## TSTP Solution File: SEV261^5 by Satallax---3.5

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV261^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n020.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
% DateTime : Tue Mar 30 22:05:13 EDT 2021

% Result   : Theorem 26.02s
% Output   : Proof 26.02s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  179
% Syntax   : Number of formulae    :  197 (  23 unt;  13 typ;  12 def)
%            Number of atoms       :  713 ( 154 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  722 ( 301   ~; 102   |;   0   &; 104   @)
%                                         (  81 <=>; 134  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   67 (  67   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   98 (  96 usr;  89 con; 0-2 aty)
%            Number of variables   :  182 ( 127   ^  55   !;   0   ?; 182   :)

%------------------------------------------------------------------------------
thf(ty_a,type,
a: \$tType ).

thf(ty_eigen__14,type,
eigen__14: a > \$o ).

thf(ty_eigen__6,type,
eigen__6: a > \$o ).

thf(ty_eigen__2,type,
eigen__2: a > \$o ).

thf(ty_eigen__7,type,
eigen__7: a ).

thf(ty_eigen__1,type,
eigen__1: a > \$o ).

thf(ty_eigen__0,type,
eigen__0: a > \$o ).

thf(ty_eigen__4,type,
eigen__4: a ).

thf(ty_eigen__5,type,
eigen__5: ( a > \$o ) > \$o ).

thf(ty_eigen__11,type,
eigen__11: a > \$o ).

thf(ty_eigen__3,type,
eigen__3: a ).

thf(ty_eigen__8,type,
eigen__8: a ).

thf(ty_eigen__18,type,
eigen__18: a > \$o ).

thf(h0,assumption,
! [X1: ( a > \$o ) > \$o,X2: a > \$o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).

thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: a > \$o] :
~ ( ( X1
= ( ^ [X2: a] : \$false ) )
=> ( ( X1
!= ( ^ [X2: a] : \$false ) )
=> ( X1
= ( ^ [X2: a] : ~ \$false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).

thf(h1,assumption,
! [X1: a > \$o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).

thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__1
@ ^ [X1: a] :
( ( eigen__2 @ X1 )
!= \$false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: a > \$o] :
~ ! [X2: a > \$o] :
( ~ ( ~ ( ( ( eigen__0
!= ( ^ [X3: a] : \$false ) )
=> ( eigen__0
= ( ^ [X3: a] : ~ \$false ) ) )
=> ~ ( ( X1
!= ( ^ [X3: a] : \$false ) )
=> ( X1
= ( ^ [X3: a] : ~ \$false ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ( ( eigen__0 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : \$false ) )
=> ( X2
= ( ^ [X3: a] : ~ \$false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: a > \$o] :
~ ( ~ ( ! [X2: a > \$o] :
( ( eigen__5 @ X2 )
=> ( ( X2
!= ( ^ [X3: a] : \$false ) )
=> ( X2
= ( ^ [X3: a] : ~ \$false ) ) ) )
=> ( X1
!= ( ^ [X2: a] :
~ ! [X3: a > \$o] :
( ( eigen__5 @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
=> ( ( X1
!= ( ^ [X2: a] : \$false ) )
=> ( X1
= ( ^ [X2: a] : ~ \$false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).

thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__0
@ ^ [X1: a > \$o] :
~ ( ( X1
= ( ^ [X2: a] : ~ \$false ) )
=> ( ( X1
!= ( ^ [X2: a] : \$false ) )
=> ( X1
= ( ^ [X2: a] : ~ \$false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).

thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: a > \$o] :
~ ! [X2: a > \$o,X3: a > \$o] :
( ~ ( ~ ( ( ( X1
!= ( ^ [X4: a] : \$false ) )
=> ( X1
= ( ^ [X4: a] : ~ \$false ) ) )
=> ~ ( ( X2
!= ( ^ [X4: a] : \$false ) )
=> ( X2
= ( ^ [X4: a] : ~ \$false ) ) ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( ( X3
!= ( ^ [X4: a] : \$false ) )
=> ( X3
= ( ^ [X4: a] : ~ \$false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(eigendef_eigen__18,definition,
( eigen__18
= ( eps__0
@ ^ [X1: a > \$o] :
~ ( ( eigen__5 @ X1 )
=> ~ ( X1 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__18])]) ).

thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: a] :
( ( eigen__6 @ X1 )
!= ( ~ \$false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).

thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: a > \$o] :
~ ( ~ ( ~ ( ( ( eigen__0
!= ( ^ [X2: a] : \$false ) )
=> ( eigen__0
= ( ^ [X2: a] : ~ \$false ) ) )
=> ~ ( ( eigen__1
!= ( ^ [X2: a] : \$false ) )
=> ( eigen__1
= ( ^ [X2: a] : ~ \$false ) ) ) )
=> ( X1
!= ( ^ [X2: a] :
~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__1 @ X2 ) ) ) ) )
=> ( ( X1
!= ( ^ [X2: a] : \$false ) )
=> ( X1
= ( ^ [X2: a] : ~ \$false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__1
@ ^ [X1: a] :
( ( eigen__2 @ X1 )
!= ( ~ \$false ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__1
@ ^ [X1: a] :
( ( eigen__6 @ X1 )
!= \$false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).

thf(h2,assumption,
! [X1: ( ( a > \$o ) > \$o ) > \$o,X2: ( a > \$o ) > \$o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).

thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__2
@ ^ [X1: ( a > \$o ) > \$o] :
~ ! [X2: a > \$o] :
( ~ ( ! [X3: a > \$o] :
( ( X1 @ X3 )
=> ( ( X3
!= ( ^ [X4: a] : \$false ) )
=> ( X3
= ( ^ [X4: a] : ~ \$false ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > \$o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : \$false ) )
=> ( X2
= ( ^ [X3: a] : ~ \$false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).

thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: a > \$o] :
( ( X1
= ( ^ [X2: a] : \$false ) )
=> ( ( X1
!= ( ^ [X2: a] : \$false ) )
=> ( X1
= ( ^ [X2: a] : ~ \$false ) ) ) )
=> ~ ! [X1: a > \$o] :
( ( X1
= ( ^ [X2: a] : ~ \$false ) )
=> ( ( X1
!= ( ^ [X2: a] : \$false ) )
=> ( X1
= ( ^ [X2: a] : ~ \$false ) ) ) ) )
=> ~ ! [X1: ( a > \$o ) > \$o,X2: a > \$o] :
( ~ ( ! [X3: a > \$o] :
( ( X1 @ X3 )
=> ( ( X3
!= ( ^ [X4: a] : \$false ) )
=> ( X3
= ( ^ [X4: a] : ~ \$false ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > \$o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : \$false ) )
=> ( X2
= ( ^ [X3: a] : ~ \$false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
( sP2
<=> ! [X1: a > \$o] :
( ( eigen__5 @ X1 )
=> ~ ( X1 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
( sP3
<=> ( ( eigen__6 @ eigen__7 )
= \$false ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
( sP4
<=> ( eigen__18
= ( ^ [X1: a] : ~ \$false ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
( sP5
<=> ( eigen__0
= ( ^ [X1: a] : ~ \$false ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
( sP6
<=> ! [X1: a > \$o] :
( ~ ( ~ ( ( ( eigen__0
!= ( ^ [X2: a] : \$false ) )
=> sP5 )
=> ~ ( ( eigen__1
!= ( ^ [X2: a] : \$false ) )
=> ( eigen__1
= ( ^ [X2: a] : ~ \$false ) ) ) )
=> ( X1
!= ( ^ [X2: a] :
~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__1 @ X2 ) ) ) ) )
=> ( ( X1
!= ( ^ [X2: a] : \$false ) )
=> ( X1
= ( ^ [X2: a] : ~ \$false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
( sP7
<=> ( ( eigen__2 @ eigen__4 )
= ( ~ \$false ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
( sP8
<=> ( eigen__2 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
( sP9
<=> ( ( eigen__2
!= ( ^ [X1: a] : \$false ) )
=> ( eigen__2
= ( ^ [X1: a] : ~ \$false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ eigen__3 )
=> ~ ( eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
( sP11
<=> ( eigen__11
= ( ^ [X1: a] : \$false ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
( sP12
<=> ( eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
( sP13
<=> ( eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
( sP14
<=> ( eigen__5 @ eigen__18 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( eigen__2 @ X1 )
= ( ~ \$false ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
( sP16
<=> ( eigen__6
= ( ^ [X1: a] : \$false ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
( sP17
<=> ( eigen__1
= ( ^ [X1: a] : ~ \$false ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
( sP18
<=> ! [X1: a > \$o] :
( ( eigen__5 @ X1 )
=> ~ ( X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
( sP19
<=> ( eigen__6 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
( sP20
<=> ! [X1: ( a > \$o ) > \$o,X2: a > \$o] :
( ~ ( ! [X3: a > \$o] :
( ( X1 @ X3 )
=> ( ( X3
!= ( ^ [X4: a] : \$false ) )
=> ( X3
= ( ^ [X4: a] : ~ \$false ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ! [X4: a > \$o] :
( ( X1 @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : \$false ) )
=> ( X2
= ( ^ [X3: a] : ~ \$false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
( sP21
<=> \$false ),
introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
( sP22
<=> ( eigen__6
= ( ^ [X1: a] : ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
( sP23
<=> ! [X1: a] :
( ( eigen__2 @ X1 )
= sP21 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
( sP24
<=> ( eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
( sP25
<=> ( sP13
= ( ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
( sP26
<=> ( ( eigen__0 @ eigen__3 )
= sP21 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
( sP27
<=> ! [X1: a] :
( ( eigen__6 @ X1 )
= ( ~ ! [X2: a > \$o] :
( ( eigen__5 @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
( sP28
<=> ( eigen__0
= ( ^ [X1: a] : sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
( sP29
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
= ( ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
( sP30
<=> ! [X1: a > \$o] :
( ~ ( ! [X2: a > \$o] :
( ( eigen__5 @ X2 )
=> ( ( X2
!= ( ^ [X3: a] : sP21 ) )
=> ( X2
= ( ^ [X3: a] : ~ sP21 ) ) ) )
=> ( X1
!= ( ^ [X2: a] :
~ ! [X3: a > \$o] :
( ( eigen__5 @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
=> ( ( X1
!= ( ^ [X2: a] : sP21 ) )
=> ( X1
= ( ^ [X2: a] : ~ sP21 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
( sP31
<=> ( sP19
= ( ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
( sP32
<=> ! [X1: a] :
( ( eigen__18 @ X1 )
= sP21 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
( sP33
<=> ( sP8 = sP21 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
( sP34
<=> ( ~ sP16
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
( sP35
<=> ( eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
( sP36
<=> ( ( eigen__1 @ eigen__3 )
= sP21 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
( sP37
<=> ( sP8
= ( ~ sP10 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
( sP38
<=> ! [X1: a > \$o,X2: a > \$o] :
( ~ ( ~ ( ( ~ sP28
=> sP5 )
=> ~ ( ( X1
!= ( ^ [X3: a] : sP21 ) )
=> ( X1
= ( ^ [X3: a] : ~ sP21 ) ) ) )
=> ( X2
!= ( ^ [X3: a] :
~ ( ( eigen__0 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) )
=> ( ( X2
!= ( ^ [X3: a] : sP21 ) )
=> ( X2
= ( ^ [X3: a] : ~ sP21 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
( sP39
<=> ( sP11
=> ( ~ sP11
=> ( eigen__11
= ( ^ [X1: a] : ~ sP21 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
( sP40
<=> ( sP12
= ( ~ sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
( sP41
<=> ( ( eigen__18 @ eigen__7 )
= sP21 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
( sP42
<=> ( ~ ( ! [X1: a > \$o] :
( ( eigen__5 @ X1 )
=> ( ( X1
!= ( ^ [X2: a] : sP21 ) )
=> ( X1
= ( ^ [X2: a] : ~ sP21 ) ) ) )
=> ( eigen__6
!= ( ^ [X1: a] :
~ ! [X2: a > \$o] :
( ( eigen__5 @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) )
=> sP34 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
( sP43
<=> ( ! [X1: a > \$o] :
( ( eigen__5 @ X1 )
=> ( ( X1
!= ( ^ [X2: a] : sP21 ) )
=> ( X1
= ( ^ [X2: a] : ~ sP21 ) ) ) )
=> ( eigen__6
!= ( ^ [X1: a] :
~ ! [X2: a > \$o] :
( ( eigen__5 @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
( sP44
<=> ( ( eigen__18
!= ( ^ [X1: a] : sP21 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
( sP45
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
= sP21 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
( sP46
<=> ( eigen__0 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
( sP47
<=> ( eigen__18 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
( sP48
<=> ( eigen__2
= ( ^ [X1: a] : sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
( sP49
<=> ( eigen__6
= ( ^ [X1: a] :
~ ! [X2: a > \$o] :
( ( eigen__5 @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
( sP50
<=> ( sP24
= ( ~ ( sP35
=> ~ sP13 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
( sP51
<=> ( sP14
=> sP44 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
( sP52
<=> ( ~ ( ( ~ sP28
=> sP5 )
=> ~ ( ( eigen__1
!= ( ^ [X1: a] : sP21 ) )
=> sP17 ) )
=> ( eigen__2
!= ( ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
( sP53
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
( sP54
<=> ( ( ~ sP28
=> sP5 )
=> ~ ( ( eigen__1
!= ( ^ [X1: a] : sP21 ) )
=> sP17 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
( sP55
<=> ( eigen__5
@ ^ [X1: a] : ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
( sP56
<=> ! [X1: a] :
( ( eigen__6 @ X1 )
= ( ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
( sP57
<=> ( sP14
=> ~ sP47 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
( sP58
<=> ! [X1: a > \$o] :
( ( X1
= ( ^ [X2: a] : ~ sP21 ) )
=> ( ( X1
!= ( ^ [X2: a] : sP21 ) )
=> ( X1
= ( ^ [X2: a] : ~ sP21 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(sP59,plain,
( sP59
<=> ( sP35
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).

