ sP31 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44_308,plain,
( sP44
<=> ( f2 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45_309,plain,
( sP45
<=> ( f3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46_310,plain,
( sP46
<=> ( f3
= ( ^ [X1: $o] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47_311,plain,
( sP47
<=> ( ( f2
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ X2 ) )
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48_312,plain,
( sP48
<=> ( eigen__18 = sP10 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49_313,plain,
( sP49
<=> ( ( f2 @ eigen__9 )
= eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50_314,plain,
( sP50
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP46
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51_315,plain,
( sP51
<=> ! [X1: $o] :
( ( f3 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52_316,plain,
( sP52
<=> ( sP8 = $false ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53_317,plain,
( sP53
<=> ( f2
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54_318,plain,
( sP54
<=> ( ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( eigen__1 != eigen__0 ) )
=> ~ ( sP37
=> ( eigen__1 != eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55_319,plain,
( sP55
<=> ( ( f2
= ( ^ [X1: $o] : X1 ) )
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56_320,plain,
( sP56
<=> ( ( f0 @ ~ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57_321,plain,
( sP57
<=> ( f2
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58_322,plain,
( sP58
<=> ( sP12 = $false ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59_323,plain,
( sP59
<=> eigen__8 ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60_324,plain,
( sP60
<=> ! [X1: $o] :
( ( f0 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61_325,plain,
( sP61
<=> ( ~ ( ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP37
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP27
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( sP37
=> ~ sP25 ) )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62_326,plain,
( sP62
<=> ( sP12
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63_327,plain,
( sP63
<=> ( sP16
=> ~ sP32 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64_328,plain,
( sP64
<=> ( ~ ( ~ sP23
=> ~ sP31 )
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65_329,plain,
( sP65
<=> ! [X1: $o] :
( ( f3 @ X1 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66_330,plain,
( sP66
<=> ( ~ sP23
=> ~ sP31 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67_331,plain,
( sP67
<=> ! [X1: $o] :
( ( f2 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68_332,plain,
( sP68
<=> ( f0
= ( ^ [X1: $o] : ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69_333,plain,
( sP69
<=> ! [X1: $i,X2: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP21
=> ( X3 != eigen__0 ) )
=> ~ ( sP68
=> ( X3 != eigen__1 ) ) )
=> ~ ( ( f0
= ( ^ [X4: $o] : X4 ) )
=> ( X3 != X1 ) ) )
=> ~ ( ( f0
= ( ^ [X4: $o] : ~ $false ) )
=> ( X3 != X2 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X4: $o] : $false ) )
=> ( X3 != eigen__0 ) )
=> ~ ( sP37
=> ( X3 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X4: $o] : X4 ) )
=> ( X3 != X1 ) ) )
=> ~ ( sP27
=> ( X3 != X2 ) ) ) )
!= eigen__1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X4: $o] : $false ) )
=> ( X3 != eigen__0 ) )
=> ~ ( sP57
=> ( X3 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X4: $o] : X4 ) )
=> ( X3 != X1 ) ) )
=> ~ ( sP53
=> ( X3 != X2 ) ) ) )
!= X1 ) )
=> ( ( eps
@ ^ [X3: $i] :
( ~ ( ~ ( ( sP46
=> ( X3 != eigen__0 ) )
=> ~ ( sP3
=> ( X3 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X4: $o] : X4 ) )
=> ( X3 != X1 ) ) )
=> ~ ( ( f3
= ( ^ [X4: $o] : ~ $false ) )
=> ( X3 != X2 ) ) ) )
!= X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70_334,plain,
( sP70
<=> ( ( f1 @ sP10 )
= ( ~ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71_335,plain,
( sP71
<=> ( ( ~ $false )
= eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72_336,plain,
( sP72
<=> ( f1 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73_337,plain,
( sP73
<=> eigen__9 ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74_338,plain,
( sP74
<=> ( ( f0
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP21
=> ( X1 != eigen__0 ) )
=> ~ ( sP68
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75_339,plain,
( sP75
<=> ( f3 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76_340,plain,
( sP76
<=> ( ~ sP63
=> ~ sP74 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77_341,plain,
( sP77
<=> ( ( ( f2
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP57
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP53
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( sP57
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP57
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP53
