TSTP Solution File: SEU904^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU904^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 : 600s
% DateTime : Tue Jul 19 14:10:46 EDT 2022
% Result : Theorem 36.83s 36.85s
% Output : Proof 36.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 134
% Syntax : Number of formulae : 157 ( 34 unt; 14 typ; 11 def)
% Number of atoms : 602 ( 84 equ; 0 cnn)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 2976 ( 769 ~; 66 |; 0 &;1476 @)
% ( 55 <=>; 610 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 152 ( 152 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 75 usr; 68 con; 0-2 aty)
% Number of variables : 477 ( 11 ^ 466 !; 0 ?; 477 :)
% 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 > 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 > b ).
thf(ty_eigen__11,type,
eigen__11: g ).
thf(ty_eigen__3,type,
eigen__3: g > g > g ).
thf(ty_eigen__10,type,
eigen__10: g ).
thf(ty_eigen__8,type,
eigen__8: g ).
thf(h0,assumption,
! [X1: g > $o,X2: g] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: g] :
~ ( ~ ( ( eigen__2 @ eigen__8 )
=> ~ ( eigen__2 @ X1 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: ( g > g > g ) > $o,X2: g > g > g] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__1
@ ^ [X1: g > g > g] :
~ ! [X2: b > $o,X3: b > b > b,X4: a > $o,X5: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( eigen__2 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: b,X7: b] :
( ~ ( ( X2 @ X6 )
=> ~ ( X2 @ X7 ) )
=> ( X2 @ ( X3 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X2 @ ( eigen__0 @ X6 ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( ( eigen__0 @ ( X1 @ X6 @ X7 ) )
= ( X3 @ ( eigen__0 @ X6 ) @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X6: b,X7: b] :
( ~ ( ( X2 @ X6 )
=> ~ ( X2 @ X7 ) )
=> ( X2 @ ( X3 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X4 @ ( eigen__1 @ X6 ) ) ) )
=> ~ ! [X6: b,X7: b] :
( ~ ( ( X2 @ X6 )
=> ~ ( X2 @ X7 ) )
=> ( ( eigen__1 @ ( X3 @ X6 @ X7 ) )
= ( X5 @ ( eigen__1 @ X6 ) @ ( eigen__1 @ X7 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( eigen__2 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X4 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( X1 @ X6 @ X7 ) ) )
= ( X5 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h2,assumption,
! [X1: ( b > a ) > $o,X2: b > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__2
@ ^ [X1: b > a] :
~ ! [X2: g > $o,X3: g > g > g,X4: b > $o,X5: b > b > b,X6: a > $o,X7: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
=> ~ ! [X8: b,X9: b] :
( ~ ( ( X4 @ X8 )
=> ~ ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__0 @ X8 ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( ( eigen__0 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( eigen__0 @ X8 ) @ ( eigen__0 @ X9 ) ) ) ) )
=> ~ ! [X8: b,X9: b] :
( ~ ( ( X4 @ X8 )
=> ~ ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X6 @ X8 )
=> ~ ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) ) )
=> ~ ! [X8: b,X9: b] :
( ~ ( ( X4 @ X8 )
=> ~ ( X4 @ X9 ) )
=> ( ( X1 @ ( X5 @ X8 @ X9 ) )
= ( X7 @ ( X1 @ X8 ) @ ( X1 @ X9 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X6 @ X8 )
=> ~ ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( ( X1 @ ( eigen__0 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( eigen__0 @ X8 ) ) @ ( X1 @ ( eigen__0 @ X9 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h3,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__3
@ ^ [X1: a > $o] :
~ ! [X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: g,X4: g] :
( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( eigen__2 @ ( eigen__3 @ X3 @ X4 ) ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( eigen__4 @ X3 )
=> ~ ( eigen__4 @ X4 ) )
=> ( eigen__4 @ ( eigen__5 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( eigen__4 @ ( eigen__0 @ X3 ) ) ) )
=> ~ ! [X3: g,X4: g] :
( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X3 @ X4 ) )
