%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : GRA082^1 : TPTP v9.2.0. Released v9.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 01:32:21 PM UTC 2025
% Result : Unsatisfiable 2.29s 2.48s
% Output : Proof 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1137
% Syntax : Number of formulae : 1141 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 3295 ( 104 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 8625 (1968 ~; 957 |; 0 &;4507 @)
% ( 520 <=>; 673 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 528 ( 526 usr; 524 con; 0-2 aty)
% Number of variables : 184 ( 4 ^; 179 !; 1 ?; 184 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_b,type,
b: $i > $i > $o ).
thf(ty_r,type,
r: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( ( eigen__0 @ X1 )
= ( eigen__0 @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
!= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eigen__1
!= ( eigen__0 @ eigen__1 ) )
=> ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ~ ( ( b @ ( eigen__0 @ eigen__1 ) @ X1 )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__1
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( b @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
!= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ~ ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
!= X1 )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ~ ( ~ sP19
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
!= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ( ( eigen__0 @ eigen__1 )
!= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) )
=> ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ eigen__1 ) )
=> ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( ( eigen__0 @ eigen__1 )
!= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( eigen__1
!= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( eigen__0 @ eigen__1 )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ sP25 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( eigen__1
!= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ~ ( sP45
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( b @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
!= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ eigen__1 ) @ eigen__1 )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( r @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
=> sP46 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i] :
( ~ ( ~ sP44
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ~ ( sP22
=> ~ sP25 )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) )
=> ~ sP45 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
= ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP62
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( sP62
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( b @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ! [X1: $i] :
( ( ( eigen__0 @ eigen__1 )
= ( eigen__0 @ X1 ) )
=> ( eigen__1 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
!= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ~ ( sP22
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ! [X1: $i] :
( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
= ( eigen__0 @ X1 ) )
=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( ~ ( ~ ( sP25
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP50 )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( b @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( ~ sP4
=> ~ ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ! [X1: $i] :
( ~ ( ~ ( sP62
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( ~ sP44
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( ~ ( ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ sP62 )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [X1: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( b @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( sP61
=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( ~ sP48
=> ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ! [X1: $i] :
( ~ ( ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( b @ eigen__1 @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( ~ ( ( b @ eigen__1 @ ( eigen__0 @ eigen__1 ) )
=> ~ ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP97 ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP50 )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ( ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ( ( ( eigen__0 @ eigen__1 )
!= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ( ~ ( sP25
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( ~ sP47
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( ~ sP3
=> ( b @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( ~ ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
!= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( ( eigen__1
!= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ! [X1: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ( ~ sP43
=> sP121 ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ( ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
!= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130,plain,
( sP130
<=> ( ~ sP63
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131,plain,
( sP131
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132,plain,
( sP132
<=> ! [X1: $i] :
( ~ ( sP111
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133,plain,
( sP133
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP97 ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134,plain,
( sP134
<=> ( ~ sP33
=> sP97 ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135,plain,
( sP135
<=> ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136,plain,
( sP136
<=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137,plain,
( sP137
<=> ( ~ ( ~ ( sP50
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ sP62 )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP137])]) ).
thf(sP138,plain,
( sP138
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ eigen__1 @ X1 )
=> ~ ( r @ eigen__1 @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139,plain,
( sP139
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ sP62 )
=> ~ sP125 ) ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140,plain,
( sP140
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141,plain,
( sP141
<=> ( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142,plain,
( sP142
<=> ! [X1: $i] :
( ~ ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
!= X1 )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143,plain,
( sP143
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144,plain,
( sP144
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145,plain,
( sP145
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP125
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146,plain,
( sP146
<=> ( ( ( eigen__0 @ eigen__1 )
!= eigen__1 )
=> sP62 ) ),
introduced(definition,[new_symbols(definition,[sP146])]) ).
thf(sP147,plain,
( sP147
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP147])]) ).
thf(sP148,plain,
( sP148
<=> ( sP110
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP148])]) ).
thf(sP149,plain,
( sP149
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP149])]) ).
thf(sP150,plain,
( sP150
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP150])]) ).
thf(sP151,plain,
( sP151
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP136 ) ),
introduced(definition,[new_symbols(definition,[sP151])]) ).
thf(sP152,plain,
( sP152
<=> ( ~ sP54
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP152])]) ).
thf(sP153,plain,
( sP153
<=> ! [X1: $i] :
( ~ ( sP110
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP153])]) ).
thf(sP154,plain,
( sP154
<=> ( ( ( eigen__0 @ eigen__1 )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP154])]) ).
thf(sP155,plain,
( sP155
<=> ( ~ ( ~ sP53
=> ~ sP120 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP155])]) ).
thf(sP156,plain,
( sP156
<=> ( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ sP25 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP156])]) ).
thf(sP157,plain,
( sP157
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP157])]) ).
thf(sP158,plain,
( sP158
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ sP50 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP158])]) ).
thf(sP159,plain,
( sP159
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP25
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP159])]) ).
thf(sP160,plain,
( sP160
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP160])]) ).
thf(sP161,plain,
( sP161
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ sP149 ) ),
introduced(definition,[new_symbols(definition,[sP161])]) ).
thf(sP162,plain,
( sP162
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP149 ) ),
introduced(definition,[new_symbols(definition,[sP162])]) ).
thf(sP163,plain,
( sP163
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP163])]) ).
thf(sP164,plain,
( sP164
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP164])]) ).
thf(sP165,plain,
( sP165
<=> ( ( eigen__0 @ eigen__1 )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP165])]) ).
thf(sP166,plain,
( sP166
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP166])]) ).
thf(sP167,plain,
( sP167
<=> ! [X1: $i] :
( ~ sP104
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP167])]) ).
thf(sP168,plain,
( sP168
<=> ( ~ ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
!= eigen__1 )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP168])]) ).
thf(sP169,plain,
( sP169
<=> ( ( eigen__0 @ eigen__1 )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP169])]) ).
thf(sP170,plain,
( sP170
<=> ( sP22
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP170])]) ).
thf(sP171,plain,
( sP171
<=> ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP171])]) ).
thf(sP172,plain,
( sP172
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP172])]) ).
thf(sP173,plain,
( sP173
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP173])]) ).
thf(sP174,plain,
( sP174
<=> ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP174])]) ).
thf(sP175,plain,
( sP175
<=> ( sP149
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP175])]) ).
thf(sP176,plain,
( sP176
<=> ( sP25
=> ~ sP160 ) ),
introduced(definition,[new_symbols(definition,[sP176])]) ).
thf(sP177,plain,
( sP177
<=> ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP177])]) ).
thf(sP178,plain,
( sP178
<=> ( ~ ( sP177
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP178])]) ).
thf(sP179,plain,
( sP179
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP179])]) ).
thf(sP180,plain,
( sP180
<=> ( ~ sP151
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP180])]) ).
thf(sP181,plain,
( sP181
<=> ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP181])]) ).
thf(sP182,plain,
( sP182
<=> ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP182])]) ).
thf(sP183,plain,
( sP183
<=> ( ~ sP69
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP183])]) ).
thf(sP184,plain,
( sP184
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP157 )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP184])]) ).
thf(sP185,plain,
( sP185
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP185])]) ).
thf(sP186,plain,
( sP186
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP186])]) ).
thf(sP187,plain,
( sP187
<=> ( ~ sP74
=> ~ sP125 ) ),
introduced(definition,[new_symbols(definition,[sP187])]) ).
thf(sP188,plain,
( sP188
<=> ( ~ sP15
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP188])]) ).
thf(sP189,plain,
( sP189
<=> ( ~ sP79
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP189])]) ).
thf(sP190,plain,
( sP190
<=> ! [X1: $i] :
( ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= ( eigen__0 @ X1 ) )
=> ( ( eigen__0 @ eigen__1 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP190])]) ).
thf(sP191,plain,
( sP191
<=> ( ~ sP99
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP191])]) ).
thf(sP192,plain,
( sP192
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP192])]) ).
thf(sP193,plain,
( sP193
<=> ( ~ ( sP50
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP193])]) ).
thf(sP194,plain,
( sP194
<=> ! [X1: $i] :
( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ X1 ) )
=> ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP194])]) ).
thf(sP195,plain,
( sP195
<=> ( sP45
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP195])]) ).
thf(sP196,plain,
( sP196
<=> ! [X1: $i] :
( ~ sP79
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP196])]) ).
thf(sP197,plain,
( sP197
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP197])]) ).
thf(sP198,plain,
( sP198
<=> ( ~ sP35
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP198])]) ).
thf(sP199,plain,
( sP199
<=> ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP199])]) ).
thf(sP200,plain,
( sP200
<=> ( sP111
=> ~ sP157 ) ),
introduced(definition,[new_symbols(definition,[sP200])]) ).
thf(sP201,plain,
( sP201
<=> ! [X1: $i] :
( ~ ( ~ sP131
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP201])]) ).
thf(sP202,plain,
( sP202
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP202])]) ).
thf(sP203,plain,
( sP203
<=> ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP203])]) ).
thf(sP204,plain,
( sP204
<=> ( sP22
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP204])]) ).
thf(sP205,plain,
( sP205
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP205])]) ).
thf(sP206,plain,
( sP206
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP206])]) ).
thf(sP207,plain,
( sP207
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> sP106 ) ),
introduced(definition,[new_symbols(definition,[sP207])]) ).
thf(sP208,plain,
( sP208
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP208])]) ).
thf(sP209,plain,
( sP209
<=> ( ~ ( sP62
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP209])]) ).
thf(sP210,plain,
( sP210
<=> ! [X1: $i,X2: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP210])]) ).
thf(sP211,plain,
( sP211
<=> ( ~ ( ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
!= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> sP110 ) ),
introduced(definition,[new_symbols(definition,[sP211])]) ).
thf(sP212,plain,
( sP212
<=> ( ~ ( ~ sP19
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP212])]) ).
thf(sP213,plain,
( sP213
<=> ( sP21
=> ( ( eigen__0 @ eigen__1 )
= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP213])]) ).
thf(sP214,plain,
( sP214
<=> ! [X1: $i] :
( ~ sP158
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP214])]) ).
thf(sP215,plain,
( sP215
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP215])]) ).
thf(sP216,plain,
( sP216
<=> ( ~ sP179
=> ~ sP125 ) ),
introduced(definition,[new_symbols(definition,[sP216])]) ).
thf(sP217,plain,
( sP217
<=> ( ~ sP131
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP217])]) ).
thf(sP218,plain,
( sP218
<=> ( sP117
=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP218])]) ).
thf(sP219,plain,
( sP219
<=> ( ~ sP79
=> ~ sP215 ) ),
introduced(definition,[new_symbols(definition,[sP219])]) ).
thf(sP220,plain,
( sP220
<=> ( ~ ( ~ sP165
=> ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> sP135 ) ),
introduced(definition,[new_symbols(definition,[sP220])]) ).
thf(sP221,plain,
( sP221
<=> ( ~ sP85
=> ~ sP136 ) ),
introduced(definition,[new_symbols(definition,[sP221])]) ).
thf(sP222,plain,
( sP222
<=> ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP222])]) ).
thf(sP223,plain,
( sP223
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP223])]) ).
thf(sP224,plain,
( sP224
<=> ( ~ sP140
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP224])]) ).
thf(sP225,plain,
( sP225
<=> ( sP121
=> ~ sP203 ) ),
introduced(definition,[new_symbols(definition,[sP225])]) ).
thf(sP226,plain,
( sP226
<=> ! [X1: $i] :
( ( eigen__0 @ X1 )
!= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP226])]) ).
thf(sP227,plain,
( sP227
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP227])]) ).
thf(sP228,plain,
( sP228
<=> ! [X1: $i] :
( ~ sP26
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP228])]) ).
thf(sP229,plain,
( sP229
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP229])]) ).
thf(sP230,plain,
( sP230
<=> ( ( eigen__0 @ eigen__1 )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP230])]) ).
thf(sP231,plain,
( sP231
<=> ! [X1: $i] :
( ~ ( ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
!= X1 )
=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP231])]) ).
thf(sP232,plain,
( sP232
<=> ( ~ sP117
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP232])]) ).
thf(sP233,plain,
( sP233
<=> ( ~ sP26
=> ~ sP120 ) ),
introduced(definition,[new_symbols(definition,[sP233])]) ).
thf(sP234,plain,
( sP234
<=> ( ~ ( ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP234])]) ).
thf(sP235,plain,
( sP235
<=> ( sP215
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP235])]) ).
thf(sP236,plain,
( sP236
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP236])]) ).
thf(sP237,plain,
( sP237
<=> ( sP110
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP237])]) ).
thf(sP238,plain,
( sP238
<=> ! [X1: $i] :
( ~ sP32
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP238])]) ).
thf(sP239,plain,
( sP239
<=> ( sP157
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP239])]) ).
thf(sP240,plain,
( sP240
<=> ! [X1: $i] :
( ~ ( ( eigen__1 != X1 )
=> ( r @ eigen__1 @ X1 ) )
=> ( b @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP240])]) ).
thf(sP241,plain,
( sP241
<=> ( sP150
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP241])]) ).
thf(sP242,plain,
( sP242
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP242])]) ).
thf(sP243,plain,
( sP243
<=> ( ~ ( ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
!= eigen__1 )
=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP243])]) ).
thf(sP244,plain,
( sP244
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP244])]) ).
