TSTP Solution File: SEV420^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEV420^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 18:06:19 EDT 2022
% Result : Theorem 1.98s 2.21s
% Output : Proof 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 53
% Syntax : Number of formulae : 64 ( 32 unt; 6 typ; 26 def)
% Number of atoms : 377 ( 144 equ; 0 cnn)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 1393 ( 422 ~; 12 |; 0 &; 529 @)
% ( 12 <=>; 418 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 106 ( 106 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 37 con; 0-2 aty)
% Number of variables : 319 ( 76 ^ 243 !; 0 ?; 319 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
eigen__2: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i > $o ).
thf(ty_eigen__3,type,
eigen__3: $i > $o ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(h0,assumption,
! [X1: ( $i > $o ) > $o,X2: $i > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i > $o] :
~ ( ~ ( ~ ( ~ ! [X2: $i > $i] :
( ( ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i,X4: $i] :
( ~ ( ~ ( ( eigen__0 @ X3 )
=> ~ ( eigen__0 @ X4 ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( eigen__1 @ X3 )
=> ~ ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( ( X2 @ X4 )
!= X3 ) ) ) ) )
=> ! [X2: $i > $i] :
( ( ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i,X4: $i] :
( ~ ( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( eigen__2 @ X4 )
=> ( ( X2 @ X4 )
!= X3 ) ) ) ) ) )
=> ( ( ^ [X2: $i] :
~ ( ( eigen__1 @ X2 )
=> ~ ( X1 @ X2 ) ) )
!= ( ^ [X2: $i] : $false ) ) )
=> ~ ! [X2: $i > $i] :
~ ( ! [X3: $i] :
( ( ~ ( eigen__0 @ X3 )
=> ( eigen__2 @ X3 ) )
=> ( ~ ( eigen__1 @ ( X2 @ X3 ) )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ! [X3: $i,X4: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X3 )
=> ( eigen__2 @ X3 ) )
=> ~ ( ~ ( eigen__0 @ X4 )
=> ( eigen__2 @ X4 ) ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) )
=> ( X3 = X4 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o] :
( ~ ( ~ ( ~ ! [X4: $i > $i] :
( ( ! [X5: $i] :
( ( eigen__0 @ X5 )
=> ( X1 @ ( X4 @ X5 ) ) )
=> ! [X5: $i,X6: $i] :
( ~ ( ~ ( ( eigen__0 @ X5 )
=> ~ ( eigen__0 @ X6 ) )
=> ( ( X4 @ X5 )
!= ( X4 @ X6 ) ) )
=> ( X5 = X6 ) ) )
=> ~ ( ! [X5: $i] :
( ( eigen__0 @ X5 )
=> ( X1 @ ( X4 @ X5 ) ) )
=> ! [X5: $i] :
( ( X1 @ X5 )
=> ~ ! [X6: $i] :
( ( eigen__0 @ X6 )
=> ( ( X4 @ X6 )
!= X5 ) ) ) ) )
=> ! [X4: $i > $i] :
( ( ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) )
=> ! [X5: $i,X6: $i] :
( ~ ( ~ ( ( X2 @ X5 )
=> ~ ( X2 @ X6 ) )
=> ( ( X4 @ X5 )
!= ( X4 @ X6 ) ) )
=> ( X5 = X6 ) ) )
=> ~ ( ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) )
=> ! [X5: $i] :
( ( X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X6 )
=> ( ( X4 @ X6 )
!= X5 ) ) ) ) ) )
=> ( ( ^ [X4: $i] :
~ ( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) ) )
!= ( ^ [X4: $i] : $false ) ) )
=> ~ ! [X4: $i > $i] :
~ ( ! [X5: $i] :
( ( ~ ( eigen__0 @ X5 )
=> ( X2 @ X5 ) )
=> ( ~ ( X1 @ ( X4 @ X5 ) )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ! [X5: $i,X6: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X5 )
=> ( X2 @ X5 ) )
=> ~ ( ~ ( eigen__0 @ X6 )
=> ( X2 @ X6 ) ) )
=> ( ( X4 @ X5 )
!= ( X4 @ X6 ) ) )
=> ( X5 = X6 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ~ ( ~ ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X1 @ X6 )
=> ~ ( X1 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X6 )
=> ~ ! [X7: $i] :
( ( X1 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) )
=> ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X3 @ X6 )
=> ~ ( X3 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) ) )
=> ( ( ^ [X5: $i] :
~ ( ( X2 @ X5 )
=> ~ ( X4 @ X5 ) ) )
!= ( ^ [X5: $i] : $false ) ) )
=> ~ ! [X5: $i > $i] :
~ ( ! [X6: $i] :
( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ( ~ ( X2 @ ( X5 @ X6 ) )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( ~ ( X1 @ X7 )
=> ( X3 @ X7 ) ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(h1,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__1 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__1
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i > $o] :
~ ! [X2: $i > $o] :
( ~ ( ~ ( ~ ! [X3: $i > $i] :
( ( ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ ( X3 @ X4 ) ) )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( eigen__0 @ X4 )
=> ~ ( eigen__0 @ X5 ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) )
=> ( X4 = X5 ) ) )
=> ~ ( ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( eigen__1 @ X4 )
=> ~ ! [X5: $i] :
( ( eigen__0 @ X5 )
=> ( ( X3 @ X5 )
!= X4 ) ) ) ) )
=> ! [X3: $i > $i] :
( ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) )
=> ( X4 = X5 ) ) )
=> ~ ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X5 )
=> ( ( X3 @ X5 )
!= X4 ) ) ) ) ) )
=> ( ( ^ [X3: $i] :
~ ( ( eigen__1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
!= ( ^ [X3: $i] : $false ) ) )
=> ~ ! [X3: $i > $i] :
~ ( ! [X4: $i] :
( ( ~ ( eigen__0 @ X4 )
=> ( X1 @ X4 ) )
=> ( ~ ( eigen__1 @ ( X3 @ X4 ) )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ( ~ ( eigen__0 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) )
=> ( X4 = X5 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__1
@ ^ [X1: $i] :
~ ( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__8 )
=> ( eigen__2 @ eigen__8 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__8 != X1 ) )
=> ( eigen__8 = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ~ ( ~ ( ~ ! [X4: $i > $i] :
( ( ! [X5: $i] :
( ( eigen__0 @ X5 )
=> ( X1 @ ( X4 @ X5 ) ) )
=> ! [X5: $i,X6: $i] :
( ~ ( ~ ( ( eigen__0 @ X5 )
=> ~ ( eigen__0 @ X6 ) )
=> ( ( X4 @ X5 )
!= ( X4 @ X6 ) ) )
=> ( X5 = X6 ) ) )
=> ~ ( ! [X5: $i] :
( ( eigen__0 @ X5 )
=> ( X1 @ ( X4 @ X5 ) ) )
=> ! [X5: $i] :
( ( X1 @ X5 )
=> ~ ! [X6: $i] :
( ( eigen__0 @ X6 )
=> ( ( X4 @ X6 )
!= X5 ) ) ) ) )
=> ! [X4: $i > $i] :
( ( ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) )
=> ! [X5: $i,X6: $i] :
( ~ ( ~ ( ( X2 @ X5 )
=> ~ ( X2 @ X6 ) )
=> ( ( X4 @ X5 )
!= ( X4 @ X6 ) ) )
=> ( X5 = X6 ) ) )
=> ~ ( ! [X5: $i] :
( ( X2 @ X5 )
=> ( X3 @ ( X4 @ X5 ) ) )
=> ! [X5: $i] :
( ( X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X6 )
=> ( ( X4 @ X6 )
!= X5 ) ) ) ) ) )
=> ( ( ^ [X4: $i] :
~ ( ( X1 @ X4 )
=> ~ ( X3 @ X4 ) ) )
!= ( ^ [X4: $i] : $false ) ) )
=> ~ ! [X4: $i > $i] :
~ ( ! [X5: $i] :
( ( ~ ( eigen__0 @ X5 )
=> ( X2 @ X5 ) )
=> ( ~ ( X1 @ ( X4 @ X5 ) )
=> ( X3 @ ( X4 @ X5 ) ) ) )
=> ! [X5: $i,X6: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X5 )
=> ( X2 @ X5 ) )
=> ~ ( ~ ( eigen__0 @ X6 )
=> ( X2 @ X6 ) ) )
=> ( ( X4 @ X5 )
!= ( X4 @ X6 ) ) )
=> ( X5 = X6 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $i] :
~ ( ! [X2: $i] :
( ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) )
=> ( ~ ( eigen__1 @ ( X1 @ X2 ) )
=> ( eigen__3 @ ( X1 @ X2 ) ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) )
=> ~ ( ~ ( eigen__0 @ X3 )
=> ( eigen__2 @ X3 ) ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ~ ( ~ ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__0 @ X2 )
