TSTP Solution File: SET047^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET047^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 15:15:33 EDT 2023
% Result : Theorem 21.47s 20.44s
% Output : Proof 21.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 53
% Syntax : Number of formulae : 61 ( 23 unt; 8 typ; 12 def)
% Number of atoms : 150 ( 34 equ; 1 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 219 ( 26 ~; 23 |; 2 &; 150 @)
% ( 15 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 33 con; 0-3 aty)
% Number of variables : 52 ( 29 ^; 21 !; 2 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_element,type,
element: $i > $i > mworld > $o ).
thf(ty_set_equal,type,
set_equal: $i > $i > mworld > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
( ( element @ X1 @ eigen__1 @ mactual )
!= ( element @ X1 @ eigen__0 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
( ( element @ X1 @ eigen__0 @ mactual )
!= ( element @ X1 @ eigen__1 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i] :
( ( set_equal @ X1 @ X2 @ mactual )
= ( ! [X3: $i] :
( ( element @ X3 @ X1 @ mactual )
= ( element @ X3 @ X2 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( element @ X1 @ eigen__1 @ mactual )
= ( element @ X1 @ eigen__0 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( set_equal @ eigen__1 @ X1 @ mactual )
= ( ! [X2: $i] :
( ( element @ X2 @ eigen__1 @ mactual )
= ( element @ X2 @ X1 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( set_equal @ eigen__1 @ eigen__0 @ mactual )
= sP2 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( element @ eigen__2 @ eigen__1 @ mactual )
= ( element @ eigen__2 @ eigen__0 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( set_equal @ eigen__1 @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( element @ eigen__3 @ eigen__1 @ mactual )
= ( element @ eigen__3 @ eigen__0 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( set_equal @ eigen__0 @ X1 @ mactual )
= ( ! [X2: $i] :
( ( element @ X2 @ eigen__0 @ mactual )
= ( element @ X2 @ X1 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( set_equal @ eigen__0 @ eigen__1 @ mactual )
= ( ! [X1: $i] :
( ( element @ X1 @ eigen__0 @ mactual )
= ( element @ X1 @ eigen__1 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( element @ eigen__3 @ eigen__0 @ mactual )
= ( element @ eigen__3 @ eigen__1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( set_equal @ eigen__0 @ eigen__1 @ mactual )
= sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( set_equal @ eigen__0 @ eigen__1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( element @ eigen__2 @ eigen__0 @ mactual )
= ( element @ eigen__2 @ eigen__1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( element @ X1 @ eigen__0 @ mactual )
= ( element @ X1 @ eigen__1 @ 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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(pel43,conjecture,
! [X1: $i,X2: $i] :
( ( set_equal @ X1 @ X2 @ mactual )
= ( set_equal @ X2 @ X1 @ mactual ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( set_equal @ X1 @ X2 @ mactual )
= ( set_equal @ X2 @ X1 @ mactual ) ),
inference(assume_negation,[status(cth)],[pel43]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( set_equal @ eigen__0 @ X1 @ mactual )
= ( set_equal @ X1 @ eigen__0 @ mactual ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP14
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP10
| sP7 ),
inference(symeq,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| sP13 ),
inference(symeq,[status(thm)],]) ).
thf(5,plain,
( sP2
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(6,plain,
( sP14
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(7,plain,
( ~ sP4
| ~ sP6
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP4
| sP6
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP9
| ~ sP12
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP9
| sP12
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP1
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP11
| ~ sP12
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP11
| sP12
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(pel43_1,axiom,
sP1 ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,pel43_1,h3]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,17,h3]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,18,h2]) ).
thf(20,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[19,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( set_equal @ X1 @ X2 @ mactual )
= ( set_equal @ X2 @ X1 @ mactual ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[19,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET047^1 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.33 % CPULimit : 300
% 0.19/0.33 % WCLimit : 300
% 0.19/0.33 % DateTime : Sat Aug 26 13:23:26 EDT 2023
% 0.19/0.33 % CPUTime :
% 21.47/20.44 % SZS status Theorem
% 21.47/20.44 % Mode: cade22grackle2x798d
% 21.47/20.44 % Steps: 199
% 21.47/20.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------