%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : GRA118^1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 : Tue May 5 06:31:28 PM UTC 2026
% Result : Unsatisfiable 11.99s 12.02s
% Output : Proof 5.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 731
% Syntax : Number of formulae : 732 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 2296 ( 338 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 5579 (1214 ~; 612 |; 0 &;2801 @)
% ( 350 <=>; 602 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 356 ( 354 usr; 353 con; 0-2 aty)
% Number of variables : 73 ( 0 ^; 73 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_r,type,
r: $i > $i > $o ).
thf(ty_c,type,
c: $i ).
thf(ty_f,type,
f: $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( f @ X1 )
!= c ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( f @ ( f @ ( f @ eigen__0 ) ) )
= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ eigen__0 ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( f @ ( f @ eigen__0 ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= c ) )
=> ( ( f @ c )
= c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ eigen__0 ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ c ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= c ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= c )
=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( c
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ c ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ~ ( r @ c @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) )
=> ( ( f @ c )
= c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) )
=> ( ( f @ ( f @ c ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( ( f @ ( f @ c ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ c ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= c ) )
=> ( ( f @ ( f @ c ) )
= c ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) )
=> ( ( f @ c )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= c )
=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( c
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( r @ ( f @ ( f @ c ) ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP4
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( f @ c )
= c ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ ( ~ ( ~ sP30
=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( r @ ( f @ c ) @ c )
=> ( r @ c @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= c )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ( c
= ( f @ c ) ) )
=> ~ sP29 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) )
=> ~ ( r @ c @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= c ) )
=> ( ( f @ ( f @ c ) )
= c ) )
=> ~ sP27 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ c ) )
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X2 ) )
=> ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ sP7
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( ( f @ ( f @ c ) )
= ( f @ c ) )
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( c
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ ( ~ sP11
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i] :
( ( ( f @ c )
= ( f @ X1 ) )
=> ( c = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $i] :
( ( ( f @ ( f @ c ) )
= ( f @ X1 ) )
=> ( ( f @ c )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ~ ( ~ ( ~ sP42
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) )
=> sP28 )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ ( ~ sP11
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ sP42
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= c ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) )
=> sP29 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ ( ~ ( ~ sP51
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( c
= ( f @ ( f @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= c ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ sP41
=> ~ ( r @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) )
=> ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( ~ sP30
=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ( f @ ( f @ eigen__0 ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= c ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) )
=> ~ sP28 )
=> ~ sP29 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ~ ( ~ ( ~ sP14
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ c ) ) )
=> ~ sP62 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ( ( f @ ( f @ c ) )
!= c )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ~ ( ~ sP45
=> ~ sP16 )
=> ~ ( r @ c @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( ( f @ ( f @ ( f @ eigen__0 ) ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ c )
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( ( c
= ( f @ c ) )
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ~ sP19 )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( sP58
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( c = X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ~ ( r @ c @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) )
=> sP28 )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) )
=> ~ sP28 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X1 ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ c ) )
=> sP79 ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X2 ) )
=> ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( ~ sP67
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( ( f @ eigen__0 )
= c ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( ~ ( ~ ( ~ sP25
=> sP16 )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) )
=> ( r @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( ~ ( ~ sP18
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( ~ sP55
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> sP28 )
=> ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( ~ ( ~ ( ~ sP18
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> sP86 )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ! [X1: $i] :
( ( ( f @ ( f @ eigen__0 ) )
= ( f @ X1 ) )
=> ( ( f @ eigen__0 )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> sP86 )
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( ( r @ c @ ( f @ c ) )
=> ( r @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> sP86 )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( ( ( f @ c )
= ( f @ ( f @ ( f @ eigen__0 ) ) ) )
=> sP58 ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( ~ sP92
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ( ~ ( ~ ( ~ sP4
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( ~ ( ~ ( ~ sP77
=> ( c
= ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X1 ) )
=> ~ sP62 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ c ) )
= c ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ( ~ sP97
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ! [X1: $i] :
( ( r @ c @ X1 )
=> ( r @ X1 @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ( ~ ( ~ ( ~ ( ~ sP50
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ~ sP19 )
=> ~ sP16 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP86
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ c ) ) ) )
=> sP78 )
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ( ~ ( ~ ( ~ sP39
=> sP32 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( ~ ( ~ ( ~ sP17
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> sP27 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ c ) )
=> sP79 )
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c )
=> ( r @ c @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= c )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ( c = X1 ) )
=> ~ sP29 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ~ ( r @ c @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( ( ( f @ ( f @ c ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( ~ ( ~ ( ~ sP120
=> ( ( f @ c )
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ( ~ sP59
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ( ~ sP4
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( ~ sP108
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ~ sP28 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> sP101 ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ( ~ sP14
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130,plain,
( sP130
<=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131,plain,
( sP131
<=> ( sP66
=> sP90 ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132,plain,
( sP132
<=> ! [X1: $i] :
( ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 )
=> ( r @ X1 @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133,plain,
( sP133
<=> ( ~ ( ~ ( ~ sP120
=> ( ( f @ c )
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134,plain,
( sP134
<=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135,plain,
( sP135
<=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136,plain,
( sP136
<=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137,plain,
( sP137
<=> ( ~ ( ~ sP24
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP62 ) ),
introduced(definition,[new_symbols(definition,[sP137])]) ).
thf(sP138,plain,
( sP138
<=> ( ~ sP117
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139,plain,
( sP139
<=> ( ~ sP51
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140,plain,
( sP140
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> sP136 )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ c ) ) ) )
=> sP78 ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141,plain,
( sP141
<=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142,plain,
( sP142
<=> ( ~ ( ~ sP117
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143,plain,
( sP143
<=> ! [X1: $i] :
( ( c = X1 )
=> ( X1 = c ) ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144,plain,
( sP144
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ~ sP130 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145,plain,
( sP145
<=> ( ~ sP31
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146,plain,
( sP146
<=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP146])]) ).
thf(sP147,plain,
( sP147
<=> ( ~ ( ~ sP120
=> ( ( f @ c )
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP147])]) ).
thf(sP148,plain,
( sP148
<=> ( ~ ( ~ sP115
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP148])]) ).
thf(sP149,plain,
( sP149
<=> ( ~ sP26
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP149])]) ).
thf(sP150,plain,
( sP150
<=> ( ~ sP139
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP150])]) ).
thf(sP151,plain,
( sP151
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= X1 )
=> ( ( f @ ( f @ c ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP151])]) ).
thf(sP152,plain,
( sP152
<=> ( ~ ( ~ sP39
=> sP32 )
=> sP130 ) ),
introduced(definition,[new_symbols(definition,[sP152])]) ).
thf(sP153,plain,
( sP153
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP153])]) ).
thf(sP154,plain,
( sP154
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ c ) ) )
=> sP134 ) ),
introduced(definition,[new_symbols(definition,[sP154])]) ).
thf(sP155,plain,
( sP155
<=> ( ~ sP137
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP155])]) ).
thf(sP156,plain,
( sP156
<=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP156])]) ).
thf(sP157,plain,
( sP157
<=> ( ~ ( ~ ( ~ sP136
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ ( f @ ( f @ c ) ) ) ) )
=> sP146 )
=> ~ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP157])]) ).
thf(sP158,plain,
( sP158
<=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP158])]) ).
thf(sP159,plain,
( sP159
<=> ( ~ sP129
=> sP62 ) ),
introduced(definition,[new_symbols(definition,[sP159])]) ).
thf(sP160,plain,
( sP160
<=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP160])]) ).
thf(sP161,plain,
( sP161
<=> ( ~ ( ( ( f @ ( f @ c ) )
!= c )
=> sP146 )
=> ( c
= ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP161])]) ).
thf(sP162,plain,
( sP162
<=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP162])]) ).
thf(sP163,plain,
( sP163
<=> ( ~ sP57
=> sP135 ) ),
introduced(definition,[new_symbols(definition,[sP163])]) ).
