%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : GRA137^1 : 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:29:37 PM UTC 2026
% Result : Unsatisfiable 197.82s 120.09s
% Output : Proof 198.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 2216
% Syntax : Number of formulae : 2217 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 7085 ( 90 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 20371 (5354 ~;1829 |; 0 &;10149 @)
% (1045 <=>;1994 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1051 (1049 usr;1047 con; 0-2 aty)
% Number of variables : 465 ( 0 ^; 465 !; 0 ?; 465 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_s,type,
s: $i > $i ).
thf(ty_r,type,
r: $i > $i > $o ).
thf(ty_z,type,
z: $i ).
thf(ty_b,type,
b: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( ( s @ X1 )
= ( s @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ~ ( ( ( s @ ( s @ z ) )
!= X1 )
=> ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( r @ ( s @ z ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ z )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
!= ( s @ z ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ~ ( ( ( s @ z )
!= X1 )
=> ( r @ ( s @ z ) @ X1 ) )
=> ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ z @ X2 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( ( s @ ( s @ z ) )
= ( s @ z ) )
=> ( ( s @ z )
= z ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) )
=> ( ( s @ ( s @ z ) )
= z ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( ( s @ z )
!= z )
=> ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP20
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ~ ( ( r @ z @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( s @ ( s @ ( s @ z ) ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ~ ( ( ( s @ ( s @ z ) )
!= ( s @ ( s @ ( s @ z ) ) ) )
=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ ( ~ ( ( r @ z @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ~ sP9
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ~ sP4
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ sP60 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ~ ( ~ ( ~ ( ~ sP67
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X3 ) )
=> ~ ( r @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ~ ( ~ ( ~ sP25
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( r @ z @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP61
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( ~ sP61
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ( ( ( s @ z )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ( ~ ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ z )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( ~ sP54
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( ( r @ z @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ! [X1: $i] :
( ~ ( ~ sP54
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ( ~ ( ( ( s @ ( s @ z ) )
!= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> sP57 )
=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ! [X1: $i] :
( ~ ( ~ sP92
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( ~ sP17
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( ~ sP47
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ! [X1: $i] :
( ~ ( ~ sP30
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ( ~ sP109
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( ~ ( sP57
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( ~ ( ~ sP46
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ( ( b @ z @ ( s @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP61
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ( ~ sP10
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130,plain,
( sP130
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131,plain,
( sP131
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ z ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132,plain,
( sP132
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133,plain,
( sP133
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP121 ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134,plain,
( sP134
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135,plain,
( sP135
<=> ( ~ sP102
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136,plain,
( sP136
<=> ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137,plain,
( sP137
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP137])]) ).
thf(sP138,plain,
( sP138
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
!= ( s @ ( s @ z ) ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139,plain,
( sP139
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140,plain,
( sP140
<=> ! [X1: $i] :
( ~ ( ~ sP112
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141,plain,
( sP141
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142,plain,
( sP142
<=> ( ~ ( ~ sP67
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143,plain,
( sP143
<=> ( ~ sP133
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144,plain,
( sP144
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145,plain,
( sP145
<=> ! [X1: $i] :
( ~ ( ~ sP142
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146,plain,
( sP146
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP146])]) ).
thf(sP147,plain,
( sP147
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ z )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP147])]) ).
thf(sP148,plain,
( sP148
<=> ( ~ ( ~ ( ( r @ z @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ sP83 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP148])]) ).
thf(sP149,plain,
( sP149
<=> ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP149])]) ).
thf(sP150,plain,
( sP150
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP150])]) ).
thf(sP151,plain,
( sP151
<=> ( ~ sP38
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP151])]) ).
thf(sP152,plain,
( sP152
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP152])]) ).
thf(sP153,plain,
( sP153
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP153])]) ).
thf(sP154,plain,
( sP154
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP154])]) ).
thf(sP155,plain,
( sP155
<=> ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP155])]) ).
thf(sP156,plain,
( sP156
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP156])]) ).
thf(sP157,plain,
( sP157
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP157])]) ).
thf(sP158,plain,
( sP158
<=> ! [X1: $i] :
( ~ ( ~ ( sP49
=> ~ sP57 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP158])]) ).
thf(sP159,plain,
( sP159
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ ( s @ z ) ) )
=> sP70 )
=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP159])]) ).
thf(sP160,plain,
( sP160
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP160])]) ).
thf(sP161,plain,
( sP161
<=> ( z
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP161])]) ).
thf(sP162,plain,
( sP162
<=> ( ( ( s @ ( s @ z ) )
!= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> sP57 ) ),
introduced(definition,[new_symbols(definition,[sP162])]) ).
thf(sP163,plain,
( sP163
<=> ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP163])]) ).
thf(sP164,plain,
( sP164
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP164])]) ).
thf(sP165,plain,
( sP165
<=> ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP165])]) ).
thf(sP166,plain,
( sP166
<=> ( ~ ( ( ( s @ ( s @ z ) )
!= z )
=> ( r @ ( s @ ( s @ z ) ) @ z ) )
=> ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP166])]) ).
thf(sP167,plain,
( sP167
<=> ( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP167])]) ).
thf(sP168,plain,
( sP168
<=> ( ~ ( ~ sP61
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP168])]) ).
thf(sP169,plain,
( sP169
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP107
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP169])]) ).
thf(sP170,plain,
( sP170
<=> ( ~ ( ~ ( sP70
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP170])]) ).
thf(sP171,plain,
( sP171
<=> ( ~ sP142
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP171])]) ).
thf(sP172,plain,
( sP172
<=> ( ( b @ ( s @ ( s @ z ) ) @ z )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP172])]) ).
thf(sP173,plain,
( sP173
<=> ( sP83
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP173])]) ).
thf(sP174,plain,
( sP174
<=> ( sP49
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP174])]) ).
thf(sP175,plain,
( sP175
<=> ! [X1: $i] :
( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ X1 ) )
=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP175])]) ).
thf(sP176,plain,
( sP176
<=> ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP176])]) ).
thf(sP177,plain,
( sP177
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP177])]) ).
thf(sP178,plain,
( sP178
<=> ( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP178])]) ).
thf(sP179,plain,
( sP179
<=> ( ~ sP12
=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP179])]) ).
thf(sP180,plain,
( sP180
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP180])]) ).
thf(sP181,plain,
( sP181
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP181])]) ).
thf(sP182,plain,
( sP182
<=> ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP182])]) ).
thf(sP183,plain,
( sP183
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP183])]) ).
thf(sP184,plain,
( sP184
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> sP121 ) ),
introduced(definition,[new_symbols(definition,[sP184])]) ).
thf(sP185,plain,
( sP185
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP117
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP185])]) ).
thf(sP186,plain,
( sP186
<=> ( ( r @ z @ ( s @ ( s @ z ) ) )
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP186])]) ).
thf(sP187,plain,
( sP187
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP187])]) ).
thf(sP188,plain,
( sP188
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( sP156
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP188])]) ).
thf(sP189,plain,
( sP189
<=> ( ~ ( ~ ( sP70
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP189])]) ).
thf(sP190,plain,
( sP190
<=> ( ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP190])]) ).
thf(sP191,plain,
( sP191
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP191])]) ).
thf(sP192,plain,
( sP192
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP192])]) ).
thf(sP193,plain,
( sP193
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP193])]) ).
thf(sP194,plain,
( sP194
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
!= z )
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) )
=> sP105 ) ),
introduced(definition,[new_symbols(definition,[sP194])]) ).
thf(sP195,plain,
( sP195
<=> ! [X1: $i] :
( ~ ( ~ sP186
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP195])]) ).
thf(sP196,plain,
( sP196
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP117
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP196])]) ).
thf(sP197,plain,
( sP197
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP197])]) ).
thf(sP198,plain,
( sP198
<=> ( ~ ( ~ sP165
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP198])]) ).
thf(sP199,plain,
( sP199
<=> ( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) )
=> ~ ( r @ ( s @ z ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP199])]) ).
thf(sP200,plain,
( sP200
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ sP83 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP200])]) ).
thf(sP201,plain,
( sP201
<=> ( ( b @ z @ ( s @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP201])]) ).
thf(sP202,plain,
( sP202
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP202])]) ).
thf(sP203,plain,
( sP203
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP203])]) ).
thf(sP204,plain,
( sP204
<=> ( sP150
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP204])]) ).
thf(sP205,plain,
( sP205
<=> ( ~ ( ~ sP164
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP205])]) ).
thf(sP206,plain,
( sP206
<=> ( ~ ( ~ sP153
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP206])]) ).
thf(sP207,plain,
( sP207
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP207])]) ).
thf(sP208,plain,
( sP208
<=> ( ~ sP184
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP208])]) ).
thf(sP209,plain,
( sP209
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ z )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP209])]) ).
thf(sP210,plain,
( sP210
<=> ! [X1: $i] :
( ~ ( ~ sP198
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP210])]) ).
thf(sP211,plain,
( sP211
<=> ( z
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP211])]) ).
thf(sP212,plain,
( sP212
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP118
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP212])]) ).
thf(sP213,plain,
( sP213
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP213])]) ).
thf(sP214,plain,
( sP214
<=> ! [X1: $i] :
( ~ ( ~ sP72
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP214])]) ).
thf(sP215,plain,
( sP215
<=> ( ~ sP129
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP215])]) ).
thf(sP216,plain,
( sP216
<=> ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP216])]) ).
thf(sP217,plain,
( sP217
<=> ( ~ ( ~ sP161
=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP217])]) ).
thf(sP218,plain,
( sP218
<=> ( ~ ( ~ ( ~ ( ~ sP97
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP218])]) ).
thf(sP219,plain,
( sP219
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP33
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP219])]) ).
thf(sP220,plain,
( sP220
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP70 ) ),
introduced(definition,[new_symbols(definition,[sP220])]) ).
thf(sP221,plain,
( sP221
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP221])]) ).
thf(sP222,plain,
( sP222
<=> ( ~ ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ z ) )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP222])]) ).
thf(sP223,plain,
( sP223
<=> ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP223])]) ).
thf(sP224,plain,
( sP224
<=> ( ~ sP153
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP224])]) ).
thf(sP225,plain,
( sP225
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP225])]) ).
thf(sP226,plain,
( sP226
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP226])]) ).
thf(sP227,plain,
( sP227
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ sP57 )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP227])]) ).
thf(sP228,plain,
( sP228
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP228])]) ).
thf(sP229,plain,
( sP229
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP229])]) ).
thf(sP230,plain,
( sP230
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP165
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP230])]) ).
thf(sP231,plain,
( sP231
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP231])]) ).
thf(sP232,plain,
( sP232
<=> ! [X1: $i] :
( ~ ( ~ ( sP83
=> ~ sP60 )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP232])]) ).
thf(sP233,plain,
( sP233
<=> ! [X1: $i] :
( ~ ( ~ sP100
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP233])]) ).
thf(sP234,plain,
( sP234
<=> ( ~ sP89
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP234])]) ).
thf(sP235,plain,
( sP235
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP235])]) ).
thf(sP236,plain,
( sP236
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP236])]) ).
thf(sP237,plain,
( sP237
<=> ( ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP237])]) ).
thf(sP238,plain,
( sP238
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP156 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP238])]) ).
thf(sP239,plain,
( sP239
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP239])]) ).
thf(sP240,plain,
( sP240
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP240])]) ).
thf(sP241,plain,
( sP241
<=> ( ~ ( ~ ( ~ ( ~ ( sP150
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP241])]) ).
thf(sP242,plain,
( sP242
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP242])]) ).
thf(sP243,plain,
( sP243
<=> ( ~ ( ( z
!= ( s @ z ) )
=> sP83 )
=> ( b @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP243])]) ).
thf(sP244,plain,
( sP244
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP156 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP244])]) ).
thf(sP245,plain,
( sP245
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP245])]) ).
thf(sP246,plain,
( sP246
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP246])]) ).
thf(sP247,plain,
( sP247
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP247])]) ).
thf(sP248,plain,
( sP248
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP248])]) ).
thf(sP249,plain,
( sP249
<=> ! [X1: $i] :
( ( s @ X1 )
!= z ) ),
introduced(definition,[new_symbols(definition,[sP249])]) ).
thf(sP250,plain,
( sP250
<=> ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP250])]) ).
thf(sP251,plain,
( sP251
<=> ( ~ sP186
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP251])]) ).
thf(sP252,plain,
( sP252
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP252])]) ).
thf(sP253,plain,
( sP253
<=> ( ~ sP235
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP253])]) ).
thf(sP254,plain,
( sP254
<=> ! [X1: $i] :
( ~ ( ~ ( sP57
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP254])]) ).
thf(sP255,plain,
( sP255
<=> ( ~ sP103
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP255])]) ).
thf(sP256,plain,
( sP256
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP36
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP256])]) ).
thf(sP257,plain,
( sP257
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ z )
=> ~ sP150 )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP257])]) ).
thf(sP258,plain,
( sP258
<=> ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP258])]) ).
thf(sP259,plain,
( sP259
<=> ( ~ ( ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP259])]) ).
thf(sP260,plain,
( sP260
<=> ( ~ ( ~ ( ~ sP89
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP260])]) ).
thf(sP261,plain,
( sP261
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP261])]) ).
thf(sP262,plain,
( sP262
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP262])]) ).
thf(sP263,plain,
( sP263
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ ( s @ z ) ) )
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP263])]) ).
thf(sP264,plain,
( sP264
<=> ( ~ ( ~ ( sP49
=> ~ sP57 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP264])]) ).
thf(sP265,plain,
( sP265
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP70 )
=> ~ sP49 )
=> ~ sP70 ) ),
introduced(definition,[new_symbols(definition,[sP265])]) ).
thf(sP266,plain,
( sP266
<=> ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP266])]) ).
thf(sP267,plain,
( sP267
<=> ( ~ ( ~ sP21
=> ~ sP70 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP267])]) ).
thf(sP268,plain,
( sP268
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP268])]) ).
thf(sP269,plain,
( sP269
<=> ( ~ ( ~ ( ~ sP97
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP156 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP269])]) ).
thf(sP270,plain,
( sP270
<=> ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP270])]) ).
thf(sP271,plain,
( sP271
<=> ( ( ( s @ z )
!= ( s @ ( s @ ( s @ z ) ) ) )
=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP271])]) ).
thf(sP272,plain,
( sP272
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP272])]) ).
thf(sP273,plain,
( sP273
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP273])]) ).
thf(sP274,plain,
( sP274
<=> ( ~ ( ~ ( ~ sP216
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP262 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP274])]) ).
thf(sP275,plain,
( sP275
<=> ( ~ ( ~ ( sP60
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP221 ) ),
introduced(definition,[new_symbols(definition,[sP275])]) ).
thf(sP276,plain,
( sP276
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ sP172
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP276])]) ).
thf(sP277,plain,
( sP277
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP156 ) ),
introduced(definition,[new_symbols(definition,[sP277])]) ).
thf(sP278,plain,
( sP278
<=> ( ~ ( ( z
!= ( s @ ( s @ z ) ) )
=> ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP278])]) ).
thf(sP279,plain,
( sP279
<=> ( ~ ( ~ sP63
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP279])]) ).
thf(sP280,plain,
( sP280
<=> ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP280])]) ).
thf(sP281,plain,
( sP281
<=> ( ( s @ z )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP281])]) ).
thf(sP282,plain,
( sP282
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP282])]) ).
thf(sP283,plain,
( sP283
<=> ( ~ ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP60 )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP283])]) ).
thf(sP284,plain,
( sP284
<=> ( ~ ( ~ sP176
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP284])]) ).
thf(sP285,plain,
( sP285
<=> ( b @ z @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP285])]) ).
thf(sP286,plain,
( sP286
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP286])]) ).
thf(sP287,plain,
( sP287
<=> ( ~ ( ~ sP282
=> ~ sP285 )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP287])]) ).
thf(sP288,plain,
( sP288
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP288])]) ).
thf(sP289,plain,
( sP289
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP70 )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP289])]) ).
thf(sP290,plain,
( sP290
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP113
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP290])]) ).
thf(sP291,plain,
( sP291
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP291])]) ).
thf(sP292,plain,
( sP292
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( sP150
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP292])]) ).
thf(sP293,plain,
( sP293
<=> ( ~ ( ~ sP62
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP293])]) ).
thf(sP294,plain,
( sP294
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( sP285
=> ~ sP280 )
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP294])]) ).
thf(sP295,plain,
( sP295
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP295])]) ).
thf(sP296,plain,
( sP296
<=> ( sP213
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP296])]) ).
thf(sP297,plain,
( sP297
<=> ! [X1: $i] :
( ~ ( ~ sP229
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP297])]) ).
thf(sP298,plain,
( sP298
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP298])]) ).
thf(sP299,plain,
( sP299
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP299])]) ).
thf(sP300,plain,
( sP300
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP104
=> ~ sP280 )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP300])]) ).
thf(sP301,plain,
( sP301
<=> ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP301])]) ).
thf(sP302,plain,
( sP302
<=> ( ~ ( ~ ( ~ sP95
=> ~ sP262 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP302])]) ).
thf(sP303,plain,
( sP303
<=> ( ~ sP161
=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP303])]) ).
thf(sP304,plain,
( sP304
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP304])]) ).
thf(sP305,plain,
( sP305
<=> ( ~ ( ~ sP92
=> ~ sP156 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP305])]) ).
thf(sP306,plain,
( sP306
<=> ( ~ sP39
=> ~ ( b @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP306])]) ).
thf(sP307,plain,
( sP307
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP307])]) ).
thf(sP308,plain,
( sP308
<=> ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP308])]) ).
thf(sP309,plain,
( sP309
<=> ( ~ ( ~ sP237
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP309])]) ).
thf(sP310,plain,
( sP310
<=> ! [X1: $i] :
( ~ ( ~ sP174
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP310])]) ).
thf(sP311,plain,
( sP311
<=> ( ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ sP60 ) ),
introduced(definition,[new_symbols(definition,[sP311])]) ).
thf(sP312,plain,
( sP312
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ z )
=> ~ sP150 )
=> ~ sP280 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP312])]) ).
thf(sP313,plain,
( sP313
<=> ( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP288 )
=> ~ sP83 )
=> ~ sP288 ) ),
introduced(definition,[new_symbols(definition,[sP313])]) ).
thf(sP314,plain,
( sP314
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP156 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP314])]) ).
thf(sP315,plain,
( sP315
<=> ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP315])]) ).
thf(sP316,plain,
( sP316
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ z ) )
=> sP288 ) ),
introduced(definition,[new_symbols(definition,[sP316])]) ).
thf(sP317,plain,
( sP317
<=> ( ~ ( sP291
=> ~ sP83 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP317])]) ).
thf(sP318,plain,
( sP318
<=> ( ~ ( ~ sP155
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP285 ) ),
introduced(definition,[new_symbols(definition,[sP318])]) ).
thf(sP319,plain,
( sP319
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP288
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP319])]) ).
thf(sP320,plain,
( sP320
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP320])]) ).
thf(sP321,plain,
( sP321
<=> ( ~ ( ~ ( ~ sP118
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP321])]) ).
thf(sP322,plain,
( sP322
<=> ( ~ ( sP156
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP322])]) ).
thf(sP323,plain,
( sP323
<=> ( ~ ( ~ ( ~ sP97
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP323])]) ).
thf(sP324,plain,
( sP324
<=> ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP70 )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP324])]) ).
thf(sP325,plain,
( sP325
<=> ( ~ ( sP156
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP325])]) ).
thf(sP326,plain,
( sP326
<=> ( ~ ( ~ sP284
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP326])]) ).
thf(sP327,plain,
( sP327
<=> ( sP70
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP327])]) ).
thf(sP328,plain,
( sP328
<=> ! [X1: $i] :
( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ X1 ) )
=> ( ( s @ ( s @ ( s @ z ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP328])]) ).
thf(sP329,plain,
( sP329
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP329])]) ).
thf(sP330,plain,
( sP330
<=> ( ~ sP118
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP330])]) ).
thf(sP331,plain,
( sP331
<=> ( sP156
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP331])]) ).
thf(sP332,plain,
( sP332
<=> ( ~ ( ~ sP186
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP332])]) ).
thf(sP333,plain,
( sP333
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP95
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP333])]) ).
thf(sP334,plain,
( sP334
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP334])]) ).
thf(sP335,plain,
( sP335
<=> ( ~ sP152
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP335])]) ).
thf(sP336,plain,
( sP336
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( r @ X1 @ X2 )
=> ~ ( r @ X2 @ X3 ) )
=> ~ ( r @ X1 @ X4 ) )
=> ~ ( r @ X2 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP336])]) ).
thf(sP337,plain,
( sP337
<=> ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP337])]) ).
thf(sP338,plain,
( sP338
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) )
=> ~ ( b @ X2 @ X4 ) )
=> ~ ( b @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP338])]) ).
thf(sP339,plain,
( sP339
<=> ( ~ ( ~ ( ~ ( ~ sP155
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ sP280 )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP339])]) ).
thf(sP340,plain,
( sP340
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP340])]) ).
thf(sP341,plain,
( sP341
<=> ! [X1: $i] :
( ~ ( ~ ( sP57
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP341])]) ).
thf(sP342,plain,
( sP342
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ sP150 )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP342])]) ).
thf(sP343,plain,
( sP343
<=> ( sP49
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP343])]) ).
thf(sP344,plain,
( sP344
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP344])]) ).
thf(sP345,plain,
( sP345
<=> ( ~ sP207
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP345])]) ).
thf(sP346,plain,
( sP346
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ X1 )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ ( s @ z ) @ X3 ) )
=> ~ ( r @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP346])]) ).
thf(sP347,plain,
( sP347
<=> ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP347])]) ).
thf(sP348,plain,
( sP348
<=> ( ~ ( ~ ( ~ ( sP150
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP348])]) ).
thf(sP349,plain,
( sP349
<=> ! [X1: $i] :
( ~ ( ~ ( sP270
=> ~ sP213 )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP349])]) ).
thf(sP350,plain,
( sP350
<=> ( ~ sP90
=> ~ sP285 ) ),
introduced(definition,[new_symbols(definition,[sP350])]) ).
thf(sP351,plain,
( sP351
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP221
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP351])]) ).
thf(sP352,plain,
( sP352
<=> ( sP83
=> ~ sP60 ) ),
introduced(definition,[new_symbols(definition,[sP352])]) ).
thf(sP353,plain,
( sP353
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP353])]) ).
thf(sP354,plain,
( sP354
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP61
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP354])]) ).
thf(sP355,plain,
( sP355
<=> ( ~ sP201
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP355])]) ).
thf(sP356,plain,
( sP356
<=> ( ~ ( ~ ( ~ sP172
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP356])]) ).
thf(sP357,plain,
( sP357
<=> ! [X1: $i] :
( ~ ( ~ sP62
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP357])]) ).
thf(sP358,plain,
( sP358
<=> ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP358])]) ).
thf(sP359,plain,
( sP359
<=> ( ( ( s @ ( s @ z ) )
!= ( s @ z ) )
=> ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP359])]) ).
thf(sP360,plain,
( sP360
<=> ( ~ ( ~ sP281
=> sP60 )
=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP360])]) ).
thf(sP361,plain,
( sP361
<=> ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP361])]) ).
thf(sP362,plain,
( sP362
<=> ( ~ sP165
=> ~ sP262 ) ),
introduced(definition,[new_symbols(definition,[sP362])]) ).
thf(sP363,plain,
( sP363
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP363])]) ).
thf(sP364,plain,
( sP364
<=> ( ~ ( ~ sP33
=> ~ sP280 )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP364])]) ).
thf(sP365,plain,
( sP365
<=> ( ~ ( ( z
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP365])]) ).
thf(sP366,plain,
( sP366
<=> ( sP60
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP366])]) ).
thf(sP367,plain,
( sP367
<=> ( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP291 )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP221 ) ),
introduced(definition,[new_symbols(definition,[sP367])]) ).
thf(sP368,plain,
( sP368
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ z ) )
=> ~ sP280 )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP368])]) ).
thf(sP369,plain,
( sP369
<=> ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ z ) )
=> ~ sP280 )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP369])]) ).
thf(sP370,plain,
( sP370
<=> ( ~ sP281
=> sP60 ) ),
introduced(definition,[new_symbols(definition,[sP370])]) ).
thf(sP371,plain,
( sP371
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP371])]) ).
thf(sP372,plain,
( sP372
<=> ( ~ ( ~ sP97
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP372])]) ).
thf(sP373,plain,
( sP373
<=> ( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP373])]) ).
thf(sP374,plain,
( sP374
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP374])]) ).
thf(sP375,plain,
( sP375
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP375])]) ).
thf(sP376,plain,
( sP376
<=> ( ~ sP113
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP376])]) ).
thf(sP377,plain,
( sP377
<=> ( ~ sP245
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP377])]) ).
thf(sP378,plain,
( sP378
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP285 ) ),
introduced(definition,[new_symbols(definition,[sP378])]) ).
thf(sP379,plain,
( sP379
<=> ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP288 )
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP379])]) ).
thf(sP380,plain,
( sP380
<=> ( sP285
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP380])]) ).
thf(sP381,plain,
( sP381
<=> ( ~ ( ~ sP72
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP60 ) ),
introduced(definition,[new_symbols(definition,[sP381])]) ).
thf(sP382,plain,
( sP382
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP382])]) ).
