TSTP Solution File: SYO248^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO248^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 : 600s
% DateTime : Thu Jul 21 19:31:05 EDT 2022
% Result : Theorem 35.76s 35.75s
% Output : Proof 35.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 163
% Syntax : Number of formulae : 168 ( 10 unt; 13 typ; 1 def)
% Number of atoms : 774 ( 209 equ; 0 cnn)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 1083 ( 334 ~; 101 |; 0 &; 374 @)
% ( 74 <=>; 200 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 90 ( 88 usr; 88 con; 0-2 aty)
% Number of variables : 27 ( 1 ^ 26 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_h,type,
h: $i ).
thf(ty_a,type,
a: $i ).
thf(ty_d,type,
d: $i ).
thf(ty_cc,type,
cc: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_dd,type,
dd: $i ).
thf(ty_e,type,
e: $i ).
thf(ty_hh,type,
hh: $i ).
thf(ty_bb,type,
bb: $i ).
thf(ty_c,type,
c: $i ).
thf(ty_ee,type,
ee: $i ).
thf(ty_aa,type,
aa: $i ).
thf(h0,assumption,
! [X1: ( $i > $i > $o ) > $o,X2: $i > $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > $i > $o] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X1 @ a )
= ( X1 @ aa ) )
=> ( ( X1 @ b )
!= ( X1 @ bb ) ) )
=> ( ( X1 @ e )
!= ( X1 @ hh ) ) )
=> ( ( X1 @ c )
= ( X1 @ dd ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ a )
= ( X1 @ aa ) )
=> ( ( X1 @ h )
!= ( X1 @ hh ) ) )
=> ( ( X1 @ b )
!= ( X1 @ cc ) ) )
=> ( ( X1 @ d )
!= ( X1 @ ee ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X1 @ c )
= ( X1 @ cc ) )
=> ( ( X1 @ cc )
!= ( X1 @ d ) ) )
=> ( ( X1 @ d )
!= ( X1 @ dd ) ) )
=> ( ( X1 @ a )
= ( X1 @ bb ) ) )
=> ( ( X1 @ e )
!= ( X1 @ hh ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ a )
= ( X1 @ aa ) )
=> ( ( X1 @ d )
!= ( X1 @ dd ) ) )
=> ( ( X1 @ b )
= ( X1 @ cc ) ) )
=> ( ( X1 @ e )
= ( X1 @ hh ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ e )
= ( X1 @ ee ) )
=> ( ( X1 @ h )
!= ( X1 @ hh ) ) )
=> ( ( X1 @ c )
!= ( X1 @ dd ) ) )
=> ( ( X1 @ a )
!= ( X1 @ bb ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X1 @ b )
= ( X1 @ bb ) )
=> ( ( X1 @ bb )
!= ( X1 @ c ) ) )
=> ( ( X1 @ c )
!= ( X1 @ cc ) ) )
=> ( ( X1 @ e )
= ( X1 @ hh ) ) )
=> ( ( X1 @ d )
= ( X1 @ ee ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X1 @ a )
= ( X1 @ aa ) )
=> ( ( X1 @ b )
!= ( X1 @ bb ) ) )
=> ( ( X1 @ c )
!= ( X1 @ cc ) ) )
=> ( ( X1 @ d )
!= ( X1 @ dd ) ) )
=> ( ( X1 @ e )
!= ( X1 @ ee ) ) )
=> ( ( X1 @ h )
!= ( X1 @ hh ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ bb ) ) )
=> ( ( eigen__0 @ e )
!= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ c )
= ( eigen__0 @ dd ) ) )
=> ~ ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ cc ) ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ ee ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( eigen__0 @ c )
= ( eigen__0 @ cc ) )
=> ( ( eigen__0 @ cc )
!= ( eigen__0 @ d ) ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ dd ) ) )
=> ( ( eigen__0 @ a )
= ( eigen__0 @ bb ) ) )
=> ( ( eigen__0 @ e )
!= ( eigen__0 @ hh ) ) ) )
=> ~ ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ dd ) ) )
=> ( ( eigen__0 @ b )
= ( eigen__0 @ cc ) ) )
=> ( ( eigen__0 @ e )
= ( eigen__0 @ hh ) ) ) )
=> ~ ( ~ ( ~ ( ( ( eigen__0 @ e )
= ( eigen__0 @ ee ) )
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ c )
!= ( eigen__0 @ dd ) ) )
=> ( ( eigen__0 @ a )
!= ( eigen__0 @ bb ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( eigen__0 @ b )
= ( eigen__0 @ bb ) )
=> ( ( eigen__0 @ bb )
!= ( eigen__0 @ c ) ) )
=> ( ( eigen__0 @ c )
!= ( eigen__0 @ cc ) ) )
=> ( ( eigen__0 @ e )
= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ d )
= ( eigen__0 @ ee ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ bb ) ) )
=> ( ( eigen__0 @ c )
!= ( eigen__0 @ cc ) ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ dd ) ) )
=> ( ( eigen__0 @ e )
!= ( eigen__0 @ ee ) ) )
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
( ( ( eigen__0 @ c )
= ( eigen__0 @ dd ) )
=> ( ( ( eigen__0 @ dd )
= X1 )
=> ( ( eigen__0 @ c )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( eigen__0 @ c )
= ( eigen__0 @ b ) )
=> ( ( eigen__0 @ bb )
= ( eigen__0 @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ dd ) ) )
=> ( ( eigen__0 @ b )
= ( eigen__0 @ cc ) ) )
=> ( ( eigen__0 @ e )
= ( eigen__0 @ hh ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o] :
( ( ( eigen__0 @ c )
= X1 )
=> ( X1
