TSTP Solution File: SEV149^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV149^5 : 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 : n004.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 18:05:05 EDT 2022
% Result : Theorem 63.06s 63.17s
% Output : Proof 63.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 135
% Syntax : Number of formulae : 153 ( 23 unt; 13 typ; 12 def)
% Number of atoms : 474 ( 12 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1934 ( 492 ~; 70 |; 0 &; 784 @)
% ( 59 <=>; 529 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 109 ( 109 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 74 usr; 68 con; 0-2 aty)
% Number of variables : 376 ( 12 ^ 364 !; 0 ?; 376 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_eigen__2,type,
eigen__2: a ).
thf(ty_eigen__7,type,
eigen__7: a ).
thf(ty_eigen__30,type,
eigen__30: a > $o ).
thf(ty_eigen__1,type,
eigen__1: a > a > $o ).
thf(ty_eigen__0,type,
eigen__0: a > a > $o ).
thf(ty_eigen__4,type,
eigen__4: a > $o ).
thf(ty_eigen__11,type,
eigen__11: a > $o ).
thf(ty_eigen__3,type,
eigen__3: a ).
thf(ty_eigen__10,type,
eigen__10: a > $o ).
thf(ty_eigen__8,type,
eigen__8: a ).
thf(ty_eigen__9,type,
eigen__9: a ).
thf(ty_eigen__31,type,
eigen__31: a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__11,definition,
( eigen__11
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__11])]) ).
thf(h1,assumption,
! [X1: a > $o,X2: a] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__1
@ ^ [X1: a] :
~ ( ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X3 )
=> ( eigen__1 @ eigen__2 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(h2,assumption,
! [X1: ( a > a > $o ) > $o,X2: a > a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__2 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__2
@ ^ [X1: a > a > $o] :
~ ! [X2: a,X3: a] :
( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( X1 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( X1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( eigen__0 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( eigen__0 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__2
@ ^ [X1: a > a > $o] :
~ ! [X2: a > a > $o,X3: a,X4: a] :
( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: a] :
~ ( ~ ( ( eigen__4 @ eigen__7 )
=> ~ ( ~ ( eigen__0 @ eigen__7 @ X1 )
=> ( eigen__1 @ eigen__7 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__31,definition,
( eigen__31
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__7 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__31])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__1
@ ^ [X1: a] :
~ ( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__1
@ ^ [X1: a] :
~ ! [X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__30,definition,
( eigen__30
= ( eps__0
@ ^ [X1: a > $o] :
~ ( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__7 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__8 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__30])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a > a > $o,X2: a,X3: a] :
( ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ( eigen__0 @ X2 @ X5 )
=> ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ( eigen__0 @ X5 @ X6 )
=> ( X1 @ X5 @ X6 ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( X1 @ X2 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( X1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( eigen__0 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( eigen__0 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X5 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ eigen__2 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ X2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( eigen__0 @ eigen__2 @ eigen__9 )
=> ( eigen__1 @ eigen__2 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ( eigen__0 @ X1 @ X2 )
=> ( eigen__1 @ X1 @ X2 ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( eigen__4 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__10 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__10 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__10 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X2 )
=> ( eigen__1 @ eigen__2 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__1 @ eigen__2 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__7 )
=> ~ ( ~ ( eigen__0 @ eigen__7 @ X1 )
=> ( eigen__1 @ eigen__7 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__0 @ eigen__7 @ eigen__8 )
=> ( eigen__30 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ~ ( ( eigen__4 @ eigen__7 )
=> ~ ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__7 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__7 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( eigen__0 @ eigen__2 @ eigen__9 )
=> ( eigen__10 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__0 @ eigen__7 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__0 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ~ ( ( eigen__4 @ eigen__7 )
=> ~ ( ~ ( eigen__0 @ eigen__7 @ eigen__8 )
=> ( eigen__1 @ eigen__7 @ eigen__8 ) ) )
=> ( eigen__4 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( eigen__1 @ eigen__2 @ X1 )
=> ( eigen__11 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP3
=> ( eigen__4 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ~ sP5
=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__9 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ~ ( sP17
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__11 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__11 @ X2 ) ) )
=> ( eigen__11 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__2 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: a] :
( ( eigen__0 @ eigen__7 @ X1 )
=> ( eigen__30 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X2 )
=> ( eigen__1 @ eigen__2 @ X2 ) )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( ~ ( eigen__0 @ X2 @ X3 )