thf(sP245,plain,
( sP245
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP50
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP245])]) ).
thf(sP246,plain,
( sP246
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP246])]) ).
thf(sP247,plain,
( sP247
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP247])]) ).
thf(sP248,plain,
( sP248
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
= ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP248])]) ).
thf(sP249,plain,
( sP249
<=> ( ~ ( sP50
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ sP120 ) ),
introduced(definition,[new_symbols(definition,[sP249])]) ).
thf(sP250,plain,
( sP250
<=> ( ~ sP158
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP250])]) ).
thf(sP251,plain,
( sP251
<=> ( eigen__1
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP251])]) ).
thf(sP252,plain,
( sP252
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP215 )
=> ~ sP120 )
=> ~ sP136 ) ),
introduced(definition,[new_symbols(definition,[sP252])]) ).
thf(sP253,plain,
( sP253
<=> ! [X1: $i] :
( ~ ( ~ sP199
=> ~ sP50 )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP253])]) ).
thf(sP254,plain,
( sP254
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP22 )
=> ~ sP62 )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP254])]) ).
thf(sP255,plain,
( sP255
<=> ( ~ ( ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ sP203 )
=> ~ sP111 ) ),
introduced(definition,[new_symbols(definition,[sP255])]) ).
thf(sP256,plain,
( sP256
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
!= eigen__1 )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP256])]) ).
thf(sP257,plain,
( sP257
<=> ( ~ sP172
=> sP50 ) ),
introduced(definition,[new_symbols(definition,[sP257])]) ).
thf(sP258,plain,
( sP258
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> sP248 ) ),
introduced(definition,[new_symbols(definition,[sP258])]) ).
thf(sP259,plain,
( sP259
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP259])]) ).
thf(sP260,plain,
( sP260
<=> ! [X1: $i] :
( ~ sP69
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP260])]) ).
thf(sP261,plain,
( sP261
<=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP261])]) ).
thf(sP262,plain,
( sP262
<=> ( ~ sP7
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP262])]) ).
thf(sP263,plain,
( sP263
<=> ( ~ sP224
=> sP157 ) ),
introduced(definition,[new_symbols(definition,[sP263])]) ).
thf(sP264,plain,
( sP264
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( r @ X1 @ X2 )
=> ~ ( r @ X1 @ X3 ) )
=> ~ ( r @ X2 @ X3 ) )
=> ~ ( r @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP264])]) ).
thf(sP265,plain,
( sP265
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP265])]) ).
thf(sP266,plain,
( sP266
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP266])]) ).
thf(sP267,plain,
( sP267
<=> ( ~ sP176
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP267])]) ).
thf(sP268,plain,
( sP268
<=> ! [X1: $i] :
( ~ ( sP121
=> ~ ( b @ eigen__1 @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP268])]) ).
thf(sP269,plain,
( sP269
<=> ( sP98
=> ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP269])]) ).
thf(sP270,plain,
( sP270
<=> ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP270])]) ).
thf(sP271,plain,
( sP271
<=> ( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP50 )
=> ~ sP136 )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP271])]) ).
thf(sP272,plain,
( sP272
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP272])]) ).
thf(sP273,plain,
( sP273
<=> ( ~ sP61
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP273])]) ).
thf(sP274,plain,
( sP274
<=> ( r @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP274])]) ).
thf(sP275,plain,
( sP275
<=> ( ~ sP217
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP275])]) ).
thf(sP276,plain,
( sP276
<=> ( b @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP276])]) ).
thf(sP277,plain,
( sP277
<=> ! [X1: $i] :
( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) )
= ( eigen__0 @ X1 ) )
=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP277])]) ).
thf(sP278,plain,
( sP278
<=> ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP278])]) ).
thf(sP279,plain,
( sP279
<=> ( ~ sP185
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP279])]) ).
thf(sP280,plain,
( sP280
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP280])]) ).
thf(sP281,plain,
( sP281
<=> ( sP274
=> ~ sP120 ) ),
introduced(definition,[new_symbols(definition,[sP281])]) ).
thf(sP282,plain,
( sP282
<=> ( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP150 )
=> ~ sP177 ) ),
introduced(definition,[new_symbols(definition,[sP282])]) ).
thf(sP283,plain,
( sP283
<=> ( ~ ( ~ sP127
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP283])]) ).
thf(sP284,plain,
( sP284
<=> ( ( eigen__0 @ eigen__1 )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP284])]) ).
thf(sP285,plain,
( sP285
<=> ( sP278
=> sP169 ) ),
introduced(definition,[new_symbols(definition,[sP285])]) ).
thf(sP286,plain,
( sP286
<=> ! [X1: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ~ ( b @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP286])]) ).
thf(sP287,plain,
( sP287
<=> ( ~ ( sP121
=> ~ sP276 )
=> ~ sP149 ) ),
introduced(definition,[new_symbols(definition,[sP287])]) ).
thf(sP288,plain,
( sP288
<=> ( ~ ( ~ sP248
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> sP266 ) ),
introduced(definition,[new_symbols(definition,[sP288])]) ).
thf(sP289,plain,
( sP289
<=> ( ~ sP244
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP289])]) ).
thf(sP290,plain,
( sP290
<=> ( ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
!= eigen__1 )
=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP290])]) ).
thf(sP291,plain,
( sP291
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP22 )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP291])]) ).
thf(sP292,plain,
( sP292
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP292])]) ).
thf(sP293,plain,
( sP293
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP293])]) ).
thf(sP294,plain,
( sP294
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP294])]) ).
thf(sP295,plain,
( sP295
<=> ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP295])]) ).
thf(sP296,plain,
( sP296
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP296])]) ).
thf(sP297,plain,
( sP297
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP297])]) ).
thf(sP298,plain,
( sP298
<=> ( sP125
=> ~ sP295 ) ),
introduced(definition,[new_symbols(definition,[sP298])]) ).
thf(sP299,plain,
( sP299
<=> ! [X1: $i] :
( ~ ( sP149
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP299])]) ).
thf(sP300,plain,
( sP300
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ sP62 )
=> ~ ( r @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP300])]) ).
thf(sP301,plain,
( sP301
<=> ( ~ sP148
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP301])]) ).
thf(sP302,plain,
( sP302
<=> ( ~ ( ~ ( sP215
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) )
=> ~ sP125 ) ),
introduced(definition,[new_symbols(definition,[sP302])]) ).
thf(sP303,plain,
( sP303
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP303])]) ).
thf(sP304,plain,
( sP304
<=> ! [X1: $i] :
( ~ ( ~ sP127
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP304])]) ).
thf(sP305,plain,
( sP305
<=> ( sP157
=> ~ sP97 ) ),
introduced(definition,[new_symbols(definition,[sP305])]) ).
thf(sP306,plain,
( sP306
<=> ( r @ eigen__1 @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP306])]) ).
thf(sP307,plain,
( sP307
<=> ! [X1: $i,X2: $i] :
( ~ ( ( b @ eigen__1 @ X1 )
=> ~ ( b @ eigen__1 @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP307])]) ).
thf(sP308,plain,
( sP308
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP303 ) ),
introduced(definition,[new_symbols(definition,[sP308])]) ).
thf(sP309,plain,
( sP309
<=> ( ~ sP225
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP309])]) ).
thf(sP310,plain,
( sP310
<=> ! [X1: $i] :
( ~ ( ~ ( sP215
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) )
=> ~ ( r @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP310])]) ).
thf(sP311,plain,
( sP311
<=> ! [X1: $i] :
( ~ ( sP177
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP311])]) ).
thf(sP312,plain,
( sP312
<=> ! [X1: $i] :
( ~ ( sP135
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP312])]) ).
thf(sP313,plain,
( sP313
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP313])]) ).
thf(sP314,plain,
( sP314
<=> ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP314])]) ).
thf(sP315,plain,
( sP315
<=> ! [X1: $i] :
( ~ ( sP266
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP315])]) ).
thf(sP316,plain,
( sP316
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP316])]) ).
thf(sP317,plain,
( sP317
<=> ( sP215
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP317])]) ).
thf(sP318,plain,
( sP318
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ sP97 ) ),
introduced(definition,[new_symbols(definition,[sP318])]) ).
thf(sP319,plain,
( sP319
<=> ( sP276
=> ~ ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP319])]) ).
thf(sP320,plain,
( sP320
<=> ( ~ sP237
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP320])]) ).
thf(sP321,plain,
( sP321
<=> ! [X1: $i] :
( ~ ( ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP321])]) ).
thf(sP322,plain,
( sP322
<=> ( sP50
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP322])]) ).
thf(sP323,plain,
( sP323
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP323])]) ).
thf(sP324,plain,
( sP324
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP274
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP324])]) ).
thf(sP325,plain,
( sP325
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> sP172 ) ),
introduced(definition,[new_symbols(definition,[sP325])]) ).
thf(sP326,plain,
( sP326
<=> $false ),
introduced(definition,[new_symbols(definition,[sP326])]) ).
thf(sP327,plain,
( sP327
<=> ( sP248
=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP327])]) ).
thf(sP328,plain,
( sP328
<=> ! [X1: $i,X2: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP328])]) ).
thf(sP329,plain,
( sP329
<=> ( ~ sP270
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP329])]) ).
thf(sP330,plain,
( sP330
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP330])]) ).
thf(sP331,plain,
( sP331
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP331])]) ).
thf(sP332,plain,
( sP332
<=> ( ~ ( ~ sP21
=> sP136 )
=> ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP332])]) ).
thf(sP333,plain,
( sP333
<=> ( eigen__1
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP333])]) ).
thf(sP334,plain,
( sP334
<=> ( ~ sP235
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP334])]) ).
thf(sP335,plain,
( sP335
<=> ! [X1: $i] :
( ~ sP20
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP335])]) ).
thf(sP336,plain,
( sP336
<=> ! [X1: $i] :
( ~ sP47
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP336])]) ).
thf(sP337,plain,
( sP337
<=> ( ~ sP40
=> ~ sP177 ) ),
introduced(definition,[new_symbols(definition,[sP337])]) ).
thf(sP338,plain,
( sP338
<=> ( ~ sP317
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP338])]) ).
thf(sP339,plain,
( sP339
<=> ( sP266
=> ~ sP157 ) ),
introduced(definition,[new_symbols(definition,[sP339])]) ).
thf(sP340,plain,
( sP340
<=> ( eigen__1
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP340])]) ).
thf(sP341,plain,
( sP341
<=> ( sP46
=> sP333 ) ),
introduced(definition,[new_symbols(definition,[sP341])]) ).
thf(sP342,plain,
( sP342
<=> ( ~ sP293
=> ~ sP136 ) ),
introduced(definition,[new_symbols(definition,[sP342])]) ).
thf(sP343,plain,
( sP343
<=> ( sP303
=> ~ sP149 ) ),
introduced(definition,[new_symbols(definition,[sP343])]) ).
thf(sP344,plain,
( sP344
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
!= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP344])]) ).
thf(sP345,plain,
( sP345
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP242 ) ),
introduced(definition,[new_symbols(definition,[sP345])]) ).
thf(sP346,plain,
( sP346
<=> ( r @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP346])]) ).
thf(sP347,plain,
( sP347
<=> ( ~ ( ~ sP345
=> ~ sP45 )
=> ~ sP215 ) ),
introduced(definition,[new_symbols(definition,[sP347])]) ).
thf(sP348,plain,
( sP348
<=> ( ~ sP127
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP348])]) ).
thf(sP349,plain,
( sP349
<=> ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP349])]) ).
thf(sP350,plain,
( sP350
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP110 ) ),
introduced(definition,[new_symbols(definition,[sP350])]) ).
thf(sP351,plain,
( sP351
<=> ( ~ sP305
=> ~ sP121 ) ),
introduced(definition,[new_symbols(definition,[sP351])]) ).
thf(sP352,plain,
( sP352
<=> ( sP272
=> ~ sP272 ) ),
introduced(definition,[new_symbols(definition,[sP352])]) ).
thf(sP353,plain,
( sP353
<=> ! [X1: $i] :
( ~ sP6
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP353])]) ).
thf(sP354,plain,
( sP354
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP22
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP354])]) ).
thf(sP355,plain,
( sP355
<=> ! [X1: $i] :
( ~ ( ( ( eigen__0 @ eigen__1 )
!= X1 )
=> ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ( b @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP355])]) ).
thf(sP356,plain,
( sP356
<=> ( ~ sP21
=> sP136 ) ),
introduced(definition,[new_symbols(definition,[sP356])]) ).
thf(sP357,plain,
( sP357
<=> ! [X1: $i] :
( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
= ( eigen__0 @ X1 ) )
=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP357])]) ).
thf(sP358,plain,
( sP358
<=> ( ~ sP20
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP358])]) ).
thf(sP359,plain,
( sP359
<=> ( ~ sP105
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP359])]) ).
thf(sP360,plain,
( sP360
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP360])]) ).
thf(sP361,plain,
( sP361
<=> ! [X1: $i] :
( ~ sP244
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP361])]) ).
thf(sP362,plain,
( sP362
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP362])]) ).
thf(sP363,plain,
( sP363
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP363])]) ).
thf(sP364,plain,
( sP364
<=> ( ~ ( sP276
=> ~ sP203 )
=> ~ sP177 ) ),
introduced(definition,[new_symbols(definition,[sP364])]) ).
