%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SYO250^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:07:55 AM UTC 2026
% Result : Theorem 1.09s 0.45s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 1
% Syntax : Number of formulae : 51 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 4147 (4096 equ; 0 cnn)
% Maximal formula atoms : 90 ( 81 avg)
% Number of connectives : 19889 (13139 ~;3578 |; 380 &;2752 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 72 ( 8 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 1 usr; 2 con; 0-13 aty)
% Number of variables : 601 ( 0 ^; 541 !; 60 ?; 601 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_SY90,type,
sK1_SY90: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(1,conjecture,
? [Xa: $i,Xaa: $i,Xb: $i,Xbb: $i,Xc: $i,Xcc: $i,Xd: $i,Xdd: $i,Xe: $i,Xee: $i,Xh: $i,Xhh: $i] :
( ( ( Xa != Xaa )
& ( Xa != Xb )
& ( Xa != Xbb )
& ( Xa != Xc )
& ( Xa != Xcc )
& ( Xa != Xd )
& ( Xa != Xdd )
& ( Xa != Xe )
& ( Xa != Xee )
& ( Xa != Xh )
& ( Xa != Xhh )
& ( Xaa != Xb )
& ( Xaa != Xbb )
& ( Xaa != Xc )
& ( Xaa != Xcc )
& ( Xaa != Xd )
& ( Xaa != Xdd )
& ( Xaa != Xe )
& ( Xaa != Xee )
& ( Xaa != Xh )
& ( Xaa != Xhh )
& ( Xb != Xbb )
& ( Xb != Xc )
& ( Xb != Xcc )
& ( Xb != Xd )
& ( Xb != Xdd )
& ( Xb != Xe )
& ( Xb != Xee )
& ( Xb != Xh )
& ( Xb != Xhh )
& ( Xc != Xcc )
& ( Xc != Xd )
& ( Xc != Xdd )
& ( Xc != Xe )
& ( Xc != Xee )
& ( Xc != Xh )
& ( Xc != Xhh )
& ( Xcc != Xd )
& ( Xcc != Xdd )
& ( Xcc != Xe )
& ( Xcc != Xee )
& ( Xcc != Xh )
& ( Xcc != Xhh )
& ( Xd != Xdd )
& ( Xd != Xe )
& ( Xd != Xee )
& ( Xd != Xh )
& ( Xd != Xhh )
& ( Xdd != Xe )
& ( Xdd != Xee )
& ( Xdd != Xh )
& ( Xdd != Xhh )
& ( Xe != Xee )
& ( Xe != Xh )
& ( Xe != Xhh )
& ( Xee != Xh )
& ( Xee != Xhh )
& ( Xh != Xhh ) )
=> ! [P: $i > $i] :
( ( ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xe )
= ( P @ Xhh ) ) )
=> ( ( P @ Xc )
= ( P @ Xdd ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xb )
= ( P @ Xcc ) ) )
=> ( ( P @ Xd )
!= ( P @ Xee ) ) )
& ( ( ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xcc )
= ( P @ Xd ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xa )
!= ( P @ Xbb ) ) )
=> ( ( P @ Xe )
!= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xb )
!= ( P @ Xcc ) ) )
=> ( ( P @ Xe )
= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xe )
= ( P @ Xee ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xc )
= ( P @ Xdd ) ) )
=> ( ( P @ Xa )
!= ( P @ Xbb ) ) )
& ( ( ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xbb )
= ( P @ Xc ) )
& ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xe )
!= ( P @ Xhh ) ) )
=> ( ( P @ Xd )
= ( P @ Xee ) ) ) )
=> ( ( ( P @ Xa )
!= ( P @ Xaa ) )
| ( ( P @ Xb )
!= ( P @ Xbb ) )
| ( ( P @ Xc )
!= ( P @ Xcc ) )
| ( ( P @ Xd )
!= ( P @ Xdd ) )
| ( ( P @ Xe )
!= ( P @ Xee ) )
| ( ( P @ Xh )
!= ( P @ Xhh ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSIXFRIENDS) ).
thf(2,negated_conjecture,
( ( ? [Xa: $i,Xaa: $i,Xb: $i,Xbb: $i,Xc: $i,Xcc: $i,Xd: $i,Xdd: $i,Xe: $i,Xee: $i,Xh: $i,Xhh: $i] :
( ( ( Xa != Xaa )
& ( Xa != Xb )
& ( Xa != Xbb )
& ( Xa != Xc )
& ( Xa != Xcc )
& ( Xa != Xd )
& ( Xa != Xdd )
& ( Xa != Xe )
& ( Xa != Xee )
& ( Xa != Xh )
& ( Xa != Xhh )
& ( Xaa != Xb )
& ( Xaa != Xbb )
& ( Xaa != Xc )
& ( Xaa != Xcc )
& ( Xaa != Xd )
& ( Xaa != Xdd )
& ( Xaa != Xe )
& ( Xaa != Xee )
& ( Xaa != Xh )
& ( Xaa != Xhh )
& ( Xb != Xbb )
& ( Xb != Xc )
& ( Xb != Xcc )
& ( Xb != Xd )
& ( Xb != Xdd )
& ( Xb != Xe )
& ( Xb != Xee )
& ( Xb != Xh )
& ( Xb != Xhh )
& ( Xc != Xcc )
& ( Xc != Xd )
& ( Xc != Xdd )
& ( Xc != Xe )
& ( Xc != Xee )
& ( Xc != Xh )
& ( Xc != Xhh )
& ( Xcc != Xd )
& ( Xcc != Xdd )
& ( Xcc != Xe )
& ( Xcc != Xee )
& ( Xcc != Xh )
& ( Xcc != Xhh )
& ( Xd != Xdd )
& ( Xd != Xe )
& ( Xd != Xee )
& ( Xd != Xh )
& ( Xd != Xhh )
& ( Xdd != Xe )
& ( Xdd != Xee )
& ( Xdd != Xh )
& ( Xdd != Xhh )
& ( Xe != Xee )
& ( Xe != Xh )
& ( Xe != Xhh )
& ( Xee != Xh )
& ( Xee != Xhh )
& ( Xh != Xhh ) )
=> ! [P: $i > $i] :
( ( ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xe )
= ( P @ Xhh ) ) )
=> ( ( P @ Xc )
= ( P @ Xdd ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xb )
= ( P @ Xcc ) ) )
=> ( ( P @ Xd )
!= ( P @ Xee ) ) )
& ( ( ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xcc )
= ( P @ Xd ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xa )
!= ( P @ Xbb ) ) )
=> ( ( P @ Xe )
!= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xb )
!= ( P @ Xcc ) ) )
=> ( ( P @ Xe )
= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xe )
= ( P @ Xee ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xc )
= ( P @ Xdd ) ) )
=> ( ( P @ Xa )
!= ( P @ Xbb ) ) )
& ( ( ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xbb )
= ( P @ Xc ) )
& ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xe )
!= ( P @ Xhh ) ) )
=> ( ( P @ Xd )
= ( P @ Xee ) ) ) )
=> ( ( ( P @ Xa )
!= ( P @ Xaa ) )
| ( ( P @ Xb )
!= ( P @ Xbb ) )
| ( ( P @ Xc )
!= ( P @ Xcc ) )
| ( ( P @ Xd )
!= ( P @ Xdd ) )
| ( ( P @ Xe )
!= ( P @ Xee ) )
| ( ( P @ Xh )
!= ( P @ Xhh ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ? [Xa: $i,Xaa: $i,Xb: $i,Xbb: $i,Xc: $i,Xcc: $i,Xd: $i,Xdd: $i,Xe: $i,Xee: $i,Xh: $i,Xhh: $i] :
( ( ( Xa != Xaa )
& ( Xa != Xb )
& ( Xa != Xbb )
& ( Xa != Xc )
& ( Xa != Xcc )
& ( Xa != Xd )
& ( Xa != Xdd )
& ( Xa != Xe )
& ( Xa != Xee )
& ( Xa != Xh )
& ( Xa != Xhh )
& ( Xaa != Xb )
& ( Xaa != Xbb )
& ( Xaa != Xc )
& ( Xaa != Xcc )
& ( Xaa != Xd )
& ( Xaa != Xdd )
& ( Xaa != Xe )
& ( Xaa != Xee )
& ( Xaa != Xh )
& ( Xaa != Xhh )
& ( Xb != Xbb )
& ( Xb != Xc )
& ( Xb != Xcc )
& ( Xb != Xd )
& ( Xb != Xdd )
& ( Xb != Xe )
& ( Xb != Xee )
& ( Xb != Xh )
& ( Xb != Xhh )
& ( Xc != Xcc )
& ( Xc != Xd )
& ( Xc != Xdd )
& ( Xc != Xe )
& ( Xc != Xee )
& ( Xc != Xh )
& ( Xc != Xhh )
& ( Xcc != Xd )
& ( Xcc != Xdd )
& ( Xcc != Xe )
& ( Xcc != Xee )
& ( Xcc != Xh )
& ( Xcc != Xhh )
& ( Xd != Xdd )
& ( Xd != Xe )
& ( Xd != Xee )
& ( Xd != Xh )
& ( Xd != Xhh )
& ( Xdd != Xe )
& ( Xdd != Xee )
& ( Xdd != Xh )
& ( Xdd != Xhh )
& ( Xe != Xee )
& ( Xe != Xh )
& ( Xe != Xhh )
& ( Xee != Xh )
& ( Xee != Xhh )
& ( Xh != Xhh ) )
=> ! [P: $i > $i] :
( ( ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xe )
= ( P @ Xhh ) ) )
=> ( ( P @ Xc )
= ( P @ Xdd ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xb )
= ( P @ Xcc ) ) )
=> ( ( P @ Xd )
!= ( P @ Xee ) ) )
& ( ( ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xcc )
= ( P @ Xd ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xa )
!= ( P @ Xbb ) ) )
=> ( ( P @ Xe )
!= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xb )
!= ( P @ Xcc ) ) )
=> ( ( P @ Xe )
= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xe )
= ( P @ Xee ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xc )
= ( P @ Xdd ) ) )
=> ( ( P @ Xa )
!= ( P @ Xbb ) ) )
& ( ( ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xbb )
= ( P @ Xc ) )
& ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xe )
!= ( P @ Xhh ) ) )
=> ( ( P @ Xd )
= ( P @ Xee ) ) ) )
=> ( ( ( P @ Xa )
!= ( P @ Xaa ) )
| ( ( P @ Xb )
!= ( P @ Xbb ) )
| ( ( P @ Xc )
!= ( P @ Xcc ) )
| ( ( P @ Xd )
!= ( P @ Xdd ) )
| ( ( P @ Xe )
!= ( P @ Xee ) )
| ( ( P @ Xh )
!= ( P @ Xhh ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [Xa: $i,Xaa: $i,Xb: $i,Xbb: $i,Xc: $i,Xcc: $i,Xd: $i,Xdd: $i,Xe: $i,Xee: $i,Xh: $i,Xhh: $i] :
( ( ( Xa != Xaa )
& ( Xa != Xb )
& ( Xa != Xbb )
& ( Xa != Xc )
& ( Xa != Xcc )
& ( Xa != Xd )
& ( Xa != Xdd )
& ( Xa != Xe )
& ( Xa != Xee )
& ( Xa != Xh )
& ( Xa != Xhh )
& ( Xaa != Xb )
& ( Xaa != Xbb )
& ( Xaa != Xc )
& ( Xaa != Xcc )
& ( Xaa != Xd )
& ( Xaa != Xdd )
& ( Xaa != Xe )
& ( Xaa != Xee )
& ( Xaa != Xh )
& ( Xaa != Xhh )
& ( Xb != Xbb )
& ( Xb != Xc )
& ( Xb != Xcc )
& ( Xb != Xd )
& ( Xb != Xdd )
& ( Xb != Xe )
& ( Xb != Xee )
& ( Xb != Xh )
& ( Xb != Xhh )
& ( Xc != Xcc )
& ( Xc != Xd )
& ( Xc != Xdd )
& ( Xc != Xe )
& ( Xc != Xee )
& ( Xc != Xh )
& ( Xc != Xhh )
& ( Xcc != Xd )
& ( Xcc != Xdd )
& ( Xcc != Xe )
& ( Xcc != Xee )
& ( Xcc != Xh )
& ( Xcc != Xhh )
& ( Xd != Xdd )
& ( Xd != Xe )
& ( Xd != Xee )
& ( Xd != Xh )
& ( Xd != Xhh )
& ( Xdd != Xe )
& ( Xdd != Xee )
& ( Xdd != Xh )
& ( Xdd != Xhh )
& ( Xe != Xee )
& ( Xe != Xh )
& ( Xe != Xhh )
& ( Xee != Xh )
& ( Xee != Xhh )
& ( Xh != Xhh ) )
=> ! [P: $i > $i] :
( ( ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xe )
= ( P @ Xhh ) ) )
=> ( ( P @ Xc )
= ( P @ Xdd ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xb )
= ( P @ Xcc ) ) )
=> ( ( P @ Xd )
!= ( P @ Xee ) ) )
& ( ( ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xcc )
= ( P @ Xd ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xa )
!= ( P @ Xbb ) ) )
=> ( ( P @ Xe )
!= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xb )
!= ( P @ Xcc ) ) )
=> ( ( P @ Xe )
= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xe )
= ( P @ Xee ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xc )
= ( P @ Xdd ) ) )
=> ( ( P @ Xa )
!= ( P @ Xbb ) ) )
& ( ( ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xbb )
= ( P @ Xc ) )
& ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xe )
!= ( P @ Xhh ) ) )
=> ( ( P @ Xd )
= ( P @ Xee ) ) ) )
=> ( ( ( P @ Xa )
!= ( P @ Xaa ) )
| ( ( P @ Xb )
!= ( P @ Xbb ) )
| ( ( P @ Xc )
!= ( P @ Xcc ) )
| ( ( P @ Xd )
!= ( P @ Xdd ) )
| ( ( P @ Xe )
!= ( P @ Xee ) )
| ( ( P @ Xh )
!= ( P @ Xhh ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ? [Xa: $i,Xaa: $i,Xb: $i,Xbb: $i,Xc: $i,Xcc: $i,Xd: $i,Xdd: $i,Xe: $i,Xee: $i,Xh: $i,Xhh: $i] :
( ( ( Xa != Xaa )
& ( Xa != Xb )
& ( Xa != Xbb )
& ( Xa != Xc )
& ( Xa != Xcc )
& ( Xa != Xd )
& ( Xa != Xdd )
& ( Xa != Xe )
& ( Xa != Xee )
& ( Xa != Xh )
& ( Xa != Xhh )
& ( Xaa != Xb )
& ( Xaa != Xbb )
& ( Xaa != Xc )
& ( Xaa != Xcc )
& ( Xaa != Xd )
& ( Xaa != Xdd )
& ( Xaa != Xe )
& ( Xaa != Xee )
& ( Xaa != Xh )
& ( Xaa != Xhh )
& ( Xb != Xbb )
& ( Xb != Xc )
& ( Xb != Xcc )
& ( Xb != Xd )
& ( Xb != Xdd )
& ( Xb != Xe )
& ( Xb != Xee )
& ( Xb != Xh )
& ( Xb != Xhh )
& ( Xc != Xcc )
& ( Xc != Xd )
& ( Xc != Xdd )
& ( Xc != Xe )
& ( Xc != Xee )
& ( Xc != Xh )
& ( Xc != Xhh )
& ( Xcc != Xd )
& ( Xcc != Xdd )
& ( Xcc != Xe )
& ( Xcc != Xee )
& ( Xcc != Xh )
& ( Xcc != Xhh )
& ( Xd != Xdd )
& ( Xd != Xe )
& ( Xd != Xee )
& ( Xd != Xh )
& ( Xd != Xhh )
& ( Xdd != Xe )
& ( Xdd != Xee )
& ( Xdd != Xh )
& ( Xdd != Xhh )
& ( Xe != Xee )
& ( Xe != Xh )
& ( Xe != Xhh )
& ( Xee != Xh )
& ( Xee != Xhh )
& ( Xh != Xhh ) )
=> ! [P: $i > $i] :
( ( ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xe )
= ( P @ Xhh ) ) )
=> ( ( P @ Xc )
= ( P @ Xdd ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xb )
= ( P @ Xcc ) ) )
=> ( ( P @ Xd )
!= ( P @ Xee ) ) )
& ( ( ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xcc )
= ( P @ Xd ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xa )
!= ( P @ Xbb ) ) )
=> ( ( P @ Xe )
!= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xa )
= ( P @ Xaa ) )
& ( ( P @ Xd )
= ( P @ Xdd ) )
& ( ( P @ Xb )
!= ( P @ Xcc ) ) )
=> ( ( P @ Xe )
= ( P @ Xhh ) ) )
& ( ( ( ( P @ Xe )
= ( P @ Xee ) )
& ( ( P @ Xh )
= ( P @ Xhh ) )
& ( ( P @ Xc )
= ( P @ Xdd ) ) )
=> ( ( P @ Xa )
!= ( P @ Xbb ) ) )
& ( ( ( ( P @ Xb )
= ( P @ Xbb ) )
& ( ( P @ Xbb )
= ( P @ Xc ) )
& ( ( P @ Xc )
= ( P @ Xcc ) )
& ( ( P @ Xe )
!= ( P @ Xhh ) ) )
=> ( ( P @ Xd )
= ( P @ Xee ) ) ) )
=> ( ( ( P @ Xa )
!= ( P @ Xaa ) )
| ( ( P @ Xb )
!= ( P @ Xbb ) )
| ( ( P @ Xc )
!= ( P @ Xcc ) )
| ( ( P @ Xd )
!= ( P @ Xdd ) )
| ( ( P @ Xe )
!= ( P @ Xee ) )
| ( ( P @ Xh )
!= ( P @ Xhh ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(6,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ! [SX8: $i] :
~ ~ ! [SX9: $i] :
~ ~ ! [SX10: $i] :
~ ~ ! [SX11: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( ( SX0 != SX2 ) ) )
| ~ ( ( SX0 != SX3 ) ) )
| ~ ( ( SX0 != SX4 ) ) )
| ~ ( ( SX0 != SX5 ) ) )
| ~ ( ( SX0 != SX6 ) ) )
| ~ ( ( SX0 != SX7 ) ) )
| ~ ( ( SX0 != SX8 ) ) )
| ~ ( ( SX0 != SX9 ) ) )
| ~ ( ( SX0 != SX10 ) ) )
| ~ ( ( SX0 != SX11 ) ) )
| ~ ( ( SX1 != SX2 ) ) )
| ~ ( ( SX1 != SX3 ) ) )
| ~ ( ( SX1 != SX4 ) ) )
| ~ ( ( SX1 != SX5 ) ) )
| ~ ( ( SX1 != SX6 ) ) )
| ~ ( ( SX1 != SX7 ) ) )
| ~ ( ( SX1 != SX8 ) ) )
| ~ ( ( SX1 != SX9 ) ) )
| ~ ( ( SX1 != SX10 ) ) )
| ~ ( ( SX1 != SX11 ) ) )
| ~ ( ( SX2 != SX3 ) ) )
| ~ ( ( SX2 != SX4 ) ) )
| ~ ( ( SX2 != SX5 ) ) )
| ~ ( ( SX2 != SX6 ) ) )
| ~ ( ( SX2 != SX7 ) ) )
| ~ ( ( SX2 != SX8 ) ) )
| ~ ( ( SX2 != SX9 ) ) )
| ~ ( ( SX2 != SX10 ) ) )
| ~ ( ( SX2 != SX11 ) ) )
| ~ ( ( SX4 != SX5 ) ) )
| ~ ( ( SX4 != SX6 ) ) )
| ~ ( ( SX4 != SX7 ) ) )
| ~ ( ( SX4 != SX8 ) ) )
| ~ ( ( SX4 != SX9 ) ) )
| ~ ( ( SX4 != SX10 ) ) )
| ~ ( ( SX4 != SX11 ) ) )
| ~ ( ( SX5 != SX6 ) ) )
| ~ ( ( SX5 != SX7 ) ) )
| ~ ( ( SX5 != SX8 ) ) )
| ~ ( ( SX5 != SX9 ) ) )
| ~ ( ( SX5 != SX10 ) ) )
| ~ ( ( SX5 != SX11 ) ) )
| ~ ( ( SX6 != SX7 ) ) )
| ~ ( ( SX6 != SX8 ) ) )
| ~ ( ( SX6 != SX9 ) ) )
| ~ ( ( SX6 != SX10 ) ) )
| ~ ( ( SX6 != SX11 ) ) )
| ~ ( ( SX7 != SX8 ) ) )
| ~ ( ( SX7 != SX9 ) ) )
| ~ ( ( SX7 != SX10 ) ) )
| ~ ( ( SX7 != SX11 ) ) )
| ~ ( ( SX8 != SX9 ) ) )
| ~ ( ( SX8 != SX10 ) ) )
| ~ ( ( SX8 != SX11 ) ) )
| ~ ( ( SX9 != SX10 ) ) )
| ~ ( ( SX9 != SX11 ) ) )
| ~ ( ( SX10 != SX11 ) ) )
| ! [SX12: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX2 )
!= ( SX12 @ SX3 ) ) )
| ( ( SX12 @ SX8 )
!= ( SX12 @ SX11 ) ) )
| ( ( SX12 @ SX4 )
= ( SX12 @ SX7 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX10 )
!= ( SX12 @ SX11 ) ) )
| ( ( SX12 @ SX2 )
!= ( SX12 @ SX5 ) ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX9 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX4 )
!= ( SX12 @ SX5 ) )
| ( ( SX12 @ SX5 )
!= ( SX12 @ SX6 ) ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX7 ) ) )
| ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX3 ) ) ) )
| ( ( SX12 @ SX8 )
!= ( SX12 @ SX11 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX7 ) ) )
| ~ ( ( ( SX12 @ SX2 )
!= ( SX12 @ SX5 ) ) ) )
| ( ( SX12 @ SX8 )
= ( SX12 @ SX11 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX8 )
!= ( SX12 @ SX9 ) )
| ( ( SX12 @ SX10 )
!= ( SX12 @ SX11 ) ) )
| ( ( SX12 @ SX4 )
!= ( SX12 @ SX7 ) ) )
| ( ( SX12 @ SX0 )
!= ( SX12 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX2 )
!= ( SX12 @ SX3 ) )
| ( ( SX12 @ SX3 )
!= ( SX12 @ SX4 ) ) )
| ( ( SX12 @ SX4 )
!= ( SX12 @ SX5 ) ) )
| ~ ( ( ( SX12 @ SX8 )
!= ( SX12 @ SX11 ) ) ) )
| ( ( SX12 @ SX6 )
= ( SX12 @ SX9 ) ) ) )
| ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX2 )
!= ( SX12 @ SX3 ) )
| ( ( SX12 @ SX4 )
!= ( SX12 @ SX5 ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX7 ) )
| ( ( SX12 @ SX8 )
!= ( SX12 @ SX9 ) )
| ( ( SX12 @ SX10 )
!= ( SX12 @ SX11 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ! [SX8: $i] :
~ ~ ! [SX9: $i] :
~ ~ ! [SX10: $i] :
~ ~ ! [SX11: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( ( SX0 != SX2 ) ) )
| ~ ( ( SX0 != SX3 ) ) )
| ~ ( ( SX0 != SX4 ) ) )
| ~ ( ( SX0 != SX5 ) ) )
| ~ ( ( SX0 != SX6 ) ) )
| ~ ( ( SX0 != SX7 ) ) )
| ~ ( ( SX0 != SX8 ) ) )
| ~ ( ( SX0 != SX9 ) ) )
| ~ ( ( SX0 != SX10 ) ) )
| ~ ( ( SX0 != SX11 ) ) )
| ~ ( ( SX1 != SX2 ) ) )
| ~ ( ( SX1 != SX3 ) ) )
| ~ ( ( SX1 != SX4 ) ) )
| ~ ( ( SX1 != SX5 ) ) )
| ~ ( ( SX1 != SX6 ) ) )
| ~ ( ( SX1 != SX7 ) ) )
| ~ ( ( SX1 != SX8 ) ) )
| ~ ( ( SX1 != SX9 ) ) )
| ~ ( ( SX1 != SX10 ) ) )
| ~ ( ( SX1 != SX11 ) ) )
| ~ ( ( SX2 != SX3 ) ) )
| ~ ( ( SX2 != SX4 ) ) )
| ~ ( ( SX2 != SX5 ) ) )
| ~ ( ( SX2 != SX6 ) ) )
| ~ ( ( SX2 != SX7 ) ) )
| ~ ( ( SX2 != SX8 ) ) )
| ~ ( ( SX2 != SX9 ) ) )
| ~ ( ( SX2 != SX10 ) ) )
| ~ ( ( SX2 != SX11 ) ) )
| ~ ( ( SX4 != SX5 ) ) )
| ~ ( ( SX4 != SX6 ) ) )
| ~ ( ( SX4 != SX7 ) ) )
| ~ ( ( SX4 != SX8 ) ) )
| ~ ( ( SX4 != SX9 ) ) )
| ~ ( ( SX4 != SX10 ) ) )
| ~ ( ( SX4 != SX11 ) ) )
| ~ ( ( SX5 != SX6 ) ) )
