TSTP Solution File: SET044^23 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET044^23 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n028.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 04:50:16 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 50
% Syntax : Number of formulae : 58 ( 20 unt; 6 typ; 11 def)
% Number of atoms : 155 ( 25 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 282 ( 54 ~; 20 |; 0 &; 160 @)
% ( 14 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 30 con; 0-3 aty)
% Number of variables : 47 ( 24 ^ 23 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_element,type,
element: $i > $i > mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_mactual,type,
mactual: mworld ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ( element @ X2 @ X1 @ mactual )
= ( ~ ( element @ X2 @ eigen__0 @ mactual ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ( ( element @ X1 @ eigen__0 @ mactual )
= ( element @ X1 @ X1 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( element @ eigen__1 @ eigen__1 @ mactual )
= ( ~ ( element @ eigen__1 @ eigen__0 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ( element @ X2 @ X1 @ mactual )
= ( ~ ( element @ X2 @ eigen__0 @ mactual ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( eiw_di @ eigen__1 @ mactual )
=> ( ( element @ eigen__1 @ eigen__0 @ mactual )
= ( element @ eigen__1 @ eigen__1 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eiw_di @ eigen__1 @ mactual )
=> ~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ( ( element @ X1 @ eigen__1 @ mactual )
= ( ~ ( element @ X1 @ eigen__0 @ mactual ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eiw_di @ eigen__0 @ mactual )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( eiw_di @ eigen__1 @ mactual )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( element @ eigen__1 @ eigen__0 @ mactual )
= ( element @ eigen__1 @ eigen__1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eiw_di @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ mactual )
=> ( ( element @ X3 @ X2 @ mactual )
= ( ~ ( element @ X3 @ X1 @ mactual ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( element @ eigen__1 @ eigen__1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ( ( element @ X1 @ eigen__1 @ mactual )
= ( ~ ( element @ X1 @ eigen__0 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( eiw_di @ eigen__1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( element @ eigen__1 @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(def_mlocal,definition,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ).
thf(def_mforall_di,definition,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(pel40,conjecture,
( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ( element @ X2 @ X1 @ mactual )
= ( element @ X2 @ X2 @ mactual ) ) ) )
=> ~ sP10 ) ).
thf(h1,negated_conjecture,
~ ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ( element @ X2 @ X1 @ mactual )
= ( element @ X2 @ X2 @ mactual ) ) ) )
=> ~ sP10 ),
inference(assume_negation,[status(cth)],[pel40]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ( element @ X2 @ X1 @ mactual )
= ( element @ X2 @ X2 @ mactual ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP10,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP9
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP9,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP11
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP11
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| ~ sP14
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| sP14
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| ~ sP13
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP4
| ~ sP13
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP5
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP5
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP3
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(12,plain,
( ~ sP10
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP6
| ~ sP9
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h5,h6,h3]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,14,h5,h6]) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h2,15,h4]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,16,h2,h3]) ).
thf(18,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[17,h0]) ).
thf(0,theorem,
( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ( element @ X2 @ X1 @ mactual )
= ( element @ X2 @ X2 @ mactual ) ) ) )
=> ~ sP10 ),
inference(contra,[status(thm),contra(discharge,[h1])],[17,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET044^23 : TPTP v8.1.0. Released v8.1.0.
% 0.08/0.15 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jul 10 07:32:27 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % Mode: mode213
% 0.14/0.40 % Inferences: 14
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------