%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : GRA119^1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 06:29:30 PM UTC 2026
% Result : Unsatisfiable 1.14s 1.37s
% Output : Proof 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 636
% Syntax : Number of formulae : 637 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 2036 ( 322 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 5386 (1112 ~; 530 |; 0 &;2875 @)
% ( 305 <=>; 564 =>; 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 : 310 ( 308 usr; 307 con; 0-2 aty)
% Number of variables : 67 ( 0 ^; 67 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_f,type,
f: $i > $i ).
thf(ty_c,type,
c: $i ).
thf(ty_r,type,
r: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [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,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ( c
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( r @ ( f @ c ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( r @ c @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [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,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ~ ( ( ( f @ c )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ c )
= ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= c ) )
=> ( ( f @ c )
= c ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [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,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( r @ ( f @ c ) @ ( f @ ( f @ c ) ) )
=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ~ sP19
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( c
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ c )
=> ( r @ c @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ sP13
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( ~ ( ~ ( ~ ( ( c
!= ( f @ c ) )
=> ( c
= ( f @ ( f @ c ) ) ) )
=> ( ( f @ c )
= ( f @ ( f @ c ) ) ) )
=> ~ ( r @ c @ ( f @ c ) ) )
=> ~ ( r @ c @ ( f @ ( f @ c ) ) ) )
=> ~ ( r @ ( f @ c ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) )
=> ( c
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ c ) ) )
=> ~ ( r @ c @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i] :
( ( r @ ( f @ ( f @ c ) ) @ X1 )
=> ( r @ X1 @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( c
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ c ) ) )
=> ~ ( r @ c @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( c
= ( f @ ( f @ c ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ c ) ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ sP28
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ c ) )
=> ( ( 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,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ ( ~ ( ~ ( ~ sP17
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ~ sP15 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) )
=> ( c
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( r @ c @ ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) )
=> ( c
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ ( ~ ( ( ( 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,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( ( f @ c )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ c )
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ ( ~ sP36
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ( f @ c )
= ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ~ ( ( c
!= ( f @ c ) )
=> ( c
= ( f @ ( f @ c ) ) ) )
=> ( ( f @ c )
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ~ ( ~ ( ~ sP17
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ ( ~ sP3
=> ( ( f @ c )
= c ) )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ ( ~ ( ~ sP39
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ( c = X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) )
=> ~ ( r @ c @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( c
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) )
=> ( c
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ~ ( ~ ( ~ ( ~ ( ~ sP61
=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= ( f @ ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( ~ ( ~ sP12
=> ( r @ ( f @ c ) @ ( f @ ( f @ c ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
= ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ~ ( ~ sP54
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ c ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( r @ ( f @ ( f @ c ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( ( c
!= ( f @ c ) )
=> sP59 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP39
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ c )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ c )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ( r @ ( f @ c ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ~ ( ~ ( ~ ( ~ ( ~ sP61
=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( ~ ( ~ sP52
=> ( r @ c @ ( f @ c ) ) )
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( ~ sP78
=> ( r @ ( f @ c ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( c
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( ~ ( ~ ( ~ ( ~ sP18
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ! [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,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( ~ ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( ~ sP32
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( ~ ( ~ ( ~ ( ~ sP57
=> ( c
= ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) )
=> sP15 )
=> ( r @ c @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( ~ ( ~ sP42
=> sP72 )
=> sP64 ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ( ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( r @ ( f @ ( f @ c ) ) @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( ( f @ ( f @ ( f @ c ) ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP39 )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ( ~ sP54
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ( ~ sP51
=> ~ sP72 ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( ~ ( ~ ( ~ ( ~ ( ~ sP91
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ( c
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ( r @ c @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( ~ ( ~ ( ~ sP57
=> ( c
= ( f @ c ) ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( ~ sP52
=> ~ ( r @ c @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= X1 )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X2 ) )
=> ( X1 = X2 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X2 ) )
=> ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( ~ sP47
=> sP77 ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ( ~ sP91
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( ~ ( ~ sP61
=> sP91 )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP61 )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ( ~ ( ~ ( ~ ( ~ sP61
=> sP39 )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ c ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP91
=> ( ( 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,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ( ~ ( ~ sP105
=> ( c
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ( ( r @ c @ ( f @ c ) )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ( ~ sP108
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ~ sP67 )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( c
!= ( f @ c ) )
=> ( c = X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ( r @ c @ ( f @ c ) ) )
=> ( r @ c @ X1 ) )
=> ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( ~ sP8
=> sP71 ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
!= c )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ c ) ) ) )
=> sP59 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( ~ ( ~ ( ( c
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP59 )
=> sP96 )
=> ( r @ c @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP101
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( ~ sP39
=> sP61 ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ! [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,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ( ~ ( ( c
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP59 )
=> sP96 ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
!= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> sP72 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( ~ ( ~ ( ~ sP93
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= c ) )
=> ( ( f @ c )
= c ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ( ~ ( ~ ( ~ ( ( ( f @ c )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP118 )
=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ( ~ ( ~ ( ( ( f @ c )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP118 ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ! [X1: $i] :
( ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 )
=> ( r @ X1 @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130,plain,
( sP130
<=> ( r @ c @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131,plain,
( sP131
<=> ( ~ sP57
=> ( c
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132,plain,
( sP132
<=> ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> sP128 ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133,plain,
( sP133
<=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134,plain,
( sP134
<=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135,plain,
( sP135
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP91
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( c = X1 ) )
=> sP113 )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ( r @ c @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136,plain,
( sP136
<=> ( ( ( f @ ( f @ c ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137,plain,
( sP137
<=> ( ~ ( ~ ( ~ sP39
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP137])]) ).
thf(sP138,plain,
( sP138
<=> ( ~ sP131
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139,plain,
( sP139
<=> ( ~ ( ~ sP42
=> ~ sP72 )
=> ~ sP64 ) ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140,plain,
( sP140
<=> ( ~ sP102
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141,plain,
( sP141
<=> ( ~ ( ~ ( ~ sP24
=> ~ sP113 )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) )
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142,plain,
( sP142
<=> ( ~ sP132
=> ~ sP77 ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143,plain,
( sP143
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144,plain,
( sP144
<=> ( ~ sP22
=> ~ sP99 ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145,plain,
( sP145
<=> ( ~ sP39
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146,plain,
( sP146
<=> ( ~ ( ~ sP56
=> ~ sP71 )
=> ~ sP72 ) ),
introduced(definition,[new_symbols(definition,[sP146])]) ).
thf(sP147,plain,
( sP147
<=> ( ~ sP91
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP147])]) ).
thf(sP148,plain,
( sP148
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP148])]) ).
thf(sP149,plain,
( sP149
<=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP149])]) ).
thf(sP150,plain,
( sP150
<=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP150])]) ).
