TSTP Solution File: SET002^3 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET002^3 : 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 : n007.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 15:15:00 EDT 2023
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mworld,type,
mworld: $tType ).
thf(ty_union,type,
union: $i > $i > $i ).
thf(ty_subset,type,
subset: $i > $i > mworld > $o ).
thf(ty_mactual,type,
mactual: mworld ).
thf(ty_qmltpeq,type,
qmltpeq: $i > $i > mworld > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(sP1,plain,
( sP1
<=> ( ( subset @ eigen__0 @ eigen__0 @ mactual )
=> ( qmltpeq @ ( union @ eigen__0 @ eigen__0 ) @ eigen__0 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( subset @ eigen__0 @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 @ mactual )
=> ( qmltpeq @ ( union @ X1 @ X2 ) @ X2 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] : ( subset @ X1 @ X1 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( subset @ eigen__0 @ X1 @ mactual )
=> ( qmltpeq @ ( union @ eigen__0 @ X1 ) @ X1 @ mactual ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( qmltpeq @ ( union @ eigen__0 @ eigen__0 ) @ eigen__0 @ mactual ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
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] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_di,definition,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(prove_idempotency_of_union,conjecture,
! [X1: $i] : ( qmltpeq @ ( union @ X1 @ X1 ) @ X1 @ mactual ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i] : ( qmltpeq @ ( union @ X1 @ X1 ) @ X1 @ mactual ),
inference(assume_negation,[status(cth)],[prove_idempotency_of_union]) ).
thf(h1,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP1
| ~ sP2
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP4
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP3
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(reflexivity_of_subset,axiom,
sP4 ).
thf(subset_union,axiom,
sP3 ).
thf(5,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,h1,reflexivity_of_subset,subset_union]) ).
thf(6,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,5,h1]) ).
thf(0,theorem,
! [X1: $i] : ( qmltpeq @ ( union @ X1 @ X1 ) @ X1 @ mactual ),
inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET002^3 : TPTP v8.1.2. Released v8.1.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n007.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 14:46:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % Mode: cade22grackle2xfee4
% 0.21/0.44 % Steps: 40
% 0.21/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------