TSTP Solution File: SET926^11 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET926^11 : 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 : n011.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 : Thu Aug 31 15:19:10 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_set_difference,type,
set_difference: $i > $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_in,type,
in: $i > $i > mworld > $o ).
thf(ty_singleton,type,
singleton: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eiw_di,type,
eiw_di: $i > mworld > $o ).
thf(ty_empty_set,type,
empty_set: $i ).
thf(ty_empty,type,
empty: $i > mworld > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ X1 ) @ ( singleton @ eigen__0 ) @ mactual )
= ( ~ ( in @ eigen__0 @ X1 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ eigen__1 ) @ empty_set @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( eiw_di @ eigen__0 @ mactual )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP2
= ( in @ eigen__0 @ eigen__1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eiw_di @ eigen__0 @ mactual )
=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ X1 ) @ empty_set @ mactual )
= ( in @ eigen__0 @ X1 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( in @ eigen__0 @ eigen__1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ eigen__1 ) @ ( singleton @ eigen__0 ) @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eiw_di @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eiw_di @ eigen__1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ X1 ) @ empty_set @ mactual )
= ( in @ eigen__0 @ X1 @ mactual ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP7 = ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP10
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
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(t69_zfmisc_1,conjecture,
! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) ) ) ),
inference(assume_negation,[status(cth)],[t69_zfmisc_1]) ).
thf(h1,assumption,
~ ( sP9
=> ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ X1 ) @ empty_set @ mactual )
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ X1 ) @ ( singleton @ eigen__0 ) @ mactual ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
sP9,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ X1 ) @ empty_set @ mactual )
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__0 ) @ X1 ) @ ( singleton @ eigen__0 ) @ mactual ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP10
=> ( ~ sP2
=> sP7 ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP10,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( ~ sP2
=> sP7 ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ( eiw_di @ eigen__2 @ mactual )
=> ( empty @ eigen__2 @ mactual ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
eiw_di @ eigen__2 @ mactual,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( empty @ eigen__2 @ mactual ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( ( eiw_di @ eigen__3 @ mactual )
=> ~ ( empty @ eigen__3 @ mactual ) ),
introduced(assumption,[]) ).
thf(h13,assumption,
eiw_di @ eigen__3 @ mactual,
introduced(assumption,[]) ).
thf(h14,assumption,
empty @ eigen__3 @ mactual,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP4
| sP2
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP13
| sP7
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP12
| ~ sP10
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP15
| ~ sP10
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP11
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP1
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| ~ sP9
| sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP5
| ~ sP9
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(l36_zfmisc_1,axiom,
sP8 ).
thf(l34_zfmisc_1,axiom,
sP14 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h13,h14,h12,h10,h11,h9,h7,h8,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h2,h5,h7,h8,l36_zfmisc_1,l34_zfmisc_1]) ).
thf(12,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h10,h11,h9,h7,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,11,h13,h14]) ).
thf(rc1_xboole_0,axiom,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ~ ( empty @ X1 @ mactual ) ) ).
thf(13,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h11,h9,h7,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__3)],[rc1_xboole_0,12,h12]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,13,h10,h11]) ).
thf(rc2_xboole_0,axiom,
~ ! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ( empty @ X1 @ mactual ) ) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[rc2_xboole_0,14,h9]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,15,h7,h8]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,16,h5,h6]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,17,h4]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,18,h2,h3]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,19,h1]) ).
thf(0,theorem,
! [X1: $i] :
( ( eiw_di @ X1 @ mactual )
=> ! [X2: $i] :
( ( eiw_di @ X2 @ mactual )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET926^11 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 11:01:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 % SZS status Theorem
% 0.19/0.57 % Mode: cade22grackle2xfee4
% 0.19/0.57 % Steps: 3736
% 0.19/0.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------