%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV420^1 : TPTP v9.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 02:55:52 PM UTC 2025
% Result : Theorem 21.24s 21.45s
% Output : Proof 21.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 170
% Syntax : Number of formulae : 233 ( 96 unt; 0 typ; 38 def)
% Number of atoms : 894 ( 231 equ; 5 cnn)
% Maximal formula atoms : 29 ( 3 avg)
% Number of connectives : 2126 ( 669 ~; 66 |; 10 &; 757 @)
% ( 39 <=>; 585 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 91 usr; 86 con; 0-2 aty)
% Number of variables : 366 ( 96 ^; 265 !; 5 ?; 366 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__14,type,
eigen__14: $i ).
thf(ty_eigen__18,type,
eigen__18: $i ).
thf(ty_eigen__71,type,
eigen__71: $i ).
thf(ty_eigen__128,type,
eigen__128: $i ).
thf(ty_eigen__98,type,
eigen__98: $i ).
thf(ty_eigen__72,type,
eigen__72: $i ).
thf(ty_eigen__93,type,
eigen__93: $i ).
thf(ty_eigen__76,type,
eigen__76: $i ).
thf(ty_eigen__32,type,
eigen__32: $i ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__54,type,
eigen__54: $i ).
thf(ty_eigen__102,type,
eigen__102: $i ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(ty_eigen__53,type,
eigen__53: $i ).
thf(ty_eigen__137,type,
eigen__137: $i ).
thf(ty_eigen__133,type,
eigen__133: $i ).
thf(ty_eigen__95,type,
eigen__95: $i ).
thf(ty_eigen__104,type,
eigen__104: $i ).
thf(ty_eigen__165,type,
eigen__165: $i ).
thf(ty_eigen__5,type,
eigen__5: $i > $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_eigen__73,type,
eigen__73: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__107,type,
eigen__107: $i ).
thf(ty_eigen__57,type,
eigen__57: $i ).
thf(ty_eigen__143,type,
eigen__143: $i ).
thf(ty_eigen__28,type,
eigen__28: $i ).
thf(ty_eigen__4,type,
eigen__4: $i > $i ).
thf(ty_eigen__29,type,
eigen__29: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__71,definition,
( eigen__71
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__57 )
=> ( eigen__2 @ eigen__57 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__57 != X1 ) )
=> ( eigen__57 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__71])]) ).
thf(eigendef_eigen__93,definition,
( eigen__93
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__76 )
=> ( eigen__2 @ eigen__76 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__76 != X1 ) )
=> ( eigen__76 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__93])]) ).
thf(eigendef_eigen__137,definition,
( eigen__137
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__133 )
=> ( eigen__2 @ eigen__133 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__133 != X1 ) )
=> ( eigen__133 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__137])]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__13 )
=> ( eigen__2 @ eigen__13 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__13 != X1 ) )
=> ( eigen__13 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
thf(eigendef_eigen__32,definition,
( eigen__32
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__32])]) ).
thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__143,definition,
( eigen__143
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__143])]) ).
thf(eigendef_eigen__98,definition,
( eigen__98
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__98])]) ).
thf(eigendef_eigen__165,definition,
( eigen__165
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__143 )
=> ( eigen__2 @ eigen__143 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__143 != X1 ) )
=> ( eigen__143 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__165])]) ).
thf(eigendef_eigen__53,definition,
( eigen__53
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__32 )
=> ( eigen__2 @ eigen__32 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__32 != X1 ) )
=> ( eigen__32 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__53])]) ).
thf(eigendef_eigen__102,definition,
( eigen__102
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__98 )
=> ( eigen__2 @ eigen__98 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__98 != X1 ) )
=> ( eigen__98 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__102])]) ).
thf(eigendef_eigen__28,definition,
( eigen__28
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__18 )
=> ( eigen__2 @ eigen__18 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__18 != X1 ) )
=> ( eigen__18 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__28])]) ).
