TSTP Solution File: HWV003-2 by Gandalf---c-2.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : HWV003-2 : TPTP v3.4.2. Released v2.7.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art09.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 39.5s
% Output : Assurance 39.5s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/HWV/HWV003-2+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 4 3)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 4 3)
% (binary-posweight-lex-big-order 30 #f 4 3)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(sum,sum_def) | -equal(carry,carry_def).
% was split for some strategies as:
% -equal(sum,sum_def).
% -equal(carry,carry_def).
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(37,40,0,74,0,0,15670,4,1127,15672,50,1132,15672,40,1132,15709,0,1132,25515,3,1433,28112,4,1583,30262,5,1733,30262,1,1733,30262,50,1734,30262,40,1734,30299,0,1734,40163,3,2035,42626,4,2185,44439,5,2335,44439,1,2335,44439,50,2336,44439,40,2336,44476,0,2336,65358,3,3837)
%
%
% START OF PROOF
% 44440 [] equal(X,X).
% 44441 [] equal(or(X,Y),or(Y,X)).
% 44442 [] equal(and(X,Y),and(Y,X)).
% 44443 [] equal(or(or(X,Y),Z),or(X,or(Y,Z))).
% 44444 [] equal(and(and(X,Y),Z),and(X,and(Y,Z))).
% 44445 [] equal(or(X,ll0),X).
% 44446 [] equal(and(X,ll1),X).
% 44447 [] equal(and(X,or(Y,Z)),or(and(X,Y),and(X,Z))).
% 44448 [] equal(or(X,and(Y,Z)),and(or(X,Y),or(X,Z))).
% 44449 [] equal(or(X,not(X)),ll1).
% 44450 [] equal(and(X,not(X)),ll0).
% 44451 [] equal(or(X,X),X).
% 44452 [] equal(and(X,X),X).
% 44453 [] equal(not(not(X)),X).
% 44454 [] equal(not(ll0),ll1).
% 44455 [] equal(not(ll1),ll0).
% 44456 [] equal(or(X,ll1),ll1).
% 44457 [] equal(and(X,ll0),ll0).
% 44458 [] equal(or(X,and(X,Y)),X).
% 44459 [] equal(and(X,or(X,Y)),X).
% 44460 [] equal(not(or(X,Y)),and(not(X),not(Y))).
% 44461 [] equal(not(and(X,Y)),or(not(X),not(Y))).
% 44462 [] equal(or(and(not(X),Y),and(X,not(Y))),xor(X,Y)).
% 44463 [] equal(xor(X,Y),xor(Y,X)).
% 44464 [] equal(xor(X,xor(Y,Z)),xor(xor(X,Y),Z)).
% 44465 [] equal(xor(a,xor(b,cin)),sum_def).
% 44466 [] equal(or(and(cin,or(a,b)),and(not(cin),and(a,b))),carry_def).
% 44467 [] equal(not(and(a,b)),t1).
% 44468 [] equal(not(and(a,t1)),t2).
% 44469 [] equal(not(and(b,t1)),t3).
% 44470 [] equal(not(and(t2,t3)),t4).
% 44471 [] equal(not(and(t4,cin)),t5).
% 44472 [] equal(not(and(t4,t5)),t6).
% 44473 [] equal(not(and(t5,cin)),t7).
% 44474 [] equal(not(and(t6,t7)),sum).
% 44475 [] equal(not(and(t1,t5)),carry).
% 44476 [] -equal(sum,sum_def) | -equal(carry,carry_def).
% 44477 [para:44467.1.1,44453.1.1.1] equal(not(t1),and(a,b)).
% 44478 [para:44453.1.1,44449.1.1.2] equal(or(not(X),X),ll1).
% 44479 [para:44453.1.1,44450.1.1.2] equal(and(not(X),X),ll0).
% 44480 [para:44468.1.1,44453.1.1.1] equal(not(t2),and(a,t1)).
% 44481 [para:44469.1.1,44453.1.1.1] equal(not(t3),and(b,t1)).
% 44482 [para:44470.1.1,44453.1.1.1] equal(not(t4),and(t2,t3)).
% 44483 [para:44471.1.1,44453.1.1.1] equal(not(t5),and(t4,cin)).
% 44484 [para:44472.1.1,44453.1.1.1] equal(not(t6),and(t4,t5)).
% 44485 [para:44473.1.1,44453.1.1.1] equal(not(t7),and(t5,cin)).
