%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV231+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:31:48 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 30 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 2975 (2693 equ)
% Maximal formula atoms : 70 ( 99 avg)
% Number of connectives : 4042 (1202 ~; 174 |;2543 &)
% ( 80 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 13 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 105 ( 105 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 64 ( 62 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_select2_type,type,
a_select2: ( $i * $i ) > $i ).
tff(n5_type,type,
n5: $i ).
tff(xinit_noise_type,type,
xinit_noise: $i ).
tff(n0_type,type,
n0: $i ).
tff(n4_type,type,
n4: $i ).
tff(n3_type,type,
n3: $i ).
tff(n2_type,type,
n2: $i ).
tff(n1_type,type,
n1: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(a_select3_type,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(r_ds1_filter_type,type,
r_ds1_filter: $i ).
tff(q_ds1_filter_type,type,
q_ds1_filter: $i ).
tff(1,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ( ( ! [A: $i,B: $i] :
( ~ ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
| ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
& ! [C: $i,D: $i] :
( ~ ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
| ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) ) ) )
=> $true )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(3,plain,
( ( ( n0 = a_select2(xinit_noise,n5) )
| ~ leq(n5,n5)
| ( ( n0 = n5 )
& ( n4 = n3 ) )
| ( ( n0 = n5 )
& ( n5 = n3 ) )
| ( ( n1 = n5 )
& ( n4 = n3 ) )
| ( ( n1 = n5 )
& ( n5 = n3 ) )
| ( ( n2 = n5 )
& ( n4 = n3 ) )
| ( ( n2 = n5 )
& ( n5 = n3 ) )
| $true
| ( ( n3 = n5 )
& ( n4 = n3 ) )
| ( ( n3 = n5 )
& ( n5 = n3 ) )
| ( ( n4 = n3 )
& ( n4 = n5 ) )
| ( n4 = n3 )
| ( ( n4 = n5 )
& ( n5 = n3 ) )
| ( n5 = n3 )
| ( n4 != n5 )
| ( n5 != n3 )
| ~ leq(n0,n3)
| ~ leq(n0,n5)
| ~ leq(n3,n5) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
( ( ( n5 = n3 )
& $true )
<=> ( n5 = n3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,plain,
( ( n5 = n5 )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( ( ( n5 = n3 )
& ( n5 = n5 ) )
<=> ( ( n5 = n3 )
& $true ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ( ( n5 = n3 )
& ( n5 = n5 ) )
<=> ( n5 = n3 ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
( ( ( n4 = n3 )
& $true )
<=> ( n4 = n3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
( ( ( n4 = n3 )
& ( n5 = n5 ) )
<=> ( ( n4 = n3 )
& $true ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(10,plain,
( ( ( n4 = n3 )
& ( n5 = n5 ) )
<=> ( n4 = n3 ) ),
inference(transitivity,[status(thm)],[9,8]) ).
