%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU558^2 : TPTP v9.2.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n002.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 02:32:09 PM UTC 2025
% Result : Theorem 32.75s 32.80s
% Output : Proof 32.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 138
% Syntax : Number of formulae : 154 ( 27 unt; 0 typ; 6 def)
% Number of atoms : 494 ( 67 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 794 ( 86 ~; 80 |; 0 &; 427 @)
% ( 61 <=>; 140 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 74 usr; 71 con; 0-2 aty)
% Number of variables : 135 ( 21 ^; 114 !; 0 ?; 135 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_in,type,
in: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__11,type,
eigen__11: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__0 @ X1 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [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,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( in @ eigen__11 @ eigen__1 )
=> ( ( eigen__2 @ eigen__11 )
=> ( in @ eigen__11 @ ( dsetconstr @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( in @ eigen__6 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ eigen__6 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( eigen__11 = X1 )
=> ( ( eigen__2 @ eigen__11 )
= ( eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ eigen__11 @ ( dsetconstr @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ eigen__6 @ eigen__0 )
=> ( ( eigen__3 @ eigen__6 )
=> ( in @ eigen__6 @ ( dsetconstr @ eigen__0 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__2 @ eigen__6 )
= ( eigen__3 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( dsetconstr @ eigen__0 @ eigen__2 )
= ( dsetconstr @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( in @ eigen__11 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) )
=> ( sP8
=> ( ( dsetconstr @ eigen__0 @ eigen__2 )
= ( dsetconstr @ eigen__1 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) )
=> ( in @ X1 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) )
=> ( eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( in @ eigen__6 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( in @ eigen__6 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__1 @ X1 ) )
=> ( X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( dsetconstr @ eigen__1 @ eigen__2 )
= ( dsetconstr @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( eigen__6 = X1 )
=> ( ( eigen__2 @ eigen__6 )
= ( eigen__3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( in @ eigen__6 @ eigen__1 )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( in @ eigen__11 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( in @ eigen__11 @ eigen__1 )
=> ( ( eigen__2 @ eigen__11 )
= ( eigen__3 @ eigen__11 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP18
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( eigen__2 @ eigen__11 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( in @ eigen__6 @ ( dsetconstr @ eigen__0 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( eigen__2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( eigen__3 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__1 @ X1 ) )
=> ( in @ X2 @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP8
=> ( ( dsetconstr @ eigen__0 @ eigen__2 )
= ( dsetconstr @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( in @ eigen__11 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ( in @ eigen__6 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( in @ eigen__6 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( eigen__2 @ eigen__6 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( eigen__2 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( dsetconstr @ eigen__0 @ X1 ) )
=> ( in @ X2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( eigen__0 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP31
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ( dsetconstr @ eigen__0 @ eigen__3 )
= ( dsetconstr @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ( eigen__3 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ( in @ eigen__11 @ eigen__0 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( eigen__2 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ( dsetconstr @ eigen__0 @ eigen__2 )
= ( dsetconstr @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP24
=> ( eigen__3 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> $false ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( sP24
=> sP34 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( eigen__3 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( in @ eigen__6 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [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,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( in @ eigen__11 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( eigen__1 = eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ! [X1: $i > $o,X2: $i] :
( ( in @ X2 @ eigen__1 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP24
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( sP38 = sP50 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [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,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( in @ eigen__6 @ ( dsetconstr @ eigen__0 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: $i] :
( ( in @ X1 @ ( dsetconstr @ eigen__0 @ eigen__2 ) )
=> ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__1 )
=> ( ( eigen__2 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ eigen__1 @ eigen__2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(def_dsetconstrI,definition,
( dsetconstrI
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X2 @ X3 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ).
thf(def_dsetconstrEL,definition,
( dsetconstrEL
= ( ! [X1: $i,X2: $i > $o,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
@ ( in @ X3 @ X1 ) ) ) ) ).