| ~ ( ( SX5 != SX7 ) ) )
| ~ ( ( SX5 != SX8 ) ) )
| ~ ( ( SX5 != SX9 ) ) )
| ~ ( ( SX5 != SX10 ) ) )
| ~ ( ( SX5 != SX11 ) ) )
| ~ ( ( SX6 != SX7 ) ) )
| ~ ( ( SX6 != SX8 ) ) )
| ~ ( ( SX6 != SX9 ) ) )
| ~ ( ( SX6 != SX10 ) ) )
| ~ ( ( SX6 != SX11 ) ) )
| ~ ( ( SX7 != SX8 ) ) )
| ~ ( ( SX7 != SX9 ) ) )
| ~ ( ( SX7 != SX10 ) ) )
| ~ ( ( SX7 != SX11 ) ) )
| ~ ( ( SX8 != SX9 ) ) )
| ~ ( ( SX8 != SX10 ) ) )
| ~ ( ( SX8 != SX11 ) ) )
| ~ ( ( SX9 != SX10 ) ) )
| ~ ( ( SX9 != SX11 ) ) )
| ~ ( ( SX10 != SX11 ) ) )
| ! [SX12: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX2 )
!= ( SX12 @ SX3 ) ) )
| ( ( SX12 @ SX8 )
!= ( SX12 @ SX11 ) ) )
| ( ( SX12 @ SX4 )
= ( SX12 @ SX7 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX10 )
!= ( SX12 @ SX11 ) ) )
| ( ( SX12 @ SX2 )
!= ( SX12 @ SX5 ) ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX9 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX4 )
!= ( SX12 @ SX5 ) )
| ( ( SX12 @ SX5 )
!= ( SX12 @ SX6 ) ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX7 ) ) )
| ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX3 ) ) ) )
| ( ( SX12 @ SX8 )
!= ( SX12 @ SX11 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX7 ) ) )
| ~ ( ( ( SX12 @ SX2 )
!= ( SX12 @ SX5 ) ) ) )
| ( ( SX12 @ SX8 )
= ( SX12 @ SX11 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX8 )
!= ( SX12 @ SX9 ) )
| ( ( SX12 @ SX10 )
!= ( SX12 @ SX11 ) ) )
| ( ( SX12 @ SX4 )
!= ( SX12 @ SX7 ) ) )
| ( ( SX12 @ SX0 )
!= ( SX12 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX2 )
!= ( SX12 @ SX3 ) )
| ( ( SX12 @ SX3 )
!= ( SX12 @ SX4 ) ) )
| ( ( SX12 @ SX4 )
!= ( SX12 @ SX5 ) ) )
| ~ ( ( ( SX12 @ SX8 )
!= ( SX12 @ SX11 ) ) ) )
| ( ( SX12 @ SX6 )
= ( SX12 @ SX9 ) ) ) )
| ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX2 )
!= ( SX12 @ SX3 ) )
| ( ( SX12 @ SX4 )
!= ( SX12 @ SX5 ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX7 ) )
| ( ( SX12 @ SX8 )
!= ( SX12 @ SX9 ) )
| ( ( SX12 @ SX10 )
!= ( SX12 @ SX11 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ! [SX6: $i] :
~ ~ ! [SX7: $i] :
~ ~ ! [SX8: $i] :
~ ~ ! [SX9: $i] :
~ ~ ! [SX10: $i] :
~ ~ ! [SX11: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( ( SX0 != SX2 ) ) )
| ~ ( ( SX0 != SX3 ) ) )
| ~ ( ( SX0 != SX4 ) ) )
| ~ ( ( SX0 != SX5 ) ) )
| ~ ( ( SX0 != SX6 ) ) )
| ~ ( ( SX0 != SX7 ) ) )
| ~ ( ( SX0 != SX8 ) ) )
| ~ ( ( SX0 != SX9 ) ) )
| ~ ( ( SX0 != SX10 ) ) )
| ~ ( ( SX0 != SX11 ) ) )
| ~ ( ( SX1 != SX2 ) ) )
| ~ ( ( SX1 != SX3 ) ) )
| ~ ( ( SX1 != SX4 ) ) )
| ~ ( ( SX1 != SX5 ) ) )
| ~ ( ( SX1 != SX6 ) ) )
| ~ ( ( SX1 != SX7 ) ) )
| ~ ( ( SX1 != SX8 ) ) )
| ~ ( ( SX1 != SX9 ) ) )
| ~ ( ( SX1 != SX10 ) ) )
| ~ ( ( SX1 != SX11 ) ) )
| ~ ( ( SX2 != SX3 ) ) )
| ~ ( ( SX2 != SX4 ) ) )
| ~ ( ( SX2 != SX5 ) ) )
| ~ ( ( SX2 != SX6 ) ) )
| ~ ( ( SX2 != SX7 ) ) )
| ~ ( ( SX2 != SX8 ) ) )
| ~ ( ( SX2 != SX9 ) ) )
| ~ ( ( SX2 != SX10 ) ) )
| ~ ( ( SX2 != SX11 ) ) )
| ~ ( ( SX4 != SX5 ) ) )
| ~ ( ( SX4 != SX6 ) ) )
| ~ ( ( SX4 != SX7 ) ) )
| ~ ( ( SX4 != SX8 ) ) )
| ~ ( ( SX4 != SX9 ) ) )
| ~ ( ( SX4 != SX10 ) ) )
| ~ ( ( SX4 != SX11 ) ) )
| ~ ( ( SX5 != SX6 ) ) )
| ~ ( ( SX5 != SX7 ) ) )
| ~ ( ( SX5 != SX8 ) ) )
| ~ ( ( SX5 != SX9 ) ) )
| ~ ( ( SX5 != SX10 ) ) )
| ~ ( ( SX5 != SX11 ) ) )
| ~ ( ( SX6 != SX7 ) ) )
| ~ ( ( SX6 != SX8 ) ) )
| ~ ( ( SX6 != SX9 ) ) )
| ~ ( ( SX6 != SX10 ) ) )
| ~ ( ( SX6 != SX11 ) ) )
| ~ ( ( SX7 != SX8 ) ) )
| ~ ( ( SX7 != SX9 ) ) )
| ~ ( ( SX7 != SX10 ) ) )
| ~ ( ( SX7 != SX11 ) ) )
| ~ ( ( SX8 != SX9 ) ) )
| ~ ( ( SX8 != SX10 ) ) )
| ~ ( ( SX8 != SX11 ) ) )
| ~ ( ( SX9 != SX10 ) ) )
| ~ ( ( SX9 != SX11 ) ) )
| ~ ( ( SX10 != SX11 ) ) )
| ! [SX12: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX2 )
!= ( SX12 @ SX3 ) ) )
| ( ( SX12 @ SX8 )
!= ( SX12 @ SX11 ) ) )
| ( ( SX12 @ SX4 )
= ( SX12 @ SX7 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX10 )
!= ( SX12 @ SX11 ) ) )
| ( ( SX12 @ SX2 )
!= ( SX12 @ SX5 ) ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX9 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX4 )
!= ( SX12 @ SX5 ) )
| ( ( SX12 @ SX5 )
!= ( SX12 @ SX6 ) ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX7 ) ) )
| ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX3 ) ) ) )
| ( ( SX12 @ SX8 )
!= ( SX12 @ SX11 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX7 ) ) )
| ~ ( ( ( SX12 @ SX2 )
!= ( SX12 @ SX5 ) ) ) )
| ( ( SX12 @ SX8 )
= ( SX12 @ SX11 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX8 )
!= ( SX12 @ SX9 ) )
| ( ( SX12 @ SX10 )
!= ( SX12 @ SX11 ) ) )
| ( ( SX12 @ SX4 )
!= ( SX12 @ SX7 ) ) )
| ( ( SX12 @ SX0 )
!= ( SX12 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SX12 @ SX2 )
!= ( SX12 @ SX3 ) )
| ( ( SX12 @ SX3 )
!= ( SX12 @ SX4 ) ) )
| ( ( SX12 @ SX4 )
!= ( SX12 @ SX5 ) ) )
| ~ ( ( ( SX12 @ SX8 )
!= ( SX12 @ SX11 ) ) ) )
| ( ( SX12 @ SX6 )
= ( SX12 @ SX9 ) ) ) )
| ( ( SX12 @ SX0 )
!= ( SX12 @ SX1 ) )
| ( ( SX12 @ SX2 )
!= ( SX12 @ SX3 ) )
| ( ( SX12 @ SX4 )
!= ( SX12 @ SX5 ) )
| ( ( SX12 @ SX6 )
!= ( SX12 @ SX7 ) )
| ( ( SX12 @ SX8 )
!= ( SX12 @ SX9 ) )
| ( ( SX12 @ SX10 )
!= ( SX12 @ SX11 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7]) ).
thf(9,plain,
! [SV1: $i] :
( ( ~ ~ ! [SY13: $i] :
~ ~ ! [SY14: $i] :
~ ~ ! [SY15: $i] :
~ ~ ! [SY16: $i] :
~ ~ ! [SY17: $i] :
~ ~ ! [SY18: $i] :
~ ~ ! [SY19: $i] :
~ ~ ! [SY20: $i] :
~ ~ ! [SY21: $i] :
~ ~ ! [SY22: $i] :
~ ~ ! [SY23: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SY13 ) )
| ~ ( ( SV1 != SY14 ) ) )
| ~ ( ( SV1 != SY15 ) ) )
| ~ ( ( SV1 != SY16 ) ) )
| ~ ( ( SV1 != SY17 ) ) )
| ~ ( ( SV1 != SY18 ) ) )
| ~ ( ( SV1 != SY19 ) ) )
| ~ ( ( SV1 != SY20 ) ) )
| ~ ( ( SV1 != SY21 ) ) )
| ~ ( ( SV1 != SY22 ) ) )
| ~ ( ( SV1 != SY23 ) ) )
| ~ ( ( SY13 != SY14 ) ) )
| ~ ( ( SY13 != SY15 ) ) )
| ~ ( ( SY13 != SY16 ) ) )
| ~ ( ( SY13 != SY17 ) ) )
| ~ ( ( SY13 != SY18 ) ) )
| ~ ( ( SY13 != SY19 ) ) )
| ~ ( ( SY13 != SY20 ) ) )
| ~ ( ( SY13 != SY21 ) ) )
| ~ ( ( SY13 != SY22 ) ) )
| ~ ( ( SY13 != SY23 ) ) )
| ~ ( ( SY14 != SY15 ) ) )
| ~ ( ( SY14 != SY16 ) ) )
| ~ ( ( SY14 != SY17 ) ) )
| ~ ( ( SY14 != SY18 ) ) )
| ~ ( ( SY14 != SY19 ) ) )
| ~ ( ( SY14 != SY20 ) ) )
| ~ ( ( SY14 != SY21 ) ) )
| ~ ( ( SY14 != SY22 ) ) )
| ~ ( ( SY14 != SY23 ) ) )
| ~ ( ( SY16 != SY17 ) ) )
| ~ ( ( SY16 != SY18 ) ) )
| ~ ( ( SY16 != SY19 ) ) )
| ~ ( ( SY16 != SY20 ) ) )
| ~ ( ( SY16 != SY21 ) ) )
| ~ ( ( SY16 != SY22 ) ) )
| ~ ( ( SY16 != SY23 ) ) )
| ~ ( ( SY17 != SY18 ) ) )
| ~ ( ( SY17 != SY19 ) ) )
| ~ ( ( SY17 != SY20 ) ) )
| ~ ( ( SY17 != SY21 ) ) )
| ~ ( ( SY17 != SY22 ) ) )
| ~ ( ( SY17 != SY23 ) ) )
| ~ ( ( SY18 != SY19 ) ) )
| ~ ( ( SY18 != SY20 ) ) )
| ~ ( ( SY18 != SY21 ) ) )
| ~ ( ( SY18 != SY22 ) ) )
| ~ ( ( SY18 != SY23 ) ) )
| ~ ( ( SY19 != SY20 ) ) )
| ~ ( ( SY19 != SY21 ) ) )
| ~ ( ( SY19 != SY22 ) ) )
| ~ ( ( SY19 != SY23 ) ) )
| ~ ( ( SY20 != SY21 ) ) )
| ~ ( ( SY20 != SY22 ) ) )
| ~ ( ( SY20 != SY23 ) ) )
| ~ ( ( SY21 != SY22 ) ) )
| ~ ( ( SY21 != SY23 ) ) )
| ~ ( ( SY22 != SY23 ) ) )
| ! [SY24: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY14 )
!= ( SY24 @ SY15 ) ) )
| ( ( SY24 @ SY20 )
!= ( SY24 @ SY23 ) ) )
| ( ( SY24 @ SY16 )
= ( SY24 @ SY19 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY22 )
!= ( SY24 @ SY23 ) ) )
| ( ( SY24 @ SY14 )
!= ( SY24 @ SY17 ) ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY21 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SY16 )
!= ( SY24 @ SY17 ) )
| ( ( SY24 @ SY17 )
!= ( SY24 @ SY18 ) ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY19 ) ) )
| ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY15 ) ) ) )
| ( ( SY24 @ SY20 )
!= ( SY24 @ SY23 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY19 ) ) )
| ~ ( ( ( SY24 @ SY14 )
!= ( SY24 @ SY17 ) ) ) )
| ( ( SY24 @ SY20 )
= ( SY24 @ SY23 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SY20 )
!= ( SY24 @ SY21 ) )
| ( ( SY24 @ SY22 )
!= ( SY24 @ SY23 ) ) )
| ( ( SY24 @ SY16 )
!= ( SY24 @ SY19 ) ) )
| ( ( SY24 @ SV1 )
!= ( SY24 @ SY15 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SY14 )
!= ( SY24 @ SY15 ) )
| ( ( SY24 @ SY15 )
!= ( SY24 @ SY16 ) ) )
| ( ( SY24 @ SY16 )
!= ( SY24 @ SY17 ) ) )
| ~ ( ( ( SY24 @ SY20 )
!= ( SY24 @ SY23 ) ) ) )
| ( ( SY24 @ SY18 )
= ( SY24 @ SY21 ) ) ) )
| ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY14 )
!= ( SY24 @ SY15 ) )
| ( ( SY24 @ SY16 )
!= ( SY24 @ SY17 ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY19 ) )
| ( ( SY24 @ SY20 )
!= ( SY24 @ SY21 ) )
| ( ( SY24 @ SY22 )
!= ( SY24 @ SY23 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(10,plain,
! [SV1: $i] :
( ( ~ ! [SY13: $i] :
~ ~ ! [SY14: $i] :
~ ~ ! [SY15: $i] :
~ ~ ! [SY16: $i] :
~ ~ ! [SY17: $i] :
~ ~ ! [SY18: $i] :
~ ~ ! [SY19: $i] :
~ ~ ! [SY20: $i] :
~ ~ ! [SY21: $i] :
~ ~ ! [SY22: $i] :
~ ~ ! [SY23: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SY13 ) )
| ~ ( ( SV1 != SY14 ) ) )
| ~ ( ( SV1 != SY15 ) ) )
| ~ ( ( SV1 != SY16 ) ) )
| ~ ( ( SV1 != SY17 ) ) )
| ~ ( ( SV1 != SY18 ) ) )
| ~ ( ( SV1 != SY19 ) ) )
| ~ ( ( SV1 != SY20 ) ) )
| ~ ( ( SV1 != SY21 ) ) )
| ~ ( ( SV1 != SY22 ) ) )
| ~ ( ( SV1 != SY23 ) ) )
| ~ ( ( SY13 != SY14 ) ) )
| ~ ( ( SY13 != SY15 ) ) )
| ~ ( ( SY13 != SY16 ) ) )
| ~ ( ( SY13 != SY17 ) ) )
| ~ ( ( SY13 != SY18 ) ) )
| ~ ( ( SY13 != SY19 ) ) )
| ~ ( ( SY13 != SY20 ) ) )
| ~ ( ( SY13 != SY21 ) ) )
| ~ ( ( SY13 != SY22 ) ) )
| ~ ( ( SY13 != SY23 ) ) )
| ~ ( ( SY14 != SY15 ) ) )
| ~ ( ( SY14 != SY16 ) ) )
| ~ ( ( SY14 != SY17 ) ) )
| ~ ( ( SY14 != SY18 ) ) )
| ~ ( ( SY14 != SY19 ) ) )
| ~ ( ( SY14 != SY20 ) ) )
| ~ ( ( SY14 != SY21 ) ) )
| ~ ( ( SY14 != SY22 ) ) )
| ~ ( ( SY14 != SY23 ) ) )
| ~ ( ( SY16 != SY17 ) ) )
| ~ ( ( SY16 != SY18 ) ) )
| ~ ( ( SY16 != SY19 ) ) )
| ~ ( ( SY16 != SY20 ) ) )
| ~ ( ( SY16 != SY21 ) ) )
| ~ ( ( SY16 != SY22 ) ) )
| ~ ( ( SY16 != SY23 ) ) )
| ~ ( ( SY17 != SY18 ) ) )
| ~ ( ( SY17 != SY19 ) ) )
| ~ ( ( SY17 != SY20 ) ) )
| ~ ( ( SY17 != SY21 ) ) )
| ~ ( ( SY17 != SY22 ) ) )
| ~ ( ( SY17 != SY23 ) ) )
| ~ ( ( SY18 != SY19 ) ) )
| ~ ( ( SY18 != SY20 ) ) )
| ~ ( ( SY18 != SY21 ) ) )
| ~ ( ( SY18 != SY22 ) ) )
| ~ ( ( SY18 != SY23 ) ) )
| ~ ( ( SY19 != SY20 ) ) )
| ~ ( ( SY19 != SY21 ) ) )
| ~ ( ( SY19 != SY22 ) ) )
| ~ ( ( SY19 != SY23 ) ) )
| ~ ( ( SY20 != SY21 ) ) )
| ~ ( ( SY20 != SY22 ) ) )
| ~ ( ( SY20 != SY23 ) ) )
| ~ ( ( SY21 != SY22 ) ) )
| ~ ( ( SY21 != SY23 ) ) )
| ~ ( ( SY22 != SY23 ) ) )
| ! [SY24: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY14 )
!= ( SY24 @ SY15 ) ) )
| ( ( SY24 @ SY20 )
!= ( SY24 @ SY23 ) ) )
| ( ( SY24 @ SY16 )
= ( SY24 @ SY19 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY22 )
!= ( SY24 @ SY23 ) ) )
| ( ( SY24 @ SY14 )
!= ( SY24 @ SY17 ) ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY21 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SY16 )
!= ( SY24 @ SY17 ) )
| ( ( SY24 @ SY17 )
!= ( SY24 @ SY18 ) ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY19 ) ) )
| ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY15 ) ) ) )
| ( ( SY24 @ SY20 )
!= ( SY24 @ SY23 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY19 ) ) )
| ~ ( ( ( SY24 @ SY14 )
!= ( SY24 @ SY17 ) ) ) )
| ( ( SY24 @ SY20 )
= ( SY24 @ SY23 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SY20 )
!= ( SY24 @ SY21 ) )
| ( ( SY24 @ SY22 )
!= ( SY24 @ SY23 ) ) )
| ( ( SY24 @ SY16 )
!= ( SY24 @ SY19 ) ) )
| ( ( SY24 @ SV1 )
!= ( SY24 @ SY15 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SY14 )
!= ( SY24 @ SY15 ) )
| ( ( SY24 @ SY15 )
!= ( SY24 @ SY16 ) ) )
| ( ( SY24 @ SY16 )
!= ( SY24 @ SY17 ) ) )
| ~ ( ( ( SY24 @ SY20 )
!= ( SY24 @ SY23 ) ) ) )
| ( ( SY24 @ SY18 )
= ( SY24 @ SY21 ) ) ) )
| ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY14 )
!= ( SY24 @ SY15 ) )
| ( ( SY24 @ SY16 )
!= ( SY24 @ SY17 ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY19 ) )
| ( ( SY24 @ SY20 )
!= ( SY24 @ SY21 ) )
| ( ( SY24 @ SY22 )
!= ( SY24 @ SY23 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(11,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
~ ~ ! [SY14: $i] :
~ ~ ! [SY15: $i] :
~ ~ ! [SY16: $i] :
~ ~ ! [SY17: $i] :
~ ~ ! [SY18: $i] :
~ ~ ! [SY19: $i] :
~ ~ ! [SY20: $i] :
~ ~ ! [SY21: $i] :
~ ~ ! [SY22: $i] :
~ ~ ! [SY23: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SY13 ) )
| ~ ( ( SV1 != SY14 ) ) )
| ~ ( ( SV1 != SY15 ) ) )
| ~ ( ( SV1 != SY16 ) ) )
| ~ ( ( SV1 != SY17 ) ) )
| ~ ( ( SV1 != SY18 ) ) )
| ~ ( ( SV1 != SY19 ) ) )
| ~ ( ( SV1 != SY20 ) ) )
| ~ ( ( SV1 != SY21 ) ) )
| ~ ( ( SV1 != SY22 ) ) )
| ~ ( ( SV1 != SY23 ) ) )
| ~ ( ( SY13 != SY14 ) ) )
| ~ ( ( SY13 != SY15 ) ) )
| ~ ( ( SY13 != SY16 ) ) )
| ~ ( ( SY13 != SY17 ) ) )
| ~ ( ( SY13 != SY18 ) ) )
| ~ ( ( SY13 != SY19 ) ) )
| ~ ( ( SY13 != SY20 ) ) )
| ~ ( ( SY13 != SY21 ) ) )
| ~ ( ( SY13 != SY22 ) ) )
| ~ ( ( SY13 != SY23 ) ) )
| ~ ( ( SY14 != SY15 ) ) )
| ~ ( ( SY14 != SY16 ) ) )
| ~ ( ( SY14 != SY17 ) ) )
| ~ ( ( SY14 != SY18 ) ) )
| ~ ( ( SY14 != SY19 ) ) )
| ~ ( ( SY14 != SY20 ) ) )
| ~ ( ( SY14 != SY21 ) ) )
| ~ ( ( SY14 != SY22 ) ) )
| ~ ( ( SY14 != SY23 ) ) )
| ~ ( ( SY16 != SY17 ) ) )
| ~ ( ( SY16 != SY18 ) ) )
| ~ ( ( SY16 != SY19 ) ) )
| ~ ( ( SY16 != SY20 ) ) )
| ~ ( ( SY16 != SY21 ) ) )
| ~ ( ( SY16 != SY22 ) ) )
| ~ ( ( SY16 != SY23 ) ) )
| ~ ( ( SY17 != SY18 ) ) )
| ~ ( ( SY17 != SY19 ) ) )
| ~ ( ( SY17 != SY20 ) ) )
| ~ ( ( SY17 != SY21 ) ) )
| ~ ( ( SY17 != SY22 ) ) )
| ~ ( ( SY17 != SY23 ) ) )
| ~ ( ( SY18 != SY19 ) ) )
| ~ ( ( SY18 != SY20 ) ) )
| ~ ( ( SY18 != SY21 ) ) )
| ~ ( ( SY18 != SY22 ) ) )
| ~ ( ( SY18 != SY23 ) ) )
| ~ ( ( SY19 != SY20 ) ) )
| ~ ( ( SY19 != SY21 ) ) )
| ~ ( ( SY19 != SY22 ) ) )
| ~ ( ( SY19 != SY23 ) ) )
| ~ ( ( SY20 != SY21 ) ) )
| ~ ( ( SY20 != SY22 ) ) )
| ~ ( ( SY20 != SY23 ) ) )
| ~ ( ( SY21 != SY22 ) ) )
| ~ ( ( SY21 != SY23 ) ) )
| ~ ( ( SY22 != SY23 ) ) )
| ! [SY24: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY14 )
!= ( SY24 @ SY15 ) ) )
| ( ( SY24 @ SY20 )
!= ( SY24 @ SY23 ) ) )
| ( ( SY24 @ SY16 )
= ( SY24 @ SY19 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY22 )
!= ( SY24 @ SY23 ) ) )
| ( ( SY24 @ SY14 )
!= ( SY24 @ SY17 ) ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY21 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SY16 )
!= ( SY24 @ SY17 ) )
| ( ( SY24 @ SY17 )
!= ( SY24 @ SY18 ) ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY19 ) ) )
| ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY15 ) ) ) )
| ( ( SY24 @ SY20 )
!= ( SY24 @ SY23 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY19 ) ) )
| ~ ( ( ( SY24 @ SY14 )
!= ( SY24 @ SY17 ) ) ) )
| ( ( SY24 @ SY20 )
= ( SY24 @ SY23 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SY20 )
!= ( SY24 @ SY21 ) )
| ( ( SY24 @ SY22 )
!= ( SY24 @ SY23 ) ) )
| ( ( SY24 @ SY16 )
!= ( SY24 @ SY19 ) ) )
| ( ( SY24 @ SV1 )
!= ( SY24 @ SY15 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY24 @ SY14 )
!= ( SY24 @ SY15 ) )
| ( ( SY24 @ SY15 )
!= ( SY24 @ SY16 ) ) )
| ( ( SY24 @ SY16 )
!= ( SY24 @ SY17 ) ) )
| ~ ( ( ( SY24 @ SY20 )
!= ( SY24 @ SY23 ) ) ) )
| ( ( SY24 @ SY18 )
= ( SY24 @ SY21 ) ) ) )
| ( ( SY24 @ SV1 )
!= ( SY24 @ SY13 ) )
| ( ( SY24 @ SY14 )
!= ( SY24 @ SY15 ) )
| ( ( SY24 @ SY16 )
!= ( SY24 @ SY17 ) )
| ( ( SY24 @ SY18 )
!= ( SY24 @ SY19 ) )
| ( ( SY24 @ SY20 )
!= ( SY24 @ SY21 ) )
| ( ( SY24 @ SY22 )
!= ( SY24 @ SY23 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(12,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY25: $i] :
~ ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ! [SY28: $i] :
~ ~ ! [SY29: $i] :
~ ~ ! [SY30: $i] :
~ ~ ! [SY31: $i] :
~ ~ ! [SY32: $i] :
~ ~ ! [SY33: $i] :
~ ~ ! [SY34: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SY25 ) ) )
| ~ ( ( SV1 != SY26 ) ) )
| ~ ( ( SV1 != SY27 ) ) )
| ~ ( ( SV1 != SY28 ) ) )
| ~ ( ( SV1 != SY29 ) ) )
| ~ ( ( SV1 != SY30 ) ) )