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78_342,plain,
( sP78
<=> ( f0
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79_343,plain,
( sP79
<=> eigen__16 ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80_344,plain,
( sP80
<=> ( f1 @ eigen__18 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81_345,plain,
( sP81
<=> ( sP57
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP57
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP53
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82_346,plain,
( sP82
<=> ( ~ ( ~ sP54
=> ~ ( ( f1
= ( ^ [X1: $o] : X1 ) )
=> ( eigen__1 != eigen__2 ) ) )
=> ~ ( sP27
=> ( eigen__1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83_347,plain,
( sP83
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( ( f2
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP57
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f2
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP53
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84_348,plain,
( sP84
<=> ( ~ sP76
=> ~ ( ( f0
= ( ^ [X1: $o] : ~ $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP21
=> ( X1 != eigen__0 ) )
=> ~ ( sP68
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85_349,plain,
( sP85
<=> ( ( ( f1
= ( ^ [X1: $o] : $false ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( ( f1
= ( ^ [X2: $o] : $false ) )
=> ( X1 != eigen__0 ) )
=> ~ ( sP37
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP27
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( sP37
=> ~ sP25 ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86_350,plain,
( sP86
<=> ! [X1: $o] :
( ( f1 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87_351,plain,
( sP87
<=> ( ( f0 @ $false )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88_352,plain,
( sP88
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( sP21
=> ( X1 != eigen__0 ) )
=> ~ ( sP68
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89_353,plain,
( sP89
<=> ! [X1: $o] :
( ( f3 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90_354,plain,
( sP90
<=> ( ( ~ $false )
= sP59 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91_355,plain,
( sP91
<=> ( f1
= ( ^ [X1: $o] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92_356,plain,
( sP92
<=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP21
=> ( X1 != eigen__0 ) )
=> ~ ( sP68
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f0
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93_357,plain,
( sP93
<=> ( sP27
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP91
=> ( X1 != eigen__0 ) )
=> ~ ( sP37
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f1
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP27
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94_358,plain,
( sP94
<=> ( f0
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95_359,plain,
( sP95
<=> ( eigen__0 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96_360,plain,
( sP96
<=> ( ( f3
= ( ^ [X1: $o] : ~ $false ) )
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97_361,plain,
( sP97
<=> ! [X1: $o] :
( ( f2 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98_362,plain,
( sP98
<=> ( ~ ( ~ ( ( ( f2
= ( ^ [X1: $o] : $false ) )
=> ( eigen__2 != eigen__0 ) )
=> ~ ( sP57
=> ( eigen__2 != eigen__1 ) ) )
=> ~ sP14 )
=> ~ ( sP53
=> ( eigen__2 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99_363,plain,
( sP99
<=> ( ( f3 @ $false )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100_364,plain,
( sP100
<=> ( sP37
=> ( eigen__1 != eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101_365,plain,
( sP101
<=> ( $false = sP79 ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102_366,plain,
( sP102
<=> ( sP80 = $false ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103_367,plain,
( sP103
<=> ( sP8
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104_368,plain,
( sP104
<=> ( ( sP46
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP46
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) )
=> ~ ( sP3
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP46
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105_369,plain,
( sP105
<=> ( f3 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106_370,plain,
( sP106
<=> ( f1
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107_371,plain,
( sP107
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP21
=> ( X5 != X1 ) )
=> ~ ( sP68
=> ( X5 != X2 ) ) )
=> ~ ( sP78
=> ( X5 != X3 ) ) )
=> ~ ( sP94
=> ( X5 != X4 ) ) ) )
= X1 )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP91
=> ( X5 != X1 ) )
=> ~ ( sP37
=> ( X5 != X2 ) ) )
=> ~ ( sP106
=> ( X5 != X3 ) ) )
=> ~ ( sP27
=> ( X5 != X4 ) ) ) )
!= X2 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( ( f2
= ( ^ [X6: $o] : $false ) )
=> ( X5 != X1 ) )
=> ~ ( sP57
=> ( X5 != X2 ) ) )
=> ~ ( ( f2
= ( ^ [X6: $o] : X6 ) )
=> ( X5 != X3 ) ) )
=> ~ ( sP53
=> ( X5 != X4 ) ) ) )
