TSTP Solution File: PLA054^4 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : PLA054^4 : 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 : n005.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 13:02:28 EDT 2023
% Result : Theorem 0.20s 0.72s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 121
% Syntax : Number of formulae : 131 ( 26 unt; 14 typ; 12 def)
% Number of atoms : 389 ( 12 equ; 1 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 870 ( 156 ~; 52 |; 2 &; 451 @)
% ( 46 <=>; 163 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 70 usr; 67 con; 0-3 aty)
% Number of variables : 129 ( 29 ^; 98 !; 2 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_open,type,
open: $i > mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_h,type,
h: $i > mworld > $o ).
thf(ty_combo,type,
combo: $i > $i > mworld > $o ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_o,type,
o: $i ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__2,type,
eigen__2: mworld ).
thf(ty_d,type,
d: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_closed,type,
closed: $i > mworld > $o ).
thf(h0,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__0 @ X1 )
=> ( open @ d @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__1
@ ^ [X1: $i] :
~ ( ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ( ~ ( ( closed @ d @ X2 )
=> ( ( combo @ d @ d @ X2 )
=> ~ ( h @ X1 @ X2 ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( open @ d @ X3 ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ( ~ ( ( closed @ d @ X2 )
=> ( ~ ( combo @ d @ d @ X2 )
=> ~ ( h @ o @ X2 ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( closed @ d @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld,X2: mworld,X3: mworld] :
( ~ ( ( mrel @ X1 @ X2 )
=> ~ ( mrel @ X2 @ X3 ) )
=> ( mrel @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( mrel @ mactual @ eigen__0 )
=> ~ ( mrel @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ( ( combo @ d @ o @ X1 )
=> ~ ( h @ o @ X1 ) ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( open @ d @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ sP2
=> ( mrel @ mactual @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( closed @ d @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i] :
~ ( ! [X3: mworld] :
( ( mrel @ eigen__0 @ X3 )
=> ~ ( ( combo @ d @ X1 @ X3 )
=> ~ ( h @ X2 @ X3 ) ) )
=> ! [X3: mworld] :
( ( mrel @ eigen__0 @ X3 )
=> ( open @ d @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ( ~ ( ( closed @ d @ X2 )
=> ( ( combo @ d @ d @ X2 )
=> ~ ( h @ X1 @ X2 ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( open @ d @ X3 ) ) ) )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ( ~ ( ( closed @ d @ X2 )
=> ( ~ ( combo @ d @ d @ X2 )
=> ~ ( h @ o @ X2 ) ) )
=> ! [X3: mworld] :
( ( mrel @ X2 @ X3 )
=> ( closed @ d @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( mrel @ eigen__2 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( mrel @ mactual @ eigen__2 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( mrel @ mactual @ eigen__2 )
=> ( ~ ( sP5
=> ( ( combo @ d @ d @ eigen__2 )
=> ~ ( h @ eigen__5 @ eigen__2 ) ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( open @ d @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( h @ eigen__5 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( combo @ d @ eigen__4 @ eigen__2 )
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( mrel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ( ( closed @ d @ X1 )
=> ( ( combo @ d @ d @ X1 )
=> ~ ( h @ eigen__5 @ X1 ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( open @ d @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP14
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( ~ ( ( closed @ d @ X1 )
=> ( ~ ( combo @ d @ d @ X1 )
=> ~ ( h @ o @ X1 ) ) )
=> ! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( closed @ d @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ! [X3: mworld] :
( ( mrel @ mactual @ X3 )
=> ( ~ ( ( closed @ d @ X3 )
=> ( ( combo @ d @ X1 @ X3 )
=> ~ ( h @ X2 @ X3 ) ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( open @ d @ X4 ) ) ) )
=> ~ ! [X3: mworld] :
( ( mrel @ mactual @ X3 )
=> ( ~ ( ( closed @ d @ X3 )
=> ( ~ ( combo @ d @ X1 @ X3 )
=> ~ ( h @ o @ X3 ) ) )
=> ! [X4: mworld] :
( ( mrel @ X3 @ X4 )
=> ( closed @ d @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: mworld] :
( ~ ( ( mrel @ mactual @ eigen__0 )
=> ~ ( mrel @ eigen__0 @ X1 ) )
=> ( mrel @ mactual @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( open @ d @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( sP5
=> ( ( combo @ d @ d @ eigen__2 )
=> ~ sP11 ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( open @ d @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( combo @ d @ d @ eigen__2 )
=> ~ ( h @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( mrel @ mactual @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ( ( combo @ d @ eigen__4 @ X1 )
=> ~ ( h @ eigen__5 @ X1 ) ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( open @ d @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ( ( combo @ d @ d @ X1 )
=> ~ ( h @ eigen__1 @ X1 ) ) )
=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( open @ d @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
~ ( ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ~ ( ( combo @ d @ d @ X2 )
=> ~ ( h @ X1 @ X2 ) ) )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( open @ d @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP13
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( mrel @ mactual @ mactual )
=> ! [X1: $i,X2: $i] :
~ ! [X3: $i] :
( ! [X4: mworld] :
( ( mrel @ mactual @ X4 )
=> ( ~ ( ( closed @ X1 @ X4 )
=> ( ( combo @ X1 @ X2 @ X4 )
=> ~ ( h @ X3 @ X4 ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( open @ X1 @ X5 ) ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ mactual @ X4 )
=> ( ~ ( ( closed @ X1 @ X4 )
=> ( ~ ( combo @ X1 @ X2 @ X4 )
=> ~ ( h @ o @ X4 ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( closed @ X1 @ X5 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: mworld,X2: mworld] :
( ~ ( ( mrel @ mactual @ X1 )
=> ~ ( mrel @ X1 @ X2 ) )
=> ( mrel @ mactual @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
~ ( ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ~ ( ( combo @ d @ o @ X2 )
=> ~ ( h @ X1 @ X2 ) ) )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( open @ d @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP13
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
~ ( ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ~ ( ( combo @ d @ eigen__4 @ X2 )
=> ~ ( h @ X1 @ X2 ) ) )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( open @ d @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP8
