%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU903^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n031.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 02:52:55 PM UTC 2025
% Result : Theorem 18.46s 18.71s
% Output : Proof 18.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 104
% Syntax : Number of formulae : 126 ( 33 unt; 0 typ; 10 def)
% Number of atoms : 472 ( 76 equ; 0 cnn)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 1871 ( 419 ~; 56 |; 0 &; 914 @)
% ( 47 <=>; 435 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 99 ( 99 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 66 usr; 59 con; 0-2 aty)
% Number of variables : 311 ( 10 ^; 301 !; 0 ?; 311 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_eigen__6,type,
eigen__6: a > $o ).
thf(ty_eigen__2,type,
eigen__2: g > $o ).
thf(ty_eigen__7,type,
eigen__7: a > a ).
thf(ty_eigen__1,type,
eigen__1: b > a ).
thf(ty_eigen__0,type,
eigen__0: g > b ).
thf(ty_eigen__4,type,
eigen__4: b > $o ).
thf(ty_eigen__5,type,
eigen__5: b > b ).
thf(ty_eigen__3,type,
eigen__3: g > g ).
thf(ty_eigen__10,type,
eigen__10: g ).
thf(ty_eigen__8,type,
eigen__8: g ).
thf(h0,assumption,
! [X1: ( g > g ) > $o,X2: g > g] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: g > g] :
~ ! [X2: b > $o,X3: b > b,X4: a > $o,X5: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( eigen__2 @ ( X1 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X2 @ ( X3 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X2 @ ( eigen__0 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( ( eigen__0 @ ( X1 @ X6 ) )
= ( X3 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X2 @ ( X3 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X4 @ ( eigen__1 @ X6 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( ( eigen__1 @ ( X3 @ X6 ) )
= ( X5 @ ( eigen__1 @ X6 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( eigen__2 @ ( X1 @ X6 ) ) )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X4 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( ( eigen__1 @ ( eigen__0 @ ( X1 @ X6 ) ) )
= ( X5 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h1,assumption,
! [X1: ( b > a ) > $o,X2: b > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__1
@ ^ [X1: b > a] :
~ ! [X2: g > $o,X3: g > g,X4: b > $o,X5: b > b,X6: a > $o,X7: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__0 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( ( eigen__0 @ ( X3 @ X8 ) )
= ( X5 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( eigen__0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h2,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__2
@ ^ [X1: a > $o] :
~ ! [X2: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( eigen__2 @ ( eigen__3 @ X3 ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( eigen__4 @ ( eigen__5 @ X3 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( eigen__4 @ ( eigen__0 @ X3 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( ( eigen__0 @ ( eigen__3 @ X3 ) )
= ( eigen__5 @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( eigen__4 @ ( eigen__5 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( X1 @ ( eigen__1 @ X3 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( ( eigen__1 @ ( eigen__5 @ X3 ) )
= ( X2 @ ( eigen__1 @ X3 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( eigen__2 @ ( eigen__3 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X3 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h3,assumption,
! [X1: ( g > b ) > $o,X2: g > b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__3
@ ^ [X1: g > b] :
~ ! [X2: b > a,X3: g > $o,X4: g > g,X5: b > $o,X6: b > b,X7: a > $o,X8: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X1 @ ( X4 @ X9 ) )
= ( X6 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( ( X2 @ ( X6 @ X9 ) )
= ( X8 @ ( X2 @ X9 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h4,assumption,
! [X1: g > $o,X2: g] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__4 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__4
@ ^ [X1: g] :
~ ( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__4
@ ^ [X1: g] :
~ ( ( eigen__2 @ X1 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(h5,assumption,
! [X1: ( g > $o ) > $o,X2: g > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__5 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__5
@ ^ [X1: g > $o] :
~ ! [X2: g > g,X3: b > $o,X4: b > b,X5: a > $o,X6: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X7: g] :
( ( X1 @ X7 )
=> ( X1 @ ( X2 @ X7 ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X3 @ ( X4 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__0 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( ( eigen__0 @ ( X2 @ X7 ) )
= ( X4 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X3 @ ( X4 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X5 @ X7 )
=> ( X5 @ ( X6 @ X7 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X5 @ ( eigen__1 @ X7 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( ( eigen__1 @ ( X4 @ X7 ) )
= ( X6 @ ( eigen__1 @ X7 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X7: g] :
( ( X1 @ X7 )
=> ( X1 @ ( X2 @ X7 ) ) )
=> ~ ! [X7: a] :
( ( X5 @ X7 )
=> ( X5 @ ( X6 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X5 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( ( eigen__1 @ ( eigen__0 @ ( X2 @ X7 ) ) )
= ( X6 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(h6,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__6 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__6
@ ^ [X1: b > $o] :
~ ! [X2: b > b,X3: a > $o,X4: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( eigen__2 @ ( eigen__3 @ X5 ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X1 @ ( X2 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X1 @ ( eigen__0 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( ( eigen__0 @ ( eigen__3 @ X5 ) )
