%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYN393^4.004 : 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 11:43:24 EDT 2022
% Result : Theorem 138.49s 138.48s
% Output : Proof 138.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 329
% Syntax : Number of formulae : 348 ( 38 unt; 20 typ; 34 def)
% Number of atoms : 2732 ( 34 equ; 0 cnn)
% Maximal formula atoms : 205 ( 8 avg)
% Number of connectives : 6543 ( 967 ~; 195 |; 0 &;3238 @)
% ( 134 <=>;2007 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 177 ( 174 usr; 171 con; 0-2 aty)
% ( 2 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1159 ( 42 ^1117 !; 0 ?;1159 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a4,type,
a4: $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_a3,type,
a3: $i > $o ).
thf(ty_eigen__16,type,
eigen__16: $i ).
thf(ty_eigen__25,type,
eigen__25: $i ).
thf(ty_eigen__7,type,
eigen__7: $i ).
thf(ty_a1,type,
a1: $i > $o ).
thf(ty_eigen__1,type,
eigen__1: $i ).
thf(ty_eigen__15,type,
eigen__15: $i ).
thf(ty_a2,type,
a2: $i > $o ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__4,type,
eigen__4: $i ).
thf(ty_eigen__26,type,
eigen__26: $i ).
thf(ty_eigen__27,type,
eigen__27: $i ).
thf(ty_irel,type,
irel: $i > $i > $o ).
thf(ty_eigen__10,type,
eigen__10: $i ).
thf(ty_eigen__8,type,
eigen__8: $i ).
thf(ty_eigen__13,type,
eigen__13: $i ).
thf(ty_eigen__20,type,
eigen__20: $i ).
thf(ty_eigen__9,type,
eigen__9: $i ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__1,definition,
( eigen__1
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__1])]) ).
thf(eigendef_eigen__15,definition,
( eigen__15
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__15])]) ).
thf(eigendef_eigen__0,definition,
( eigen__0
= ( eps__0
@ ^ [X1: $i] :
~ ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__0])]) ).
thf(eigendef_eigen__10,definition,
( eigen__10
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__4 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__10])]) ).
thf(eigendef_eigen__8,definition,
( eigen__8
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__1 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__8])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(eigendef_eigen__13,definition,
( eigen__13
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__7 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__13])]) ).
thf(eigendef_eigen__4,definition,
( eigen__4
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__1 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__4])]) ).
thf(eigendef_eigen__16,definition,
( eigen__16
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__4 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__16])]) ).
thf(eigendef_eigen__26,definition,
( eigen__26
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__26])]) ).
thf(eigendef_eigen__20,definition,
( eigen__20
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__9 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__20])]) ).
thf(eigendef_eigen__9,definition,
( eigen__9
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__9])]) ).
thf(eigendef_eigen__25,definition,
( eigen__25
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__7 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__25])]) ).
thf(eigendef_eigen__7,definition,
( eigen__7
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__7])]) ).
thf(eigendef_eigen__27,definition,
( eigen__27
= ( eps__0
@ ^ [X1: $i] :
~ ( ( irel @ eigen__9 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__27])]) ).
thf(sP1,plain,
( sP1
<=> ( ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( irel @ eigen__1 @ eigen__4 )
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a3 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( irel @ eigen__4 @ eigen__10 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a4 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( irel @ eigen__9 @ eigen__27 )
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a2 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( irel @ eigen__1 @ eigen__8 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP9
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ( a3 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ( a3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a2 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a1 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ! [X1: $i] :
( ( irel @ eigen__25 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__25 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( irel @ eigen__0 @ eigen__2 )
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a4 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a4 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ( a3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ( a3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( irel @ eigen__4 @ eigen__16 )
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a2 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ! [X1: $i] :
( ( irel @ eigen__26 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__26 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( irel @ eigen__1 @ eigen__4 )
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) )
=> ~ sP15 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( irel @ eigen__2 @ eigen__9 ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ( a3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__26 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__26 @ X1 )
=> ( a2 @ X1 ) ) )
=> ~ sP21 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( sP7
=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ( a3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( irel @ eigen__0 @ eigen__2 )
=> ~ ( sP4
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a4 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( sP32
=> ~ sP15 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ! [X1: $i] :
( ( irel @ eigen__10 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__10 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__25 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__25 @ X1 )
=> ( a2 @ X1 ) ) )
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ( sP25
=> ~ ( sP34
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ( a3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ! [X1: $i] :
( ( irel @ eigen__26 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__26 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( ( irel @ eigen__9 @ eigen__20 )
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ sP18 ) ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(sP42,plain,
( sP42
<=> ( sP28
=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP42])]) ).