thf(sP151,plain,
( sP151
<=> ( ~ sP86
=> sP99 ) ),
introduced(definition,[new_symbols(definition,[sP151])]) ).
thf(sP152,plain,
( sP152
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP152])]) ).
thf(sP153,plain,
( sP153
<=> ( ~ ( ~ sP24
=> ~ sP113 )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP153])]) ).
thf(sP154,plain,
( sP154
<=> ( sP133
=> sP72 ) ),
introduced(definition,[new_symbols(definition,[sP154])]) ).
thf(sP155,plain,
( sP155
<=> ( ~ sP12
=> ( r @ ( f @ c ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP155])]) ).
thf(sP156,plain,
( sP156
<=> ( sP90
=> ( r @ ( f @ c ) @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP156])]) ).
thf(sP157,plain,
( sP157
<=> ( ~ sP68
=> sP133 ) ),
introduced(definition,[new_symbols(definition,[sP157])]) ).
thf(sP158,plain,
( sP158
<=> ( ~ sP106
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP158])]) ).
thf(sP159,plain,
( sP159
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ c )
!= X1 )
=> ( ( f @ c )
= X2 ) )
=> ( X1 = X2 ) )
=> ( r @ ( f @ c ) @ X1 ) )
=> ( r @ ( f @ c ) @ X2 ) )
=> ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP159])]) ).
thf(sP160,plain,
( sP160
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP160])]) ).
thf(sP161,plain,
( sP161
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ c ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ~ sP77 )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP161])]) ).
thf(sP162,plain,
( sP162
<=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP162])]) ).
thf(sP163,plain,
( sP163
<=> ( ~ ( ~ ( ~ ( ( ( f @ ( f @ c ) )
!= ( f @ c ) )
=> sP162 )
=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP90 )
=> sP71 ) ),
introduced(definition,[new_symbols(definition,[sP163])]) ).
thf(sP164,plain,
( sP164
<=> ! [X1: $i] :
( ( r @ c @ X1 )
=> ( r @ X1 @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP164])]) ).
thf(sP165,plain,
( sP165
<=> ! [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,[sP165])]) ).
thf(sP166,plain,
( sP166
<=> ( ~ ( ~ sP106
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP113 ) ),
introduced(definition,[new_symbols(definition,[sP166])]) ).
thf(sP167,plain,
( sP167
<=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP167])]) ).
thf(sP168,plain,
( sP168
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP168])]) ).
thf(sP169,plain,
( sP169
<=> ( ~ sP35
=> sP90 ) ),
introduced(definition,[new_symbols(definition,[sP169])]) ).
thf(sP170,plain,
( sP170
<=> ( ~ ( ~ sP117
=> sP83 )
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP170])]) ).
thf(sP171,plain,
( sP171
<=> ( ~ sP56
=> ~ sP71 ) ),
introduced(definition,[new_symbols(definition,[sP171])]) ).
thf(sP172,plain,
( sP172
<=> ( ~ sP48
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP172])]) ).
thf(sP173,plain,
( sP173
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP173])]) ).
thf(sP174,plain,
( sP174
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( c
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( c = X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> sP130 )
=> ( r @ c @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP174])]) ).
thf(sP175,plain,
( sP175
<=> ( ~ sP61
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP175])]) ).
thf(sP176,plain,
( sP176
<=> ( ~ sP105
=> ( c
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP176])]) ).
thf(sP177,plain,
( sP177
<=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP177])]) ).
thf(sP178,plain,
( sP178
<=> ( ~ sP145
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP178])]) ).
thf(sP179,plain,
( sP179
<=> ( ~ ( ~ sP79
=> sP72 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP179])]) ).
thf(sP180,plain,
( sP180
<=> ( ~ ( ~ ( ~ ( ~ ( ~ sP61
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> sP134 )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ sP77 )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP180])]) ).
thf(sP181,plain,
( sP181
<=> ( ~ ( ~ ( ~ ( ~ sP61
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) )
=> sP134 )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ~ sP77 ) ),
introduced(definition,[new_symbols(definition,[sP181])]) ).
thf(sP182,plain,
( sP182
<=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP182])]) ).
thf(sP183,plain,
( sP183
<=> ( ( f @ c )
= c ) ),
introduced(definition,[new_symbols(definition,[sP183])]) ).
thf(sP184,plain,
( sP184
<=> ( ~ sP175
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP184])]) ).
thf(sP185,plain,
( sP185
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP39
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> sP160 )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ c ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP185])]) ).
thf(sP186,plain,
( sP186
<=> ( ~ sP144
=> ~ sP167 ) ),
introduced(definition,[new_symbols(definition,[sP186])]) ).
thf(sP187,plain,
( sP187
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP50
=> ( ( f @ c )
= X1 ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ( r @ ( f @ c ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP187])]) ).
thf(sP188,plain,
( sP188
<=> ( ~ sP17
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP188])]) ).
thf(sP189,plain,
( sP189
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP189])]) ).
thf(sP190,plain,
( sP190
<=> ( ~ sP151
=> sP182 ) ),
introduced(definition,[new_symbols(definition,[sP190])]) ).
thf(sP191,plain,
( sP191
<=> ( ~ sP106
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP191])]) ).
thf(sP192,plain,
( sP192
<=> ( r @ c @ ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP192])]) ).
thf(sP193,plain,
( sP193
<=> ( ~ sP128
=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP193])]) ).
thf(sP194,plain,
( sP194
<=> ( ~ ( ~ ( ~ sP18
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) )
=> ~ sP167 )
=> ~ sP182 ) ),
introduced(definition,[new_symbols(definition,[sP194])]) ).
thf(sP195,plain,
( sP195
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP101
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> sP133 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP195])]) ).
thf(sP196,plain,
( sP196
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP61
=> ( ( 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,[sP196])]) ).
thf(sP197,plain,
( sP197
<=> ( ~ sP163
=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP197])]) ).
thf(sP198,plain,
( sP198
<=> ( ~ sP188
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP198])]) ).
thf(sP199,plain,
( sP199
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( c
!= ( f @ c ) )
=> ( c = X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ~ sP192 )
=> ~ ( r @ c @ X1 ) )
=> ~ ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP199])]) ).
thf(sP200,plain,
( sP200
<=> ( ~ sP101
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP200])]) ).
thf(sP201,plain,
( sP201
<=> ! [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,[sP201])]) ).
thf(sP202,plain,
( sP202
<=> ( ~ sP110
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP202])]) ).
thf(sP203,plain,
( sP203
<=> ! [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,[sP203])]) ).
thf(sP204,plain,
( sP204
<=> ( ~ sP2
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP204])]) ).
thf(sP205,plain,
( sP205
<=> ( ~ sP126
=> sP72 ) ),
introduced(definition,[new_symbols(definition,[sP205])]) ).
thf(sP206,plain,
( sP206
<=> ( ~ sP119
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP206])]) ).