= ( X2 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X1 @ ( X2 @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X3 @ ( eigen__1 @ X5 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( ( eigen__1 @ ( X2 @ X5 ) )
= ( X4 @ ( eigen__1 @ X5 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( eigen__2 @ ( eigen__3 @ X5 ) ) )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X3 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X5 ) ) )
= ( X4 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(h7,assumption,
! [X1: ( a > a ) > $o,X2: a > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__7 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__7
@ ^ [X1: a > a] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( eigen__2 @ ( eigen__3 @ X2 ) ) )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( eigen__4 @ ( eigen__5 @ X2 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( eigen__4 @ ( eigen__0 @ X2 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( ( eigen__0 @ ( eigen__3 @ X2 ) )
= ( eigen__5 @ ( eigen__0 @ X2 ) ) ) ) )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( eigen__4 @ ( eigen__5 @ X2 ) ) ) )
=> ~ ! [X2: a] :
( ( eigen__6 @ X2 )
=> ( eigen__6 @ ( X1 @ X2 ) ) ) )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( eigen__6 @ ( eigen__1 @ X2 ) ) ) )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( ( eigen__1 @ ( eigen__5 @ X2 ) )
= ( X1 @ ( eigen__1 @ X2 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( eigen__2 @ ( eigen__3 @ X2 ) ) )
=> ~ ! [X2: a] :
( ( eigen__6 @ X2 )
=> ( eigen__6 @ ( X1 @ X2 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X2 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(h8,assumption,
! [X1: ( b > b ) > $o,X2: b > b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__8 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__8
@ ^ [X1: b > b] :
~ ! [X2: a > $o,X3: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( eigen__2 @ ( eigen__3 @ X4 ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( eigen__4 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( eigen__4 @ ( eigen__0 @ X4 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( ( eigen__0 @ ( eigen__3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( eigen__4 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( X2 @ ( eigen__1 @ X4 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( ( eigen__1 @ ( X1 @ X4 ) )
= ( X3 @ ( eigen__1 @ X4 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( eigen__2 @ ( eigen__3 @ X4 ) ) )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( X2 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X4 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b > a,X2: g > $o,X3: g > g,X4: b > $o,X5: b > b,X6: a > $o,X7: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__0 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( ( eigen__0 @ ( X3 @ X8 ) )
= ( X5 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) ) )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
=> ~ ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( eigen__0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( eigen__2 @ eigen__8 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__4 @ ( eigen__0 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP3
=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o,X2: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( eigen__2 @ ( eigen__3 @ X3 ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( eigen__4 @ ( eigen__5 @ X3 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( eigen__4 @ ( eigen__0 @ X3 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( ( eigen__0 @ ( eigen__3 @ X3 ) )
= ( eigen__5 @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( eigen__4 @ ( eigen__5 @ X3 ) ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( X1 @ ( eigen__1 @ X3 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( ( eigen__1 @ ( eigen__5 @ X3 ) )
= ( X2 @ ( eigen__1 @ X3 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( eigen__2 @ ( eigen__3 @ X3 ) ) )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X3 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__4 @ ( eigen__0 @ X1 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__0 @ ( eigen__3 @ X1 ) )
= ( eigen__5 @ ( eigen__0 @ X1 ) ) ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ ! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( ( eigen__1 @ ( eigen__5 @ X1 ) )
= ( eigen__7 @ ( eigen__1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( eigen__4 @ ( eigen__0 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( sP7
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__10 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( eigen__0 @ ( eigen__3 @ eigen__8 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: b > $o,X2: b > b,X3: a > $o,X4: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( eigen__2 @ ( eigen__3 @ X5 ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X1 @ ( X2 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X1 @ ( eigen__0 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( ( eigen__0 @ ( eigen__3 @ X5 ) )
= ( X2 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X1 @ ( X2 @ X5 ) ) ) )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X3 @ ( eigen__1 @ X5 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( ( eigen__1 @ ( X2 @ X5 ) )
= ( X4 @ ( eigen__1 @ X5 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( eigen__2 @ ( eigen__3 @ X5 ) ) )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X3 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X5 ) ) )
= ( X4 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ( eigen__6 @ X1 )
=> ( eigen__6 @ ( eigen__7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__0 @ ( eigen__3 @ X1 ) )
= ( eigen__5 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: b > $o] :
( ( X1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 ) ) )