thf(sP43,plain,
( sP43
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) )
=> sP27 )
=> ~ ( sP27
=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP43])]) ).
thf(sP44,plain,
( sP44
<=> ( sP3
=> ~ ( sP37
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__10 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__10 @ X1 )
=> ( a1 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP44])]) ).
thf(sP45,plain,
( sP45
<=> ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) )
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP45])]) ).
thf(sP46,plain,
( sP46
<=> ( sP34
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ( a3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP46])]) ).
thf(sP47,plain,
( sP47
<=> ( sP17
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP47])]) ).
thf(sP48,plain,
( sP48
<=> ( ( irel @ eigen__7 @ eigen__13 )
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP48])]) ).
thf(sP49,plain,
( sP49
<=> ( ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a3 @ X1 ) )
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP49])]) ).
thf(sP50,plain,
( sP50
<=> ( sP27
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP50])]) ).
thf(sP51,plain,
( sP51
<=> ( sP3
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__10 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__10 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ sP37 ) ) ),
introduced(definition,[new_symbols(definition,[sP51])]) ).
thf(sP52,plain,
( sP52
<=> ( ( irel @ eigen__7 @ eigen__13 )
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP52])]) ).
thf(sP53,plain,
( sP53
<=> ( ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__20 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP53])]) ).
thf(sP54,plain,
( sP54
<=> ! [X1: $i] :
( ( irel @ eigen__1 @ X1 )
=> ( a4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP54])]) ).
thf(sP55,plain,
( sP55
<=> ( sP9
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP55])]) ).
thf(sP56,plain,
( sP56
<=> ( ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ( a3 @ X1 ) )
=> sP12 ) ),
introduced(definition,[new_symbols(definition,[sP56])]) ).
thf(sP57,plain,
( sP57
<=> ( ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) ) ) ) )
=> sP7 ) ),
introduced(definition,[new_symbols(definition,[sP57])]) ).
thf(sP58,plain,
( sP58
<=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP58])]) ).
thf(sP59,plain,
( sP59
<=> ( ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP59])]) ).
thf(sP60,plain,
( sP60
<=> ( ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ( a3 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP60])]) ).
thf(sP61,plain,
( sP61
<=> ! [X1: $i] :
( ( irel @ eigen__8 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP61])]) ).
thf(sP62,plain,
( sP62
<=> ( ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP62])]) ).
thf(sP63,plain,
( sP63
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a1 @ X1 ) ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP63])]) ).
thf(sP64,plain,
( sP64
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP64])]) ).
thf(sP65,plain,
( sP65
<=> ( ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__15 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP65])]) ).
thf(sP66,plain,
( sP66
<=> ( ( sP24
=> sP54 )
=> ~ ( sP54
=> sP24 ) ) ),
introduced(definition,[new_symbols(definition,[sP66])]) ).
thf(sP67,plain,
( sP67
<=> ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ( a3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP67])]) ).
thf(sP68,plain,
( sP68
<=> ( ( irel @ eigen__8 @ eigen__15 )
=> ~ ( sP65
=> ~ sP20 ) ) ),
introduced(definition,[new_symbols(definition,[sP68])]) ).
thf(sP69,plain,
( sP69
<=> ( sP54
=> sP33 ) ),
introduced(definition,[new_symbols(definition,[sP69])]) ).
thf(sP70,plain,
( sP70
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ( a4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP70])]) ).
thf(sP71,plain,
( sP71
<=> ( sP12
=> sP67 ) ),
introduced(definition,[new_symbols(definition,[sP71])]) ).
thf(sP72,plain,
( sP72
<=> ( ( irel @ eigen__8 @ eigen__15 )
=> ~ ( sP20
=> ~ sP65 ) ) ),
introduced(definition,[new_symbols(definition,[sP72])]) ).