thf(sP207,plain,
( sP207
<=> ( ~ ( ~ sP81
=> ~ sP113 )
=> ~ sP77 ) ),
introduced(definition,[new_symbols(definition,[sP207])]) ).
thf(sP208,plain,
( sP208
<=> ( ~ sP24
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP208])]) ).
thf(sP209,plain,
( sP209
<=> ( c
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP209])]) ).
thf(sP210,plain,
( sP210
<=> ( ( ( f @ ( f @ c ) )
!= ( f @ c ) )
=> sP162 ) ),
introduced(definition,[new_symbols(definition,[sP210])]) ).
thf(sP211,plain,
( sP211
<=> ( ~ sP104
=> sP192 ) ),
introduced(definition,[new_symbols(definition,[sP211])]) ).
thf(sP212,plain,
( sP212
<=> ( ~ sP158
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP212])]) ).
thf(sP213,plain,
( sP213
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP213])]) ).
thf(sP214,plain,
( sP214
<=> ! [X1: $i] :
( ( r @ ( f @ c ) @ X1 )
=> ( r @ X1 @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP214])]) ).
thf(sP215,plain,
( sP215
<=> ( ~ sP142
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP215])]) ).
thf(sP216,plain,
( sP216
<=> ( ~ sP206
=> sP167 ) ),
introduced(definition,[new_symbols(definition,[sP216])]) ).
thf(sP217,plain,
( sP217
<=> ( ~ sP148
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP217])]) ).
thf(sP218,plain,
( sP218
<=> ( ~ sP177
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP218])]) ).
thf(sP219,plain,
( sP219
<=> ( ( f @ c )
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP219])]) ).
thf(sP220,plain,
( sP220
<=> ( ~ sP117
=> sP83 ) ),
introduced(definition,[new_symbols(definition,[sP220])]) ).
thf(sP221,plain,
( sP221
<=> ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP61 )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP221])]) ).
thf(sP222,plain,
( sP222
<=> ( sP83
=> sP71 ) ),
introduced(definition,[new_symbols(definition,[sP222])]) ).
thf(sP223,plain,
( sP223
<=> ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP61 ) ),
introduced(definition,[new_symbols(definition,[sP223])]) ).
thf(sP224,plain,
( sP224
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP50
=> ( ( f @ c )
= X1 ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ~ ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ c ) ) ) ) )
=> ~ ( r @ ( f @ c ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP224])]) ).
thf(sP225,plain,
( sP225
<=> ( ~ sP91
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP225])]) ).
thf(sP226,plain,
( sP226
<=> ( ~ ( ~ ( ~ sP50
=> sP183 )
=> sP91 )
=> ~ ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP226])]) ).
thf(sP227,plain,
( sP227
<=> ( ~ sP218
=> sP59 ) ),
introduced(definition,[new_symbols(definition,[sP227])]) ).
thf(sP228,plain,
( sP228
<=> ( ( c
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP59 ) ),
introduced(definition,[new_symbols(definition,[sP228])]) ).
thf(sP229,plain,
( sP229
<=> ( ~ sP136
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP229])]) ).
thf(sP230,plain,
( sP230
<=> ( ~ sP18
=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP230])]) ).
thf(sP231,plain,
( sP231
<=> ( ~ sP50
=> sP183 ) ),
introduced(definition,[new_symbols(definition,[sP231])]) ).
thf(sP232,plain,
( sP232
<=> ( ( f @ ( f @ c ) )
= ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP232])]) ).
thf(sP233,plain,
( sP233
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( c != X1 )
=> ( c = X2 ) )
=> ( X1 = X2 ) )
=> ~ ( r @ c @ X1 ) )
=> ~ ( r @ c @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP233])]) ).
thf(sP234,plain,
( sP234
<=> ( ~ sP231
=> sP91 ) ),
introduced(definition,[new_symbols(definition,[sP234])]) ).
thf(sP235,plain,
( sP235
<=> ( ~ ( ~ sP121
=> sP162 )
=> sP160 ) ),
introduced(definition,[new_symbols(definition,[sP235])]) ).
thf(sP236,plain,
( sP236
<=> ( ~ sP204
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP236])]) ).
thf(sP237,plain,
( sP237
<=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ c ) ),
introduced(definition,[new_symbols(definition,[sP237])]) ).
thf(sP238,plain,
( sP238
<=> ( ~ sP61
=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP238])]) ).
thf(sP239,plain,
( sP239
<=> ( ~ sP3
=> sP183 ) ),
introduced(definition,[new_symbols(definition,[sP239])]) ).
thf(sP240,plain,
( sP240
<=> ( sP72
=> sP133 ) ),
introduced(definition,[new_symbols(definition,[sP240])]) ).
thf(sP241,plain,
( sP241
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP241])]) ).
thf(sP242,plain,
( sP242
<=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP242])]) ).
thf(sP243,plain,
( sP243
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ ( f @ ( f @ c ) ) )
!= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) )
=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP243])]) ).
thf(sP244,plain,
( sP244
<=> ( ~ sP93
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP244])]) ).
thf(sP245,plain,
( sP245
<=> ( r @ ( f @ ( f @ ( f @ c ) ) ) @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP245])]) ).
thf(sP246,plain,
( sP246
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP93
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> sP182 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) )
=> ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP246])]) ).
thf(sP247,plain,
( sP247
<=> ( ~ sP139
=> ~ sP237 ) ),
introduced(definition,[new_symbols(definition,[sP247])]) ).
thf(sP248,plain,
( sP248
<=> ( ~ ( ~ sP210
=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
=> sP90 ) ),
introduced(definition,[new_symbols(definition,[sP248])]) ).
thf(sP249,plain,
( sP249
<=> ( ~ sP38
=> sP213 ) ),
introduced(definition,[new_symbols(definition,[sP249])]) ).
thf(sP250,plain,
( sP250
<=> ( ~ sP193
=> sP241 ) ),
introduced(definition,[new_symbols(definition,[sP250])]) ).
thf(sP251,plain,
( sP251
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( ( f @ c )
!= X1 )
=> ( ( f @ c )
= X2 ) )
=> ( X1 = X2 ) )
=> ~ ( r @ ( f @ c ) @ X1 ) )
=> ~ ( r @ ( f @ c ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP251])]) ).
thf(sP252,plain,
( sP252
<=> ( ( f @ ( f @ c ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP252])]) ).
thf(sP253,plain,
( sP253
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP177
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ( c = X1 ) )
=> sP237 )
=> ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ( r @ c @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP253])]) ).
thf(sP254,plain,
( sP254
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP148
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ ( f @ c ) ) )
= X1 ) )
=> ~ sP99 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ ( f @ c ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP254])]) ).