= ( eigen__5 @ ( eigen__0 @ X3 ) @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( eigen__4 @ X3 )
=> ~ ( eigen__4 @ X4 ) )
=> ( eigen__4 @ ( eigen__5 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( X1 @ ( eigen__1 @ X3 ) ) ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( eigen__4 @ X3 )
=> ~ ( eigen__4 @ X4 ) )
=> ( ( eigen__1 @ ( eigen__5 @ X3 @ X4 ) )
= ( X2 @ ( eigen__1 @ X3 ) @ ( eigen__1 @ X4 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X3: g,X4: g] :
( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( eigen__2 @ ( eigen__3 @ X3 @ X4 ) ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X3: g,X4: g] :
( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X3 @ X4 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(h4,assumption,
! [X1: ( g > b ) > $o,X2: g > b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__4 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__4
@ ^ [X1: g > b] :
~ ! [X2: b > a,X3: g > $o,X4: g > g > g,X5: b > $o,X6: b > b > b,X7: a > $o,X8: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: b,X10: b] :
( ~ ( ( X5 @ X9 )
=> ~ ( X5 @ X10 ) )
=> ( X5 @ ( X6 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( ( X1 @ ( X4 @ X9 @ X10 ) )
= ( X6 @ ( X1 @ X9 ) @ ( X1 @ X10 ) ) ) ) )
=> ~ ! [X9: b,X10: b] :
( ~ ( ( X5 @ X9 )
=> ~ ( X5 @ X10 ) )
=> ( X5 @ ( X6 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b,X10: b] :
( ~ ( ( X5 @ X9 )
=> ~ ( X5 @ X10 ) )
=> ( ( X2 @ ( X6 @ X9 @ X10 ) )
= ( X8 @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 @ X10 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) @ ( X2 @ ( X1 @ X10 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [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__0
@ ^ [X1: g] :
~ ! [X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ) ),
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 > g,X3: b > $o,X4: b > b > b,X5: a > $o,X6: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( X1 @ ( X2 @ X7 @ X8 ) ) )
=> ~ ! [X7: b,X8: b] :
( ~ ( ( X3 @ X7 )
=> ~ ( X3 @ X8 ) )
=> ( X3 @ ( X4 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__0 @ X7 ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__0 @ ( X2 @ X7 @ X8 ) )
= ( X4 @ ( eigen__0 @ X7 ) @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X7: b,X8: b] :
( ~ ( ( X3 @ X7 )
=> ~ ( X3 @ X8 ) )
=> ( X3 @ ( X4 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X5 @ X7 )
=> ~ ( X5 @ X8 ) )
=> ( X5 @ ( X6 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X5 @ ( eigen__1 @ X7 ) ) ) )
=> ~ ! [X7: b,X8: b] :
( ~ ( ( X3 @ X7 )
=> ~ ( X3 @ X8 ) )
=> ( ( eigen__1 @ ( X4 @ X7 @ X8 ) )
= ( X6 @ ( eigen__1 @ X7 ) @ ( eigen__1 @ X8 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( X1 @ ( X2 @ X7 @ X8 ) ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X5 @ X7 )
=> ~ ( X5 @ X8 ) )
=> ( X5 @ ( X6 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X5 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( X2 @ X7 @ X8 ) ) )
= ( X6 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) @ ( eigen__1 @ ( eigen__0 @ X8 ) ) ) ) ) ) ) ) ),
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 > b,X3: a > $o,X4: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: g,X6: g] :
( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ( eigen__2 @ ( eigen__3 @ X5 @ X6 ) ) )
=> ~ ! [X5: b,X6: b] :
( ~ ( ( X1 @ X5 )
=> ~ ( X1 @ X6 ) )
=> ( X1 @ ( X2 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X1 @ ( eigen__0 @ X5 ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X5 @ X6 ) )
= ( X2 @ ( eigen__0 @ X5 ) @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X5: b,X6: b] :
( ~ ( ( X1 @ X5 )
=> ~ ( X1 @ X6 ) )
=> ( X1 @ ( X2 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X3 @ ( eigen__1 @ X5 ) ) ) )
=> ~ ! [X5: b,X6: b] :
( ~ ( ( X1 @ X5 )
=> ~ ( X1 @ X6 ) )
=> ( ( eigen__1 @ ( X2 @ X5 @ X6 ) )
= ( X4 @ ( eigen__1 @ X5 ) @ ( eigen__1 @ X6 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X5: g,X6: g] :
( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ( eigen__2 @ ( eigen__3 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X3 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X5 @ X6 ) ) )
= ( X4 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(h7,assumption,
! [X1: ( a > a > a ) > $o,X2: a > a > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__7 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__7
@ ^ [X1: a > a > a] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X2: g,X3: g] :
( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( eigen__2 @ ( eigen__3 @ X2 @ X3 ) ) )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__4 @ X2 )
=> ~ ( eigen__4 @ X3 ) )
=> ( eigen__4 @ ( eigen__5 @ X2 @ X3 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( eigen__4 @ ( eigen__0 @ X2 ) ) ) )
=> ~ ! [X2: g,X3: g] :
( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X2 @ X3 ) )
= ( eigen__5 @ ( eigen__0 @ X2 ) @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__4 @ X2 )
=> ~ ( eigen__4 @ X3 ) )
=> ( eigen__4 @ ( eigen__5 @ X2 @ X3 ) ) ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__6 @ X2 )
=> ~ ( eigen__6 @ X3 ) )
=> ( eigen__6 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ ! [X2: b] :
( ( eigen__4 @ X2 )
=> ( eigen__6 @ ( eigen__1 @ X2 ) ) ) )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__4 @ X2 )
=> ~ ( eigen__4 @ X3 ) )
=> ( ( eigen__1 @ ( eigen__5 @ X2 @ X3 ) )
= ( X1 @ ( eigen__1 @ X2 ) @ ( eigen__1 @ X3 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X2: g,X3: g] :
( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( eigen__2 @ ( eigen__3 @ X2 @ X3 ) ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__6 @ X2 )
=> ~ ( eigen__6 @ X3 ) )
=> ( eigen__6 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__2 @ X2 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) )
=> ~ ! [X2: g,X3: g] :
( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X2 @ X3 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(h8,assumption,
! [X1: ( b > b > b ) > $o,X2: b > b > b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__8 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__8
@ ^ [X1: b > b > b] :
~ ! [X2: a > $o,X3: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X4: g,X5: g] :
( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ( eigen__2 @ ( eigen__3 @ X4 @ X5 ) ) )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( eigen__4 @ X4 )
=> ~ ( eigen__4 @ X5 ) )
=> ( eigen__4 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( eigen__4 @ ( eigen__0 @ X4 ) ) ) )
=> ~ ! [X4: g,X5: g] :
( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X4 @ X5 ) )
= ( X1 @ ( eigen__0 @ X4 ) @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( eigen__4 @ X4 )
=> ~ ( eigen__4 @ X5 ) )
=> ( eigen__4 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( X2 @ ( eigen__1 @ X4 ) ) ) )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( eigen__4 @ X4 )
=> ~ ( eigen__4 @ X5 ) )
=> ( ( eigen__1 @ ( X1 @ X4 @ X5 ) )
= ( X3 @ ( eigen__1 @ X4 ) @ ( eigen__1 @ X5 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X4: g,X5: g] :
( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ( eigen__2 @ ( eigen__3 @ X4 @ X5 ) ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( X2 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: g,X5: g] :
( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X4 @ X5 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: b > a,X2: g > $o,X3: g > g > g,X4: b > $o,X5: b > b > b,X6: a > $o,X7: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
=> ~ ! [X8: b,X9: b] :
( ~ ( ( X4 @ X8 )
=> ~ ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__0 @ X8 ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( ( eigen__0 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( eigen__0 @ X8 ) @ ( eigen__0 @ X9 ) ) ) ) )
=> ~ ! [X8: b,X9: b] :
( ~ ( ( X4 @ X8 )
=> ~ ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X6 @ X8 )
=> ~ ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) ) )
=> ~ ! [X8: b,X9: b] :
