TSTP Solution File: PUZ093^5 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : PUZ093^5 : 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 : Mon Jul 18 18:26:02 EDT 2022
% Result : Theorem 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 47 ( 7 unt; 2 typ; 1 def)
% Number of atoms : 544 ( 473 equ; 0 cnn)
% Maximal formula atoms : 33 ( 12 avg)
% Number of connectives : 2175 ( 729 ~; 19 |; 0 &; 948 @)
% ( 19 <=>; 460 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 22 con; 0-2 aty)
% Number of variables : 94 ( 1 ^ 93 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
eigen__1: $i > $i ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(h0,assumption,
! [X1: ( $i > $i ) > $o,X2: $i > $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $i] :
~ ( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
~ ! [X12: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X12 @ eigen__0 )
= ( X12 @ X1 ) )
=> ( ( X12 @ X2 )
!= ( X12 @ X3 ) ) )
=> ( ( X12 @ X8 )
!= ( X12 @ X11 ) ) )
=> ( ( X12 @ X4 )
= ( X12 @ X7 ) ) )
=> ~ ( ~ ( ~ ( ( ( X12 @ eigen__0 )
= ( X12 @ X1 ) )
=> ( ( X12 @ X10 )
!= ( X12 @ X11 ) ) )
=> ( ( X12 @ X2 )
!= ( X12 @ X5 ) ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X9 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X12 @ X4 )
= ( X12 @ X5 ) )
=> ( ( X12 @ X5 )
!= ( X12 @ X6 ) ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X7 ) ) )
=> ( ( X12 @ eigen__0 )
= ( X12 @ X3 ) ) )
=> ( ( X12 @ X8 )
!= ( X12 @ X11 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X12 @ eigen__0 )
= ( X12 @ X1 ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X7 ) ) )
=> ( ( X12 @ X2 )
= ( X12 @ X5 ) ) )
=> ( ( X12 @ X8 )
= ( X12 @ X11 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X12 @ X8 )
= ( X12 @ X9 ) )
=> ( ( X12 @ X10 )
!= ( X12 @ X11 ) ) )
=> ( ( X12 @ X4 )
!= ( X12 @ X7 ) ) )
=> ( ( X12 @ eigen__0 )
!= ( X12 @ X3 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X12 @ X2 )
= ( X12 @ X3 ) )
=> ( ( X12 @ X3 )
!= ( X12 @ X4 ) ) )
=> ( ( X12 @ X4 )
!= ( X12 @ X5 ) ) )
=> ( ( X12 @ X8 )
= ( X12 @ X11 ) ) )
=> ( ( X12 @ X6 )
= ( X12 @ X9 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X12 @ eigen__0 )
= ( X12 @ X1 ) )
=> ( ( X12 @ X2 )
!= ( X12 @ X3 ) ) )
=> ( ( X12 @ X4 )
!= ( X12 @ X5 ) ) )
=> ( ( X12 @ X6 )
!= ( X12 @ X7 ) ) )
=> ( ( X12 @ X8 )
!= ( X12 @ X9 ) ) )
=> ( ( X12 @ X10 )
!= ( X12 @ X11 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
~ ! [X7: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X7 @ eigen__0 )
= ( X7 @ eigen__0 ) )
=> ( ( X7 @ eigen__0 )
!= ( X7 @ eigen__0 ) ) )
=> ( ( X7 @ X3 )
!= ( X7 @ X6 ) ) )
=> ( ( X7 @ eigen__0 )
= ( X7 @ X2 ) ) )
=> ~ ( ~ ( ~ ( ( ( X7 @ eigen__0 )
= ( X7 @ eigen__0 ) )
=> ( ( X7 @ X5 )
!= ( X7 @ X6 ) ) )
=> ( ( X7 @ eigen__0 )
!= ( X7 @ eigen__0 ) ) )
=> ( ( X7 @ X1 )
!= ( X7 @ X4 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X7 @ eigen__0 )
= ( X7 @ eigen__0 ) )
=> ( ( X7 @ eigen__0 )
!= ( X7 @ X1 ) ) )
=> ( ( X7 @ X1 )
!= ( X7 @ X2 ) ) )
=> ( ( X7 @ eigen__0 )
= ( X7 @ eigen__0 ) ) )
=> ( ( X7 @ X3 )
!= ( X7 @ X6 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X7 @ eigen__0 )
= ( X7 @ eigen__0 ) )
=> ( ( X7 @ X1 )
!= ( X7 @ X2 ) ) )
=> ( ( X7 @ eigen__0 )
= ( X7 @ eigen__0 ) ) )
=> ( ( X7 @ X3 )
= ( X7 @ X6 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X7 @ X3 )
= ( X7 @ X4 ) )