thf(sP60,plain,
( sP60
<=> ( eigen__1
= ( ^ [X1: a] : sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).

thf(sP61,plain,
( sP61
<=> ( ~ sP60
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).

thf(sP62,plain,
( sP62
<=> ! [X1: a > \$o,X2: a > \$o,X3: a > \$o] :
( ~ ( ~ ( ( ( X1
!= ( ^ [X4: a] : sP21 ) )
=> ( X1
= ( ^ [X4: a] : ~ sP21 ) ) )
=> ~ ( ( X2
!= ( ^ [X4: a] : sP21 ) )
=> ( X2
= ( ^ [X4: a] : ~ sP21 ) ) ) )
=> ( X3
!= ( ^ [X4: a] :
~ ( ( X1 @ X4 )
=> ~ ( X2 @ X4 ) ) ) ) )
=> ( ( X3
!= ( ^ [X4: a] : sP21 ) )
=> ( X3
= ( ^ [X4: a] : ~ sP21 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).

thf(sP63,plain,
( sP63
<=> ( sP19
= ( ~ sP18 ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).

thf(sP64,plain,
( sP64
<=> ( eigen__18
= ( ^ [X1: a] : sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).

thf(sP65,plain,
( sP65
<=> ! [X1: a] :
( ( eigen__2 @ X1 )
= ( ~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).

thf(sP66,plain,
( sP66
<=> ( ~ sP1
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).

thf(sP67,plain,
( sP67
<=> ! [X1: a] :
( ( eigen__6 @ X1 )
= sP21 ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).

thf(sP68,plain,
( sP68
<=> ( eigen__14
= ( ^ [X1: a] : ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).

thf(sP69,plain,
( sP69
<=> ( ~ sP52
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).

thf(sP70,plain,
( sP70
<=> ( eigen__2
= ( ^ [X1: a] :
~ ( ( eigen__0 @ X1 )
=> ~ ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).

thf(sP71,plain,
( sP71
<=> ! [X1: a] :
( ( eigen__1 @ X1 )
= ( ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).

thf(sP72,plain,
( sP72
<=> ! [X1: a > \$o] :
( ( X1
= ( ^ [X2: a] : sP21 ) )
=> ( ( X1
!= ( ^ [X2: a] : sP21 ) )
=> ( X1
= ( ^ [X2: a] : ~ sP21 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).

