TSTP Solution File: GRA027^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : GRA027^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:03:55 EDT 2023
% Result : Theorem 1.13s 1.34s
% Output : Proof 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 179
% Syntax : Number of formulae : 200 ( 26 unt; 15 typ; 15 def)
% Number of atoms : 901 ( 114 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1142 ( 344 ~; 138 |; 0 &; 374 @)
% ( 71 <=>; 215 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 156 ( 156 >; 0 *; 0 +; 0 <<)
% Number of symbols : 91 ( 89 usr; 78 con; 0-2 aty)
% Number of variables : 98 ( 15 ^; 83 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1057,type,
eigen__1057: $o ).
thf(ty_eigen__1046,type,
eigen__1046: $o > $o ).
thf(ty_eigen__1047,type,
eigen__1047: ( $o > $o ) > $o ).
thf(ty_eigen__1049,type,
eigen__1049: ( $o > $o ) > $o ).
thf(ty_eigen__1040,type,
eigen__1040: $o > $o ).
thf(ty_eigen__1048,type,
eigen__1048: ( $o > $o ) > $o ).
thf(ty_eigen__1043,type,
eigen__1043: $o > $o ).
thf(ty_eigen__1042,type,
eigen__1042: $o > $o ).
thf(ty_eigen__1045,type,
eigen__1045: $o > $o ).
thf(ty_eigen__1041,type,
eigen__1041: $o > $o ).
thf(ty_eigen__1039,type,
eigen__1039: $o > $o ).
thf(ty_eigen__1050,type,
eigen__1050: ( $o > $o ) > $o ).
thf(ty_eigen__1044,type,
eigen__1044: $o > $o ).
thf(ty_eigen__1054,type,
eigen__1054: $o ).
thf(ty_eigen__1058,type,
eigen__1058: $o ).
thf(h0,assumption,
! [X1: ( $o > $o ) > $o,X2: $o > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1045,definition,
( eigen__1045
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__1041 )
=> ( X2 @ eigen__1043 ) )
=> ( X2 @ X1 ) )
=> ( X3 @ eigen__1041 ) )
=> ~ ( X3 @ eigen__1043 ) )
=> ( X3 @ X1 ) )
=> ( ~ ( ( ( eigen__1043 @ $false )
!= ( eigen__1041 @ $false ) )
=> ( ( X1 @ $false )
= ( eigen__1041 @ $false ) ) )
=> ( ( X1 @ $false )
= ( eigen__1043 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1045])]) ).
thf(h1,assumption,
! [X1: ( ( $o > $o ) > $o ) > $o,X2: ( $o > $o ) > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1048,definition,
( eigen__1048
= ( eps__1
@ ^ [X1: ( $o > $o ) > $o] :
~ ! [X2: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__1042 )
=> ( X1 @ eigen__1044 ) )
=> ( X1 @ eigen__1046 ) )
=> ( X2 @ eigen__1042 ) )
=> ~ ( X2 @ eigen__1044 ) )
=> ( X2 @ eigen__1046 ) )
=> ( ~ ( ( ( eigen__1044 @ $false )
= ( eigen__1042 @ $false ) )
=> ( ( eigen__1046 @ $false )
!= ( eigen__1042 @ $false ) ) )
=> ( ( eigen__1046 @ $false )
!= ( eigen__1044 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1048])]) ).
thf(eigendef_eigen__1044,definition,
( eigen__1044
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__1042 )
=> ( X3 @ X1 ) )
=> ( X3 @ X2 ) )
=> ( X4 @ eigen__1042 ) )
=> ~ ( X4 @ X1 ) )
=> ( X4 @ X2 ) )
=> ( ~ ( ( ( X1 @ $false )
= ( eigen__1042 @ $false ) )
=> ( ( X2 @ $false )
!= ( eigen__1042 @ $false ) ) )
=> ( ( X2 @ $false )
!= ( X1 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1044])]) ).
thf(eigendef_eigen__1040,definition,
( eigen__1040
= ( eps__0
@ ^ [X1: $o > $o] :
~ ( ( ( eigen__1039 @ $false )
= ( X1 @ $false ) )
=> ( ( X1 @ $false )
= ( eigen__1039 @ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1040])]) ).
