TSTP Solution File: SYO225^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO225^5 : 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 : n025.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 : Thu Jul 21 19:30:58 EDT 2022
% Result : Theorem 36.82s 36.88s
% Output : Proof 36.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 150
% Syntax : Number of formulae : 179 ( 40 unt; 14 typ; 17 def)
% Number of atoms : 670 ( 108 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 4082 (1107 ~; 74 |; 0 &;1962 @)
% ( 63 <=>; 876 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 303 ( 303 >; 0 *; 0 +; 0 <<)
% Number of symbols : 91 ( 89 usr; 82 con; 0-2 aty)
% Number of variables : 700 ( 17 ^ 683 !; 0 ?; 700 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_b,type,
b: $tType ).
thf(ty_g,type,
g: $tType ).
thf(ty_eigen__14,type,
eigen__14: g ).
thf(ty_eigen__6,type,
eigen__6: g > b ).
thf(ty_eigen__12,type,
eigen__12: a > $o ).
thf(ty_eigen__16,type,
eigen__16: g ).
thf(ty_eigen__7,type,
eigen__7: b > a ).
thf(ty_eigen__11,type,
eigen__11: b > b > b ).
thf(ty_eigen__17,type,
eigen__17: g ).
thf(ty_eigen__10,type,
eigen__10: b > $o ).
thf(ty_eigen__8,type,
eigen__8: g > $o ).
thf(ty_eigen__13,type,
eigen__13: a > a > a ).
thf(ty_eigen__9,type,
eigen__9: g > g > g ).
thf(h0,assumption,
! [X1: ( b > b > b ) > $o,X2: b > b > b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: b > b > b] :
~ ! [X2: a > $o,X3: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X4: g,X5: g] :
( ~ ( ( eigen__8 @ X4 )
=> ~ ( eigen__8 @ X5 ) )
=> ( eigen__8 @ ( eigen__9 @ X4 @ X5 ) ) )
=> ~ ! [X4: g] :
( ( eigen__8 @ X4 )
=> ( eigen__10 @ ( eigen__6 @ X4 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__8 @ X4 )
=> ( eigen__10 @ ( eigen__6 @ X4 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__8 @ X4 )
=> ( eigen__10 @ ( eigen__6 @ X4 ) ) ) )
=> ~ ! [X4: g,X5: g] :
( ~ ( ( eigen__8 @ X4 )
=> ~ ( eigen__8 @ X5 ) )
=> ( ( eigen__6 @ ( eigen__9 @ X4 @ X5 ) )
= ( X1 @ ( eigen__6 @ X4 ) @ ( eigen__6 @ X5 ) ) ) ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__10 @ X4 )
=> ( X2 @ ( eigen__7 @ X4 ) ) ) )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( eigen__10 @ X4 )
=> ~ ( eigen__10 @ X5 ) )
=> ( ( eigen__7 @ ( X1 @ X4 @ X5 ) )
= ( X3 @ ( eigen__7 @ X4 ) @ ( eigen__7 @ X5 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X4: g,X5: g] :
( ~ ( ( eigen__8 @ X4 )
=> ~ ( eigen__8 @ X5 ) )
=> ( eigen__8 @ ( eigen__9 @ X4 @ X5 ) ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__8 @ X4 )
=> ( X2 @ ( eigen__7 @ ( eigen__6 @ X4 ) ) ) ) )
=> ~ ! [X4: g,X5: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X4 )
=> ~ ( eigen__8 @ X5 ) )
=> ~ ( eigen__8 @ X4 ) )
=> ~ ( eigen__8 @ X5 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X4 @ X5 ) ) )
= ( X3 @ ( eigen__7 @ ( eigen__6 @ X4 ) ) @ ( eigen__7 @ ( eigen__6 @ X5 ) ) ) ) ) ) ) ) ),
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: g > b,X5: b > a,X6: g > $o,X7: g > g > g,X8: b > $o,X9: b > b > b,X10: a > $o,X11: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X12: g,X13: g] :
( ~ ( ( X6 @ X12 )
=> ~ ( X6 @ X13 ) )
=> ( X6 @ ( X7 @ X12 @ X13 ) ) )
=> ~ ! [X12: g] :
( ( X6 @ X12 )
=> ( X8 @ ( X4 @ X12 ) ) ) )
=> ~ ! [X12: g] :
( ( X6 @ X12 )
=> ( X8 @ ( X4 @ X12 ) ) ) )
=> ~ ! [X12: g] :
( ( X6 @ X12 )
=> ( X8 @ ( X4 @ X12 ) ) ) )
=> ~ ! [X12: g,X13: g] :
( ~ ( ( X6 @ X12 )
=> ~ ( X6 @ X13 ) )
=> ( ( X4 @ ( X7 @ X12 @ X13 ) )
= ( X9 @ ( X4 @ X12 ) @ ( X4 @ X13 ) ) ) ) )
=> ~ ! [X12: a,X13: a] :
( ~ ( ( X10 @ X12 )
=> ~ ( X10 @ X13 ) )
=> ( X10 @ ( X11 @ X12 @ X13 ) ) ) )
=> ~ ! [X12: b] :
( ( X8 @ X12 )
=> ( X10 @ ( X5 @ X12 ) ) ) )
=> ~ ! [X12: b,X13: b] :
( ~ ( ( X8 @ X12 )
=> ~ ( X8 @ X13 ) )
=> ( ( X5 @ ( X9 @ X12 @ X13 ) )
= ( X11 @ ( X5 @ X12 ) @ ( X5 @ X13 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X12: g,X13: g] :
( ~ ( ( X6 @ X12 )
=> ~ ( X6 @ X13 ) )
=> ( X6 @ ( X7 @ X12 @ X13 ) ) )
=> ~ ! [X12: a,X13: a] :
( ~ ( ( X10 @ X12 )
=> ~ ( X10 @ X13 ) )
=> ( X10 @ ( X11 @ X12 @ X13 ) ) ) )
=> ~ ! [X12: g] :
( ( X6 @ X12 )
=> ( X10 @ ( X5 @ ( X4 @ X12 ) ) ) ) )
=> ~ ! [X12: g,X13: g] :
( ~ ( ~ ( ~ ( ( X6 @ X12 )
=> ~ ( X6 @ X13 ) )
=> ~ ( X6 @ X12 ) )
=> ~ ( X6 @ X13 ) )
=> ( ( X5 @ ( X4 @ ( X7 @ X12 @ X13 ) ) )
= ( X11 @ ( X5 @ ( X4 @ X12 ) ) @ ( X5 @ ( X4 @ X13 ) ) ) ) ) ) ) ) ),
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: g > b,X7: b > a,X8: g > $o,X9: g > g > g,X10: b > $o,X11: b > b > b,X12: a > $o,X13: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X14: g,X15: g] :
( ~ ( ( X8 @ X14 )
=> ~ ( X8 @ X15 ) )
=> ( X8 @ ( X9 @ X14 @ X15 ) ) )
=> ~ ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) ) )
=> ~ ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) ) )
=> ~ ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) ) )
=> ~ ! [X14: g,X15: g] :
( ~ ( ( X8 @ X14 )
=> ~ ( X8 @ X15 ) )
=> ( ( X6 @ ( X9 @ X14 @ X15 ) )
= ( X11 @ ( X6 @ X14 ) @ ( X6 @ X15 ) ) ) ) )
=> ~ ! [X14: a,X15: a] :
( ~ ( ( X12 @ X14 )
=> ~ ( X12 @ X15 ) )
=> ( X12 @ ( X13 @ X14 @ X15 ) ) ) )
=> ~ ! [X14: b] :
( ( X10 @ X14 )
=> ( X12 @ ( X7 @ X14 ) ) ) )
=> ~ ! [X14: b,X15: b] :
( ~ ( ( X10 @ X14 )
=> ~ ( X10 @ X15 ) )
=> ( ( X7 @ ( X11 @ X14 @ X15 ) )
= ( X13 @ ( X7 @ X14 ) @ ( X7 @ X15 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X14: g,X15: g] :
( ~ ( ( X8 @ X14 )
=> ~ ( X8 @ X15 ) )
=> ( X8 @ ( X9 @ X14 @ X15 ) ) )
=> ~ ! [X14: a,X15: a] :
( ~ ( ( X12 @ X14 )
=> ~ ( X12 @ X15 ) )
=> ( X12 @ ( X13 @ X14 @ X15 ) ) ) )
=> ~ ! [X14: g] :
( ( X8 @ X14 )
=> ( X12 @ ( X7 @ ( X6 @ X14 ) ) ) ) )
=> ~ ! [X14: g,X15: g] :
( ~ ( ~ ( ~ ( ( X8 @ X14 )
=> ~ ( X8 @ X15 ) )
=> ~ ( X8 @ X14 ) )
=> ~ ( X8 @ X15 ) )
=> ( ( X7 @ ( X6 @ ( X9 @ X14 @ X15 ) ) )
= ( X13 @ ( X7 @ ( X6 @ X14 ) ) @ ( X7 @ ( X6 @ X15 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h3,assumption,
! [X1: g > $o,X2: g] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__3 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__17,definition,
( eigen__17
= ( eps__3
@ ^ [X1: g] :
~ ( ~ ( ~ ( ~ ( ( eigen__8 @ eigen__14 )
=> ~ ( eigen__8 @ X1 ) )
=> ~ ( eigen__8 @ eigen__14 ) )
=> ~ ( eigen__8 @ X1 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ eigen__14 @ X1 ) ) )
= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ eigen__14 ) ) @ ( eigen__7 @ ( eigen__6 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__17])]) ).
