TSTP Solution File: SEU486^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU486^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n006.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 13:52:25 EDT 2022
% Result : Theorem 2.00s 2.35s
% Output : Proof 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 100
% Syntax : Number of formulae : 111 ( 43 unt; 6 typ; 35 def)
% Number of atoms : 362 ( 90 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1826 ( 429 ~; 35 |; 0 &; 892 @)
% ( 31 <=>; 438 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 207 ( 207 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 67 con; 0-2 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 495 ( 49 ^ 446 !; 0 ?; 495 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_eigen__7,type,
eigen__7: $i > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__0,type,
eigen__0: $i > $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_eigen__8,type,
eigen__8: $i > $i > $o ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__0 @ eigen__1 @ eigen__2 ) )
=> ~ ! [X2: $i] :
( ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ( ( eigen__2 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ eigen__2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X3 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(h1,assumption,
! [X1: ( $i > $i > $o ) > $o,X2: $i > $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__1
@ ^ [X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) )
=> ~ ( ( X2 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X3 ) ) ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ X2 )
=> ~ ( eigen__0 @ eigen__1 @ X1 ) )
=> ~ ! [X3: $i] :
( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ( ( X1 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__1
@ ^ [X1: $i > $i > $o] :
~ ( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( ( X1 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) )
=> ~ ( ( X1 != X2 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X2 ) ) ) )
=> ~ ! [X4: $i] :
( ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X3 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( eigen__7 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( eigen__0 @ eigen__1 @ eigen__3 )
=> ~ ( eigen__0 @ eigen__1 @ eigen__2 ) )
=> ~ ! [X1: $i] :
( ( ( eigen__3 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__3 @ X1 ) ) )
=> ~ ( ( eigen__2 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__7 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( eigen__1 != eigen__3 )
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ ( sP5
=> ~ ( ( eigen__1 != eigen__2 )
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ) )
=> ~ ! [X1: $i] :
( ( ( eigen__3 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__3 @ X1 ) ) )
=> ~ ( ( eigen__2 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i,X2: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ X2 )
=> ~ ( eigen__0 @ eigen__1 @ X1 ) )
=> ~ ! [X3: $i] :
( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ( ( X1 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__8 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__7 @ X1 @ X2 )
=> ~ ( eigen__7 @ X2 @ X3 ) )
=> ( eigen__7 @ X1 @ X3 ) )
=> ~ sP4 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i] :
( ~ ( ( ( eigen__1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ eigen__1 @ X2 ) ) )
=> ~ ( ( eigen__1 != X1 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ eigen__1 @ X1 ) ) ) )
=> ~ ! [X3: $i] :
( ( ( X2 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) ) )
=> ~ ( ( X1 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i] :
( ~ ( ( eigen__0 @ eigen__1 @ X1 )
=> ~ ( eigen__0 @ eigen__1 @ eigen__2 ) )
=> ~ ! [X2: $i] :
( ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ( ( eigen__2 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ eigen__2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( eigen__0 @ eigen__1 @ eigen__3 )
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__7 @ X1 @ X2 )
=> ~ ( eigen__7 @ X2 @ X3 ) )
=> ( eigen__7 @ X1 @ X3 ) )
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( ( eigen__3 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__3 @ X1 ) ) )
=> ~ ( ( eigen__2 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ~ ( ( ( eigen__1 != X1 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ X1 ) ) )
=> ~ ( ( eigen__1 != eigen__2 )
=> ! [X2: $i > $i > $o] :