thf(eigendef_eigen__1046,definition,
( eigen__1046
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__1042 )
=> ( X2 @ eigen__1044 ) )
=> ( X2 @ X1 ) )
=> ( X3 @ eigen__1042 ) )
=> ~ ( X3 @ eigen__1044 ) )
=> ( X3 @ X1 ) )
=> ( ~ ( ( ( eigen__1044 @ $false )
= ( eigen__1042 @ $false ) )
=> ( ( X1 @ $false )
!= ( eigen__1042 @ $false ) ) )
=> ( ( X1 @ $false )
!= ( eigen__1044 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1046])]) ).
thf(eigendef_eigen__1047,definition,
( eigen__1047
= ( eps__1
@ ^ [X1: ( $o > $o ) > $o] :
~ ! [X2: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__1041 )
=> ( X1 @ eigen__1043 ) )
=> ( X1 @ eigen__1045 ) )
=> ( X2 @ eigen__1041 ) )
=> ~ ( X2 @ eigen__1043 ) )
=> ( X2 @ eigen__1045 ) )
=> ( ~ ( ( ( eigen__1043 @ $false )
!= ( eigen__1041 @ $false ) )
=> ( ( eigen__1045 @ $false )
= ( eigen__1041 @ $false ) ) )
=> ( ( eigen__1045 @ $false )
= ( eigen__1043 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1047])]) ).
thf(eigendef_eigen__1049,definition,
( eigen__1049
= ( eps__1
@ ^ [X1: ( $o > $o ) > $o] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__1047 @ eigen__1041 )
=> ( eigen__1047 @ eigen__1043 ) )
=> ( eigen__1047 @ eigen__1045 ) )
=> ( X1 @ eigen__1041 ) )
=> ~ ( X1 @ eigen__1043 ) )
=> ( X1 @ eigen__1045 ) )
=> ( ~ ( ( ( eigen__1043 @ $false )
!= ( eigen__1041 @ $false ) )
=> ( ( eigen__1045 @ $false )
= ( eigen__1041 @ $false ) ) )
=> ( ( eigen__1045 @ $false )
= ( eigen__1043 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1049])]) ).
thf(eigendef_eigen__1043,definition,
( eigen__1043
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__1041 )
=> ( X3 @ X1 ) )
=> ( X3 @ X2 ) )
=> ( X4 @ eigen__1041 ) )
=> ~ ( X4 @ X1 ) )
=> ( X4 @ X2 ) )
=> ( ~ ( ( ( X1 @ $false )
!= ( eigen__1041 @ $false ) )
=> ( ( X2 @ $false )
= ( eigen__1041 @ $false ) ) )
=> ( ( X2 @ $false )
= ( X1 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1043])]) ).
thf(h2,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1058,definition,
( eigen__1058
= ( eps__2
@ ^ [X1: $o] :
( ( eigen__1042 @ X1 )
!= ( eigen__1046 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1058])]) ).
thf(eigendef_eigen__1057,definition,
( eigen__1057
= ( eps__2
@ ^ [X1: $o] :
( ( eigen__1044 @ X1 )
!= ( eigen__1046 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1057])]) ).
thf(eigendef_eigen__1041,definition,
( eigen__1041
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ( X4 @ X3 ) )
=> ( X5 @ X1 ) )
=> ~ ( X5 @ X2 ) )
=> ( X5 @ X3 ) )
=> ( ~ ( ( ( X2 @ $false )
!= ( X1 @ $false ) )
=> ( ( X3 @ $false )
= ( X1 @ $false ) ) )
=> ( ( X3 @ $false )
= ( X2 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1041])]) ).
thf(eigendef_eigen__1039,definition,
( eigen__1039
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o] :
( ( ( X1 @ $false )
= ( X2 @ $false ) )
=> ( ( X2 @ $false )
= ( X1 @ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1039])]) ).