thf(h4,assumption,
! [X1: ( g > b ) > $o,X2: g > b] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__4 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( 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: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [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: 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 ) )
=> ~ ( X3 @ X9 ) )
=> ~ ( X3 @ X10 ) )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 @ X10 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) @ ( X2 @ ( X1 @ X10 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(eigendef_eigen__14,definition,
( eigen__14
= ( eps__3
@ ^ [X1: g] :
~ ! [X2: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ~ ( eigen__8 @ X1 ) )
=> ~ ( eigen__8 @ X2 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X1 @ X2 ) ) )
= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ X1 ) ) @ ( eigen__7 @ ( eigen__6 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__14])]) ).
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: g > b,X8: b > a,X9: g > $o,X10: g > g > g,X11: b > $o,X12: b > b > b,X13: a > $o,X14: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X15: g,X16: g] :
( ~ ( ( X9 @ X15 )
=> ~ ( X9 @ X16 ) )
=> ( X9 @ ( X10 @ X15 @ X16 ) ) )
=> ~ ! [X15: g] :
( ( X9 @ X15 )
=> ( X11 @ ( X7 @ X15 ) ) ) )
=> ~ ! [X15: g] :
( ( X9 @ X15 )
=> ( X11 @ ( X7 @ X15 ) ) ) )
=> ~ ! [X15: g] :
( ( X9 @ X15 )
=> ( X11 @ ( X7 @ X15 ) ) ) )
=> ~ ! [X15: g,X16: g] :
( ~ ( ( X9 @ X15 )
=> ~ ( X9 @ X16 ) )
=> ( ( X7 @ ( X10 @ X15 @ X16 ) )
= ( X12 @ ( X7 @ X15 ) @ ( X7 @ X16 ) ) ) ) )
=> ~ ! [X15: a,X16: a] :
( ~ ( ( X13 @ X15 )
=> ~ ( X13 @ X16 ) )
=> ( X13 @ ( X14 @ X15 @ X16 ) ) ) )
=> ~ ! [X15: b] :
( ( X11 @ X15 )
=> ( X13 @ ( X8 @ X15 ) ) ) )
=> ~ ! [X15: b,X16: b] :
( ~ ( ( X11 @ X15 )
=> ~ ( X11 @ X16 ) )
=> ( ( X8 @ ( X12 @ X15 @ X16 ) )
= ( X14 @ ( X8 @ X15 ) @ ( X8 @ X16 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X15: g,X16: g] :
( ~ ( ( X9 @ X15 )
=> ~ ( X9 @ X16 ) )
=> ( X9 @ ( X10 @ X15 @ X16 ) ) )
=> ~ ! [X15: a,X16: a] :
( ~ ( ( X13 @ X15 )
=> ~ ( X13 @ X16 ) )
=> ( X13 @ ( X14 @ X15 @ X16 ) ) ) )
=> ~ ! [X15: g] :
( ( X9 @ X15 )
=> ( X13 @ ( X8 @ ( X7 @ X15 ) ) ) ) )
=> ~ ! [X15: g,X16: g] :
( ~ ( ~ ( ~ ( ( X9 @ X15 )
=> ~ ( X9 @ X16 ) )
=> ~ ( X9 @ X15 ) )
=> ~ ( X9 @ X16 ) )
=> ( ( X8 @ ( X7 @ ( X10 @ X15 @ X16 ) ) )
= ( X14 @ ( X8 @ ( X7 @ X15 ) ) @ ( X8 @ ( X7 @ X16 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h5,assumption,
! [X1: ( b > $o ) > $o,X2: b > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__5 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__5
@ ^ [X1: b > $o] :
~ ! [X2: b > b > b,X3: a > $o,X4: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: g,X6: g] :
( ~ ( ( eigen__8 @ X5 )
=> ~ ( eigen__8 @ X6 ) )
=> ( eigen__8 @ ( eigen__9 @ X5 @ X6 ) ) )
=> ~ ! [X5: g] :
( ( eigen__8 @ X5 )
=> ( X1 @ ( eigen__6 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__8 @ X5 )
=> ( X1 @ ( eigen__6 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__8 @ X5 )
=> ( X1 @ ( eigen__6 @ X5 ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ( eigen__8 @ X5 )
=> ~ ( eigen__8 @ X6 ) )
=> ( ( eigen__6 @ ( eigen__9 @ X5 @ X6 ) )
= ( X2 @ ( eigen__6 @ X5 ) @ ( eigen__6 @ X6 ) ) ) ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X3 @ ( eigen__7 @ X5 ) ) ) )
=> ~ ! [X5: b,X6: b] :
( ~ ( ( X1 @ X5 )
=> ~ ( X1 @ X6 ) )
=> ( ( eigen__7 @ ( X2 @ X5 @ X6 ) )
= ( X4 @ ( eigen__7 @ X5 ) @ ( eigen__7 @ X6 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X5: g,X6: g] :
( ~ ( ( eigen__8 @ X5 )
=> ~ ( eigen__8 @ X6 ) )
=> ( eigen__8 @ ( eigen__9 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__8 @ X5 )
=> ( X3 @ ( eigen__7 @ ( eigen__6 @ X5 ) ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X5 )
=> ~ ( eigen__8 @ X6 ) )
=> ~ ( eigen__8 @ X5 ) )
=> ~ ( eigen__8 @ X6 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X5 @ X6 ) ) )
= ( X4 @ ( eigen__7 @ ( eigen__6 @ X5 ) ) @ ( eigen__7 @ ( eigen__6 @ X6 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(h6,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__6 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__12,definition,
( eigen__12
= ( eps__6
@ ^ [X1: a > $o] :
~ ! [X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X3: g,X4: g] :
( ~ ( ( eigen__8 @ X3 )
=> ~ ( eigen__8 @ X4 ) )
=> ( eigen__8 @ ( eigen__9 @ X3 @ X4 ) ) )
=> ~ ! [X3: g] :
( ( eigen__8 @ X3 )
=> ( eigen__10 @ ( eigen__6 @ X3 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__8 @ X3 )
=> ( eigen__10 @ ( eigen__6 @ X3 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__8 @ X3 )
=> ( eigen__10 @ ( eigen__6 @ X3 ) ) ) )
=> ~ ! [X3: g,X4: g] :
( ~ ( ( eigen__8 @ X3 )
=> ~ ( eigen__8 @ X4 ) )
=> ( ( eigen__6 @ ( eigen__9 @ X3 @ X4 ) )
= ( eigen__11 @ ( eigen__6 @ X3 ) @ ( eigen__6 @ X4 ) ) ) ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__10 @ X3 )
=> ( X1 @ ( eigen__7 @ X3 ) ) ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( eigen__10 @ X3 )
=> ~ ( eigen__10 @ X4 ) )
=> ( ( eigen__7 @ ( eigen__11 @ X3 @ X4 ) )
= ( X2 @ ( eigen__7 @ X3 ) @ ( eigen__7 @ X4 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X3: g,X4: g] :
( ~ ( ( eigen__8 @ X3 )
=> ~ ( eigen__8 @ X4 ) )
=> ( eigen__8 @ ( eigen__9 @ X3 @ X4 ) ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__8 @ X3 )
=> ( X1 @ ( eigen__7 @ ( eigen__6 @ X3 ) ) ) ) )
=> ~ ! [X3: g,X4: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X3 )
=> ~ ( eigen__8 @ X4 ) )
=> ~ ( eigen__8 @ X3 ) )
=> ~ ( eigen__8 @ X4 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X3 @ X4 ) ) )
= ( X2 @ ( eigen__7 @ ( eigen__6 @ X3 ) ) @ ( eigen__7 @ ( eigen__6 @ X4 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__12])]) ).