thf(sP365,plain,
( sP365
<=> ( ~ sP239
=> ~ ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP365])]) ).
thf(sP366,plain,
( sP366
<=> ( ~ sP334
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP366])]) ).
thf(sP367,plain,
( sP367
<=> ( sP215
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP367])]) ).
thf(sP368,plain,
( sP368
<=> ( ~ sP292
=> ~ sP276 ) ),
introduced(definition,[new_symbols(definition,[sP368])]) ).
thf(sP369,plain,
( sP369
<=> ( eigen__1
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP369])]) ).
thf(sP370,plain,
( sP370
<=> ( sP160
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP370])]) ).
thf(sP371,plain,
( sP371
<=> ( ~ sP86
=> ~ sP120 ) ),
introduced(definition,[new_symbols(definition,[sP371])]) ).
thf(sP372,plain,
( sP372
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ eigen__1 ) @ X1 )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP372])]) ).
thf(sP373,plain,
( sP373
<=> ! [X1: $i] :
( ~ ( sP323
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP373])]) ).
thf(sP374,plain,
( sP374
<=> ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP374])]) ).
thf(sP375,plain,
( sP375
<=> ( ~ sP87
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP375])]) ).
thf(sP376,plain,
( sP376
<=> ( ~ sP232
=> sP330 ) ),
introduced(definition,[new_symbols(definition,[sP376])]) ).
thf(sP377,plain,
( sP377
<=> ( ~ sP352
=> ~ sP272 ) ),
introduced(definition,[new_symbols(definition,[sP377])]) ).
thf(sP378,plain,
( sP378
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP378])]) ).
thf(sP379,plain,
( sP379
<=> ( ~ sP146
=> ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP379])]) ).
thf(sP380,plain,
( sP380
<=> ( ~ ( ~ ( sP280
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) )
=> ~ sP295 ) ),
introduced(definition,[new_symbols(definition,[sP380])]) ).
thf(sP381,plain,
( sP381
<=> ( ~ sP278
=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP381])]) ).
thf(sP382,plain,
( sP382
<=> ( ~ sP41
=> sP177 ) ),
introduced(definition,[new_symbols(definition,[sP382])]) ).
thf(sP383,plain,
( sP383
<=> ( ~ sP36
=> ~ sP323 ) ),
introduced(definition,[new_symbols(definition,[sP383])]) ).
thf(sP384,plain,
( sP384
<=> ! [X1: $i] :
( ~ ( sP362
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP384])]) ).
thf(sP385,plain,
( sP385
<=> ( ~ sP129
=> ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP385])]) ).
thf(sP386,plain,
( sP386
<=> ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP386])]) ).
thf(sP387,plain,
( sP387
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP387])]) ).
thf(sP388,plain,
( sP388
<=> ( ~ ( ~ sP369
=> sP346 )
=> ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP388])]) ).
thf(sP389,plain,
( sP389
<=> ! [X1: $i] :
( ~ sP171
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP389])]) ).
thf(sP390,plain,
( sP390
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP390])]) ).
thf(sP391,plain,
( sP391
<=> ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP391])]) ).
thf(sP392,plain,
( sP392
<=> ( ~ ( sP135
=> ~ sP177 )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP392])]) ).
thf(sP393,plain,
( sP393
<=> ( ~ sP345
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP393])]) ).
thf(sP394,plain,
( sP394
<=> ( ~ sP257
=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP394])]) ).
thf(sP395,plain,
( sP395
<=> ( ~ ( ~ sP298
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP395])]) ).
thf(sP396,plain,
( sP396
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP396])]) ).
thf(sP397,plain,
( sP397
<=> ( ( eigen__0 @ eigen__1 )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP397])]) ).
thf(sP398,plain,
( sP398
<=> ( sP330
=> ~ sP266 ) ),
introduced(definition,[new_symbols(definition,[sP398])]) ).
thf(sP399,plain,
( sP399
<=> ! [X1: $i] :
( ~ ( sP330
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP399])]) ).
thf(sP400,plain,
( sP400
<=> ( ~ sP348
=> ~ sP125 ) ),
introduced(definition,[new_symbols(definition,[sP400])]) ).
thf(sP401,plain,
( sP401
<=> ( ~ sP197
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP401])]) ).
thf(sP402,plain,
( sP402
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP402])]) ).
thf(sP403,plain,
( sP403
<=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP403])]) ).
thf(sP404,plain,
( sP404
<=> ( sP362
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP404])]) ).
thf(sP405,plain,
( sP405
<=> ( sP280
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP405])]) ).
thf(sP406,plain,
( sP406
<=> ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP406])]) ).
thf(sP407,plain,
( sP407
<=> ! [X1: $i] :
( ~ ( sP374
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP407])]) ).
thf(sP408,plain,
( sP408
<=> ( ~ sP93
=> ~ sP177 ) ),
introduced(definition,[new_symbols(definition,[sP408])]) ).
thf(sP409,plain,
( sP409
<=> ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP409])]) ).
thf(sP410,plain,
( sP410
<=> ! [X1: $i] :
( ~ ( sP203
=> ~ ( b @ eigen__1 @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP410])]) ).
thf(sP411,plain,
( sP411
<=> ( ~ sP249
=> ~ sP136 ) ),
introduced(definition,[new_symbols(definition,[sP411])]) ).
thf(sP412,plain,
( sP412
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( b @ X1 @ X2 )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP412])]) ).
thf(sP413,plain,
( sP413
<=> ( b @ eigen__1 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP413])]) ).
thf(sP414,plain,
( sP414
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP390
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP414])]) ).
thf(sP415,plain,
( sP415
<=> ( ~ sP241
=> ~ sP374 ) ),
introduced(definition,[new_symbols(definition,[sP415])]) ).
thf(sP416,plain,
( sP416
<=> ( sP396
=> sP98 ) ),
introduced(definition,[new_symbols(definition,[sP416])]) ).
thf(sP417,plain,
( sP417
<=> ! [X1: $i] :
( ~ sP262
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP417])]) ).
thf(sP418,plain,
( sP418
<=> ! [X1: $i] :
( ~ ( sP409
=> ~ ( b @ eigen__1 @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP418])]) ).
thf(sP419,plain,
( sP419
<=> ( ~ sP133
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP419])]) ).
thf(sP420,plain,
( sP420
<=> ! [X1: $i] :
( ~ sP216
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP420])]) ).
thf(sP421,plain,
( sP421
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP421])]) ).
thf(sP422,plain,
( sP422
<=> ( ~ sP248
=> sP390 ) ),
introduced(definition,[new_symbols(definition,[sP422])]) ).
thf(sP423,plain,
( sP423
<=> ! [X1: $i] :
( ~ ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
!= X1 )
=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP423])]) ).
thf(sP424,plain,
( sP424
<=> ( ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP424])]) ).
thf(sP425,plain,
( sP425
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP425])]) ).
thf(sP426,plain,
( sP426
<=> ( ~ sP318
=> ~ sP362 ) ),
introduced(definition,[new_symbols(definition,[sP426])]) ).
thf(sP427,plain,
( sP427
<=> ( ~ sP104
=> ~ sP136 ) ),
introduced(definition,[new_symbols(definition,[sP427])]) ).
thf(sP428,plain,
( sP428
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP428])]) ).
thf(sP429,plain,
( sP429
<=> ( ~ sP6
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP429])]) ).
thf(sP430,plain,
( sP430
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) )
=> ~ sP421 ) ),
introduced(definition,[new_symbols(definition,[sP430])]) ).
thf(sP431,plain,
( sP431
<=> ( ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP431])]) ).
thf(sP432,plain,
( sP432
<=> ( b @ ( eigen__0 @ eigen__1 ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP432])]) ).
thf(sP433,plain,
( sP433
<=> ( sP150
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP433])]) ).
thf(sP434,plain,
( sP434
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP434])]) ).
thf(sP435,plain,
( sP435
<=> ! [X1: $i] :
( ~ ( sP276
=> ~ ( b @ eigen__1 @ X1 ) )
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP435])]) ).
thf(sP436,plain,
( sP436
<=> ( ~ sP107
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP436])]) ).
thf(sP437,plain,
( sP437
<=> ( sP323
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP437])]) ).
thf(sP438,plain,
( sP438
<=> ( ~ sP344
=> sP150 ) ),
introduced(definition,[new_symbols(definition,[sP438])]) ).
thf(sP439,plain,
( sP439
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP439])]) ).
thf(sP440,plain,
( sP440
<=> ( ~ sP76
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP440])]) ).
thf(sP441,plain,
( sP441
<=> ( ~ sP165
=> sP274 ) ),
introduced(definition,[new_symbols(definition,[sP441])]) ).
thf(sP442,plain,
( sP442
<=> ! [X1: $i] :
( ~ sP291
=> ~ ( r @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP442])]) ).
thf(sP443,plain,
( sP443
<=> ( ~ sP227
=> sP215 ) ),
introduced(definition,[new_symbols(definition,[sP443])]) ).
thf(sP444,plain,
( sP444
<=> ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP444])]) ).
thf(sP445,plain,
( sP445
<=> ( ~ sP124
=> sP409 ) ),
introduced(definition,[new_symbols(definition,[sP445])]) ).
thf(sP446,plain,
( sP446
<=> ( sP121
=> ~ sP276 ) ),
introduced(definition,[new_symbols(definition,[sP446])]) ).
thf(sP447,plain,
( sP447
<=> ( ~ sP152
=> sP303 ) ),
introduced(definition,[new_symbols(definition,[sP447])]) ).
thf(sP448,plain,
( sP448
<=> ( ~ sP200
=> ~ sP444 ) ),
introduced(definition,[new_symbols(definition,[sP448])]) ).
thf(sP449,plain,
( sP449
<=> ( ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
=> sP165 ) ),
introduced(definition,[new_symbols(definition,[sP449])]) ).
thf(sP450,plain,
( sP450
<=> ( sP135
=> ~ sP177 ) ),
introduced(definition,[new_symbols(definition,[sP450])]) ).
thf(sP451,plain,
( sP451
<=> ( ~ sP19
=> ~ sP403 ) ),
introduced(definition,[new_symbols(definition,[sP451])]) ).
thf(sP452,plain,
( sP452
<=> ( ( eigen__0 @ ( eigen__0 @ eigen__1 ) )
= ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP452])]) ).
thf(sP453,plain,
( sP453
<=> ( ~ sP428
=> sP280 ) ),
introduced(definition,[new_symbols(definition,[sP453])]) ).
thf(sP454,plain,
( sP454
<=> ( ~ sP343
=> ~ sP276 ) ),
introduced(definition,[new_symbols(definition,[sP454])]) ).
thf(sP455,plain,
( sP455
<=> ( sP434
=> ~ sP421 ) ),
introduced(definition,[new_symbols(definition,[sP455])]) ).
thf(sP456,plain,
( sP456
<=> ( ~ sP298
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP456])]) ).
thf(sP457,plain,
( sP457
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP434
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP457])]) ).
thf(sP458,plain,
( sP458
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP458])]) ).
thf(sP459,plain,
( sP459
<=> ! [X1: $i] :
( ~ sP267
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP459])]) ).
thf(sP460,plain,
( sP460
<=> ( sP177
=> ~ ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP460])]) ).
thf(sP461,plain,
( sP461
<=> ! [X1: $i,X2: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP461])]) ).
thf(sP462,plain,
( sP462
<=> ( b @ ( eigen__0 @ eigen__1 ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP462])]) ).
thf(sP463,plain,
( sP463
<=> ( ~ sP94
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP463])]) ).
thf(sP464,plain,
( sP464
<=> ( ~ sP262
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP464])]) ).
thf(sP465,plain,
( sP465
<=> ( ~ sP267
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP465])]) ).
thf(sP466,plain,
( sP466
<=> ! [X1: $i,X2: $i] :
( ~ ( ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP466])]) ).
thf(sP467,plain,
( sP467
<=> ( ~ sP405
=> ~ sP421 ) ),
introduced(definition,[new_symbols(definition,[sP467])]) ).
thf(sP468,plain,
( sP468
<=> ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP468])]) ).
thf(sP469,plain,
( sP469
<=> ( ~ sP369
=> sP346 ) ),
introduced(definition,[new_symbols(definition,[sP469])]) ).
thf(sP470,plain,
( sP470
<=> ( ~ ( sP362
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) )
=> ~ sP149 ) ),
introduced(definition,[new_symbols(definition,[sP470])]) ).
thf(sP471,plain,
( sP471
<=> ( ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 )
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP471])]) ).
thf(sP472,plain,
( sP472
<=> ( ~ sP52
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP472])]) ).
thf(sP473,plain,
( sP473
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP473])]) ).
thf(sP474,plain,
( sP474
<=> ! [X1: $i] :
( ~ ( sP391
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP474])]) ).
thf(sP475,plain,
( sP475
<=> ( ~ ( sP391
=> ~ sP374 )
=> ~ sP149 ) ),
introduced(definition,[new_symbols(definition,[sP475])]) ).
thf(sP476,plain,
( sP476
<=> ( ~ sP199
=> ~ sP50 ) ),
introduced(definition,[new_symbols(definition,[sP476])]) ).
thf(sP477,plain,
( sP477
<=> ! [X1: $i,X2: $i] :
( ~ ( ( X1 != X2 )
=> ( r @ X1 @ X2 ) )
=> ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP477])]) ).