tff(11,plain,
( ( $true
& $true )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( n3 = n3 )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( ( n3 = n3 )
& ( n5 = n5 ) )
<=> ( $true
& $true ) ),
inference(monotonicity,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ( n3 = n3 )
& ( n5 = n5 ) )
<=> $true ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ( ( n0 = a_select2(xinit_noise,n5) )
| ~ leq(n5,n5)
| ( ( n0 = n5 )
& ( n4 = n3 ) )
| ( ( n0 = n5 )
& ( n5 = n3 ) )
| ( ( n1 = n5 )
& ( n4 = n3 ) )
| ( ( n1 = n5 )
& ( n5 = n3 ) )
| ( ( n2 = n5 )
& ( n4 = n3 ) )
| ( ( n2 = n5 )
& ( n5 = n3 ) )
| ( ( n3 = n3 )
& ( n5 = n5 ) )
| ( ( n3 = n5 )
& ( n4 = n3 ) )
| ( ( n3 = n5 )
& ( n5 = n3 ) )
| ( ( n4 = n3 )
& ( n4 = n5 ) )
| ( ( n4 = n3 )
& ( n5 = n5 ) )
| ( ( n4 = n5 )
& ( n5 = n3 ) )
| ( ( n5 = n3 )
& ( n5 = n5 ) )
| ( n4 != n5 )
| ( n5 != n3 )
| ~ leq(n0,n3)
| ~ leq(n0,n5)
| ~ leq(n3,n5) )
<=> ( ( n0 = a_select2(xinit_noise,n5) )
| ~ leq(n5,n5)
| ( ( n0 = n5 )
& ( n4 = n3 ) )
| ( ( n0 = n5 )
& ( n5 = n3 ) )
| ( ( n1 = n5 )
& ( n4 = n3 ) )
| ( ( n1 = n5 )
& ( n5 = n3 ) )
| ( ( n2 = n5 )
& ( n4 = n3 ) )
| ( ( n2 = n5 )
& ( n5 = n3 ) )
| $true
| ( ( n3 = n5 )
& ( n4 = n3 ) )
| ( ( n3 = n5 )
& ( n5 = n3 ) )
| ( ( n4 = n3 )
& ( n4 = n5 ) )
| ( n4 = n3 )
| ( ( n4 = n5 )
& ( n5 = n3 ) )
| ( n5 = n3 )
| ( n4 != n5 )
| ( n5 != n3 )
| ~ leq(n0,n3)
| ~ leq(n0,n5)
| ~ leq(n3,n5) ) ),
inference(monotonicity,[status(thm)],[14,10,7]) ).
tff(16,plain,
( ( ( n0 = a_select2(xinit_noise,n5) )
| ~ leq(n5,n5)
| ( ( n0 = n5 )
& ( n4 = n3 ) )
| ( ( n0 = n5 )
& ( n5 = n3 ) )
| ( ( n1 = n5 )
& ( n4 = n3 ) )
| ( ( n1 = n5 )
& ( n5 = n3 ) )
| ( ( n2 = n5 )
& ( n4 = n3 ) )
| ( ( n2 = n5 )
& ( n5 = n3 ) )
| ( ( n3 = n3 )
& ( n5 = n5 ) )
| ( ( n3 = n5 )
& ( n4 = n3 ) )
| ( ( n3 = n5 )
& ( n5 = n3 ) )
| ( ( n4 = n3 )
& ( n4 = n5 ) )
| ( ( n4 = n3 )
& ( n5 = n5 ) )
| ( ( n4 = n5 )
& ( n5 = n3 ) )
| ( ( n5 = n3 )
& ( n5 = n5 ) )
| ( n4 != n5 )
| ( n5 != n3 )
| ~ leq(n0,n3)
| ~ leq(n0,n5)
| ~ leq(n3,n5) )
<=> $true ),
inference(transitivity,[status(thm)],[15,3]) ).
tff(17,plain,
( ! [E: $i,F: $i] :
( ( n0 = a_select2(xinit_noise,n5) )
| ~ leq(n5,n5)
| ( ( n0 = n5 )
& ( n4 = n3 ) )
| ( ( n0 = n5 )
& ( n5 = n3 ) )
| ( ( n1 = n5 )
& ( n4 = n3 ) )
| ( ( n1 = n5 )
& ( n5 = n3 ) )
| ( ( n2 = n5 )
& ( n4 = n3 ) )
| ( ( n2 = n5 )
& ( n5 = n3 ) )
| ( ( n3 = n3 )
& ( n5 = n5 ) )
| ( ( n3 = n5 )
& ( n4 = n3 ) )