thf(h7,assumption,
! [X1: ( g > $o ) > $o,X2: g > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__7 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__7
@ ^ [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: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__6 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__6 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__6 @ X7 ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__6 @ ( X2 @ X7 @ X8 ) )
= ( X4 @ ( eigen__6 @ X7 ) @ ( eigen__6 @ X8 ) ) ) ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X5 @ X7 )
=> ~ ( X5 @ X8 ) )
=> ( X5 @ ( X6 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X5 @ ( eigen__7 @ X7 ) ) ) )
=> ~ ! [X7: b,X8: b] :
( ~ ( ( X3 @ X7 )
=> ~ ( X3 @ X8 ) )
=> ( ( eigen__7 @ ( X4 @ X7 @ X8 ) )
= ( X6 @ ( eigen__7 @ X7 ) @ ( eigen__7 @ 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__7 @ ( eigen__6 @ X7 ) ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ~ ( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ~ ( X1 @ X7 ) )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( X2 @ X7 @ X8 ) ) )
= ( X6 @ ( eigen__7 @ ( eigen__6 @ X7 ) ) @ ( eigen__7 @ ( eigen__6 @ X8 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__7
@ ^ [X1: g > $o] :
~ ! [X2: g > g > g,X3: b > $o,X4: b > b > b,X5: g > b,X6: b > a,X7: g > $o,X8: g > g > g,X9: b > $o,X10: b > b > b,X11: a > $o,X12: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X13: g,X14: g] :
( ~ ( ( X7 @ X13 )
=> ~ ( X7 @ X14 ) )
=> ( X7 @ ( X8 @ X13 @ X14 ) ) )
=> ~ ! [X13: g] :
( ( X7 @ X13 )
=> ( X9 @ ( X5 @ X13 ) ) ) )
=> ~ ! [X13: g] :
( ( X7 @ X13 )
=> ( X9 @ ( X5 @ X13 ) ) ) )
=> ~ ! [X13: g] :
( ( X7 @ X13 )
=> ( X9 @ ( X5 @ X13 ) ) ) )
=> ~ ! [X13: g,X14: g] :
( ~ ( ( X7 @ X13 )
=> ~ ( X7 @ X14 ) )
=> ( ( X5 @ ( X8 @ X13 @ X14 ) )
= ( X10 @ ( X5 @ X13 ) @ ( X5 @ X14 ) ) ) ) )
=> ~ ! [X13: a,X14: a] :
( ~ ( ( X11 @ X13 )
=> ~ ( X11 @ X14 ) )
=> ( X11 @ ( X12 @ X13 @ X14 ) ) ) )
=> ~ ! [X13: b] :
( ( X9 @ X13 )
=> ( X11 @ ( X6 @ X13 ) ) ) )
=> ~ ! [X13: b,X14: b] :
( ~ ( ( X9 @ X13 )
=> ~ ( X9 @ X14 ) )
=> ( ( X6 @ ( X10 @ X13 @ X14 ) )
= ( X12 @ ( X6 @ X13 ) @ ( X6 @ X14 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X13: g,X14: g] :
( ~ ( ( X7 @ X13 )
=> ~ ( X7 @ X14 ) )
=> ( X7 @ ( X8 @ X13 @ X14 ) ) )
=> ~ ! [X13: a,X14: a] :
( ~ ( ( X11 @ X13 )
=> ~ ( X11 @ X14 ) )
=> ( X11 @ ( X12 @ X13 @ X14 ) ) ) )
=> ~ ! [X13: g] :
( ( X7 @ X13 )
=> ( X11 @ ( X6 @ ( X5 @ X13 ) ) ) ) )
=> ~ ! [X13: g,X14: g] :
( ~ ( ~ ( ~ ( ( X7 @ X13 )
=> ~ ( X7 @ X14 ) )
=> ~ ( X7 @ X13 ) )
=> ~ ( X7 @ X14 ) )
=> ( ( X6 @ ( X5 @ ( X8 @ X13 @ X14 ) ) )
= ( X12 @ ( X6 @ ( X5 @ X13 ) ) @ ( X6 @ ( X5 @ X14 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(h8,assumption,
! [X1: ( a > a > a ) > $o,X2: a > a > a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__8 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__8
@ ^ [X1: a > a > a] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X2: g,X3: g] :
( ~ ( ( eigen__8 @ X2 )
=> ~ ( eigen__8 @ X3 ) )
=> ( eigen__8 @ ( eigen__9 @ X2 @ X3 ) ) )
=> ~ ! [X2: g] :
( ( eigen__8 @ X2 )
=> ( eigen__10 @ ( eigen__6 @ X2 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__8 @ X2 )
=> ( eigen__10 @ ( eigen__6 @ X2 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__8 @ X2 )
=> ( eigen__10 @ ( eigen__6 @ X2 ) ) ) )
=> ~ ! [X2: g,X3: g] :
( ~ ( ( eigen__8 @ X2 )
=> ~ ( eigen__8 @ X3 ) )
=> ( ( eigen__6 @ ( eigen__9 @ X2 @ X3 ) )
= ( eigen__11 @ ( eigen__6 @ X2 ) @ ( eigen__6 @ X3 ) ) ) ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__12 @ X2 )
=> ~ ( eigen__12 @ X3 ) )
=> ( eigen__12 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ ! [X2: b] :
( ( eigen__10 @ X2 )
=> ( eigen__12 @ ( eigen__7 @ X2 ) ) ) )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__10 @ X2 )
=> ~ ( eigen__10 @ X3 ) )
=> ( ( eigen__7 @ ( eigen__11 @ X2 @ X3 ) )
= ( X1 @ ( eigen__7 @ X2 ) @ ( eigen__7 @ X3 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X2: g,X3: g] :
( ~ ( ( eigen__8 @ X2 )
=> ~ ( eigen__8 @ X3 ) )
=> ( eigen__8 @ ( eigen__9 @ X2 @ X3 ) ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__12 @ X2 )
=> ~ ( eigen__12 @ X3 ) )
=> ( eigen__12 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__8 @ X2 )
=> ( eigen__12 @ ( eigen__7 @ ( eigen__6 @ X2 ) ) ) ) )
=> ~ ! [X2: g,X3: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X2 )
=> ~ ( eigen__8 @ X3 ) )
=> ~ ( eigen__8 @ X2 ) )
=> ~ ( eigen__8 @ X3 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X2 @ X3 ) ) )
= ( X1 @ ( eigen__7 @ ( eigen__6 @ X2 ) ) @ ( eigen__7 @ ( eigen__6 @ X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__5
@ ^ [X1: b > $o] :
~ ! [X2: b > b > b,X3: g > b,X4: b > a,X5: g > $o,X6: g > g > g,X7: b > $o,X8: b > b > b,X9: a > $o,X10: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X11: g,X12: g] :
( ~ ( ( X5 @ X11 )
=> ~ ( X5 @ X12 ) )
=> ( X5 @ ( X6 @ X11 @ X12 ) ) )
=> ~ ! [X11: g] :
( ( X5 @ X11 )
=> ( X7 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: g] :
( ( X5 @ X11 )
=> ( X7 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: g] :
( ( X5 @ X11 )
=> ( X7 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: g,X12: g] :
( ~ ( ( X5 @ X11 )
=> ~ ( X5 @ X12 ) )
=> ( ( X3 @ ( X6 @ X11 @ X12 ) )
= ( X8 @ ( X3 @ X11 ) @ ( X3 @ X12 ) ) ) ) )
=> ~ ! [X11: a,X12: a] :
( ~ ( ( X9 @ X11 )
=> ~ ( X9 @ X12 ) )
=> ( X9 @ ( X10 @ X11 @ X12 ) ) ) )
=> ~ ! [X11: b] :
( ( X7 @ X11 )
=> ( X9 @ ( X4 @ X11 ) ) ) )
=> ~ ! [X11: b,X12: b] :
( ~ ( ( X7 @ X11 )
=> ~ ( X7 @ X12 ) )
=> ( ( X4 @ ( X8 @ X11 @ X12 ) )
= ( X10 @ ( X4 @ X11 ) @ ( X4 @ X12 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X11: g,X12: g] :
( ~ ( ( X5 @ X11 )
=> ~ ( X5 @ X12 ) )
=> ( X5 @ ( X6 @ X11 @ X12 ) ) )
=> ~ ! [X11: a,X12: a] :
( ~ ( ( X9 @ X11 )
=> ~ ( X9 @ X12 ) )
=> ( X9 @ ( X10 @ X11 @ X12 ) ) ) )
=> ~ ! [X11: g] :
( ( X5 @ X11 )
=> ( X9 @ ( X4 @ ( X3 @ X11 ) ) ) ) )
=> ~ ! [X11: g,X12: g] :
( ~ ( ~ ( ~ ( ( X5 @ X11 )
=> ~ ( X5 @ X12 ) )
=> ~ ( X5 @ X11 ) )
=> ~ ( X5 @ X12 ) )
=> ( ( X4 @ ( X3 @ ( X6 @ X11 @ X12 ) ) )
= ( X10 @ ( X4 @ ( X3 @ X11 ) ) @ ( X4 @ ( X3 @ X12 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__3
@ ^ [X1: g] :