thf(sP164,plain,
( sP164
<=> ( ~ ( ~ sP136
=> sP79 )
=> ( ( f @ ( f @ c ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP164])]) ).
thf(sP165,plain,
( sP165
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP126
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X1 ) )
=> ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP165])]) ).
thf(sP166,plain,
( sP166
<=> ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) )
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP166])]) ).
thf(sP167,plain,
( sP167
<=> ( ~ sP114
=> ( r @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP167])]) ).
thf(sP168,plain,
( sP168
<=> ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> sP134 ) ),
introduced(definition,[new_symbols(definition,[sP168])]) ).
thf(sP169,plain,
( sP169
<=> ( ~ ( ~ ( ~ sP22
=> sP32 )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) )
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP169])]) ).
thf(sP170,plain,
( sP170
<=> ( ( f @ ( f @ c ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP170])]) ).
thf(sP171,plain,
( sP171
<=> ( ~ ( ~ sP71
=> ~ sP16 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP171])]) ).
thf(sP172,plain,
( sP172
<=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP172])]) ).
thf(sP173,plain,
( sP173
<=> ( ~ ( ~ sP138
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ c ) )
=> ~ ( r @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP173])]) ).
thf(sP174,plain,
( sP174
<=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP174])]) ).
thf(sP175,plain,
( sP175
<=> ( ( ( f @ c )
= ( f @ ( f @ c ) ) )
=> ( c
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP175])]) ).
thf(sP176,plain,
( sP176
<=> ( ~ sP54
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP176])]) ).
thf(sP177,plain,
( sP177
<=> ( ~ sP70
=> ( c
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP177])]) ).
thf(sP178,plain,
( sP178
<=> ( ~ sP126
=> sP79 ) ),
introduced(definition,[new_symbols(definition,[sP178])]) ).
thf(sP179,plain,
( sP179
<=> ( ~ sP136
=> sP79 ) ),
introduced(definition,[new_symbols(definition,[sP179])]) ).
thf(sP180,plain,
( sP180
<=> ( ~ sP145
=> sP158 ) ),
introduced(definition,[new_symbols(definition,[sP180])]) ).
thf(sP181,plain,
( sP181
<=> ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP181])]) ).
thf(sP182,plain,
( sP182
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP182])]) ).
thf(sP183,plain,
( sP183
<=> ( ( f @ c )
= ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP183])]) ).
thf(sP184,plain,
( sP184
<=> ! [X1: $i,X2: $i] :
( ( r @ X1 @ X2 )
=> ( r @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP184])]) ).
thf(sP185,plain,
( sP185
<=> ( ~ sP123
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP185])]) ).
thf(sP186,plain,
( sP186
<=> ( ~ ( ~ sP22
=> sP32 )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP186])]) ).
thf(sP187,plain,
( sP187
<=> ( ~ ( ~ sP172
=> sP170 )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP187])]) ).
thf(sP188,plain,
( sP188
<=> ( ~ sP17
=> sP134 ) ),
introduced(definition,[new_symbols(definition,[sP188])]) ).
thf(sP189,plain,
( sP189
<=> ( ~ sP50
=> sP134 ) ),
introduced(definition,[new_symbols(definition,[sP189])]) ).
thf(sP190,plain,
( sP190
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> sP136 )
=> sP174 ) ),
introduced(definition,[new_symbols(definition,[sP190])]) ).
thf(sP191,plain,
( sP191
<=> ( ~ sP25
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP191])]) ).
thf(sP192,plain,
( sP192
<=> ( sP183
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP192])]) ).
thf(sP193,plain,
( sP193
<=> ( ~ sP150
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP193])]) ).
thf(sP194,plain,
( sP194
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP194])]) ).
thf(sP195,plain,
( sP195
<=> ( ~ ( ~ sP65
=> ~ sP78 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP195])]) ).
thf(sP196,plain,
( sP196
<=> ( ~ sP93
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP196])]) ).
thf(sP197,plain,
( sP197
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP136
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ~ sP27 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP197])]) ).
thf(sP198,plain,
( sP198
<=> ! [X1: $i] :
( ( r @ ( f @ c ) @ X1 )
=> ( r @ X1 @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP198])]) ).
thf(sP199,plain,
( sP199
<=> ( ~ sP142
=> ( r @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP199])]) ).
thf(sP200,plain,
( sP200
<=> ( c
= ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP200])]) ).
thf(sP201,plain,
( sP201
<=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP201])]) ).
thf(sP202,plain,
( sP202
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP134
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP202])]) ).
thf(sP203,plain,
( sP203
<=> ( ~ sP46
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP203])]) ).
thf(sP204,plain,
( sP204
<=> ( ~ sP162
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP204])]) ).
thf(sP205,plain,
( sP205
<=> ( ~ sP139
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP205])]) ).
thf(sP206,plain,
( sP206
<=> ( ~ sP120
=> sP183 ) ),
introduced(definition,[new_symbols(definition,[sP206])]) ).
thf(sP207,plain,
( sP207
<=> ( ~ ( ~ sP15
=> ~ sP135 )
=> ~ ( r @ ( f @ c ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP207])]) ).
thf(sP208,plain,
( sP208
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP208])]) ).
thf(sP209,plain,
( sP209
<=> ( ~ sP15
=> ~ sP135 ) ),
introduced(definition,[new_symbols(definition,[sP209])]) ).
thf(sP210,plain,
( sP210
<=> ! [X1: $i] :
( ( ( f @ c )
= X1 )
=> ( X1
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP210])]) ).
thf(sP211,plain,
( sP211
<=> ( ~ sP45
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP211])]) ).
thf(sP212,plain,
( sP212
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> sP78 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP212])]) ).
thf(sP213,plain,
( sP213
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> sP158 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP213])]) ).
thf(sP214,plain,
( sP214
<=> ( ~ ( ~ sP5
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP214])]) ).
thf(sP215,plain,
( sP215
<=> ( ~ sP99
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP215])]) ).
thf(sP216,plain,
( sP216
<=> ( ~ sP22
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP216])]) ).
thf(sP217,plain,
( sP217
<=> ( r @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP217])]) ).
thf(sP218,plain,
( sP218
<=> ( c
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP218])]) ).
thf(sP219,plain,
( sP219
<=> ( ~ ( ~ ( ~ sP24
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ sP62 )
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP219])]) ).
thf(sP220,plain,
( sP220
<=> ( ~ sP177
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP220])]) ).
thf(sP221,plain,
( sP221
<=> ( ~ ( ~ sP168
=> sP86 )
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP221])]) ).
thf(sP222,plain,
( sP222
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP160
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP222])]) ).
thf(sP223,plain,
( sP223
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) )
=> sP162 ) ),
introduced(definition,[new_symbols(definition,[sP223])]) ).
thf(sP224,plain,
( sP224
<=> ( ~ sP191
=> sP194 ) ),
introduced(definition,[new_symbols(definition,[sP224])]) ).
thf(sP225,plain,
( sP225
<=> ! [X1: $i] :
( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ X1 ) )
=> ( ( f @ ( f @ ( f @ eigen__0 ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP225])]) ).
thf(sP226,plain,
( sP226
<=> ( ~ sP23
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP226])]) ).
thf(sP227,plain,
( sP227
<=> ( ~ sP52
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP227])]) ).
thf(sP228,plain,
( sP228
<=> ( ~ sP77
=> sP218 ) ),
introduced(definition,[new_symbols(definition,[sP228])]) ).
thf(sP229,plain,
( sP229
<=> ! [X1: $i] :
( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP229])]) ).
thf(sP230,plain,
( sP230
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ c ) )
=> sP162 ) ),
introduced(definition,[new_symbols(definition,[sP230])]) ).
thf(sP231,plain,
( sP231
<=> ( ~ ( ~ sP223
=> sP101 )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP231])]) ).