=> ( eigen__1 @ X2 @ X3 ) ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a > $o] :
( ~ ( ! [X2: a] :
( ( eigen__1 @ eigen__7 @ X2 )
=> ( X1 @ X2 ) )
=> ~ ! [X2: a,X3: a] :
( ~ ( ( X1 @ X2 )
=> ~ ( eigen__1 @ X2 @ X3 ) )
=> ( X1 @ X3 ) ) )
=> ( X1 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( sP17
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__11 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__11 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ~ ( ( eigen__4 @ eigen__7 )
=> ~ ( ~ sP15
=> sP24 ) )
=> ( eigen__4 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( eigen__0 @ eigen__2 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( eigen__4 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ~ sP10
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__4 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ( eigen__4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: a] :
( ( ~ ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__0 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__0 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( eigen__1 @ eigen__2 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( eigen__1 @ X3 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ( eigen__1 @ eigen__7 @ eigen__8 )
=> ( eigen__31 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ sP7
=> ( eigen__10 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ~ ( ! [X1: a] :
( ( eigen__1 @ eigen__7 @ X1 )
=> ( eigen__31 @ X1 ) )
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__31 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__31 @ X2 ) ) )
=> ( eigen__31 @ eigen__8 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( eigen__0 @ eigen__7 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ! [X1: a] :
( ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__10 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( sP9
=> ( eigen__11 @ eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ! [X1: a,X2: a] :
( ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ( eigen__0 @ X1 @ X4 )
=> ( eigen__1 @ X1 @ X4 ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ( eigen__0 @ X4 @ X5 )
=> ( eigen__1 @ X4 @ X5 ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X1 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( ~ ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__0 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__0 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) )
=> ! [X6: a > $o] :
( ~ ( ! [X7: a] :
( ( eigen__1 @ X4 @ X7 )
=> ( X6 @ X7 ) )
=> ~ ! [X7: a,X8: a] :
( ~ ( ( X6 @ X7 )
=> ~ ( eigen__1 @ X7 @ X8 ) )
=> ( X6 @ X8 ) ) )
=> ( X6 @ X5 ) ) ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a > a > $o,X2: a > a > $o,X3: a,X4: a] :
( ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ( X1 @ X3 @ X6 )
=> ( X2 @ X3 @ X6 ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ( X1 @ X6 @ X7 )
=> ( X2 @ X6 @ X7 ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( ~ ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X1 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X1 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) )
=> ! [X7: a > $o] :
( ~ ( ! [X8: a] :
( ( X2 @ X3 @ X8 )
=> ( X7 @ X8 ) )
=> ~ ! [X8: a,X9: a] :
( ~ ( ( X7 @ X8 )
=> ~ ( X2 @ X8 @ X9 ) )
=> ( X7 @ X9 ) ) )
=> ( X7 @ X6 ) ) )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( ~ ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X1 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X1 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) )
=> ! [X8: a > $o] :
( ~ ( ! [X9: a] :
( ( X2 @ X6 @ X9 )
=> ( X8 @ X9 ) )
=> ~ ! [X9: a,X10: a] :
( ~ ( ( X8 @ X9 )
=> ~ ( X2 @ X9 @ X10 ) )
=> ( X8 @ X10 ) ) )
=> ( X8 @ X7 ) ) ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ! [X1: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X1 )
=> ( eigen__1 @ eigen__2 @ X1 ) )
=> ( eigen__4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ! [X1: a] :
( ( eigen__1 @ eigen__7 @ X1 )
=> ( eigen__31 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( ~ sP15
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ~ sP30
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( eigen__1 @ eigen__7 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ! [X1: a,X2: a] :
( ~ ( ( eigen__4 @ X1 )
=> ~ ( ~ ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__0 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) )
=> ! [X3: a > $o] :
( ~ ( ! [X4: a] :
( ( eigen__1 @ X1 @ X4 )
=> ( X3 @ X4 ) )
=> ~ ! [X4: a,X5: a] :
( ~ ( ( X3 @ X4 )
=> ~ ( eigen__1 @ X4 @ X5 ) )
=> ( X3 @ X5 ) ) )
=> ( X3 @ X2 ) ) ) )
=> ( eigen__4 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( eigen__10 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( eigen__31 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( eigen__4 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( eigen__30 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP28
=> ~ sP42 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP19
=> sP48 ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ! [X1: a] :
( ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ( eigen__0 @ eigen__2 @ X3 )
=> ( eigen__1 @ eigen__2 @ X3 ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ( eigen__0 @ X3 @ X4 )
=> ( eigen__1 @ X3 @ X4 ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) )
=> ! [X2: a > $o] :
( ~ ( ! [X3: a] :
( ( ~ ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__0 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__0 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ~ ( ! [X5: a] :
( ( eigen__1 @ eigen__2 @ X5 )
=> ( X4 @ X5 ) )
=> ~ ! [X5: a,X6: a] :
( ~ ( ( X4 @ X5 )
=> ~ ( eigen__1 @ X5 @ X6 ) )
=> ( X4 @ X6 ) ) )
=> ( X4 @ X3 ) ) )
=> ( X2 @ X3 ) )
=> ~ ! [X3: a,X4: a] :
( ~ ( ( X2 @ X3 )