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_setext,definition,
( setext
= ( ! [X1: $i,X2: $i] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X1 )
@ ( in @ X3 @ X2 ) )
@ ( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( in @ X3 @ X2 )
@ ( in @ X3 @ X1 ) )
@ ( X1 = X2 ) ) ) ) ) ).
thf(dsetconstr__Cong,conjecture,
( sP4
=> ( sP29
=> ( sP13
=> ( sP58
=> ! [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,
~ ( sP4
=> ( sP29
=> ( sP13
=> ( sP58
=> ! [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,
sP4,
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP29
=> ( sP13
=> ( sP58
=> ! [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,
sP29,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ( sP13
=> ( sP58
=> ! [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,
sP13,
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP58
=> ! [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,
sP58,
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,
~ ( sP40
=> ! [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,
sP40,
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,
~ ( sP2
=> sP46 ),
introduced(assumption,[]) ).
thf(h16,assumption,
sP2,
introduced(assumption,[]) ).
thf(h17,assumption,
~ sP46,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP57
| sP38
| ~ sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP7
| sP12
| ~ sP21
| sP48 ),
inference(mating_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP10
| ~ sP45
| sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP28
| sP19
| ~ sP42
| sP48 ),
inference(mating_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP25
| ~ sP34
| sP57 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP34
| sP53
| ~ sP54
| sP48 ),
inference(mating_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP23
| ~ sP51
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP18
| sP51
| ~ sP40
| sP48 ),
inference(mating_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP6
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP27
| ~ sP38
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP22
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP41
| ~ sP31
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP44
| ~ sP53
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP47
| ~ sP24
| sP50 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP49
| ~ sP24
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP3
| ~ sP34
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP26
| ~ sP18
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP37
| ~ sP59
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP5
| ~ sP59
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP9
| ~ sP18
| sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP2
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP16
| sP47 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP15
| sP49 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP61
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP2
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP30
| sP37 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP35
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP43
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(29,plain,
( sP42
| sP48
| ~ sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( sP11
| sP48
| ~ sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP11
| sP21 ),
inference(symeq,[status(thm)],[]) ).
thf(32,plain,
( sP56
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( sP56
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP36
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP36
| sP59 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP8
| ~ sP56 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(37,plain,
( ~ sP33
| ~ sP8
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP60
| ~ sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(39,plain,
~ sP48,
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( ~ sP14
| ~ sP60
| sP33 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP55
| sP61 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP17
| sP43 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
( ~ sP32
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(44,plain,
( ~ sP39
| sP35 ),
inference(all_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP20
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP1
| sP30 ),
inference(all_rule,[status(thm)],[]) ).
thf(47,plain,
( ~ sP52
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(48,plain,
( ~ sP4
| sP55 ),
inference(all_rule,[status(thm)],[]) ).
thf(49,plain,
( ~ sP4
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(50,plain,
( ~ sP29
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(51,plain,
( ~ sP29
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(52,plain,
( ~ sP13
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(53,plain,
( ~ sP13
| sP1 ),
inference(all_rule,[status(thm)],[]) ).
thf(54,plain,
( ~ sP58
| sP52 ),
inference(all_rule,[status(thm)],[]) ).
thf(55,plain,
( ~ sP40
| sP54 ),
inference(symeq,[status(thm)],[]) ).
thf(56,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,h2,h4,h6,h8,h12,h16,h17]) ).
thf(57,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])],[h15,56,h16,h17]) ).
thf(58,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)],[h14,57,h15]) ).
thf(59,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)],[h13,58,h14]) ).
thf(60,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])],[h11,59,h12,h13]) ).
thf(61,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)],[h10,60,h11]) ).
thf(62,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)],[h9,61,h10]) ).
thf(63,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,62,h8,h9]) ).
thf(64,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,63,h6,h7]) ).
thf(65,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,64,h4,h5]) ).
thf(66,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,65,h2,h3]) ).
thf(67,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[66,h0]) ).
thf(0,theorem,
( sP4
=> ( sP29
=> ( sP13
=> ( sP58
=> ! [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])],[66,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU558^2 : TPTP v9.2.0. Bugfixed v4.0.0.
% 0.13/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Oct 8 21:44:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 32.75/32.80 % SZS status Theorem
% 32.75/32.80 % Mode: cade22grackle2x798d
% 32.75/32.80 % Steps: 92067
% 32.75/32.80 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------