%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : GRA138^1 : 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 : n029.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 3.04s 3.20s
% Output : Proof 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 1533
% Syntax : Number of formulae : 1534 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 4519 ( 82 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 11437 (2951 ~;1279 |; 0 &;5501 @)
% ( 696 <=>;1010 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 702 ( 700 usr; 698 con; 0-2 aty)
% Number of variables : 260 ( 0 ^; 260 !; 0 ?; 260 :)
% 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
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( ( s @ X1 )
= ( s @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( 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,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( 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 @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ( s @ ( s @ z ) )
= ( s @ z ) )
=> ( ( s @ z )
= z ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( r @ z @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ X1 )
=> ~ ( r @ ( s @ z ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ~ ( ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ z @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( b @ z @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( r @ z @ ( s @ z ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ( ~ ( ( 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 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( ( r @ z @ ( s @ ( s @ z ) ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( ( r @ z @ ( s @ z ) )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ sP22 )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP19 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( s @ z )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( ( s @ ( s @ z ) )
!= ( s @ z ) )
=> ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP14 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( b @ ( s @ z ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ ( ~ ( ( 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 ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ ( ~ ( ( 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 ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ sP7
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( s @ z )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: $i] :
( ~ ( ~ ( sP22
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ~ ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP19 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ( s @ z )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ ( ( r @ z @ ( s @ ( s @ z ) ) )
=> ~ ( r @ z @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i] :
( ~ ( ( ( s @ ( s @ z ) )
!= X1 )
=> ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ! [X1: $i] :
( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ X1 ) )
=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( sP22
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ~ ( ~ ( ( 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,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ! [X1: $i] :
( ~ ( ~ sP74
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( r @ z @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( ( z
!= ( s @ ( s @ ( s @ z ) ) ) )
=> ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP19 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP80 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( ~ ( ~ sP61
=> sP22 )
=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP22
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ sP62 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ( ~ ( ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP22 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( ~ sP53
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ! [X1: $i] :
( ~ ( ~ ( sP22
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= z )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP80 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP22 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( sP80
=> ~ ( r @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ! [X1: $i] :
( ~ sP7
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( z
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ z ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( ( z
!= ( s @ z ) )
=> ( r @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ! [X1: $i] :
( ( ( s @ z )
= ( s @ X1 ) )
=> ( z = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ z @ X1 )
=> ~ ( r @ z @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ( ~ ( ~ ( sP15
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ( ~ ( sP14
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ z ) ) )
=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ( ~ sP55
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( ~ sP46
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( ~ ( ~ ( sP113
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ( ~ ( ( 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,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ! [X1: $i] :
( ~ sP59
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( ~ ( ( 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,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ( ~ ( sP67
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ( ( ( 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,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ( ~ ( ~ ( sP124
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ z @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ sP62 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ( ( ( 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,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP62
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130,plain,
( sP130
<=> ( r @ z @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131,plain,
( sP131
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132,plain,
( sP132
<=> ( sP15
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133,plain,
( sP133
<=> ( ~ sP93
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134,plain,
( sP134
<=> ( ~ ( sP124
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP80 ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135,plain,
( sP135
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136,plain,
( sP136
<=> ( ~ ( ~ ( ( 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 @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137,plain,
( sP137
<=> ! [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,[sP137])]) ).
thf(sP138,plain,
( sP138
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139,plain,
( sP139
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140,plain,
( sP140
<=> ( ~ ( ~ ( sP19
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141,plain,
( sP141
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
!= ( s @ z ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142,plain,
( sP142
<=> ! [X1: $i] :
( ~ sP26
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143,plain,
( sP143
<=> ( ~ sP7
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144,plain,
( sP144
<=> ( z
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145,plain,
( sP145
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146,plain,
( sP146
<=> ( ~ sP59
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP146])]) ).
thf(sP147,plain,
( sP147
<=> ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP147])]) ).
thf(sP148,plain,
( sP148
<=> ! [X1: $i] :
( ~ ( ~ sP73
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP148])]) ).
thf(sP149,plain,
( sP149
<=> ( ~ ( ~ sP100
=> sP124 )
=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP149])]) ).
thf(sP150,plain,
( sP150
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP150])]) ).
thf(sP151,plain,
( sP151
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP151])]) ).
thf(sP152,plain,
( sP152
<=> ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP152])]) ).
thf(sP153,plain,
( sP153
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP153])]) ).
thf(sP154,plain,
( sP154
<=> ( ~ ( ~ sP34
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP154])]) ).
thf(sP155,plain,
( sP155
<=> ( ~ ( ~ ( sP62
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP155])]) ).
thf(sP156,plain,
( sP156
<=> ( ~ sP38
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP156])]) ).
thf(sP157,plain,
( sP157
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP157])]) ).
thf(sP158,plain,
( sP158
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP158])]) ).
thf(sP159,plain,
( sP159
<=> ( ( ( s @ ( s @ z ) )
!= z )
=> ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP159])]) ).
thf(sP160,plain,
( sP160
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) )
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP160])]) ).
thf(sP161,plain,
( sP161
<=> ( ~ ( sP22
=> ~ sP113 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP161])]) ).
thf(sP162,plain,
( sP162
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP162])]) ).
thf(sP163,plain,
( sP163
<=> ( r @ ( s @ z ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP163])]) ).
thf(sP164,plain,
( sP164
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP164])]) ).
thf(sP165,plain,
( sP165
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP165])]) ).
thf(sP166,plain,
( sP166
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ sP19 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP166])]) ).
thf(sP167,plain,
( sP167
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ sP62 )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP167])]) ).
thf(sP168,plain,
( sP168
<=> ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP168])]) ).
thf(sP169,plain,
( sP169
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP169])]) ).
thf(sP170,plain,
( sP170
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP170])]) ).
thf(sP171,plain,
( sP171
<=> ( ~ ( ~ sP74
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP171])]) ).
thf(sP172,plain,
( sP172
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP172])]) ).
thf(sP173,plain,
( sP173
<=> ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP173])]) ).
thf(sP174,plain,
( sP174
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP174])]) ).
thf(sP175,plain,
( sP175
<=> ! [X1: $i] :
( ~ sP151
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP175])]) ).
thf(sP176,plain,
( sP176
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP176])]) ).
thf(sP177,plain,
( sP177
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) )
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP177])]) ).
thf(sP178,plain,
( sP178
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( b @ X1 @ X2 )
=> ~ ( b @ X1 @ X3 ) )
=> ~ ( b @ X2 @ X3 ) )
=> ~ ( b @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP178])]) ).
thf(sP179,plain,
( sP179
<=> ( r @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP179])]) ).
thf(sP180,plain,
( sP180
<=> ( ~ sP28
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP180])]) ).
thf(sP181,plain,
( sP181
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP181])]) ).
thf(sP182,plain,
( sP182
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP182])]) ).
thf(sP183,plain,
( sP183
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( 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,[sP183])]) ).
thf(sP184,plain,
( sP184
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP184])]) ).
thf(sP185,plain,
( sP185
<=> ! [X1: $i] :
( ~ ( ~ ( sP163
=> ~ sP49 )
=> ~ sP78 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP185])]) ).
thf(sP186,plain,
( sP186
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP186])]) ).
thf(sP187,plain,
( sP187
<=> ( ~ ( ~ sP157
=> ~ sP78 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP187])]) ).
thf(sP188,plain,
( sP188
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP188])]) ).
thf(sP189,plain,
( sP189
<=> ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP189])]) ).
thf(sP190,plain,
( sP190
<=> ( ~ ( ~ ( sP163
=> ~ sP49 )
=> ~ sP78 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP190])]) ).
thf(sP191,plain,
( sP191
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP191])]) ).
thf(sP192,plain,
( sP192
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP192])]) ).
thf(sP193,plain,
( sP193
<=> ( ~ sP128
=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP193])]) ).
thf(sP194,plain,
( sP194
<=> ( sP62
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP194])]) ).
thf(sP195,plain,
( sP195
<=> ( ~ sP156
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP195])]) ).
thf(sP196,plain,
( sP196
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP196])]) ).
thf(sP197,plain,
( sP197
<=> ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP197])]) ).
thf(sP198,plain,
( sP198
<=> ( ~ ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP198])]) ).
thf(sP199,plain,
( sP199
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP199])]) ).
thf(sP200,plain,
( sP200
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP200])]) ).
thf(sP201,plain,
( sP201
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP150
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP201])]) ).
thf(sP202,plain,
( sP202
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP202])]) ).
thf(sP203,plain,
( sP203
<=> ( ~ sP21
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP203])]) ).
thf(sP204,plain,
( sP204
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP80 ) ),
introduced(definition,[new_symbols(definition,[sP204])]) ).
thf(sP205,plain,
( sP205
<=> ( ~ sP147
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP205])]) ).
thf(sP206,plain,
( sP206
<=> ( ~ sP11
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP206])]) ).
thf(sP207,plain,
( sP207
<=> ( ~ ( ~ ( sP113
=> ~ sP22 )
=> ~ sP49 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP207])]) ).
thf(sP208,plain,
( sP208
<=> ! [X1: $i,X2: $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 ) ) ),
introduced(definition,[new_symbols(definition,[sP208])]) ).
thf(sP209,plain,
( sP209
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP209])]) ).
thf(sP210,plain,
( sP210
<=> ( ~ sP100
=> sP124 ) ),
introduced(definition,[new_symbols(definition,[sP210])]) ).
thf(sP211,plain,
( sP211
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP211])]) ).
thf(sP212,plain,
( sP212
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP212])]) ).
thf(sP213,plain,
( sP213
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP213])]) ).
thf(sP214,plain,
( sP214
<=> ( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ sP130 )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP214])]) ).
thf(sP215,plain,
( sP215
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP215])]) ).
thf(sP216,plain,
( sP216
<=> ! [X1: $i] :
( ~ sP84
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP216])]) ).
thf(sP217,plain,
( sP217
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP78
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP217])]) ).
thf(sP218,plain,
( sP218
<=> ( sP80
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP218])]) ).
thf(sP219,plain,
( sP219
<=> ( sP14
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP219])]) ).
thf(sP220,plain,
( sP220
<=> ( sP19
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP220])]) ).
thf(sP221,plain,
( sP221
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ z ) @ X1 )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP221])]) ).
thf(sP222,plain,
( sP222
<=> ( ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP222])]) ).
thf(sP223,plain,
( sP223
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP223])]) ).
thf(sP224,plain,
( sP224
<=> ( ~ ( ~ sP91
=> ~ sP80 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP224])]) ).
thf(sP225,plain,
( sP225
<=> ( ~ sP199
=> ~ sP124 ) ),
introduced(definition,[new_symbols(definition,[sP225])]) ).
thf(sP226,plain,
( sP226
<=> ( ~ sP161
=> ~ sP173 ) ),
introduced(definition,[new_symbols(definition,[sP226])]) ).
thf(sP227,plain,
( sP227
<=> ( ~ sP97
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP227])]) ).
thf(sP228,plain,
( sP228
<=> ( ~ ( ~ ( sP173
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP228])]) ).
thf(sP229,plain,
( sP229
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ sP211 ) ),
introduced(definition,[new_symbols(definition,[sP229])]) ).
thf(sP230,plain,
( sP230
<=> ( ~ sP28
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP230])]) ).
thf(sP231,plain,
( sP231
<=> ! [X1: $i] :
( ~ sP28
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP231])]) ).
thf(sP232,plain,
( sP232
<=> ( ~ sP134
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP232])]) ).
thf(sP233,plain,
( sP233
<=> ! [X1: $i] :
( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ X1 ) )
=> ( ( s @ ( s @ z ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP233])]) ).
thf(sP234,plain,
( sP234
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP150 )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP234])]) ).
thf(sP235,plain,
( sP235
<=> ( ~ ( ( ( s @ z )
!= z )
=> sP163 )
=> ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP235])]) ).
thf(sP236,plain,
( sP236
<=> ! [X1: $i] :
( ~ sP205
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP236])]) ).
thf(sP237,plain,
( sP237
<=> ( ~ sP90
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP237])]) ).
thf(sP238,plain,
( sP238
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ sP14 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP238])]) ).
thf(sP239,plain,
( sP239
<=> ( ~ sP35
=> ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP239])]) ).
thf(sP240,plain,
( sP240
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ sP150 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP240])]) ).
thf(sP241,plain,
( sP241
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP241])]) ).
thf(sP242,plain,
( sP242
<=> ! [X1: $i] :
( ~ sP111
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP242])]) ).
thf(sP243,plain,
( sP243
<=> ( sP150
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP243])]) ).
thf(sP244,plain,
( sP244
<=> ( b @ z @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP244])]) ).
thf(sP245,plain,
( sP245
<=> ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP245])]) ).
thf(sP246,plain,
( sP246
<=> ( ~ ( sP22
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP246])]) ).
thf(sP247,plain,
( sP247
<=> ( sP124
=> ~ sP191 ) ),
introduced(definition,[new_symbols(definition,[sP247])]) ).
thf(sP248,plain,
( sP248
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP248])]) ).
thf(sP249,plain,
( sP249
<=> ( ~ ( ~ sP74
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ sP163 ) ),
introduced(definition,[new_symbols(definition,[sP249])]) ).
thf(sP250,plain,
( sP250
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP250])]) ).
thf(sP251,plain,
( sP251
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP251])]) ).
thf(sP252,plain,
( sP252
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP252])]) ).
thf(sP253,plain,
( sP253
<=> ( ~ ( ~ sP196
=> ~ sP211 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP253])]) ).
thf(sP254,plain,
( sP254
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP254])]) ).
thf(sP255,plain,
( sP255
<=> ( ~ sP135
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP255])]) ).
thf(sP256,plain,
( sP256
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP19
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP256])]) ).
thf(sP257,plain,
( sP257
<=> ( ~ sP194
=> ~ sP244 ) ),
introduced(definition,[new_symbols(definition,[sP257])]) ).
thf(sP258,plain,
( sP258
<=> ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ ( s @ z ) ) ) )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP258])]) ).
thf(sP259,plain,
( sP259
<=> ! [X1: $i] :
( ~ ( ~ sP220
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP259])]) ).
thf(sP260,plain,
( sP260
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP260])]) ).
thf(sP261,plain,
( sP261
<=> ! [X1: $i] :
( ~ ( ~ sP44
=> ~ sP19 )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP261])]) ).
thf(sP262,plain,
( sP262
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
!= ( s @ ( s @ z ) ) )
=> sP67 )
=> sP158 ) ),
introduced(definition,[new_symbols(definition,[sP262])]) ).
thf(sP263,plain,
( sP263
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP263])]) ).
thf(sP264,plain,
( sP264
<=> ( sP163
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP264])]) ).
thf(sP265,plain,
( sP265
<=> ( sP211
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP265])]) ).
thf(sP266,plain,
( sP266
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP163 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP266])]) ).
thf(sP267,plain,
( sP267
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP267])]) ).
thf(sP268,plain,
( sP268
<=> ( sP80
=> ~ sP179 ) ),
introduced(definition,[new_symbols(definition,[sP268])]) ).
thf(sP269,plain,
( sP269
<=> ( ~ ( ~ sP188
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP269])]) ).
thf(sP270,plain,
( sP270
<=> ! [X1: $i] :
( ~ ( ~ ( sP113
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP270])]) ).
thf(sP271,plain,
( sP271
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP271])]) ).
thf(sP272,plain,
( sP272
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP272])]) ).
thf(sP273,plain,
( sP273
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ sP22 )
=> ~ sP78 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP273])]) ).
thf(sP274,plain,
( sP274
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP274])]) ).
thf(sP275,plain,
( sP275
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP275])]) ).
thf(sP276,plain,
( sP276
<=> ( ~ ( ~ sP189
=> ~ sP130 )
=> ~ sP173 ) ),
introduced(definition,[new_symbols(definition,[sP276])]) ).
thf(sP277,plain,
( sP277
<=> ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP163 ) ),
introduced(definition,[new_symbols(definition,[sP277])]) ).
thf(sP278,plain,
( sP278
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP278])]) ).
thf(sP279,plain,
( sP279
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP279])]) ).
thf(sP280,plain,
( sP280
<=> ( ~ sP91
=> ~ sP80 ) ),
introduced(definition,[new_symbols(definition,[sP280])]) ).
thf(sP281,plain,
( sP281
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP281])]) ).
thf(sP282,plain,
( sP282
<=> ! [X1: $i] :
( ~ ( ( ( s @ z )
!= X1 )
=> ( r @ ( s @ z ) @ X1 ) )
=> ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP282])]) ).
thf(sP283,plain,
( sP283
<=> ( ~ ( sP211
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP283])]) ).
thf(sP284,plain,
( sP284
<=> ( ( ( s @ ( s @ z ) )
!= ( s @ ( s @ ( s @ z ) ) ) )
=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP284])]) ).
thf(sP285,plain,
( sP285
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP285])]) ).
thf(sP286,plain,
( sP286
<=> ! [X1: $i] :
( ~ ( ~ ( sP78
=> ~ sP179 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP286])]) ).
thf(sP287,plain,
( sP287
<=> ! [X1: $i] :
( ~ sP176
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP287])]) ).
thf(sP288,plain,
( sP288
<=> ( ~ sP283
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP288])]) ).
thf(sP289,plain,
( sP289
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP289])]) ).
thf(sP290,plain,
( sP290
<=> ( ~ sP26
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP290])]) ).
thf(sP291,plain,
( sP291
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP291])]) ).
thf(sP292,plain,
( sP292
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ z ) )
=> sP191 )
=> sP223 ) ),
introduced(definition,[new_symbols(definition,[sP292])]) ).
thf(sP293,plain,
( sP293
<=> ( sP202
=> sP100 ) ),
introduced(definition,[new_symbols(definition,[sP293])]) ).
