TSTP Solution File: SYO248^5 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO248^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n032.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 : Fri Sep 1 04:46:01 EDT 2023
% Result : Theorem 1.10s 1.31s
% Output : Proof 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 147
% Syntax : Number of formulae : 165 ( 30 unt; 15 typ; 2 def)
% Number of atoms : 568 ( 153 equ; 0 cnn)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 997 ( 345 ~; 87 |; 0 &; 347 @)
% ( 56 <=>; 162 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 72 usr; 72 con; 0-2 aty)
% Number of variables : 14 ( 2 ^; 12 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_h,type,
h: $i ).
thf(ty_cc,type,
cc: $i ).
thf(ty_b,type,
b: $i ).
thf(ty_dd,type,
dd: $i ).
thf(ty_d,type,
d: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_bb,type,
bb: $i ).
thf(ty_aa,type,
aa: $i ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(ty_ee,type,
ee: $i ).
thf(ty_hh,type,
hh: $i ).
thf(ty_c,type,
c: $i ).
thf(ty_a,type,
a: $i ).
thf(ty_e,type,
e: $i ).
thf(ty_eigen__12,type,
eigen__12: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__0
@ ^ [X1: $i] :
( ( eigen__0 @ bb @ X1 )
!= ( eigen__0 @ c @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: $i] :
( ( eigen__0 @ cc @ X1 )
!= ( eigen__0 @ d @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__0 @ d )
= ( eigen__0 @ ee ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__0 @ e )
= ( eigen__0 @ ee ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP2
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eigen__0 @ e )
= ( eigen__0 @ hh ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ cc ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ ( ~ ( ( ( eigen__0 @ b )
= ( eigen__0 @ bb ) )
=> ( ( eigen__0 @ bb )
!= ( eigen__0 @ c ) ) )
=> ( ( eigen__0 @ c )
!= ( eigen__0 @ cc ) ) )
=> sP4 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ b )
!= ( eigen__0 @ bb ) ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0 @ cc @ eigen__13 )
= ( eigen__0 @ d @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ~ ( ~ ( ( ( eigen__0 @ c )
= ( eigen__0 @ cc ) )
=> ( ( eigen__0 @ cc )
!= ( eigen__0 @ d ) ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ dd ) ) )
=> ( ( eigen__0 @ a )
= ( eigen__0 @ bb ) ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( ( eigen__0 @ b )
= ( eigen__0 @ bb ) )
=> ( ( eigen__0 @ bb )
!= ( eigen__0 @ c ) ) )
=> ( ( eigen__0 @ c )
!= ( eigen__0 @ cc ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__0 @ cc @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eigen__0 @ c @ X1 )
= ( eigen__0 @ dd @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__0 @ bb )
= ( eigen__0 @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__0 @ c @ eigen__12 )
= sP11 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eigen__0 @ b )
= ( eigen__0 @ bb ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eigen__0 @ bb @ X1 )
= ( eigen__0 @ c @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ dd ) ) )
=> ( ( eigen__0 @ b )
= ( eigen__0 @ cc ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) )
=> ( ( eigen__0 @ d )
!= ( eigen__0 @ dd ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP3
=> ( ( eigen__0 @ c )
!= ( eigen__0 @ dd ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP15
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( eigen__0 @ bb @ eigen__12 )
= ( eigen__0 @ c @ eigen__12 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 @ cc @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( eigen__0 @ a )
= ( eigen__0 @ aa ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__0 @ d @ eigen__13 )
= ( eigen__0 @ dd @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( eigen__0 @ b @ X1 )
= ( eigen__0 @ cc @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP23
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( eigen__0 @ c )
= ( eigen__0 @ dd ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( eigen__0 @ b @ X1 )
= ( eigen__0 @ bb @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP10
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( sP23
=> ( ( eigen__0 @ h )
!= ( eigen__0 @ hh ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP17
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP5
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ( eigen__0 @ c @ eigen__13 )
= sP22 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( eigen__0 @ c @ eigen__13 )
= ( eigen__0 @ dd @ eigen__13 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( eigen__0 @ d @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: $i] :
( ( eigen__0 @ c @ X1 )
= ( eigen__0 @ cc @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( eigen__0 @ d )
= ( eigen__0 @ dd ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( eigen__0 @ a )
= ( eigen__0 @ bb ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( eigen__0 @ h )
= ( eigen__0 @ hh ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ( eigen__0 @ cc )
= ( eigen__0 @ d ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__0 @ bb @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( eigen__0 @ b )
= ( eigen__0 @ cc ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( eigen__0 @ b @ eigen__12 )
= sP41 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( eigen__0 @ b @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ sP19
=> ~ sP38 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ sP7
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ ( ~ ( ( ( eigen__0 @ c )
= ( eigen__0 @ cc ) )
=> ~ sP40 )
=> ~ sP37 )
=> sP38 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__0 @ c @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( eigen__0 @ c @ eigen__12 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( eigen__0 @ cc @ X1 )
= ( eigen__0 @ d @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [X1: $i] :
( ( eigen__0 @ d @ X1 )
= ( eigen__0 @ dd @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ~ ( ( ( eigen__0 @ c )
= ( eigen__0 @ cc ) )
=> ~ sP40 )
=> ~ sP37 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ( eigen__0 @ c )
= ( eigen__0 @ cc ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( sP53
=> ~ sP40 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP44 = sP11 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( eigen__0 @ dd @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(cSIXFRIENDS_AGAIN,conjecture,
! [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 ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [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 ) ) ) ),
inference(assume_negation,[status(cth)],[cSIXFRIENDS_AGAIN]) ).