thf(sP478,plain,
( sP478
<=> ( ~ sP82
=> ~ sP374 ) ),
introduced(definition,[new_symbols(definition,[sP478])]) ).
thf(sP479,plain,
( sP479
<=> ( sP409
=> ~ sP203 ) ),
introduced(definition,[new_symbols(definition,[sP479])]) ).
thf(sP480,plain,
( sP480
<=> ( sP50
=> ~ sP439 ) ),
introduced(definition,[new_symbols(definition,[sP480])]) ).
thf(sP481,plain,
( sP481
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP45
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP481])]) ).
thf(sP482,plain,
( sP482
<=> ( ~ sP161
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP482])]) ).
thf(sP483,plain,
( sP483
<=> ( ~ sP479
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP483])]) ).
thf(sP484,plain,
( sP484
<=> ( sP473
=> ~ sP215 ) ),
introduced(definition,[new_symbols(definition,[sP484])]) ).
thf(sP485,plain,
( sP485
<=> ( sP391
=> ~ sP374 ) ),
introduced(definition,[new_symbols(definition,[sP485])]) ).
thf(sP486,plain,
( sP486
<=> ! [X1: $i] :
( ~ sP377
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP486])]) ).
thf(sP487,plain,
( sP487
<=> ! [X1: $i] :
( ~ sP112
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP487])]) ).
thf(sP488,plain,
( sP488
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP488])]) ).
thf(sP489,plain,
( sP489
<=> ( ~ sP32
=> ~ sP274 ) ),
introduced(definition,[new_symbols(definition,[sP489])]) ).
thf(sP490,plain,
( sP490
<=> ( ~ ( ~ sP430
=> ~ sP62 )
=> ~ sP295 ) ),
introduced(definition,[new_symbols(definition,[sP490])]) ).
thf(sP491,plain,
( sP491
<=> ( sP421
=> ~ sP473 ) ),
introduced(definition,[new_symbols(definition,[sP491])]) ).
thf(sP492,plain,
( sP492
<=> ( sP413
=> ~ sP203 ) ),
introduced(definition,[new_symbols(definition,[sP492])]) ).
thf(sP493,plain,
( sP493
<=> ( ~ sP209
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP493])]) ).
thf(sP494,plain,
( sP494
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ ( eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP494])]) ).
thf(sP495,plain,
( sP495
<=> ( sP62
=> ~ sP274 ) ),
introduced(definition,[new_symbols(definition,[sP495])]) ).
thf(sP496,plain,
( sP496
<=> ( sP101
=> sP140 ) ),
introduced(definition,[new_symbols(definition,[sP496])]) ).
thf(sP497,plain,
( sP497
<=> ( ~ sP265
=> ~ sP203 ) ),
introduced(definition,[new_symbols(definition,[sP497])]) ).
thf(sP498,plain,
( sP498
<=> ! [X1: $i] :
( ~ ( sP488
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP498])]) ).
thf(sP499,plain,
( sP499
<=> ( ~ sP273
=> sP149 ) ),
introduced(definition,[new_symbols(definition,[sP499])]) ).
thf(sP500,plain,
( sP500
<=> ! [X1: $i] :
( ~ sP342
=> ~ ( r @ ( eigen__0 @ eigen__1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP500])]) ).
thf(sP501,plain,
( sP501
<=> ( sP105
=> sP363 ) ),
introduced(definition,[new_symbols(definition,[sP501])]) ).
thf(sP502,plain,
( sP502
<=> ( ~ sP59
=> ~ sP488 ) ),
introduced(definition,[new_symbols(definition,[sP502])]) ).
thf(sP503,plain,
( sP503
<=> ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP503])]) ).
thf(sP504,plain,
( sP504
<=> ( sP276
=> ~ sP203 ) ),
introduced(definition,[new_symbols(definition,[sP504])]) ).
thf(sP505,plain,
( sP505
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP505])]) ).
thf(sP506,plain,
( sP506
<=> ! [X1: $i] :
( ~ sP187
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP506])]) ).
thf(sP507,plain,
( sP507
<=> ( ~ sP484
=> ~ sP120 ) ),
introduced(definition,[new_symbols(definition,[sP507])]) ).
thf(sP508,plain,
( sP508
<=> ( ~ sP433
=> ~ sP444 ) ),
introduced(definition,[new_symbols(definition,[sP508])]) ).
thf(sP509,plain,
( sP509
<=> ( ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) )
= ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP509])]) ).
thf(sP510,plain,
( sP510
<=> ! [X1: $i] :
( ~ sP52
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP510])]) ).
thf(sP511,plain,
( sP511
<=> ( ~ sP32
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP511])]) ).
thf(sP512,plain,
( sP512
<=> ( ~ sP53
=> ~ sP120 ) ),
introduced(definition,[new_symbols(definition,[sP512])]) ).
thf(sP513,plain,
( sP513
<=> ( ~ sP6
=> ~ sP421 ) ),
introduced(definition,[new_symbols(definition,[sP513])]) ).
thf(sP514,plain,
( sP514
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP295
=> ~ ( r @ eigen__1 @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP514])]) ).
thf(sP515,plain,
( sP515
<=> ( ~ sP216
=> ~ sP136 ) ),
introduced(definition,[new_symbols(definition,[sP515])]) ).
thf(sP516,plain,
( sP516
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP242
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) @ X1 ) )
=> ~ ( r @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP516])]) ).
thf(sP517,plain,
( sP517
<=> ( sP25
=> ~ sP390 ) ),
introduced(definition,[new_symbols(definition,[sP517])]) ).
thf(sP518,plain,
( sP518
<=> ( b @ ( eigen__0 @ ( eigen__0 @ ( eigen__0 @ eigen__1 ) ) ) @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP518])]) ).
thf(sP519,plain,
( sP519
<=> ( sP362
=> ~ sP494 ) ),
introduced(definition,[new_symbols(definition,[sP519])]) ).
thf(sP520,plain,
( sP520
<=> ( ~ sP430
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP520])]) ).
thf(def_inj,definition,
( inj
= ( ^ [X1: $i > $i] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( ( X1 @ X2 )
= ( X1 @ X3 ) )
@ ( X2 = X3 ) ) ) ) ).
thf(def_surj,definition,
( surj
= ( ^ [X1: $i > $i] :
! [X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
= X2 ) ) ) ).
thf(h0,assumption,
~ ( sP1
=> ! [X1: $i] :
~ ! [X2: $i] :
( ( eigen__0 @ X2 )
!= X1 ) ),
introduced(assumption,[]) ).
thf(h1,assumption,
sP1,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
~ ! [X2: $i] :
( ( eigen__0 @ X2 )
!= X1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP226,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP409
| sP323
| sP326
| ~ sP251 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP374
| sP391
| ~ sP284
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP444
| sP391
| ~ sP251
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP50
| sP280
| ~ sP284
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP503
| sP280
| ~ sP251
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP276
| sP149
| sP326
| ~ sP251 ),
inference(mating_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP374
| sP149
| sP326
| ~ sP181 ),
inference(mating_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP462
| sP303
| sP326
| ~ sP284 ),
inference(mating_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP444
| sP303
| sP326
| ~ sP181 ),
inference(mating_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP203
| sP121
| ~ sP181
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP179
| ~ sP421
| ~ sP215 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP216
| sP179
| ~ sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP484
| ~ sP473
| ~ sP215 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP507
| sP484
| ~ sP120 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP131
| ~ sP473
| ~ sP434 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP217
| sP131
| ~ sP274 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP317
| ~ sP215
| ~ sP421 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP338
| sP317
| ~ sP403 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP367
| ~ sP215
| ~ sP473 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP151
| sP367
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP235
| ~ sP215
| ~ sP434 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP334
| sP235
| ~ sP468 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP455
| ~ sP434
| ~ sP421 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP349
| sP455
| ~ sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP296
| ~ sP434
| ~ sP473 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP244
| sP296
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP166
| ~ sP434
| ~ sP215 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP104
| sP166
| ~ sP439 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP489
| sP32
| ~ sP274 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP491
| ~ sP421
| ~ sP473 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP32
| sP491
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP511
| sP32
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP515
| sP216
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP88
| sP520
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP139
| sP520
| ~ sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP490
| sP520
| ~ sP295 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP430
| ~ sP473
| ~ sP421 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP520
| sP430
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP252
| sP507
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP275
| sP217
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP147
| sP338
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP302
| sP338
| ~ sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP180
| sP151
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP366
| sP334
| ~ sP439 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP14
| sP349
| ~ sP314 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP289
| sP244
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP427
| sP104
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP222
| ~ sP314
| ~ sP295 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP174
| sP222
| ~ sP434 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP195
| ~ sP45
| ~ sP274 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP52
| sP195
| ~ sP434 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP405
| ~ sP280
| ~ sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP467
| sP405
| ~ sP421 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP259
| ~ sP280
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP158
| sP259
| ~ sP473 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP73
| ~ sP242
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP47
| sP73
| ~ sP434 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP238
| sP489 ),
inference(all_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP238
| sP511 ),
inference(all_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP420
| sP515 ),
inference(all_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP300
| sP88 ),
inference(all_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP300
| sP139 ),
inference(all_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP300
| sP490 ),
inference(all_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP64
| sP252 ),
inference(all_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP201
| sP275 ),
inference(all_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP310
| sP147 ),
inference(all_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP310
| sP302 ),
inference(all_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP95
| sP180 ),
inference(all_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP114
| sP366 ),
inference(all_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP28
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(71,plain,
( ~ sP361
| sP289 ),
inference(all_rule,[status(thm)],[]) ).
thf(72,plain,
( ~ sP167
| sP427 ),
inference(all_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP34
| sP174
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP472
| sP52
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP163
| sP467
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP380
| sP467
| ~ sP295 ),
inference(prop_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP250
| sP158
| ~ sP274 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( ~ sP378
| ~ sP439
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP6
| sP378
| ~ sP261 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
( ~ sP182
| ~ sP346
| ~ sP314 ),
inference(prop_rule,[status(thm)],[]) ).
thf(81,plain,
( ~ sP171
| sP182
| ~ sP242 ),
inference(prop_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP113
| sP47
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP170
| ~ sP22
| ~ sP242 ),
inference(prop_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP79
| sP170
| ~ sP314 ),
inference(prop_rule,[status(thm)],[]) ).
thf(85,plain,
( ~ sP345
| ~ sP390
| ~ sP242 ),
inference(prop_rule,[status(thm)],[]) ).
thf(86,plain,
( ~ sP393
| sP345
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(87,plain,
( ~ sP308
| ~ sP488
| ~ sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(88,plain,
( ~ sP66
| sP308
| ~ sP444 ),
inference(prop_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP162
| ~ sP488
| ~ sP149 ),
inference(prop_rule,[status(thm)],[]) ).
thf(90,plain,
( ~ sP109
| sP162
| ~ sP374 ),
inference(prop_rule,[status(thm)],[]) ).
thf(91,plain,
( ~ sP185
| ~ sP323
| ~ sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(92,plain,
( ~ sP279
| sP185
| ~ sP518 ),
inference(prop_rule,[status(thm)],[]) ).
thf(93,plain,
( ~ sP161
| ~ sP323
| ~ sP149 ),
inference(prop_rule,[status(thm)],[]) ).
thf(94,plain,
( ~ sP482
| sP161
| ~ sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(95,plain,
( ~ sP437
| ~ sP323
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(96,plain,
( ~ sP173
| sP437
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(97,plain,
( ~ sP152
| sP54
| sP421 ),
inference(prop_rule,[status(thm)],[]) ).
thf(98,plain,
( ~ sP447
| sP152
| sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(99,plain,
( ~ sP273
| sP61
| sP473 ),
inference(prop_rule,[status(thm)],[]) ).
thf(100,plain,
( ~ sP499
| sP273
| sP149 ),
inference(prop_rule,[status(thm)],[]) ).
thf(101,plain,
( ~ sP443
| sP227
| sP215 ),
inference(prop_rule,[status(thm)],[]) ).
thf(102,plain,
( ~ sP57
| sP443
| sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(103,plain,
( ~ sP359
| sP105
| sP434 ),
inference(prop_rule,[status(thm)],[]) ).
thf(104,plain,
( ~ sP2
| sP359
| sP323 ),
inference(prop_rule,[status(thm)],[]) ).
thf(105,plain,
( ~ sP402
| sP238 ),
inference(all_rule,[status(thm)],[]) ).
thf(106,plain,
( ~ sP402
| sP420 ),
inference(all_rule,[status(thm)],[]) ).
thf(107,plain,
( ~ sP103
| sP300 ),
inference(all_rule,[status(thm)],[]) ).
thf(108,plain,
( ~ sP103
| sP64 ),
inference(all_rule,[status(thm)],[]) ).
thf(109,plain,
( ~ sP103
| sP201 ),
inference(all_rule,[status(thm)],[]) ).
thf(110,plain,
( ~ sP102
| sP310 ),
inference(all_rule,[status(thm)],[]) ).
thf(111,plain,
( ~ sP102
| sP95 ),
inference(all_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP102
| sP114 ),
inference(all_rule,[status(thm)],[]) ).
thf(113,plain,
( ~ sP457
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(114,plain,
( ~ sP457
| sP361 ),
inference(all_rule,[status(thm)],[]) ).
thf(115,plain,
( ~ sP457
| sP167 ),
inference(all_rule,[status(thm)],[]) ).