~ ( ( eigen__8 @ X1 )
=> ( eigen__12 @ ( eigen__7 @ ( eigen__6 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( 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__8 @ X6 )
=> ~ ( eigen__8 @ X7 ) )
=> ( eigen__8 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: g] :
( ( eigen__8 @ X6 )
=> ( X2 @ ( eigen__6 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__8 @ X6 )
=> ( X2 @ ( eigen__6 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__8 @ X6 )
=> ( X2 @ ( eigen__6 @ X6 ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ( eigen__8 @ X6 )
=> ~ ( eigen__8 @ X7 ) )
=> ( ( eigen__6 @ ( X1 @ X6 @ X7 ) )
= ( X3 @ ( eigen__6 @ X6 ) @ ( eigen__6 @ X7 ) ) ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X4 @ ( eigen__7 @ X6 ) ) ) )
=> ~ ! [X6: b,X7: b] :
( ~ ( ( X2 @ X6 )
=> ~ ( X2 @ X7 ) )
=> ( ( eigen__7 @ ( X3 @ X6 @ X7 ) )
= ( X5 @ ( eigen__7 @ X6 ) @ ( eigen__7 @ X7 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X6: g,X7: g] :
( ~ ( ( eigen__8 @ X6 )
=> ~ ( eigen__8 @ X7 ) )
=> ( eigen__8 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__8 @ X6 )
=> ( X4 @ ( eigen__7 @ ( eigen__6 @ X6 ) ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X6 )
=> ~ ( eigen__8 @ X7 ) )
=> ~ ( eigen__8 @ X6 ) )
=> ~ ( eigen__8 @ X7 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( X1 @ X6 @ X7 ) ) )
= ( X5 @ ( eigen__7 @ ( eigen__6 @ X6 ) ) @ ( eigen__7 @ ( eigen__6 @ X7 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( 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: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__6 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__6 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__6 @ X8 ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( ( eigen__6 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( eigen__6 @ X8 ) @ ( eigen__6 @ 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__6 @ X8 ) ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ~ ( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ~ ( X2 @ X8 ) )
=> ~ ( X2 @ X9 ) )
=> ( ( X1 @ ( eigen__6 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( eigen__6 @ X8 ) ) @ ( X1 @ ( eigen__6 @ X9 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: b > b > b] :
~ ! [X2: g > b,X3: b > a,X4: g > $o,X5: g > g > g,X6: b > $o,X7: b > b > b,X8: a > $o,X9: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X10: g,X11: g] :
( ~ ( ( X4 @ X10 )
=> ~ ( X4 @ X11 ) )
=> ( X4 @ ( X5 @ X10 @ X11 ) ) )
=> ~ ! [X10: g] :
( ( X4 @ X10 )
=> ( X6 @ ( X2 @ X10 ) ) ) )
=> ~ ! [X10: g] :
( ( X4 @ X10 )
=> ( X6 @ ( X2 @ X10 ) ) ) )
=> ~ ! [X10: g] :
( ( X4 @ X10 )
=> ( X6 @ ( X2 @ X10 ) ) ) )
=> ~ ! [X10: g,X11: g] :
( ~ ( ( X4 @ X10 )
=> ~ ( X4 @ X11 ) )
=> ( ( X2 @ ( X5 @ X10 @ X11 ) )
= ( X7 @ ( X2 @ X10 ) @ ( X2 @ X11 ) ) ) ) )
=> ~ ! [X10: a,X11: a] :
( ~ ( ( X8 @ X10 )
=> ~ ( X8 @ X11 ) )
=> ( X8 @ ( X9 @ X10 @ X11 ) ) ) )
=> ~ ! [X10: b] :
( ( X6 @ X10 )
=> ( X8 @ ( X3 @ X10 ) ) ) )
=> ~ ! [X10: b,X11: b] :
( ~ ( ( X6 @ X10 )
=> ~ ( X6 @ X11 ) )
=> ( ( X3 @ ( X7 @ X10 @ X11 ) )
= ( X9 @ ( X3 @ X10 ) @ ( X3 @ X11 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X10: g,X11: g] :
( ~ ( ( X4 @ X10 )
=> ~ ( X4 @ X11 ) )
=> ( X4 @ ( X5 @ X10 @ X11 ) ) )
=> ~ ! [X10: a,X11: a] :
( ~ ( ( X8 @ X10 )
=> ~ ( X8 @ X11 ) )
=> ( X8 @ ( X9 @ X10 @ X11 ) ) ) )
=> ~ ! [X10: g] :
( ( X4 @ X10 )
=> ( X8 @ ( X3 @ ( X2 @ X10 ) ) ) ) )
=> ~ ! [X10: g,X11: g] :
( ~ ( ~ ( ~ ( ( X4 @ X10 )
=> ~ ( X4 @ X11 ) )
=> ~ ( X4 @ X10 ) )
=> ~ ( X4 @ X11 ) )
=> ( ( X3 @ ( X2 @ ( X5 @ X10 @ X11 ) ) )
= ( X9 @ ( X3 @ ( X2 @ X10 ) ) @ ( X3 @ ( X2 @ X11 ) ) ) ) ) ) ) ) ),
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: g > b,X7: b > a,X8: g > $o,X9: g > g > g,X10: b > $o,X11: b > b > b,X12: a > $o,X13: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X14: g,X15: g] :
( ~ ( ( X8 @ X14 )
=> ~ ( X8 @ X15 ) )
=> ( X8 @ ( X9 @ X14 @ X15 ) ) )
=> ~ ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) ) )
=> ~ ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) ) )
=> ~ ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) ) )
=> ~ ! [X14: g,X15: g] :
( ~ ( ( X8 @ X14 )
=> ~ ( X8 @ X15 ) )
=> ( ( X6 @ ( X9 @ X14 @ X15 ) )
= ( X11 @ ( X6 @ X14 ) @ ( X6 @ X15 ) ) ) ) )
=> ~ ! [X14: a,X15: a] :
( ~ ( ( X12 @ X14 )
=> ~ ( X12 @ X15 ) )
=> ( X12 @ ( X13 @ X14 @ X15 ) ) ) )
=> ~ ! [X14: b] :
( ( X10 @ X14 )
=> ( X12 @ ( X7 @ X14 ) ) ) )
=> ~ ! [X14: b,X15: b] :
( ~ ( ( X10 @ X14 )
=> ~ ( X10 @ X15 ) )
=> ( ( X7 @ ( X11 @ X14 @ X15 ) )
= ( X13 @ ( X7 @ X14 ) @ ( X7 @ X15 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X14: g,X15: g] :
( ~ ( ( X8 @ X14 )
=> ~ ( X8 @ X15 ) )
=> ( X8 @ ( X9 @ X14 @ X15 ) ) )
=> ~ ! [X14: a,X15: a] :
( ~ ( ( X12 @ X14 )
=> ~ ( X12 @ X15 ) )
=> ( X12 @ ( X13 @ X14 @ X15 ) ) ) )
=> ~ ! [X14: g] :
( ( X8 @ X14 )
=> ( X12 @ ( X7 @ ( X6 @ X14 ) ) ) ) )
=> ~ ! [X14: g,X15: g] :
( ~ ( ~ ( ~ ( ( X8 @ X14 )
=> ~ ( X8 @ X15 ) )
=> ~ ( X8 @ X14 ) )
=> ~ ( X8 @ X15 ) )
=> ( ( X7 @ ( X6 @ ( X9 @ X14 @ X15 ) ) )
= ( X13 @ ( X7 @ ( X6 @ X14 ) ) @ ( X7 @ ( X6 @ X15 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ! [X1: g,X2: g] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ( eigen__8 @ ( eigen__9 @ X1 @ X2 ) ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__12 @ X1 )
=> ~ ( eigen__12 @ X2 ) )
=> ( eigen__12 @ ( eigen__13 @ X1 @ X2 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__8 @ X1 )
=> ( eigen__12 @ ( eigen__7 @ ( eigen__6 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: g,X2: g] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ( ( eigen__6 @ ( eigen__9 @ X1 @ X2 ) )
= ( eigen__11 @ ( eigen__6 @ X1 ) @ ( eigen__6 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [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: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [X9: g] :
( ( X3 @ X9 )
=> ( X5 @ ( X1 @ X9 ) ) ) )
=> ~ ! [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: 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 ) )
=> ~ ( X3 @ X9 ) )
=> ~ ( X3 @ X10 ) )
=> ( ( X2 @ ( X1 @ ( X4 @ X9 @ X10 ) ) )
= ( X8 @ ( X2 @ ( X1 @ X9 ) ) @ ( X2 @ ( X1 @ X10 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: b > $o] :
