%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV174^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 : 300s
% DateTime : Thu Oct 9 02:55:12 PM UTC 2025
% Result : Theorem 83.21s 83.53s
% Output : Proof 83.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 89
% Syntax : Number of formulae : 96 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 946 ( 268 equ; 0 cnn)
% Maximal formula atoms : 37 ( 9 avg)
% Number of connectives : 3411 (1322 ~; 58 |; 0 &;1030 @)
% ( 41 <=>; 960 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 431 ( 431 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 43 con; 0-2 aty)
% Number of variables : 690 ( 5 ^; 453 !; 0 ?; 690 :)
% ( 0 !>; 0 ?*; 0 @-; 232 @+)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_cP,type,
cP: ( a > $o ) > $o ).
thf(ty_eigen__36,type,
eigen__36: a > $o ).
thf(h0,assumption,
! [X1: ( a > $o ) > $o,X2: a > $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__36,definition,
( eigen__36
= ( eps__0
@ ^ [X1: a > $o] :
( ( ~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) )
!= ( ~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__36])]) ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a > $o,X3: a > $o] :
( ~ ( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ~ ( X2 @ X1 ) )
=> ~ ( X3 @ X1 ) )
=> ( X2 = X3 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( cP
@ @+[X1: a > $o] :
~ ( ( cP @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > $o] :
( ( ~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) )
= ( ~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) )
@ @+[X1: a] :
( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) )
= ( @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) )
@ @+[X1: a] :
( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a > $o] :
( ~ ( ~ ( ( cP @ eigen__36 )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( eigen__36 @ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( eigen__36 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( ^ [X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
= ( ^ [X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a > $o] :
( ( cP @ X1 )
=> ~ ( X1
@ @+[X2: a] :
( ( ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
!= ( @+[X3: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) ) )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( @+[X5: a > $o] :
~ ! [X6: a > $o] :
( ~ ( ~ ( ( cP @ X5 )
=> ~ ( cP @ X6 ) )
=> ! [X7: a] :
( ( X5 @ X7 )
=> ~ ( X6 @ X7 ) ) )
=> ( X5 = X6 ) )
@ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) ) )
= X3 ) )
@ X2 ) )
!= ( ~ ! [X3: a > $o] :
( ( cP @ X3 )
=> ~ ( X3 @ X2 ) ) ) )
!= ( ~ ! [X3: a > $o] :
( ( cP @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a > $o,X2: a > $o] :
( ~ ( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ~ ( X1
@ @+[X3: a] :
~ ( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( @+[X4: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X5: a > $o] :
~ ! [X6: a > $o] :
( ~ ( ~ ( ( cP @ X5 )
=> ~ ( cP @ X6 ) )
=> ! [X7: a] :
( ( X5 @ X7 )
=> ~ ( X6 @ X7 ) ) )
=> ( X5 = X6 ) ) )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( @+[X6: a > $o] :
~ ! [X7: a > $o] :
( ~ ( ~ ( ( cP @ X6 )
=> ~ ( cP @ X7 ) )
=> ! [X8: a] :
( ( X6 @ X8 )
=> ~ ( X7 @ X8 ) ) )
=> ( X6 = X7 ) )
@ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( ( @+[X5: a > $o] :
~ ! [X6: a > $o] :
( ~ ( ~ ( ( cP @ X5 )
=> ~ ( cP @ X6 ) )
=> ! [X7: a] :
( ( X5 @ X7 )
=> ~ ( X6 @ X7 ) ) )
=> ( X5 = X6 ) ) )
= X4 ) )
@ X3 ) ) ) )
=> ~ ( X2
@ @+[X3: a] :
~ ( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( @+[X4: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X5: a > $o] :
~ ! [X6: a > $o] :
( ~ ( ~ ( ( cP @ X5 )
=> ~ ( cP @ X6 ) )
=> ! [X7: a] :
( ( X5 @ X7 )
=> ~ ( X6 @ X7 ) ) )
=> ( X5 = X6 ) ) )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( @+[X6: a > $o] :
~ ! [X7: a > $o] :
( ~ ( ~ ( ( cP @ X6 )
=> ~ ( cP @ X7 ) )
=> ! [X8: a] :
( ( X6 @ X8 )
=> ~ ( X7 @ X8 ) ) )
=> ( X6 = X7 ) )
@ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( ( @+[X5: a > $o] :
~ ! [X6: a > $o] :
( ~ ( ~ ( ( cP @ X5 )
=> ~ ( cP @ X6 ) )
=> ! [X7: a] :
( ( X5 @ X7 )
=> ~ ( X6 @ X7 ) ) )
=> ( X5 = X6 ) ) )
= X4 ) )
@ X3 ) ) ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ ( ~ ( ( cP
@ @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( cP
@ @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ) )
=> ! [X1: a] :
( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
=> ~ ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) )
=> ( ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
= ( @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a] :
( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( ^ [X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) )
= ( ^ [X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) )
@ @+[X1: a] :
~ ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
=> ~ ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) )
=> ~ ( @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) )
@ @+[X1: a] :
~ ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