thf(sP232,plain,
( sP232
<=> ( ~ sP106
=> ( r @ c @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP232])]) ).
thf(sP233,plain,
( sP233
<=> ( ~ sP117
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP233])]) ).
thf(sP234,plain,
( sP234
<=> ( ~ ( ~ sP223
=> sP101 )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP234])]) ).
thf(sP235,plain,
( sP235
<=> ( ~ sP228
=> sP135 ) ),
introduced(definition,[new_symbols(definition,[sP235])]) ).
thf(sP236,plain,
( sP236
<=> ( sP146
=> ( ( f @ c )
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP236])]) ).
thf(sP237,plain,
( sP237
<=> ( ~ ( ~ sP18
=> ~ sP158 )
=> ~ sP156 ) ),
introduced(definition,[new_symbols(definition,[sP237])]) ).
thf(sP238,plain,
( sP238
<=> ( ~ ( ~ sP146
=> sP170 )
=> sP162 ) ),
introduced(definition,[new_symbols(definition,[sP238])]) ).
thf(sP239,plain,
( sP239
<=> ( ( f @ ( f @ ( f @ eigen__0 ) ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP239])]) ).
thf(sP240,plain,
( sP240
<=> ( ~ sP164
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP240])]) ).
thf(sP241,plain,
( sP241
<=> ( r @ c @ ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP241])]) ).
thf(sP242,plain,
( sP242
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X2 ) )
=> ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP242])]) ).
thf(sP243,plain,
( sP243
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP146
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP243])]) ).
thf(sP244,plain,
( sP244
<=> ! [X1: $i] :
( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ X1 ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP244])]) ).
thf(sP245,plain,
( sP245
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP245])]) ).
thf(sP246,plain,
( sP246
<=> ( ~ sP116
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP246])]) ).
thf(sP247,plain,
( sP247
<=> ( ~ ( ~ ( ~ sP141
=> sP170 )
=> sP101 )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP247])]) ).
thf(sP248,plain,
( sP248
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP141
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X1 ) )
=> sP62 )
=> ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP248])]) ).
thf(sP249,plain,
( sP249
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> sP16 )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP249])]) ).
thf(sP250,plain,
( sP250
<=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP250])]) ).
thf(sP251,plain,
( sP251
<=> ( ~ sP11
=> ~ sP158 ) ),
introduced(definition,[new_symbols(definition,[sP251])]) ).
thf(sP252,plain,
( sP252
<=> ( ( f @ ( f @ ( f @ eigen__0 ) ) )
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP252])]) ).
thf(sP253,plain,
( sP253
<=> ( r @ c @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP253])]) ).
thf(sP254,plain,
( sP254
<=> ( ( f @ c )
= ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP254])]) ).
thf(sP255,plain,
( sP255
<=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP255])]) ).
thf(sP256,plain,
( sP256
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP136
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> sP27 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ c ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP256])]) ).
thf(sP257,plain,
( sP257
<=> ( sP21
=> sP126 ) ),
introduced(definition,[new_symbols(definition,[sP257])]) ).
thf(sP258,plain,
( sP258
<=> ( ~ sP231
=> ~ sP194 ) ),
introduced(definition,[new_symbols(definition,[sP258])]) ).
thf(sP259,plain,
( sP259
<=> ( ~ sP113
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP259])]) ).
thf(sP260,plain,
( sP260
<=> ( ~ sP65
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP260])]) ).
thf(sP261,plain,
( sP261
<=> ( ~ sP86
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP261])]) ).
thf(sP262,plain,
( sP262
<=> ( sP2
=> sP254 ) ),
introduced(definition,[new_symbols(definition,[sP262])]) ).
thf(sP263,plain,
( sP263
<=> ( ~ ( ~ sP24
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP263])]) ).
thf(sP264,plain,
( sP264
<=> ( ~ sP204
=> sP218 ) ),
introduced(definition,[new_symbols(definition,[sP264])]) ).
thf(sP265,plain,
( sP265
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( X1 != X2 )
=> ( X1 = X3 ) )
=> ( X2 = X3 ) )
=> ( r @ X1 @ X2 ) )
=> ( r @ X1 @ X3 ) )
=> ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP265])]) ).
thf(sP266,plain,
( sP266
<=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP266])]) ).
thf(sP267,plain,
( sP267
<=> ( ~ sP164
=> ~ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP267])]) ).
thf(sP268,plain,
( sP268
<=> ( ~ sP65
=> sP78 ) ),
introduced(definition,[new_symbols(definition,[sP268])]) ).
thf(sP269,plain,
( sP269
<=> ( ~ sP261
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP269])]) ).
thf(sP270,plain,
( sP270
<=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP270])]) ).
thf(sP271,plain,
( sP271
<=> ( ~ sP267
=> ~ sP201 ) ),
introduced(definition,[new_symbols(definition,[sP271])]) ).
thf(sP272,plain,
( sP272
<=> ( ~ ( ~ sP189
=> ~ sP19 )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP272])]) ).
thf(sP273,plain,
( sP273
<=> ( ( f @ c )
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP273])]) ).
thf(sP274,plain,
( sP274
<=> ( ~ sP136
=> sP255 ) ),
introduced(definition,[new_symbols(definition,[sP274])]) ).
thf(sP275,plain,
( sP275
<=> ! [X1: $i] :
( ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ X1 ) )
=> ( ( f @ ( f @ c ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP275])]) ).
thf(sP276,plain,
( sP276
<=> ( sP16
=> sP124 ) ),
introduced(definition,[new_symbols(definition,[sP276])]) ).
thf(sP277,plain,
( sP277
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP126
=> ( ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ~ sP250 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP277])]) ).
thf(sP278,plain,
( sP278
<=> ( ~ sP168
=> sP86 ) ),
introduced(definition,[new_symbols(definition,[sP278])]) ).
thf(sP279,plain,
( sP279
<=> ! [X1: $i,X2: $i] :
( ( ( f @ X1 )
= ( f @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP279])]) ).
thf(sP280,plain,
( sP280
<=> ( ~ sP115
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP280])]) ).
thf(sP281,plain,
( sP281
<=> ( ~ sP148
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP281])]) ).
thf(sP282,plain,
( sP282
<=> ( sP270
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP282])]) ).
thf(sP283,plain,
( sP283
<=> ( ~ sP121
=> ~ sP124 ) ),
introduced(definition,[new_symbols(definition,[sP283])]) ).
thf(sP284,plain,
( sP284
<=> ( sP172
=> sP183 ) ),
introduced(definition,[new_symbols(definition,[sP284])]) ).
thf(sP285,plain,
( sP285
<=> ( ~ sP94
=> sP130 ) ),
introduced(definition,[new_symbols(definition,[sP285])]) ).
thf(sP286,plain,
( sP286
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP286])]) ).
thf(sP287,plain,
( sP287
<=> ( sP160
=> sP146 ) ),
introduced(definition,[new_symbols(definition,[sP287])]) ).
thf(sP288,plain,
( sP288
<=> ( sP73
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP288])]) ).
thf(sP289,plain,
( sP289
<=> ( ~ sP189
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP289])]) ).
thf(sP290,plain,
( sP290
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP290])]) ).
thf(sP291,plain,
( sP291
<=> ( sP136
=> sP73 ) ),
introduced(definition,[new_symbols(definition,[sP291])]) ).
thf(sP292,plain,
( sP292
<=> ( ~ sP115
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP292])]) ).
thf(sP293,plain,
( sP293
<=> ( ~ sP55
=> sP78 ) ),
introduced(definition,[new_symbols(definition,[sP293])]) ).
thf(sP294,plain,
( sP294
<=> ( ~ sP290
=> sP208 ) ),
introduced(definition,[new_symbols(definition,[sP294])]) ).