% 44486 [para:44474.1.1,44453.1.1.1] equal(not(sum),and(t6,t7)).
% 44487 [para:44475.1.1,44453.1.1.1] equal(not(carry),and(t1,t5)).
% 44490 [para:44441.1.1,44445.1.1] equal(or(ll0,X),X).
% 44491 [para:44441.1.1,44456.1.1] equal(or(ll1,X),ll1).
% 44492 [para:44441.1.1,44466.1.1,demod:44460,44477] equal(or(not(or(cin,t1)),and(cin,or(a,b))),carry_def).
% 44493 [para:44441.1.1,44466.1.1.1.2,demod:44460,44477] equal(or(and(cin,or(b,a)),not(or(cin,t1))),carry_def).
% 44494 [para:44442.1.1,44446.1.1] equal(and(ll1,X),X).
% 44499 [para:44442.1.1,44457.1.1] equal(and(ll0,X),ll0).
% 44508 [para:44442.1.1,44477.1.2] equal(not(t1),and(b,a)).
% 44509 [para:44442.1.1,44480.1.2] equal(not(t2),and(t1,a)).
% 44510 [para:44442.1.1,44481.1.2] equal(not(t3),and(t1,b)).
% 44511 [para:44442.1.1,44482.1.2] equal(not(t4),and(t3,t2)).
% 44512 [para:44442.1.1,44483.1.2] equal(not(t5),and(cin,t4)).
% 44513 [para:44442.1.1,44484.1.2] equal(not(t6),and(t5,t4)).
% 44514 [para:44442.1.1,44485.1.2] equal(not(t7),and(cin,t5)).
% 44515 [para:44442.1.1,44486.1.2] equal(not(sum),and(t7,t6)).
% 44516 [para:44442.1.1,44487.1.2] equal(not(carry),and(t5,t1)).
% 44517 [para:44443.1.1,44451.1.1] equal(or(X,or(Y,or(X,Y))),or(X,Y)).
% 44519 [para:44449.1.1,44443.1.1.1,demod:44491] equal(ll1,or(X,or(not(X),Y))).
% 44520 [para:44478.1.1,44443.1.1.1,demod:44491] equal(ll1,or(not(X),or(X,Y))).
% 44521 [para:44443.1.1,44441.1.1] equal(or(X,or(Y,Z)),or(Z,or(X,Y))).
% 44523 [para:44441.1.1,44443.1.1.1,demod:44443] equal(or(X,or(Y,Z)),or(Y,or(X,Z))).
% 44524 [para:44444.1.1,44452.1.1] equal(and(X,and(Y,and(X,Y))),and(X,Y)).
% 44525 [para:44452.1.1,44444.1.1.1] equal(and(X,Y),and(X,and(X,Y))).
% 44526 [para:44450.1.1,44444.1.1.1,demod:44499] equal(ll0,and(X,and(not(X),Y))).
% 44527 [para:44479.1.1,44444.1.1.1,demod:44499] equal(ll0,and(not(X),and(X,Y))).
% 44528 [para:44477.1.2,44444.1.1.1] equal(and(not(t1),X),and(a,and(b,X))).
% 44529 [para:44480.1.2,44444.1.1.1] equal(and(not(t2),X),and(a,and(t1,X))).
% 44530 [para:44481.1.2,44444.1.1.1] equal(and(not(t3),X),and(b,and(t1,X))).
% 44531 [para:44482.1.2,44444.1.1.1] equal(and(not(t4),X),and(t2,and(t3,X))).
% 44532 [para:44483.1.2,44444.1.1.1] equal(and(not(t5),X),and(t4,and(cin,X))).
% 44533 [para:44484.1.2,44444.1.1.1] equal(and(not(t6),X),and(t4,and(t5,X))).
% 44534 [para:44485.1.2,44444.1.1.1] equal(and(not(t7),X),and(t5,and(cin,X))).
% 44537 [para:44444.1.1,44442.1.1] equal(and(X,and(Y,Z)),and(Z,and(X,Y))).
% 44540 [para:44452.1.1,44447.1.2.2] equal(and(X,or(Y,X)),or(and(X,Y),X)).
% 44541 [para:44446.1.1,44447.1.2.2,demod:44446,44456] equal(X,or(and(X,Y),X)).
% 44542 [para:44450.1.1,44447.1.2.1,demod:44490] equal(and(X,or(not(X),Y)),and(X,Y)).