thf(sP294,plain,
( sP294
<=> ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP294])]) ).
thf(sP295,plain,
( sP295
<=> ! [X1: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ sP130 )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP295])]) ).
thf(sP296,plain,
( sP296
<=> ! [X1: $i] :
( ( s @ X1 )
!= z ) ),
introduced(definition,[new_symbols(definition,[sP296])]) ).
thf(sP297,plain,
( sP297
<=> ( ~ sP205
=> ~ sP158 ) ),
introduced(definition,[new_symbols(definition,[sP297])]) ).
thf(sP298,plain,
( sP298
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ sP62 )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP298])]) ).
thf(sP299,plain,
( sP299
<=> ( ~ ( ~ sP125
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP299])]) ).
thf(sP300,plain,
( sP300
<=> ( sP124
=> ~ sP281 ) ),
introduced(definition,[new_symbols(definition,[sP300])]) ).
thf(sP301,plain,
( sP301
<=> ( ~ ( ~ sP73
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP301])]) ).
thf(sP302,plain,
( sP302
<=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP302])]) ).
thf(sP303,plain,
( sP303
<=> ( ~ sP144
=> sP80 ) ),
introduced(definition,[new_symbols(definition,[sP303])]) ).
thf(sP304,plain,
( sP304
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP302 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP304])]) ).
thf(sP305,plain,
( sP305
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ z @ X1 )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP305])]) ).
thf(sP306,plain,
( sP306
<=> ( ~ ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> sP211 ) ),
introduced(definition,[new_symbols(definition,[sP306])]) ).
thf(sP307,plain,
( sP307
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP307])]) ).
thf(sP308,plain,
( sP308
<=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP308])]) ).
thf(sP309,plain,
( sP309
<=> ! [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 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP309])]) ).
thf(sP310,plain,
( sP310
<=> ( ~ sP161
=> ~ sP163 ) ),
introduced(definition,[new_symbols(definition,[sP310])]) ).
thf(sP311,plain,
( sP311
<=> ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP244 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP311])]) ).
thf(sP312,plain,
( sP312
<=> ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP312])]) ).
thf(sP313,plain,
( sP313
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP173
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP313])]) ).
thf(sP314,plain,
( sP314
<=> ( ~ sP245
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP314])]) ).
thf(sP315,plain,
( sP315
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP315])]) ).
thf(sP316,plain,
( sP316
<=> ( ~ ( ~ ( sP191
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP49 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP316])]) ).
thf(sP317,plain,
( sP317
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP158
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP317])]) ).
thf(sP318,plain,
( sP318
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP318])]) ).
thf(sP319,plain,
( sP319
<=> ! [X1: $i,X2: $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 ) ) ),
introduced(definition,[new_symbols(definition,[sP319])]) ).
thf(sP320,plain,
( sP320
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP320])]) ).
thf(sP321,plain,
( sP321
<=> ( sP130
=> ~ sP80 ) ),
introduced(definition,[new_symbols(definition,[sP321])]) ).
thf(sP322,plain,
( sP322
<=> ( sP173
=> ~ sP308 ) ),
introduced(definition,[new_symbols(definition,[sP322])]) ).
thf(sP323,plain,
( sP323
<=> ( ~ ( ( ( s @ z )
!= ( s @ ( s @ ( s @ z ) ) ) )
=> sP308 )
=> sP302 ) ),
introduced(definition,[new_symbols(definition,[sP323])]) ).
thf(sP324,plain,
( sP324
<=> ( ~ sP311
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP324])]) ).
thf(sP325,plain,
( sP325
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP124
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP325])]) ).
thf(sP326,plain,
( sP326
<=> ( ~ ( sP191
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP326])]) ).
thf(sP327,plain,
( sP327
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP263
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP327])]) ).
thf(sP328,plain,
( sP328
<=> ! [X1: $i] :
( ~ ( ~ sP157
=> ~ sP78 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP328])]) ).
thf(sP329,plain,
( sP329
<=> ! [X1: $i] :
( ~ ( ~ sP132
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP329])]) ).
thf(sP330,plain,
( sP330
<=> ( ~ sP202
=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP330])]) ).
thf(sP331,plain,
( sP331
<=> ( ~ sP213
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP331])]) ).
thf(sP332,plain,
( sP332
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP332])]) ).
thf(sP333,plain,
( sP333
<=> ! [X1: $i] :
( ~ ( ~ sP268
=> ~ sP332 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP333])]) ).
thf(sP334,plain,
( sP334
<=> ( ~ ( ~ sP58
=> sP49 )
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP334])]) ).
thf(sP335,plain,
( sP335
<=> ( ~ sP229
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP335])]) ).
thf(sP336,plain,
( sP336
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP223
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP336])]) ).
thf(sP337,plain,
( sP337
<=> ( ~ ( ~ ( sP78
=> ~ sP130 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ sP173 ) ),
introduced(definition,[new_symbols(definition,[sP337])]) ).
thf(sP338,plain,
( sP338
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP281 ) ),
introduced(definition,[new_symbols(definition,[sP338])]) ).
thf(sP339,plain,
( sP339
<=> ( ~ sP203
=> ~ sP263 ) ),
introduced(definition,[new_symbols(definition,[sP339])]) ).
thf(sP340,plain,
( sP340
<=> ! [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,[sP340])]) ).
thf(sP341,plain,
( sP341
<=> ! [X1: $i] :
~ ( b @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP341])]) ).
thf(sP342,plain,
( sP342
<=> ( z
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP342])]) ).
thf(sP343,plain,
( sP343
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP191
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP343])]) ).
thf(sP344,plain,
( sP344
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP302 ) ),
introduced(definition,[new_symbols(definition,[sP344])]) ).
thf(sP345,plain,
( sP345
<=> ! [X1: $i] :
( ~ sP37
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP345])]) ).
thf(sP346,plain,
( sP346
<=> ( sP172
=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP346])]) ).
thf(sP347,plain,
( sP347
<=> ! [X1: $i] :
( ~ ( ( ( s @ ( s @ ( s @ z ) ) )
!= X1 )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP347])]) ).
thf(sP348,plain,
( sP348
<=> ! [X1: $i] :
( ~ sP241
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP348])]) ).
thf(sP349,plain,
( sP349
<=> ( ~ ( sP158
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP349])]) ).
thf(sP350,plain,
( sP350
<=> ( sP124
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP350])]) ).
thf(sP351,plain,
( sP351
<=> ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP351])]) ).
thf(sP352,plain,
( sP352
<=> ( ~ sP241
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP352])]) ).
thf(sP353,plain,
( sP353
<=> ! [X1: $i] :
( ~ sP315
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP353])]) ).
thf(sP354,plain,
( sP354
<=> ( sP61
=> sP48 ) ),
introduced(definition,[new_symbols(definition,[sP354])]) ).
thf(sP355,plain,
( sP355
<=> ( ~ sP89
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP355])]) ).
thf(sP356,plain,
( sP356
<=> ! [X1: $i] :
( ~ ( ~ ( sP62
=> ~ sP158 )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP356])]) ).
thf(sP357,plain,
( sP357
<=> ( ~ sP121
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP357])]) ).
thf(sP358,plain,
( sP358
<=> ( ~ sP73
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP358])]) ).
thf(sP359,plain,
( sP359
<=> ! [X1: $i] :
( ~ sP326
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP359])]) ).
thf(sP360,plain,
( sP360
<=> ( ~ sP74
=> ~ sP263 ) ),
introduced(definition,[new_symbols(definition,[sP360])]) ).
thf(sP361,plain,
( sP361
<=> ( ~ ( ~ ( sP113
=> ~ sP332 )
=> ~ sP308 )
=> ~ sP263 ) ),
introduced(definition,[new_symbols(definition,[sP361])]) ).
thf(sP362,plain,
( sP362
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP263 ) ),
introduced(definition,[new_symbols(definition,[sP362])]) ).
thf(sP363,plain,
( sP363
<=> ! [X1: $i] :
( ~ ( ~ ( sP78
=> ~ sP130 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP363])]) ).
thf(sP364,plain,
( sP364
<=> ( z
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP364])]) ).
thf(sP365,plain,
( sP365
<=> ! [X1: $i] :
( ~ sP168
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP365])]) ).
thf(sP366,plain,
( sP366
<=> ( ~ sP257
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP366])]) ).
thf(sP367,plain,
( sP367
<=> ( ~ sP268
=> ~ sP332 ) ),
introduced(definition,[new_symbols(definition,[sP367])]) ).
thf(sP368,plain,
( sP368
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP67
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP368])]) ).
thf(sP369,plain,
( sP369
<=> ! [X1: $i] :
( ~ sP349
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP369])]) ).
thf(sP370,plain,
( sP370
<=> ( ~ sP132
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP370])]) ).
thf(sP371,plain,
( sP371
<=> ( ~ sP169
=> ~ sP163 ) ),
introduced(definition,[new_symbols(definition,[sP371])]) ).
thf(sP372,plain,
( sP372
<=> ( ~ sP125
=> ~ sP308 ) ),
introduced(definition,[new_symbols(definition,[sP372])]) ).
thf(sP373,plain,
( sP373
<=> ( ~ ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ z ) )
=> sP263 )
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP373])]) ).
thf(sP374,plain,
( sP374
<=> ( ~ sP280
=> ~ sP332 ) ),
introduced(definition,[new_symbols(definition,[sP374])]) ).
thf(sP375,plain,
( sP375
<=> ! [X1: $i] :
( ~ ( ~ sP267
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP375])]) ).
thf(sP376,plain,
( sP376
<=> ! [X1: $i] :
( ~ sP117
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP376])]) ).
thf(sP377,plain,
( sP377
<=> ! [X1: $i] :
( ~ sP93
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP377])]) ).
thf(sP378,plain,
( sP378
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP67 ) ),
introduced(definition,[new_symbols(definition,[sP378])]) ).
thf(sP379,plain,
( sP379
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP379])]) ).
thf(sP380,plain,
( sP380
<=> ( ( s @ z )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP380])]) ).
thf(sP381,plain,
( sP381
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP211 ) ),
introduced(definition,[new_symbols(definition,[sP381])]) ).
thf(sP382,plain,
( sP382
<=> ! [X1: $i] :
( ~ sP283
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP382])]) ).
thf(sP383,plain,
( sP383
<=> ( ~ ( ~ sP182
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP383])]) ).
thf(sP384,plain,
( sP384
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP384])]) ).
thf(sP385,plain,
( sP385
<=> ( b @ ( s @ ( s @ z ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP385])]) ).
thf(sP386,plain,
( sP386
<=> ( ~ ( ~ sP362
=> ~ sP191 )
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP386])]) ).
thf(sP387,plain,
( sP387
<=> ( ~ sP197
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP387])]) ).
thf(sP388,plain,
( sP388
<=> ( ~ sP206
=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP388])]) ).
thf(sP389,plain,
( sP389
<=> ! [X1: $i] :
( ~ ( ~ sP338
=> ~ sP67 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP389])]) ).
thf(sP390,plain,
( sP390
<=> ( ~ sP387
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP390])]) ).
thf(sP391,plain,
( sP391
<=> ( ~ sP135
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP391])]) ).
thf(sP392,plain,
( sP392
<=> ( ~ ( ~ sP362
=> ~ sP191 )
=> ~ sP308 ) ),
introduced(definition,[new_symbols(definition,[sP392])]) ).
thf(sP393,plain,
( sP393
<=> ( ~ sP204
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP393])]) ).
thf(sP394,plain,
( sP394
<=> ( ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ z ) ) ) )
=> sP32 ) ),
introduced(definition,[new_symbols(definition,[sP394])]) ).
thf(sP395,plain,
( sP395
<=> ( ~ sP111
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP395])]) ).
thf(sP396,plain,
( sP396
<=> ( ~ sP251
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP396])]) ).
thf(sP397,plain,
( sP397
<=> ! [X1: $i] :
( ~ ( ~ sP165
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP397])]) ).
thf(sP398,plain,
( sP398
<=> ( ~ ( ~ sP188
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP398])]) ).
thf(sP399,plain,
( sP399
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP399])]) ).
thf(sP400,plain,
( sP400
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP400])]) ).
thf(sP401,plain,
( sP401
<=> ! [X1: $i] :
( ~ ( ~ sP294
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP401])]) ).
thf(sP402,plain,
( sP402
<=> ( ~ ( sP49
=> ~ sP308 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP402])]) ).
thf(sP403,plain,
( sP403
<=> ! [X1: $i] :
( ~ sP335
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP403])]) ).
thf(sP404,plain,
( sP404
<=> ( sP113
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP404])]) ).
thf(sP405,plain,
( sP405
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP405])]) ).
thf(sP406,plain,
( sP406
<=> ( sP263
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP406])]) ).
thf(sP407,plain,
( sP407
<=> ( sP211
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP407])]) ).
thf(sP408,plain,
( sP408
<=> ( r @ ( s @ z ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP408])]) ).
thf(sP409,plain,
( sP409
<=> ( ( b @ ( s @ z ) @ z )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP409])]) ).
thf(sP410,plain,
( sP410
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP410])]) ).
thf(sP411,plain,
( sP411
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP411])]) ).
thf(sP412,plain,
( sP412
<=> ( ~ ( sP78
=> ~ sP130 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP412])]) ).
thf(sP413,plain,
( sP413
<=> ( ~ sP404
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP413])]) ).
thf(sP414,plain,
( sP414
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( r @ X1 @ X2 )
=> ~ ( r @ X1 @ X3 ) )
=> ~ ( r @ X2 @ X3 ) )
=> ~ ( r @ X3 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP414])]) ).
thf(sP415,plain,
( sP415
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP15
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP415])]) ).
thf(sP416,plain,
( sP416
<=> ! [X1: $i] :
( ~ sP311
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP416])]) ).
thf(sP417,plain,
( sP417
<=> ( sP113
=> ~ sP332 ) ),
introduced(definition,[new_symbols(definition,[sP417])]) ).
thf(sP418,plain,
( sP418
<=> ( ~ sP247
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP418])]) ).
thf(sP419,plain,
( sP419
<=> ! [X1: $i] :
( ~ ( ~ sP243
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP419])]) ).
thf(sP420,plain,
( sP420
<=> ( ~ sP165
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP420])]) ).
thf(sP421,plain,
( sP421
<=> ( sP22
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP421])]) ).
thf(sP422,plain,
( sP422
<=> ( ~ sP378
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP422])]) ).
thf(sP423,plain,
( sP423
<=> ( ( s @ ( s @ z ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP423])]) ).
thf(sP424,plain,
( sP424
<=> ( sP53
=> ( ( s @ ( s @ z ) )
= ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP424])]) ).
thf(sP425,plain,
( sP425
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP425])]) ).
thf(sP426,plain,
( sP426
<=> ( ~ ( ~ sP196
=> ~ sP211 )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP426])]) ).
thf(sP427,plain,
( sP427
<=> ( sP62
=> ~ sP158 ) ),
introduced(definition,[new_symbols(definition,[sP427])]) ).
thf(sP428,plain,
( sP428
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP428])]) ).
thf(sP429,plain,
( sP429
<=> ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP429])]) ).
thf(sP430,plain,
( sP430
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP430])]) ).
thf(sP431,plain,
( sP431
<=> ( ~ sP152
=> ~ sP179 ) ),
introduced(definition,[new_symbols(definition,[sP431])]) ).
thf(sP432,plain,
( sP432
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP432])]) ).
thf(sP433,plain,
( sP433
<=> ! [X1: $i] :
( ~ sP213
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP433])]) ).
thf(sP434,plain,
( sP434
<=> ! [X1: $i] :
( ~ ( ~ sP318
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP434])]) ).
thf(sP435,plain,
( sP435
<=> ( ~ sP58
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP435])]) ).
thf(sP436,plain,
( sP436
<=> ( ~ ( ~ sP294
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP158 ) ),
introduced(definition,[new_symbols(definition,[sP436])]) ).
thf(sP437,plain,
( sP437
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP437])]) ).
thf(sP438,plain,
( sP438
<=> ! [X1: $i] :
( ~ sP251
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP438])]) ).
thf(sP439,plain,
( sP439
<=> ( ~ sP350
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP439])]) ).
thf(sP440,plain,
( sP440
<=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP440])]) ).
thf(sP441,plain,
( sP441
<=> ! [X1: $i] :
( ~ sP372
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP441])]) ).
thf(sP442,plain,
( sP442
<=> ! [X1: $i] :
( ~ sP122
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP442])]) ).
thf(sP443,plain,
( sP443
<=> ( ~ sP311
=> ~ sP211 ) ),
introduced(definition,[new_symbols(definition,[sP443])]) ).
thf(sP444,plain,
( sP444
<=> ( ~ ( ~ sP430
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ sP312 ) ),
introduced(definition,[new_symbols(definition,[sP444])]) ).
thf(sP445,plain,
( sP445
<=> ( ~ sP34
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP445])]) ).
thf(sP446,plain,
( sP446
<=> ( ~ ( ~ sP410
=> ~ sP385 )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP446])]) ).
thf(sP447,plain,
( sP447
<=> ( sP440
=> sP380 ) ),
introduced(definition,[new_symbols(definition,[sP447])]) ).
thf(sP448,plain,
( sP448
<=> ! [X1: $i] :
( ~ sP402
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP448])]) ).
thf(sP449,plain,
( sP449
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP449])]) ).
thf(sP450,plain,
( sP450
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ X1 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP450])]) ).
thf(sP451,plain,
( sP451
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ z ) @ z )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP451])]) ).
thf(sP452,plain,
( sP452
<=> ( ~ ( ~ sP294
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP452])]) ).