( ( X1 @ ( eigen__6 @ ( eigen__9 @ eigen__14 @ eigen__17 ) ) )
=> ! [X2: b] :
( ( ( eigen__6 @ ( eigen__9 @ eigen__14 @ eigen__17 ) )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__10 @ ( eigen__6 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: g > g > g,X2: b > $o,X3: b > b > b,X4: a > $o,X5: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X6: g,X7: g] :
( ~ ( ( eigen__8 @ X6 )
=> ~ ( eigen__8 @ X7 ) )
=> ( eigen__8 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: g] :
( ( eigen__8 @ X6 )
=> ( X2 @ ( eigen__6 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__8 @ X6 )
=> ( X2 @ ( eigen__6 @ X6 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__8 @ X6 )
=> ( X2 @ ( eigen__6 @ X6 ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ( eigen__8 @ X6 )
=> ~ ( eigen__8 @ X7 ) )
=> ( ( eigen__6 @ ( X1 @ X6 @ X7 ) )
= ( X3 @ ( eigen__6 @ X6 ) @ ( eigen__6 @ X7 ) ) ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: b] :
( ( X2 @ X6 )
=> ( X4 @ ( eigen__7 @ X6 ) ) ) )
=> ~ ! [X6: b,X7: b] :
( ~ ( ( X2 @ X6 )
=> ~ ( X2 @ X7 ) )
=> ( ( eigen__7 @ ( X3 @ X6 @ X7 ) )
= ( X5 @ ( eigen__7 @ X6 ) @ ( eigen__7 @ X7 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X6: g,X7: g] :
( ~ ( ( eigen__8 @ X6 )
=> ~ ( eigen__8 @ X7 ) )
=> ( eigen__8 @ ( X1 @ X6 @ X7 ) ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X4 @ X6 )
=> ~ ( X4 @ X7 ) )
=> ( X4 @ ( X5 @ X6 @ X7 ) ) ) )
=> ~ ! [X6: g] :
( ( eigen__8 @ X6 )
=> ( X4 @ ( eigen__7 @ ( eigen__6 @ X6 ) ) ) ) )
=> ~ ! [X6: g,X7: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X6 )
=> ~ ( eigen__8 @ X7 ) )
=> ~ ( eigen__8 @ X6 ) )
=> ~ ( eigen__8 @ X7 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( X1 @ X6 @ X7 ) ) )
= ( X5 @ ( eigen__7 @ ( eigen__6 @ X6 ) ) @ ( eigen__7 @ ( eigen__6 @ X7 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( eigen__12 @ ( eigen__7 @ ( eigen__6 @ eigen__16 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: b] :
( ( ( eigen__6 @ ( eigen__9 @ eigen__14 @ eigen__17 ) )
= X1 )
=> ( ( eigen__7 @ X1 )
!= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ eigen__14 ) ) @ ( eigen__7 @ ( eigen__6 @ eigen__17 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( eigen__8 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ ( ( eigen__8 @ eigen__14 )
=> ~ ( eigen__8 @ eigen__17 ) )
=> ~ ( eigen__8 @ eigen__14 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ ( ~ sP11
=> ~ ( eigen__8 @ eigen__17 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ eigen__14 @ eigen__17 ) ) )
= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ eigen__14 ) ) @ ( eigen__7 @ ( eigen__6 @ eigen__17 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( eigen__8 @ eigen__17 )
=> ( eigen__10 @ ( eigen__6 @ eigen__17 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: b > $o,X2: b > b > b,X3: g > b,X4: b > a,X5: g > $o,X6: g > g > g,X7: b > $o,X8: b > b > b,X9: a > $o,X10: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X11: g,X12: g] :
( ~ ( ( X5 @ X11 )
=> ~ ( X5 @ X12 ) )
=> ( X5 @ ( X6 @ X11 @ X12 ) ) )
=> ~ ! [X11: g] :
( ( X5 @ X11 )
=> ( X7 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: g] :
( ( X5 @ X11 )
=> ( X7 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: g] :
( ( X5 @ X11 )
=> ( X7 @ ( X3 @ X11 ) ) ) )
=> ~ ! [X11: g,X12: g] :
( ~ ( ( X5 @ X11 )
=> ~ ( X5 @ X12 ) )
=> ( ( X3 @ ( X6 @ X11 @ X12 ) )
= ( X8 @ ( X3 @ X11 ) @ ( X3 @ X12 ) ) ) ) )
=> ~ ! [X11: a,X12: a] :
( ~ ( ( X9 @ X11 )
=> ~ ( X9 @ X12 ) )
=> ( X9 @ ( X10 @ X11 @ X12 ) ) ) )
=> ~ ! [X11: b] :
( ( X7 @ X11 )
=> ( X9 @ ( X4 @ X11 ) ) ) )
=> ~ ! [X11: b,X12: b] :
( ~ ( ( X7 @ X11 )
=> ~ ( X7 @ X12 ) )
=> ( ( X4 @ ( X8 @ X11 @ X12 ) )
= ( X10 @ ( X4 @ X11 ) @ ( X4 @ X12 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X11: g,X12: g] :
( ~ ( ( X5 @ X11 )
=> ~ ( X5 @ X12 ) )
=> ( X5 @ ( X6 @ X11 @ X12 ) ) )
=> ~ ! [X11: a,X12: a] :
( ~ ( ( X9 @ X11 )
=> ~ ( X9 @ X12 ) )
=> ( X9 @ ( X10 @ X11 @ X12 ) ) ) )
=> ~ ! [X11: g] :
( ( X5 @ X11 )
=> ( X9 @ ( X4 @ ( X3 @ X11 ) ) ) ) )
=> ~ ! [X11: g,X12: g] :
( ~ ( ~ ( ~ ( ( X5 @ X11 )
=> ~ ( X5 @ X12 ) )
=> ~ ( X5 @ X11 ) )
=> ~ ( X5 @ X12 ) )
=> ( ( X4 @ ( X3 @ ( X6 @ X11 @ X12 ) ) )
= ( X10 @ ( X4 @ ( X3 @ X11 ) ) @ ( X4 @ ( X3 @ X12 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( eigen__7 @ ( eigen__11 @ ( eigen__6 @ eigen__14 ) @ ( eigen__6 @ eigen__17 ) ) )
= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ eigen__14 ) ) @ ( eigen__7 @ ( eigen__6 @ eigen__17 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__12 @ X1 )
=> ~ ( eigen__12 @ X2 ) )
=> ( eigen__12 @ ( eigen__13 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ ( sP6
=> ~ ( eigen__10 @ ( eigen__6 @ eigen__17 ) ) )
=> sP15 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( eigen__8 @ eigen__14 )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ ( ~ ( ~ ( ~ ( ! [X1: g,X2: g] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ( eigen__8 @ ( eigen__9 @ X1 @ X2 ) ) )
=> ~ ! [X1: g] :
( ( eigen__8 @ X1 )
=> ( eigen__10 @ ( eigen__6 @ X1 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__8 @ X1 )
=> ( eigen__10 @ ( eigen__6 @ X1 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__8 @ X1 )
=> ( eigen__10 @ ( eigen__6 @ X1 ) ) ) )
=> ~ sP3 )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( ~ ( ! [X1: g,X2: g] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ( eigen__8 @ ( eigen__9 @ X1 @ X2 ) ) )
=> ~ ! [X1: g] :
( ( eigen__8 @ X1 )
=> ( eigen__10 @ ( eigen__6 @ X1 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__8 @ X1 )
=> ( eigen__10 @ ( eigen__6 @ X1 ) ) ) )
=> ~ ! [X1: g] :
( ( eigen__8 @ X1 )
=> ( eigen__10 @ ( eigen__6 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: g] :
( ( eigen__8 @ X1 )
=> ( eigen__10 @ ( eigen__6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( eigen__8 @ eigen__17 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ~ sP20
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: b > b > b] : sP4 ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( eigen__6 @ ( eigen__9 @ eigen__14 @ eigen__17 ) )
= ( eigen__11 @ ( eigen__6 @ eigen__14 ) @ ( eigen__6 @ eigen__17 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP10
