TSTP Solution File: SEV101^5 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV101^5 : 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 : n015.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 19:32:37 EDT 2023
% Result : Theorem 0.18s 0.53s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 39
% Syntax : Number of formulae : 48 ( 13 unt; 4 typ; 4 def)
% Number of atoms : 113 ( 4 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 271 ( 57 ~; 18 |; 0 &; 117 @)
% ( 16 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 20 con; 0-2 aty)
% Number of variables : 69 ( 10 ^; 59 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__112,type,
eigen__112: $i > $o ).
thf(ty_eigen__120,type,
eigen__120: $i > $o ).
thf(ty_eigen__132,type,
eigen__132: $i ).
thf(ty_eigen__126,type,
eigen__126: $i > $o ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__112,definition,
( eigen__112
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__112])]) ).
thf(eigendef_eigen__126,definition,
( eigen__126
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ! [X2: $i] :
( ( eigen__112 @ X2 )
=> ( eigen__120 @ X2 ) )
=> ~ ! [X2: $i] :
( ( eigen__120 @ X2 )
=> ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__112 @ X2 )
=> ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__126])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__132,definition,
( eigen__132
= ( eps__1
@ ^ [X1: $i] :
~ ( ( eigen__112 @ X1 )
=> ( eigen__126 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__132])]) ).
thf(eigendef_eigen__120,definition,
( eigen__120
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ! [X3: $i] :
( ( eigen__112 @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( eigen__112 @ X3 )
=> ( X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__120])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ! [X2: $i > $o,X3: $i] :
( ~ ( X1 @ X2 @ X2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ! [X5: $i] :
( ~ ( X1 @ X2 @ X3 @ X5 )
=> ( X3 @ X5 ) )
=> ~ ! [X5: $i] :
( ~ ( X1 @ X3 @ X4 @ X5 )
=> ( X4 @ X5 ) ) )
=> ! [X5: $i] :
( ~ ( X1 @ X2 @ X4 @ X5 )
=> ( X4 @ X5 ) ) ) )
=> ! [X2: $i] :
( X1
@ ^ [X3: $i] : ~ $false
@ ^ [X3: $i] : $false
@ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__112 @ eigen__132 )
=> ( eigen__126 @ eigen__132 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__126 @ eigen__132 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ! [X1: $i] :
( ( eigen__112 @ X1 )
=> ( eigen__120 @ X1 ) )
=> ~ ! [X1: $i] :
( ( eigen__120 @ X1 )
=> ( eigen__126 @ X1 ) ) )
=> ! [X1: $i] :
( ( eigen__112 @ X1 )
=> ( eigen__126 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__112 @ eigen__132 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eigen__112 @ X1 )
=> ( eigen__126 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ! [X3: $i] :
( ( eigen__112 @ X3 )
=> ( X1 @ X3 ) )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( eigen__112 @ X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: $i] :
( ( eigen__112 @ X1 )
=> ( eigen__120 @ X1 ) )
=> ~ ! [X1: $i] :
( ( eigen__120 @ X1 )
=> ( eigen__126 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ! [X3: $i > $o,X4: $i] :
( ~ ( X2 @ X3 @ X3 @ X4 )
=> ( X1 @ X3 @ X3 @ X4 ) )
=> ~ ! [X3: $i > $o,X4: $i > $o,X5: $i > $o] :
( ~ ( ! [X6: $i] :
( ~ ( X2 @ X3 @ X4 @ X6 )
=> ( X1 @ X3 @ X4 @ X6 ) )
=> ~ ! [X6: $i] :
( ~ ( X2 @ X4 @ X5 @ X6 )
=> ( X1 @ X4 @ X5 @ X6 ) ) )
=> ! [X6: $i] :
( ~ ( X2 @ X3 @ X5 @ X6 )
=> ( X1 @ X3 @ X5 @ X6 ) ) ) )
=> ! [X3: $i] :
( ~ ( X2
@ ^ [X4: $i] : ~ $false
@ ^ [X4: $i] : $false
@ X3 )
=> ( X1
@ ^ [X4: $i] : ~ $false
@ ^ [X4: $i] : $false
@ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__120 @ eigen__132 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__112 @ X1 )
=> ( eigen__120 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__120 @ eigen__132 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i > $o] :
( ~ ( sP11
=> ~ ! [X2: $i] :
( ( eigen__120 @ X2 )
=> ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__112 @ X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( eigen__120 @ X1 )
=> ( eigen__126 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP5
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ X4 ) )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(cTHM120E_pme,conjecture,
~ sP9 ).
thf(h2,negated_conjecture,
sP9,
inference(assume_negation,[status(cth)],[cTHM120E_pme]) ).
thf(1,plain,
( ~ sP15
| ~ sP5
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| ~ sP12
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP14
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP8
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP8
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP2
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP2
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP6
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__132]) ).
thf(10,plain,
( sP4
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP4
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP13
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__126]) ).
thf(13,plain,
( sP7
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__120]) ).
thf(14,plain,
( sP16
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__112]) ).
thf(15,plain,
( ~ sP1
| ~ sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP9
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h2]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[17,h1]) ).
thf(19,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[18,h0]) ).
thf(0,theorem,
~ sP9,
inference(contra,[status(thm),contra(discharge,[h2])],[17,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV101^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Aug 24 04:01:35 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.53 % SZS status Theorem
% 0.18/0.53 % Mode: cade22grackle2xfee4
% 0.18/0.53 % Steps: 3822
% 0.18/0.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------