TSTP Solution File: SYO898^9 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO898^9 : 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 : n026.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 04:48:32 EDT 2023
% Result : Theorem 0.14s 0.36s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 35
% Syntax : Number of formulae : 41 ( 16 unt; 6 typ; 9 def)
% Number of atoms : 76 ( 9 equ; 1 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 100 ( 22 ~; 10 |; 2 &; 43 @)
% ( 10 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 22 con; 0-2 aty)
% Number of variables : 33 ( 24 ^; 8 !; 1 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_q,type,
q: mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_p,type,
p: mworld > $o ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(h0,assumption,
! [X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: mworld] :
~ ~ ( mrel @ mactual @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ( ( q @ X1 )
=> ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( mrel @ mactual @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mworld] :
~ ( mrel @ mactual @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( p @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( p @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mworld] :
~ ! [X2: mworld] :
~ ( mrel @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP2
=> ~ ( ( q @ eigen__0 )
=> sP4 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP2
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( q @ eigen__0 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
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(con,conjecture,
( sP5
=> ~ sP1 ) ).
thf(h1,negated_conjecture,
~ ( sP5
=> ~ sP1 ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h2,assumption,
sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP9
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP7
| ~ sP2
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| ~ sP2
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( sP3
| sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(7,plain,
( ~ sP6
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(mrel_serial,axiom,
sP6 ).
thf(8,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,3,4,5,6,7,h2,h3,mrel_serial]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,8,h2,h3]) ).
thf(10,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0]) ).
thf(0,theorem,
( sP5
=> ~ sP1 ),
inference(contra,[status(thm),contra(discharge,[h1])],[9,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO898^9 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 08:27:48 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % SZS status Theorem
% 0.14/0.36 % Mode: cade22grackle2xfee4
% 0.14/0.36 % Steps: 32
% 0.14/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------