%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU704^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 02:45:57 PM UTC 2025
% Result : Theorem 1.12s 1.61s
% Output : Proof 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 104
% Syntax : Number of formulae : 113 ( 17 unt; 0 typ; 9 def)
% Number of atoms : 514 ( 143 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 1050 ( 312 ~; 62 |; 0 &; 354 @)
% ( 48 <=>; 274 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 63 usr; 61 con; 0-2 aty)
% Number of variables : 151 ( 58 ^; 93 !; 0 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__1,type,
eigen__1: $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_emptyset,type,
emptyset: $i ).
thf(ty_eigen__3,type,
eigen__3: $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(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( eigen__1
=> ( X3 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X3 != X1 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( eigen__1
=> ( X3 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X3 != X1 ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: $o] :
~ ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ eigen__0
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( eigen__1
=> ( X4 != X1 ) )
=> ~ ( ~ eigen__1
=> ( X4 != X2 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( eigen__1
=> ( X4 != X1 ) )
=> ~ ( ~ eigen__1
=> ( X4 != X2 ) ) ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( in @ X4
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) )
=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( in @ eigen__3
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) )
!= ( setadjoin @ eigen__3 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ eigen__1
=> ( in @ eigen__3
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ~ ! [X4: $i] :
( ( in @ X4
@ ( dsetconstr @ eigen__0
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X5: $i] :
( ( X1
=> ( X5 != X2 ) )
=> ~ ( ~ X1
=> ( X5 != X3 ) ) ) )
!= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( eigen__1
=> ( X3 != X1 ) )
=> ~ ( ~ eigen__1
=> ( X3 != X2 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( in @ eigen__2
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X1
=> ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ eigen__1
=> ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( X1
=> ( ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP7
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( eigen__1
=> sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( ~ eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) )
= ( setadjoin @ eigen__3 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( in @ eigen__3 @ eigen__0 )
=> ( eigen__1
=> sP12 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( in @ eigen__3
@ ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ X1
=> ( in @ X3
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( eigen__1
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ eigen__1
=> ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( dsetconstr @ eigen__0
@ ^ [X1: $i] :
( ( eigen__1
=> ( X1 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X1 != eigen__3 ) ) ) )
= ( setadjoin @ eigen__3 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( ~ eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) )
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__1
=> ( in @ eigen__2
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i] :
( ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != eigen__3 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != eigen__3 ) ) ) )
!= ( setadjoin @ X1 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $o,X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ! [X3: $i] :
( ( in @ X3 @ eigen__0 )
=> ( ~ X1
=> ( ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( X1
=> ( X4 != X2 ) )
=> ~ ( ~ X1
=> ( X4 != X3 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__1
=> ( in @ eigen__2
@ ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( in @ eigen__2 @ eigen__0 )
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( eigen__1
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( eigen__1
=> ( X2 != eigen__2 ) )
=> ~ ( ~ eigen__1
=> ( X2 != X1 ) ) ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( in @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ~ ! [X5: $i] :
( ( in @ X5
@ ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) ) )
=> ( ( dsetconstr @ X1
@ ^ [X6: $i] :
( ( X2
=> ( X6 != X3 ) )
=> ~ ( ~ X2
=> ( X6 != X4 ) ) ) )
!= ( setadjoin @ X5 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( eigen__1
=> ( in @ X1
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( eigen__1
=> ( X3 != X1 ) )
=> ~ ( ~ eigen__1
=> ( X3 != X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ~ ! [X3: $i] :
( ( in @ X3
@ ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( eigen__1
=> ( X4 != X1 ) )
=> ~ ( ~ eigen__1
=> ( X4 != X2 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X4: $i] :
( ( eigen__1
=> ( X4 != X1 ) )
=> ~ ( ~ eigen__1
=> ( X4 != X2 ) ) ) )
!= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( in @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP1
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> eigen__1 ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( sP37
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( X2
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) )
= ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP30
=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP37
=> ( X3 != eigen__2 ) )
=> ~ ( ~ sP37
=> ( X3 != X1 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP37