thf(sP453,plain,
( sP453
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP453])]) ).
thf(sP454,plain,
( sP454
<=> ( sP49
=> ~ sP308 ) ),
introduced(definition,[new_symbols(definition,[sP454])]) ).
thf(sP455,plain,
( sP455
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP455])]) ).
thf(sP456,plain,
( sP456
<=> ( ~ ( ~ sP20
=> ~ sP312 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP456])]) ).
thf(sP457,plain,
( sP457
<=> ( sP449
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP457])]) ).
thf(sP458,plain,
( sP458
<=> ( b @ z @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP458])]) ).
thf(sP459,plain,
( sP459
<=> ! [X1: $i] :
( ~ sP411
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP459])]) ).
thf(sP460,plain,
( sP460
<=> ( ~ sP115
=> sP62 ) ),
introduced(definition,[new_symbols(definition,[sP460])]) ).
thf(sP461,plain,
( sP461
<=> ! [X1: $i] :
( ~ ( ~ sP265
=> ~ sP449 )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP461])]) ).
thf(sP462,plain,
( sP462
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ sP455 ) ),
introduced(definition,[new_symbols(definition,[sP462])]) ).
thf(sP463,plain,
( sP463
<=> ! [X1: $i] :
( ~ sP314
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP463])]) ).
thf(sP464,plain,
( sP464
<=> ( ~ sP380
=> sP308 ) ),
introduced(definition,[new_symbols(definition,[sP464])]) ).
thf(sP465,plain,
( sP465
<=> ( ~ sP44
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP465])]) ).
thf(sP466,plain,
( sP466
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP466])]) ).
thf(sP467,plain,
( sP467
<=> ( sP78
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP467])]) ).
thf(sP468,plain,
( sP468
<=> ( ~ ( sP312
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ sP385 ) ),
introduced(definition,[new_symbols(definition,[sP468])]) ).
thf(sP469,plain,
( sP469
<=> ( ~ sP338
=> ~ sP67 ) ),
introduced(definition,[new_symbols(definition,[sP469])]) ).
thf(sP470,plain,
( sP470
<=> ( sP158
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP470])]) ).
thf(sP471,plain,
( sP471
<=> ( ~ sP243
=> ~ sP429 ) ),
introduced(definition,[new_symbols(definition,[sP471])]) ).
thf(sP472,plain,
( sP472
<=> ( ~ ( ~ sP409
=> ~ sP429 )
=> ~ sP449 ) ),
introduced(definition,[new_symbols(definition,[sP472])]) ).
thf(sP473,plain,
( sP473
<=> ( ( ( s @ z )
!= z )
=> sP163 ) ),
introduced(definition,[new_symbols(definition,[sP473])]) ).
thf(sP474,plain,
( sP474
<=> ( ~ sP157
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP474])]) ).
thf(sP475,plain,
( sP475
<=> ( ~ sP251
=> ~ sP244 ) ),
introduced(definition,[new_symbols(definition,[sP475])]) ).
thf(sP476,plain,
( sP476
<=> ( ~ sP251
=> ~ sP429 ) ),
introduced(definition,[new_symbols(definition,[sP476])]) ).
thf(sP477,plain,
( sP477
<=> ( ~ sP246
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP477])]) ).
thf(sP478,plain,
( sP478
<=> ( ~ sP159
=> sP385 ) ),
introduced(definition,[new_symbols(definition,[sP478])]) ).
thf(sP479,plain,
( sP479
<=> ( ~ sP278
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP479])]) ).
thf(sP480,plain,
( sP480
<=> ( ~ ( ~ sP294
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP480])]) ).
thf(sP481,plain,
( sP481
<=> ( ~ sP122
=> ~ sP173 ) ),
introduced(definition,[new_symbols(definition,[sP481])]) ).
thf(sP482,plain,
( sP482
<=> ( ~ ( ~ sP277
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP482])]) ).
thf(sP483,plain,
( sP483
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP130
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP483])]) ).
thf(sP484,plain,
( sP484
<=> ( ~ sP81
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP484])]) ).
thf(sP485,plain,
( sP485
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP485])]) ).
thf(sP486,plain,
( sP486
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ sP455 ) ),
introduced(definition,[new_symbols(definition,[sP486])]) ).
thf(sP487,plain,
( sP487
<=> ! [X1: $i] :
( ~ ( ~ sP264
=> ~ sP179 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP487])]) ).
thf(sP488,plain,
( sP488
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP488])]) ).
thf(sP489,plain,
( sP489
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP489])]) ).
thf(sP490,plain,
( sP490
<=> ( ~ sP367
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP490])]) ).
thf(sP491,plain,
( sP491
<=> ( ~ sP209
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP491])]) ).
thf(sP492,plain,
( sP492
<=> ( ~ sP97
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP492])]) ).
thf(sP493,plain,
( sP493
<=> ( sP488
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP493])]) ).
thf(sP494,plain,
( sP494
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ z ) )
=> ( ( s @ ( s @ ( s @ z ) ) )
= z ) ) ),
introduced(definition,[new_symbols(definition,[sP494])]) ).
thf(sP495,plain,
( sP495
<=> ( ~ ( ~ sP264
=> ~ sP179 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP495])]) ).
thf(sP496,plain,
( sP496
<=> ( ~ sP427
=> ~ sP458 ) ),
introduced(definition,[new_symbols(definition,[sP496])]) ).
thf(sP497,plain,
( sP497
<=> ( ( s @ z )
= z ) ),
introduced(definition,[new_symbols(definition,[sP497])]) ).
thf(sP498,plain,
( sP498
<=> ! [X1: $i] :
( ~ sP156
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP498])]) ).
thf(sP499,plain,
( sP499
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ z ) )
=> sP191 ) ),
introduced(definition,[new_symbols(definition,[sP499])]) ).
thf(sP500,plain,
( sP500
<=> ( ~ sP294
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP500])]) ).
thf(sP501,plain,
( sP501
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP113
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP501])]) ).
thf(sP502,plain,
( sP502
<=> ! [X1: $i] :
( ~ ( ~ sP196
=> ~ sP211 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP502])]) ).
thf(sP503,plain,
( sP503
<=> ( ~ sP106
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP503])]) ).
thf(sP504,plain,
( sP504
<=> ( ~ ( ~ sP264
=> ~ sP179 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP504])]) ).
thf(sP505,plain,
( sP505
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP505])]) ).
thf(sP506,plain,
( sP506
<=> ( ~ sP445
=> ~ sP80 ) ),
introduced(definition,[new_symbols(definition,[sP506])]) ).
thf(sP507,plain,
( sP507
<=> ( ~ sP371
=> ~ sP80 ) ),
introduced(definition,[new_symbols(definition,[sP507])]) ).
thf(sP508,plain,
( sP508
<=> ( ~ sP29
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP508])]) ).
thf(sP509,plain,
( sP509
<=> ( sP78
=> ~ sP179 ) ),
introduced(definition,[new_symbols(definition,[sP509])]) ).
thf(sP510,plain,
( sP510
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP510])]) ).
thf(sP511,plain,
( sP511
<=> ( ~ ( ~ sP322
=> ~ sP332 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP511])]) ).
thf(sP512,plain,
( sP512
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP512])]) ).
thf(sP513,plain,
( sP513
<=> ( sP312
=> ~ sP302 ) ),
introduced(definition,[new_symbols(definition,[sP513])]) ).
thf(sP514,plain,
( sP514
<=> ( sP223
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP514])]) ).
thf(sP515,plain,
( sP515
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP515])]) ).
thf(sP516,plain,
( sP516
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP244
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP516])]) ).
thf(sP517,plain,
( sP517
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP517])]) ).
thf(sP518,plain,
( sP518
<=> ( sP312
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP518])]) ).
thf(sP519,plain,
( sP519
<=> ( ~ ( ~ ( sP130
=> ~ sP78 )
=> ~ sP49 )
=> ~ sP437 ) ),
introduced(definition,[new_symbols(definition,[sP519])]) ).
thf(sP520,plain,
( sP520
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP520])]) ).
thf(sP521,plain,
( sP521
<=> ! [X1: $i] :
( ~ sP81
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP521])]) ).
thf(sP522,plain,
( sP522
<=> ! [X1: $i] :
( ~ sP413
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP522])]) ).
thf(sP523,plain,
( sP523
<=> ( ~ sP37
=> ~ sP425 ) ),
introduced(definition,[new_symbols(definition,[sP523])]) ).
thf(sP524,plain,
( sP524
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP510 ) ),
introduced(definition,[new_symbols(definition,[sP524])]) ).
thf(sP525,plain,
( sP525
<=> ( ~ sP417
=> ~ sP308 ) ),
introduced(definition,[new_symbols(definition,[sP525])]) ).
thf(sP526,plain,
( sP526
<=> ( sP158
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP526])]) ).
thf(sP527,plain,
( sP527
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP527])]) ).
thf(sP528,plain,
( sP528
<=> ! [X1: $i] :
( ~ sP183
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP528])]) ).
thf(sP529,plain,
( sP529
<=> ! [X1: $i] :
( ~ ( ~ sP20
=> ~ sP312 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP529])]) ).
thf(sP530,plain,
( sP530
<=> ( ~ sP335
=> ~ sP449 ) ),
introduced(definition,[new_symbols(definition,[sP530])]) ).
thf(sP531,plain,
( sP531
<=> ( ~ sP322
=> ~ sP332 ) ),
introduced(definition,[new_symbols(definition,[sP531])]) ).
thf(sP532,plain,
( sP532
<=> ( ~ sP277
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP532])]) ).
thf(sP533,plain,
( sP533
<=> ( sP163
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP533])]) ).
thf(sP534,plain,
( sP534
<=> ( ~ sP358
=> ~ sP263 ) ),
introduced(definition,[new_symbols(definition,[sP534])]) ).
thf(sP535,plain,
( sP535
<=> ( ~ sP360
=> ~ sP173 ) ),
introduced(definition,[new_symbols(definition,[sP535])]) ).
thf(sP536,plain,
( sP536
<=> ! [X1: $i] :
( ( ( s @ ( s @ z ) )
= ( s @ X1 ) )
=> ( ( s @ z )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP536])]) ).
thf(sP537,plain,
( sP537
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP537])]) ).
thf(sP538,plain,
( sP538
<=> ( ~ ( ~ sP514
=> ~ sP312 )
=> ~ sP385 ) ),
introduced(definition,[new_symbols(definition,[sP538])]) ).
thf(sP539,plain,
( sP539
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP80
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP539])]) ).
thf(sP540,plain,
( sP540
<=> ( ~ ( ~ sP514
=> ~ sP312 )
=> ~ sP505 ) ),
introduced(definition,[new_symbols(definition,[sP540])]) ).
thf(sP541,plain,
( sP541
<=> ( sP512
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP541])]) ).
thf(sP542,plain,
( sP542
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP542])]) ).
thf(sP543,plain,
( sP543
<=> ( ~ sP205
=> ~ sP449 ) ),
introduced(definition,[new_symbols(definition,[sP543])]) ).
thf(sP544,plain,
( sP544
<=> ( sP191
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP544])]) ).
thf(sP545,plain,
( sP545
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP545])]) ).
thf(sP546,plain,
( sP546
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP546])]) ).
thf(sP547,plain,
( sP547
<=> ! [X1: $i] :
( ~ sP225
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP547])]) ).
thf(sP548,plain,
( sP548
<=> ! [X1: $i] :
( ~ ( ( z != X1 )
=> ( r @ z @ X1 ) )
=> ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP548])]) ).
thf(sP549,plain,
( sP549
<=> ( ~ sP84
=> ~ sP312 ) ),
introduced(definition,[new_symbols(definition,[sP549])]) ).
thf(sP550,plain,
( sP550
<=> ! [X1: $i] :
( ~ sP257
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP550])]) ).
thf(sP551,plain,
( sP551
<=> ( ~ ( ~ sP20
=> ~ sP312 )
=> ~ sP488 ) ),
introduced(definition,[new_symbols(definition,[sP551])]) ).
thf(sP552,plain,
( sP552
<=> ( ( b @ ( s @ z ) @ z )
=> ~ sP302 ) ),
introduced(definition,[new_symbols(definition,[sP552])]) ).
thf(sP553,plain,
( sP553
<=> ( ~ sP196
=> ~ sP211 ) ),
introduced(definition,[new_symbols(definition,[sP553])]) ).
thf(sP554,plain,
( sP554
<=> ( sP510
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP554])]) ).
thf(sP555,plain,
( sP555
<=> ( ~ sP32
=> sP173 ) ),
introduced(definition,[new_symbols(definition,[sP555])]) ).
thf(sP556,plain,
( sP556
<=> ! [X1: $i] :
( ~ sP371
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP556])]) ).
thf(sP557,plain,
( sP557
<=> ( ~ ( ( r @ ( s @ ( s @ z ) ) @ z )
=> ~ sP22 )
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP557])]) ).
thf(sP558,plain,
( sP558
<=> ( sP32
=> sP364 ) ),
introduced(definition,[new_symbols(definition,[sP558])]) ).
thf(sP559,plain,
( sP559
<=> ( b @ ( s @ z ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP559])]) ).
thf(sP560,plain,
( sP560
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP560])]) ).
thf(sP561,plain,
( sP561
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP425
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP561])]) ).
thf(sP562,plain,
( sP562
<=> ( ( s @ ( s @ ( s @ z ) ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP562])]) ).
thf(sP563,plain,
( sP563
<=> ( sP263
=> ~ sP520 ) ),
introduced(definition,[new_symbols(definition,[sP563])]) ).
thf(sP564,plain,
( sP564
<=> ( ~ ( ~ sP267
=> ~ sP517 )
=> ~ sP455 ) ),
introduced(definition,[new_symbols(definition,[sP564])]) ).
thf(sP565,plain,
( sP565
<=> ! [X1: $i] :
( ~ sP418
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP565])]) ).
thf(sP566,plain,
( sP566
<=> ! [X1: $i] :
( ~ sP160
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP566])]) ).
thf(sP567,plain,
( sP567
<=> ! [X1: $i] :
( ~ sP97
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP567])]) ).
thf(sP568,plain,
( sP568
<=> ! [X1: $i,X2: $i] :
( ~ ( ( X1 != X2 )
=> ( r @ X1 @ X2 ) )
=> ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP568])]) ).
thf(sP569,plain,
( sP569
<=> ( ~ sP439
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP569])]) ).
thf(sP570,plain,
( sP570
<=> ( ( s @ ( s @ z ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP570])]) ).
thf(sP571,plain,
( sP571
<=> ! [X1: $i] :
( ~ sP134
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP571])]) ).
thf(sP572,plain,
( sP572
<=> ( ~ sP351
=> ~ sP488 ) ),
introduced(definition,[new_symbols(definition,[sP572])]) ).
thf(sP573,plain,
( sP573
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ z ) )
=> sP263 ) ),
introduced(definition,[new_symbols(definition,[sP573])]) ).
thf(sP574,plain,
( sP574
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP574])]) ).
thf(sP575,plain,
( sP575
<=> ( ~ sP335
=> ~ sP515 ) ),
introduced(definition,[new_symbols(definition,[sP575])]) ).
thf(sP576,plain,
( sP576
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP576])]) ).
thf(sP577,plain,
( sP577
<=> ( ~ sP572
=> ~ sP302 ) ),
introduced(definition,[new_symbols(definition,[sP577])]) ).
thf(sP578,plain,
( sP578
<=> ! [X1: $i] :
( ~ sP203
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP578])]) ).
thf(sP579,plain,
( sP579
<=> ( ~ sP160
=> ~ sP173 ) ),
introduced(definition,[new_symbols(definition,[sP579])]) ).
thf(sP580,plain,
( sP580
<=> ! [X1: $i] :
( ~ sP278
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP580])]) ).
thf(sP581,plain,
( sP581
<=> ( ~ sP411
=> ~ sP429 ) ),
introduced(definition,[new_symbols(definition,[sP581])]) ).
thf(sP582,plain,
( sP582
<=> ( ~ ( ~ sP554
=> ~ sP19 )
=> ~ sP302 ) ),
introduced(definition,[new_symbols(definition,[sP582])]) ).
thf(sP583,plain,
( sP583
<=> ( ~ sP557
=> ~ sP432 ) ),
introduced(definition,[new_symbols(definition,[sP583])]) ).
thf(sP584,plain,
( sP584
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP49
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP584])]) ).
thf(sP585,plain,
( sP585
<=> ( r @ ( s @ ( s @ z ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP585])]) ).
thf(sP586,plain,
( sP586
<=> ( ~ ( ~ sP533
=> ~ sP78 )
=> ~ sP437 ) ),
introduced(definition,[new_symbols(definition,[sP586])]) ).
thf(sP587,plain,
( sP587
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP302
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP587])]) ).
thf(sP588,plain,
( sP588
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP588])]) ).
thf(sP589,plain,
( sP589
<=> ( ~ sP508
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP589])]) ).
thf(sP590,plain,
( sP590
<=> ! [X1: $i] :
( ~ sP89
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP590])]) ).
thf(sP591,plain,
( sP591
<=> ( sP585
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP591])]) ).
thf(sP592,plain,
( sP592
<=> ! [X1: $i] :
( ~ ( ~ sP514
=> ~ sP312 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP592])]) ).
thf(sP593,plain,
( sP593
<=> ( sP281
=> ~ sP191 ) ),
introduced(definition,[new_symbols(definition,[sP593])]) ).
thf(sP594,plain,
( sP594
<=> ( ~ sP20
=> ~ sP312 ) ),
introduced(definition,[new_symbols(definition,[sP594])]) ).
thf(sP595,plain,
( sP595
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP595])]) ).
