%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU497^1 : TPTP v9.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 02:43:17 PM UTC 2025
% Result : Theorem 1.52s 1.77s
% Output : Proof 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 129
% Syntax : Number of formulae : 141 ( 48 unt; 0 typ; 36 def)
% Number of atoms : 445 ( 115 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 825 ( 237 ~; 62 |; 0 &; 305 @)
% ( 48 <=>; 172 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 91 ( 91 >; 0 *; 0 +; 0 <<)
% Number of symbols : 89 ( 86 usr; 87 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 159 ( 50 ^; 109 !; 0 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
eigen__6: $i ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__5,type,
eigen__5: $i ).
thf(ty_eigen__3,type,
eigen__3: $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] :
~ ! [X2: $i] :
( ~ ( ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( ( X2 != X1 )
=> ( eigen__0 @ X2 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ( ( eigen__5 != X1 )
=> ( eigen__0 @ eigen__5 @ X1 ) )
=> ~ ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) ) )
=> ( ( eigen__5 != X2 )
=> ( eigen__0 @ eigen__5 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h1,assumption,
! [X1: ( $i > $i > $o ) > $o,X2: $i > $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ( ~ ( ! [X2: $i] :
( ( X2 != X2 )
=> ( X1 @ X2 @ X2 ) )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( ( X3 != X2 )
=> ( X1 @ X3 @ X2 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( ( X3 != X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ( ( X2 != X4 )
=> ( X1 @ X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( X1 != X1 )
=> ( eigen__0 @ X1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( ( eigen__3 != X1 )
=> ( eigen__0 @ eigen__3 @ X1 ) )
=> ~ ( ( X1 != eigen__3 )
=> ( eigen__0 @ X1 @ eigen__3 ) ) )
=> ( eigen__3 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( ( eigen__5 != eigen__6 )
=> ( eigen__0 @ eigen__5 @ eigen__6 ) )
=> ~ ( ( eigen__6 != X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) )
=> ( ( eigen__5 != X1 )
=> ( eigen__0 @ eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( ( X2 != X3 )
=> ( eigen__0 @ X2 @ X3 ) ) )
=> ( ( X1 != X3 )
=> ( eigen__0 @ X1 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X1 ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) )
=> ~ ( ~ ( ! [X1: $i] :
( ( X1 != X1 )
=> ( eigen__0 @ X1 @ X1 ) )
=> ~ ! [X1: $i,X2: $i] :
( ~ ( ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( ( X2 != X1 )
=> ( eigen__0 @ X2 @ X1 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( ( X2 != X3 )
=> ( eigen__0 @ X2 @ X3 ) ) )
=> ( ( X1 != X3 )
=> ( eigen__0 @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__4 = eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__4 @ X1 )
=> ~ ( eigen__0 @ X1 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__0 @ eigen__5 @ eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i] :
( ( X1 != X1 )
=> ( eigen__0 @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__6 != eigen__7 )
=> ( eigen__0 @ eigen__6 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ~ ( sP4
=> ~ ( eigen__0 @ eigen__6 @ X1 ) )
=> ( eigen__0 @ eigen__5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( eigen__0 @ X1 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP5
=> ~ ! [X1: $i,X2: $i] :
( ~ ( ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( ( X2 != X1 )
=> ( eigen__0 @ X2 @ X1 ) ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ~ ( ( ( eigen__5 != eigen__6 )
=> sP4 )
=> ~ sP6 )
=> ( ( eigen__5 != eigen__7 )
=> ( eigen__0 @ eigen__5 @ eigen__7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( eigen__5 = eigen__6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( eigen__5 = X1 )
=> ( X1 = eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__3 != eigen__4 )
=> ( eigen__0 @ eigen__3 @ eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( ( X2 != X3 )
=> ( eigen__0 @ X2 @ X3 ) ) )
=> ( ( X1 != X3 )
=> ( eigen__0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP4
=> ~ ( eigen__0 @ eigen__6 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__5 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__0 @ eigen__5 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i,X2: $i] :
( ~ ( ( ( eigen__5 != X1 )
=> ( eigen__0 @ eigen__5 @ X1 ) )
=> ~ ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) ) )
=> ( ( eigen__5 != X2 )
=> ( eigen__0 @ eigen__5 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__3 = eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__2 = eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ sP15
=> ( eigen__0 @ eigen__5 @ eigen__7 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP11
=> ( eigen__6 = eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__0 @ eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( eigen__0 @ eigen__5 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( sP13
=> ~ ( ~ sP2
=> sP22 ) )
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( eigen__4 = X1 )
=> ( X1 = eigen__4 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( sP23
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__6 = eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) )
=> ~ ( ~ ( ! [X2: $i] :
( ( X2 != X2 )
=> ( X1 @ X2 @ X2 ) )
=> ~ ! [X2: $i,X3: $i] :
( ~ ( ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( ( X3 != X2 )
=> ( X1 @ X3 @ X2 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ~ ( ( X3 != X4 )
=> ( X1 @ X3 @ X4 ) ) )
=> ( ( X2 != X4 )
=> ( X1 @ X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( ~ sP11
=> sP4 )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ~ ( ( ~ sP11
=> sP4 )
=> ~ ( ( eigen__6 != X1 )
=> ( eigen__0 @ eigen__6 @ X1 ) ) )
=> ( ( eigen__5 != X1 )
=> ( eigen__0 @ eigen__5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [X1: $i,X2: $i] :
( ~ ( ( ( X1 != X2 )
=> ( eigen__0 @ X1 @ X2 ) )
=> ~ ( ( X2 != X1 )
=> ( eigen__0 @ X2 @ X1 ) ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( eigen__6 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__5 = eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: $i] :
( ~ ( ( ( eigen__3 != X1 )
=> ( eigen__0 @ eigen__3 @ X1 ) )
=> ~ ( ( X1 != eigen__3 )
=> ( eigen__0 @ X1 @ eigen__3 ) ) )
=> ( eigen__3 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ sP19
=> ( eigen__0 @ eigen__2 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP2
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ~ sP9
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP2
=> sP18 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( eigen__5 = eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP22
=> ~ sP24 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( sP13
=> ~ sP40 ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( ~ sP43
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ sP11
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__7 = eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(def_subrel,definition,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_inv,definition,
( inv
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_idem,definition,
( idem
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ ( X1 @ X2 ) )
= ( X1 @ X2 ) ) ) ) ).
