TSTP Solution File: SYO892^15 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO892^15 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 : 600s
% DateTime : Thu Jul 21 19:35:12 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: mworld ).
thf(ty_mrel,type,
mrel: mworld > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_f,type,
f: $i > mworld > $o ).
thf(sP1,plain,
( sP1
<=> ( eiw_di @ eigen__1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eiw_di @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: mworld,X2: mworld,X3: $i] :
( ~ ( ( eiw_di @ X3 @ X1 )
=> ~ ( mrel @ X1 @ X2 ) )
=> ( eiw_di @ X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: mworld,X2: $i] :
( ~ ( ( eiw_di @ X2 @ mactual )
=> ~ ( mrel @ mactual @ X1 ) )
=> ( eiw_di @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( mrel @ mactual @ eigen__0 )
=> ~ ( f @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP2
=> ( f @ eigen__1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( ( eiw_di @ X1 @ mactual )
=> ~ ( mrel @ mactual @ eigen__0 ) )
=> ( eiw_di @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ eigen__0 )
=> ( f @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ( f @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( f @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( sP1
=> ~ ( mrel @ mactual @ eigen__0 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP1
=> ~ ( mrel @ mactual @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( mrel @ mactual @ eigen__0 ) ),
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] :
( ( 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] :
( ( 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] :
( ( 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 )
=> ( f @ X2 @ X1 ) ) )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ( f @ X1 @ X2 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( f @ X2 @ X1 ) ) )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ( f @ X1 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(h1,assumption,
~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( f @ X2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ( f @ X1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP13
=> ~ sP8 ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP13,
introduced(assumption,[]) ).
thf(h5,assumption,
sP8,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP1
=> ~ sP9 ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP1,
introduced(assumption,[]) ).
thf(h8,assumption,
sP9,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| sP12
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| ~ sP1
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP8
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP6
| ~ sP2
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP9
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP5
| ~ sP13
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(eiw_di_cumul,axiom,
sP3 ).
thf(10,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,eiw_di_cumul,h4,h5,h7,h8]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,10,h7,h8]) ).
thf(12,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h2,11,h6]) ).
thf(13,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,12,h4,h5]) ).
thf(14,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h1,13,h3]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,14,h1,h2]) ).
thf(0,theorem,
( ~ ! [X1: mworld] :
( ( mrel @ mactual @ X1 )
=> ~ ! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( f @ X2 @ X1 ) ) )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ! [X2: mworld] :
( ( mrel @ mactual @ X2 )
=> ~ ( f @ X1 @ X2 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO892^15 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n018.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 : 600
% 0.13/0.34 % DateTime : Sat Jul 9 02:18:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 10
% 0.13/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------