%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEV382^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 19:34:24 EDT 2023
% Result : Theorem 81.02s 81.42s
% Output : Proof 81.02s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( ( @+[X2: a > a > $o] :
~ ! [X3: a > $o] :
( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( X2 @ X6 @ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X2 @ X5 @ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ @+[X2: a] :
~ ( ( @+[X3: a > a > $o] :
~ ! [X4: a > $o] :
( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( X3 @ X7 @ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( X3 @ X6 @ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X2
@ X1 )
=> ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 ) )
@ X1 )
=> ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ @+[X2: a] :
~ ( ( @+[X3: a > a > $o] :
~ ! [X4: a > $o] :
( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( X3 @ X7 @ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( X3 @ X6 @ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X2
@ X1 )
=> ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 ) ) ) )
=> ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ! [X1: a] :
( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 )
=> ~ ( ~ ( @+[X1: a > $o] :
~ ( ~ ( ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ~ ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) )
=> ! [X2: a] : ( X1 @ X2 ) )
@ @+[X1: a] :
~ ( ~ ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 )
=> ~ ! [X2: a] :
( ( @+[X3: a > a > $o] :
~ ! [X4: a > $o] :
( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( X3 @ X7 @ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( X3 @ X6 @ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X2
@ X1 )
=> ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 ) ) ) )
=> ~ ! [X1: a] :
( ( @+[X2: a > a > $o] :
~ ! [X3: a > $o] :
( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( X2 @ X6 @ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X2 @ X5 @ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X1
@ @+[X2: a] :
~ ( ~ ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 )
=> ~ ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( @+[X4: a > $o] :
~ ( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( @+[X8: a > a > $o] :
~ ! [X9: a > $o] :
( ~ ( ! [X10: a > $o] :
( ~ ! [X11: a] :
~ ( X10 @ X11 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ~ ! [X12: a] :
( ( X8 @ X12 @ X11 )
=> ~ ( X10 @ X12 ) ) ) )
=> ~ ! [X10: a] :
( ! [X11: a] :
( ( X8 @ X11 @ X10 )
=> ( X9 @ X11 ) )
=> ( X9 @ X10 ) ) )
=> ! [X10: a] : ( X9 @ X10 ) )
@ X7
@ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X3 ) ) ) )
=> ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a] :
( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ~ ( @+[X1: a > $o] :
~ ( ~ ( ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ~ ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) )
=> ! [X2: a] : ( X1 @ X2 ) )
@ @+[X1: a] :
~ ( ~ ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 )
=> ~ ! [X2: a] :
( ( @+[X3: a > a > $o] :
~ ! [X4: a > $o] :
( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( X3 @ X7 @ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( X3 @ X6 @ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X2
@ X1 )
=> ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 ) ) ) )
=> ~ ! [X1: a] :
( ( @+[X2: a > a > $o] :
~ ! [X3: a > $o] :
( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( X2 @ X6 @ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X2 @ X5 @ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X1
@ @+[X2: a] :
~ ( ~ ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 )
=> ~ ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( @+[X4: a > $o] :
~ ( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( @+[X8: a > a > $o] :
~ ! [X9: a > $o] :
( ~ ( ! [X10: a > $o] :
( ~ ! [X11: a] :
~ ( X10 @ X11 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ~ ! [X12: a] :
( ( X8 @ X12 @ X11 )
=> ~ ( X10 @ X12 ) ) ) )
=> ~ ! [X10: a] :
( ! [X11: a] :
( ( X8 @ X11 @ X10 )
=> ( X9 @ X11 ) )
=> ( X9 @ X10 ) ) )
=> ! [X10: a] : ( X9 @ X10 ) )
@ X7
@ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X3 ) ) ) )
=> ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( @+[X2: a > a > $o] :
~ ! [X3: a > $o] :
( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( X2 @ X6 @ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X2 @ X5 @ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X1
@ @+[X2: a] :
~ ( ~ ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 )
=> ~ ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( @+[X4: a > $o] :
~ ( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( @+[X8: a > a > $o] :
~ ! [X9: a > $o] :
( ~ ( ! [X10: a > $o] :
( ~ ! [X11: a] :
~ ( X10 @ X11 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ~ ! [X12: a] :
( ( X8 @ X12 @ X11 )
=> ~ ( X10 @ X12 ) ) ) )
=> ~ ! [X10: a] :
( ! [X11: a] :
( ( X8 @ X11 @ X10 )
=> ( X9 @ X11 ) )
=> ( X9 @ X10 ) ) )
=> ! [X10: a] : ( X9 @ X10 ) )
@ X7
@ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X3 ) ) ) )
=> ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a > $o] :
( ~ ! [X2: a] :
~ ( X1 @ X2 )
=> ~ ( ( X1
@ @+[X2: a] :
~ ( ( X1 @ X2 )
=> ~ ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ~ ( X1 @ X3 ) ) ) )
=> ~ ! [X2: a] :
( ( @+[X3: a > a > $o] :
~ ! [X4: a > $o] :
( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( X3 @ X7 @ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( X3 @ X6 @ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X2
@ @+[X3: a] :
~ ( ( X1 @ X3 )
=> ~ ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ~ ( X1 @ X4 ) ) ) )
=> ~ ( X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( @+[X1: a > $o] :
~ ( ~ ( ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ~ ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) )
=> ! [X2: a] : ( X1 @ X2 ) )
@ @+[X1: a] :
~ ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( @+[X1: a > a > $o] :
~ ! [X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 @ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X1 @ X4 @ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ @+[X1: a] :
~ ( ( @+[X2: a > a > $o] :
~ ! [X3: a > $o] :
( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( X2 @ X6 @ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X2 @ X5 @ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X1
@ @+[X2: a] :
~ ( ~ ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 )
=> ~ ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( @+[X4: a > $o] :
~ ( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( @+[X8: a > a > $o] :
~ ! [X9: a > $o] :
( ~ ( ! [X10: a > $o] :
( ~ ! [X11: a] :
~ ( X10 @ X11 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ~ ! [X12: a] :
( ( X8 @ X12 @ X11 )
=> ~ ( X10 @ X12 ) ) ) )
=> ~ ! [X10: a] :
( ! [X11: a] :
( ( X8 @ X11 @ X10 )
=> ( X9 @ X11 ) )
=> ( X9 @ X10 ) ) )
=> ! [X10: a] : ( X9 @ X10 ) )
@ X7
@ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X3 ) ) ) )
=> ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 ) )
@ @+[X1: a] :
~ ( ~ ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 )
=> ~ ! [X2: a] :
( ( @+[X3: a > a > $o] :
~ ! [X4: a > $o] :
( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( X3 @ X7 @ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( X3 @ X6 @ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X2
@ X1 )
=> ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 ) ) ) )
=> ( @+[X1: a > $o] :
~ ( ~ ( ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ~ ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) )
=> ! [X2: a] : ( X1 @ X2 ) )
@ @+[X1: a] :
~ ( ( @+[X2: a > a > $o] :
~ ! [X3: a > $o] :
( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( X2 @ X6 @ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( X2 @ X5 @ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X1
@ @+[X2: a] :
~ ( ~ ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 )
=> ~ ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( @+[X4: a > $o] :
~ ( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( @+[X8: a > a > $o] :
~ ! [X9: a > $o] :
( ~ ( ! [X10: a > $o] :
( ~ ! [X11: a] :
~ ( X10 @ X11 )
=> ~ ! [X11: a] :
( ( X10 @ X11 )
=> ~ ! [X12: a] :
( ( X8 @ X12 @ X11 )
=> ~ ( X10 @ X12 ) ) ) )
=> ~ ! [X10: a] :
( ! [X11: a] :
( ( X8 @ X11 @ X10 )
=> ( X9 @ X11 ) )
=> ( X9 @ X10 ) ) )
=> ! [X10: a] : ( X9 @ X10 ) )
@ X7
@ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X3 ) ) ) )
=> ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( @+[X1: a > $o] :
~ ( ~ ( ! [X2: a > $o] :
( ~ ! [X3: a] :
~ ( X2 @ X3 )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ~ ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ~ ( X2 @ X4 ) ) ) )