thf(eigendef_eigen__1042,definition,
( eigen__1042
= ( eps__0
@ ^ [X1: $o > $o] :
~ ! [X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ( X4 @ X3 ) )
=> ( X5 @ X1 ) )
=> ~ ( X5 @ X2 ) )
=> ( X5 @ X3 ) )
=> ( ~ ( ( ( X2 @ $false )
= ( X1 @ $false ) )
=> ( ( X3 @ $false )
!= ( X1 @ $false ) ) )
=> ( ( X3 @ $false )
!= ( X2 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1042])]) ).
thf(eigendef_eigen__1054,definition,
( eigen__1054
= ( eps__2
@ ^ [X1: $o] :
( ( eigen__1042 @ X1 )
!= ( eigen__1044 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1054])]) ).
thf(eigendef_eigen__1050,definition,
( eigen__1050
= ( eps__1
@ ^ [X1: ( $o > $o ) > $o] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__1048 @ eigen__1042 )
=> ( eigen__1048 @ eigen__1044 ) )
=> ( eigen__1048 @ eigen__1046 ) )
=> ( X1 @ eigen__1042 ) )
=> ~ ( X1 @ eigen__1044 ) )
=> ( X1 @ eigen__1046 ) )
=> ( ~ ( ( ( eigen__1044 @ $false )
= ( eigen__1042 @ $false ) )
=> ( ( eigen__1046 @ $false )
!= ( eigen__1042 @ $false ) ) )
=> ( ( eigen__1046 @ $false )
!= ( eigen__1044 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1050])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ( ( eigen__1043 @ $false )
!= ( eigen__1041 @ $false ) )
=> ( ( eigen__1045 @ $false )
= ( eigen__1041 @ $false ) ) )
=> ( ( eigen__1045 @ $false )
= ( eigen__1043 @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__1050 @ eigen__1046 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: ( $o > $o ) > $o,X2: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__1041 )
=> ( X1 @ eigen__1043 ) )
=> ( X1 @ eigen__1045 ) )
=> ( X2 @ eigen__1041 ) )
=> ~ ( X2 @ eigen__1043 ) )
=> ( X2 @ eigen__1045 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__1048 @ eigen__1042 )
=> ( eigen__1048 @ eigen__1044 ) )
=> ( eigen__1048 @ eigen__1046 ) )
=> ( X1 @ eigen__1042 ) )
=> ~ ( X1 @ eigen__1044 ) )
=> ( X1 @ eigen__1046 ) )
=> ( ~ ( ( ( eigen__1044 @ $false )
= ( eigen__1042 @ $false ) )
=> ( ( eigen__1046 @ $false )
!= ( eigen__1042 @ $false ) ) )
=> ( ( eigen__1046 @ $false )
!= ( eigen__1044 @ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ ( ~ ( ( eigen__1048 @ eigen__1042 )
=> ( eigen__1048 @ eigen__1044 ) )
=> ( eigen__1048 @ eigen__1046 ) )
=> ( eigen__1050 @ eigen__1042 ) )
=> ~ ( eigen__1050 @ eigen__1044 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__1047 @ eigen__1041 )
=> ( eigen__1047 @ eigen__1043 ) )
=> ( eigen__1047 @ eigen__1045 ) )
=> ( eigen__1049 @ eigen__1041 ) )
=> ~ ( eigen__1049 @ eigen__1043 ) )
=> ( eigen__1049 @ eigen__1045 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__1043 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ( ~ sP5
=> sP2 )
=> ( ~ ( ( ( eigen__1044 @ $false )
= ( eigen__1042 @ $false ) )
=> ( ( eigen__1046 @ $false )
!= ( eigen__1042 @ $false ) ) )
=> ( ( eigen__1046 @ $false )
!= ( eigen__1044 @ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1039 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__1040 @ $false )
= sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__1054 = eigen__1058 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ! [X1: $o > $o,X2: $o > $o] :
( ( ( X1 @ $false )
= ( X2 @ $false ) )
=> ( ( X2 @ $false )
= ( X1 @ $false ) ) )
=> ~ ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ( X4 @ X3 ) )
=> ( X5 @ X1 ) )
=> ~ ( X5 @ X2 ) )
=> ( X5 @ X3 ) )
=> ( ~ ( ( ( X2 @ $false )
= ( X1 @ $false ) )
=> ( ( X3 @ $false )
!= ( X1 @ $false ) ) )
=> ( ( X3 @ $false )
!= ( X2 @ $false ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eigen__1042 = eigen__1046 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $o > $o] :
( ( sP9
= ( X1 @ $false ) )
=> ( ( X1 @ $false )
= sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP7
= ( eigen__1041 @ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( ( eigen__1044 @ $false )
= ( eigen__1042 @ $false ) )
=> ( ( eigen__1046 @ $false )
!= ( eigen__1042 @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__1046 @ $false )