thf(sP73,plain,
( sP73
<=> ( ~ sP28
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).

thf(sP74,plain,
( sP74
<=> ( eigen__2
= ( ^ [X1: a] : ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).

thf(sP75,plain,
( sP75
<=> ! [X1: a > \$o] :
( ( eigen__5 @ X1 )
=> ( ( X1
!= ( ^ [X2: a] : sP21 ) )
=> ( X1
= ( ^ [X2: a] : ~ sP21 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).

thf(sP76,plain,
( sP76
<=> ( sP72
=> ~ sP58 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).

thf(sP77,plain,
( sP77
<=> ( sP68
=> ( ( eigen__14
!= ( ^ [X1: a] : sP21 ) )
=> sP68 ) ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).

thf(sP78,plain,
( sP78
<=> ( ~ sP11
=> ( eigen__11
= ( ^ [X1: a] : ~ sP21 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).

thf(sP79,plain,
( sP79
<=> ( ( eigen__14
!= ( ^ [X1: a] : sP21 ) )
=> sP68 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).

thf(sP80,plain,
( sP80
<=> ! [X1: a] :
( ( eigen__0 @ X1 )
= sP21 ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).

thf(sP81,plain,
( sP81
<=> ( sP35
= ( ~ sP21 ) ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).

thf(cINDISCRETE_TOPOLOGY_pme,conjecture,
~ sP66 ).

thf(h3,negated_conjecture,
sP66,
inference(assume_negation,[status(cth)],[cINDISCRETE_TOPOLOGY_pme]) ).

thf(1,plain,
( ~ sP41
| ~ sP47
| sP21 ),
inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
( ~ sP32
| sP41 ),
inference(all_rule,[status(thm)],]) ).

thf(3,plain,
( ~ sP64
| sP32 ),
inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
( ~ sP14
| sP55
| ~ sP4 ),
inference(mating_rule,[status(thm)],]) ).

thf(5,plain,
( ~ sP75
| sP51 ),
inference(all_rule,[status(thm)],]) ).

thf(6,plain,
( ~ sP51
| ~ sP14
| sP44 ),
inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
( ~ sP44
| sP64
| sP4 ),
inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
( sP57
| sP47 ),
inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
( sP57
| sP14 ),
inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
( sP2
| ~ sP57 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).

thf(11,plain,
( ~ sP40
| ~ sP12
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
( ~ sP18
| ~ sP55 ),
inference(all_rule,[status(thm)],]) ).

thf(13,plain,
( ~ sP63
| sP19
| sP18 ),
inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
( ~ sP27
| sP40 ),
inference(all_rule,[status(thm)],]) ).

thf(15,plain,
( ~ sP27
| sP63 ),
inference(all_rule,[status(thm)],]) ).

thf(16,plain,
( sP79
| ~ sP68 ),
inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
( sP77
| ~ sP79 ),
inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
( sP77
| sP68 ),
inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
( sP58
| ~ sP77 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__14]) ).

thf(20,plain,
( sP78
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
( sP39
| ~ sP78 ),
inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
( sP39
| sP11 ),
inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
( sP72
| ~ sP39 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).

thf(24,plain,
( sP10
| sP53 ),
inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
( sP10
| sP46 ),
inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
( ~ sP37
| ~ sP8
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
( ~ sP26
| ~ sP46
| sP21 ),
inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
( ~ sP36
| ~ sP53
| sP21 ),
inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
( ~ sP59
| ~ sP35
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
( ~ sP50
| sP24
| sP59 ),
inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
( ~ sP81
| sP35
| sP21 ),
inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
( ~ sP25
| sP13
| sP21 ),
inference(prop_rule,[status(thm)],]) ).

thf(33,plain,
( ~ sP65
| sP37 ),
inference(all_rule,[status(thm)],]) ).

thf(34,plain,
( ~ sP80
| sP26 ),
inference(all_rule,[status(thm)],]) ).

thf(35,plain,
( ~ sP45
| sP36 ),
inference(all_rule,[status(thm)],]) ).

thf(36,plain,
( ~ sP65
| sP50 ),
inference(all_rule,[status(thm)],]) ).