=> ( ( X7 @ X5 )
!= ( X7 @ X6 ) ) )
=> ( ( X7 @ eigen__0 )
!= ( X7 @ X2 ) ) )
=> ( ( X7 @ eigen__0 )
!= ( X7 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X7 @ eigen__0 )
= ( X7 @ eigen__0 ) )
=> ( ( X7 @ eigen__0 )
!= ( X7 @ eigen__0 ) ) )
=> ( ( X7 @ eigen__0 )
!= ( X7 @ eigen__0 ) ) )
=> ( ( X7 @ X3 )
= ( X7 @ X6 ) ) )
=> ( ( X7 @ X1 )
= ( X7 @ X4 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X7 @ eigen__0 )
= ( X7 @ eigen__0 ) )
=> ( ( X7 @ eigen__0 )
!= ( X7 @ eigen__0 ) ) )
=> ( ( X7 @ eigen__0 )
!= ( X7 @ eigen__0 ) ) )
=> ( ( X7 @ X1 )
!= ( X7 @ X2 ) ) )
=> ( ( X7 @ X3 )
!= ( X7 @ X4 ) ) )
=> ( ( X7 @ X5 )
!= ( X7 @ X6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: $i,X2: $i,X3: $i] :
~ ! [X4: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X4 @ eigen__0 )
= ( X4 @ eigen__0 ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ X3 ) ) )
=> ( ( X4 @ eigen__0 )
= ( X4 @ eigen__0 ) ) )
=> ~ ( ~ ( ~ ( ( ( X4 @ eigen__0 )
= ( X4 @ eigen__0 ) )
=> ( ( X4 @ X2 )
!= ( X4 @ X3 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ X1 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X4 @ eigen__0 )
= ( X4 @ eigen__0 ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ X3 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X4 @ eigen__0 )
= ( X4 @ eigen__0 ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
= ( X4 @ X3 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X4 @ eigen__0 )
= ( X4 @ X1 ) )
=> ( ( X4 @ X2 )
!= ( X4 @ X3 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X4 @ eigen__0 )
= ( X4 @ eigen__0 ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
= ( X4 @ X3 ) ) )
=> ( ( X4 @ eigen__0 )
= ( X4 @ X1 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X4 @ eigen__0 )
= ( X4 @ eigen__0 ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ eigen__0 ) ) )
=> ( ( X4 @ eigen__0 )
!= ( X4 @ X1 ) ) )
=> ( ( X4 @ X2 )
!= ( X4 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
~ ! [X9: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X9 @ eigen__0 )
= ( X9 @ eigen__0 ) )
=> ( ( X9 @ eigen__0 )
!= ( X9 @ eigen__0 ) ) )
=> ( ( X9 @ X5 )
!= ( X9 @ X8 ) ) )
=> ( ( X9 @ X1 )
= ( X9 @ X4 ) ) )
=> ~ ( ~ ( ~ ( ( ( X9 @ eigen__0 )
= ( X9 @ eigen__0 ) )
=> ( ( X9 @ X7 )
!= ( X9 @ X8 ) ) )
=> ( ( X9 @ eigen__0 )
!= ( X9 @ X2 ) ) )
=> ( ( X9 @ X3 )
!= ( X9 @ X6 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X9 @ X1 )
= ( X9 @ X2 ) )
=> ( ( X9 @ X2 )
!= ( X9 @ X3 ) ) )
=> ( ( X9 @ X3 )
!= ( X9 @ X4 ) ) )
=> ( ( X9 @ eigen__0 )
= ( X9 @ eigen__0 ) ) )
=> ( ( X9 @ X5 )
!= ( X9 @ X8 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X9 @ eigen__0 )
= ( X9 @ eigen__0 ) )
=> ( ( X9 @ X3 )
!= ( X9 @ X4 ) ) )
=> ( ( X9 @ eigen__0 )
= ( X9 @ X2 ) ) )
=> ( ( X9 @ X5 )
= ( X9 @ X8 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X9 @ X5 )
= ( X9 @ X6 ) )
=> ( ( X9 @ X7 )
!= ( X9 @ X8 ) ) )
=> ( ( X9 @ X1 )
!= ( X9 @ X4 ) ) )
=> ( ( X9 @ eigen__0 )
!= ( X9 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X9 @ eigen__0 )
= ( X9 @ eigen__0 ) )
=> ( ( X9 @ eigen__0 )
!= ( X9 @ X1 ) ) )
=> ( ( X9 @ X1 )
!= ( X9 @ X2 ) ) )
=> ( ( X9 @ X5 )
= ( X9 @ X8 ) ) )
=> ( ( X9 @ X3 )
= ( X9 @ X6 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X9 @ eigen__0 )
= ( X9 @ eigen__0 ) )
=> ( ( X9 @ eigen__0 )
!= ( X9 @ eigen__0 ) ) )
=> ( ( X9 @ X1 )
!= ( X9 @ X2 ) ) )
=> ( ( X9 @ X3 )
!= ( X9 @ X4 ) ) )