| ~ ( ( SV1 != SY31 ) ) )
| ~ ( ( SV1 != SY32 ) ) )
| ~ ( ( SV1 != SY33 ) ) )
| ~ ( ( SV1 != SY34 ) ) )
| ~ ( ( SV2 != SY25 ) ) )
| ~ ( ( SV2 != SY26 ) ) )
| ~ ( ( SV2 != SY27 ) ) )
| ~ ( ( SV2 != SY28 ) ) )
| ~ ( ( SV2 != SY29 ) ) )
| ~ ( ( SV2 != SY30 ) ) )
| ~ ( ( SV2 != SY31 ) ) )
| ~ ( ( SV2 != SY32 ) ) )
| ~ ( ( SV2 != SY33 ) ) )
| ~ ( ( SV2 != SY34 ) ) )
| ~ ( ( SY25 != SY26 ) ) )
| ~ ( ( SY25 != SY27 ) ) )
| ~ ( ( SY25 != SY28 ) ) )
| ~ ( ( SY25 != SY29 ) ) )
| ~ ( ( SY25 != SY30 ) ) )
| ~ ( ( SY25 != SY31 ) ) )
| ~ ( ( SY25 != SY32 ) ) )
| ~ ( ( SY25 != SY33 ) ) )
| ~ ( ( SY25 != SY34 ) ) )
| ~ ( ( SY27 != SY28 ) ) )
| ~ ( ( SY27 != SY29 ) ) )
| ~ ( ( SY27 != SY30 ) ) )
| ~ ( ( SY27 != SY31 ) ) )
| ~ ( ( SY27 != SY32 ) ) )
| ~ ( ( SY27 != SY33 ) ) )
| ~ ( ( SY27 != SY34 ) ) )
| ~ ( ( SY28 != SY29 ) ) )
| ~ ( ( SY28 != SY30 ) ) )
| ~ ( ( SY28 != SY31 ) ) )
| ~ ( ( SY28 != SY32 ) ) )
| ~ ( ( SY28 != SY33 ) ) )
| ~ ( ( SY28 != SY34 ) ) )
| ~ ( ( SY29 != SY30 ) ) )
| ~ ( ( SY29 != SY31 ) ) )
| ~ ( ( SY29 != SY32 ) ) )
| ~ ( ( SY29 != SY33 ) ) )
| ~ ( ( SY29 != SY34 ) ) )
| ~ ( ( SY30 != SY31 ) ) )
| ~ ( ( SY30 != SY32 ) ) )
| ~ ( ( SY30 != SY33 ) ) )
| ~ ( ( SY30 != SY34 ) ) )
| ~ ( ( SY31 != SY32 ) ) )
| ~ ( ( SY31 != SY33 ) ) )
| ~ ( ( SY31 != SY34 ) ) )
| ~ ( ( SY32 != SY33 ) ) )
| ~ ( ( SY32 != SY34 ) ) )
| ~ ( ( SY33 != SY34 ) ) )
| ! [SY35: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY25 )
!= ( SY35 @ SY26 ) ) )
| ( ( SY35 @ SY31 )
!= ( SY35 @ SY34 ) ) )
| ( ( SY35 @ SY27 )
= ( SY35 @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY33 )
!= ( SY35 @ SY34 ) ) )
| ( ( SY35 @ SY25 )
!= ( SY35 @ SY28 ) ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY32 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SY27 )
!= ( SY35 @ SY28 ) )
| ( ( SY35 @ SY28 )
!= ( SY35 @ SY29 ) ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY30 ) ) )
| ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SY26 ) ) ) )
| ( ( SY35 @ SY31 )
!= ( SY35 @ SY34 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY30 ) ) )
| ~ ( ( ( SY35 @ SY25 )
!= ( SY35 @ SY28 ) ) ) )
| ( ( SY35 @ SY31 )
= ( SY35 @ SY34 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SY31 )
!= ( SY35 @ SY32 ) )
| ( ( SY35 @ SY33 )
!= ( SY35 @ SY34 ) ) )
| ( ( SY35 @ SY27 )
!= ( SY35 @ SY30 ) ) )
| ( ( SY35 @ SV1 )
!= ( SY35 @ SY26 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SY25 )
!= ( SY35 @ SY26 ) )
| ( ( SY35 @ SY26 )
!= ( SY35 @ SY27 ) ) )
| ( ( SY35 @ SY27 )
!= ( SY35 @ SY28 ) ) )
| ~ ( ( ( SY35 @ SY31 )
!= ( SY35 @ SY34 ) ) ) )
| ( ( SY35 @ SY29 )
= ( SY35 @ SY32 ) ) ) )
| ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY25 )
!= ( SY35 @ SY26 ) )
| ( ( SY35 @ SY27 )
!= ( SY35 @ SY28 ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY30 ) )
| ( ( SY35 @ SY31 )
!= ( SY35 @ SY32 ) )
| ( ( SY35 @ SY33 )
!= ( SY35 @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(13,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ! [SY25: $i] :
~ ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ! [SY28: $i] :
~ ~ ! [SY29: $i] :
~ ~ ! [SY30: $i] :
~ ~ ! [SY31: $i] :
~ ~ ! [SY32: $i] :
~ ~ ! [SY33: $i] :
~ ~ ! [SY34: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SY25 ) ) )
| ~ ( ( SV1 != SY26 ) ) )
| ~ ( ( SV1 != SY27 ) ) )
| ~ ( ( SV1 != SY28 ) ) )
| ~ ( ( SV1 != SY29 ) ) )
| ~ ( ( SV1 != SY30 ) ) )
| ~ ( ( SV1 != SY31 ) ) )
| ~ ( ( SV1 != SY32 ) ) )
| ~ ( ( SV1 != SY33 ) ) )
| ~ ( ( SV1 != SY34 ) ) )
| ~ ( ( SV2 != SY25 ) ) )
| ~ ( ( SV2 != SY26 ) ) )
| ~ ( ( SV2 != SY27 ) ) )
| ~ ( ( SV2 != SY28 ) ) )
| ~ ( ( SV2 != SY29 ) ) )
| ~ ( ( SV2 != SY30 ) ) )
| ~ ( ( SV2 != SY31 ) ) )
| ~ ( ( SV2 != SY32 ) ) )
| ~ ( ( SV2 != SY33 ) ) )
| ~ ( ( SV2 != SY34 ) ) )
| ~ ( ( SY25 != SY26 ) ) )
| ~ ( ( SY25 != SY27 ) ) )
| ~ ( ( SY25 != SY28 ) ) )
| ~ ( ( SY25 != SY29 ) ) )
| ~ ( ( SY25 != SY30 ) ) )
| ~ ( ( SY25 != SY31 ) ) )
| ~ ( ( SY25 != SY32 ) ) )
| ~ ( ( SY25 != SY33 ) ) )
| ~ ( ( SY25 != SY34 ) ) )
| ~ ( ( SY27 != SY28 ) ) )
| ~ ( ( SY27 != SY29 ) ) )
| ~ ( ( SY27 != SY30 ) ) )
| ~ ( ( SY27 != SY31 ) ) )
| ~ ( ( SY27 != SY32 ) ) )
| ~ ( ( SY27 != SY33 ) ) )
| ~ ( ( SY27 != SY34 ) ) )
| ~ ( ( SY28 != SY29 ) ) )
| ~ ( ( SY28 != SY30 ) ) )
| ~ ( ( SY28 != SY31 ) ) )
| ~ ( ( SY28 != SY32 ) ) )
| ~ ( ( SY28 != SY33 ) ) )
| ~ ( ( SY28 != SY34 ) ) )
| ~ ( ( SY29 != SY30 ) ) )
| ~ ( ( SY29 != SY31 ) ) )
| ~ ( ( SY29 != SY32 ) ) )
| ~ ( ( SY29 != SY33 ) ) )
| ~ ( ( SY29 != SY34 ) ) )
| ~ ( ( SY30 != SY31 ) ) )
| ~ ( ( SY30 != SY32 ) ) )
| ~ ( ( SY30 != SY33 ) ) )
| ~ ( ( SY30 != SY34 ) ) )
| ~ ( ( SY31 != SY32 ) ) )
| ~ ( ( SY31 != SY33 ) ) )
| ~ ( ( SY31 != SY34 ) ) )
| ~ ( ( SY32 != SY33 ) ) )
| ~ ( ( SY32 != SY34 ) ) )
| ~ ( ( SY33 != SY34 ) ) )
| ! [SY35: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY25 )
!= ( SY35 @ SY26 ) ) )
| ( ( SY35 @ SY31 )
!= ( SY35 @ SY34 ) ) )
| ( ( SY35 @ SY27 )
= ( SY35 @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY33 )
!= ( SY35 @ SY34 ) ) )
| ( ( SY35 @ SY25 )
!= ( SY35 @ SY28 ) ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY32 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SY27 )
!= ( SY35 @ SY28 ) )
| ( ( SY35 @ SY28 )
!= ( SY35 @ SY29 ) ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY30 ) ) )
| ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SY26 ) ) ) )
| ( ( SY35 @ SY31 )
!= ( SY35 @ SY34 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY30 ) ) )
| ~ ( ( ( SY35 @ SY25 )
!= ( SY35 @ SY28 ) ) ) )
| ( ( SY35 @ SY31 )
= ( SY35 @ SY34 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SY31 )
!= ( SY35 @ SY32 ) )
| ( ( SY35 @ SY33 )
!= ( SY35 @ SY34 ) ) )
| ( ( SY35 @ SY27 )
!= ( SY35 @ SY30 ) ) )
| ( ( SY35 @ SV1 )
!= ( SY35 @ SY26 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SY25 )
!= ( SY35 @ SY26 ) )
| ( ( SY35 @ SY26 )
!= ( SY35 @ SY27 ) ) )
| ( ( SY35 @ SY27 )
!= ( SY35 @ SY28 ) ) )
| ~ ( ( ( SY35 @ SY31 )
!= ( SY35 @ SY34 ) ) ) )
| ( ( SY35 @ SY29 )
= ( SY35 @ SY32 ) ) ) )
| ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY25 )
!= ( SY35 @ SY26 ) )
| ( ( SY35 @ SY27 )
!= ( SY35 @ SY28 ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY30 ) )
| ( ( SY35 @ SY31 )
!= ( SY35 @ SY32 ) )
| ( ( SY35 @ SY33 )
!= ( SY35 @ SY34 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY25: $i] :
~ ~ ! [SY26: $i] :
~ ~ ! [SY27: $i] :
~ ~ ! [SY28: $i] :
~ ~ ! [SY29: $i] :
~ ~ ! [SY30: $i] :
~ ~ ! [SY31: $i] :
~ ~ ! [SY32: $i] :
~ ~ ! [SY33: $i] :
~ ~ ! [SY34: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SY25 ) ) )
| ~ ( ( SV1 != SY26 ) ) )
| ~ ( ( SV1 != SY27 ) ) )
| ~ ( ( SV1 != SY28 ) ) )
| ~ ( ( SV1 != SY29 ) ) )
| ~ ( ( SV1 != SY30 ) ) )
| ~ ( ( SV1 != SY31 ) ) )
| ~ ( ( SV1 != SY32 ) ) )
| ~ ( ( SV1 != SY33 ) ) )
| ~ ( ( SV1 != SY34 ) ) )
| ~ ( ( SV2 != SY25 ) ) )
| ~ ( ( SV2 != SY26 ) ) )
| ~ ( ( SV2 != SY27 ) ) )
| ~ ( ( SV2 != SY28 ) ) )
| ~ ( ( SV2 != SY29 ) ) )
| ~ ( ( SV2 != SY30 ) ) )
| ~ ( ( SV2 != SY31 ) ) )
| ~ ( ( SV2 != SY32 ) ) )
| ~ ( ( SV2 != SY33 ) ) )
| ~ ( ( SV2 != SY34 ) ) )
| ~ ( ( SY25 != SY26 ) ) )
| ~ ( ( SY25 != SY27 ) ) )
| ~ ( ( SY25 != SY28 ) ) )
| ~ ( ( SY25 != SY29 ) ) )
| ~ ( ( SY25 != SY30 ) ) )
| ~ ( ( SY25 != SY31 ) ) )
| ~ ( ( SY25 != SY32 ) ) )
| ~ ( ( SY25 != SY33 ) ) )
| ~ ( ( SY25 != SY34 ) ) )
| ~ ( ( SY27 != SY28 ) ) )
| ~ ( ( SY27 != SY29 ) ) )
| ~ ( ( SY27 != SY30 ) ) )
| ~ ( ( SY27 != SY31 ) ) )
| ~ ( ( SY27 != SY32 ) ) )
| ~ ( ( SY27 != SY33 ) ) )
| ~ ( ( SY27 != SY34 ) ) )
| ~ ( ( SY28 != SY29 ) ) )
| ~ ( ( SY28 != SY30 ) ) )
| ~ ( ( SY28 != SY31 ) ) )
| ~ ( ( SY28 != SY32 ) ) )
| ~ ( ( SY28 != SY33 ) ) )
| ~ ( ( SY28 != SY34 ) ) )
| ~ ( ( SY29 != SY30 ) ) )
| ~ ( ( SY29 != SY31 ) ) )
| ~ ( ( SY29 != SY32 ) ) )
| ~ ( ( SY29 != SY33 ) ) )
| ~ ( ( SY29 != SY34 ) ) )
| ~ ( ( SY30 != SY31 ) ) )
| ~ ( ( SY30 != SY32 ) ) )
| ~ ( ( SY30 != SY33 ) ) )
| ~ ( ( SY30 != SY34 ) ) )
| ~ ( ( SY31 != SY32 ) ) )
| ~ ( ( SY31 != SY33 ) ) )
| ~ ( ( SY31 != SY34 ) ) )
| ~ ( ( SY32 != SY33 ) ) )
| ~ ( ( SY32 != SY34 ) ) )
| ~ ( ( SY33 != SY34 ) ) )
| ! [SY35: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY25 )
!= ( SY35 @ SY26 ) ) )
| ( ( SY35 @ SY31 )
!= ( SY35 @ SY34 ) ) )
| ( ( SY35 @ SY27 )
= ( SY35 @ SY30 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY33 )
!= ( SY35 @ SY34 ) ) )
| ( ( SY35 @ SY25 )
!= ( SY35 @ SY28 ) ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY32 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SY27 )
!= ( SY35 @ SY28 ) )
| ( ( SY35 @ SY28 )
!= ( SY35 @ SY29 ) ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY30 ) ) )
| ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SY26 ) ) ) )
| ( ( SY35 @ SY31 )
!= ( SY35 @ SY34 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY30 ) ) )
| ~ ( ( ( SY35 @ SY25 )
!= ( SY35 @ SY28 ) ) ) )
| ( ( SY35 @ SY31 )
= ( SY35 @ SY34 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SY31 )
!= ( SY35 @ SY32 ) )
| ( ( SY35 @ SY33 )
!= ( SY35 @ SY34 ) ) )
| ( ( SY35 @ SY27 )
!= ( SY35 @ SY30 ) ) )
| ( ( SY35 @ SV1 )
!= ( SY35 @ SY26 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY35 @ SY25 )
!= ( SY35 @ SY26 ) )
| ( ( SY35 @ SY26 )
!= ( SY35 @ SY27 ) ) )
| ( ( SY35 @ SY27 )
!= ( SY35 @ SY28 ) ) )
| ~ ( ( ( SY35 @ SY31 )
!= ( SY35 @ SY34 ) ) ) )
| ( ( SY35 @ SY29 )
= ( SY35 @ SY32 ) ) ) )
| ( ( SY35 @ SV1 )
!= ( SY35 @ SV2 ) )
| ( ( SY35 @ SY25 )
!= ( SY35 @ SY26 ) )
| ( ( SY35 @ SY27 )
!= ( SY35 @ SY28 ) )
| ( ( SY35 @ SY29 )
!= ( SY35 @ SY30 ) )
| ( ( SY35 @ SY31 )
!= ( SY35 @ SY32 ) )
| ( ( SY35 @ SY33 )
!= ( SY35 @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(15,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ! [SY41: $i] :
~ ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ! [SY44: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SY36 ) ) )
| ~ ( ( SV1 != SY37 ) ) )
| ~ ( ( SV1 != SY38 ) ) )
| ~ ( ( SV1 != SY39 ) ) )
| ~ ( ( SV1 != SY40 ) ) )
| ~ ( ( SV1 != SY41 ) ) )
| ~ ( ( SV1 != SY42 ) ) )
| ~ ( ( SV1 != SY43 ) ) )
| ~ ( ( SV1 != SY44 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SY36 ) ) )
| ~ ( ( SV2 != SY37 ) ) )
| ~ ( ( SV2 != SY38 ) ) )
| ~ ( ( SV2 != SY39 ) ) )
| ~ ( ( SV2 != SY40 ) ) )
| ~ ( ( SV2 != SY41 ) ) )
| ~ ( ( SV2 != SY42 ) ) )
| ~ ( ( SV2 != SY43 ) ) )
| ~ ( ( SV2 != SY44 ) ) )
| ~ ( ( SV3 != SY36 ) ) )
| ~ ( ( SV3 != SY37 ) ) )
| ~ ( ( SV3 != SY38 ) ) )
| ~ ( ( SV3 != SY39 ) ) )
| ~ ( ( SV3 != SY40 ) ) )
| ~ ( ( SV3 != SY41 ) ) )
| ~ ( ( SV3 != SY42 ) ) )
| ~ ( ( SV3 != SY43 ) ) )
| ~ ( ( SV3 != SY44 ) ) )
| ~ ( ( SY37 != SY38 ) ) )
| ~ ( ( SY37 != SY39 ) ) )
| ~ ( ( SY37 != SY40 ) ) )
| ~ ( ( SY37 != SY41 ) ) )
| ~ ( ( SY37 != SY42 ) ) )
| ~ ( ( SY37 != SY43 ) ) )
| ~ ( ( SY37 != SY44 ) ) )
| ~ ( ( SY38 != SY39 ) ) )
| ~ ( ( SY38 != SY40 ) ) )
| ~ ( ( SY38 != SY41 ) ) )
| ~ ( ( SY38 != SY42 ) ) )
| ~ ( ( SY38 != SY43 ) ) )
| ~ ( ( SY38 != SY44 ) ) )
| ~ ( ( SY39 != SY40 ) ) )
| ~ ( ( SY39 != SY41 ) ) )
| ~ ( ( SY39 != SY42 ) ) )
| ~ ( ( SY39 != SY43 ) ) )
| ~ ( ( SY39 != SY44 ) ) )
| ~ ( ( SY40 != SY41 ) ) )
| ~ ( ( SY40 != SY42 ) ) )
| ~ ( ( SY40 != SY43 ) ) )
| ~ ( ( SY40 != SY44 ) ) )
| ~ ( ( SY41 != SY42 ) ) )
| ~ ( ( SY41 != SY43 ) ) )
| ~ ( ( SY41 != SY44 ) ) )
| ~ ( ( SY42 != SY43 ) ) )
| ~ ( ( SY42 != SY44 ) ) )
| ~ ( ( SY43 != SY44 ) ) )
| ! [SY45: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SV3 )
!= ( SY45 @ SY36 ) ) )
| ( ( SY45 @ SY41 )
!= ( SY45 @ SY44 ) ) )
| ( ( SY45 @ SY37 )
= ( SY45 @ SY40 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SY43 )
!= ( SY45 @ SY44 ) ) )
| ( ( SY45 @ SV3 )
!= ( SY45 @ SY38 ) ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY42 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SY37 )
!= ( SY45 @ SY38 ) )
| ( ( SY45 @ SY38 )
!= ( SY45 @ SY39 ) ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY40 ) ) )
| ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SY36 ) ) ) )
| ( ( SY45 @ SY41 )
!= ( SY45 @ SY44 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY40 ) ) )
| ~ ( ( ( SY45 @ SV3 )
!= ( SY45 @ SY38 ) ) ) )
| ( ( SY45 @ SY41 )
= ( SY45 @ SY44 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SY41 )
!= ( SY45 @ SY42 ) )
| ( ( SY45 @ SY43 )
!= ( SY45 @ SY44 ) ) )
| ( ( SY45 @ SY37 )
!= ( SY45 @ SY40 ) ) )
| ( ( SY45 @ SV1 )
!= ( SY45 @ SY36 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV3 )
!= ( SY45 @ SY36 ) )
| ( ( SY45 @ SY36 )
!= ( SY45 @ SY37 ) ) )
| ( ( SY45 @ SY37 )
!= ( SY45 @ SY38 ) ) )
| ~ ( ( ( SY45 @ SY41 )
!= ( SY45 @ SY44 ) ) ) )
| ( ( SY45 @ SY39 )
= ( SY45 @ SY42 ) ) ) )
| ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SV3 )
!= ( SY45 @ SY36 ) )
| ( ( SY45 @ SY37 )
!= ( SY45 @ SY38 ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY40 ) )
| ( ( SY45 @ SY41 )
!= ( SY45 @ SY42 ) )
| ( ( SY45 @ SY43 )
!= ( SY45 @ SY44 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(16,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ! [SY41: $i] :
~ ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ! [SY44: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SY36 ) ) )
| ~ ( ( SV1 != SY37 ) ) )
| ~ ( ( SV1 != SY38 ) ) )
| ~ ( ( SV1 != SY39 ) ) )
| ~ ( ( SV1 != SY40 ) ) )
| ~ ( ( SV1 != SY41 ) ) )
| ~ ( ( SV1 != SY42 ) ) )
| ~ ( ( SV1 != SY43 ) ) )
| ~ ( ( SV1 != SY44 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SY36 ) ) )
| ~ ( ( SV2 != SY37 ) ) )
| ~ ( ( SV2 != SY38 ) ) )
| ~ ( ( SV2 != SY39 ) ) )
| ~ ( ( SV2 != SY40 ) ) )
| ~ ( ( SV2 != SY41 ) ) )
| ~ ( ( SV2 != SY42 ) ) )
| ~ ( ( SV2 != SY43 ) ) )
| ~ ( ( SV2 != SY44 ) ) )
| ~ ( ( SV3 != SY36 ) ) )
| ~ ( ( SV3 != SY37 ) ) )
| ~ ( ( SV3 != SY38 ) ) )
| ~ ( ( SV3 != SY39 ) ) )
| ~ ( ( SV3 != SY40 ) ) )
| ~ ( ( SV3 != SY41 ) ) )
| ~ ( ( SV3 != SY42 ) ) )
| ~ ( ( SV3 != SY43 ) ) )
| ~ ( ( SV3 != SY44 ) ) )
| ~ ( ( SY37 != SY38 ) ) )
| ~ ( ( SY37 != SY39 ) ) )
| ~ ( ( SY37 != SY40 ) ) )
| ~ ( ( SY37 != SY41 ) ) )
| ~ ( ( SY37 != SY42 ) ) )
| ~ ( ( SY37 != SY43 ) ) )
| ~ ( ( SY37 != SY44 ) ) )
| ~ ( ( SY38 != SY39 ) ) )
| ~ ( ( SY38 != SY40 ) ) )
| ~ ( ( SY38 != SY41 ) ) )
| ~ ( ( SY38 != SY42 ) ) )
| ~ ( ( SY38 != SY43 ) ) )
| ~ ( ( SY38 != SY44 ) ) )
| ~ ( ( SY39 != SY40 ) ) )
| ~ ( ( SY39 != SY41 ) ) )
| ~ ( ( SY39 != SY42 ) ) )
| ~ ( ( SY39 != SY43 ) ) )
| ~ ( ( SY39 != SY44 ) ) )
| ~ ( ( SY40 != SY41 ) ) )
| ~ ( ( SY40 != SY42 ) ) )
| ~ ( ( SY40 != SY43 ) ) )
| ~ ( ( SY40 != SY44 ) ) )
| ~ ( ( SY41 != SY42 ) ) )
| ~ ( ( SY41 != SY43 ) ) )
| ~ ( ( SY41 != SY44 ) ) )
| ~ ( ( SY42 != SY43 ) ) )
| ~ ( ( SY42 != SY44 ) ) )
| ~ ( ( SY43 != SY44 ) ) )
| ! [SY45: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SV3 )
!= ( SY45 @ SY36 ) ) )
| ( ( SY45 @ SY41 )
!= ( SY45 @ SY44 ) ) )
| ( ( SY45 @ SY37 )
= ( SY45 @ SY40 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SY43 )
!= ( SY45 @ SY44 ) ) )
| ( ( SY45 @ SV3 )
!= ( SY45 @ SY38 ) ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY42 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SY37 )
!= ( SY45 @ SY38 ) )
| ( ( SY45 @ SY38 )
!= ( SY45 @ SY39 ) ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY40 ) ) )
| ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SY36 ) ) ) )
| ( ( SY45 @ SY41 )
!= ( SY45 @ SY44 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY40 ) ) )
| ~ ( ( ( SY45 @ SV3 )
!= ( SY45 @ SY38 ) ) ) )
| ( ( SY45 @ SY41 )
= ( SY45 @ SY44 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SY41 )
!= ( SY45 @ SY42 ) )
| ( ( SY45 @ SY43 )
!= ( SY45 @ SY44 ) ) )
| ( ( SY45 @ SY37 )
!= ( SY45 @ SY40 ) ) )
| ( ( SY45 @ SV1 )
!= ( SY45 @ SY36 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV3 )
!= ( SY45 @ SY36 ) )
| ( ( SY45 @ SY36 )
!= ( SY45 @ SY37 ) ) )
| ( ( SY45 @ SY37 )
!= ( SY45 @ SY38 ) ) )
| ~ ( ( ( SY45 @ SY41 )
!= ( SY45 @ SY44 ) ) ) )
| ( ( SY45 @ SY39 )
= ( SY45 @ SY42 ) ) ) )
| ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SV3 )
