%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : LCL713^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 Aug 31 08:04:41 EDT 2023
% Result : Theorem 81.37s 81.61s
% Output : Proof 81.37s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(sP1,plain,
( sP1
<=> ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ @+[X1: $i] :
~ ( ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) ) )
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $i > $o] :
( ~ ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 )
=> ~ ( X1 @ X2 ) )
=> ! [X2: $i] :
( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 )
=> ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X2
@ @+[X3: $i] :
~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 )
=> ~ ( X1 @ X3 ) ) )
=> ~ ( X1
@ @+[X3: $i] :
~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 )
=> ~ ( X1 @ X3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ @+[X1: $i] :
~ ! [X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 ) ) )
=> ~ ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ @+[X1: $i] :
~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 )
=> ( ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) ) )
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 ) ) ) ) )
=> ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 ) )
@ @+[X1: $i] :
~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 )
=> ( ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) ) )
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ @+[X1: $i] :
~ ! [X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 ) ) )
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP1
=> ( ~ sP4
=> ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 ) )
@ @+[X1: $i] :
~ ( ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) ) )
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ~ sP4
=> ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 ) )
@ @+[X1: $i] :
~ ( ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) ) )
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 ) )
@ @+[X1: $i] :
~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 )
=> ( ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) ) )
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ~ ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 )
=> ( ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) ) )
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 ) ) )
=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 )
=> ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ X1
@ @+[X2: $i] :
~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 )
=> ( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ @+[X3: $i] :
~ ! [X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) ) )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X2 ) ) ) )
=> ( ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) ) )
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 )
=> ( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ @+[X3: $i] :
~ ! [X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) ) )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X2 ) ) ) ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ @+[X2: $i] :
~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 )
=> ( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ @+[X3: $i] :
~ ! [X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) ) )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP7
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i,X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ @+[X1: $i] :
~ ! [X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( @+[X1: $i > $i > $o] :
~ ( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) )
@ @+[X1: $i] :
~ ! [X2: $i] :
( ~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X1 )
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 ) )
@ @+[X1: $i] :
~ ( ~ ( sP10
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP10
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: $i,X2: $i > $o] :
( ~ ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X3 )
=> ~ ( X2 @ X3 ) )
=> ! [X3: $i] :
( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X1
@ X3 )
=> ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X3
@ @+[X4: $i] :
~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 )
=> ~ ( X2 @ X4 ) ) )
=> ~ ( X2
@ @+[X4: $i] :
~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 )
=> ~ ( X2 @ X4 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 )
=> ( ~ ( sP10
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: $i] :
( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X1 )
=> ~ ( ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ X1
@ @+[X2: $i] :
~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 )
=> ( ~ ( sP10
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X2 ) ) ) )
=> ( ~ ( sP10
=> ~ ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i,X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X2
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ @+[X2: $i] :
~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 )
=> ( ~ ( sP10
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X2 ) ) ) ) )
=> ( @+[X2: $i > $i > $o] :
~ ( ! [X3: $i,X4: $i > $o] :
( ~ ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ( X4 @ X5 ) )
=> ! [X5: $i] :
( ( X2 @ X3 @ X5 )
=> ~ ! [X6: $i] :
( ( X2 @ X5 @ X6 )
=> ~ ( X4 @ X6 ) ) ) )
=> ! [X3: $i,X4: $i,X5: $i] :
( ~ ( ( X2 @ X3 @ X4 )
=> ~ ( X2 @ X3 @ X5 ) )
=> ( X2 @ X4 @ X5 ) ) )
@ @+[X2: $i] :
~ ! [X3: $i] :
( ~ ( ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X2 )
=> ~ ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ @+[X4: $i] :
~ ! [X5: $i,X6: $i] :