thf(sP383,plain,
( sP383
<=> ( ~ ( ~ ( sP60
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP383])]) ).
thf(sP384,plain,
( sP384
<=> ( ~ ( ( r @ z @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP384])]) ).
thf(sP385,plain,
( sP385
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP385])]) ).
thf(sP386,plain,
( sP386
<=> ( ~ ( ~ sP89
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP386])]) ).
thf(sP387,plain,
( sP387
<=> ! [X1: $i] :
( ~ ( ~ ( sP60
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP387])]) ).
thf(sP388,plain,
( sP388
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ sP155
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP388])]) ).
thf(sP389,plain,
( sP389
<=> ( ~ ( ~ ( sP334
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP389])]) ).
thf(sP390,plain,
( sP390
<=> ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
!= ( s @ ( s @ ( s @ z ) ) ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP390])]) ).
thf(sP391,plain,
( sP391
<=> ( ~ sP21
=> ~ sP70 ) ),
introduced(definition,[new_symbols(definition,[sP391])]) ).
thf(sP392,plain,
( sP392
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP104
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP392])]) ).
thf(sP393,plain,
( sP393
<=> ( ~ sP61
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP393])]) ).
thf(sP394,plain,
( sP394
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP394])]) ).
thf(sP395,plain,
( sP395
<=> ! [X1: $i] :
( ~ ( ~ sP318
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP395])]) ).
thf(sP396,plain,
( sP396
<=> ! [X1: $i] :
( ~ ( ~ sP311
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP396])]) ).
thf(sP397,plain,
( sP397
<=> ( sP270
=> ~ sP213 ) ),
introduced(definition,[new_symbols(definition,[sP397])]) ).
thf(sP398,plain,
( sP398
<=> ( ~ ( ~ ( ~ ( sP280
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP398])]) ).
thf(sP399,plain,
( sP399
<=> ( ~ ( ~ sP137
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP399])]) ).
thf(sP400,plain,
( sP400
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP152
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP400])]) ).
thf(sP401,plain,
( sP401
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP401])]) ).
thf(sP402,plain,
( sP402
<=> ( ~ ( ~ sP190
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP402])]) ).
thf(sP403,plain,
( sP403
<=> ( ~ ( ~ ( sP280
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP403])]) ).
thf(sP404,plain,
( sP404
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP404])]) ).
thf(sP405,plain,
( sP405
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= z )
=> sP291 ) ),
introduced(definition,[new_symbols(definition,[sP405])]) ).
thf(sP406,plain,
( sP406
<=> ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP60 ) ),
introduced(definition,[new_symbols(definition,[sP406])]) ).
thf(sP407,plain,
( sP407
<=> ( ~ sP67
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP407])]) ).
thf(sP408,plain,
( sP408
<=> ( ~ sP120
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP408])]) ).
thf(sP409,plain,
( sP409
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP286
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP409])]) ).
thf(sP410,plain,
( sP410
<=> ( ~ sP345
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP410])]) ).
thf(sP411,plain,
( sP411
<=> ! [X1: $i] :
( ~ ( ~ sP26
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP411])]) ).
thf(sP412,plain,
( sP412
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP277
=> ~ sP329 )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP412])]) ).
thf(sP413,plain,
( sP413
<=> ( ~ ( ~ sP91
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP413])]) ).
thf(sP414,plain,
( sP414
<=> ( ~ ( ( b @ z @ ( s @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP414])]) ).
thf(sP415,plain,
( sP415
<=> ! [X1: $i] :
( ~ ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
!= X1 )
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP415])]) ).
thf(sP416,plain,
( sP416
<=> ( ~ sP36
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP416])]) ).
thf(sP417,plain,
( sP417
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP417])]) ).
thf(sP418,plain,
( sP418
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP345
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP418])]) ).
thf(sP419,plain,
( sP419
<=> ( ~ ( ~ ( ~ sP204
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP285 )
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP419])]) ).
thf(sP420,plain,
( sP420
<=> ! [X1: $i] :
( ~ ( ~ ( sP121
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP420])]) ).
thf(sP421,plain,
( sP421
<=> ! [X1: $i] :
( ~ ( ~ ( sP334
=> ~ sP83 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP421])]) ).
thf(sP422,plain,
( sP422
<=> ( ~ ( ~ ( ~ sP380
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP422])]) ).
thf(sP423,plain,
( sP423
<=> ! [X1: $i] :
( ~ ( ~ sP295
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP423])]) ).
thf(sP424,plain,
( sP424
<=> ( ~ ( ~ sP112
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP424])]) ).
thf(sP425,plain,
( sP425
<=> ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ z ) )
=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= z ) ) ),
introduced(definition,[new_symbols(definition,[sP425])]) ).
thf(sP426,plain,
( sP426
<=> ( ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP426])]) ).
thf(sP427,plain,
( sP427
<=> ( sP150
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP427])]) ).
thf(sP428,plain,
( sP428
<=> ( ~ sP152
=> ~ ( b @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP428])]) ).
thf(sP429,plain,
( sP429
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP429])]) ).
thf(sP430,plain,
( sP430
<=> ( ~ sP306
=> ~ sP156 ) ),
introduced(definition,[new_symbols(definition,[sP430])]) ).
thf(sP431,plain,
( sP431
<=> ( ~ sP416
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP431])]) ).
thf(sP432,plain,
( sP432
<=> ( ~ ( ~ ( sP83
=> ~ sP270 )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP432])]) ).
thf(sP433,plain,
( sP433
<=> ( ~ ( ~ ( ~ ( sP156
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP404 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP433])]) ).
thf(sP434,plain,
( sP434
<=> ( ~ sP89
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP434])]) ).
thf(sP435,plain,
( sP435
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP435])]) ).
thf(sP436,plain,
( sP436
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ sP105 ) ),
introduced(definition,[new_symbols(definition,[sP436])]) ).
thf(sP437,plain,
( sP437
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ z ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP437])]) ).
thf(sP438,plain,
( sP438
<=> ( ~ sP186
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP438])]) ).
thf(sP439,plain,
( sP439
<=> ( ~ sP330
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP439])]) ).
thf(sP440,plain,
( sP440
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ sP216
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP262 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP440])]) ).
thf(sP441,plain,
( sP441
<=> ! [X1: $i] :
( ( ( s @ ( s @ z ) )
= ( s @ X1 ) )
=> ( ( s @ z )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP441])]) ).
thf(sP442,plain,
( sP442
<=> ( ~ ( ~ sP225
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP442])]) ).
thf(sP443,plain,
( sP443
<=> ( ~ sP273
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP443])]) ).
thf(sP444,plain,
( sP444
<=> ( ~ ( ~ ( ~ sP340
=> ~ sP262 )
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP444])]) ).
thf(sP445,plain,
( sP445
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP445])]) ).
thf(sP446,plain,
( sP446
<=> ( ~ sP327
=> ~ sP291 ) ),
introduced(definition,[new_symbols(definition,[sP446])]) ).
thf(sP447,plain,
( sP447
<=> ( sP83
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP447])]) ).
thf(sP448,plain,
( sP448
<=> ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP448])]) ).
thf(sP449,plain,
( sP449
<=> ( ~ ( sP60
=> ~ sP291 )
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP449])]) ).
thf(sP450,plain,
( sP450
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP450])]) ).
thf(sP451,plain,
( sP451
<=> ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP451])]) ).
thf(sP452,plain,
( sP452
<=> ( ~ ( ( ( s @ ( s @ z ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> sP385 )
=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP452])]) ).
thf(sP453,plain,
( sP453
<=> ( ~ sP414
=> ~ sP262 ) ),
introduced(definition,[new_symbols(definition,[sP453])]) ).
thf(sP454,plain,
( sP454
<=> ( ( ( s @ ( s @ z ) )
!= ( s @ ( s @ ( s @ z ) ) ) )
=> sP213 ) ),
introduced(definition,[new_symbols(definition,[sP454])]) ).
thf(sP455,plain,
( sP455
<=> ( ~ sP397
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP455])]) ).
thf(sP456,plain,
( sP456
<=> ( ~ ( ~ ( sP156
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP456])]) ).
thf(sP457,plain,
( sP457
<=> ( ~ sP117
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP457])]) ).
thf(sP458,plain,
( sP458
<=> ( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP458])]) ).
thf(sP459,plain,
( sP459
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP459])]) ).
thf(sP460,plain,
( sP460
<=> ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP156 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP460])]) ).
thf(sP461,plain,
( sP461
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP461])]) ).
thf(sP462,plain,
( sP462
<=> ( ~ sP384
=> ~ sP385 ) ),
introduced(definition,[new_symbols(definition,[sP462])]) ).
thf(sP463,plain,
( sP463
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP463])]) ).
thf(sP464,plain,
( sP464
<=> ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP464])]) ).
thf(sP465,plain,
( sP465
<=> ( ~ ( ~ sP107
=> ~ sP285 )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP465])]) ).
thf(sP466,plain,
( sP466
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP466])]) ).
thf(sP467,plain,
( sP467
<=> ( ~ ( ~ ( sP213
=> ~ sP288 )
=> ~ sP461 )
=> ~ sP288 ) ),
introduced(definition,[new_symbols(definition,[sP467])]) ).
thf(sP468,plain,
( sP468
<=> ! [X1: $i] :
( ~ ( ~ sP10
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP468])]) ).
thf(sP469,plain,
( sP469
<=> ( sP280
=> ~ ( b @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP469])]) ).
thf(sP470,plain,
( sP470
<=> ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP470])]) ).
thf(sP471,plain,
( sP471
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( sP280
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP404 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP471])]) ).
thf(sP472,plain,
( sP472
<=> ( sP445
=> ~ sP463 ) ),
introduced(definition,[new_symbols(definition,[sP472])]) ).
thf(sP473,plain,
( sP473
<=> ( ~ ( ( r @ z @ ( s @ ( s @ z ) ) )
=> ~ sP461 )
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP473])]) ).
thf(sP474,plain,
( sP474
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ sP150 )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP474])]) ).
thf(sP475,plain,
( sP475
<=> ( ~ sP2
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP475])]) ).
thf(sP476,plain,
( sP476
<=> ( ~ ( ~ sP181
=> ~ sP150 )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP476])]) ).
thf(sP477,plain,
( sP477
<=> ( ~ ( ( ( s @ z )
!= ( s @ ( s @ z ) ) )
=> sP270 )
=> sP448 ) ),
introduced(definition,[new_symbols(definition,[sP477])]) ).
thf(sP478,plain,
( sP478
<=> ( ( s @ z )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP478])]) ).
thf(sP479,plain,
( sP479
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP479])]) ).
thf(sP480,plain,
( sP480
<=> ! [X1: $i] :
( ~ ( ~ ( sP213
=> ~ sP334 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP480])]) ).
thf(sP481,plain,
( sP481
<=> ( ~ ( ~ sP211
=> ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> sP280 ) ),
introduced(definition,[new_symbols(definition,[sP481])]) ).
thf(sP482,plain,
( sP482
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP482])]) ).
thf(sP483,plain,
( sP483
<=> ! [X1: $i] :
( ~ ( ~ sP453
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP483])]) ).
thf(sP484,plain,
( sP484
<=> ( ~ sP266
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP484])]) ).
thf(sP485,plain,
( sP485
<=> ( ~ ( ~ ( ~ ( ~ sP126
=> ~ sP448 )
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP485])]) ).
thf(sP486,plain,
( sP486
<=> ( ~ sP340
=> ~ sP262 ) ),
introduced(definition,[new_symbols(definition,[sP486])]) ).
thf(sP487,plain,
( sP487
<=> ( ~ sP244
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP487])]) ).
thf(sP488,plain,
( sP488
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP216
=> ~ sP445 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP488])]) ).
thf(sP489,plain,
( sP489
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP489])]) ).
thf(sP490,plain,
( sP490
<=> ( z
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP490])]) ).
thf(sP491,plain,
( sP491
<=> ( sP213
=> ~ sP334 ) ),
introduced(definition,[new_symbols(definition,[sP491])]) ).
thf(sP492,plain,
( sP492
<=> ( ~ ( ~ sP250
=> ~ sP463 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP492])]) ).
thf(sP493,plain,
( sP493
<=> ! [X1: $i] :
( ~ ( ~ sP46
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP493])]) ).
thf(sP494,plain,
( sP494
<=> ! [X1: $i] :
( ~ ( ~ sP91
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP494])]) ).
thf(sP495,plain,
( sP495
<=> ( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP334 )
=> ~ ( r @ ( s @ z ) @ z ) )
=> ~ sP334 ) ),
introduced(definition,[new_symbols(definition,[sP495])]) ).
thf(sP496,plain,
( sP496
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP496])]) ).
thf(sP497,plain,
( sP497
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ sP126
=> ~ sP448 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP497])]) ).
thf(sP498,plain,
( sP498
<=> ( ~ sP100
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP498])]) ).
thf(sP499,plain,
( sP499
<=> ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP499])]) ).
thf(sP500,plain,
( sP500
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP500])]) ).
thf(sP501,plain,
( sP501
<=> ( ~ sP490
=> sP83 ) ),
introduced(definition,[new_symbols(definition,[sP501])]) ).
thf(sP502,plain,
( sP502
<=> ( ~ sP324
=> ~ sP70 ) ),
introduced(definition,[new_symbols(definition,[sP502])]) ).
thf(sP503,plain,
( sP503
<=> ( ~ ( ~ sP26
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP503])]) ).
thf(sP504,plain,
( sP504
<=> ( ~ ( ~ sP30
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP504])]) ).
thf(sP505,plain,
( sP505
<=> ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP505])]) ).
thf(sP506,plain,
( sP506
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ sP380
=> ~ sP150 )
=> ~ sP479 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP506])]) ).
thf(sP507,plain,
( sP507
<=> ( ~ sP153
=> ~ ( b @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP507])]) ).
thf(sP508,plain,
( sP508
<=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP508])]) ).
thf(sP509,plain,
( sP509
<=> ( ~ sP25
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP509])]) ).
thf(sP510,plain,
( sP510
<=> ( ~ sP364
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP510])]) ).
thf(sP511,plain,
( sP511
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP511])]) ).
thf(sP512,plain,
( sP512
<=> ( ~ sP258
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP512])]) ).
thf(sP513,plain,
( sP513
<=> ( ~ sP311
=> ~ sP385 ) ),
introduced(definition,[new_symbols(definition,[sP513])]) ).
thf(sP514,plain,
( sP514
<=> ( r @ z @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP514])]) ).
thf(sP515,plain,
( sP515
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ sP126
=> ~ sP448 )
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP515])]) ).
thf(sP516,plain,
( sP516
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP470
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP516])]) ).
thf(sP517,plain,
( sP517
<=> ( ~ sP59
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP517])]) ).
thf(sP518,plain,
( sP518
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ ( sP404
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP463 )
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP518])]) ).
thf(sP519,plain,
( sP519
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP150
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP519])]) ).
thf(sP520,plain,
( sP520
<=> ! [X1: $i] :
( ~ ( ~ sP372
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP520])]) ).
thf(sP521,plain,
( sP521
<=> ! [X1: $i] :
( ~ ( ~ sP492
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP521])]) ).
thf(sP522,plain,
( sP522
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP486
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP522])]) ).
thf(sP523,plain,
( sP523
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP523])]) ).
thf(sP524,plain,
( sP524
<=> ( ~ sP393
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP524])]) ).
thf(sP525,plain,
( sP525
<=> ( ~ ( ~ sP216
=> ~ sP445 )
=> ~ sP262 ) ),
introduced(definition,[new_symbols(definition,[sP525])]) ).
thf(sP526,plain,
( sP526
<=> ! [X1: $i] :
( ~ ( ~ sP287
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP526])]) ).
thf(sP527,plain,
( sP527
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP334 )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP527])]) ).
thf(sP528,plain,
( sP528
<=> ( ~ sP141
=> ~ sP334 ) ),
introduced(definition,[new_symbols(definition,[sP528])]) ).
thf(sP529,plain,
( sP529
<=> ( ~ ( ~ ( ~ sP325
=> ~ sP489 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ sP156 ) ),
introduced(definition,[new_symbols(definition,[sP529])]) ).
thf(sP530,plain,
( sP530
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP121
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP530])]) ).
thf(sP531,plain,
( sP531
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP404 )
=> ~ sP523 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP531])]) ).
thf(sP532,plain,
( sP532
<=> ( ( s @ z )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP532])]) ).
thf(sP533,plain,
( sP533
<=> ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ ( s @ z ) ) ) )
=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP533])]) ).
thf(sP534,plain,
( sP534
<=> ( ~ ( ~ ( sP70
=> ~ sP213 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP213 ) ),
introduced(definition,[new_symbols(definition,[sP534])]) ).
thf(sP535,plain,
( sP535
<=> ( ~ sP428
=> ~ sP285 ) ),
introduced(definition,[new_symbols(definition,[sP535])]) ).
thf(sP536,plain,
( sP536
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP536])]) ).
thf(sP537,plain,
( sP537
<=> ( sP70
=> ~ sP461 ) ),
introduced(definition,[new_symbols(definition,[sP537])]) ).
thf(sP538,plain,
( sP538
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP538])]) ).
thf(sP539,plain,
( sP539
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP539])]) ).
thf(sP540,plain,
( sP540
<=> ! [X1: $i] :
( ~ ( ~ sP181
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP540])]) ).
thf(sP541,plain,
( sP541
<=> ( ~ ( ~ ( ~ sP126
=> ~ sP448 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP541])]) ).
thf(sP542,plain,
( sP542
<=> ! [X1: $i] :
( ~ ( ~ sP39
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP542])]) ).
thf(sP543,plain,
( sP543
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP472
=> ~ sP262 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP543])]) ).
thf(sP544,plain,
( sP544
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP134
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP544])]) ).
thf(sP545,plain,
( sP545
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP545])]) ).
thf(sP546,plain,
( sP546
<=> ! [X1: $i] :
( ~ ( ~ ( sP70
=> ~ sP213 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP546])]) ).
thf(sP547,plain,
( sP547
<=> ! [X1: $i] :
( ~ ( ~ sP402
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP547])]) ).
thf(sP548,plain,
( sP548
<=> ! [X1: $i] :
( ~ ( ~ sP426
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP548])]) ).
thf(sP549,plain,
( sP549
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP95
=> ~ sP262 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP549])]) ).
thf(sP550,plain,
( sP550
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ sP329 )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP550])]) ).
thf(sP551,plain,
( sP551
<=> ( ~ sP422
=> ~ sP285 ) ),
introduced(definition,[new_symbols(definition,[sP551])]) ).
thf(sP552,plain,
( sP552
<=> ( sP280
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP552])]) ).
thf(sP553,plain,
( sP553
<=> ( ( b @ z @ ( s @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP553])]) ).
thf(sP554,plain,
( sP554
<=> ( ~ sP277
=> ~ sP329 ) ),
introduced(definition,[new_symbols(definition,[sP554])]) ).
thf(sP555,plain,
( sP555
<=> ( ~ sP541
=> ~ ( b @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP555])]) ).
thf(sP556,plain,
( sP556
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( r @ z @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP556])]) ).
thf(sP557,plain,
( sP557
<=> ( z
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP557])]) ).
thf(sP558,plain,
( sP558
<=> ! [X1: $i] :
( ~ ( ~ sP101
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP558])]) ).
thf(sP559,plain,
( sP559
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP285
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP559])]) ).
thf(sP560,plain,
( sP560
<=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP560])]) ).
thf(sP561,plain,
( sP561
<=> ! [X1: $i] :
( ~ ( ~ sP21
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP561])]) ).
thf(sP562,plain,
( sP562
<=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP562])]) ).
thf(sP563,plain,
( sP563
<=> ! [X1: $i] :
( ~ ( ~ sP507
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP563])]) ).
thf(sP564,plain,
( sP564
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP564])]) ).
thf(sP565,plain,
( sP565
<=> ( ~ ( ~ sP96
=> ~ sP70 )
=> ~ sP514 ) ),
introduced(definition,[new_symbols(definition,[sP565])]) ).
thf(sP566,plain,
( sP566
<=> ( ~ sP469
=> ~ sP564 ) ),
introduced(definition,[new_symbols(definition,[sP566])]) ).
thf(sP567,plain,
( sP567
<=> ! [X1: $i] :
( ~ ( ~ ( sP60
=> ~ sP70 )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP567])]) ).
thf(sP568,plain,
( sP568
<=> ( ~ sP557
=> sP514 ) ),
introduced(definition,[new_symbols(definition,[sP568])]) ).
thf(sP569,plain,
( sP569
<=> ( ~ sP474
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP569])]) ).
thf(sP570,plain,
( sP570
<=> ( ~ sP224
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP570])]) ).
thf(sP571,plain,
( sP571
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP508
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP571])]) ).
thf(sP572,plain,
( sP572
<=> ( ( b @ z @ ( s @ z ) )
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP572])]) ).
thf(sP573,plain,
( sP573
<=> ( ~ sP299
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP573])]) ).
thf(sP574,plain,
( sP574
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ z )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP574])]) ).
thf(sP575,plain,
( sP575
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP448 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP575])]) ).
thf(sP576,plain,
( sP576
<=> ( ~ sP137
=> ~ sP560 ) ),
introduced(definition,[new_symbols(definition,[sP576])]) ).
thf(sP577,plain,
( sP577
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) )
=> ~ ( r @ z @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP577])]) ).
thf(sP578,plain,
( sP578
<=> ( sP280
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP578])]) ).
thf(sP579,plain,
( sP579
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP579])]) ).
thf(sP580,plain,
( sP580
<=> ! [X1: $i] :
( ~ ( ~ sP63
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP580])]) ).
thf(sP581,plain,
( sP581
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP334 )
=> ~ sP291 ) ),
introduced(definition,[new_symbols(definition,[sP581])]) ).
thf(sP582,plain,
( sP582
<=> ! [X1: $i] :
( ~ ( ~ sP247
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP582])]) ).
thf(sP583,plain,
( sP583
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP583])]) ).
thf(sP584,plain,
( sP584
<=> ( ~ ( ~ sP482
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP562 ) ),
introduced(definition,[new_symbols(definition,[sP584])]) ).
thf(sP585,plain,
( sP585
<=> ( b @ z @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP585])]) ).
thf(sP586,plain,
( sP586
<=> ! [X1: $i] :
( ~ ( ~ ( ~ ( ~ sP204
=> ~ sP479 )
=> ~ sP285 )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP586])]) ).
thf(sP587,plain,
( sP587
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP587])]) ).
thf(sP588,plain,
( sP588
<=> ( ~ ( ~ sP104
=> ~ sP280 )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP588])]) ).
thf(sP589,plain,
( sP589
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ z )
=> ~ sP150 )
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP589])]) ).
thf(sP590,plain,
( sP590
<=> ( ~ ( ~ ( ~ sP20
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ sP448 ) ),
introduced(definition,[new_symbols(definition,[sP590])]) ).
thf(sP591,plain,
( sP591
<=> ( ( s @ z )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP591])]) ).
thf(sP592,plain,
( sP592
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ z @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP592])]) ).
thf(sP593,plain,
( sP593
<=> ! [X1: $i] :
( ~ ( ~ sP137
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP593])]) ).
thf(sP594,plain,
( sP594
<=> ! [X1: $i] :
( ~ ( ~ ( sP60
=> ~ sP291 )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP594])]) ).
thf(sP595,plain,
( sP595
<=> ( ~ sP394
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP595])]) ).
thf(sP596,plain,
( sP596
<=> ( ~ sP43
=> ~ sP562 ) ),
introduced(definition,[new_symbols(definition,[sP596])]) ).
thf(sP597,plain,
( sP597
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X3 ) )
=> ~ ( r @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP597])]) ).
thf(sP598,plain,
( sP598
<=> ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP598])]) ).
thf(sP599,plain,
( sP599
<=> ( ~ sP431
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP599])]) ).
thf(sP600,plain,
( sP600
<=> ( ~ sP570
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP600])]) ).
thf(sP601,plain,
( sP601
<=> ( sP583
=> ~ sP514 ) ),
introduced(definition,[new_symbols(definition,[sP601])]) ).
thf(sP602,plain,
( sP602
<=> ( ~ sP271
=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP602])]) ).
thf(sP603,plain,
( sP603
<=> ! [X1: $i] :
( ~ ( ~ sP456
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP603])]) ).
thf(sP604,plain,
( sP604
<=> ( ~ ( ~ ( sP150
=> ~ sP489 )
=> ~ sP404 )
=> ~ sP463 ) ),
introduced(definition,[new_symbols(definition,[sP604])]) ).
thf(sP605,plain,
( sP605
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP564 )
=> ~ sP329 )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP605])]) ).
thf(sP606,plain,
( sP606
<=> ( b @ ( s @ ( s @ z ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP606])]) ).
thf(sP607,plain,
( sP607
<=> ( sP334
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP607])]) ).
thf(sP608,plain,
( sP608
<=> ( ~ sP524
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP608])]) ).
thf(sP609,plain,
( sP609
<=> ( ~ ( ~ ( sP57
=> ~ sP291 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) )
=> ~ sP291 ) ),
introduced(definition,[new_symbols(definition,[sP609])]) ).
thf(sP610,plain,
( sP610
<=> ( ~ sP19
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP610])]) ).
thf(sP611,plain,
( sP611
<=> ( ~ sP164
=> ~ sP545 ) ),
introduced(definition,[new_symbols(definition,[sP611])]) ).
