%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : GRA162^1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:29:42 PM UTC 2026
% Result : Unsatisfiable 1.73s 1.96s
% Output : Proof 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 848
% Syntax : Number of formulae : 849 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 2423 ( 81 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 6194 (1398 ~; 676 |; 0 &;3222 @)
% ( 404 <=>; 494 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 410 ( 408 usr; 406 con; 0-2 aty)
% Number of variables : 133 ( 0 ^; 133 !; 0 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_s,type,
s: $i > $i ).
thf(ty_r,type,
r: $i > $i > $o ).
thf(ty_z,type,
z: $i ).
thf(ty_b,type,
b: $i > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( ( s @ X1 )
= ( s @ X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( b @ z @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( b @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( z
!= ( s @ ( s @ z ) ) )
=> ( r @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( s @ ( s @ z ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ~ ( ~ ( sP5
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( s @ ( s @ z ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP20 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( ~ sP17
=> ( r @ ( s @ ( s @ z ) ) @ z ) )
=> ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( z
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ ( ( ( s @ z )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ ( ~ ( sP5
=> ~ sP33 )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( ( s @ z )
!= ( s @ ( s @ ( s @ z ) ) ) )
=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( sP5
=> ~ sP33 )
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( s @ z )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ ( sP20
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ ( ( ( s @ ( s @ z ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( z
!= ( s @ z ) )
=> ( r @ z @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP19
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ z @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( ( s @ z )
!= z )
=> ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ ( sP20
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ ( ~ ( sP33
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ sP39
=> ~ ( r @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ( ( 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,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( s @ ( s @ ( s @ z ) ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP33
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ( s @ z )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP5
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ~ ( ~ ( sP19
=> ~ sP2 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ~ sP52
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( r @ X1 @ X2 )
=> ~ ( r @ X1 @ X3 ) )
=> ~ ( r @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) )
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ z ) ) @ X1 )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X3 ) )
=> ~ ( b @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ~ ( ~ ( sP33
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP61 )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ ( s @ z ) ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( sP14
=> ( ( s @ z )
= z ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( ~ sP10
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( ~ sP48
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP19 )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ! [X1: $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 ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( ~ ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ z ) )
=> sP24 )
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( ~ ( sP19
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( ( s @ z )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ z ) @ z ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( sP55
=> ~ ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ! [X1: $i] :
( ( ( s @ z )
= ( s @ X1 ) )
=> ( z = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ! [X1: $i,X2: $i] :
( ~ ( ( r @ z @ X1 )
=> ~ ( r @ z @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ( sP69
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ! [X1: $i] :
( ~ ( ~ sP8
=> ~ ( b @ z @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( ~ sP28
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ( ~ ( ~ sP31
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X3 ) )
=> ~ ( b @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ! [X1: $i] :
( ~ ( ~ sP22
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ( ~ sP51
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( ~ sP45
=> ( b @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP55 ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ! [X1: $i] :
( ~ ( ~ ( sP19
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP100 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) )
=> ~ sP100 ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ! [X1: $i] :
( ~ ( ( ( s @ ( s @ ( s @ z ) ) )
!= X1 )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
!= ( s @ z ) )
=> sP36 )
=> sP109 ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( b @ ( s @ z ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP61 ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( ~ sP3
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ! [X1: $i] :
( ~ ( ~ sP66
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( ~ ( ~ sP14
=> sP96 )
=> sP108 ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( sP109
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ( ~ sP37
=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ! [X1: $i] :
( ~ ( ( ( s @ ( s @ z ) )
!= X1 )
=> ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ sP108 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ! [X1: $i] :
( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ X1 ) )
=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X3 ) )
=> ~ ( b @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ! [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,[sP129])]) ).
thf(sP130,plain,
( sP130
<=> ( sP96
=> ~ sP55 ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131,plain,
( sP131
<=> ( ~ sP6
=> ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132,plain,
( sP132
<=> ( ~ ( ~ sP57
=> ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133,plain,
( sP133
<=> ( ~ ( sP19
=> ~ sP2 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134,plain,
( sP134
<=> ( ~ sP59
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(sP135,plain,
( sP135
<=> ( r @ z @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP135])]) ).
thf(sP136,plain,
( sP136
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP136])]) ).
thf(sP137,plain,
( sP137
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP137])]) ).
thf(sP138,plain,
( sP138
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP100
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP138])]) ).
thf(sP139,plain,
( sP139
<=> ( ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP139])]) ).
thf(sP140,plain,
( sP140
<=> ! [X1: $i] :
( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP19 )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP140])]) ).
thf(sP141,plain,
( sP141
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP141])]) ).
thf(sP142,plain,
( sP142
<=> ( ~ ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP142])]) ).
thf(sP143,plain,
( sP143
<=> ( ~ ( ~ ( sP108
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP143])]) ).
thf(sP144,plain,
( sP144
<=> ! [X1: $i] :
( ~ ( ~ sP56
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP144])]) ).
thf(sP145,plain,
( sP145
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP145])]) ).
thf(sP146,plain,
( sP146
<=> ! [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,[sP146])]) ).
thf(sP147,plain,
( sP147
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP147])]) ).
thf(sP148,plain,
( sP148
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ z ) @ X1 )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ ( s @ z ) @ X3 ) )
=> ~ ( b @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP148])]) ).
thf(sP149,plain,
( sP149
<=> ( ~ sP21
=> ~ sP145 ) ),
introduced(definition,[new_symbols(definition,[sP149])]) ).
thf(sP150,plain,
( sP150
<=> ( sP88
=> ~ ( r @ ( s @ z ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP150])]) ).
thf(sP151,plain,
( sP151
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP69
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP151])]) ).
thf(sP152,plain,
( sP152
<=> ( ~ ( sP100
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP152])]) ).
thf(sP153,plain,
( sP153
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP153])]) ).
thf(sP154,plain,
( sP154
<=> ! [X1: $i] :
( ~ ( ( r @ ( s @ z ) @ z )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP154])]) ).
thf(sP155,plain,
( sP155
<=> ( ~ ( ~ ( sP100
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP61 )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP155])]) ).
thf(sP156,plain,
( sP156
<=> ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP156])]) ).
thf(sP157,plain,
( sP157
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ sP100 ) ),
introduced(definition,[new_symbols(definition,[sP157])]) ).
thf(sP158,plain,
( sP158
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP158])]) ).
thf(sP159,plain,
( sP159
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP159])]) ).
thf(sP160,plain,
( sP160
<=> ! [X1: $i,X2: $i] :
( ~ ( ( r @ ( s @ ( s @ z ) ) @ X1 )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP160])]) ).
thf(sP161,plain,
( sP161
<=> ( sP100
=> ~ sP116 ) ),
introduced(definition,[new_symbols(definition,[sP161])]) ).
thf(sP162,plain,
( sP162
<=> ( ~ ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= z )
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP162])]) ).
thf(sP163,plain,
( sP163
<=> ( ~ sP161
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP163])]) ).
thf(sP164,plain,
( sP164
<=> ! [X1: $i] :
( ~ ( ~ ( sP100
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP164])]) ).
thf(sP165,plain,
( sP165
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP165])]) ).
thf(sP166,plain,
( sP166
<=> ( ( s @ z )
= z ) ),
introduced(definition,[new_symbols(definition,[sP166])]) ).
thf(sP167,plain,
( sP167
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= z )
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP167])]) ).
thf(sP168,plain,
( sP168
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP168])]) ).
thf(sP169,plain,
( sP169
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP108
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP169])]) ).
thf(sP170,plain,
( sP170
<=> ( r @ ( s @ z ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP170])]) ).
thf(sP171,plain,
( sP171
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP171])]) ).
thf(sP172,plain,
( sP172
<=> ( sP99
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP172])]) ).
thf(sP173,plain,
( sP173
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP173])]) ).
thf(sP174,plain,
( sP174
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ sP13 )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP174])]) ).
thf(sP175,plain,
( sP175
<=> ( ~ sP30
=> ~ sP165 ) ),
introduced(definition,[new_symbols(definition,[sP175])]) ).
thf(sP176,plain,
( sP176
<=> ( ~ ( sP165
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ sP89 ) ),
introduced(definition,[new_symbols(definition,[sP176])]) ).
thf(sP177,plain,
( sP177
<=> ( sP19
=> ~ ( b @ z @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP177])]) ).
thf(sP178,plain,
( sP178
<=> ( sP137
=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP178])]) ).
thf(sP179,plain,
( sP179
<=> ( ~ sP66
=> ~ sP108 ) ),
introduced(definition,[new_symbols(definition,[sP179])]) ).
thf(sP180,plain,
( sP180
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ z @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ z @ X2 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP180])]) ).
thf(sP181,plain,
( sP181
<=> ( ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP181])]) ).
thf(sP182,plain,
( sP182
<=> ( ~ ( sP170
=> ~ sP88 )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP182])]) ).
thf(sP183,plain,
( sP183
<=> ( ~ ( sP173
=> ~ sP19 )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP183])]) ).
thf(sP184,plain,
( sP184
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP184])]) ).
thf(sP185,plain,
( sP185
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> sP165 ) ),
introduced(definition,[new_symbols(definition,[sP185])]) ).
thf(sP186,plain,
( sP186
<=> ( ~ sP157
=> ~ sP171 ) ),
introduced(definition,[new_symbols(definition,[sP186])]) ).
thf(sP187,plain,
( sP187
<=> ( ~ sP50
=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP187])]) ).
thf(sP188,plain,
( sP188
<=> ! [X1: $i] :
( ~ ( ~ sP121
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP188])]) ).
thf(sP189,plain,
( sP189
<=> ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ sP69 )
=> ~ sP171 ) ),
introduced(definition,[new_symbols(definition,[sP189])]) ).
thf(sP190,plain,
( sP190
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP190])]) ).
thf(sP191,plain,
( sP191
<=> ( ~ sP25
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP191])]) ).
thf(sP192,plain,
( sP192
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP125
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP192])]) ).
thf(sP193,plain,
( sP193
<=> ( ~ sP159
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP193])]) ).
thf(sP194,plain,
( sP194
<=> ! [X1: $i] :
( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP194])]) ).