thf(sP255,plain,
( sP255
<=> ( ~ sP52
=> sP192 ) ),
introduced(definition,[new_symbols(definition,[sP255])]) ).
thf(sP256,plain,
( sP256
<=> ( ~ ( ~ sP137
=> ~ sP77 )
=> ~ sP90 ) ),
introduced(definition,[new_symbols(definition,[sP256])]) ).
thf(sP257,plain,
( sP257
<=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP257])]) ).
thf(sP258,plain,
( sP258
<=> ( ~ sP244
=> sP183 ) ),
introduced(definition,[new_symbols(definition,[sP258])]) ).
thf(sP259,plain,
( sP259
<=> ( r @ ( f @ c ) @ ( f @ ( f @ ( f @ c ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP259])]) ).
thf(sP260,plain,
( sP260
<=> ( ~ sP241
=> sP93 ) ),
introduced(definition,[new_symbols(definition,[sP260])]) ).
thf(sP261,plain,
( sP261
<=> $false ),
introduced(definition,[new_symbols(definition,[sP261])]) ).
thf(sP262,plain,
( sP262
<=> ( ~ sP238
=> sP134 ) ),
introduced(definition,[new_symbols(definition,[sP262])]) ).
thf(sP263,plain,
( sP263
<=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP263])]) ).
thf(sP264,plain,
( sP264
<=> ! [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,[sP264])]) ).
thf(sP265,plain,
( sP265
<=> ( ~ ( ~ sP85
=> ~ sP133 )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP265])]) ).
thf(sP266,plain,
( sP266
<=> ( ~ sP88
=> sP237 ) ),
introduced(definition,[new_symbols(definition,[sP266])]) ).
thf(sP267,plain,
( sP267
<=> ( ~ sP79
=> sP72 ) ),
introduced(definition,[new_symbols(definition,[sP267])]) ).
thf(sP268,plain,
( sP268
<=> ! [X1: $i,X2: $i] :
( ( r @ X1 @ X2 )
=> ( r @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP268])]) ).
thf(sP269,plain,
( sP269
<=> ( ~ sP265
=> ~ sP182 ) ),
introduced(definition,[new_symbols(definition,[sP269])]) ).
thf(sP270,plain,
( sP270
<=> ( ~ sP215
=> ~ sP118 ) ),
introduced(definition,[new_symbols(definition,[sP270])]) ).
thf(sP271,plain,
( sP271
<=> ( ~ sP186
=> ~ sP160 ) ),
introduced(definition,[new_symbols(definition,[sP271])]) ).
thf(sP272,plain,
( sP272
<=> ( sP71
=> sP83 ) ),
introduced(definition,[new_symbols(definition,[sP272])]) ).
thf(sP273,plain,
( sP273
<=> ( ~ sP148
=> sP96 ) ),
introduced(definition,[new_symbols(definition,[sP273])]) ).
thf(sP274,plain,
( sP274
<=> ( ~ sP226
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP274])]) ).
thf(sP275,plain,
( sP275
<=> ( ~ sP121
=> sP162 ) ),
introduced(definition,[new_symbols(definition,[sP275])]) ).
thf(sP276,plain,
( sP276
<=> ( ~ sP137
=> ~ sP77 ) ),
introduced(definition,[new_symbols(definition,[sP276])]) ).
thf(sP277,plain,
( sP277
<=> ( ~ sP241
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= c ) ) ),
introduced(definition,[new_symbols(definition,[sP277])]) ).
thf(sP278,plain,
( sP278
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= c ) ),
introduced(definition,[new_symbols(definition,[sP278])]) ).
thf(sP279,plain,
( sP279
<=> ( ~ sP274
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP279])]) ).
thf(sP280,plain,
( sP280
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP134
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ( ( f @ c )
= X1 ) )
=> ~ sP15 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ c ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP280])]) ).
thf(sP281,plain,
( sP281
<=> ( ~ sP210
=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP281])]) ).
thf(sP282,plain,
( sP282
<=> ( ( f @ ( f @ ( f @ c ) ) )
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP282])]) ).
thf(sP283,plain,
( sP283
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP96
=> ( ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) )
= X1 ) )
=> ( ( f @ ( f @ c ) )
= X1 ) )
=> ~ sP167 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( f @ ( f @ c ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP283])]) ).
thf(sP284,plain,
( sP284
<=> ( ~ sP101
=> sP134 ) ),
introduced(definition,[new_symbols(definition,[sP284])]) ).
thf(sP285,plain,
( sP285
<=> ( ( f @ c )
= ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP285])]) ).
thf(sP286,plain,
( sP286
<=> ( ~ sP81
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP286])]) ).
thf(sP287,plain,
( sP287
<=> ( ~ sP262
=> ~ sP213 ) ),
introduced(definition,[new_symbols(definition,[sP287])]) ).
thf(sP288,plain,
( sP288
<=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP288])]) ).
thf(sP289,plain,
( sP289
<=> ( ~ sP184
=> ~ sP213 ) ),
introduced(definition,[new_symbols(definition,[sP289])]) ).
thf(sP290,plain,
( sP290
<=> ( ~ sP61
=> sP91 ) ),
introduced(definition,[new_symbols(definition,[sP290])]) ).
thf(sP291,plain,
( sP291
<=> ( c
= ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP291])]) ).
thf(sP292,plain,
( sP292
<=> ( ~ sP42
=> ~ sP72 ) ),
introduced(definition,[new_symbols(definition,[sP292])]) ).
thf(sP293,plain,
( sP293
<=> ( ~ sP230
=> ~ sP167 ) ),
introduced(definition,[new_symbols(definition,[sP293])]) ).
thf(sP294,plain,
( sP294
<=> ( ~ sP5
=> sP167 ) ),
introduced(definition,[new_symbols(definition,[sP294])]) ).
thf(sP295,plain,
( sP295
<=> ( ~ sP190
=> sP77 ) ),
introduced(definition,[new_symbols(definition,[sP295])]) ).
thf(sP296,plain,
( sP296
<=> ( ( f @ ( f @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) )
= ( f @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP296])]) ).
thf(sP297,plain,
( sP297
<=> ( ~ sP36
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP297])]) ).
thf(sP298,plain,
( sP298
<=> ( r @ ( f @ c ) @ ( f @ ( f @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP298])]) ).
thf(sP299,plain,
( sP299
<=> ( ~ sP19
=> sP160 ) ),
introduced(definition,[new_symbols(definition,[sP299])]) ).
thf(sP300,plain,
( sP300
<=> ( ~ sP85
=> ~ sP133 ) ),
introduced(definition,[new_symbols(definition,[sP300])]) ).
thf(sP301,plain,
( sP301
<=> ( ~ sP42
=> sP72 ) ),
introduced(definition,[new_symbols(definition,[sP301])]) ).