thf(sP612,plain,
( sP612
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ z @ X1 )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ z @ X3 ) )
=> ~ ( r @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP612])]) ).
thf(sP613,plain,
( sP613
<=> ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP613])]) ).
thf(sP614,plain,
( sP614
<=> ( ~ sP263
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP614])]) ).
thf(sP615,plain,
( sP615
<=> ( ~ sP239
=> ~ sP500 ) ),
introduced(definition,[new_symbols(definition,[sP615])]) ).
thf(sP616,plain,
( sP616
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP616])]) ).
thf(sP617,plain,
( sP617
<=> ( sP445
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP617])]) ).
thf(sP618,plain,
( sP618
<=> ( ~ sP513
=> ~ sP508 ) ),
introduced(definition,[new_symbols(definition,[sP618])]) ).
thf(sP619,plain,
( sP619
<=> ( ~ sP505
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP619])]) ).
thf(sP620,plain,
( sP620
<=> ( ~ sP62
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP620])]) ).
thf(sP621,plain,
( sP621
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP33
=> ~ sP280 )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP621])]) ).
thf(sP622,plain,
( sP622
<=> ( sP291
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP622])]) ).
thf(sP623,plain,
( sP623
<=> ( ~ sP225
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP623])]) ).
thf(sP624,plain,
( sP624
<=> ( ~ sP451
=> ~ sP562 ) ),
introduced(definition,[new_symbols(definition,[sP624])]) ).
thf(sP625,plain,
( sP625
<=> ( sP60
=> ~ sP70 ) ),
introduced(definition,[new_symbols(definition,[sP625])]) ).
thf(sP626,plain,
( sP626
<=> ( ~ sP622
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP626])]) ).
thf(sP627,plain,
( sP627
<=> ( sP508
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP627])]) ).
thf(sP628,plain,
( sP628
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP404 )
=> ~ sP523 ) ),
introduced(definition,[new_symbols(definition,[sP628])]) ).
thf(sP629,plain,
( sP629
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP629])]) ).
thf(sP630,plain,
( sP630
<=> ! [X1: $i] :
( ~ ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= X1 )
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP630])]) ).
thf(sP631,plain,
( sP631
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP479 ) ),
introduced(definition,[new_symbols(definition,[sP631])]) ).
thf(sP632,plain,
( sP632
<=> ( ( s @ ( s @ z ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP632])]) ).
thf(sP633,plain,
( sP633
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP633])]) ).
thf(sP634,plain,
( sP634
<=> ( ~ ( ~ sP126
=> ~ sP448 )
=> ~ sP606 ) ),
introduced(definition,[new_symbols(definition,[sP634])]) ).
thf(sP635,plain,
( sP635
<=> ( ~ sP106
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP635])]) ).
thf(sP636,plain,
( sP636
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP636])]) ).
thf(sP637,plain,
( sP637
<=> ! [X1: $i] :
( ~ ( ~ sP59
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP637])]) ).
thf(sP638,plain,
( sP638
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP404 )
=> ~ sP156 ) ),
introduced(definition,[new_symbols(definition,[sP638])]) ).
thf(sP639,plain,
( sP639
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP639])]) ).
thf(sP640,plain,
( sP640
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ ( sP150
=> ~ sP489 )
=> ~ sP404 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP640])]) ).
thf(sP641,plain,
( sP641
<=> ( ~ ( ~ sP174
=> ~ sP121 )
=> ~ sP385 ) ),
introduced(definition,[new_symbols(definition,[sP641])]) ).
thf(sP642,plain,
( sP642
<=> ( ~ sP632
=> ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP642])]) ).
thf(sP643,plain,
( sP643
<=> ( ~ sP216
=> ~ sP445 ) ),
introduced(definition,[new_symbols(definition,[sP643])]) ).
thf(sP644,plain,
( sP644
<=> ( ~ ( ~ sP28
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP644])]) ).
thf(sP645,plain,
( sP645
<=> ( ~ sP52
=> ~ sP585 ) ),
introduced(definition,[new_symbols(definition,[sP645])]) ).
thf(sP646,plain,
( sP646
<=> ! [X1: $i] :
( ~ ( ~ sP443
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP646])]) ).
thf(sP647,plain,
( sP647
<=> ( ~ sP26
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP647])]) ).
thf(sP648,plain,
( sP648
<=> ( ~ sP402
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP648])]) ).
thf(sP649,plain,
( sP649
<=> ( ~ sP301
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP649])]) ).
thf(sP650,plain,
( sP650
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP650])]) ).
thf(sP651,plain,
( sP651
<=> ( ~ sP615
=> ~ sP562 ) ),
introduced(definition,[new_symbols(definition,[sP651])]) ).
thf(sP652,plain,
( sP652
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP652])]) ).
thf(sP653,plain,
( sP653
<=> ( ~ sP375
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP653])]) ).
thf(sP654,plain,
( sP654
<=> ! [X1: $i] :
( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ X1 ) )
=> ( ( s @ ( s @ z ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP654])]) ).
thf(sP655,plain,
( sP655
<=> ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP288 ) ),
introduced(definition,[new_symbols(definition,[sP655])]) ).
thf(sP656,plain,
( sP656
<=> ( sP650
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP656])]) ).
thf(sP657,plain,
( sP657
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP657])]) ).
thf(sP658,plain,
( sP658
<=> ( ~ sP361
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP658])]) ).
thf(sP659,plain,
( sP659
<=> ( ~ sP181
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP659])]) ).
thf(sP660,plain,
( sP660
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP660])]) ).
thf(sP661,plain,
( sP661
<=> ( ( s @ ( s @ z ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP661])]) ).
thf(sP662,plain,
( sP662
<=> ( ~ sP112
=> ~ sP633 ) ),
introduced(definition,[new_symbols(definition,[sP662])]) ).
thf(sP663,plain,
( sP663
<=> ( ~ ( ~ sP572
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP479 ) ),
introduced(definition,[new_symbols(definition,[sP663])]) ).
thf(sP664,plain,
( sP664
<=> ( ~ sP658
=> ~ sP633 ) ),
introduced(definition,[new_symbols(definition,[sP664])]) ).
thf(sP665,plain,
( sP665
<=> ! [X1: $i] :
( ~ ( ~ sP474
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP665])]) ).
thf(sP666,plain,
( sP666
<=> ( ~ sP269
=> ~ sP448 ) ),
introduced(definition,[new_symbols(definition,[sP666])]) ).
thf(sP667,plain,
( sP667
<=> ! [X1: $i] :
( ~ ( ~ sP312
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP667])]) ).
thf(sP668,plain,
( sP668
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP668])]) ).
thf(sP669,plain,
( sP669
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP355
=> ~ sP657 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP669])]) ).
thf(sP670,plain,
( sP670
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP509
=> ~ sP489 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP670])]) ).
thf(sP671,plain,
( sP671
<=> ( sP463
=> ~ sP657 ) ),
introduced(definition,[new_symbols(definition,[sP671])]) ).
thf(sP672,plain,
( sP672
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ X1 @ X2 )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) )
=> ~ ( b @ X3 @ X4 ) )
=> ~ ( b @ X3 @ X5 ) )
=> ~ ( b @ X4 @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[sP672])]) ).
thf(sP673,plain,
( sP673
<=> ( ~ ( ~ ( ~ sP380
=> ~ sP150 )
=> ~ sP564 )
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP673])]) ).
thf(sP674,plain,
( sP674
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP674])]) ).
thf(sP675,plain,
( sP675
<=> ( ~ sP625
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP675])]) ).
thf(sP676,plain,
( sP676
<=> ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP676])]) ).
thf(sP677,plain,
( sP677
<=> ( ~ sP223
=> ~ sP60 ) ),
introduced(definition,[new_symbols(definition,[sP677])]) ).
thf(sP678,plain,
( sP678
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP678])]) ).
thf(sP679,plain,
( sP679
<=> ( ~ ( ~ sP97
=> ~ sP489 )
=> ~ sP156 ) ),
introduced(definition,[new_symbols(definition,[sP679])]) ).
thf(sP680,plain,
( sP680
<=> ( ~ sP491
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP680])]) ).
thf(sP681,plain,
( sP681
<=> ( ~ ( ~ ( sP404
=> ~ sP650 )
=> ~ sP463 )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP681])]) ).
thf(sP682,plain,
( sP682
<=> ( sP657
=> ~ sP463 ) ),
introduced(definition,[new_symbols(definition,[sP682])]) ).
thf(sP683,plain,
( sP683
<=> ( ~ sP176
=> ~ sP329 ) ),
introduced(definition,[new_symbols(definition,[sP683])]) ).
thf(sP684,plain,
( sP684
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ X1 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) )
=> ~ ( b @ X2 @ X4 ) )
=> ~ ( b @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP684])]) ).
thf(sP685,plain,
( sP685
<=> ( b @ ( s @ z ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP685])]) ).
thf(sP686,plain,
( sP686
<=> ( ~ sP321
=> ~ sP479 ) ),
introduced(definition,[new_symbols(definition,[sP686])]) ).
thf(sP687,plain,
( sP687
<=> ( ~ sP499
=> ~ sP514 ) ),
introduced(definition,[new_symbols(definition,[sP687])]) ).
thf(sP688,plain,
( sP688
<=> ( sP57
=> ~ sP221 ) ),
introduced(definition,[new_symbols(definition,[sP688])]) ).
thf(sP689,plain,
( sP689
<=> ! [X1: $i] :
( ~ ( ~ sP239
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP689])]) ).
thf(sP690,plain,
( sP690
<=> ( ~ sP94
=> sP560 ) ),
introduced(definition,[new_symbols(definition,[sP690])]) ).
thf(sP691,plain,
( sP691
<=> ( ~ sP447
=> ~ sP514 ) ),
introduced(definition,[new_symbols(definition,[sP691])]) ).
thf(sP692,plain,
( sP692
<=> ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP692])]) ).
thf(sP693,plain,
( sP693
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ sP606 ) ),
introduced(definition,[new_symbols(definition,[sP693])]) ).
thf(sP694,plain,
( sP694
<=> ( ~ ( sP57
=> ~ sP291 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP694])]) ).
thf(sP695,plain,
( sP695
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP334 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP695])]) ).
thf(sP696,plain,
( sP696
<=> ( ~ sP91
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP696])]) ).
thf(sP697,plain,
( sP697
<=> ( ~ sP45
=> sP334 ) ),
introduced(definition,[new_symbols(definition,[sP697])]) ).
thf(sP698,plain,
( sP698
<=> ( sP245
=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP698])]) ).
thf(sP699,plain,
( sP699
<=> ! [X1: $i] :
( ~ ( ~ sP96
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP699])]) ).
thf(sP700,plain,
( sP700
<=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP700])]) ).
thf(sP701,plain,
( sP701
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP671
=> ~ sP606 )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP701])]) ).
thf(sP702,plain,
( sP702
<=> ( ~ sP376
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP702])]) ).
thf(sP703,plain,
( sP703
<=> ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP514 ) ),
introduced(definition,[new_symbols(definition,[sP703])]) ).
thf(sP704,plain,
( sP704
<=> ! [X1: $i] :
( ~ ( ~ sP616
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP704])]) ).
thf(sP705,plain,
( sP705
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP564 ) ),
introduced(definition,[new_symbols(definition,[sP705])]) ).
thf(sP706,plain,
( sP706
<=> ( sP404
=> ~ sP650 ) ),
introduced(definition,[new_symbols(definition,[sP706])]) ).
thf(sP707,plain,
( sP707
<=> ( ~ sP675
=> ~ sP70 ) ),
introduced(definition,[new_symbols(definition,[sP707])]) ).
thf(sP708,plain,
( sP708
<=> ! [X1: $i] :
( ~ ( ~ sP187
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP708])]) ).
thf(sP709,plain,
( sP709
<=> ( ~ sP126
=> ~ sP448 ) ),
introduced(definition,[new_symbols(definition,[sP709])]) ).
thf(sP710,plain,
( sP710
<=> ( ~ ( ~ sP613
=> ~ sP83 )
=> ~ sP652 ) ),
introduced(definition,[new_symbols(definition,[sP710])]) ).
thf(sP711,plain,
( sP711
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP711])]) ).
thf(sP712,plain,
( sP712
<=> ! [X1: $i] :
( ~ ( ~ ( ~ sP28
=> ~ sP650 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP712])]) ).
thf(sP713,plain,
( sP713
<=> ( ~ sP41
=> sP685 ) ),
introduced(definition,[new_symbols(definition,[sP713])]) ).
thf(sP714,plain,
( sP714
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP714])]) ).
thf(sP715,plain,
( sP715
<=> ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP715])]) ).
thf(sP716,plain,
( sP716
<=> ( ~ sP595
=> ~ sP700 ) ),
introduced(definition,[new_symbols(definition,[sP716])]) ).
thf(sP717,plain,
( sP717
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP566
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP717])]) ).
thf(sP718,plain,
( sP718
<=> ( ~ sP668
=> sP583 ) ),
introduced(definition,[new_symbols(definition,[sP718])]) ).
thf(sP719,plain,
( sP719
<=> ( ~ sP168
=> ~ sP676 ) ),
introduced(definition,[new_symbols(definition,[sP719])]) ).
thf(sP720,plain,
( sP720
<=> ( ~ sP380
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP720])]) ).
thf(sP721,plain,
( sP721
<=> ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP291 ) ),
introduced(definition,[new_symbols(definition,[sP721])]) ).
thf(sP722,plain,
( sP722
<=> ( ~ ( ~ sP443
=> ~ sP404 )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP722])]) ).
thf(sP723,plain,
( sP723
<=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP723])]) ).
thf(sP724,plain,
( sP724
<=> ! [X1: $i] :
( ~ ( ~ sP173
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP724])]) ).
thf(sP725,plain,
( sP725
<=> ( ~ sP697
=> sP479 ) ),
introduced(definition,[new_symbols(definition,[sP725])]) ).
thf(sP726,plain,
( sP726
<=> ( ~ ( sP606
=> ~ sP489 )
=> ~ sP692 ) ),
introduced(definition,[new_symbols(definition,[sP726])]) ).
thf(sP727,plain,
( sP727
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP514
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ z @ X2 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP727])]) ).
thf(sP728,plain,
( sP728
<=> ( ~ sP680
=> ~ sP334 ) ),
introduced(definition,[new_symbols(definition,[sP728])]) ).
thf(sP729,plain,
( sP729
<=> ( ~ sP104
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP729])]) ).
thf(sP730,plain,
( sP730
<=> ( ~ sP33
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP730])]) ).
thf(sP731,plain,
( sP731
<=> ( ~ ( sP150
=> ~ sP489 )
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP731])]) ).
thf(sP732,plain,
( sP732
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP732])]) ).
thf(sP733,plain,
( sP733
<=> ( ~ sP220
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP733])]) ).
thf(sP734,plain,
( sP734
<=> ( ~ sP390
=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP734])]) ).
thf(sP735,plain,
( sP735
<=> ! [X1: $i] :
( ~ ( ~ sP106
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP735])]) ).
thf(sP736,plain,
( sP736
<=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP736])]) ).
thf(sP737,plain,
( sP737
<=> ( sP150
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP737])]) ).
thf(sP738,plain,
( sP738
<=> ( sP57
=> ~ sP291 ) ),
introduced(definition,[new_symbols(definition,[sP738])]) ).
thf(sP739,plain,
( sP739
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( r @ z @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP739])]) ).
thf(sP740,plain,
( sP740
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP657 ) ),
introduced(definition,[new_symbols(definition,[sP740])]) ).
thf(sP741,plain,
( sP741
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP155
=> ~ sP479 )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP741])]) ).
thf(sP742,plain,
( sP742
<=> ( ~ sP272
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP742])]) ).
thf(sP743,plain,
( sP743
<=> ( ~ sP97
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP743])]) ).
thf(sP744,plain,
( sP744
<=> ( ~ ( sP562
=> ~ sP334 )
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP744])]) ).
thf(sP745,plain,
( sP745
<=> ( ~ sP136
=> ~ sP585 ) ),
introduced(definition,[new_symbols(definition,[sP745])]) ).
thf(sP746,plain,
( sP746
<=> ( ~ sP155
=> ~ sP479 ) ),
introduced(definition,[new_symbols(definition,[sP746])]) ).
thf(sP747,plain,
( sP747
<=> ( ~ sP81
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP747])]) ).
thf(sP748,plain,
( sP748
<=> ! [X1: $i] :
( ~ ( ~ sP434
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP748])]) ).
thf(sP749,plain,
( sP749
<=> ! [X1: $i] :
( ~ ( ~ sP146
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP749])]) ).
thf(sP750,plain,
( sP750
<=> ( ~ sP601
=> ~ sP633 ) ),
introduced(definition,[new_symbols(definition,[sP750])]) ).
thf(sP751,plain,
( sP751
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ z ) ) )
=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP751])]) ).
thf(sP752,plain,
( sP752
<=> ( ~ sP720
=> ~ sP479 ) ),
introduced(definition,[new_symbols(definition,[sP752])]) ).
thf(sP753,plain,
( sP753
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP49
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP753])]) ).
thf(sP754,plain,
( sP754
<=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP754])]) ).
thf(sP755,plain,
( sP755
<=> ( ~ sP550
=> ~ sP560 ) ),
introduced(definition,[new_symbols(definition,[sP755])]) ).
thf(sP756,plain,
( sP756
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP414
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP756])]) ).
thf(sP757,plain,
( sP757
<=> ( ~ sP645
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP757])]) ).
thf(sP758,plain,
( sP758
<=> ( ~ sP92
=> ~ sP156 ) ),
introduced(definition,[new_symbols(definition,[sP758])]) ).
thf(sP759,plain,
( sP759
<=> ( ~ ( sP70
=> ~ sP213 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP759])]) ).
thf(sP760,plain,
( sP760
<=> ( sP334
=> ~ sP514 ) ),
introduced(definition,[new_symbols(definition,[sP760])]) ).
thf(sP761,plain,
( sP761
<=> ( ~ sP511
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP761])]) ).
thf(sP762,plain,
( sP762
<=> ( sP448
=> ~ sP700 ) ),
introduced(definition,[new_symbols(definition,[sP762])]) ).
thf(sP763,plain,
( sP763
<=> ( ~ sP46
=> ~ sP685 ) ),
introduced(definition,[new_symbols(definition,[sP763])]) ).
thf(sP764,plain,
( sP764
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ z @ X1 )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) )
=> ~ ( b @ X2 @ X4 ) )
=> ~ ( b @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP764])]) ).
thf(sP765,plain,
( sP765
<=> ( ~ ( sP121
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP765])]) ).
thf(sP766,plain,
( sP766
<=> ( sP404
=> ~ sP479 ) ),
introduced(definition,[new_symbols(definition,[sP766])]) ).
thf(sP767,plain,
( sP767
<=> ( sP121
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP767])]) ).
thf(sP768,plain,
( sP768
<=> ( ~ ( ~ sP187
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP768])]) ).
thf(sP769,plain,
( sP769
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP769])]) ).
thf(sP770,plain,
( sP770
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP770])]) ).
thf(sP771,plain,
( sP771
<=> ! [X1: $i] :
( ~ ( ~ sP299
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP771])]) ).
thf(sP772,plain,
( sP772
<=> ! [X1: $i] :
( ~ ( ~ sP296
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP772])]) ).
thf(sP773,plain,
( sP773
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP773])]) ).
thf(sP774,plain,
( sP774
<=> ( ~ sP134
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP774])]) ).
thf(sP775,plain,
( sP775
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP775])]) ).
thf(sP776,plain,
( sP776
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP776])]) ).
thf(sP777,plain,
( sP777
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP777])]) ).
thf(sP778,plain,
( sP778
<=> ( ~ sP720
=> ~ sP564 ) ),
introduced(definition,[new_symbols(definition,[sP778])]) ).
thf(sP779,plain,
( sP779
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP153
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP779])]) ).
thf(sP780,plain,
( sP780
<=> ( ~ sP537
=> ~ sP652 ) ),
introduced(definition,[new_symbols(definition,[sP780])]) ).
thf(sP781,plain,
( sP781
<=> ( ~ sP325
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP781])]) ).
thf(sP782,plain,
( sP782
<=> ( ~ sP352
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP782])]) ).
thf(sP783,plain,
( sP783
<=> ( ~ sP635
=> ~ sP213 ) ),
introduced(definition,[new_symbols(definition,[sP783])]) ).
thf(sP784,plain,
( sP784
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP784])]) ).
thf(sP785,plain,
( sP785
<=> ( ~ sP96
=> ~ sP70 ) ),
introduced(definition,[new_symbols(definition,[sP785])]) ).
thf(sP786,plain,
( sP786
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP353
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP786])]) ).
thf(sP787,plain,
( sP787
<=> ( ~ sP750
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP787])]) ).
thf(sP788,plain,
( sP788
<=> ( sP288
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP788])]) ).
thf(sP789,plain,
( sP789
<=> ( ~ sP72
=> ~ sP769 ) ),
introduced(definition,[new_symbols(definition,[sP789])]) ).
thf(sP790,plain,
( sP790
<=> ( ~ sP705
=> ~ sP329 ) ),
introduced(definition,[new_symbols(definition,[sP790])]) ).
thf(sP791,plain,
( sP791
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP791])]) ).
thf(sP792,plain,
( sP792
<=> ( ~ sP51
=> ~ sP121 ) ),
introduced(definition,[new_symbols(definition,[sP792])]) ).
thf(sP793,plain,
( sP793
<=> ( sP291
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP793])]) ).
thf(sP794,plain,
( sP794
<=> ( sP156
=> ~ sP657 ) ),
introduced(definition,[new_symbols(definition,[sP794])]) ).
thf(sP795,plain,
( sP795
<=> ( ~ sP317
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP795])]) ).
thf(sP796,plain,
( sP796
<=> ( ~ sP107
=> ~ sP285 ) ),
introduced(definition,[new_symbols(definition,[sP796])]) ).
thf(sP797,plain,
( sP797
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP172
=> ~ sP585 )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP797])]) ).
thf(sP798,plain,
( sP798
<=> ( ~ sP274
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP798])]) ).
thf(sP799,plain,
( sP799
<=> ( sP773
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP799])]) ).
thf(sP800,plain,
( sP800
<=> ( ~ sP590
=> ~ sP285 ) ),
introduced(definition,[new_symbols(definition,[sP800])]) ).
thf(sP801,plain,
( sP801
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP489
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP801])]) ).
thf(sP802,plain,
( sP802
<=> ( ~ ( ~ sP601
=> ~ sP770 )
=> ~ sP514 ) ),
introduced(definition,[new_symbols(definition,[sP802])]) ).
thf(sP803,plain,
( sP803
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP36
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP803])]) ).
thf(sP804,plain,
( sP804
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP378
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP804])]) ).
thf(sP805,plain,
( sP805
<=> ( sP606
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP805])]) ).
thf(sP806,plain,
( sP806
<=> ( ~ sP355
=> ~ sP657 ) ),
introduced(definition,[new_symbols(definition,[sP806])]) ).
thf(sP807,plain,
( sP807
<=> ( ~ sP455
=> ~ sP213 ) ),
introduced(definition,[new_symbols(definition,[sP807])]) ).
thf(sP808,plain,
( sP808
<=> ( ~ ( sP479
=> ~ sP564 )
=> ~ sP585 ) ),
introduced(definition,[new_symbols(definition,[sP808])]) ).
thf(sP809,plain,
( sP809
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP60
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP809])]) ).
thf(sP810,plain,
( sP810
<=> ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP773 ) ),
introduced(definition,[new_symbols(definition,[sP810])]) ).
thf(sP811,plain,
( sP811
<=> ( ~ sP755
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP811])]) ).
thf(sP812,plain,
( sP812
<=> ( ~ sP356
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP812])]) ).
thf(sP813,plain,
( sP813
<=> ( ~ sP405
=> sP657 ) ),
introduced(definition,[new_symbols(definition,[sP813])]) ).
thf(sP814,plain,
( sP814
<=> ( ~ sP465
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP814])]) ).
thf(sP815,plain,
( sP815
<=> ( ~ sP450
=> ~ sP692 ) ),
introduced(definition,[new_symbols(definition,[sP815])]) ).
thf(sP816,plain,
( sP816
<=> ( ~ sP63
=> ~ sP700 ) ),
introduced(definition,[new_symbols(definition,[sP816])]) ).
thf(sP817,plain,
( sP817
<=> ( ~ ( ~ sP20
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ sP685 ) ),
introduced(definition,[new_symbols(definition,[sP817])]) ).
thf(sP818,plain,
( sP818
<=> ( ~ sP30
=> ~ sP508 ) ),
introduced(definition,[new_symbols(definition,[sP818])]) ).
thf(sP819,plain,
( sP819
<=> ( ~ sP706
=> ~ sP463 ) ),
introduced(definition,[new_symbols(definition,[sP819])]) ).
thf(sP820,plain,
( sP820
<=> ( ~ sP37
=> ~ sP221 ) ),
introduced(definition,[new_symbols(definition,[sP820])]) ).
thf(sP821,plain,
( sP821
<=> ( r @ ( s @ z ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP821])]) ).
thf(sP822,plain,
( sP822
<=> ( ~ sP703
=> ~ sP770 ) ),
introduced(definition,[new_symbols(definition,[sP822])]) ).