thf(eigendef_eigen__128,definition,
( eigen__128
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__107 )
=> ( eigen__2 @ eigen__107 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__107 != X1 ) )
=> ( eigen__107 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__128])]) ).
thf(eigendef_eigen__76,definition,
( eigen__76
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__76])]) ).
thf(eigendef_eigen__133,definition,
( eigen__133
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__133])]) ).
thf(eigendef_eigen__57,definition,
( eigen__57
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__57])]) ).
thf(eigendef_eigen__107,definition,
( eigen__107
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__107])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__133 )
=> ( eigen__2 @ eigen__133 ) )
=> ~ ( ~ ( eigen__0 @ eigen__137 )
=> ( eigen__2 @ eigen__137 ) ) )
=> ( eigen__133 != eigen__137 ) )
=> ( eigen__133 = eigen__137 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__98 )
=> ( eigen__2 @ eigen__98 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__98 != X1 ) )
=> ( eigen__98 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__76 )
=> ( eigen__2 @ eigen__76 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__76 != X1 ) )
=> ( eigen__76 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__57 )
=> ( eigen__2 @ eigen__57 ) )
=> ~ ( ~ ( eigen__0 @ eigen__71 )
=> ( eigen__2 @ eigen__71 ) ) )
=> ( eigen__57 != eigen__71 ) )
=> ( eigen__57 = eigen__71 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__143 )
=> ( eigen__2 @ eigen__143 ) )
=> ~ ( ~ ( eigen__0 @ eigen__165 )
=> ( eigen__2 @ eigen__165 ) ) )
=> ( eigen__143 != eigen__165 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__18 )
=> ( eigen__2 @ eigen__18 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__18 != X1 ) )
=> ( eigen__18 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__32 )
=> ( eigen__2 @ eigen__32 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__32 != X1 ) )
=> ( eigen__32 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__107 = eigen__128 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__13 = eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__107 )
=> ( eigen__2 @ eigen__107 ) )
=> ~ ( ~ ( eigen__0 @ eigen__128 )
=> ( eigen__2 @ eigen__128 ) ) )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__143 )
=> ( eigen__2 @ eigen__143 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__143 != X1 ) )
=> ( eigen__143 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__18 )
=> ( eigen__2 @ eigen__18 ) )
=> ~ ( ~ ( eigen__0 @ eigen__28 )
=> ( eigen__2 @ eigen__28 ) ) )
=> ( eigen__18 != eigen__28 ) )
=> ( eigen__18 = eigen__28 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__13 )
=> ( eigen__2 @ eigen__13 ) )
=> ~ ( ~ ( eigen__0 @ eigen__14 )
=> ( eigen__2 @ eigen__14 ) ) )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__76 = eigen__93 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__107 )
=> ( eigen__2 @ eigen__107 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__107 != X1 ) )
=> ( eigen__107 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__98 )
=> ( eigen__2 @ eigen__98 ) )
=> ~ ( ~ ( eigen__0 @ eigen__102 )
=> ( eigen__2 @ eigen__102 ) ) )
=> ( eigen__98 != eigen__102 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( eigen__57 = eigen__71 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__18 = eigen__28 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__98 = eigen__102 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__76 )
=> ( eigen__2 @ eigen__76 ) )
=> ~ ( ~ ( eigen__0 @ eigen__93 )
=> ( eigen__2 @ eigen__93 ) ) )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__57 )
=> ( eigen__2 @ eigen__57 ) )
=> ~ ( ~ ( eigen__0 @ eigen__71 )
=> ( eigen__2 @ eigen__71 ) ) )
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__32 )
=> ( eigen__2 @ eigen__32 ) )
=> ~ ( ~ ( eigen__0 @ eigen__53 )
=> ( eigen__2 @ eigen__53 ) ) )
=> ( eigen__32 != eigen__53 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ! [X1: $i] :
( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ( ~ ( eigen__1 @ X1 )
=> ( eigen__3 @ X1 ) ) )
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__133 )
=> ( eigen__2 @ eigen__133 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__133 != X1 ) )
=> ( eigen__133 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__133 = eigen__137 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP16
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i > $i] :
~ ( ! [X2: $i] :
( ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) )
=> ( ~ ( eigen__1 @ ( X1 @ X2 ) )
=> ( eigen__3 @ ( X1 @ X2 ) ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) )
=> ~ ( ~ ( eigen__0 @ X3 )
=> ( eigen__2 @ X3 ) ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP20
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__57 )
=> ( eigen__2 @ eigen__57 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__57 != X1 ) )
=> ( eigen__57 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP22
=> ( eigen__32 = eigen__53 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( eigen__32 = eigen__53 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ sP13
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP5
=> ( eigen__143 = eigen__165 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__18 )
=> ( eigen__2 @ eigen__18 ) )
=> ~ ( ~ ( eigen__0 @ eigen__28 )
=> ( eigen__2 @ eigen__28 ) ) )
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__143 = eigen__165 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__13 )
=> ( eigen__2 @ eigen__13 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__13 != X1 ) )
=> ( eigen__13 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ sP10
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__133 )
=> ( eigen__2 @ eigen__133 ) )
=> ~ ( ~ ( eigen__0 @ eigen__137 )
=> ( eigen__2 @ eigen__137 ) ) )
=> ~ sP26 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(def_in,definition,
( in
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_is_a,definition,
( is_a
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : $false ) ) ).
thf(def_unord_pair,definition,
( unord_pair
= ( ^ [X1: $i,X2: $i,X3: $i] :
( ( X3 = X1 )
| ( X3 = X2 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).
thf(def_union,definition,
( union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_excl_union,definition,
( excl_union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) )
| ( ( (~) @ ( X1 @ X3 ) )
& ( X2 @ X3 ) ) ) ) ) ).
thf(def_intersection,definition,
( intersection
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_setminus,definition,
( setminus
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
& ( (~) @ ( X2 @ X3 ) ) ) ) ) ).
thf(def_complement,definition,
( complement
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_disjoint,definition,
( disjoint
= ( ^ [X1: $i > $o,X2: $i > $o] :
( ( intersection @ X1 @ X2 )
= emptyset ) ) ) ).
thf(def_subset,definition,
( subset
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X3 )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_meets,definition,
( meets
= ( ^ [X1: $i > $o,X2: $i > $o] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ).
thf(def_misses,definition,
( misses
= ( ^ [X1: $i > $o,X2: $i > $o] :
( (~)
@ ? [X3: $i] :
( ( X1 @ X3 )
& ( X2 @ X3 ) ) ) ) ) ).
thf(def_is_function,definition,
( is_function
= ( ^ [X1: $i > $o,X2: $i > $i,X3: $i > $o] :
! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X4 )
@ ( X3 @ ( X2 @ X4 ) ) ) ) ) ).
thf(def_injection,definition,
( injection
= ( ^ [X1: $i > $o,X2: $i > $i,X3: $i > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( is_function @ X1 @ X2 @ X3 )
@ ! [X4: $i,X5: $i] :
( ^ [X6: $o,X7: $o] :
( X6
=> X7 )
@ ( ( X1 @ X4 )
& ( X1 @ X5 )
& ( ( X2 @ X4 )
= ( X2 @ X5 ) ) )
@ ( X4 = X5 ) ) ) ) ) ).
thf(def_surjection,definition,
( surjection
= ( ^ [X1: $i > $o,X2: $i > $i,X3: $i > $o] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( is_function @ X1 @ X2 @ X3 )
@ ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X3 @ X4 )
@ ? [X5: $i] :
( ( X1 @ X5 )
& ( ( X2 @ X5 )
= X4 ) ) ) ) ) ) ).