thf(sP596,plain,
( sP596
<=> ( ~ ( ~ sP409
=> ~ sP429 )
=> ~ sP515 ) ),
introduced(definition,[new_symbols(definition,[sP596])]) ).
thf(sP597,plain,
( sP597
<=> ( ~ sP422
=> ~ sP332 ) ),
introduced(definition,[new_symbols(definition,[sP597])]) ).
thf(sP598,plain,
( sP598
<=> ( ~ sP533
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP598])]) ).
thf(sP599,plain,
( sP599
<=> ( ~ sP82
=> sP244 ) ),
introduced(definition,[new_symbols(definition,[sP599])]) ).
thf(sP600,plain,
( sP600
<=> ( ~ sP349
=> ~ sP211 ) ),
introduced(definition,[new_symbols(definition,[sP600])]) ).
thf(sP601,plain,
( sP601
<=> ( ~ sP457
=> ~ sP559 ) ),
introduced(definition,[new_symbols(definition,[sP601])]) ).
thf(sP602,plain,
( sP602
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP602])]) ).
thf(sP603,plain,
( sP603
<=> ( ~ sP314
=> ~ sP455 ) ),
introduced(definition,[new_symbols(definition,[sP603])]) ).
thf(sP604,plain,
( sP604
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( r @ ( s @ ( s @ z ) ) @ X1 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP604])]) ).
thf(sP605,plain,
( sP605
<=> ! [X1: $i] :
( ~ sP55
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP605])]) ).
thf(sP606,plain,
( sP606
<=> ( ~ ( ~ sP409
=> ~ sP429 )
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP606])]) ).
thf(sP607,plain,
( sP607
<=> ( ~ sP265
=> ~ sP449 ) ),
introduced(definition,[new_symbols(definition,[sP607])]) ).
thf(sP608,plain,
( sP608
<=> ( ~ sP554
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP608])]) ).
thf(sP609,plain,
( sP609
<=> ! [X1: $i] :
( ~ sP508
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP609])]) ).
thf(sP610,plain,
( sP610
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP312
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP610])]) ).
thf(sP611,plain,
( sP611
<=> ( sP244
=> ~ sP458 ) ),
introduced(definition,[new_symbols(definition,[sP611])]) ).
thf(sP612,plain,
( sP612
<=> ( ~ sP26
=> ~ sP437 ) ),
introduced(definition,[new_symbols(definition,[sP612])]) ).
thf(sP613,plain,
( sP613
<=> ( sP67
=> ~ sP432 ) ),
introduced(definition,[new_symbols(definition,[sP613])]) ).
thf(sP614,plain,
( sP614
<=> ( sP11
=> sP602 ) ),
introduced(definition,[new_symbols(definition,[sP614])]) ).
thf(sP615,plain,
( sP615
<=> ! [X1: $i] :
( ~ ( ~ sP182
=> ~ sP458 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP615])]) ).
thf(sP616,plain,
( sP616
<=> ( sP545
=> ~ sP560 ) ),
introduced(definition,[new_symbols(definition,[sP616])]) ).
thf(sP617,plain,
( sP617
<=> ( ~ sP61
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP617])]) ).
thf(sP618,plain,
( sP618
<=> ! [X1: $i] :
( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ X1 ) )
=> ( ( s @ ( s @ ( s @ z ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP618])]) ).
thf(sP619,plain,
( sP619
<=> ( sP425
=> ~ sP560 ) ),
introduced(definition,[new_symbols(definition,[sP619])]) ).
thf(sP620,plain,
( sP620
<=> ( ~ sP189
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP620])]) ).
thf(sP621,plain,
( sP621
<=> ( sP505
=> ~ sP385 ) ),
introduced(definition,[new_symbols(definition,[sP621])]) ).
thf(sP622,plain,
( sP622
<=> ! [X1: $i] :
( ~ sP431
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP622])]) ).
thf(sP623,plain,
( sP623
<=> ( ~ sP123
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP623])]) ).
thf(sP624,plain,
( sP624
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP14
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP624])]) ).
thf(sP625,plain,
( sP625
<=> ( ~ sP410
=> ~ sP385 ) ),
introduced(definition,[new_symbols(definition,[sP625])]) ).
thf(sP626,plain,
( sP626
<=> ! [X1: $i] :
( ~ sP121
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP626])]) ).
thf(sP627,plain,
( sP627
<=> ( ~ sP26
=> ~ sP489 ) ),
introduced(definition,[new_symbols(definition,[sP627])]) ).
thf(sP628,plain,
( sP628
<=> ( ~ ( ~ sP509
=> ~ sP437 )
=> ~ sP263 ) ),
introduced(definition,[new_symbols(definition,[sP628])]) ).
thf(sP629,plain,
( sP629
<=> ( ~ sP372
=> ~ sP263 ) ),
introduced(definition,[new_symbols(definition,[sP629])]) ).
thf(sP630,plain,
( sP630
<=> ( ~ sP371
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP630])]) ).
thf(sP631,plain,
( sP631
<=> ( sP22
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP631])]) ).
thf(sP632,plain,
( sP632
<=> ( sP588
=> ~ sP520 ) ),
introduced(definition,[new_symbols(definition,[sP632])]) ).
thf(sP633,plain,
( sP633
<=> ( sP602
=> sP423 ) ),
introduced(definition,[new_symbols(definition,[sP633])]) ).
thf(sP634,plain,
( sP634
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP432
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP634])]) ).
thf(sP635,plain,
( sP635
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP635])]) ).
thf(sP636,plain,
( sP636
<=> ( ~ sP28
=> ~ sP113 ) ),
introduced(definition,[new_symbols(definition,[sP636])]) ).
thf(sP637,plain,
( sP637
<=> ( sP489
=> ~ sP432 ) ),
introduced(definition,[new_symbols(definition,[sP637])]) ).
thf(sP638,plain,
( sP638
<=> ( ~ sP264
=> ~ sP179 ) ),
introduced(definition,[new_symbols(definition,[sP638])]) ).
thf(sP639,plain,
( sP639
<=> ( ~ sP89
=> ~ sP437 ) ),
introduced(definition,[new_symbols(definition,[sP639])]) ).
thf(sP640,plain,
( sP640
<=> ( sP560
=> ~ sP510 ) ),
introduced(definition,[new_symbols(definition,[sP640])]) ).
thf(sP641,plain,
( sP641
<=> ( sP455
=> ~ sP385 ) ),
introduced(definition,[new_symbols(definition,[sP641])]) ).
thf(sP642,plain,
( sP642
<=> ( sP130
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP642])]) ).
thf(sP643,plain,
( sP643
<=> ( ~ sP59
=> ~ sP163 ) ),
introduced(definition,[new_symbols(definition,[sP643])]) ).
thf(sP644,plain,
( sP644
<=> ( ~ sP121
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP644])]) ).
thf(sP645,plain,
( sP645
<=> ( ~ sP220
=> ~ sP312 ) ),
introduced(definition,[new_symbols(definition,[sP645])]) ).
thf(sP646,plain,
( sP646
<=> ( ~ sP537
=> sP67 ) ),
introduced(definition,[new_symbols(definition,[sP646])]) ).
thf(sP647,plain,
( sP647
<=> ( ~ sP311
=> ~ sP510 ) ),
introduced(definition,[new_symbols(definition,[sP647])]) ).
thf(sP648,plain,
( sP648
<=> ( sP429
=> ~ sP244 ) ),
introduced(definition,[new_symbols(definition,[sP648])]) ).
thf(sP649,plain,
( sP649
<=> ( ~ sP526
=> ~ sP385 ) ),
introduced(definition,[new_symbols(definition,[sP649])]) ).
thf(sP650,plain,
( sP650
<=> ( ~ sP430
=> ~ sP560 ) ),
introduced(definition,[new_symbols(definition,[sP650])]) ).
thf(sP651,plain,
( sP651
<=> ! [X1: $i] :
~ ( r @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP651])]) ).
thf(sP652,plain,
( sP652
<=> ( ~ sP188
=> ~ sP510 ) ),
introduced(definition,[new_symbols(definition,[sP652])]) ).
thf(sP653,plain,
( sP653
<=> ( ~ sP183
=> ~ sP332 ) ),
introduced(definition,[new_symbols(definition,[sP653])]) ).
thf(sP654,plain,
( sP654
<=> ! [X1: $i] :
( ~ ( ~ sP409
=> ~ sP429 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP654])]) ).
thf(sP655,plain,
( sP655
<=> ! [X1: $i] :
( ~ ( ~ sP642
=> ~ sP49 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP655])]) ).
thf(sP656,plain,
( sP656
<=> ( ~ sP471
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP656])]) ).
thf(sP657,plain,
( sP657
<=> ( ~ sP402
=> ~ sP588 ) ),
introduced(definition,[new_symbols(definition,[sP657])]) ).
thf(sP658,plain,
( sP658
<=> ( ~ sP469
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP658])]) ).
thf(sP659,plain,
( sP659
<=> ( ~ sP284
=> sP455 ) ),
introduced(definition,[new_symbols(definition,[sP659])]) ).
thf(sP660,plain,
( sP660
<=> ( ~ sP320
=> ~ sP458 ) ),
introduced(definition,[new_symbols(definition,[sP660])]) ).
thf(sP661,plain,
( sP661
<=> ( ~ sP509
=> ~ sP437 ) ),
introduced(definition,[new_symbols(definition,[sP661])]) ).
thf(sP662,plain,
( sP662
<=> ( ~ sP37
=> ~ sP510 ) ),
introduced(definition,[new_symbols(definition,[sP662])]) ).
thf(sP663,plain,
( sP663
<=> ( ~ sP318
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP663])]) ).
thf(sP664,plain,
( sP664
<=> ( ~ sP555
=> sP312 ) ),
introduced(definition,[new_symbols(definition,[sP664])]) ).
thf(sP665,plain,
( sP665
<=> ( ~ sP514
=> ~ sP312 ) ),
introduced(definition,[new_symbols(definition,[sP665])]) ).
thf(sP666,plain,
( sP666
<=> ( ~ sP409
=> ~ sP429 ) ),
introduced(definition,[new_symbols(definition,[sP666])]) ).
thf(sP667,plain,
( sP667
<=> ( ~ sP168
=> ~ sP505 ) ),
introduced(definition,[new_symbols(definition,[sP667])]) ).
thf(sP668,plain,
( sP668
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP668])]) ).
thf(sP669,plain,
( sP669
<=> ( sP505
=> ~ sP488 ) ),
introduced(definition,[new_symbols(definition,[sP669])]) ).
thf(sP670,plain,
( sP670
<=> ( ~ sP213
=> ~ sP510 ) ),
introduced(definition,[new_symbols(definition,[sP670])]) ).
thf(sP671,plain,
( sP671
<=> ( ~ sP303
=> sP458 ) ),
introduced(definition,[new_symbols(definition,[sP671])]) ).
thf(sP672,plain,
( sP672
<=> ( ~ sP94
=> sP510 ) ),
introduced(definition,[new_symbols(definition,[sP672])]) ).
thf(sP673,plain,
( sP673
<=> ( ~ sP642
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP673])]) ).
thf(sP674,plain,
( sP674
<=> ( ~ sP637
=> ~ sP130 ) ),
introduced(definition,[new_symbols(definition,[sP674])]) ).
thf(sP675,plain,
( sP675
<=> ( ~ sP620
=> ~ sP308 ) ),
introduced(definition,[new_symbols(definition,[sP675])]) ).
thf(sP676,plain,
( sP676
<=> ( sP302
=> ~ sP559 ) ),
introduced(definition,[new_symbols(definition,[sP676])]) ).
thf(sP677,plain,
( sP677
<=> ( sP449
=> ~ sP515 ) ),
introduced(definition,[new_symbols(definition,[sP677])]) ).
thf(sP678,plain,
( sP678
<=> ( ~ sP104
=> sP78 ) ),
introduced(definition,[new_symbols(definition,[sP678])]) ).
thf(sP679,plain,
( sP679
<=> ! [X1: $i] :
( ~ sP445
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP679])]) ).
thf(sP680,plain,
( sP680
<=> ( ~ sP663
=> ~ sP437 ) ),
introduced(definition,[new_symbols(definition,[sP680])]) ).
thf(sP681,plain,
( sP681
<=> ! [X1: $i] :
( ~ sP279
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP681])]) ).
thf(sP682,plain,
( sP682
<=> $false ),
introduced(definition,[new_symbols(definition,[sP682])]) ).
thf(sP683,plain,
( sP683
<=> ( ~ sP69
=> ~ sP449 ) ),
introduced(definition,[new_symbols(definition,[sP683])]) ).
thf(sP684,plain,
( sP684
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP684])]) ).
thf(sP685,plain,
( sP685
<=> ( ~ sP371
=> ~ sP78 ) ),
introduced(definition,[new_symbols(definition,[sP685])]) ).
thf(sP686,plain,
( sP686
<=> ( sP588
=> ~ sP263 ) ),
introduced(definition,[new_symbols(definition,[sP686])]) ).
thf(sP687,plain,
( sP687
<=> ( ~ sP362
=> ~ sP191 ) ),
introduced(definition,[new_symbols(definition,[sP687])]) ).
thf(sP688,plain,
( sP688
<=> ! [X1: $i] :
( ~ sP531
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP688])]) ).
thf(sP689,plain,
( sP689
<=> ( ~ sP111
=> ~ sP425 ) ),
introduced(definition,[new_symbols(definition,[sP689])]) ).
thf(sP690,plain,
( sP690
<=> ( ~ sP267
=> ~ sP517 ) ),
introduced(definition,[new_symbols(definition,[sP690])]) ).
thf(sP691,plain,
( sP691
<=> ! [X1: $i] :
( ~ sP650
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP691])]) ).
thf(sP692,plain,
( sP692
<=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP692])]) ).
thf(sP693,plain,
( sP693
<=> ( ~ sP182
=> ~ sP458 ) ),
introduced(definition,[new_symbols(definition,[sP693])]) ).
thf(sP694,plain,
( sP694
<=> ( sP517
=> ~ sP150 ) ),
introduced(definition,[new_symbols(definition,[sP694])]) ).
thf(sP695,plain,
( sP695
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP576
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP695])]) ).
thf(sP696,plain,
( sP696
<=> ! [X1: $i] :
( ~ sP608
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP696])]) ).
thf(1,plain,
( ~ sP432
| sP27
| ~ sP58
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP449
| sP466
| ~ sP58
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP489
| sP27
| ~ sP104
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP62
| sP466
| ~ sP104
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP125
| ~ sP432
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP372
| sP125
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP613
| ~ sP67
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP122
| sP613
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP34
| ~ sP437
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP445
| sP34
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP74
| ~ sP437
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP360
| sP74
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP378
| ~ sP437
| ~ sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP422
| sP378
| ~ sP520 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP194
| ~ sP62
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP257
| sP194
| ~ sP244 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP677
| ~ sP449
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP344
| sP677
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP470
| ~ sP158
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP349
| sP470
| ~ sP455 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP188
| ~ sP515
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP652
| sP188
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP430
| ~ sP515
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP650
| sP430
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP637
| ~ sP489
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP674
| sP637
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP214
| sP674
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP629
| sP372
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP299
| sP372
| ~ sP520 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP481
| sP122
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP506
| sP445
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP154
| sP445
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP249
| sP360
| ~ sP163 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP535
| sP360
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP171
| sP360
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP597
| sP422
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP427
| ~ sP62
| ~ sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP496
| sP427
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP155
| sP496
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP366
| sP257
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP298
| sP601
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP457
| ~ sP449
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP601
| sP457
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP50
| sP344
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP119
| sP344
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP127
| sP649
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP526
| ~ sP158
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP649
| sP526
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP600
| sP349
| ~ sP211 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP398
| sP652
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP269
| sP652
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP23
| sP652
| ~ sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP162
| sP650
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP444
| sP650
| ~ sP312 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP648
| ~ sP429
| ~ sP244 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP311
| sP648
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP509
| ~ sP78
| ~ sP179 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP661
| sP509
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP219
| ~ sP14
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP111
| sP219
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP454
| ~ sP49
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP402
| sP454
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP669
| ~ sP505
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP176
| sP669
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP462
| ~ sP505
| ~ sP455 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP213
| sP462
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP631
| ~ sP22
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP161
| sP631
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP73
| ~ sP22
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP358
| sP73
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(71,plain,
( ~ sP407
| ~ sP211
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( ~ sP283
| sP407
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP265
| ~ sP211
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP607
| sP265
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP541
| ~ sP512
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP315
| sP541
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP184
| ~ sP512
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( ~ sP7
| sP184
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP132
| ~ sP15
| ~ sP223 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
( ~ sP370
| sP132
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(81,plain,
( ~ sP338
| ~ sP668
| ~ sP281 ),
inference(prop_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP469
| sP338
| ~ sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP295
| sP214 ),
inference(all_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP441
| sP629 ),
inference(all_rule,[status(thm)],[]) ).
thf(85,plain,
( ~ sP441
| sP299 ),
inference(all_rule,[status(thm)],[]) ).
thf(86,plain,
( ~ sP442
| sP481 ),
inference(all_rule,[status(thm)],[]) ).
thf(87,plain,
( ~ sP679
| sP506 ),
inference(all_rule,[status(thm)],[]) ).
thf(88,plain,
( ~ sP679
| sP154 ),
inference(all_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP77
| sP249 ),
inference(all_rule,[status(thm)],[]) ).
thf(90,plain,
( ~ sP77
| sP535 ),
inference(all_rule,[status(thm)],[]) ).
thf(91,plain,
( ~ sP77
| sP171 ),
inference(all_rule,[status(thm)],[]) ).
