TSTP Solution File: SYO891^16 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO891^16 : 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 : n023.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 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_p,type,
p: $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: mworld ).
thf(sP1,plain,
( sP1
<=> ( p @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( eiw_di @ eigen__0 @ mactual )
=> ~ ( mrel @ mactual @ eigen__1 ) )
=> ( eiw_di @ eigen__0 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eiw_di @ eigen__0 @ eigen__1 )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__1 )
=> ~ ( p @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eiw_di @ eigen__0 @ mactual )
=> ~ ( mrel @ mactual @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ mactual )
=> ~ ( mrel @ mactual @ eigen__1 ) )
=> ( eiw_di @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( mrel @ mactual @ eigen__1 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ~ ( p @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( mrel @ mactual @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eiw_di @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eiw_di @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ mactual )
=> ~ ( mrel @ mactual @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: mworld,X2: mworld,X3: $i] :
( ~ ( ( eiw_di @ X3 @ X1 )
=> ~ ( mrel @ X1 @ X2 ) )
=> ( eiw_di @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
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: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( qmltpeq @ X1 @ X3 @ X2 ) ) ) )
=> ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ( p @ X1 @ X2 ) ) )
=> ~ sP8 ) ) ).
thf(h0,negated_conjecture,
~ ( ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( qmltpeq @ X1 @ X3 @ X2 ) ) ) )
=> ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ( p @ X1 @ X2 ) ) )
=> ~ sP8 ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( qmltpeq @ X1 @ X3 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ( p @ X1 @ X2 ) ) )
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ( p @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP8,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP11
=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ( p @ eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP11,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ( p @ eigen__0 @ X1 ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP9
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP9,
introduced(assumption,[]) ).
thf(h10,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| ~ sP11
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP5
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| ~ sP10
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP7
| ~ sP9
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP12
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(eiw_di_cumul,axiom,
sP13 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,h6,h9,h10,h4,eiw_di_cumul]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,10,h9,h10]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h7,11,h8]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,12,h6,h7]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h3,13,h5]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,14,h3,h4]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,15,h1,h2]) ).
thf(0,theorem,
( ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ! [X3: $i] :
( ( eiw_di @ X3 @ X2 )
=> ~ ( qmltpeq @ X1 @ X3 @ X2 ) ) ) )
=> ( ~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ( p @ X1 @ X2 ) ) )
=> ~ sP8 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO891^16 : TPTP v8.1.2. Released v8.1.0.
% 0.10/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n023.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 : Sat Aug 26 07:17:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % Mode: cade22grackle2xfee4
% 0.19/0.41 % Steps: 97
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------