%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV150^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 02:56:21 PM UTC 2025
% Result : Theorem 156.91s 157.38s
% Output : Proof 156.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 275
% Syntax : Number of formulae : 312 ( 56 unt; 0 typ; 18 def)
% Number of atoms : 954 ( 27 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 2911 ( 763 ~; 156 |; 0 &;1128 @)
% ( 129 <=>; 735 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 157 ( 155 usr; 148 con; 0-2 aty)
% Number of variables : 515 ( 42 ^; 473 !; 0 ?; 515 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__58,type,
eigen__58: a > $o ).
thf(ty_eigen__6,type,
eigen__6: a ).
thf(ty_eigen__12,type,
eigen__12: a > $o ).
thf(ty_eigen__69,type,
eigen__69: a ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__74,type,
eigen__74: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__60,type,
eigen__60: a ).
thf(ty_eigen__5,type,
eigen__5: a ).
thf(ty_eigen__59,type,
eigen__59: a ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__63,type,
eigen__63: a ).
thf(ty_eigen__13,type,
eigen__13: a > $o ).
thf(ty_eigen__70,type,
eigen__70: a ).
thf(ty_eigen__68,type,
eigen__68: a ).
thf(ty_eigen__62,type,
eigen__62: a ).
thf(ty_eigen__22,type,
eigen__22: a > $o ).
thf(ty_eigen__23,type,
eigen__23: a > $o ).
thf(ty_eigen__64,type,
eigen__64: a ).
thf(ty_eigen__76,type,
eigen__76: a ).
thf(ty_eigen__61,type,
eigen__61: a ).
thf(h0,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__68,definition,
( eigen__68
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__58 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__68])]) ).
thf(eigendef_eigen__62,definition,
( eigen__62
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__58 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__62])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a] :
~ ( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__5 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__22,definition,
( eigen__22
= ( 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__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__22])]) ).
thf(eigendef_eigen__63,definition,
( eigen__63
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__59 @ X1 )
=> ( eigen__58 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__63])]) ).
thf(eigendef_eigen__69,definition,
( eigen__69
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__59 @ X1 )
=> ( eigen__58 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__69])]) ).
thf(eigendef_eigen__23,definition,
( eigen__23
= ( 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__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__23])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__1
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__5 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__64,definition,
( eigen__64
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__58 @ eigen__62 )
=> ~ ( eigen__0 @ eigen__62 @ X1 ) )
=> ( eigen__58 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__64])]) ).
thf(eigendef_eigen__74,definition,
( eigen__74
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__58 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__74])]) ).
thf(eigendef_eigen__60,definition,
( eigen__60
= ( 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__58 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__60])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__4 @ eigen__5 )
=> ~ ( ~ ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__5 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__76,definition,
( eigen__76
= ( eps__0
@ ^ [X1: a] :
~ ( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__58 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__76])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( 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__5])]) ).
thf(eigendef_eigen__61,definition,
( eigen__61
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__58 @ eigen__59 )
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__59 @ 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__59 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) )
=> ( eigen__58 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__61])]) ).
thf(eigendef_eigen__70,definition,
( eigen__70
= ( eps__0
@ ^ [X1: a] :
~ ( ~ ( ( eigen__58 @ eigen__68 )
=> ~ ( eigen__1 @ eigen__68 @ X1 ) )
=> ( eigen__58 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__70])]) ).
thf(eigendef_eigen__59,definition,
( eigen__59
= ( eps__0
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__58 @ 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__58 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__59])]) ).
