TSTP Solution File: SYO068^4.020 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO068^4.020 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 04:45:03 EDT 2023
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 302
% Syntax : Number of formulae : 308 ( 50 unt; 24 typ; 20 def)
% Number of atoms : 1022 ( 20 equ; 3 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 1636 ( 173 ~; 168 |; 1 &; 766 @)
% ( 128 <=>; 400 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 176 ( 172 usr; 153 con; 0-2 aty)
% Number of variables : 315 ( 34 ^; 279 !; 2 ?; 315 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_p16,type,
p16: $i > $o ).
thf(ty_p3,type,
p3: $i > $o ).
thf(ty_p7,type,
p7: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_p9,type,
p9: $i > $o ).
thf(ty_p5,type,
p5: $i > $o ).
thf(ty_p2,type,
p2: $i > $o ).
thf(ty_p15,type,
p15: $i > $o ).
thf(ty_p1,type,
p1: $i > $o ).
thf(ty_p20,type,
p20: $i > $o ).
thf(ty_p6,type,
p6: $i > $o ).
thf(ty_p14,type,
p14: $i > $o ).
thf(ty_p8,type,
p8: $i > $o ).
thf(ty_p19,type,
p19: $i > $o ).
thf(ty_p13,type,
p13: $i > $o ).
thf(ty_p4,type,
p4: $i > $o ).
thf(ty_p0,type,
p0: $i > $o ).
thf(ty_p11,type,
p11: $i > $o ).
thf(ty_p10,type,
p10: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_p18,type,
p18: $i > $o ).
thf(ty_p17,type,
p17: $i > $o ).
thf(ty_p12,type,
p12: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__0 @ X1 )
=> ( p20 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p17 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p17 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p16 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p16 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p16 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p15 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p11 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p10 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p10 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p10 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p9 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p16 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p15 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p12 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p6 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p6 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p13 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p7 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p6 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p20 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p19 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p4 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p3 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p6 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p15 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p14 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP8
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p12 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p11 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p8 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p8 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p7 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p17 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p16 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p10 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p9 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p7 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p6 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p7 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p6 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p6 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ( p0 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p6 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p15 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( irel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p17 @ X1 ) )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p19 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p17 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p16 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p19 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p19 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p18 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p20 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP20
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p11 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p10 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p15 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p14 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP8
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP35
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p18 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p13 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p12 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP39
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p18 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p7 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP49
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP33
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP33
=> ( sP47
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p17 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP33
=> sP43 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP47
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p18 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p17 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP33
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( sP33
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p14 @ X1 ) )
=> sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP33
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p8 @ X1 ) )
=> sP49 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p3 @ X1 ) )
=> sP50 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p18 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p17 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( sP33
=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p4 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( sP33
=> sP44 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP40
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p4 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p14 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p14 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p13 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP47
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p17 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p16 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p16 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p15 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP10
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p14 @ X1 ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p4 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p10 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p10 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p9 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p17 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p6 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p6 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p8 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p7 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( sP35
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p19 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p18 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p10 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p9 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( sP33
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p16 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p9 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p9 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p8 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( sP33
=> ( sP50
=> sP70 ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p18 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p18 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p17 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p11 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p10 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p8 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p7 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p13 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p13 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p12 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( p0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ! [X1: $i] : ( p20 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( sP33
=> ( sP78
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p9 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p20 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p20 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p19 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p14 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p19 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p18 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p5 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p5 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p4 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( sP33
=> sP79 ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p16 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p15 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( sP33
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( sP33
=> ( sP70
=> sP13 ) ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p9 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p9 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p8 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ( sP97
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p14 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p13 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( sP33
=> ( sP40
=> sP94 ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p14 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p13 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ( sP78
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p9 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p12 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p11 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p12 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p12 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p11 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p11 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p11 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p10 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( sP32
