TSTP Solution File: SET926^7 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET926^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 15:19:11 EDT 2023
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: mu ).
thf(ty_empty_set,type,
empty_set: mu ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_set_difference,type,
set_difference: mu > mu > mu ).
thf(ty_in,type,
in: mu > mu > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: mu ).
thf(ty_singleton,type,
singleton: mu > mu ).
thf(ty_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ~ ( ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
=> ( in @ X2 @ X3 @ X1 ) )
=> ~ ( ( in @ X2 @ X3 @ X1 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( in @ eigen__1 @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ sP2
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ eigen__2 ) @ ( singleton @ eigen__1 ) @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ eigen__2 ) @ ( singleton @ eigen__1 ) @ eigen__0 )
=> ~ sP2 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( exists_in_world @ eigen__2 @ eigen__0 )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ empty_set @ eigen__0 )
=> ( in @ eigen__1 @ X1 @ eigen__0 ) )
=> ~ ( ( in @ eigen__1 @ X1 @ eigen__0 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ empty_set @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ~ ( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ eigen__0 )
=> ( in @ X1 @ X2 @ eigen__0 ) )
=> ~ ( ( in @ X1 @ X2 @ eigen__0 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( exists_in_world @ eigen__2 @ eigen__0 )
=> ~ ( ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ eigen__2 ) @ empty_set @ eigen__0 )
=> sP2 )
=> ~ ( sP2
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ eigen__2 ) @ empty_set @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ eigen__2 ) @ ( singleton @ eigen__1 ) @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ~ ( ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 )
=> ~ ( in @ X2 @ X3 @ X1 ) )
=> ~ ( ~ ( in @ X2 @ X3 @ X1 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ eigen__2 ) @ empty_set @ eigen__0 )
=> sP2 )
=> ~ ( sP2
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ eigen__2 ) @ empty_set @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( exists_in_world @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP12
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP12
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ ( singleton @ eigen__1 ) @ eigen__0 )
=> ~ ( in @ eigen__1 @ X1 @ eigen__0 ) )
=> ~ ( ~ ( in @ eigen__1 @ X1 @ eigen__0 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ ( singleton @ eigen__1 ) @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP2
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ eigen__2 ) @ empty_set @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( exists_in_world @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ eigen__2 ) @ empty_set @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ~ ( ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ eigen__0 )
=> ~ ( in @ X1 @ X2 @ eigen__0 ) )
=> ~ ( ~ ( in @ X1 @ X2 @ eigen__0 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ ( singleton @ eigen__1 ) @ eigen__0 )
=> ~ ( in @ eigen__1 @ X1 @ eigen__0 ) )
=> ~ ( ~ ( in @ eigen__1 @ X1 @ eigen__0 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ ( singleton @ eigen__1 ) @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( exists_in_world @ X3 @ X2 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(t69_zfmisc_1,conjecture,
! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[t69_zfmisc_1]) ).
thf(h1,assumption,
~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ eigen__0 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP12
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ empty_set @ eigen__0 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ ( singleton @ eigen__1 ) @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP12,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ empty_set @ eigen__0 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ eigen__1 ) @ X1 ) @ ( singleton @ eigen__1 ) @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP16
=> ( ~ sP17
=> sP9 ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP16,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ sP17
=> sP9 ),
introduced(assumption,[]) ).
thf(h8,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(h9,assumption,
~ sP9,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP3
| sP2
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP4
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| ~ sP16
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP19
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP15
| ~ sP2
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP11
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP8
| ~ sP16
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP6
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| ~ sP12
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP13
| ~ sP12
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP18
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP7
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP10
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(l36_zfmisc_1,axiom,
sP1 ).
thf(l34_zfmisc_1,axiom,
sP10 ).
thf(15,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h3,h6,h8,h9,l36_zfmisc_1,l34_zfmisc_1]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,15,h8,h9]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,16,h6,h7]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,17,h5]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,18,h3,h4]) ).
thf(20,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,19,h2]) ).
thf(21,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,20,h1]) ).
thf(0,theorem,
! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ( ~ ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ empty_set @ X1 )
=> ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X3 ) @ ( singleton @ X2 ) @ X1 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET926^7 : TPTP v8.1.2. Released v5.5.0.
% 0.13/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 16:18:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % Mode: cade22sinegrackle2x6978
% 0.21/0.45 % Steps: 454
% 0.21/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------