thf(sP195,plain,
( sP195
<=> ! [X1: $i] :
( ~ ( ~ sP21
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP195])]) ).
thf(sP196,plain,
( sP196
<=> ( ~ sP105
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP196])]) ).
thf(sP197,plain,
( sP197
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( ~ ( ( b @ X1 @ X2 )
=> ~ ( b @ X2 @ X3 ) )
=> ~ ( b @ X1 @ X4 ) )
=> ~ ( b @ X2 @ X4 ) ) ),
introduced(definition,[new_symbols(definition,[sP197])]) ).
thf(sP198,plain,
( sP198
<=> ( z
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP198])]) ).
thf(sP199,plain,
( sP199
<=> ( ~ ( ( 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,[sP199])]) ).
thf(sP200,plain,
( sP200
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP200])]) ).
thf(sP201,plain,
( sP201
<=> ( ~ ( sP99
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP201])]) ).
thf(sP202,plain,
( sP202
<=> ( sP20
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP202])]) ).
thf(sP203,plain,
( sP203
<=> ( ~ ( ~ sP87
=> sP80 )
=> sP69 ) ),
introduced(definition,[new_symbols(definition,[sP203])]) ).
thf(sP204,plain,
( sP204
<=> ( ~ ( sP20
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> ~ ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP204])]) ).
thf(sP205,plain,
( sP205
<=> ( ~ ( ~ sP64
=> sP89 )
=> sP53 ) ),
introduced(definition,[new_symbols(definition,[sP205])]) ).
thf(sP206,plain,
( sP206
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP206])]) ).
thf(sP207,plain,
( sP207
<=> ( ~ sP121
=> ~ sP53 ) ),
introduced(definition,[new_symbols(definition,[sP207])]) ).
thf(sP208,plain,
( sP208
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ ( s @ ( s @ z ) ) ) )
=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP208])]) ).
thf(sP209,plain,
( sP209
<=> ! [X1: $i] :
( ~ ( ( z != X1 )
=> ( r @ z @ X1 ) )
=> ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP209])]) ).
thf(sP210,plain,
( sP210
<=> ! [X1: $i] :
( ~ ( sP55
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP210])]) ).
thf(sP211,plain,
( sP211
<=> ( ~ ( sP13
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) )
=> ~ sP89 ) ),
introduced(definition,[new_symbols(definition,[sP211])]) ).
thf(sP212,plain,
( sP212
<=> ( sP108
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP212])]) ).
thf(sP213,plain,
( sP213
<=> ( sP100
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP213])]) ).
thf(sP214,plain,
( sP214
<=> ( ~ sP56
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP214])]) ).
thf(sP215,plain,
( sP215
<=> ( ~ sP22
=> ~ sP53 ) ),
introduced(definition,[new_symbols(definition,[sP215])]) ).
thf(sP216,plain,
( sP216
<=> ( ~ sP130
=> ~ sP88 ) ),
introduced(definition,[new_symbols(definition,[sP216])]) ).
thf(sP217,plain,
( sP217
<=> ( ~ sP122
=> sP55 ) ),
introduced(definition,[new_symbols(definition,[sP217])]) ).
thf(sP218,plain,
( sP218
<=> ( ~ sP117
=> ~ sP53 ) ),
introduced(definition,[new_symbols(definition,[sP218])]) ).
thf(sP219,plain,
( sP219
<=> ! [X1: $i] :
( ~ ( ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP219])]) ).
thf(sP220,plain,
( sP220
<=> ( ( ( s @ ( s @ ( s @ z ) ) )
!= ( s @ z ) )
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP220])]) ).
thf(sP221,plain,
( sP221
<=> ! [X1: $i] :
( ~ ( ( ( s @ z )
!= X1 )
=> ( r @ ( s @ z ) @ X1 ) )
=> ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP221])]) ).
thf(sP222,plain,
( sP222
<=> ! [X1: $i] :
( ~ ( ~ sP159
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP222])]) ).
thf(sP223,plain,
( sP223
<=> ( ~ sP139
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP223])]) ).
thf(sP224,plain,
( sP224
<=> ! [X1: $i] :
( ~ ( ~ sP157
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP224])]) ).
thf(sP225,plain,
( sP225
<=> ! [X1: $i] :
( ~ ( ~ ( sP33
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP225])]) ).
thf(sP226,plain,
( sP226
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP226])]) ).
thf(sP227,plain,
( sP227
<=> ! [X1: $i,X2: $i] :
( ~ ( ( X1 != X2 )
=> ( r @ X1 @ X2 ) )
=> ( b @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP227])]) ).
thf(sP228,plain,
( sP228
<=> ( ~ ( ~ sP190
=> sP92 )
=> sP125 ) ),
introduced(definition,[new_symbols(definition,[sP228])]) ).
thf(sP229,plain,
( sP229
<=> ! [X1: $i] :
( ~ ( ~ sP31
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP229])]) ).
thf(sP230,plain,
( sP230
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP230])]) ).
thf(sP231,plain,
( sP231
<=> ! [X1: $i] :
( ~ ( sP135
=> ~ ( r @ z @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP231])]) ).
thf(sP232,plain,
( sP232
<=> ( r @ z @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP232])]) ).
thf(sP233,plain,
( sP233
<=> ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ sP108 ) ),
introduced(definition,[new_symbols(definition,[sP233])]) ).
thf(sP234,plain,
( sP234
<=> ( ~ sP75
=> sP33 ) ),
introduced(definition,[new_symbols(definition,[sP234])]) ).
thf(sP235,plain,
( sP235
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP235])]) ).
thf(sP236,plain,
( sP236
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X3 ) )
=> ~ ( b @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP236])]) ).
thf(sP237,plain,
( sP237
<=> ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
!= ( s @ z ) )
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP237])]) ).
thf(sP238,plain,
( sP238
<=> ( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ sP99 )
=> ~ ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP238])]) ).
thf(sP239,plain,
( sP239
<=> ( ~ sP91
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP239])]) ).
thf(sP240,plain,
( sP240
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP240])]) ).
thf(sP241,plain,
( sP241
<=> ( sP135
=> ~ sP232 ) ),
introduced(definition,[new_symbols(definition,[sP241])]) ).
thf(sP242,plain,
( sP242
<=> ( ~ sP15
=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP242])]) ).
thf(sP243,plain,
( sP243
<=> ( ~ ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP243])]) ).
thf(sP244,plain,
( sP244
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP244])]) ).
thf(sP245,plain,
( sP245
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP245])]) ).
thf(sP246,plain,
( sP246
<=> ! [X1: $i] :
( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ X1 ) )
=> ( ( s @ ( s @ ( s @ z ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP246])]) ).
thf(sP247,plain,
( sP247
<=> ( ( s @ ( s @ z ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP247])]) ).
thf(sP248,plain,
( sP248
<=> ( sP33
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP248])]) ).
thf(sP249,plain,
( sP249
<=> ( ~ sP233
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP249])]) ).
thf(sP250,plain,
( sP250
<=> ( ~ sP214
=> ~ sP53 ) ),
introduced(definition,[new_symbols(definition,[sP250])]) ).
thf(sP251,plain,
( sP251
<=> ! [X1: $i] :
( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP251])]) ).
thf(sP252,plain,
( sP252
<=> ( z
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP252])]) ).
thf(sP253,plain,
( sP253
<=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP253])]) ).
thf(sP254,plain,
( sP254
<=> ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP254])]) ).
thf(sP255,plain,
( sP255
<=> ( ~ sP43
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP255])]) ).
thf(sP256,plain,
( sP256
<=> ( ~ ( sP100
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ sP61 ) ),
introduced(definition,[new_symbols(definition,[sP256])]) ).
thf(sP257,plain,
( sP257
<=> ! [X1: $i] :
( ( ( s @ ( s @ ( s @ z ) ) )
= ( s @ X1 ) )
=> ( ( s @ ( s @ z ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP257])]) ).
thf(sP258,plain,
( sP258
<=> ( ~ sP82
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP258])]) ).
thf(sP259,plain,
( sP259
<=> ( ~ sP193
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP259])]) ).
thf(sP260,plain,
( sP260
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP260])]) ).
thf(sP261,plain,
( sP261
<=> ( b @ z @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP261])]) ).
thf(sP262,plain,
( sP262
<=> ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP262])]) ).
thf(sP263,plain,
( sP263
<=> ( ~ sP85
=> ~ sP261 ) ),
introduced(definition,[new_symbols(definition,[sP263])]) ).
thf(sP264,plain,
( sP264
<=> ( ~ sP118
=> sP100 ) ),
introduced(definition,[new_symbols(definition,[sP264])]) ).
thf(sP265,plain,
( sP265
<=> ( sP20
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP265])]) ).
thf(sP266,plain,
( sP266
<=> ( ~ sP14
=> sP96 ) ),
introduced(definition,[new_symbols(definition,[sP266])]) ).
thf(sP267,plain,
( sP267
<=> ( ~ sP242
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP267])]) ).
thf(sP268,plain,
( sP268
<=> ( r @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP268])]) ).
thf(sP269,plain,
( sP269
<=> ( sP24
=> ~ sP165 ) ),
introduced(definition,[new_symbols(definition,[sP269])]) ).
thf(sP270,plain,
( sP270
<=> ( ~ ( ~ sP29
=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP270])]) ).
thf(sP271,plain,
( sP271
<=> ( ~ sP179
=> ~ sP100 ) ),
introduced(definition,[new_symbols(definition,[sP271])]) ).
thf(sP272,plain,
( sP272
<=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP272])]) ).
thf(sP273,plain,
( sP273
<=> ( ~ sP150
=> ~ sP89 ) ),
introduced(definition,[new_symbols(definition,[sP273])]) ).
thf(sP274,plain,
( sP274
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ z ) ) )
=> sP254 ) ),
introduced(definition,[new_symbols(definition,[sP274])]) ).
thf(sP275,plain,
( sP275
<=> ( sP13
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP275])]) ).
thf(sP276,plain,
( sP276
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( sP145
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP276])]) ).
thf(sP277,plain,
( sP277
<=> ( sP24
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP277])]) ).
thf(sP278,plain,
( sP278
<=> ( sP100
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP278])]) ).