thf(sP73,plain,
( sP73
<=> ( sP21
=> ~ sP40 ) ),
introduced(definition,[new_symbols(definition,[sP73])]) ).
thf(sP74,plain,
( sP74
<=> ( ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__27 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP74])]) ).
thf(sP75,plain,
( sP75
<=> ( irel @ eigen__7 @ eigen__13 ) ),
introduced(definition,[new_symbols(definition,[sP75])]) ).
thf(sP76,plain,
( sP76
<=> ( sP53
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP76])]) ).
thf(sP77,plain,
( sP77
<=> ( irel @ eigen__9 @ eigen__27 ) ),
introduced(definition,[new_symbols(definition,[sP77])]) ).
thf(sP78,plain,
( sP78
<=> ! [X1: $i] :
( ( irel @ eigen__9 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP78])]) ).
thf(sP79,plain,
( sP79
<=> ( irel @ eigen__8 @ eigen__15 ) ),
introduced(definition,[new_symbols(definition,[sP79])]) ).
thf(sP80,plain,
( sP80
<=> ( sP49
=> ~ ( sP22
=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a3 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP80])]) ).
thf(sP81,plain,
( sP81
<=> ( sP65
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP81])]) ).
thf(sP82,plain,
( sP82
<=> ( irel @ eigen__0 @ eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP82])]) ).
thf(sP83,plain,
( sP83
<=> ( sP82
=> ~ ( sP69
=> ~ sP1 ) ) ),
introduced(definition,[new_symbols(definition,[sP83])]) ).
thf(sP84,plain,
( sP84
<=> ( ! [X1: $i] :
( ( irel @ eigen__10 @ X1 )
=> ( a2 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__10 @ X1 )
=> ( a1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP84])]) ).
thf(sP85,plain,
( sP85
<=> ( sP54
=> sP24 ) ),
introduced(definition,[new_symbols(definition,[sP85])]) ).
thf(sP86,plain,
( sP86
<=> ( irel @ eigen__4 @ eigen__16 ) ),
introduced(definition,[new_symbols(definition,[sP86])]) ).
thf(sP87,plain,
( sP87
<=> ( sP56
=> ~ sP71 ) ),
introduced(definition,[new_symbols(definition,[sP87])]) ).
thf(sP88,plain,
( sP88
<=> ( sP42
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a3 @ X1 ) )
=> sP28 ) ) ),
introduced(definition,[new_symbols(definition,[sP88])]) ).
thf(sP89,plain,
( sP89
<=> ( sP27
=> sP61 ) ),
introduced(definition,[new_symbols(definition,[sP89])]) ).
thf(sP90,plain,
( sP90
<=> ! [X1: $i] :
( ( irel @ eigen__7 @ X1 )
=> ( a3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP90])]) ).
thf(sP91,plain,
( sP91
<=> ( irel @ eigen__8 @ eigen__26 ) ),
introduced(definition,[new_symbols(definition,[sP91])]) ).
thf(sP92,plain,
( sP92
<=> ( sP37
=> ~ sP84 ) ),
introduced(definition,[new_symbols(definition,[sP92])]) ).
thf(sP93,plain,
( sP93
<=> ( sP4
=> ~ ( sP64
=> sP70 ) ) ),
introduced(definition,[new_symbols(definition,[sP93])]) ).
thf(sP94,plain,
( sP94
<=> ( ( ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) )
=> sP70 )
=> ~ ( sP70
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP94])]) ).
thf(sP95,plain,
( sP95
<=> ( sP70
=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP95])]) ).
thf(sP96,plain,
( sP96
<=> ( sP84
=> ~ sP37 ) ),
introduced(definition,[new_symbols(definition,[sP96])]) ).
thf(sP97,plain,
( sP97
<=> ( sP91
=> ~ sP30 ) ),
introduced(definition,[new_symbols(definition,[sP97])]) ).
thf(sP98,plain,
( sP98
<=> ( irel @ eigen__1 @ eigen__4 ) ),
introduced(definition,[new_symbols(definition,[sP98])]) ).
thf(sP99,plain,
( sP99
<=> ( sP86
=> ~ ( ( ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a2 @ X1 ) ) )
=> ~ sP62 ) ) ),
introduced(definition,[new_symbols(definition,[sP99])]) ).
