TSTP Solution File: SEV150^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV150^5 : 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 : n002.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 : Thu Aug 31 19:32:45 EDT 2023
% Result : Theorem 5.74s 5.89s
% Output : Proof 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 300
% Syntax : Number of formulae : 337 ( 56 unt; 25 typ; 18 def)
% Number of atoms : 950 ( 27 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 2912 ( 761 ~; 156 |; 0 &;1131 @)
% ( 129 <=>; 735 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 127 ( 127 >; 0 *; 0 +; 0 <<)
% Number of symbols : 157 ( 155 usr; 148 con; 0-2 aty)
% Number of variables : 512 ( 42 ^; 470 !; 0 ?; 512 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__113,type,
eigen__113: a ).
thf(ty_eigen__112,type,
eigen__112: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__51,type,
eigen__51: a > $o ).
thf(ty_eigen__110,type,
eigen__110: a ).
thf(ty_eigen__111,type,
eigen__111: a ).
thf(ty_eigen__114,type,
eigen__114: a ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__115,type,
eigen__115: a ).
thf(ty_eigen__17,type,
eigen__17: a > $o ).
thf(ty_eigen__105,type,
eigen__105: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__116,type,
eigen__116: a ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__119,type,
eigen__119: a ).
thf(ty_eigen__77,type,
eigen__77: a > $o ).
thf(ty_eigen__109,type,
eigen__109: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__50,type,
eigen__50: a > $o ).
thf(ty_eigen__106,type,
eigen__106: a ).
thf(ty_eigen__16,type,
eigen__16: a > $o ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__106,definition,
( eigen__106
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__77 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__106])]) ).
thf(eigendef_eigen__110,definition,
( eigen__110
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__77 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__77 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__110])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__119,definition,
( eigen__119
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__114 @ X1 )
=> ( eigen__77 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__119])]) ).
thf(eigendef_eigen__116,definition,
( eigen__116
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__114 @ X1 )
=> ( eigen__77 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__116])]) ).
thf(eigendef_eigen__114,definition,
( eigen__114
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__77 @ X1 )
=> ~ ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ( eigen__77 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__114])]) ).
thf(eigendef_eigen__50,definition,
( eigen__50
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__50])]) ).
thf(eigendef_eigen__109,definition,
( eigen__109
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__77 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__77 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__109])]) ).
thf(eigendef_eigen__115,definition,
( eigen__115
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__77 @ eigen__114 )
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__114 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__114 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) )
=> ( eigen__77 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__115])]) ).
thf(eigendef_eigen__105,definition,
( eigen__105
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__77 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__105])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__112,definition,
( eigen__112
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__77 @ eigen__110 )
=> ~ ( eigen__0 @ eigen__110 @ X1 ) )
=> ( eigen__77 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__112])]) ).
thf(eigendef_eigen__51,definition,
( eigen__51
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__51])]) ).
thf(eigendef_eigen__113,definition,
( eigen__113
= ( eps__0
@ ^ [X1: a] :
~ ( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__77 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__113])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: a] :
~ ( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(eigendef_eigen__111,definition,
( eigen__111
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__77 @ eigen__109 )
=> ~ ( eigen__1 @ eigen__109 @ X1 ) )
=> ( eigen__77 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__111])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__77 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__77 @ X1 )
=> ~ ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ( eigen__77 @ X2 ) ) )
=> ( eigen__77 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__77 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__77 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__16 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__77 @ X1 ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__77 @ eigen__113 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__114 @ X1 )
=> ( eigen__77 @ X1 ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__6 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__6 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( eigen__0 @ eigen__2 @ eigen__5 )
=> ( eigen__1 @ eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: a] :
( ~ ( ( eigen__77 @ eigen__109 )
=> ~ ( ~ ( eigen__0 @ eigen__109 @ X1 )
=> ( eigen__1 @ eigen__109 @ X1 ) ) )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__1 @ eigen__109 @ eigen__111 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__50 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( eigen__0 @ eigen__114 @ X1 )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__77 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__77 @ X1 )
=> ~ ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ( eigen__77 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__0 @ eigen__114 @ eigen__116 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__17 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__17 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__17 @ X2 ) ) )
=> ( eigen__17 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__77 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__77 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( ~ ( eigen__0 @ eigen__2 @ eigen__106 )
=> ( eigen__1 @ eigen__2 @ eigen__106 ) )
=> ( eigen__77 @ eigen__106 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ ( eigen__0 @ eigen__2 @ eigen__105 )
=> ( eigen__1 @ eigen__2 @ eigen__105 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ( ! [X1: a] :
( ( eigen__1 @ eigen__114 @ X1 )
=> ( eigen__77 @ X1 ) )
=> ~ sP21 )
=> ( eigen__77 @ eigen__115 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__1 @ eigen__2 @ eigen__105 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: a] :
( ~ ( ( eigen__77 @ eigen__109 )
=> ~ ( eigen__1 @ eigen__109 @ X1 ) )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ~ ( ( eigen__77 @ eigen__114 )
=> ~ ( ~ ( eigen__0 @ eigen__114 @ X1 )
=> ( eigen__1 @ eigen__114 @ X1 ) ) )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ~ ( ( eigen__77 @ eigen__110 )
=> ~ ( eigen__0 @ eigen__110 @ X1 ) )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ ( sP6
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) )
=> ( eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( eigen__1 @ eigen__2 @ eigen__5 )
=> ( eigen__17 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ! [X1: a] :
( ( eigen__1 @ eigen__114 @ X1 )
=> ( eigen__77 @ X1 ) )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a] :
( ( eigen__1 @ eigen__6 @ X1 )
=> ( eigen__51 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( eigen__77 @ eigen__109 )