thf(def_bijection,definition,
( bijection
= ( ^ [X1: $i > $o,X2: $i > $i,X3: $i > $o] :
( ( injection @ X1 @ X2 @ X3 )
& ( surjection @ X1 @ X2 @ X3 ) ) ) ) ).
thf(def_equinumerous,definition,
( equinumerous
= ( ^ [X1: $i > $o,X2: $i > $o] :
? [X3: $i > $i] : ( bijection @ X1 @ X3 @ X2 ) ) ) ).
thf(def_embedding,definition,
( embedding
= ( ^ [X1: $i > $o,X2: $i > $o] :
? [X3: $i > $i] : ( injection @ X1 @ X3 @ X2 ) ) ) ).
thf(prove,conjecture,
! [X1: $i > $o,X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ~ ( ~ ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X1 @ X6 )
=> ~ ( X1 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X6 )
=> ~ ! [X7: $i] :
( ( X1 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) )
=> ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X3 @ X6 )
=> ~ ( X3 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) ) )
=> ( ( ^ [X5: $i] :
~ ( ( X2 @ X5 )
=> ~ ( X4 @ X5 ) ) )
!= ( ^ [X5: $i] : $false ) ) )
=> ~ ! [X5: $i > $i] :
~ ( ! [X6: $i] :
( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ( ~ ( X2 @ ( X5 @ X6 ) )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( ~ ( X1 @ X7 )
=> ( X3 @ X7 ) ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ~ ( ~ ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X1 @ X6 )
=> ~ ( X1 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X6 )
=> ~ ! [X7: $i] :
( ( X1 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) )
=> ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X3 @ X6 )
=> ~ ( X3 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) ) )
=> ( ( ^ [X5: $i] :
~ ( ( X2 @ X5 )
=> ~ ( X4 @ X5 ) ) )
!= ( ^ [X5: $i] : $false ) ) )
=> ~ ! [X5: $i > $i] :
~ ( ! [X6: $i] :
( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ( ~ ( X2 @ ( X5 @ X6 ) )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( ~ ( X1 @ X7 )
=> ( X3 @ X7 ) ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(h2,assumption,
~ ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ~ ( ~ ! [X4: $i > $i] :
( ( ! [X5: $i] :
( ( eigen__0 @ X5 )
=> ( X1 @ ( X4 @ X5 ) ) )
=> ! [X5: $i,X6: $i] :
( ~ ( ~ ( ( eigen__0 @ X5 )
=> ~ ( eigen__0 @ X6 ) )
=> ( ( X4 @ X5 )
!= ( X4 @ X6 ) ) )
=> ( X5 = X6 ) ) )
=> ~ ( ! [X5: $i] :
( ( eigen__0 @ X5 )
=> ( X1 @ ( X4 @ X5 ) ) )
=> ! [X5: $i] :
( ( X1 @ X5 )
=> ~ ! [X6: $i] :
( ( eigen__0 @ X6 )
=> ( ( X4 @ X6 )
!= X5 ) ) ) ) )
=> ! [X4: $i > $i] :
( ( ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) )
=> ! [X5: $i,X6: $i] :
( ~ ( ~ ( ( X2 @ X5 )
=> ~ ( X2 @ X6 ) )
=> ( ( X4 @ X5 )
!= ( X4 @ X6 ) ) )
=> ( X5 = X6 ) ) )
=> ~ ( ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) )
=> ! [X5: $i] :
( ( X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X6 )
=> ( ( X4 @ X6 )
!= X5 ) ) ) ) ) )
=> ( ( ^ [X4: $i] :
~ ( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) ) )
!= ( ^ [X4: $i] : $false ) ) )
=> ~ ! [X4: $i > $i] :
~ ( ! [X5: $i] :
( ( ~ ( eigen__0 @ X5 )
=> ( X2 @ X5 ) )
=> ( ~ ( X1 @ ( X4 @ X5 ) )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ! [X5: $i,X6: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X5 )
=> ( X2 @ X5 ) )
=> ~ ( ~ ( eigen__0 @ X6 )
=> ( X2 @ X6 ) ) )
=> ( ( X4 @ X5 )
!= ( X4 @ X6 ) ) )
=> ( X5 = X6 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ~ ( ~ ! [X3: $i > $i] :
( ( ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ ( X3 @ X4 ) ) )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( eigen__0 @ X4 )
=> ~ ( eigen__0 @ X5 ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) )
=> ( X4 = X5 ) ) )
=> ~ ( ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( eigen__1 @ X4 )
=> ~ ! [X5: $i] :
( ( eigen__0 @ X5 )
=> ( ( X3 @ X5 )
!= X4 ) ) ) ) )
=> ! [X3: $i > $i] :
( ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) )
=> ( X4 = X5 ) ) )
=> ~ ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X5 )
=> ( ( X3 @ X5 )
!= X4 ) ) ) ) ) )
=> ( ( ^ [X3: $i] :
~ ( ( eigen__1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
!= ( ^ [X3: $i] : $false ) ) )
=> ~ ! [X3: $i > $i] :