thf(sP100,plain,
( sP100
<=> ( ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__13 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP100])]) ).
thf(sP101,plain,
( sP101
<=> ( ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__16 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP101])]) ).
thf(sP102,plain,
( sP102
<=> ( ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) )
=> sP70 ) ),
introduced(definition,[new_symbols(definition,[sP102])]) ).
thf(sP103,plain,
( sP103
<=> ! [X1: $i] :
~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP103])]) ).
thf(sP104,plain,
( sP104
<=> ( irel @ eigen__2 @ eigen__7 ) ),
introduced(definition,[new_symbols(definition,[sP104])]) ).
thf(sP105,plain,
( sP105
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ( a3 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP105])]) ).
thf(sP106,plain,
( sP106
<=> ( sP25
=> ~ sP87 ) ),
introduced(definition,[new_symbols(definition,[sP106])]) ).
thf(sP107,plain,
( sP107
<=> ( sP105
=> sP28 ) ),
introduced(definition,[new_symbols(definition,[sP107])]) ).
thf(sP108,plain,
( sP108
<=> ( sP104
=> ~ ( sP45
=> ~ sP26 ) ) ),
introduced(definition,[new_symbols(definition,[sP108])]) ).
thf(sP109,plain,
( sP109
<=> ( sP62
=> ~ sP101 ) ),
introduced(definition,[new_symbols(definition,[sP109])]) ).
thf(sP110,plain,
( sP110
<=> ( sP13
=> ~ ( ! [X1: $i] :
( ( irel @ eigen__25 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__25 @ X1 )
=> ( a2 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP110])]) ).
thf(sP111,plain,
( sP111
<=> ! [X1: $i] :
( ( irel @ eigen__0 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) ) )
=> ~ ( ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a1 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a2 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a3 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a4 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP111])]) ).
thf(sP112,plain,
( sP112
<=> ( sP22
=> sP90 ) ),
introduced(definition,[new_symbols(definition,[sP112])]) ).
thf(sP113,plain,
( sP113
<=> ( sP101
=> ~ sP62 ) ),
introduced(definition,[new_symbols(definition,[sP113])]) ).
thf(sP114,plain,
( sP114
<=> ! [X1: $i] :
( ( irel @ eigen__2 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a3 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) ) )
=> ~ ( ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a2 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a1 @ X3 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP114])]) ).
thf(sP115,plain,
( sP115
<=> ( sP61
=> sP27 ) ),
introduced(definition,[new_symbols(definition,[sP115])]) ).
thf(sP116,plain,
( sP116
<=> ( ! [X1: $i] :
( ( irel @ eigen__25 @ X1 )
=> ( a1 @ X1 ) )
=> ! [X1: $i] :
( ( irel @ eigen__25 @ X1 )
=> ( a2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP116])]) ).
thf(sP117,plain,
( sP117
<=> ( ( irel @ eigen__7 @ eigen__25 )
=> ~ sP110 ) ),
introduced(definition,[new_symbols(definition,[sP117])]) ).
thf(sP118,plain,
( sP118
<=> ( irel @ eigen__7 @ eigen__25 ) ),
introduced(definition,[new_symbols(definition,[sP118])]) ).
thf(sP119,plain,
( sP119
<=> ( irel @ eigen__0 @ eigen__2 ) ),
introduced(definition,[new_symbols(definition,[sP119])]) ).
thf(sP120,plain,
( sP120
<=> ( sP45
=> ~ sP26 ) ),
introduced(definition,[new_symbols(definition,[sP120])]) ).
thf(sP121,plain,
( sP121
<=> ( ( irel @ eigen__9 @ eigen__20 )
=> ~ sP11 ) ),
introduced(definition,[new_symbols(definition,[sP121])]) ).
thf(sP122,plain,
( sP122
<=> ( sP69
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP122])]) ).
thf(sP123,plain,
( sP123
<=> ( sP64
=> sP70 ) ),
introduced(definition,[new_symbols(definition,[sP123])]) ).
thf(sP124,plain,
( sP124
<=> ( sP20
=> ~ sP65 ) ),
introduced(definition,[new_symbols(definition,[sP124])]) ).
thf(sP125,plain,
( sP125
<=> ( sP31
=> ~ sP57 ) ),
introduced(definition,[new_symbols(definition,[sP125])]) ).