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__114 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__115 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__0 @ eigen__2 @ eigen__106 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ sP10
=> ( eigen__77 @ eigen__115 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ( eigen__77 @ eigen__110 )
=> ~ ( ~ ( eigen__0 @ eigen__110 @ eigen__112 )
=> ( eigen__1 @ eigen__110 @ eigen__112 ) ) )
=> ( eigen__77 @ eigen__112 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( eigen__77 @ eigen__114 )
=> ~ ( ~ sP19
=> ( eigen__1 @ eigen__114 @ eigen__116 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__77 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__77 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__17 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP6
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( eigen__77 @ eigen__109 )
=> ~ ( ~ ( eigen__0 @ eigen__109 @ eigen__111 )
=> sP15 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ sP44
=> ( eigen__77 @ eigen__111 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP23
=> ( eigen__77 @ eigen__105 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__16 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__16 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__16 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( eigen__0 @ eigen__2 @ eigen__5 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__6 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__51 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ ( ( eigen__77 @ eigen__114 )
=> ~ ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__114 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__115 ) )
=> sP34 ) )
=> ( eigen__77 @ eigen__115 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( eigen__77 @ eigen__116 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__114 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__115 ) )
=> sP34 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ( eigen__1 @ eigen__114 @ eigen__119 )
=> ( eigen__77 @ eigen__119 ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ~ sP2
=> ( eigen__1 @ eigen__6 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ sP43
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( eigen__77 @ eigen__106 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ~ sP39
=> sP52 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( sP36
=> sP58 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__113 ) )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__113 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( eigen__1 @ eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( eigen__77 @ eigen__115 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__113 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP12
=> ( eigen__4 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ~ sP19
=> ( eigen__1 @ eigen__114 @ eigen__116 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP25
=> ( eigen__77 @ eigen__105 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [X1: a] :
( ~ ( ( eigen__77 @ eigen__110 )
=> ~ ( ~ ( eigen__0 @ eigen__110 @ X1 )
=> ( eigen__1 @ eigen__110 @ X1 ) ) )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( eigen__77 @ eigen__105 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__113 ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ~ ( eigen__0 @ eigen__114 @ eigen__119 )
=> ( eigen__1 @ eigen__114 @ eigen__119 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ~ sP8
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( eigen__77 @ eigen__109 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( eigen__0 @ eigen__110 @ eigen__112 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( ~ sP13
=> sP53 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( eigen__1 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( ( eigen__4 @ eigen__6 )
=> ~ sP56 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( ~ sP47
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__16 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( ( eigen__77 @ eigen__114 )
=> ~ sP72 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( ( eigen__77 @ eigen__114 )
=> ~ sP54 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( sP16
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__50 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__50 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( eigen__77 @ eigen__119 ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( sP2
=> ( eigen__50 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ( ~ sP36
=> ( eigen__1 @ eigen__2 @ eigen__106 ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__77 @ X1 )
=> ~ ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ( eigen__77 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( ~ ( eigen__0 @ eigen__109 @ eigen__111 )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( eigen__77 @ eigen__112 ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ( sP35
=> sP69 ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( eigen__50 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( sP61
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__114 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__115 ) ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( eigen__0 @ eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__17 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__17 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__17 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( eigen__77 @ eigen__110 ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( eigen__77 @ eigen__114 ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( ~ sP79
=> sP53 ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ( ~ sP86
=> sP96 ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ( eigen__77 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ! [X1: a] :
( ~ ( sP104
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__114 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__114 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ( ~ sP83
=> sP87 ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__6 )
=> ~ ( ~ ( eigen__0 @ eigen__6 @ X1 )
=> ( eigen__1 @ eigen__6 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ( sP103
=> ~ ( ~ sP76
=> ( eigen__1 @ eigen__110 @ eigen__112 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( sP78
=> sP50 ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ( ~ sP33
=> ( eigen__77 @ eigen__111 ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ! [X1: a] :
( ( eigen__1 @ eigen__114 @ X1 )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X2 )
=> ( eigen__1 @ eigen__2 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__77 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( sP19
=> sP52 ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( eigen__77 @ eigen__111 ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( ~ ( sP32
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__51 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__51 @ X2 ) ) )
=> sP50 ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( sP32
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__51 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__51 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ( eigen__1 @ eigen__114 @ eigen__119 ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__17 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( ~ ( sP89
=> ~ sP21 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( ~ sP76
=> ( eigen__1 @ eigen__110 @ eigen__112 ) ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ( eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ( ~ ( sP103
=> ~ sP76 )
=> sP93 ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ( sP89
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ( sP103
=> ~ sP76 ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(cTHM251A_pme,conjecture,
! [X1: a > a > $o,X2: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM251A_pme]) ).