~ ( ! [X4: $i] :
( ( ~ ( eigen__0 @ X4 )
=> ( X1 @ X4 ) )
=> ( ~ ( eigen__1 @ ( X3 @ X4 ) )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ( ~ ( eigen__0 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) )
=> ( X4 = X5 ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i > $o] :
( ~ ( ~ ( ~ ! [X2: $i > $i] :
( ( ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i,X4: $i] :
( ~ ( ~ ( ( eigen__0 @ X3 )
=> ~ ( eigen__0 @ X4 ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( eigen__1 @ X3 )
=> ~ ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( ( X2 @ X4 )
!= X3 ) ) ) ) )
=> ! [X2: $i > $i] :
( ( ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i,X4: $i] :
( ~ ( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( eigen__2 @ X4 )
=> ( ( X2 @ X4 )
!= X3 ) ) ) ) ) )
=> ( ( ^ [X2: $i] :
~ ( ( eigen__1 @ X2 )
=> ~ ( X1 @ X2 ) ) )
!= ( ^ [X2: $i] : $false ) ) )
=> ~ ! [X2: $i > $i] :
~ ( ! [X3: $i] :
( ( ~ ( eigen__0 @ X3 )
=> ( eigen__2 @ X3 ) )
=> ( ~ ( eigen__1 @ ( X2 @ X3 ) )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ! [X3: $i,X4: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X3 )
=> ( eigen__2 @ X3 ) )
=> ~ ( ~ ( eigen__0 @ X4 )
=> ( eigen__2 @ X4 ) ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) )
=> ( X3 = X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__0 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) )
=> ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__3 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) ) )
=> ( ( ^ [X1: $i] :
~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__3 @ X1 ) ) )
!= ( ^ [X1: $i] : $false ) ) )
=> ~ sP28 ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ ( ~ ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__0 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) )
=> ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__3 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) ) )
=> ( ( ^ [X1: $i] :
~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__3 @ X1 ) ) )
!= ( ^ [X1: $i] : $false ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP28,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ~ ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__0 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) )
=> ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__3 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
( ( ^ [X1: $i] :
~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__3 @ X1 ) ) )
= ( ^ [X1: $i] : $false ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__0 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__3 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ( ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ ( eigen__4 @ X1 ) ) )
=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( ( eigen__4 @ X1 )
!= ( eigen__4 @ X2 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ ( eigen__4 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( ( eigen__4 @ X2 )
!= X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
( ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ ( eigen__4 @ X1 ) ) )
=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( ( eigen__4 @ X1 )
!= ( eigen__4 @ X2 ) ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
( ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ ( eigen__4 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( ( eigen__4 @ X2 )
!= X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ! [X1: $i] :
( ( eigen__0 @ X1 )
=> ( eigen__1 @ ( eigen__4 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h16,assumption,
! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__0 @ X2 ) )
=> ( ( eigen__4 @ X1 )
!= ( eigen__4 @ X2 ) ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( sP5
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( sP34
| ~ sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( sP34
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP11
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__165]) ).