thf(sP126,plain,
( sP126
<=> ( sP6
=> ~ sP74 ) ),
introduced(definition,[new_symbols(definition,[sP126])]) ).
thf(sP127,plain,
( sP127
<=> ( sP77
=> ~ sP126 ) ),
introduced(definition,[new_symbols(definition,[sP127])]) ).
thf(sP128,plain,
( sP128
<=> ( sP24
=> sP54 ) ),
introduced(definition,[new_symbols(definition,[sP128])]) ).
thf(sP129,plain,
( sP129
<=> ( sP91
=> ~ sP73 ) ),
introduced(definition,[new_symbols(definition,[sP129])]) ).
thf(sP130,plain,
( sP130
<=> ( irel @ eigen__9 @ eigen__20 ) ),
introduced(definition,[new_symbols(definition,[sP130])]) ).
thf(sP131,plain,
( sP131
<=> ( sP104
=> ~ sP80 ) ),
introduced(definition,[new_symbols(definition,[sP131])]) ).
thf(sP132,plain,
( sP132
<=> ( sP118
=> ~ sP38 ) ),
introduced(definition,[new_symbols(definition,[sP132])]) ).
thf(sP133,plain,
( sP133
<=> ( sP82
=> ~ sP66 ) ),
introduced(definition,[new_symbols(definition,[sP133])]) ).
thf(sP134,plain,
( sP134
<=> ! [X1: $i] :
( ( irel @ eigen__4 @ X1 )
=> ~ ( ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) ) )
=> ~ ( ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a1 @ X2 ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( a2 @ X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP134])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
~ ( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(def_iatom,definition,
( iatom
= ( ^ [X1: $i > $o] : X1 ) ) ).
thf(def_inot,definition,
( inot
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).
thf(def_itrue,definition,
( itrue
= ( ^ [X1: $i] : ~ $false ) ) ).
thf(def_ifalse,definition,
( ifalse
= ( inot @ itrue ) ) ).
thf(def_iand,definition,
iand = mand ).
thf(def_ior,definition,
( ior
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplies,definition,
( iimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).
thf(def_iimplied,definition,
( iimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).
thf(def_iequiv,definition,
( iequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).
thf(def_ixor,definition,
( ixor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).
thf(def_ivalid,definition,
ivalid = !! ).
thf(def_isatisfiable,definition,
( isatisfiable
= ( ^ [X1: $i > $o] :
~ ! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_icountersatisfiable,definition,
( icountersatisfiable
= ( ^ [X1: $i > $o] :
~ ( !! @ X1 ) ) ) ).
thf(def_iinvalid,definition,
( iinvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(con,conjecture,
! [X1: $i] :
~ ( ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ sP103,
inference(assume_negation,[status(cth)],[con]) ).
thf(1,plain,
( sP63
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP63
| sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP30
| sP21 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP30
| sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP38
| sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( sP38
| sP116 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( sP11
| sP53 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP11
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP126
| ~ sP6
| ~ sP74 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP12
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP5
| ~ sP77
| ~ sP63 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP109
| sP101 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( sP109
| sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( sP124
| sP65 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( sP124
| sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP73
| ~ sP21
| ~ sP40 ),
inference(prop_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP61
| sP97 ),
inference(all_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP97
| ~ sP91
| ~ sP30 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP29
| sP100 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP29
| sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( ~ sP110
| ~ sP13
| ~ sP116 ),
inference(prop_rule,[status(thm)],]) ).
thf(22,plain,
( ~ sP58
| sP132 ),
inference(all_rule,[status(thm)],]) ).
thf(23,plain,
( ~ sP132
| ~ sP118
| ~ sP38 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP76
| ~ sP53
| ~ sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP78
| sP121 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP121
| ~ sP130
| ~ sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( sP127
| sP126 ),
inference(prop_rule,[status(thm)],]) ).
thf(28,plain,
( sP127
| sP77 ),
inference(prop_rule,[status(thm)],]) ).
thf(29,plain,
( sP92
| sP84 ),
inference(prop_rule,[status(thm)],]) ).
thf(30,plain,
( sP92
| sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(31,plain,
( ~ sP113
| ~ sP101
| ~ sP62 ),
inference(prop_rule,[status(thm)],]) ).