thf(sP279,plain,
( sP279
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP279])]) ).
thf(sP280,plain,
( sP280
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP280])]) ).
thf(sP281,plain,
( sP281
<=> ! [X1: $i] :
( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP281])]) ).
thf(sP282,plain,
( sP282
<=> ! [X1: $i] :
( ~ ( sP24
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP282])]) ).
thf(sP283,plain,
( sP283
<=> ! [X1: $i,X2: $i] :
( ~ ( ( r @ ( s @ z ) @ X1 )
=> ~ ( r @ ( s @ z ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP283])]) ).
thf(sP284,plain,
( sP284
<=> ( ( ( s @ z )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> sP88 ) ),
introduced(definition,[new_symbols(definition,[sP284])]) ).
thf(sP285,plain,
( sP285
<=> ( ~ sP29
=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP285])]) ).
thf(sP286,plain,
( sP286
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP286])]) ).
thf(sP287,plain,
( sP287
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP287])]) ).
thf(sP288,plain,
( sP288
<=> ( ~ sP218
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP288])]) ).
thf(sP289,plain,
( sP289
<=> ( ~ sP98
=> ~ sP116 ) ),
introduced(definition,[new_symbols(definition,[sP289])]) ).
thf(sP290,plain,
( sP290
<=> ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP290])]) ).
thf(sP291,plain,
( sP291
<=> ( sP15
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP291])]) ).
thf(sP292,plain,
( sP292
<=> ( ~ sP247
=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP292])]) ).
thf(sP293,plain,
( sP293
<=> ( ~ ( sP24
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) )
=> ~ sP268 ) ),
introduced(definition,[new_symbols(definition,[sP293])]) ).
thf(sP294,plain,
( sP294
<=> ( ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ z ) )
=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= z ) ) ),
introduced(definition,[new_symbols(definition,[sP294])]) ).
thf(sP295,plain,
( sP295
<=> ( sP173
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP295])]) ).
thf(sP296,plain,
( sP296
<=> ! [X1: $i] :
( ~ ( sP99
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP296])]) ).
thf(sP297,plain,
( sP297
<=> ( ~ sP248
=> ~ sP61 ) ),
introduced(definition,[new_symbols(definition,[sP297])]) ).
thf(sP298,plain,
( sP298
<=> ( b @ ( s @ z ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP298])]) ).
thf(sP299,plain,
( sP299
<=> ! [X1: $i,X2: $i] :
( ~ ( ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP299])]) ).
thf(sP300,plain,
( sP300
<=> ( b @ ( s @ ( s @ z ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP300])]) ).
thf(sP301,plain,
( sP301
<=> ( ( ( s @ z )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
=> sP252 ) ),
introduced(definition,[new_symbols(definition,[sP301])]) ).
thf(sP302,plain,
( sP302
<=> ( ~ sP181
=> ~ sP116 ) ),
introduced(definition,[new_symbols(definition,[sP302])]) ).
thf(sP303,plain,
( sP303
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP303])]) ).
thf(sP304,plain,
( sP304
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP304])]) ).
thf(sP305,plain,
( sP305
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP305])]) ).
thf(sP306,plain,
( sP306
<=> ( ~ sP111
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP306])]) ).
thf(sP307,plain,
( sP307
<=> ( ~ sP241
=> ~ sP268 ) ),
introduced(definition,[new_symbols(definition,[sP307])]) ).
thf(sP308,plain,
( sP308
<=> ( ~ sP212
=> ~ sP279 ) ),
introduced(definition,[new_symbols(definition,[sP308])]) ).
thf(sP309,plain,
( sP309
<=> ( sP305
=> ~ sP69 ) ),
introduced(definition,[new_symbols(definition,[sP309])]) ).
thf(sP310,plain,
( sP310
<=> ! [X1: $i] :
( ~ ( ~ sP28
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP310])]) ).
thf(sP311,plain,
( sP311
<=> ! [X1: $i] :
( ( ( s @ ( s @ z ) )
= ( s @ X1 ) )
=> ( ( s @ z )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP311])]) ).
thf(sP312,plain,
( sP312
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP312])]) ).
thf(sP313,plain,
( sP313
<=> ( ~ ( ~ sP244
=> sP99 )
=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP313])]) ).
thf(sP314,plain,
( sP314
<=> ( b @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP314])]) ).
thf(sP315,plain,
( sP315
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= z ) ),
introduced(definition,[new_symbols(definition,[sP315])]) ).
thf(sP316,plain,
( sP316
<=> ! [X1: $i] :
~ ( r @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP316])]) ).
thf(sP317,plain,
( sP317
<=> ( ~ sP57
=> sP268 ) ),
introduced(definition,[new_symbols(definition,[sP317])]) ).
thf(sP318,plain,
( sP318
<=> ( ~ sP183
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP318])]) ).
thf(sP319,plain,
( sP319
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP319])]) ).
thf(sP320,plain,
( sP320
<=> ! [X1: $i] :
( ~ ( sP13
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP320])]) ).
thf(sP321,plain,
( sP321
<=> ( ~ sP190
=> sP92 ) ),
introduced(definition,[new_symbols(definition,[sP321])]) ).
thf(sP322,plain,
( sP322
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP322])]) ).
thf(sP323,plain,
( sP323
<=> ( ( z
!= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) )
=> sP272 ) ),
introduced(definition,[new_symbols(definition,[sP323])]) ).
thf(sP324,plain,
( sP324
<=> ( ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP324])]) ).
thf(sP325,plain,
( sP325
<=> ( ~ sP152
=> ~ ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP325])]) ).
thf(sP326,plain,
( sP326
<=> ! [X1: $i] :
( ( s @ X1 )
!= z ) ),
introduced(definition,[new_symbols(definition,[sP326])]) ).
thf(sP327,plain,
( sP327
<=> ( z
= ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP327])]) ).
thf(sP328,plain,
( sP328
<=> ( z
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP328])]) ).
thf(sP329,plain,
( sP329
<=> ( sP173
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP329])]) ).
thf(sP330,plain,
( sP330
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP330])]) ).
thf(sP331,plain,
( sP331
<=> ( sP3
=> sP51 ) ),
introduced(definition,[new_symbols(definition,[sP331])]) ).
thf(sP332,plain,
( sP332
<=> ( ~ sP312
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP332])]) ).
thf(sP333,plain,
( sP333
<=> ( sP99
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP333])]) ).
thf(sP334,plain,
( sP334
<=> ( sP20
=> ~ sP303 ) ),
introduced(definition,[new_symbols(definition,[sP334])]) ).
thf(sP335,plain,
( sP335
<=> ( sP55
=> ~ ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP335])]) ).
thf(sP336,plain,
( sP336
<=> ( ~ sP17
=> ( r @ ( s @ ( s @ z ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP336])]) ).
thf(sP337,plain,
( sP337
<=> ( ~ sP64
=> sP89 ) ),
introduced(definition,[new_symbols(definition,[sP337])]) ).
thf(sP338,plain,
( sP338
<=> ( ( s @ z )
= ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP338])]) ).
thf(sP339,plain,
( sP339
<=> ( ~ ( ~ sP8
=> ~ ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP339])]) ).
thf(sP340,plain,
( sP340
<=> ( b @ z @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP340])]) ).
thf(sP341,plain,
( sP341
<=> ( ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ ( s @ z ) ) ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP341])]) ).
thf(sP342,plain,
( sP342
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ~ ( ( b @ z @ X1 )
=> ~ ( b @ X1 @ X2 ) )
=> ~ ( b @ z @ X3 ) )
=> ~ ( b @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP342])]) ).
thf(sP343,plain,
( sP343
<=> ( r @ ( s @ ( s @ z ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP343])]) ).
thf(sP344,plain,
( sP344
<=> ( ( s @ z )
= ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP344])]) ).
thf(sP345,plain,
( sP345
<=> ( ~ sP8
=> ~ sP340 ) ),
introduced(definition,[new_symbols(definition,[sP345])]) ).
thf(sP346,plain,
( sP346
<=> ( sP171
=> ~ sP298 ) ),
introduced(definition,[new_symbols(definition,[sP346])]) ).
thf(sP347,plain,
( sP347
<=> ( ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) )
=> ~ sP268 ) ),
introduced(definition,[new_symbols(definition,[sP347])]) ).
thf(sP348,plain,
( sP348
<=> ( r @ z @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP348])]) ).
thf(sP349,plain,
( sP349
<=> ! [X1: $i] :
( ~ ( ~ sP52
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP349])]) ).
thf(sP350,plain,
( sP350
<=> ( ~ sP172
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP350])]) ).
thf(sP351,plain,
( sP351
<=> ! [X1: $i,X2: $i] :
( ~ ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X2 ) )
=> ~ ( r @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP351])]) ).
thf(sP352,plain,
( sP352
<=> ( ~ sP335
=> ~ sP89 ) ),
introduced(definition,[new_symbols(definition,[sP352])]) ).
thf(sP353,plain,
( sP353
<=> ( sP170
=> ~ sP88 ) ),
introduced(definition,[new_symbols(definition,[sP353])]) ).
thf(sP354,plain,
( sP354
<=> ( ~ sP287
=> sP61 ) ),
introduced(definition,[new_symbols(definition,[sP354])]) ).
thf(sP355,plain,
( sP355
<=> ( sP338
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP355])]) ).
thf(sP356,plain,
( sP356
<=> ( ~ sP87
=> sP80 ) ),
introduced(definition,[new_symbols(definition,[sP356])]) ).
thf(sP357,plain,
( sP357
<=> ( r @ ( s @ z ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP357])]) ).
thf(sP358,plain,
( sP358
<=> ( sP20
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP358])]) ).
thf(sP359,plain,
( sP359
<=> ! [X1: $i] :
( ~ ( ~ sP346
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP359])]) ).
thf(sP360,plain,
( sP360
<=> ( ~ sP244
=> sP99 ) ),
introduced(definition,[new_symbols(definition,[sP360])]) ).
thf(sP361,plain,
( sP361
<=> ! [X1: $i] :
( ~ ( sP357
=> ~ ( r @ ( s @ z ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP361])]) ).