= ( eigen__1042 @ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__1042 @ eigen__1054 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $o > $o,X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__1042 )
=> ( X3 @ X1 ) )
=> ( X3 @ X2 ) )
=> ( X4 @ eigen__1042 ) )
=> ~ ( X4 @ X1 ) )
=> ( X4 @ X2 ) )
=> ( ~ ( ( ( X1 @ $false )
= ( eigen__1042 @ $false ) )
=> ( ( X2 @ $false )
!= ( eigen__1042 @ $false ) ) )
=> ( ( X2 @ $false )
!= ( X1 @ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $o > $o,X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__1041 )
=> ( X2 @ eigen__1043 ) )
=> ( X2 @ X1 ) )
=> ( X3 @ eigen__1041 ) )
=> ~ ( X3 @ eigen__1043 ) )
=> ( X3 @ X1 ) )
=> ( ~ ( ~ sP15
=> ( ( X1 @ $false )
= ( eigen__1041 @ $false ) ) )
=> ( ( X1 @ $false )
= sP7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ sP16
=> ( ( eigen__1046 @ $false )
!= ( eigen__1044 @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__1048 @ eigen__1044 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> eigen__1057 ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__1042 @ eigen__1058 )
= ( eigen__1046 @ eigen__1058 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__1046 @ eigen__1058 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( eigen__1044 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__1044 = eigen__1046 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( sP23 = eigen__1058 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP15
=> ( ( eigen__1045 @ $false )
= ( eigen__1041 @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP5
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( eigen__1046 @ $false )
= sP26 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( eigen__1048 @ eigen__1042 )
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( eigen__1047 @ eigen__1041 )
=> ( eigen__1047 @ eigen__1043 ) )
=> ( eigen__1047 @ eigen__1045 ) )
=> ( X1 @ eigen__1041 ) )
=> ~ ( X1 @ eigen__1043 ) )
=> ( X1 @ eigen__1045 ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: ( $o > $o ) > $o,X2: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X1 @ eigen__1042 )
=> ( X1 @ eigen__1044 ) )
=> ( X1 @ eigen__1046 ) )
=> ( X2 @ eigen__1042 ) )
=> ~ ( X2 @ eigen__1044 ) )
=> ( X2 @ eigen__1046 ) )
=> sP21 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( eigen__1050 @ eigen__1044 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__1048 @ eigen__1046 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $o] :
( ( eigen__1042 @ X1 )
= ( eigen__1046 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ sP32
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( eigen__1058 = eigen__1054 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( sP9
= ( eigen__1040 @ $false ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__1046 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> eigen__1058 ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( eigen__1044 @ sP23 )
= ( eigen__1046 @ sP23 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> eigen__1054 ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ( X4 @ X3 ) )
=> ( X5 @ X1 ) )
=> ~ ( X5 @ X2 ) )
=> ( X5 @ X3 ) )
=> ( ~ ( ( ( X2 @ $false )
!= ( X1 @ $false ) )
=> ( ( X3 @ $false )
= ( X1 @ $false ) ) )
=> ( ( X3 @ $false )
= ( X2 @ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( eigen__1045 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( eigen__1048 @ eigen__1042 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__1042 @ sP42 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP46
= ( eigen__1041 @ $false ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ~ sP12
=> ~ sP45 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( eigen__1042 = eigen__1044 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( sP23 = sP44 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP42 = sP23 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( eigen__1044 @ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( eigen__1040 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ! [X1: $o > $o,X2: $o > $o,X3: ( $o > $o ) > $o,X4: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X3 @ eigen__1041 )