thf(5,plain,
( sP23
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__143]) ).
thf(6,plain,
( sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP28
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,h7]) ).
thf(h17,assumption,
! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( ( eigen__4 @ X2 )
!= X1 ) ) ),
introduced(assumption,[]) ).
thf(h18,assumption,
~ ( ( eigen__0 @ eigen__72 )
=> ( eigen__1 @ ( eigen__4 @ eigen__72 ) ) ),
introduced(assumption,[]) ).
thf(h19,assumption,
eigen__0 @ eigen__72,
introduced(assumption,[]) ).
thf(h20,assumption,
~ ( eigen__1 @ ( eigen__4 @ eigen__72 ) ),
introduced(assumption,[]) ).
thf(h21,assumption,
~ ( ( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__73 @ X1 ) ) )
=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__73 @ X1 )
!= ( eigen__73 @ X2 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__73 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__3 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( ( eigen__73 @ X2 )
!= X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h22,assumption,
( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__73 @ X1 ) ) )
=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__73 @ X1 )
!= ( eigen__73 @ X2 ) ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h23,assumption,
( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__73 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__3 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( ( eigen__73 @ X2 )
!= X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h24,assumption,
~ ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__73 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h25,assumption,
! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__73 @ X1 )
!= ( eigen__73 @ X2 ) ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h26,assumption,
~ ( ( eigen__2 @ eigen__104 )
=> ( eigen__3 @ ( eigen__73 @ eigen__104 ) ) ),
introduced(assumption,[]) ).
thf(h27,assumption,
eigen__2 @ eigen__104,
introduced(assumption,[]) ).
thf(h28,assumption,
~ ( eigen__3 @ ( eigen__73 @ eigen__104 ) ),
introduced(assumption,[]) ).
thf(h29,assumption,
! [X1: $i] :
( ( eigen__3 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( ( eigen__73 @ X2 )
!= X1 ) ) ),
introduced(assumption,[]) ).
thf(9,plain,
( sP39
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP1
| ~ sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP1
| ~ sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP25
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__137]) ).
thf(13,plain,
( sP23
| ~ sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__133]) ).
thf(14,plain,
( sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP28
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h24,h27,h28,h26,h24,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[9,10,11,12,13,14,15,h7]) ).
thf(17,plain,
( sP10
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP38
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP38
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP15
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__128]) ).
thf(21,plain,
( sP23
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__107]) ).
thf(22,plain,
( sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP28
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h29,h27,h28,h26,h24,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[17,18,19,20,21,22,23,h7]) ).
thf(25,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h27,h28,h26,h24,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h24]),tab_imp(discharge,[h29])],[h23,16,24,h24,h29]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h26,h24,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,25,h27,h28]) ).
thf(27,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__104)],[h24,26,h26]) ).
thf(h30,assumption,
~ ( ( eigen__2 @ eigen__95 )
=> ( eigen__3 @ ( eigen__73 @ eigen__95 ) ) ),
introduced(assumption,[]) ).
thf(h31,assumption,
eigen__2 @ eigen__95,
introduced(assumption,[]) ).
thf(h32,assumption,
~ ( eigen__3 @ ( eigen__73 @ eigen__95 ) ),
introduced(assumption,[]) ).
thf(28,plain,
( sP16
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP27
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( sP27
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP2
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__102]) ).
thf(32,plain,
( sP23
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__98]) ).
thf(33,plain,
( sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP28
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h31,h32,h30,h24,h25,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[28,29,30,31,32,33,34,h7]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h30,h24,h25,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h31,h32])],[h30,35,h31,h32]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h24,h25,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__95)],[h24,36,h30]) ).
