TSTP Solution File: SEU645^2 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU645^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 17:20:35 EDT 2023
% Result : Theorem 20.23s 20.59s
% Output : Proof 20.23s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_setunion,type,
setunion: $i > $i ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) )
=> ( in @ ( setunion @ X1 ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i] :
( ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( eigen__0 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__0
= ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( in
@ ( setadjoin
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ emptyset )
@ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( in
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
~ ! [X3: $i] :
( ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ sP8
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
=> ( eigen__0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ~ sP9
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP4
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ~ ! [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
=> ( X1
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
=> ( ( dsetconstr @ ( setunion @ X1 )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) ) )
= eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ eigen__1 @ emptyset ) ) @ emptyset ) ) ) @ X1 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP5
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(def_dsetconstrER,definition,
( dsetconstrER
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
@ ( X2 @ X3 ) ) ) ) ).
thf(def_iskpair,definition,
( iskpair
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
& ( X1
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
thf(def_kpair,definition,
( kpair
= ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ).
thf(def_kpairp,definition,
( kpairp
= ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X1 )
& ( X1
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(def_setukpairinjL1,definition,
( setukpairinjL1
= ( ! [X1: $i,X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
@ ( X1 = X3 ) ) ) ) ).
thf(def_kfstsingleton,definition,
( kfstsingleton
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( iskpair @ X1 )
@ ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ) ) ) ) ) ).
thf(def_theprop,definition,
( theprop
= ( ! [X1: $i] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ( singleton @ X1 )
@ ( in @ ( setunion @ X1 ) @ X1 ) ) ) ) ).
thf(def_kfst,definition,
( kfst
= ( ^ [X1: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ) ) ) ) ).
thf(kfstpairEq,conjecture,
( sP12
=> ( sP7
=> ( sP20
=> ( sP16
=> ( sP1
=> ! [X1: $i,X2: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
= X1 ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP12
=> ( sP7
=> ( sP20
=> ( sP16
=> ( sP1
=> ! [X1: $i,X2: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
= X1 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[kfstpairEq]) ).
thf(h1,assumption,
sP12,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP7
=> ( sP20
=> ( sP16
=> ( sP1
=> ! [X1: $i,X2: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
= X1 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP7,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP20
=> ( sP16
=> ( sP1
=> ! [X1: $i,X2: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
= X1 ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP20,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP16
=> ( sP1
=> ! [X1: $i,X2: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
= X1 ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP16,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ( sP1
=> ! [X1: $i,X2: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
= X1 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
sP1,
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i,X2: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
= X1 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ! [X1: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ eigen__0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
= eigen__0 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP17,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP19
| ~ sP5
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP15
| ~ sP4
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP13
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP11
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP18
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| ~ sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP10
| sP8
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP9
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP12
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP20
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP16
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP1
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP3
| sP17 ),
inference(symeq,[status(thm)],]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h1,h3,h5,h7,h9,h12]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[h11,16,h12]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__0)],[h10,17,h11]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,18,h9,h10]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,19,h7,h8]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,20,h5,h6]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,21,h3,h4]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,22,h1,h2]) ).
thf(0,theorem,
( sP12
=> ( sP7
=> ( sP20
=> ( sP16
=> ( sP1
=> ! [X1: $i,X2: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
@ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) )
= X1 ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU645^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 01:54:35 EDT 2023
% 0.14/0.34 % CPUTime :
% 20.23/20.59 % SZS status Theorem
% 20.23/20.59 % Mode: cade22grackle2x798d
% 20.23/20.59 % Steps: 2133
% 20.23/20.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------