( ~ ( ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X4 @ X5 ) )
=> ( X2 @ X3 @ X5 ) )
=> ~ ! [X3: $i,X4: $i] :
( ( eigen__0 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) )
=> ( X2 @ eigen__1 @ eigen__2 ) ) ) )
=> ~ ! [X2: $i] :
( ( ( X1 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ X1 @ X2 ) ) )
=> ~ ( ( eigen__2 != X2 )
=> ! [X3: $i > $i > $o] :
( ~ ( ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X5 @ X6 ) )
=> ( X3 @ X4 @ X6 ) )
=> ~ ! [X4: $i,X5: $i] :
( ( eigen__0 @ X4 @ X5 )
=> ( X3 @ X4 @ X5 ) ) )
=> ( X3 @ eigen__2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__8 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( eigen__1 != eigen__2 )
=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( eigen__0 @ eigen__1 @ eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( ( X1 != X3 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X3 ) ) )
=> ~ ( ( X1 != X2 )
=> ! [X4: $i > $i > $o] :
( ~ ( ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X6 @ X7 ) )
=> ( X4 @ X5 @ X7 ) )
=> ~ ! [X5: $i,X6: $i] :
( ( eigen__0 @ X5 @ X6 )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X1 @ X2 ) ) ) )
=> ~ ! [X4: $i] :
( ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) )
=> ~ ( ( X2 != X3 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( X1 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X3 ) ) ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ~ ! [X5: $i] :
( ( ( X4 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X4 @ X5 ) ) )
=> ~ ( ( X3 != X5 )
=> ! [X6: $i > $i > $o] :
( ~ ( ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X8 @ X9 ) )
=> ( X6 @ X7 @ X9 ) )
=> ~ ! [X7: $i,X8: $i] :
( ( X1 @ X7 @ X8 )
=> ( X6 @ X7 @ X8 ) ) )
=> ( X6 @ X3 @ X5 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ~ ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__8 @ X1 @ X2 )
=> ~ ( eigen__8 @ X2 @ X3 ) )
=> ( eigen__8 @ X1 @ X3 ) )
=> ~ ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__8 @ X1 @ X2 ) ) )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( sP5
=> ~ sP17 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP18
=> ~ ( eigen__0 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( eigen__0 @ eigen__1 @ X1 )
=> ( eigen__7 @ eigen__1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ! [X1: $i,X2: $i] :
( ( eigen__0 @ X1 @ X2 )
=> ( eigen__8 @ X1 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( eigen__0 @ eigen__1 @ eigen__2 )
=> sP16 ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__3 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i > $i > $o] :
( ~ ( ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) )
=> ~ ! [X2: $i,X3: $i] :
( ( eigen__0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
=> ( X1 @ eigen__1 @ eigen__2 ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__0 @ X1 @ X3 )
=> ~ ( eigen__0 @ X1 @ X2 ) )
=> ~ ! [X4: $i] :
( ( ( X3 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X3 @ X4 ) ) )
=> ~ ( ( X2 != X4 )
=> ! [X5: $i > $i > $o] :
( ~ ( ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X7 @ X8 ) )
=> ( X5 @ X6 @ X8 ) )
=> ~ ! [X6: $i,X7: $i] :
( ( eigen__0 @ X6 @ X7 )
=> ( X5 @ X6 @ X7 ) ) )
=> ( X5 @ X2 @ X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ! [X1: $i,X2: $i,X3: $i] :
( ~ ( ( eigen__8 @ X1 @ X2 )
=> ~ ( eigen__8 @ X2 @ X3 ) )
=> ( eigen__8 @ X1 @ X3 ) )
=> ~ sP25 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(def_subrel,definition,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ) ).
thf(def_inv,definition,
( inv
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_idem,definition,
( idem
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] :
( ( X1 @ ( X1 @ X2 ) )
= ( X1 @ X2 ) ) ) ) ).
thf(def_infl,definition,
( infl
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).
thf(def_mono,definition,
( mono
= ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
! [X2: $i > $i > $o,X3: $i > $i > $o] :
( ( subrel @ X2 @ X3 )
=> ( subrel @ ( X1 @ X2 ) @ ( X1 @ X3 ) ) ) ) ) ).
thf(def_refl,definition,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_irrefl,definition,
( irrefl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 @ X2 ) ) ) ).
thf(def_rc,definition,
( rc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_symm,definition,
( symm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_antisymm,definition,
( antisymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) )
=> ( X2 = X3 ) ) ) ) ).