thf(37,plain,
( ~ sP29
| sP81 ),
inference(all_rule,[status(thm)],]) ).

thf(38,plain,
( ~ sP71
| sP25 ),
inference(all_rule,[status(thm)],]) ).

thf(39,plain,
( ~ sP17
| sP71 ),
inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
( ~ sP60
| sP45 ),
inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
( ~ sP5
| sP29 ),
inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
( ~ sP28
| sP80 ),
inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
( sP31
| ~ sP19
| sP21 ),
inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
( sP3
| sP12
| sP21 ),
inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
( sP56
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).

thf(46,plain,
( sP67
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).

thf(47,plain,
( sP22
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).

thf(48,plain,
( sP16
| ~ sP67 ),
inference(prop_rule,[status(thm)],]) ).

thf(49,plain,
( ~ sP49
| sP27 ),
inference(prop_rule,[status(thm)],]) ).

thf(50,plain,
( sP34
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).

thf(51,plain,
( sP34
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
( sP43
| sP49 ),
inference(prop_rule,[status(thm)],]) ).

thf(53,plain,
( sP43
| sP75 ),
inference(prop_rule,[status(thm)],]) ).

thf(54,plain,
( sP42
| ~ sP34 ),
inference(prop_rule,[status(thm)],]) ).

thf(55,plain,
( sP42
| ~ sP43 ),
inference(prop_rule,[status(thm)],]) ).

thf(56,plain,
( sP30
| ~ sP42 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).

thf(57,plain,
( sP20
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__5]) ).

thf(58,plain,
( ~ sP76
| ~ sP72
| ~ sP58 ),
inference(prop_rule,[status(thm)],]) ).

thf(59,plain,
~ sP21,
inference(prop_rule,[status(thm)],]) ).

thf(60,plain,
( sP7
| ~ sP24
| sP21 ),
inference(prop_rule,[status(thm)],]) ).

thf(61,plain,
( sP33
| sP8
| sP21 ),
inference(prop_rule,[status(thm)],]) ).

thf(62,plain,
( sP15
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).

thf(63,plain,
( sP23
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__3]) ).

thf(64,plain,
( ~ sP61
| sP60
| sP17 ),
inference(prop_rule,[status(thm)],]) ).

thf(65,plain,
( ~ sP73
| sP28
| sP5 ),
inference(prop_rule,[status(thm)],]) ).

thf(66,plain,
( sP74
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).

thf(67,plain,
( sP48
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).

thf(68,plain,
( ~ sP70
| sP65 ),
inference(prop_rule,[status(thm)],]) ).

thf(69,plain,
( sP54
| sP61 ),
inference(prop_rule,[status(thm)],]) ).

thf(70,plain,
( sP54
| sP73 ),
inference(prop_rule,[status(thm)],]) ).

thf(71,plain,
( sP9
| ~ sP74 ),
inference(prop_rule,[status(thm)],]) ).

thf(72,plain,
( sP9
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).

thf(73,plain,
( sP52
| sP70 ),
inference(prop_rule,[status(thm)],]) ).

thf(74,plain,
( sP52
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).

thf(75,plain,
( sP69
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).

thf(76,plain,
( sP69
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).

thf(77,plain,
( sP6
| ~ sP69 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(78,plain,
( sP38
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(79,plain,
( sP62
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(80,plain,
( ~ sP1
| sP76
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).

thf(81,plain,
( ~ sP66
| sP1
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).

thf(82,plain,
\$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,h3]) ).

thf(83,plain,
\$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[82,h2]) ).

thf(84,plain,
\$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[83,h1]) ).

thf(85,plain,
\$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[84,h0]) ).

thf(0,theorem,
~ sP66,
inference(contra,[status(thm),contra(discharge,[h3])],[82,h3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV261^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Mar 26 14:44:31 EDT 2021
% 0.13/0.34  % CPUTime  :
% 26.02/26.34  % SZS status Theorem
% 26.02/26.34  % Mode: mode454
% 26.02/26.34  % Inferences: 790
% 26.02/26.34  % SZS output start Proof
% See solution above
% 26.02/26.34  % SZS output end Proof
%------------------------------------------------------------------------------
```