% 44544 [para:44479.1.1,44447.1.2.1,demod:44490] equal(and(not(X),or(X,Y)),and(not(X),Y)).
% 44545 [para:44479.1.1,44447.1.2.2,demod:44445] equal(and(not(X),or(Y,X)),and(not(X),Y)).
% 44546 [para:44477.1.2,44447.1.2.1] equal(and(a,or(b,X)),or(not(t1),and(a,X))).
% 44552 [para:44482.1.2,44447.1.2.1] equal(and(t2,or(t3,X)),or(not(t4),and(t2,X))).
% 44553 [para:44482.1.2,44447.1.2.2] equal(and(t2,or(X,t3)),or(and(t2,X),not(t4))).
% 44560 [para:44486.1.2,44447.1.2.1] equal(and(t6,or(t7,X)),or(not(sum),and(t6,X))).
% 44562 [para:44487.1.2,44447.1.2.1] equal(and(t1,or(t5,X)),or(not(carry),and(t1,X))).
% 44565 [para:44442.1.1,44447.1.2.1] equal(and(X,or(Y,Z)),or(and(Y,X),and(X,Z))).
% 44568 [para:44451.1.1,44448.1.2.2] equal(or(X,and(Y,X)),and(or(X,Y),X)).
% 44569 [para:44445.1.1,44448.1.2.2,demod:44568,44445,44457] equal(X,or(X,and(Y,X))).
% 44570 [para:44449.1.1,44448.1.2.1,demod:44494] equal(or(X,and(not(X),Y)),or(X,Y)).
% 44571 [para:44449.1.1,44448.1.2.2,demod:44446] equal(or(X,and(Y,not(X))),or(X,Y)).
% 44572 [para:44478.1.1,44448.1.2.1,demod:44494] equal(or(not(X),and(X,Y)),or(not(X),Y)).
% 44573 [para:44478.1.1,44448.1.2.2,demod:44446] equal(or(not(X),and(Y,X)),or(not(X),Y)).
% 44581 [para:44508.1.2,44447.1.2.1] equal(and(b,or(a,X)),or(not(t1),and(b,X))).
% 44589 [para:44511.1.2,44444.1.1.1] equal(and(not(t4),X),and(t3,and(t2,X))).
% 44591 [para:44511.1.2,44447.1.2.2] equal(and(t3,or(X,t2)),or(and(t3,X),not(t4))).
% 44592 [para:44512.1.2,44444.1.1.1] equal(and(not(t5),X),and(cin,and(t4,X))).
% 44593 [para:44512.1.2,44447.1.2.1] equal(and(cin,or(t4,X)),or(not(t5),and(cin,X))).
% 44595 [para:44477.1.2,44458.1.1.2] equal(or(a,not(t1)),a).
% 44596 [para:44480.1.2,44458.1.1.2] equal(or(a,not(t2)),a).
% 44597 [para:44481.1.2,44458.1.1.2] equal(or(b,not(t3)),b).
% 44598 [para:44482.1.2,44458.1.1.2] equal(or(t2,not(t4)),t2).
% 44599 [para:44483.1.2,44458.1.1.2] equal(or(t4,not(t5)),t4).
% 44600 [para:44484.1.2,44458.1.1.2] equal(or(t4,not(t6)),t4).
% 44601 [para:44485.1.2,44458.1.1.2] equal(or(t5,not(t7)),t5).
% 44603 [para:44487.1.2,44458.1.1.2] equal(or(t1,not(carry)),t1).
% 44604 [para:44458.1.1,44443.1.1.1] equal(or(X,Y),or(X,or(and(X,Z),Y))).
% 44605 [para:44458.1.1,44448.1.2.2,demod:44569,44568] equal(or(X,and(Y,and(X,Z))),X).
% 44606 [para:44508.1.2,44458.1.1.2] equal(or(b,not(t1)),b).
% 44607 [para:44509.1.2,44458.1.1.2] equal(or(t1,not(t2)),t1).
% 44608 [para:44510.1.2,44458.1.1.2] equal(or(t1,not(t3)),t1).
% 44609 [para:44511.1.2,44458.1.1.2] equal(or(t3,not(t4)),t3).
% 44610 [para:44512.1.2,44458.1.1.2] equal(or(cin,not(t5)),cin).
% 44614 [para:44513.1.2,44458.1.1.2] equal(or(t5,not(t6)),t5).
% 44615 [para:44514.1.2,44444.1.1.1] equal(and(not(t7),X),and(cin,and(t5,X))).