thf(sP295,plain,
( sP295
<=> ( ~ sP5
=> ~ sP250 ) ),
introduced(definition,[new_symbols(definition,[sP295])]) ).
thf(sP296,plain,
( sP296
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X2 ) )
=> ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP296])]) ).
thf(sP297,plain,
( sP297
<=> ( ~ sP11
=> sP158 ) ),
introduced(definition,[new_symbols(definition,[sP297])]) ).
thf(sP298,plain,
( sP298
<=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP298])]) ).
thf(sP299,plain,
( sP299
<=> ( ~ ( ~ sP157
=> ~ sP78 )
=> ~ sP298 ) ),
introduced(definition,[new_symbols(definition,[sP299])]) ).
thf(sP300,plain,
( sP300
<=> ( ~ sP187
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP300])]) ).
thf(sP301,plain,
( sP301
<=> ( ~ sP274
=> sP146 ) ),
introduced(definition,[new_symbols(definition,[sP301])]) ).
thf(sP302,plain,
( sP302
<=> ( ~ sP206
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP302])]) ).
thf(sP303,plain,
( sP303
<=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP303])]) ).
thf(sP304,plain,
( sP304
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP304])]) ).
thf(sP305,plain,
( sP305
<=> ( sP255
=> sP252 ) ),
introduced(definition,[new_symbols(definition,[sP305])]) ).
thf(sP306,plain,
( sP306
<=> ( ~ sP157
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP306])]) ).
thf(sP307,plain,
( sP307
<=> ( ~ sP146
=> sP170 ) ),
introduced(definition,[new_symbols(definition,[sP307])]) ).
thf(sP308,plain,
( sP308
<=> ( ~ sP12
=> ~ sP156 ) ),
introduced(definition,[new_symbols(definition,[sP308])]) ).
thf(sP309,plain,
( sP309
<=> ( ~ sP39
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP309])]) ).
thf(sP310,plain,
( sP310
<=> ( ~ sP255
=> sP136 ) ),
introduced(definition,[new_symbols(definition,[sP310])]) ).
thf(sP311,plain,
( sP311
<=> ( ~ ( ~ sP160
=> sP303 )
=> sP86 ) ),
introduced(definition,[new_symbols(definition,[sP311])]) ).
thf(sP312,plain,
( sP312
<=> ( ~ sP18
=> sP158 ) ),
introduced(definition,[new_symbols(definition,[sP312])]) ).
thf(sP313,plain,
( sP313
<=> ( ~ sP34
=> sP194 ) ),
introduced(definition,[new_symbols(definition,[sP313])]) ).
thf(sP314,plain,
( sP314
<=> ( ~ sP300
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP314])]) ).
thf(sP315,plain,
( sP315
<=> ( sP141
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP315])]) ).
thf(sP316,plain,
( sP316
<=> ( ~ sP188
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP316])]) ).
thf(sP317,plain,
( sP317
<=> ( ~ sP10
=> sP135 ) ),
introduced(definition,[new_symbols(definition,[sP317])]) ).
thf(sP318,plain,
( sP318
<=> ( ~ sP196
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP318])]) ).
thf(sP319,plain,
( sP319
<=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP319])]) ).
thf(sP320,plain,
( sP320
<=> ( sP86
=> sP162 ) ),
introduced(definition,[new_symbols(definition,[sP320])]) ).
thf(sP321,plain,
( sP321
<=> ( ~ sP170
=> sP146 ) ),
introduced(definition,[new_symbols(definition,[sP321])]) ).
thf(sP322,plain,
( sP322
<=> ( ~ sP69
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP322])]) ).
thf(sP323,plain,
( sP323
<=> ( ~ sP18
=> ~ sP158 ) ),
introduced(definition,[new_symbols(definition,[sP323])]) ).
thf(sP324,plain,
( sP324
<=> ( ~ sP223
=> sP101 ) ),
introduced(definition,[new_symbols(definition,[sP324])]) ).
thf(sP325,plain,
( sP325
<=> ( ~ sP172
=> sP170 ) ),
introduced(definition,[new_symbols(definition,[sP325])]) ).
thf(sP326,plain,
( sP326
<=> ( sP200
=> sP162 ) ),
introduced(definition,[new_symbols(definition,[sP326])]) ).
thf(sP327,plain,
( sP327
<=> ( ~ sP169
=> sP217 ) ),
introduced(definition,[new_symbols(definition,[sP327])]) ).
thf(sP328,plain,
( sP328
<=> ( ~ sP219
=> ~ sP158 ) ),
introduced(definition,[new_symbols(definition,[sP328])]) ).
thf(sP329,plain,
( sP329
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= X1 )
=> ( ( f @ ( f @ c ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ c ) ) @ X2 ) )
=> ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP329])]) ).
thf(sP330,plain,
( sP330
<=> ( ~ sP138
=> ~ sP201 ) ),
introduced(definition,[new_symbols(definition,[sP330])]) ).
thf(sP331,plain,
( sP331
<=> ( ~ sP141
=> sP170 ) ),
introduced(definition,[new_symbols(definition,[sP331])]) ).
thf(sP332,plain,
( sP332
<=> ( ~ sP155
=> sP158 ) ),
introduced(definition,[new_symbols(definition,[sP332])]) ).
thf(sP333,plain,
( sP333
<=> ( ~ sP129
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP333])]) ).
thf(sP334,plain,
( sP334
<=> ( ~ sP160
=> sP303 ) ),
introduced(definition,[new_symbols(definition,[sP334])]) ).
thf(sP335,plain,
( sP335
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( X1 != X2 )
=> ( X1 = X3 ) )
=> ( X2 = X3 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X1 @ X3 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP335])]) ).
thf(sP336,plain,
( sP336
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP266
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ( c = X1 ) )
=> sP135 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ( r @ c @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP336])]) ).
thf(sP337,plain,
( sP337
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP134
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ~ sP319 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ~ ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP337])]) ).
thf(sP338,plain,
( sP338
<=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP338])]) ).
thf(sP339,plain,
( sP339
<=> ( ~ sP220
=> ~ sP319 ) ),
introduced(definition,[new_symbols(definition,[sP339])]) ).
thf(sP340,plain,
( sP340
<=> ( ~ sP195
=> ~ sP194 ) ),
introduced(definition,[new_symbols(definition,[sP340])]) ).
thf(sP341,plain,
( sP341
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP341])]) ).
thf(sP342,plain,
( sP342
<=> ( ~ ( ~ sP159
=> sP319 )
=> sP130 ) ),
introduced(definition,[new_symbols(definition,[sP342])]) ).
thf(sP343,plain,
( sP343
<=> ( ~ sP331
=> sP101 ) ),
introduced(definition,[new_symbols(definition,[sP343])]) ).
thf(sP344,plain,
( sP344
<=> ( ~ sP193
=> ~ sP135 ) ),
introduced(definition,[new_symbols(definition,[sP344])]) ).
thf(sP345,plain,
( sP345
<=> ( ~ sP159
=> sP319 ) ),
introduced(definition,[new_symbols(definition,[sP345])]) ).
thf(sP346,plain,
( sP346
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP290
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ~ sP158 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ eigen__0 ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP346])]) ).
thf(sP347,plain,
( sP347
<=> ! [X1: $i] :
( ( ( f @ ( f @ ( f @ eigen__0 ) ) )
= ( f @ X1 ) )
=> ( ( f @ ( f @ eigen__0 ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP347])]) ).
thf(sP348,plain,
( sP348
<=> ( ~ sP125
=> sP194 ) ),
introduced(definition,[new_symbols(definition,[sP348])]) ).
thf(sP349,plain,
( sP349
<=> ( ~ sP24
=> sP290 ) ),
introduced(definition,[new_symbols(definition,[sP349])]) ).
thf(sP350,plain,
( sP350
<=> ( ~ sP71
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP350])]) ).