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__4 @ eigen__5 )
=> ~ ( ~ ( eigen__0 @ eigen__5 @ eigen__7 )
=> ( eigen__1 @ eigen__5 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( ~ ( ( eigen__58 @ eigen__59 )
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__59 @ 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__59 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ! [X1: a] :
( ( eigen__1 @ eigen__59 @ X1 )
=> ( eigen__58 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__58 @ X2 ) ) )
=> ( eigen__58 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__0 @ eigen__2 @ eigen__74 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__58 @ eigen__70 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__23 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ( eigen__58 @ eigen__59 )
=> ~ ( ~ ( eigen__0 @ eigen__59 @ eigen__63 )
=> ( eigen__1 @ eigen__59 @ eigen__63 ) ) )
=> ( eigen__58 @ eigen__63 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( eigen__0 @ eigen__5 @ eigen__7 )
=> ( eigen__1 @ eigen__5 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__58 @ eigen__68 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__0 @ eigen__59 @ eigen__63 )
=> ( eigen__58 @ eigen__63 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__58 @ eigen__60 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__58 @ eigen__76 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 @ eigen__2 @ eigen__76 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__22 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__58 @ eigen__59 )
=> ~ ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__59 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__61 ) )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__59 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__61 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__58 @ eigen__59 )
=> ~ ( ~ ( eigen__0 @ eigen__59 @ eigen__63 )
=> ( eigen__1 @ eigen__59 @ eigen__63 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( eigen__0 @ eigen__59 @ eigen__63 )
=> ( eigen__1 @ eigen__59 @ eigen__63 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__58 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ! [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__60 ) )
=> ! [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__60 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__58 @ eigen__62 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( eigen__1 @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__59 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__61 ) )
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__59 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__61 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP5
=> ( eigen__1 @ eigen__2 @ eigen__74 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__22 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__13 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: a] :
( ( eigen__1 @ eigen__5 @ X1 )
=> ( eigen__12 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__5 )
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__5 @ 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__5 @ 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,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [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__60 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP17
=> ( eigen__58 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP2
=> ( eigen__4 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a] :
( ~ ( sP22
=> ~ ( ~ ( eigen__0 @ eigen__62 @ X1 )
=> ( eigen__1 @ eigen__62 @ X1 ) ) )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ ! [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__6 ) )
=> ! [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__6 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ ( sP7
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__23 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__23 @ X2 ) ) )
=> ( eigen__23 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP10
=> ~ ( eigen__1 @ eigen__68 @ eigen__70 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP5
=> ( eigen__58 @ eigen__74 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__59 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__58 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__58 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ! [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__58 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ 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__58 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__4 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP16
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__22 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__22 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ~ ( ! [X1: a] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__13 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__13 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__13 @ X2 ) ) )
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( eigen__1 @ eigen__2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__58 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ sP39
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ( eigen__58 @ eigen__59 )
=> ~ ( ~ ( eigen__0 @ eigen__59 @ eigen__69 )
=> ( eigen__1 @ eigen__59 @ eigen__69 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ~ sP47
=> ( eigen__58 @ eigen__69 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__5 @ 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
<=> ( sP41
=> ~ ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__5 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) )
=> sP49 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ~ ( sP28
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__12 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__12 @ X2 ) ) )
=> ( eigen__12 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ~ ( eigen__0 @ eigen__59 @ eigen__69 )
=> ( eigen__1 @ eigen__59 @ eigen__69 ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ! [X1: a] :
( ( eigen__1 @ eigen__59 @ X1 )
=> ( eigen__58 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__58 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( eigen__0 @ eigen__62 @ eigen__64 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( eigen__58 @ eigen__69 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( eigen__1 @ eigen__59 @ eigen__69 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ sP40
=> sP45 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( ~ ( sP22
=> ~ sP54 )
=> ( eigen__58 @ eigen__64 ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( eigen__0 @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( eigen__58 @ eigen__64 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: a] :
( ~ ( sP10
=> ~ ( eigen__1 @ eigen__68 @ X1 ) )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( eigen__1 @ eigen__68 @ eigen__70 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( eigen__23 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ~ ( eigen__0 @ eigen__2 @ eigen__76 )
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP23
=> ( eigen__12 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ! [X1: a] :
( ~ ( sP10
=> ~ ( ~ ( eigen__0 @ eigen__68 @ X1 )
=> ( eigen__1 @ eigen__68 @ X1 ) ) )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: a] :
( ~ ( sP41