=> ( X3 @ X1 ) )
=> ( X3 @ X2 ) )
=> ( X4 @ eigen__1041 ) )
=> ~ ( X4 @ X1 ) )
=> ( X4 @ X2 ) )
=> ( ~ ( ( ( X1 @ $false )
!= ( eigen__1041 @ $false ) )
=> ( ( X2 @ $false )
= ( eigen__1041 @ $false ) ) )
=> ( ( X2 @ $false )
= ( X1 @ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ! [X1: $o] :
( ( eigen__1042 @ X1 )
= ( eigen__1044 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( eigen__1044 @ sP44 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ! [X1: ( $o > $o ) > ( $o > $o ) > $o] :
( ~ ( ! [X2: $o > $o,X3: $o > $o] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X5 @ X2 )
=> ( X5 @ X3 ) )
=> ( X5 @ X4 ) )
=> ( X6 @ X2 ) )
=> ~ ( X6 @ X3 ) )
=> ( X6 @ X4 ) )
=> ( ~ ( ( X1 @ X3 @ X2 )
=> ~ ( X1 @ X4 @ X2 ) )
=> ~ ( X1 @ X4 @ X3 ) ) ) )
=> ~ ! [X2: $o > $o,X3: $o > $o,X4: $o > $o,X5: ( $o > $o ) > $o,X6: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X5 @ X2 )
=> ( X5 @ X3 ) )
=> ( X5 @ X4 ) )
=> ( X6 @ X2 ) )
=> ~ ( X6 @ X3 ) )
=> ( X6 @ X4 ) )
=> ( ~ ( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X4 @ X2 ) )
=> ( X1 @ X4 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $o] :
( ( eigen__1044 @ X1 )
= ( eigen__1046 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( eigen__1041 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: $o > $o,X2: ( $o > $o ) > $o,X3: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X2 @ eigen__1042 )
=> ( X2 @ eigen__1044 ) )
=> ( X2 @ X1 ) )
=> ( X3 @ eigen__1042 ) )
=> ~ ( X3 @ eigen__1044 ) )
=> ( X3 @ X1 ) )
=> ( ~ ( ( sP26
= ( eigen__1042 @ $false ) )
=> ( ( X1 @ $false )
!= ( eigen__1042 @ $false ) ) )
=> ( ( X1 @ $false )
!= sP26 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( eigen__1042 @ $false ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $o > $o,X2: $o > $o] :
( ( ( X1 @ $false )
= ( X2 @ $false ) )
=> ( ( X2 @ $false )
= ( X1 @ $false ) ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( sP46 = sP7 ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( sP18 = sP58 ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: $o > $o,X2: $o > $o,X3: $o > $o,X4: ( $o > $o ) > $o,X5: ( $o > $o ) > $o] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( X4 @ X1 )
=> ( X4 @ X2 ) )
=> ( X4 @ X3 ) )
=> ( X5 @ X1 ) )
=> ~ ( X5 @ X2 ) )
=> ( X5 @ X3 ) )
=> ( ~ ( ( ( X2 @ $false )
= ( X1 @ $false ) )
=> ( ( X3 @ $false )
!= ( X1 @ $false ) ) )
=> ( ( X3 @ $false )
!= ( X2 @ $false ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( sP9 = sP55 ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP44 = sP23 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ( ~ sP38
=> ( eigen__1050 @ eigen__1042 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( eigen__1046 @ sP23 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(ramsey_l_3_3_4,conjecture,
~ sP59 ).
thf(h3,negated_conjecture,
sP59,
inference(assume_negation,[status(cth)],[ramsey_l_3_3_4]) ).
thf(1,plain,
( sP53
| ~ sP42
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP25
| sP41
| sP42 ),
inference(mating_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP25
| sP71
| ~ sP53 ),
inference(mating_rule,[status(thm)],]) ).
thf(4,plain,
( sP39
| ~ sP42
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP48
| sP63
| sP42 ),
inference(mating_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP48
| sP18
| ~ sP39 ),
inference(mating_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP71
| sP41
| sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(8,plain,
( sP52
| ~ sP23
| ~ sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP54
| sP26
| sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP54
| sP58
| ~ sP52 ),
inference(mating_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP58
| sP26
| sP44 ),
inference(mating_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| sP63
| sP44 ),
inference(mating_rule,[status(thm)],]) ).