thf(sP302,plain,
( sP302
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( c != X1 )
=> ( c = X2 ) )
=> ( X1 = X2 ) )
=> ( r @ c @ X1 ) )
=> ( r @ c @ X2 ) )
=> ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP302])]) ).
thf(sP303,plain,
( sP303
<=> ! [X1: $i] :
( ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 )
=> ( r @ X1 @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP303])]) ).
thf(sP304,plain,
( sP304
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ~ sP177
=> ( ( f @ ( f @ ( f @ ( f @ c ) ) ) )
= X1 ) )
=> ( c = X1 ) )
=> ~ sP237 )
=> ~ ( r @ ( f @ ( f @ ( f @ ( f @ c ) ) ) ) @ X1 ) )
=> ~ ( r @ c @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP304])]) ).
thf(sP305,plain,
( sP305
<=> ( ~ sP278
=> sP93 ) ),
introduced(definition,[new_symbols(definition,[sP305])]) ).
thf(1,plain,
( ~ sP150
| sP168
| ~ sP150
| sP261 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP43
| sP189
| ~ sP43
| sP261 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP242
| sP66
| ~ sP242
| sP261 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP30
| sP296
| ~ sP30
| sP261 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP241
| sP101
| ~ sP241
| sP261 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP101
| sP168
| ~ sP98
| sP261 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP23
| sP61
| ~ sP23
| sP261 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(8,plain,
( sP43
| ~ sP128 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP150
| ~ sP282 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP242
| ~ sP149 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP98
| ~ sP101 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP30
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP282
| ~ sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP101
| ~ sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP149
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP273
| sP148
| sP96 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP22
| sP273
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP217
| sP148
| sP241 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP34
| sP217
| sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP260
| sP241
| sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP79
| sP260
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP46
| sP60
| ~ sP64 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP293
| sP230
| ~ sP167 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP144
| sP22
| ~ sP99 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP292
| sP42
| ~ sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP305
| sP278
| sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP60
| sP305
| sP209 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP244
| sP93
| sP278 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP258
| sP244
| sP183 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP125
| sP258
| sP182 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP18
| sP96
| sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP230
| sP18
| sP252 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP32
| sP148
| sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP86
| sP32
| sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP151
| sP86
| sP99 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP28
| sP34
| sP99 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP277
| sP241
| sP278 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP42
| sP277
| sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP301
| sP42
| sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP267
| sP79
| sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP193
| sP128
| sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP250
| sP193
| sP241 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP136
| sP149
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP229
| sP136
| sP241 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP152
| sP282
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP92
| sP152
| sP96 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP223
| sP282
| sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP221
| sP223
| sP241 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP284
| sP101
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP85
| sP284
| sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP200
| sP101
| sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP68
| sP200
| sP96 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP44
| sP46
| ~ sP182 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP194
| sP293
| ~ sP182 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP186
| sP144
| ~ sP167 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP139
| sP292
| ~ sP64 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP13
| sP125
| sP64 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP190
| sP151
| sP182 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP38
| sP28
| sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP88
| sP301
| sP64 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP179
| sP267
| sP182 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP119
| sP123
| sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP228
| sP291
| sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP123
| sP228
| sP96 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP127
| sP250
| sP118 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP56
| sP229
| ~ sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP19
| sP92
| sP245 ),
inference(prop_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP107
| sP221
| ~ sP245 ),
inference(prop_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP157
| sP68
| sP133 ),
inference(prop_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP300
| sP85
| ~ sP133 ),
inference(prop_rule,[status(thm)],[]) ).
thf(71,plain,
( ~ sP29
| sP44
| ~ sP192 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( ~ sP82
| sP194
| ~ sP90 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP271
| sP186
| ~ sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP247
| sP139
| ~ sP237 ),
inference(prop_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP26
| sP13
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP295
| sP190
| sP77 ),
inference(prop_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP249
| sP38
| sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( ~ sP266
| sP88
| sP237 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP37
| sP179
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
( ~ sP206
| sP119
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(81,plain,
( ~ sP126
| sP127
| sP257 ),
inference(prop_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP171
| sP56
| ~ sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP299
| sP19
| sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP51
| sP107
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(85,plain,
( ~ sP110
| sP176
| sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(86,plain,
( ~ sP143
| sP263
| sP282 ),
inference(prop_rule,[status(thm)],[]) ).
thf(87,plain,
( ~ sP132
| sP143
| sP128 ),
inference(prop_rule,[status(thm)],[]) ).
thf(88,plain,
( ~ sP142
| sP132
| ~ sP77 ),
inference(prop_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP105
| sP91
| sP282 ),
inference(prop_rule,[status(thm)],[]) ).
thf(90,plain,
( ~ sP176
| sP105
| sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(91,plain,
( ~ sP2
| sP176
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(92,plain,
( ~ sP5
| sP157
| sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(93,plain,
( ~ sP265
| sP300
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(94,plain,
( ~ sP58
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(95,plain,
( ~ sP283
| sP82 ),
inference(all_rule,[status(thm)],[]) ).
thf(96,plain,
( ~ sP254
| sP271 ),
inference(all_rule,[status(thm)],[]) ).
thf(97,plain,
( ~ sP14
| sP247 ),
inference(all_rule,[status(thm)],[]) ).
thf(98,plain,
( ~ sP246
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(99,plain,
( ~ sP70
| sP295 ),
inference(all_rule,[status(thm)],[]) ).
thf(100,plain,
( ~ sP70
| sP249 ),
inference(all_rule,[status(thm)],[]) ).
thf(101,plain,
( ~ sP124
| sP266 ),
inference(all_rule,[status(thm)],[]) ).
thf(102,plain,
( ~ sP124
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(103,plain,
( ~ sP216
| sP206
| sP167 ),
inference(prop_rule,[status(thm)],[]) ).
thf(104,plain,
( ~ sP205
| sP126
| sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(105,plain,
( ~ sP146
| sP171
| ~ sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(106,plain,
( ~ sP21
| sP299
| sP167 ),
inference(prop_rule,[status(thm)],[]) ).
thf(107,plain,
( ~ sP95
| sP51
| ~ sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(108,plain,
( ~ sP202
| sP110
| sP245 ),
inference(prop_rule,[status(thm)],[]) ).
thf(109,plain,
( ~ sP215
| sP142
| ~ sP245 ),
inference(prop_rule,[status(thm)],[]) ).
thf(110,plain,
( ~ sP204
| sP2
| ~ sP245 ),
inference(prop_rule,[status(thm)],[]) ).
thf(111,plain,
( ~ sP294
| sP5
| sP167 ),
inference(prop_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP269
| sP265
| ~ sP182 ),
inference(prop_rule,[status(thm)],[]) ).
thf(113,plain,
( ~ sP7
| sP58 ),
inference(all_rule,[status(thm)],[]) ).