thf(116,plain,
( ~ sP56
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(117,plain,
( ~ sP510
| sP472 ),
inference(all_rule,[status(thm)],[]) ).
thf(118,plain,
( ~ sP202
| ~ sP391
| ~ sP444 ),
inference(prop_rule,[status(thm)],[]) ).
thf(119,plain,
( ~ sP192
| sP202
| ~ sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP485
| ~ sP391
| ~ sP374 ),
inference(prop_rule,[status(thm)],[]) ).
thf(121,plain,
( ~ sP475
| sP485
| ~ sP149 ),
inference(prop_rule,[status(thm)],[]) ).
thf(122,plain,
( ~ sP404
| ~ sP362
| ~ sP518 ),
inference(prop_rule,[status(thm)],[]) ).
thf(123,plain,
( ~ sP247
| sP404
| ~ sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(124,plain,
( ~ sP519
| ~ sP362
| ~ sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(125,plain,
( ~ sP470
| sP519
| ~ sP149 ),
inference(prop_rule,[status(thm)],[]) ).
thf(126,plain,
( ~ sP59
| ~ sP362
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(127,plain,
( ~ sP502
| sP59
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(128,plain,
( ~ sP208
| sP163 ),
inference(all_rule,[status(thm)],[]) ).
thf(129,plain,
( ~ sP208
| sP380 ),
inference(all_rule,[status(thm)],[]) ).
thf(130,plain,
( ~ sP214
| sP250 ),
inference(all_rule,[status(thm)],[]) ).
thf(131,plain,
( ~ sP513
| sP6
| ~ sP421 ),
inference(prop_rule,[status(thm)],[]) ).
thf(132,plain,
( ~ sP429
| sP6
| ~ sP473 ),
inference(prop_rule,[status(thm)],[]) ).
thf(133,plain,
( ~ sP141
| sP171
| ~ sP421 ),
inference(prop_rule,[status(thm)],[]) ).
thf(134,plain,
( ~ sP336
| sP113 ),
inference(all_rule,[status(thm)],[]) ).
thf(135,plain,
( ~ sP189
| sP79
| ~ sP473 ),
inference(prop_rule,[status(thm)],[]) ).
thf(136,plain,
( ~ sP219
| sP79
| ~ sP215 ),
inference(prop_rule,[status(thm)],[]) ).
thf(137,plain,
( ~ sP347
| sP393
| ~ sP215 ),
inference(prop_rule,[status(thm)],[]) ).
thf(138,plain,
( ~ sP246
| ~ sP303
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(139,plain,
( ~ sP119
| sP246
| ~ sP203 ),
inference(prop_rule,[status(thm)],[]) ).
thf(140,plain,
( ~ sP4
| ~ sP303
| ~ sP323 ),
inference(prop_rule,[status(thm)],[]) ).
thf(141,plain,
( ~ sP83
| sP4
| ~ sP409 ),
inference(prop_rule,[status(thm)],[]) ).
thf(142,plain,
( ~ sP40
| ~ sP149
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(143,plain,
( ~ sP337
| sP40
| ~ sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(144,plain,
( ~ sP175
| ~ sP149
| ~ sP323 ),
inference(prop_rule,[status(thm)],[]) ).
thf(145,plain,
( ~ sP13
| sP175
| ~ sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(146,plain,
( ~ sP498
| sP66 ),
inference(all_rule,[status(thm)],[]) ).
thf(147,plain,
( ~ sP498
| sP109 ),
inference(all_rule,[status(thm)],[]) ).
thf(148,plain,
( ~ sP373
| sP279 ),
inference(all_rule,[status(thm)],[]) ).
thf(149,plain,
( ~ sP373
| sP482 ),
inference(all_rule,[status(thm)],[]) ).
thf(150,plain,
( ~ sP373
| sP173 ),
inference(all_rule,[status(thm)],[]) ).
thf(151,plain,
( ~ sP225
| ~ sP121
| ~ sP203 ),
inference(prop_rule,[status(thm)],[]) ).
thf(152,plain,
( ~ sP309
| sP225
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(153,plain,
( ~ sP36
| ~ sP121
| ~ sP409 ),
inference(prop_rule,[status(thm)],[]) ).
thf(154,plain,
( ~ sP383
| sP36
| ~ sP323 ),
inference(prop_rule,[status(thm)],[]) ).
thf(155,plain,
( ~ sP17
| sP447 ),
inference(all_rule,[status(thm)],[]) ).
thf(156,plain,
( ~ sP17
| sP499 ),
inference(all_rule,[status(thm)],[]) ).
thf(157,plain,
( ~ sP17
| sP57 ),
inference(all_rule,[status(thm)],[]) ).
thf(158,plain,
( ~ sP17
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(159,plain,
( ~ sP294
| sP402 ),
inference(all_rule,[status(thm)],[]) ).
thf(160,plain,
( ~ sP294
| sP103 ),
inference(all_rule,[status(thm)],[]) ).
thf(161,plain,
( ~ sP294
| sP102 ),
inference(all_rule,[status(thm)],[]) ).
thf(162,plain,
( ~ sP294
| sP457 ),
inference(all_rule,[status(thm)],[]) ).
thf(163,plain,
( ~ sP143
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(164,plain,
( ~ sP43
| sP251
| sP314 ),
inference(prop_rule,[status(thm)],[]) ).
thf(165,plain,
( ~ sP128
| sP43
| sP121 ),
inference(prop_rule,[status(thm)],[]) ).
thf(166,plain,
( ~ sP481
| sP510 ),
inference(all_rule,[status(thm)],[]) ).
thf(167,plain,
( ~ sP108
| sP284
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(168,plain,
( ~ sP38
| sP108
| sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(169,plain,
( ~ sP474
| sP192 ),
inference(all_rule,[status(thm)],[]) ).
thf(170,plain,
( ~ sP474
| sP475 ),
inference(all_rule,[status(thm)],[]) ).
thf(171,plain,
( ~ sP129
| sP181
| sP261 ),
inference(prop_rule,[status(thm)],[]) ).
thf(172,plain,
( ~ sP385
| sP129
| sP391 ),
inference(prop_rule,[status(thm)],[]) ).
thf(173,plain,
( ~ sP384
| sP247 ),
inference(all_rule,[status(thm)],[]) ).
thf(174,plain,
( ~ sP384
| sP470 ),
inference(all_rule,[status(thm)],[]) ).
thf(175,plain,
( ~ sP384
| sP502 ),
inference(all_rule,[status(thm)],[]) ).
thf(176,plain,
( ~ sP30
| sP208 ),
inference(all_rule,[status(thm)],[]) ).
thf(177,plain,
( ~ sP30
| sP214 ),
inference(all_rule,[status(thm)],[]) ).
thf(178,plain,
( ~ sP453
| sP428
| sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(179,plain,
( ~ sP118
| sP453
| sP362 ),
inference(prop_rule,[status(thm)],[]) ).
thf(180,plain,
( ~ sP197
| ~ sP494
| ~ sP362 ),
inference(prop_rule,[status(thm)],[]) ).
thf(181,plain,
( ~ sP401
| sP197
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(182,plain,
( ~ sP353
| sP513 ),
inference(all_rule,[status(thm)],[]) ).
thf(183,plain,
( ~ sP353
| sP429 ),
inference(all_rule,[status(thm)],[]) ).
thf(184,plain,
( ~ sP9
| sP249
| ~ sP261 ),
inference(prop_rule,[status(thm)],[]) ).
thf(185,plain,
( ~ sP389
| sP141 ),
inference(all_rule,[status(thm)],[]) ).
thf(186,plain,
( ~ sP516
| sP336 ),
inference(all_rule,[status(thm)],[]) ).
thf(187,plain,
( ~ sP33
| sP396
| sP242 ),
inference(prop_rule,[status(thm)],[]) ).
thf(188,plain,
( ~ sP134
| sP33
| sP97 ),
inference(prop_rule,[status(thm)],[]) ).
thf(189,plain,
( ~ sP318
| ~ sP330
| ~ sP97 ),
inference(prop_rule,[status(thm)],[]) ).
thf(190,plain,
( ~ sP426
| sP318
| ~ sP362 ),
inference(prop_rule,[status(thm)],[]) ).
thf(191,plain,
( ~ sP99
| ~ sP111
| ~ sP97 ),
inference(prop_rule,[status(thm)],[]) ).
thf(192,plain,
( ~ sP191
| sP99
| ~ sP391 ),
inference(prop_rule,[status(thm)],[]) ).
thf(193,plain,
( ~ sP133
| ~ sP266
| ~ sP97 ),
inference(prop_rule,[status(thm)],[]) ).
thf(194,plain,
( ~ sP419
| sP133
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(195,plain,
( ~ sP305
| ~ sP157
| ~ sP97 ),
inference(prop_rule,[status(thm)],[]) ).
thf(196,plain,
( ~ sP351
| sP305
| ~ sP121 ),
inference(prop_rule,[status(thm)],[]) ).
thf(197,plain,
( ~ sP196
| sP189 ),
inference(all_rule,[status(thm)],[]) ).
thf(198,plain,
( ~ sP196
| sP219 ),
inference(all_rule,[status(thm)],[]) ).
thf(199,plain,
( ~ sP70
| sP347 ),
inference(all_rule,[status(thm)],[]) ).
thf(200,plain,
( ~ sP343
| ~ sP303
| ~ sP149 ),
inference(prop_rule,[status(thm)],[]) ).
thf(201,plain,
( ~ sP63
| ~ sP149
| ~ sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(202,plain,
( ~ sP454
| sP343
| ~ sP276 ),
inference(prop_rule,[status(thm)],[]) ).
thf(203,plain,
( ~ sP130
| sP63
| ~ sP462 ),
inference(prop_rule,[status(thm)],[]) ).
thf(204,plain,
( ~ sP446
| ~ sP121
| ~ sP276 ),
inference(prop_rule,[status(thm)],[]) ).
thf(205,plain,
( ~ sP431
| ~ sP432
| ~ sP462 ),
inference(prop_rule,[status(thm)],[]) ).
thf(206,plain,
( ~ sP10
| sP454 ),
inference(all_rule,[status(thm)],[]) ).
thf(207,plain,
( ~ sP10
| sP119 ),
inference(all_rule,[status(thm)],[]) ).
thf(208,plain,
( ~ sP10
| sP83 ),
inference(all_rule,[status(thm)],[]) ).
thf(209,plain,
( ~ sP299
| sP130 ),
inference(all_rule,[status(thm)],[]) ).
thf(210,plain,
( ~ sP299
| sP337 ),
inference(all_rule,[status(thm)],[]) ).
thf(211,plain,
( ~ sP299
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(212,plain,
( ~ sP287
| sP446
| ~ sP149 ),
inference(prop_rule,[status(thm)],[]) ).
thf(213,plain,
( ~ sP234
| sP431
| ~ sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(214,plain,
( ~ sP466
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(215,plain,
( ~ sP466
| sP299 ),
inference(all_rule,[status(thm)],[]) ).
thf(216,plain,
( ~ sP466
| sP498 ),
inference(all_rule,[status(thm)],[]) ).
thf(217,plain,
( ~ sP466
| sP373 ),
inference(all_rule,[status(thm)],[]) ).
thf(218,plain,
( ~ sP268
| sP287 ),
inference(all_rule,[status(thm)],[]) ).
thf(219,plain,
( ~ sP268
| sP309 ),
inference(all_rule,[status(thm)],[]) ).
thf(220,plain,
( ~ sP268
| sP383 ),
inference(all_rule,[status(thm)],[]) ).
thf(221,plain,
( ~ sP321
| sP234 ),
inference(all_rule,[status(thm)],[]) ).
thf(222,plain,
( ~ sP477
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(223,plain,
( ~ sP264
| sP294 ),
inference(all_rule,[status(thm)],[]) ).
thf(224,plain,
( ~ sP412
| sP466 ),
inference(all_rule,[status(thm)],[]) ).
thf(225,plain,
( ~ sP307
| sP268 ),
inference(all_rule,[status(thm)],[]) ).
thf(226,plain,
( ~ sP138
| sP143 ),
inference(all_rule,[status(thm)],[]) ).
thf(227,plain,
( ~ sP240
| sP128 ),
inference(all_rule,[status(thm)],[]) ).
thf(228,plain,
( ~ sP5
| sP321 ),
inference(all_rule,[status(thm)],[]) ).
thf(229,plain,
( ~ sP372
| sP481 ),
inference(all_rule,[status(thm)],[]) ).
thf(230,plain,
( ~ sP355
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(231,plain,
( ~ sP210
| sP474 ),
inference(all_rule,[status(thm)],[]) ).
thf(232,plain,
( ~ sP231
| sP385 ),
inference(all_rule,[status(thm)],[]) ).
thf(233,plain,
( ~ sP461
| sP384 ),
inference(all_rule,[status(thm)],[]) ).
thf(234,plain,
( ~ sP123
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(235,plain,
( ~ sP423
| sP118 ),
inference(all_rule,[status(thm)],[]) ).
thf(236,plain,
( ~ sP49
| sP401 ),
inference(all_rule,[status(thm)],[]) ).
thf(237,plain,
( ~ sP164
| sP353 ),
inference(all_rule,[status(thm)],[]) ).