=> ~ ( ~ ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__1 @ eigen__5 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ! [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__60 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ~ ( eigen__0 @ eigen__68 @ eigen__70 )
=> sP62 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ~ sP15
=> ( eigen__4 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( sP14
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( eigen__0 @ eigen__2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( sP22
=> ~ sP54 ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( ~ ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__5 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) )
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( eigen__58 @ eigen__59 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( sP28
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__12 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__12 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ( ~ sP36
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( sP21
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__13 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__13 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__13 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ 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__58 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( ~ ( ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__58 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__58 @ X2 ) ) )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( eigen__4 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ! [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,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( sP59
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ! [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__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ! [X1: a] :
( ( eigen__0 @ eigen__59 @ X1 )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__5 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( sP7
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__23 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__23 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( eigen__0 @ eigen__59 @ eigen__63 ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ! [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,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ! [X1: a] :
( ( eigen__1 @ eigen__59 @ X1 )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__59 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( ~ sP42
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( ~ sP54
=> ( eigen__1 @ eigen__62 @ eigen__64 ) ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__58 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( ~ ( sP10
=> ~ sP69 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ( eigen__58 @ eigen__63 ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( sP73
=> sP63 ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ( sP56
=> sP55 ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( ~ ( sP22
=> ~ sP98 )
=> sP60 ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( ~ ( sP90
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__58 @ X2 ) ) )
=> ( eigen__58 @ eigen__61 ) ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ! [X1: a] :
( ~ ( sP22
=> ~ ( eigen__0 @ eigen__62 @ X1 ) )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__58 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__58 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ( eigen__12 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ( sP90
=> ~ sP108 ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ! [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__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ( ~ sP73
=> sP44 ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ( eigen__58 @ eigen__61 ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( sP44
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( sP112
=> sP84 ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ( sP64
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( ~ sP50
=> ( eigen__4 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( sP25
=> ( eigen__58 @ eigen__74 ) ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( sP22
=> ~ sP98 ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ! [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,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ( sP10
=> ~ sP69 ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ! [X1: a] :
( ~ ( sP76
=> ~ ( ~ ( eigen__0 @ eigen__59 @ X1 )
=> ( eigen__1 @ eigen__59 @ X1 ) ) )
=> ( eigen__58 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( sP34
=> sP84 ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ( sP87
=> ~ sP99 ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ( eigen__58 @ eigen__74 ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ! [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__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ! [X1: a] :
( ( eigen__0 @ eigen__5 @ X1 )
=> ( eigen__13 @ X1 ) ) ),
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,
sP122 != sP94,
introduced(assumption,[]) ).
thf(h9,assumption,
sP122,
introduced(assumption,[]) ).
thf(h10,assumption,
sP94,
introduced(assumption,[]) ).
thf(h11,assumption,
~ sP122,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP94,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ( ~ ( sP85
=> ~ sP1 )
=> sP88 ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ( sP85
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ sP88,
introduced(assumption,[]) ).
thf(h16,assumption,
sP85,
introduced(assumption,[]) ).
thf(h17,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP86
| ~ sP59
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP65
| ~ sP23
| sP109 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP102
| ~ sP73
| sP63 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP115
| ~ sP44
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP16
| sP115 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( sP42
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP97
| ~ sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP97
| ~ sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP7
| sP102 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( sP92
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP35
| ~ sP63 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP35
| ~ sP92 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP128
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__23]) ).
thf(14,plain,
( sP111
| ~ sP97 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__22]) ).
thf(15,plain,
( sP34
| ~ sP111 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP34
| ~ sP128 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP125
| ~ sP34
| sP84 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP28
| sP65 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( sP77
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP51
| ~ sP109 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP51
| ~ sP77 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP129
| sP86 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( sP81
| sP129 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP43
| ~ sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP43
| ~ sP81 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( sP91
| ~ sP43 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__13]) ).
thf(27,plain,
( sP49
| ~ sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).