thf(1,plain,
( ~ sP282
| ~ sP270
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP287
| ~ sP160
| sP146 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP127
| sP83 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP83
| sP215
| ~ sP338 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP215
| sP99
| ~ sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP99
| sP278
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP95
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP53
| sP82
| sP338 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP82
| sP221
| sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP221
| sP278
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP278
| sP168
| sP86 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP168
| sP172
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP222
| sP171 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP171
| sP350
| ~ sP338 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP350
| sP71
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP71
| sP311
| ~ sP286 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP47
| sP109 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP109
| sP97
| sP338 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP97
| sP102
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP102
| sP311
| sP286 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP311
| sP334
| sP86 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP334
| sP160
| sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP315
| ~ sP141
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP284
| ~ sP172
| sP183 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP236
| ~ sP146
| sP273 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP346
| sP203 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP203
| sP46
| ~ sP338 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP46
| sP251
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP251
| sP11
| ~ sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP213
| sP176 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP176
| sP54
| sP338 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP54
| sP297
| sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP297
| sP11
| sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP11
| sP294
| sP86 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP294
| sP290
| sP208 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP107
| sP322 ),
inference(all_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP322
| sP69
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP69
| sP333
| ~ sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP333
| sP129
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP248
| sP342 ),
inference(all_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP342
| sP345
| sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP345
| sP159
| sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP159
| sP129
| sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP129
| sP14
| sP208 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP14
| sP141
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP33
| sP281 ),
inference(all_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP281
| sP148
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP148
| sP292
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP292
| sP115
| ~ sP304 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP84
| sP285 ),
inference(all_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP285
| sP94
| sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP94
| sP280
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP280
| sP115
| sP304 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP115
| sP182
| sP208 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP182
| sP270
| sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP212
| sP259 ),
inference(all_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP259
| sP113
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP113
| sP140
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP140
| sP190
| sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP197
| sP299 ),
inference(all_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP299
| sP306
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP306
| sP157
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP157
| sP301
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP301
| sP274
| sP146 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP274
| sP136
| sP255 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP190
| sP310
| sP174 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP310
| sP255
| sP136 ),
inference(prop_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP262
| ~ sP2
| sP254 ),
inference(prop_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP8
| ~ sP124
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP337
| sP283 ),
inference(all_rule,[status(thm)],[]) ).
thf(71,plain,
( ~ sP283
| sP121
| ~ sP124 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( ~ sP121
| sP147
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP147
| sP206
| ~ sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP192
| ~ sP183
| sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP210
| sP192 ),
inference(all_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP276
| ~ sP16
| sP124 ),
inference(prop_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP202
| sP74 ),
inference(all_rule,[status(thm)],[]) ).
thf(78,plain,
( ~ sP74
| sP133
| sP124 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP133
| sP302
| sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
( ~ sP302
| sP206
| sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(81,plain,
( ~ sP206
| sP120
| sP183 ),
inference(prop_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP120
| sP134
| sP146 ),
inference(prop_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP257
| ~ sP21
| sP126 ),
inference(prop_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP210
| sP257 ),
inference(all_rule,[status(thm)],[]) ).
thf(85,plain,
( ~ sP44
| sP318 ),
inference(all_rule,[status(thm)],[]) ).
thf(86,plain,
( ~ sP318
| sP196
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(87,plain,
( ~ sP196
| sP93
| ~ sP250 ),
inference(prop_rule,[status(thm)],[]) ).
thf(88,plain,
( ~ sP93
| sP55
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP212
| sP227 ),
inference(all_rule,[status(thm)],[]) ).
thf(90,plain,
( ~ sP227
| sP52
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(91,plain,
( ~ sP52
| sP293
| sP250 ),
inference(prop_rule,[status(thm)],[]) ).
thf(92,plain,
( ~ sP293
| sP55
| sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(93,plain,
( ~ sP55
| sP42
| sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(94,plain,
( ~ sP42
| sP255
| sP126 ),
inference(prop_rule,[status(thm)],[]) ).
thf(95,plain,
( ~ sP154
| ~ sP174
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(96,plain,
( ~ sP336
| sP232 ),
inference(all_rule,[status(thm)],[]) ).
thf(97,plain,
( ~ sP232
| sP106
| sP253 ),
inference(prop_rule,[status(thm)],[]) ).
thf(98,plain,
( ~ sP106
| sP235
| sP338 ),
inference(prop_rule,[status(thm)],[]) ).
thf(99,plain,
( ~ sP235
| sP228
| sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(100,plain,
( ~ sP228
| sP77
| sP218 ),
inference(prop_rule,[status(thm)],[]) ).
thf(101,plain,
( ~ sP77
| sP266
| sP86 ),
inference(prop_rule,[status(thm)],[]) ).
thf(102,plain,
( ~ sP89
| sP112 ),
inference(all_rule,[status(thm)],[]) ).
thf(103,plain,
( ~ sP112
| sP207 ),
inference(all_rule,[status(thm)],[]) ).
thf(104,plain,
( ~ sP207
| sP209
| ~ sP217 ),
inference(prop_rule,[status(thm)],[]) ).
thf(105,plain,
( ~ sP209
| sP15
| ~ sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(106,plain,
( ~ sP15
| sP269
| ~ sP338 ),
inference(prop_rule,[status(thm)],[]) ).
thf(107,plain,
( ~ sP269
| sP261
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(108,plain,
( ~ sP261
| sP86
| sP266 ),
inference(prop_rule,[status(thm)],[]) ).
thf(109,plain,
( ~ sP95
| sP317 ),
inference(all_rule,[status(thm)],[]) ).
thf(110,plain,
( ~ sP317
| sP10
| sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(111,plain,
( ~ sP10
| sP166
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP166
| sP187
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(113,plain,
( ~ sP127
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(114,plain,
( ~ sP68
| sP314
| ~ sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(115,plain,
( ~ sP314
| sP300
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(116,plain,
( ~ sP300
| sP187
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(117,plain,
( ~ sP187
| sP325
| sP266 ),
inference(prop_rule,[status(thm)],[]) ).
thf(118,plain,
( ~ sP325
| sP172
| sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(119,plain,
( ~ sP242
| sP336 ),
inference(all_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP222
| sP344 ),
inference(all_rule,[status(thm)],[]) ).
thf(121,plain,
( ~ sP344
| sP193
| ~ sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(122,plain,
( ~ sP193
| sP150
| ~ sP194 ),
inference(prop_rule,[status(thm)],[]) ).
thf(123,plain,
( ~ sP150
| sP139
| ~ sP286 ),
inference(prop_rule,[status(thm)],[]) ).
thf(124,plain,
( ~ sP47
| sP163 ),
inference(all_rule,[status(thm)],[]) ).
thf(125,plain,
( ~ sP163
| sP57
| sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(126,plain,
( ~ sP57
| sP205
| sP194 ),
inference(prop_rule,[status(thm)],[]) ).
thf(127,plain,
( ~ sP205
| sP139
| sP286 ),
inference(prop_rule,[status(thm)],[]) ).
thf(128,plain,
( ~ sP139
| sP51
| sP266 ),
inference(prop_rule,[status(thm)],[]) ).
thf(129,plain,
( ~ sP51
| sP160
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(130,plain,
( ~ sP40
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(131,plain,
( ~ sP84
| sP180 ),
inference(all_rule,[status(thm)],[]) ).
thf(132,plain,
( ~ sP180
| sP145
| sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(133,plain,
( ~ sP145
| sP31
| sP286 ),
inference(prop_rule,[status(thm)],[]) ).
thf(134,plain,
( ~ sP31
| sP4
| sP304 ),
inference(prop_rule,[status(thm)],[]) ).
thf(135,plain,
( ~ sP341
| sP222 ),
inference(all_rule,[status(thm)],[]) ).
thf(136,plain,
( ~ sP76
| sP111 ),
inference(all_rule,[status(thm)],[]) ).