thf(92,plain,
( ~ sP5
| sP597 ),
inference(all_rule,[status(thm)],[]) ).
thf(93,plain,
( ~ sP356
| sP155 ),
inference(all_rule,[status(thm)],[]) ).
thf(94,plain,
( ~ sP550
| sP366 ),
inference(all_rule,[status(thm)],[]) ).
thf(95,plain,
( ~ sP167
| sP298 ),
inference(all_rule,[status(thm)],[]) ).
thf(96,plain,
( ~ sP304
| sP50 ),
inference(all_rule,[status(thm)],[]) ).
thf(97,plain,
( ~ sP304
| sP119 ),
inference(all_rule,[status(thm)],[]) ).
thf(98,plain,
( ~ sP88
| sP127 ),
inference(all_rule,[status(thm)],[]) ).
thf(99,plain,
( ~ sP369
| sP600 ),
inference(all_rule,[status(thm)],[]) ).
thf(100,plain,
( ~ sP13
| sP398 ),
inference(all_rule,[status(thm)],[]) ).
thf(101,plain,
( ~ sP13
| sP269 ),
inference(all_rule,[status(thm)],[]) ).
thf(102,plain,
( ~ sP13
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(103,plain,
( ~ sP691
| sP162 ),
inference(all_rule,[status(thm)],[]) ).
thf(104,plain,
( ~ sP691
| sP444 ),
inference(all_rule,[status(thm)],[]) ).
thf(105,plain,
( ~ sP57
| sP84
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(106,plain,
( ~ sP549
| sP84
| ~ sP312 ),
inference(prop_rule,[status(thm)],[]) ).
thf(107,plain,
( ~ sP31
| sP84
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(108,plain,
( ~ sP103
| ~ sP429
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(109,plain,
( ~ sP84
| sP103
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(110,plain,
( ~ sP647
| sP311
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(111,plain,
( ~ sP324
| sP311
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP443
| sP311
| ~ sP211 ),
inference(prop_rule,[status(thm)],[]) ).
thf(113,plain,
( ~ sP337
| sP412
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(114,plain,
( ~ sP467
| ~ sP78
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(115,plain,
( ~ sP412
| sP467
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(116,plain,
( ~ sP18
| sP412
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(117,plain,
( ~ sP628
| sP661
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(118,plain,
( ~ sP395
| sP111
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(119,plain,
( ~ sP689
| sP111
| ~ sP425 ),
inference(prop_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP657
| sP402
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(121,plain,
( ~ sP294
| ~ sP312
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(122,plain,
( ~ sP500
| sP294
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(123,plain,
( ~ sP660
| sP320
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(124,plain,
( ~ sP621
| ~ sP505
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(125,plain,
( ~ sP320
| sP621
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(126,plain,
( ~ sP98
| sP176
| ~ sP312 ),
inference(prop_rule,[status(thm)],[]) ).
thf(127,plain,
( ~ sP670
| sP213
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(128,plain,
( ~ sP331
| sP213
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(129,plain,
( ~ sP421
| ~ sP22
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(130,plain,
( ~ sP246
| sP421
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(131,plain,
( ~ sP477
| sP246
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(132,plain,
( ~ sP310
| sP161
| ~ sP163 ),
inference(prop_rule,[status(thm)],[]) ).
thf(133,plain,
( ~ sP226
| sP161
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(134,plain,
( ~ sP534
| sP358
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(135,plain,
( ~ sP301
| sP358
| ~ sP520 ),
inference(prop_rule,[status(thm)],[]) ).
thf(136,plain,
( ~ sP493
| ~ sP488
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(137,plain,
( ~ sP69
| sP493
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(138,plain,
( ~ sP404
| ~ sP113
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(139,plain,
( ~ sP413
| sP404
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(140,plain,
( ~ sP197
| ~ sP308
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(141,plain,
( ~ sP387
| sP197
| ~ sP512 ),
inference(prop_rule,[status(thm)],[]) ).
thf(142,plain,
( ~ sP288
| sP283
| ~ sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(143,plain,
( ~ sP145
| sP607
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(144,plain,
( ~ sP177
| sP315
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(145,plain,
( ~ sP143
| sP7
| ~ sP163 ),
inference(prop_rule,[status(thm)],[]) ).
thf(146,plain,
( ~ sP47
| sP7
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(147,plain,
( ~ sP229
| ~ sP510
| ~ sP211 ),
inference(prop_rule,[status(thm)],[]) ).
thf(148,plain,
( ~ sP335
| sP229
| ~ sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(149,plain,
( ~ sP406
| ~ sP263
| ~ sP512 ),
inference(prop_rule,[status(thm)],[]) ).
thf(150,plain,
( ~ sP241
| sP406
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(151,plain,
( ~ sP157
| ~ sP588
| ~ sP512 ),
inference(prop_rule,[status(thm)],[]) ).
thf(152,plain,
( ~ sP474
| sP157
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(153,plain,
( ~ sP222
| ~ sP332
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(154,plain,
( ~ sP89
| sP222
| ~ sP512 ),
inference(prop_rule,[status(thm)],[]) ).
thf(155,plain,
( ~ sP196
| ~ sP455
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(156,plain,
( ~ sP553
| sP196
| ~ sP211 ),
inference(prop_rule,[status(thm)],[]) ).
thf(157,plain,
( ~ sP165
| ~ sP425
| ~ sP211 ),
inference(prop_rule,[status(thm)],[]) ).
thf(158,plain,
( ~ sP420
| sP165
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(159,plain,
( ~ sP192
| ~ sP520
| ~ sP512 ),
inference(prop_rule,[status(thm)],[]) ).
thf(160,plain,
( ~ sP151
| sP192
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(161,plain,
( ~ sP110
| sP370
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(162,plain,
( ~ sP658
| sP469
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(163,plain,
( ~ sP243
| ~ sP150
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(164,plain,
( ~ sP471
| sP243
| ~ sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(165,plain,
( ~ sP350
| ~ sP124
| ~ sP668 ),
inference(prop_rule,[status(thm)],[]) ).
thf(166,plain,
( ~ sP439
| sP350
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(167,plain,
( ~ sP318
| ~ sP576
| ~ sP512 ),
inference(prop_rule,[status(thm)],[]) ).
thf(168,plain,
( ~ sP663
| sP318
| ~ sP668 ),
inference(prop_rule,[status(thm)],[]) ).
thf(169,plain,
( ~ sP381
| ~ sP545
| ~ sP211 ),
inference(prop_rule,[status(thm)],[]) ).
thf(170,plain,
( ~ sP55
| sP381
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(171,plain,
( ~ sP544
| ~ sP191
| ~ sP668 ),
inference(prop_rule,[status(thm)],[]) ).
thf(172,plain,
( ~ sP326
| sP544
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(173,plain,
( ~ sP17
| sP295 ),
inference(all_rule,[status(thm)],[]) ).
thf(174,plain,
( ~ sP634
| sP441 ),
inference(all_rule,[status(thm)],[]) ).
thf(175,plain,
( ~ sP368
| sP442 ),
inference(all_rule,[status(thm)],[]) ).
thf(176,plain,
( ~ sP260
| sP679 ),
inference(all_rule,[status(thm)],[]) ).
thf(177,plain,
( ~ sP260
| sP77 ),
inference(all_rule,[status(thm)],[]) ).
thf(178,plain,
( ~ sP260
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(179,plain,
( ~ sP129
| sP356 ),
inference(all_rule,[status(thm)],[]) ).
thf(180,plain,
( ~ sP129
| sP550 ),
inference(all_rule,[status(thm)],[]) ).
thf(181,plain,
( ~ sP120
| sP167 ),
inference(all_rule,[status(thm)],[]) ).
thf(182,plain,
( ~ sP120
| sP304 ),
inference(all_rule,[status(thm)],[]) ).
thf(183,plain,
( ~ sP317
| sP88 ),
inference(all_rule,[status(thm)],[]) ).
thf(184,plain,
( ~ sP317
| sP369 ),
inference(all_rule,[status(thm)],[]) ).
thf(185,plain,
( ~ sP307
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(186,plain,
( ~ sP307
| sP691 ),
inference(all_rule,[status(thm)],[]) ).
thf(187,plain,
( ~ sP216
| sP57 ),
inference(all_rule,[status(thm)],[]) ).
thf(188,plain,
( ~ sP216
| sP549 ),
inference(all_rule,[status(thm)],[]) ).
thf(189,plain,
( ~ sP216
| sP31 ),
inference(all_rule,[status(thm)],[]) ).
thf(190,plain,
( ~ sP416
| sP647 ),
inference(all_rule,[status(thm)],[]) ).
thf(191,plain,
( ~ sP416
| sP324 ),
inference(all_rule,[status(thm)],[]) ).
thf(192,plain,
( ~ sP416
| sP443 ),
inference(all_rule,[status(thm)],[]) ).
thf(193,plain,
( ~ sP363
| sP337 ),
inference(all_rule,[status(thm)],[]) ).
thf(194,plain,
( ~ sP363
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(195,plain,
( ~ sP286
| sP628 ),
inference(all_rule,[status(thm)],[]) ).
thf(196,plain,
( ~ sP519
| sP673
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(197,plain,
( ~ sP642
| ~ sP130
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(198,plain,
( ~ sP673
| sP642
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(199,plain,
( ~ sP242
| sP395 ),
inference(all_rule,[status(thm)],[]) ).
thf(200,plain,
( ~ sP242
| sP689 ),
inference(all_rule,[status(thm)],[]) ).
thf(201,plain,
( ~ sP448
| sP657 ),
inference(all_rule,[status(thm)],[]) ).
thf(202,plain,
( ~ sP606
| sP666
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(203,plain,
( ~ sP472
| sP666
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(204,plain,
( ~ sP596
| sP666
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(205,plain,
( ~ sP409
| ~ sP559
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(206,plain,
( ~ sP666
| sP409
| ~ sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(207,plain,
( ~ sP190
| sP598
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(208,plain,
( ~ sP586
| sP598
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(209,plain,
( ~ sP533
| ~ sP163
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(210,plain,
( ~ sP598
| sP533
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(211,plain,
( ~ sP452
| sP500
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(212,plain,
( ~ sP238
| sP500
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(213,plain,
( ~ sP436
| sP500
| ~ sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(214,plain,
( ~ sP480
| sP500
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(215,plain,
( ~ sP627
| sP26
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(216,plain,
( ~ sP290
| sP26
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(217,plain,
( ~ sP612
| sP26
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(218,plain,
( ~ sP218
| ~ sP80
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(219,plain,
( ~ sP26
| sP218
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(220,plain,
( ~ sP543
| sP205
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(221,plain,
( ~ sP297
| sP205
| ~ sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(222,plain,
( ~ sP147
| ~ sP458
| ~ sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(223,plain,
( ~ sP205
| sP147
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(224,plain,
( ~ sP52
| sP660 ),
inference(all_rule,[status(thm)],[]) ).
thf(225,plain,
( ~ sP287
| sP98 ),
inference(all_rule,[status(thm)],[]) ).
thf(226,plain,
( ~ sP433
| sP670 ),
inference(all_rule,[status(thm)],[]) ).
thf(227,plain,
( ~ sP433
| sP331 ),
inference(all_rule,[status(thm)],[]) ).
thf(228,plain,
( ~ sP92
| sP477 ),
inference(all_rule,[status(thm)],[]) ).
thf(229,plain,
( ~ sP54
| sP310 ),
inference(all_rule,[status(thm)],[]) ).
thf(230,plain,
( ~ sP54
| sP226 ),
inference(all_rule,[status(thm)],[]) ).
thf(231,plain,
( ~ sP148
| sP534 ),
inference(all_rule,[status(thm)],[]) ).
thf(232,plain,
( ~ sP148
| sP301 ),
inference(all_rule,[status(thm)],[]) ).
thf(233,plain,
( ~ sP683
| sP69
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(234,plain,
( ~ sP30
| sP413
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(235,plain,
( ~ sP207
| sP413
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(236,plain,
( ~ sP583
| sP557
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(237,plain,
( ~ sP591
| ~ sP585
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(238,plain,
( ~ sP557
| sP591
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(239,plain,
( ~ sP390
| sP387
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(240,plain,
( ~ sP382
| sP288 ),
inference(all_rule,[status(thm)],[]) ).
thf(241,plain,
( ~ sP461
| sP145 ),
inference(all_rule,[status(thm)],[]) ).
thf(242,plain,
( ~ sP353
| sP177 ),
inference(all_rule,[status(thm)],[]) ).
thf(243,plain,
( ~ sP102
| sP143 ),
inference(all_rule,[status(thm)],[]) ).
thf(244,plain,
( ~ sP102
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(245,plain,
( ~ sP530
| sP335
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(246,plain,
( ~ sP575
| sP335
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(247,plain,
( ~ sP352
| sP241
| ~ sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(248,plain,
( ~ sP187
| sP474
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(249,plain,
( ~ sP355
| sP89
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(250,plain,
( ~ sP639
| sP89
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(251,plain,
( ~ sP426
| sP553
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(252,plain,
( ~ sP41
| sP553
| ~ sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(253,plain,
( ~ sP253
| sP553
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(254,plain,
( ~ sP70
| sP420
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(255,plain,
( ~ sP96
| sP151
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(256,plain,
( ~ sP329
| sP110 ),
inference(all_rule,[status(thm)],[]) ).
thf(257,plain,
( ~ sP389
| sP658 ),
inference(all_rule,[status(thm)],[]) ).
thf(258,plain,
( ~ sP656
| sP471
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(259,plain,
( ~ sP569
| sP439
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(260,plain,
( ~ sP680
| sP663
| ~ sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(261,plain,
( ~ sP114
| sP55
| ~ sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(262,plain,
( ~ sP316
| sP326
| ~ sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(263,plain,
( ~ sP330
| sP202
| sP432 ),
inference(prop_rule,[status(thm)],[]) ).
thf(264,plain,
( ~ sP141
| sP330
| sP449 ),
inference(prop_rule,[status(thm)],[]) ).
thf(265,plain,
( ~ sP646
| sP537
| sP67 ),
inference(prop_rule,[status(thm)],[]) ).
thf(266,plain,
( ~ sP262
| sP646
| sP158 ),
inference(prop_rule,[status(thm)],[]) ).
thf(267,plain,
( ~ sP128
| sP635
| sP437 ),
inference(prop_rule,[status(thm)],[]) ).
thf(268,plain,
( ~ sP193
| sP128
| sP515 ),
inference(prop_rule,[status(thm)],[]) ).
thf(269,plain,
( ~ sP595
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(270,plain,
( ~ sP595
| sP634 ),
inference(all_rule,[status(thm)],[]) ).
thf(271,plain,
( ~ sP595
| sP368 ),
inference(all_rule,[status(thm)],[]) ).
thf(272,plain,
( ~ sP595
| sP260 ),
inference(all_rule,[status(thm)],[]) ).
thf(273,plain,
( ~ sP542
| sP129 ),
inference(all_rule,[status(thm)],[]) ).
thf(274,plain,
( ~ sP542
| sP120 ),
inference(all_rule,[status(thm)],[]) ).
thf(275,plain,
( ~ sP542
| sP317 ),
inference(all_rule,[status(thm)],[]) ).
thf(276,plain,
( ~ sP542
| sP307 ),
inference(all_rule,[status(thm)],[]) ).
thf(277,plain,
( ~ sP428
| sP216 ),
inference(all_rule,[status(thm)],[]) ).
thf(278,plain,
( ~ sP428
| sP416 ),
inference(all_rule,[status(thm)],[]) ).
thf(279,plain,
( ~ sP217
| sP363 ),
inference(all_rule,[status(thm)],[]) ).
thf(280,plain,
( ~ sP217
| sP286 ),
inference(all_rule,[status(thm)],[]) ).
thf(281,plain,
( ~ sP655
| sP519 ),
inference(all_rule,[status(thm)],[]) ).
thf(282,plain,
( ~ sP624
| sP242 ),
inference(all_rule,[status(thm)],[]) ).
thf(283,plain,
( ~ sP584
| sP448 ),
inference(all_rule,[status(thm)],[]) ).
thf(284,plain,
( ~ sP435
| sP58
| sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(285,plain,
( ~ sP334
| sP435
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(286,plain,
( ~ sP654
| sP606 ),
inference(all_rule,[status(thm)],[]) ).
thf(287,plain,
( ~ sP654
| sP472 ),
inference(all_rule,[status(thm)],[]) ).
thf(288,plain,
( ~ sP654
| sP596 ),
inference(all_rule,[status(thm)],[]) ).
thf(289,plain,
( ~ sP185
| sP190 ),
inference(all_rule,[status(thm)],[]) ).
thf(290,plain,
( ~ sP185
| sP586 ),
inference(all_rule,[status(thm)],[]) ).
thf(291,plain,
( ~ sP401
| sP452 ),
inference(all_rule,[status(thm)],[]) ).
thf(292,plain,
( ~ sP401
| sP238 ),
inference(all_rule,[status(thm)],[]) ).
thf(293,plain,
( ~ sP401
| sP436 ),
inference(all_rule,[status(thm)],[]) ).
thf(294,plain,
( ~ sP401
| sP480 ),
inference(all_rule,[status(thm)],[]) ).
thf(295,plain,
( ~ sP140
| sP645
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(296,plain,
( ~ sP230
| sP28
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(297,plain,
( ~ sP142
| sP627 ),
inference(all_rule,[status(thm)],[]) ).
thf(298,plain,
( ~ sP142
| sP290 ),
inference(all_rule,[status(thm)],[]) ).
thf(299,plain,
( ~ sP142
| sP612 ),
inference(all_rule,[status(thm)],[]) ).
