%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV232+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.23s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 31 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 1563 (1274 equ)
% Maximal formula atoms : 46 ( 50 avg)
% Number of connectives : 1991 ( 541 ~; 125 |;1215 &)
% ( 69 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 10 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 82 ( 82 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 : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 48 ( 44 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
tff(n0_type,type,
n0: $i ).
tff(a_select2_type,type,
a_select2: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(rho_type,type,
rho: $i ).
tff(n2_type,type,
n2: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(a_select3_type,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(q_ds1_filter_type,type,
q_ds1_filter: $i ).
tff(n5_type,type,
n5: $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) ) )
=> $true )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(3,plain,
( ( ~ leq(n0,n2)
| ( a_select2(rho,n1) = n0 )
| ~ leq(n0,n2)
| ~ leq(n0,n0)
| ~ leq(n2,n2)
| ( ( n0 = n2 )
& ( n1 = n0 ) )
| ( ( n0 = n2 )
& ( n2 = n0 ) )
| $true
| ( ( n1 = n2 )
& ( n1 = n0 ) )
| ( ( n1 = n2 )
& ( n2 = n0 ) )
| ( n1 = n0 )
| ( n2 = n0 )
| ( n1 != n2 )
| ( n1 != n0 ) )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
( ( $true
& ( n2 = n0 ) )
<=> ( n2 = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,plain,
( ( n2 = n2 )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( ( ( n2 = n2 )
& ( n2 = n0 ) )
<=> ( $true
& ( n2 = n0 ) ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ( ( n2 = n2 )
& ( n2 = n0 ) )
<=> ( n2 = n0 ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
( ( ( n1 = n0 )
& $true )
<=> ( n1 = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
( ( ( n1 = n0 )
& ( n2 = n2 ) )
<=> ( ( n1 = n0 )
& $true ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(10,plain,
( ( ( n1 = n0 )
& ( n2 = n2 ) )
<=> ( n1 = n0 ) ),
inference(transitivity,[status(thm)],[9,8]) ).
tff(11,plain,
( ( $true
& $true )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( n0 = n0 )
<=> $true ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( ( n0 = n0 )
& ( n2 = n2 ) )
<=> ( $true
& $true ) ),
inference(monotonicity,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ( n0 = n0 )
& ( n2 = n2 ) )
<=> $true ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ( ~ leq(n0,n2)
| ( a_select2(rho,n1) = n0 )
| ~ leq(n0,n2)
| ~ leq(n0,n0)
| ~ leq(n2,n2)
| ( ( n0 = n2 )
& ( n1 = n0 ) )
| ( ( n0 = n2 )
& ( n2 = n0 ) )
| ( ( n0 = n0 )
& ( n2 = n2 ) )
| ( ( n1 = n2 )
& ( n1 = n0 ) )
| ( ( n1 = n2 )
& ( n2 = n0 ) )
| ( ( n1 = n0 )
& ( n2 = n2 ) )
| ( ( n2 = n2 )
& ( n2 = n0 ) )
| ( n1 != n2 )
| ( n1 != n0 ) )
<=> ( ~ leq(n0,n2)
| ( a_select2(rho,n1) = n0 )
| ~ leq(n0,n2)
| ~ leq(n0,n0)
| ~ leq(n2,n2)
| ( ( n0 = n2 )
& ( n1 = n0 ) )
| ( ( n0 = n2 )
& ( n2 = n0 ) )
| $true
| ( ( n1 = n2 )
& ( n1 = n0 ) )
| ( ( n1 = n2 )
& ( n2 = n0 ) )
| ( n1 = n0 )
| ( n2 = n0 )
| ( n1 != n2 )
| ( n1 != n0 ) ) ),
inference(monotonicity,[status(thm)],[14,10,7]) ).
