TSTP Solution File: SYO889^16 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO889^16 : 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 : n004.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 : Fri Sep 1 04:48:29 EDT 2023
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 67
% Syntax : Number of formulae : 78 ( 25 unt; 9 typ; 11 def)
% Number of atoms : 186 ( 11 equ; 1 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 351 ( 67 ~; 24 |; 3 &; 175 @)
% ( 21 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 37 con; 0-2 aty)
% Number of variables : 70 ( 30 ^; 38 !; 2 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_eigen__4,type,
eigen__4: mworld ).
thf(ty_b,type,
b: $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_a,type,
a: $i > mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(h0,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: mworld] :
~ ( ( mrel @ eigen__0 @ X1 )
=> ~ ( b @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( a @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( mrel @ eigen__0 @ eigen__4 )
=> ( ( a @ eigen__1 @ eigen__4 )
=> ~ ( b @ eigen__1 @ eigen__4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( mrel @ mactual @ eigen__0 )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( ( a @ X1 @ X2 )
=> ~ ( b @ X1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ~ ( b @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( ( a @ X2 @ X3 )
=> ~ ( b @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ~ ( b @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( mrel @ eigen__0 @ eigen__4 )
=> ~ ( b @ eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( a @ eigen__1 @ eigen__4 )
=> ~ ( b @ eigen__1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mworld] :
( ( mrel @ eigen__0 @ X1 )
=> ( ( a @ eigen__1 @ X1 )
=> ~ ( b @ eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( a @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( b @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( mrel @ eigen__0 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ~ ( b @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( mrel @ mactual @ eigen__0 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eiw_di @ eigen__1 @ eigen__0 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( mrel @ mactual @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP12
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( ( a @ X1 @ X2 )
=> ~ ( b @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eiw_di @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( sP19
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
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: mworld] :
( ( mrel @ X1 @ X3 )
=> ( a @ X2 @ X3 ) ) ) )
=> ~ sP13 )
=> ~ sP5 ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( a @ X2 @ X3 ) ) ) )
=> ~ sP13 )
=> ~ sP5 ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h2,assumption,
~ ( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( a @ X2 @ X3 ) ) ) )
=> ~ sP13 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( a @ X2 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP13,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP16
=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( a @ X1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP16,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ~ ! [X2: mworld] :
( ( mrel @ eigen__0 @ X2 )
=> ( a @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP19
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP19,
introduced(assumption,[]) ).
thf(h11,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP8
| ~ sP10
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP17
| ~ sP12
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP2
| ~ sP12
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP9
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP7
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP7
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP4
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(9,plain,
( ~ sP15
| ~ sP19
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP20
| ~ sP19
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP6
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP18
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP3
| ~ sP16
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP14
| ~ sP16
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP5
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP13
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,h7,h10,h11,h5,h3]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,17,h10,h11]) ).
thf(19,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__1)],[h8,18,h9]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,19,h7,h8]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h4,20,h6]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,21,h4,h5]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,22,h2,h3]) ).
thf(24,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[23,h0]) ).
thf(0,theorem,
( ~ ( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ! [X3: mworld] :
( ( mrel @ X1 @ X3 )
=> ( a @ X2 @ X3 ) ) ) )
=> ~ sP13 )
=> ~ sP5 ),
inference(contra,[status(thm),contra(discharge,[h1])],[23,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO889^16 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : Fri Aug 25 23:59:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % Mode: cade22grackle2xfee4
% 0.19/0.43 % Steps: 431
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------