=> ( ( X9 @ X5 )
!= ( X9 @ X6 ) ) )
=> ( ( X9 @ X7 )
!= ( X9 @ X8 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ~ ( ~ ( ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
~ ! [X8: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X8 @ eigen__0 )
= ( X8 @ eigen__0 ) )
=> ( ( X8 @ eigen__0 )
!= ( X8 @ eigen__0 ) ) )
=> ( ( X8 @ X4 )
!= ( X8 @ X7 ) ) )
=> ( ( X8 @ eigen__0 )
= ( X8 @ X3 ) ) )
=> ~ ( ~ ( ~ ( ( ( X8 @ eigen__0 )
= ( X8 @ eigen__0 ) )
=> ( ( X8 @ X6 )
!= ( X8 @ X7 ) ) )
=> ( ( X8 @ eigen__0 )
!= ( X8 @ X1 ) ) )
=> ( ( X8 @ X2 )
!= ( X8 @ X5 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X8 @ eigen__0 )
= ( X8 @ X1 ) )
=> ( ( X8 @ X1 )
!= ( X8 @ X2 ) ) )
=> ( ( X8 @ X2 )
!= ( X8 @ X3 ) ) )
=> ( ( X8 @ eigen__0 )
= ( X8 @ eigen__0 ) ) )
=> ( ( X8 @ X4 )
!= ( X8 @ X7 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X8 @ eigen__0 )
= ( X8 @ eigen__0 ) )
=> ( ( X8 @ X2 )
!= ( X8 @ X3 ) ) )
=> ( ( X8 @ eigen__0 )
= ( X8 @ X1 ) ) )
=> ( ( X8 @ X4 )
= ( X8 @ X7 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X8 @ X4 )
= ( X8 @ X5 ) )
=> ( ( X8 @ X6 )
!= ( X8 @ X7 ) ) )
=> ( ( X8 @ eigen__0 )
!= ( X8 @ X3 ) ) )
=> ( ( X8 @ eigen__0 )
!= ( X8 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X8 @ eigen__0 )
= ( X8 @ eigen__0 ) )
=> ( ( X8 @ eigen__0 )
!= ( X8 @ eigen__0 ) ) )
=> ( ( X8 @ eigen__0 )
!= ( X8 @ X1 ) ) )
=> ( ( X8 @ X4 )
= ( X8 @ X7 ) ) )
=> ( ( X8 @ X2 )
= ( X8 @ X5 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X8 @ eigen__0 )
= ( X8 @ eigen__0 ) )
=> ( ( X8 @ eigen__0 )
!= ( X8 @ eigen__0 ) ) )
=> ( ( X8 @ eigen__0 )
!= ( X8 @ X1 ) ) )
=> ( ( X8 @ X2 )
!= ( X8 @ X3 ) ) )
=> ( ( X8 @ X4 )
!= ( X8 @ X5 ) ) )
=> ( ( X8 @ X6 )
!= ( X8 @ X7 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) ) )
=> ~ sP5 )
=> ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) ) ) )
=> ~ sP5 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ sP5
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X1 @ eigen__0 )
= ( X1 @ eigen__0 ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) )
=> ( ( X1 @ eigen__0 )
!= ( X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
~ ! [X5: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X5 @ eigen__0 )
= ( X5 @ eigen__0 ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ X1 )
!= ( X5 @ X4 ) ) )
=> ( ( X5 @ eigen__0 )
= ( X5 @ eigen__0 ) ) )
=> ~ ( ~ ( ~ ( ( ( X5 @ eigen__0 )
= ( X5 @ eigen__0 ) )
=> ( ( X5 @ X3 )
!= ( X5 @ X4 ) ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ X2 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X5 @ eigen__0 )
= ( X5 @ eigen__0 ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ eigen__0 )
= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ X1 )
!= ( X5 @ X4 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X5 @ eigen__0 )
= ( X5 @ eigen__0 ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ eigen__0 )
= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ X1 )
= ( X5 @ X4 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X5 @ X1 )
= ( X5 @ X2 ) )
=> ( ( X5 @ X3 )
!= ( X5 @ X4 ) ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X5 @ eigen__0 )
= ( X5 @ eigen__0 ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ X1 )
= ( X5 @ X4 ) ) )
=> ( ( X5 @ eigen__0 )
= ( X5 @ X2 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X5 @ eigen__0 )