% 44616 [para:44514.1.2,44447.1.2.1] equal(and(cin,or(t5,X)),or(not(t7),and(cin,X))).
% 44618 [para:44514.1.2,44458.1.1.2] equal(or(cin,not(t7)),cin).
% 44622 [para:44515.1.2,44458.1.1.2] equal(or(t7,not(sum)),t7).
% 44624 [para:44516.1.2,44447.1.2.1] equal(and(t5,or(t1,X)),or(not(carry),and(t5,X))).
% 44625 [para:44516.1.2,44447.1.2.2] equal(and(t5,or(X,t1)),or(and(t5,X),not(carry))).
% 44626 [para:44516.1.2,44458.1.1.2] equal(or(t5,not(carry)),t5).
% 44627 [para:44595.1.1,44441.1.1] equal(a,or(not(t1),a)).
% 44632 [para:44459.1.1,44444.1.1.1] equal(and(X,Y),and(X,and(or(X,Z),Y))).
% 44634 [para:44596.1.1,44441.1.1] equal(a,or(not(t2),a)).
% 44638 [para:44597.1.1,44441.1.1] equal(b,or(not(t3),b)).
% 44642 [para:44598.1.1,44441.1.1] equal(t2,or(not(t4),t2)).
% 44643 [para:44598.1.1,44443.1.1.1] equal(or(t2,X),or(t2,or(not(t4),X))).
% 44646 [para:44599.1.1,44441.1.1] equal(t4,or(not(t5),t4)).
% 44650 [para:44600.1.1,44441.1.1] equal(t4,or(not(t6),t4)).
% 44654 [para:44453.1.1,44460.1.2.1] equal(not(or(not(X),Y)),and(X,not(Y))).
% 44655 [para:44453.1.1,44460.1.2.2] equal(not(or(X,not(Y))),and(not(X),Y)).
% 44657 [para:44460.1.2,44444.1.1.1] equal(and(not(or(X,Y)),Z),and(not(X),and(not(Y),Z))).
% 44660 [para:44601.1.1,44441.1.1] equal(t5,or(not(t7),t5)).
% 44668 [para:44603.1.1,44441.1.1] equal(t1,or(not(carry),t1)).
% 44671 [para:44603.1.1,44448.1.2.2,demod:44569,44568] equal(or(t1,and(X,not(carry))),t1).
% 44672 [para:44606.1.1,44441.1.1] equal(b,or(not(t1),b)).
% 44676 [para:44607.1.1,44441.1.1] equal(t1,or(not(t2),t1)).
% 44680 [para:44453.1.1,44461.1.2.1] equal(not(and(not(X),Y)),or(X,not(Y))).
% 44686 [para:44608.1.1,44441.1.1] equal(t1,or(not(t3),t1)).
% 44690 [para:44454.1.1,44462.1.1.1.1,demod:44445,44499,44494] equal(X,xor(ll0,X)).
% 44691 [para:44454.1.1,44462.1.1.2.2,demod:44490,44446,44457] equal(X,xor(X,ll0)).
% 44692 [para:44455.1.1,44462.1.1.1.1,demod:44490,44494,44499] equal(not(X),xor(ll1,X)).
% 44693 [para:44455.1.1,44462.1.1.2.2,demod:44445,44457,44446] equal(not(X),xor(X,ll1)).
% 44696 [para:44453.1.1,44462.1.1.1.1,demod:44460] equal(or(and(X,Y),not(or(X,Y))),xor(not(X),Y)).
% 44698 [para:44450.1.1,44462.1.1.1,demod:44490,44450,44453] equal(ll0,xor(X,X)).
% 44704 [para:44463.1.1,44465.1.1,demod:44464] equal(xor(b,xor(cin,a)),sum_def).
% 44706 [para:44609.1.1,44441.1.1] equal(t3,or(not(t4),t3)).
% 44707 [para:44609.1.1,44443.1.1.1] equal(or(t3,X),or(t3,or(not(t4),X))).
% 44712 [para:44698.1.2,44464.1.2.1,demod:44690] equal(xor(X,xor(X,Y)),Y).
% 44716 [para:44692.1.2,44464.1.2.1,demod:44692] equal(not(xor(X,Y)),xor(not(X),Y)).
% 44717 [para:44464.1.2,44693.1.2,demod:44693] equal(not(xor(X,Y)),xor(X,not(Y))).