thf(300,plain,
( ~ sP236
| sP543 ),
inference(all_rule,[status(thm)],[]) ).
thf(301,plain,
( ~ sP236
| sP297 ),
inference(all_rule,[status(thm)],[]) ).
thf(302,plain,
( ~ sP66
| sP52 ),
inference(all_rule,[status(thm)],[]) ).
thf(303,plain,
( ~ sP66
| sP287 ),
inference(all_rule,[status(thm)],[]) ).
thf(304,plain,
( ~ sP66
| sP433 ),
inference(all_rule,[status(thm)],[]) ).
thf(305,plain,
( ~ sP87
| sP92 ),
inference(all_rule,[status(thm)],[]) ).
thf(306,plain,
( ~ sP87
| sP54 ),
inference(all_rule,[status(thm)],[]) ).
thf(307,plain,
( ~ sP87
| sP148 ),
inference(all_rule,[status(thm)],[]) ).
thf(308,plain,
( ~ sP617
| sP61
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(309,plain,
( ~ sP86
| sP617
| sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(310,plain,
( ~ sP36
| sP683 ),
inference(all_rule,[status(thm)],[]) ).
thf(311,plain,
( ~ sP522
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(312,plain,
( ~ sP522
| sP207 ),
inference(all_rule,[status(thm)],[]) ).
thf(313,plain,
( ~ sP273
| sP583 ),
inference(all_rule,[status(thm)],[]) ).
thf(314,plain,
( ~ sP164
| sP390 ),
inference(all_rule,[status(thm)],[]) ).
thf(315,plain,
( ~ sP208
| sP382 ),
inference(all_rule,[status(thm)],[]) ).
thf(316,plain,
( ~ sP208
| sP461 ),
inference(all_rule,[status(thm)],[]) ).
thf(317,plain,
( ~ sP272
| sP353 ),
inference(all_rule,[status(thm)],[]) ).
thf(318,plain,
( ~ sP272
| sP102 ),
inference(all_rule,[status(thm)],[]) ).
thf(319,plain,
( ~ sP485
| sP574
| sP512 ),
inference(prop_rule,[status(thm)],[]) ).
thf(320,plain,
( ~ sP306
| sP485
| sP211 ),
inference(prop_rule,[status(thm)],[]) ).
thf(321,plain,
( ~ sP105
| sP532
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(322,plain,
( ~ sP476
| sP251
| ~ sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(323,plain,
( ~ sP403
| sP530 ),
inference(all_rule,[status(thm)],[]) ).
thf(324,plain,
( ~ sP403
| sP575 ),
inference(all_rule,[status(thm)],[]) ).
thf(325,plain,
( ~ sP348
| sP352 ),
inference(all_rule,[status(thm)],[]) ).
thf(326,plain,
( ~ sP328
| sP187 ),
inference(all_rule,[status(thm)],[]) ).
thf(327,plain,
( ~ sP4
| sP608
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(328,plain,
( ~ sP685
| sP371
| ~ sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(329,plain,
( ~ sP492
| sP97
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(330,plain,
( ~ sP590
| sP355 ),
inference(all_rule,[status(thm)],[]) ).
thf(331,plain,
( ~ sP590
| sP639 ),
inference(all_rule,[status(thm)],[]) ).
thf(332,plain,
( ~ sP502
| sP426 ),
inference(all_rule,[status(thm)],[]) ).
thf(333,plain,
( ~ sP502
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(334,plain,
( ~ sP502
| sP253 ),
inference(all_rule,[status(thm)],[]) ).
thf(335,plain,
( ~ sP495
| sP638
| ~ sP512 ),
inference(prop_rule,[status(thm)],[]) ).
thf(336,plain,
( ~ sP589
| sP508
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(337,plain,
( ~ sP667
| sP168
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(338,plain,
( ~ sP397
| sP70 ),
inference(all_rule,[status(thm)],[]) ).
thf(339,plain,
( ~ sP175
| sP96 ),
inference(all_rule,[status(thm)],[]) ).
thf(340,plain,
( ~ sP456
| sP594
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(341,plain,
( ~ sP393
| sP204
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(342,plain,
( ~ sP644
| sP121
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(343,plain,
( ~ sP255
| sP135
| ~ sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(344,plain,
( ~ sP415
| sP329 ),
inference(all_rule,[status(thm)],[]) ).
thf(345,plain,
( ~ sP271
| sP389 ),
inference(all_rule,[status(thm)],[]) ).
thf(346,plain,
( ~ sP123
| sP172
| sP668 ),
inference(prop_rule,[status(thm)],[]) ).
thf(347,plain,
( ~ sP623
| sP123
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(348,plain,
( ~ sP419
| sP656 ),
inference(all_rule,[status(thm)],[]) ).
thf(349,plain,
( ~ sP16
| sP569 ),
inference(all_rule,[status(thm)],[]) ).
thf(350,plain,
( ~ sP434
| sP680 ),
inference(all_rule,[status(thm)],[]) ).
thf(351,plain,
( ~ sP605
| sP114 ),
inference(all_rule,[status(thm)],[]) ).
thf(352,plain,
( ~ sP359
| sP316 ),
inference(all_rule,[status(thm)],[]) ).
thf(353,plain,
( ~ sP232
| sP134
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(354,plain,
( ~ sP386
| sP687
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(355,plain,
( ~ sP581
| sP411
| ~ sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(356,plain,
( ~ sP540
| sP665
| ~ sP505 ),
inference(prop_rule,[status(thm)],[]) ).
thf(357,plain,
( ~ sP115
| sP46
| sP489 ),
inference(prop_rule,[status(thm)],[]) ).
thf(358,plain,
( ~ sP460
| sP115
| sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(359,plain,
( ~ sP678
| sP104
| sP78 ),
inference(prop_rule,[status(thm)],[]) ).
thf(360,plain,
( ~ sP137
| sP460 ),
inference(all_rule,[status(thm)],[]) ).
thf(361,plain,
( ~ sP137
| sP141 ),
inference(all_rule,[status(thm)],[]) ).
thf(362,plain,
( ~ sP137
| sP262 ),
inference(all_rule,[status(thm)],[]) ).
thf(363,plain,
( ~ sP137
| sP193 ),
inference(all_rule,[status(thm)],[]) ).
thf(364,plain,
( ~ sP3
| sP678
| sP429 ),
inference(prop_rule,[status(thm)],[]) ).
thf(365,plain,
( ~ sP651
| ~ sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(366,plain,
( ~ sP341
| ~ sP466 ),
inference(all_rule,[status(thm)],[]) ).
thf(367,plain,
( ~ sP568
| sP137 ),
inference(all_rule,[status(thm)],[]) ).
thf(368,plain,
( ~ sP414
| sP595 ),
inference(all_rule,[status(thm)],[]) ).
thf(369,plain,
( ~ sP178
| sP542 ),
inference(all_rule,[status(thm)],[]) ).
thf(370,plain,
( ~ sP305
| sP428 ),
inference(all_rule,[status(thm)],[]) ).
thf(371,plain,
( ~ sP109
| sP217 ),
inference(all_rule,[status(thm)],[]) ).
thf(372,plain,
( ~ sP548
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(373,plain,
( ~ sP483
| sP655 ),
inference(all_rule,[status(thm)],[]) ).
thf(374,plain,
( ~ sP221
| sP624 ),
inference(all_rule,[status(thm)],[]) ).
thf(375,plain,
( ~ sP12
| sP584 ),
inference(all_rule,[status(thm)],[]) ).
thf(376,plain,
( ~ sP282
| sP334 ),
inference(all_rule,[status(thm)],[]) ).
thf(377,plain,
( ~ sP451
| sP654 ),
inference(all_rule,[status(thm)],[]) ).
thf(378,plain,
( ~ sP79
| sP185 ),
inference(all_rule,[status(thm)],[]) ).
thf(379,plain,
( ~ sP610
| sP401 ),
inference(all_rule,[status(thm)],[]) ).
thf(380,plain,
( ~ sP259
| sP140 ),
inference(all_rule,[status(thm)],[]) ).
thf(381,plain,
( ~ sP231
| sP230 ),
inference(all_rule,[status(thm)],[]) ).
thf(382,plain,
( ~ sP539
| sP142 ),
inference(all_rule,[status(thm)],[]) ).
thf(383,plain,
( ~ sP68
| sP236 ),
inference(all_rule,[status(thm)],[]) ).
thf(384,plain,
( ~ sP450
| sP66 ),
inference(all_rule,[status(thm)],[]) ).
thf(385,plain,
( ~ sP604
| sP87 ),
inference(all_rule,[status(thm)],[]) ).
thf(386,plain,
( ~ sP65
| sP86 ),
inference(all_rule,[status(thm)],[]) ).
thf(387,plain,
( ~ sP138
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(388,plain,
( ~ sP501
| sP522 ),
inference(all_rule,[status(thm)],[]) ).
thf(389,plain,
( ~ sP181
| sP273 ),
inference(all_rule,[status(thm)],[]) ).
thf(390,plain,
( ~ sP170
| sP164 ),
inference(all_rule,[status(thm)],[]) ).
thf(391,plain,
( ~ sP51
| sP208 ),
inference(all_rule,[status(thm)],[]) ).
thf(392,plain,
( ~ sP400
| sP272 ),
inference(all_rule,[status(thm)],[]) ).
thf(393,plain,
( ~ sP347
| sP306 ),
inference(all_rule,[status(thm)],[]) ).
thf(394,plain,
( ~ sP266
| sP105 ),
inference(all_rule,[status(thm)],[]) ).
thf(395,plain,
( ~ sP438
| sP476 ),
inference(all_rule,[status(thm)],[]) ).
thf(396,plain,
( ~ sP285
| sP403 ),
inference(all_rule,[status(thm)],[]) ).
thf(397,plain,
( ~ sP327
| sP348 ),
inference(all_rule,[status(thm)],[]) ).
thf(398,plain,
( ~ sP250
| sP328 ),
inference(all_rule,[status(thm)],[]) ).
thf(399,plain,
( ~ sP696
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(400,plain,
( ~ sP556
| sP685 ),
inference(all_rule,[status(thm)],[]) ).
thf(401,plain,
( ~ sP567
| sP492 ),
inference(all_rule,[status(thm)],[]) ).
thf(402,plain,
( ~ sP108
| sP590 ),
inference(all_rule,[status(thm)],[]) ).
thf(403,plain,
( ~ sP8
| sP502 ),
inference(all_rule,[status(thm)],[]) ).
thf(404,plain,
( ~ sP487
| sP495 ),
inference(all_rule,[status(thm)],[]) ).
thf(405,plain,
( ~ sP609
| sP589 ),
inference(all_rule,[status(thm)],[]) ).
thf(406,plain,
( ~ sP365
| sP667 ),
inference(all_rule,[status(thm)],[]) ).
thf(407,plain,
( ~ sP561
| sP397 ),
inference(all_rule,[status(thm)],[]) ).
thf(408,plain,
( ~ sP453
| sP175 ),
inference(all_rule,[status(thm)],[]) ).
thf(409,plain,
( ~ sP529
| sP456 ),
inference(all_rule,[status(thm)],[]) ).
thf(410,plain,
( ~ sP64
| sP393 ),
inference(all_rule,[status(thm)],[]) ).
thf(411,plain,
( ~ sP626
| sP644 ),
inference(all_rule,[status(thm)],[]) ).
thf(412,plain,
( ~ sP33
| sP255 ),
inference(all_rule,[status(thm)],[]) ).
thf(413,plain,
( ~ sP274
| sP415 ),
inference(all_rule,[status(thm)],[]) ).
thf(414,plain,
( ~ sP379
| sP271 ),
inference(all_rule,[status(thm)],[]) ).
thf(415,plain,
( ~ sP340
| sP623 ),
inference(all_rule,[status(thm)],[]) ).
thf(416,plain,
( ~ sP201
| sP419 ),
inference(all_rule,[status(thm)],[]) ).
thf(417,plain,
( ~ sP325
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(418,plain,
( ~ sP695
| sP434 ),
inference(all_rule,[status(thm)],[]) ).
thf(419,plain,
( ~ sP319
| sP605 ),
inference(all_rule,[status(thm)],[]) ).
thf(420,plain,
( ~ sP343
| sP359 ),
inference(all_rule,[status(thm)],[]) ).
thf(421,plain,
( ~ sP571
| sP232 ),
inference(all_rule,[status(thm)],[]) ).
thf(422,plain,
( ~ sP131
| sP386 ),
inference(all_rule,[status(thm)],[]) ).
thf(423,plain,
( ~ sP459
| sP581 ),
inference(all_rule,[status(thm)],[]) ).
thf(424,plain,
( ~ sP592
| sP540 ),
inference(all_rule,[status(thm)],[]) ).
thf(425,plain,
( ~ sP191
| sP200
| ~ sP48
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(426,plain,
( ~ sP223
| sP248
| ~ sP48
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(427,plain,
( ~ sP616
| ~ sP545
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(428,plain,
( ~ sP117
| sP616
| ~ sP223 ),
inference(prop_rule,[status(thm)],[]) ).
thf(429,plain,
( ~ sP267
| ~ sP545
| ~ sP425 ),
inference(prop_rule,[status(thm)],[]) ).
thf(430,plain,
( ~ sP690
| sP267
| ~ sP517 ),
inference(prop_rule,[status(thm)],[]) ).
thf(431,plain,
( ~ sP362
| ~ sP576
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(432,plain,
( ~ sP687
| sP362
| ~ sP191 ),
inference(prop_rule,[status(thm)],[]) ).
thf(433,plain,
( ~ sP215
| ~ sP576
| ~ sP520 ),
inference(prop_rule,[status(thm)],[]) ).
thf(434,plain,
( ~ sP183
| sP215
| ~ sP281 ),
inference(prop_rule,[status(thm)],[]) ).
thf(435,plain,
( ~ sP579
| sP160
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(436,plain,
( ~ sP593
| ~ sP281
| ~ sP191 ),
inference(prop_rule,[status(thm)],[]) ).
thf(437,plain,
( ~ sP160
| sP593
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(438,plain,
( ~ sP538
| sP665
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(439,plain,
( ~ sP514
| ~ sP223
| ~ sP517 ),
inference(prop_rule,[status(thm)],[]) ).
thf(440,plain,
( ~ sP665
| sP514
| ~ sP312 ),
inference(prop_rule,[status(thm)],[]) ).
thf(441,plain,
( ~ sP136
| sP240
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(442,plain,
( ~ sP694
| ~ sP517
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(443,plain,
( ~ sP240
| sP694
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(444,plain,
( ~ sP234
| sP411
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(445,plain,
( ~ sP524
| ~ sP545
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(446,plain,
( ~ sP411
| sP524
| ~ sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(447,plain,
( ~ sP42
| sP117
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(448,plain,
( ~ sP564
| sP690
| ~ sP455 ),
inference(prop_rule,[status(thm)],[]) ).
thf(449,plain,
( ~ sP75
| sP225
| ~ sP179 ),
inference(prop_rule,[status(thm)],[]) ).
thf(450,plain,
( ~ sP199
| ~ sP576
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(451,plain,
( ~ sP225
| sP199
| ~ sP124 ),
inference(prop_rule,[status(thm)],[]) ).
thf(452,plain,
( ~ sP392
| sP687
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(453,plain,
( ~ sP653
| sP183
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(454,plain,
( ~ sP126
| sP418
| ~ sP163 ),
inference(prop_rule,[status(thm)],[]) ).
thf(455,plain,
( ~ sP247
| ~ sP124
| ~ sP191 ),
inference(prop_rule,[status(thm)],[]) ).
thf(456,plain,
( ~ sP418
| sP247
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(457,plain,
( ~ sP300
| ~ sP124
| ~ sP281 ),
inference(prop_rule,[status(thm)],[]) ).
thf(458,plain,
( ~ sP134
| sP300
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(459,plain,
( ~ sP9
| sP465
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(460,plain,
( ~ sP44
| ~ sP150
| ~ sP223 ),
inference(prop_rule,[status(thm)],[]) ).
thf(461,plain,
( ~ sP465
| sP44
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(462,plain,
( ~ sP566
| sP579 ),
inference(all_rule,[status(thm)],[]) ).
thf(463,plain,
( ~ sP592
| sP538 ),
inference(all_rule,[status(thm)],[]) ).
thf(464,plain,
( ~ sP153
| sP136 ),
inference(all_rule,[status(thm)],[]) ).
thf(465,plain,
( ~ sP459
| sP234 ),
inference(all_rule,[status(thm)],[]) ).
thf(466,plain,
( ~ sP376
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(467,plain,
( ~ sP375
| sP564 ),
inference(all_rule,[status(thm)],[]) ).
thf(468,plain,
( ~ sP547
| sP75 ),
inference(all_rule,[status(thm)],[]) ).
thf(469,plain,
( ~ sP131
| sP392 ),
inference(all_rule,[status(thm)],[]) ).
thf(470,plain,
( ~ sP528
| sP653 ),
inference(all_rule,[status(thm)],[]) ).
thf(471,plain,
( ~ sP565
| sP126 ),
inference(all_rule,[status(thm)],[]) ).
thf(472,plain,
( ~ sP261
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(473,plain,
( ~ sP206
| sP11
| sP281 ),
inference(prop_rule,[status(thm)],[]) ).
thf(474,plain,
( ~ sP388
| sP206
| sP517 ),
inference(prop_rule,[status(thm)],[]) ).
thf(475,plain,
( ~ sP101
| sP566 ),
inference(all_rule,[status(thm)],[]) ).
thf(476,plain,
( ~ sP336
| sP592 ),
inference(all_rule,[status(thm)],[]) ).