thf(238,plain,
( ~ sP12
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(239,plain,
( ~ sP313
| sP389 ),
inference(all_rule,[status(thm)],[]) ).
thf(240,plain,
( ~ sP236
| sP516 ),
inference(all_rule,[status(thm)],[]) ).
thf(241,plain,
( ~ sP142
| sP134 ),
inference(all_rule,[status(thm)],[]) ).
thf(242,plain,
( ~ sP399
| sP426 ),
inference(all_rule,[status(thm)],[]) ).
thf(243,plain,
( ~ sP132
| sP191 ),
inference(all_rule,[status(thm)],[]) ).
thf(244,plain,
( ~ sP315
| sP419 ),
inference(all_rule,[status(thm)],[]) ).
thf(245,plain,
( ~ sP75
| sP351 ),
inference(all_rule,[status(thm)],[]) ).
thf(246,plain,
( ~ sP354
| sP196 ),
inference(all_rule,[status(thm)],[]) ).
thf(247,plain,
( ~ sP414
| sP70 ),
inference(all_rule,[status(thm)],[]) ).
thf(248,plain,
( ~ sP90
| ~ sP61
| sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(249,plain,
( ~ sP71
| ~ sP227
| sP101 ),
inference(prop_rule,[status(thm)],[]) ).
thf(250,plain,
( ~ sP501
| ~ sP105
| sP363 ),
inference(prop_rule,[status(thm)],[]) ).
thf(251,plain,
( sP181
| ~ sP230 ),
inference(prop_rule,[status(thm)],[]) ).
thf(252,plain,
( ~ sP277
| sP90 ),
inference(all_rule,[status(thm)],[]) ).
thf(253,plain,
( ~ sP277
| sP71 ),
inference(all_rule,[status(thm)],[]) ).
thf(254,plain,
( ~ sP277
| sP501 ),
inference(all_rule,[status(thm)],[]) ).
thf(255,plain,
( ~ sP207
| ~ sP428
| sP106 ),
inference(prop_rule,[status(thm)],[]) ).
thf(256,plain,
( ~ sP416
| ~ sP396
| sP98 ),
inference(prop_rule,[status(thm)],[]) ).
thf(257,plain,
( ~ sP226
| ~ sP54 ),
inference(all_rule,[status(thm)],[]) ).
thf(258,plain,
( ~ sP1
| sP277 ),
inference(all_rule,[status(thm)],[]) ).
thf(259,plain,
( ~ sP194
| sP207 ),
inference(all_rule,[status(thm)],[]) ).
thf(260,plain,
( ~ sP80
| sP416 ),
inference(all_rule,[status(thm)],[]) ).
thf(261,plain,
( ~ sP494
| sP111
| ~ sP169
| ~ sP229 ),
inference(mating_rule,[status(thm)],[]) ).
thf(262,plain,
( ~ sP518
| sP157
| sP326
| ~ sP229 ),
inference(mating_rule,[status(thm)],[]) ).
thf(263,plain,
( ~ sP517
| ~ sP25
| ~ sP390 ),
inference(prop_rule,[status(thm)],[]) ).
thf(264,plain,
( ~ sP112
| sP517
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(265,plain,
( ~ sP176
| ~ sP25
| ~ sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(266,plain,
( ~ sP267
| sP176
| ~ sP439 ),
inference(prop_rule,[status(thm)],[]) ).
thf(267,plain,
( ~ sP254
| sP291
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(268,plain,
( ~ sP283
| sP348
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(269,plain,
( ~ sP400
| sP348
| ~ sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(270,plain,
( ~ sP127
| ~ sP160
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(271,plain,
( ~ sP348
| sP127
| ~ sP403 ),
inference(prop_rule,[status(thm)],[]) ).
thf(272,plain,
( ~ sP371
| sP86
| ~ sP120 ),
inference(prop_rule,[status(thm)],[]) ).
thf(273,plain,
( ~ sP370
| ~ sP160
| ~ sP390 ),
inference(prop_rule,[status(thm)],[]) ).
thf(274,plain,
( ~ sP86
| sP370
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(275,plain,
( ~ sP81
| sP112
| ~ sP274 ),
inference(prop_rule,[status(thm)],[]) ).
thf(276,plain,
( ~ sP465
| sP267
| ~ sP468 ),
inference(prop_rule,[status(thm)],[]) ).
thf(277,plain,
( ~ sP183
| sP69
| ~ sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(278,plain,
( ~ sP204
| ~ sP22
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(279,plain,
( ~ sP69
| sP204
| ~ sP295 ),
inference(prop_rule,[status(thm)],[]) ).
thf(280,plain,
( ~ sP316
| ~ sP390
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(281,plain,
( ~ sP291
| sP316
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(282,plain,
( ~ sP442
| sP254 ),
inference(all_rule,[status(thm)],[]) ).
thf(283,plain,
( ~ sP304
| sP283 ),
inference(all_rule,[status(thm)],[]) ).
thf(284,plain,
( ~ sP304
| sP400 ),
inference(all_rule,[status(thm)],[]) ).
thf(285,plain,
( ~ sP24
| sP371 ),
inference(all_rule,[status(thm)],[]) ).
thf(286,plain,
( ~ sP487
| sP81 ),
inference(all_rule,[status(thm)],[]) ).
thf(287,plain,
( ~ sP459
| sP465 ),
inference(all_rule,[status(thm)],[]) ).
thf(288,plain,
( ~ sP156
| sP329
| ~ sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(289,plain,
( ~ sP270
| ~ sP346
| ~ sP295 ),
inference(prop_rule,[status(thm)],[]) ).
thf(290,plain,
( ~ sP329
| sP270
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(291,plain,
( ~ sP260
| sP183 ),
inference(all_rule,[status(thm)],[]) ).
thf(292,plain,
( ~ sP398
| ~ sP330
| ~ sP266 ),
inference(prop_rule,[status(thm)],[]) ).
thf(293,plain,
( ~ sP144
| sP398
| ~ sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(294,plain,
( ~ sP94
| ~ sP330
| ~ sP111 ),
inference(prop_rule,[status(thm)],[]) ).
thf(295,plain,
( ~ sP463
| sP94
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(296,plain,
( ~ sP78
| sP425
| sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(297,plain,
( ~ sP16
| sP78
| sP111 ),
inference(prop_rule,[status(thm)],[]) ).
thf(298,plain,
( ~ sP232
| sP117
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(299,plain,
( ~ sP376
| sP232
| sP330 ),
inference(prop_rule,[status(thm)],[]) ).
thf(300,plain,
( ~ sP414
| sP442 ),
inference(all_rule,[status(thm)],[]) ).
thf(301,plain,
( ~ sP11
| sP304 ),
inference(all_rule,[status(thm)],[]) ).
thf(302,plain,
( ~ sP11
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(303,plain,
( ~ sP159
| sP487 ),
inference(all_rule,[status(thm)],[]) ).
thf(304,plain,
( ~ sP159
| sP459 ),
inference(all_rule,[status(thm)],[]) ).
thf(305,plain,
( ~ sP23
| sP156 ),
inference(all_rule,[status(thm)],[]) ).
thf(306,plain,
( ~ sP239
| ~ sP157
| ~ sP330 ),
inference(prop_rule,[status(thm)],[]) ).
thf(307,plain,
( ~ sP339
| ~ sP266
| ~ sP157 ),
inference(prop_rule,[status(thm)],[]) ).
thf(308,plain,
( ~ sP93
| ~ sP266
| ~ sP111 ),
inference(prop_rule,[status(thm)],[]) ).
thf(309,plain,
( ~ sP200
| ~ sP111
| ~ sP157 ),
inference(prop_rule,[status(thm)],[]) ).
thf(310,plain,
( ~ sP224
| sP140
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(311,plain,
( ~ sP422
| sP248
| sP390 ),
inference(prop_rule,[status(thm)],[]) ).
thf(312,plain,
( ~ sP365
| sP239
| ~ sP409 ),
inference(prop_rule,[status(thm)],[]) ).
thf(313,plain,
( ~ sP184
| sP339
| ~ sP462 ),
inference(prop_rule,[status(thm)],[]) ).
thf(314,plain,
( ~ sP408
| sP93
| ~ sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(315,plain,
( ~ sP448
| sP200
| ~ sP444 ),
inference(prop_rule,[status(thm)],[]) ).
thf(316,plain,
( ~ sP492
| ~ sP413
| ~ sP203 ),
inference(prop_rule,[status(thm)],[]) ).
thf(317,plain,
( ~ sP496
| ~ sP101
| sP140 ),
inference(prop_rule,[status(thm)],[]) ).
thf(318,plain,
( ~ sP258
| ~ sP363
| sP248 ),
inference(prop_rule,[status(thm)],[]) ).
thf(319,plain,
( ~ sP263
| sP224
| sP157 ),
inference(prop_rule,[status(thm)],[]) ).
thf(320,plain,
( ~ sP288
| sP422
| sP266 ),
inference(prop_rule,[status(thm)],[]) ).
thf(321,plain,
( ~ sP354
| sP260 ),
inference(all_rule,[status(thm)],[]) ).
thf(322,plain,
( ~ sP75
| sP365 ),
inference(all_rule,[status(thm)],[]) ).
thf(323,plain,
( ~ sP315
| sP184 ),
inference(all_rule,[status(thm)],[]) ).
thf(324,plain,
( ~ sP315
| sP408 ),
inference(all_rule,[status(thm)],[]) ).
thf(325,plain,
( ~ sP132
| sP448 ),
inference(all_rule,[status(thm)],[]) ).
thf(326,plain,
( ~ sP399
| sP144 ),
inference(all_rule,[status(thm)],[]) ).
thf(327,plain,
( ~ sP399
| sP463 ),
inference(all_rule,[status(thm)],[]) ).
thf(328,plain,
( ~ sP255
| sP492
| ~ sP111 ),
inference(prop_rule,[status(thm)],[]) ).
thf(329,plain,
( ~ sP469
| sP369
| sP346 ),
inference(prop_rule,[status(thm)],[]) ).
thf(330,plain,
( ~ sP357
| sP496 ),
inference(all_rule,[status(thm)],[]) ).
thf(331,plain,
( ~ sP357
| sP258 ),
inference(all_rule,[status(thm)],[]) ).
thf(332,plain,
( ~ sP142
| sP263 ),
inference(all_rule,[status(thm)],[]) ).
thf(333,plain,
( ~ sP142
| sP288 ),
inference(all_rule,[status(thm)],[]) ).
thf(334,plain,
( ~ sP142
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(335,plain,
( ~ sP142
| sP376 ),
inference(all_rule,[status(thm)],[]) ).
thf(336,plain,
( ~ sP236
| sP354 ),
inference(all_rule,[status(thm)],[]) ).
thf(337,plain,
( ~ sP236
| sP414 ),
inference(all_rule,[status(thm)],[]) ).
thf(338,plain,
( ~ sP236
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(339,plain,
( ~ sP236
| sP159 ),
inference(all_rule,[status(thm)],[]) ).
thf(340,plain,
( ~ sP328
| sP75 ),
inference(all_rule,[status(thm)],[]) ).
thf(341,plain,
( ~ sP328
| sP315 ),
inference(all_rule,[status(thm)],[]) ).
thf(342,plain,
( ~ sP328
| sP132 ),
inference(all_rule,[status(thm)],[]) ).
thf(343,plain,
( ~ sP328
| sP399 ),
inference(all_rule,[status(thm)],[]) ).
thf(344,plain,
( sP230
| ~ sP369 ),
inference(prop_rule,[status(thm)],[]) ).
thf(345,plain,
( ~ sP92
| sP255 ),
inference(all_rule,[status(thm)],[]) ).
thf(346,plain,
( ~ sP313
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(347,plain,
( ~ sP388
| sP469
| sP413 ),
inference(prop_rule,[status(thm)],[]) ).
thf(348,plain,
( ~ sP65
| ~ sP106
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(349,plain,
( ~ sP269
| ~ sP98
| sP452 ),
inference(prop_rule,[status(thm)],[]) ).
thf(350,plain,
( ~ sP226
| ~ sP505 ),
inference(all_rule,[status(thm)],[]) ).
thf(351,plain,
( ~ sP1
| sP357 ),
inference(all_rule,[status(thm)],[]) ).
thf(352,plain,
( ~ sP477
| sP142 ),
inference(all_rule,[status(thm)],[]) ).
thf(353,plain,
( ~ sP264
| sP236 ),
inference(all_rule,[status(thm)],[]) ).
thf(354,plain,
( ~ sP412
| sP328 ),
inference(all_rule,[status(thm)],[]) ).
thf(355,plain,
( ~ sP307
| sP92 ),
inference(all_rule,[status(thm)],[]) ).
thf(356,plain,
( ~ sP138
| sP313 ),
inference(all_rule,[status(thm)],[]) ).
thf(357,plain,
( ~ sP240
| sP388 ),
inference(all_rule,[status(thm)],[]) ).
thf(358,plain,
( ~ sP190
| sP65 ),
inference(all_rule,[status(thm)],[]) ).
thf(359,plain,
( ~ sP194
| sP269 ),
inference(all_rule,[status(thm)],[]) ).
