TSTP Solution File: SYO897^6 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO897^6 : 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 : n002.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 04:48:31 EDT 2023
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% 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_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(sP1,plain,
( sP1
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( mrel @ mactual @ mactual )
=> ~ ( q @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( q @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( mrel @ mactual @ mactual )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( mrel @ mactual @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ( q @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mworld,X2: mworld] : ( mrel @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mworld] : ( mrel @ mactual @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
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,
( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ( p @ X1 ) )
=> ( sP6
=> ~ sP1 ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ( p @ X1 ) )
=> ( sP6
=> ~ sP1 ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ( p @ X1 ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP6
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( ( mrel @ mactual @ eigen__0 )
=> ~ ( p @ eigen__0 ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
mrel @ mactual @ eigen__0,
introduced(assumption,[]) ).
thf(h5,assumption,
p @ eigen__0,
introduced(assumption,[]) ).
thf(h6,assumption,
sP6,
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP2
| ~ sP5
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| ~ sP5
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP7
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP1
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(mrel_universal,axiom,
sP7 ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h6,h7,h4,h5,h3,h1,h2,h0])],[1,2,3,4,5,6,h6,h7,mrel_universal]) ).
thf(8,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h2,7,h6,h7]) ).
thf(9,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,8,h4,h5]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,9,h3]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).
thf(0,theorem,
( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ( p @ X1 ) )
=> ( sP6
=> ~ sP1 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO897^6 : TPTP v8.1.2. Released v8.1.0.
% 0.06/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n002.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 07:23:03 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % Mode: cade22grackle2xfee4
% 0.13/0.39 % Steps: 11
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------