!= ( SY45 @ SY36 ) )
| ( ( SY45 @ SY37 )
!= ( SY45 @ SY38 ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY40 ) )
| ( ( SY45 @ SY41 )
!= ( SY45 @ SY42 ) )
| ( ( SY45 @ SY43 )
!= ( SY45 @ SY44 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(17,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY36: $i] :
~ ~ ! [SY37: $i] :
~ ~ ! [SY38: $i] :
~ ~ ! [SY39: $i] :
~ ~ ! [SY40: $i] :
~ ~ ! [SY41: $i] :
~ ~ ! [SY42: $i] :
~ ~ ! [SY43: $i] :
~ ~ ! [SY44: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SY36 ) ) )
| ~ ( ( SV1 != SY37 ) ) )
| ~ ( ( SV1 != SY38 ) ) )
| ~ ( ( SV1 != SY39 ) ) )
| ~ ( ( SV1 != SY40 ) ) )
| ~ ( ( SV1 != SY41 ) ) )
| ~ ( ( SV1 != SY42 ) ) )
| ~ ( ( SV1 != SY43 ) ) )
| ~ ( ( SV1 != SY44 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SY36 ) ) )
| ~ ( ( SV2 != SY37 ) ) )
| ~ ( ( SV2 != SY38 ) ) )
| ~ ( ( SV2 != SY39 ) ) )
| ~ ( ( SV2 != SY40 ) ) )
| ~ ( ( SV2 != SY41 ) ) )
| ~ ( ( SV2 != SY42 ) ) )
| ~ ( ( SV2 != SY43 ) ) )
| ~ ( ( SV2 != SY44 ) ) )
| ~ ( ( SV3 != SY36 ) ) )
| ~ ( ( SV3 != SY37 ) ) )
| ~ ( ( SV3 != SY38 ) ) )
| ~ ( ( SV3 != SY39 ) ) )
| ~ ( ( SV3 != SY40 ) ) )
| ~ ( ( SV3 != SY41 ) ) )
| ~ ( ( SV3 != SY42 ) ) )
| ~ ( ( SV3 != SY43 ) ) )
| ~ ( ( SV3 != SY44 ) ) )
| ~ ( ( SY37 != SY38 ) ) )
| ~ ( ( SY37 != SY39 ) ) )
| ~ ( ( SY37 != SY40 ) ) )
| ~ ( ( SY37 != SY41 ) ) )
| ~ ( ( SY37 != SY42 ) ) )
| ~ ( ( SY37 != SY43 ) ) )
| ~ ( ( SY37 != SY44 ) ) )
| ~ ( ( SY38 != SY39 ) ) )
| ~ ( ( SY38 != SY40 ) ) )
| ~ ( ( SY38 != SY41 ) ) )
| ~ ( ( SY38 != SY42 ) ) )
| ~ ( ( SY38 != SY43 ) ) )
| ~ ( ( SY38 != SY44 ) ) )
| ~ ( ( SY39 != SY40 ) ) )
| ~ ( ( SY39 != SY41 ) ) )
| ~ ( ( SY39 != SY42 ) ) )
| ~ ( ( SY39 != SY43 ) ) )
| ~ ( ( SY39 != SY44 ) ) )
| ~ ( ( SY40 != SY41 ) ) )
| ~ ( ( SY40 != SY42 ) ) )
| ~ ( ( SY40 != SY43 ) ) )
| ~ ( ( SY40 != SY44 ) ) )
| ~ ( ( SY41 != SY42 ) ) )
| ~ ( ( SY41 != SY43 ) ) )
| ~ ( ( SY41 != SY44 ) ) )
| ~ ( ( SY42 != SY43 ) ) )
| ~ ( ( SY42 != SY44 ) ) )
| ~ ( ( SY43 != SY44 ) ) )
| ! [SY45: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SV3 )
!= ( SY45 @ SY36 ) ) )
| ( ( SY45 @ SY41 )
!= ( SY45 @ SY44 ) ) )
| ( ( SY45 @ SY37 )
= ( SY45 @ SY40 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SY43 )
!= ( SY45 @ SY44 ) ) )
| ( ( SY45 @ SV3 )
!= ( SY45 @ SY38 ) ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY42 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SY37 )
!= ( SY45 @ SY38 ) )
| ( ( SY45 @ SY38 )
!= ( SY45 @ SY39 ) ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY40 ) ) )
| ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SY36 ) ) ) )
| ( ( SY45 @ SY41 )
!= ( SY45 @ SY44 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY40 ) ) )
| ~ ( ( ( SY45 @ SV3 )
!= ( SY45 @ SY38 ) ) ) )
| ( ( SY45 @ SY41 )
= ( SY45 @ SY44 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SY41 )
!= ( SY45 @ SY42 ) )
| ( ( SY45 @ SY43 )
!= ( SY45 @ SY44 ) ) )
| ( ( SY45 @ SY37 )
!= ( SY45 @ SY40 ) ) )
| ( ( SY45 @ SV1 )
!= ( SY45 @ SY36 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY45 @ SV3 )
!= ( SY45 @ SY36 ) )
| ( ( SY45 @ SY36 )
!= ( SY45 @ SY37 ) ) )
| ( ( SY45 @ SY37 )
!= ( SY45 @ SY38 ) ) )
| ~ ( ( ( SY45 @ SY41 )
!= ( SY45 @ SY44 ) ) ) )
| ( ( SY45 @ SY39 )
= ( SY45 @ SY42 ) ) ) )
| ( ( SY45 @ SV1 )
!= ( SY45 @ SV2 ) )
| ( ( SY45 @ SV3 )
!= ( SY45 @ SY36 ) )
| ( ( SY45 @ SY37 )
!= ( SY45 @ SY38 ) )
| ( ( SY45 @ SY39 )
!= ( SY45 @ SY40 ) )
| ( ( SY45 @ SY41 )
!= ( SY45 @ SY42 ) )
| ( ( SY45 @ SY43 )
!= ( SY45 @ SY44 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(18,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY46: $i] :
~ ~ ! [SY47: $i] :
~ ~ ! [SY48: $i] :
~ ~ ! [SY49: $i] :
~ ~ ! [SY50: $i] :
~ ~ ! [SY51: $i] :
~ ~ ! [SY52: $i] :
~ ~ ! [SY53: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SY46 ) ) )
| ~ ( ( SV1 != SY47 ) ) )
| ~ ( ( SV1 != SY48 ) ) )
| ~ ( ( SV1 != SY49 ) ) )
| ~ ( ( SV1 != SY50 ) ) )
| ~ ( ( SV1 != SY51 ) ) )
| ~ ( ( SV1 != SY52 ) ) )
| ~ ( ( SV1 != SY53 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SY46 ) ) )
| ~ ( ( SV2 != SY47 ) ) )
| ~ ( ( SV2 != SY48 ) ) )
| ~ ( ( SV2 != SY49 ) ) )
| ~ ( ( SV2 != SY50 ) ) )
| ~ ( ( SV2 != SY51 ) ) )
| ~ ( ( SV2 != SY52 ) ) )
| ~ ( ( SV2 != SY53 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SY46 ) ) )
| ~ ( ( SV3 != SY47 ) ) )
| ~ ( ( SV3 != SY48 ) ) )
| ~ ( ( SV3 != SY49 ) ) )
| ~ ( ( SV3 != SY50 ) ) )
| ~ ( ( SV3 != SY51 ) ) )
| ~ ( ( SV3 != SY52 ) ) )
| ~ ( ( SV3 != SY53 ) ) )
| ~ ( ( SY46 != SY47 ) ) )
| ~ ( ( SY46 != SY48 ) ) )
| ~ ( ( SY46 != SY49 ) ) )
| ~ ( ( SY46 != SY50 ) ) )
| ~ ( ( SY46 != SY51 ) ) )
| ~ ( ( SY46 != SY52 ) ) )
| ~ ( ( SY46 != SY53 ) ) )
| ~ ( ( SY47 != SY48 ) ) )
| ~ ( ( SY47 != SY49 ) ) )
| ~ ( ( SY47 != SY50 ) ) )
| ~ ( ( SY47 != SY51 ) ) )
| ~ ( ( SY47 != SY52 ) ) )
| ~ ( ( SY47 != SY53 ) ) )
| ~ ( ( SY48 != SY49 ) ) )
| ~ ( ( SY48 != SY50 ) ) )
| ~ ( ( SY48 != SY51 ) ) )
| ~ ( ( SY48 != SY52 ) ) )
| ~ ( ( SY48 != SY53 ) ) )
| ~ ( ( SY49 != SY50 ) ) )
| ~ ( ( SY49 != SY51 ) ) )
| ~ ( ( SY49 != SY52 ) ) )
| ~ ( ( SY49 != SY53 ) ) )
| ~ ( ( SY50 != SY51 ) ) )
| ~ ( ( SY50 != SY52 ) ) )
| ~ ( ( SY50 != SY53 ) ) )
| ~ ( ( SY51 != SY52 ) ) )
| ~ ( ( SY51 != SY53 ) ) )
| ~ ( ( SY52 != SY53 ) ) )
| ! [SY54: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SV3 )
!= ( SY54 @ SV4 ) ) )
| ( ( SY54 @ SY50 )
!= ( SY54 @ SY53 ) ) )
| ( ( SY54 @ SY46 )
= ( SY54 @ SY49 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SY52 )
!= ( SY54 @ SY53 ) ) )
| ( ( SY54 @ SV3 )
!= ( SY54 @ SY47 ) ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY51 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SY46 )
!= ( SY54 @ SY47 ) )
| ( ( SY54 @ SY47 )
!= ( SY54 @ SY48 ) ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY49 ) ) )
| ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV4 ) ) ) )
| ( ( SY54 @ SY50 )
!= ( SY54 @ SY53 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY49 ) ) )
| ~ ( ( ( SY54 @ SV3 )
!= ( SY54 @ SY47 ) ) ) )
| ( ( SY54 @ SY50 )
= ( SY54 @ SY53 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SY50 )
!= ( SY54 @ SY51 ) )
| ( ( SY54 @ SY52 )
!= ( SY54 @ SY53 ) ) )
| ( ( SY54 @ SY46 )
!= ( SY54 @ SY49 ) ) )
| ( ( SY54 @ SV1 )
!= ( SY54 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV3 )
!= ( SY54 @ SV4 ) )
| ( ( SY54 @ SV4 )
!= ( SY54 @ SY46 ) ) )
| ( ( SY54 @ SY46 )
!= ( SY54 @ SY47 ) ) )
| ~ ( ( ( SY54 @ SY50 )
!= ( SY54 @ SY53 ) ) ) )
| ( ( SY54 @ SY48 )
= ( SY54 @ SY51 ) ) ) )
| ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SV3 )
!= ( SY54 @ SV4 ) )
| ( ( SY54 @ SY46 )
!= ( SY54 @ SY47 ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY49 ) )
| ( ( SY54 @ SY50 )
!= ( SY54 @ SY51 ) )
| ( ( SY54 @ SY52 )
!= ( SY54 @ SY53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(19,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ! [SY46: $i] :
~ ~ ! [SY47: $i] :
~ ~ ! [SY48: $i] :
~ ~ ! [SY49: $i] :
~ ~ ! [SY50: $i] :
~ ~ ! [SY51: $i] :
~ ~ ! [SY52: $i] :
~ ~ ! [SY53: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SY46 ) ) )
| ~ ( ( SV1 != SY47 ) ) )
| ~ ( ( SV1 != SY48 ) ) )
| ~ ( ( SV1 != SY49 ) ) )
| ~ ( ( SV1 != SY50 ) ) )
| ~ ( ( SV1 != SY51 ) ) )
| ~ ( ( SV1 != SY52 ) ) )
| ~ ( ( SV1 != SY53 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SY46 ) ) )
| ~ ( ( SV2 != SY47 ) ) )
| ~ ( ( SV2 != SY48 ) ) )
| ~ ( ( SV2 != SY49 ) ) )
| ~ ( ( SV2 != SY50 ) ) )
| ~ ( ( SV2 != SY51 ) ) )
| ~ ( ( SV2 != SY52 ) ) )
| ~ ( ( SV2 != SY53 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SY46 ) ) )
| ~ ( ( SV3 != SY47 ) ) )
| ~ ( ( SV3 != SY48 ) ) )
| ~ ( ( SV3 != SY49 ) ) )
| ~ ( ( SV3 != SY50 ) ) )
| ~ ( ( SV3 != SY51 ) ) )
| ~ ( ( SV3 != SY52 ) ) )
| ~ ( ( SV3 != SY53 ) ) )
| ~ ( ( SY46 != SY47 ) ) )
| ~ ( ( SY46 != SY48 ) ) )
| ~ ( ( SY46 != SY49 ) ) )
| ~ ( ( SY46 != SY50 ) ) )
| ~ ( ( SY46 != SY51 ) ) )
| ~ ( ( SY46 != SY52 ) ) )
| ~ ( ( SY46 != SY53 ) ) )
| ~ ( ( SY47 != SY48 ) ) )
| ~ ( ( SY47 != SY49 ) ) )
| ~ ( ( SY47 != SY50 ) ) )
| ~ ( ( SY47 != SY51 ) ) )
| ~ ( ( SY47 != SY52 ) ) )
| ~ ( ( SY47 != SY53 ) ) )
| ~ ( ( SY48 != SY49 ) ) )
| ~ ( ( SY48 != SY50 ) ) )
| ~ ( ( SY48 != SY51 ) ) )
| ~ ( ( SY48 != SY52 ) ) )
| ~ ( ( SY48 != SY53 ) ) )
| ~ ( ( SY49 != SY50 ) ) )
| ~ ( ( SY49 != SY51 ) ) )
| ~ ( ( SY49 != SY52 ) ) )
| ~ ( ( SY49 != SY53 ) ) )
| ~ ( ( SY50 != SY51 ) ) )
| ~ ( ( SY50 != SY52 ) ) )
| ~ ( ( SY50 != SY53 ) ) )
| ~ ( ( SY51 != SY52 ) ) )
| ~ ( ( SY51 != SY53 ) ) )
| ~ ( ( SY52 != SY53 ) ) )
| ! [SY54: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SV3 )
!= ( SY54 @ SV4 ) ) )
| ( ( SY54 @ SY50 )
!= ( SY54 @ SY53 ) ) )
| ( ( SY54 @ SY46 )
= ( SY54 @ SY49 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SY52 )
!= ( SY54 @ SY53 ) ) )
| ( ( SY54 @ SV3 )
!= ( SY54 @ SY47 ) ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY51 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SY46 )
!= ( SY54 @ SY47 ) )
| ( ( SY54 @ SY47 )
!= ( SY54 @ SY48 ) ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY49 ) ) )
| ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV4 ) ) ) )
| ( ( SY54 @ SY50 )
!= ( SY54 @ SY53 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY49 ) ) )
| ~ ( ( ( SY54 @ SV3 )
!= ( SY54 @ SY47 ) ) ) )
| ( ( SY54 @ SY50 )
= ( SY54 @ SY53 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SY50 )
!= ( SY54 @ SY51 ) )
| ( ( SY54 @ SY52 )
!= ( SY54 @ SY53 ) ) )
| ( ( SY54 @ SY46 )
!= ( SY54 @ SY49 ) ) )
| ( ( SY54 @ SV1 )
!= ( SY54 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV3 )
!= ( SY54 @ SV4 ) )
| ( ( SY54 @ SV4 )
!= ( SY54 @ SY46 ) ) )
| ( ( SY54 @ SY46 )
!= ( SY54 @ SY47 ) ) )
| ~ ( ( ( SY54 @ SY50 )
!= ( SY54 @ SY53 ) ) ) )
| ( ( SY54 @ SY48 )
= ( SY54 @ SY51 ) ) ) )
| ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SV3 )
!= ( SY54 @ SV4 ) )
| ( ( SY54 @ SY46 )
!= ( SY54 @ SY47 ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY49 ) )
| ( ( SY54 @ SY50 )
!= ( SY54 @ SY51 ) )
| ( ( SY54 @ SY52 )
!= ( SY54 @ SY53 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(20,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY46: $i] :
~ ~ ! [SY47: $i] :
~ ~ ! [SY48: $i] :
~ ~ ! [SY49: $i] :
~ ~ ! [SY50: $i] :
~ ~ ! [SY51: $i] :
~ ~ ! [SY52: $i] :
~ ~ ! [SY53: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SY46 ) ) )
| ~ ( ( SV1 != SY47 ) ) )
| ~ ( ( SV1 != SY48 ) ) )
| ~ ( ( SV1 != SY49 ) ) )
| ~ ( ( SV1 != SY50 ) ) )
| ~ ( ( SV1 != SY51 ) ) )
| ~ ( ( SV1 != SY52 ) ) )
| ~ ( ( SV1 != SY53 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SY46 ) ) )
| ~ ( ( SV2 != SY47 ) ) )
| ~ ( ( SV2 != SY48 ) ) )
| ~ ( ( SV2 != SY49 ) ) )
| ~ ( ( SV2 != SY50 ) ) )
| ~ ( ( SV2 != SY51 ) ) )
| ~ ( ( SV2 != SY52 ) ) )
| ~ ( ( SV2 != SY53 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SY46 ) ) )
| ~ ( ( SV3 != SY47 ) ) )
| ~ ( ( SV3 != SY48 ) ) )
| ~ ( ( SV3 != SY49 ) ) )
| ~ ( ( SV3 != SY50 ) ) )
| ~ ( ( SV3 != SY51 ) ) )
| ~ ( ( SV3 != SY52 ) ) )
| ~ ( ( SV3 != SY53 ) ) )
| ~ ( ( SY46 != SY47 ) ) )
| ~ ( ( SY46 != SY48 ) ) )
| ~ ( ( SY46 != SY49 ) ) )
| ~ ( ( SY46 != SY50 ) ) )
| ~ ( ( SY46 != SY51 ) ) )
| ~ ( ( SY46 != SY52 ) ) )
| ~ ( ( SY46 != SY53 ) ) )
| ~ ( ( SY47 != SY48 ) ) )
| ~ ( ( SY47 != SY49 ) ) )
| ~ ( ( SY47 != SY50 ) ) )
| ~ ( ( SY47 != SY51 ) ) )
| ~ ( ( SY47 != SY52 ) ) )
| ~ ( ( SY47 != SY53 ) ) )
| ~ ( ( SY48 != SY49 ) ) )
| ~ ( ( SY48 != SY50 ) ) )
| ~ ( ( SY48 != SY51 ) ) )
| ~ ( ( SY48 != SY52 ) ) )
| ~ ( ( SY48 != SY53 ) ) )
| ~ ( ( SY49 != SY50 ) ) )
| ~ ( ( SY49 != SY51 ) ) )
| ~ ( ( SY49 != SY52 ) ) )
| ~ ( ( SY49 != SY53 ) ) )
| ~ ( ( SY50 != SY51 ) ) )
| ~ ( ( SY50 != SY52 ) ) )
| ~ ( ( SY50 != SY53 ) ) )
| ~ ( ( SY51 != SY52 ) ) )
| ~ ( ( SY51 != SY53 ) ) )
| ~ ( ( SY52 != SY53 ) ) )
| ! [SY54: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SV3 )
!= ( SY54 @ SV4 ) ) )
| ( ( SY54 @ SY50 )
!= ( SY54 @ SY53 ) ) )
| ( ( SY54 @ SY46 )
= ( SY54 @ SY49 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SY52 )
!= ( SY54 @ SY53 ) ) )
| ( ( SY54 @ SV3 )
!= ( SY54 @ SY47 ) ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY51 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SY46 )
!= ( SY54 @ SY47 ) )
| ( ( SY54 @ SY47 )
!= ( SY54 @ SY48 ) ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY49 ) ) )
| ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV4 ) ) ) )
| ( ( SY54 @ SY50 )
!= ( SY54 @ SY53 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY49 ) ) )
| ~ ( ( ( SY54 @ SV3 )
!= ( SY54 @ SY47 ) ) ) )
| ( ( SY54 @ SY50 )
= ( SY54 @ SY53 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SY50 )
!= ( SY54 @ SY51 ) )
| ( ( SY54 @ SY52 )
!= ( SY54 @ SY53 ) ) )
| ( ( SY54 @ SY46 )
!= ( SY54 @ SY49 ) ) )
| ( ( SY54 @ SV1 )
!= ( SY54 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY54 @ SV3 )
!= ( SY54 @ SV4 ) )
| ( ( SY54 @ SV4 )
!= ( SY54 @ SY46 ) ) )
| ( ( SY54 @ SY46 )
!= ( SY54 @ SY47 ) ) )
| ~ ( ( ( SY54 @ SY50 )
!= ( SY54 @ SY53 ) ) ) )
| ( ( SY54 @ SY48 )
= ( SY54 @ SY51 ) ) ) )
| ( ( SY54 @ SV1 )
!= ( SY54 @ SV2 ) )
| ( ( SY54 @ SV3 )
!= ( SY54 @ SV4 ) )
| ( ( SY54 @ SY46 )
!= ( SY54 @ SY47 ) )
| ( ( SY54 @ SY48 )
!= ( SY54 @ SY49 ) )
| ( ( SY54 @ SY50 )
!= ( SY54 @ SY51 ) )
| ( ( SY54 @ SY52 )
!= ( SY54 @ SY53 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(21,plain,
! [SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SY55 ) ) )
| ~ ( ( SV1 != SY56 ) ) )
| ~ ( ( SV1 != SY57 ) ) )
| ~ ( ( SV1 != SY58 ) ) )
| ~ ( ( SV1 != SY59 ) ) )
| ~ ( ( SV1 != SY60 ) ) )
| ~ ( ( SV1 != SY61 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SY55 ) ) )
| ~ ( ( SV2 != SY56 ) ) )
| ~ ( ( SV2 != SY57 ) ) )
| ~ ( ( SV2 != SY58 ) ) )
| ~ ( ( SV2 != SY59 ) ) )
| ~ ( ( SV2 != SY60 ) ) )
| ~ ( ( SV2 != SY61 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SY55 ) ) )
| ~ ( ( SV3 != SY56 ) ) )
| ~ ( ( SV3 != SY57 ) ) )
| ~ ( ( SV3 != SY58 ) ) )
| ~ ( ( SV3 != SY59 ) ) )
| ~ ( ( SV3 != SY60 ) ) )
| ~ ( ( SV3 != SY61 ) ) )
| ~ ( ( SV5 != SY55 ) ) )
| ~ ( ( SV5 != SY56 ) ) )
| ~ ( ( SV5 != SY57 ) ) )
| ~ ( ( SV5 != SY58 ) ) )
| ~ ( ( SV5 != SY59 ) ) )
| ~ ( ( SV5 != SY60 ) ) )
| ~ ( ( SV5 != SY61 ) ) )
| ~ ( ( SY55 != SY56 ) ) )
| ~ ( ( SY55 != SY57 ) ) )
| ~ ( ( SY55 != SY58 ) ) )
| ~ ( ( SY55 != SY59 ) ) )
| ~ ( ( SY55 != SY60 ) ) )
| ~ ( ( SY55 != SY61 ) ) )
| ~ ( ( SY56 != SY57 ) ) )
| ~ ( ( SY56 != SY58 ) ) )
| ~ ( ( SY56 != SY59 ) ) )
| ~ ( ( SY56 != SY60 ) ) )
| ~ ( ( SY56 != SY61 ) ) )
| ~ ( ( SY57 != SY58 ) ) )
| ~ ( ( SY57 != SY59 ) ) )
| ~ ( ( SY57 != SY60 ) ) )
| ~ ( ( SY57 != SY61 ) ) )
| ~ ( ( SY58 != SY59 ) ) )
| ~ ( ( SY58 != SY60 ) ) )
| ~ ( ( SY58 != SY61 ) ) )
| ~ ( ( SY59 != SY60 ) ) )
| ~ ( ( SY59 != SY61 ) ) )
| ~ ( ( SY60 != SY61 ) ) )
| ! [SY62: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SV3 )
!= ( SY62 @ SV4 ) ) )
| ( ( SY62 @ SY58 )
!= ( SY62 @ SY61 ) ) )
| ( ( SY62 @ SV5 )
= ( SY62 @ SY57 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SY60 )
!= ( SY62 @ SY61 ) ) )
| ( ( SY62 @ SV3 )
!= ( SY62 @ SY55 ) ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY59 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV5 )
!= ( SY62 @ SY55 ) )
| ( ( SY62 @ SY55 )
!= ( SY62 @ SY56 ) ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY57 ) ) )
| ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV4 ) ) ) )
| ( ( SY62 @ SY58 )
!= ( SY62 @ SY61 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY57 ) ) )
| ~ ( ( ( SY62 @ SV3 )
!= ( SY62 @ SY55 ) ) ) )
| ( ( SY62 @ SY58 )
= ( SY62 @ SY61 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SY58 )
!= ( SY62 @ SY59 ) )
| ( ( SY62 @ SY60 )
!= ( SY62 @ SY61 ) ) )
| ( ( SY62 @ SV5 )
!= ( SY62 @ SY57 ) ) )
| ( ( SY62 @ SV1 )
!= ( SY62 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV3 )
!= ( SY62 @ SV4 ) )
| ( ( SY62 @ SV4 )
!= ( SY62 @ SV5 ) ) )
| ( ( SY62 @ SV5 )
