TSTP Solution File: SET579^3 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET579^3 : 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 : n032.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 15:17:33 EDT 2023
% Result : Theorem 23.60s 23.85s
% Output : Proof 23.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 87
% Syntax : Number of formulae : 97 ( 24 unt; 11 typ; 12 def)
% Number of atoms : 240 ( 33 equ; 1 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 467 ( 59 ~; 35 |; 2 &; 306 @)
% ( 31 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 50 con; 0-3 aty)
% Number of variables : 72 ( 29 ^; 41 !; 2 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_difference,type,
difference: $i > $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_subset,type,
subset: $i > $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_member,type,
member: $i > $i > mworld > $o ).
thf(ty_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( member @ X1 @ eigen__0 @ mactual )
=> ( member @ X1 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ( member @ X1 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual )
=> ( member @ X1 @ eigen__0 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( member @ X1 @ eigen__0 @ mactual )
= ( ~ ( ( member @ X1 @ eigen__1 @ mactual )
=> ( member @ X1 @ eigen__2 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i] :
( ( qmltpeq @ eigen__0 @ X1 @ mactual )
= ( ~ ( ( subset @ eigen__0 @ X1 @ mactual )
=> ~ ( subset @ X1 @ eigen__0 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( member @ X2 @ ( difference @ eigen__1 @ X1 ) @ mactual )
= ( ~ ( ( member @ X2 @ eigen__1 @ mactual )
=> ( member @ X2 @ X1 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( member @ eigen__4 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( qmltpeq @ X1 @ X2 @ mactual )
= ( ~ ( ( subset @ X1 @ X2 @ mactual )
=> ~ ( subset @ X2 @ X1 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( member @ X1 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual )
=> ( member @ X1 @ eigen__0 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( subset @ eigen__0 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual )
=> ~ ( subset @ ( difference @ eigen__1 @ eigen__2 ) @ eigen__0 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( member @ eigen__4 @ eigen__0 @ mactual )
= ( ~ ( ( member @ eigen__4 @ eigen__1 @ mactual )
=> ( member @ eigen__4 @ eigen__2 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( member @ eigen__4 @ eigen__0 @ mactual )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( member @ eigen__4 @ eigen__1 @ mactual )
=> ( member @ eigen__4 @ eigen__2 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( member @ eigen__7 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( subset @ eigen__0 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual )
= ( ! [X1: $i] :
( ( member @ X1 @ eigen__0 @ mactual )
=> ( member @ X1 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( member @ eigen__4 @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( member @ X3 @ ( difference @ X1 @ X2 ) @ mactual )
= ( ~ ( ( member @ X3 @ X1 @ mactual )
=> ( member @ X3 @ X2 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( subset @ ( difference @ eigen__1 @ eigen__2 ) @ eigen__0 @ mactual )
= sP6 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( member @ eigen__7 @ eigen__1 @ mactual )
=> ( member @ eigen__7 @ eigen__2 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( member @ X1 @ eigen__0 @ mactual )
=> ( member @ X1 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( subset @ ( difference @ eigen__1 @ eigen__2 ) @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i] :
( ( subset @ ( difference @ eigen__1 @ eigen__2 ) @ X1 @ mactual )
= ( ! [X2: $i] :
( ( member @ X2 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual )
=> ( member @ X2 @ X1 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( member @ eigen__7 @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( qmltpeq @ eigen__0 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP11
=> sP20 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP11 = ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( subset @ eigen__0 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP20 = ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP21 = ~ sP7 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 @ mactual )
= ( ! [X3: $i] :
( ( member @ X3 @ X1 @ mactual )
=> ( member @ X3 @ X2 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( subset @ eigen__0 @ X1 @ mactual )
= ( ! [X2: $i] :
( ( member @ X2 @ eigen__0 @ mactual )
=> ( member @ X2 @ X1 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP4 = ~ sP10 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( member @ X1 @ ( difference @ eigen__1 @ eigen__2 ) @ mactual )
= ( ~ ( ( member @ X1 @ eigen__1 @ mactual )
=> ( member @ X1 @ eigen__2 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
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(prove_th20,conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ! [X4: $i] :
( ( member @ X4 @ X1 @ mactual )
= ( ~ ( ( member @ X4 @ X2 @ mactual )
=> ( member @ X4 @ X3 @ mactual ) ) ) )
=> ( qmltpeq @ X1 @ ( difference @ X2 @ X3 ) @ mactual ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i] :
( ! [X4: $i] :
( ( member @ X4 @ X1 @ mactual )
= ( ~ ( ( member @ X4 @ X2 @ mactual )
=> ( member @ X4 @ X3 @ mactual ) ) ) )
=> ( qmltpeq @ X1 @ ( difference @ X2 @ X3 ) @ mactual ) ),
inference(assume_negation,[status(cth)],[prove_th20]) ).
thf(h2,assumption,
~ ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( member @ X3 @ eigen__0 @ mactual )
= ( ~ ( ( member @ X3 @ X1 @ mactual )
=> ( member @ X3 @ X2 @ mactual ) ) ) )
=> ( qmltpeq @ eigen__0 @ ( difference @ X1 @ X2 ) @ mactual ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ! [X2: $i] :
( ( member @ X2 @ eigen__0 @ mactual )
= ( ~ ( ( member @ X2 @ eigen__1 @ mactual )
=> ( member @ X2 @ X1 @ mactual ) ) ) )
=> ( qmltpeq @ eigen__0 @ ( difference @ eigen__1 @ X1 ) @ mactual ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP1
=> sP21 ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(h6,assumption,
~ sP21,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP25
| sP20
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP23
| ~ sP11
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| ~ sP13
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP29
| sP4
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP25 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP30
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP30
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( sP22
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP22
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP9
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP9
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP7
| ~ sP24
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP6
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(15,plain,
( sP17
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(16,plain,
( ~ sP26
| sP21
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP15
| sP18
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP12
| sP24
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP3
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP2
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP19
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP28
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP14
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP27
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP27
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(difference_defn,axiom,
sP14 ).
thf(equal_defn,axiom,
sP5 ).
thf(subset_defn,axiom,
sP27 ).
thf(27,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,difference_defn,equal_defn,subset_defn,h5,h6]) ).
thf(28,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,27,h5,h6]) ).
thf(29,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,28,h4]) ).
thf(30,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,29,h3]) ).
thf(31,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,30,h2]) ).
thf(32,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[31,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i,X3: $i] :
( ! [X4: $i] :
( ( member @ X4 @ X1 @ mactual )
= ( ~ ( ( member @ X4 @ X2 @ mactual )
=> ( member @ X4 @ X3 @ mactual ) ) ) )
=> ( qmltpeq @ X1 @ ( difference @ X2 @ X3 ) @ mactual ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[31,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET579^3 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.31 % Computer : n032.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Aug 26 16:02:13 EDT 2023
% 0.10/0.31 % CPUTime :
% 23.60/23.85 % SZS status Theorem
% 23.60/23.85 % Mode: cade22grackle2x798d
% 23.60/23.85 % Steps: 33261
% 23.60/23.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------