TSTP Solution File: SYO069^4.002 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO069^4.002 : 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 : n032.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 195.45s 195.70s
% Output : Proof 195.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 201
% Syntax : Number of formulae : 212 ( 32 unt; 15 typ; 25 def)
% Number of atoms : 945 ( 25 equ; 3 cnn)
% Maximal formula atoms : 56 ( 4 avg)
% Number of connectives : 1804 ( 166 ~; 103 |; 1 &; 941 @)
% ( 80 <=>; 513 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 119 ( 115 usr; 110 con; 0-2 aty)
% Number of variables : 335 ( 39 ^; 294 !; 2 ?; 335 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__38,type,
eigen__38: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__37,type,
eigen__37: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_a1,type,
a1: $i > $o ).
thf(ty_eigen__43,type,
eigen__43: $i ).
thf(ty_f,type,
f: $i > $o ).
thf(ty_b2,type,
b2: $i > $o ).
thf(ty_a0,type,
a0: $i > $o ).
thf(ty_b0,type,
b0: $i > $o ).
thf(ty_eigen__42,type,
eigen__42: $i ).
thf(ty_a2,type,
a2: $i > $o ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_b1,type,
b1: $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__42,definition,
( eigen__42
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__42])]) ).
thf(eigendef_eigen__43,definition,
( eigen__43
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__42 @ X1 )
=> ( b0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__43])]) ).
thf(eigendef_eigen__37,definition,
( eigen__37
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__37])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__5 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(eigendef_eigen__38,definition,
( eigen__38
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__37 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__38])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( irel @ X1 @ X2 )
=> ~ ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( irel @ eigen__5 @ eigen__7 )
=> ~ ( irel @ eigen__7 @ eigen__42 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( irel @ eigen__5 @ eigen__42 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP6
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( irel @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ~ ( sP8
=> ~ ( irel @ eigen__7 @ X1 ) )
=> ( irel @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( irel @ eigen__0 @ eigen__7 )
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a1 @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) ) )
=> ( sP7
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( f @ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( irel @ eigen__37 @ eigen__38 )
=> ( a2 @ eigen__38 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ( irel @ eigen__0 @ eigen__5 )
=> ~ sP8 )
=> ( irel @ eigen__0 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__7 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__7 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a1 @ X1 ) ) )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) ) )
=> ( sP7
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( f @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( irel @ eigen__7 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( irel @ eigen__42 @ eigen__43 )
=> ( b0 @ eigen__43 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__0 @ eigen__5 )
=> ~ ( irel @ eigen__5 @ X1 ) )
=> ( irel @ eigen__0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__0 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( irel @ eigen__42 @ eigen__43 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( b0 @ eigen__43 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ! [X1: $i] :
( ( irel @ eigen__37 @ X1 )
=> ( b1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__37 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( irel @ eigen__0 @ eigen__7 )
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( f @ X1 ) ) )
=> ( sP7
=> ( ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a1 @ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ ( ( irel @ eigen__7 @ eigen__37 )
=> ~ ( irel @ eigen__37 @ eigen__38 ) )
=> ( irel @ eigen__7 @ eigen__38 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( irel @ eigen__7 @ eigen__38 )
=> ( a2 @ eigen__38 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( irel @ eigen__0 @ eigen__5 )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( irel @ eigen__7 @ eigen__37 )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( irel @ eigen__7 @ eigen__42 )
=> ( ! [X1: $i] :
( ( irel @ eigen__42 @ X1 )
=> ( b2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__42 @ X1 )
=> ( b0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ~ ( sP5
=> ~ ( irel @ eigen__42 @ X1 ) )
=> ( irel @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( irel @ eigen__5 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) ) )
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( irel @ eigen__5 @ X1 )
=> ( b0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ~ ( ( irel @ eigen__7 @ eigen__37 )
=> ~ ( irel @ eigen__37 @ X1 ) )
=> ( irel @ eigen__7 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( a1 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP16
=> sP38 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( irel @ eigen__7 @ eigen__42 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( irel @ eigen__0 @ eigen__0 )
=> ~ ( sP1
=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a2 @ X1 ) ) )
=> sP4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP1
=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a2 @ X1 ) ) )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( irel @ eigen__5 @ eigen__43 )
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i] :
( ( irel @ eigen__37 @ X1 )
=> ( a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( irel @ eigen__7 @ eigen__38 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP8
=> sP38 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP35
=> sP33 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( a2 @ eigen__38 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a1 @ X1 ) ) )
=> ( ( sP21
=> sP27 )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a2 @ X1 ) ) )
=> ~ sP1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ! [X1: $i] :
( ( irel @ eigen__42 @ X1 )
=> ( b2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__42 @ X1 )
=> ( b0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a2 @ X1 ) ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ( irel @ eigen__7 @ eigen__37 )
=> ~ ( irel @ eigen__37 @ eigen__38 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) ) )
=> ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( b0 @ X3 ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: $i,X2: $i] :
( ~ ( ( irel @ eigen__5 @ X1 )
=> ~ ( irel @ X1 @ X2 ) )
=> ( irel @ eigen__5 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP47
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ( sP21
=> sP27 )
=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a2 @ X1 ) ) )
=> ~ sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $i] : ( irel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( a2 @ X1 ) ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( sP7
=> sP34 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ( irel @ eigen__0 @ eigen__5 )
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( sP21
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP7
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( f @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( irel @ eigen__7 @ eigen__37 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP5