( ~ ( ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X5 )
=> ~ ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X4
@ X6 ) )
=> ( @+[X7: $i > $i > $o] :
~ ( ! [X8: $i,X9: $i > $o] :
( ~ ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ( X9 @ X10 ) )
=> ! [X10: $i] :
( ( X7 @ X8 @ X10 )
=> ~ ! [X11: $i] :
( ( X7 @ X10 @ X11 )
=> ~ ( X9 @ X11 ) ) ) )
=> ! [X8: $i,X9: $i,X10: $i] :
( ~ ( ( X7 @ X8 @ X9 )
=> ~ ( X7 @ X8 @ X10 ) )
=> ( X7 @ X9 @ X10 ) ) )
@ X5
@ X6 ) )
@ X3 ) )
=> ( @+[X4: $i > $i > $o] :
~ ( ! [X5: $i,X6: $i > $o] :
( ~ ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ( X6 @ X7 ) )
=> ! [X7: $i] :
( ( X4 @ X5 @ X7 )
=> ~ ! [X8: $i] :
( ( X4 @ X7 @ X8 )
=> ~ ( X6 @ X8 ) ) ) )
=> ! [X5: $i,X6: $i,X7: $i] :
( ~ ( ( X4 @ X5 @ X6 )
=> ~ ( X4 @ X5 @ X7 ) )
=> ( X4 @ X6 @ X7 ) ) )
@ X2
@ X3 ) )
@ @+[X2: $i] :
~ ( ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ X1
@ X2 )
=> ( ~ ( sP10
=> ~ ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i,X5: $i] :
( ~ ( ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X4 )
=> ~ ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X3
@ X5 ) )
=> ( @+[X6: $i > $i > $o] :
~ ( ! [X7: $i,X8: $i > $o] :
( ~ ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ( X8 @ X9 ) )
=> ! [X9: $i] :
( ( X6 @ X7 @ X9 )
=> ~ ! [X10: $i] :
( ( X6 @ X9 @ X10 )
=> ~ ( X8 @ X10 ) ) ) )
=> ! [X7: $i,X8: $i,X9: $i] :
( ~ ( ( X6 @ X7 @ X8 )
=> ~ ( X6 @ X7 @ X9 ) )
=> ( X6 @ X8 @ X9 ) ) )
@ X4
@ X5 ) )
@ X2 ) )
=> ( @+[X3: $i > $i > $o] :
~ ( ! [X4: $i,X5: $i > $o] :
( ~ ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ( X5 @ X6 ) )
=> ! [X6: $i] :
( ( X3 @ X4 @ X6 )
=> ~ ! [X7: $i] :
( ( X3 @ X6 @ X7 )
=> ~ ( X5 @ X7 ) ) ) )
=> ! [X4: $i,X5: $i,X6: $i] :
( ~ ( ( X3 @ X4 @ X5 )
=> ~ ( X3 @ X4 @ X6 ) )
=> ( X3 @ X5 @ X6 ) ) )
@ @+[X3: $i] :
~ ! [X4: $i] :
( ~ ( ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X3 )
=> ~ ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ @+[X5: $i] :
~ ! [X6: $i,X7: $i] :
( ~ ( ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X6 )
=> ~ ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X5
@ X7 ) )
=> ( @+[X8: $i > $i > $o] :
~ ( ! [X9: $i,X10: $i > $o] :
( ~ ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ( X10 @ X11 ) )
=> ! [X11: $i] :
( ( X8 @ X9 @ X11 )
=> ~ ! [X12: $i] :
( ( X8 @ X11 @ X12 )
=> ~ ( X10 @ X12 ) ) ) )
=> ! [X9: $i,X10: $i,X11: $i] :
( ~ ( ( X8 @ X9 @ X10 )
=> ~ ( X8 @ X9 @ X11 ) )
=> ( X8 @ X10 @ X11 ) ) )
@ X6
@ X7 ) )
@ X4 ) )
=> ( @+[X5: $i > $i > $o] :
~ ( ! [X6: $i,X7: $i > $o] :
( ~ ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ( X7 @ X8 ) )
=> ! [X8: $i] :
( ( X5 @ X6 @ X8 )
=> ~ ! [X9: $i] :
( ( X5 @ X8 @ X9 )
=> ~ ( X7 @ X9 ) ) ) )
=> ! [X6: $i,X7: $i,X8: $i] :
( ~ ( ( X5 @ X6 @ X7 )
=> ~ ( X5 @ X6 @ X8 ) )
=> ( X5 @ X7 @ X8 ) ) )
@ X3
@ X4 ) )
@ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(def_meq_ind,definition,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
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] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( (~) @ ( X1 @ X3 @ X4 ) )
| ( X2 @ X4 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] :
( ( X1 @ X2 @ X3 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X4 )
@ ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X3 )
@ ? [X5: $i] :
( ( X1 @ X2 @ X5 )
& ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( ( X1 @ X3 @ X4 )
| ( X3 = X4 )
| ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ? [X5: $i] :
( ( X1 @ X3 @ X5 )
& ( X1 @ X4 @ X5 ) ) ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(conj,conjecture,
! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(h1,assumption,
sP13,
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h3,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP11,
introduced(assumption,[]) ).
thf(h5,assumption,
sP10,
introduced(assumption,[]) ).
thf(h6,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( sP3
| ~ sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP9
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP9
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP4
| ~ sP10
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP6
| sP4
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP12
| ~ sP10
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP5
| ~ sP1
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP15
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP14
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP8
| sP14
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP2
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(12,plain,
( ~ sP13
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h1,h5,h6,h4]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0,h0]),tab_negimp(discharge,[h5,h6])],[h3,13,h5,h6]) ).
thf(15,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0,h0]),tab_negimp(discharge,[h3,h4])],[h2,14,h3,h4]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0,h0]),tab_negimp(discharge,[h1,h2])],[h0,15,h1,h2]) ).
thf(0,theorem,
! [X1: $i > $i > $o] :
( ! [X2: $i,X3: $i > $o] :
( ~ ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ( X3 @ X4 ) )
=> ! [X4: $i] :
( ( X1 @ X2 @ X4 )
=> ~ ! [X5: $i] :
( ( X1 @ X4 @ X5 )
=> ~ ( X3 @ X5 ) ) ) )
=> ! [X2: $i,X3: $i,X4: $i] :
( ~ ( ( X1 @ X2 @ X3 )
=> ~ ( X1 @ X2 @ X4 ) )
=> ( X1 @ X3 @ X4 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL713^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% 0.11/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Aug 25 01:33:08 EDT 2023
% 0.11/0.33 % CPUTime :
% 81.37/81.61 % SZS status Theorem
% 81.37/81.61 % Mode: cade22grackle2x4fb9
% 81.37/81.61 % Steps: 285
% 81.37/81.61 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------