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i,X2: $i] :
~ ! [X3: $i] :
( ! [X4: mworld] :
( ( mrel @ mactual @ X4 )
=> ( ~ ( ( closed @ X1 @ X4 )
=> ( ( combo @ X1 @ X2 @ X4 )
=> ~ ( h @ X3 @ X4 ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( open @ X1 @ X5 ) ) ) )
=> ~ ! [X4: mworld] :
( ( mrel @ mactual @ X4 )
=> ( ~ ( ( closed @ X1 @ X4 )
=> ( ~ ( combo @ X1 @ X2 @ X4 )
=> ~ ( h @ o @ X4 ) ) )
=> ! [X5: mworld] :
( ( mrel @ X4 @ X5 )
=> ( closed @ X1 @ X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i,X3: $i] :
~ ! [X4: $i] :
( ! [X5: mworld] :
( ( mrel @ X1 @ X5 )
=> ( ~ ( ( closed @ X2 @ X5 )
=> ( ( combo @ X2 @ X3 @ X5 )
=> ~ ( h @ X4 @ X5 ) ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( open @ X2 @ X6 ) ) ) )
=> ~ ! [X5: mworld] :
( ( mrel @ X1 @ X5 )
=> ( ~ ( ( closed @ X2 @ X5 )
=> ( ~ ( combo @ X2 @ X3 @ X5 )
=> ~ ( h @ o @ X5 ) ) )
=> ! [X6: mworld] :
( ( mrel @ X5 @ X6 )
=> ( closed @ X2 @ X6 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: mworld] : ( mrel @ X1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ( ( combo @ d @ d @ X1 )
=> ~ ( h @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( mrel @ mactual @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( combo @ d @ d @ eigen__2 )
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP13
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( open @ d @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP5
=> sP37 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ( ( combo @ d @ eigen__4 @ X1 )
=> ~ ( h @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( mrel @ mactual @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( combo @ d @ d @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: mworld] :
( ( mrel @ eigen__2 @ X1 )
=> ( open @ d @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( closed @ d @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
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(con,conjecture,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: $i,X3: $i] :
~ ( ! [X4: mworld] :
( ( mrel @ X1 @ X4 )
=> ~ ( ( combo @ d @ X2 @ X4 )
=> ~ ( h @ X3 @ X4 ) ) )
=> ! [X4: mworld] :
( ( mrel @ X1 @ X4 )
=> ( open @ d @ X4 ) ) ) ) ).
thf(h2,negated_conjecture,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: $i,X3: $i] :
~ ( ! [X4: mworld] :
( ( mrel @ X1 @ X4 )
=> ~ ( ( combo @ d @ X2 @ X4 )
=> ~ ( h @ X3 @ X4 ) ) )
=> ! [X4: mworld] :
( ( mrel @ X1 @ X4 )
=> ( open @ d @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h3,assumption,
~ ( sP36
=> ~ sP6 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP36,
introduced(assumption,[]) ).
thf(h5,assumption,
sP6,
introduced(assumption,[]) ).
thf(h6,assumption,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( combo @ d @ eigen__1 @ X1 ) ),
introduced(assumption,[]) ).
thf(1,plain,
( sP12
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP38
| ~ sP13
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP41
| sP38 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP22
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP30
| ~ sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP37
| ~ sP43
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP40
| ~ sP5
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP19
| sP40
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP31
| ~ sP8
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP44
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP10
| ~ sP21
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP20
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP29
| ~ sP13
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP2
| ~ sP36
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP4
| sP2
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP9
| ~ sP21
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP34
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP45
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP14
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP35
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP17
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP27
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(24,plain,
( sP23
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP24
| ~ sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( sP15
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP7
| ~ sP15 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__5]) ).
thf(28,plain,
( ~ sP16
| ~ sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP6
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP32
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(31,plain,
( sP25
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP25
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP39
| ~ sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(34,plain,
( sP3
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP28
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP6
| sP28 ),
inference(all_rule,[status(thm)],]) ).
thf(37,plain,
( ~ sP26
| ~ sP42
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( ~ sP34
| sP42 ),
inference(all_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP1
| sP27 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP33
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(ax2,axiom,
sP45 ).
thf(ax1,axiom,
sP33 ).
thf(mrel_transitive,axiom,
sP1 ).
thf(mrel_reflexive,axiom,
sP34 ).
thf(41,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,h4,h5,ax2,ax1,mrel_transitive,mrel_reflexive]) ).
thf(ax5,axiom,
~ ! [X1: $i] :
~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ( combo @ d @ X1 @ X2 ) ) ).
thf(42,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[ax5,41,h6]) ).
thf(43,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,42,h4,h5]) ).
thf(44,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,43,h3]) ).
thf(45,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[44,h1]) ).
thf(46,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[45,h0]) ).
thf(0,theorem,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: $i,X3: $i] :
~ ( ! [X4: mworld] :
( ( mrel @ X1 @ X4 )
=> ~ ( ( combo @ d @ X2 @ X4 )
=> ~ ( h @ X3 @ X4 ) ) )
=> ! [X4: mworld] :
( ( mrel @ X1 @ X4 )
=> ( open @ d @ X4 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[44,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : PLA054^4 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 06:00:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.72 % SZS status Theorem
% 0.20/0.72 % Mode: cade22grackle2xfee4
% 0.20/0.72 % Steps: 3923
% 0.20/0.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------