!= X3 ) )
=> ( ( eps
@ ^ [X5: $i] :
( ~ ( ~ ( ( sP46
=> ( X5 != X1 ) )
=> ~ ( sP3
=> ( X5 != X2 ) ) )
=> ~ ( ( f3
= ( ^ [X6: $o] : X6 ) )
=> ( X5 != X3 ) ) )
=> ~ ( ( f3
= ( ^ [X6: $o] : ~ $false ) )
=> ( X5 != X4 ) ) ) )
!= X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108_372,plain,
( sP108
<=> ( sP3
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP46
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109_373,plain,
( sP109
<=> ( ~ sP39
=> ~ ( sP94
=> ( eigen__0 != eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110_374,plain,
( sP110
<=> ( f2
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111_375,plain,
( sP111
<=> ( ( f2 @ sP59 )
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112_376,plain,
( sP112
<=> ( ( f3
= ( ^ [X1: $o] : X1 ) )
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP46
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : X2 ) )
=> ( X1 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X2: $o] : ~ $false ) )
=> ( X1 != eigen__3 ) ) ) )
!= eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113_377,plain,
( sP113
<=> ( sP94
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP21
=> ( X1 != eigen__0 ) )
=> ~ ( sP68
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP78
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP94
=> ( X1 != eigen__3 ) ) ) )
!= eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114_378,plain,
( sP114
<=> ( f0 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115_379,plain,
( sP115
<=> ( f0 @ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116_380,plain,
( sP116
<=> eigen__18 ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117_381,plain,
( sP117
<=> ( ( f0 @ ~ $false )
= $false ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118_382,plain,
( sP118
<=> ! [X1: $o] :
( ( f2 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119_383,plain,
( sP119
<=> ( ~ sP54
=> ~ ( sP106
=> ( eigen__1 != eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120_384,plain,
( sP120
<=> ( f2
= ( ^ [X1: $o] : $false ) ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121_385,plain,
( sP121
<=> ( f2 @ sP59 ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122_386,plain,
( sP122
<=> ! [X1: $i] :
~ ( ~ ( ~ ( ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP21
=> ( X2 != eigen__0 ) )
=> ~ ( sP68
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP78
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP94
=> ( X2 != X1 ) ) ) )
= eigen__0 )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP91
=> ( X2 != eigen__0 ) )
=> ~ ( sP37
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP106
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP27
=> ( X2 != X1 ) ) ) )
!= eigen__1 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP120
=> ( X2 != eigen__0 ) )
=> ~ ( sP57
=> ( X2 != eigen__1 ) ) )
=> ~ ( sP110
=> ( X2 != eigen__2 ) ) )
=> ~ ( sP53
=> ( X2 != X1 ) ) ) )
!= eigen__2 ) )
=> ( ( eps
@ ^ [X2: $i] :
( ~ ( ~ ( ( sP46
=> ( X2 != eigen__0 ) )
=> ~ ( sP3
=> ( X2 != eigen__1 ) ) )
=> ~ ( ( f3
= ( ^ [X3: $o] : X3 ) )
=> ( X2 != eigen__2 ) ) )
=> ~ ( ( f3
= ( ^ [X3: $o] : ~ $false ) )
=> ( X2 != X1 ) ) ) )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123_387,plain,
( sP123
<=> ( f3
= ( ^ [X1: $o] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124_388,plain,
( sP124
<=> ( sP34 = $false ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125_389,plain,
( sP125
<=> ! [X1: $o] :
( ( f3 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126_390,plain,
( sP126
<=> ! [X1: $o] :
( ( f0 @ X1 )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127_391,plain,
( sP127
<=> ( sP123
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128_392,plain,
( sP128
<=> ( ~ ( ( sP120
=> ( eigen__2 != eigen__0 ) )
=> ~ ( sP57
=> ( eigen__2 != eigen__1 ) ) )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129_393,plain,
( sP129
<=> ( f3
= ( ^ [X1: $o] : X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130_394,plain,
( sP130
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131_395,plain,
( sP131
<=> ( f1 @ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132_396,plain,
( sP132
<=> ( sP116
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133_397,plain,
( sP133
<=> eigen__4 ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134_398,plain,
( sP134
<=> ( sP72
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135_399,plain,
( sP135
<=> ( sP105 = $false ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136_400,plain,
( sP136
<=> ( sP75 = $false ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137_401,plain,
( sP137
<=> ( sP120
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP120
=> ( X1 != eigen__0 ) )
=> ~ ( sP57
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP110
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP53
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP137])]) ).