=> ~ ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a] :
( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
=> ~ ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( @+[X1: a > $o] :
~ ( ( cP @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) )
@ @+[X1: a] :
( @+[X2: a > $o] :
~ ( ( cP @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) )
@ @+[X1: a] :
( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( sP2
=> ~ ! [X1: a] :
~ ( @+[X2: a > $o] :
~ ( ( cP @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
@ X1 ) )
=> ( ( ( ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) )
@ @+[X1: a] :
( ( ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) )
!= ( @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) )
@ @+[X1: a] :
( ( ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ) )
!= ( ~ sP7 ) )
!= ( ~ sP7 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a > $o] :
( ~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ~ ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ @+[X2: a] :
~ ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( @+[X3: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) ) )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( @+[X5: a > $o] :
~ ! [X6: a > $o] :
( ~ ( ~ ( ( cP @ X5 )
=> ~ ( cP @ X6 ) )
=> ! [X7: a] :
( ( X5 @ X7 )
=> ~ ( X6 @ X7 ) ) )
=> ( X5 = X6 ) )
@ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) ) )
= X3 ) )
@ X2 ) ) ) )
=> ~ ( X1
@ @+[X2: a] :
~ ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( @+[X3: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) ) )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( @+[X5: a > $o] :
~ ! [X6: a > $o] :
( ~ ( ~ ( ( cP @ X5 )
=> ~ ( cP @ X6 ) )
=> ! [X7: a] :
( ( X5 @ X7 )
=> ~ ( X6 @ X7 ) ) )
=> ( X5 = X6 ) )
@ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) ) )
= X3 ) )
@ X2 ) ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) )
@ @+[X1: a] :
~ ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
=> ~ ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) )
@ @+[X1: a] :
( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) )
@ @+[X1: a] :
~ ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
=> ~ ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> $false ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ ( ~ ( ( cP
@ @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( cP
@ @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ) )
=> sP12 )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( sP2
=> sP14 ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: a > $o] :
( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) )
@ @+[X1: a] :
( ( ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) )
!= ( @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) )
@ @+[X1: a] :
( ( ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ) )
= ( ~ sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) )
@ @+[X1: a] :
( ( ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) )
= ( @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) )
@ @+[X1: a] :
( ( ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
!= ( @+[X2: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( @+[X4: a > $o] :
~ ! [X5: a > $o] :
( ~ ( ~ ( ( cP @ X4 )
=> ~ ( cP @ X5 ) )
=> ! [X6: a] :
( ( X4 @ X6 )
=> ~ ( X5 @ X6 ) ) )
=> ( X4 = X5 ) )
@ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) ) )
= X2 ) )
@ X1 ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2 @ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( ( ~ ( ~ ( ~ ( ( cP
@ @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( cP @ eigen__36 ) )
=> ! [X1: a] :
( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
=> ~ ( eigen__36 @ X1 ) ) )
=> ( ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
= eigen__36 ) ) )
= ( ~ sP5 ) ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( ~ ( ( cP
@ @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( cP
@ @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ) )
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ! [X1: a] :
~ ( @+[X2: a > $o] :
~ ( ( cP @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ! [X1: a > $o] :
( ( cP @ X1 )
=> ( X1
@ @+[X2: a] : ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ( ~ ( ~ ( ( cP
@ @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( cP
@ @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ) )
=> ~ sP20 )
=> ~ sP18 ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ! [X1: a > $o] :
( ~ ( ( sP2
=> ~ sP29 )
=> ( ( X1
@ @+[X2: a] :
( ( X1 @ X2 )
!= ( ~ ! [X3: a > $o] :
( ( cP @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
!= ( ~ ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ( X2
@ @+[X3: a] :
( ( X1 @ X3 )
!= ( ~ ! [X4: a > $o] :
( ( cP @ X4 )
=> ~ ( X4 @ X3 ) ) ) ) ) ) ) ) )
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ( ~ sP16
=> ~ sP22 ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( ( ~ sP25 ) = ( ~ sP7 ) ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(sP35,plain,
( sP35
<=> ( ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
= ( @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP35])]) ).