thf(sP823,plain,
( sP823
<=> ( ~ sP211
=> ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP823])]) ).
thf(sP824,plain,
( sP824
<=> ( ~ sP443
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP824])]) ).
thf(sP825,plain,
( sP825
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP334
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( r @ z @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP825])]) ).
thf(sP826,plain,
( sP826
<=> ( ~ sP172
=> ~ sP585 ) ),
introduced(definition,[new_symbols(definition,[sP826])]) ).
thf(sP827,plain,
( sP827
<=> ( ~ sP649
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP827])]) ).
thf(sP828,plain,
( sP828
<=> ( ~ sP229
=> ~ sP606 ) ),
introduced(definition,[new_symbols(definition,[sP828])]) ).
thf(sP829,plain,
( sP829
<=> ! [X1: $i] :
( ~ ( ~ sP4
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP829])]) ).
thf(sP830,plain,
( sP830
<=> ( ~ sP681
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP830])]) ).
thf(sP831,plain,
( sP831
<=> ( ~ sP492
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP831])]) ).
thf(sP832,plain,
( sP832
<=> ! [X1: $i] :
( ~ ( ~ sP141
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP832])]) ).
thf(sP833,plain,
( sP833
<=> ( sP70
=> ~ sP213 ) ),
introduced(definition,[new_symbols(definition,[sP833])]) ).
thf(sP834,plain,
( sP834
<=> ( ~ sP578
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP834])]) ).
thf(sP835,plain,
( sP835
<=> ( ~ sP826
=> ~ sP685 ) ),
introduced(definition,[new_symbols(definition,[sP835])]) ).
thf(sP836,plain,
( sP836
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP355
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP836])]) ).
thf(sP837,plain,
( sP837
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP837])]) ).
thf(sP838,plain,
( sP838
<=> ( sP511
=> sP777 ) ),
introduced(definition,[new_symbols(definition,[sP838])]) ).
thf(sP839,plain,
( sP839
<=> ( sP60
=> ~ sP773 ) ),
introduced(definition,[new_symbols(definition,[sP839])]) ).
thf(sP840,plain,
( sP840
<=> ! [X1: $i] :
( ~ ( ~ sP224
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP840])]) ).
thf(sP841,plain,
( sP841
<=> ( sP514
=> ~ sP461 ) ),
introduced(definition,[new_symbols(definition,[sP841])]) ).
thf(sP842,plain,
( sP842
<=> ( r @ ( s @ ( s @ z ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP842])]) ).
thf(sP843,plain,
( sP843
<=> ( ~ sP810
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP843])]) ).
thf(sP844,plain,
( sP844
<=> ( ~ sP311
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP844])]) ).
thf(sP845,plain,
( sP845
<=> ( ~ sP359
=> ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP845])]) ).
thf(sP846,plain,
( sP846
<=> ( ~ sP374
=> ~ sP606 ) ),
introduced(definition,[new_symbols(definition,[sP846])]) ).
thf(sP847,plain,
( sP847
<=> ( ~ sP781
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP847])]) ).
thf(sP848,plain,
( sP848
<=> ( ~ sP517
=> ~ sP842 ) ),
introduced(definition,[new_symbols(definition,[sP848])]) ).
thf(sP849,plain,
( sP849
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP849])]) ).
thf(sP850,plain,
( sP850
<=> ( sP606
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP850])]) ).
thf(sP851,plain,
( sP851
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP57
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP851])]) ).
thf(sP852,plain,
( sP852
<=> ! [X1: $i] :
( ~ ( ~ sP237
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP852])]) ).
thf(sP853,plain,
( sP853
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP853])]) ).
thf(sP854,plain,
( sP854
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP700
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP854])]) ).
thf(sP855,plain,
( sP855
<=> ( ~ sP61
=> ~ sP853 ) ),
introduced(definition,[new_symbols(definition,[sP855])]) ).
thf(sP856,plain,
( sP856
<=> ( ~ sP776
=> ~ sP723 ) ),
introduced(definition,[new_symbols(definition,[sP856])]) ).
thf(sP857,plain,
( sP857
<=> ! [X1: $i] :
( ~ ( ~ sP721
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP857])]) ).
thf(sP858,plain,
( sP858
<=> ( sP773
=> ~ sP334 ) ),
introduced(definition,[new_symbols(definition,[sP858])]) ).
thf(sP859,plain,
( sP859
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP107
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP859])]) ).
thf(sP860,plain,
( sP860
<=> ! [X1: $i] :
( ~ ( ~ sP679
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP860])]) ).
thf(sP861,plain,
( sP861
<=> ! [X1: $i] :
( ~ ( ~ sP447
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP861])]) ).
thf(sP862,plain,
( sP862
<=> ( sP57
=> ~ sP773 ) ),
introduced(definition,[new_symbols(definition,[sP862])]) ).
thf(sP863,plain,
( sP863
<=> ( ~ sP572
=> ~ sP700 ) ),
introduced(definition,[new_symbols(definition,[sP863])]) ).
thf(sP864,plain,
( sP864
<=> ( ~ sP237
=> ~ sP842 ) ),
introduced(definition,[new_symbols(definition,[sP864])]) ).
thf(sP865,plain,
( sP865
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ ( s @ z ) ) )
=> sP70 ) ),
introduced(definition,[new_symbols(definition,[sP865])]) ).
thf(sP866,plain,
( sP866
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP562
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP866])]) ).
thf(sP867,plain,
( sP867
<=> ! [X1: $i] :
( ~ ( ( ( s @ ( s @ ( s @ z ) ) )
!= X1 )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP867])]) ).
thf(sP868,plain,
( sP868
<=> ( ~ sP98
=> sP404 ) ),
introduced(definition,[new_symbols(definition,[sP868])]) ).
thf(sP869,plain,
( sP869
<=> ( ~ sP784
=> ~ sP700 ) ),
introduced(definition,[new_symbols(definition,[sP869])]) ).
thf(sP870,plain,
( sP870
<=> ! [X1: $i] :
( ~ ( ~ sP550
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP870])]) ).
thf(sP871,plain,
( sP871
<=> ( ~ sP119
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP871])]) ).
thf(sP872,plain,
( sP872
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP28
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP872])]) ).
thf(sP873,plain,
( sP873
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP213
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP873])]) ).
thf(sP874,plain,
( sP874
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP685
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP874])]) ).
thf(sP875,plain,
( sP875
<=> ( ~ sP607
=> ~ sP288 ) ),
introduced(definition,[new_symbols(definition,[sP875])]) ).
thf(sP876,plain,
( sP876
<=> ( ~ ( sP700
=> ~ sP723 )
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP876])]) ).
thf(sP877,plain,
( sP877
<=> ! [X1: $i] :
( ~ ( ~ ( sP213
=> ~ sP288 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP877])]) ).
thf(sP878,plain,
( sP878
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP509
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP878])]) ).
thf(sP879,plain,
( sP879
<=> ( ~ sP482
=> ~ sP773 ) ),
introduced(definition,[new_symbols(definition,[sP879])]) ).
thf(sP880,plain,
( sP880
<=> ( sP156
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP880])]) ).
thf(sP881,plain,
( sP881
<=> ( ~ sP236
=> ~ sP650 ) ),
introduced(definition,[new_symbols(definition,[sP881])]) ).
thf(sP882,plain,
( sP882
<=> ( ~ sP532
=> sP270 ) ),
introduced(definition,[new_symbols(definition,[sP882])]) ).
thf(sP883,plain,
( sP883
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP404 ) ),
introduced(definition,[new_symbols(definition,[sP883])]) ).
thf(sP884,plain,
( sP884
<=> ( sP489
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP884])]) ).
thf(sP885,plain,
( sP885
<=> ( sP777
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP885])]) ).
thf(sP886,plain,
( sP886
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP291
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( r @ z @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP886])]) ).
thf(sP887,plain,
( sP887
<=> ( ~ sP721
=> ~ sP754 ) ),
introduced(definition,[new_symbols(definition,[sP887])]) ).
thf(sP888,plain,
( sP888
<=> ( ~ sP702
=> ~ sP692 ) ),
introduced(definition,[new_symbols(definition,[sP888])]) ).
thf(sP889,plain,
( sP889
<=> ( ~ sP79
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP889])]) ).
thf(sP890,plain,
( sP890
<=> ( ~ sP844
=> ~ sP60 ) ),
introduced(definition,[new_symbols(definition,[sP890])]) ).
thf(sP891,plain,
( sP891
<=> ( ~ sP259
=> ~ sP508 ) ),
introduced(definition,[new_symbols(definition,[sP891])]) ).
thf(sP892,plain,
( sP892
<=> ! [X1: $i] :
( ~ ( ~ ( sP769
=> ~ sP70 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP892])]) ).
thf(sP893,plain,
( sP893
<=> ( ~ sP251
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP893])]) ).
thf(sP894,plain,
( sP894
<=> ( sP723
=> ~ sP685 ) ),
introduced(definition,[new_symbols(definition,[sP894])]) ).
thf(sP895,plain,
( sP895
<=> ( ~ sP828
=> ~ sP657 ) ),
introduced(definition,[new_symbols(definition,[sP895])]) ).
thf(sP896,plain,
( sP896
<=> ( ~ ( ~ sP616
=> ~ sP633 )
=> ~ sP652 ) ),
introduced(definition,[new_symbols(definition,[sP896])]) ).
thf(sP897,plain,
( sP897
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP70 )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP897])]) ).
thf(sP898,plain,
( sP898
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP898])]) ).
thf(sP899,plain,
( sP899
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP463
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP899])]) ).
thf(sP900,plain,
( sP900
<=> ( ~ ( sP213
=> ~ sP288 )
=> ~ sP461 ) ),
introduced(definition,[new_symbols(definition,[sP900])]) ).
thf(sP901,plain,
( sP901
<=> ( ~ sP343
=> ~ sP769 ) ),
introduced(definition,[new_symbols(definition,[sP901])]) ).
thf(sP902,plain,
( sP902
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ ( ~ sP204
=> ~ sP479 )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP902])]) ).
thf(sP903,plain,
( sP903
<=> ( sP225
=> sP245 ) ),
introduced(definition,[new_symbols(definition,[sP903])]) ).
thf(sP904,plain,
( sP904
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP89
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP904])]) ).
thf(sP905,plain,
( sP905
<=> ( ( s @ z )
= z ) ),
introduced(definition,[new_symbols(definition,[sP905])]) ).
thf(sP906,plain,
( sP906
<=> ( ~ sP472
=> ~ sP262 ) ),
introduced(definition,[new_symbols(definition,[sP906])]) ).
thf(sP907,plain,
( sP907
<=> ( ~ sP101
=> ~ sP270 ) ),
introduced(definition,[new_symbols(definition,[sP907])]) ).
thf(sP908,plain,
( sP908
<=> ( ~ ( ~ sP198
=> ~ sP545 )
=> ~ sP676 ) ),
introduced(definition,[new_symbols(definition,[sP908])]) ).
thf(sP909,plain,
( sP909
<=> ( ~ sP20
=> ~ sP853 ) ),
introduced(definition,[new_symbols(definition,[sP909])]) ).
thf(sP910,plain,
( sP910
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP910])]) ).
thf(sP911,plain,
( sP911
<=> ( ~ sP616
=> ~ sP633 ) ),
introduced(definition,[new_symbols(definition,[sP911])]) ).
thf(sP912,plain,
( sP912
<=> ( ~ sP190
=> ~ sP650 ) ),
introduced(definition,[new_symbols(definition,[sP912])]) ).
thf(sP913,plain,
( sP913
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP538
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP913])]) ).
thf(sP914,plain,
( sP914
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP113
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP914])]) ).
thf(sP915,plain,
( sP915
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP325
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP915])]) ).
thf(sP916,plain,
( sP916
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) )
=> sP661 ) ),
introduced(definition,[new_symbols(definition,[sP916])]) ).
thf(sP917,plain,
( sP917
<=> ( ~ sP88
=> ~ sP692 ) ),
introduced(definition,[new_symbols(definition,[sP917])]) ).
thf(sP918,plain,
( sP918
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP683
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP918])]) ).
thf(sP919,plain,
( sP919
<=> ( ~ sP358
=> ~ sP821 ) ),
introduced(definition,[new_symbols(definition,[sP919])]) ).
thf(sP920,plain,
( sP920
<=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP920])]) ).
thf(sP921,plain,
( sP921
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP436
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP921])]) ).
thf(sP922,plain,
( sP922
<=> ( ~ sP601
=> ~ sP770 ) ),
introduced(definition,[new_symbols(definition,[sP922])]) ).
thf(sP923,plain,
( sP923
<=> ! [X1: $i] :
( ~ ( ~ sP52
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP923])]) ).
thf(sP924,plain,
( sP924
<=> ( ~ sP296
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP924])]) ).
thf(sP925,plain,
( sP925
<=> ( ~ sP426
=> ~ sP213 ) ),
introduced(definition,[new_symbols(definition,[sP925])]) ).
thf(sP926,plain,
( sP926
<=> ! [X1: $i] :
( ~ ( ~ sP815
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP926])]) ).
thf(sP927,plain,
( sP927
<=> ( ~ ( ~ sP318
=> ~ sP692 )
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP927])]) ).
thf(sP928,plain,
( sP928
<=> ( sP700
=> ~ sP448 ) ),
introduced(definition,[new_symbols(definition,[sP928])]) ).
thf(sP929,plain,
( sP929
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ z ) @ X1 )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) )
=> ~ ( b @ X2 @ X4 ) )
=> ~ ( b @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP929])]) ).
thf(sP930,plain,
( sP930
<=> ( ~ sP377
=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP930])]) ).
thf(sP931,plain,
( sP931
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X3 ) )
=> ~ ( r @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP931])]) ).
thf(sP932,plain,
( sP932
<=> ! [X1: $i] :
( ~ ( ~ sP482
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP932])]) ).
thf(sP933,plain,
( sP933
<=> ( ~ sP644
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP933])]) ).
thf(sP934,plain,
( sP934
<=> ( ~ ( ~ sP470
=> ~ sP692 )
=> ~ sP156 ) ),
introduced(definition,[new_symbols(definition,[sP934])]) ).
thf(sP935,plain,
( sP935
<=> ( sP479
=> ~ sP564 ) ),
introduced(definition,[new_symbols(definition,[sP935])]) ).
thf(sP936,plain,
( sP936
<=> ( ~ sP498
=> ~ sP445 ) ),
introduced(definition,[new_symbols(definition,[sP936])]) ).
thf(sP937,plain,
( sP937
<=> ! [X1: $i] :
( ~ ( ~ sP182
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP937])]) ).
thf(sP938,plain,
( sP938
<=> ! [X1: $i] :
( ~ ( ( z != X1 )
=> ( r @ z @ X1 ) )
=> ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP938])]) ).
thf(sP939,plain,
( sP939
<=> ( ~ ( ~ sP95
=> ~ sP262 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP939])]) ).
thf(sP940,plain,
( sP940
<=> ( ~ ( ~ sP457
=> ~ sP479 )
=> ~ sP685 ) ),
introduced(definition,[new_symbols(definition,[sP940])]) ).
thf(sP941,plain,
( sP941
<=> ( ~ sP746
=> ~ sP585 ) ),
introduced(definition,[new_symbols(definition,[sP941])]) ).
thf(sP942,plain,
( sP942
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP657
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP942])]) ).
thf(sP943,plain,
( sP943
<=> ( ~ sP95
=> ~ sP262 ) ),
introduced(definition,[new_symbols(definition,[sP943])]) ).
thf(sP944,plain,
( sP944
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP876
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP944])]) ).
thf(sP945,plain,
( sP945
<=> ! [X1: $i] :
( ~ ( ~ sP862
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP945])]) ).
thf(sP946,plain,
( sP946
<=> ! [X1: $i] :
( ~ ( ~ sP410
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP946])]) ).
thf(sP947,plain,
( sP947
<=> ! [X1: $i] :
( ~ ( ~ sP760
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP947])]) ).
thf(sP948,plain,
( sP948
<=> ( ~ ( sP57
=> ~ sP652 )
=> ~ sP461 ) ),
introduced(definition,[new_symbols(definition,[sP948])]) ).
thf(sP949,plain,
( sP949
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP585
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP949])]) ).
thf(sP950,plain,
( sP950
<=> ( ~ sP204
=> ~ sP479 ) ),
introduced(definition,[new_symbols(definition,[sP950])]) ).
thf(sP951,plain,
( sP951
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP951])]) ).
thf(sP952,plain,
( sP952
<=> ( ~ sP760
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP952])]) ).
thf(sP953,plain,
( sP953
<=> ( ~ sP880
=> ~ sP700 ) ),
introduced(definition,[new_symbols(definition,[sP953])]) ).
thf(sP954,plain,
( sP954
<=> ! [X1: $i,X2: $i] :
( ~ ( ( X1 != X2 )
=> ( r @ X1 @ X2 ) )
=> ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP954])]) ).
thf(sP955,plain,
( sP955
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP163
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP955])]) ).
thf(sP956,plain,
( sP956
<=> ( ~ sP875
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP956])]) ).
thf(sP957,plain,
( sP957
<=> ( ~ sP624
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP957])]) ).
thf(sP958,plain,
( sP958
<=> ( sP700
=> ~ sP723 ) ),
introduced(definition,[new_symbols(definition,[sP958])]) ).
thf(sP959,plain,
( sP959
<=> ( ~ sP460
=> ~ sP685 ) ),
introduced(definition,[new_symbols(definition,[sP959])]) ).
thf(sP960,plain,
( sP960
<=> ! [X1: $i] :
( ~ ( ~ sP781
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP960])]) ).
thf(sP961,plain,
( sP961
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP479
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP961])]) ).
thf(sP962,plain,
( sP962
<=> ( ~ sP709
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP962])]) ).
thf(sP963,plain,
( sP963
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP589
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP963])]) ).
thf(sP964,plain,
( sP964
<=> ( ~ sP962
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP964])]) ).
thf(sP965,plain,
( sP965
<=> ( ~ sP613
=> ~ sP83 ) ),
introduced(definition,[new_symbols(definition,[sP965])]) ).
thf(sP966,plain,
( sP966
<=> ( ~ sP282
=> ~ sP285 ) ),
introduced(definition,[new_symbols(definition,[sP966])]) ).
thf(sP967,plain,
( sP967
<=> ( ~ sP846
=> ~ sP585 ) ),
introduced(definition,[new_symbols(definition,[sP967])]) ).
thf(sP968,plain,
( sP968
<=> ! [X1: $i] :
( ~ ( ~ sP234
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP968])]) ).
thf(sP969,plain,
( sP969
<=> ( ~ sP677
=> ~ sP769 ) ),
introduced(definition,[new_symbols(definition,[sP969])]) ).
thf(sP970,plain,
( sP970
<=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP970])]) ).
thf(sP971,plain,
( sP971
<=> ( ~ sP486
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP971])]) ).
thf(sP972,plain,
( sP972
<=> ( ~ sP135
=> ~ sP606 ) ),
introduced(definition,[new_symbols(definition,[sP972])]) ).
thf(sP973,plain,
( sP973
<=> ( sP213
=> ~ sP288 ) ),
introduced(definition,[new_symbols(definition,[sP973])]) ).
thf(sP974,plain,
( sP974
<=> ( sP562
=> ~ sP334 ) ),
introduced(definition,[new_symbols(definition,[sP974])]) ).
thf(sP975,plain,
( sP975
<=> ( sP769
=> ~ sP70 ) ),
introduced(definition,[new_symbols(definition,[sP975])]) ).
thf(sP976,plain,
( sP976
<=> ( ~ sP671
=> ~ sP606 ) ),
introduced(definition,[new_symbols(definition,[sP976])]) ).
thf(sP977,plain,
( sP977
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ X1 )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X3 ) )
=> ~ ( r @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP977])]) ).
thf(sP978,plain,
( sP978
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP819
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP978])]) ).
thf(sP979,plain,
( sP979
<=> ( ~ sP470
=> ~ sP692 ) ),
introduced(definition,[new_symbols(definition,[sP979])]) ).
thf(sP980,plain,
( sP980
<=> ( ~ sP950
=> ~ sP285 ) ),
introduced(definition,[new_symbols(definition,[sP980])]) ).
thf(sP981,plain,
( sP981
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP650
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP981])]) ).
thf(sP982,plain,
( sP982
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) )
=> ~ ( b @ X2 @ X4 ) )
=> ~ ( b @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP982])]) ).
thf(sP983,plain,
( sP983
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP983])]) ).
thf(sP984,plain,
( sP984
<=> ! [X1: $i] :
( ~ ( ~ sP403
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP984])]) ).
thf(sP985,plain,
( sP985
<=> ( ~ sP736
=> sP385 ) ),
introduced(definition,[new_symbols(definition,[sP985])]) ).
thf(sP986,plain,
( sP986
<=> ( ~ sP925
=> ~ sP562 ) ),
introduced(definition,[new_symbols(definition,[sP986])]) ).
thf(sP987,plain,
( sP987
<=> ( ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP334 ) ),
introduced(definition,[new_symbols(definition,[sP987])]) ).
thf(sP988,plain,
( sP988
<=> ( sP288
=> ~ sP821 ) ),
introduced(definition,[new_symbols(definition,[sP988])]) ).
thf(sP989,plain,
( sP989
<=> ! [X1: $i] :
( ~ ( ~ sP358
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP989])]) ).
thf(sP990,plain,
( sP990
<=> ( ~ sP967
=> ~ sP692 ) ),
introduced(definition,[new_symbols(definition,[sP990])]) ).
thf(sP991,plain,
( sP991
<=> ! [X1: $i] :
( ~ ( ~ sP537
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP991])]) ).
thf(sP992,plain,
( sP992
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP992])]) ).
thf(sP993,plain,
( sP993
<=> ( ~ sP839
=> ~ sP562 ) ),
introduced(definition,[new_symbols(definition,[sP993])]) ).
thf(sP994,plain,
( sP994
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP273
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP994])]) ).
thf(sP995,plain,
( sP995
<=> ! [X1: $i] :
( ~ ( ~ sP258
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP995])]) ).
thf(sP996,plain,
( sP996
<=> ( ~ sP337
=> ~ sP514 ) ),
introduced(definition,[new_symbols(definition,[sP996])]) ).
thf(sP997,plain,
( sP997
<=> ( ~ sP457
=> ~ sP479 ) ),
introduced(definition,[new_symbols(definition,[sP997])]) ).
thf(sP998,plain,
( sP998
<=> ( sP970
=> ~ sP70 ) ),
introduced(definition,[new_symbols(definition,[sP998])]) ).
thf(sP999,plain,
( sP999
<=> ( ~ sP187
=> ~ sP770 ) ),
introduced(definition,[new_symbols(definition,[sP999])]) ).
thf(sP1000,plain,
( sP1000
<=> ( ~ sP366
=> ~ sP508 ) ),
introduced(definition,[new_symbols(definition,[sP1000])]) ).
thf(sP1001,plain,
( sP1001
<=> ( ~ sP453
=> ~ sP523 ) ),
introduced(definition,[new_symbols(definition,[sP1001])]) ).
thf(sP1002,plain,
( sP1002
<=> ( ~ sP941
=> ~ sP280 ) ),
introduced(definition,[new_symbols(definition,[sP1002])]) ).
thf(sP1003,plain,
( sP1003
<=> ( sP821
=> ~ sP970 ) ),
introduced(definition,[new_symbols(definition,[sP1003])]) ).
thf(sP1004,plain,
( sP1004
<=> ( ~ sP284
=> ~ sP560 ) ),
introduced(definition,[new_symbols(definition,[sP1004])]) ).
thf(sP1005,plain,
( sP1005
<=> ( ~ sP855
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP1005])]) ).
thf(sP1006,plain,
( sP1006
<=> ! [X1: $i] :
( ~ ( ~ sP627
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1006])]) ).
thf(sP1007,plain,
( sP1007
<=> ( sP60
=> ~ sP291 ) ),
introduced(definition,[new_symbols(definition,[sP1007])]) ).
thf(sP1008,plain,
( sP1008
<=> ( ~ sP160
=> ~ sP821 ) ),
introduced(definition,[new_symbols(definition,[sP1008])]) ).
thf(sP1009,plain,
( sP1009
<=> ( ~ sP174
=> ~ sP121 ) ),
introduced(definition,[new_symbols(definition,[sP1009])]) ).
thf(sP1010,plain,
( sP1010
<=> ( ~ sP588
=> ~ sP951 ) ),
introduced(definition,[new_symbols(definition,[sP1010])]) ).
thf(sP1011,plain,
( sP1011
<=> ( sP270
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP1011])]) ).
thf(sP1012,plain,
( sP1012
<=> ( ~ sP369
=> ~ sP585 ) ),
introduced(definition,[new_symbols(definition,[sP1012])]) ).
thf(sP1013,plain,
( sP1013
<=> ! [X1: $i] :
( ~ ( ~ sP601
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1013])]) ).
thf(sP1014,plain,
( sP1014
<=> ( ~ sP58
=> ~ sP463 ) ),
introduced(definition,[new_symbols(definition,[sP1014])]) ).
thf(sP1015,plain,
( sP1015
<=> ( ~ sP535
=> ~ sP448 ) ),
introduced(definition,[new_symbols(definition,[sP1015])]) ).