thf(sP138_402,plain,
( sP138
<=> ! [X1: $o] :
( ( f0 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139_403,plain,
( sP139
<=> ( sP37
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140_404,plain,
( sP140
<=> ( sP34
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141_405,plain,
( sP141
<=> ( f0 @ ~ $false ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142_406,plain,
( sP142
<=> ( sP91
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP91
=> ( X1 != eigen__0 ) )
=> ~ ( sP37
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP106
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP27
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143_407,plain,
( sP143
<=> ( f2 @ sP73 ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144_408,plain,
( sP144
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145_409,plain,
( sP145
<=> ( ~ sP43
=> ~ sP47 ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146_410,plain,
( sP146
<=> ( sP45
= ( ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP146])]) ).
thf(sP147,plain,
( sP147
<=> ( sP46
=> ( ( eps
@ ^ [X1: $i] :
( ~ ( ~ ( ( sP46
=> ( X1 != eigen__0 ) )
=> ~ ( sP3
=> ( X1 != eigen__1 ) ) )
=> ~ ( sP129
=> ( X1 != eigen__2 ) ) )
=> ~ ( sP123
=> ( X1 != eigen__3 ) ) ) )
!= eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP147])]) ).
thf(sP148,plain,
( sP148
<=> $false ),
introduced(definition,[new_symbols(definition,[sP148])]) ).
thf(sP149,plain,
( sP149
<=> ! [X1: $o] :
( ( f1 @ X1 )
= ( ~ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP149])]) ).
thf(def_case_411,definition,
( case
= ( ^ [X1: $o > $o,X2: $i,X3: $i,X4: $i,X5: $i] :
( eps
@ ^ [X6: $i] :
( ~ ( ~ ( ( ( X1
= ( ^ [X7: $o] : sP148 ) )
=> ( X6 != X2 ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ X7 ) )
=> ( X6 != X3 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : X7 ) )
=> ( X6 != X4 ) ) )
=> ~ ( ( X1
= ( ^ [X7: $o] : ~ sP148 ) )
=> ( X6 != X5 ) ) ) ) ) ) ).
thf(conj_412,conjecture,
sP107 ).
thf(h2_413,negated_conjecture,
~ sP107,
inference(assume_negation,[status(cth)],[conj]) ).
thf('1_414',plain,
( sP139
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf('2_415',plain,
( ~ sP86
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf('3_416',plain,
( ~ sP91
| sP86 ),
inference(prop_rule,[status(thm)],]) ).
thf('4_417',plain,
( sP142
| sP91 ),
inference(prop_rule,[status(thm)],]) ).
thf('5_418',plain,
( ~ sP138
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf('6_419',plain,
( ~ sP68
| sP138 ),
inference(prop_rule,[status(thm)],]) ).
thf('7_420',plain,
( sP32
| sP68 ),
inference(prop_rule,[status(thm)],]) ).
thf('8_421',plain,
( sP16
| sP92 ),
inference(prop_rule,[status(thm)],]) ).
thf('9_422',plain,
( ~ sP67
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf('10_423',plain,
( ~ sP57
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf('11_424',plain,
( sP81
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf('12_425',plain,
( ~ sP124
| ~ sP34
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf('13_426',plain,
( ~ sP97
| sP124 ),
inference(all_rule,[status(thm)],]) ).
thf('14_427',plain,
( ~ sP120
| sP97 ),
inference(prop_rule,[status(thm)],]) ).
thf('15_428',plain,
( sP137
| sP120 ),
inference(prop_rule,[status(thm)],]) ).
thf('16_429',plain,
( sP48
| sP116
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf('17_430',plain,
( sP40
| ~ sP10
| ~ sP79 ),
inference(prop_rule,[status(thm)],]) ).
thf('18_431',plain,
( sP132
| ~ sP116
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf('19_432',plain,
( sP101
| sP148
| sP79 ),
inference(prop_rule,[status(thm)],]) ).
thf('20_433',plain,
( ~ sP35
| ~ sP28
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf('21_434',plain,
( ~ sP20
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf('22_435',plain,
( ~ sP106
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf('23_436',plain,
( sP5
| sP106 ),
inference(prop_rule,[status(thm)],]) ).
thf('24_437',plain,
( ~ sP85
| ~ sP142
| ~ sP139 ),
inference(prop_rule,[status(thm)],]) ).