( ~ ( ( X4 @ X8 )
=> ~ ( X4 @ X9 ) )
=> ( ( X1 @ ( X5 @ X8 @ X9 ) )
= ( X7 @ ( X1 @ X8 ) @ ( X1 @ X9 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X6 @ X8 )
=> ~ ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( ( X1 @ ( eigen__0 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( eigen__0 @ X8 ) ) @ ( X1 @ ( eigen__0 @ X9 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: g] :
( ~ ( ( eigen__2 @ eigen__8 )
=> ~ ( eigen__2 @ X1 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 @ X1 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( eigen__2 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a > $o,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: g,X4: g] :
( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( eigen__2 @ ( eigen__3 @ X3 @ X4 ) ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( eigen__4 @ X3 )
=> ~ ( eigen__4 @ X4 ) )
=> ( eigen__4 @ ( eigen__5 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( eigen__4 @ ( eigen__0 @ X3 ) ) ) )
=> ~ ! [X3: g,X4: g] :
( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X3 @ X4 ) )
= ( eigen__5 @ ( eigen__0 @ X3 ) @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( eigen__4 @ X3 )
=> ~ ( eigen__4 @ X4 ) )
=> ( eigen__4 @ ( eigen__5 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__4 @ X3 )
=> ( X1 @ ( eigen__1 @ X3 ) ) ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( eigen__4 @ X3 )
=> ~ ( eigen__4 @ X4 ) )
=> ( ( eigen__1 @ ( eigen__5 @ X3 @ X4 ) )
= ( X2 @ ( eigen__1 @ X3 ) @ ( eigen__1 @ X4 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X3: g,X4: g] :
( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( eigen__2 @ ( eigen__3 @ X3 @ X4 ) ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) )
=> ~ ! [X3: g,X4: g] :
( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X3 @ X4 ) ) )
= ( X2 @ ( eigen__1 @ ( eigen__0 @ X3 ) ) @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( eigen__4 @ ( eigen__0 @ eigen__11 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( eigen__4 @ ( eigen__0 @ eigen__8 ) )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( eigen__2 @ ( eigen__3 @ X1 @ X2 ) ) )
=> ~ ! [X1: b,X2: b] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__4 @ X2 ) )
=> ( eigen__4 @ ( eigen__5 @ X1 @ X2 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__4 @ ( eigen__0 @ X1 ) ) ) )
=> ~ ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) )
= ( eigen__5 @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ) )
=> ~ ! [X1: b,X2: b] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__4 @ X2 ) )
=> ( eigen__4 @ ( eigen__5 @ X1 @ X2 ) ) ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__6 @ X1 )
=> ~ ( eigen__6 @ X2 ) )
=> ( eigen__6 @ ( eigen__7 @ X1 @ X2 ) ) ) )
=> ~ ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ) )
=> ~ ! [X1: b,X2: b] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__4 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__5 @ X1 @ X2 ) )
= ( eigen__7 @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__11 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__11 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__11 ) ) )
!= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__11 ) ) ) )
=> ! [X1: b] :
( ( ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__11 ) )
= X1 )
=> ( ( eigen__1 @ X1 )
!= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__11 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP8
=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__11 ) ) )
!= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__11 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( eigen__4 @ ( eigen__0 @ eigen__10 ) )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__10 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: g] :
( ~ ( ( eigen__2 @ eigen__8 )
=> ~ ( eigen__2 @ X1 ) )
=> ( ( eigen__0 @ ( eigen__3 @ eigen__8 @ X1 ) )
= ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: b,X2: b > $o] :
( ( X2 @ X1 )