thf(38,plain,
( sP20
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( sP29
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP29
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( sP3
| ~ sP29 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__93]) ).
thf(42,plain,
( sP23
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__76]) ).
thf(43,plain,
( sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP28
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(45,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h29,h25,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[38,39,40,41,42,43,44,h7]) ).
thf(46,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h25,h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h24]),tab_imp(discharge,[h29])],[h23,37,45,h24,h29]) ).
thf(47,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h22,h23,h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h24]),tab_imp(discharge,[h25])],[h22,27,46,h24,h25]) ).
thf(48,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,47,h22,h23]) ).
thf(49,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h19,h20,h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__73)],[h11,48,h21]) ).
thf(50,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h18,h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h18,49,h19,h20]) ).
thf(51,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h15,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__72)],[h15,50,h18]) ).
thf(h33,assumption,
~ ( ( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__5 @ X1 ) ) )
=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__5 @ X1 )
!= ( eigen__5 @ X2 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__5 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__3 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( ( eigen__5 @ X2 )
!= X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h34,assumption,
( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__5 @ X1 ) ) )
=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__5 @ X1 )
!= ( eigen__5 @ X2 ) ) )
=> ( X1 = X2 ) ) ),
introduced(assumption,[]) ).
thf(h35,assumption,
( ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__5 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__3 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( ( eigen__5 @ X2 )
!= X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h36,assumption,
~ ! [X1: $i] :
( ( eigen__2 @ X1 )
=> ( eigen__3 @ ( eigen__5 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h37,assumption,
! [X1: $i,X2: $i] :
( ~ ( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__5 @ X1 )
!= ( eigen__5 @ X2 ) ) )
=> ( X1 = X2 ) ),
introduced(assumption,[]) ).
thf(h38,assumption,
~ ( ( eigen__2 @ eigen__29 )
=> ( eigen__3 @ ( eigen__5 @ eigen__29 ) ) ),
introduced(assumption,[]) ).
thf(h39,assumption,
eigen__2 @ eigen__29,
introduced(assumption,[]) ).
thf(h40,assumption,
~ ( eigen__3 @ ( eigen__5 @ eigen__29 ) ),
introduced(assumption,[]) ).
thf(h41,assumption,
! [X1: $i] :
( ( eigen__3 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( ( eigen__5 @ X2 )
!= X1 ) ) ),
introduced(assumption,[]) ).
thf(h42,assumption,
~ ( ( eigen__2 @ eigen__54 )
=> ( eigen__3 @ ( eigen__5 @ eigen__54 ) ) ),
introduced(assumption,[]) ).
thf(h43,assumption,
eigen__2 @ eigen__54,
introduced(assumption,[]) ).
thf(h44,assumption,
~ ( eigen__3 @ ( eigen__5 @ eigen__54 ) ),
introduced(assumption,[]) ).
thf(52,plain,
( sP21
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( sP4
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( sP4
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(55,plain,
( sP30
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__71]) ).
thf(56,plain,
( sP23
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__57]) ).
thf(57,plain,
( sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(58,plain,
( ~ sP28
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(59,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h43,h44,h42,h36,h39,h40,h38,h36,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[52,53,54,55,56,57,58,h7]) ).
thf(60,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h42,h36,h39,h40,h38,h36,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h43,h44])],[h42,59,h43,h44]) ).
thf(61,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h36,h39,h40,h38,h36,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h42]),tab_negall(eigenvar,eigen__54)],[h36,60,h42]) ).
thf(62,plain,
( sP22
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(63,plain,
( sP31
| ~ sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(64,plain,
( sP31
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(65,plain,
( sP7
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__53]) ).
thf(66,plain,
( sP23
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__32]) ).
thf(67,plain,
( sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(68,plain,
( ~ sP28
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(69,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h41,h39,h40,h38,h36,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[62,63,64,65,66,67,68,h7]) ).