thf('25_438',plain,
( sP103
| ~ sP8
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf('26_439',plain,
( sP52
| sP8
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf('27_440',plain,
( ~ sP136
| ~ sP75
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf('28_441',plain,
( ~ sP62
| sP12
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf('29_442',plain,
( ~ sP126
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf('30_443',plain,
( ~ sP78
| sP126 ),
inference(prop_rule,[status(thm)],]) ).
thf('31_444',plain,
( sP74
| sP78 ),
inference(prop_rule,[status(thm)],]) ).
thf('32_445',plain,
( ~ sP63
| ~ sP16
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf('33_446',plain,
( ~ sP51
| sP136 ),
inference(all_rule,[status(thm)],]) ).
thf('34_447',plain,
( ~ sP3
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf('35_448',plain,
( sP108
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf('36_449',plain,
( ~ sP89
| sP135 ),
inference(all_rule,[status(thm)],]) ).
thf('37_450',plain,
( ~ sP46
| sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf('38_451',plain,
( sP147
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf('39_452',plain,
( sP71
| sP148
| ~ sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf('40_453',plain,
( sP7
| sP73
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf('41_454',plain,
( sP90
| sP148
| ~ sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf('42_455',plain,
( sP55
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP77
| ~ sP137
| ~ sP81 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP80
| sP131
| ~ sP48 ),
inference(mating_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP131
| sP72
| ~ sP40 ),
inference(mating_rule,[status(thm)],]) ).
thf(46,plain,
( sP70
| ~ sP131
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP70
| sP131
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( sP149
| ~ sP70 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__19]) ).
thf(49,plain,
( sP37
| ~ sP149 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP80
| sP12
| ~ sP132 ),
inference(mating_rule,[status(thm)],]) ).
thf(51,plain,
( sP102
| sP80
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP86
| ~ sP102 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__18]) ).
thf(53,plain,
( ~ sP28
| sP72
| ~ sP101 ),
inference(mating_rule,[status(thm)],]) ).
thf(54,plain,
( sP134
| ~ sP72
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP13
| ~ sP134 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__16]) ).
thf(56,plain,
( ~ sP13
| sP62 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP27
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( sP93
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP61
| sP85
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP115
| sP141
| ~ sP103 ),
inference(mating_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP115
| sP114
| ~ sP52 ),
inference(mating_rule,[status(thm)],]) ).
thf(62,plain,
( sP2
| sP115
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( sP19
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__14]) ).
thf(64,plain,
( sP21
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP56
| sP141
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP4
| sP114
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP60
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP94
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( sP113
| sP94 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP76
| sP63
| ~ sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
sP130,
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
sP95,
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( sP22
| sP148
| ~ sP133 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( sP6
| sP148
| sP133 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP135
| ~ sP105
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP125
| sP135 ),
inference(all_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP129
| sP125 ),
inference(prop_rule,[status(thm)],]) ).
thf(78,plain,
( sP112
| sP129 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( ~ sP104
| ~ sP147
| ~ sP108 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( ~ sP34
| sP143
| ~ sP71 ),
inference(mating_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP143
| sP121
| ~ sP7 ),
inference(mating_rule,[status(thm)],]) ).
thf(82,plain,
( sP49
| ~ sP143
| ~ sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(83,plain,
( sP49
| sP143
| sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( sP118
| ~ sP49 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9]) ).
thf(85,plain,
( sP110
| ~ sP118 ),
inference(prop_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP34
| sP121
| ~ sP90 ),
inference(mating_rule,[status(thm)],]) ).
thf(87,plain,
( sP111
| ~ sP121
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(88,plain,
( sP36
| ~ sP111 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(89,plain,
sP144,
inference(prop_rule,[status(thm)],]) ).
thf(90,plain,
( ~ sP38
| sP44
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(91,plain,
( ~ sP36
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(92,plain,
( ~ sP53
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(93,plain,
( sP47
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(94,plain,
( ~ sP43
| sP77
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(95,plain,
( ~ sP100
| ~ sP37
| ~ sP130 ),
inference(prop_rule,[status(thm)],]) ).
thf(96,plain,
( sP54
| sP100 ),
inference(prop_rule,[status(thm)],]) ).
thf(97,plain,
( sP119
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(98,plain,
( sP82
| ~ sP119 ),
inference(prop_rule,[status(thm)],]) ).
thf(99,plain,
( ~ sP30
| sP61
| ~ sP93 ),
inference(prop_rule,[status(thm)],]) ).