=> ! [X3: b] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: b > $o,X2: b > b > b,X3: a > $o,X4: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: g,X6: g] :
( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ( eigen__2 @ ( eigen__3 @ X5 @ X6 ) ) )
=> ~ ! [X5: b,X6: b] :
( ~ ( ( X1 @ X5 )
=> ~ ( X1 @ X6 ) )
=> ( X1 @ ( X2 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X1 @ ( eigen__0 @ X5 ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X5 @ X6 ) )
= ( X2 @ ( eigen__0 @ X5 ) @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X5: b,X6: b] :
( ~ ( ( X1 @ X5 )
=> ~ ( X1 @ X6 ) )
=> ( X1 @ ( X2 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X3 @ ( eigen__1 @ X5 ) ) ) )
=> ~ ! [X5: b,X6: b] :
( ~ ( ( X1 @ X5 )
=> ~ ( X1 @ X6 ) )
=> ( ( eigen__1 @ ( X2 @ X5 @ X6 ) )
= ( X4 @ ( eigen__1 @ X5 ) @ ( eigen__1 @ X6 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X5: g,X6: g] :
( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ( eigen__2 @ ( eigen__3 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__2 @ X5 )
=> ( X3 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ( eigen__2 @ X5 )
=> ~ ( eigen__2 @ X6 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X5 @ X6 ) ) )
= ( X4 @ ( eigen__1 @ ( eigen__0 @ X5 ) ) @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__4 @ ( eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ sP6
=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__11 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__11 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( ~ ( ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( eigen__2 @ ( eigen__3 @ X1 @ X2 ) ) )
=> ~ ! [X1: b,X2: b] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__4 @ X2 ) )
=> ( eigen__4 @ ( eigen__5 @ X1 @ X2 ) ) ) )
=> ~ sP15 )
=> ~ ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) )
= ( eigen__5 @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__6 @ X1 )
=> ~ ( eigen__6 @ X2 ) )
=> ( eigen__6 @ ( eigen__7 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__4 @ ( eigen__0 @ eigen__10 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: b] :
( ~ ( ( eigen__4 @ ( eigen__0 @ eigen__8 ) )
=> ~ ( eigen__4 @ X1 ) )
=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ X1 ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( eigen__1 @ ( eigen__5 @ ( eigen__0 @ eigen__8 ) @ ( eigen__0 @ eigen__11 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__11 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( ( eigen__2 @ eigen__8 )
=> ~ ( eigen__2 @ eigen__11 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__11 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__11 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: b > b > b,X2: a > $o,X3: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X4: g,X5: g] :
( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ( eigen__2 @ ( eigen__3 @ X4 @ X5 ) ) )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( eigen__4 @ X4 )
=> ~ ( eigen__4 @ X5 ) )
=> ( eigen__4 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ sP15 )
=> ~ ! [X4: g,X5: g] :
( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X4 @ X5 ) )
= ( X1 @ ( eigen__0 @ X4 ) @ ( eigen__0 @ X5 ) ) ) ) )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( eigen__4 @ X4 )
=> ~ ( eigen__4 @ X5 ) )
=> ( eigen__4 @ ( X1 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__4 @ X4 )
=> ( X2 @ ( eigen__1 @ X4 ) ) ) )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( eigen__4 @ X4 )
=> ~ ( eigen__4 @ X5 ) )
=> ( ( eigen__1 @ ( X1 @ X4 @ X5 ) )
= ( X3 @ ( eigen__1 @ X4 ) @ ( eigen__1 @ X5 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X4: g,X5: g] :
( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ( eigen__2 @ ( eigen__3 @ X4 @ X5 ) ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__2 @ X4 )
=> ( X2 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) ) ) )
=> ~ ! [X4: g,X5: g] :
( ~ ( ( eigen__2 @ X4 )
=> ~ ( eigen__2 @ X5 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X4 @ X5 ) ) )