=> ( X3 != eigen__2 ) )
=> ~ ( ~ sP37
=> ( X3 != X1 ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ sP37
=> ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP37
=> ( X3 != X1 ) )
=> ~ ( ~ sP37
=> ( X3 != X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ! [X2: $i] :
( ( in @ X2 @ eigen__0 )
=> ( ~ sP37
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP37
=> ( X3 != X1 ) )
=> ~ ( ~ sP37
=> ( X3 != X2 ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( sP34
=> ~ sP26 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ~ ! [X2: $i] :
( ( in @ X2
@ ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP37
=> ( X3 != eigen__2 ) )
=> ~ ( ~ sP37
=> ( X3 != X1 ) ) ) ) )
=> ( ( dsetconstr @ eigen__0
@ ^ [X3: $i] :
( ( sP37
=> ( X3 != eigen__2 ) )
=> ~ ( ~ sP37
=> ( X3 != X1 ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ~ sP37
=> sP23 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: $i] :
( ( in @ X1 @ eigen__0 )
=> ( sP37
=> ( ( dsetconstr @ eigen__0
@ ^ [X2: $i] :
( ( sP37
=> ( X2 != eigen__2 ) )
=> ~ ( ~ sP37
=> ( X2 != X1 ) ) ) )
= ( setadjoin @ eigen__2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: $i,X2: $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ~ X2
=> ( ( dsetconstr @ X1
@ ^ [X5: $i] :
( ( X2
=> ( X5 != X3 ) )
=> ~ ( ~ X2
=> ( X5 != X4 ) ) ) )
= ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( sP34
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i] :
~ ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X1
!= ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).
thf(def_iffalseProp1,definition,
iffalseProp1 = sP1 ).
thf(def_iffalseProp2,definition,
iffalseProp2 = sP47 ).
thf(def_iftrueProp1,definition,
iftrueProp1 = sP19 ).
thf(def_iftrueProp2,definition,
iftrueProp2 = sP39 ).
thf(ifSingleton,conjecture,
sP36 ).
thf(h2,negated_conjecture,
~ sP36,
inference(assume_negation,[status(cth)],[ifSingleton]) ).
thf(1,plain,
( ~ sP1
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP18
| sP41 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP41
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP9
| ~ sP30
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP21
| sP48 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP48
| ~ sP34
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP4
| sP37
| sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP8
| sP32 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP32
| sP25 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP25
| ~ sP30
| sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP28
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP14
| ~ sP34
| sP38 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP38
| ~ sP37
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP3
| ~ sP17
| ~ sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP13
| ~ sP7
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP47
| sP27 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP27
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP42
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP22
| ~ sP30
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP24
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP15
| ~ sP34
| sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP45
| sP37
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP19
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP26
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP39
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP11
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP6
| sP29 ),
inference(all_rule,[status(thm)],[]) ).
thf(28,plain,
( ~ sP29
| ~ sP30
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP46
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP16
| ~ sP34
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP20
| ~ sP37
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP26
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( sP43
| sP26 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP43
| sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP44
| ~ sP43 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(36,plain,
( sP40
| ~ sP44 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( sP40
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP33
| ~ sP40 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(39,plain,
( sP5
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(40,plain,
( sP31
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(41,plain,
( sP2
| ~ sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(42,plain,
( sP2
| sP39 ),
inference(prop_rule,[status(thm)],[]) ).
thf(43,plain,
( sP10
| ~ sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP10
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( sP35
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( sP35
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( sP36
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( sP36
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,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,h2]) ).
thf(50,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[49,h1]) ).
thf(51,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[50,h0]) ).
thf(0,theorem,
sP36,
inference(contra,[status(thm),contra(discharge,[h2])],[49,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SEU704^2 : TPTP v9.2.0. Released v3.7.0.
% 0.05/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 8 20:56:53 EDT 2025
% 0.15/0.35 % CPUTime :
% 1.12/1.61 % SZS status Theorem
% 1.12/1.61 % Mode: mode506
% 1.12/1.61 % Inferences: 20728
% 1.12/1.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------