thf(28,plain,
( sP75
| ~ sP49 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP75
| ~ sP91 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP50
| ~ sP41
| ~ sP75 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP118
| sP50
| sP119 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP29
| sP118 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP1
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP9
| sP59
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP2
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP2
| sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( sP32
| ~ sP119 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP32
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( sP67
| ~ sP32 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(40,plain,
( ~ sP112
| sP73
| sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP85
| sP125 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( sP116
| ~ sP84 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP116
| sP112 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP71
| ~ sP116 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(45,plain,
( sP105
| ~ sP67 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(46,plain,
( ~ sP15
| ~ sP71
| ~ sP105 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP70
| sP15
| sP88 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP122
| sP70 ),
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,
~ ( ~ ( sP80
=> ~ sP20 )
=> sP45 ),
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( sP80
=> ~ sP20 ),
introduced(assumption,[]) ).
thf(h20,assumption,
~ sP45,
introduced(assumption,[]) ).
thf(h21,assumption,
sP80,
introduced(assumption,[]) ).
thf(h22,assumption,
sP20,
introduced(assumption,[]) ).
thf(53,plain,
( ~ sP117
| ~ sP64
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( sP64
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( sP69
| ~ sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(56,plain,
( ~ sP123
| ~ sP10
| ~ sP69 ),
inference(prop_rule,[status(thm)],[]) ).
thf(57,plain,
( ~ sP100
| sP123
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( sP25
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(59,plain,
( ~ sP120
| ~ sP25
| sP127 ),
inference(prop_rule,[status(thm)],[]) ).
thf(60,plain,
( sP52
| ~ sP56 ),
inference(prop_rule,[status(thm)],[]) ).
thf(61,plain,
( ~ sP47
| ~ sP76
| ~ sP52 ),
inference(prop_rule,[status(thm)],[]) ).
thf(62,plain,
( ~ sP48
| sP47
| sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( ~ sP66
| sP100 ),
inference(all_rule,[status(thm)],[]) ).
thf(64,plain,
( ~ sP80
| sP117 ),
inference(all_rule,[status(thm)],[]) ).
thf(65,plain,
( sP72
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(66,plain,
( sP72
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(67,plain,
( sP87
| ~ sP72 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__76]) ).
thf(68,plain,
( ~ sP126
| ~ sP87
| ~ sP99 ),
inference(prop_rule,[status(thm)],[]) ).
thf(69,plain,
( ~ sP83
| sP126
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(70,plain,
( ~ sP80
| sP120 ),
inference(all_rule,[status(thm)],[]) ).
thf(71,plain,
( sP37
| ~ sP127 ),
inference(prop_rule,[status(thm)],[]) ).
thf(72,plain,
( sP37
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(73,plain,
( sP113
| ~ sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__74]) ).
thf(74,plain,
( ~ sP39
| ~ sP113
| ~ sP108 ),
inference(prop_rule,[status(thm)],[]) ).
thf(75,plain,
( ~ sP46
| sP39
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(76,plain,
( ~ sP20
| sP66 ),
inference(all_rule,[status(thm)],[]) ).
thf(77,plain,
( sP36
| sP62 ),
inference(prop_rule,[status(thm)],[]) ).
thf(78,plain,
( sP36
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( sP78
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(80,plain,
( sP78
| ~ sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(81,plain,
( sP61
| ~ sP78 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__70]) ).
thf(82,plain,
( ~ sP124
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(83,plain,
( sP103
| ~ sP55 ),
inference(prop_rule,[status(thm)],[]) ).
thf(84,plain,
( sP103
| sP56 ),
inference(prop_rule,[status(thm)],[]) ).
thf(85,plain,
( sP95
| ~ sP103 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__69]) ).
thf(86,plain,
( sP99
| ~ sP61 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__68]) ).
thf(87,plain,
( ~ sP53
| ~ sP95
| ~ sP99 ),
inference(prop_rule,[status(thm)],[]) ).