thf(sP36,plain,
( sP36
<=> ( ~ sP31
=> sP35 ) ),
introduced(definition,[new_symbols(definition,[sP36])]) ).
thf(sP37,plain,
( sP37
<=> ( ( cP
@ @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( cP
@ @+[X1: a > $o] :
~ ( ~ ( ~ ( ( cP
@ @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
=> ~ ( cP @ X1 ) )
=> ! [X2: a] :
( ( @+[X3: a > $o] :
~ ! [X4: a > $o] :
( ~ ( ~ ( ( cP @ X3 )
=> ~ ( cP @ X4 ) )
=> ! [X5: a] :
( ( X3 @ X5 )
=> ~ ( X4 @ X5 ) ) )
=> ( X3 = X4 ) )
@ X2 )
=> ~ ( X1 @ X2 ) ) )
=> ( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) ) )
= X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP37])]) ).
thf(sP38,plain,
( sP38
<=> ( ~ ( ~ ( ( cP
@ @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
=> ~ ( cP @ eigen__36 ) )
=> ! [X1: a] :
( ( @+[X2: a > $o] :
~ ! [X3: a > $o] :
( ~ ( ~ ( ( cP @ X2 )
=> ~ ( cP @ X3 ) )
=> ! [X4: a] :
( ( X2 @ X4 )
=> ~ ( X3 @ X4 ) ) )
=> ( X2 = X3 ) )
@ X1 )
=> ~ ( eigen__36 @ X1 ) ) )
=> ( ( @+[X1: a > $o] :
~ ! [X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) )
= eigen__36 ) ) ),
introduced(definition,[new_symbols(definition,[sP38])]) ).
thf(sP39,plain,
( sP39
<=> ! [X1: a > $o,X2: a > $o] :
( ~ ( ~ ( ( cP @ X1 )
=> ~ ( cP @ X2 ) )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ~ ( X2 @ X3 ) ) )
=> ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP39])]) ).
thf(sP40,plain,
( sP40
<=> ( ~ sP37
=> ~ sP20 ) ),
introduced(definition,[new_symbols(definition,[sP40])]) ).
thf(sP41,plain,
( sP41
<=> ( sP2
=> ~ sP29 ) ),
introduced(definition,[new_symbols(definition,[sP41])]) ).
thf(cTHM555_pme,conjecture,
( ~ ( ! [X1: a > $o] :
( ( cP @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) )
=> ~ sP1 )
=> ~ ! [X1: a > $o] :
( ~ ( ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
= ( ~ ! [X3: a > $o] :
( ( cP @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
=> ~ sP39 ) ) ).
thf(h1,negated_conjecture,
~ ( ~ ( ! [X1: a > $o] :
( ( cP @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) )
=> ~ sP1 )
=> ~ ! [X1: a > $o] :
( ~ ( ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
= ( ~ ! [X3: a > $o] :
( ( cP @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
=> ~ sP39 ) ),
inference(assume_negation,[status(cth)],[cTHM555_pme]) ).
