TSTP Solution File: PLA053^18 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : PLA053^18 : 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 13:02:27 EDT 2023
% Result : Theorem 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 65
% Syntax : Number of formulae : 76 ( 26 unt; 11 typ; 11 def)
% Number of atoms : 194 ( 11 equ; 1 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 429 ( 81 ~; 18 |; 3 &; 227 @)
% ( 18 <=>; 82 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 35 con; 0-2 aty)
% Number of variables : 76 ( 30 ^; 44 !; 2 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(ty_defused,type,
defused: $i > mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_bomb,type,
bomb: $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_h,type,
h: $i > mworld > $o ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( ~ ( ( bomb @ eigen__1 @ X2 )
=> ~ ( h @ X1 @ X2 ) )
=> ( defused @ eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X1 )
=> ~ ! [X4: mworld] :
( ( mrel @ X1 @ X4 )
=> ( ~ ( ( bomb @ X2 @ X4 )
=> ~ ( h @ X3 @ X4 ) )
=> ( defused @ X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( mrel @ mactual @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eiw_di @ eigen__1 @ eigen__0 )
=> ~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( ~ ( ( bomb @ eigen__1 @ X2 )
=> ~ ( h @ X1 @ X2 ) )
=> ( defused @ eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ eigen__0 )
=> ~ ! [X3: mworld] :
( ( mrel @ eigen__0 @ X3 )
=> ( ~ ( ( bomb @ X1 @ X3 )
=> ~ ( h @ X2 @ X3 ) )
=> ( defused @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eiw_di @ eigen__9 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ( bomb @ eigen__1 @ eigen__0 )
=> ~ ( h @ eigen__9 @ eigen__0 ) )
=> ( defused @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mworld] : ( mrel @ eigen__0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ~ ( ( bomb @ eigen__1 @ X1 )
=> ~ ( h @ eigen__9 @ X1 ) )
=> ( defused @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( mrel @ eigen__0 @ eigen__0 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eiw_di @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( mrel @ eigen__0 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP5
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP5
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: mworld,X2: mworld] : ( mrel @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( ~ ( ( bomb @ eigen__1 @ X2 )
=> ~ ( h @ X1 @ X2 ) )
=> ( defused @ eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ( ~ ( ( bomb @ eigen__1 @ eigen__0 )
=> ~ ( h @ X1 @ eigen__0 ) )
=> ( defused @ eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP2
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
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] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( 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(con,conjecture,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X1 )
=> ~ ( ~ ( ( bomb @ X2 @ X1 )
=> ~ ( h @ X3 @ X1 ) )
=> ( defused @ X2 @ X1 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X1 )
=> ~ ( ~ ( ( bomb @ X2 @ X1 )
=> ~ ( h @ X3 @ X1 ) )
=> ( defused @ X2 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h2,assumption,
~ ( sP2
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ eigen__0 )
=> ~ ( ~ ( ( bomb @ X1 @ eigen__0 )
=> ~ ( h @ X2 @ eigen__0 ) )
=> ( defused @ X1 @ eigen__0 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP2,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ eigen__0 )
=> ~ ( ~ ( ( bomb @ X1 @ eigen__0 )
=> ~ ( h @ X2 @ eigen__0 ) )
=> ( defused @ X1 @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP10
=> ~ sP16 ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP10,
introduced(assumption,[]) ).
thf(h7,assumption,
sP16,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( ( eiw_di @ eigen__2 @ mactual )
=> ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ~ ( ( bomb @ X2 @ X1 )
=> ~ ( h @ eigen__2 @ X1 ) )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( bomb @ X2 @ X3 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
eiw_di @ eigen__2 @ mactual,
introduced(assumption,[]) ).
thf(h10,assumption,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( ~ ( ( bomb @ X2 @ X1 )
=> ~ ( h @ eigen__2 @ X1 ) )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( bomb @ X2 @ X3 ) ) ) ) ),
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP12
| ~ sP5
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP9
| ~ sP11
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP13
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP13
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP15
| ~ sP13 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(8,plain,
( ~ sP3
| ~ sP10
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP17
| ~ sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP14
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP1
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(ax3,axiom,
sP1 ).
thf(mrel_universal,axiom,
sP14 ).
thf(14,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,h3,h6,h7,ax3,mrel_universal]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,14,h9,h10]) ).
thf(ax2,axiom,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ( ~ ( ( bomb @ X3 @ X2 )
=> ~ ( h @ X1 @ X2 ) )
=> ! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( bomb @ X3 @ X4 ) ) ) ) ) ) ).
thf(16,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__2)],[ax2,15,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,16,h6,h7]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,17,h5]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,18,h3,h4]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,19,h2]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X1 )
=> ~ ( ~ ( ( bomb @ X2 @ X1 )
=> ~ ( h @ X3 @ X1 ) )
=> ( defused @ X2 @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[20,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PLA053^18 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13 % 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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 06:10:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 % Mode: cade22grackle2xfee4
% 0.21/0.48 % Steps: 856
% 0.21/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------