=> ( eigen__10 @ ( eigen__6 @ eigen__16 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ~ sP11
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: b,X2: b > $o] :
( ( X2 @ X1 )
=> ! [X3: b] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP2
=> ~ ! [X1: g,X2: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ~ ( eigen__8 @ X1 ) )
=> ~ ( eigen__8 @ X2 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X1 @ X2 ) ) )
= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ X1 ) ) @ ( eigen__7 @ ( eigen__6 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( eigen__10 @ ( eigen__6 @ eigen__16 ) )
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP10
=> sP8 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: b,X2: b] :
( ~ ( ( eigen__10 @ X1 )
=> ~ ( eigen__10 @ X2 ) )
=> ( ( eigen__7 @ ( eigen__11 @ X1 @ X2 ) )
= ( eigen__13 @ ( eigen__7 @ X1 ) @ ( eigen__7 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: a > $o,X2: a > a > a] :
( ~ ( ~ ( ~ ( ~ sP23
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: b] :
( ( eigen__10 @ X3 )
=> ( X1 @ ( eigen__7 @ X3 ) ) ) )
=> ~ ! [X3: b,X4: b] :
( ~ ( ( eigen__10 @ X3 )
=> ~ ( eigen__10 @ X4 ) )
=> ( ( eigen__7 @ ( eigen__11 @ X3 @ X4 ) )
= ( X2 @ ( eigen__7 @ X3 ) @ ( eigen__7 @ X4 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X3: g,X4: g] :
( ~ ( ( eigen__8 @ X3 )
=> ~ ( eigen__8 @ X4 ) )
=> ( eigen__8 @ ( eigen__9 @ X3 @ X4 ) ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X1 @ X3 )
=> ~ ( X1 @ X4 ) )
=> ( X1 @ ( X2 @ X3 @ X4 ) ) ) )
=> ~ ! [X3: g] :
( ( eigen__8 @ X3 )
=> ( X1 @ ( eigen__7 @ ( eigen__6 @ X3 ) ) ) ) )
=> ~ ! [X3: g,X4: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X3 )
=> ~ ( eigen__8 @ X4 ) )
=> ~ ( eigen__8 @ X3 ) )
=> ~ ( eigen__8 @ X4 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X3 @ X4 ) ) )
= ( X2 @ ( eigen__7 @ ( eigen__6 @ X3 ) ) @ ( eigen__7 @ ( eigen__6 @ X4 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ! [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: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__6 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__6 @ X7 ) ) ) )
=> ~ ! [X7: g] :
( ( X1 @ X7 )
=> ( X3 @ ( eigen__6 @ X7 ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__6 @ ( X2 @ X7 @ X8 ) )
= ( X4 @ ( eigen__6 @ X7 ) @ ( eigen__6 @ X8 ) ) ) ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X5 @ X7 )
=> ~ ( X5 @ X8 ) )
=> ( X5 @ ( X6 @ X7 @ X8 ) ) ) )
=> ~ ! [X7: b] :
( ( X3 @ X7 )
=> ( X5 @ ( eigen__7 @ X7 ) ) ) )
=> ~ ! [X7: b,X8: b] :
( ~ ( ( X3 @ X7 )
=> ~ ( X3 @ X8 ) )
=> ( ( eigen__7 @ ( X4 @ X7 @ X8 ) )
= ( X6 @ ( eigen__7 @ X7 ) @ ( eigen__7 @ 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__7 @ ( eigen__6 @ X7 ) ) ) ) )
=> ~ ! [X7: g,X8: g] :
( ~ ( ~ ( ~ ( ( X1 @ X7 )
=> ~ ( X1 @ X8 ) )
=> ~ ( X1 @ X7 ) )
=> ~ ( X1 @ X8 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( X2 @ X7 @ X8 ) ) )
= ( X6 @ ( eigen__7 @ ( eigen__6 @ X7 ) ) @ ( eigen__7 @ ( eigen__6 @ X8 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ! [X1: b > $o,X2: b > b > b,X3: a > $o,X4: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X5: g,X6: g] :
( ~ ( ( eigen__8 @ X5 )
=> ~ ( eigen__8 @ X6 ) )
=> ( eigen__8 @ ( eigen__9 @ X5 @ X6 ) ) )
=> ~ ! [X5: g] :
( ( eigen__8 @ X5 )
=> ( X1 @ ( eigen__6 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__8 @ X5 )
=> ( X1 @ ( eigen__6 @ X5 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__8 @ X5 )
=> ( X1 @ ( eigen__6 @ X5 ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ( eigen__8 @ X5 )
=> ~ ( eigen__8 @ X6 ) )
=> ( ( eigen__6 @ ( eigen__9 @ X5 @ X6 ) )
= ( X2 @ ( eigen__6 @ X5 ) @ ( eigen__6 @ X6 ) ) ) ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: b] :
( ( X1 @ X5 )
=> ( X3 @ ( eigen__7 @ X5 ) ) ) )
=> ~ ! [X5: b,X6: b] :
( ~ ( ( X1 @ X5 )
=> ~ ( X1 @ X6 ) )
=> ( ( eigen__7 @ ( X2 @ X5 @ X6 ) )
= ( X4 @ ( eigen__7 @ X5 ) @ ( eigen__7 @ X6 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X5: g,X6: g] :
( ~ ( ( eigen__8 @ X5 )
=> ~ ( eigen__8 @ X6 ) )
=> ( eigen__8 @ ( eigen__9 @ X5 @ X6 ) ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X3 @ X5 )
=> ~ ( X3 @ X6 ) )
=> ( X3 @ ( X4 @ X5 @ X6 ) ) ) )
=> ~ ! [X5: g] :
( ( eigen__8 @ X5 )
=> ( X3 @ ( eigen__7 @ ( eigen__6 @ X5 ) ) ) ) )
=> ~ ! [X5: g,X6: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X5 )
=> ~ ( eigen__8 @ X6 ) )
=> ~ ( eigen__8 @ X5 ) )
=> ~ ( eigen__8 @ X6 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X5 @ X6 ) ) )
= ( X4 @ ( eigen__7 @ ( eigen__6 @ X5 ) ) @ ( eigen__7 @ ( eigen__6 @ X6 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ eigen__14 )
=> ~ ( eigen__8 @ X1 ) )
=> ~ ( eigen__8 @ eigen__14 ) )
=> ~ ( eigen__8 @ X1 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ eigen__14 @ X1 ) ) )
= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ eigen__14 ) ) @ ( eigen__7 @ ( eigen__6 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ~ ( ! [X1: g,X2: g] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ( eigen__8 @ ( eigen__9 @ X1 @ X2 ) ) )
=> ~ sP21 )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( eigen__8 @ eigen__14 )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: g,X2: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ~ ( eigen__8 @ X1 ) )
=> ~ ( eigen__8 @ X2 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X1 @ X2 ) ) )
= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ X1 ) ) @ ( eigen__7 @ ( eigen__6 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( sP25
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ! [X1: g,X2: g] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ( eigen__8 @ ( eigen__9 @ X1 @ X2 ) ) )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ ( ~ sP19
=> ~ ! [X1: b] :
( ( eigen__10 @ X1 )
=> ( eigen__12 @ ( eigen__7 @ X1 ) ) ) )
=> ~ sP32 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ! [X1: g,X2: g] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ( eigen__8 @ ( eigen__9 @ X1 @ X2 ) ) )
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ! [X1: g > $o,X2: g > g > g,X3: b > $o,X4: b > b > b,X5: g > b,X6: b > a,X7: g > $o,X8: g > g > g,X9: b > $o,X10: b > b > b,X11: a > $o,X12: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ! [X13: g,X14: g] :
( ~ ( ( X7 @ X13 )
=> ~ ( X7 @ X14 ) )