thf(114,plain,
( ~ sP7
| sP283 ),
inference(all_rule,[status(thm)],[]) ).
thf(115,plain,
( ~ sP7
| sP254 ),
inference(all_rule,[status(thm)],[]) ).
thf(116,plain,
( ~ sP7
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(117,plain,
( ~ sP103
| sP246 ),
inference(all_rule,[status(thm)],[]) ).
thf(118,plain,
( ~ sP103
| sP70 ),
inference(all_rule,[status(thm)],[]) ).
thf(119,plain,
( ~ sP103
| sP124 ),
inference(all_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP174
| sP216 ),
inference(all_rule,[status(thm)],[]) ).
thf(121,plain,
( ~ sP75
| sP205 ),
inference(all_rule,[status(thm)],[]) ).
thf(122,plain,
( ~ sP114
| sP146 ),
inference(all_rule,[status(thm)],[]) ).
thf(123,plain,
( ~ sP243
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(124,plain,
( ~ sP173
| sP95 ),
inference(all_rule,[status(thm)],[]) ).
thf(125,plain,
( ~ sP97
| sP202
| sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(126,plain,
( ~ sP270
| sP215
| ~ sP118 ),
inference(prop_rule,[status(thm)],[]) ).
thf(127,plain,
( ~ sP236
| sP204
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(128,plain,
( ~ sP195
| sP294 ),
inference(all_rule,[status(thm)],[]) ).
thf(129,plain,
( ~ sP120
| sP269 ),
inference(all_rule,[status(thm)],[]) ).
thf(130,plain,
( ~ sP25
| ~ sP64
| sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(131,plain,
( ~ sP4
| ~ sP167
| sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(132,plain,
( ~ sP11
| ~ sP99
| sP245 ),
inference(prop_rule,[status(thm)],[]) ).
thf(133,plain,
( ~ sP240
| ~ sP72
| sP133 ),
inference(prop_rule,[status(thm)],[]) ).
thf(134,plain,
( ~ sP129
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(135,plain,
( ~ sP129
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(136,plain,
( ~ sP129
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(137,plain,
( ~ sP129
| sP240 ),
inference(all_rule,[status(thm)],[]) ).
thf(138,plain,
( ~ sP9
| ~ sP130
| sP64 ),
inference(prop_rule,[status(thm)],[]) ).
thf(139,plain,
( ~ sP154
| ~ sP133
| sP72 ),
inference(prop_rule,[status(thm)],[]) ).
thf(140,plain,
( ~ sP268
| sP129 ),
inference(all_rule,[status(thm)],[]) ).
thf(141,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(142,plain,
( ~ sP264
| sP103 ),
inference(all_rule,[status(thm)],[]) ).
thf(143,plain,
( ~ sP164
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(144,plain,
( ~ sP302
| sP174 ),
inference(all_rule,[status(thm)],[]) ).
thf(145,plain,
( ~ sP159
| sP75 ),
inference(all_rule,[status(thm)],[]) ).
thf(146,plain,
( ~ sP10
| sP114 ),
inference(all_rule,[status(thm)],[]) ).
thf(147,plain,
( ~ sP165
| sP243 ),
inference(all_rule,[status(thm)],[]) ).
thf(148,plain,
( ~ sP203
| sP173 ),
inference(all_rule,[status(thm)],[]) ).
thf(149,plain,
( ~ sP135
| sP97 ),
inference(all_rule,[status(thm)],[]) ).
thf(150,plain,
( ~ sP161
| sP270 ),
inference(all_rule,[status(thm)],[]) ).
thf(151,plain,
( ~ sP109
| sP236 ),
inference(all_rule,[status(thm)],[]) ).
thf(152,plain,
( ~ sP303
| sP154 ),
inference(all_rule,[status(thm)],[]) ).
thf(153,plain,
( ~ sP84
| sP195 ),
inference(all_rule,[status(thm)],[]) ).
thf(154,plain,
( ~ sP201
| sP120 ),
inference(all_rule,[status(thm)],[]) ).
thf(155,plain,
( sP23
| ~ sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(156,plain,
( sP162
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(157,plain,
( sP61
| ~ sP232 ),
inference(prop_rule,[status(thm)],[]) ).
thf(158,plain,
( ~ sP36
| sP227
| ~ sP237 ),
inference(prop_rule,[status(thm)],[]) ).
thf(159,plain,
( ~ sP54
| sP239
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(160,plain,
( ~ sP198
| sP188
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(161,plain,
( ~ sP218
| sP177
| sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(162,plain,
( ~ sP227
| sP218
| sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(163,plain,
( ~ sP117
| sP227
| sP237 ),
inference(prop_rule,[status(thm)],[]) ).
thf(164,plain,
( ~ sP17
| sP288
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(165,plain,
( ~ sP188
| sP17
| sP252 ),
inference(prop_rule,[status(thm)],[]) ).
thf(166,plain,
( ~ sP297
| sP36
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(167,plain,
( ~ sP94
| sP54
| ~ sP237 ),
inference(prop_rule,[status(thm)],[]) ).
thf(168,plain,
( ~ sP53
| sP198
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(169,plain,
( ~ sP57
| sP177
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(170,plain,
( ~ sP131
| sP57
| sP209 ),
inference(prop_rule,[status(thm)],[]) ).
thf(171,plain,
( ~ sP138
| sP131
| sP237 ),
inference(prop_rule,[status(thm)],[]) ).
thf(172,plain,
( ~ sP100
| sP138
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(173,plain,
( ~ sP220
| sP117
| sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(174,plain,
( ~ sP3
| sP134
| sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(175,plain,
( ~ sP239
| sP3
| sP183 ),
inference(prop_rule,[status(thm)],[]) ).
thf(176,plain,
( ~ sP191
| sP106
| sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(177,plain,
( ~ sP290
| sP61
| sP91 ),
inference(prop_rule,[status(thm)],[]) ).
thf(178,plain,
( ~ sP106
| sP290
| sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(179,plain,
( ~ sP158
| sP106
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(180,plain,
( ~ sP238
| sP61
| sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(181,plain,
( ~ sP262
| sP238
| sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(182,plain,
( ~ sP287
| sP262
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(183,plain,
( ~ sP175
| sP61
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(184,plain,
( ~ sP184
| sP175
| sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(185,plain,
( ~ sP289
| sP184
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(186,plain,
( ~ sP49
| sP297
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(187,plain,
( ~ sP69
| sP94
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(188,plain,
( ~ sP41
| sP53
| ~ sP90 ),
inference(prop_rule,[status(thm)],[]) ).
thf(189,plain,
( ~ sP87
| sP100
| sP192 ),
inference(prop_rule,[status(thm)],[]) ).