thf(32,plain,
( ~ sP134
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(33,plain,
( ~ sP19
| ~ sP86
| ~ sP109 ),
inference(prop_rule,[status(thm)],]) ).
thf(34,plain,
( ~ sP81
| ~ sP65
| ~ sP20 ),
inference(prop_rule,[status(thm)],]) ).
thf(35,plain,
( ~ sP17
| sP72 ),
inference(all_rule,[status(thm)],]) ).
thf(36,plain,
( ~ sP72
| ~ sP79
| ~ sP124 ),
inference(prop_rule,[status(thm)],]) ).
thf(37,plain,
( sP129
| sP73 ),
inference(prop_rule,[status(thm)],]) ).
thf(38,plain,
( sP129
| sP91 ),
inference(prop_rule,[status(thm)],]) ).
thf(39,plain,
( ~ sP8
| ~ sP100
| ~ sP59 ),
inference(prop_rule,[status(thm)],]) ).
thf(40,plain,
( ~ sP22
| sP48 ),
inference(all_rule,[status(thm)],]) ).
thf(41,plain,
( ~ sP48
| ~ sP75
| ~ sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(42,plain,
( sP117
| sP110 ),
inference(prop_rule,[status(thm)],]) ).
thf(43,plain,
( sP117
| sP118 ),
inference(prop_rule,[status(thm)],]) ).
thf(44,plain,
( sP41
| sP76 ),
inference(prop_rule,[status(thm)],]) ).
thf(45,plain,
( sP41
| sP130 ),
inference(prop_rule,[status(thm)],]) ).
thf(46,plain,
( sP78
| ~ sP127 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__27]) ).
thf(47,plain,
( ~ sP96
| ~ sP84
| ~ sP37 ),
inference(prop_rule,[status(thm)],]) ).
thf(48,plain,
( ~ sP28
| sP44 ),
inference(all_rule,[status(thm)],]) ).
thf(49,plain,
( ~ sP44
| ~ sP3
| ~ sP92 ),
inference(prop_rule,[status(thm)],]) ).
thf(50,plain,
( sP99
| sP113 ),
inference(prop_rule,[status(thm)],]) ).
thf(51,plain,
( sP99
| sP86 ),
inference(prop_rule,[status(thm)],]) ).
thf(52,plain,
( sP68
| sP81 ),
inference(prop_rule,[status(thm)],]) ).
thf(53,plain,
( sP68
| sP79 ),
inference(prop_rule,[status(thm)],]) ).
thf(54,plain,
( sP17
| ~ sP129 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__26]) ).
thf(55,plain,
( sP52
| sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(56,plain,
( sP52
| sP75 ),
inference(prop_rule,[status(thm)],]) ).
thf(57,plain,
( sP22
| ~ sP117 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__25]) ).
thf(58,plain,
( sP12
| ~ sP41 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__20]) ).
thf(59,plain,
( ~ sP60
| ~ sP67
| sP78 ),
inference(prop_rule,[status(thm)],]) ).
thf(60,plain,
( ~ sP34
| ~ sP78
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(61,plain,
( sP51
| sP96 ),
inference(prop_rule,[status(thm)],]) ).
thf(62,plain,
( sP51
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(63,plain,
( sP28
| ~ sP99 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__16]) ).
thf(64,plain,
( sP61
| ~ sP68 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).
thf(65,plain,
( ~ sP47
| ~ sP17
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(66,plain,
( ~ sP50
| ~ sP27
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(67,plain,
( sP58
| ~ sP52 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).
thf(68,plain,
( ~ sP112
| ~ sP22
| sP90 ),
inference(prop_rule,[status(thm)],]) ).
thf(69,plain,
( ~ sP49
| ~ sP90
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(70,plain,
( sP71
| ~ sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(71,plain,
( sP71
| sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(72,plain,
( sP56
| ~ sP12 ),
inference(prop_rule,[status(thm)],]) ).
thf(73,plain,
( sP56
| sP67 ),
inference(prop_rule,[status(thm)],]) ).
thf(74,plain,
( sP46
| sP60 ),
inference(prop_rule,[status(thm)],]) ).
thf(75,plain,
( sP46
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(76,plain,
( sP134
| ~ sP51 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__10]) ).