= ( eigen__0 @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ cc ) ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ ee ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eigen__0 @ bb )
= ( eigen__0 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( ( eigen__0 @ cc )
= X1 )
=> ( ( X1 = X2 )
=> ( ( eigen__0 @ cc )
= X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__0 @ d )
= ( eigen__0 @ dd ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__0 @ b )
= ( eigen__0 @ cc ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ bb ) ) )
=> ( ( eigen__0 @ e )
!= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ c )
= ( eigen__0 @ dd ) ) )
=> ~ sP6 )
=> ~ ( ~ ( ~ ( ~ ( ( ( eigen__0 @ c )
= ( eigen__0 @ cc ) )
=> ( ( eigen__0 @ cc )
!= ( eigen__0 @ d ) ) )
=> ~ sP9 )
=> ( ( eigen__0 @ a )
= ( eigen__0 @ bb ) ) )
=> ( ( eigen__0 @ e )
!= ( eigen__0 @ hh ) ) ) )
=> ~ sP4 )
=> ~ ( ~ ( ~ ( ( ( eigen__0 @ e )
= ( eigen__0 @ ee ) )
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ c )
!= ( eigen__0 @ dd ) ) )
=> ( ( eigen__0 @ a )
!= ( eigen__0 @ bb ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ~ sP9 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 @ c )
= ( eigen__0 @ cc ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ bb ) ) )
=> ~ sP13 )
=> ~ sP9 )
=> ( ( eigen__0 @ e )
!= ( eigen__0 @ ee ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eigen__0 @ dd )
= ( eigen__0 @ d ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( eigen__0 @ cc )
= ( eigen__0 @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__0 @ e )
= ( eigen__0 @ ee ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ ( ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ bb ) ) )
=> ( ( eigen__0 @ e )
!= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ c )
= ( eigen__0 @ dd ) ) )
=> ~ sP6 )
=> ~ ( ~ ( ~ ( ~ ( sP13
=> ( ( eigen__0 @ cc )
!= ( eigen__0 @ d ) ) )
=> ~ sP9 )
=> ( ( eigen__0 @ a )
= ( eigen__0 @ bb ) ) )
=> ( ( eigen__0 @ e )
!= ( eigen__0 @ hh ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( ( eigen__0 @ c )
= ( eigen__0 @ d ) )
=> ( ( eigen__0 @ cc )
= ( eigen__0 @ d ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( sP17
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ c )
!= ( eigen__0 @ dd ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i > $o] :
( ( ( eigen__0 @ d )
= X1 )
=> ( X1
= ( eigen__0 @ d ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP17
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i > $o] :
( ( ( eigen__0 @ b )
= X1 )
=> ( X1
= ( eigen__0 @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( eigen__0 @ a )
= ( eigen__0 @ bb ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP15
=> ( ( eigen__0 @ c )
= ( eigen__0 @ d ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ bb ) ) )
=> ~ sP13 )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( ~ ( ~ ( ( ( eigen__0 @ b )
= ( eigen__0 @ bb ) )
=> ( ( eigen__0 @ bb )
!= ( eigen__0 @ c ) ) )
=> ~ sP13 )
=> ( ( eigen__0 @ e )
= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ d )
= ( eigen__0 @ ee ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eigen__0 @ e )
= ( eigen__0 @ hh ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( eigen__0 @ h )
= ( eigen__0 @ hh ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( ( eigen__0 @ b )
= ( eigen__0 @ bb ) )
=> ( ( eigen__0 @ bb )
!= ( eigen__0 @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ~ sP30 )
=> ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( ( eigen__0 @ c )
= X1 )
=> ( ( X1 = X2 )
=> ( ( eigen__0 @ c )
= X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ ( ~ sP31
=> ~ sP13 )
=> sP29 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( sP13
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( ( eigen__0 @ bb )
= X1 )
=> ( ( X2 = X1 )
=> ( ( eigen__0 @ bb )
= X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ bb ) ) )
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i > $o] :
( sP7
=> ( ( X1
= ( eigen__0 @ b ) )
=> ( ( eigen__0 @ bb )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( eigen__0 @ c )
= ( eigen__0 @ dd ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ bb ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( X1 = X2 )
=> ( ( X2 = X3 )
=> ( X1 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP39
=> sP26 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( eigen__0 @ c )
= ( eigen__0 @ d ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ ( ~ ( sP13
=> ( ( eigen__0 @ cc )
!= ( eigen__0 @ d ) ) )
=> ~ sP9 )
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( ( eigen__0 @ b )