thf(sP362,plain,
( sP362
<=> ( ~ sP200
=> ~ sP55 ) ),
introduced(definition,[new_symbols(definition,[sP362])]) ).
thf(sP363,plain,
( sP363
<=> ( ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) )
= ( s @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP363])]) ).
thf(sP364,plain,
( sP364
<=> ( ~ sP149
=> ~ ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP364])]) ).
thf(sP365,plain,
( sP365
<=> ( ~ sP31
=> ~ sP305 ) ),
introduced(definition,[new_symbols(definition,[sP365])]) ).
thf(sP366,plain,
( sP366
<=> ( r @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP366])]) ).
thf(sP367,plain,
( sP367
<=> ( b @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP367])]) ).
thf(sP368,plain,
( sP368
<=> ( b @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) @ ( s @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP368])]) ).
thf(sP369,plain,
( sP369
<=> $false ),
introduced(definition,[new_symbols(definition,[sP369])]) ).
thf(sP370,plain,
( sP370
<=> ( ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z )
=> ~ sP99 ) ),
introduced(definition,[new_symbols(definition,[sP370])]) ).
thf(sP371,plain,
( sP371
<=> ( ~ sP189
=> ~ sP108 ) ),
introduced(definition,[new_symbols(definition,[sP371])]) ).
thf(sP372,plain,
( sP372
<=> ( ~ sP322
=> ~ sP232 ) ),
introduced(definition,[new_symbols(definition,[sP372])]) ).
thf(sP373,plain,
( sP373
<=> ( sP24
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP373])]) ).
thf(sP374,plain,
( sP374
<=> ( sP5
=> ~ sP33 ) ),
introduced(definition,[new_symbols(definition,[sP374])]) ).
thf(sP375,plain,
( sP375
<=> ! [X1: $i] :
( ~ ( ~ ( sP19
=> ~ sP2 )
=> ~ ( b @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( b @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP375])]) ).
thf(sP376,plain,
( sP376
<=> ( ~ sP292
=> sP279 ) ),
introduced(definition,[new_symbols(definition,[sP376])]) ).
thf(sP377,plain,
( sP377
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP377])]) ).
thf(sP378,plain,
( sP378
<=> ! [X1: $i] :
( ~ ( ~ sP324
=> ~ ( b @ ( s @ z ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP378])]) ).
thf(sP379,plain,
( sP379
<=> ( sP55
=> ~ sP96 ) ),
introduced(definition,[new_symbols(definition,[sP379])]) ).
thf(sP380,plain,
( sP380
<=> ( b @ ( s @ z ) @ ( s @ ( s @ z ) ) ) ),
introduced(definition,[new_symbols(definition,[sP380])]) ).
thf(sP381,plain,
( sP381
<=> ( sP19
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP381])]) ).
thf(sP382,plain,
( sP382
<=> ( sP165
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ) ),
introduced(definition,[new_symbols(definition,[sP382])]) ).
thf(sP383,plain,
( sP383
<=> ( ~ sP249
=> ~ sP69 ) ),
introduced(definition,[new_symbols(definition,[sP383])]) ).
thf(sP384,plain,
( sP384
<=> ( ~ sP4
=> ~ sP290 ) ),
introduced(definition,[new_symbols(definition,[sP384])]) ).
thf(sP385,plain,
( sP385
<=> ( sP190
=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP385])]) ).
thf(sP386,plain,
( sP386
<=> ! [X1: $i] :
~ ( b @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP386])]) ).
thf(sP387,plain,
( sP387
<=> ( ~ sP269
=> ~ sP88 ) ),
introduced(definition,[new_symbols(definition,[sP387])]) ).
thf(sP388,plain,
( sP388
<=> ! [X1: $i] :
( ~ ( sP96
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( r @ ( s @ z ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP388])]) ).
thf(sP389,plain,
( sP389
<=> ( ~ sP215
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP389])]) ).
thf(sP390,plain,
( sP390
<=> ( ~ sP277
=> ~ sP170 ) ),
introduced(definition,[new_symbols(definition,[sP390])]) ).
thf(sP391,plain,
( sP391
<=> ( sP235
=> sP87 ) ),
introduced(definition,[new_symbols(definition,[sP391])]) ).
thf(sP392,plain,
( sP392
<=> ( ~ sP54
=> ~ sP232 ) ),
introduced(definition,[new_symbols(definition,[sP392])]) ).
thf(sP393,plain,
( sP393
<=> ( ~ sP379
=> ~ sP36 ) ),
introduced(definition,[new_symbols(definition,[sP393])]) ).
thf(sP394,plain,
( sP394
<=> ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP394])]) ).
thf(sP395,plain,
( sP395
<=> ( ( s @ ( s @ ( s @ ( s @ z ) ) ) )
= ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP395])]) ).
thf(sP396,plain,
( sP396
<=> ! [X1: $i] :
( ~ ( sP394
=> ~ ( r @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) )
=> ~ ( r @ z @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP396])]) ).
thf(sP397,plain,
( sP397
<=> ! [X1: $i] :
( ~ ( sP377
=> ~ ( r @ ( s @ ( s @ ( s @ z ) ) ) @ X1 ) )
=> ~ ( r @ ( s @ ( s @ z ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP397])]) ).
thf(sP398,plain,
( sP398
<=> ( r @ ( s @ ( s @ ( s @ z ) ) ) @ z ) ),
introduced(definition,[new_symbols(definition,[sP398])]) ).
thf(sP399,plain,
( sP399
<=> ( ~ sP163
=> ~ sP116 ) ),
introduced(definition,[new_symbols(definition,[sP399])]) ).
thf(sP400,plain,
( sP400
<=> ( ~ sP347
=> ~ sP377 ) ),
introduced(definition,[new_symbols(definition,[sP400])]) ).
thf(sP401,plain,
( sP401
<=> ( ~ sP208
=> sP173 ) ),
introduced(definition,[new_symbols(definition,[sP401])]) ).
thf(sP402,plain,
( sP402
<=> ( r @ ( s @ ( s @ z ) ) @ ( s @ ( s @ ( s @ z ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP402])]) ).
thf(sP403,plain,
( sP403
<=> ! [X1: $i] :
( ~ ( ~ sP95
=> ~ ( b @ ( s @ ( s @ z ) ) @ X1 ) )
=> ~ ( b @ ( s @ ( s @ ( s @ ( s @ z ) ) ) ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP403])]) ).
thf(sP404,plain,
( sP404
<=> ( ~ sP207
=> ~ sP116 ) ),
introduced(definition,[new_symbols(definition,[sP404])]) ).
thf(1,plain,
( ~ sP92
| sP168
| ~ sP304
| sP369 ),
inference(mating_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP125
| sP368
| ~ sP304
| sP369 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP53
| sP368
| ~ sP328
| sP369 ),
inference(mating_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP207
| sP121
| ~ sP53 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP121
| ~ sP109
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP215
| sP22
| ~ sP53 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP22
| ~ sP240
| ~ sP145 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP218
| sP117
| ~ sP53 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP117
| ~ sP125
| ~ sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP404
| sP207
| ~ sP116 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP389
| sP215
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP288
| sP218
| ~ sP290 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP214
| sP56
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP56
| ~ sP145
| ~ sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP188
| sP404 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP104
| sP389 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP9
| sP288 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP243
| sP324
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP250
| sP214
| ~ sP53 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP25
| sP346
| ~ sP145 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP149
| sP21
| ~ sP145 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP248
| ~ sP33
| ~ sP367 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP297
| sP248
| ~ sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP256
| sP278
| ~ sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP60
| sP188 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP230
| sP104 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP192
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP324
| ~ sP380
| ~ sP367 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP103
| sP243
| ~ sP367 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP8
| ~ sP261
| ~ sP367 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP345
| sP8
| ~ sP340 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP339
| sP345
| ~ sP367 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP144
| sP250 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP382
| ~ sP165
| ~ sP398 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP176
| sP382
| ~ sP89 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP346
| ~ sP171
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP191
| sP25
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP21
| ~ sP305
| ~ sP367 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP364
| sP149
| ~ sP367 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP275
| ~ sP13
| ~ sP394 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP211
| sP275
| ~ sP89 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP74
| sP297
| ~ sP367 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP278
| ~ sP100
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP155
| sP256
| ~ sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP237
| sP363
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP115
| sP237
| sP109 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP50
| sP137
| sP366 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP187
| sP50
| sP240 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP321
| sP190
| sP92 ),
inference(prop_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP228
| sP321
| sP125 ),
inference(prop_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP379
| ~ sP55
| ~ sP96 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP393
| sP379
| ~ sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP91
| ~ sP55
| ~ sP402 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP239
| sP91
| ~ sP366 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP48
| ~ sP55
| ~ sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP78
| sP48
| ~ sP92 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP102
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP102
| sP230 ),
inference(all_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP102
| sP192 ),
inference(all_rule,[status(thm)],[]) ).
thf(60,plain,
( ~ sP284
| sP338
| sP88 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP34
| sP284
| sP298 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP378
| sP103 ),
inference(all_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP97
| sP339 ),
inference(all_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP217
| sP122
| sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( ~ sP42
| sP217
| sP367 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( ~ sP130
| ~ sP96
| ~ sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( ~ sP216
| sP130
| ~ sP88 ),
inference(prop_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP276
| sP144 ),
inference(all_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP81
| sP176 ),
inference(all_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP185
| sP235
| sP165 ),
inference(prop_rule,[status(thm)],[]) ).
thf(71,plain,
( ~ sP142
| sP185
| sP145 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( ~ sP359
| sP191 ),
inference(all_rule,[status(thm)],[]) ).
thf(73,plain,
( ~ sP147
| ~ sP377
| ~ sP165 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( ~ sP107
| sP147
| ~ sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP269
| ~ sP24
| ~ sP165 ),
inference(prop_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP387
| sP269
| ~ sP88 ),
inference(prop_rule,[status(thm)],[]) ).
thf(77,plain,
( ~ sP59
| ~ sP398
| ~ sP165 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( ~ sP134
| sP59
| ~ sP272 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP195
| sP364 ),
inference(all_rule,[status(thm)],[]) ).