thf(360,plain,
( ~ sP503
| sP50
| ~ sP8
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(361,plain,
( ~ sP518
| sP458
| ~ sP333
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(362,plain,
( ~ sP494
| sP458
| ~ sP165
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(363,plain,
( ~ sP50
| sP439
| ~ sP169
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(364,plain,
( ~ sP439
| sP272
| ~ sP278
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(365,plain,
( ~ sP50
| sP272
| ~ sP165
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(366,plain,
( ~ sP503
| sP272
| ~ sP333
| sP326 ),
inference(mating_rule,[status(thm)],[]) ).
thf(367,plain,
( ~ sP403
| sP503
| sP326
| ~ sP278 ),
inference(mating_rule,[status(thm)],[]) ).
thf(368,plain,
( ~ sP352
| ~ sP272
| ~ sP272 ),
inference(prop_rule,[status(thm)],[]) ).
thf(369,plain,
( ~ sP377
| sP352
| ~ sP272 ),
inference(prop_rule,[status(thm)],[]) ).
thf(370,plain,
( ~ sP212
| sP451
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(371,plain,
( ~ sP293
| ~ sP439
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(372,plain,
( ~ sP342
| sP293
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(373,plain,
( ~ sP271
| sP342
| ~ sP274 ),
inference(prop_rule,[status(thm)],[]) ).
thf(374,plain,
( ~ sP58
| sP377
| ~ sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(375,plain,
( ~ sP223
| sP377
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(376,plain,
( ~ sP221
| sP85
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(377,plain,
( ~ sP44
| ~ sP503
| ~ sP439 ),
inference(prop_rule,[status(thm)],[]) ).
thf(378,plain,
( ~ sP85
| sP44
| ~ sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(379,plain,
( ~ sP411
| sP249
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(380,plain,
( ~ sP480
| ~ sP50
| ~ sP439 ),
inference(prop_rule,[status(thm)],[]) ).
thf(381,plain,
( ~ sP249
| sP480
| ~ sP120 ),
inference(prop_rule,[status(thm)],[]) ).
thf(382,plain,
( ~ sP19
| ~ sP439
| ~ sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(383,plain,
( ~ sP451
| sP19
| ~ sP403 ),
inference(prop_rule,[status(thm)],[]) ).
thf(384,plain,
( ~ sP29
| sP212 ),
inference(all_rule,[status(thm)],[]) ).
thf(385,plain,
( ~ sP500
| sP271 ),
inference(all_rule,[status(thm)],[]) ).
thf(386,plain,
( ~ sP486
| sP58 ),
inference(all_rule,[status(thm)],[]) ).
thf(387,plain,
( ~ sP486
| sP223 ),
inference(all_rule,[status(thm)],[]) ).
thf(388,plain,
( ~ sP358
| sP20
| ~ sP403 ),
inference(prop_rule,[status(thm)],[]) ).
thf(389,plain,
( ~ sP116
| ~ sP295
| ~ sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(390,plain,
( ~ sP20
| sP116
| ~ sP439 ),
inference(prop_rule,[status(thm)],[]) ).
thf(391,plain,
( ~ sP375
| sP87
| ~ sP403 ),
inference(prop_rule,[status(thm)],[]) ).
thf(392,plain,
( ~ sP281
| ~ sP274
| ~ sP120 ),
inference(prop_rule,[status(thm)],[]) ).
thf(393,plain,
( ~ sP87
| sP281
| ~ sP439 ),
inference(prop_rule,[status(thm)],[]) ).
thf(394,plain,
( ~ sP493
| sP209
| ~ sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(395,plain,
( ~ sP495
| ~ sP62
| ~ sP274 ),
inference(prop_rule,[status(thm)],[]) ).
thf(396,plain,
( ~ sP209
| sP495
| ~ sP295 ),
inference(prop_rule,[status(thm)],[]) ).
thf(397,plain,
( ~ sP395
| sP456
| ~ sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(398,plain,
( ~ sP298
| ~ sP125
| ~ sP295 ),
inference(prop_rule,[status(thm)],[]) ).
thf(399,plain,
( ~ sP456
| sP298
| ~ sP468 ),
inference(prop_rule,[status(thm)],[]) ).
thf(400,plain,
( ~ sP233
| sP26
| ~ sP120 ),
inference(prop_rule,[status(thm)],[]) ).
thf(401,plain,
( ~ sP68
| sP221 ),
inference(all_rule,[status(thm)],[]) ).
thf(402,plain,
( ~ sP12
| sP411 ),
inference(all_rule,[status(thm)],[]) ).
thf(403,plain,
( ~ sP164
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(404,plain,
( ~ sP164
| sP500 ),
inference(all_rule,[status(thm)],[]) ).
thf(405,plain,
( ~ sP205
| sP486 ),
inference(all_rule,[status(thm)],[]) ).
thf(406,plain,
( ~ sP335
| sP358 ),
inference(all_rule,[status(thm)],[]) ).
thf(407,plain,
( ~ sP51
| sP375 ),
inference(all_rule,[status(thm)],[]) ).
thf(408,plain,
( ~ sP84
| sP493 ),
inference(all_rule,[status(thm)],[]) ).
thf(409,plain,
( ~ sP18
| sP395 ),
inference(all_rule,[status(thm)],[]) ).
thf(410,plain,
( ~ sP471
| ~ sP503
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(411,plain,
( ~ sP322
| ~ sP50
| ~ sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(412,plain,
( ~ sP26
| sP471
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(413,plain,
( ~ sP193
| sP322
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(414,plain,
( ~ sP199
| ~ sP295
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(415,plain,
( ~ sP137
| sP193
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(416,plain,
( ~ sP186
| ~ sP518
| ~ sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(417,plain,
( ~ sP265
| ~ sP518
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(418,plain,
( ~ sP35
| ~ sP494
| ~ sP518 ),
inference(prop_rule,[status(thm)],[]) ).
thf(419,plain,
( ~ sP386
| ~ sP494
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(420,plain,
( ~ sP433
| ~ sP150
| ~ sP518 ),
inference(prop_rule,[status(thm)],[]) ).
thf(421,plain,
( ~ sP241
| ~ sP150
| ~ sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(422,plain,
( ~ sP360
| ~ sP458
| ~ sP518 ),
inference(prop_rule,[status(thm)],[]) ).
thf(423,plain,
( ~ sP15
| ~ sP458
| ~ sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(424,plain,
( ~ sP476
| sP199
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(425,plain,
( ~ sP256
| sP387
| sP503 ),
inference(prop_rule,[status(thm)],[]) ).
thf(426,plain,
( ~ sP257
| sP172
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(427,plain,
( ~ sP344
| sP509
| sP439 ),
inference(prop_rule,[status(thm)],[]) ).
thf(428,plain,
( ~ sP228
| sP233 ),
inference(all_rule,[status(thm)],[]) ).
thf(429,plain,
( ~ sP42
| sP137 ),
inference(all_rule,[status(thm)],[]) ).
thf(430,plain,
( ~ sP55
| sP186
| ~ sP276 ),
inference(prop_rule,[status(thm)],[]) ).
thf(431,plain,
( ~ sP497
| sP265
| ~ sP203 ),
inference(prop_rule,[status(thm)],[]) ).
thf(432,plain,
( ~ sP198
| sP35
| ~ sP462 ),
inference(prop_rule,[status(thm)],[]) ).
thf(433,plain,
( ~ sP282
| sP386
| ~ sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(434,plain,
( ~ sP508
| sP433
| ~ sP444 ),
inference(prop_rule,[status(thm)],[]) ).
thf(435,plain,
( ~ sP415
| sP241
| ~ sP374 ),
inference(prop_rule,[status(thm)],[]) ).
thf(436,plain,
( ~ sP31
| sP360
| ~ sP518 ),
inference(prop_rule,[status(thm)],[]) ).
thf(437,plain,
( ~ sP188
| sP15
| ~ sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(438,plain,
( ~ sP76
| ~ sP409
| ~ sP276 ),
inference(prop_rule,[status(thm)],[]) ).
thf(439,plain,
( ~ sP479
| ~ sP409
| ~ sP203 ),
inference(prop_rule,[status(thm)],[]) ).
thf(440,plain,
( ~ sP100
| sP476
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(441,plain,
( ~ sP107
| ~ sP135
| ~ sP462 ),
inference(prop_rule,[status(thm)],[]) ).
thf(442,plain,
( ~ sP450
| ~ sP135
| ~ sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(443,plain,
( ~ sP237
| ~ sP110
| ~ sP444 ),
inference(prop_rule,[status(thm)],[]) ).
thf(444,plain,
( ~ sP148
| ~ sP110
| ~ sP374 ),
inference(prop_rule,[status(thm)],[]) ).
thf(445,plain,
( ~ sP327
| ~ sP248
| sP387 ),
inference(prop_rule,[status(thm)],[]) ).
thf(446,plain,
( ~ sP325
| ~ sP425
| sP172 ),
inference(prop_rule,[status(thm)],[]) ).
thf(447,plain,
( ~ sP218
| ~ sP117
| sP509 ),
inference(prop_rule,[status(thm)],[]) ).
thf(448,plain,
( ~ sP168
| sP256
| sP518 ),
inference(prop_rule,[status(thm)],[]) ).
thf(449,plain,
( ~ sP394
| sP257
| sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(450,plain,
( ~ sP438
| sP344
| sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(451,plain,
( ~ sP331
| sP228 ),
inference(all_rule,[status(thm)],[]) ).
thf(452,plain,
( ~ sP331
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(453,plain,
( ~ sP245
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(454,plain,
( ~ sP245
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(455,plain,
( ~ sP89
| sP55 ),
inference(all_rule,[status(thm)],[]) ).
thf(456,plain,
( ~ sP89
| sP497 ),
inference(all_rule,[status(thm)],[]) ).
thf(457,plain,
( ~ sP49
| sP198 ),
inference(all_rule,[status(thm)],[]) ).
thf(458,plain,
( ~ sP49
| sP282 ),
inference(all_rule,[status(thm)],[]) ).
thf(459,plain,
( ~ sP126
| sP508 ),
inference(all_rule,[status(thm)],[]) ).
thf(460,plain,
( ~ sP126
| sP415 ),
inference(all_rule,[status(thm)],[]) ).
thf(461,plain,
( ~ sP27
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(462,plain,
( ~ sP27
| sP188 ),
inference(all_rule,[status(thm)],[]) ).
thf(463,plain,
( ~ sP440
| sP76
| ~ sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(464,plain,
( ~ sP483
| sP479
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(465,plain,
( ~ sP253
| sP100 ),
inference(all_rule,[status(thm)],[]) ).
thf(466,plain,
( ~ sP124
| sP333
| sP295 ),
inference(prop_rule,[status(thm)],[]) ).
thf(467,plain,
( ~ sP319
| ~ sP276
| ~ sP409 ),
inference(prop_rule,[status(thm)],[]) ).
thf(468,plain,
( ~ sP436
| sP107
| ~ sP518 ),
inference(prop_rule,[status(thm)],[]) ).
thf(469,plain,
( ~ sP392
| sP450
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(470,plain,
( ~ sP441
| sP165
| sP274 ),
inference(prop_rule,[status(thm)],[]) ).
thf(471,plain,
( ~ sP320
| sP237
| ~ sP518 ),
inference(prop_rule,[status(thm)],[]) ).
thf(472,plain,
( ~ sP301
| sP148
| ~ sP494 ),
inference(prop_rule,[status(thm)],[]) ).
thf(473,plain,
( ~ sP381
| sP278
| sP468 ),
inference(prop_rule,[status(thm)],[]) ).
thf(474,plain,
( ~ sP350
| ~ sP374
| ~ sP110 ),
inference(prop_rule,[status(thm)],[]) ).
thf(475,plain,
( ~ sP80
| sP327 ),
inference(all_rule,[status(thm)],[]) ).
thf(476,plain,
( ~ sP80
| sP325 ),
inference(all_rule,[status(thm)],[]) ).
thf(477,plain,
( ~ sP80
| sP218 ),
inference(all_rule,[status(thm)],[]) ).
thf(478,plain,
( ~ sP423
| sP168 ),
inference(all_rule,[status(thm)],[]) ).
thf(479,plain,
( ~ sP423
| sP394 ),
inference(all_rule,[status(thm)],[]) ).
thf(480,plain,
( ~ sP423
| sP438 ),
inference(all_rule,[status(thm)],[]) ).
thf(481,plain,
( ~ sP123
| sP331 ),
inference(all_rule,[status(thm)],[]) ).
thf(482,plain,
( ~ sP123
| sP245 ),
inference(all_rule,[status(thm)],[]) ).
thf(483,plain,
( ~ sP123
| sP164 ),
inference(all_rule,[status(thm)],[]) ).
thf(484,plain,
( ~ sP123
| sP205 ),
inference(all_rule,[status(thm)],[]) ).
thf(485,plain,
( ~ sP461
| sP89 ),
inference(all_rule,[status(thm)],[]) ).
thf(486,plain,
( ~ sP461
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(487,plain,
( ~ sP461
| sP126 ),
inference(all_rule,[status(thm)],[]) ).
thf(488,plain,
( ~ sP461
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(489,plain,
( ~ sP341
| ~ sP46
| sP333 ),
inference(prop_rule,[status(thm)],[]) ).
thf(490,plain,
( ~ sP418
| sP440 ),
inference(all_rule,[status(thm)],[]) ).
thf(491,plain,
( ~ sP418
| sP483 ),
inference(all_rule,[status(thm)],[]) ).