tff(16,plain,
( ( ~ leq(n0,n2)
| ( a_select2(rho,n1) = n0 )
| ~ leq(n0,n2)
| ~ leq(n0,n0)
| ~ leq(n2,n2)
| ( ( n0 = n2 )
& ( n1 = n0 ) )
| ( ( n0 = n2 )
& ( n2 = n0 ) )
| ( ( n0 = n0 )
& ( n2 = n2 ) )
| ( ( n1 = n2 )
& ( n1 = n0 ) )
| ( ( n1 = n2 )
& ( n2 = n0 ) )
| ( ( n1 = n0 )
& ( n2 = n2 ) )
| ( ( n2 = n2 )
& ( n2 = n0 ) )
| ( n1 != n2 )
| ( n1 != n0 ) )
<=> $true ),
inference(transitivity,[status(thm)],[15,3]) ).
tff(17,plain,
( ! [C: $i,D: $i] :
( ~ leq(n0,n2)
| ( a_select2(rho,n1) = n0 )
| ~ leq(n0,n2)
| ~ leq(n0,n0)
| ~ leq(n2,n2)
| ( ( n0 = n2 )
& ( n1 = n0 ) )
| ( ( n0 = n2 )
& ( n2 = n0 ) )
| ( ( n0 = n0 )
& ( n2 = n2 ) )
| ( ( n1 = n2 )
& ( n1 = n0 ) )
| ( ( n1 = n2 )
& ( n2 = n0 ) )
| ( ( n1 = n0 )
& ( n2 = n2 ) )
| ( ( n2 = n2 )
& ( n2 = n0 ) )
| ( n1 != n2 )
| ( n1 != n0 ) )
<=> ( ~ leq(n0,n2)
| ( a_select2(rho,n1) = n0 )
| ~ leq(n0,n2)
| ~ leq(n0,n0)
| ~ leq(n2,n2)
| ( ( n0 = n2 )
& ( n1 = n0 ) )
| ( ( n0 = n2 )
& ( n2 = n0 ) )
| ( ( n0 = n0 )
& ( n2 = n2 ) )
| ( ( n1 = n2 )
& ( n1 = n0 ) )
| ( ( n1 = n2 )
& ( n2 = n0 ) )
| ( ( n1 = n0 )
& ( n2 = n2 ) )
| ( ( n2 = n2 )
& ( n2 = n0 ) )
| ( n1 != n2 )
| ( n1 != n0 ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(18,plain,
( ! [C: $i,D: $i] :
( ( a_select2(rho,n1) = n0 )
| ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ~ ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) ) )
<=> ! [C: $i,D: $i] :
( ~ leq(n0,n2)
| ( a_select2(rho,n1) = n0 )
| ~ leq(n0,n2)
| ~ leq(n0,n0)
| ~ leq(n2,n2)
| ( ( n0 = n2 )
& ( n1 = n0 ) )
| ( ( n0 = n2 )
& ( n2 = n0 ) )
| ( ( n0 = n0 )
& ( n2 = n2 ) )
| ( ( n1 = n2 )
& ( n1 = n0 ) )
| ( ( n1 = n2 )
& ( n2 = n0 ) )
| ( ( n1 = n0 )
& ( n2 = n2 ) )
| ( ( n2 = n2 )
& ( n2 = n0 ) )
| ( n1 != n2 )
| ( n1 != n0 ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(19,plain,
( ! [C: $i,D: $i] :
( ( a_select2(rho,n1) = n0 )
| ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ~ ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) ) )
<=> ( ~ leq(n0,n2)
| ( a_select2(rho,n1) = n0 )
| ~ leq(n0,n2)
| ~ leq(n0,n0)
| ~ leq(n2,n2)
| ( ( n0 = n2 )
& ( n1 = n0 ) )
| ( ( n0 = n2 )
& ( n2 = n0 ) )
| ( ( n0 = n0 )
& ( n2 = n2 ) )
| ( ( n1 = n2 )
& ( n1 = n0 ) )
| ( ( n1 = n2 )
& ( n2 = n0 ) )
| ( ( n1 = n0 )
& ( n2 = n2 ) )
| ( ( n2 = n2 )
& ( n2 = n0 ) )
| ( n1 != n2 )
| ( n1 != n0 ) ) ),
inference(transitivity,[status(thm)],[18,17]) ).