thf(77,plain,
( ~ sP107
| ~ sP105
| sP28 ),
inference(prop_rule,[status(thm)],]) ).
thf(78,plain,
( ~ sP42
| ~ sP28
| sP105 ),
inference(prop_rule,[status(thm)],]) ).
thf(79,plain,
( sP89
| ~ sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(80,plain,
( sP89
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(81,plain,
( sP115
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(82,plain,
( sP115
| sP61 ),
inference(prop_rule,[status(thm)],]) ).
thf(83,plain,
( sP16
| sP47 ),
inference(prop_rule,[status(thm)],]) ).
thf(84,plain,
( sP16
| sP50 ),
inference(prop_rule,[status(thm)],]) ).
thf(85,plain,
( sP26
| ~ sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(86,plain,
( sP26
| sP90 ),
inference(prop_rule,[status(thm)],]) ).
thf(87,plain,
( sP45
| ~ sP90 ),
inference(prop_rule,[status(thm)],]) ).
thf(88,plain,
( sP45
| sP58 ),
inference(prop_rule,[status(thm)],]) ).
thf(89,plain,
( sP80
| sP112 ),
inference(prop_rule,[status(thm)],]) ).
thf(90,plain,
( sP80
| sP49 ),
inference(prop_rule,[status(thm)],]) ).
thf(91,plain,
( ~ sP87
| ~ sP56
| ~ sP71 ),
inference(prop_rule,[status(thm)],]) ).
thf(92,plain,
( ~ sP114
| sP39 ),
inference(all_rule,[status(thm)],]) ).
thf(93,plain,
( ~ sP39
| ~ sP25
| ~ sP46 ),
inference(prop_rule,[status(thm)],]) ).
thf(94,plain,
( sP15
| ~ sP105 ),
inference(prop_rule,[status(thm)],]) ).
thf(95,plain,
( sP15
| sP134 ),
inference(prop_rule,[status(thm)],]) ).
thf(96,plain,
( sP32
| ~ sP134 ),
inference(prop_rule,[status(thm)],]) ).
thf(97,plain,
( sP32
| sP105 ),
inference(prop_rule,[status(thm)],]) ).
thf(98,plain,
( sP88
| sP107 ),
inference(prop_rule,[status(thm)],]) ).
thf(99,plain,
( sP88
| sP42 ),
inference(prop_rule,[status(thm)],]) ).
thf(100,plain,
( ~ sP43
| ~ sP115
| ~ sP89 ),
inference(prop_rule,[status(thm)],]) ).
thf(101,plain,
( ~ sP33
| sP55 ),
inference(all_rule,[status(thm)],]) ).
thf(102,plain,
( ~ sP55
| ~ sP9
| ~ sP16 ),
inference(prop_rule,[status(thm)],]) ).
thf(103,plain,
( ~ sP120
| ~ sP45
| ~ sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(104,plain,
( ~ sP64
| sP131 ),
inference(all_rule,[status(thm)],]) ).
thf(105,plain,
( ~ sP131
| ~ sP104
| ~ sP80 ),
inference(prop_rule,[status(thm)],]) ).
thf(106,plain,
( sP106
| sP87 ),
inference(prop_rule,[status(thm)],]) ).
thf(107,plain,
( sP106
| sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(108,plain,
( ~ sP36
| ~ sP32
| ~ sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(109,plain,
( ~ sP24
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(110,plain,
( ~ sP2
| ~ sP98
| ~ sP88 ),
inference(prop_rule,[status(thm)],]) ).
thf(111,plain,
( sP10
| sP43 ),
inference(prop_rule,[status(thm)],]) ).
thf(112,plain,
( sP10
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(113,plain,
( sP108
| sP120 ),
inference(prop_rule,[status(thm)],]) ).
thf(114,plain,
( sP108
| sP104 ),
inference(prop_rule,[status(thm)],]) ).
thf(115,plain,
( sP64
| ~ sP106 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).
thf(116,plain,
( sP23
| sP36 ),
inference(prop_rule,[status(thm)],]) ).
thf(117,plain,
( sP23
| sP98 ),
inference(prop_rule,[status(thm)],]) ).
thf(118,plain,
( sP24
| ~ sP10 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).