= ( eigen__0 @ bb ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ sP18
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP13
=> ( sP10
=> ( ( eigen__0 @ c )
= ( eigen__0 @ b ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ sP11
=> ~ sP28 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i > $i > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X1 @ a )
= ( X1 @ aa ) )
=> ( ( X1 @ b )
!= ( X1 @ bb ) ) )
=> ( ( X1 @ e )
!= ( X1 @ hh ) ) )
=> ( ( X1 @ c )
= ( X1 @ dd ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ a )
= ( X1 @ aa ) )
=> ( ( X1 @ h )
!= ( X1 @ hh ) ) )
=> ( ( X1 @ b )
!= ( X1 @ cc ) ) )
=> ( ( X1 @ d )
!= ( X1 @ ee ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X1 @ c )
= ( X1 @ cc ) )
=> ( ( X1 @ cc )
!= ( X1 @ d ) ) )
=> ( ( X1 @ d )
!= ( X1 @ dd ) ) )
=> ( ( X1 @ a )
= ( X1 @ bb ) ) )
=> ( ( X1 @ e )
!= ( X1 @ hh ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ a )
= ( X1 @ aa ) )
=> ( ( X1 @ d )
!= ( X1 @ dd ) ) )
=> ( ( X1 @ b )
= ( X1 @ cc ) ) )
=> ( ( X1 @ e )
= ( X1 @ hh ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ e )
= ( X1 @ ee ) )
=> ( ( X1 @ h )
!= ( X1 @ hh ) ) )
=> ( ( X1 @ c )
!= ( X1 @ dd ) ) )
=> ( ( X1 @ a )
!= ( X1 @ bb ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X1 @ b )
= ( X1 @ bb ) )
=> ( ( X1 @ bb )
!= ( X1 @ c ) ) )
=> ( ( X1 @ c )
!= ( X1 @ cc ) ) )
=> ( ( X1 @ e )
= ( X1 @ hh ) ) )
=> ( ( X1 @ d )
= ( X1 @ ee ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X1 @ a )
= ( X1 @ aa ) )
=> ( ( X1 @ b )
!= ( X1 @ bb ) ) )
=> ( ( X1 @ c )
!= ( X1 @ cc ) ) )
=> ( ( X1 @ d )
!= ( X1 @ dd ) ) )
=> ( ( X1 @ e )
!= ( X1 @ ee ) ) )
=> ( ( X1 @ h )
!= ( X1 @ hh ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ( eigen__0 @ d )
= ( eigen__0 @ ee ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: $i > $o] :
( sP13
=> ( ( X1
= ( eigen__0 @ cc ) )
=> ( ( eigen__0 @ c )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ sP41
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ~ ( sP13
=> ( ( eigen__0 @ cc )
!= ( eigen__0 @ d ) ) )
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ sP45
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP13
=> ( ( eigen__0 @ cc )
!= ( eigen__0 @ d ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ( eigen__0 @ cc )
= ( eigen__0 @ d ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ~ sP20
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP51
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ~ sP31
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ! [X1: $i > $o,X2: $i > $o] :
( ( ( eigen__0 @ c )
= X1 )
=> ( ( X2 = X1 )
=> ( ( eigen__0 @ c )
= X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ( ( eigen__0 @ b )
= ( eigen__0 @ bb ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( X1 = X2 )
=> ( ( X3 = X2 )
=> ( X1 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ~ sP37
=> sP39 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ( sP10
=> ( ( eigen__0 @ c )
= ( eigen__0 @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP16
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( ~ sP14
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( sP66
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( sP9
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ( eigen__0 @ c )
= ( eigen__0 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( ( eigen__0 @ bb )
= ( eigen__0 @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ! [X1: $i > $o] :
( sP16
=> ( ( ( eigen__0 @ c )
= X1 )
=> ( ( eigen__0 @ cc )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(cSIXFRIENDS_AGAIN,conjecture,
sP50 ).
thf(h1,negated_conjecture,
~ sP50,
inference(assume_negation,[status(cth)],[cSIXFRIENDS_AGAIN]) ).
thf(1,plain,
( ~ sP74
| sP68 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP68
| ~ sP16
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP19
| ~ sP44
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP2
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP43
| ~ sP39
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP26
| ~ sP15
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP33
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP42
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP8
| sP74 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP42
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP38
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP22
| ~ sP7
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP3