= ( X3 @ ( eigen__1 @ ( eigen__0 @ X4 ) ) @ ( eigen__1 @ ( eigen__0 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( eigen__4 @ ( eigen__0 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: b] :
( ( eigen__4 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( eigen__2 @ ( eigen__3 @ X1 @ X2 ) ) )
=> ~ ! [X1: b,X2: b] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__4 @ X2 ) )
=> ( eigen__4 @ ( eigen__5 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: g] :
( ( eigen__2 @ X1 )
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ sP26
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: b,X2: b] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__4 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__5 @ X1 @ X2 ) )
= ( eigen__7 @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ~ sP7
=> ~ ( ~ ( ~ ( ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( eigen__2 @ ( eigen__3 @ X1 @ X2 ) ) )
=> ~ sP18 )
=> ~ sP27 )
=> ~ ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ( eigen__2 @ eigen__11 )
=> sP5 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ~ ( ~ ( ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( eigen__2 @ ( eigen__3 @ X1 @ X2 ) ) )
=> ~ sP18 )
=> ~ sP27 )
=> ~ ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( sP3
=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__10 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ ( ( eigen__2 @ eigen__8 )
=> ~ ( eigen__2 @ eigen__11 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( eigen__6 @ ( eigen__1 @ ( eigen__0 @ eigen__10 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( eigen__2 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ sP17
=> ~ ! [X1: b,X2: b] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( eigen__4 @ X2 ) )
=> ( eigen__4 @ ( eigen__5 @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: b] :
( ( ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__11 ) )
= X1 )
=> ( ( eigen__1 @ X1 )
!= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__11 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( ~ sP37
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: g > $o,X2: g > g > g,X3: b > $o,X4: b > b > b,X5: a > $o,X6: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( X1 @ ( X2 @ X7 @ X8 ) ) )
=> ~ ! [X7: b,X8: b] :
( ~ ( ( X3 @ X7 )
=> ~ ( X3 @ X8 ) )
=> ( X3 @ ( X4 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__0 @ X7 ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__0 @ ( X2 @ X7 @ X8 ) )
= ( X4 @ ( eigen__0 @ X7 ) @ ( eigen__0 @ X8 ) ) ) ) )
=> ~ ! [X7: b,X8: b] :
( ~ ( ( X3 @ X7 )
=> ~ ( X3 @ X8 ) )
=> ( X3 @ ( X4 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X5 @ X7 )
=> ~ ( X5 @ X8 ) )
=> ( X5 @ ( X6 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X5 @ ( eigen__1 @ X7 ) ) ) )
=> ~ ! [X7: b,X8: b] :
( ~ ( ( X3 @ X7 )
=> ~ ( X3 @ X8 ) )
=> ( ( eigen__1 @ ( X4 @ X7 @ X8 ) )
= ( X6 @ ( eigen__1 @ X7 ) @ ( eigen__1 @ X8 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( X1 @ ( X2 @ X7 @ X8 ) ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X5 @ X7 )
=> ~ ( X5 @ X8 ) )
=> ( X5 @ ( X6 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X5 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( X2 @ X7 @ X8 ) ) )
= ( X6 @ ( eigen__1 @ ( eigen__0 @ X7 ) ) @ ( eigen__1 @ ( eigen__0 @ X8 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( eigen__2 @ eigen__11 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ! [X1: g > b,X2: b > a,X3: g > $o,X4: g > g > g,X5: b > $o,X6: b > b > b,X7: a > $o,X8: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: b,X10: b] :
( ~ ( ( X5 @ X9 )
=> ~ ( X5 @ X10 ) )
=> ( X5 @ ( X6 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( ( X1 @ ( X4 @ X9 @ X10 ) )
= ( X6 @ ( X1 @ X9 ) @ ( X1 @ X10 ) ) ) ) )
=> ~ ! [X9: b,X10: b] :
( ~ ( ( X5 @ X9 )
=> ~ ( X5 @ X10 ) )
=> ( X5 @ ( X6 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: b] :
( ( X5 @ X9 )
=> ( X7 @ ( X2 @ X9 ) ) ) )