!= ( SY62 @ SY55 ) ) )
| ~ ( ( ( SY62 @ SY58 )
!= ( SY62 @ SY61 ) ) ) )
| ( ( SY62 @ SY56 )
= ( SY62 @ SY59 ) ) ) )
| ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SV3 )
!= ( SY62 @ SV4 ) )
| ( ( SY62 @ SV5 )
!= ( SY62 @ SY55 ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY57 ) )
| ( ( SY62 @ SY58 )
!= ( SY62 @ SY59 ) )
| ( ( SY62 @ SY60 )
!= ( SY62 @ SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(22,plain,
! [SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SY55 ) ) )
| ~ ( ( SV1 != SY56 ) ) )
| ~ ( ( SV1 != SY57 ) ) )
| ~ ( ( SV1 != SY58 ) ) )
| ~ ( ( SV1 != SY59 ) ) )
| ~ ( ( SV1 != SY60 ) ) )
| ~ ( ( SV1 != SY61 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SY55 ) ) )
| ~ ( ( SV2 != SY56 ) ) )
| ~ ( ( SV2 != SY57 ) ) )
| ~ ( ( SV2 != SY58 ) ) )
| ~ ( ( SV2 != SY59 ) ) )
| ~ ( ( SV2 != SY60 ) ) )
| ~ ( ( SV2 != SY61 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SY55 ) ) )
| ~ ( ( SV3 != SY56 ) ) )
| ~ ( ( SV3 != SY57 ) ) )
| ~ ( ( SV3 != SY58 ) ) )
| ~ ( ( SV3 != SY59 ) ) )
| ~ ( ( SV3 != SY60 ) ) )
| ~ ( ( SV3 != SY61 ) ) )
| ~ ( ( SV5 != SY55 ) ) )
| ~ ( ( SV5 != SY56 ) ) )
| ~ ( ( SV5 != SY57 ) ) )
| ~ ( ( SV5 != SY58 ) ) )
| ~ ( ( SV5 != SY59 ) ) )
| ~ ( ( SV5 != SY60 ) ) )
| ~ ( ( SV5 != SY61 ) ) )
| ~ ( ( SY55 != SY56 ) ) )
| ~ ( ( SY55 != SY57 ) ) )
| ~ ( ( SY55 != SY58 ) ) )
| ~ ( ( SY55 != SY59 ) ) )
| ~ ( ( SY55 != SY60 ) ) )
| ~ ( ( SY55 != SY61 ) ) )
| ~ ( ( SY56 != SY57 ) ) )
| ~ ( ( SY56 != SY58 ) ) )
| ~ ( ( SY56 != SY59 ) ) )
| ~ ( ( SY56 != SY60 ) ) )
| ~ ( ( SY56 != SY61 ) ) )
| ~ ( ( SY57 != SY58 ) ) )
| ~ ( ( SY57 != SY59 ) ) )
| ~ ( ( SY57 != SY60 ) ) )
| ~ ( ( SY57 != SY61 ) ) )
| ~ ( ( SY58 != SY59 ) ) )
| ~ ( ( SY58 != SY60 ) ) )
| ~ ( ( SY58 != SY61 ) ) )
| ~ ( ( SY59 != SY60 ) ) )
| ~ ( ( SY59 != SY61 ) ) )
| ~ ( ( SY60 != SY61 ) ) )
| ! [SY62: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SV3 )
!= ( SY62 @ SV4 ) ) )
| ( ( SY62 @ SY58 )
!= ( SY62 @ SY61 ) ) )
| ( ( SY62 @ SV5 )
= ( SY62 @ SY57 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SY60 )
!= ( SY62 @ SY61 ) ) )
| ( ( SY62 @ SV3 )
!= ( SY62 @ SY55 ) ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY59 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV5 )
!= ( SY62 @ SY55 ) )
| ( ( SY62 @ SY55 )
!= ( SY62 @ SY56 ) ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY57 ) ) )
| ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV4 ) ) ) )
| ( ( SY62 @ SY58 )
!= ( SY62 @ SY61 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY57 ) ) )
| ~ ( ( ( SY62 @ SV3 )
!= ( SY62 @ SY55 ) ) ) )
| ( ( SY62 @ SY58 )
= ( SY62 @ SY61 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SY58 )
!= ( SY62 @ SY59 ) )
| ( ( SY62 @ SY60 )
!= ( SY62 @ SY61 ) ) )
| ( ( SY62 @ SV5 )
!= ( SY62 @ SY57 ) ) )
| ( ( SY62 @ SV1 )
!= ( SY62 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV3 )
!= ( SY62 @ SV4 ) )
| ( ( SY62 @ SV4 )
!= ( SY62 @ SV5 ) ) )
| ( ( SY62 @ SV5 )
!= ( SY62 @ SY55 ) ) )
| ~ ( ( ( SY62 @ SY58 )
!= ( SY62 @ SY61 ) ) ) )
| ( ( SY62 @ SY56 )
= ( SY62 @ SY59 ) ) ) )
| ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SV3 )
!= ( SY62 @ SV4 ) )
| ( ( SY62 @ SV5 )
!= ( SY62 @ SY55 ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY57 ) )
| ( ( SY62 @ SY58 )
!= ( SY62 @ SY59 ) )
| ( ( SY62 @ SY60 )
!= ( SY62 @ SY61 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(23,plain,
! [SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY55: $i] :
~ ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ! [SY58: $i] :
~ ~ ! [SY59: $i] :
~ ~ ! [SY60: $i] :
~ ~ ! [SY61: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SY55 ) ) )
| ~ ( ( SV1 != SY56 ) ) )
| ~ ( ( SV1 != SY57 ) ) )
| ~ ( ( SV1 != SY58 ) ) )
| ~ ( ( SV1 != SY59 ) ) )
| ~ ( ( SV1 != SY60 ) ) )
| ~ ( ( SV1 != SY61 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SY55 ) ) )
| ~ ( ( SV2 != SY56 ) ) )
| ~ ( ( SV2 != SY57 ) ) )
| ~ ( ( SV2 != SY58 ) ) )
| ~ ( ( SV2 != SY59 ) ) )
| ~ ( ( SV2 != SY60 ) ) )
| ~ ( ( SV2 != SY61 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SY55 ) ) )
| ~ ( ( SV3 != SY56 ) ) )
| ~ ( ( SV3 != SY57 ) ) )
| ~ ( ( SV3 != SY58 ) ) )
| ~ ( ( SV3 != SY59 ) ) )
| ~ ( ( SV3 != SY60 ) ) )
| ~ ( ( SV3 != SY61 ) ) )
| ~ ( ( SV5 != SY55 ) ) )
| ~ ( ( SV5 != SY56 ) ) )
| ~ ( ( SV5 != SY57 ) ) )
| ~ ( ( SV5 != SY58 ) ) )
| ~ ( ( SV5 != SY59 ) ) )
| ~ ( ( SV5 != SY60 ) ) )
| ~ ( ( SV5 != SY61 ) ) )
| ~ ( ( SY55 != SY56 ) ) )
| ~ ( ( SY55 != SY57 ) ) )
| ~ ( ( SY55 != SY58 ) ) )
| ~ ( ( SY55 != SY59 ) ) )
| ~ ( ( SY55 != SY60 ) ) )
| ~ ( ( SY55 != SY61 ) ) )
| ~ ( ( SY56 != SY57 ) ) )
| ~ ( ( SY56 != SY58 ) ) )
| ~ ( ( SY56 != SY59 ) ) )
| ~ ( ( SY56 != SY60 ) ) )
| ~ ( ( SY56 != SY61 ) ) )
| ~ ( ( SY57 != SY58 ) ) )
| ~ ( ( SY57 != SY59 ) ) )
| ~ ( ( SY57 != SY60 ) ) )
| ~ ( ( SY57 != SY61 ) ) )
| ~ ( ( SY58 != SY59 ) ) )
| ~ ( ( SY58 != SY60 ) ) )
| ~ ( ( SY58 != SY61 ) ) )
| ~ ( ( SY59 != SY60 ) ) )
| ~ ( ( SY59 != SY61 ) ) )
| ~ ( ( SY60 != SY61 ) ) )
| ! [SY62: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SV3 )
!= ( SY62 @ SV4 ) ) )
| ( ( SY62 @ SY58 )
!= ( SY62 @ SY61 ) ) )
| ( ( SY62 @ SV5 )
= ( SY62 @ SY57 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SY60 )
!= ( SY62 @ SY61 ) ) )
| ( ( SY62 @ SV3 )
!= ( SY62 @ SY55 ) ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY59 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV5 )
!= ( SY62 @ SY55 ) )
| ( ( SY62 @ SY55 )
!= ( SY62 @ SY56 ) ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY57 ) ) )
| ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV4 ) ) ) )
| ( ( SY62 @ SY58 )
!= ( SY62 @ SY61 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY57 ) ) )
| ~ ( ( ( SY62 @ SV3 )
!= ( SY62 @ SY55 ) ) ) )
| ( ( SY62 @ SY58 )
= ( SY62 @ SY61 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SY58 )
!= ( SY62 @ SY59 ) )
| ( ( SY62 @ SY60 )
!= ( SY62 @ SY61 ) ) )
| ( ( SY62 @ SV5 )
!= ( SY62 @ SY57 ) ) )
| ( ( SY62 @ SV1 )
!= ( SY62 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY62 @ SV3 )
!= ( SY62 @ SV4 ) )
| ( ( SY62 @ SV4 )
!= ( SY62 @ SV5 ) ) )
| ( ( SY62 @ SV5 )
!= ( SY62 @ SY55 ) ) )
| ~ ( ( ( SY62 @ SY58 )
!= ( SY62 @ SY61 ) ) ) )
| ( ( SY62 @ SY56 )
= ( SY62 @ SY59 ) ) ) )
| ( ( SY62 @ SV1 )
!= ( SY62 @ SV2 ) )
| ( ( SY62 @ SV3 )
!= ( SY62 @ SV4 ) )
| ( ( SY62 @ SV5 )
!= ( SY62 @ SY55 ) )
| ( ( SY62 @ SY56 )
!= ( SY62 @ SY57 ) )
| ( ( SY62 @ SY58 )
!= ( SY62 @ SY59 ) )
| ( ( SY62 @ SY60 )
!= ( SY62 @ SY61 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(24,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY63: $i] :
~ ~ ! [SY64: $i] :
~ ~ ! [SY65: $i] :
~ ~ ! [SY66: $i] :
~ ~ ! [SY67: $i] :
~ ~ ! [SY68: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SY63 ) ) )
| ~ ( ( SV1 != SY64 ) ) )
| ~ ( ( SV1 != SY65 ) ) )
| ~ ( ( SV1 != SY66 ) ) )
| ~ ( ( SV1 != SY67 ) ) )
| ~ ( ( SV1 != SY68 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SY63 ) ) )
| ~ ( ( SV2 != SY64 ) ) )
| ~ ( ( SV2 != SY65 ) ) )
| ~ ( ( SV2 != SY66 ) ) )
| ~ ( ( SV2 != SY67 ) ) )
| ~ ( ( SV2 != SY68 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SY63 ) ) )
| ~ ( ( SV3 != SY64 ) ) )
| ~ ( ( SV3 != SY65 ) ) )
| ~ ( ( SV3 != SY66 ) ) )
| ~ ( ( SV3 != SY67 ) ) )
| ~ ( ( SV3 != SY68 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SY63 ) ) )
| ~ ( ( SV5 != SY64 ) ) )
| ~ ( ( SV5 != SY65 ) ) )
| ~ ( ( SV5 != SY66 ) ) )
| ~ ( ( SV5 != SY67 ) ) )
| ~ ( ( SV5 != SY68 ) ) )
| ~ ( ( SV6 != SY63 ) ) )
| ~ ( ( SV6 != SY64 ) ) )
| ~ ( ( SV6 != SY65 ) ) )
| ~ ( ( SV6 != SY66 ) ) )
| ~ ( ( SV6 != SY67 ) ) )
| ~ ( ( SV6 != SY68 ) ) )
| ~ ( ( SY63 != SY64 ) ) )
| ~ ( ( SY63 != SY65 ) ) )
| ~ ( ( SY63 != SY66 ) ) )
| ~ ( ( SY63 != SY67 ) ) )
| ~ ( ( SY63 != SY68 ) ) )
| ~ ( ( SY64 != SY65 ) ) )
| ~ ( ( SY64 != SY66 ) ) )
| ~ ( ( SY64 != SY67 ) ) )
| ~ ( ( SY64 != SY68 ) ) )
| ~ ( ( SY65 != SY66 ) ) )
| ~ ( ( SY65 != SY67 ) ) )
| ~ ( ( SY65 != SY68 ) ) )
| ~ ( ( SY66 != SY67 ) ) )
| ~ ( ( SY66 != SY68 ) ) )
| ~ ( ( SY67 != SY68 ) ) )
| ! [SY69: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SV3 )
!= ( SY69 @ SV4 ) ) )
| ( ( SY69 @ SY65 )
!= ( SY69 @ SY68 ) ) )
| ( ( SY69 @ SV5 )
= ( SY69 @ SY64 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SY67 )
!= ( SY69 @ SY68 ) ) )
| ( ( SY69 @ SV3 )
!= ( SY69 @ SV6 ) ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY66 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV5 )
!= ( SY69 @ SV6 ) )
| ( ( SY69 @ SV6 )
!= ( SY69 @ SY63 ) ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY64 ) ) )
| ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV4 ) ) ) )
| ( ( SY69 @ SY65 )
!= ( SY69 @ SY68 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY64 ) ) )
| ~ ( ( ( SY69 @ SV3 )
!= ( SY69 @ SV6 ) ) ) )
| ( ( SY69 @ SY65 )
= ( SY69 @ SY68 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SY65 )
!= ( SY69 @ SY66 ) )
| ( ( SY69 @ SY67 )
!= ( SY69 @ SY68 ) ) )
| ( ( SY69 @ SV5 )
!= ( SY69 @ SY64 ) ) )
| ( ( SY69 @ SV1 )
!= ( SY69 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV3 )
!= ( SY69 @ SV4 ) )
| ( ( SY69 @ SV4 )
!= ( SY69 @ SV5 ) ) )
| ( ( SY69 @ SV5 )
!= ( SY69 @ SV6 ) ) )
| ~ ( ( ( SY69 @ SY65 )
!= ( SY69 @ SY68 ) ) ) )
| ( ( SY69 @ SY63 )
= ( SY69 @ SY66 ) ) ) )
| ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SV3 )
!= ( SY69 @ SV4 ) )
| ( ( SY69 @ SV5 )
!= ( SY69 @ SV6 ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY64 ) )
| ( ( SY69 @ SY65 )
!= ( SY69 @ SY66 ) )
| ( ( SY69 @ SY67 )
!= ( SY69 @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(25,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ! [SY63: $i] :
~ ~ ! [SY64: $i] :
~ ~ ! [SY65: $i] :
~ ~ ! [SY66: $i] :
~ ~ ! [SY67: $i] :
~ ~ ! [SY68: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SY63 ) ) )
| ~ ( ( SV1 != SY64 ) ) )
| ~ ( ( SV1 != SY65 ) ) )
| ~ ( ( SV1 != SY66 ) ) )
| ~ ( ( SV1 != SY67 ) ) )
| ~ ( ( SV1 != SY68 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SY63 ) ) )
| ~ ( ( SV2 != SY64 ) ) )
| ~ ( ( SV2 != SY65 ) ) )
| ~ ( ( SV2 != SY66 ) ) )
| ~ ( ( SV2 != SY67 ) ) )
| ~ ( ( SV2 != SY68 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SY63 ) ) )
| ~ ( ( SV3 != SY64 ) ) )
| ~ ( ( SV3 != SY65 ) ) )
| ~ ( ( SV3 != SY66 ) ) )
| ~ ( ( SV3 != SY67 ) ) )
| ~ ( ( SV3 != SY68 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SY63 ) ) )
| ~ ( ( SV5 != SY64 ) ) )
| ~ ( ( SV5 != SY65 ) ) )
| ~ ( ( SV5 != SY66 ) ) )
| ~ ( ( SV5 != SY67 ) ) )
| ~ ( ( SV5 != SY68 ) ) )
| ~ ( ( SV6 != SY63 ) ) )
| ~ ( ( SV6 != SY64 ) ) )
| ~ ( ( SV6 != SY65 ) ) )
| ~ ( ( SV6 != SY66 ) ) )
| ~ ( ( SV6 != SY67 ) ) )
| ~ ( ( SV6 != SY68 ) ) )
| ~ ( ( SY63 != SY64 ) ) )
| ~ ( ( SY63 != SY65 ) ) )
| ~ ( ( SY63 != SY66 ) ) )
| ~ ( ( SY63 != SY67 ) ) )
| ~ ( ( SY63 != SY68 ) ) )
| ~ ( ( SY64 != SY65 ) ) )
| ~ ( ( SY64 != SY66 ) ) )
| ~ ( ( SY64 != SY67 ) ) )
| ~ ( ( SY64 != SY68 ) ) )
| ~ ( ( SY65 != SY66 ) ) )
| ~ ( ( SY65 != SY67 ) ) )
| ~ ( ( SY65 != SY68 ) ) )
| ~ ( ( SY66 != SY67 ) ) )
| ~ ( ( SY66 != SY68 ) ) )
| ~ ( ( SY67 != SY68 ) ) )
| ! [SY69: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SV3 )
!= ( SY69 @ SV4 ) ) )
| ( ( SY69 @ SY65 )
!= ( SY69 @ SY68 ) ) )
| ( ( SY69 @ SV5 )
= ( SY69 @ SY64 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SY67 )
!= ( SY69 @ SY68 ) ) )
| ( ( SY69 @ SV3 )
!= ( SY69 @ SV6 ) ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY66 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV5 )
!= ( SY69 @ SV6 ) )
| ( ( SY69 @ SV6 )
!= ( SY69 @ SY63 ) ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY64 ) ) )
| ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV4 ) ) ) )
| ( ( SY69 @ SY65 )
!= ( SY69 @ SY68 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY64 ) ) )
| ~ ( ( ( SY69 @ SV3 )
!= ( SY69 @ SV6 ) ) ) )
| ( ( SY69 @ SY65 )
= ( SY69 @ SY68 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SY65 )
!= ( SY69 @ SY66 ) )
| ( ( SY69 @ SY67 )
!= ( SY69 @ SY68 ) ) )
| ( ( SY69 @ SV5 )
!= ( SY69 @ SY64 ) ) )
| ( ( SY69 @ SV1 )
!= ( SY69 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV3 )
!= ( SY69 @ SV4 ) )
| ( ( SY69 @ SV4 )
!= ( SY69 @ SV5 ) ) )
| ( ( SY69 @ SV5 )
!= ( SY69 @ SV6 ) ) )
| ~ ( ( ( SY69 @ SY65 )
!= ( SY69 @ SY68 ) ) ) )
| ( ( SY69 @ SY63 )
= ( SY69 @ SY66 ) ) ) )
| ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SV3 )
!= ( SY69 @ SV4 ) )
| ( ( SY69 @ SV5 )
!= ( SY69 @ SV6 ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY64 ) )
| ( ( SY69 @ SY65 )
!= ( SY69 @ SY66 ) )
| ( ( SY69 @ SY67 )
!= ( SY69 @ SY68 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(26,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY63: $i] :
~ ~ ! [SY64: $i] :
~ ~ ! [SY65: $i] :
~ ~ ! [SY66: $i] :
~ ~ ! [SY67: $i] :
~ ~ ! [SY68: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SY63 ) ) )
| ~ ( ( SV1 != SY64 ) ) )
| ~ ( ( SV1 != SY65 ) ) )
| ~ ( ( SV1 != SY66 ) ) )
| ~ ( ( SV1 != SY67 ) ) )
| ~ ( ( SV1 != SY68 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SY63 ) ) )
| ~ ( ( SV2 != SY64 ) ) )
| ~ ( ( SV2 != SY65 ) ) )
| ~ ( ( SV2 != SY66 ) ) )
| ~ ( ( SV2 != SY67 ) ) )
| ~ ( ( SV2 != SY68 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SY63 ) ) )
| ~ ( ( SV3 != SY64 ) ) )
| ~ ( ( SV3 != SY65 ) ) )
| ~ ( ( SV3 != SY66 ) ) )
| ~ ( ( SV3 != SY67 ) ) )
| ~ ( ( SV3 != SY68 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SY63 ) ) )
| ~ ( ( SV5 != SY64 ) ) )
| ~ ( ( SV5 != SY65 ) ) )
| ~ ( ( SV5 != SY66 ) ) )
| ~ ( ( SV5 != SY67 ) ) )
| ~ ( ( SV5 != SY68 ) ) )
| ~ ( ( SV6 != SY63 ) ) )
| ~ ( ( SV6 != SY64 ) ) )
| ~ ( ( SV6 != SY65 ) ) )
| ~ ( ( SV6 != SY66 ) ) )
| ~ ( ( SV6 != SY67 ) ) )
| ~ ( ( SV6 != SY68 ) ) )
| ~ ( ( SY63 != SY64 ) ) )
| ~ ( ( SY63 != SY65 ) ) )
| ~ ( ( SY63 != SY66 ) ) )
| ~ ( ( SY63 != SY67 ) ) )
| ~ ( ( SY63 != SY68 ) ) )
| ~ ( ( SY64 != SY65 ) ) )
| ~ ( ( SY64 != SY66 ) ) )
| ~ ( ( SY64 != SY67 ) ) )
| ~ ( ( SY64 != SY68 ) ) )
| ~ ( ( SY65 != SY66 ) ) )
| ~ ( ( SY65 != SY67 ) ) )
| ~ ( ( SY65 != SY68 ) ) )
| ~ ( ( SY66 != SY67 ) ) )
| ~ ( ( SY66 != SY68 ) ) )
| ~ ( ( SY67 != SY68 ) ) )
| ! [SY69: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SV3 )
!= ( SY69 @ SV4 ) ) )
| ( ( SY69 @ SY65 )
!= ( SY69 @ SY68 ) ) )
| ( ( SY69 @ SV5 )
= ( SY69 @ SY64 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SY67 )
!= ( SY69 @ SY68 ) ) )
| ( ( SY69 @ SV3 )
!= ( SY69 @ SV6 ) ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY66 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV5 )
!= ( SY69 @ SV6 ) )
| ( ( SY69 @ SV6 )
!= ( SY69 @ SY63 ) ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY64 ) ) )
| ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV4 ) ) ) )
| ( ( SY69 @ SY65 )
!= ( SY69 @ SY68 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY64 ) ) )
| ~ ( ( ( SY69 @ SV3 )
!= ( SY69 @ SV6 ) ) ) )
| ( ( SY69 @ SY65 )
= ( SY69 @ SY68 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SY65 )
!= ( SY69 @ SY66 ) )
| ( ( SY69 @ SY67 )
!= ( SY69 @ SY68 ) ) )
| ( ( SY69 @ SV5 )
!= ( SY69 @ SY64 ) ) )
| ( ( SY69 @ SV1 )
!= ( SY69 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY69 @ SV3 )
!= ( SY69 @ SV4 ) )
| ( ( SY69 @ SV4 )
!= ( SY69 @ SV5 ) ) )
| ( ( SY69 @ SV5 )
!= ( SY69 @ SV6 ) ) )
| ~ ( ( ( SY69 @ SY65 )
!= ( SY69 @ SY68 ) ) ) )
| ( ( SY69 @ SY63 )
= ( SY69 @ SY66 ) ) ) )
| ( ( SY69 @ SV1 )
!= ( SY69 @ SV2 ) )
| ( ( SY69 @ SV3 )
!= ( SY69 @ SV4 ) )
| ( ( SY69 @ SV5 )
!= ( SY69 @ SV6 ) )
| ( ( SY69 @ SY63 )
!= ( SY69 @ SY64 ) )
| ( ( SY69 @ SY65 )
!= ( SY69 @ SY66 ) )
| ( ( SY69 @ SY67 )
!= ( SY69 @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(27,plain,
! [SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY70: $i] :
~ ~ ! [SY71: $i] :
~ ~ ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ! [SY74: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SY70 ) ) )