| ~ sP72
| sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP65
| sP36 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP36
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP37
| sP41
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP66
| sP37
| sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP61
| ~ sP51
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP32
| sP61
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP6
| sP32
| ~ sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP70
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP70
| sP66 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP58
| ~ sP13
| ~ sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP55
| sP58
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP45
| sP55
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP57
| sP45
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP18
| sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP18
| ~ sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP40
| ~ sP51
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP53
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP48
| ~ sP13
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP67
| ~ sP10
| sP72 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP12
| sP40
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP4
| sP12
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP47
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP47
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP23
| ~ sP17
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP20
| sP23
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP60
| sP20
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP11
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP11
| ~ sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP31
| ~ sP64
| ~ sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP62
| sP31
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP34
| sP62
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP28
| sP34
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP49
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP49
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP46
| ~ sP64
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP24
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP56
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(51,plain,
( sP41
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP41
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( ~ sP65
| sP63 ),
inference(all_rule,[status(thm)],]) ).
thf(54,plain,
( ~ sP63
| sP53 ),
inference(all_rule,[status(thm)],]) ).
thf(55,plain,
( ~ sP35
| ~ sP13
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( ~ sP5
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(57,plain,
( ~ sP56
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(58,plain,
( sP54
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( sP54
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP71
| ~ sP9
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( ~ sP21
| sP71 ),
inference(all_rule,[status(thm)],]) ).
thf(62,plain,
( ~ sP56
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(63,plain,
( sP27
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( sP27
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( sP14
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( sP14
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
sP65,
inference(eq_trans_sym_r,[status(thm)],]) ).
thf(68,plain,
sP42,
inference(eq_trans,[status(thm)],]) ).
thf(69,plain,
sP56,
inference(eq_sym,[status(thm)],]) ).
thf(70,plain,
( sP69
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( sP69
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( sP1
| ~ sP69 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( sP1
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( sP50
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(75,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h1]) ).
thf(76,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[75,h0]) ).
thf(0,theorem,
sP50,
inference(contra,[status(thm),contra(discharge,[h1])],[75,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYO248^5 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 22:17:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 35.76/35.75 % SZS status Theorem
% 35.76/35.75 % Mode: mode466
% 35.76/35.75 % Inferences: 1501
% 35.76/35.75 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------