=> ~ ! [X9: b,X10: b] :
( ~ ( ( X5 @ X9 )
=> ~ ( X5 @ X10 ) )
=> ( ( X2 @ ( X6 @ X9 @ X10 ) )
= ( X8 @ ( X2 @ X9 ) @ ( X2 @ X10 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( X3 @ ( X4 @ X9 @ X10 ) ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X7 @ X9 )
=> ~ ( X7 @ X10 ) )
=> ( X7 @ ( X8 @ X9 @ X10 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X7 @ ( X2 @ ( X1 @ X9 ) ) ) ) )
=> ~ ! [X9: g,X10: g] :
( ~ ( ( X3 @ X9 )
=> ~ ( X3 @ X10 ) )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 @ X10 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) @ ( X2 @ ( X1 @ X10 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ! [X1: b > $o] :
( ( X1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__11 ) ) )
=> ! [X2: b] :
( ( ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__11 ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP36
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: a > a > a] :
( ~ ( ~ ( ~ ( ~ sP37
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__6 @ X2 )
=> ~ ( eigen__6 @ X3 ) )
=> ( eigen__6 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ sP25 )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__4 @ X2 )
=> ~ ( eigen__4 @ X3 ) )
=> ( ( eigen__1 @ ( eigen__5 @ X2 @ X3 ) )
= ( X1 @ ( eigen__1 @ X2 ) @ ( eigen__1 @ X3 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X2: g,X3: g] :
( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( eigen__2 @ ( eigen__3 @ X2 @ X3 ) ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__6 @ X2 )
=> ~ ( eigen__6 @ X3 ) )
=> ( eigen__6 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ sP27 )
=> ~ ! [X2: g,X3: g] :
( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X2 @ X3 ) ) )
= ( X1 @ ( eigen__1 @ ( eigen__0 @ X2 ) ) @ ( eigen__1 @ ( eigen__0 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP3
=> sP19 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( ~ sP39
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ X1 ) ) @ ( eigen__1 @ ( eigen__0 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ~ ( ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( eigen__2 @ ( eigen__3 @ X1 @ X2 ) ) )
=> ~ sP18 )
=> ~ sP27 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ! [X1: g > g > g,X2: b > $o,X3: b > b > b,X4: a > $o,X5: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( eigen__2 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: b,X7: b] :
( ~ ( ( X2 @ X6 )
=> ~ ( X2 @ X7 ) )
=> ( X2 @ ( X3 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X2 @ ( eigen__0 @ X6 ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( ( eigen__0 @ ( X1 @ X6 @ X7 ) )
= ( X3 @ ( eigen__0 @ X6 ) @ ( eigen__0 @ X7 ) ) ) ) )
=> ~ ! [X6: b,X7: b] :
( ~ ( ( X2 @ X6 )
=> ~ ( X2 @ X7 ) )
=> ( X2 @ ( X3 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X4 @ ( eigen__1 @ X6 ) ) ) )
=> ~ ! [X6: b,X7: b] :
( ~ ( ( X2 @ X6 )
=> ~ ( X2 @ X7 ) )
=> ( ( eigen__1 @ ( X3 @ X6 @ X7 ) )
= ( X5 @ ( eigen__1 @ X6 ) @ ( eigen__1 @ X7 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( eigen__2 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__2 @ X6 )
=> ( X4 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ( eigen__2 @ X6 )
=> ~ ( eigen__2 @ X7 ) )
=> ( ( eigen__1 @ ( eigen__0 @ ( X1 @ X6 @ X7 ) ) )
= ( X5 @ ( eigen__1 @ ( eigen__0 @ X6 ) ) @ ( eigen__1 @ ( eigen__0 @ X7 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP36
=> ~ sP41 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( ( eigen__0 @ ( eigen__3 @ X1 @ X2 ) )
= ( eigen__5 @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: g,X2: g] :
( ~ ( ( eigen__2 @ X1 )
=> ~ ( eigen__2 @ X2 ) )
=> ( eigen__2 @ ( eigen__3 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ( eigen__1 @ ( eigen__0 @ ( eigen__3 @ eigen__8 @ eigen__11 ) ) )
= ( eigen__7 @ ( eigen__1 @ ( eigen__0 @ eigen__8 ) ) @ ( eigen__1 @ ( eigen__0 @ eigen__11 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP53
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(cTHM126_pme,conjecture,
sP42 ).
