%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU481^1 : 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 : n001.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 02:43:15 PM UTC 2025
% Result : Theorem 13.18s 13.38s
% Output : Proof 13.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 83
% Syntax : Number of formulae : 94 ( 44 unt; 0 typ; 34 def)
% Number of atoms : 255 ( 38 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 707 ( 157 ~; 29 |; 0 &; 348 @)
% ( 25 <=>; 143 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 123 ( 123 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 62 usr; 61 con; 0-2 aty)
% ( 5 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 209 ( 48 ^; 161 !; 0 ?; 209 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__26,type,
eigen__26: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__8,type,
eigen__8: $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] :
( ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ~ ( eigen__1 @ X2 ) )
=> ~ ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: $i > $o] :
~ ( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( eigen__0 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h2,assumption,
! [X1: ( $i > $i > $o ) > $o,X2: $i > $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__2
@ ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) )
=> ( !! @ X2 ) )
=> ! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] :
~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__0 @ eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__26,definition,
( eigen__26
= ( eps__2
@ ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__3 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__26])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i > $o] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) )
=> ( !! @ X1 ) )
=> ! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( eigen__0 @ X2 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__0 @ eigen__3 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ~ ( eigen__0 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__3 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__26 @ X1 @ X2 )
=> ~ ( eigen__26 @ X2 @ X3 ) )
=> ( eigen__26 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__26 @ X1 @ X2 ) ) )
=> ( eigen__26 @ eigen__3 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( sP4
=> ~ ( eigen__1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ! [X1: $i] :
~ ( eigen__1 @ X1 )
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__1 @ X1 )
=> ~ ( eigen__0 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__1 @ eigen__8 )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i] :
~ ( eigen__1 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__3 @ X1 )
=> ( eigen__26 @ eigen__3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ! [X1: $i] :
( ! [X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ~ ( eigen__1 @ X2 ) )
=> ~ ( eigen__1 @ X1 ) )
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__1 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__3 @ X1 ) )
=> ~ ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i > $o] :
( ! [X2: $i] :
( ! [X3: $i] :
( ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) )
=> ( !! @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP12
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: $i > $i > $o] :
( ! [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) )
=> ( !! @ X2 ) )
=> ! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP2
=> ( eigen__26 @ eigen__3 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i] :
( ! [X2: $i] :
( ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) )
=> ~ ( eigen__1 @ X2 ) )
=> ~ ( eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__26 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__26 @ X1 @ X2 )
=> ~ ( eigen__26 @ X2 @ X3 ) )
=> ( eigen__26 @ X1 @ X3 ) )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP15
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__26 @ eigen__3 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i > $o] :
( ~ ! [X2: $i] :
~ ( X1 @ X2 )
=> ~ ! [X2: $i] :
( ( X1 @ X2 )
=> ~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( eigen__0 @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
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(induction_implies_termination,conjecture,
sP18 ).
thf(h3,negated_conjecture,
~ sP18,
inference(assume_negation,[status(cth)],[induction_implies_termination]) ).
thf(1,plain,
( ~ sP21
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP11
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP19
| ~ sP2
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP22
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP5
| ~ sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP5
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP4
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__26]) ).
thf(8,plain,
( ~ sP15
| sP6 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP6
| ~ sP4
| ~ sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP9
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP9
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP8
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(13,plain,
( ~ sP3
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP17
| ~ sP12
| ~ sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP23
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( sP23
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP20
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(18,plain,
( ~ sP16
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP13
| ~ sP20
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP7
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP7
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP25
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(23,plain,
( sP1
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP1
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( sP18
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__0]) ).
thf(26,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,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,h3]) ).
thf(27,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[26,h2]) ).
thf(28,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[27,h1]) ).
thf(29,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[28,h0]) ).
thf(0,theorem,
sP18,
inference(contra,[status(thm),contra(discharge,[h3])],[26,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU481^1 : TPTP v9.2.0. Released v3.6.0.
% 0.13/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Oct 8 21:00:08 EDT 2025
% 0.21/0.35 % CPUTime :
% 13.18/13.38 % SZS status Theorem
% 13.18/13.38 % Mode: mode454
% 13.18/13.38 % Inferences: 198
% 13.18/13.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------