thf(80,plain,
( ~ sP320
| sP211 ),
inference(all_rule,[status(thm)],[]) ).
thf(81,plain,
( ~ sP287
| sP304
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(82,plain,
( ~ sP354
| sP287
| sP61 ),
inference(prop_rule,[status(thm)],[]) ).
thf(83,plain,
( ~ sP30
| ~ sP303
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(84,plain,
( ~ sP175
| sP30
| ~ sP165 ),
inference(prop_rule,[status(thm)],[]) ).
thf(85,plain,
( ~ sP200
| ~ sP330
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(86,plain,
( ~ sP362
| sP200
| ~ sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(87,plain,
( ~ sP358
| ~ sP20
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(88,plain,
( ~ sP12
| sP358
| ~ sP88 ),
inference(prop_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP245
| ~ sP394
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(90,plain,
( ~ sP174
| sP245
| ~ sP272 ),
inference(prop_rule,[status(thm)],[]) ).
thf(91,plain,
( ~ sP225
| sP74 ),
inference(all_rule,[status(thm)],[]) ).
thf(92,plain,
( ~ sP164
| sP155 ),
inference(all_rule,[status(thm)],[]) ).
thf(93,plain,
( ~ sP337
| sP64
| sP89 ),
inference(prop_rule,[status(thm)],[]) ).
thf(94,plain,
( ~ sP150
| ~ sP88
| ~ sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(95,plain,
( ~ sP335
| ~ sP55
| ~ sP343 ),
inference(prop_rule,[status(thm)],[]) ).
thf(96,plain,
( ~ sP205
| sP337
| sP53 ),
inference(prop_rule,[status(thm)],[]) ).
thf(97,plain,
( ~ sP323
| sP328
| sP272 ),
inference(prop_rule,[status(thm)],[]) ).
thf(98,plain,
( ~ sP273
| sP150
| ~ sP89 ),
inference(prop_rule,[status(thm)],[]) ).
thf(99,plain,
( ~ sP353
| ~ sP170
| ~ sP88 ),
inference(prop_rule,[status(thm)],[]) ).
thf(100,plain,
( ~ sP352
| sP335
| ~ sP89 ),
inference(prop_rule,[status(thm)],[]) ).
thf(101,plain,
( ~ sP146
| sP205 ),
inference(all_rule,[status(thm)],[]) ).
thf(102,plain,
( ~ sP146
| sP115 ),
inference(all_rule,[status(thm)],[]) ).
thf(103,plain,
( ~ sP146
| sP187 ),
inference(all_rule,[status(thm)],[]) ).
thf(104,plain,
( ~ sP146
| sP228 ),
inference(all_rule,[status(thm)],[]) ).
thf(105,plain,
( ~ sP199
| sP323
| sP340 ),
inference(prop_rule,[status(thm)],[]) ).
thf(106,plain,
( ~ sP32
| sP273 ),
inference(all_rule,[status(thm)],[]) ).
thf(107,plain,
( ~ sP182
| sP353
| ~ sP272 ),
inference(prop_rule,[status(thm)],[]) ).
thf(108,plain,
( ~ sP210
| sP352 ),
inference(all_rule,[status(thm)],[]) ).
thf(109,plain,
( ~ sP210
| sP393 ),
inference(all_rule,[status(thm)],[]) ).
thf(110,plain,
( ~ sP210
| sP239 ),
inference(all_rule,[status(thm)],[]) ).
thf(111,plain,
( ~ sP210
| sP78 ),
inference(all_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP316
| ~ sP168 ),
inference(all_rule,[status(thm)],[]) ).
thf(113,plain,
( ~ sP386
| ~ sP368 ),
inference(all_rule,[status(thm)],[]) ).
thf(114,plain,
( ~ sP227
| sP146 ),
inference(all_rule,[status(thm)],[]) ).
thf(115,plain,
( ~ sP197
| sP102 ),
inference(all_rule,[status(thm)],[]) ).
thf(116,plain,
( ~ sP209
| sP199 ),
inference(all_rule,[status(thm)],[]) ).
thf(117,plain,
( ~ sP283
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(118,plain,
( ~ sP221
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(119,plain,
( ~ sP154
| sP182 ),
inference(all_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP226
| sP378 ),
inference(all_rule,[status(thm)],[]) ).
thf(121,plain,
( ~ sP180
| sP97 ),
inference(all_rule,[status(thm)],[]) ).
thf(122,plain,
( ~ sP160
| sP210 ),
inference(all_rule,[status(thm)],[]) ).
thf(123,plain,
( ~ sP124
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(124,plain,
( ~ sP388
| sP216 ),
inference(all_rule,[status(thm)],[]) ).
thf(125,plain,
( ~ sP236
| sP276 ),
inference(all_rule,[status(thm)],[]) ).
thf(126,plain,
( ~ sP351
| sP81 ),
inference(all_rule,[status(thm)],[]) ).
thf(127,plain,
( ~ sP114
| sP142 ),
inference(all_rule,[status(thm)],[]) ).
thf(128,plain,
( ~ sP158
| sP359 ),
inference(all_rule,[status(thm)],[]) ).
thf(129,plain,
( ~ sP397
| sP107 ),
inference(all_rule,[status(thm)],[]) ).
thf(130,plain,
( ~ sP282
| sP387 ),
inference(all_rule,[status(thm)],[]) ).
thf(131,plain,
( ~ sP194
| sP134 ),
inference(all_rule,[status(thm)],[]) ).
thf(132,plain,
( ~ sP184
| sP195 ),
inference(all_rule,[status(thm)],[]) ).
thf(133,plain,
( ~ sP299
| sP320 ),
inference(all_rule,[status(thm)],[]) ).
thf(134,plain,
( ~ sP129
| sP354 ),
inference(all_rule,[status(thm)],[]) ).
thf(135,plain,
( ~ sP251
| sP175 ),
inference(all_rule,[status(thm)],[]) ).
thf(136,plain,
( ~ sP281
| sP362 ),
inference(all_rule,[status(thm)],[]) ).
thf(137,plain,
( ~ sP11
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(138,plain,
( ~ sP396
| sP174 ),
inference(all_rule,[status(thm)],[]) ).
thf(139,plain,
( ~ sP26
| sP225 ),
inference(all_rule,[status(thm)],[]) ).
thf(140,plain,
( ~ sP138
| sP164 ),
inference(all_rule,[status(thm)],[]) ).
thf(141,plain,
( ~ sP330
| sP319
| ~ sP87
| sP369 ),
inference(mating_rule,[status(thm)],[]) ).
thf(142,plain,
( ~ sP33
| sP280
| ~ sP87
| sP369 ),
inference(mating_rule,[status(thm)],[]) ).
thf(143,plain,
( ~ sP394
| sP319
| ~ sP29
| sP369 ),
inference(mating_rule,[status(thm)],[]) ).
thf(144,plain,
( ~ sP290
| sP280
| ~ sP29
| sP369 ),
inference(mating_rule,[status(thm)],[]) ).
thf(145,plain,
( ~ sP63
| sP52
| ~ sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(146,plain,
( ~ sP82
| sP295
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(147,plain,
( ~ sP295
| ~ sP173
| ~ sP305 ),
inference(prop_rule,[status(thm)],[]) ).
thf(148,plain,
( ~ sP186
| sP157
| ~ sP171 ),
inference(prop_rule,[status(thm)],[]) ).
thf(149,plain,
( ~ sP365
| sP31
| ~ sP305 ),
inference(prop_rule,[status(thm)],[]) ).
thf(150,plain,
( ~ sP31
| ~ sP314
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(151,plain,
( ~ sP163
| sP161
| ~ sP290 ),
inference(prop_rule,[status(thm)],[]) ).
thf(152,plain,
( ~ sP399
| sP163
| ~ sP116 ),
inference(prop_rule,[status(thm)],[]) ).
thf(153,plain,
( ~ sP161
| ~ sP100
| ~ sP116 ),
inference(prop_rule,[status(thm)],[]) ).
thf(154,plain,
( ~ sP152
| sP213
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(155,plain,
( ~ sP325
| sP152
| ~ sP380 ),
inference(prop_rule,[status(thm)],[]) ).
thf(156,plain,
( ~ sP213
| ~ sP100
| ~ sP380 ),
inference(prop_rule,[status(thm)],[]) ).
thf(157,plain,
( ~ sP52
| ~ sP33
| ~ sP108 ),
inference(prop_rule,[status(thm)],[]) ).
thf(158,plain,
( ~ sP47
| sP63
| ~ sP279 ),
inference(prop_rule,[status(thm)],[]) ).
thf(159,plain,
( ~ sP183
| sP329
| ~ sP290 ),
inference(prop_rule,[status(thm)],[]) ).
thf(160,plain,
( ~ sP318
| sP183
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(161,plain,
( ~ sP329
| ~ sP173
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(162,plain,
( ~ sP258
| sP82
| ~ sP305 ),
inference(prop_rule,[status(thm)],[]) ).
thf(163,plain,
( ~ sP38
| sP374
| ~ sP261 ),
inference(prop_rule,[status(thm)],[]) ).
thf(164,plain,
( ~ sP35
| sP38
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(165,plain,
( ~ sP374
| ~ sP5
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(166,plain,
( ~ sP4
| sP95
| ~ sP300 ),
inference(prop_rule,[status(thm)],[]) ).
thf(167,plain,
( ~ sP384
| sP4
| ~ sP290 ),
inference(prop_rule,[status(thm)],[]) ).
thf(168,plain,
( ~ sP95
| ~ sP69
| ~ sP290 ),
inference(prop_rule,[status(thm)],[]) ).
thf(169,plain,
( ~ sP179
| sP66
| ~ sP108 ),
inference(prop_rule,[status(thm)],[]) ).
thf(170,plain,
( ~ sP271
| sP179
| ~ sP100 ),
inference(prop_rule,[status(thm)],[]) ).
thf(171,plain,
( ~ sP66
| ~ sP69
| ~ sP100 ),
inference(prop_rule,[status(thm)],[]) ).