thf(88,plain,
( ~ sP4
| sP53
| sP114 ),
inference(prop_rule,[status(thm)],[]) ).
thf(89,plain,
( sP19
| ~ sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(90,plain,
( ~ sP18
| ~ sP76
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(91,plain,
( ~ sP8
| sP18
| sP101 ),
inference(prop_rule,[status(thm)],[]) ).
thf(92,plain,
( sP98
| ~ sP54 ),
inference(prop_rule,[status(thm)],[]) ).
thf(93,plain,
( ~ sP121
| ~ sP22
| ~ sP98 ),
inference(prop_rule,[status(thm)],[]) ).
thf(94,plain,
( ~ sP104
| sP121
| sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(95,plain,
( ~ sP33
| sP104 ),
inference(all_rule,[status(thm)],[]) ).
thf(96,plain,
( ~ sP20
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(97,plain,
( sP74
| sP54 ),
inference(prop_rule,[status(thm)],[]) ).
thf(98,plain,
( sP74
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(99,plain,
( sP58
| ~ sP60 ),
inference(prop_rule,[status(thm)],[]) ).
thf(100,plain,
( sP58
| ~ sP74 ),
inference(prop_rule,[status(thm)],[]) ).
thf(101,plain,
( sP107
| ~ sP58 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__64]) ).
thf(102,plain,
( ~ sP124
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(103,plain,
( sP11
| ~ sP101 ),
inference(prop_rule,[status(thm)],[]) ).
thf(104,plain,
( sP11
| sP93 ),
inference(prop_rule,[status(thm)],[]) ).
thf(105,plain,
( sP90
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__63]) ).
thf(106,plain,
( sP108
| ~ sP107 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__62]) ).
thf(107,plain,
( ~ sP110
| ~ sP90
| ~ sP108 ),
inference(prop_rule,[status(thm)],[]) ).
thf(108,plain,
( ~ sP106
| sP110
| sP114 ),
inference(prop_rule,[status(thm)],[]) ).
thf(109,plain,
( ~ sP20
| sP124 ),
inference(all_rule,[status(thm)],[]) ).
thf(110,plain,
( ~ sP96
| sP106 ),
inference(all_rule,[status(thm)],[]) ).
thf(111,plain,
( ~ sP38
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(112,plain,
( ~ sP24
| sP96
| sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(113,plain,
( sP17
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(114,plain,
( sP17
| sP76 ),
inference(prop_rule,[status(thm)],[]) ).
thf(115,plain,
( sP31
| ~ sP114 ),
inference(prop_rule,[status(thm)],[]) ).
thf(116,plain,
( sP31
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(117,plain,
( sP3
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__61]) ).
thf(118,plain,
( ~ sP68
| sP46 ),
inference(all_rule,[status(thm)],[]) ).
thf(119,plain,
( ~ sP30
| sP83 ),
inference(all_rule,[status(thm)],[]) ).
thf(120,plain,
( ~ sP21
| sP68
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(121,plain,
( sP79
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(122,plain,
( sP79
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(123,plain,
( sP89
| ~ sP79 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__60]) ).
thf(124,plain,
( sP82
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__59]) ).
thf(125,plain,
( ~ sP40
| ~ sP89
| ~ sP82 ),
inference(prop_rule,[status(thm)],[]) ).
thf(126,plain,
( ~ sP57
| sP40
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(127,plain,
( ~ sP94
| sP57 ),
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__58)],[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
% 0.09/0.11 % Problem : SEV150^5 : TPTP v9.2.0. Released v4.0.0.
% 0.09/0.11 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.31 % Computer : n029.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 8 19:44:08 EDT 2025
% 0.10/0.32 % CPUTime :
% 156.91/157.38 % SZS status Theorem
% 156.91/157.38 % Mode: mode406
% 156.91/157.38 % Inferences: 16318
% 156.91/157.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------