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ( f @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( b0 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) ) )
=> sP65 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( irel @ eigen__0 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( ~ sP3
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( irel @ eigen__0 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ! [X1: $i] :
( ( irel @ eigen__42 @ X1 )
=> ( b0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( irel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a0 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( f @ X1 ) ) )
=> sP62 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( irel @ eigen__37 @ eigen__38 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( ~ sP67
=> ( irel @ eigen__5 @ eigen__43 ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( sP75
=> ~ sP51 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( irel @ eigen__5 @ eigen__43 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
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] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h2,assumption,
sP58,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP67
| ~ sP5
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP78
| sP67
| sP80 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP32
| sP78 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| ~ sP8
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP71
| sP3
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP57
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP9
| sP71 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP43
| ~ sP80
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP35
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP55
| ~ sP66
| ~ sP77 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP25
| sP55
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP36
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP14
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP26
| ~ sP45
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP53
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP29
| ~ sP70
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP13
| sP29
| sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP57
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP18
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP2
| sP57 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP19
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( sP34
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP62
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP62
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP76
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP24
| ~ sP72
| ~ sP76 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP17
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP17
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP73
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__43]) ).
thf(30,plain,
( sP52
| ~ sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP31
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP31
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP6
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__42]) ).
thf(34,plain,
( ~ sP7
| ~ sP6
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP65
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP69
| ~ sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP12
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP12
| sP77 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP44
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__38]) ).
thf(40,plain,
( sP23
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP30
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP30
| sP66 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP37
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__37]) ).
thf(44,plain,
( ~ sP39
| ~ sP16
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP74
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP28
| ~ sP37
| sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP15
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( sP15
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP10
| ~ sP72
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP60
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP2
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(52,plain,
( ~ sP48
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP56
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( sP61
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP59
| ~ sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP59
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( sP51
| ~ sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP79
| ~ sP75
| ~ sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( sP46
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( sP46
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( sP33
| ~ sP46 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(62,plain,
( sP49
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( sP49
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( sP63
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( sP63
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( sP21
| ~ sP63 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(67,plain,
( ~ sP64
| ~ sP21
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( sP4
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( sP54
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP1
| ~ sP27
| sP68 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( sP42
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( sP42
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( ~ sP41
| ~ sP75
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP56
| sP79 ),
inference(all_rule,[status(thm)],]) ).
thf(75,plain,
( ~ sP48
| sP41 ),
inference(all_rule,[status(thm)],]) ).
thf(76,plain,
( sP11
| ~ sP68 ),
inference(prop_rule,[status(thm)],]) ).
thf(77,plain,
( sP11
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(78,plain,
( sP47
| ~ sP68 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( sP47
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( ~ sP58
| ~ sP47
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP2
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP60
| sP75 ),
inference(all_rule,[status(thm)],]) ).
thf(trans_axiom,axiom,
sP2 ).
thf(refl_axiom,axiom,
sP60 ).
thf(83,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,h2,trans_axiom,refl_axiom]) ).
thf(84,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,83,h2]) ).
thf(85,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[84,h0]) ).
thf(0,theorem,
! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) ) )
=> ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( b0 @ X4 ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a0 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( f @ X3 ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( f @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[84,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO069^4.002 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.09 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sat Aug 26 04:24:43 EDT 2023
% 0.09/0.29 % CPUTime :
% 195.45/195.70 % SZS status Theorem
% 195.45/195.70 % Mode: cade22grackle2x2d0b
% 195.45/195.70 % Steps: 221585
% 195.45/195.70 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------