thf(sP1016,plain,
( sP1016
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP461
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( r @ ( s @ z ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1016])]) ).
thf(sP1017,plain,
( sP1017
<=> ( ~ sP509
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP1017])]) ).
thf(sP1018,plain,
( sP1018
<=> ! [X1: $i] :
( ~ ( ~ sP327
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1018])]) ).
thf(sP1019,plain,
( sP1019
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP743
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1019])]) ).
thf(sP1020,plain,
( sP1020
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP448
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1020])]) ).
thf(sP1021,plain,
( sP1021
<=> ! [X1: $i] :
( ~ ( ~ sP688
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1021])]) ).
thf(sP1022,plain,
( sP1022
<=> ! [X1: $i] :
( ~ ( ~ sP298
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1022])]) ).
thf(sP1023,plain,
( sP1023
<=> ( sP514
=> ~ sP842 ) ),
introduced(definition,[new_symbols(definition,[sP1023])]) ).
thf(sP1024,plain,
( sP1024
<=> ( z
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1024])]) ).
thf(sP1025,plain,
( sP1025
<=> ( ~ sP198
=> ~ sP545 ) ),
introduced(definition,[new_symbols(definition,[sP1025])]) ).
thf(sP1026,plain,
( sP1026
<=> ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1026])]) ).
thf(sP1027,plain,
( sP1027
<=> ( ~ sP1024
=> sP754 ) ),
introduced(definition,[new_symbols(definition,[sP1027])]) ).
thf(sP1028,plain,
( sP1028
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP869
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1028])]) ).
thf(sP1029,plain,
( sP1029
<=> ( ~ sP84
=> ~ sP983 ) ),
introduced(definition,[new_symbols(definition,[sP1029])]) ).
thf(sP1030,plain,
( sP1030
<=> ! [X1: $i] :
( ~ ( ~ sP788
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1030])]) ).
thf(sP1031,plain,
( sP1031
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ~ ( ~ ( sP853
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1031])]) ).
thf(sP1032,plain,
( sP1032
<=> ( ~ sP626
=> ~ sP1026 ) ),
introduced(definition,[new_symbols(definition,[sP1032])]) ).
thf(sP1033,plain,
( sP1033
<=> ( sP57
=> ~ sP652 ) ),
introduced(definition,[new_symbols(definition,[sP1033])]) ).
thf(sP1034,plain,
( sP1034
<=> ( ~ sP250
=> ~ sP463 ) ),
introduced(definition,[new_symbols(definition,[sP1034])]) ).
thf(sP1035,plain,
( sP1035
<=> ! [X1: $i] :
( ~ ( ~ sP817
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1035])]) ).
thf(sP1036,plain,
( sP1036
<=> ( ~ sP924
=> ~ sP769 ) ),
introduced(definition,[new_symbols(definition,[sP1036])]) ).
thf(sP1037,plain,
( sP1037
<=> ( ~ sP948
=> ~ sP652 ) ),
introduced(definition,[new_symbols(definition,[sP1037])]) ).
thf(sP1038,plain,
( sP1038
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1038])]) ).
thf(sP1039,plain,
( sP1039
<=> ( ~ sP318
=> ~ sP692 ) ),
introduced(definition,[new_symbols(definition,[sP1039])]) ).
thf(sP1040,plain,
( sP1040
<=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1040])]) ).
thf(sP1041,plain,
( sP1041
<=> ( ~ sP28
=> ~ sP650 ) ),
introduced(definition,[new_symbols(definition,[sP1041])]) ).
thf(sP1042,plain,
( sP1042
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP628
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1042])]) ).
thf(sP1043,plain,
( sP1043
<=> ! [X1: $i] :
( ~ ( ~ sP841
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1043])]) ).
thf(sP1044,plain,
( sP1044
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ~ sP720
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1044])]) ).
thf(sP1045,plain,
( sP1045
<=> ( ~ sP1005
=> ~ sP723 ) ),
introduced(definition,[new_symbols(definition,[sP1045])]) ).
thf(1,plain,
( ~ sP375
| sP531
| ~ sP445 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP653
| sP375
| ~ sP951 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP340
| ~ sP951
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP486
| sP340
| ~ sP262 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP631
| ~ sP951
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP104
| sP631
| ~ sP105 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP705
| ~ sP951
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP790
| sP705
| ~ sP329 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP883
| ~ sP951
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP628
| sP883
| ~ sP523 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP472
| ~ sP445
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP906
| sP472
| ~ sP262 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP617
| ~ sP445
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP436
| sP617
| ~ sP105 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP277
| ~ sP445
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP554
| sP277
| ~ sP329 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP198
| sP362
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP165
| ~ sP676
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP362
| sP165
| ~ sP262 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP284
| sP683
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP176
| ~ sP676
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP683
| sP176
| ~ sP329 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP552
| ~ sP280
| ~ sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP163
| sP552
| ~ sP951 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP971
| sP486
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP729
| sP104
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP550
| sP790
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP531
| sP628
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP216
| ~ sP692
| ~ sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP643
| sP216
| ~ sP445 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP164
| sP906
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP100
| sP436
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP137
| sP554
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP103
| sP54
| ~ sP583 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP54
| ~ sP500
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP615
| sP239
| ~ sP500 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP999
| sP187
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP911
| sP616
| ~ sP633 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP616
| ~ sP678
| ~ sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP1025
| sP198
| ~ sP545 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP1004
| sP284
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP453
| sP414
| ~ sP262 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP553
| ~ sP585
| ~ sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP414
| sP553
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP943
| sP95
| ~ sP262 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP308
| ~ sP685
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP95
| sP308
| ~ sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP10
| sP163
| ~ sP262 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP444
| sP971
| ~ sP545 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP588
| sP729
| ~ sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP755
| sP550
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP525
| sP643
| ~ sP262 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP611
| sP164
| ~ sP545 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP498
| sP100
| ~ sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP576
| sP137
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP255
| sP103
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP922
| sP601
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP802
| sP922
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP601
| ~ sP583
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP750
| sP601
| ~ sP633 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP787
| sP750
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP112
| ~ sP583
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP662
| sP112
| ~ sP633 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP424
| sP662
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP651
| sP615
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP239
| ~ sP633
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP768
| sP999
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP187
| ~ sP633
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP896
| sP911
| ~ sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP647
| sP26
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(71,plain,
( ~ sP908
| sP1025
| ~ sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( ~ sP326
| sP1004
| ~ sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP505
| sP627
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP1001
| sP453
| ~ sP523 ),
inference(prop_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP939
| sP943
| ~ sP1038 ),
inference(prop_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP765
| sP767
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP767
| ~ sP121
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( ~ sP129
| sP10
| ~ sP329 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP87
| sP444
| ~ sP951 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
( ~ sP1010
| sP588
| ~ sP951 ),
inference(prop_rule,[status(thm)],[]) ).
thf(81,plain,
( ~ sP811
| sP755
| ~ sP951 ),
inference(prop_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP391
| sP21
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP21
| ~ sP221
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP274
| sP525
| ~ sP1038 ),
inference(prop_rule,[status(thm)],[]) ).
thf(85,plain,
( ~ sP205
| sP611
| ~ sP445 ),
inference(prop_rule,[status(thm)],[]) ).
thf(86,plain,
( ~ sP936
| sP498
| ~ sP445 ),
inference(prop_rule,[status(thm)],[]) ).
thf(87,plain,
( ~ sP399
| sP576
| ~ sP445 ),
inference(prop_rule,[status(thm)],[]) ).
thf(88,plain,
( ~ sP108
| sP255 ),
inference(all_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP1013
| sP802 ),
inference(all_rule,[status(thm)],[]) ).
thf(90,plain,
( ~ sP1013
| sP787 ),
inference(all_rule,[status(thm)],[]) ).
thf(91,plain,
( ~ sP140
| sP424 ),
inference(all_rule,[status(thm)],[]) ).
thf(92,plain,
( ~ sP689
| sP651 ),
inference(all_rule,[status(thm)],[]) ).
thf(93,plain,
( ~ sP708
| sP768 ),
inference(all_rule,[status(thm)],[]) ).
thf(94,plain,
( ~ sP704
| sP896 ),
inference(all_rule,[status(thm)],[]) ).
thf(95,plain,
( ~ sP703
| sP715
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(96,plain,
( ~ sP822
| sP703
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(97,plain,
( ~ sP715
| ~ sP754
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(98,plain,
( ~ sP658
| sP361
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(99,plain,
( ~ sP664
| sP658
| ~ sP633 ),
inference(prop_rule,[status(thm)],[]) ).
thf(100,plain,
( ~ sP361
| ~ sP754
| ~ sP633 ),
inference(prop_rule,[status(thm)],[]) ).
thf(101,plain,
( ~ sP26
| ~ sP754
| ~ sP678 ),
inference(prop_rule,[status(thm)],[]) ).
thf(102,plain,
( ~ sP503
| sP647
| ~ sP678 ),
inference(prop_rule,[status(thm)],[]) ).
thf(103,plain,
( ~ sP210
| sP908 ),
inference(all_rule,[status(thm)],[]) ).
thf(104,plain,
( ~ sP73
| sP326 ),
inference(all_rule,[status(thm)],[]) ).
thf(105,plain,
( ~ sP619
| sP505
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(106,plain,
( ~ sP627
| ~ sP508
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(107,plain,
( ~ sP919
| sP358
| ~ sP821 ),
inference(prop_rule,[status(thm)],[]) ).
thf(108,plain,
( ~ sP199
| sP919
| ~ sP583 ),
inference(prop_rule,[status(thm)],[]) ).
thf(109,plain,
( ~ sP358
| ~ sP508
| ~ sP583 ),
inference(prop_rule,[status(thm)],[]) ).
thf(110,plain,
( ~ sP127
| sP1001
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(111,plain,
( ~ sP302
| sP939
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP48
| sP765
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(113,plain,
( ~ sP215
| sP129
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(114,plain,
( ~ sP522
| sP87 ),
inference(all_rule,[status(thm)],[]) ).
thf(115,plain,
( ~ sP300
| sP1010 ),
inference(all_rule,[status(thm)],[]) ).
thf(116,plain,
( ~ sP870
| sP811 ),
inference(all_rule,[status(thm)],[]) ).
thf(117,plain,
( ~ sP197
| sP653 ),
inference(all_rule,[status(thm)],[]) ).
thf(118,plain,
( ~ sP267
| sP391
| ~ sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(119,plain,
( ~ sP688
| ~ sP57
| ~ sP221 ),
inference(prop_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP37
| sP688
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(121,plain,
( ~ sP798
| sP274
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(122,plain,
( ~ sP69
| sP205 ),
inference(all_rule,[status(thm)],[]) ).
thf(123,plain,
( ~ sP233
| sP936 ),
inference(all_rule,[status(thm)],[]) ).
thf(124,plain,
( ~ sP593
| sP399 ),
inference(all_rule,[status(thm)],[]) ).
thf(125,plain,
( ~ sP202
| sP108 ),
inference(all_rule,[status(thm)],[]) ).
thf(126,plain,
( ~ sP556
| sP1013 ),
inference(all_rule,[status(thm)],[]) ).
thf(127,plain,
( ~ sP556
| sP140 ),
inference(all_rule,[status(thm)],[]) ).
thf(128,plain,
( ~ sP344
| sP689 ),
inference(all_rule,[status(thm)],[]) ).
thf(129,plain,
( ~ sP344
| sP708 ),
inference(all_rule,[status(thm)],[]) ).
thf(130,plain,
( ~ sP307
| sP704 ),
inference(all_rule,[status(thm)],[]) ).
thf(131,plain,
( ~ sP466
| sP822 ),
inference(all_rule,[status(thm)],[]) ).
thf(132,plain,
( ~ sP77
| sP664 ),
inference(all_rule,[status(thm)],[]) ).
thf(133,plain,
( ~ sP411
| sP503 ),
inference(all_rule,[status(thm)],[]) ).
thf(134,plain,
( ~ sP230
| sP210 ),
inference(all_rule,[status(thm)],[]) ).
thf(135,plain,
( ~ sP918
| sP73 ),
inference(all_rule,[status(thm)],[]) ).
thf(136,plain,
( ~ sP1006
| sP619 ),
inference(all_rule,[status(thm)],[]) ).
thf(137,plain,
( ~ sP989
| sP199 ),
inference(all_rule,[status(thm)],[]) ).
thf(138,plain,
( ~ sP483
| sP127 ),
inference(all_rule,[status(thm)],[]) ).
thf(139,plain,
( ~ sP549
| sP302 ),
inference(all_rule,[status(thm)],[]) ).
thf(140,plain,
( ~ sP420
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(141,plain,
( ~ sP468
| sP215 ),
inference(all_rule,[status(thm)],[]) ).
thf(142,plain,
( ~ sP177
| sP522 ),
inference(all_rule,[status(thm)],[]) ).
thf(143,plain,
( ~ sP392
| sP300 ),
inference(all_rule,[status(thm)],[]) ).
thf(144,plain,
( ~ sP605
| sP870 ),
inference(all_rule,[status(thm)],[]) ).
thf(145,plain,
( ~ sP1042
| sP197 ),
inference(all_rule,[status(thm)],[]) ).
thf(146,plain,
( ~ sP1009
| sP174
| ~ sP121 ),
inference(prop_rule,[status(thm)],[]) ).
thf(147,plain,
( ~ sP561
| sP267 ),
inference(all_rule,[status(thm)],[]) ).
thf(148,plain,
( ~ sP820
| sP37
| ~ sP221 ),
inference(prop_rule,[status(thm)],[]) ).
thf(149,plain,
( ~ sP440
| sP798 ),
inference(all_rule,[status(thm)],[]) ).
thf(150,plain,
( ~ sP543
| sP69 ),
inference(all_rule,[status(thm)],[]) ).
thf(151,plain,
( ~ sP921
| sP233 ),
inference(all_rule,[status(thm)],[]) ).
thf(152,plain,
( ~ sP412
| sP593 ),
inference(all_rule,[status(thm)],[]) ).
thf(153,plain,
( ~ sP133
| sP247
| ~ sP121 ),
inference(prop_rule,[status(thm)],[]) ).
thf(154,plain,
( ~ sP1000
| sP366
| ~ sP508 ),
inference(prop_rule,[status(thm)],[]) ).
thf(155,plain,
( ~ sP168
| sP393
| ~ sP545 ),
inference(prop_rule,[status(thm)],[]) ).
thf(156,plain,
( ~ sP390
| sP629
| sP500 ),
inference(prop_rule,[status(thm)],[]) ).
thf(157,plain,
( ~ sP734
| sP390
| sP1038 ),
inference(prop_rule,[status(thm)],[]) ).
thf(158,plain,
( ~ sP761
| sP511
| sP770 ),
inference(prop_rule,[status(thm)],[]) ).
thf(159,plain,
( ~ sP138
| sP761
| sP262 ),
inference(prop_rule,[status(thm)],[]) ).
thf(160,plain,
( ~ sP12
| sP732
| sP633 ),
inference(prop_rule,[status(thm)],[]) ).
thf(161,plain,
( ~ sP179
| sP12
| sP329 ),
inference(prop_rule,[status(thm)],[]) ).
thf(162,plain,
( ~ sP623
| sP225
| sP678 ),
inference(prop_rule,[status(thm)],[]) ).
thf(163,plain,
( ~ sP442
| sP623
| sP523 ),
inference(prop_rule,[status(thm)],[]) ).
thf(164,plain,
( ~ sP597
| sP202 ),
inference(all_rule,[status(thm)],[]) ).
thf(165,plain,
( ~ sP597
| sP556 ),
inference(all_rule,[status(thm)],[]) ).
thf(166,plain,
( ~ sP597
| sP344 ),
inference(all_rule,[status(thm)],[]) ).
thf(167,plain,
( ~ sP597
| sP307 ),
inference(all_rule,[status(thm)],[]) ).
thf(168,plain,
( ~ sP539
| sP466 ),
inference(all_rule,[status(thm)],[]) ).
thf(169,plain,
( ~ sP539
| sP77 ),
inference(all_rule,[status(thm)],[]) ).
thf(170,plain,
( ~ sP539
| sP411 ),
inference(all_rule,[status(thm)],[]) ).
thf(171,plain,
( ~ sP579
| sP230 ),
inference(all_rule,[status(thm)],[]) ).
thf(172,plain,
( ~ sP579
| sP918 ),
inference(all_rule,[status(thm)],[]) ).
thf(173,plain,
( ~ sP571
| sP1006 ),
inference(all_rule,[status(thm)],[]) ).
thf(174,plain,
( ~ sP571
| sP989 ),
inference(all_rule,[status(thm)],[]) ).
thf(175,plain,
( ~ sP94
| sP478
| sP508 ),
inference(prop_rule,[status(thm)],[]) ).
thf(176,plain,
( ~ sP690
| sP94
| sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(177,plain,
( ~ sP818
| sP30
| ~ sP508 ),
inference(prop_rule,[status(thm)],[]) ).
thf(178,plain,
( ~ sP504
| sP818
| ~ sP754 ),
inference(prop_rule,[status(thm)],[]) ).
thf(179,plain,
( ~ sP756
| sP483 ),
inference(all_rule,[status(thm)],[]) ).
thf(180,plain,
( ~ sP333
| sP549 ),
inference(all_rule,[status(thm)],[]) ).
thf(181,plain,
( ~ sP985
| sP736
| sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(182,plain,
( ~ sP452
| sP985
| sP545 ),
inference(prop_rule,[status(thm)],[]) ).
thf(183,plain,
( ~ sP384
| sP1023
| ~ sP754 ),
inference(prop_rule,[status(thm)],[]) ).
thf(184,plain,
( ~ sP462
| sP384
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(185,plain,
( ~ sP530
| sP420 ),
inference(all_rule,[status(thm)],[]) ).
thf(186,plain,
( ~ sP184
| sP711
| sP121 ),
inference(prop_rule,[status(thm)],[]) ).
thf(187,plain,
( ~ sP208
| sP184
| sP951 ),
inference(prop_rule,[status(thm)],[]) ).
thf(188,plain,
( ~ sP51
| sP987
| ~ sP754 ),
inference(prop_rule,[status(thm)],[]) ).
thf(189,plain,
( ~ sP792
| sP51
| ~ sP121 ),
inference(prop_rule,[status(thm)],[]) ).
thf(190,plain,
( ~ sP259
| sP426
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(191,plain,
( ~ sP891
| sP259
| ~ sP508 ),
inference(prop_rule,[status(thm)],[]) ).
thf(192,plain,
( ~ sP955
| sP468 ),
inference(all_rule,[status(thm)],[]) ).
thf(193,plain,
( ~ sP775
| sP177 ),
inference(all_rule,[status(thm)],[]) ).
thf(194,plain,
( ~ sP775
| sP392 ),
inference(all_rule,[status(thm)],[]) ).
thf(195,plain,
( ~ sP775
| sP605 ),
inference(all_rule,[status(thm)],[]) ).
thf(196,plain,
( ~ sP775
| sP1042 ),
inference(all_rule,[status(thm)],[]) ).
thf(197,plain,
( ~ sP641
| sP1009
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(198,plain,
( ~ sP351
| sP561 ),
inference(all_rule,[status(thm)],[]) ).
thf(199,plain,
( ~ sP183
| sP791
| sP221 ),
inference(prop_rule,[status(thm)],[]) ).
thf(200,plain,
( ~ sP86
| sP183
| sP445 ),
inference(prop_rule,[status(thm)],[]) ).
thf(201,plain,
( ~ sP513
| sP311
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(202,plain,
( ~ sP618
| sP513
| ~ sP508 ),
inference(prop_rule,[status(thm)],[]) ).
thf(203,plain,
( ~ sP1021
| sP820 ),
inference(all_rule,[status(thm)],[]) ).
thf(204,plain,
( ~ sP438
| sP186
| ~ sP754 ),
inference(prop_rule,[status(thm)],[]) ).
thf(205,plain,
( ~ sP332
| sP438
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(206,plain,
( ~ sP488
| sP440 ),
inference(all_rule,[status(thm)],[]) ).
thf(207,plain,
( ~ sP31
| sP543 ),
inference(all_rule,[status(thm)],[]) ).
thf(208,plain,
( ~ sP31
| sP921 ),
inference(all_rule,[status(thm)],[]) ).
thf(209,plain,
( ~ sP31
| sP412 ),
inference(all_rule,[status(thm)],[]) ).
thf(210,plain,
( ~ sP143
| sP133
| ~ sP221 ),
inference(prop_rule,[status(thm)],[]) ).
thf(211,plain,
( ~ sP275
| sP1000
| ~ sP221 ),
inference(prop_rule,[status(thm)],[]) ).
thf(212,plain,
( ~ sP887
| sP721
| ~ sP754 ),
inference(prop_rule,[status(thm)],[]) ).
thf(213,plain,
( ~ sP367
| sP887
| ~ sP221 ),
inference(prop_rule,[status(thm)],[]) ).
thf(214,plain,
( ~ sP719
| sP168
| ~ sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(215,plain,
( ~ sP718
| sP668
| sP583 ),
inference(prop_rule,[status(thm)],[]) ).
thf(216,plain,
( ~ sP194
| sP718
| sP105 ),
inference(prop_rule,[status(thm)],[]) ).
thf(217,plain,
( ~ sP1027
| sP1024
| sP754 ),
inference(prop_rule,[status(thm)],[]) ).
thf(218,plain,
( ~ sP415
| sP734 ),
inference(all_rule,[status(thm)],[]) ).
thf(219,plain,
( ~ sP415
| sP138 ),
inference(all_rule,[status(thm)],[]) ).
thf(220,plain,
( ~ sP415
| sP194 ),
inference(all_rule,[status(thm)],[]) ).
thf(221,plain,
( ~ sP415
| sP179 ),
inference(all_rule,[status(thm)],[]) ).
thf(222,plain,
( ~ sP415
| sP442 ),
inference(all_rule,[status(thm)],[]) ).
thf(223,plain,
( ~ sP365
| sP1027
| sP676 ),
inference(prop_rule,[status(thm)],[]) ).
thf(224,plain,
( ~ sP954
| sP415 ),
inference(all_rule,[status(thm)],[]) ).
thf(225,plain,
( ~ sP336
| sP597 ),
inference(all_rule,[status(thm)],[]) ).
thf(226,plain,
( ~ sP612
| sP539 ),
inference(all_rule,[status(thm)],[]) ).
thf(227,plain,
( ~ sP938
| sP365 ),
inference(all_rule,[status(thm)],[]) ).
thf(228,plain,
( ~ sP764
| sP579 ),
inference(all_rule,[status(thm)],[]) ).
thf(229,plain,
( ~ sP346
| sP571 ),
inference(all_rule,[status(thm)],[]) ).
thf(230,plain,
( ~ sP22
| sP690 ),
inference(all_rule,[status(thm)],[]) ).
thf(231,plain,
( ~ sP116
| sP504 ),
inference(all_rule,[status(thm)],[]) ).
thf(232,plain,
( ~ sP949
| sP756 ),
inference(all_rule,[status(thm)],[]) ).
thf(233,plain,
( ~ sP874
| sP333 ),
inference(all_rule,[status(thm)],[]) ).
thf(234,plain,
( ~ sP5
| sP452 ),
inference(all_rule,[status(thm)],[]) ).
thf(235,plain,
( ~ sP382
| sP462 ),
inference(all_rule,[status(thm)],[]) ).
thf(236,plain,
( ~ sP931
| sP530 ),
inference(all_rule,[status(thm)],[]) ).
thf(237,plain,
( ~ sP867
| sP208 ),
inference(all_rule,[status(thm)],[]) ).
thf(238,plain,
( ~ sP114
| sP792 ),
inference(all_rule,[status(thm)],[]) ).
thf(239,plain,
( ~ sP548
| sP891 ),
inference(all_rule,[status(thm)],[]) ).
thf(240,plain,
( ~ sP252
| sP955 ),
inference(all_rule,[status(thm)],[]) ).
thf(241,plain,
( ~ sP982
| sP775 ),
inference(all_rule,[status(thm)],[]) ).
thf(242,plain,
( ~ sP310
| sP641 ),
inference(all_rule,[status(thm)],[]) ).
thf(243,plain,
( ~ sP78
| sP351 ),
inference(all_rule,[status(thm)],[]) ).
thf(244,plain,
( ~ sP630
| sP86 ),
inference(all_rule,[status(thm)],[]) ).
thf(245,plain,
( ~ sP396
| sP618 ),
inference(all_rule,[status(thm)],[]) ).
thf(246,plain,
( ~ sP851
| sP1021 ),
inference(all_rule,[status(thm)],[]) ).
thf(247,plain,
( ~ sP195
| sP332 ),
inference(all_rule,[status(thm)],[]) ).
thf(248,plain,
( ~ sP459
| sP488 ),
inference(all_rule,[status(thm)],[]) ).
thf(249,plain,
( ~ sP338
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(250,plain,
( ~ sP582
| sP143 ),
inference(all_rule,[status(thm)],[]) ).
thf(251,plain,
( ~ sP14
| sP275 ),
inference(all_rule,[status(thm)],[]) ).
thf(252,plain,
( ~ sP857
| sP367 ),
inference(all_rule,[status(thm)],[]) ).
thf(253,plain,
( ~ sP85
| sP719 ),
inference(all_rule,[status(thm)],[]) ).