=> sP42 ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p9 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( sP40
=> sP94 ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( sP70
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p0 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p20 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p19 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( sP50
=> sP70 ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( p20 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( sP39
=> sP118 ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p9 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p8 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ( ( irel @ eigen__0 @ eigen__1 )
=> sP120 ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( sP33
=> sP61 ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( p8 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p15 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p15 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( p14 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( p3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ( sP125
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( irel @ X2 @ X3 )
@ ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
( iand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
( ivalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(con,conjecture,
! [X1: $i] : ( p0 @ X1 ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i] : ( p0 @ X1 ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h2,assumption,
~ sP88,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP90
| sP120 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP28
| ~ sP33
| sP88 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP13
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP116
| ~ sP70
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP119
| ~ sP50
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP61
| ~ sP110
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP72
| ~ sP94
| sP110 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP115
| ~ sP40
| sP94 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP30
| ~ sP95
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP48
| ~ sP49
| sP95 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP128
| ~ sP125
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP79
| ~ sP114
| sP125 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP108
| ~ sP78
| sP114 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP4
| ~ sP20
| sP78 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP43
| ~ sP8
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP12
| ~ sP10
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP71
| ~ sP97
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP19
| ~ sP32
| sP97 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP6
| ~ sP81
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP36
| ~ sP74
| sP81 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP67
| ~ sP47
| sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP44
| ~ sP35
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP46
| ~ sP39
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP103
| ~ sP33
| sP116 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP83
| ~ sP33
| sP119 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP124
| ~ sP33
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP63
| ~ sP33
| sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP106
| ~ sP33
| sP115 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP27
| ~ sP33
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP26
| ~ sP33
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP60
| ~ sP33
| sP128 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP100
| ~ sP33
| sP79 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP91
| ~ sP33
| sP108 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP52
| ~ sP33
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP54
| ~ sP33
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP80
| ~ sP33
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP59
| ~ sP33
| sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP56
| ~ sP33
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP11
| ~ sP33
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP102
| ~ sP33
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP53
| ~ sP33
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP64
| ~ sP33
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP16
| ~ sP33
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP57
| sP103 ),
inference(all_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP38
| sP83 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP89
| sP124 ),
inference(all_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP127
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP96
| sP106 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP18
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP25
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP86
| sP60 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP122
| sP100 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP24
| sP91 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP85
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP109
| sP54 ),
inference(all_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP45
| sP80 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP107
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP42
| sP56 ),
inference(all_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP101
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP23
| sP102 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP62
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP98
| sP64 ),
inference(all_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP118
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP31
| ~ sP70
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP2
| ~ sP50
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP15
| ~ sP110
| sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( ~ sP17
| ~ sP94
| sP127 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP65
| ~ sP40
| sP96 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP9
| ~ sP95
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP51
| ~ sP49
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP22
| ~ sP125
| sP86 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( ~ sP82
| ~ sP114
| sP122 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( ~ sP5
| ~ sP78
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP41
| ~ sP20
| sP85 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP21
| ~ sP8
| sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP69
| ~ sP10
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP105
| ~ sP97
| sP107 ),
inference(prop_rule,[status(thm)],]) ).
thf(78,plain,
( ~ sP113
| ~ sP32
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( ~ sP3
| ~ sP81
| sP101 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( ~ sP34
| ~ sP74
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP55
| ~ sP47
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP77
| ~ sP35
| sP98 ),
inference(prop_rule,[status(thm)],]) ).
thf(83,plain,
( sP123
| ~ sP120 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( sP39
| ~ sP123 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(85,plain,
( ~ sP121
| ~ sP39
| sP118 ),
inference(prop_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP93
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(87,plain,
( ~ sP117
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(88,plain,
( ~ sP29
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(89,plain,
( ~ sP58
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(90,plain,
( ~ sP7
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(91,plain,
( ~ sP99
| sP65 ),
inference(all_rule,[status(thm)],]) ).
thf(92,plain,
( ~ sP75
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(93,plain,
( ~ sP14
| sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(94,plain,
( ~ sP76
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(95,plain,
( ~ sP104
| sP82 ),
inference(all_rule,[status(thm)],]) ).
thf(96,plain,
( ~ sP73
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(97,plain,
( ~ sP112
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(98,plain,
( ~ sP111
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(99,plain,
( ~ sP87
| sP69 ),
inference(all_rule,[status(thm)],]) ).
thf(100,plain,
( ~ sP66
| sP105 ),
inference(all_rule,[status(thm)],]) ).
thf(101,plain,
( ~ sP126
| sP113 ),
inference(all_rule,[status(thm)],]) ).
thf(102,plain,
( ~ sP68
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(103,plain,
( ~ sP1
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(104,plain,
( ~ sP84
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(105,plain,
( ~ sP37
| sP77 ),
inference(all_rule,[status(thm)],]) ).
thf(106,plain,
( ~ sP92
| sP121 ),
inference(all_rule,[status(thm)],]) ).
thf(axiom21,axiom,
sP92 ).
thf(axiom20,axiom,
sP37 ).
thf(axiom19,axiom,
sP84 ).
thf(axiom18,axiom,
sP1 ).
thf(axiom17,axiom,
sP68 ).
thf(axiom16,axiom,
sP126 ).
thf(axiom15,axiom,
sP66 ).
thf(axiom14,axiom,
sP87 ).
thf(axiom13,axiom,
sP111 ).
thf(axiom12,axiom,
sP112 ).
thf(axiom11,axiom,
sP73 ).
thf(axiom10,axiom,
sP104 ).
thf(axiom9,axiom,
sP76 ).
thf(axiom8,axiom,
sP14 ).
thf(axiom7,axiom,
sP75 ).
thf(axiom6,axiom,
sP99 ).
thf(axiom5,axiom,
sP7 ).
thf(axiom4,axiom,
sP58 ).
thf(axiom3,axiom,
sP29 ).
thf(axiom2,axiom,
sP117 ).
thf(axiom1,axiom,
sP90 ).
thf(refl_axiom,axiom,
sP93 ).
thf(107,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[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,h2,axiom21,axiom20,axiom19,axiom18,axiom17,axiom16,axiom15,axiom14,axiom13,axiom12,axiom11,axiom10,axiom9,axiom8,axiom7,axiom6,axiom5,axiom4,axiom3,axiom2,axiom1,refl_axiom]) ).
thf(108,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,107,h2]) ).
thf(109,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[108,h0]) ).
thf(0,theorem,
! [X1: $i] : ( p0 @ X1 ),
inference(contra,[status(thm),contra(discharge,[h1])],[108,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO068^4.020 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 01:42:06 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % Mode: cade22grackle2xfee4
% 0.19/0.46 % Steps: 398
% 0.19/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------