| ( ( n3 = n5 )
& ( n5 = n3 ) )
| ( ( n4 = n3 )
& ( n4 = n5 ) )
| ( ( n4 = n3 )
& ( n5 = n5 ) )
| ( ( n4 = n5 )
& ( n5 = n3 ) )
| ( ( n5 = n3 )
& ( n5 = n5 ) )
| ( n4 != n5 )
| ( n5 != n3 )
| ~ leq(n0,n3)
| ~ leq(n0,n5)
| ~ leq(n3,n5) )
<=> ( ( n0 = a_select2(xinit_noise,n5) )
| ~ leq(n5,n5)
| ( ( n0 = n5 )
& ( n4 = n3 ) )
| ( ( n0 = n5 )
& ( n5 = n3 ) )
| ( ( n1 = n5 )
& ( n4 = n3 ) )
| ( ( n1 = n5 )
& ( n5 = n3 ) )
| ( ( n2 = n5 )
& ( n4 = n3 ) )
| ( ( n2 = n5 )
& ( n5 = n3 ) )
| ( ( n3 = n3 )
& ( n5 = n5 ) )
| ( ( n3 = n5 )
& ( n4 = n3 ) )
| ( ( n3 = n5 )
& ( n5 = n3 ) )
| ( ( n4 = n3 )
& ( n4 = n5 ) )
| ( ( n4 = n3 )
& ( n5 = n5 ) )
| ( ( n4 = n5 )
& ( n5 = n3 ) )
| ( ( n5 = n3 )
& ( n5 = n5 ) )
| ( n4 != n5 )
| ( n5 != n3 )
| ~ leq(n0,n3)
| ~ leq(n0,n5)
| ~ leq(n3,n5) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(18,plain,
( ! [E: $i,F: $i] :
( ( n0 = a_select2(xinit_noise,n5) )
| ~ ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
| ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) ) )
<=> ! [E: $i,F: $i] :
( ( n0 = a_select2(xinit_noise,n5) )
| ~ leq(n5,n5)
| ( ( n0 = n5 )
& ( n4 = n3 ) )
| ( ( n0 = n5 )
& ( n5 = n3 ) )
| ( ( n1 = n5 )
& ( n4 = n3 ) )
| ( ( n1 = n5 )
& ( n5 = n3 ) )
| ( ( n2 = n5 )
& ( n4 = n3 ) )
| ( ( n2 = n5 )
& ( n5 = n3 ) )
| ( ( n3 = n3 )
& ( n5 = n5 ) )
| ( ( n3 = n5 )
& ( n4 = n3 ) )
| ( ( n3 = n5 )
& ( n5 = n3 ) )
| ( ( n4 = n3 )
& ( n4 = n5 ) )
| ( ( n4 = n3 )
& ( n5 = n5 ) )
| ( ( n4 = n5 )
& ( n5 = n3 ) )
| ( ( n5 = n3 )
& ( n5 = n5 ) )
| ( n4 != n5 )
| ( n5 != n3 )
| ~ leq(n0,n3)
| ~ leq(n0,n5)
| ~ leq(n3,n5) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(19,plain,
( ! [E: $i,F: $i] :
( ( n0 = a_select2(xinit_noise,n5) )
| ~ ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
| ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) ) )
<=> ( ( n0 = a_select2(xinit_noise,n5) )
| ~ leq(n5,n5)
| ( ( n0 = n5 )
& ( n4 = n3 ) )
| ( ( n0 = n5 )
& ( n5 = n3 ) )
| ( ( n1 = n5 )
& ( n4 = n3 ) )
| ( ( n1 = n5 )
& ( n5 = n3 ) )
| ( ( n2 = n5 )
& ( n4 = n3 ) )
| ( ( n2 = n5 )
& ( n5 = n3 ) )
| ( ( n3 = n3 )
& ( n5 = n5 ) )
| ( ( n3 = n5 )
& ( n4 = n3 ) )
| ( ( n3 = n5 )
& ( n5 = n3 ) )
| ( ( n4 = n3 )
& ( n4 = n5 ) )
| ( ( n4 = n3 )
& ( n5 = n5 ) )
| ( ( n4 = n5 )
& ( n5 = n3 ) )
| ( ( n5 = n3 )
& ( n5 = n5 ) )
| ( n4 != n5 )
| ( n5 != n3 )
| ~ leq(n0,n3)
| ~ leq(n0,n5)
| ~ leq(n3,n5) ) ),
inference(transitivity,[status(thm)],[18,17]) ).