thf(254,plain,
( ~ sP25
| ~ sP983
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(255,plain,
( ~ sP509
| sP25
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(256,plain,
( ~ sP207
| ~ sP463
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(257,plain,
( ~ sP345
| sP207
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(258,plain,
( ~ sP880
| ~ sP156
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(259,plain,
( ~ sP953
| sP880
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(260,plain,
( ~ sP1017
| sP509
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(261,plain,
( ~ sP740
| ~ sP983
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(262,plain,
( ~ sP450
| sP740
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(263,plain,
( ~ sP815
| sP450
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(264,plain,
( ~ sP410
| sP345
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(265,plain,
( ~ sP671
| ~ sP463
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(266,plain,
( ~ sP976
| sP671
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(267,plain,
( ~ sP4
| sP976
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(268,plain,
( ~ sP639
| ~ sP657
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(269,plain,
( ~ sP538
| sP639
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(270,plain,
( ~ sP146
| sP538
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(271,plain,
( ~ sP682
| ~ sP657
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(272,plain,
( ~ sP378
| sP682
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(273,plain,
( ~ sP229
| sP378
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(274,plain,
( ~ sP456
| sP953
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(275,plain,
( ~ sP331
| ~ sP156
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(276,plain,
( ~ sP325
| sP331
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(277,plain,
( ~ sP781
| sP325
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(278,plain,
( ~ sP39
| sP322
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(279,plain,
( ~ sP598
| ~ sP723
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(280,plain,
( ~ sP273
| sP598
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(281,plain,
( ~ sP884
| ~ sP489
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(282,plain,
( ~ sP28
| sP884
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(283,plain,
( ~ sP706
| ~ sP404
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(284,plain,
( ~ sP819
| sP706
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(285,plain,
( ~ sP79
| sP1017
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(286,plain,
( ~ sP435
| sP815
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(287,plain,
( ~ sP47
| sP410
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(288,plain,
( ~ sP58
| sP4
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(289,plain,
( ~ sP93
| sP146
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(290,plain,
( ~ sP828
| sP229
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(291,plain,
( ~ sP433
| sP456
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(292,plain,
( ~ sP847
| sP781
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(293,plain,
( ~ sP794
| ~ sP156
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(294,plain,
( ~ sP322
| sP794
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(295,plain,
( ~ sP306
| sP39
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(296,plain,
( ~ sP182
| sP484
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(297,plain,
( ~ sP266
| ~ sP692
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(298,plain,
( ~ sP484
| sP266
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(299,plain,
( ~ sP492
| sP1034
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(300,plain,
( ~ sP250
| ~ sP692
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(301,plain,
( ~ sP1034
| sP250
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(302,plain,
( ~ sP376
| sP113
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(303,plain,
( ~ sP17
| ~ sP692
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(304,plain,
( ~ sP113
| sP17
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(305,plain,
( ~ sP231
| sP273
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(306,plain,
( ~ sP443
| sP273
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(307,plain,
( ~ sP393
| sP61
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(308,plain,
( ~ sP855
| sP61
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(309,plain,
( ~ sP149
| ~ sP723
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(310,plain,
( ~ sP61
| sP149
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(311,plain,
( ~ sP91
| sP61
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(312,plain,
( ~ sP224
| sP153
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(313,plain,
( ~ sP507
| sP153
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(314,plain,
( ~ sP1041
| sP28
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(315,plain,
( ~ sP796
| sP107
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(316,plain,
( ~ sP122
| ~ sP489
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(317,plain,
( ~ sP107
| sP122
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(318,plain,
( ~ sP737
| ~ sP150
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(319,plain,
( ~ sP731
| sP737
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(320,plain,
( ~ sP958
| ~ sP700
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(321,plain,
( ~ sP876
| sP958
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(322,plain,
( ~ sP681
| sP819
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(323,plain,
( ~ sP730
| sP33
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(324,plain,
( ~ sP766
| ~ sP404
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(325,plain,
( ~ sP33
| sP766
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(326,plain,
( ~ sP656
| ~ sP650
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(327,plain,
( ~ sP134
| sP656
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(328,plain,
( ~ sP889
| sP79
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(329,plain,
( ~ sP242
| sP435
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(330,plain,
( ~ sP115
| sP47
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(331,plain,
( ~ sP1014
| sP58
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(332,plain,
( ~ sP82
| sP93
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(333,plain,
( ~ sP895
| sP828
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(334,plain,
( ~ sP16
| sP433
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(335,plain,
( ~ sP529
| sP847
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(336,plain,
( ~ sP430
| sP306
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(337,plain,
( ~ sP88
| sP182
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(338,plain,
( ~ sP831
| sP492
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(339,plain,
( ~ sP702
| sP376
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(340,plain,
( ~ sP806
| sP355
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(341,plain,
( ~ sP201
| ~ sP585
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(342,plain,
( ~ sP355
| sP201
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(343,plain,
( ~ sP90
| sP231
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(344,plain,
( ~ sP824
| sP443
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(345,plain,
( ~ sP524
| sP393
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(346,plain,
( ~ sP1005
| sP855
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(347,plain,
( ~ sP696
| sP91
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(348,plain,
( ~ sP570
| sP224
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(349,plain,
( ~ sP894
| ~ sP723
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(350,plain,
( ~ sP153
| sP894
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(351,plain,
( ~ sP206
| sP507
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(352,plain,
( ~ sP934
| sP979
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(353,plain,
( ~ sP470
| ~ sP685
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(354,plain,
( ~ sP979
| sP470
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(355,plain,
( ~ sP372
| sP743
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(356,plain,
( ~ sP679
| sP743
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(357,plain,
( ~ sP97
| ~ sP448
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(358,plain,
( ~ sP743
| sP97
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(359,plain,
( ~ sP142
| sP407
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(360,plain,
( ~ sP67
| ~ sP285
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(361,plain,
( ~ sP407
| sP67
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(362,plain,
( ~ sP644
| sP1041
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(363,plain,
( ~ sP465
| sP796
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(364,plain,
( ~ sP92
| sP856
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(365,plain,
( ~ sP776
| ~ sP853
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(366,plain,
( ~ sP856
| sP776
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(367,plain,
( ~ sP102
| sP726
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(368,plain,
( ~ sP850
| ~ sP606
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(369,plain,
( ~ sP726
| sP850
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(370,plain,
( ~ sP604
| sP731
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(371,plain,
( ~ sP638
| sP876
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(372,plain,
( ~ sP403
| sP834
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(373,plain,
( ~ sP578
| ~ sP280
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(374,plain,
( ~ sP834
| sP578
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(375,plain,
( ~ sP830
| sP681
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(376,plain,
( ~ sP364
| sP730
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(377,plain,
( ~ sP439
| sP330
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(378,plain,
( ~ sP118
| ~ sP479
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(379,plain,
( ~ sP330
| sP118
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(380,plain,
( ~ sP774
| sP134
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(381,plain,
( ~ sP19
| sP799
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(382,plain,
( ~ sP799
| ~ sP773
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(383,plain,
( ~ sP759
| sP833
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(384,plain,
( ~ sP879
| sP482
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(385,plain,
( ~ sP670
| sP889 ),
inference(all_rule,[status(thm)],[]) ).
thf(386,plain,
( ~ sP926
| sP242 ),
inference(all_rule,[status(thm)],[]) ).
thf(387,plain,
( ~ sP946
| sP115 ),
inference(all_rule,[status(thm)],[]) ).
thf(388,plain,
( ~ sP829
| sP1014 ),
inference(all_rule,[status(thm)],[]) ).
thf(389,plain,
( ~ sP749
| sP82 ),
inference(all_rule,[status(thm)],[]) ).
thf(390,plain,
( ~ sP297
| sP895 ),
inference(all_rule,[status(thm)],[]) ).
thf(391,plain,
( ~ sP603
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(392,plain,
( ~ sP960
| sP529 ),
inference(all_rule,[status(thm)],[]) ).
thf(393,plain,
( ~ sP542
| sP430 ),
inference(all_rule,[status(thm)],[]) ).
thf(394,plain,
( ~ sP917
| sP88
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(395,plain,
( ~ sP228
| sP831
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(396,plain,
( ~ sP888
| sP702
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(397,plain,
( ~ sP993
| sP839
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(398,plain,
( ~ sP136
| sP806
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(399,plain,
( ~ sP350
| sP90
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(400,plain,
( ~ sP722
| sP824
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(401,plain,
( ~ sP608
| sP524
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(402,plain,
( ~ sP1045
| sP1005
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(403,plain,
( ~ sP413
| sP696
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(404,plain,
( ~ sP600
| sP570
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(405,plain,
( ~ sP44
| sP206
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(406,plain,
( ~ sP460
| sP934
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(407,plain,
( ~ sP120
| sP862
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(408,plain,
( ~ sP323
| sP372
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(409,plain,
( ~ sP269
| sP679
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(410,plain,
( ~ sP171
| sP142
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(411,plain,
( ~ sP933
| sP644
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(412,plain,
( ~ sP814
| sP465
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(413,plain,
( ~ sP758
| sP92
| ~ sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(414,plain,
( ~ sP135
| sP102
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(415,plain,
( ~ sP247
| ~ sP769
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(416,plain,
( ~ sP289
| sP975
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(417,plain,
( ~ sP975
| ~ sP769
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(418,plain,
( ~ sP348
| sP604
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(419,plain,
( ~ sP244
| sP638
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(420,plain,
( ~ sP398
| sP403
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(421,plain,
( ~ sP363
| sP830
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(422,plain,
( ~ sP510
| sP364
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(423,plain,
( ~ sP299
| sP575
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(424,plain,
( ~ sP321
| sP439
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(425,plain,
( ~ sP9
| sP774
| ~ sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(426,plain,
( ~ sP610
| sP19
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(427,plain,
( ~ sP581
| sP858
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(428,plain,
( ~ sP18
| sP581
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(429,plain,
( ~ sP858
| ~ sP773
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(430,plain,
( ~ sP534
| sP759
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(431,plain,
( ~ sP833
| ~ sP70
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(432,plain,
( ~ sP446
| sP327
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(433,plain,
( ~ sP189
| sP446
| ~ sP842 ),
inference(prop_rule,[status(thm)],[]) ).
thf(434,plain,
( ~ sP327
| ~ sP70
| ~ sP842 ),
inference(prop_rule,[status(thm)],[]) ).
thf(435,plain,
( ~ sP537
| ~ sP70
| ~ sP461 ),
inference(prop_rule,[status(thm)],[]) ).
thf(436,plain,
( ~ sP780
| sP537
| ~ sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(437,plain,
( ~ sP170
| sP780
| ~ sP461 ),
inference(prop_rule,[status(thm)],[]) ).
thf(438,plain,
( ~ sP584
| sP879
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(439,plain,
( ~ sP482
| ~ sP652
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(440,plain,
( ~ sP220
| sP429
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(441,plain,
( ~ sP733
| sP220
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(442,plain,
( ~ sP429
| ~ sP652
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(443,plain,
( ~ sP878
| sP670 ),
inference(all_rule,[status(thm)],[]) ).
thf(444,plain,
( ~ sP191
| sP926 ),
inference(all_rule,[status(thm)],[]) ).
thf(445,plain,
( ~ sP418
| sP946 ),
inference(all_rule,[status(thm)],[]) ).
thf(446,plain,
( ~ sP701
| sP829 ),
inference(all_rule,[status(thm)],[]) ).
thf(447,plain,
( ~ sP913
| sP749 ),
inference(all_rule,[status(thm)],[]) ).
thf(448,plain,
( ~ sP804
| sP297 ),
inference(all_rule,[status(thm)],[]) ).
thf(449,plain,
( ~ sP188
| sP603 ),
inference(all_rule,[status(thm)],[]) ).
thf(450,plain,
( ~ sP915
| sP960 ),
inference(all_rule,[status(thm)],[]) ).
thf(451,plain,
( ~ sP154
| sP542 ),
inference(all_rule,[status(thm)],[]) ).
thf(452,plain,
( ~ sP843
| sP810
| ~ sP1026 ),
inference(prop_rule,[status(thm)],[]) ).
thf(453,plain,
( ~ sP178
| sP843
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(454,plain,
( ~ sP810
| ~ sP970
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(455,plain,
( ~ sP324
| sP998
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(456,plain,
( ~ sP502
| sP324
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(457,plain,
( ~ sP998
| ~ sP970
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(458,plain,
( ~ sP721
| ~ sP970
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(459,plain,
( ~ sP965
| sP613
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(460,plain,
( ~ sP710
| sP965
| ~ sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(461,plain,
( ~ sP613
| ~ sP970
| ~ sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(462,plain,
( ~ sP937
| sP917 ),
inference(all_rule,[status(thm)],[]) ).
thf(463,plain,
( ~ sP521
| sP228 ),
inference(all_rule,[status(thm)],[]) ).
thf(464,plain,
( ~ sP290
| sP888 ),
inference(all_rule,[status(thm)],[]) ).
thf(465,plain,
( ~ sP383
| sP993
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(466,plain,
( ~ sP839
| ~ sP60
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(467,plain,
( ~ sP675
| sP625
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(468,plain,
( ~ sP707
| sP675
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(469,plain,
( ~ sP625
| ~ sP60
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(470,plain,
( ~ sP449
| sP1007
| ~ sP821 ),
inference(prop_rule,[status(thm)],[]) ).
thf(471,plain,
( ~ sP6
| sP449
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(472,plain,
( ~ sP1007
| ~ sP60
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(473,plain,
( ~ sP366
| ~ sP60
| ~ sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(474,plain,
( ~ sP745
| sP136
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(475,plain,
( ~ sP139
| sP350 ),
inference(all_rule,[status(thm)],[]) ).
thf(476,plain,
( ~ sP646
| sP722 ),
inference(all_rule,[status(thm)],[]) ).
thf(477,plain,
( ~ sP85
| sP608 ),
inference(all_rule,[status(thm)],[]) ).
thf(478,plain,
( ~ sP354
| sP1045 ),
inference(all_rule,[status(thm)],[]) ).
thf(479,plain,
( ~ sP494
| sP413 ),
inference(all_rule,[status(thm)],[]) ).
thf(480,plain,
( ~ sP840
| sP600 ),
inference(all_rule,[status(thm)],[]) ).
thf(481,plain,
( ~ sP563
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(482,plain,
( ~ sP959
| sP460
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(483,plain,
( ~ sP408
| sP120
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(484,plain,
( ~ sP862
| ~ sP57
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(485,plain,
( ~ sP694
| sP738
| ~ sP842 ),
inference(prop_rule,[status(thm)],[]) ).
thf(486,plain,
( ~ sP609
| sP694
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(487,plain,
( ~ sP738
| ~ sP57
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(488,plain,
( ~ sP1033
| ~ sP57
| ~ sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(489,plain,
( ~ sP948
| sP1033
| ~ sP461 ),
inference(prop_rule,[status(thm)],[]) ).
thf(490,plain,
( ~ sP1037
| sP948
| ~ sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(491,plain,
( ~ sP218
| sP323
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(492,plain,
( ~ sP666
| sP269
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(493,plain,
( ~ sP76
| sP171
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(494,plain,
( ~ sP712
| sP933 ),
inference(all_rule,[status(thm)],[]) ).
thf(495,plain,
( ~ sP169
| sP814 ),
inference(all_rule,[status(thm)],[]) ).
thf(496,plain,
( ~ sP84
| sP335
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(497,plain,
( ~ sP335
| sP152
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(498,plain,
( ~ sP305
| sP758
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(499,plain,
( ~ sP972
| sP135
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(500,plain,
( ~ sP265
| sP289
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(501,plain,
( ~ sP528
| sP141
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(502,plain,
( ~ sP80
| sP528
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(503,plain,
( ~ sP141
| ~ sP769
| ~ sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(504,plain,
( ~ sP789
| sP72
| ~ sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(505,plain,
( ~ sP241
| sP348
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(506,plain,
( ~ sP924
| sP296
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(507,plain,
( ~ sP487
| sP244
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(508,plain,
( ~ sP677
| sP223
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(509,plain,
( ~ sP125
| sP398
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(510,plain,
( ~ sP518
| sP363 ),
inference(all_rule,[status(thm)],[]) ).
thf(511,plain,
( ~ sP621
| sP510 ),
inference(all_rule,[status(thm)],[]) ).
thf(512,plain,
( ~ sP901
| sP343
| ~ sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(513,plain,
( ~ sP573
| sP299
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(514,plain,
( ~ sP686
| sP321
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(515,plain,
( ~ sP56
| sP9
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(516,plain,
( ~ sP626
| sP622
| ~ sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(517,plain,
( ~ sP1032
| sP626
| ~ sP1026 ),
inference(prop_rule,[status(thm)],[]) ).
thf(518,plain,
( ~ sP622
| ~ sP291
| ~ sP1026 ),
inference(prop_rule,[status(thm)],[]) ).
thf(519,plain,
( ~ sP785
| sP96
| ~ sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(520,plain,
( ~ sP565
| sP785
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(521,plain,
( ~ sP371
| sP610 ),
inference(all_rule,[status(thm)],[]) ).
thf(522,plain,
( ~ sP695
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(523,plain,
( ~ sP546
| sP534 ),
inference(all_rule,[status(thm)],[]) ).
thf(524,plain,
( ~ sP1018
| sP189 ),
inference(all_rule,[status(thm)],[]) ).
thf(525,plain,
( ~ sP991
| sP170 ),
inference(all_rule,[status(thm)],[]) ).
thf(526,plain,
( ~ sP932
| sP584 ),
inference(all_rule,[status(thm)],[]) ).
thf(527,plain,
( ~ sP32
| sP733 ),
inference(all_rule,[status(thm)],[]) ).
thf(528,plain,
( ~ sP496
| sP878 ),
inference(all_rule,[status(thm)],[]) ).
thf(529,plain,
( ~ sP496
| sP191 ),
inference(all_rule,[status(thm)],[]) ).
thf(530,plain,
( ~ sP899
| sP418 ),
inference(all_rule,[status(thm)],[]) ).
thf(531,plain,
( ~ sP899
| sP701 ),
inference(all_rule,[status(thm)],[]) ).
thf(532,plain,
( ~ sP942
| sP913 ),
inference(all_rule,[status(thm)],[]) ).
thf(533,plain,
( ~ sP942
| sP804 ),
inference(all_rule,[status(thm)],[]) ).
thf(534,plain,
( ~ sP64
| sP188 ),
inference(all_rule,[status(thm)],[]) ).
thf(535,plain,
( ~ sP64
| sP915 ),
inference(all_rule,[status(thm)],[]) ).
thf(536,plain,
( ~ sP64
| sP154 ),
inference(all_rule,[status(thm)],[]) ).
thf(537,plain,
( ~ sP304
| sP178 ),
inference(all_rule,[status(thm)],[]) ).
thf(538,plain,
( ~ sP897
| sP502 ),
inference(all_rule,[status(thm)],[]) ).
thf(539,plain,
( ~ sP587
| sP710 ),
inference(all_rule,[status(thm)],[]) ).
thf(540,plain,
( ~ sP193
| sP937 ),
inference(all_rule,[status(thm)],[]) ).
thf(541,plain,
( ~ sP24
| sP521 ),
inference(all_rule,[status(thm)],[]) ).
thf(542,plain,
( ~ sP914
| sP290 ),
inference(all_rule,[status(thm)],[]) ).
thf(543,plain,
( ~ sP387
| sP383 ),
inference(all_rule,[status(thm)],[]) ).
thf(544,plain,
( ~ sP567
| sP707 ),
inference(all_rule,[status(thm)],[]) ).
thf(545,plain,
( ~ sP594
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(546,plain,
( ~ sP669
| sP745 ),
inference(all_rule,[status(thm)],[]) ).
thf(547,plain,
( ~ sP994
| sP139 ),
inference(all_rule,[status(thm)],[]) ).
thf(548,plain,
( ~ sP994
| sP646 ),
inference(all_rule,[status(thm)],[]) ).
thf(549,plain,
( ~ sP128
| sP85 ),
inference(all_rule,[status(thm)],[]) ).
thf(550,plain,
( ~ sP128
| sP354 ),
inference(all_rule,[status(thm)],[]) ).
thf(551,plain,
( ~ sP128
| sP494 ),
inference(all_rule,[status(thm)],[]) ).
thf(552,plain,
( ~ sP779
| sP840 ),
inference(all_rule,[status(thm)],[]) ).
thf(553,plain,
( ~ sP779
| sP563 ),
inference(all_rule,[status(thm)],[]) ).
thf(554,plain,
( ~ sP314
| sP959 ),
inference(all_rule,[status(thm)],[]) ).
thf(555,plain,
( ~ sP1011
| ~ sP270
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(556,plain,
( ~ sP2
| sP1011
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(557,plain,
( ~ sP475
| sP2
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(558,plain,
( ~ sP251
| sP186
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(559,plain,
( ~ sP893
| sP251
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(560,plain,
( ~ sP945
| sP408 ),
inference(all_rule,[status(thm)],[]) ).
thf(561,plain,
( ~ sP254
| sP609 ),
inference(all_rule,[status(thm)],[]) ).
thf(562,plain,
( ~ sP341
| sP1037 ),
inference(all_rule,[status(thm)],[]) ).
thf(563,plain,
( ~ sP311
| ~ sP461
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(564,plain,
( ~ sP844
| sP311
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(565,plain,
( ~ sP890
| sP844
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(566,plain,
( ~ sP520
| sP218 ),
inference(all_rule,[status(thm)],[]) ).
thf(567,plain,
( ~ sP860
| sP666 ),
inference(all_rule,[status(thm)],[]) ).
thf(568,plain,
( ~ sP145
| sP76 ),
inference(all_rule,[status(thm)],[]) ).
thf(569,plain,
( ~ sP872
| sP712 ),
inference(all_rule,[status(thm)],[]) ).
thf(570,plain,
( ~ sP859
| sP169 ),
inference(all_rule,[status(thm)],[]) ).
thf(571,plain,
( ~ sP1029
| sP84
| ~ sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(572,plain,
( ~ sP111
| sP305 ),
inference(all_rule,[status(thm)],[]) ).
thf(573,plain,
( ~ sP8
| sP972 ),
inference(all_rule,[status(thm)],[]) ).
thf(574,plain,
( ~ sP258
| ~ sP1026
| ~ sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(575,plain,
( ~ sP512
| sP258
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(576,plain,
( ~ sP167
| sP512
| ~ sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(577,plain,
( ~ sP892
| sP265 ),
inference(all_rule,[status(thm)],[]) ).
thf(578,plain,
( ~ sP832
| sP80 ),
inference(all_rule,[status(thm)],[]) ).
thf(579,plain,
( ~ sP72
| ~ sP288
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(580,plain,
( ~ sP381
| sP789
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(581,plain,
( ~ sP272
| sP298
| ~ sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(582,plain,
( ~ sP742
| sP272
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(583,plain,
( ~ sP292
| sP241 ),
inference(all_rule,[status(thm)],[]) ).
thf(584,plain,
( ~ sP964
| sP962
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(585,plain,
( ~ sP296
| ~ sP213
| ~ sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(586,plain,
( ~ sP1036
| sP924
| ~ sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(587,plain,
( ~ sP238
| sP487 ),
inference(all_rule,[status(thm)],[]) ).
thf(588,plain,
( ~ sP223
| ~ sP562
| ~ sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(589,plain,
( ~ sP969
| sP677
| ~ sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(590,plain,
( ~ sP984
| sP125 ),
inference(all_rule,[status(thm)],[]) ).
thf(591,plain,
( ~ sP978
| sP518 ),
inference(all_rule,[status(thm)],[]) ).
thf(592,plain,
( ~ sP219
| sP621 ),
inference(all_rule,[status(thm)],[]) ).
thf(593,plain,
( ~ sP343
| ~ sP49
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(594,plain,
( ~ sP264
| sP901
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(595,plain,
( ~ sP569
| sP474
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(596,plain,
( ~ sP673
| sP778
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(597,plain,
( ~ sP157
| sP573
| ~ sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(598,plain,
( ~ sP3
| sP686 ),
inference(all_rule,[status(thm)],[]) ).
thf(599,plain,
( ~ sP544
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(600,plain,
( ~ sP386
| sP434
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(601,plain,
( ~ sP1039
| sP318
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(602,plain,
( ~ sP990
| sP967
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(603,plain,
( ~ sP317
| sP793
| ~ sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(604,plain,
( ~ sP795
| sP317
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(605,plain,
( ~ sP132
| sP1032 ),
inference(all_rule,[status(thm)],[]) ).
thf(606,plain,
( ~ sP96
| ~ sP291
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(607,plain,
( ~ sP699
| sP565 ),
inference(all_rule,[status(thm)],[]) ).
thf(608,plain,
( ~ sP377
| sP245
| sP773 ),
inference(prop_rule,[status(thm)],[]) ).
thf(609,plain,
( ~ sP930
| sP377
| sP983 ),
inference(prop_rule,[status(thm)],[]) ).
thf(610,plain,
( ~ sP865
| sP910
| sP70 ),
inference(prop_rule,[status(thm)],[]) ).
thf(611,plain,
( ~ sP159
| sP865
| sP463 ),
inference(prop_rule,[status(thm)],[]) ).
thf(612,plain,
( ~ sP246
| sP371 ),
inference(all_rule,[status(thm)],[]) ).