thf(492,plain,
( ~ sP514
| sP253 ),
inference(all_rule,[status(thm)],[]) ).
thf(493,plain,
( ~ sP514
| sP335 ),
inference(all_rule,[status(thm)],[]) ).
thf(494,plain,
( ~ sP445
| sP124
| sP409 ),
inference(prop_rule,[status(thm)],[]) ).
thf(495,plain,
( ~ sP449
| ~ sP452
| sP165 ),
inference(prop_rule,[status(thm)],[]) ).
thf(496,plain,
( ~ sP96
| sP319
| ~ sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(497,plain,
( ~ sP312
| sP436 ),
inference(all_rule,[status(thm)],[]) ).
thf(498,plain,
( ~ sP312
| sP392 ),
inference(all_rule,[status(thm)],[]) ).
thf(499,plain,
( ~ sP324
| sP51 ),
inference(all_rule,[status(thm)],[]) ).
thf(500,plain,
( ~ sP220
| sP441
| sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(501,plain,
( ~ sP153
| sP320 ),
inference(all_rule,[status(thm)],[]) ).
thf(502,plain,
( ~ sP153
| sP301 ),
inference(all_rule,[status(thm)],[]) ).
thf(503,plain,
( ~ sP211
| sP381
| sP110 ),
inference(prop_rule,[status(thm)],[]) ).
thf(504,plain,
( sP229
| ~ sP278 ),
inference(prop_rule,[status(thm)],[]) ).
thf(505,plain,
( ~ sP67
| sP350
| ~ sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(506,plain,
( ~ sP226
| ~ sP140 ),
inference(all_rule,[status(thm)],[]) ).
thf(507,plain,
( ~ sP1
| sP80 ),
inference(all_rule,[status(thm)],[]) ).
thf(508,plain,
( ~ sP477
| sP423 ),
inference(all_rule,[status(thm)],[]) ).
thf(509,plain,
( ~ sP264
| sP123 ),
inference(all_rule,[status(thm)],[]) ).
thf(510,plain,
( ~ sP412
| sP461 ),
inference(all_rule,[status(thm)],[]) ).
thf(511,plain,
( ~ sP77
| sP341 ),
inference(all_rule,[status(thm)],[]) ).
thf(512,plain,
( ~ sP307
| sP418 ),
inference(all_rule,[status(thm)],[]) ).
thf(513,plain,
( ~ sP138
| sP514 ),
inference(all_rule,[status(thm)],[]) ).
thf(514,plain,
( ~ sP240
| sP445 ),
inference(all_rule,[status(thm)],[]) ).
thf(515,plain,
( ~ sP190
| sP449 ),
inference(all_rule,[status(thm)],[]) ).
thf(516,plain,
( ~ sP435
| sP96 ),
inference(all_rule,[status(thm)],[]) ).
thf(517,plain,
( ~ sP5
| sP312 ),
inference(all_rule,[status(thm)],[]) ).
thf(518,plain,
( ~ sP372
| sP324 ),
inference(all_rule,[status(thm)],[]) ).
thf(519,plain,
( ~ sP355
| sP220 ),
inference(all_rule,[status(thm)],[]) ).
thf(520,plain,
( ~ sP72
| sP84 ),
inference(all_rule,[status(thm)],[]) ).
thf(521,plain,
( ~ sP145
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(522,plain,
( ~ sP210
| sP153 ),
inference(all_rule,[status(thm)],[]) ).
thf(523,plain,
( ~ sP231
| sP211 ),
inference(all_rule,[status(thm)],[]) ).
thf(524,plain,
( ~ sP407
| sP67 ),
inference(all_rule,[status(thm)],[]) ).
thf(525,plain,
( ~ sP7
| ~ sP403
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(526,plain,
( ~ sP262
| sP7
| ~ sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(527,plain,
( ~ sP464
| sP262
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(528,plain,
( ~ sP292
| ~ sP444
| ~ sP374 ),
inference(prop_rule,[status(thm)],[]) ).
thf(529,plain,
( ~ sP74
| ~ sP62
| ~ sP120 ),
inference(prop_rule,[status(thm)],[]) ).
thf(530,plain,
( ~ sP356
| sP21
| sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(531,plain,
( ~ sP417
| sP464 ),
inference(all_rule,[status(thm)],[]) ).
thf(532,plain,
( ~ sP368
| sP292
| ~ sP276 ),
inference(prop_rule,[status(thm)],[]) ).
thf(533,plain,
( ~ sP53
| ~ sP306
| ~ sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(534,plain,
( ~ sP512
| sP53
| ~ sP120 ),
inference(prop_rule,[status(thm)],[]) ).
thf(535,plain,
( ~ sP460
| ~ sP177
| ~ sP462 ),
inference(prop_rule,[status(thm)],[]) ).
thf(536,plain,
( ~ sP187
| sP74
| ~ sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(537,plain,
( ~ sP424
| ~ sP509
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(538,plain,
( ~ sP290
| sP406
| sP403 ),
inference(prop_rule,[status(thm)],[]) ).
thf(539,plain,
( ~ sP243
| sP290
| sP444 ),
inference(prop_rule,[status(thm)],[]) ).
thf(540,plain,
( ~ sP332
| sP356
| sP374 ),
inference(prop_rule,[status(thm)],[]) ).
thf(541,plain,
( ~ sP122
| sP417 ),
inference(all_rule,[status(thm)],[]) ).
thf(542,plain,
( ~ sP286
| sP368 ),
inference(all_rule,[status(thm)],[]) ).
thf(543,plain,
( ~ sP82
| ~ sP203
| ~ sP276 ),
inference(prop_rule,[status(thm)],[]) ).
thf(544,plain,
( ~ sP478
| sP82
| ~ sP374 ),
inference(prop_rule,[status(thm)],[]) ).
thf(545,plain,
( ~ sP155
| sP512
| ~ sP403 ),
inference(prop_rule,[status(thm)],[]) ).
thf(546,plain,
( ~ sP178
| sP460
| ~ sP444 ),
inference(prop_rule,[status(thm)],[]) ).
thf(547,plain,
( ~ sP41
| sP169
| sP120 ),
inference(prop_rule,[status(thm)],[]) ).
thf(548,plain,
( ~ sP60
| sP187
| ~ sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(549,plain,
( ~ sP39
| ~ sP172
| sP406 ),
inference(prop_rule,[status(thm)],[]) ).
thf(550,plain,
( ~ sP194
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(551,plain,
( ~ sP194
| sP424 ),
inference(all_rule,[status(thm)],[]) ).
thf(552,plain,
( ~ sP231
| sP243 ),
inference(all_rule,[status(thm)],[]) ).
thf(553,plain,
( ~ sP231
| sP332 ),
inference(all_rule,[status(thm)],[]) ).
thf(554,plain,
( ~ sP297
| sP122 ),
inference(all_rule,[status(thm)],[]) ).
thf(555,plain,
( ~ sP210
| sP286 ),
inference(all_rule,[status(thm)],[]) ).
thf(556,plain,
( ~ sP210
| sP407 ),
inference(all_rule,[status(thm)],[]) ).
thf(557,plain,
( ~ sP410
| sP478 ),
inference(all_rule,[status(thm)],[]) ).
thf(558,plain,
( ~ sP48
| sP340
| sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(559,plain,
( ~ sP91
| sP48
| sP203 ),
inference(prop_rule,[status(thm)],[]) ).
thf(560,plain,
( sP278
| ~ sP169 ),
inference(prop_rule,[status(thm)],[]) ).
thf(561,plain,
( ~ sP285
| ~ sP278
| sP169 ),
inference(prop_rule,[status(thm)],[]) ).
thf(562,plain,
( ~ sP37
| sP155 ),
inference(all_rule,[status(thm)],[]) ).
thf(563,plain,
( ~ sP504
| ~ sP276
| ~ sP203 ),
inference(prop_rule,[status(thm)],[]) ).
thf(564,plain,
( ~ sP364
| sP504
| ~ sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(565,plain,
( ~ sP311
| sP178 ),
inference(all_rule,[status(thm)],[]) ).
thf(566,plain,
( ~ sP382
| sP41
| sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(567,plain,
( ~ sP506
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(568,plain,
( sP165
| ~ sP340 ),
inference(prop_rule,[status(thm)],[]) ).
thf(569,plain,
( ~ sP226
| ~ sP387 ),
inference(all_rule,[status(thm)],[]) ).
thf(570,plain,
( ~ sP1
| sP194 ),
inference(all_rule,[status(thm)],[]) ).
thf(571,plain,
( ~ sP477
| sP231 ),
inference(all_rule,[status(thm)],[]) ).
thf(572,plain,
( ~ sP264
| sP297 ),
inference(all_rule,[status(thm)],[]) ).
thf(573,plain,
( ~ sP412
| sP210 ),
inference(all_rule,[status(thm)],[]) ).
thf(574,plain,
( ~ sP307
| sP410 ),
inference(all_rule,[status(thm)],[]) ).
thf(575,plain,
( ~ sP138
| sP145 ),
inference(all_rule,[status(thm)],[]) ).
thf(576,plain,
( ~ sP240
| sP91 ),
inference(all_rule,[status(thm)],[]) ).
thf(577,plain,
( ~ sP190
| sP285 ),
inference(all_rule,[status(thm)],[]) ).
thf(578,plain,
( ~ sP206
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(579,plain,
( ~ sP435
| sP364 ),
inference(all_rule,[status(thm)],[]) ).
thf(580,plain,
( ~ sP5
| sP311 ),
inference(all_rule,[status(thm)],[]) ).
thf(581,plain,
( ~ sP355
| sP382 ),
inference(all_rule,[status(thm)],[]) ).
thf(582,plain,
( ~ sP72
| sP506 ),
inference(all_rule,[status(thm)],[]) ).
thf(583,plain,
~ sP326,
inference(prop_rule,[status(thm)],[]) ).
thf(584,plain,
( ~ sP146
| sP397
| sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(585,plain,
( ~ sP379
| sP146
| sP462 ),
inference(prop_rule,[status(thm)],[]) ).
thf(586,plain,
( ~ sP355
| sP379 ),
inference(all_rule,[status(thm)],[]) ).
thf(587,plain,
( ~ sP372
| sP72 ),
inference(all_rule,[status(thm)],[]) ).
thf(588,plain,
( ~ sP3
| sP8
| sP306 ),
inference(prop_rule,[status(thm)],[]) ).
thf(589,plain,
( ~ sP115
| sP3
| sP276 ),
inference(prop_rule,[status(thm)],[]) ).
thf(590,plain,
( ~ sP213
| ~ sP21
| sP397 ),
inference(prop_rule,[status(thm)],[]) ).
thf(591,plain,
( sP169
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(592,plain,
( ~ sP190
| sP213 ),
inference(all_rule,[status(thm)],[]) ).
thf(593,plain,
( ~ sP154
| ~ sP169
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(594,plain,
( ~ sP226
| ~ sP406 ),
inference(all_rule,[status(thm)],[]) ).
thf(595,plain,
( ~ sP1
| sP190 ),
inference(all_rule,[status(thm)],[]) ).
thf(596,plain,
( ~ sP477
| sP355 ),
inference(all_rule,[status(thm)],[]) ).
thf(597,plain,
( ~ sP264
| sP372 ),
inference(all_rule,[status(thm)],[]) ).
thf(598,plain,
( ~ sP412
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(599,plain,
( ~ sP77
| sP154 ),
inference(all_rule,[status(thm)],[]) ).
thf(600,plain,
( ~ sP307
| sP435 ),
inference(all_rule,[status(thm)],[]) ).
thf(601,plain,
( ~ sP138
| sP206 ),
inference(all_rule,[status(thm)],[]) ).
thf(602,plain,
( ~ sP240
| sP115 ),
inference(all_rule,[status(thm)],[]) ).
thf(603,plain,
( ~ sP226
| ~ sP397 ),
inference(all_rule,[status(thm)],[]) ).
thf(604,plain,
( ~ sP1
| sP77 ),
inference(all_rule,[status(thm)],[]) ).
thf(605,plain,
( ~ sP477
| sP240 ),
inference(all_rule,[status(thm)],[]) ).
thf(606,plain,
( ~ sP264
| sP138 ),
inference(all_rule,[status(thm)],[]) ).
thf(607,plain,
( ~ sP412
| sP307 ),
inference(all_rule,[status(thm)],[]) ).
thf(axb,axiom,
sP412 ).
thf(axr,axiom,
sP264 ).
thf(rb_cov,axiom,
sP477 ).
thf(608,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,axb,axr,rb_cov,h1,h3]) ).
thf(609,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,608,h3]) ).
thf(610,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,609,h1,h2]) ).
thf(inf,axiom,
~ ! [X1: $i > $i] :
( ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X1 @ X3 ) )
=> ( X2 = X3 ) )
=> ! [X2: $i] :
~ ! [X3: $i] :
( ( X1 @ X3 )
!= X2 ) ) ).
thf(611,plain,
$false,
inference(tab_negall,[status(thm),tab_negall(discharge,[h0]),tab_negall(eigenvar,eigen__0)],[inf,610,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA082^1 : TPTP v9.2.0. Released v9.0.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 15:42:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 2.29/2.48 % SZS status Unsatisfiable
% 2.29/2.48 % Mode: cade22grackle2xfee4
% 2.29/2.48 % Steps: 6078
% 2.29/2.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------