= ( X5 @ eigen__0 ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ eigen__0 )
!= ( X5 @ eigen__0 ) ) )
=> ( ( X5 @ X1 )
!= ( X5 @ X2 ) ) )
=> ( ( X5 @ X3 )
!= ( X5 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: $i,X2: $i] :
~ ! [X3: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ X2 ) ) )
=> ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) ) )
=> ~ ( ~ ( ~ ( ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) )
=> ( ( X3 @ X1 )
!= ( X3 @ X2 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ X2 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
= ( X3 @ X2 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) )
=> ( ( X3 @ X1 )
!= ( X3 @ X2 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
= ( X3 @ X2 ) ) )
=> ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X3 @ eigen__0 )
= ( X3 @ eigen__0 ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ eigen__0 )
!= ( X3 @ eigen__0 ) ) )
=> ( ( X3 @ X1 )
!= ( X3 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ~ sP8
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i] :
~ ! [X11: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X11 @ eigen__0 )
= ( X11 @ eigen__0 ) )
=> ( ( X11 @ X1 )
!= ( X11 @ X2 ) ) )
=> ( ( X11 @ X7 )
!= ( X11 @ X10 ) ) )
=> ( ( X11 @ X3 )
= ( X11 @ X6 ) ) )
=> ~ ( ~ ( ~ ( ( ( X11 @ eigen__0 )
= ( X11 @ eigen__0 ) )
=> ( ( X11 @ X9 )
!= ( X11 @ X10 ) ) )
=> ( ( X11 @ X1 )
!= ( X11 @ X4 ) ) )
=> ( ( X11 @ X5 )
!= ( X11 @ X8 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X11 @ X3 )
= ( X11 @ X4 ) )
=> ( ( X11 @ X4 )
!= ( X11 @ X5 ) ) )
=> ( ( X11 @ X5 )
!= ( X11 @ X6 ) ) )
=> ( ( X11 @ eigen__0 )
= ( X11 @ X2 ) ) )
=> ( ( X11 @ X7 )
!= ( X11 @ X10 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X11 @ eigen__0 )
= ( X11 @ eigen__0 ) )
=> ( ( X11 @ X5 )
!= ( X11 @ X6 ) ) )
=> ( ( X11 @ X1 )
= ( X11 @ X4 ) ) )
=> ( ( X11 @ X7 )
= ( X11 @ X10 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X11 @ X7 )
= ( X11 @ X8 ) )
=> ( ( X11 @ X9 )
!= ( X11 @ X10 ) ) )
=> ( ( X11 @ X3 )
!= ( X11 @ X6 ) ) )
=> ( ( X11 @ eigen__0 )
!= ( X11 @ X2 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X11 @ X1 )
= ( X11 @ X2 ) )
=> ( ( X11 @ X2 )
!= ( X11 @ X3 ) ) )
=> ( ( X11 @ X3 )
!= ( X11 @ X4 ) ) )
=> ( ( X11 @ X7 )
= ( X11 @ X10 ) ) )
=> ( ( X11 @ X5 )
= ( X11 @ X8 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X11 @ eigen__0 )
= ( X11 @ eigen__0 ) )
=> ( ( X11 @ X1 )
!= ( X11 @ X2 ) ) )
=> ( ( X11 @ X3 )
!= ( X11 @ X4 ) ) )
=> ( ( X11 @ X5 )
!= ( X11 @ X6 ) ) )
=> ( ( X11 @ X7 )
!= ( X11 @ X8 ) ) )
=> ( ( X11 @ X9 )
!= ( X11 @ X10 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i,X12: $i] :
~ ! [X13: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X13 @ X1 )
= ( X13 @ X2 ) )
=> ( ( X13 @ X3 )
!= ( X13 @ X4 ) ) )
=> ( ( X13 @ X9 )
!= ( X13 @ X12 ) ) )
=> ( ( X13 @ X5 )
= ( X13 @ X8 ) ) )
=> ~ ( ~ ( ~ ( ( ( X13 @ X1 )
= ( X13 @ X2 ) )
=> ( ( X13 @ X11 )
!= ( X13 @ X12 ) ) )
=> ( ( X13 @ X3 )
!= ( X13 @ X6 ) ) )
=> ( ( X13 @ X7 )
!= ( X13 @ X10 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X13 @ X5 )
= ( X13 @ X6 ) )
=> ( ( X13 @ X6 )
!= ( X13 @ X7 ) ) )
=> ( ( X13 @ X7 )
!= ( X13 @ X8 ) ) )
=> ( ( X13 @ X1 )
= ( X13 @ X4 ) ) )
=> ( ( X13 @ X9 )
!= ( X13 @ X12 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X13 @ X1 )
= ( X13 @ X2 ) )
=> ( ( X13 @ X7 )
!= ( X13 @ X8 ) ) )
=> ( ( X13 @ X3 )
= ( X13 @ X6 ) ) )