=> ! [X2: b] :
( ( ( eigen__0 @ ( eigen__3 @ eigen__8 ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__4 @ ( eigen__0 @ X1 ) ) ) )
=> ~ sP14 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: b > b,X2: a > $o,X3: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( eigen__2 @ ( eigen__3 @ X4 ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( eigen__4 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( eigen__4 @ ( eigen__0 @ X4 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( ( eigen__0 @ ( eigen__3 @ X4 ) )
= ( X1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( eigen__4 @ ( X1 @ X4 ) ) ) )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( X2 @ ( eigen__1 @ X4 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( ( eigen__1 @ ( X1 @ X4 ) )
= ( X3 @ ( eigen__1 @ X4 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( eigen__2 @ ( eigen__3 @ X4 ) ) )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( X2 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X4 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP9
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__4 @ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( eigen__2 @ eigen__8 )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( ( eigen__1 @ ( eigen__5 @ X1 ) )
= ( eigen__7 @ ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ~ sP6
=> ~ ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ sP13 )
=> ~ sP22 )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( eigen__2 @ eigen__8 )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ sP13 )
=> ~ sP22 )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ( eigen__2 @ eigen__10 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__10 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__10 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__2 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ sP16
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__4 @ ( eigen__5 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ sP31
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: g > $o,X2: g > g,X3: b > $o,X4: b > b,X5: a > $o,X6: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X7: g] :
( ( X1 @ X7 )
=> ( X1 @ ( X2 @ X7 ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X3 @ ( X4 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__0 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( ( eigen__0 @ ( X2 @ X7 ) )
= ( X4 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X3 @ ( X4 @ X7 ) ) ) )
=> ~ ! [X7: a] :
( ( X5 @ X7 )
=> ( X5 @ ( X6 @ X7 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X5 @ ( eigen__1 @ X7 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( ( eigen__1 @ ( X4 @ X7 ) )
= ( X6 @ ( eigen__1 @ X7 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X7: g] :
( ( X1 @ X7 )
=> ( X1 @ ( X2 @ X7 ) ) )
=> ~ ! [X7: a] :
( ( X5 @ X7 )
=> ( X5 @ ( X6 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X5 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( ( eigen__1 @ ( eigen__0 @ ( X2 @ X7 ) ) )
= ( X6 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ sP10
=> ! [X1: b] :
( ( ( eigen__0 @ ( eigen__3 @ eigen__8 ) )
= X1 )
=> ( ( eigen__1 @ X1 )
!= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ~ sP17
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g,X5: b > $o,X6: b > b,X7: a > $o,X8: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X1 @ ( X4 @ X9 ) )
= ( X6 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X5 @ ( X6 @ X9 ) ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( ( X2 @ ( X6 @ X9 ) )
= ( X8 @ ( X2 @ X9 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g] :
( ( X3 @ X9 )
=> ( X3 @ ( X4 @ X9 ) ) )
=> ~ ! [X9: a] :
( ( X7 @ X9 )
=> ( X7 @ ( X8 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ! [X1: b,X2: b > $o] :
( ( X2 @ X1 )
=> ! [X3: b] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: a > a] :
( ~ ( ~ ( ~ ( ~ sP31
=> ~ ! [X2: a] :
( ( eigen__6 @ X2 )
=> ( eigen__6 @ ( X1 @ X2 ) ) ) )
=> ~ sP21 )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( ( eigen__1 @ ( eigen__5 @ X2 ) )
= ( X1 @ ( eigen__1 @ X2 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( eigen__2 @ ( eigen__3 @ X2 ) ) )
=> ~ ! [X2: a] :
( ( eigen__6 @ X2 )
=> ( eigen__6 @ ( X1 @ X2 ) ) ) )
=> ~ sP22 )
=> ~ ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X2 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ( eigen__2 @ eigen__10 )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP32
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__2 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: b] :
( ( ( eigen__0 @ ( eigen__3 @ eigen__8 ) )
= X1 )
=> ( ( eigen__1 @ X1 )
!= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( ~ ( ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) )
=> ~ sP13 )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: g > g,X2: b > $o,X3: b > b,X4: a > $o,X5: a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( eigen__2 @ ( X1 @ X6 ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X2 @ ( X3 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X2 @ ( eigen__0 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( ( eigen__0 @ ( X1 @ X6 ) )
= ( X3 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X2 @ ( X3 @ X6 ) ) ) )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X4 @ ( eigen__1 @ X6 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( ( eigen__1 @ ( X3 @ X6 ) )
= ( X5 @ ( eigen__1 @ X6 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( eigen__2 @ ( X1 @ X6 ) ) )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X4 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( ( eigen__1 @ ( eigen__0 @ ( X1 @ X6 ) ) )
= ( X5 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__2 @ ( eigen__3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP46
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(cTHM131_pme,conjecture,
sP36 ).