thf(h2,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP32 )
=> ~ sP9 )
=> ~ sP31 )
=> ~ sP45 )
=> ~ sP6 )
=> ( ~ ( ~ ( ~ ( ~ sP26
=> ~ sP53 )
=> ~ sP37 )
=> ~ sP2 )
=> ~ sP39 ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP32 )
=> ~ sP9 )
=> ~ sP31 )
=> ~ sP45 )
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( ~ ( ~ ( ~ ( ~ sP26
=> ~ sP53 )
=> ~ sP37 )
=> ~ sP2 )
=> ~ sP39 ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( ~ ( ~ ( ~ ( sP46
=> ~ sP32 )
=> ~ sP9 )
=> ~ sP31 )
=> ~ sP45 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP6,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ ( ~ ( sP46
=> ~ sP32 )
=> ~ sP9 )
=> ~ sP31 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP45,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ~ ( sP46
=> ~ sP32 )
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP31,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP46
=> ~ sP32 ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP9,
introduced(assumption,[]) ).
thf(h13,assumption,
sP46,
introduced(assumption,[]) ).
thf(h14,assumption,
sP32,
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( ~ ( ~ ( ~ sP26
=> ~ sP53 )
=> ~ sP37 )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP39,
introduced(assumption,[]) ).
thf(h17,assumption,
~ ( ~ ( ~ sP26
=> ~ sP53 )
=> ~ sP37 ),
introduced(assumption,[]) ).
thf(h18,assumption,
sP2,
introduced(assumption,[]) ).
thf(h19,assumption,
~ ( ~ sP26
=> ~ sP53 ),
introduced(assumption,[]) ).
thf(h20,assumption,
sP37,
introduced(assumption,[]) ).
thf(h21,assumption,
~ sP26,
introduced(assumption,[]) ).
thf(h22,assumption,
sP53,
introduced(assumption,[]) ).
thf(h23,assumption,
sP23,
introduced(assumption,[]) ).
thf(h24,assumption,
sP15,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP24
| ~ sP35
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP24
| sP35
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP33
| ~ sP48
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP33
| sP48
| ~ sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP34
| ~ sP48
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP34
| sP48
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP51
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP36
| sP33 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP12
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP14
| ~ sP49
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP14
| sP49
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP43
| ~ sP44
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP43
| sP44
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP55
| ~ sP44
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP55
| sP44
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP36
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP28
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP25
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( sP8
| ~ sP22
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP8
| sP22
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP50
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(22,plain,
( sP40
| ~ sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP54
| ~ sP53
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP52
| sP54
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP21
| ~ sP41
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP21
| sP41
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP16
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).
thf(28,plain,
( sP13
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP20
| ~ sP15
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP10
| sP20
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP26
| ~ sP23
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP7
| sP26
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP30
| ~ sP23
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP5
| sP30
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP47
| sP52
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP42
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP18
| ~ sP23
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP17
| sP18
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP3
| ~ sP2
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP19
| sP3
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP29
| sP10
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( ~ sP27
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP46
| sP7
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( ~ sP32
| sP5
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP9
| sP47
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( ~ sP31
| sP17
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP45
| sP19
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP6
| sP29
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP15
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( ~ sP53
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( ~ sP37
| sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,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,h13,h14,h12,h10,h8,h6,h23,h24,h22,h20,h18,h16]) ).
thf(53,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h21,52,h23,h24]) ).
thf(54,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h19,53,h21,h22]) ).
thf(55,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h19,h20])],[h17,54,h19,h20]) ).
thf(56,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,55,h17,h18]) ).
thf(57,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h4,56,h15,h16]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,57,h13,h14]) ).
thf(59,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h9,58,h11,h12]) ).
thf(60,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,59,h9,h10]) ).
thf(61,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,60,h7,h8]) ).
thf(62,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h3,61,h5,h6]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,62,h3,h4]) ).
thf(64,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,63,h2]) ).
thf(65,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[64,h0]) ).
thf(0,theorem,
! [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 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[64,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SYO248^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.08 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Sat Aug 26 03:18:13 EDT 2023
% 0.08/0.28 % CPUTime :
% 1.10/1.31 % SZS status Theorem
% 1.10/1.31 % Mode: cade22grackle2xfee4
% 1.10/1.31 % Steps: 4313
% 1.10/1.31 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------