thf(def_infl,definition,
( infl
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).
thf(def_mono,definition,
( mono
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o] :
( ( subrel @ X2 @ X3 )
=> ( subrel @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_refl,definition,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irrefl,definition,
( irrefl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) ).
thf(def_rc,definition,
( rc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_symm,definition,
( symm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_antisymm,definition,
( antisymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) ).
thf(def_asymm,definition,
( asymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_sc,definition,
( sc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_trans,definition,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_tc,definition,
( tc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ( trans @ X4 )
=> ~ ( subrel @ X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ).
thf(def_trc,definition,
( trc
= ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).
thf(def_trsc,definition,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).
thf(def_po,definition,
( po
= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ( refl @ X1 )
=> ~ ( antisymm @ X1 ) )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_so,definition,
( so
= ( ^ [X1: $i > $i > $o] :
~ ( ( asymm @ X1 )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_total,definition,
( total
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_term,definition,
( term
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ).
thf(def_ind,definition,
( ind
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( tc @ X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) )
=> ( !! @ X2 ) ) ) ) ).
thf(def_innf,definition,
( innf
= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_nfof,definition,
( nfof
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( trc @ X1 @ X3 @ X2 )
=> ~ ( innf @ X1 @ X2 ) ) ) ) ).
thf(def_norm,definition,
( norm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( nfof @ X1 @ X3 @ X2 ) ) ) ).
thf(def_join,definition,
( join
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ! [X4: $i] :
( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X3 @ X4 ) ) ) ) ).
thf(def_lconfl,definition,
( lconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_sconfl,definition,
( sconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_confl,definition,
( confl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_cr,definition,
( cr
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( trsc @ X1 @ X2 @ X3 )
=> ( join @ X1 @ X2 @ X3 ) ) ) ) ).
thf(strict_order_induces_partial_order,conjecture,
sP31 ).
thf(h2,negated_conjecture,
~ sP31,
inference(assume_negation,[status(cth)],[strict_order_induces_partial_order]) ).
thf(1,plain,
( ~ sP30
| sP43
| ~ sP35
| ~ sP30 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP21
| ~ sP11
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP12
| sP21 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
sP36,
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP4
| sP25
| ~ sP36
| ~ sP30 ),
inference(mating_rule,[status(thm)],[]) ).
thf(6,plain,
sP48,
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP47
| sP11
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP37
| sP25
| ~ sP35
| ~ sP48 ),
inference(mating_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP16
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP7
| sP20 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP20
| sP15
| sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP15
| ~ sP4
| ~ sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP6
| sP30
| sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP32
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP32
| sP47 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP26
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP8
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( sP46
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP46
| ~ sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP10
| ~ sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP10
| ~ sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP33
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(23,plain,
( sP17
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(24,plain,
sP19,
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP13
| sP18
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP44
| ~ sP22
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( ~ sP40
| sP2
| sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( sP45
| sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP45
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP3
| sP44 ),
inference(all_rule,[status(thm)],[]) ).
thf(31,plain,
( sP39
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(32,plain,
( ~ sP23
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(33,plain,
( ~ sP42
| ~ sP2
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( ~ sP28
| sP42 ),
inference(all_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP26
| sP28 ),
inference(all_rule,[status(thm)],[]) ).
thf(36,plain,
sP26,
inference(eq_sym,[status(thm)],[]) ).
thf(37,plain,
( sP27
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP27
| ~ sP45 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( sP14
| ~ sP17 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(40,plain,
( sP38
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(41,plain,
( sP34
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(42,plain,
( sP5
| ~ sP39 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(43,plain,
( sP29
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(44,plain,
( sP29
| sP23 ),
inference(prop_rule,[status(thm)],[]) ).
thf(45,plain,
( ~ sP9
| ~ sP5
| ~ sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(46,plain,
( ~ sP41
| sP9
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(47,plain,
( sP1
| sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(48,plain,
( sP1
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(49,plain,
( sP31
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(50,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,h2]) ).
thf(51,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[50,h1]) ).
thf(52,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[51,h0]) ).
thf(0,theorem,
sP31,
inference(contra,[status(thm),contra(discharge,[h2])],[50,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SEU497^1 : TPTP v9.2.0. Released v3.6.0.
% 0.09/0.15 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.37 % Computer : n019.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Oct 8 21:30:23 EDT 2025
% 0.15/0.37 % CPUTime :
% 1.52/1.77 % SZS status Theorem
% 1.52/1.77 % Mode: mode506
% 1.52/1.77 % Inferences: 226277
% 1.52/1.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------