=> ( ( X13 @ X9 )
= ( X13 @ X12 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X13 @ X9 )
= ( X13 @ X10 ) )
=> ( ( X13 @ X11 )
!= ( X13 @ X12 ) ) )
=> ( ( X13 @ X5 )
!= ( X13 @ X8 ) ) )
=> ( ( X13 @ X1 )
!= ( X13 @ X4 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X13 @ X3 )
= ( X13 @ X4 ) )
=> ( ( X13 @ X4 )
!= ( X13 @ X5 ) ) )
=> ( ( X13 @ X5 )
!= ( X13 @ X6 ) ) )
=> ( ( X13 @ X9 )
= ( X13 @ X12 ) ) )
=> ( ( X13 @ X7 )
= ( X13 @ X10 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X13 @ X1 )
= ( X13 @ X2 ) )
=> ( ( X13 @ X3 )
!= ( X13 @ X4 ) ) )
=> ( ( X13 @ X5 )
!= ( X13 @ X6 ) ) )
=> ( ( X13 @ X7 )
!= ( X13 @ X8 ) ) )
=> ( ( X13 @ X9 )
!= ( X13 @ X10 ) ) )
=> ( ( X13 @ X11 )
!= ( X13 @ X12 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
~ ! [X6: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X6 @ eigen__0 )
= ( X6 @ eigen__0 ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ eigen__0 ) ) )
=> ( ( X6 @ X2 )
!= ( X6 @ X5 ) ) )
=> ( ( X6 @ eigen__0 )
= ( X6 @ X1 ) ) )
=> ~ ( ~ ( ~ ( ( ( X6 @ eigen__0 )
= ( X6 @ eigen__0 ) )
=> ( ( X6 @ X4 )
!= ( X6 @ X5 ) ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ eigen__0 ) ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ X3 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X6 @ eigen__0 )
= ( X6 @ eigen__0 ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ eigen__0 ) ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ X1 ) ) )
=> ( ( X6 @ eigen__0 )
= ( X6 @ eigen__0 ) ) )
=> ( ( X6 @ X2 )
!= ( X6 @ X5 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X6 @ eigen__0 )
= ( X6 @ eigen__0 ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ X1 ) ) )
=> ( ( X6 @ eigen__0 )
= ( X6 @ eigen__0 ) ) )
=> ( ( X6 @ X2 )
= ( X6 @ X5 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X6 @ X2 )
= ( X6 @ X3 ) )
=> ( ( X6 @ X4 )
!= ( X6 @ X5 ) ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ X1 ) ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X6 @ eigen__0 )
= ( X6 @ eigen__0 ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ eigen__0 ) ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ eigen__0 ) ) )
=> ( ( X6 @ X2 )
= ( X6 @ X5 ) ) )
=> ( ( X6 @ eigen__0 )
= ( X6 @ X3 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X6 @ eigen__0 )
= ( X6 @ eigen__0 ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ eigen__0 ) ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ eigen__0 ) ) )
=> ( ( X6 @ eigen__0 )
!= ( X6 @ X1 ) ) )
=> ( ( X6 @ X2 )
!= ( X6 @ X3 ) ) )
=> ( ( X6 @ X4 )
!= ( X6 @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: $i] :
~ ! [X2: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ X1 ) ) )
=> ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) ) )
=> ~ ( ~ ( ~ ( ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ X1 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ X1 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
= ( X2 @ X1 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ X1 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
= ( X2 @ X1 ) ) )
=> ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X2 @ eigen__0 )
= ( X2 @ eigen__0 ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ eigen__0 ) ) )
=> ( ( X2 @ eigen__0 )
!= ( X2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ~ sP7
=> ~ ( ~ ( ~ ( ~ ( ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
!= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) ) )
=> ( ( eigen__1 @ eigen__0 )
= ( eigen__1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP17
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
~ ! [X10: $i > $i] :
( ~ ( ~ ( ~ ( ~ ( ~ ( ( ~ ( ~ ( ( ( X10 @ eigen__0 )
= ( X10 @ eigen__0 ) )
=> ( ( X10 @ eigen__0 )
!= ( X10 @ X1 ) ) )
=> ( ( X10 @ X6 )
!= ( X10 @ X9 ) ) )
=> ( ( X10 @ X2 )
= ( X10 @ X5 ) ) )
=> ~ ( ~ ( ~ ( ( ( X10 @ eigen__0 )
= ( X10 @ eigen__0 ) )
=> ( ( X10 @ X8 )
!= ( X10 @ X9 ) ) )
=> ( ( X10 @ eigen__0 )
!= ( X10 @ X3 ) ) )
=> ( ( X10 @ X4 )
!= ( X10 @ X7 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X10 @ X2 )
= ( X10 @ X3 ) )
=> ( ( X10 @ X3 )
!= ( X10 @ X4 ) ) )
=> ( ( X10 @ X4 )
!= ( X10 @ X5 ) ) )
=> ( ( X10 @ eigen__0 )
= ( X10 @ X1 ) ) )
=> ( ( X10 @ X6 )
!= ( X10 @ X9 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X10 @ eigen__0 )
= ( X10 @ eigen__0 ) )
=> ( ( X10 @ X4 )
!= ( X10 @ X5 ) ) )
=> ( ( X10 @ eigen__0 )
= ( X10 @ X3 ) ) )
=> ( ( X10 @ X6 )
= ( X10 @ X9 ) ) ) )
=> ~ ( ~ ( ~ ( ( ( X10 @ X6 )
= ( X10 @ X7 ) )
=> ( ( X10 @ X8 )
!= ( X10 @ X9 ) ) )
=> ( ( X10 @ X2 )
!= ( X10 @ X5 ) ) )
=> ( ( X10 @ eigen__0 )
!= ( X10 @ X1 ) ) ) )
=> ~ ( ~ ( ~ ( ~ ( ( ( X10 @ eigen__0 )
= ( X10 @ X1 ) )
=> ( ( X10 @ X1 )
!= ( X10 @ X2 ) ) )
=> ( ( X10 @ X2 )
!= ( X10 @ X3 ) ) )
=> ( ( X10 @ X6 )
= ( X10 @ X9 ) ) )
=> ( ( X10 @ X4 )
= ( X10 @ X7 ) ) ) )
=> ( ~ ( ~ ( ~ ( ~ ( ( ( X10 @ eigen__0 )
= ( X10 @ eigen__0 ) )
=> ( ( X10 @ eigen__0 )
!= ( X10 @ X1 ) ) )
=> ( ( X10 @ X2 )
!= ( X10 @ X3 ) ) )
=> ( ( X10 @ X4 )
!= ( X10 @ X5 ) ) )
=> ( ( X10 @ X6 )
!= ( X10 @ X7 ) ) )
=> ( ( X10 @ X8 )
!= ( X10 @ X9 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(cSIXFRIENDS_PTH,conjecture,
~ sP14 ).
thf(h1,negated_conjecture,
sP14,
inference(assume_negation,[status(cth)],[cSIXFRIENDS_PTH]) ).
thf(1,plain,
( sP8
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP7
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP12
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP17
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP18
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP18
| ~ sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP9
| ~ sP18 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(8,plain,
( ~ sP16
| ~ sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP11
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP3
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP10
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP2
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP4
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP19
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP13
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP1
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP14
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h1]) ).
thf(21,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[20,h0]) ).
thf(0,theorem,
~ sP14,
inference(contra,[status(thm),contra(discharge,[h1])],[20,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ093^5 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat May 28 20:48:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.38 % SZS status Theorem
% 0.18/0.38 % Mode: mode213
% 0.18/0.38 % Inferences: 32
% 0.18/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------