%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU558^2 : TPTP v9.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -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 Oct 9 02:43:39 PM UTC 2025
% Result : Theorem 5.66s 5.85s
% Output : Proof 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 140
% Syntax : Number of formulae : 156 ( 29 unt; 0 typ; 6 def)
% Number of atoms : 492 ( 76 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 727 ( 87 ~; 76 |; 0 &; 361 @)
% ( 62 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 75 usr; 72 con; 0-2 aty)
% Number of variables : 108 ( 2 ^; 106 !; 0 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( X1 = X2 )
=> ( ( eigen__2 @ X1 )
= ( eigen__3 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__3 @ eigen__5 )
=> ( in @ eigen__5 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( eigen__3 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__0 @ X1 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( in @ eigen__5 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( eigen__5 = X1 )
=> ( ( eigen__2 @ eigen__5 )
= ( eigen__3 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ eigen__5 @ eigen__1 )
=> ( ( eigen__5 = eigen__5 )
=> ( ( eigen__2 @ eigen__5 )
= ( eigen__3 @ eigen__5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ X2 @ X1 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) )
=> ( ( dsetconstr @ eigen__0 @ eigen__2 )
= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( in @ eigen__4 @ eigen__0 )
=> ( ( eigen__2 @ eigen__4 )
=> ( in @ eigen__4 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ) ) ),
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 @ eigen__0 )
=> ( ( eigen__2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( in @ eigen__4 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__4 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( in @ eigen__5 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( in @ eigen__5 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( in @ eigen__4 @ ( dsetconstr @ eigen__1 @ eigen__3 ) )
=> ( eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__3 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( in @ eigen__4 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( eigen__4 = X1 )
=> ( ( eigen__2 @ eigen__4 )
= ( eigen__3 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( in @ eigen__5 @ eigen__1 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__2 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( ( eigen__2 @ eigen__5 )
= sP19 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) )
=> ( eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__1 @ X1 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( eigen__0 = eigen__1 )
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) )
=> ( sP3
=> ( ( dsetconstr @ eigen__0 @ eigen__2 )
= ( dsetconstr @ eigen__1 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( in @ eigen__4 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP22
=> ( in @ eigen__4 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( in @ eigen__5 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( in @ eigen__5 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( eigen__5 = X1 )
=> ( ( eigen__2 @ eigen__5 )
= ( eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( eigen__4 = X1 )
=> ( sP22
= ( eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP17
=> sP36 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( dsetconstr @ eigen__0 @ eigen__2 )
= ( dsetconstr @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP17
=> ( eigen__2 @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP31
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ( eigen__5 = eigen__5 )
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP3
=> sP41 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__1 @ X1 ) )
=> ( in @ X2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__0 @ X1 ) )
=> ( in @ X2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP15
=> ( sP22 = sP35 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( in @ eigen__4 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ X3 @ X1 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP31
=> ( in @ eigen__4 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( in @ eigen__4 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP22 = sP35 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( sP17
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( eigen__2 @ eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $i] :
( ( eigen__0 = X1 )
=> ( X1 = eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( eigen__5 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( sP14
=> sP51 ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(def_dsetconstrI,definition,
dsetconstrI = sP5 ).
thf(def_dsetconstrEL,definition,
dsetconstrEL = sP23 ).
thf(def_dsetconstrER,definition,
dsetconstrER = sP12 ).
thf(def_setext,definition,
setext = sP54 ).
thf(dsetconstr__Cong,conjecture,
( sP5
=> ( sP23
=> ( sP12
=> ( sP54
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i > $o,X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X5 = X6 )
=> ( ( X3 @ X5 )
= ( X4 @ X6 ) ) ) ) )
=> ( ( dsetconstr @ X1 @ X3 )
= ( dsetconstr @ X2 @ X4 ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ( sP5
=> ( sP23
=> ( sP12
=> ( sP54
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i > $o,X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X5 = X6 )
=> ( ( X3 @ X5 )
= ( X4 @ X6 ) ) ) ) )
=> ( ( dsetconstr @ X1 @ X3 )
= ( dsetconstr @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[dsetconstr__Cong]) ).