thf(13,plain,
( sP28
| ~ sP23
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP41
| sP25
| sP42 ),
inference(mating_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP71
| sP25
| ~ sP28 ),
inference(mating_rule,[status(thm)],]) ).
thf(16,plain,
( sP11
| ~ sP44
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP63
| sP48
| sP42 ),
inference(mating_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP18
| sP48
| ~ sP11 ),
inference(mating_rule,[status(thm)],]) ).
thf(19,plain,
( sP24
| ~ sP48
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP24
| sP48
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP37
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__1058]) ).
thf(22,plain,
( sP13
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP47
| sP36
| ~ sP13 ),
inference(mating_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP41
| sP71
| sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(25,plain,
( sP69
| ~ sP44
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP26
| sP54
| sP23 ),
inference(mating_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP58
| sP54
| ~ sP69 ),
inference(mating_rule,[status(thm)],]) ).
thf(28,plain,
( sP43
| ~ sP54
| ~ sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP43
| sP54
| sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP60
| ~ sP43 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__1057]) ).
thf(31,plain,
( sP27
| ~ sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP35
| sP2
| ~ sP27 ),
inference(mating_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP26
| sP58
| sP44 ),
inference(mating_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP63
| sP18
| sP44 ),
inference(mating_rule,[status(thm)],]) ).
thf(35,plain,
( sP66
| ~ sP18
| ~ sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP66
| sP18
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP57
| ~ sP66 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__1054]) ).
thf(38,plain,
( sP51
| ~ sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP47
| sP22
| ~ sP51 ),
inference(mating_rule,[status(thm)],]) ).
thf(40,plain,
( sP32
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP32
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP38
| ~ sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP38
| ~ sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP70
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP5
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP5
| ~ sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP17
| ~ sP41
| sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP17
| sP41
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP31
| ~ sP41
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP31
| sP41
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP16
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP21
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( sP21
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( sP30
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP30
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP8
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( sP8
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(58,plain,
( sP49
| ~ sP46
| ~ sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(59,plain,
( sP49
| sP46
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( sP15
| ~ sP7
| ~ sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( sP15
| sP7
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(62,plain,
( sP65
| ~ sP46
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( sP65
| sP46
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(64,plain,
( sP29
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(65,plain,
( sP29
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( sP1
| ~ sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( sP1
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(68,plain,
( sP6
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( sP4
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1050]) ).
thf(70,plain,
( sP33
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1049]) ).
thf(71,plain,
( sP34
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1048]) ).
thf(72,plain,
( sP3
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1047]) ).
thf(73,plain,
( sP62
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1046]) ).
thf(74,plain,
( sP20
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1045]) ).
thf(75,plain,
( sP19
| ~ sP62 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1044]) ).
thf(76,plain,
( sP56
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1043]) ).
thf(77,plain,
( sP67
| ~ sP19 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1042]) ).
thf(78,plain,
( sP45
| ~ sP56 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1041]) ).
thf(79,plain,
( sP10
| ~ sP55
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( sP10
| sP55
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( ~ sP68
| ~ sP9
| sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
( ~ sP68
| sP9
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(83,plain,
( sP40
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( sP40
| sP68 ),
inference(prop_rule,[status(thm)],]) ).
thf(85,plain,
( sP14
| ~ sP40 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1040]) ).
thf(86,plain,
( sP64
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1039]) ).
thf(87,plain,
( ~ sP12
| ~ sP64
| ~ sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(88,plain,
( ~ sP50
| sP12
| ~ sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(89,plain,
( ~ sP59
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(90,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,h3]) ).
thf(91,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[90,h2]) ).
thf(92,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[91,h1]) ).
thf(93,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[92,h0]) ).
thf(0,theorem,
~ sP59,
inference(contra,[status(thm),contra(discharge,[h3])],[90,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRA027^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 03:36:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.13/1.34 % SZS status Theorem
% 1.13/1.34 % Mode: cade22grackle2xfee4
% 1.13/1.34 % Steps: 20850
% 1.13/1.34 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------