thf(h9,negated_conjecture,
~ sP36,
inference(assume_negation,[status(cth)],[cTHM131_pme]) ).
thf(1,plain,
( ~ sP20
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP26
| ~ sP30
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP20
| sP39 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP39
| ~ sP41
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( sP17
| sP46 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP19
| ~ sP9
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP42
| sP19 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP34
| sP10
| sP42 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP15
| sP34 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP14
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP23
| ~ sP30
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP37
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
sP37,
inference(eq_ind,[status(thm)],[]) ).
thf(14,plain,
( sP35
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( sP35
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP21
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP8
| ~ sP7
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP16
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP16
| ~ sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( sP28
| ~ sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( sP28
| sP41 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( sP31
| ~ sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( sP2
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( sP2
| sP30 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP24
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( ~ sP4
| ~ sP3
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP22
| ~ sP28 ),
inference(eigen_choice_rule,[status(thm),assumptions([h4])],[h4,eigendef_eigen__10]) ).
thf(28,plain,
( ~ sP47
| ~ sP46
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( sP32
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(30,plain,
( sP32
| ~ sP31 ),
inference(prop_rule,[status(thm)],[]) ).
thf(31,plain,
( sP43
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h4])],[h4,eigendef_eigen__8]) ).
thf(32,plain,
( ~ sP44
| sP47
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( sP40
| sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP40
| ~ sP32 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( ~ sP27
| sP44
| ~ sP43 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP6
| sP24 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( sP6
| ~ sP40 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( sP25
| sP27 ),
inference(prop_rule,[status(thm)],[]) ).
thf(39,plain,
( sP25
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP38
| ~ sP25 ),
inference(eigen_choice_rule,[status(thm),assumptions([h7])],[h7,eigendef_eigen__7]) ).
thf(41,plain,
( sP5
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__6]) ).
thf(42,plain,
( sP18
| ~ sP5 ),
inference(eigen_choice_rule,[status(thm),assumptions([h8])],[h8,eigendef_eigen__5]) ).
thf(43,plain,
( sP11
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h6])],[h6,eigendef_eigen__4]) ).
thf(44,plain,
( sP45
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(45,plain,
( sP33
| ~ sP45 ),
inference(eigen_choice_rule,[status(thm),assumptions([h5])],[h5,eigendef_eigen__2]) ).
thf(46,plain,
( sP1
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1]) ).
thf(47,plain,
( sP36
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__0]) ).
thf(48,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,h9]) ).
thf(49,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h7,h6,h5,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h8])],[48,h8]) ).
thf(50,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h6,h5,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h7])],[49,h7]) ).
thf(51,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h5,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h6])],[50,h6]) ).
thf(52,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h5])],[51,h5]) ).
thf(53,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h3,h2,h1,h0]),eigenvar_choice(discharge,[h4])],[52,h4]) ).
thf(54,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h2,h1,h0]),eigenvar_choice(discharge,[h3])],[53,h3]) ).
thf(55,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h1,h0]),eigenvar_choice(discharge,[h2])],[54,h2]) ).
thf(56,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h0]),eigenvar_choice(discharge,[h1])],[55,h1]) ).
thf(57,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9]),eigenvar_choice(discharge,[h0])],[56,h0]) ).
thf(0,theorem,
sP36,
inference(contra,[status(thm),contra(discharge,[h9])],[48,h9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU903^5 : TPTP v9.2.0. Released v4.0.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 22:00:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 18.46/18.71 % SZS status Theorem
% 18.46/18.71 % Mode: mode485
% 18.46/18.71 % Inferences: 63
% 18.46/18.71 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------