thf(613,plain,
( ~ sP246
| sP695 ),
inference(all_rule,[status(thm)],[]) ).
thf(614,plain,
( ~ sP66
| sP546 ),
inference(all_rule,[status(thm)],[]) ).
thf(615,plain,
( ~ sP66
| sP1018 ),
inference(all_rule,[status(thm)],[]) ).
thf(616,plain,
( ~ sP66
| sP991 ),
inference(all_rule,[status(thm)],[]) ).
thf(617,plain,
( ~ sP636
| sP932 ),
inference(all_rule,[status(thm)],[]) ).
thf(618,plain,
( ~ sP636
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(619,plain,
( ~ sP782
| sP352
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(620,plain,
( ~ sP55
| sP782
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(621,plain,
( ~ sP406
| sP1003
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(622,plain,
( ~ sP283
| sP406
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(623,plain,
( ~ sP649
| sP301
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(624,plain,
( ~ sP827
| sP649
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(625,plain,
( ~ sP338
| sP496 ),
inference(all_rule,[status(thm)],[]) ).
thf(626,plain,
( ~ sP338
| sP899 ),
inference(all_rule,[status(thm)],[]) ).
thf(627,plain,
( ~ sP338
| sP942 ),
inference(all_rule,[status(thm)],[]) ).
thf(628,plain,
( ~ sP338
| sP64 ),
inference(all_rule,[status(thm)],[]) ).
thf(629,plain,
( ~ sP837
| sP304 ),
inference(all_rule,[status(thm)],[]) ).
thf(630,plain,
( ~ sP837
| sP897 ),
inference(all_rule,[status(thm)],[]) ).
thf(631,plain,
( ~ sP837
| sP857 ),
inference(all_rule,[status(thm)],[]) ).
thf(632,plain,
( ~ sP837
| sP587 ),
inference(all_rule,[status(thm)],[]) ).
thf(633,plain,
( ~ sP459
| sP193 ),
inference(all_rule,[status(thm)],[]) ).
thf(634,plain,
( ~ sP459
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(635,plain,
( ~ sP459
| sP914 ),
inference(all_rule,[status(thm)],[]) ).
thf(636,plain,
( ~ sP809
| sP387 ),
inference(all_rule,[status(thm)],[]) ).
thf(637,plain,
( ~ sP809
| sP567 ),
inference(all_rule,[status(thm)],[]) ).
thf(638,plain,
( ~ sP809
| sP594 ),
inference(all_rule,[status(thm)],[]) ).
thf(639,plain,
( ~ sP809
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(640,plain,
( ~ sP836
| sP669 ),
inference(all_rule,[status(thm)],[]) ).
thf(641,plain,
( ~ sP536
| sP994 ),
inference(all_rule,[status(thm)],[]) ).
thf(642,plain,
( ~ sP536
| sP128 ),
inference(all_rule,[status(thm)],[]) ).
thf(643,plain,
( ~ sP536
| sP779 ),
inference(all_rule,[status(thm)],[]) ).
thf(644,plain,
( ~ sP516
| sP314 ),
inference(all_rule,[status(thm)],[]) ).
thf(645,plain,
( ~ sP227
| sP475 ),
inference(all_rule,[status(thm)],[]) ).
thf(646,plain,
( ~ sP186
| ~ sP514
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(647,plain,
( ~ sP195
| sP893 ),
inference(all_rule,[status(thm)],[]) ).
thf(648,plain,
( ~ sP851
| sP945 ),
inference(all_rule,[status(thm)],[]) ).
thf(649,plain,
( ~ sP851
| sP254 ),
inference(all_rule,[status(thm)],[]) ).
thf(650,plain,
( ~ sP851
| sP341 ),
inference(all_rule,[status(thm)],[]) ).
thf(651,plain,
( ~ sP162
| sP1040
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(652,plain,
( ~ sP110
| sP162
| sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(653,plain,
( ~ sP396
| sP890 ),
inference(all_rule,[status(thm)],[]) ).
thf(654,plain,
( ~ sP1019
| sP520 ),
inference(all_rule,[status(thm)],[]) ).
thf(655,plain,
( ~ sP1019
| sP860 ),
inference(all_rule,[status(thm)],[]) ).
thf(656,plain,
( ~ sP7
| sP145 ),
inference(all_rule,[status(thm)],[]) ).
thf(657,plain,
( ~ sP801
| sP872 ),
inference(all_rule,[status(thm)],[]) ).
thf(658,plain,
( ~ sP801
| sP859 ),
inference(all_rule,[status(thm)],[]) ).
thf(659,plain,
( ~ sP13
| sP1029 ),
inference(all_rule,[status(thm)],[]) ).
thf(660,plain,
( ~ sP417
| sP111 ),
inference(all_rule,[status(thm)],[]) ).
thf(661,plain,
( ~ sP209
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(662,plain,
( ~ sP995
| sP167 ),
inference(all_rule,[status(thm)],[]) ).
thf(663,plain,
( ~ sP714
| sP582 ),
inference(all_rule,[status(thm)],[]) ).
thf(664,plain,
( ~ sP714
| sP892 ),
inference(all_rule,[status(thm)],[]) ).
thf(665,plain,
( ~ sP714
| sP832 ),
inference(all_rule,[status(thm)],[]) ).
thf(666,plain,
( ~ sP98
| sP849
| sP769 ),
inference(prop_rule,[status(thm)],[]) ).
thf(667,plain,
( ~ sP868
| sP98
| sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(668,plain,
( ~ sP214
| sP381 ),
inference(all_rule,[status(thm)],[]) ).
thf(669,plain,
( ~ sP298
| ~ sP334
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(670,plain,
( ~ sP1022
| sP742 ),
inference(all_rule,[status(thm)],[]) ).
thf(671,plain,
( ~ sP640
| sP292 ),
inference(all_rule,[status(thm)],[]) ).
thf(672,plain,
( ~ sP485
| sP964
| ~ sP404 ),
inference(prop_rule,[status(thm)],[]) ).
thf(673,plain,
( ~ sP772
| sP1036 ),
inference(all_rule,[status(thm)],[]) ).
thf(674,plain,
( ~ sP944
| sP238 ),
inference(all_rule,[status(thm)],[]) ).
thf(675,plain,
( ~ sP53
| sP969 ),
inference(all_rule,[status(thm)],[]) ).
thf(676,plain,
( ~ sP471
| sP984 ),
inference(all_rule,[status(thm)],[]) ).
thf(677,plain,
( ~ sP75
| sP978 ),
inference(all_rule,[status(thm)],[]) ).
thf(678,plain,
( ~ sP75
| sP219 ),
inference(all_rule,[status(thm)],[]) ).
thf(679,plain,
( ~ sP158
| sP264 ),
inference(all_rule,[status(thm)],[]) ).
thf(680,plain,
( ~ sP342
| sP569
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(681,plain,
( ~ sP71
| sP673
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(682,plain,
( ~ sP771
| sP157 ),
inference(all_rule,[status(thm)],[]) ).
thf(683,plain,
( ~ sP212
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(684,plain,
( ~ sP11
| sP544 ),
inference(all_rule,[status(thm)],[]) ).
thf(685,plain,
( ~ sP260
| sP386
| ~ sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(686,plain,
( ~ sP927
| sP1039
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(687,plain,
( ~ sP373
| sP990
| ~ sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(688,plain,
( ~ sP793
| ~ sP291
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(689,plain,
( ~ sP352
| ~ sP83
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(690,plain,
( ~ sP1003
| ~ sP821
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(691,plain,
( ~ sP301
| ~ sP842
| ~ sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(692,plain,
( ~ sP405
| sP660
| sP291 ),
inference(prop_rule,[status(thm)],[]) ).
thf(693,plain,
( ~ sP437
| sP777
| sP652 ),
inference(prop_rule,[status(thm)],[]) ).
thf(694,plain,
( ~ sP200
| sP795 ),
inference(all_rule,[status(thm)],[]) ).
thf(695,plain,
( ~ sP903
| ~ sP225
| sP245 ),
inference(prop_rule,[status(thm)],[]) ).
thf(696,plain,
( ~ sP533
| ~ sP629
| sP910 ),
inference(prop_rule,[status(thm)],[]) ).
thf(697,plain,
( ~ sP425
| ~ sP732
| sP660 ),
inference(prop_rule,[status(thm)],[]) ).
thf(698,plain,
( ~ sP838
| ~ sP511
| sP777 ),
inference(prop_rule,[status(thm)],[]) ).
thf(699,plain,
( ~ sP813
| sP405
| sP657 ),
inference(prop_rule,[status(thm)],[]) ).
thf(700,plain,
( ~ sP131
| sP437
| sP156 ),
inference(prop_rule,[status(thm)],[]) ).
thf(701,plain,
( ~ sP886
| sP132 ),
inference(all_rule,[status(thm)],[]) ).
thf(702,plain,
( ~ sP886
| sP699 ),
inference(all_rule,[status(thm)],[]) ).
thf(703,plain,
( ~ sP886
| sP200 ),
inference(all_rule,[status(thm)],[]) ).
thf(704,plain,
( ~ sP303
| sP161
| sP970 ),
inference(prop_rule,[status(thm)],[]) ).
thf(705,plain,
( ~ sP370
| sP281
| sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(706,plain,
( ~ sP711
| sP629 ),
inference(symeq,[status(thm)],[]) ).
thf(707,plain,
( ~ sP791
| sP225 ),
inference(symeq,[status(thm)],[]) ).
thf(708,plain,
( ~ sP175
| sP903 ),
inference(all_rule,[status(thm)],[]) ).
thf(709,plain,
( ~ sP175
| sP533 ),
inference(all_rule,[status(thm)],[]) ).
thf(710,plain,
( ~ sP175
| sP425 ),
inference(all_rule,[status(thm)],[]) ).
thf(711,plain,
( ~ sP175
| sP838 ),
inference(all_rule,[status(thm)],[]) ).
thf(712,plain,
( ~ sP630
| sP930 ),
inference(all_rule,[status(thm)],[]) ).
thf(713,plain,
( ~ sP630
| sP159 ),
inference(all_rule,[status(thm)],[]) ).
thf(714,plain,
( ~ sP630
| sP813 ),
inference(all_rule,[status(thm)],[]) ).
thf(715,plain,
( ~ sP630
| sP131 ),
inference(all_rule,[status(thm)],[]) ).
thf(716,plain,
( ~ sP78
| sP246 ),
inference(all_rule,[status(thm)],[]) ).
thf(717,plain,
( ~ sP78
| sP66 ),
inference(all_rule,[status(thm)],[]) ).
thf(718,plain,
( ~ sP78
| sP886 ),
inference(all_rule,[status(thm)],[]) ).
thf(719,plain,
( ~ sP78
| sP636 ),
inference(all_rule,[status(thm)],[]) ).
thf(720,plain,
( ~ sP478
| sP732 ),
inference(symeq,[status(thm)],[]) ).
thf(721,plain,
( ~ sP217
| sP303
| sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(722,plain,
( ~ sP736
| sP511 ),
inference(symeq,[status(thm)],[]) ).
thf(723,plain,
( ~ sP232
| sP55 ),
inference(all_rule,[status(thm)],[]) ).
thf(724,plain,
( ~ sP360
| sP370
| sP723 ),
inference(prop_rule,[status(thm)],[]) ).
thf(725,plain,
( ~ sP674
| sP283 ),
inference(all_rule,[status(thm)],[]) ).
thf(726,plain,
( ~ sP192
| sP827 ),
inference(all_rule,[status(thm)],[]) ).
thf(727,plain,
( ~ sP1024
| sP668 ),
inference(symeq,[status(thm)],[]) ).
thf(728,plain,
( ~ sP249
| ~ sP668 ),
inference(all_rule,[status(thm)],[]) ).
thf(729,plain,
( ~ sP1
| sP175 ),
inference(all_rule,[status(thm)],[]) ).
thf(730,plain,
( ~ sP954
| sP630 ),
inference(all_rule,[status(thm)],[]) ).
thf(731,plain,
( ~ sP336
| sP78 ),
inference(all_rule,[status(thm)],[]) ).
thf(732,plain,
( ~ sP672
| sP338 ),
inference(all_rule,[status(thm)],[]) ).
thf(733,plain,
( ~ sP612
| sP837 ),
inference(all_rule,[status(thm)],[]) ).
thf(734,plain,
( ~ sP938
| sP217 ),
inference(all_rule,[status(thm)],[]) ).
thf(735,plain,
( ~ sP764
| sP459 ),
inference(all_rule,[status(thm)],[]) ).
thf(736,plain,
( ~ sP29
| sP232 ),
inference(all_rule,[status(thm)],[]) ).
thf(737,plain,
( ~ sP346
| sP809 ),
inference(all_rule,[status(thm)],[]) ).
thf(738,plain,
( ~ sP22
| sP360 ),
inference(all_rule,[status(thm)],[]) ).
thf(739,plain,
( ~ sP577
| sP674 ),
inference(all_rule,[status(thm)],[]) ).
thf(740,plain,
( ~ sP949
| sP836 ),
inference(all_rule,[status(thm)],[]) ).
thf(741,plain,
( ~ sP929
| sP536 ),
inference(all_rule,[status(thm)],[]) ).
thf(742,plain,
( ~ sP874
| sP516 ),
inference(all_rule,[status(thm)],[]) ).
thf(743,plain,
( ~ sP23
| sP227 ),
inference(all_rule,[status(thm)],[]) ).
thf(744,plain,
( ~ sP727
| sP195 ),
inference(all_rule,[status(thm)],[]) ).
thf(745,plain,
( ~ sP977
| sP851 ),
inference(all_rule,[status(thm)],[]) ).
thf(746,plain,
( ~ sP5
| sP110 ),
inference(all_rule,[status(thm)],[]) ).
thf(747,plain,
( ~ sP1016
| sP396 ),
inference(all_rule,[status(thm)],[]) ).
thf(748,plain,
( ~ sP739
| sP192 ),
inference(all_rule,[status(thm)],[]) ).
thf(749,plain,
( ~ sP1020
| sP1019 ),
inference(all_rule,[status(thm)],[]) ).
thf(750,plain,
( ~ sP559
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(751,plain,
( ~ sP684
| sP801 ),
inference(all_rule,[status(thm)],[]) ).
thf(752,plain,
( ~ sP400
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(753,plain,
( ~ sP1031
| sP417 ),
inference(all_rule,[status(thm)],[]) ).
thf(754,plain,
( ~ sP574
| sP209 ),
inference(all_rule,[status(thm)],[]) ).
thf(755,plain,
( ~ sP592
| sP995 ),
inference(all_rule,[status(thm)],[]) ).
thf(756,plain,
( ~ sP931
| sP714 ),
inference(all_rule,[status(thm)],[]) ).
thf(757,plain,
( ~ sP867
| sP868 ),
inference(all_rule,[status(thm)],[]) ).
thf(758,plain,
( ~ sP319
| sP214 ),
inference(all_rule,[status(thm)],[]) ).
thf(759,plain,
( ~ sP825
| sP1022 ),
inference(all_rule,[status(thm)],[]) ).
thf(760,plain,
( ~ sP519
| sP640 ),
inference(all_rule,[status(thm)],[]) ).
thf(761,plain,
( ~ sP515
| sP485 ),
inference(all_rule,[status(thm)],[]) ).
thf(762,plain,
( ~ sP873
| sP772 ),
inference(all_rule,[status(thm)],[]) ).
thf(763,plain,
( ~ sP854
| sP944 ),
inference(all_rule,[status(thm)],[]) ).
thf(764,plain,
( ~ sP866
| sP53 ),
inference(all_rule,[status(thm)],[]) ).
thf(765,plain,
( ~ sP252
| sP471 ),
inference(all_rule,[status(thm)],[]) ).
thf(766,plain,
( ~ sP982
| sP75 ),
inference(all_rule,[status(thm)],[]) ).
thf(767,plain,
( ~ sP753
| sP158 ),
inference(all_rule,[status(thm)],[]) ).
thf(768,plain,
( ~ sP665
| sP342 ),
inference(all_rule,[status(thm)],[]) ).
thf(769,plain,
( ~ sP294
| sP71 ),
inference(all_rule,[status(thm)],[]) ).
thf(770,plain,
( ~ sP130
| sP771 ),
inference(all_rule,[status(thm)],[]) ).
thf(771,plain,
( ~ sP961
| sP212 ),
inference(all_rule,[status(thm)],[]) ).
thf(772,plain,
( ~ sP981
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(773,plain,
( ~ sP748
| sP260 ),
inference(all_rule,[status(thm)],[]) ).
thf(774,plain,
( ~ sP395
| sP927 ),
inference(all_rule,[status(thm)],[]) ).
thf(775,plain,
( ~ sP240
| sP373 ),
inference(all_rule,[status(thm)],[]) ).
thf(776,plain,
( ~ sP295
| sP846
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(777,plain,
( ~ sP967
| sP846
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(778,plain,
( ~ sP716
| sP595
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(779,plain,
( ~ sP394
| ~ sP650
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(780,plain,
( ~ sP595
| sP394
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(781,plain,
( ~ sP287
| sP966
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(782,plain,
( ~ sP282
| ~ sP479
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(783,plain,
( ~ sP966
| sP282
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(784,plain,
( ~ sP46
| sP808
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(785,plain,
( ~ sP38
| sP295
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(786,plain,
( ~ sP374
| ~ sP650
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(787,plain,
( ~ sP846
| sP374
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(788,plain,
( ~ sP236
| sP716
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(789,plain,
( ~ sP235
| sP287
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(790,plain,
( ~ sP763
| sP46
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(791,plain,
( ~ sP935
| ~ sP479
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(792,plain,
( ~ sP808
| sP935
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(793,plain,
( ~ sP402
| sP912
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(794,plain,
( ~ sP190
| ~ sP280
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(795,plain,
( ~ sP912
| sP190
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(796,plain,
( ~ sP928
| ~ sP700
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(797,plain,
( ~ sP575
| sP928
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(798,plain,
( ~ sP181
| sP575
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(799,plain,
( ~ sP980
| sP950
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(800,plain,
( ~ sP234
| sP89
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(801,plain,
( ~ sP434
| sP89
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(802,plain,
( ~ sP427
| ~ sP150
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(803,plain,
( ~ sP89
| sP427
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(804,plain,
( ~ sP151
| sP38
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(805,plain,
( ~ sP881
| sP236
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(806,plain,
( ~ sP253
| sP235
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(807,plain,
( ~ sP124
| sP763
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(808,plain,
( ~ sP648
| sP402
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(809,plain,
( ~ sP816
| sP63
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(810,plain,
( ~ sP63
| sP566
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(811,plain,
( ~ sP469
| ~ sP280
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(812,plain,
( ~ sP566
| sP469
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(813,plain,
( ~ sP663
| sP863
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(814,plain,
( ~ sP572
| ~ sP585
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(815,plain,
( ~ sP863
| sP572
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(816,plain,
( ~ sP659
| sP181
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(817,plain,
( ~ sP318
| sP746
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(818,plain,
( ~ sP1002
| sP941
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(819,plain,
( ~ sP155
| ~ sP700
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(820,plain,
( ~ sP746
| sP155
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(821,plain,
( ~ sP941
| sP746
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(822,plain,
( ~ sP109
| ~ sP685
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(823,plain,
( ~ sP117
| sP109
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(824,plain,
( ~ sP457
| sP117
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(825,plain,
( ~ sP762
| ~ sP448
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(826,plain,
( ~ sP286
| sP762
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(827,plain,
( ~ sP62
| sP286
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(828,plain,
( ~ sP752
| sP720
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(829,plain,
( ~ sP380
| ~ sP285
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(830,plain,
( ~ sP720
| sP380
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(831,plain,
( ~ sP778
| sP720
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(832,plain,
( ~ sP419
| sP980
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(833,plain,
( ~ sP204
| ~ sP150
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(834,plain,
( ~ sP950
| sP204
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(835,plain,
( ~ sP81
| sP234
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(836,plain,
( ~ sP474
| sP869
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(837,plain,
( ~ sP784
| ~ sP853
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(838,plain,
( ~ sP869
| sP784
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(839,plain,
( ~ sP312
| sP589
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(840,plain,
( ~ sP805
| ~ sP606
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(841,plain,
( ~ sP589
| sP805
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(842,plain,
( ~ sP423
| sP151 ),
inference(all_rule,[status(thm)],[]) ).
thf(843,plain,
( ~ sP15
| sP881 ),
inference(all_rule,[status(thm)],[]) ).
thf(844,plain,
( ~ sP526
| sP253 ),
inference(all_rule,[status(thm)],[]) ).
thf(845,plain,
( ~ sP493
| sP124 ),
inference(all_rule,[status(thm)],[]) ).
thf(846,plain,
( ~ sP27
| sP648
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(847,plain,
( ~ sP279
| sP816
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(848,plain,
( ~ sP369
| sP663
| ~ sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(849,plain,
( ~ sP476
| sP659
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(850,plain,
( ~ sP339
| sP1002
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(851,plain,
( ~ sP997
| sP457
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(852,plain,
( ~ sP620
| sP62
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(853,plain,
( ~ sP962
| sP709
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(854,plain,
( ~ sP422
| sP752
| ~ sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(855,plain,
( ~ sP144
| sP419
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(856,plain,
( ~ sP747
| sP81
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(857,plain,
( ~ sP257
| sP312
| ~ sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(858,plain,
( ~ sP174
| ~ sP49
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(859,plain,
( ~ sP320
| sP423 ),
inference(all_rule,[status(thm)],[]) ).
thf(860,plain,
( ~ sP320
| sP240 ),
inference(all_rule,[status(thm)],[]) ).
thf(861,plain,
( ~ sP226
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(862,plain,
( ~ sP261
| sP526 ),
inference(all_rule,[status(thm)],[]) ).
thf(863,plain,
( ~ sP401
| sP493 ),
inference(all_rule,[status(thm)],[]) ).
thf(864,plain,
( ~ sP547
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(865,plain,
( ~ sP580
| sP279 ),
inference(all_rule,[status(thm)],[]) ).
thf(866,plain,
( ~ sP907
| sP101
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(867,plain,
( ~ sP40
| sP907
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(868,plain,
( ~ sP101
| ~ sP562
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(869,plain,
( ~ sP744
| sP974
| ~ sP821 ),
inference(prop_rule,[status(thm)],[]) ).
thf(870,plain,
( ~ sP495
| sP744
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(871,plain,
( ~ sP974
| ~ sP562
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(872,plain,
( ~ sP1012
| sP369
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(873,plain,
( ~ sP540
| sP476 ),
inference(all_rule,[status(thm)],[]) ).
thf(874,plain,
( ~ sP388
| sP339 ),
inference(all_rule,[status(thm)],[]) ).
thf(875,plain,
( ~ sP940
| sP997
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(876,plain,
( ~ sP680
| sP491
| ~ sP842 ),
inference(prop_rule,[status(thm)],[]) ).
thf(877,plain,
( ~ sP728
| sP680
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(878,plain,
( ~ sP491
| ~ sP213
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(879,plain,
( ~ sP973
| ~ sP213
| ~ sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(880,plain,
( ~ sP900
| sP973
| ~ sP461 ),
inference(prop_rule,[status(thm)],[]) ).
thf(881,plain,
( ~ sP467
| sP900
| ~ sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(882,plain,
( ~ sP293
| sP620
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(883,plain,
( ~ sP551
| sP422
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(884,plain,
( ~ sP586
| sP144 ),
inference(all_rule,[status(thm)],[]) ).
thf(885,plain,
( ~ sP968
| sP747 ),
inference(all_rule,[status(thm)],[]) ).
thf(886,plain,
( ~ sP147
| sP257
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(887,plain,
( ~ sP119
| sP788
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(888,plain,
( ~ sP871
| sP119
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(889,plain,
( ~ sP788
| ~ sP288
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(890,plain,
( ~ sP687
| sP499
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(891,plain,
( ~ sP458
| sP687
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(892,plain,
( ~ sP499
| ~ sP1026
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(893,plain,
( ~ sP379
| sP655
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(894,plain,
( ~ sP313
| sP379
| ~ sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(895,plain,
( ~ sP981
| sP320 ),
inference(all_rule,[status(thm)],[]) ).
thf(896,plain,
( ~ sP981
| sP226 ),
inference(all_rule,[status(thm)],[]) ).
thf(897,plain,
( ~ sP961
| sP261 ),
inference(all_rule,[status(thm)],[]) ).
thf(898,plain,
( ~ sP961
| sP401 ),
inference(all_rule,[status(thm)],[]) ).
thf(899,plain,
( ~ sP65
| sP547 ),
inference(all_rule,[status(thm)],[]) ).
thf(900,plain,
( ~ sP717
| sP580 ),
inference(all_rule,[status(thm)],[]) ).
thf(901,plain,
( ~ sP558
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(902,plain,
( ~ sP527
| sP495 ),
inference(all_rule,[status(thm)],[]) ).
thf(903,plain,
( ~ sP74
| sP1012 ),
inference(all_rule,[status(thm)],[]) ).
thf(904,plain,
( ~ sP130
| sP540 ),
inference(all_rule,[status(thm)],[]) ).
thf(905,plain,
( ~ sP741
| sP395 ),
inference(all_rule,[status(thm)],[]) ).