thf(477,plain,
( ~ sP384
| sP153 ),
inference(all_rule,[status(thm)],[]) ).
thf(478,plain,
( ~ sP319
| sP459 ),
inference(all_rule,[status(thm)],[]) ).
thf(479,plain,
( ~ sP319
| sP376 ),
inference(all_rule,[status(thm)],[]) ).
thf(480,plain,
( ~ sP319
| sP375 ),
inference(all_rule,[status(thm)],[]) ).
thf(481,plain,
( ~ sP695
| sP547 ),
inference(all_rule,[status(thm)],[]) ).
thf(482,plain,
( ~ sP695
| sP131 ),
inference(all_rule,[status(thm)],[]) ).
thf(483,plain,
( ~ sP695
| sP528 ),
inference(all_rule,[status(thm)],[]) ).
thf(484,plain,
( ~ sP209
| sP399
| sP576 ),
inference(prop_rule,[status(thm)],[]) ).
thf(485,plain,
( ~ sP491
| sP209
| sP545 ),
inference(prop_rule,[status(thm)],[]) ).
thf(486,plain,
( ~ sP210
| sP100
| sP124 ),
inference(prop_rule,[status(thm)],[]) ).
thf(487,plain,
( ~ sP499
| sP684
| sP191 ),
inference(prop_rule,[status(thm)],[]) ).
thf(488,plain,
( ~ sP293
| ~ sP202
| sP100 ),
inference(prop_rule,[status(thm)],[]) ).
thf(489,plain,
( ~ sP112
| ~ sP537
| sP684 ),
inference(prop_rule,[status(thm)],[]) ).
thf(490,plain,
( ~ sP258
| ~ sP635
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(491,plain,
( ~ sP149
| sP210
| sP150 ),
inference(prop_rule,[status(thm)],[]) ).
thf(492,plain,
( ~ sP292
| sP499
| sP223 ),
inference(prop_rule,[status(thm)],[]) ).
thf(493,plain,
( ~ sP325
| sP565 ),
inference(all_rule,[status(thm)],[]) ).
thf(494,plain,
( ~ sP325
| sP571 ),
inference(all_rule,[status(thm)],[]) ).
thf(495,plain,
( ~ sP201
| sP261 ),
inference(all_rule,[status(thm)],[]) ).
thf(496,plain,
( ~ sP72
| sP293 ),
inference(all_rule,[status(thm)],[]) ).
thf(497,plain,
( ~ sP72
| sP112 ),
inference(all_rule,[status(thm)],[]) ).
thf(498,plain,
( ~ sP72
| sP258 ),
inference(all_rule,[status(thm)],[]) ).
thf(499,plain,
( ~ sP340
| sP149 ),
inference(all_rule,[status(thm)],[]) ).
thf(500,plain,
( ~ sP340
| sP292 ),
inference(all_rule,[status(thm)],[]) ).
thf(501,plain,
( ~ sP340
| sP388 ),
inference(all_rule,[status(thm)],[]) ).
thf(502,plain,
( ~ sP379
| sP325 ),
inference(all_rule,[status(thm)],[]) ).
thf(503,plain,
( ~ sP379
| sP343 ),
inference(all_rule,[status(thm)],[]) ).
thf(504,plain,
( ~ sP379
| sP101 ),
inference(all_rule,[status(thm)],[]) ).
thf(505,plain,
( ~ sP274
| sP201 ),
inference(all_rule,[status(thm)],[]) ).
thf(506,plain,
( ~ sP274
| sP336 ),
inference(all_rule,[status(thm)],[]) ).
thf(507,plain,
( ~ sP274
| sP384 ),
inference(all_rule,[status(thm)],[]) ).
thf(508,plain,
( ~ sP354
| ~ sP61
| sP48 ),
inference(prop_rule,[status(thm)],[]) ).
thf(509,plain,
( ~ sP60
| ~ sP574
| sP440 ),
inference(prop_rule,[status(thm)],[]) ).
thf(510,plain,
( ~ sP346
| ~ sP172
| sP399 ),
inference(prop_rule,[status(thm)],[]) ).
thf(511,plain,
( ~ sP296
| ~ sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(512,plain,
( ~ sP2
| sP72 ),
inference(all_rule,[status(thm)],[]) ).
thf(513,plain,
( ~ sP651
| ~ sP200 ),
inference(all_rule,[status(thm)],[]) ).
thf(514,plain,
( ~ sP341
| ~ sP248 ),
inference(all_rule,[status(thm)],[]) ).
thf(515,plain,
( ~ sP568
| sP340 ),
inference(all_rule,[status(thm)],[]) ).
thf(516,plain,
( ~ sP414
| sP379 ),
inference(all_rule,[status(thm)],[]) ).
thf(517,plain,
( ~ sP178
| sP274 ),
inference(all_rule,[status(thm)],[]) ).
thf(518,plain,
( ~ sP536
| sP354 ),
inference(all_rule,[status(thm)],[]) ).
thf(519,plain,
( ~ sP233
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(520,plain,
( ~ sP51
| sP319 ),
inference(all_rule,[status(thm)],[]) ).
thf(521,plain,
( ~ sP400
| sP695 ),
inference(all_rule,[status(thm)],[]) ).
thf(522,plain,
( ~ sP347
| sP491 ),
inference(all_rule,[status(thm)],[]) ).
thf(523,plain,
( ~ sP618
| sP346 ),
inference(all_rule,[status(thm)],[]) ).
thf(524,plain,
( ~ sP263
| sP527
| ~ sP380
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(525,plain,
( ~ sP560
| sP252
| ~ sP380
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(526,plain,
( ~ sP195
| sP156
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(527,plain,
( ~ sP446
| sP625
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(528,plain,
( ~ sP619
| ~ sP425
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(529,plain,
( ~ sP405
| sP619
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(530,plain,
( ~ sP24
| sP405
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(531,plain,
( ~ sP391
| sP135
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(532,plain,
( ~ sP357
| sP121
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(533,plain,
( ~ sP174
| ~ sP455
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(534,plain,
( ~ sP121
| sP174
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(535,plain,
( ~ sP95
| sP204
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(536,plain,
( ~ sP632
| ~ sP588
| ~ sP520 ),
inference(prop_rule,[status(thm)],[]) ).
thf(537,plain,
( ~ sP204
| sP632
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(538,plain,
( ~ sP45
| sP204
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(539,plain,
( ~ sP484
| sP81
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(540,plain,
( ~ sP563
| ~ sP263
| ~ sP520 ),
inference(prop_rule,[status(thm)],[]) ).
thf(541,plain,
( ~ sP81
| sP563
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(542,plain,
( ~ sP383
| sP693
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(543,plain,
( ~ sP182
| ~ sP510
| ~ sP425 ),
inference(prop_rule,[status(thm)],[]) ).
thf(544,plain,
( ~ sP693
| sP182
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(545,plain,
( ~ sP551
| sP594
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(546,plain,
( ~ sP20
| ~ sP560
| ~ sP425 ),
inference(prop_rule,[status(thm)],[]) ).
thf(547,plain,
( ~ sP594
| sP20
| ~ sP312 ),
inference(prop_rule,[status(thm)],[]) ).
thf(548,plain,
( ~ sP38
| ~ sP520
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(549,plain,
( ~ sP156
| sP38
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(550,plain,
( ~ sP498
| sP195 ),
inference(all_rule,[status(thm)],[]) ).
thf(551,plain,
( ~ sP410
| ~ sP425
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(552,plain,
( ~ sP625
| sP410
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(553,plain,
( ~ sP43
| sP446 ),
inference(all_rule,[status(thm)],[]) ).
thf(554,plain,
( ~ sP309
| sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(555,plain,
( ~ sP611
| ~ sP244
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(556,plain,
( ~ sP168
| sP611
| ~ sP425 ),
inference(prop_rule,[status(thm)],[]) ).
thf(557,plain,
( ~ sP29
| ~ sP308
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(558,plain,
( ~ sP508
| sP29
| ~ sP520 ),
inference(prop_rule,[status(thm)],[]) ).
thf(559,plain,
( ~ sP339
| sP203
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(560,plain,
( ~ sP21
| ~ sP130
| ~ sP179 ),
inference(prop_rule,[status(thm)],[]) ).
thf(561,plain,
( ~ sP203
| sP21
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(562,plain,
( ~ sP25
| sP198
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(563,plain,
( ~ sP552
| ~ sP559
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(564,plain,
( ~ sP198
| sP552
| ~ sP244 ),
inference(prop_rule,[status(thm)],[]) ).
thf(565,plain,
( ~ sP504
| sP638
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(566,plain,
( ~ sP264
| ~ sP163
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(567,plain,
( ~ sP638
| sP264
| ~ sP179 ),
inference(prop_rule,[status(thm)],[]) ).
thf(568,plain,
( ~ sP511
| sP531
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(569,plain,
( ~ sP228
| sP531
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(570,plain,
( ~ sP322
| ~ sP173
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(571,plain,
( ~ sP531
| sP322
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(572,plain,
( ~ sP479
| sP278
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(573,plain,
( ~ sP76
| sP278
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(574,plain,
( ~ sP513
| ~ sP312
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(575,plain,
( ~ sP278
| sP513
| ~ sP455 ),
inference(prop_rule,[status(thm)],[]) ).
thf(576,plain,
( ~ sP490
| sP367
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(577,plain,
( ~ sP268
| ~ sP80
| ~ sP179 ),
inference(prop_rule,[status(thm)],[]) ).
thf(578,plain,
( ~ sP367
| sP268
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(579,plain,
( ~ sP662
| sP37
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(580,plain,
( ~ sP523
| sP37
| ~ sP425 ),
inference(prop_rule,[status(thm)],[]) ).
thf(581,plain,
( ~ sP40
| ~ sP458
| ~ sP244 ),
inference(prop_rule,[status(thm)],[]) ).
thf(582,plain,
( ~ sP37
| sP40
| ~ sP455 ),
inference(prop_rule,[status(thm)],[]) ).
thf(583,plain,
( ~ sP641
| ~ sP455
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(584,plain,
( ~ sP135
| sP641
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(585,plain,
( ~ sP33
| sP391 ),
inference(all_rule,[status(thm)],[]) ).
thf(586,plain,
( ~ sP626
| sP357 ),
inference(all_rule,[status(thm)],[]) ).
thf(587,plain,
( ~ sP139
| sP186
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(588,plain,
( ~ sP486
| ~ sP488
| ~ sP455 ),
inference(prop_rule,[status(thm)],[]) ).
thf(589,plain,
( ~ sP186
| sP486
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(590,plain,
( ~ sP116
| sP525
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(591,plain,
( ~ sP361
| sP525
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(592,plain,
( ~ sP417
| ~ sP113
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(593,plain,
( ~ sP525
| sP417
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(594,plain,
( ~ sP83
| sP431
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(595,plain,
( ~ sP152
| ~ sP585
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(596,plain,
( ~ sP431
| sP152
| ~ sP179 ),
inference(prop_rule,[status(thm)],[]) ).
thf(597,plain,
( ~ sP227
| sP97
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(598,plain,
( ~ sP582
| sP608
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(599,plain,
( ~ sP64
| sP95 ),
inference(all_rule,[status(thm)],[]) ).
thf(600,plain,
( ~ sP64
| sP45 ),
inference(all_rule,[status(thm)],[]) ).
thf(601,plain,
( ~ sP521
| sP484 ),
inference(all_rule,[status(thm)],[]) ).
thf(602,plain,
( ~ sP615
| sP383 ),
inference(all_rule,[status(thm)],[]) ).
thf(603,plain,
( ~ sP529
| sP551 ),
inference(all_rule,[status(thm)],[]) ).
thf(604,plain,
( ~ sP475
| sP251
| ~ sP244 ),
inference(prop_rule,[status(thm)],[]) ).
thf(605,plain,
( ~ sP453
| sP498 ),
inference(all_rule,[status(thm)],[]) ).
thf(606,plain,
( ~ sP561
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(607,plain,
( ~ sP561
| sP309 ),
inference(all_rule,[status(thm)],[]) ).
thf(608,plain,
( ~ sP578
| sP339 ),
inference(all_rule,[status(thm)],[]) ).
thf(609,plain,
( ~ sP63
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(610,plain,
( ~ sP487
| sP504 ),
inference(all_rule,[status(thm)],[]) ).
thf(611,plain,
( ~ sP374
| sP280
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(612,plain,
( ~ sP603
| sP314
| ~ sP455 ),
inference(prop_rule,[status(thm)],[]) ).
thf(613,plain,
( ~ sP688
| sP511 ),
inference(all_rule,[status(thm)],[]) ).
thf(614,plain,
( ~ sP688
| sP228 ),
inference(all_rule,[status(thm)],[]) ).
thf(615,plain,
( ~ sP580
| sP479 ),
inference(all_rule,[status(thm)],[]) ).
thf(616,plain,
( ~ sP580
| sP76 ),
inference(all_rule,[status(thm)],[]) ).
thf(617,plain,
( ~ sP180
| sP28
| ~ sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(618,plain,
( ~ sP333
| sP490 ),
inference(all_rule,[status(thm)],[]) ).
thf(619,plain,
( ~ sP345
| sP662 ),
inference(all_rule,[status(thm)],[]) ).
thf(620,plain,
( ~ sP345
| sP523 ),
inference(all_rule,[status(thm)],[]) ).
thf(621,plain,
( ~ sP8
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(622,plain,
( ~ sP8
| sP626 ),
inference(all_rule,[status(thm)],[]) ).
thf(623,plain,
( ~ sP71
| sP139 ),
inference(all_rule,[status(thm)],[]) ).
thf(624,plain,
( ~ sP270
| sP116 ),
inference(all_rule,[status(thm)],[]) ).
thf(625,plain,
( ~ sP270
| sP361 ),
inference(all_rule,[status(thm)],[]) ).
thf(626,plain,
( ~ sP622
| sP83 ),
inference(all_rule,[status(thm)],[]) ).
thf(627,plain,
( ~ sP686
| ~ sP588
| ~ sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(628,plain,
( ~ sP169
| ~ sP263
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(629,plain,
( ~ sP554
| ~ sP510
| ~ sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(630,plain,
( ~ sP640
| ~ sP560
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(631,plain,
( ~ sP97
| sP686
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(632,plain,
( ~ sP371
| sP169
| ~ sP163 ),
inference(prop_rule,[status(thm)],[]) ).
thf(633,plain,
( ~ sP608
| sP554
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(634,plain,
( ~ sP279
| sP640
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(635,plain,
( ~ sP676
| ~ sP302
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(636,plain,
( ~ sP277
| ~ sP308
| ~ sP163 ),
inference(prop_rule,[status(thm)],[]) ).
thf(637,plain,
( ~ sP630
| sP371
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(638,plain,
( ~ sP507
| sP371
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(639,plain,
( ~ sP1
| sP608
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(640,plain,
( ~ sP212
| sP279
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(641,plain,
( ~ sP251
| sP676
| ~ sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(642,plain,
( ~ sP532
| sP277
| ~ sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(643,plain,
( ~ sP94
| sP562
| sP588 ),
inference(prop_rule,[status(thm)],[]) ).
thf(644,plain,
( ~ sP573
| sP602
| sP263 ),
inference(prop_rule,[status(thm)],[]) ).
thf(645,plain,
( ~ sP90
| sP53
| sP520 ),
inference(prop_rule,[status(thm)],[]) ).
thf(646,plain,
( ~ sP567
| sP227 ),
inference(all_rule,[status(thm)],[]) ).
thf(647,plain,
( ~ sP556
| sP630 ),
inference(all_rule,[status(thm)],[]) ).
thf(648,plain,
( ~ sP556
| sP507 ),
inference(all_rule,[status(thm)],[]) ).
thf(649,plain,
( ~ sP696
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(650,plain,
( ~ sP696
| sP582 ),
inference(all_rule,[status(thm)],[]) ).
thf(651,plain,
( ~ sP681
| sP212 ),
inference(all_rule,[status(thm)],[]) ).
thf(652,plain,
( ~ sP396
| sP251
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(653,plain,
( ~ sP482
| sP532
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(654,plain,
( ~ sP494
| ~ sP684
| sP562 ),
inference(prop_rule,[status(thm)],[]) ).
thf(655,plain,
( ~ sP614
| ~ sP11
| sP602 ),
inference(prop_rule,[status(thm)],[]) ).
thf(656,plain,
( ~ sP672
| sP94
| sP510 ),
inference(prop_rule,[status(thm)],[]) ).
thf(657,plain,
( ~ sP373
| sP573
| sP560 ),
inference(prop_rule,[status(thm)],[]) ).
thf(658,plain,
( ~ sP237
| sP90
| sP425 ),
inference(prop_rule,[status(thm)],[]) ).
thf(659,plain,
( ~ sP250
| sP567 ),
inference(all_rule,[status(thm)],[]) ).
thf(660,plain,
( ~ sP250
| sP64 ),
inference(all_rule,[status(thm)],[]) ).
thf(661,plain,
( ~ sP327
| sP556 ),
inference(all_rule,[status(thm)],[]) ).
thf(662,plain,
( ~ sP327
| sP521 ),
inference(all_rule,[status(thm)],[]) ).
thf(663,plain,
( ~ sP285
| sP696 ),
inference(all_rule,[status(thm)],[]) ).
thf(664,plain,
( ~ sP285
| sP615 ),
inference(all_rule,[status(thm)],[]) ).
thf(665,plain,
( ~ sP546
| sP681 ),
inference(all_rule,[status(thm)],[]) ).
thf(666,plain,
( ~ sP546
| sP529 ),
inference(all_rule,[status(thm)],[]) ).