| ~ ( ( SV1 != SY71 ) ) )
| ~ ( ( SV1 != SY72 ) ) )
| ~ ( ( SV1 != SY73 ) ) )
| ~ ( ( SV1 != SY74 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SY70 ) ) )
| ~ ( ( SV2 != SY71 ) ) )
| ~ ( ( SV2 != SY72 ) ) )
| ~ ( ( SV2 != SY73 ) ) )
| ~ ( ( SV2 != SY74 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SY70 ) ) )
| ~ ( ( SV3 != SY71 ) ) )
| ~ ( ( SV3 != SY72 ) ) )
| ~ ( ( SV3 != SY73 ) ) )
| ~ ( ( SV3 != SY74 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SY70 ) ) )
| ~ ( ( SV5 != SY71 ) ) )
| ~ ( ( SV5 != SY72 ) ) )
| ~ ( ( SV5 != SY73 ) ) )
| ~ ( ( SV5 != SY74 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SY70 ) ) )
| ~ ( ( SV6 != SY71 ) ) )
| ~ ( ( SV6 != SY72 ) ) )
| ~ ( ( SV6 != SY73 ) ) )
| ~ ( ( SV6 != SY74 ) ) )
| ~ ( ( SV7 != SY70 ) ) )
| ~ ( ( SV7 != SY71 ) ) )
| ~ ( ( SV7 != SY72 ) ) )
| ~ ( ( SV7 != SY73 ) ) )
| ~ ( ( SV7 != SY74 ) ) )
| ~ ( ( SY70 != SY71 ) ) )
| ~ ( ( SY70 != SY72 ) ) )
| ~ ( ( SY70 != SY73 ) ) )
| ~ ( ( SY70 != SY74 ) ) )
| ~ ( ( SY71 != SY72 ) ) )
| ~ ( ( SY71 != SY73 ) ) )
| ~ ( ( SY71 != SY74 ) ) )
| ~ ( ( SY72 != SY73 ) ) )
| ~ ( ( SY72 != SY74 ) ) )
| ~ ( ( SY73 != SY74 ) ) )
| ! [SY75: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SV3 )
!= ( SY75 @ SV4 ) ) )
| ( ( SY75 @ SY71 )
!= ( SY75 @ SY74 ) ) )
| ( ( SY75 @ SV5 )
= ( SY75 @ SY70 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SY73 )
!= ( SY75 @ SY74 ) ) )
| ( ( SY75 @ SV3 )
!= ( SY75 @ SV6 ) ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY72 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV5 )
!= ( SY75 @ SV6 ) )
| ( ( SY75 @ SV6 )
!= ( SY75 @ SV7 ) ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY70 ) ) )
| ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV4 ) ) ) )
| ( ( SY75 @ SY71 )
!= ( SY75 @ SY74 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY70 ) ) )
| ~ ( ( ( SY75 @ SV3 )
!= ( SY75 @ SV6 ) ) ) )
| ( ( SY75 @ SY71 )
= ( SY75 @ SY74 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SY71 )
!= ( SY75 @ SY72 ) )
| ( ( SY75 @ SY73 )
!= ( SY75 @ SY74 ) ) )
| ( ( SY75 @ SV5 )
!= ( SY75 @ SY70 ) ) )
| ( ( SY75 @ SV1 )
!= ( SY75 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV3 )
!= ( SY75 @ SV4 ) )
| ( ( SY75 @ SV4 )
!= ( SY75 @ SV5 ) ) )
| ( ( SY75 @ SV5 )
!= ( SY75 @ SV6 ) ) )
| ~ ( ( ( SY75 @ SY71 )
!= ( SY75 @ SY74 ) ) ) )
| ( ( SY75 @ SV7 )
= ( SY75 @ SY72 ) ) ) )
| ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SV3 )
!= ( SY75 @ SV4 ) )
| ( ( SY75 @ SV5 )
!= ( SY75 @ SV6 ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY70 ) )
| ( ( SY75 @ SY71 )
!= ( SY75 @ SY72 ) )
| ( ( SY75 @ SY73 )
!= ( SY75 @ SY74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(28,plain,
! [SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ! [SY70: $i] :
~ ~ ! [SY71: $i] :
~ ~ ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ! [SY74: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SY70 ) ) )
| ~ ( ( SV1 != SY71 ) ) )
| ~ ( ( SV1 != SY72 ) ) )
| ~ ( ( SV1 != SY73 ) ) )
| ~ ( ( SV1 != SY74 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SY70 ) ) )
| ~ ( ( SV2 != SY71 ) ) )
| ~ ( ( SV2 != SY72 ) ) )
| ~ ( ( SV2 != SY73 ) ) )
| ~ ( ( SV2 != SY74 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SY70 ) ) )
| ~ ( ( SV3 != SY71 ) ) )
| ~ ( ( SV3 != SY72 ) ) )
| ~ ( ( SV3 != SY73 ) ) )
| ~ ( ( SV3 != SY74 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SY70 ) ) )
| ~ ( ( SV5 != SY71 ) ) )
| ~ ( ( SV5 != SY72 ) ) )
| ~ ( ( SV5 != SY73 ) ) )
| ~ ( ( SV5 != SY74 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SY70 ) ) )
| ~ ( ( SV6 != SY71 ) ) )
| ~ ( ( SV6 != SY72 ) ) )
| ~ ( ( SV6 != SY73 ) ) )
| ~ ( ( SV6 != SY74 ) ) )
| ~ ( ( SV7 != SY70 ) ) )
| ~ ( ( SV7 != SY71 ) ) )
| ~ ( ( SV7 != SY72 ) ) )
| ~ ( ( SV7 != SY73 ) ) )
| ~ ( ( SV7 != SY74 ) ) )
| ~ ( ( SY70 != SY71 ) ) )
| ~ ( ( SY70 != SY72 ) ) )
| ~ ( ( SY70 != SY73 ) ) )
| ~ ( ( SY70 != SY74 ) ) )
| ~ ( ( SY71 != SY72 ) ) )
| ~ ( ( SY71 != SY73 ) ) )
| ~ ( ( SY71 != SY74 ) ) )
| ~ ( ( SY72 != SY73 ) ) )
| ~ ( ( SY72 != SY74 ) ) )
| ~ ( ( SY73 != SY74 ) ) )
| ! [SY75: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SV3 )
!= ( SY75 @ SV4 ) ) )
| ( ( SY75 @ SY71 )
!= ( SY75 @ SY74 ) ) )
| ( ( SY75 @ SV5 )
= ( SY75 @ SY70 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SY73 )
!= ( SY75 @ SY74 ) ) )
| ( ( SY75 @ SV3 )
!= ( SY75 @ SV6 ) ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY72 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV5 )
!= ( SY75 @ SV6 ) )
| ( ( SY75 @ SV6 )
!= ( SY75 @ SV7 ) ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY70 ) ) )
| ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV4 ) ) ) )
| ( ( SY75 @ SY71 )
!= ( SY75 @ SY74 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY70 ) ) )
| ~ ( ( ( SY75 @ SV3 )
!= ( SY75 @ SV6 ) ) ) )
| ( ( SY75 @ SY71 )
= ( SY75 @ SY74 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SY71 )
!= ( SY75 @ SY72 ) )
| ( ( SY75 @ SY73 )
!= ( SY75 @ SY74 ) ) )
| ( ( SY75 @ SV5 )
!= ( SY75 @ SY70 ) ) )
| ( ( SY75 @ SV1 )
!= ( SY75 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV3 )
!= ( SY75 @ SV4 ) )
| ( ( SY75 @ SV4 )
!= ( SY75 @ SV5 ) ) )
| ( ( SY75 @ SV5 )
!= ( SY75 @ SV6 ) ) )
| ~ ( ( ( SY75 @ SY71 )
!= ( SY75 @ SY74 ) ) ) )
| ( ( SY75 @ SV7 )
= ( SY75 @ SY72 ) ) ) )
| ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SV3 )
!= ( SY75 @ SV4 ) )
| ( ( SY75 @ SV5 )
!= ( SY75 @ SV6 ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY70 ) )
| ( ( SY75 @ SY71 )
!= ( SY75 @ SY72 ) )
| ( ( SY75 @ SY73 )
!= ( SY75 @ SY74 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(29,plain,
! [SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY70: $i] :
~ ~ ! [SY71: $i] :
~ ~ ! [SY72: $i] :
~ ~ ! [SY73: $i] :
~ ~ ! [SY74: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SY70 ) ) )
| ~ ( ( SV1 != SY71 ) ) )
| ~ ( ( SV1 != SY72 ) ) )
| ~ ( ( SV1 != SY73 ) ) )
| ~ ( ( SV1 != SY74 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SY70 ) ) )
| ~ ( ( SV2 != SY71 ) ) )
| ~ ( ( SV2 != SY72 ) ) )
| ~ ( ( SV2 != SY73 ) ) )
| ~ ( ( SV2 != SY74 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SY70 ) ) )
| ~ ( ( SV3 != SY71 ) ) )
| ~ ( ( SV3 != SY72 ) ) )
| ~ ( ( SV3 != SY73 ) ) )
| ~ ( ( SV3 != SY74 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SY70 ) ) )
| ~ ( ( SV5 != SY71 ) ) )
| ~ ( ( SV5 != SY72 ) ) )
| ~ ( ( SV5 != SY73 ) ) )
| ~ ( ( SV5 != SY74 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SY70 ) ) )
| ~ ( ( SV6 != SY71 ) ) )
| ~ ( ( SV6 != SY72 ) ) )
| ~ ( ( SV6 != SY73 ) ) )
| ~ ( ( SV6 != SY74 ) ) )
| ~ ( ( SV7 != SY70 ) ) )
| ~ ( ( SV7 != SY71 ) ) )
| ~ ( ( SV7 != SY72 ) ) )
| ~ ( ( SV7 != SY73 ) ) )
| ~ ( ( SV7 != SY74 ) ) )
| ~ ( ( SY70 != SY71 ) ) )
| ~ ( ( SY70 != SY72 ) ) )
| ~ ( ( SY70 != SY73 ) ) )
| ~ ( ( SY70 != SY74 ) ) )
| ~ ( ( SY71 != SY72 ) ) )
| ~ ( ( SY71 != SY73 ) ) )
| ~ ( ( SY71 != SY74 ) ) )
| ~ ( ( SY72 != SY73 ) ) )
| ~ ( ( SY72 != SY74 ) ) )
| ~ ( ( SY73 != SY74 ) ) )
| ! [SY75: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SV3 )
!= ( SY75 @ SV4 ) ) )
| ( ( SY75 @ SY71 )
!= ( SY75 @ SY74 ) ) )
| ( ( SY75 @ SV5 )
= ( SY75 @ SY70 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SY73 )
!= ( SY75 @ SY74 ) ) )
| ( ( SY75 @ SV3 )
!= ( SY75 @ SV6 ) ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY72 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV5 )
!= ( SY75 @ SV6 ) )
| ( ( SY75 @ SV6 )
!= ( SY75 @ SV7 ) ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY70 ) ) )
| ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV4 ) ) ) )
| ( ( SY75 @ SY71 )
!= ( SY75 @ SY74 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY70 ) ) )
| ~ ( ( ( SY75 @ SV3 )
!= ( SY75 @ SV6 ) ) ) )
| ( ( SY75 @ SY71 )
= ( SY75 @ SY74 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SY71 )
!= ( SY75 @ SY72 ) )
| ( ( SY75 @ SY73 )
!= ( SY75 @ SY74 ) ) )
| ( ( SY75 @ SV5 )
!= ( SY75 @ SY70 ) ) )
| ( ( SY75 @ SV1 )
!= ( SY75 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY75 @ SV3 )
!= ( SY75 @ SV4 ) )
| ( ( SY75 @ SV4 )
!= ( SY75 @ SV5 ) ) )
| ( ( SY75 @ SV5 )
!= ( SY75 @ SV6 ) ) )
| ~ ( ( ( SY75 @ SY71 )
!= ( SY75 @ SY74 ) ) ) )
| ( ( SY75 @ SV7 )
= ( SY75 @ SY72 ) ) ) )
| ( ( SY75 @ SV1 )
!= ( SY75 @ SV2 ) )
| ( ( SY75 @ SV3 )
!= ( SY75 @ SV4 ) )
| ( ( SY75 @ SV5 )
!= ( SY75 @ SV6 ) )
| ( ( SY75 @ SV7 )
!= ( SY75 @ SY70 ) )
| ( ( SY75 @ SY71 )
!= ( SY75 @ SY72 ) )
| ( ( SY75 @ SY73 )
!= ( SY75 @ SY74 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(30,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY76: $i] :
~ ~ ! [SY77: $i] :
~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SY76 ) ) )
| ~ ( ( SV1 != SY77 ) ) )
| ~ ( ( SV1 != SY78 ) ) )
| ~ ( ( SV1 != SY79 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SY76 ) ) )
| ~ ( ( SV2 != SY77 ) ) )
| ~ ( ( SV2 != SY78 ) ) )
| ~ ( ( SV2 != SY79 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SY76 ) ) )
| ~ ( ( SV3 != SY77 ) ) )
| ~ ( ( SV3 != SY78 ) ) )
| ~ ( ( SV3 != SY79 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SY76 ) ) )
| ~ ( ( SV5 != SY77 ) ) )
| ~ ( ( SV5 != SY78 ) ) )
| ~ ( ( SV5 != SY79 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SY76 ) ) )
| ~ ( ( SV6 != SY77 ) ) )
| ~ ( ( SV6 != SY78 ) ) )
| ~ ( ( SV6 != SY79 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SY76 ) ) )
| ~ ( ( SV7 != SY77 ) ) )
| ~ ( ( SV7 != SY78 ) ) )
| ~ ( ( SV7 != SY79 ) ) )
| ~ ( ( SV8 != SY76 ) ) )
| ~ ( ( SV8 != SY77 ) ) )
| ~ ( ( SV8 != SY78 ) ) )
| ~ ( ( SV8 != SY79 ) ) )
| ~ ( ( SY76 != SY77 ) ) )
| ~ ( ( SY76 != SY78 ) ) )
| ~ ( ( SY76 != SY79 ) ) )
| ~ ( ( SY77 != SY78 ) ) )
| ~ ( ( SY77 != SY79 ) ) )
| ~ ( ( SY78 != SY79 ) ) )
| ! [SY80: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SV3 )
!= ( SY80 @ SV4 ) ) )
| ( ( SY80 @ SY76 )
!= ( SY80 @ SY79 ) ) )
| ( ( SY80 @ SV5 )
= ( SY80 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SY78 )
!= ( SY80 @ SY79 ) ) )
| ( ( SY80 @ SV3 )
!= ( SY80 @ SV6 ) ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SY77 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV5 )
!= ( SY80 @ SV6 ) )
| ( ( SY80 @ SV6 )
!= ( SY80 @ SV7 ) ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SV8 ) ) )
| ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV4 ) ) ) )
| ( ( SY80 @ SY76 )
!= ( SY80 @ SY79 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SV8 ) ) )
| ~ ( ( ( SY80 @ SV3 )
!= ( SY80 @ SV6 ) ) ) )
| ( ( SY80 @ SY76 )
= ( SY80 @ SY79 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SY76 )
!= ( SY80 @ SY77 ) )
| ( ( SY80 @ SY78 )
!= ( SY80 @ SY79 ) ) )
| ( ( SY80 @ SV5 )
!= ( SY80 @ SV8 ) ) )
| ( ( SY80 @ SV1 )
!= ( SY80 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV3 )
!= ( SY80 @ SV4 ) )
| ( ( SY80 @ SV4 )
!= ( SY80 @ SV5 ) ) )
| ( ( SY80 @ SV5 )
!= ( SY80 @ SV6 ) ) )
| ~ ( ( ( SY80 @ SY76 )
!= ( SY80 @ SY79 ) ) ) )
| ( ( SY80 @ SV7 )
= ( SY80 @ SY77 ) ) ) )
| ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SV3 )
!= ( SY80 @ SV4 ) )
| ( ( SY80 @ SV5 )
!= ( SY80 @ SV6 ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SV8 ) )
| ( ( SY80 @ SY76 )
!= ( SY80 @ SY77 ) )
| ( ( SY80 @ SY78 )
!= ( SY80 @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ! [SY76: $i] :
~ ~ ! [SY77: $i] :
~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SY76 ) ) )
| ~ ( ( SV1 != SY77 ) ) )
| ~ ( ( SV1 != SY78 ) ) )
| ~ ( ( SV1 != SY79 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SY76 ) ) )
| ~ ( ( SV2 != SY77 ) ) )
| ~ ( ( SV2 != SY78 ) ) )
| ~ ( ( SV2 != SY79 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SY76 ) ) )
| ~ ( ( SV3 != SY77 ) ) )
| ~ ( ( SV3 != SY78 ) ) )
| ~ ( ( SV3 != SY79 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SY76 ) ) )
| ~ ( ( SV5 != SY77 ) ) )
| ~ ( ( SV5 != SY78 ) ) )
| ~ ( ( SV5 != SY79 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SY76 ) ) )
| ~ ( ( SV6 != SY77 ) ) )
| ~ ( ( SV6 != SY78 ) ) )
| ~ ( ( SV6 != SY79 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SY76 ) ) )
| ~ ( ( SV7 != SY77 ) ) )
| ~ ( ( SV7 != SY78 ) ) )
| ~ ( ( SV7 != SY79 ) ) )
| ~ ( ( SV8 != SY76 ) ) )
| ~ ( ( SV8 != SY77 ) ) )
| ~ ( ( SV8 != SY78 ) ) )
| ~ ( ( SV8 != SY79 ) ) )
| ~ ( ( SY76 != SY77 ) ) )
| ~ ( ( SY76 != SY78 ) ) )
| ~ ( ( SY76 != SY79 ) ) )
| ~ ( ( SY77 != SY78 ) ) )
| ~ ( ( SY77 != SY79 ) ) )
| ~ ( ( SY78 != SY79 ) ) )
| ! [SY80: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SV3 )
!= ( SY80 @ SV4 ) ) )
| ( ( SY80 @ SY76 )
!= ( SY80 @ SY79 ) ) )
| ( ( SY80 @ SV5 )
= ( SY80 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SY78 )
!= ( SY80 @ SY79 ) ) )
| ( ( SY80 @ SV3 )
!= ( SY80 @ SV6 ) ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SY77 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV5 )
!= ( SY80 @ SV6 ) )
| ( ( SY80 @ SV6 )
!= ( SY80 @ SV7 ) ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SV8 ) ) )
| ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV4 ) ) ) )
| ( ( SY80 @ SY76 )
!= ( SY80 @ SY79 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SV8 ) ) )
| ~ ( ( ( SY80 @ SV3 )
!= ( SY80 @ SV6 ) ) ) )
| ( ( SY80 @ SY76 )
= ( SY80 @ SY79 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SY76 )
!= ( SY80 @ SY77 ) )
| ( ( SY80 @ SY78 )
!= ( SY80 @ SY79 ) ) )
| ( ( SY80 @ SV5 )
!= ( SY80 @ SV8 ) ) )
| ( ( SY80 @ SV1 )
!= ( SY80 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV3 )
!= ( SY80 @ SV4 ) )
| ( ( SY80 @ SV4 )
!= ( SY80 @ SV5 ) ) )
| ( ( SY80 @ SV5 )
!= ( SY80 @ SV6 ) ) )
| ~ ( ( ( SY80 @ SY76 )
!= ( SY80 @ SY79 ) ) ) )
| ( ( SY80 @ SV7 )
= ( SY80 @ SY77 ) ) ) )
| ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SV3 )
!= ( SY80 @ SV4 ) )
| ( ( SY80 @ SV5 )
!= ( SY80 @ SV6 ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SV8 ) )
| ( ( SY80 @ SY76 )
!= ( SY80 @ SY77 ) )
| ( ( SY80 @ SY78 )
!= ( SY80 @ SY79 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(32,plain,
! [SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY76: $i] :
~ ~ ! [SY77: $i] :
~ ~ ! [SY78: $i] :
~ ~ ! [SY79: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SY76 ) ) )
| ~ ( ( SV1 != SY77 ) ) )
| ~ ( ( SV1 != SY78 ) ) )
| ~ ( ( SV1 != SY79 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SY76 ) ) )
| ~ ( ( SV2 != SY77 ) ) )
| ~ ( ( SV2 != SY78 ) ) )
| ~ ( ( SV2 != SY79 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SY76 ) ) )
| ~ ( ( SV3 != SY77 ) ) )
| ~ ( ( SV3 != SY78 ) ) )
| ~ ( ( SV3 != SY79 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SY76 ) ) )
| ~ ( ( SV5 != SY77 ) ) )
| ~ ( ( SV5 != SY78 ) ) )
| ~ ( ( SV5 != SY79 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SY76 ) ) )
| ~ ( ( SV6 != SY77 ) ) )
| ~ ( ( SV6 != SY78 ) ) )
| ~ ( ( SV6 != SY79 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SY76 ) ) )
| ~ ( ( SV7 != SY77 ) ) )
| ~ ( ( SV7 != SY78 ) ) )
| ~ ( ( SV7 != SY79 ) ) )
| ~ ( ( SV8 != SY76 ) ) )
| ~ ( ( SV8 != SY77 ) ) )
| ~ ( ( SV8 != SY78 ) ) )
| ~ ( ( SV8 != SY79 ) ) )
| ~ ( ( SY76 != SY77 ) ) )
| ~ ( ( SY76 != SY78 ) ) )
| ~ ( ( SY76 != SY79 ) ) )
| ~ ( ( SY77 != SY78 ) ) )
| ~ ( ( SY77 != SY79 ) ) )
| ~ ( ( SY78 != SY79 ) ) )
| ! [SY80: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SV3 )
!= ( SY80 @ SV4 ) ) )
| ( ( SY80 @ SY76 )
!= ( SY80 @ SY79 ) ) )
| ( ( SY80 @ SV5 )
= ( SY80 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SY78 )
!= ( SY80 @ SY79 ) ) )
| ( ( SY80 @ SV3 )
!= ( SY80 @ SV6 ) ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SY77 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV5 )
!= ( SY80 @ SV6 ) )
| ( ( SY80 @ SV6 )
!= ( SY80 @ SV7 ) ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SV8 ) ) )
| ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV4 ) ) ) )
| ( ( SY80 @ SY76 )
!= ( SY80 @ SY79 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SV8 ) ) )