thf(906,plain,
( ~ sP741
| sP388 ),
inference(all_rule,[status(thm)],[]) ).
thf(907,plain,
( ~ sP185
| sP940 ),
inference(all_rule,[status(thm)],[]) ).
thf(908,plain,
( ~ sP455
| sP397
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(909,plain,
( ~ sP807
| sP455
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(910,plain,
( ~ sP397
| ~ sP270
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(911,plain,
( ~ sP480
| sP728 ),
inference(all_rule,[status(thm)],[]) ).
thf(912,plain,
( ~ sP877
| sP467 ),
inference(all_rule,[status(thm)],[]) ).
thf(913,plain,
( ~ sP925
| sP426
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(914,plain,
( ~ sP986
| sP925
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(915,plain,
( ~ sP357
| sP293 ),
inference(all_rule,[status(thm)],[]) ).
thf(916,plain,
( ~ sP506
| sP551 ),
inference(all_rule,[status(thm)],[]) ).
thf(917,plain,
( ~ sP902
| sP586 ),
inference(all_rule,[status(thm)],[]) ).
thf(918,plain,
( ~ sP904
| sP968 ),
inference(all_rule,[status(thm)],[]) ).
thf(919,plain,
( ~ sP904
| sP748 ),
inference(all_rule,[status(thm)],[]) ).
thf(920,plain,
( ~ sP667
| sP147 ),
inference(all_rule,[status(thm)],[]) ).
thf(921,plain,
( ~ sP356
| sP835
| ~ sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(922,plain,
( ~ sP952
| sP760
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(923,plain,
( ~ sP389
| sP952
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(924,plain,
( ~ sP1030
| sP871 ),
inference(all_rule,[status(thm)],[]) ).
thf(925,plain,
( ~ sP753
| sP310 ),
inference(all_rule,[status(thm)],[]) ).
thf(926,plain,
( ~ sP248
| sP458 ),
inference(all_rule,[status(thm)],[]) ).
thf(927,plain,
( ~ sP655
| ~ sP1026
| ~ sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(928,plain,
( ~ sP180
| sP313 ),
inference(all_rule,[status(thm)],[]) ).
thf(929,plain,
( ~ sP43
| sP173
| ~ sP1026 ),
inference(prop_rule,[status(thm)],[]) ).
thf(930,plain,
( ~ sP596
| sP43
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(931,plain,
( ~ sP624
| sP451
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(932,plain,
( ~ sP957
| sP624
| ~ sP1026 ),
inference(prop_rule,[status(thm)],[]) ).
thf(933,plain,
( ~ sP635
| sP106
| ~ sP1026 ),
inference(prop_rule,[status(thm)],[]) ).
thf(934,plain,
( ~ sP783
| sP635
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(935,plain,
( ~ sP982
| sP981 ),
inference(all_rule,[status(thm)],[]) ).
thf(936,plain,
( ~ sP982
| sP961 ),
inference(all_rule,[status(thm)],[]) ).
thf(937,plain,
( ~ sP252
| sP65 ),
inference(all_rule,[status(thm)],[]) ).
thf(938,plain,
( ~ sP252
| sP717 ),
inference(all_rule,[status(thm)],[]) ).
thf(939,plain,
( ~ sP866
| sP558 ),
inference(all_rule,[status(thm)],[]) ).
thf(940,plain,
( ~ sP866
| sP527 ),
inference(all_rule,[status(thm)],[]) ).
thf(941,plain,
( ~ sP368
| sP74 ),
inference(all_rule,[status(thm)],[]) ).
thf(942,plain,
( ~ sP854
| sP130 ),
inference(all_rule,[status(thm)],[]) ).
thf(943,plain,
( ~ sP854
| sP741 ),
inference(all_rule,[status(thm)],[]) ).
thf(944,plain,
( ~ sP196
| sP185 ),
inference(all_rule,[status(thm)],[]) ).
thf(945,plain,
( ~ sP349
| sP807 ),
inference(all_rule,[status(thm)],[]) ).
thf(946,plain,
( ~ sP873
| sP480 ),
inference(all_rule,[status(thm)],[]) ).
thf(947,plain,
( ~ sP873
| sP877 ),
inference(all_rule,[status(thm)],[]) ).
thf(948,plain,
( ~ sP426
| ~ sP461
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(949,plain,
( ~ sP548
| sP986 ),
inference(all_rule,[status(thm)],[]) ).
thf(950,plain,
( ~ sP409
| sP357 ),
inference(all_rule,[status(thm)],[]) ).
thf(951,plain,
( ~ sP1044
| sP506 ),
inference(all_rule,[status(thm)],[]) ).
thf(952,plain,
( ~ sP1044
| sP294 ),
inference(all_rule,[status(thm)],[]) ).
thf(953,plain,
( ~ sP519
| sP902 ),
inference(all_rule,[status(thm)],[]) ).
thf(954,plain,
( ~ sP519
| sP904 ),
inference(all_rule,[status(thm)],[]) ).
thf(955,plain,
( ~ sP1028
| sP665 ),
inference(all_rule,[status(thm)],[]) ).
thf(956,plain,
( ~ sP963
| sP667 ),
inference(all_rule,[status(thm)],[]) ).
thf(957,plain,
( ~ sP812
| sP356
| ~ sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(958,plain,
( ~ sP760
| ~ sP334
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(959,plain,
( ~ sP607
| ~ sP334
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(960,plain,
( ~ sP988
| ~ sP288
| ~ sP821 ),
inference(prop_rule,[status(thm)],[]) ).
thf(961,plain,
( ~ sP875
| sP607
| ~ sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(962,plain,
( ~ sP160
| sP988
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(963,plain,
( ~ sP987
| ~ sP1026
| ~ sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(964,plain,
( ~ sP956
| sP875
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(965,plain,
( ~ sP1008
| sP160
| ~ sP821 ),
inference(prop_rule,[status(thm)],[]) ).
thf(966,plain,
( ~ sP173
| ~ sP83
| ~ sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(967,plain,
( ~ sP451
| ~ sP821
| ~ sP1026 ),
inference(prop_rule,[status(thm)],[]) ).
thf(968,plain,
( ~ sP106
| ~ sP514
| ~ sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(969,plain,
( ~ sP263
| sP992
| sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(970,plain,
( ~ sP697
| sP45
| sP334 ),
inference(prop_rule,[status(thm)],[]) ).
thf(971,plain,
( ~ sP316
| sP898
| sP288 ),
inference(prop_rule,[status(thm)],[]) ).
thf(972,plain,
( ~ sP947
| sP389 ),
inference(all_rule,[status(thm)],[]) ).
thf(973,plain,
( ~ sP421
| sP956 ),
inference(all_rule,[status(thm)],[]) ).
thf(974,plain,
( ~ sP123
| sP1008 ),
inference(all_rule,[status(thm)],[]) ).
thf(975,plain,
( ~ sP698
| ~ sP245
| sP992 ),
inference(prop_rule,[status(thm)],[]) ).
thf(976,plain,
( ~ sP885
| ~ sP777
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(977,plain,
( ~ sP751
| ~ sP910
| sP898 ),
inference(prop_rule,[status(thm)],[]) ).
thf(978,plain,
( ~ sP614
| sP263
| sP650 ),
inference(prop_rule,[status(thm)],[]) ).
thf(979,plain,
( ~ sP725
| sP697
| sP479 ),
inference(prop_rule,[status(thm)],[]) ).
thf(980,plain,
( ~ sP222
| sP316
| sP564 ),
inference(prop_rule,[status(thm)],[]) ).
thf(981,plain,
( ~ sP825
| sP947 ),
inference(all_rule,[status(thm)],[]) ).
thf(982,plain,
( ~ sP825
| sP421 ),
inference(all_rule,[status(thm)],[]) ).
thf(983,plain,
( ~ sP319
| sP1030 ),
inference(all_rule,[status(thm)],[]) ).
thf(984,plain,
( ~ sP319
| sP123 ),
inference(all_rule,[status(thm)],[]) ).
thf(985,plain,
( ~ sP823
| sP211
| sP1026 ),
inference(prop_rule,[status(thm)],[]) ).
thf(986,plain,
( ~ sP271
| sP591
| sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(987,plain,
( ~ sP454
| sP920
| sP213 ),
inference(prop_rule,[status(thm)],[]) ).
thf(988,plain,
( ~ sP328
| sP698 ),
inference(all_rule,[status(thm)],[]) ).
thf(989,plain,
( ~ sP328
| sP885 ),
inference(all_rule,[status(thm)],[]) ).
thf(990,plain,
( ~ sP328
| sP751 ),
inference(all_rule,[status(thm)],[]) ).
thf(991,plain,
( ~ sP867
| sP614 ),
inference(all_rule,[status(thm)],[]) ).
thf(992,plain,
( ~ sP867
| sP725 ),
inference(all_rule,[status(thm)],[]) ).
thf(993,plain,
( ~ sP867
| sP222 ),
inference(all_rule,[status(thm)],[]) ).
thf(994,plain,
( ~ sP931
| sP753 ),
inference(all_rule,[status(thm)],[]) ).
thf(995,plain,
( ~ sP931
| sP825 ),
inference(all_rule,[status(thm)],[]) ).
thf(996,plain,
( ~ sP931
| sP319 ),
inference(all_rule,[status(thm)],[]) ).
thf(997,plain,
( ~ sP281
| sP777 ),
inference(symeq,[status(thm)],[]) ).
thf(998,plain,
( ~ sP592
| sP248 ),
inference(all_rule,[status(thm)],[]) ).
thf(999,plain,
( ~ sP592
| sP114 ),
inference(all_rule,[status(thm)],[]) ).
thf(1000,plain,
( ~ sP592
| sP180 ),
inference(all_rule,[status(thm)],[]) ).
thf(1001,plain,
( ~ sP481
| sP823
| sP280 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1002,plain,
( ~ sP1040
| sP910 ),
inference(symeq,[status(thm)],[]) ).
thf(1003,plain,
( ~ sP724
| sP596 ),
inference(all_rule,[status(thm)],[]) ).
thf(1004,plain,
( ~ sP602
| sP271
| sP700 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1005,plain,
( ~ sP268
| sP957 ),
inference(all_rule,[status(thm)],[]) ).
thf(1006,plain,
( ~ sP735
| sP783 ),
inference(all_rule,[status(thm)],[]) ).
thf(1007,plain,
( ~ sP50
| sP454
| sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1008,plain,
( ~ sP849
| sP245 ),
inference(symeq,[status(thm)],[]) ).
thf(1009,plain,
( ~ sP161
| sP660 ),
inference(symeq,[status(thm)],[]) ).
thf(1010,plain,
( ~ sP249
| ~ sP660 ),
inference(all_rule,[status(thm)],[]) ).
thf(1011,plain,
( ~ sP1
| sP328 ),
inference(all_rule,[status(thm)],[]) ).
thf(1012,plain,
( ~ sP954
| sP867 ),
inference(all_rule,[status(thm)],[]) ).
thf(1013,plain,
( ~ sP336
| sP931 ),
inference(all_rule,[status(thm)],[]) ).
thf(1014,plain,
( ~ sP672
| sP982 ),
inference(all_rule,[status(thm)],[]) ).
thf(1015,plain,
( ~ sP612
| sP592 ),
inference(all_rule,[status(thm)],[]) ).
thf(1016,plain,
( ~ sP938
| sP481 ),
inference(all_rule,[status(thm)],[]) ).
thf(1017,plain,
( ~ sP764
| sP252 ),
inference(all_rule,[status(thm)],[]) ).
thf(1018,plain,
( ~ sP29
| sP724 ),
inference(all_rule,[status(thm)],[]) ).
thf(1019,plain,
( ~ sP346
| sP866 ),
inference(all_rule,[status(thm)],[]) ).
thf(1020,plain,
( ~ sP22
| sP602 ),
inference(all_rule,[status(thm)],[]) ).
thf(1021,plain,
( ~ sP577
| sP268 ),
inference(all_rule,[status(thm)],[]) ).
thf(1022,plain,
( ~ sP949
| sP368 ),
inference(all_rule,[status(thm)],[]) ).
thf(1023,plain,
( ~ sP929
| sP854 ),
inference(all_rule,[status(thm)],[]) ).
thf(1024,plain,
( ~ sP874
| sP196 ),
inference(all_rule,[status(thm)],[]) ).
thf(1025,plain,
( ~ sP23
| sP349 ),
inference(all_rule,[status(thm)],[]) ).
thf(1026,plain,
( ~ sP727
| sP735 ),
inference(all_rule,[status(thm)],[]) ).
thf(1027,plain,
( ~ sP977
| sP873 ),
inference(all_rule,[status(thm)],[]) ).
thf(1028,plain,
( ~ sP5
| sP50 ),
inference(all_rule,[status(thm)],[]) ).
thf(1029,plain,
( ~ sP1016
| sP548 ),
inference(all_rule,[status(thm)],[]) ).
thf(1030,plain,
( ~ sP1020
| sP409 ),
inference(all_rule,[status(thm)],[]) ).
thf(1031,plain,
( ~ sP99
| sP515 ),
inference(all_rule,[status(thm)],[]) ).
thf(1032,plain,
( ~ sP559
| sP1044 ),
inference(all_rule,[status(thm)],[]) ).
thf(1033,plain,
( ~ sP684
| sP519 ),
inference(all_rule,[status(thm)],[]) ).
thf(1034,plain,
( ~ sP1031
| sP1028 ),
inference(all_rule,[status(thm)],[]) ).
thf(1035,plain,
( ~ sP574
| sP963 ),
inference(all_rule,[status(thm)],[]) ).
thf(1036,plain,
( ~ sP276
| sP812 ),
inference(all_rule,[status(thm)],[]) ).
thf(1037,plain,
( ~ sP835
| sP826
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1038,plain,
( ~ sP172
| ~ sP606
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1039,plain,
( ~ sP826
| sP172
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1040,plain,
( ~ sP52
| sP353
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1041,plain,
( ~ sP645
| sP52
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1042,plain,
( ~ sP693
| ~ sP853
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1043,plain,
( ~ sP353
| sP693
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1044,plain,
( ~ sP757
| sP645
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1045,plain,
( ~ sP590
| sP817
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1046,plain,
( ~ sP817
| sP909
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1047,plain,
( ~ sP20
| ~ sP285
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1048,plain,
( ~ sP909
| sP20
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1049,plain,
( ~ sP535
| sP428
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1050,plain,
( ~ sP347
| ~ sP448
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1051,plain,
( ~ sP152
| sP347
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1052,plain,
( ~ sP428
| sP152
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1053,plain,
( ~ sP923
| sP757 ),
inference(all_rule,[status(thm)],[]) ).
thf(1054,plain,
( ~ sP800
| sP590
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1055,plain,
( ~ sP634
| sP709
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1056,plain,
( ~ sP541
| sP634
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1057,plain,
( ~ sP126
| ~ sP585
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1058,plain,
( ~ sP709
| sP126
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1059,plain,
( ~ sP1015
| sP535
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1060,plain,
( ~ sP431
| sP416
| ~ sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1061,plain,
( ~ sP315
| ~ sP685
| ~ sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1062,plain,
( ~ sP36
| sP315
| ~ sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1063,plain,
( ~ sP416
| sP36
| ~ sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1064,plain,
( ~ sP797
| sP276 ),
inference(all_rule,[status(thm)],[]) ).
thf(1065,plain,
( ~ sP786
| sP923 ),
inference(all_rule,[status(thm)],[]) ).
thf(1066,plain,
( ~ sP1035
| sP800 ),
inference(all_rule,[status(thm)],[]) ).
thf(1067,plain,
( ~ sP555
| sP541
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1068,plain,
( ~ sP68
| sP1015 ),
inference(all_rule,[status(thm)],[]) ).
thf(1069,plain,
( ~ sP599
| sP431
| ~ sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1070,plain,
( ~ sP574
| sP797 ),
inference(all_rule,[status(thm)],[]) ).
thf(1071,plain,
( ~ sP1031
| sP786 ),
inference(all_rule,[status(thm)],[]) ).
thf(1072,plain,
( ~ sP42
| sP1035 ),
inference(all_rule,[status(thm)],[]) ).
thf(1073,plain,
( ~ sP497
| sP555 ),
inference(all_rule,[status(thm)],[]) ).
thf(1074,plain,
( ~ sP400
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(1075,plain,
( ~ sP256
| sP599 ),
inference(all_rule,[status(thm)],[]) ).
thf(1076,plain,
( ~ sP684
| sP574 ),
inference(all_rule,[status(thm)],[]) ).
thf(1077,plain,
( ~ sP684
| sP1031 ),
inference(all_rule,[status(thm)],[]) ).
thf(1078,plain,
( ~ sP559
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(1079,plain,
( ~ sP99
| sP497 ),
inference(all_rule,[status(thm)],[]) ).
thf(1080,plain,
( ~ sP1020
| sP400 ),
inference(all_rule,[status(thm)],[]) ).
thf(1081,plain,
( ~ sP803
| sP256 ),
inference(all_rule,[status(thm)],[]) ).
thf(1082,plain,
( ~ sP237
| ~ sP461
| ~ sP821 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1083,plain,
( ~ sP864
| sP237
| ~ sP842 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1084,plain,
( ~ sP1023
| ~ sP514
| ~ sP842 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1085,plain,
( ~ sP841
| ~ sP514
| ~ sP461 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1086,plain,
( ~ sP59
| ~ sP270
| ~ sP842 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1087,plain,
( ~ sP309
| sP864
| ~ sP821 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1088,plain,
( ~ sP473
| sP841
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1089,plain,
( ~ sP447
| ~ sP83
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1090,plain,
( ~ sP517
| sP59
| ~ sP821 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1091,plain,
( ~ sP359
| sP661
| sP461 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1092,plain,
( ~ sP852
| sP309 ),
inference(all_rule,[status(thm)],[]) ).
thf(1093,plain,
( ~ sP148
| sP473
| ~ sP461 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1094,plain,
( ~ sP691
| sP447
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1095,plain,
( ~ sP848
| sP517
| ~ sP842 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1096,plain,
( ~ sP337
| sP464
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1097,plain,
( ~ sP464
| ~ sP821
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1098,plain,
( ~ sP916
| ~ sP992
| sP661 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1099,plain,
( ~ sP642
| sP632
| sP842 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1100,plain,
( ~ sP166
| sP642
| sP606 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1101,plain,
( ~ sP845
| sP359
| sP853 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1102,plain,
( ~ sP1016
| sP852 ),
inference(all_rule,[status(thm)],[]) ).
thf(1103,plain,
( ~ sP1043
| sP148 ),
inference(all_rule,[status(thm)],[]) ).
thf(1104,plain,
( ~ sP432
| sP691
| ~ sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1105,plain,
( ~ sP637
| sP848 ),
inference(all_rule,[status(thm)],[]) ).
thf(1106,plain,
( ~ sP882
| sP532
| sP270 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1107,plain,
( ~ sP996
| sP337
| ~ sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1108,plain,
( ~ sP35
| ~ sP898
| sP632 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1109,plain,
( ~ sP654
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(1110,plain,
( ~ sP654
| sP916 ),
inference(all_rule,[status(thm)],[]) ).
thf(1111,plain,
( ~ sP5
| sP166 ),
inference(all_rule,[status(thm)],[]) ).
thf(1112,plain,
( ~ sP5
| sP845 ),
inference(all_rule,[status(thm)],[]) ).
thf(1113,plain,
( ~ sP977
| sP739 ),
inference(all_rule,[status(thm)],[]) ).
thf(1114,plain,
( ~ sP977
| sP1016 ),
inference(all_rule,[status(thm)],[]) ).
thf(1115,plain,
( ~ sP727
| sP382 ),
inference(all_rule,[status(thm)],[]) ).
thf(1116,plain,
( ~ sP727
| sP1043 ),
inference(all_rule,[status(thm)],[]) ).
thf(1117,plain,
( ~ sP568
| sP557
| sP514 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1118,plain,
( ~ sP278
| sP568
| sP285 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1119,plain,
( ~ sP920
| sP992 ),
inference(symeq,[status(thm)],[]) ).
thf(1120,plain,
( ~ sP861
| sP432 ),
inference(all_rule,[status(thm)],[]) ).
thf(1121,plain,
( ~ sP23
| sP637 ),
inference(all_rule,[status(thm)],[]) ).
thf(1122,plain,
( ~ sP477
| sP882
| sP448 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1123,plain,
( ~ sP203
| sP996 ),
inference(all_rule,[status(thm)],[]) ).
thf(1124,plain,
( ~ sP591
| sP898 ),
inference(symeq,[status(thm)],[]) ).
thf(1125,plain,
( ~ sP211
| sP45 ),
inference(symeq,[status(thm)],[]) ).
thf(1126,plain,
( ~ sP249
| ~ sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(1127,plain,
( ~ sP1
| sP654 ),
inference(all_rule,[status(thm)],[]) ).
thf(1128,plain,
( ~ sP954
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(1129,plain,
( ~ sP336
| sP977 ),
inference(all_rule,[status(thm)],[]) ).
thf(1130,plain,
( ~ sP672
| sP684 ),
inference(all_rule,[status(thm)],[]) ).
thf(1131,plain,
( ~ sP612
| sP727 ),
inference(all_rule,[status(thm)],[]) ).
thf(1132,plain,
( ~ sP938
| sP278 ),
inference(all_rule,[status(thm)],[]) ).
thf(1133,plain,
( ~ sP764
| sP559 ),
inference(all_rule,[status(thm)],[]) ).
thf(1134,plain,
( ~ sP29
| sP861 ),
inference(all_rule,[status(thm)],[]) ).
thf(1135,plain,
( ~ sP346
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(1136,plain,
( ~ sP22
| sP477 ),
inference(all_rule,[status(thm)],[]) ).
thf(1137,plain,
( ~ sP577
| sP203 ),
inference(all_rule,[status(thm)],[]) ).
thf(1138,plain,
( ~ sP949
| sP99 ),
inference(all_rule,[status(thm)],[]) ).
thf(1139,plain,
( ~ sP929
| sP1020 ),
inference(all_rule,[status(thm)],[]) ).
thf(1140,plain,
( ~ sP874
| sP803 ),
inference(all_rule,[status(thm)],[]) ).
thf(1141,plain,
( ~ sP929
| sP874 ),
inference(all_rule,[status(thm)],[]) ).
thf(1142,plain,
( ~ sP30
| ~ sP821
| ~ sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1143,plain,
( ~ sP41
| sP905
| sP821 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1144,plain,
( ~ sP713
| sP41
| sP685 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1145,plain,
( ~ sP577
| sP116 ),
inference(all_rule,[status(thm)],[]) ).
thf(1146,plain,
( ~ sP22
| sP713 ),
inference(all_rule,[status(thm)],[]) ).
thf(1147,plain,
( ~ sP346
| sP577 ),
inference(all_rule,[status(thm)],[]) ).
thf(1148,plain,
( ~ sP501
| sP490
| sP83 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1149,plain,
( ~ sP243
| sP501
| sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1150,plain,
( ~ sP34
| ~ sP661
| sP905 ),
inference(prop_rule,[status(thm)],[]) ).
thf(1151,plain,
( ~ sP532
| sP661 ),
inference(symeq,[status(thm)],[]) ).
thf(1152,plain,
( ~ sP557
| sP632 ),
inference(symeq,[status(thm)],[]) ).
thf(1153,plain,
( ~ sP441
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(1154,plain,
( ~ sP249
| ~ sP632 ),
inference(all_rule,[status(thm)],[]) ).
thf(1155,plain,
( ~ sP1
| sP441 ),
inference(all_rule,[status(thm)],[]) ).
thf(1156,plain,
( ~ sP954
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(1157,plain,
( ~ sP336
| sP346 ),
inference(all_rule,[status(thm)],[]) ).
thf(1158,plain,
( ~ sP672
| sP929 ),
inference(all_rule,[status(thm)],[]) ).
thf(1159,plain,
( ~ sP612
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(1160,plain,
( ~ sP938
| sP243 ),
inference(all_rule,[status(thm)],[]) ).
thf(1161,plain,
( ~ sP764
| sP949 ),
inference(all_rule,[status(thm)],[]) ).
thf(1162,plain,
( ~ sP490
| sP905 ),
inference(symeq,[status(thm)],[]) ).
thf(1163,plain,
( ~ sP249
| ~ sP905 ),
inference(all_rule,[status(thm)],[]) ).
thf(1164,plain,
( ~ sP954
| sP938 ),
inference(all_rule,[status(thm)],[]) ).
thf(1165,plain,
( ~ sP336
| sP612 ),
inference(all_rule,[status(thm)],[]) ).
thf(1166,plain,
( ~ sP672
| sP764 ),
inference(all_rule,[status(thm)],[]) ).
thf(axb,axiom,
sP672 ).
thf(axr,axiom,
sP336 ).
thf(rb,axiom,
sP954 ).
thf(sinj,axiom,
sP1 ).
thf(snz,axiom,
sP249 ).
thf(1167,plain,
$false,
inference(prop_unsat,[status(thm)],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,axb,axr,rb,sinj,snz]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA137^1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 23:07:45 EDT 2026
% 0.14/0.33 % CPUTime :
% 197.82/120.09 % SZS status Unsatisfiable
% 197.82/120.09 % Mode: cade22grackle2x052f
% 197.82/120.09 % Steps: 30306
% 197.82/120.09 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------