thf(70,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h39,h40,h38,h36,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h36]),tab_imp(discharge,[h41])],[h35,61,69,h36,h41]) ).
thf(71,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h38,h36,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h39,h40])],[h38,70,h39,h40]) ).
thf(72,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h36,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h38]),tab_negall(eigenvar,eigen__29)],[h36,71,h38]) ).
thf(h45,assumption,
~ ( ( eigen__2 @ eigen__15 )
=> ( eigen__3 @ ( eigen__5 @ eigen__15 ) ) ),
introduced(assumption,[]) ).
thf(h46,assumption,
eigen__2 @ eigen__15,
introduced(assumption,[]) ).
thf(h47,assumption,
~ ( eigen__3 @ ( eigen__5 @ eigen__15 ) ),
introduced(assumption,[]) ).
thf(73,plain,
( sP35
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(74,plain,
( sP12
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(75,plain,
( sP12
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(76,plain,
( sP6
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__28]) ).
thf(77,plain,
( sP23
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).
thf(78,plain,
( sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(79,plain,
( ~ sP28
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(80,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h46,h47,h45,h36,h37,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[73,74,75,76,77,78,79,h7]) ).
thf(81,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h45,h36,h37,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h46,h47])],[h45,80,h46,h47]) ).
thf(82,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h36,h37,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__15)],[h36,81,h45]) ).
thf(83,plain,
( sP13
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(84,plain,
( sP33
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(85,plain,
( sP33
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(86,plain,
( sP37
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).
thf(87,plain,
( sP23
| ~ sP37 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(88,plain,
( sP24
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(89,plain,
( ~ sP28
| ~ sP24 ),
inference(all_rule,[status(thm)],[]) ).
thf(90,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h41,h37,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[83,84,85,86,87,88,89,h7]) ).
thf(91,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h37,h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h36]),tab_imp(discharge,[h41])],[h35,82,90,h36,h41]) ).
thf(92,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h34,h35,h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h36]),tab_imp(discharge,[h37])],[h34,72,91,h36,h37]) ).
thf(93,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h33,h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,92,h34,h35]) ).
thf(94,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h17,h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h33]),tab_negall(eigenvar,eigen__5)],[h11,93,h33]) ).
thf(95,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h16,h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h17])],[h14,51,94,h15,h17]) ).
thf(96,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h13,h14,h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h16])],[h13,8,95,h15,h16]) ).
thf(97,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,96,h13,h14]) ).
thf(98,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__4)],[h10,97,h12]) ).
thf(99,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,98,h10,h11]) ).
thf(100,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,99,h8,h9]) ).
thf(101,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,100,h6,h7]) ).
thf(102,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__3)],[h4,101,h5]) ).
thf(103,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,102,h4]) ).
thf(104,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,103,h3]) ).
thf(105,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,104,h2]) ).
thf(106,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[105,h0]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ~ ( ~ ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X1 @ X6 )
=> ~ ( X1 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X6 )
=> ~ ! [X7: $i] :
( ( X1 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) )
=> ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X3 @ X6 )
=> ~ ( X3 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) ) )
=> ( ( ^ [X5: $i] :
~ ( ( X2 @ X5 )
=> ~ ( X4 @ X5 ) ) )
!= ( ^ [X5: $i] : $false ) ) )
=> ~ ! [X5: $i > $i] :
~ ( ! [X6: $i] :
( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ( ~ ( X2 @ ( X5 @ X6 ) )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( ~ ( X1 @ X7 )
=> ( X3 @ X7 ) ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[105,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SEV420^1 : TPTP v9.2.0. Released v4.1.0.
% 0.07/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 19:04:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 21.24/21.45 % SZS status Theorem
% 21.24/21.45 % Mode: cade22grackle2x798d
% 21.24/21.45 % Steps: 14111
% 21.24/21.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------