| ~ ( ( ( SY80 @ SV3 )
!= ( SY80 @ SV6 ) ) ) )
| ( ( SY80 @ SY76 )
= ( SY80 @ SY79 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SY76 )
!= ( SY80 @ SY77 ) )
| ( ( SY80 @ SY78 )
!= ( SY80 @ SY79 ) ) )
| ( ( SY80 @ SV5 )
!= ( SY80 @ SV8 ) ) )
| ( ( SY80 @ SV1 )
!= ( SY80 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY80 @ SV3 )
!= ( SY80 @ SV4 ) )
| ( ( SY80 @ SV4 )
!= ( SY80 @ SV5 ) ) )
| ( ( SY80 @ SV5 )
!= ( SY80 @ SV6 ) ) )
| ~ ( ( ( SY80 @ SY76 )
!= ( SY80 @ SY79 ) ) ) )
| ( ( SY80 @ SV7 )
= ( SY80 @ SY77 ) ) ) )
| ( ( SY80 @ SV1 )
!= ( SY80 @ SV2 ) )
| ( ( SY80 @ SV3 )
!= ( SY80 @ SV4 ) )
| ( ( SY80 @ SV5 )
!= ( SY80 @ SV6 ) )
| ( ( SY80 @ SV7 )
!= ( SY80 @ SV8 ) )
| ( ( SY80 @ SY76 )
!= ( SY80 @ SY77 ) )
| ( ( SY80 @ SY78 )
!= ( SY80 @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(33,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY81: $i] :
~ ~ ! [SY82: $i] :
~ ~ ! [SY83: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SY81 ) ) )
| ~ ( ( SV1 != SY82 ) ) )
| ~ ( ( SV1 != SY83 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SY81 ) ) )
| ~ ( ( SV2 != SY82 ) ) )
| ~ ( ( SV2 != SY83 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SY81 ) ) )
| ~ ( ( SV3 != SY82 ) ) )
| ~ ( ( SV3 != SY83 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SY81 ) ) )
| ~ ( ( SV5 != SY82 ) ) )
| ~ ( ( SV5 != SY83 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SY81 ) ) )
| ~ ( ( SV6 != SY82 ) ) )
| ~ ( ( SV6 != SY83 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SY81 ) ) )
| ~ ( ( SV7 != SY82 ) ) )
| ~ ( ( SV7 != SY83 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SY81 ) ) )
| ~ ( ( SV8 != SY82 ) ) )
| ~ ( ( SV8 != SY83 ) ) )
| ~ ( ( SV9 != SY81 ) ) )
| ~ ( ( SV9 != SY82 ) ) )
| ~ ( ( SV9 != SY83 ) ) )
| ~ ( ( SY81 != SY82 ) ) )
| ~ ( ( SY81 != SY83 ) ) )
| ~ ( ( SY82 != SY83 ) ) )
| ! [SY84: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SV3 )
!= ( SY84 @ SV4 ) ) )
| ( ( SY84 @ SV9 )
!= ( SY84 @ SY83 ) ) )
| ( ( SY84 @ SV5 )
= ( SY84 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SY82 )
!= ( SY84 @ SY83 ) ) )
| ( ( SY84 @ SV3 )
!= ( SY84 @ SV6 ) ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SY81 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV5 )
!= ( SY84 @ SV6 ) )
| ( ( SY84 @ SV6 )
!= ( SY84 @ SV7 ) ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SV8 ) ) )
| ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV4 ) ) ) )
| ( ( SY84 @ SV9 )
!= ( SY84 @ SY83 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SV8 ) ) )
| ~ ( ( ( SY84 @ SV3 )
!= ( SY84 @ SV6 ) ) ) )
| ( ( SY84 @ SV9 )
= ( SY84 @ SY83 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV9 )
!= ( SY84 @ SY81 ) )
| ( ( SY84 @ SY82 )
!= ( SY84 @ SY83 ) ) )
| ( ( SY84 @ SV5 )
!= ( SY84 @ SV8 ) ) )
| ( ( SY84 @ SV1 )
!= ( SY84 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV3 )
!= ( SY84 @ SV4 ) )
| ( ( SY84 @ SV4 )
!= ( SY84 @ SV5 ) ) )
| ( ( SY84 @ SV5 )
!= ( SY84 @ SV6 ) ) )
| ~ ( ( ( SY84 @ SV9 )
!= ( SY84 @ SY83 ) ) ) )
| ( ( SY84 @ SV7 )
= ( SY84 @ SY81 ) ) ) )
| ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SV3 )
!= ( SY84 @ SV4 ) )
| ( ( SY84 @ SV5 )
!= ( SY84 @ SV6 ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SV8 ) )
| ( ( SY84 @ SV9 )
!= ( SY84 @ SY81 ) )
| ( ( SY84 @ SY82 )
!= ( SY84 @ SY83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(34,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ! [SY81: $i] :
~ ~ ! [SY82: $i] :
~ ~ ! [SY83: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SY81 ) ) )
| ~ ( ( SV1 != SY82 ) ) )
| ~ ( ( SV1 != SY83 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SY81 ) ) )
| ~ ( ( SV2 != SY82 ) ) )
| ~ ( ( SV2 != SY83 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SY81 ) ) )
| ~ ( ( SV3 != SY82 ) ) )
| ~ ( ( SV3 != SY83 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SY81 ) ) )
| ~ ( ( SV5 != SY82 ) ) )
| ~ ( ( SV5 != SY83 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SY81 ) ) )
| ~ ( ( SV6 != SY82 ) ) )
| ~ ( ( SV6 != SY83 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SY81 ) ) )
| ~ ( ( SV7 != SY82 ) ) )
| ~ ( ( SV7 != SY83 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SY81 ) ) )
| ~ ( ( SV8 != SY82 ) ) )
| ~ ( ( SV8 != SY83 ) ) )
| ~ ( ( SV9 != SY81 ) ) )
| ~ ( ( SV9 != SY82 ) ) )
| ~ ( ( SV9 != SY83 ) ) )
| ~ ( ( SY81 != SY82 ) ) )
| ~ ( ( SY81 != SY83 ) ) )
| ~ ( ( SY82 != SY83 ) ) )
| ! [SY84: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SV3 )
!= ( SY84 @ SV4 ) ) )
| ( ( SY84 @ SV9 )
!= ( SY84 @ SY83 ) ) )
| ( ( SY84 @ SV5 )
= ( SY84 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SY82 )
!= ( SY84 @ SY83 ) ) )
| ( ( SY84 @ SV3 )
!= ( SY84 @ SV6 ) ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SY81 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV5 )
!= ( SY84 @ SV6 ) )
| ( ( SY84 @ SV6 )
!= ( SY84 @ SV7 ) ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SV8 ) ) )
| ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV4 ) ) ) )
| ( ( SY84 @ SV9 )
!= ( SY84 @ SY83 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SV8 ) ) )
| ~ ( ( ( SY84 @ SV3 )
!= ( SY84 @ SV6 ) ) ) )
| ( ( SY84 @ SV9 )
= ( SY84 @ SY83 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV9 )
!= ( SY84 @ SY81 ) )
| ( ( SY84 @ SY82 )
!= ( SY84 @ SY83 ) ) )
| ( ( SY84 @ SV5 )
!= ( SY84 @ SV8 ) ) )
| ( ( SY84 @ SV1 )
!= ( SY84 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV3 )
!= ( SY84 @ SV4 ) )
| ( ( SY84 @ SV4 )
!= ( SY84 @ SV5 ) ) )
| ( ( SY84 @ SV5 )
!= ( SY84 @ SV6 ) ) )
| ~ ( ( ( SY84 @ SV9 )
!= ( SY84 @ SY83 ) ) ) )
| ( ( SY84 @ SV7 )
= ( SY84 @ SY81 ) ) ) )
| ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SV3 )
!= ( SY84 @ SV4 ) )
| ( ( SY84 @ SV5 )
!= ( SY84 @ SV6 ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SV8 ) )
| ( ( SY84 @ SV9 )
!= ( SY84 @ SY81 ) )
| ( ( SY84 @ SY82 )
!= ( SY84 @ SY83 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(35,plain,
! [SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY81: $i] :
~ ~ ! [SY82: $i] :
~ ~ ! [SY83: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SY81 ) ) )
| ~ ( ( SV1 != SY82 ) ) )
| ~ ( ( SV1 != SY83 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SY81 ) ) )
| ~ ( ( SV2 != SY82 ) ) )
| ~ ( ( SV2 != SY83 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SY81 ) ) )
| ~ ( ( SV3 != SY82 ) ) )
| ~ ( ( SV3 != SY83 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SY81 ) ) )
| ~ ( ( SV5 != SY82 ) ) )
| ~ ( ( SV5 != SY83 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SY81 ) ) )
| ~ ( ( SV6 != SY82 ) ) )
| ~ ( ( SV6 != SY83 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SY81 ) ) )
| ~ ( ( SV7 != SY82 ) ) )
| ~ ( ( SV7 != SY83 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SY81 ) ) )
| ~ ( ( SV8 != SY82 ) ) )
| ~ ( ( SV8 != SY83 ) ) )
| ~ ( ( SV9 != SY81 ) ) )
| ~ ( ( SV9 != SY82 ) ) )
| ~ ( ( SV9 != SY83 ) ) )
| ~ ( ( SY81 != SY82 ) ) )
| ~ ( ( SY81 != SY83 ) ) )
| ~ ( ( SY82 != SY83 ) ) )
| ! [SY84: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SV3 )
!= ( SY84 @ SV4 ) ) )
| ( ( SY84 @ SV9 )
!= ( SY84 @ SY83 ) ) )
| ( ( SY84 @ SV5 )
= ( SY84 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SY82 )
!= ( SY84 @ SY83 ) ) )
| ( ( SY84 @ SV3 )
!= ( SY84 @ SV6 ) ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SY81 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV5 )
!= ( SY84 @ SV6 ) )
| ( ( SY84 @ SV6 )
!= ( SY84 @ SV7 ) ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SV8 ) ) )
| ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV4 ) ) ) )
| ( ( SY84 @ SV9 )
!= ( SY84 @ SY83 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SV8 ) ) )
| ~ ( ( ( SY84 @ SV3 )
!= ( SY84 @ SV6 ) ) ) )
| ( ( SY84 @ SV9 )
= ( SY84 @ SY83 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV9 )
!= ( SY84 @ SY81 ) )
| ( ( SY84 @ SY82 )
!= ( SY84 @ SY83 ) ) )
| ( ( SY84 @ SV5 )
!= ( SY84 @ SV8 ) ) )
| ( ( SY84 @ SV1 )
!= ( SY84 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY84 @ SV3 )
!= ( SY84 @ SV4 ) )
| ( ( SY84 @ SV4 )
!= ( SY84 @ SV5 ) ) )
| ( ( SY84 @ SV5 )
!= ( SY84 @ SV6 ) ) )
| ~ ( ( ( SY84 @ SV9 )
!= ( SY84 @ SY83 ) ) ) )
| ( ( SY84 @ SV7 )
= ( SY84 @ SY81 ) ) ) )
| ( ( SY84 @ SV1 )
!= ( SY84 @ SV2 ) )
| ( ( SY84 @ SV3 )
!= ( SY84 @ SV4 ) )
| ( ( SY84 @ SV5 )
!= ( SY84 @ SV6 ) )
| ( ( SY84 @ SV7 )
!= ( SY84 @ SV8 ) )
| ( ( SY84 @ SV9 )
!= ( SY84 @ SY81 ) )
| ( ( SY84 @ SY82 )
!= ( SY84 @ SY83 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(36,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY85: $i] :
~ ~ ! [SY86: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SY85 ) ) )
| ~ ( ( SV1 != SY86 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SY85 ) ) )
| ~ ( ( SV2 != SY86 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SY85 ) ) )
| ~ ( ( SV3 != SY86 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SY85 ) ) )
| ~ ( ( SV5 != SY86 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SY85 ) ) )
| ~ ( ( SV6 != SY86 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SY85 ) ) )
| ~ ( ( SV7 != SY86 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SY85 ) ) )
| ~ ( ( SV8 != SY86 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SY85 ) ) )
| ~ ( ( SV9 != SY86 ) ) )
| ~ ( ( SV10 != SY85 ) ) )
| ~ ( ( SV10 != SY86 ) ) )
| ~ ( ( SY85 != SY86 ) ) )
| ! [SY87: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SV3 )
!= ( SY87 @ SV4 ) ) )
| ( ( SY87 @ SV9 )
!= ( SY87 @ SY86 ) ) )
| ( ( SY87 @ SV5 )
= ( SY87 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SY85 )
!= ( SY87 @ SY86 ) ) )
| ( ( SY87 @ SV3 )
!= ( SY87 @ SV6 ) ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV5 )
!= ( SY87 @ SV6 ) )
| ( ( SY87 @ SV6 )
!= ( SY87 @ SV7 ) ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV8 ) ) )
| ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV4 ) ) ) )
| ( ( SY87 @ SV9 )
!= ( SY87 @ SY86 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV8 ) ) )
| ~ ( ( ( SY87 @ SV3 )
!= ( SY87 @ SV6 ) ) ) )
| ( ( SY87 @ SV9 )
= ( SY87 @ SY86 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV9 )
!= ( SY87 @ SV10 ) )
| ( ( SY87 @ SY85 )
!= ( SY87 @ SY86 ) ) )
| ( ( SY87 @ SV5 )
!= ( SY87 @ SV8 ) ) )
| ( ( SY87 @ SV1 )
!= ( SY87 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV3 )
!= ( SY87 @ SV4 ) )
| ( ( SY87 @ SV4 )
!= ( SY87 @ SV5 ) ) )
| ( ( SY87 @ SV5 )
!= ( SY87 @ SV6 ) ) )
| ~ ( ( ( SY87 @ SV9 )
!= ( SY87 @ SY86 ) ) ) )
| ( ( SY87 @ SV7 )
= ( SY87 @ SV10 ) ) ) )
| ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SV3 )
!= ( SY87 @ SV4 ) )
| ( ( SY87 @ SV5 )
!= ( SY87 @ SV6 ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV8 ) )
| ( ( SY87 @ SV9 )
!= ( SY87 @ SV10 ) )
| ( ( SY87 @ SY85 )
!= ( SY87 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(37,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ! [SY85: $i] :
~ ~ ! [SY86: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SY85 ) ) )
| ~ ( ( SV1 != SY86 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SY85 ) ) )
| ~ ( ( SV2 != SY86 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SY85 ) ) )
| ~ ( ( SV3 != SY86 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SY85 ) ) )
| ~ ( ( SV5 != SY86 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SY85 ) ) )
| ~ ( ( SV6 != SY86 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SY85 ) ) )
| ~ ( ( SV7 != SY86 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SY85 ) ) )
| ~ ( ( SV8 != SY86 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SY85 ) ) )
| ~ ( ( SV9 != SY86 ) ) )
| ~ ( ( SV10 != SY85 ) ) )
| ~ ( ( SV10 != SY86 ) ) )
| ~ ( ( SY85 != SY86 ) ) )
| ! [SY87: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SV3 )
!= ( SY87 @ SV4 ) ) )
| ( ( SY87 @ SV9 )
!= ( SY87 @ SY86 ) ) )
| ( ( SY87 @ SV5 )
= ( SY87 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SY85 )
!= ( SY87 @ SY86 ) ) )
| ( ( SY87 @ SV3 )
!= ( SY87 @ SV6 ) ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV5 )
!= ( SY87 @ SV6 ) )
| ( ( SY87 @ SV6 )
!= ( SY87 @ SV7 ) ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV8 ) ) )
| ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV4 ) ) ) )
| ( ( SY87 @ SV9 )
!= ( SY87 @ SY86 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV8 ) ) )
| ~ ( ( ( SY87 @ SV3 )
!= ( SY87 @ SV6 ) ) ) )
| ( ( SY87 @ SV9 )
= ( SY87 @ SY86 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV9 )
!= ( SY87 @ SV10 ) )
| ( ( SY87 @ SY85 )
!= ( SY87 @ SY86 ) ) )
| ( ( SY87 @ SV5 )
!= ( SY87 @ SV8 ) ) )
| ( ( SY87 @ SV1 )
!= ( SY87 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV3 )
!= ( SY87 @ SV4 ) )
| ( ( SY87 @ SV4 )
!= ( SY87 @ SV5 ) ) )
| ( ( SY87 @ SV5 )
!= ( SY87 @ SV6 ) ) )
| ~ ( ( ( SY87 @ SV9 )
!= ( SY87 @ SY86 ) ) ) )
| ( ( SY87 @ SV7 )
= ( SY87 @ SV10 ) ) ) )
| ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SV3 )
!= ( SY87 @ SV4 ) )
| ( ( SY87 @ SV5 )
!= ( SY87 @ SV6 ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV8 ) )
| ( ( SY87 @ SV9 )
!= ( SY87 @ SV10 ) )
| ( ( SY87 @ SY85 )
!= ( SY87 @ SY86 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(38,plain,
! [SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY85: $i] :
~ ~ ! [SY86: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SY85 ) ) )
| ~ ( ( SV1 != SY86 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SY85 ) ) )
| ~ ( ( SV2 != SY86 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SY85 ) ) )
| ~ ( ( SV3 != SY86 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SY85 ) ) )
| ~ ( ( SV5 != SY86 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SY85 ) ) )
| ~ ( ( SV6 != SY86 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SY85 ) ) )
| ~ ( ( SV7 != SY86 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SY85 ) ) )
| ~ ( ( SV8 != SY86 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SY85 ) ) )
| ~ ( ( SV9 != SY86 ) ) )
| ~ ( ( SV10 != SY85 ) ) )
| ~ ( ( SV10 != SY86 ) ) )
| ~ ( ( SY85 != SY86 ) ) )
| ! [SY87: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SV3 )
!= ( SY87 @ SV4 ) ) )
| ( ( SY87 @ SV9 )
!= ( SY87 @ SY86 ) ) )
| ( ( SY87 @ SV5 )
= ( SY87 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SY85 )
!= ( SY87 @ SY86 ) ) )
| ( ( SY87 @ SV3 )
!= ( SY87 @ SV6 ) ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV5 )
!= ( SY87 @ SV6 ) )
| ( ( SY87 @ SV6 )
!= ( SY87 @ SV7 ) ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV8 ) ) )
| ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV4 ) ) ) )
| ( ( SY87 @ SV9 )
!= ( SY87 @ SY86 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV8 ) ) )
| ~ ( ( ( SY87 @ SV3 )
!= ( SY87 @ SV6 ) ) ) )
| ( ( SY87 @ SV9 )
= ( SY87 @ SY86 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV9 )
!= ( SY87 @ SV10 ) )
| ( ( SY87 @ SY85 )
!= ( SY87 @ SY86 ) ) )
| ( ( SY87 @ SV5 )
!= ( SY87 @ SV8 ) ) )
| ( ( SY87 @ SV1 )
!= ( SY87 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY87 @ SV3 )
!= ( SY87 @ SV4 ) )
| ( ( SY87 @ SV4 )
!= ( SY87 @ SV5 ) ) )
| ( ( SY87 @ SV5 )
!= ( SY87 @ SV6 ) ) )
| ~ ( ( ( SY87 @ SV9 )
!= ( SY87 @ SY86 ) ) ) )
| ( ( SY87 @ SV7 )
= ( SY87 @ SV10 ) ) ) )
| ( ( SY87 @ SV1 )
!= ( SY87 @ SV2 ) )
| ( ( SY87 @ SV3 )
!= ( SY87 @ SV4 ) )
| ( ( SY87 @ SV5 )
!= ( SY87 @ SV6 ) )
| ( ( SY87 @ SV7 )
!= ( SY87 @ SV8 ) )
| ( ( SY87 @ SV9 )
!= ( SY87 @ SV10 ) )
| ( ( SY87 @ SY85 )
!= ( SY87 @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(39,plain,
! [SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ! [SY88: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SV11 ) ) )
| ~ ( ( SV1 != SY88 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SV11 ) ) )
| ~ ( ( SV2 != SY88 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SV11 ) ) )
| ~ ( ( SV3 != SY88 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SV11 ) ) )