=> ~ ( ~ ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__0 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__0 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) )
=> ! [X5: a > $o] :
( ~ ( ! [X6: a] :
( ( eigen__1 @ X3 @ X6 )
=> ( X5 @ X6 ) )
=> ~ ! [X6: a,X7: a] :
( ~ ( ( X5 @ X6 )
=> ~ ( eigen__1 @ X6 @ X7 ) )
=> ( X5 @ X7 ) ) )
=> ( X5 @ X4 ) ) ) )
=> ( X2 @ X4 ) ) )
=> ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( sP28
=> ~ ( ~ sP35
=> sP44 ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ( ~ sP35
=> sP44 ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP22
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__30 @ X1 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ( eigen__30 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( sP41
=> ~ ! [X1: a,X2: a] :
( ~ ( ( eigen__31 @ X1 )
=> ~ ( eigen__1 @ X1 @ X2 ) )
=> ( eigen__31 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ~ sP55
=> sP49 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ( eigen__11 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( eigen__4 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(cTHM251B_pme,conjecture,
sP39 ).
thf(h3,negated_conjecture,
~ sP39,
inference(assume_negation,[status(cth)],[cTHM251B_pme]) ).
thf(1,plain,
( ~ sP41
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP32
| ~ sP44
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP22
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP12
| ~ sP35
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP56
| sP41 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP55
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP34
| ~ sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP34
| ~ sP56 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP57
| ~ sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP57
| ~ sP55 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP24
| ~ sP34 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__31]) ).
thf(12,plain,
( sP15
| ~ sP57 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__30]) ).
thf(13,plain,
( sP42
| ~ sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP42
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP13
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP26
| sP50
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP50
| ~ sP28
| ~ sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP17
| sP37 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP37
| ~ sP9
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP36
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP14
| ~ sP27
| sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( sP25
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP7
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP20
| ~ sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP20
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP33
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP33
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP21
| ~ sP20 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).
thf(29,plain,
( sP5
| ~ sP33 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(30,plain,
( sP19
| ~ sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP19
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP51
| ~ sP19
| sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP31
| sP51 ),
inference(all_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP3
| sP27
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( sP18
| ~ sP48 ),
inference(prop_rule,[status(thm)],]) ).
thf(36,plain,
( sP18
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP40
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9]) ).
thf(38,plain,
( ~ sP54
| sP35
| sP44 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP45
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(40,plain,
( sP53
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(41,plain,
( sP53
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP16
| ~ sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP16
| ~ sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP11
| ~ sP16 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(45,plain,
( sP4
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).
thf(46,plain,
( ~ sP10
| ~ sP40
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(47,plain,
( ~ sP29
| sP10
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP23
| sP29 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( sP30
| sP45 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( sP30
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP43
| ~ sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP43
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( sP2
| ~ sP43 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(54,plain,
( sP8
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(55,plain,
( sP8
| sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP52
| ~ sP8 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__3]) ).
thf(57,plain,
( sP38
| ~ sP52 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).
thf(58,plain,
( sP1
| ~ sP38 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__1]) ).
thf(59,plain,
( sP39
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__0]) ).
thf(60,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,h3]) ).
thf(61,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[60,h2]) ).
thf(62,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[61,h1]) ).
thf(63,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[62,h0]) ).
thf(0,theorem,
sP39,
inference(contra,[status(thm),contra(discharge,[h3])],[60,h3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV149^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 28 15:40:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 63.06/63.17 % SZS status Theorem
% 63.06/63.17 % Mode: mode371
% 63.06/63.17 % Inferences: 19493
% 63.06/63.17 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------