thf(137,plain,
( ~ sP111
| sP272
| ~ sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(138,plain,
( ~ sP272
| sP289
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(139,plain,
( ~ sP289
| sP189
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(140,plain,
( ~ sP189
| sP50
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(141,plain,
( ~ sP50
| sP174
| sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(142,plain,
( ~ sP33
| sP105 ),
inference(all_rule,[status(thm)],[]) ).
thf(143,plain,
( ~ sP105
| sP185
| ~ sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(144,plain,
( ~ sP185
| sP123
| ~ sP286 ),
inference(prop_rule,[status(thm)],[]) ).
thf(145,plain,
( ~ sP123
| sP4
| ~ sP304 ),
inference(prop_rule,[status(thm)],[]) ).
thf(146,plain,
( ~ sP4
| sP153
| sP290 ),
inference(prop_rule,[status(thm)],[]) ).
thf(147,plain,
( ~ sP153
| sP270
| sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(148,plain,
( ~ sP132
| sP276 ),
inference(all_rule,[status(thm)],[]) ).
thf(149,plain,
( ~ sP64
| sP144 ),
inference(all_rule,[status(thm)],[]) ).
thf(150,plain,
( ~ sP144
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(151,plain,
( ~ sP60
| sP41
| ~ sP217 ),
inference(prop_rule,[status(thm)],[]) ).
thf(152,plain,
( ~ sP41
| sP7
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(153,plain,
( ~ sP7
| sP309
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(154,plain,
( ~ sP296
| sP63 ),
inference(all_rule,[status(thm)],[]) ).
thf(155,plain,
( ~ sP63
| sP167 ),
inference(all_rule,[status(thm)],[]) ).
thf(156,plain,
( ~ sP167
| sP114
| sP217 ),
inference(prop_rule,[status(thm)],[]) ).
thf(157,plain,
( ~ sP114
| sP152
| sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(158,plain,
( ~ sP152
| sP309
| sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(159,plain,
( ~ sP309
| sP39
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(160,plain,
( ~ sP39
| sP208
| sP101 ),
inference(prop_rule,[status(thm)],[]) ).
thf(161,plain,
( ~ sP341
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(162,plain,
( ~ sP33
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(163,plain,
( ~ sP36
| sP258
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(164,plain,
( ~ sP258
| sP231
| ~ sP194 ),
inference(prop_rule,[status(thm)],[]) ).
thf(165,plain,
( ~ sP231
| sP324
| ~ sP304 ),
inference(prop_rule,[status(thm)],[]) ).
thf(166,plain,
( ~ sP40
| sP84 ),
inference(all_rule,[status(thm)],[]) ).
thf(167,plain,
( ~ sP84
| sP88 ),
inference(all_rule,[status(thm)],[]) ).
thf(168,plain,
( ~ sP88
| sP67
| sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(169,plain,
( ~ sP67
| sP234
| sP194 ),
inference(prop_rule,[status(thm)],[]) ).
thf(170,plain,
( ~ sP234
| sP324
| sP304 ),
inference(prop_rule,[status(thm)],[]) ).
thf(171,plain,
( ~ sP324
| sP223
| sP101 ),
inference(prop_rule,[status(thm)],[]) ).
thf(172,plain,
( ~ sP223
| sP270
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(173,plain,
( ~ sP248
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(174,plain,
( ~ sP56
| sP122
| sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(175,plain,
( ~ sP122
| sP59
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(176,plain,
( ~ sP59
| sP343
| sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(177,plain,
( ~ sP107
| sP308 ),
inference(all_rule,[status(thm)],[]) ).
thf(178,plain,
( ~ sP308
| sP12
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(179,plain,
( ~ sP12
| sP247
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(180,plain,
( ~ sP247
| sP343
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(181,plain,
( ~ sP343
| sP331
| sP101 ),
inference(prop_rule,[status(thm)],[]) ).
thf(182,plain,
( ~ sP331
| sP141
| sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(183,plain,
( ~ sP346
| sP96 ),
inference(all_rule,[status(thm)],[]) ).
thf(184,plain,
( ~ sP96
| sP237
| ~ sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(185,plain,
( ~ sP237
| sP323
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(186,plain,
( ~ sP323
| sP18
| ~ sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(187,plain,
( ~ sP213
| sP104 ),
inference(all_rule,[status(thm)],[]) ).
thf(188,plain,
( ~ sP104
| sP92
| sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(189,plain,
( ~ sP92
| sP312
| sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(190,plain,
( ~ sP312
| sP18
| sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(191,plain,
( ~ sP18
| sP128
| sP266 ),
inference(prop_rule,[status(thm)],[]) ).
thf(192,plain,
( ~ sP128
| sP290
| sP101 ),
inference(prop_rule,[status(thm)],[]) ).
thf(193,plain,
( ~ sP256
| sP246 ),
inference(all_rule,[status(thm)],[]) ).
thf(194,plain,
( ~ sP246
| sP116
| sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(195,plain,
( ~ sP116
| sP316
| sP250 ),
inference(prop_rule,[status(thm)],[]) ).
thf(196,plain,
( ~ sP316
| sP188
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(197,plain,
( ~ sP197
| sP214 ),
inference(all_rule,[status(thm)],[]) ).
thf(198,plain,
( ~ sP214
| sP295
| ~ sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(199,plain,
( ~ sP295
| sP5
| ~ sP250 ),
inference(prop_rule,[status(thm)],[]) ).
thf(200,plain,
( ~ sP5
| sP188
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(201,plain,
( ~ sP188
| sP17
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(202,plain,
( ~ sP17
| sP136
| sP126 ),
inference(prop_rule,[status(thm)],[]) ).
thf(203,plain,
( ~ sP119
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(204,plain,
( ~ sP13
| sP149
| ~ sP241 ),
inference(prop_rule,[status(thm)],[]) ).
thf(205,plain,
( ~ sP149
| sP26
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(206,plain,
( ~ sP26
| sP161
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(207,plain,
( ~ sP132
| sP118 ),
inference(all_rule,[status(thm)],[]) ).
thf(208,plain,
( ~ sP118
| ~ sP194
| sP241 ),
inference(prop_rule,[status(thm)],[]) ).
thf(209,plain,
( ~ sP161
| sP321
| sP200 ),
inference(prop_rule,[status(thm)],[]) ).
thf(210,plain,
( ~ sP321
| sP170
| sP146 ),
inference(prop_rule,[status(thm)],[]) ).
thf(211,plain,
( ~ sP291
| ~ sP136
| sP73 ),
inference(prop_rule,[status(thm)],[]) ).
thf(212,plain,
( ~ sP265
| sP242 ),
inference(all_rule,[status(thm)],[]) ).
thf(213,plain,
( ~ sP335
| sP89 ),
inference(all_rule,[status(thm)],[]) ).
thf(214,plain,
( ~ sP151
| sP127 ),
inference(all_rule,[status(thm)],[]) ).
thf(215,plain,
( ~ sP329
| sP95 ),
inference(all_rule,[status(thm)],[]) ).
thf(216,plain,
( ~ sP296
| sP213 ),
inference(all_rule,[status(thm)],[]) ).
thf(217,plain,
( ~ sP265
| sP296 ),
inference(all_rule,[status(thm)],[]) ).
thf(218,plain,
( ~ sP64
| sP346 ),
inference(all_rule,[status(thm)],[]) ).
thf(219,plain,
( ~ sP335
| sP64 ),
inference(all_rule,[status(thm)],[]) ).
thf(220,plain,
( ~ sP151
| sP107 ),
inference(all_rule,[status(thm)],[]) ).
thf(221,plain,
( ~ sP107
| sP328 ),
inference(all_rule,[status(thm)],[]) ).