thf(h2,assumption,
sP5,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP23
=> ( sP12
=> ( sP54
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i > $o,X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X5 = X6 )
=> ( ( X3 @ X5 )
= ( X4 @ X6 ) ) ) ) )
=> ( ( dsetconstr @ X1 @ X3 )
= ( dsetconstr @ X2 @ X4 ) ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP23,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP12
=> ( sP54
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i > $o,X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X5 = X6 )
=> ( ( X3 @ X5 )
= ( X4 @ X6 ) ) ) ) )
=> ( ( dsetconstr @ X1 @ X3 )
= ( dsetconstr @ X2 @ X4 ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
sP12,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP54
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i > $o,X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X5 = X6 )
=> ( ( X3 @ X5 )
= ( X4 @ X6 ) ) ) ) )
=> ( ( dsetconstr @ X1 @ X3 )
= ( dsetconstr @ X2 @ X4 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP54,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i > $o,X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X5 = X6 )
=> ( ( X3 @ X5 )
= ( X4 @ X6 ) ) ) ) )
=> ( ( dsetconstr @ X1 @ X3 )
= ( dsetconstr @ X2 @ X4 ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ! [X1: $i] :
( ( eigen__0 = X1 )
=> ! [X2: $i > $o,X3: $i > $o] :
( ! [X4: $i] :
( ( in @ X4 @ eigen__0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( X4 = X5 )
=> ( ( X2 @ X4 )
= ( X3 @ X5 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0 @ X2 )
= ( dsetconstr @ X1 @ X3 ) ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP38
=> ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__1 )
=> ( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0 @ X1 )
= ( dsetconstr @ eigen__1 @ X2 ) ) ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
sP38,
introduced(assumption,[]) ).
thf(h13,assumption,
~ ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ! [X4: $i] :
( ( in @ X4 @ eigen__1 )
=> ( ( X3 = X4 )
=> ( ( X1 @ X3 )
= ( X2 @ X4 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0 @ X1 )
= ( dsetconstr @ eigen__1 @ X2 ) ) ),
introduced(assumption,[]) ).
thf(h14,assumption,
~ ! [X1: $i > $o] :
( ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__1 )
=> ( ( X2 = X3 )
=> ( ( eigen__2 @ X2 )
= ( X1 @ X3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0 @ eigen__2 )
= ( dsetconstr @ eigen__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h15,assumption,
~ ( sP1
=> sP41 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP1,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP41,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP24
| ~ sP59
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
sP61,
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP45
| ~ sP61
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP9
| ~ sP34
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
sP15,
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP57
| sP22
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP39
| sP62 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP62
| ~ sP14
| sP51 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP51
| ~ sP15
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP20
| ~ sP53
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP36
| sP34
| ~ sP61
| ~ sP38 ),
inference(mating_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP14
| sP53
| ~ sP15
| ~ sP28 ),
inference(mating_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP37
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP1
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP8
| ~ sP36
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP5
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP49
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP4
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP21
| ~ sP34
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP2
| ~ sP19
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP12
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP7
| sP50 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP50
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP42
| ~ sP17
| sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP23
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP48
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP43
| sP40 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP40
| ~ sP17
| sP36 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( sP58
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP58
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP5
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP6
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP13
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP11
| ~ sP53
| sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( ~ sP32
| ~ sP22
| sP56 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP12
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP26
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( ~ sP25
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP18
| ~ sP31
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP23
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP47
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP27
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP44
| ~ sP31
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( sP55
| ~ sP56 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP55
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( sP52
| ~ sP58 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(48,plain,
( sP3
| ~ sP55 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(49,plain,
( ~ sP54
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP10
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP30
| ~ sP52
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP46
| ~ sP3
| sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP29
| ~ sP38
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP60
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP33
| sP60 ),
inference(all_rule,[status(thm)],[]) ).
thf(56,plain,
sP33,
inference(eq_sym,[status(thm)],[]) ).
thf(57,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h14,h12,h13,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,h2,h4,h6,h8,h12,h16,h17]) ).
thf(58,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h15,h14,h12,h13,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,57,h16,h17]) ).
thf(59,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h14,h12,h13,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__3)],[h14,58,h15]) ).
thf(60,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__2)],[h13,59,h14]) ).
thf(61,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,60,h12,h13]) ).
thf(62,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h10,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__1)],[h10,61,h11]) ).
thf(63,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__0)],[h9,62,h10]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,63,h8,h9]) ).
thf(65,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,64,h6,h7]) ).
thf(66,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,65,h4,h5]) ).
thf(67,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,66,h2,h3]) ).
thf(68,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[67,h0]) ).
thf(0,theorem,
( sP5
=> ( sP23
=> ( sP12
=> ( sP54
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X3: $i > $o,X4: $i > $o] :
( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X5 = X6 )
=> ( ( X3 @ X5 )
= ( X4 @ X6 ) ) ) ) )
=> ( ( dsetconstr @ X1 @ X3 )
= ( dsetconstr @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[67,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU558^2 : TPTP v9.2.0. Bugfixed v4.0.0.
% 0.03/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n007.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 : Wed Oct 8 21:44:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 5.66/5.85 % SZS status Theorem
% 5.66/5.85 % Mode: mode515
% 5.66/5.85 % Inferences: 648
% 5.66/5.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------