thf(119,plain,
( sP114
| ~ sP108 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).
thf(120,plain,
( ~ sP123
| ~ sP64
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(121,plain,
( ~ sP4
| ~ sP70
| sP64 ),
inference(prop_rule,[status(thm)],]) ).
thf(122,plain,
( sP33
| ~ sP23 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).
thf(123,plain,
( ~ sP85
| ~ sP54
| sP24 ),
inference(prop_rule,[status(thm)],]) ).
thf(124,plain,
( ~ sP128
| ~ sP24
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(125,plain,
( sP95
| ~ sP114 ),
inference(prop_rule,[status(thm)],]) ).
thf(126,plain,
( sP95
| sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(127,plain,
( sP102
| ~ sP70 ),
inference(prop_rule,[status(thm)],]) ).
thf(128,plain,
( sP102
| sP114 ),
inference(prop_rule,[status(thm)],]) ).
thf(129,plain,
( sP93
| sP123 ),
inference(prop_rule,[status(thm)],]) ).
thf(130,plain,
( sP93
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(131,plain,
( sP1
| ~ sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(132,plain,
( sP1
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(133,plain,
( sP69
| ~ sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(134,plain,
( sP69
| sP54 ),
inference(prop_rule,[status(thm)],]) ).
thf(135,plain,
( sP66
| sP85 ),
inference(prop_rule,[status(thm)],]) ).
thf(136,plain,
( sP66
| sP128 ),
inference(prop_rule,[status(thm)],]) ).
thf(137,plain,
( ~ sP94
| ~ sP102
| ~ sP95 ),
inference(prop_rule,[status(thm)],]) ).
thf(138,plain,
( ~ sP111
| sP35 ),
inference(all_rule,[status(thm)],]) ).
thf(139,plain,
( ~ sP35
| ~ sP119
| ~ sP93 ),
inference(prop_rule,[status(thm)],]) ).
thf(140,plain,
( ~ sP122
| ~ sP69
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(141,plain,
( ~ sP7
| sP133 ),
inference(all_rule,[status(thm)],]) ).
thf(142,plain,
( ~ sP133
| ~ sP82
| ~ sP66 ),
inference(prop_rule,[status(thm)],]) ).
thf(143,plain,
( sP14
| sP94 ),
inference(prop_rule,[status(thm)],]) ).
thf(144,plain,
( sP14
| sP119 ),
inference(prop_rule,[status(thm)],]) ).
thf(145,plain,
( sP83
| sP122 ),
inference(prop_rule,[status(thm)],]) ).
thf(146,plain,
( sP83
| sP82 ),
inference(prop_rule,[status(thm)],]) ).
thf(147,plain,
( sP7
| ~ sP14 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(148,plain,
( sP111
| ~ sP83 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).
thf(149,plain,
( sP57
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(150,plain,
( sP57
| sP111 ),
inference(prop_rule,[status(thm)],]) ).
thf(151,plain,
( sP31
| ~ sP111 ),
inference(prop_rule,[status(thm)],]) ).
thf(152,plain,
( sP31
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(153,plain,
( ~ sP125
| ~ sP31
| ~ sP57 ),
inference(prop_rule,[status(thm)],]) ).
thf(154,plain,
( sP103
| sP125 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).
thf(155,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,h1]) ).
thf(156,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[155,h0]) ).
thf(0,theorem,
! [X1: $i] :
~ ( ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) ) ) )
=> ! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ~ ( ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ( a4 @ X3 ) )
=> ! [X3: $i] :
( ( irel @ X2 @ X3 )
=> ~ ( ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) ) )
=> ~ ( ~ ~ ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ( a3 @ X4 ) )
=> ! [X4: $i] :
( ( irel @ X3 @ X4 )
=> ~ ( ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) ) )
=> ~ ( ~ ~ ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a2 @ X5 ) )
=> ! [X5: $i] :
( ( irel @ X4 @ X5 )
=> ( a1 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[155,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN393^4.004 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Tue Jul 12 08:22:09 EDT 2022
% 0.15/0.36 % CPUTime :
% 138.49/138.48 % SZS status Theorem
% 138.49/138.48 % Mode: mode398
% 138.49/138.48 % Inferences: 3367
% 138.49/138.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------