thf(def_asymm,definition,
( asymm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_sc,definition,
( sc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ X3 @ X2 )
=> ( X1 @ X2 @ X3 ) ) ) ) ).
thf(def_trans,definition,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X3 @ X4 ) )
=> ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_tc,definition,
( tc
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ~ ( ( trans @ X4 )
=> ~ ( subrel @ X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ) ).
thf(def_trc,definition,
( trc
= ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).
thf(def_trsc,definition,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).
thf(def_po,definition,
( po
= ( ^ [X1: $i > $i > $o] :
~ ( ~ ( ( refl @ X1 )
=> ~ ( antisymm @ X1 ) )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_so,definition,
( so
= ( ^ [X1: $i > $i > $o] :
~ ( ( asymm @ X1 )
=> ~ ( trans @ X1 ) ) ) ) ).
thf(def_total,definition,
( total
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ~ ( ( X2 != X3 )
=> ( X1 @ X2 @ X3 ) )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_term,definition,
( term
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ~ ! [X3: $i] :
~ ( X2 @ X3 )
=> ~ ! [X3: $i] :
( ( X2 @ X3 )
=> ~ ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ).
thf(def_ind,definition,
( ind
= ( ^ [X1: $i > $i > $o] :
! [X2: $i > $o] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( tc @ X1 @ X3 @ X4 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) )
=> ( !! @ X2 ) ) ) ) ).
thf(def_innf,definition,
( innf
= ( ^ [X1: $i > $i > $o,X2: $i] :
! [X3: $i] :
~ ( X1 @ X2 @ X3 ) ) ) ).
thf(def_nfof,definition,
( nfof
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ( ( trc @ X1 @ X3 @ X2 )
=> ~ ( innf @ X1 @ X2 ) ) ) ) ).
thf(def_norm,definition,
( norm
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
~ ! [X3: $i] :
~ ( nfof @ X1 @ X3 @ X2 ) ) ) ).
thf(def_join,definition,
( join
= ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
~ ! [X4: $i] :
( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X3 @ X4 ) ) ) ) ).
thf(def_lconfl,definition,
( lconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_sconfl,definition,
( sconfl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_confl,definition,
( confl
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( trc @ X1 @ X2 @ X4 )
=> ~ ( trc @ X1 @ X2 @ X3 ) )
=> ( join @ X1 @ X4 @ X3 ) ) ) ) ).
thf(def_cr,definition,
( cr
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( trsc @ X1 @ X2 @ X3 )
=> ( join @ X1 @ X2 @ X3 ) ) ) ) ).
thf(confluence_implies_local_confluence,conjecture,
sP20 ).
thf(h2,negated_conjecture,
~ sP20,
inference(assume_negation,[status(cth)],[confluence_implies_local_confluence]) ).
thf(1,plain,
( ~ sP25
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP26 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP26
| ~ sP30
| sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP31
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP24
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP12
| ~ sP18
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP13
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP21
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( sP21
| ~ sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( sP9
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP9
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP28
| ~ sP21 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(14,plain,
( sP27
| ~ sP9 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__7]) ).
thf(15,plain,
( sP5
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( sP17
| ~ sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP10
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP15
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP6
| sP22
| ~ sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( ~ sP22
| ~ sP5
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP19
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(22,plain,
( sP23
| sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP23
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( sP3
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( sP3
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(26,plain,
( sP11
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(27,plain,
( sP7
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(28,plain,
( sP29
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(29,plain,
( sP1
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP1
| sP19 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( sP20
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).
thf(32,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([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,h2]) ).
thf(33,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[32,h1]) ).
thf(34,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[33,h0]) ).
thf(0,theorem,
sP20,
inference(contra,[status(thm),contra(discharge,[h2])],[32,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU486^1 : TPTP v8.1.0. Released v3.6.0.
% 0.04/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n006.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 : Sun Jun 19 10:26:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.00/2.35 % SZS status Theorem
% 2.00/2.35 % Mode: mode506
% 2.00/2.35 % Inferences: 81831
% 2.00/2.35 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------