tff(20,plain,
( ! [E: $i,F: $i] :
( ( n0 = a_select2(xinit_noise,n5) )
| ~ ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
| ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[19,16]) ).
tff(21,plain,
^ [E: $i,F: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5) )
<=> ( leq(n0,E)
& leq(n0,F)
& leq(E,n5) ) )),
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
<=> ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) ) )),
rewrite(( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
<=> ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) ) )),
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
<=> ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) ) )),
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) ) )),
rewrite(( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) ) )),
( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
<=> ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) ) )),
( ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) )
<=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) )),
rewrite(( ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) )
<=> ( ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
| ( n0 = a_select2(xinit_noise,n5) ) ) )),
( ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) )
<=> ( ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
| ( n0 = a_select2(xinit_noise,n5) ) ) )),
( ( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) )
<=> ( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
| ( n0 = a_select2(xinit_noise,n5) ) ) ) )),
rewrite(( ( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
| ( n0 = a_select2(xinit_noise,n5) ) ) )
<=> ( ( n0 = a_select2(xinit_noise,n5) )
| ~ ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
| ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) ) ) )),
( ( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) )
<=> ( ( n0 = a_select2(xinit_noise,n5) )
| ~ ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
| ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [E: $i,F: $i] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) )
<=> ! [E: $i,F: $i] :
( ( n0 = a_select2(xinit_noise,n5) )
| ~ ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
| ~ ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [E: $i,F: $i] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ( ! [A: $i,B: $i] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
=> ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
& ! [C: $i,D: $i] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) ) ) )
<=> ( ! [A: $i,B: $i] :
( ~ ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
| ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
& ! [C: $i,D: $i] :
( ~ ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
| ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ( ! [A: $i,B: $i] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
=> ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
& ! [C: $i,D: $i] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) ) ) )
=> ! [E: $i,F: $i] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) ) )
<=> ( ( ! [A: $i,B: $i] :
( ~ ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
| ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
& ! [C: $i,D: $i] :
( ~ ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
| ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) ) ) )
=> $true ) ),
inference(monotonicity,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ( ! [A: $i,B: $i] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
=> ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
& ! [C: $i,D: $i] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) ) ) )
=> ! [E: $i,F: $i] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[25,2]) ).
tff(27,plain,
( ~ ( ( ! [A: $i,B: $i] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
=> ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
& ! [C: $i,D: $i] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) ) ) )
=> ! [E: $i,F: $i] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ~ ( ( ! [A: $i,B: $i] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
=> ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
& ! [C: $i,D: $i] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) ) ) )
=> ! [E: $i,F: $i] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) ) )
<=> $false ),
inference(transitivity,[status(thm)],[27,1]) ).
tff(29,axiom,
~ ( ( ! [A: $i,B: $i] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
=> ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
& ! [C: $i,D: $i] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) ) ) )
=> ! [E: $i,F: $i] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n5)
& leq(F,n5) )
=> ( ( ~ ( ( n0 = F )
& ( n4 = E ) )
& ~ ( ( n0 = F )
& ( n5 = E ) )
& ~ ( ( n1 = F )
& ( n4 = E ) )
& ~ ( ( n1 = F )
& ( n5 = E ) )
& ~ ( ( n2 = F )
& ( n4 = E ) )
& ~ ( ( n2 = F )
& ( n5 = E ) )
& ~ ( ( n3 = E )
& ( n5 = F ) )
& ~ ( ( n3 = F )
& ( n4 = E ) )
& ~ ( ( n3 = F )
& ( n5 = E ) )
& ~ ( ( n4 = E )
& ( n4 = F ) )
& ~ ( ( n4 = E )
& ( n5 = F ) )
& ~ ( ( n4 = F )
& ( n5 = E ) )
& ~ ( ( n5 = E )
& ( n5 = F ) )
& ( n3 = E )
& ( n4 = F )
& ( n5 = E )
& ( n5 = F ) )
=> ( n0 = a_select2(xinit_noise,n5) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0801) ).
tff(30,plain,
$false,
inference(modus_ponens,[status(thm)],[29,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV231+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 09:33:46 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------