=> ~ ( eigen__0 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__0 @ X2 )
=> ( eigen__1 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__1 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) )
=> ! [X1: $i > $i] :
( ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i,X3: $i] :
( ~ ( ~ ( ( eigen__2 @ X2 )
=> ~ ( eigen__2 @ X3 ) )
=> ( ( X1 @ X2 )
!= ( X1 @ X3 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( ! [X2: $i] :
( ( eigen__2 @ X2 )
=> ( eigen__3 @ ( X1 @ X2 ) ) )
=> ! [X2: $i] :
( ( eigen__3 @ X2 )
=> ~ ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( ( X1 @ X3 )
!= X2 ) ) ) ) ) )
=> ( ( ^ [X1: $i] :
~ ( ( eigen__1 @ X1 )
=> ~ ( eigen__3 @ X1 ) ) )
!= ( ^ [X1: $i] : $false ) ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( ( ~ ( eigen__0 @ eigen__8 )
=> ( eigen__2 @ eigen__8 ) )
=> ~ ( ~ ( eigen__0 @ eigen__9 )
=> ( eigen__2 @ eigen__9 ) ) )
=> ( eigen__8 != eigen__9 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ! [X1: $i] :
( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ( ~ ( eigen__1 @ X1 )
=> ( eigen__3 @ X1 ) ) )
=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ eigen__8 )
=> ( eigen__2 @ eigen__8 ) )
=> ~ ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) ) )
=> ( eigen__8 != X1 ) )
=> ( eigen__8 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i > $o,X2: $i > $o] :
( ~ ( ~ ( ~ ! [X3: $i > $i] :
( ( ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ ( X3 @ X4 ) ) )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( eigen__0 @ X4 )
=> ~ ( eigen__0 @ X5 ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) )
=> ( X4 = X5 ) ) )
=> ~ ( ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( eigen__1 @ ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( eigen__1 @ X4 )
=> ~ ! [X5: $i] :
( ( eigen__0 @ X5 )
=> ( ( X3 @ X5 )
!= X4 ) ) ) ) )
=> ! [X3: $i > $i] :
( ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) )
=> ( X4 = X5 ) ) )
=> ~ ( ! [X4: $i] :
( ( X1 @ X4 )
=> ( X2 @ ( X3 @ X4 ) ) )
=> ! [X4: $i] :
( ( X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X5 )
=> ( ( X3 @ X5 )
!= X4 ) ) ) ) ) )
=> ( ( ^ [X3: $i] :
~ ( ( eigen__1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
!= ( ^ [X3: $i] : $false ) ) )
=> ~ ! [X3: $i > $i] :
~ ( ! [X4: $i] :
( ( ~ ( eigen__0 @ X4 )
=> ( X1 @ X4 ) )
=> ( ~ ( eigen__1 @ ( X3 @ X4 ) )
=> ( X2 @ ( X3 @ X4 ) ) ) )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X4 )
=> ( X1 @ X4 ) )
=> ~ ( ~ ( eigen__0 @ X5 )
=> ( X1 @ X5 ) ) )
=> ( ( X3 @ X4 )
!= ( X3 @ X5 ) ) )
=> ( X4 = X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: $i > $o,X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ~ ( ~ ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X1 @ X6 )
=> ~ ( X1 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X6 )
=> ~ ! [X7: $i] :
( ( X1 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) )
=> ! [X5: $i > $i] :
( ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X3 @ X6 )
=> ~ ( X3 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) ) )
=> ( ( ^ [X5: $i] :
~ ( ( X2 @ X5 )
=> ~ ( X4 @ X5 ) ) )
!= ( ^ [X5: $i] : $false ) ) )
=> ~ ! [X5: $i > $i] :
~ ( ! [X6: $i] :
( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ( ~ ( X2 @ ( X5 @ X6 ) )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( ~ ( X1 @ X7 )
=> ( X3 @ X7 ) ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__8 = eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: $i > $o] :