thf(h3,assumption,
~ ! [X1: a > a > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( X1 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( X1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( eigen__0 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( eigen__0 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
( ( ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
!= ( ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: a] :
( ( ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
= ( ^ [X2: a] :
! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
( ( ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X3 )
=> ( eigen__1 @ eigen__2 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
!= ( ^ [X1: a] :
! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: a] :
( ( ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X3 )
=> ( eigen__1 @ eigen__2 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
= ( ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP116 != sP101,
introduced(assumption,[]) ).
thf(h9,assumption,
sP116,
introduced(assumption,[]) ).
thf(h10,assumption,
sP101,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP116,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP101,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( sP80
=> ~ sP1 )
=> sP85 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP80
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP85,
introduced(assumption,[]) ).
thf(h16,assumption,
sP80,
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP113
| ~ sP78
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP32
| sP113 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( sP121
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP88
| ~ sP2
| sP96 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP16
| sP88 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP86
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP120
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP120
| ~ sP121 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP107
| ~ sP96 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP107
| ~ sP86 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP49
| ~ sP120 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__51]) ).
thf(12,plain,
( sP43
| ~ sP107 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__50]) ).
thf(13,plain,
( sP57
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP57
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP13
| ~ sP126
| ~ sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP77
| sP13
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP11
| sP77 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP30
| ~ sP62
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP123
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( sP102
| sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP48
| ~ sP100
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP82
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( sP47
| sP82 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP20
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP20
| ~ sP102 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP81
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP81
| ~ sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP5
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__17]) ).
thf(30,plain,
( sP94
| ~ sP81 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__16]) ).
thf(31,plain,
( sP35
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP35
| ~ sP94 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP95
| ~ sP35
| sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP80
| sP95 ),
inference(all_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP56
| sP2
| sP78 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP79
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP79
| sP126 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP106
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP106
| ~ sP79 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP111
| ~ sP106 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(41,plain,
( sP97
| ~ sP111 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(42,plain,
( ~ sP12
| sP100
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP65
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP65
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP6
| ~ sP65 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(46,plain,
( ~ sP42
| ~ sP6
| ~ sP97 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP29
| sP42
| sP85 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP116
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h14,h15,h13,h9,h10,h8,h7,h6,h5,h4,h3,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,h9,h16,h17,h15]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h15,h13,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h14,49,h16,h17]) ).
thf(51,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,50,h14,h15]) ).
thf(52,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__4)],[h10,51,h13]) ).
thf(h18,assumption,
~ ( ~ ( sP73
=> ~ sP40 )
=> sP108 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP73
=> ~ sP40 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP108,
introduced(assumption,[]) ).
thf(h21,assumption,
sP73,
introduced(assumption,[]) ).
thf(h22,assumption,
sP40,
introduced(assumption,[]) ).
thf(53,plain,
( sP72
| ~ sP122 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP83
| ~ sP104
| ~ sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP110
| sP83
| sP87 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP27
| sP110 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( sP66
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( ~ sP39
| ~ sP104
| ~ sP66 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( ~ sP59
| sP39
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP27
| sP59 ),
inference(all_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP40
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( sP125
| ~ sP76 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( ~ sP112
| ~ sP103
| ~ sP125 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( ~ sP38
| sP112
| sP93 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( ~ sP68
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP40
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(67,plain,
( sP92
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( ~ sP44
| ~ sP75
| ~ sP92 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP45
| sP44
| sP119 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( ~ sP14
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(71,plain,
( ~ sP40
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(72,plain,
( sP90
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( ~ sP22
| ~ sP90
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( ~ sP73
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(75,plain,
( sP23
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(76,plain,
( ~ sP46
| ~ sP23
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(77,plain,
( ~ sP73
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(78,plain,
( sP55
| ~ sP87 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( sP55
| sP122 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( sP115
| ~ sP55 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__119]) ).