thf(190,plain,
( ~ sP170
| sP220
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(191,plain,
( ~ sP248
| sP281
| sP90 ),
inference(prop_rule,[status(thm)],[]) ).
thf(192,plain,
( ~ sP210
| sP252
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(193,plain,
( ~ sP281
| sP210
| sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(194,plain,
( ~ sP166
| sP191
| sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(195,plain,
( ~ sP212
| sP158
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(196,plain,
( ~ sP181
| sP287
| ~ sP77 ),
inference(prop_rule,[status(thm)],[]) ).
thf(197,plain,
( ~ sP108
| sP289
| ~ sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(198,plain,
( ~ sP235
| sP275
| sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(199,plain,
( ~ sP121
| sP39
| sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(200,plain,
( ~ sP275
| sP121
| sP162 ),
inference(prop_rule,[status(thm)],[]) ).
thf(201,plain,
( ~ sP304
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(202,plain,
( ~ sP280
| sP69 ),
inference(all_rule,[status(thm)],[]) ).
thf(203,plain,
( ~ sP63
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(204,plain,
( ~ sP253
| sP87 ),
inference(all_rule,[status(thm)],[]) ).
thf(205,plain,
( ~ sP253
| sP170 ),
inference(all_rule,[status(thm)],[]) ).
thf(206,plain,
( ~ sP163
| sP248
| sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(207,plain,
( ~ sP62
| sP166
| sP237 ),
inference(prop_rule,[status(thm)],[]) ).
thf(208,plain,
( ~ sP76
| sP212
| ~ sP237 ),
inference(prop_rule,[status(thm)],[]) ).
thf(209,plain,
( ~ sP180
| sP181
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(210,plain,
( ~ sP112
| sP108
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(211,plain,
( ~ sP8
| sP235
| sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(212,plain,
( ~ sP201
| sP304 ),
inference(all_rule,[status(thm)],[]) ).
thf(213,plain,
( ~ sP201
| sP280 ),
inference(all_rule,[status(thm)],[]) ).
thf(214,plain,
( ~ sP201
| sP63 ),
inference(all_rule,[status(thm)],[]) ).
thf(215,plain,
( ~ sP84
| sP253 ),
inference(all_rule,[status(thm)],[]) ).
thf(216,plain,
( ~ sP197
| sP163
| sP257 ),
inference(prop_rule,[status(thm)],[]) ).
thf(217,plain,
( ~ sP16
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(218,plain,
( ~ sP196
| sP76 ),
inference(all_rule,[status(thm)],[]) ).
thf(219,plain,
( ~ sP196
| sP180 ),
inference(all_rule,[status(thm)],[]) ).
thf(220,plain,
( ~ sP196
| sP112 ),
inference(all_rule,[status(thm)],[]) ).
thf(221,plain,
( ~ sP116
| sP8
| sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(222,plain,
( ~ sP222
| ~ sP83
| sP71 ),
inference(prop_rule,[status(thm)],[]) ).
thf(223,plain,
( ~ sP303
| sP222 ),
inference(all_rule,[status(thm)],[]) ).
thf(224,plain,
( ~ sP89
| ~ sP257
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(225,plain,
( ~ sP272
| ~ sP71
| sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(226,plain,
( ~ sP268
| sP303 ),
inference(all_rule,[status(thm)],[]) ).
thf(227,plain,
( ~ sP1
| sP201 ),
inference(all_rule,[status(thm)],[]) ).
thf(228,plain,
( ~ sP264
| sP84 ),
inference(all_rule,[status(thm)],[]) ).
thf(229,plain,
( ~ sP214
| sP89 ),
inference(all_rule,[status(thm)],[]) ).
thf(230,plain,
( ~ sP31
| sP272 ),
inference(all_rule,[status(thm)],[]) ).
thf(231,plain,
( ~ sP40
| sP197 ),
inference(all_rule,[status(thm)],[]) ).
thf(232,plain,
( ~ sP165
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(233,plain,
( ~ sP203
| sP196 ),
inference(all_rule,[status(thm)],[]) ).
thf(234,plain,
( ~ sP185
| sP116 ),
inference(all_rule,[status(thm)],[]) ).
thf(235,plain,
( sP39
| ~ sP252 ),
inference(prop_rule,[status(thm)],[]) ).
thf(236,plain,
( sP50
| ~ sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(237,plain,
( sP232
| ~ sP219 ),
inference(prop_rule,[status(thm)],[]) ).
thf(238,plain,
( ~ sP137
| sP178
| ~ sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(239,plain,
( ~ sP145
| sP39
| sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(240,plain,
( ~ sP178
| sP145
| sP252 ),
inference(prop_rule,[status(thm)],[]) ).
thf(241,plain,
( ~ sP55
| sP178
| sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(242,plain,
( ~ sP286
| sP81
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(243,plain,
( ~ sP207
| sP286
| ~ sP77 ),
inference(prop_rule,[status(thm)],[]) ).
thf(244,plain,
( ~ sP208
| sP24
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(245,plain,
( ~ sP153
| sP208
| ~ sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(246,plain,
( ~ sP276
| sP137
| ~ sP77 ),
inference(prop_rule,[status(thm)],[]) ).
thf(247,plain,
( ~ sP225
| sP91
| sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(248,plain,
( ~ sP81
| sP225
| sP209 ),
inference(prop_rule,[status(thm)],[]) ).
thf(249,plain,
( ~ sP47
| sP81
| sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(250,plain,
( ~ sP104
| sP47
| sP77 ),
inference(prop_rule,[status(thm)],[]) ).
thf(251,plain,
( ~ sP147
| sP91
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(252,plain,
( ~ sP24
| sP147
| sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(253,plain,
( ~ sP35
| sP55
| sP77 ),
inference(prop_rule,[status(thm)],[]) ).
thf(254,plain,
( ~ sP12
| sP172
| sP259 ),
inference(prop_rule,[status(thm)],[]) ).
thf(255,plain,
( ~ sP48
| sP50
| sP219 ),
inference(prop_rule,[status(thm)],[]) ).
thf(256,plain,
( ~ sP172
| sP48
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(257,plain,
( ~ sP33
| sP207
| ~ sP192 ),
inference(prop_rule,[status(thm)],[]) ).
thf(258,plain,
( ~ sP141
| sP153
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(259,plain,
( ~ sP256
| sP276
| ~ sP90 ),
inference(prop_rule,[status(thm)],[]) ).
thf(260,plain,
( ~ sP211
| sP104
| sP192 ),
inference(prop_rule,[status(thm)],[]) ).
thf(261,plain,
( ~ sP169
| sP35
| sP90 ),
inference(prop_rule,[status(thm)],[]) ).
thf(262,plain,
( ~ sP155
| sP12
| sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(263,plain,
( ~ sP231
| sP50
| sP183 ),
inference(prop_rule,[status(thm)],[]) ).