tff(20,plain,
( ! [C: $i,D: $i] :
( ( a_select2(rho,n1) = n0 )
| ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ~ ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) ) )
<=> $true ),
inference(transitivity,[status(thm)],[19,16]) ).
tff(21,plain,
^ [C: $i,D: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2) )
<=> ( leq(n0,C)
& leq(n0,D)
& leq(C,n2) ) )),
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
<=> ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) ) )),
rewrite(( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
<=> ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) ) )),
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
<=> ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) ) )),
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) ) ) )),
rewrite(( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) ) ) )),
rewrite(( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) ) ) )),
rewrite(( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) ) ) )),
rewrite(( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D ) ) )),
rewrite(( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C ) ) )),
rewrite(( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D ) ) )),
rewrite(( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) ) )),
rewrite(( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) ) )),
( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
<=> ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) ) )),
( ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) )
<=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) )),
rewrite(( ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) )
<=> ( ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ( a_select2(rho,n1) = n0 ) ) )),
( ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) )
<=> ( ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ( a_select2(rho,n1) = n0 ) ) )),
( ( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) )
<=> ( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ( a_select2(rho,n1) = n0 ) ) ) )),
rewrite(( ( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ( a_select2(rho,n1) = n0 ) ) )
<=> ( ( a_select2(rho,n1) = n0 )
| ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ~ ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) ) ) )),
( ( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) )
<=> ( ( a_select2(rho,n1) = n0 )
| ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ~ ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [C: $i,D: $i] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) )
<=> ! [C: $i,D: $i] :
( ( a_select2(rho,n1) = n0 )
| ~ ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
| ~ ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [C: $i,D: $i] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,n2) )
=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
^ [A: $i,B: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5) )
<=> ( leq(n0,A)
& leq(n0,B)
& leq(A,n5) ) )),
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
<=> ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) ) )),
rewrite(( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
<=> ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) ) )),
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) )
<=> ( leq(n0,A)
& leq(n0,B)
& leq(A,n5)
& leq(B,n5) ) )),
( ( ( 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) ) )
<=> ( ( 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) ) ) )),
rewrite(( ( ( 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) ) )
<=> ( ~ ( 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) ) ) )),
( ( ( 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) ) )
<=> ( ~ ( 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) ) ) )),
inference(bind,[status(th)],[]) ).
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) ) )
<=> ! [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) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
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) )
=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) ) )
<=> ( ! [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) ) )
=> $true ) ),
inference(monotonicity,[status(thm)],[25,23]) ).
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) )
=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) ) )
<=> $true ),
inference(transitivity,[status(thm)],[26,2]) ).
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) )
=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) ) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,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) )
=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) ) )
<=> $false ),
inference(transitivity,[status(thm)],[28,1]) ).
tff(30,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) )
=> ( ( ~ ( ( n0 = C )
& ( n1 = D ) )
& ~ ( ( n0 = C )
& ( n2 = D ) )
& ~ ( ( n0 = D )
& ( n2 = C ) )
& ~ ( ( n1 = C )
& ( n1 = D ) )
& ~ ( ( n1 = C )
& ( n2 = D ) )
& ~ ( ( n1 = D )
& ( n2 = C ) )
& ~ ( ( n2 = C )
& ( n2 = D ) )
& ( n0 = D )
& ( n1 = C )
& ( n1 = D )
& ( n2 = C ) )
=> ( a_select2(rho,n1) = n0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0841) ).
tff(31,plain,
$false,
inference(modus_ponens,[status(thm)],[30,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SWV232+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.05/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 09:32:24 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.23/0.40 % SZS status Theorem
% 0.23/0.40 % SZS output start Proof
% See solution above
% 0.23/0.43 % E exiting
%------------------------------------------------------------------------------