thf(81,plain,
( ~ sP31
| ~ sP115
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
( sP118
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(83,plain,
( sP118
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( sP17
| ~ sP118 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__116]) ).
thf(85,plain,
( ~ sP10
| ~ sP17
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(86,plain,
( ~ sP24
| sP31
| sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(87,plain,
( ~ sP37
| sP10
| sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(88,plain,
( ~ sP34
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(89,plain,
( ~ sP99
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(90,plain,
( ~ sP54
| sP99
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(91,plain,
( sP84
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(92,plain,
( sP84
| sP104 ),
inference(prop_rule,[status(thm)],]) ).
thf(93,plain,
( sP51
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(94,plain,
( sP51
| ~ sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(95,plain,
( ~ sP124
| sP128
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(96,plain,
( ~ sP74
| sP8
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(97,plain,
( ~ sP71
| sP124 ),
inference(all_rule,[status(thm)],]) ).
thf(98,plain,
( ~ sP64
| sP74 ),
inference(all_rule,[status(thm)],]) ).
thf(99,plain,
( ~ sP61
| sP64
| sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(100,plain,
( sP109
| ~ sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__115]) ).
thf(101,plain,
( sP98
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(102,plain,
( sP98
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(103,plain,
( sP91
| ~ sP109 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__114]) ).
thf(104,plain,
( sP105
| ~ sP98 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__113]) ).
thf(105,plain,
( ~ sP18
| ~ sP105
| ~ sP91 ),
inference(prop_rule,[status(thm)],]) ).
thf(106,plain,
( ~ sP3
| sP18
| sP108 ),
inference(prop_rule,[status(thm)],]) ).
thf(107,plain,
( sP129
| sP76 ),
inference(prop_rule,[status(thm)],]) ).
thf(108,plain,
( sP129
| sP103 ),
inference(prop_rule,[status(thm)],]) ).
thf(109,plain,
( sP127
| ~ sP93 ),
inference(prop_rule,[status(thm)],]) ).
thf(110,plain,
( sP127
| ~ sP129 ),
inference(prop_rule,[status(thm)],]) ).
thf(111,plain,
( sP28
| ~ sP127 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__112]) ).
thf(112,plain,
( sP33
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(113,plain,
( sP33
| sP75 ),
inference(prop_rule,[status(thm)],]) ).
thf(114,plain,
( sP114
| ~ sP119 ),
inference(prop_rule,[status(thm)],]) ).
thf(115,plain,
( sP114
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(116,plain,
( sP26
| ~ sP114 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__111]) ).
thf(117,plain,
( sP4
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__110]) ).
thf(118,plain,
( sP21
| ~ sP26 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__109]) ).
thf(119,plain,
( sP60
| ~ sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(120,plain,
( sP60
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(121,plain,
( sP117
| ~ sP60 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__106]) ).
thf(122,plain,
( ~ sP8
| ~ sP117
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(123,plain,
( sP67
| ~ sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(124,plain,
( sP67
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(125,plain,
( sP89
| ~ sP67 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__105]) ).
thf(126,plain,
( ~ sP128
| ~ sP89
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(127,plain,
( ~ sP101
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(128,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h21,h22,h19,h20,h18,h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[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,h21,h22,h20,h12]) ).
thf(129,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h18,h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,128,h21,h22]) ).
thf(130,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,129,h19,h20]) ).
thf(131,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h12,h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__77)],[h11,130,h18]) ).
thf(132,plain,
$false,
inference(tab_be,[status(thm),assumptions([h8,h7,h6,h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h9,h10]),tab_be(discharge,[h11,h12])],[h8,52,131,h9,h10,h11,h12]) ).
thf(133,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h6,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,132,h8]) ).
thf(134,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h6,h5,h4,h3,h2,h1,h0]),tab_fe(discharge,[h7])],[h6,133,h7]) ).
thf(135,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,134,h6]) ).
thf(136,plain,
$false,
inference(tab_fe,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_fe(discharge,[h5])],[h4,135,h5]) ).
thf(137,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,136,h4]) ).
thf(138,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,137,h3]) ).
thf(139,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[138,h1]) ).
thf(140,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[139,h0]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > a > $o] :
( ( ^ [X3: a,X4: a] :
! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
= ( ^ [X3: a,X4: a] :
! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[138,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEV150^5 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 02:10:01 EDT 2023
% 0.15/0.37 % CPUTime :
% 5.74/5.89 % SZS status Theorem
% 5.74/5.89 % Mode: cade22grackle2xfee4
% 5.74/5.89 % Steps: 65503
% 5.74/5.89 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------