thf(172,plain,
( ~ sP157
| ~ sP314
| ~ sP100 ),
inference(prop_rule,[status(thm)],[]) ).
thf(173,plain,
( ~ sP113
| sP186
| ~ sP100 ),
inference(prop_rule,[status(thm)],[]) ).
thf(174,plain,
( ~ sP101
| sP365
| ~ sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(175,plain,
( ~ sP90
| sP399 ),
inference(all_rule,[status(thm)],[]) ).
thf(176,plain,
( ~ sP71
| sP325 ),
inference(all_rule,[status(thm)],[]) ).
thf(177,plain,
( ~ sP349
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(178,plain,
( ~ sP18
| sP318 ),
inference(all_rule,[status(thm)],[]) ).
thf(179,plain,
( ~ sP112
| sP258 ),
inference(all_rule,[status(thm)],[]) ).
thf(180,plain,
( ~ sP16
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(181,plain,
( ~ sP403
| sP384 ),
inference(all_rule,[status(thm)],[]) ).
thf(182,plain,
( ~ sP119
| sP271 ),
inference(all_rule,[status(thm)],[]) ).
thf(183,plain,
( ~ sP224
| sP113 ),
inference(all_rule,[status(thm)],[]) ).
thf(184,plain,
( ~ sP229
| sP101 ),
inference(all_rule,[status(thm)],[]) ).
thf(185,plain,
( ~ sP309
| ~ sP305
| ~ sP69 ),
inference(prop_rule,[status(thm)],[]) ).
thf(186,plain,
( ~ sP189
| sP309
| ~ sP171 ),
inference(prop_rule,[status(thm)],[]) ).
thf(187,plain,
( ~ sP371
| sP189
| ~ sP108 ),
inference(prop_rule,[status(thm)],[]) ).
thf(188,plain,
( ~ sP334
| ~ sP20
| ~ sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(189,plain,
( ~ sP204
| sP334
| ~ sP357 ),
inference(prop_rule,[status(thm)],[]) ).
thf(190,plain,
( ~ sP141
| ~ sP303
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(191,plain,
( ~ sP23
| sP141
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(192,plain,
( ~ sP111
| ~ sP303
| ~ sP330 ),
inference(prop_rule,[status(thm)],[]) ).
thf(193,plain,
( ~ sP306
| sP111
| ~ sP377 ),
inference(prop_rule,[status(thm)],[]) ).
thf(194,plain,
( ~ sP75
| sP286
| sP330 ),
inference(prop_rule,[status(thm)],[]) ).
thf(195,plain,
( ~ sP234
| sP75
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(196,plain,
( ~ sP208
| sP395
| sP303 ),
inference(prop_rule,[status(thm)],[]) ).
thf(197,plain,
( ~ sP401
| sP208
| sP173 ),
inference(prop_rule,[status(thm)],[]) ).
thf(198,plain,
( ~ sP138
| sP90 ),
inference(all_rule,[status(thm)],[]) ).
thf(199,plain,
( ~ sP138
| sP71 ),
inference(all_rule,[status(thm)],[]) ).
thf(200,plain,
( ~ sP26
| sP349 ),
inference(all_rule,[status(thm)],[]) ).
thf(201,plain,
( ~ sP83
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(202,plain,
( ~ sP83
| sP112 ),
inference(all_rule,[status(thm)],[]) ).
thf(203,plain,
( ~ sP172
| ~ sP99
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(204,plain,
( ~ sP350
| sP172
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(205,plain,
( ~ sP58
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(206,plain,
( ~ sP151
| sP403 ),
inference(all_rule,[status(thm)],[]) ).
thf(207,plain,
( ~ sP151
| sP119 ),
inference(all_rule,[status(thm)],[]) ).
thf(208,plain,
( ~ sP356
| sP87
| sP80 ),
inference(prop_rule,[status(thm)],[]) ).
thf(209,plain,
( ~ sP203
| sP356
| sP69 ),
inference(prop_rule,[status(thm)],[]) ).
thf(210,plain,
( ~ sP136
| sP224 ),
inference(all_rule,[status(thm)],[]) ).
thf(211,plain,
( ~ sP136
| sP229 ),
inference(all_rule,[status(thm)],[]) ).
thf(212,plain,
( ~ sP360
| sP244
| sP99 ),
inference(prop_rule,[status(thm)],[]) ).
thf(213,plain,
( ~ sP313
| sP360
| sP314 ),
inference(prop_rule,[status(thm)],[]) ).
thf(214,plain,
( ~ sP68
| sP371 ),
inference(all_rule,[status(thm)],[]) ).
thf(215,plain,
( ~ sP249
| sP233
| ~ sP314 ),
inference(prop_rule,[status(thm)],[]) ).
thf(216,plain,
( ~ sP383
| sP249
| ~ sP69 ),
inference(prop_rule,[status(thm)],[]) ).
thf(217,plain,
( ~ sP54
| ~ sP394
| ~ sP330 ),
inference(prop_rule,[status(thm)],[]) ).
thf(218,plain,
( ~ sP265
| ~ sP20
| ~ sP394 ),
inference(prop_rule,[status(thm)],[]) ).
thf(219,plain,
( ~ sP202
| ~ sP20
| ~ sP330 ),
inference(prop_rule,[status(thm)],[]) ).
thf(220,plain,
( ~ sP262
| ~ sP330
| ~ sP394 ),
inference(prop_rule,[status(thm)],[]) ).
thf(221,plain,
( ~ sP167
| sP315
| sP394 ),
inference(prop_rule,[status(thm)],[]) ).
thf(222,plain,
( ~ sP118
| sP3
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(223,plain,
( ~ sP392
| sP54
| ~ sP232 ),
inference(prop_rule,[status(thm)],[]) ).
thf(224,plain,
( ~ sP41
| sP265
| ~ sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(225,plain,
( ~ sP46
| sP202
| ~ sP268 ),
inference(prop_rule,[status(thm)],[]) ).
thf(226,plain,
( ~ sP153
| sP262
| ~ sP343 ),
inference(prop_rule,[status(thm)],[]) ).
thf(227,plain,
( ~ sP333
| ~ sP99
| ~ sP398 ),
inference(prop_rule,[status(thm)],[]) ).
thf(228,plain,
( ~ sP294
| ~ sP363
| sP315 ),
inference(prop_rule,[status(thm)],[]) ).
thf(229,plain,
( ~ sP178
| ~ sP137
| sP286 ),
inference(prop_rule,[status(thm)],[]) ).
thf(230,plain,
( ~ sP385
| ~ sP190
| sP395 ),
inference(prop_rule,[status(thm)],[]) ).
thf(231,plain,
( ~ sP162
| sP167
| sP290 ),
inference(prop_rule,[status(thm)],[]) ).
thf(232,plain,
( ~ sP264
| sP118
| sP100 ),
inference(prop_rule,[status(thm)],[]) ).
thf(233,plain,
( ~ sP396
| sP392 ),
inference(all_rule,[status(thm)],[]) ).
thf(234,plain,
( ~ sP11
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(235,plain,
( ~ sP11
| sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(236,plain,
( ~ sP11
| sP204 ),
inference(all_rule,[status(thm)],[]) ).
thf(237,plain,
( ~ sP281
| sP153 ),
inference(all_rule,[status(thm)],[]) ).
thf(238,plain,
( ~ sP251
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(239,plain,
( ~ sP251
| sP306 ),
inference(all_rule,[status(thm)],[]) ).
thf(240,plain,
( ~ sP285
| sP29
| sP348 ),
inference(prop_rule,[status(thm)],[]) ).
thf(241,plain,
( ~ sP201
| sP333
| ~ sP394 ),
inference(prop_rule,[status(thm)],[]) ).
thf(242,plain,
( sP304
| ~ sP244 ),
inference(prop_rule,[status(thm)],[]) ).
thf(243,plain,
( ~ sP370
| ~ sP398
| ~ sP99 ),
inference(prop_rule,[status(thm)],[]) ).
thf(244,plain,
( ~ sP127
| sP294 ),
inference(all_rule,[status(thm)],[]) ).
thf(245,plain,
( ~ sP127
| sP178 ),
inference(all_rule,[status(thm)],[]) ).
thf(246,plain,
( ~ sP127
| sP385 ),
inference(all_rule,[status(thm)],[]) ).
thf(247,plain,
( ~ sP129
| sP162 ),
inference(all_rule,[status(thm)],[]) ).
thf(248,plain,
( ~ sP129
| sP264 ),
inference(all_rule,[status(thm)],[]) ).
thf(249,plain,
( ~ sP129
| sP234 ),
inference(all_rule,[status(thm)],[]) ).
thf(250,plain,
( ~ sP129
| sP401 ),
inference(all_rule,[status(thm)],[]) ).
thf(251,plain,
( ~ sP299
| sP396 ),
inference(all_rule,[status(thm)],[]) ).
thf(252,plain,
( ~ sP299
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(253,plain,
( ~ sP299
| sP281 ),
inference(all_rule,[status(thm)],[]) ).
thf(254,plain,
( ~ sP299
| sP251 ),
inference(all_rule,[status(thm)],[]) ).
thf(255,plain,
( ~ sP128
| sP138 ),
inference(all_rule,[status(thm)],[]) ).
thf(256,plain,
( ~ sP128
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(257,plain,
( ~ sP128
| sP83 ),
inference(all_rule,[status(thm)],[]) ).
thf(258,plain,
( ~ sP355
| ~ sP338
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(259,plain,
( ~ sP270
| sP285
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(260,plain,
( ~ sP86
| ~ sP122
| sP344 ),
inference(prop_rule,[status(thm)],[]) ).
thf(261,plain,
( ~ sP391
| ~ sP235
| sP87 ),
inference(prop_rule,[status(thm)],[]) ).
thf(262,plain,
( ~ sP296
| sP201 ),
inference(all_rule,[status(thm)],[]) ).
thf(263,plain,
( ~ sP296
| sP350 ),
inference(all_rule,[status(thm)],[]) ).
thf(264,plain,
( ~ sP238
| sP370
| ~ sP348 ),
inference(prop_rule,[status(thm)],[]) ).
