TSTP Solution File: SEV084^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV084^5 : 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 : 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
% WCLimit : 300s
% DateTime : Thu Aug 31 19:32:34 EDT 2023
% Result : Theorem 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of formulae : 37 ( 10 unt; 4 typ; 3 def)
% Number of atoms : 81 ( 3 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 161 ( 38 ~; 14 |; 0 &; 56 @)
% ( 12 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 21 ( 5 ^; 16 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__134,type,
eigen__134: $i > $o ).
thf(ty_eigen__133,type,
eigen__133: $i > $o ).
thf(ty_eigen__132,type,
eigen__132: $i > $o ).
thf(ty_eigen__119,type,
eigen__119: $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__134,definition,
( eigen__134
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ( ( eigen__132 @ eigen__119 )
=> ( eigen__133 @ eigen__119 ) )
=> ~ ( ( eigen__133 @ eigen__119 )
=> ( X1 @ eigen__119 ) ) )
=> ( ( eigen__132 @ eigen__119 )
=> ( X1 @ eigen__119 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__134])]) ).
thf(eigendef_eigen__132,definition,
( eigen__132
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ( ( X1 @ eigen__119 )
=> ( X2 @ eigen__119 ) )
=> ~ ( ( X2 @ eigen__119 )
=> ( X3 @ eigen__119 ) ) )
=> ( ( X1 @ eigen__119 )
=> ( X3 @ eigen__119 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__132])]) ).
thf(eigendef_eigen__133,definition,
( eigen__133
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ( ( eigen__132 @ eigen__119 )
=> ( X1 @ eigen__119 ) )
=> ~ ( ( X1 @ eigen__119 )
=> ( X2 @ eigen__119 ) ) )
=> ( ( eigen__132 @ eigen__119 )
=> ( X2 @ eigen__119 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__133])]) ).
thf(sP1,plain,
( sP1
<=> ( ( eigen__132 @ eigen__119 )
=> ( eigen__133 @ eigen__119 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__134 @ eigen__119 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( sP1
=> ~ ( ( eigen__133 @ eigen__119 )
=> sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ( ( X1 @ eigen__119 )
=> ( X2 @ eigen__119 ) )
=> ~ ( ( X2 @ eigen__119 )
=> ( X3 @ eigen__119 ) ) )
=> ( ( X1 @ eigen__119 )
=> ( X3 @ eigen__119 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ sP3
=> ( ( eigen__132 @ eigen__119 )
=> sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__132 @ eigen__119 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__132 @ eigen__119 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( ~ ( X1
@ ^ [X2: $i] : ~ $false
@ ^ [X2: $i] : $false )
=> ~ ! [X2: $i > $o] : ( X1 @ X2 @ X2 ) )
=> ~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $o] :
( ~ ( sP1
=> ~ ( ( eigen__133 @ eigen__119 )
=> ( X1 @ eigen__119 ) ) )
=> ( sP7
=> ( X1 @ eigen__119 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ( sP7
=> ( X1 @ eigen__119 ) )
=> ~ ( ( X1 @ eigen__119 )
=> ( X2 @ eigen__119 ) ) )
=> ( sP7
=> ( X2 @ eigen__119 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__133 @ eigen__119 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__133 @ eigen__119 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(cTHM120J_pme,conjecture,
~ sP8 ).
thf(h1,negated_conjecture,
sP8,
inference(assume_negation,[status(cth)],[cTHM120J_pme]) ).
thf(1,plain,
( ~ sP11
| ~ sP12
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP1
| ~ sP7
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP6
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP3
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP3
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP5
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP5
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP9
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__134]) ).
thf(10,plain,
( sP10
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__133]) ).
thf(11,plain,
( sP4
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__132]) ).
thf(12,plain,
( ~ sP8
| ~ sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h1]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0]) ).
thf(0,theorem,
~ sP8,
inference(contra,[status(thm),contra(discharge,[h1])],[13,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV084^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : lash -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 : 300
% 0.13/0.34 % DateTime : Thu Aug 24 03:21:00 EDT 2023
% 0.21/0.34 % CPUTime :
% 0.21/0.49 % SZS status Theorem
% 0.21/0.49 % Mode: cade22grackle2xfee4
% 0.21/0.49 % Steps: 53443
% 0.21/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------