thf(h9,negated_conjecture,
~ sP42,
inference(assume_negation,[status(cth)],[cTHM126_pme]) ).
thf(1,plain,
( ~ sP15
| sP46 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP46
| ~ sP3
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP15
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP44
| ~ sP36
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP15
| sP31 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP31
| ~ sP41
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP26
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP52
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP12
| sP34 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP34
| sP51
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| ~ sP8
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP38
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP9
| sP54
| sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP43
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP13
| sP43 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
sP13,
inference(eq_ind,[status(thm)],]) ).
thf(17,plain,
( sP28
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP28
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP51
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP51
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP25
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP11
| ~ sP19
| sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP17
| sP52 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP17
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP22
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP22
| ~ sP51 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP29
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP20
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP16
| sP6
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP6
| ~ sP24
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP33
| ~ sP35 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP33
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP37
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP2
| ~ sP22 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(35,plain,
( sP27
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(36,plain,
( ~ sP55
| ~ sP53
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP39
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP39
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP48
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(40,plain,
( ~ sP49
| sP55
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP47
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP47
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( ~ sP32
| sP49
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP7
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP7
| ~ sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP30
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP30
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( sP45
| ~ sP30 ),
inference(eigen_choice_rule,[status(thm),assumptions([h7])],[h7,eigendef_eigen__7]) ).
thf(49,plain,
( sP4
| ~ sP45 ),
inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__6]) ).
thf(50,plain,
( sP23
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h8])],[h8,eigendef_eigen__5]) ).
thf(51,plain,
( sP14
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h6])],[h6,eigendef_eigen__4]) ).
thf(52,plain,
( sP50
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__3]) ).
thf(53,plain,
( sP40
| ~ sP50 ),
inference(eigen_choice_rule,[status(thm),assumptions([h5])],[h5,eigendef_eigen__2]) ).
thf(54,plain,
( sP1
| ~ sP40 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__1]) ).
thf(55,plain,
( sP42
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h4])],[h4,eigendef_eigen__0]) ).
thf(56,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,h9]) ).
thf(57,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h7,h6,h5,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h8])],[56,h8]) ).
thf(58,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h6,h5,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h7])],[57,h7]) ).
thf(59,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h5,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h6])],[58,h6]) ).
thf(60,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h5])],[59,h5]) ).
thf(61,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h3,h2,h1,h0]),eigenvar_choice(discharge,[h4])],[60,h4]) ).
thf(62,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h2,h1,h0]),eigenvar_choice(discharge,[h3])],[61,h3]) ).
thf(63,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h1,h0]),eigenvar_choice(discharge,[h2])],[62,h2]) ).
thf(64,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h0]),eigenvar_choice(discharge,[h1])],[63,h1]) ).
thf(65,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9]),eigenvar_choice(discharge,[h0])],[64,h0]) ).
thf(0,theorem,
sP42,
inference(contra,[status(thm),contra(discharge,[h9])],[56,h9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU904^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 10:30:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 36.83/36.85 % SZS status Theorem
% 36.83/36.85 % Mode: mode485
% 36.83/36.85 % Inferences: 62
% 36.83/36.85 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------