( ~ ( ~ ( ~ ! [X2: $i > $i] :
( ( ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i,X4: $i] :
( ~ ( ~ ( ( eigen__0 @ X3 )
=> ~ ( eigen__0 @ X4 ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( ! [X3: $i] :
( ( eigen__0 @ X3 )
=> ( eigen__1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( eigen__1 @ X3 )
=> ~ ! [X4: $i] :
( ( eigen__0 @ X4 )
=> ( ( X2 @ X4 )
!= X3 ) ) ) ) )
=> ! [X2: $i > $i] :
( ( ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i,X4: $i] :
( ~ ( ~ ( ( eigen__2 @ X3 )
=> ~ ( eigen__2 @ X4 ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( ! [X3: $i] :
( ( eigen__2 @ X3 )
=> ( X1 @ ( X2 @ X3 ) ) )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ! [X4: $i] :
( ( eigen__2 @ X4 )
=> ( ( X2 @ X4 )
!= X3 ) ) ) ) ) )
=> ( ( ^ [X2: $i] :
~ ( ( eigen__1 @ X2 )
=> ~ ( X1 @ X2 ) ) )
!= ( ^ [X2: $i] : $false ) ) )
=> ~ ! [X2: $i > $i] :
~ ( ! [X3: $i] :
( ( ~ ( eigen__0 @ X3 )
=> ( eigen__2 @ X3 ) )
=> ( ~ ( eigen__1 @ ( X2 @ X3 ) )
=> ( X1 @ ( X2 @ X3 ) ) ) )
=> ! [X3: $i,X4: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X3 )
=> ( eigen__2 @ X3 ) )
=> ~ ( ~ ( eigen__0 @ X4 )
=> ( eigen__2 @ X4 ) ) )
=> ( ( X2 @ X3 )
!= ( X2 @ X4 ) ) )
=> ( X3 = X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ~ sP4
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i,X2: $i] :
( ~ ( ~ ( ( ~ ( eigen__0 @ X1 )
=> ( eigen__2 @ X1 ) )
=> ~ ( ~ ( eigen__0 @ X2 )
=> ( eigen__2 @ X2 ) ) )
=> ( X1 != X2 ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(def_in,definition,
( in
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_is_a,definition,
( is_a
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).
thf(def_emptyset,definition,
( emptyset
= ( ^ [X1: $i] : $false ) ) ).
thf(def_unord_pair,definition,
( unord_pair
= ( ^ [X1: $i,X2: $i,X3: $i] :
( ( X3 != X1 )
=> ( X3 = X2 ) ) ) ) ).
thf(def_singleton,definition,
( singleton
= ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).
thf(def_union,definition,
( union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_excl_union,definition,
( excl_union
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ~ ( ~ ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ) ).
thf(def_intersection,definition,
( intersection
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_setminus,definition,
( setminus
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_complement,definition,
( complement
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_disjoint,definition,
( disjoint
= ( ^ [X1: $i > $o,X2: $i > $o] :
( ( intersection @ X1 @ X2 )
= emptyset ) ) ) ).
thf(def_subset,definition,
( subset
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_meets,definition,
( meets
= ( ^ [X1: $i > $o,X2: $i > $o] :
~ ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_misses,definition,
( misses
= ( ^ [X1: $i > $o,X2: $i > $o] :
! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_is_function,definition,
( is_function
= ( ^ [X1: $i > $o,X2: $i > $i,X3: $i > $o] :
! [X4: $i] :
( ( X1 @ X4 )
=> ( X3 @ ( X2 @ X4 ) ) ) ) ) ).
thf(def_injection,definition,
( injection
= ( ^ [X1: $i > $o,X2: $i > $i,X3: $i > $o] :
( ( is_function @ X1 @ X2 @ X3 )
=> ! [X4: $i,X5: $i] :
( ~ ( ~ ( ( X1 @ X4 )
=> ~ ( X1 @ X5 ) )
=> ( ( X2 @ X4 )
!= ( X2 @ X5 ) ) )
=> ( X4 = X5 ) ) ) ) ) ).
thf(def_surjection,definition,
( surjection
= ( ^ [X1: $i > $o,X2: $i > $i,X3: $i > $o] :
( ( is_function @ X1 @ X2 @ X3 )
=> ! [X4: $i] :
( ( X3 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X5 )
=> ( ( X2 @ X5 )
!= X4 ) ) ) ) ) ) ).