thf(h2,assumption,
~ ( sP30
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP32,
introduced(assumption,[]) ).
thf(h4,assumption,
sP30,
introduced(assumption,[]) ).
thf(h5,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP10
| sP26 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP39
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP24
| sP38 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( sP27
| ~ sP38
| ~ sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP25
| ~ sP26
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(6,plain,
( sP25
| ~ sP26
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP34
| sP25
| sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP34
| ~ sP25
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP16
| ~ sP41
| ~ sP34 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP33
| sP16
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP3
| ~ sP27 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__36]) ).
thf(12,plain,
( sP11
| ~ sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP29
| ~ sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP32
| sP33 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP4
| sP10 ),
inference(choice_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP12
| sP13 ),
inference(choice_rule,[status(thm)],[]) ).
thf(17,plain,
~ sP21,
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP11
| sP6 ),
inference(symeq,[status(thm)],[]) ).
thf(19,plain,
( ~ sP19
| sP15
| sP21
| ~ sP11 ),
inference(mating_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP10
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP35
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP40
| sP37
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(23,plain,
( ~ sP31
| sP40
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
( ~ sP36
| sP31
| sP35 ),
inference(prop_rule,[status(thm)],[]) ).
thf(25,plain,
( ~ sP17
| sP36 ),
inference(all_rule,[status(thm)],[]) ).
thf(26,plain,
( sP28
| ~ sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(27,plain,
( sP28
| ~ sP37 ),
inference(prop_rule,[status(thm)],[]) ).
thf(28,plain,
( sP9
| ~ sP28 ),
inference(prop_rule,[status(thm)],[]) ).
thf(29,plain,
( ~ sP15
| sP19
| sP21
| ~ sP6 ),
inference(mating_rule,[status(thm)],[]) ).
thf(30,plain,
( ~ sP9
| sP24 ),
inference(choice_rule,[status(thm)],[]) ).
thf(31,plain,
( ~ sP24
| sP39 ),
inference(choice_rule,[status(thm)],[]) ).
thf(32,plain,
( sP12
| sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(33,plain,
( sP12
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(34,plain,
( sP4
| ~ sP15
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(35,plain,
( sP4
| sP15
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(36,plain,
( sP22
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(37,plain,
( ~ sP23
| ~ sP2
| sP14 ),
inference(prop_rule,[status(thm)],[]) ).
thf(38,plain,
( ~ sP8
| sP17 ),
inference(all_rule,[status(thm)],[]) ).
thf(39,plain,
( sP41
| sP29 ),
inference(prop_rule,[status(thm)],[]) ).
thf(40,plain,
( sP41
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(41,plain,
( ~ sP30
| sP23 ),
inference(all_rule,[status(thm)],[]) ).
thf(42,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(43,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h5,h2,h3,h1,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,h4,h5,h3]) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,43,h4,h5]) ).
thf(45,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,44,h2,h3]) ).
thf(46,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[45,h0]) ).
thf(0,theorem,
( ~ ( ! [X1: a > $o] :
( ( cP @ X1 )
=> ~ ! [X2: a] :
~ ( X1 @ X2 ) )
=> ~ sP1 )
=> ~ ! [X1: a > $o] :
( ~ ( ! [X2: a > $o] :
( ( cP @ X2 )
=> ~ ! [X3: a] :
~ ( X2 @ X3 ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
= ( ~ ! [X3: a > $o] :
( ( cP @ X3 )
=> ~ ( X3 @ X2 ) ) ) ) )
=> ~ sP39 ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[45,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEV174^5 : TPTP v9.2.0. Released v4.0.0.
% 0.09/0.11 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.32 % Computer : n015.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Wed Oct 8 19:34:23 EDT 2025
% 0.10/0.32 % CPUTime :
% 83.21/83.53 % SZS status Theorem
% 83.21/83.53 % Mode: cade22grackle2x4fb9
% 83.21/83.53 % Steps: 9431
% 83.21/83.53 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------