thf(222,plain,
( ~ sP328
| sP219
| ~ sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(223,plain,
( ~ sP219
| sP263
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(224,plain,
( ~ sP263
| sP349
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(225,plain,
( ~ sP329
| sP248 ),
inference(all_rule,[status(thm)],[]) ).
thf(226,plain,
( ~ sP248
| sP332 ),
inference(all_rule,[status(thm)],[]) ).
thf(227,plain,
( ~ sP332
| sP155
| sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(228,plain,
( ~ sP155
| sP137
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(229,plain,
( ~ sP137
| sP349
| sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(230,plain,
( ~ sP349
| sP24
| sP290 ),
inference(prop_rule,[status(thm)],[]) ).
thf(231,plain,
( ~ sP24
| sP141
| sP172 ),
inference(prop_rule,[status(thm)],[]) ).
thf(232,plain,
( ~ sP103
| ~ sP254
| sP58 ),
inference(prop_rule,[status(thm)],[]) ).
thf(233,plain,
( ~ sP175
| ~ sP273
| sP218 ),
inference(prop_rule,[status(thm)],[]) ).
thf(234,plain,
( ~ sP275
| sP154 ),
inference(all_rule,[status(thm)],[]) ).
thf(235,plain,
( ~ sP275
| sP282 ),
inference(all_rule,[status(thm)],[]) ).
thf(236,plain,
( ~ sP275
| sP287 ),
inference(all_rule,[status(thm)],[]) ).
thf(237,plain,
( ~ sP326
| ~ sP200
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(238,plain,
( ~ sP143
| sP326 ),
inference(all_rule,[status(thm)],[]) ).
thf(239,plain,
( ~ sP244
| sP320 ),
inference(all_rule,[status(thm)],[]) ).
thf(240,plain,
( ~ sP320
| ~ sP86
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(241,plain,
( ~ sP81
| sP72 ),
inference(all_rule,[status(thm)],[]) ).
thf(242,plain,
( ~ sP72
| sP211
| ~ sP253 ),
inference(prop_rule,[status(thm)],[]) ).
thf(243,plain,
( ~ sP211
| sP45
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(244,plain,
( ~ sP45
| sP264
| ~ sP194 ),
inference(prop_rule,[status(thm)],[]) ).
thf(245,plain,
( ~ sP264
| sP204
| sP218 ),
inference(prop_rule,[status(thm)],[]) ).
thf(246,plain,
( ~ sP204
| sP162
| sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(247,plain,
( ~ sP341
| sP81 ),
inference(all_rule,[status(thm)],[]) ).
thf(248,plain,
( ~ sP40
| sP249 ),
inference(all_rule,[status(thm)],[]) ).
thf(249,plain,
( ~ sP249
| sP91 ),
inference(all_rule,[status(thm)],[]) ).
thf(250,plain,
( ~ sP91
| sP224
| sP217 ),
inference(prop_rule,[status(thm)],[]) ).
thf(251,plain,
( ~ sP224
| sP191
| sP194 ),
inference(prop_rule,[status(thm)],[]) ).
thf(252,plain,
( ~ sP191
| sP25
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(253,plain,
( ~ sP25
| sP230
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(254,plain,
( ~ sP230
| sP303
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(255,plain,
( ~ sP341
| sP76 ),
inference(all_rule,[status(thm)],[]) ).
thf(256,plain,
( ~ sP243
| sP348 ),
inference(all_rule,[status(thm)],[]) ).
thf(257,plain,
( ~ sP348
| sP125
| sP194 ),
inference(prop_rule,[status(thm)],[]) ).
thf(258,plain,
( ~ sP125
| sP108
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(259,plain,
( ~ sP108
| sP238
| sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(260,plain,
( ~ sP238
| sP307
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(261,plain,
( ~ sP307
| sP146
| sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(262,plain,
( ~ sP329
| sP243 ),
inference(all_rule,[status(thm)],[]) ).
thf(263,plain,
( ~ sP225
| sP291 ),
inference(all_rule,[status(thm)],[]) ).
thf(264,plain,
( ~ sP229
| sP85 ),
inference(all_rule,[status(thm)],[]) ).
thf(265,plain,
( ~ sP85
| ~ sP208
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(266,plain,
( ~ sP44
| sP340 ),
inference(all_rule,[status(thm)],[]) ).
thf(267,plain,
( ~ sP340
| sP195
| ~ sP194 ),
inference(prop_rule,[status(thm)],[]) ).
thf(268,plain,
( ~ sP195
| sP260
| ~ sP201 ),
inference(prop_rule,[status(thm)],[]) ).
thf(269,plain,
( ~ sP260
| sP65
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(270,plain,
( ~ sP212
| sP313 ),
inference(all_rule,[status(thm)],[]) ).
thf(271,plain,
( ~ sP313
| sP34
| sP194 ),
inference(prop_rule,[status(thm)],[]) ).
thf(272,plain,
( ~ sP34
| sP268
| sP201 ),
inference(prop_rule,[status(thm)],[]) ).
thf(273,plain,
( ~ sP268
| sP65
| sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(274,plain,
( ~ sP65
| sP30
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(275,plain,
( ~ sP30
| sP255
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(276,plain,
( ~ sP245
| sP277 ),
inference(all_rule,[status(thm)],[]) ).
thf(277,plain,
( ~ sP277
| sP173 ),
inference(all_rule,[status(thm)],[]) ).
thf(278,plain,
( ~ sP173
| sP330
| ~ sP217 ),
inference(prop_rule,[status(thm)],[]) ).
thf(279,plain,
( ~ sP330
| sP138
| ~ sP201 ),
inference(prop_rule,[status(thm)],[]) ).
thf(280,plain,
( ~ sP138
| sP117
| ~ sP250 ),
inference(prop_rule,[status(thm)],[]) ).
thf(281,plain,
( ~ sP87
| sP165 ),
inference(all_rule,[status(thm)],[]) ).
thf(282,plain,
( ~ sP165
| sP199 ),
inference(all_rule,[status(thm)],[]) ).
thf(283,plain,
( ~ sP199
| sP142
| sP217 ),
inference(prop_rule,[status(thm)],[]) ).
thf(284,plain,
( ~ sP142
| sP233
| sP201 ),
inference(prop_rule,[status(thm)],[]) ).
thf(285,plain,
( ~ sP233
| sP117
| sP250 ),
inference(prop_rule,[status(thm)],[]) ).
thf(286,plain,
( ~ sP117
| sP178
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(287,plain,
( ~ sP178
| sP126
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(288,plain,
( ~ sP245
| sP197 ),
inference(all_rule,[status(thm)],[]) ).
thf(289,plain,
( ~ sP197
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(290,plain,
( ~ sP38
| sP271
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(291,plain,
( ~ sP271
| sP267
| ~ sP201 ),
inference(prop_rule,[status(thm)],[]) ).
thf(292,plain,
( ~ sP267
| sP164
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(293,plain,
( ~ sP87
| sP256 ),
inference(all_rule,[status(thm)],[]) ).
thf(294,plain,
( ~ sP256
| sP226 ),
inference(all_rule,[status(thm)],[]) ).
thf(295,plain,
( ~ sP226
| sP23
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(296,plain,
( ~ sP23
| sP240
| sP201 ),
inference(prop_rule,[status(thm)],[]) ).
thf(297,plain,
( ~ sP240
| sP164
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(298,plain,
( ~ sP164
| sP179
| sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(299,plain,
( ~ sP179
| sP136
| sP79 ),
inference(prop_rule,[status(thm)],[]) ).
thf(300,plain,
( ~ sP49
| sP262 ),
inference(all_rule,[status(thm)],[]) ).
thf(301,plain,
( ~ sP49
| sP236 ),
inference(all_rule,[status(thm)],[]) ).
thf(302,plain,
( ~ sP49
| sP315 ),
inference(all_rule,[status(thm)],[]) ).