thf(667,plain,
( ~ sP82
| sP342
| sP179 ),
inference(prop_rule,[status(thm)],[]) ).
thf(668,plain,
( ~ sP438
| sP396 ),
inference(all_rule,[status(thm)],[]) ).
thf(669,plain,
( ~ sP438
| sP475 ),
inference(all_rule,[status(thm)],[]) ).
thf(670,plain,
( ~ sP266
| sP482 ),
inference(all_rule,[status(thm)],[]) ).
thf(671,plain,
( ~ sP464
| sP380
| sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(672,plain,
( ~ sP284
| sP692
| sP332 ),
inference(prop_rule,[status(thm)],[]) ).
thf(673,plain,
( ~ sP618
| sP494 ),
inference(all_rule,[status(thm)],[]) ).
thf(674,plain,
( ~ sP618
| sP614 ),
inference(all_rule,[status(thm)],[]) ).
thf(675,plain,
( ~ sP347
| sP672 ),
inference(all_rule,[status(thm)],[]) ).
thf(676,plain,
( ~ sP347
| sP373 ),
inference(all_rule,[status(thm)],[]) ).
thf(677,plain,
( ~ sP347
| sP237 ),
inference(all_rule,[status(thm)],[]) ).
thf(678,plain,
( ~ sP400
| sP250 ),
inference(all_rule,[status(thm)],[]) ).
thf(679,plain,
( ~ sP400
| sP327 ),
inference(all_rule,[status(thm)],[]) ).
thf(680,plain,
( ~ sP400
| sP453 ),
inference(all_rule,[status(thm)],[]) ).
thf(681,plain,
( ~ sP51
| sP285 ),
inference(all_rule,[status(thm)],[]) ).
thf(682,plain,
( ~ sP51
| sP546 ),
inference(all_rule,[status(thm)],[]) ).
thf(683,plain,
( ~ sP51
| sP561 ),
inference(all_rule,[status(thm)],[]) ).
thf(684,plain,
( sP48
| ~ sP342 ),
inference(prop_rule,[status(thm)],[]) ).
thf(685,plain,
( ~ sP516
| sP365 ),
inference(all_rule,[status(thm)],[]) ).
thf(686,plain,
( ~ sP599
| sP82
| sP244 ),
inference(prop_rule,[status(thm)],[]) ).
thf(687,plain,
( ~ sP447
| ~ sP440
| sP380 ),
inference(prop_rule,[status(thm)],[]) ).
thf(688,plain,
( ~ sP587
| sP438 ),
inference(all_rule,[status(thm)],[]) ).
thf(689,plain,
( ~ sP170
| sP266 ),
inference(all_rule,[status(thm)],[]) ).
thf(690,plain,
( ~ sP170
| sP609 ),
inference(all_rule,[status(thm)],[]) ).
thf(691,plain,
( ~ sP323
| sP464
| sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(692,plain,
( ~ sP659
| sP284
| sP455 ),
inference(prop_rule,[status(thm)],[]) ).
thf(693,plain,
( ~ sP289
| ~ sP399
| sP692 ),
inference(prop_rule,[status(thm)],[]) ).
thf(694,plain,
( ~ sP146
| sP59
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(695,plain,
( ~ sP577
| sP572
| ~ sP302 ),
inference(prop_rule,[status(thm)],[]) ).
thf(696,plain,
( ~ sP675
| sP620
| ~ sP308 ),
inference(prop_rule,[status(thm)],[]) ).
thf(697,plain,
( ~ sP296
| ~ sP100 ),
inference(all_rule,[status(thm)],[]) ).
thf(698,plain,
( ~ sP2
| sP618 ),
inference(all_rule,[status(thm)],[]) ).
thf(699,plain,
( ~ sP651
| ~ sP527 ),
inference(all_rule,[status(thm)],[]) ).
thf(700,plain,
( ~ sP341
| ~ sP252 ),
inference(all_rule,[status(thm)],[]) ).
thf(701,plain,
( ~ sP568
| sP347 ),
inference(all_rule,[status(thm)],[]) ).
thf(702,plain,
( ~ sP414
| sP400 ),
inference(all_rule,[status(thm)],[]) ).
thf(703,plain,
( ~ sP178
| sP51 ),
inference(all_rule,[status(thm)],[]) ).
thf(704,plain,
( ~ sP305
| sP516 ),
inference(all_rule,[status(thm)],[]) ).
thf(705,plain,
( ~ sP548
| sP599 ),
inference(all_rule,[status(thm)],[]) ).
thf(706,plain,
( ~ sP536
| sP447 ),
inference(all_rule,[status(thm)],[]) ).
thf(707,plain,
( ~ sP483
| sP578 ),
inference(all_rule,[status(thm)],[]) ).
thf(708,plain,
( ~ sP221
| sP587 ),
inference(all_rule,[status(thm)],[]) ).
thf(709,plain,
( ~ sP12
| sP170 ),
inference(all_rule,[status(thm)],[]) ).
thf(710,plain,
( ~ sP282
| sP323 ),
inference(all_rule,[status(thm)],[]) ).
thf(711,plain,
( ~ sP451
| sP63 ),
inference(all_rule,[status(thm)],[]) ).
thf(712,plain,
( ~ sP79
| sP487 ),
inference(all_rule,[status(thm)],[]) ).
thf(713,plain,
( ~ sP85
| sP374 ),
inference(all_rule,[status(thm)],[]) ).
thf(714,plain,
( ~ sP463
| sP603 ),
inference(all_rule,[status(thm)],[]) ).
thf(715,plain,
( ~ sP313
| sP688 ),
inference(all_rule,[status(thm)],[]) ).
thf(716,plain,
( ~ sP610
| sP580 ),
inference(all_rule,[status(thm)],[]) ).
thf(717,plain,
( ~ sP231
| sP180 ),
inference(all_rule,[status(thm)],[]) ).
thf(718,plain,
( ~ sP539
| sP333 ),
inference(all_rule,[status(thm)],[]) ).
thf(719,plain,
( ~ sP68
| sP345 ),
inference(all_rule,[status(thm)],[]) ).
thf(720,plain,
( ~ sP450
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(721,plain,
( ~ sP604
| sP108 ),
inference(all_rule,[status(thm)],[]) ).
thf(722,plain,
( ~ sP65
| sP659 ),
inference(all_rule,[status(thm)],[]) ).
thf(723,plain,
( ~ sP233
| sP289 ),
inference(all_rule,[status(thm)],[]) ).
thf(724,plain,
( ~ sP118
| sP146 ),
inference(all_rule,[status(thm)],[]) ).
thf(725,plain,
( ~ sP166
| sP577 ),
inference(all_rule,[status(thm)],[]) ).
thf(726,plain,
( ~ sP138
| sP71 ),
inference(all_rule,[status(thm)],[]) ).
thf(727,plain,
( ~ sP501
| sP270 ),
inference(all_rule,[status(thm)],[]) ).
thf(728,plain,
( ~ sP181
| sP622 ),
inference(all_rule,[status(thm)],[]) ).
thf(729,plain,
( ~ sP10
| sP675 ),
inference(all_rule,[status(thm)],[]) ).
thf(730,plain,
( ~ sP189
| ~ sP585
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(731,plain,
( ~ sP291
| ~ sP488
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(732,plain,
( ~ sP620
| sP189
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(733,plain,
( ~ sP93
| sP291
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(734,plain,
( ~ sP518
| ~ sP312
| ~ sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(735,plain,
( ~ sP276
| sP620
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(736,plain,
( ~ sP133
| sP93
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(737,plain,
( ~ sP351
| ~ sP458
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(738,plain,
( ~ sP572
| sP351
| ~ sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(739,plain,
( ~ sP99
| ~ sP80
| ~ sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(740,plain,
( ~ sP59
| sP99
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(741,plain,
( ~ sP468
| sP518
| ~ sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(742,plain,
( ~ sP245
| ~ sP559
| ~ sP312 ),
inference(prop_rule,[status(thm)],[]) ).
thf(743,plain,
( ~ sP91
| ~ sP163
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(744,plain,
( ~ sP35
| sP570
| sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(745,plain,
( ~ sP10
| sP276 ),
inference(all_rule,[status(thm)],[]) ).
thf(746,plain,
( ~ sP377
| sP133 ),
inference(all_rule,[status(thm)],[]) ).
thf(747,plain,
( ~ sP643
| sP59
| ~ sP163 ),
inference(prop_rule,[status(thm)],[]) ).
thf(748,plain,
( ~ sP321
| ~ sP130
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(749,plain,
( ~ sP28
| sP321
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(750,plain,
( ~ sP220
| ~ sP19
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(751,plain,
( ~ sP645
| sP220
| ~ sP312 ),
inference(prop_rule,[status(thm)],[]) ).
thf(752,plain,
( ~ sP254
| sP468
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(753,plain,
( ~ sP314
| sP245
| ~ sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(754,plain,
( ~ sP280
| sP91
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(755,plain,
( ~ sP424
| ~ sP53
| sP570 ),
inference(prop_rule,[status(thm)],[]) ).
thf(756,plain,
( ~ sP159
| sP423
| sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(757,plain,
( ~ sP478
| sP159
| sP385 ),
inference(prop_rule,[status(thm)],[]) ).
thf(758,plain,
( ~ sP239
| sP35
| sP488 ),
inference(prop_rule,[status(thm)],[]) ).
thf(759,plain,
( ~ sP181
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(760,plain,
( ~ sP138
| sP377 ),
inference(all_rule,[status(thm)],[]) ).
thf(761,plain,
( ~ sP118
| sP643 ),
inference(all_rule,[status(thm)],[]) ).
thf(762,plain,
( ~ sP636
| sP28
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(763,plain,
( ~ sP275
| sP254 ),
inference(all_rule,[status(thm)],[]) ).
thf(764,plain,
( ~ sP555
| sP32
| sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(765,plain,
( ~ sP224
| sP280
| ~ sP585 ),
inference(prop_rule,[status(thm)],[]) ).
thf(766,plain,
( ~ sP56
| sP280
| ~ sP113 ),
inference(prop_rule,[status(thm)],[]) ).
thf(767,plain,
( ~ sP633
| ~ sP602
| sP423 ),
inference(prop_rule,[status(thm)],[]) ).
thf(768,plain,
( ~ sP233
| sP633 ),
inference(all_rule,[status(thm)],[]) ).
thf(769,plain,
( ~ sP233
| sP424 ),
inference(all_rule,[status(thm)],[]) ).
thf(770,plain,
( ~ sP65
| sP478 ),
inference(all_rule,[status(thm)],[]) ).
thf(771,plain,
( ~ sP65
| sP239 ),
inference(all_rule,[status(thm)],[]) ).
thf(772,plain,
( ~ sP604
| sP181 ),
inference(all_rule,[status(thm)],[]) ).
thf(773,plain,
( ~ sP604
| sP501 ),
inference(all_rule,[status(thm)],[]) ).
thf(774,plain,
( ~ sP450
| sP138 ),
inference(all_rule,[status(thm)],[]) ).
thf(775,plain,
( ~ sP68
| sP166 ),
inference(all_rule,[status(thm)],[]) ).
thf(776,plain,
( ~ sP539
| sP118 ),
inference(all_rule,[status(thm)],[]) ).
thf(777,plain,
( ~ sP303
| sP144
| sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(778,plain,
( ~ sP671
| sP303
| sP458 ),
inference(prop_rule,[status(thm)],[]) ).
thf(779,plain,
( ~ sP394
| ~ sP692
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(780,plain,
( ~ sP231
| sP636 ),
inference(all_rule,[status(thm)],[]) ).
thf(781,plain,
( ~ sP610
| sP275 ),
inference(all_rule,[status(thm)],[]) ).
thf(782,plain,
( ~ sP664
| sP555
| sP312 ),
inference(prop_rule,[status(thm)],[]) ).
thf(783,plain,
( ~ sP85
| sP224 ),
inference(all_rule,[status(thm)],[]) ).
thf(784,plain,
( ~ sP85
| sP56 ),
inference(all_rule,[status(thm)],[]) ).
thf(785,plain,
( sP380
| ~ sP144 ),
inference(prop_rule,[status(thm)],[]) ).
thf(786,plain,
( ~ sP296
| ~ sP562 ),
inference(all_rule,[status(thm)],[]) ).
thf(787,plain,
( ~ sP2
| sP233 ),
inference(all_rule,[status(thm)],[]) ).
thf(788,plain,
( ~ sP568
| sP65 ),
inference(all_rule,[status(thm)],[]) ).
thf(789,plain,
( ~ sP414
| sP604 ),
inference(all_rule,[status(thm)],[]) ).
thf(790,plain,
( ~ sP178
| sP450 ),
inference(all_rule,[status(thm)],[]) ).
thf(791,plain,
( ~ sP305
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(792,plain,
( ~ sP109
| sP539 ),
inference(all_rule,[status(thm)],[]) ).
thf(793,plain,
( ~ sP548
| sP671 ),
inference(all_rule,[status(thm)],[]) ).
thf(794,plain,
( ~ sP536
| sP394 ),
inference(all_rule,[status(thm)],[]) ).
thf(795,plain,
( ~ sP483
| sP231 ),
inference(all_rule,[status(thm)],[]) ).
thf(796,plain,
( ~ sP256
| sP259 ),
inference(all_rule,[status(thm)],[]) ).
thf(797,plain,
( ~ sP221
| sP610 ),
inference(all_rule,[status(thm)],[]) ).
thf(798,plain,
( ~ sP12
| sP313 ),
inference(all_rule,[status(thm)],[]) ).
thf(799,plain,
( ~ sP282
| sP664 ),
inference(all_rule,[status(thm)],[]) ).
thf(800,plain,
( ~ sP451
| sP463 ),
inference(all_rule,[status(thm)],[]) ).
thf(801,plain,
( ~ sP79
| sP85 ),
inference(all_rule,[status(thm)],[]) ).
thf(802,plain,
( ~ sP163
| sP408
| ~ sP364
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(803,plain,
( ~ sP559
| sP39
| ~ sP364
| sP682 ),
inference(mating_rule,[status(thm)],[]) ).
thf(804,plain,
~ sP682,
inference(prop_rule,[status(thm)],[]) ).
thf(805,plain,
( ~ sP473
| sP497
| sP163 ),
inference(prop_rule,[status(thm)],[]) ).
thf(806,plain,
( ~ sP235
| sP473
| sP559 ),
inference(prop_rule,[status(thm)],[]) ).
thf(807,plain,
( ~ sP282
| sP235 ),
inference(all_rule,[status(thm)],[]) ).
thf(808,plain,
( ~ sP12
| sP79 ),
inference(all_rule,[status(thm)],[]) ).
thf(809,plain,
( ~ sP221
| sP451 ),
inference(all_rule,[status(thm)],[]) ).
thf(810,plain,
( ~ sP106
| sP364
| sP130 ),
inference(prop_rule,[status(thm)],[]) ).
thf(811,plain,
( ~ sP503
| sP106
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(812,plain,
( ~ sP6
| ~ sP570
| sP497 ),
inference(prop_rule,[status(thm)],[]) ).
thf(813,plain,
( ~ sP536
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(814,plain,
( ~ sP558
| ~ sP32
| sP364 ),
inference(prop_rule,[status(thm)],[]) ).
thf(815,plain,
( ~ sP296
| ~ sP423 ),
inference(all_rule,[status(thm)],[]) ).
thf(816,plain,
( ~ sP2
| sP536 ),
inference(all_rule,[status(thm)],[]) ).
thf(817,plain,
( ~ sP651
| ~ sP408 ),
inference(all_rule,[status(thm)],[]) ).
thf(818,plain,
( ~ sP341
| ~ sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(819,plain,
( ~ sP568
| sP282 ),
inference(all_rule,[status(thm)],[]) ).
thf(820,plain,
( ~ sP414
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(821,plain,
( ~ sP178
| sP221 ),
inference(all_rule,[status(thm)],[]) ).
thf(822,plain,
( ~ sP107
| sP558 ),
inference(all_rule,[status(thm)],[]) ).
thf(823,plain,
( ~ sP305
| sP256 ),
inference(all_rule,[status(thm)],[]) ).
thf(824,plain,
( ~ sP109
| sP483 ),
inference(all_rule,[status(thm)],[]) ).
thf(825,plain,
( ~ sP548
| sP503 ),
inference(all_rule,[status(thm)],[]) ).
thf(826,plain,
( ~ sP296
| ~ sP497 ),
inference(all_rule,[status(thm)],[]) ).
thf(827,plain,
( ~ sP2
| sP107 ),
inference(all_rule,[status(thm)],[]) ).
thf(828,plain,
( ~ sP568
| sP548 ),
inference(all_rule,[status(thm)],[]) ).
thf(829,plain,
( ~ sP414
| sP109 ),
inference(all_rule,[status(thm)],[]) ).
thf(830,plain,
( ~ sP178
| sP305 ),
inference(all_rule,[status(thm)],[]) ).
thf(axb,axiom,
sP178 ).
thf(axr,axiom,
sP414 ).
thf(rb,axiom,
sP568 ).
thf(bi,axiom,
sP341 ).
thf(ri,axiom,
sP651 ).
thf(sinj,axiom,
sP2 ).
thf(snz,axiom,
sP296 ).
thf(831,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,axb,axr,rb,bi,ri,sinj,snz]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA138^1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.17/0.34 % Computer : n029.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 23:18:14 EDT 2026
% 0.17/0.34 % CPUTime :
% 3.04/3.20 % SZS status Unsatisfiable
% 3.04/3.20 % Mode: cade22grackle2xfee4
% 3.04/3.20 % Steps: 5905
% 3.04/3.20 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------