=> ( X7 @ ( X8 @ X13 @ X14 ) ) )
=> ~ ! [X13: g] :
( ( X7 @ X13 )
=> ( X9 @ ( X5 @ X13 ) ) ) )
=> ~ ! [X13: g] :
( ( X7 @ X13 )
=> ( X9 @ ( X5 @ X13 ) ) ) )
=> ~ ! [X13: g] :
( ( X7 @ X13 )
=> ( X9 @ ( X5 @ X13 ) ) ) )
=> ~ ! [X13: g,X14: g] :
( ~ ( ( X7 @ X13 )
=> ~ ( X7 @ X14 ) )
=> ( ( X5 @ ( X8 @ X13 @ X14 ) )
= ( X10 @ ( X5 @ X13 ) @ ( X5 @ X14 ) ) ) ) )
=> ~ ! [X13: a,X14: a] :
( ~ ( ( X11 @ X13 )
=> ~ ( X11 @ X14 ) )
=> ( X11 @ ( X12 @ X13 @ X14 ) ) ) )
=> ~ ! [X13: b] :
( ( X9 @ X13 )
=> ( X11 @ ( X6 @ X13 ) ) ) )
=> ~ ! [X13: b,X14: b] :
( ~ ( ( X9 @ X13 )
=> ~ ( X9 @ X14 ) )
=> ( ( X6 @ ( X10 @ X13 @ X14 ) )
= ( X12 @ ( X6 @ X13 ) @ ( X6 @ X14 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X13: g,X14: g] :
( ~ ( ( X7 @ X13 )
=> ~ ( X7 @ X14 ) )
=> ( X7 @ ( X8 @ X13 @ X14 ) ) )
=> ~ ! [X13: a,X14: a] :
( ~ ( ( X11 @ X13 )
=> ~ ( X11 @ X14 ) )
=> ( X11 @ ( X12 @ X13 @ X14 ) ) ) )
=> ~ ! [X13: g] :
( ( X7 @ X13 )
=> ( X11 @ ( X6 @ ( X5 @ X13 ) ) ) ) )
=> ~ ! [X13: g,X14: g] :
( ~ ( ~ ( ~ ( ( X7 @ X13 )
=> ~ ( X7 @ X14 ) )
=> ~ ( X7 @ X13 ) )
=> ~ ( X7 @ X14 ) )
=> ( ( X6 @ ( X5 @ ( X8 @ X13 @ X14 ) ) )
= ( X12 @ ( X6 @ ( X5 @ X13 ) ) @ ( X6 @ ( X5 @ X14 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: g] :
( ~ ( ( eigen__8 @ eigen__14 )
=> ~ ( eigen__8 @ X1 ) )
=> ( ( eigen__6 @ ( eigen__9 @ eigen__14 @ X1 ) )
= ( eigen__11 @ ( eigen__6 @ eigen__14 ) @ ( eigen__6 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ! [X1: b] :
( ( eigen__10 @ X1 )
=> ( eigen__12 @ ( eigen__7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ! [X1: g > b] : sP1 ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ! [X1: b] :
( ~ ( sP6
=> ~ ( eigen__10 @ X1 ) )
=> ( ( eigen__7 @ ( eigen__11 @ ( eigen__6 @ eigen__14 ) @ X1 ) )
= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ eigen__14 ) ) @ ( eigen__7 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( eigen__10 @ ( eigen__6 @ eigen__17 ) ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ eigen__14 @ eigen__17 ) ) )
!= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ eigen__14 ) ) @ ( eigen__7 @ ( eigen__6 @ eigen__17 ) ) ) )
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ! [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: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__6 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__6 @ X8 ) ) ) )
=> ~ ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( eigen__6 @ X8 ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ( ( eigen__6 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( eigen__6 @ X8 ) @ ( eigen__6 @ 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__6 @ X8 ) ) ) ) )
=> ~ ! [X8: g,X9: g] :
( ~ ( ~ ( ~ ( ( X2 @ X8 )
=> ~ ( X2 @ X9 ) )
=> ~ ( X2 @ X8 ) )
=> ~ ( X2 @ X9 ) )
=> ( ( X1 @ ( eigen__6 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( eigen__6 @ X8 ) ) @ ( X1 @ ( eigen__6 @ X9 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ~ sP38
=> sP25 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ! [X1: b > b > b,X2: a > $o,X3: a > a > a] :
( ~ ( ~ ( ~ ( ~ ( ~ sP20
=> ~ ! [X4: g,X5: g] :
( ~ ( ( eigen__8 @ X4 )
=> ~ ( eigen__8 @ X5 ) )
=> ( ( eigen__6 @ ( eigen__9 @ X4 @ X5 ) )
= ( X1 @ ( eigen__6 @ X4 ) @ ( eigen__6 @ X5 ) ) ) ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: b] :
( ( eigen__10 @ X4 )
=> ( X2 @ ( eigen__7 @ X4 ) ) ) )
=> ~ ! [X4: b,X5: b] :
( ~ ( ( eigen__10 @ X4 )
=> ~ ( eigen__10 @ X5 ) )
=> ( ( eigen__7 @ ( X1 @ X4 @ X5 ) )
= ( X3 @ ( eigen__7 @ X4 ) @ ( eigen__7 @ X5 ) ) ) ) )
=> ~ ( ~ ( ~ ( ! [X4: g,X5: g] :
( ~ ( ( eigen__8 @ X4 )
=> ~ ( eigen__8 @ X5 ) )
=> ( eigen__8 @ ( eigen__9 @ X4 @ X5 ) ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X2 @ X4 )
=> ~ ( X2 @ X5 ) )
=> ( X2 @ ( X3 @ X4 @ X5 ) ) ) )
=> ~ ! [X4: g] :
( ( eigen__8 @ X4 )
=> ( X2 @ ( eigen__7 @ ( eigen__6 @ X4 ) ) ) ) )
=> ~ ! [X4: g,X5: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X4 )
=> ~ ( eigen__8 @ X5 ) )
=> ~ ( eigen__8 @ X4 ) )
=> ~ ( eigen__8 @ X5 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X4 @ X5 ) ) )
= ( X3 @ ( eigen__7 @ ( eigen__6 @ X4 ) ) @ ( eigen__7 @ ( eigen__6 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: g,X2: g] :
( ~ ( ( eigen__8 @ X1 )
=> ~ ( eigen__8 @ X2 ) )
=> ( eigen__8 @ ( eigen__9 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ eigen__14 @ eigen__17 ) ) )
= ( eigen__13 @ ( eigen__7 @ ( eigen__6 @ eigen__14 ) ) @ ( eigen__7 @ ( eigen__6 @ eigen__17 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( eigen__10 @ ( eigen__6 @ eigen__16 ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ sP42
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: a > a > a] :
( ~ ( ~ ( ~ ( ~ sP23
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__12 @ X2 )
=> ~ ( eigen__12 @ X3 ) )
=> ( eigen__12 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ sP46 )
=> ~ ! [X2: b,X3: b] :
( ~ ( ( eigen__10 @ X2 )
=> ~ ( eigen__10 @ X3 ) )
=> ( ( eigen__7 @ ( eigen__11 @ X2 @ X3 ) )
= ( X1 @ ( eigen__7 @ X2 ) @ ( eigen__7 @ X3 ) ) ) ) )
=> ~ ( ~ ( ~ ( sP54
=> ~ ! [X2: a,X3: a] :
( ~ ( ( eigen__12 @ X2 )
=> ~ ( eigen__12 @ X3 ) )
=> ( eigen__12 @ ( X1 @ X2 @ X3 ) ) ) )
=> ~ ! [X2: g] :
( ( eigen__8 @ X2 )
=> ( eigen__12 @ ( eigen__7 @ ( eigen__6 @ X2 ) ) ) ) )
=> ~ ! [X2: g,X3: g] :
( ~ ( ~ ( ~ ( ( eigen__8 @ X2 )
=> ~ ( eigen__8 @ X3 ) )
=> ~ ( eigen__8 @ X2 ) )
=> ~ ( eigen__8 @ X3 ) )
=> ( ( eigen__7 @ ( eigen__6 @ ( eigen__9 @ X2 @ X3 ) ) )
= ( X1 @ ( eigen__7 @ ( eigen__6 @ X2 ) ) @ ( eigen__7 @ ( eigen__6 @ X3 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( eigen__8 @ eigen__14 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ! [X1: g > g > g] : sP14 ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ( sP6
=> ~ sP49 ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ! [X1: g] :
( ( eigen__8 @ X1 )
=> ( eigen__12 @ ( eigen__7 @ ( eigen__6 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ~ sP19
=> ~ sP46 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(cTHM126_CORRECTED_pme,conjecture,
sP47 ).
thf(h9,negated_conjecture,
~ sP47,
inference(assume_negation,[status(cth)],[cTHM126_CORRECTED_pme]) ).
thf(1,plain,
( ~ sP21
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP18
| ~ sP59