thf(303,plain,
( ~ sP49
| sP284 ),
inference(all_rule,[status(thm)],[]) ).
thf(304,plain,
( ~ sP275
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(305,plain,
( ~ sP20
| ~ sP303
| sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(306,plain,
( ~ sP119
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(307,plain,
( ~ sP37
| sP339
| ~ sP253 ),
inference(prop_rule,[status(thm)],[]) ).
thf(308,plain,
( ~ sP339
| sP220
| ~ sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(309,plain,
( ~ sP220
| sP177
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(310,plain,
( ~ sP177
| sP70
| sP218 ),
inference(prop_rule,[status(thm)],[]) ).
thf(311,plain,
( ~ sP70
| sP170
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(312,plain,
( ~ sP151
| sP119 ),
inference(all_rule,[status(thm)],[]) ).
thf(313,plain,
( ~ sP151
| sP337 ),
inference(all_rule,[status(thm)],[]) ).
thf(314,plain,
( ~ sP329
| sP202 ),
inference(all_rule,[status(thm)],[]) ).
thf(315,plain,
( ~ sP202
| sP327 ),
inference(all_rule,[status(thm)],[]) ).
thf(316,plain,
( ~ sP327
| sP169
| sP217 ),
inference(prop_rule,[status(thm)],[]) ).
thf(317,plain,
( ~ sP169
| sP186
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(318,plain,
( ~ sP186
| sP216
| sP319 ),
inference(prop_rule,[status(thm)],[]) ).
thf(319,plain,
( ~ sP216
| sP22
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(320,plain,
( ~ sP22
| sP134
| sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(321,plain,
( ~ sP198
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(322,plain,
( ~ sP225
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(323,plain,
( ~ sP9
| ~ sP126
| sP239 ),
inference(prop_rule,[status(thm)],[]) ).
thf(324,plain,
( ~ sP48
| sP103 ),
inference(all_rule,[status(thm)],[]) ).
thf(325,plain,
( ~ sP48
| sP175 ),
inference(all_rule,[status(thm)],[]) ).
thf(326,plain,
( ~ sP49
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(327,plain,
( ~ sP43
| ~ sP134
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(328,plain,
( ~ sP347
| sP288 ),
inference(all_rule,[status(thm)],[]) ).
thf(329,plain,
( ~ sP288
| ~ sP73
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(330,plain,
( ~ sP279
| sP244 ),
inference(all_rule,[status(thm)],[]) ).
thf(331,plain,
( ~ sP1
| ~ sP266 ),
inference(all_rule,[status(thm)],[]) ).
thf(332,plain,
( ~ sP265
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(333,plain,
( ~ sP335
| sP341 ),
inference(all_rule,[status(thm)],[]) ).
thf(334,plain,
( ~ sP184
| sP132 ),
inference(all_rule,[status(thm)],[]) ).
thf(335,plain,
( ~ sP1
| ~ sP101 ),
inference(all_rule,[status(thm)],[]) ).
thf(336,plain,
( ~ sP279
| sP229 ),
inference(all_rule,[status(thm)],[]) ).
thf(337,plain,
( ~ sP229
| sP181 ),
inference(all_rule,[status(thm)],[]) ).
thf(338,plain,
( ~ sP181
| ~ sP290
| sP255 ),
inference(prop_rule,[status(thm)],[]) ).
thf(339,plain,
( ~ sP87
| sP212 ),
inference(all_rule,[status(thm)],[]) ).
thf(340,plain,
( ~ sP265
| sP87 ),
inference(all_rule,[status(thm)],[]) ).
thf(341,plain,
( ~ sP245
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(342,plain,
( ~ sP335
| sP245 ),
inference(all_rule,[status(thm)],[]) ).
thf(343,plain,
( ~ sP80
| ~ sP58
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(344,plain,
( ~ sP143
| sP80 ),
inference(all_rule,[status(thm)],[]) ).
thf(345,plain,
( ~ sP110
| sP100 ),
inference(all_rule,[status(thm)],[]) ).
thf(346,plain,
( ~ sP100
| ~ sP253
| sP217 ),
inference(prop_rule,[status(thm)],[]) ).
thf(347,plain,
( ~ sP198
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(348,plain,
( ~ sP35
| ~ sP217
| sP253 ),
inference(prop_rule,[status(thm)],[]) ).
thf(349,plain,
( ~ sP75
| ~ sP218
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(350,plain,
( ~ sP143
| sP75 ),
inference(all_rule,[status(thm)],[]) ).
thf(351,plain,
( ~ sP279
| sP275 ),
inference(all_rule,[status(thm)],[]) ).
thf(352,plain,
( ~ sP1
| ~ sP162 ),
inference(all_rule,[status(thm)],[]) ).
thf(353,plain,
( ~ sP265
| sP329 ),
inference(all_rule,[status(thm)],[]) ).
thf(354,plain,
( ~ sP335
| sP151 ),
inference(all_rule,[status(thm)],[]) ).
thf(355,plain,
( ~ sP1
| ~ sP79 ),
inference(all_rule,[status(thm)],[]) ).
thf(356,plain,
( ~ sP279
| sP225 ),
inference(all_rule,[status(thm)],[]) ).
thf(357,plain,
( ~ sP225
| sP305 ),
inference(all_rule,[status(thm)],[]) ).
thf(358,plain,
( ~ sP305
| ~ sP255
| sP252 ),
inference(prop_rule,[status(thm)],[]) ).
thf(359,plain,
( ~ sP279
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(360,plain,
( ~ sP1
| ~ sP170 ),
inference(all_rule,[status(thm)],[]) ).
thf(361,plain,
( ~ sP184
| sP198 ),
inference(all_rule,[status(thm)],[]) ).
thf(362,plain,
( ~ sP1
| ~ sP239 ),
inference(all_rule,[status(thm)],[]) ).
thf(363,plain,
( ~ sP61
| sP210 ),
inference(all_rule,[status(thm)],[]) ).
thf(364,plain,
( ~ sP279
| sP347 ),
inference(all_rule,[status(thm)],[]) ).
thf(365,plain,
( ~ sP347
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(366,plain,
( ~ sP3
| ~ sP252
| sP66 ),
inference(prop_rule,[status(thm)],[]) ).
thf(367,plain,
( ~ sP279
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(368,plain,
( ~ sP1
| ~ sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(369,plain,
( ~ sP184
| sP110 ),
inference(all_rule,[status(thm)],[]) ).
thf(370,plain,
( ~ sP1
| ~ sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(371,plain,
( ~ sP61
| sP143 ),
inference(all_rule,[status(thm)],[]) ).
thf(372,plain,
sP61,
inference(eq_sym,[status(thm)],[]) ).
thf(373,plain,
( ~ sP279
| sP98 ),
inference(all_rule,[status(thm)],[]) ).
thf(374,plain,
( ~ sP98
| sP131 ),
inference(all_rule,[status(thm)],[]) ).
thf(375,plain,
( ~ sP131
| ~ sP66
| sP90 ),
inference(prop_rule,[status(thm)],[]) ).
thf(376,plain,
( ~ sP1
| ~ sP90 ),
inference(all_rule,[status(thm)],[]) ).
thf(rsym,axiom,
sP184 ).
thf(rno3cl,axiom,
sP335 ).
thf(rno3acl,axiom,
sP265 ).
thf(pfnc,axiom,
sP1 ).
thf(pfinj,axiom,
sP279 ).
thf(377,plain,
$false,
inference(prop_unsat,[status(thm)],[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,rsym,rno3cl,rno3acl,pfnc,pfinj]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA118^1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 21:24:57 EDT 2026
% 0.16/0.34 % CPUTime :
% 11.99/12.02 % SZS status Unsatisfiable
% 11.99/12.02 % Mode: mode515
% 11.99/12.02 % Inferences: 17756
% 11.99/12.02 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------