thf(265,plain,
( ~ sP326
| ~ sP64 ),
inference(all_rule,[status(thm)],[]) ).
thf(266,plain,
( ~ sP1
| sP127 ),
inference(all_rule,[status(thm)],[]) ).
thf(267,plain,
( ~ sP316
| ~ sP319 ),
inference(all_rule,[status(thm)],[]) ).
thf(268,plain,
( ~ sP386
| ~ sP280 ),
inference(all_rule,[status(thm)],[]) ).
thf(269,plain,
( ~ sP227
| sP129 ),
inference(all_rule,[status(thm)],[]) ).
thf(270,plain,
( ~ sP65
| sP299 ),
inference(all_rule,[status(thm)],[]) ).
thf(271,plain,
( ~ sP197
| sP128 ),
inference(all_rule,[status(thm)],[]) ).
thf(272,plain,
( ~ sP93
| sP355 ),
inference(all_rule,[status(thm)],[]) ).
thf(273,plain,
( ~ sP342
| sP58 ),
inference(all_rule,[status(thm)],[]) ).
thf(274,plain,
( ~ sP209
| sP270 ),
inference(all_rule,[status(thm)],[]) ).
thf(275,plain,
( ~ sP311
| sP86 ),
inference(all_rule,[status(thm)],[]) ).
thf(276,plain,
( ~ sP73
| sP151 ),
inference(all_rule,[status(thm)],[]) ).
thf(277,plain,
( ~ sP124
| sP203 ),
inference(all_rule,[status(thm)],[]) ).
thf(278,plain,
( ~ sP257
| sP391 ),
inference(all_rule,[status(thm)],[]) ).
thf(279,plain,
( ~ sP236
| sP136 ),
inference(all_rule,[status(thm)],[]) ).
thf(280,plain,
( ~ sP351
| sP296 ),
inference(all_rule,[status(thm)],[]) ).
thf(281,plain,
( ~ sP114
| sP313 ),
inference(all_rule,[status(thm)],[]) ).
thf(282,plain,
( ~ sP194
| sP238 ),
inference(all_rule,[status(thm)],[]) ).
thf(283,plain,
( ~ sP184
| sP68 ),
inference(all_rule,[status(thm)],[]) ).
thf(284,plain,
( ~ sP126
| sP383 ),
inference(all_rule,[status(thm)],[]) ).
thf(285,plain,
( ~ sP398
| sP206
| ~ sP252
| sP369 ),
inference(mating_rule,[status(thm)],[]) ).
thf(286,plain,
( ~ sP19
| sP260
| ~ sP252
| sP369 ),
inference(mating_rule,[status(thm)],[]) ).
thf(287,plain,
( ~ sP233
| ~ sP305
| ~ sP108 ),
inference(prop_rule,[status(thm)],[]) ).
thf(288,plain,
( ~ sP302
| sP181
| ~ sP116 ),
inference(prop_rule,[status(thm)],[]) ).
thf(289,plain,
( ~ sP79
| sP302
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(290,plain,
( ~ sP181
| ~ sP253
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(291,plain,
( ~ sP193
| sP159
| ~ sP305 ),
inference(prop_rule,[status(thm)],[]) ).
thf(292,plain,
( ~ sP259
| sP193
| ~ sP380 ),
inference(prop_rule,[status(thm)],[]) ).
thf(293,plain,
( ~ sP159
| ~ sP171
| ~ sP380 ),
inference(prop_rule,[status(thm)],[]) ).
thf(294,plain,
( ~ sP140
| sP79 ),
inference(all_rule,[status(thm)],[]) ).
thf(295,plain,
( ~ sP85
| sP177
| ~ sP305 ),
inference(prop_rule,[status(thm)],[]) ).
thf(296,plain,
( ~ sP263
| sP85
| ~ sP261 ),
inference(prop_rule,[status(thm)],[]) ).
thf(297,plain,
( ~ sP222
| sP259 ),
inference(all_rule,[status(thm)],[]) ).
thf(298,plain,
( ~ sP184
| sP126 ),
inference(all_rule,[status(thm)],[]) ).
thf(299,plain,
( ~ sP67
| sP140 ),
inference(all_rule,[status(thm)],[]) ).
thf(300,plain,
( ~ sP308
| sP212
| ~ sP279 ),
inference(prop_rule,[status(thm)],[]) ).
thf(301,plain,
( ~ sP143
| sP308
| ~ sP253 ),
inference(prop_rule,[status(thm)],[]) ).
thf(302,plain,
( ~ sP381
| ~ sP19
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(303,plain,
( ~ sP177
| ~ sP19
| ~ sP261 ),
inference(prop_rule,[status(thm)],[]) ).
thf(304,plain,
( ~ sP133
| sP381
| ~ sP171 ),
inference(prop_rule,[status(thm)],[]) ).
thf(305,plain,
( ~ sP322
| ~ sP398
| ~ sP377 ),
inference(prop_rule,[status(thm)],[]) ).
thf(306,plain,
( ~ sP277
| ~ sP24
| ~ sP398 ),
inference(prop_rule,[status(thm)],[]) ).
thf(307,plain,
( ~ sP373
| ~ sP24
| ~ sP377 ),
inference(prop_rule,[status(thm)],[]) ).
thf(308,plain,
( ~ sP312
| ~ sP377
| ~ sP398 ),
inference(prop_rule,[status(thm)],[]) ).
thf(309,plain,
( ~ sP62
| sP133
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(310,plain,
( ~ sP105
| sP51
| sP398 ),
inference(prop_rule,[status(thm)],[]) ).
thf(311,plain,
( ~ sP220
| sP254
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(312,plain,
( ~ sP242
| sP15
| sP377 ),
inference(prop_rule,[status(thm)],[]) ).
thf(313,plain,
( ~ sP372
| sP322
| ~ sP232 ),
inference(prop_rule,[status(thm)],[]) ).
thf(314,plain,
( ~ sP390
| sP277
| ~ sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(315,plain,
( ~ sP293
| sP373
| ~ sP268 ),
inference(prop_rule,[status(thm)],[]) ).
thf(316,plain,
( ~ sP332
| sP312
| ~ sP343 ),
inference(prop_rule,[status(thm)],[]) ).
thf(317,plain,
( ~ sP375
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(318,plain,
( ~ sP110
| sP263 ),
inference(all_rule,[status(thm)],[]) ).
thf(319,plain,
( ~ sP347
| ~ sP357
| ~ sP268 ),
inference(prop_rule,[status(thm)],[]) ).
thf(320,plain,
( ~ sP331
| ~ sP3
| sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(321,plain,
( ~ sP274
| ~ sP286
| sP254 ),
inference(prop_rule,[status(thm)],[]) ).
thf(322,plain,
( ~ sP341
| ~ sP395
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(323,plain,
( ~ sP196
| sP105
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(324,plain,
( ~ sP84
| sP220
| sP171 ),
inference(prop_rule,[status(thm)],[]) ).
thf(325,plain,
( ~ sP267
| sP242
| sP305 ),
inference(prop_rule,[status(thm)],[]) ).
thf(326,plain,
( ~ sP194
| sP372 ),
inference(all_rule,[status(thm)],[]) ).
thf(327,plain,
( ~ sP282
| sP390 ),
inference(all_rule,[status(thm)],[]) ).
thf(328,plain,
( ~ sP282
| sP293 ),
inference(all_rule,[status(thm)],[]) ).
thf(329,plain,
( ~ sP397
| sP332 ),
inference(all_rule,[status(thm)],[]) ).
thf(330,plain,
( ~ sP44
| sP375 ),
inference(all_rule,[status(thm)],[]) ).
thf(331,plain,
( ~ sP44
| sP110 ),
inference(all_rule,[status(thm)],[]) ).
thf(332,plain,
( ~ sP158
| sP222 ),
inference(all_rule,[status(thm)],[]) ).
thf(333,plain,
( ~ sP400
| sP347
| ~ sP377 ),
inference(prop_rule,[status(thm)],[]) ).
thf(334,plain,
( ~ sP37
| sP40
| sP357 ),
inference(prop_rule,[status(thm)],[]) ).
thf(335,plain,
( ~ sP292
| sP247
| sP402 ),
inference(prop_rule,[status(thm)],[]) ).
thf(336,plain,
( ~ sP246
| sP331 ),
inference(all_rule,[status(thm)],[]) ).
thf(337,plain,
( ~ sP246
| sP274 ),
inference(all_rule,[status(thm)],[]) ).
thf(338,plain,
( ~ sP246
| sP341 ),
inference(all_rule,[status(thm)],[]) ).
thf(339,plain,
( ~ sP114
| sP196 ),
inference(all_rule,[status(thm)],[]) ).
thf(340,plain,
( ~ sP114
| sP84 ),
inference(all_rule,[status(thm)],[]) ).
thf(341,plain,
( ~ sP114
| sP267 ),
inference(all_rule,[status(thm)],[]) ).
thf(342,plain,
( ~ sP351
| sP194 ),
inference(all_rule,[status(thm)],[]) ).
thf(343,plain,
( ~ sP351
| sP282 ),
inference(all_rule,[status(thm)],[]) ).
thf(344,plain,
( ~ sP351
| sP397 ),
inference(all_rule,[status(thm)],[]) ).
thf(345,plain,
( ~ sP236
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(346,plain,
( ~ sP236
| sP158 ),
inference(all_rule,[status(thm)],[]) ).
thf(347,plain,
( ~ sP236
| sP184 ),
inference(all_rule,[status(thm)],[]) ).
thf(348,plain,
( ~ sP301
| ~ sP344
| sP252 ),
inference(prop_rule,[status(thm)],[]) ).
thf(349,plain,
( sP87
| ~ sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(350,plain,
( ~ sP361
| sP400 ),
inference(all_rule,[status(thm)],[]) ).
thf(351,plain,
( ~ sP123
| sP37
| sP253 ),
inference(prop_rule,[status(thm)],[]) ).
thf(352,plain,
( ~ sP376
| sP292
| sP279 ),
inference(prop_rule,[status(thm)],[]) ).
thf(353,plain,
( sP244
| ~ sP247 ),
inference(prop_rule,[status(thm)],[]) ).