thf(def_bijection,definition,
( bijection
= ( ^ [X1: $i > $o,X2: $i > $i,X3: $i > $o] :
~ ( ( injection @ X1 @ X2 @ X3 )
=> ~ ( surjection @ X1 @ X2 @ X3 ) ) ) ) ).
thf(def_equinumerous,definition,
( equinumerous
= ( ^ [X1: $i > $o,X2: $i > $o] :
~ ! [X3: $i > $i] :
~ ( bijection @ X1 @ X3 @ X2 ) ) ) ).
thf(def_embedding,definition,
( embedding
= ( ^ [X1: $i > $o,X2: $i > $o] :
~ ! [X3: $i > $i] :
~ ( injection @ X1 @ X3 @ X2 ) ) ) ).
thf(prove,conjecture,
! [X1: $i > $o,X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ~ ( ~ ! [X5: $i > $i] :
~ ~ ( ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X1 @ X6 )
=> ~ ( X1 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X6 )
=> ~ ! [X7: $i] :
( ( X1 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) )
=> ~ ~ ! [X5: $i > $i] :
~ ~ ( ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X3 @ X6 )
=> ~ ( X3 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) ) )
=> ( ( ^ [X5: $i] :
~ ( ( X2 @ X5 )
=> ~ ( X4 @ X5 ) ) )
!= ( ^ [X5: $i] : $false ) ) )
=> ~ ! [X5: $i > $i] :
~ ( ! [X6: $i] :
( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ( ~ ( X2 @ ( X5 @ X6 ) )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( ~ ( X1 @ X7 )
=> ( X3 @ X7 ) ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) ) ) ).
thf(h2,negated_conjecture,
~ sP8,
inference(assume_negation,[status(cth)],[prove]) ).
thf(1,plain,
( sP4
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP11
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP11
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP6
| ~ sP11 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__9]) ).
thf(5,plain,
( sP12
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).
thf(6,plain,
( sP5
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| ~ sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( sP3
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( sP10
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(10,plain,
( sP7
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(11,plain,
( sP1
| ~ sP7 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(12,plain,
( sP8
| ~ sP1 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2]) ).
thf(14,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[13,h1]) ).
thf(15,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[14,h0]) ).
thf(0,theorem,
! [X1: $i > $o,X2: $i > $o,X3: $i > $o,X4: $i > $o] :
( ~ ( ~ ( ~ ! [X5: $i > $i] :
~ ~ ( ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X1 @ X6 )
=> ~ ( X1 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X1 @ X6 )
=> ( X2 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X2 @ X6 )
=> ~ ! [X7: $i] :
( ( X1 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) )
=> ~ ~ ! [X5: $i > $i] :
~ ~ ( ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( X3 @ X6 )
=> ~ ( X3 @ X7 ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) )
=> ~ ( ! [X6: $i] :
( ( X3 @ X6 )
=> ( X4 @ ( X5 @ X6 ) ) )
=> ! [X6: $i] :
( ( X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X7 )
=> ( ( X5 @ X7 )
!= X6 ) ) ) ) ) )
=> ( ( ^ [X5: $i] :
~ ( ( X2 @ X5 )
=> ~ ( X4 @ X5 ) ) )
!= ( ^ [X5: $i] : $false ) ) )
=> ~ ! [X5: $i > $i] :
~ ( ! [X6: $i] :
( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ( ~ ( X2 @ ( X5 @ X6 ) )
=> ( X4 @ ( X5 @ X6 ) ) ) )
=> ! [X6: $i,X7: $i] :
( ~ ( ~ ( ( ~ ( X1 @ X6 )
=> ( X3 @ X6 ) )
=> ~ ( ~ ( X1 @ X7 )
=> ( X3 @ X7 ) ) )
=> ( ( X5 @ X6 )
!= ( X5 @ X7 ) ) )
=> ( X6 = X7 ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h2])],[13,h2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV420^1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n013.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 : Tue Jun 28 17:03:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.21 % SZS status Theorem
% 1.98/2.21 % Mode: mode506
% 1.98/2.21 % Inferences: 58285
% 1.98/2.21 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------