TSTP Solution File: SEV088^5 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV088^5 : 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 : n012.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 : Tue Jul 19 18:04:48 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 23
% Syntax : Number of formulae : 33 ( 15 unt; 0 typ; 5 def)
% Number of atoms : 79 ( 5 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 142 ( 50 ~; 10 |; 0 &; 47 @)
% ( 10 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 19 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 48 ( 5 ^ 43 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i] : ~ $false ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: $i] :
~ ~ $false ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ! [X2: $i] : ~ $false
=> ~ ! [X2: $i] : ~ $false )
=> ! [X2: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ! [X3: $i] : ~ $false
=> ~ ! [X3: $i] : ~ $false )
=> ! [X3: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ! [X4: $i] : ~ $false
=> ~ ! [X4: $i] : ~ $false )
=> ! [X4: $i] : ~ $false ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ( !! @ ( X1 @ X2 @ X3 ) )
=> ~ ( !! @ ( X1 @ X3 @ X4 ) ) )
=> ( !! @ ( X1 @ X2 @ X4 ) ) )
=> ~ ! [X2: $i > $o] : ( !! @ ( X1 @ X2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] : ~ $false ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( sP2
=> ~ sP2 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> $false ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i > $o,X2: $i > $o] : sP3 ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [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 > $o,X4: $i] :
( ~ ( X2 @ X3 @ X3 @ X4 )
=> ( X1 @ X3 @ X3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] : sP3
=> ~ ! [X1: $i > $o,X2: $i] : ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $o] : sP2 ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $o] : sP5 ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o] : sP3 ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(cTHM120G_pme,conjecture,
~ sP6 ).
thf(h2,negated_conjecture,
sP6,
inference(assume_negation,[status(cth)],[cTHM120G_pme]) ).
thf(1,plain,
( sP3
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
~ sP4,
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP10
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(4,plain,
( sP2
| sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(5,plain,
( sP5
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(6,plain,
( sP8
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(7,plain,
( sP9
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(8,plain,
( ~ sP7
| ~ sP9
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h2]) ).
thf(12,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[11,h1]) ).
thf(13,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[12,h0]) ).
thf(0,theorem,
~ sP6,
inference(contra,[status(thm),contra(discharge,[h2])],[11,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEV088^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 28 17:07:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.35 % SZS status Theorem
% 0.13/0.35 % Mode: mode213
% 0.13/0.35 % Inferences: 124
% 0.13/0.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------