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP41
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP21
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP13
| ~ sP22
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP11
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP11
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP21
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP26
| ~ sP10
| sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP37
| ~ sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP40
| ~ sP25
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP9
| sP40 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP50
| sP55
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP5
| sP50 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( sP27
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP27
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP46
| sP30 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP30
| ~ sP56
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP3
| sP45 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP45
| sP52 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP52
| sP38
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP28
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
sP28,
inference(eq_ind,[status(thm)],]) ).
thf(24,plain,
( sP20
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP20
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP12
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP12
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP32
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(29,plain,
( ~ sP48
| sP17 ),
inference(all_rule,[status(thm)],]) ).
thf(30,plain,
( ~ sP17
| sP61
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP61
| ~ sP6
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( sP31
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( sP31
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( sP23
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP23
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP36
| ~ sP12 ),
inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__17]) ).
thf(37,plain,
( sP62
| ~ sP31 ),
inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__16]) ).
thf(38,plain,
( ~ sP43
| ~ sP54
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( sP19
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( sP19
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP39
| ~ sP36 ),
inference(eigen_choice_rule,[status(thm),assumptions([h3])],[h3,eigendef_eigen__14]) ).
thf(42,plain,
( ~ sP2
| sP43
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP63
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP63
| ~ sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( ~ sP29
| sP2
| ~ sP39 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP42
| sP32 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( sP42
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( sP57
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(49,plain,
( sP57
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( sP58
| ~ sP57 ),
inference(eigen_choice_rule,[status(thm),assumptions([h8])],[h8,eigendef_eigen__13]) ).
thf(51,plain,
( sP33
| ~ sP58 ),
inference(eigen_choice_rule,[status(thm),assumptions([h6])],[h6,eigendef_eigen__12]) ).
thf(52,plain,
( sP53
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(53,plain,
( sP35
| ~ sP53 ),
inference(eigen_choice_rule,[status(thm),assumptions([h5])],[h5,eigendef_eigen__10]) ).
thf(54,plain,
( sP7
| ~ sP35 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9]) ).
thf(55,plain,
( sP34
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h7])],[h7,eigendef_eigen__8]) ).
thf(56,plain,
( sP51
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__7]) ).
thf(57,plain,
( sP4
| ~ sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h4])],[h4,eigendef_eigen__6]) ).
thf(58,plain,
( sP24
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(59,plain,
( sP14
| ~ sP24 ),
inference(eigen_choice_rule,[status(thm),assumptions([h5])],[h5,eigendef_eigen__4]) ).
thf(60,plain,
( sP60
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__3]) ).
thf(61,plain,
( sP44
| ~ sP60 ),
inference(eigen_choice_rule,[status(thm),assumptions([h7])],[h7,eigendef_eigen__2]) ).
thf(62,plain,
( sP1
| ~ sP44 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__1]) ).
thf(63,plain,
( sP47
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h4])],[h4,eigendef_eigen__0]) ).
thf(64,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h8,h7,h6,h5,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,h9]) ).
thf(65,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h7,h6,h5,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h8])],[64,h8]) ).
thf(66,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h6,h5,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h7])],[65,h7]) ).
thf(67,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h5,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h6])],[66,h6]) ).
thf(68,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h4,h3,h2,h1,h0]),eigenvar_choice(discharge,[h5])],[67,h5]) ).
thf(69,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h3,h2,h1,h0]),eigenvar_choice(discharge,[h4])],[68,h4]) ).
thf(70,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h2,h1,h0]),eigenvar_choice(discharge,[h3])],[69,h3]) ).
thf(71,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h1,h0]),eigenvar_choice(discharge,[h2])],[70,h2]) ).
thf(72,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9,h0]),eigenvar_choice(discharge,[h1])],[71,h1]) ).
thf(73,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h9]),eigenvar_choice(discharge,[h0])],[72,h0]) ).
thf(0,theorem,
sP47,
inference(contra,[status(thm),contra(discharge,[h9])],[64,h9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO225^5 : 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
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 19:08:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 36.82/36.88 % SZS status Theorem
% 36.82/36.88 % Mode: mode485
% 36.82/36.88 % Inferences: 94
% 36.82/36.88 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------