thf(100,plain,
( ~ sP33
| ~ sP82 ),
inference(all_rule,[status(thm)],]) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ) ).
thf(101,plain,
( sP30
| sP33 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(102,plain,
( ~ sP11
| ~ sP21
| ~ sP95 ),
inference(prop_rule,[status(thm)],]) ).
thf(103,plain,
( sP15
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(104,plain,
( sP39
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(105,plain,
( sP109
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(106,plain,
( ~ sP84
| sP76
| ~ sP113 ),
inference(prop_rule,[status(thm)],]) ).
thf(107,plain,
( ~ sP88
| ~ sP109 ),
inference(all_rule,[status(thm)],]) ).
thf(108,plain,
( sP84
| sP88 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(109,plain,
sP18,
inference(prop_rule,[status(thm)],]) ).
thf(110,plain,
( ~ sP75
| sP45
| ~ sP22 ),
inference(mating_rule,[status(thm)],]) ).
thf(111,plain,
( ~ sP105
| sP45
| ~ sP6 ),
inference(mating_rule,[status(thm)],]) ).
thf(112,plain,
( sP146
| ~ sP45
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(113,plain,
( sP65
| ~ sP146 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).
thf(114,plain,
( sP123
| ~ sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(115,plain,
( sP96
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(116,plain,
( ~ sP41
| sP104
| ~ sP112 ),
inference(prop_rule,[status(thm)],]) ).
thf(117,plain,
( ~ sP14
| ~ sP110
| ~ sP144 ),
inference(prop_rule,[status(thm)],]) ).
thf(118,plain,
( sP128
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(119,plain,
( sP98
| ~ sP128 ),
inference(prop_rule,[status(thm)],]) ).
thf(120,plain,
( ~ sP145
| sP43
| ~ sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(121,plain,
( ~ sP83
| ~ sP98 ),
inference(all_rule,[status(thm)],]) ).
thf(122,plain,
( sP145
| sP83 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(123,plain,
( ~ sP23
| ~ sP92
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(124,plain,
( ~ sP127
| ~ sP123
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(125,plain,
( sP42
| sP127 ),
inference(prop_rule,[status(thm)],]) ).
thf(126,plain,
( ~ sP29
| sP41
| ~ sP96 ),
inference(prop_rule,[status(thm)],]) ).
thf(127,plain,
( ~ sP24
| ~ sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(128,plain,
( sP29
| sP24 ),
inference(choice_rule,[status(thm)],[choiceax]) ).
thf(129,plain,
( ~ sP66
| sP23
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(130,plain,
( ~ sP64
| sP66
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(131,plain,
( sP122
| sP64 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(132,plain,
( sP69
| ~ sP122 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(133,plain,
~ sP148,
inference(prop_rule,[status(thm)],]) ).
thf(134,plain,
( sP17
| ~ sP69 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(135,plain,
( ~ sP87
| ~ sP114
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(136,plain,
( ~ sP117
| ~ sP141
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(137,plain,
( ~ sP9
| sP28
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(138,plain,
( ~ sP58
| ~ sP12
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(139,plain,
( ~ sP26
| ~ sP44
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(140,plain,
( ~ sP140
| sP34
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(141,plain,
( ~ sP99
| sP105
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(142,plain,
( ~ sP1
| sP75
| sP148 ),
inference(prop_rule,[status(thm)],]) ).
thf(143,plain,
( sP107
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(f0f,axiom,
sP87 ).
thf(f0t,axiom,
sP117 ).
thf(f1f,axiom,
sP9 ).
thf(f1t,axiom,
sP58 ).
thf(f2f,axiom,
sP26 ).
thf(f2t,axiom,
sP140 ).
thf(f3f,axiom,
sP99 ).
thf(f3t,axiom,
sP1 ).
thf(144,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,f0f,f0t,f1f,f1t,f2f,f2t,f3f,f3t,h2]) ).
thf(145,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[144,h1]) ).
thf(146,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[145,h0]) ).
thf(0,theorem,
sP107,
inference(contra,[status(thm),contra(discharge,[h2])],[144,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO544^1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n012.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 : 600
% 0.13/0.34 % DateTime : Sat Jul 9 11:08:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.89/1.14 % SZS status Theorem
% 0.89/1.14 % Mode: mode213
% 0.89/1.14 % Inferences: 6541
% 0.89/1.14 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------