thf(264,plain,
( ~ sP234
| sP231
| sP91 ),
inference(prop_rule,[status(thm)],[]) ).
thf(265,plain,
( ~ sP226
| sP234
| ~ sP259 ),
inference(prop_rule,[status(thm)],[]) ).
thf(266,plain,
( ~ sP274
| sP226
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(267,plain,
( ~ sP109
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(268,plain,
( ~ sP109
| sP141 ),
inference(all_rule,[status(thm)],[]) ).
thf(269,plain,
( ~ sP74
| sP256 ),
inference(all_rule,[status(thm)],[]) ).
thf(270,plain,
( ~ sP135
| sP211 ),
inference(all_rule,[status(thm)],[]) ).
thf(271,plain,
( ~ sP185
| sP169 ),
inference(all_rule,[status(thm)],[]) ).
thf(272,plain,
( ~ sP65
| sP155
| sP160 ),
inference(prop_rule,[status(thm)],[]) ).
thf(273,plain,
( ~ sP279
| sP274
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(274,plain,
( ~ sP203
| sP109 ),
inference(all_rule,[status(thm)],[]) ).
thf(275,plain,
( ~ sP203
| sP161 ),
inference(all_rule,[status(thm)],[]) ).
thf(276,plain,
( ~ sP203
| sP74 ),
inference(all_rule,[status(thm)],[]) ).
thf(277,plain,
( ~ sP165
| sP135 ),
inference(all_rule,[status(thm)],[]) ).
thf(278,plain,
( ~ sP165
| sP185 ),
inference(all_rule,[status(thm)],[]) ).
thf(279,plain,
( ~ sP187
| sP65 ),
inference(all_rule,[status(thm)],[]) ).
thf(280,plain,
( ~ sP224
| sP279 ),
inference(all_rule,[status(thm)],[]) ).
thf(281,plain,
( ~ sP1
| sP203 ),
inference(all_rule,[status(thm)],[]) ).
thf(282,plain,
( ~ sP264
| sP165 ),
inference(all_rule,[status(thm)],[]) ).
thf(283,plain,
( ~ sP159
| sP187 ),
inference(all_rule,[status(thm)],[]) ).
thf(284,plain,
( ~ sP251
| sP224 ),
inference(all_rule,[status(thm)],[]) ).
thf(285,plain,
( sP252
| ~ sP183 ),
inference(prop_rule,[status(thm)],[]) ).
thf(286,plain,
( sP219
| ~ sP209 ),
inference(prop_rule,[status(thm)],[]) ).
thf(287,plain,
~ sP261,
inference(prop_rule,[status(thm)],[]) ).
thf(288,plain,
( ~ sP122
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(289,plain,
( ~ sP255
| sP52
| sP192 ),
inference(prop_rule,[status(thm)],[]) ).
thf(290,plain,
( ~ sP78
| sP255
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(291,plain,
( ~ sP80
| sP78
| sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(292,plain,
( ~ sP73
| sP209
| sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(293,plain,
( ~ sP52
| sP73
| sP219 ),
inference(prop_rule,[status(thm)],[]) ).
thf(294,plain,
( ~ sP102
| sP52
| ~ sP192 ),
inference(prop_rule,[status(thm)],[]) ).
thf(295,plain,
( ~ sP140
| sP102
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(296,plain,
( ~ sP27
| sP140
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(297,plain,
( ~ sP156
| ~ sP90
| sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(298,plain,
( ~ sP31
| sP156 ),
inference(all_rule,[status(thm)],[]) ).
thf(299,plain,
( ~ sP20
| ~ sP298
| sP90 ),
inference(prop_rule,[status(thm)],[]) ).
thf(300,plain,
( ~ sP268
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(301,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(302,plain,
( ~ sP264
| sP122 ),
inference(all_rule,[status(thm)],[]) ).
thf(303,plain,
( ~ sP214
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(304,plain,
( ~ sP115
| sP80 ),
inference(all_rule,[status(thm)],[]) ).
thf(305,plain,
( ~ sP199
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(306,plain,
( ~ sP111
| ~ sP192
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(307,plain,
( ~ sP268
| sP214 ),
inference(all_rule,[status(thm)],[]) ).
thf(308,plain,
( ~ sP1
| sP251 ),
inference(all_rule,[status(thm)],[]) ).
thf(309,plain,
( ~ sP264
| sP159 ),
inference(all_rule,[status(thm)],[]) ).
thf(310,plain,
( ~ sP164
| sP111 ),
inference(all_rule,[status(thm)],[]) ).
thf(311,plain,
( ~ sP302
| sP115 ),
inference(all_rule,[status(thm)],[]) ).
thf(312,plain,
( ~ sP233
| sP199 ),
inference(all_rule,[status(thm)],[]) ).
thf(313,plain,
( ~ sP268
| sP164 ),
inference(all_rule,[status(thm)],[]) ).
thf(314,plain,
( ~ sP1
| sP233 ),
inference(all_rule,[status(thm)],[]) ).
thf(315,plain,
( ~ sP264
| sP302 ),
inference(all_rule,[status(thm)],[]) ).
thf(316,plain,
( sP288
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(317,plain,
( sP148
| ~ sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(318,plain,
( sP168
| ~ sP148 ),
inference(prop_rule,[status(thm)],[]) ).
thf(319,plain,
( sP134
| ~ sP91 ),
inference(prop_rule,[status(thm)],[]) ).
thf(320,plain,
( sP96
| ~ sP134 ),
inference(prop_rule,[status(thm)],[]) ).
thf(321,plain,
( sP66
| ~ sP96 ),
inference(prop_rule,[status(thm)],[]) ).
thf(322,plain,
( sP93
| ~ sP177 ),
inference(prop_rule,[status(thm)],[]) ).
thf(323,plain,
( sP189
| ~ sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(324,plain,
( sP296
| ~ sP278 ),
inference(prop_rule,[status(thm)],[]) ).
thf(f64ck,axiom,
~ sP168 ).
thf(f63ck,axiom,
~ sP66 ).
thf(f62ck,axiom,
~ sP189 ).
thf(f6ck,axiom,
~ sP296 ).
thf(rn3acl,axiom,
sP264 ).
thf(rn3cl,axiom,
sP1 ).
thf(rsym,axiom,
sP268 ).
thf(325,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,f64ck,f63ck,f62ck,f6ck,rn3acl,rn3cl,rsym]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA119^1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.18/0.34 % Computer : n028.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Mon May 4 21:40:15 EDT 2026
% 0.18/0.34 % CPUTime :
% 1.14/1.37 % SZS status Unsatisfiable
% 1.14/1.37 % Mode: cade22grackle2xfee4
% 1.14/1.37 % Steps: 2303
% 1.14/1.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------