TSTP Solution File: SEU645^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU645^2 : TPTP v8.1.0. Released v3.7.0.
% 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 : Tue Jul 19 13:55:03 EDT 2022
% Result : Theorem 11.31s 10.52s
% Output : Proof 11.31s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_setunion,type,
setunion: $i > $i ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_setadjoin,type,
setadjoin: $i > $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
<=> ( 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,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [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,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [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,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [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,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( 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,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [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,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [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,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ( eigen__0 = X1 )
=> ( X1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( 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,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [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,[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 ) ) ) ) )
=> ( ( 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 ) ) )
=> sP11 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( 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,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [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,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP7
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [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,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP2
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP3
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP11
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [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,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [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,[sP23])]) ).
thf(def_dsetconstrER,definition,
dsetconstrER = sP6 ).
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 = sP22 ).
thf(def_kfstsingleton,definition,
( kfstsingleton
= ( ! [X1: $i] :
( ( iskpair @ X1 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ) ) ) ) ) ).
thf(def_theprop,definition,
( theprop
= ( ! [X1: $i] :
( ( 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,
( sP6
=> ( sP5
=> ( sP22
=> ( sP12
=> ( 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,
~ ( sP6
=> ( sP5
=> ( sP22
=> ( sP12
=> ( 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,
sP6,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP5
=> ( sP22
=> ( sP12
=> ( 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,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP22
=> ( sP12
=> ( 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,
sP22,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP12
=> ( 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,
sP12,
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,
~ sP14,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP9
| ~ sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP20
| sP3
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP23
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP17
| ~ sP7
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP12
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP15
| sP21 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP21
| ~ sP11
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| sP23 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP13
| sP18
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP6
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP4
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP1
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP5
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP22
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP19
| ~ sP2
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP10
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP16
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
sP16,
inference(eq_sym,[status(thm)],]) ).
thf(19,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h12,h11,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h1,h3,h5,h7,h9,h12]) ).
thf(20,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)],[h11,19,h12]) ).
thf(21,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)],[h10,20,h11]) ).
thf(22,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,21,h9,h10]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,22,h7,h8]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,23,h5,h6]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,24,h3,h4]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,25,h1,h2]) ).
thf(0,theorem,
( sP6
=> ( sP5
=> ( sP22
=> ( sP12
=> ( 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])],[26,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU645^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 20 13:41:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 11.31/10.52 % SZS status Theorem
% 11.31/10.52 % Mode: mode515
% 11.31/10.52 % Inferences: 412
% 11.31/10.52 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------