=> ~ ! [X2: a] :
( ! [X3: a] :
( ( @+[X4: a > a > $o] :
~ ! [X5: a > $o] :
( ~ ( ! [X6: a > $o] :
( ~ ! [X7: a] :
~ ( X6 @ X7 )
=> ~ ! [X7: a] :
( ( X6 @ X7 )
=> ~ ! [X8: a] :
( ( X4 @ X8 @ X7 )
=> ~ ( X6 @ X8 ) ) ) )
=> ~ ! [X6: a] :
( ! [X7: a] :
( ( X4 @ X7 @ X6 )
=> ( X5 @ X7 ) )
=> ( X5 @ X6 ) ) )
=> ! [X6: a] : ( X5 @ X6 ) )
@ X3
@ X2 )
=> ( X1 @ X3 ) )
=> ( X1 @ X2 ) ) )
=> ! [X2: a] : ( X1 @ X2 ) )
@ @+[X1: a] :
~ ( ~ ( @+[X2: a > $o] :
~ ( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( @+[X5: a > a > $o] :
~ ! [X6: a > $o] :
( ~ ( ! [X7: a > $o] :
( ~ ! [X8: a] :
~ ( X7 @ X8 )
=> ~ ! [X8: a] :
( ( X7 @ X8 )
=> ~ ! [X9: a] :
( ( X5 @ X9 @ X8 )
=> ~ ( X7 @ X9 ) ) ) )
=> ~ ! [X7: a] :
( ! [X8: a] :
( ( X5 @ X8 @ X7 )
=> ( X6 @ X8 ) )
=> ( X6 @ X7 ) ) )
=> ! [X7: a] : ( X6 @ X7 ) )
@ X4
@ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) )
@ X1 )
=> ~ ! [X2: a] :
( ( @+[X3: a > a > $o] :
~ ! [X4: a > $o] :
( ~ ( ! [X5: a > $o] :
( ~ ! [X6: a] :
~ ( X5 @ X6 )
=> ~ ! [X6: a] :
( ( X5 @ X6 )
=> ~ ! [X7: a] :
( ( X3 @ X7 @ X6 )
=> ~ ( X5 @ X7 ) ) ) )
=> ~ ! [X5: a] :
( ! [X6: a] :
( ( X3 @ X6 @ X5 )
=> ( X4 @ X6 ) )
=> ( X4 @ X5 ) ) )
=> ! [X5: a] : ( X4 @ X5 ) )
@ X2
@ X1 )
=> ( @+[X3: a > $o] :
~ ( ~ ( ! [X4: a > $o] :
( ~ ! [X5: a] :
~ ( X4 @ X5 )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ~ ! [X6: a] :
( ( @+[X7: a > a > $o] :
~ ! [X8: a > $o] :
( ~ ( ! [X9: a > $o] :
( ~ ! [X10: a] :
~ ( X9 @ X10 )
=> ~ ! [X10: a] :
( ( X9 @ X10 )
=> ~ ! [X11: a] :
( ( X7 @ X11 @ X10 )
=> ~ ( X9 @ X11 ) ) ) )
=> ~ ! [X9: a] :
( ! [X10: a] :
( ( X7 @ X10 @ X9 )
=> ( X8 @ X10 ) )
=> ( X8 @ X9 ) ) )
=> ! [X9: a] : ( X8 @ X9 ) )
@ X6
@ X5 )
=> ~ ( X4 @ X6 ) ) ) )
=> ~ ! [X4: a] :
( ! [X5: a] :
( ( @+[X6: a > a > $o] :
~ ! [X7: a > $o] :
( ~ ( ! [X8: a > $o] :
( ~ ! [X9: a] :
~ ( X8 @ X9 )
=> ~ ! [X9: a] :
( ( X8 @ X9 )
=> ~ ! [X10: a] :
( ( X6 @ X10 @ X9 )
=> ~ ( X8 @ X10 ) ) ) )
=> ~ ! [X8: a] :
( ! [X9: a] :
( ( X6 @ X9 @ X8 )
=> ( X7 @ X9 ) )
=> ( X7 @ X8 ) ) )
=> ! [X8: a] : ( X7 @ X8 ) )
@ X5
@ X4 )
=> ( X3 @ X5 ) )
=> ( X3 @ X4 ) ) )
=> ! [X4: a] : ( X3 @ X4 ) )
@ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( sP8
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(cTRANS_IND,conjecture,
! [X1: a > a > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 @ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X1 @ X4 @ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: a > a > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 @ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X1 @ X4 @ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) ),
inference(assume_negation,[status(cth)],[cTRANS_IND]) ).
thf(h1,assumption,
~ ( sP6
=> ~ sP1 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP7,
introduced(assumption,[]) ).
thf(h3,assumption,
sP6,
introduced(assumption,[]) ).
thf(h4,assumption,
sP1,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP5
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP10
| ~ sP8
| sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP1
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( sP4
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP3
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP2
| sP3
| ~ sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP6
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h3,h4,h1,h2,h0,h0])],[1,2,3,4,5,6,7,8,h3,h4,h2]) ).
thf(10,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0,h0]),tab_negimp(discharge,[h3,h4])],[h1,9,h3,h4]) ).
thf(11,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0,h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).
thf(0,theorem,
! [X1: a > a > $o,X2: a > $o] :
( ~ ( ! [X3: a > $o] :
( ~ ! [X4: a] :
~ ( X3 @ X4 )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ~ ! [X5: a] :
( ( X1 @ X5 @ X4 )
=> ~ ( X3 @ X5 ) ) ) )
=> ~ ! [X3: a] :
( ! [X4: a] :
( ( X1 @ X4 @ X3 )
=> ( X2 @ X4 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] : ( X2 @ X3 ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV382^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.10/0.31 % Computer : n017.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Aug 24 02:28:54 EDT 2023
% 0.10/0.31 % CPUTime :
% 81.02/81.42 % SZS status Theorem
% 81.02/81.42 % Mode: cade22grackle2x4fb9
% 81.02/81.42 % Steps: 520
% 81.02/81.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------