thf(354,plain,
( ~ sP326
| ~ sP315 ),
inference(all_rule,[status(thm)],[]) ).
thf(355,plain,
( ~ sP1
| sP246 ),
inference(all_rule,[status(thm)],[]) ).
thf(356,plain,
( ~ sP316
| ~ sP206 ),
inference(all_rule,[status(thm)],[]) ).
thf(357,plain,
( ~ sP386
| ~ sP260 ),
inference(all_rule,[status(thm)],[]) ).
thf(358,plain,
( ~ sP227
| sP114 ),
inference(all_rule,[status(thm)],[]) ).
thf(359,plain,
( ~ sP65
| sP351 ),
inference(all_rule,[status(thm)],[]) ).
thf(360,plain,
( ~ sP197
| sP236 ),
inference(all_rule,[status(thm)],[]) ).
thf(361,plain,
( ~ sP93
| sP301 ),
inference(all_rule,[status(thm)],[]) ).
thf(362,plain,
( ~ sP148
| sP67 ),
inference(all_rule,[status(thm)],[]) ).
thf(363,plain,
( ~ sP283
| sP361 ),
inference(all_rule,[status(thm)],[]) ).
thf(364,plain,
( ~ sP221
| sP123 ),
inference(all_rule,[status(thm)],[]) ).
thf(365,plain,
( ~ sP124
| sP376 ),
inference(all_rule,[status(thm)],[]) ).
thf(366,plain,
( ~ sP7
| sP143 ),
inference(all_rule,[status(thm)],[]) ).
thf(367,plain,
( ~ sP28
| ~ sP108
| ~ sP116 ),
inference(prop_rule,[status(thm)],[]) ).
thf(368,plain,
( ~ sP212
| ~ sP108
| ~ sP380 ),
inference(prop_rule,[status(thm)],[]) ).
thf(369,plain,
( ~ sP98
| sP28
| ~ sP300 ),
inference(prop_rule,[status(thm)],[]) ).
thf(370,plain,
( ~ sP156
| ~ sP380
| ~ sP300 ),
inference(prop_rule,[status(thm)],[]) ).
thf(371,plain,
( ~ sP289
| sP98
| ~ sP116 ),
inference(prop_rule,[status(thm)],[]) ).
thf(372,plain,
( ~ sP10
| sP156
| ~ sP116 ),
inference(prop_rule,[status(thm)],[]) ).
thf(373,plain,
( ~ sP266
| sP14
| sP96 ),
inference(prop_rule,[status(thm)],[]) ).
thf(374,plain,
( ~ sP310
| sP289 ),
inference(all_rule,[status(thm)],[]) ).
thf(375,plain,
( ~ sP77
| sP10
| ~ sP300 ),
inference(prop_rule,[status(thm)],[]) ).
thf(376,plain,
( ~ sP139
| ~ sP268
| ~ sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(377,plain,
( ~ sP291
| ~ sP15
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(378,plain,
( ~ sP336
| sP17
| sP343 ),
inference(prop_rule,[status(thm)],[]) ).
thf(379,plain,
( ~ sP27
| sP336
| sP300 ),
inference(prop_rule,[status(thm)],[]) ).
thf(380,plain,
( ~ sP120
| sP266
| sP108 ),
inference(prop_rule,[status(thm)],[]) ).
thf(381,plain,
( ~ sP169
| sP310 ),
inference(all_rule,[status(thm)],[]) ).
thf(382,plain,
( ~ sP169
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(383,plain,
( ~ sP70
| sP77 ),
inference(all_rule,[status(thm)],[]) ).
thf(384,plain,
( ~ sP223
| sP139
| ~ sP343 ),
inference(prop_rule,[status(thm)],[]) ).
thf(385,plain,
( ~ sP317
| sP57
| sP268 ),
inference(prop_rule,[status(thm)],[]) ).
thf(386,plain,
( ~ sP39
| ~ sP170
| ~ sP268 ),
inference(prop_rule,[status(thm)],[]) ).
thf(387,plain,
( ~ sP72
| ~ sP254
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(388,plain,
( ~ sP257
| sP72 ),
inference(all_rule,[status(thm)],[]) ).
thf(389,plain,
( ~ sP257
| sP291 ),
inference(all_rule,[status(thm)],[]) ).
thf(390,plain,
( ~ sP124
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(391,plain,
( ~ sP124
| sP120 ),
inference(all_rule,[status(thm)],[]) ).
thf(392,plain,
( ~ sP160
| sP388 ),
inference(all_rule,[status(thm)],[]) ).
thf(393,plain,
( ~ sP73
| sP169 ),
inference(all_rule,[status(thm)],[]) ).
thf(394,plain,
( ~ sP6
| sP327
| sP232 ),
inference(prop_rule,[status(thm)],[]) ).
thf(395,plain,
( ~ sP131
| sP6
| sP261 ),
inference(prop_rule,[status(thm)],[]) ).
thf(396,plain,
( sP247
| ~ sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(397,plain,
( ~ sP241
| ~ sP135
| ~ sP232 ),
inference(prop_rule,[status(thm)],[]) ).
thf(398,plain,
( ~ sP307
| sP241
| ~ sP268 ),
inference(prop_rule,[status(thm)],[]) ).
thf(399,plain,
( ~ sP226
| sP70 ),
inference(all_rule,[status(thm)],[]) ).
thf(400,plain,
( ~ sP219
| sP223 ),
inference(all_rule,[status(thm)],[]) ).
thf(401,plain,
( ~ sP132
| sP317
| sP380 ),
inference(prop_rule,[status(thm)],[]) ).
thf(402,plain,
( ~ sP49
| sP39
| ~ sP232 ),
inference(prop_rule,[status(thm)],[]) ).
thf(403,plain,
( sP40
| ~ sP327 ),
inference(prop_rule,[status(thm)],[]) ).
thf(404,plain,
( ~ sP326
| ~ sP51 ),
inference(all_rule,[status(thm)],[]) ).
thf(405,plain,
( ~ sP1
| sP257 ),
inference(all_rule,[status(thm)],[]) ).
thf(406,plain,
( ~ sP227
| sP124 ),
inference(all_rule,[status(thm)],[]) ).
thf(407,plain,
( ~ sP65
| sP160 ),
inference(all_rule,[status(thm)],[]) ).
thf(408,plain,
( ~ sP197
| sP73 ),
inference(all_rule,[status(thm)],[]) ).
thf(409,plain,
( ~ sP342
| sP180 ),
inference(all_rule,[status(thm)],[]) ).
thf(410,plain,
( ~ sP209
| sP131 ),
inference(all_rule,[status(thm)],[]) ).
thf(411,plain,
( ~ sP231
| sP307 ),
inference(all_rule,[status(thm)],[]) ).
thf(412,plain,
( ~ sP148
| sP226 ),
inference(all_rule,[status(thm)],[]) ).
thf(413,plain,
( ~ sP283
| sP219 ),
inference(all_rule,[status(thm)],[]) ).
thf(414,plain,
( ~ sP221
| sP132 ),
inference(all_rule,[status(thm)],[]) ).
thf(415,plain,
( ~ sP154
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(416,plain,
~ sP369,
inference(prop_rule,[status(thm)],[]) ).
thf(417,plain,
( ~ sP45
| sP166
| sP170 ),
inference(prop_rule,[status(thm)],[]) ).
thf(418,plain,
( ~ sP106
| sP45
| sP116 ),
inference(prop_rule,[status(thm)],[]) ).
thf(419,plain,
( ~ sP221
| sP106 ),
inference(all_rule,[status(thm)],[]) ).
thf(420,plain,
( ~ sP283
| sP154 ),
inference(all_rule,[status(thm)],[]) ).
thf(421,plain,
( ~ sP43
| sP198
| sP135 ),
inference(prop_rule,[status(thm)],[]) ).
thf(422,plain,
( ~ sP255
| sP43
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(423,plain,
( ~ sP76
| ~ sP14
| sP166 ),
inference(prop_rule,[status(thm)],[]) ).
thf(424,plain,
( sP57
| ~ sP198 ),
inference(prop_rule,[status(thm)],[]) ).
thf(425,plain,
( ~ sP311
| sP76 ),
inference(all_rule,[status(thm)],[]) ).
thf(426,plain,
( ~ sP326
| ~ sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(427,plain,
( ~ sP1
| sP311 ),
inference(all_rule,[status(thm)],[]) ).
thf(428,plain,
( ~ sP227
| sP221 ),
inference(all_rule,[status(thm)],[]) ).
thf(429,plain,
( ~ sP65
| sP283 ),
inference(all_rule,[status(thm)],[]) ).
thf(430,plain,
( ~ sP197
| sP148 ),
inference(all_rule,[status(thm)],[]) ).
thf(431,plain,
( ~ sP94
| sP231 ),
inference(all_rule,[status(thm)],[]) ).
thf(432,plain,
( ~ sP209
| sP255 ),
inference(all_rule,[status(thm)],[]) ).
thf(433,plain,
( ~ sP326
| ~ sP166 ),
inference(all_rule,[status(thm)],[]) ).
thf(434,plain,
( ~ sP1
| sP93 ),
inference(all_rule,[status(thm)],[]) ).
thf(435,plain,
( ~ sP227
| sP209 ),
inference(all_rule,[status(thm)],[]) ).
thf(436,plain,
( ~ sP65
| sP94 ),
inference(all_rule,[status(thm)],[]) ).
thf(437,plain,
( ~ sP197
| sP342 ),
inference(all_rule,[status(thm)],[]) ).
thf(axb,axiom,
sP197 ).
thf(axr,axiom,
sP65 ).
thf(rb,axiom,
sP227 ).
thf(bi,axiom,
sP386 ).
thf(ri,axiom,
sP316 ).
thf(sinj,axiom,
sP1 ).
thf(snz,axiom,
sP326 ).
thf(438,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,axb,axr,rb,bi,ri,sinj,snz]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA162^1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:31:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 1.73/1.96 % SZS status Unsatisfiable
% 1.73/1.96 % Mode: cade22grackle2xfee4
% 1.73/1.96 % Steps: 5752
% 1.73/1.96 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------