| ~ ( ( SV5 != SY88 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SV11 ) ) )
| ~ ( ( SV6 != SY88 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SV11 ) ) )
| ~ ( ( SV7 != SY88 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SV11 ) ) )
| ~ ( ( SV8 != SY88 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SV11 ) ) )
| ~ ( ( SV9 != SY88 ) ) )
| ~ ( ( SV10 != SV11 ) ) )
| ~ ( ( SV10 != SY88 ) ) )
| ~ ( ( SV11 != SY88 ) ) )
| ! [SY89: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV3 )
!= ( SY89 @ SV4 ) ) )
| ( ( SY89 @ SV9 )
!= ( SY89 @ SY88 ) ) )
| ( ( SY89 @ SV5 )
= ( SY89 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV11 )
!= ( SY89 @ SY88 ) ) )
| ( ( SY89 @ SV3 )
!= ( SY89 @ SV6 ) ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV5 )
!= ( SY89 @ SV6 ) )
| ( ( SY89 @ SV6 )
!= ( SY89 @ SV7 ) ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV8 ) ) )
| ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV4 ) ) ) )
| ( ( SY89 @ SV9 )
!= ( SY89 @ SY88 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV8 ) ) )
| ~ ( ( ( SY89 @ SV3 )
!= ( SY89 @ SV6 ) ) ) )
| ( ( SY89 @ SV9 )
= ( SY89 @ SY88 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV9 )
!= ( SY89 @ SV10 ) )
| ( ( SY89 @ SV11 )
!= ( SY89 @ SY88 ) ) )
| ( ( SY89 @ SV5 )
!= ( SY89 @ SV8 ) ) )
| ( ( SY89 @ SV1 )
!= ( SY89 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV3 )
!= ( SY89 @ SV4 ) )
| ( ( SY89 @ SV4 )
!= ( SY89 @ SV5 ) ) )
| ( ( SY89 @ SV5 )
!= ( SY89 @ SV6 ) ) )
| ~ ( ( ( SY89 @ SV9 )
!= ( SY89 @ SY88 ) ) ) )
| ( ( SY89 @ SV7 )
= ( SY89 @ SV10 ) ) ) )
| ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV3 )
!= ( SY89 @ SV4 ) )
| ( ( SY89 @ SV5 )
!= ( SY89 @ SV6 ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV8 ) )
| ( ( SY89 @ SV9 )
!= ( SY89 @ SV10 ) )
| ( ( SY89 @ SV11 )
!= ( SY89 @ SY88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ! [SY88: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SV11 ) ) )
| ~ ( ( SV1 != SY88 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SV11 ) ) )
| ~ ( ( SV2 != SY88 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SV11 ) ) )
| ~ ( ( SV3 != SY88 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SV11 ) ) )
| ~ ( ( SV5 != SY88 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SV11 ) ) )
| ~ ( ( SV6 != SY88 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SV11 ) ) )
| ~ ( ( SV7 != SY88 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SV11 ) ) )
| ~ ( ( SV8 != SY88 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SV11 ) ) )
| ~ ( ( SV9 != SY88 ) ) )
| ~ ( ( SV10 != SV11 ) ) )
| ~ ( ( SV10 != SY88 ) ) )
| ~ ( ( SV11 != SY88 ) ) )
| ! [SY89: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV3 )
!= ( SY89 @ SV4 ) ) )
| ( ( SY89 @ SV9 )
!= ( SY89 @ SY88 ) ) )
| ( ( SY89 @ SV5 )
= ( SY89 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV11 )
!= ( SY89 @ SY88 ) ) )
| ( ( SY89 @ SV3 )
!= ( SY89 @ SV6 ) ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV5 )
!= ( SY89 @ SV6 ) )
| ( ( SY89 @ SV6 )
!= ( SY89 @ SV7 ) ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV8 ) ) )
| ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV4 ) ) ) )
| ( ( SY89 @ SV9 )
!= ( SY89 @ SY88 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV8 ) ) )
| ~ ( ( ( SY89 @ SV3 )
!= ( SY89 @ SV6 ) ) ) )
| ( ( SY89 @ SV9 )
= ( SY89 @ SY88 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV9 )
!= ( SY89 @ SV10 ) )
| ( ( SY89 @ SV11 )
!= ( SY89 @ SY88 ) ) )
| ( ( SY89 @ SV5 )
!= ( SY89 @ SV8 ) ) )
| ( ( SY89 @ SV1 )
!= ( SY89 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV3 )
!= ( SY89 @ SV4 ) )
| ( ( SY89 @ SV4 )
!= ( SY89 @ SV5 ) ) )
| ( ( SY89 @ SV5 )
!= ( SY89 @ SV6 ) ) )
| ~ ( ( ( SY89 @ SV9 )
!= ( SY89 @ SY88 ) ) ) )
| ( ( SY89 @ SV7 )
= ( SY89 @ SV10 ) ) ) )
| ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV3 )
!= ( SY89 @ SV4 ) )
| ( ( SY89 @ SV5 )
!= ( SY89 @ SV6 ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV8 ) )
| ( ( SY89 @ SV9 )
!= ( SY89 @ SV10 ) )
| ( ( SY89 @ SV11 )
!= ( SY89 @ SY88 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
! [SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY88: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SV11 ) ) )
| ~ ( ( SV1 != SY88 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SV11 ) ) )
| ~ ( ( SV2 != SY88 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SV11 ) ) )
| ~ ( ( SV3 != SY88 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SV11 ) ) )
| ~ ( ( SV5 != SY88 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SV11 ) ) )
| ~ ( ( SV6 != SY88 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SV11 ) ) )
| ~ ( ( SV7 != SY88 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SV11 ) ) )
| ~ ( ( SV8 != SY88 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SV11 ) ) )
| ~ ( ( SV9 != SY88 ) ) )
| ~ ( ( SV10 != SV11 ) ) )
| ~ ( ( SV10 != SY88 ) ) )
| ~ ( ( SV11 != SY88 ) ) )
| ! [SY89: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV3 )
!= ( SY89 @ SV4 ) ) )
| ( ( SY89 @ SV9 )
!= ( SY89 @ SY88 ) ) )
| ( ( SY89 @ SV5 )
= ( SY89 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV11 )
!= ( SY89 @ SY88 ) ) )
| ( ( SY89 @ SV3 )
!= ( SY89 @ SV6 ) ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV5 )
!= ( SY89 @ SV6 ) )
| ( ( SY89 @ SV6 )
!= ( SY89 @ SV7 ) ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV8 ) ) )
| ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV4 ) ) ) )
| ( ( SY89 @ SV9 )
!= ( SY89 @ SY88 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV8 ) ) )
| ~ ( ( ( SY89 @ SV3 )
!= ( SY89 @ SV6 ) ) ) )
| ( ( SY89 @ SV9 )
= ( SY89 @ SY88 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV9 )
!= ( SY89 @ SV10 ) )
| ( ( SY89 @ SV11 )
!= ( SY89 @ SY88 ) ) )
| ( ( SY89 @ SV5 )
!= ( SY89 @ SV8 ) ) )
| ( ( SY89 @ SV1 )
!= ( SY89 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY89 @ SV3 )
!= ( SY89 @ SV4 ) )
| ( ( SY89 @ SV4 )
!= ( SY89 @ SV5 ) ) )
| ( ( SY89 @ SV5 )
!= ( SY89 @ SV6 ) ) )
| ~ ( ( ( SY89 @ SV9 )
!= ( SY89 @ SY88 ) ) ) )
| ( ( SY89 @ SV7 )
= ( SY89 @ SV10 ) ) ) )
| ( ( SY89 @ SV1 )
!= ( SY89 @ SV2 ) )
| ( ( SY89 @ SV3 )
!= ( SY89 @ SV4 ) )
| ( ( SY89 @ SV5 )
!= ( SY89 @ SV6 ) )
| ( ( SY89 @ SV7 )
!= ( SY89 @ SV8 ) )
| ( ( SY89 @ SV9 )
!= ( SY89 @ SV10 ) )
| ( ( SY89 @ SV11 )
!= ( SY89 @ SY88 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(42,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SV11 ) ) )
| ~ ( ( SV1 != SV12 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SV11 ) ) )
| ~ ( ( SV2 != SV12 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SV11 ) ) )
| ~ ( ( SV3 != SV12 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SV11 ) ) )
| ~ ( ( SV5 != SV12 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SV11 ) ) )
| ~ ( ( SV6 != SV12 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SV11 ) ) )
| ~ ( ( SV7 != SV12 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SV11 ) ) )
| ~ ( ( SV8 != SV12 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SV11 ) ) )
| ~ ( ( SV9 != SV12 ) ) )
| ~ ( ( SV10 != SV11 ) ) )
| ~ ( ( SV10 != SV12 ) ) )
| ~ ( ( SV11 != SV12 ) ) )
| ! [SY90: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV1 )
!= ( SY90 @ SV2 ) )
| ( ( SY90 @ SV3 )
!= ( SY90 @ SV4 ) ) )
| ( ( SY90 @ SV9 )
!= ( SY90 @ SV12 ) ) )
| ( ( SY90 @ SV5 )
= ( SY90 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV1 )
!= ( SY90 @ SV2 ) )
| ( ( SY90 @ SV11 )
!= ( SY90 @ SV12 ) ) )
| ( ( SY90 @ SV3 )
!= ( SY90 @ SV6 ) ) )
| ( ( SY90 @ SV7 )
!= ( SY90 @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV5 )
!= ( SY90 @ SV6 ) )
| ( ( SY90 @ SV6 )
!= ( SY90 @ SV7 ) ) )
| ( ( SY90 @ SV7 )
!= ( SY90 @ SV8 ) ) )
| ~ ( ( ( SY90 @ SV1 )
!= ( SY90 @ SV4 ) ) ) )
| ( ( SY90 @ SV9 )
!= ( SY90 @ SV12 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV1 )
!= ( SY90 @ SV2 ) )
| ( ( SY90 @ SV7 )
!= ( SY90 @ SV8 ) ) )
| ~ ( ( ( SY90 @ SV3 )
!= ( SY90 @ SV6 ) ) ) )
| ( ( SY90 @ SV9 )
= ( SY90 @ SV12 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV9 )
!= ( SY90 @ SV10 ) )
| ( ( SY90 @ SV11 )
!= ( SY90 @ SV12 ) ) )
| ( ( SY90 @ SV5 )
!= ( SY90 @ SV8 ) ) )
| ( ( SY90 @ SV1 )
!= ( SY90 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV3 )
!= ( SY90 @ SV4 ) )
| ( ( SY90 @ SV4 )
!= ( SY90 @ SV5 ) ) )
| ( ( SY90 @ SV5 )
!= ( SY90 @ SV6 ) ) )
| ~ ( ( ( SY90 @ SV9 )
!= ( SY90 @ SV12 ) ) ) )
| ( ( SY90 @ SV7 )
= ( SY90 @ SV10 ) ) ) )
| ( ( SY90 @ SV1 )
!= ( SY90 @ SV2 ) )
| ( ( SY90 @ SV3 )
!= ( SY90 @ SV4 ) )
| ( ( SY90 @ SV5 )
!= ( SY90 @ SV6 ) )
| ( ( SY90 @ SV7 )
!= ( SY90 @ SV8 ) )
| ( ( SY90 @ SV9 )
!= ( SY90 @ SV10 ) )
| ( ( SY90 @ SV11 )
!= ( SY90 @ SV12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(43,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SV11 ) ) )
| ~ ( ( SV1 != SV12 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SV11 ) ) )
| ~ ( ( SV2 != SV12 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SV11 ) ) )
| ~ ( ( SV3 != SV12 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SV11 ) ) )
| ~ ( ( SV5 != SV12 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SV11 ) ) )
| ~ ( ( SV6 != SV12 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SV11 ) ) )
| ~ ( ( SV7 != SV12 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SV11 ) ) )
| ~ ( ( SV8 != SV12 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SV11 ) ) )
| ~ ( ( SV9 != SV12 ) ) )
| ~ ( ( SV10 != SV11 ) ) )
| ~ ( ( SV10 != SV12 ) ) )
| ~ ( ( SV11 != SV12 ) ) )
| ! [SY90: $i > $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV1 )
!= ( SY90 @ SV2 ) )
| ( ( SY90 @ SV3 )
!= ( SY90 @ SV4 ) ) )
| ( ( SY90 @ SV9 )
!= ( SY90 @ SV12 ) ) )
| ( ( SY90 @ SV5 )
= ( SY90 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV1 )
!= ( SY90 @ SV2 ) )
| ( ( SY90 @ SV11 )
!= ( SY90 @ SV12 ) ) )
| ( ( SY90 @ SV3 )
!= ( SY90 @ SV6 ) ) )
| ( ( SY90 @ SV7 )
!= ( SY90 @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV5 )
!= ( SY90 @ SV6 ) )
| ( ( SY90 @ SV6 )
!= ( SY90 @ SV7 ) ) )
| ( ( SY90 @ SV7 )
!= ( SY90 @ SV8 ) ) )
| ~ ( ( ( SY90 @ SV1 )
!= ( SY90 @ SV4 ) ) ) )
| ( ( SY90 @ SV9 )
!= ( SY90 @ SV12 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV1 )
!= ( SY90 @ SV2 ) )
| ( ( SY90 @ SV7 )
!= ( SY90 @ SV8 ) ) )
| ~ ( ( ( SY90 @ SV3 )
!= ( SY90 @ SV6 ) ) ) )
| ( ( SY90 @ SV9 )
= ( SY90 @ SV12 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV9 )
!= ( SY90 @ SV10 ) )
| ( ( SY90 @ SV11 )
!= ( SY90 @ SV12 ) ) )
| ( ( SY90 @ SV5 )
!= ( SY90 @ SV8 ) ) )
| ( ( SY90 @ SV1 )
!= ( SY90 @ SV4 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( SY90 @ SV3 )
!= ( SY90 @ SV4 ) )
| ( ( SY90 @ SV4 )
!= ( SY90 @ SV5 ) ) )
| ( ( SY90 @ SV5 )
!= ( SY90 @ SV6 ) ) )
| ~ ( ( ( SY90 @ SV9 )
!= ( SY90 @ SV12 ) ) ) )
| ( ( SY90 @ SV7 )
= ( SY90 @ SV10 ) ) ) )
| ( ( SY90 @ SV1 )
!= ( SY90 @ SV2 ) )
| ( ( SY90 @ SV3 )
!= ( SY90 @ SV4 ) )
| ( ( SY90 @ SV5 )
!= ( SY90 @ SV6 ) )
| ( ( SY90 @ SV7 )
!= ( SY90 @ SV8 ) )
| ( ( SY90 @ SV9 )
!= ( SY90 @ SV10 ) )
| ( ( SY90 @ SV11 )
!= ( SY90 @ SV12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SV11 ) ) )
| ~ ( ( SV1 != SV12 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SV11 ) ) )
| ~ ( ( SV2 != SV12 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SV11 ) ) )
| ~ ( ( SV3 != SV12 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SV11 ) ) )
| ~ ( ( SV5 != SV12 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SV11 ) ) )
| ~ ( ( SV6 != SV12 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SV11 ) ) )
| ~ ( ( SV7 != SV12 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SV11 ) ) )
| ~ ( ( SV8 != SV12 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SV11 ) ) )
| ~ ( ( SV9 != SV12 ) ) )
| ~ ( ( SV10 != SV11 ) ) )
| ~ ( ( SV10 != SV12 ) ) )
| ~ ( ( SV11 != SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(46,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SV11 ) ) )
| ~ ( ( SV1 != SV12 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SV11 ) ) )
| ~ ( ( SV2 != SV12 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SV11 ) ) )
| ~ ( ( SV3 != SV12 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SV11 ) ) )
| ~ ( ( SV5 != SV12 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SV11 ) ) )
| ~ ( ( SV6 != SV12 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SV11 ) ) )
| ~ ( ( SV7 != SV12 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SV11 ) ) )
| ~ ( ( SV8 != SV12 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SV11 ) ) )
| ~ ( ( SV9 != SV12 ) ) )
| ~ ( ( SV10 != SV11 ) ) )
| ~ ( ( SV10 != SV12 ) ) )
| ~ ( ( SV11 != SV12 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV12: $i,SV11: $i,SV10: $i,SV9: $i,SV8: $i,SV7: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( SV1 != SV2 ) )
| ~ ( ( SV1 != SV3 ) ) )
| ~ ( ( SV1 != SV4 ) ) )
| ~ ( ( SV1 != SV5 ) ) )
| ~ ( ( SV1 != SV6 ) ) )
| ~ ( ( SV1 != SV7 ) ) )
| ~ ( ( SV1 != SV8 ) ) )
| ~ ( ( SV1 != SV9 ) ) )
| ~ ( ( SV1 != SV10 ) ) )
| ~ ( ( SV1 != SV11 ) ) )
| ~ ( ( SV1 != SV12 ) ) )
| ~ ( ( SV2 != SV3 ) ) )
| ~ ( ( SV2 != SV4 ) ) )
| ~ ( ( SV2 != SV5 ) ) )
| ~ ( ( SV2 != SV6 ) ) )
| ~ ( ( SV2 != SV7 ) ) )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ( ( SV2 != SV9 ) ) )
| ~ ( ( SV2 != SV10 ) ) )
| ~ ( ( SV2 != SV11 ) ) )
| ~ ( ( SV2 != SV12 ) ) )
| ~ ( ( SV3 != SV4 ) ) )
| ~ ( ( SV3 != SV5 ) ) )
| ~ ( ( SV3 != SV6 ) ) )
| ~ ( ( SV3 != SV7 ) ) )
| ~ ( ( SV3 != SV8 ) ) )
| ~ ( ( SV3 != SV9 ) ) )
| ~ ( ( SV3 != SV10 ) ) )
| ~ ( ( SV3 != SV11 ) ) )
| ~ ( ( SV3 != SV12 ) ) )
| ~ ( ( SV5 != SV6 ) ) )
| ~ ( ( SV5 != SV7 ) ) )
| ~ ( ( SV5 != SV8 ) ) )
| ~ ( ( SV5 != SV9 ) ) )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ( ( SV5 != SV11 ) ) )
| ~ ( ( SV5 != SV12 ) ) )
| ~ ( ( SV6 != SV7 ) ) )
| ~ ( ( SV6 != SV8 ) ) )
| ~ ( ( SV6 != SV9 ) ) )
| ~ ( ( SV6 != SV10 ) ) )
| ~ ( ( SV6 != SV11 ) ) )
| ~ ( ( SV6 != SV12 ) ) )
| ~ ( ( SV7 != SV8 ) ) )
| ~ ( ( SV7 != SV9 ) ) )
| ~ ( ( SV7 != SV10 ) ) )
| ~ ( ( SV7 != SV11 ) ) )
| ~ ( ( SV7 != SV12 ) ) )
| ~ ( ( SV8 != SV9 ) ) )
| ~ ( ( SV8 != SV10 ) ) )
| ~ ( ( SV8 != SV11 ) ) )
| ~ ( ( SV8 != SV12 ) ) )
| ~ ( ( SV9 != SV10 ) ) )
| ~ ( ( SV9 != SV11 ) ) )
| ~ ( ( SV9 != SV12 ) ) )
| ~ ( ( SV10 != SV11 ) ) )
| ~ ( ( SV10 != SV12 ) ) )
| ~ ( ( SV11 != SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV12: $i,SV11: $i] :
( ( ~ ( ( SV11 != SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(57,plain,
! [SV12: $i,SV11: $i] :
( ( SV11 != SV12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(63,plain,
! [SV12: $i,SV11: $i] :
( ( SV11 = SV12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
$false = $true,
inference(flexflex,[status(thm)],[63]) ).
thf(65,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO250^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 17:36:58 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.09/0.45
% 1.09/0.45 No.of.Axioms: 0
% 1.09/0.45
% 1.09/0.45 Length.of.Defs: 0
% 1.09/0.45
% 1.09/0.45 Contains.Choice.Funs: false
% 1.09/0.45 .............................
% 1.09/0.45
% 1.09/0.45 ********************************
% 1.09/0.45 * All subproblems solved! *
% 1.09/0.45 ********************************
% 1.09/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:0,translation:fof_full)
% 1.09/0.45
% 1.09/0.45 %**** Beginning of derivation protocol ****
% 1.09/0.45 % SZS output start CNFRefutation
% See solution above
% 1.09/0.45
% 1.09/0.45 %**** End of derivation protocol ****
% 1.09/0.45 %**** no. of clauses in derivation: 51 ****
% 1.09/0.45 %**** clause counter: 64 ****
% 1.09/0.45
% 1.09/0.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:64,loop_count:0,foatp_calls:0,translation:fof_full)
%------------------------------------------------------------------------------