% 44718 [para:44610.1.1,44441.1.1] equal(cin,or(not(t5),cin)).
% 44722 [para:44614.1.1,44441.1.1] equal(t5,or(not(t6),t5)).
% 44726 [para:44618.1.1,44441.1.1] equal(cin,or(not(t7),cin)).
% 44730 [para:44622.1.1,44441.1.1] equal(t7,or(not(sum),t7)).
% 44734 [para:44626.1.1,44441.1.1] equal(t5,or(not(carry),t5)).
% 44739 [para:44627.1.2,44448.1.2.1,demod:44546] equal(and(a,or(b,X)),and(a,or(not(t1),X))).
% 44740 [para:44627.1.2,44448.1.2.2] equal(or(not(t1),and(X,a)),and(or(not(t1),X),a)).
% 44741 [para:44627.1.2,44459.1.1.2] equal(and(not(t1),a),not(t1)).
% 44745 [para:44634.1.2,44459.1.1.2] equal(and(not(t2),a),not(t2)).
% 44749 [para:44638.1.2,44459.1.1.2] equal(and(not(t3),b),not(t3)).
% 44757 [para:44646.1.2,44459.1.1.2] equal(and(not(t5),t4),not(t5)).
% 44765 [para:44650.1.2,44459.1.1.2] equal(and(not(t6),t4),not(t6)).
% 44777 [para:44668.1.2,44459.1.1.2] equal(and(not(carry),t1),not(carry)).
% 44779 [para:44672.1.2,44448.1.2.1,demod:44581] equal(and(b,or(a,X)),and(b,or(not(t1),X))).
% 44781 [para:44672.1.2,44459.1.1.2] equal(and(not(t1),b),not(t1)).
% 44784 [para:44493.1.1,44459.1.1.2,demod:44444] equal(and(cin,and(or(b,a),carry_def)),and(cin,or(b,a))).
% 44788 [para:44676.1.2,44459.1.1.2] equal(and(not(t2),t1),not(t2)).
% 44792 [para:44686.1.2,44459.1.1.2] equal(and(not(t3),t1),not(t3)).
% 44798 [para:44718.1.2,44448.1.2.1,demod:44593] equal(and(cin,or(t4,X)),and(cin,or(not(t5),X))).
% 44800 [para:44718.1.2,44459.1.1.2] equal(and(not(t5),cin),not(t5)).
% 44804 [para:44722.1.2,44459.1.1.2] equal(and(not(t6),t5),not(t6)).
% 44819 [para:44442.1.1,44541.1.2.1] equal(X,or(and(Y,X),X)).
% 44821 [para:44541.1.2,44448.1.2.1,demod:44447] equal(and(X,or(Y,Z)),and(X,or(and(X,Y),Z))).
% 44824 [para:44541.1.2,44459.1.1.2,demod:44444] equal(and(X,and(Y,X)),and(X,Y)).
% 44825 [para:44741.1.1,44442.1.1] equal(not(t1),and(a,not(t1))).
% 44829 [para:44741.1.1,44462.1.1.1,demod:44453,44509,44461,44572] equal(t2,xor(t1,a)).
% 44830 [para:44829.1.2,44463.1.1] equal(t2,xor(a,t1)).
% 44835 [para:44459.1.1,44569.1.2.2,demod:44443] equal(or(X,Y),or(X,or(Y,X))).
% 44837 [para:44712.1.1,44463.1.1,demod:44464] equal(X,xor(Y,xor(X,Y))).
% 44838 [para:44829.1.2,44712.1.1.2] equal(xor(t1,t2),a).
% 44839 [para:44830.1.2,44712.1.1.2] equal(xor(a,t2),t1).
% 44840 [para:44838.1.1,44463.1.1] equal(a,xor(t2,t1)).
% 44842 [para:44839.1.1,44463.1.1] equal(t1,xor(t2,a)).
% 44846 [para:44745.1.1,44442.1.1] equal(not(t2),and(a,not(t2))).
% 44850 [para:44745.1.1,44462.1.1.1,demod:44842,44461,44572] equal(not(and(t2,a)),t1).
% 44851 [para:44850.1.1,44453.1.1.1] equal(not(t1),and(t2,a)).
% 44854 [para:44517.1.1,44448.1.2.1,demod:44448,44835] equal(or(X,and(or(Y,X),Z)),or(X,and(Y,Z))).
% 44856 [para:44851.1.2,44442.1.1] equal(not(t1),and(a,t2)).
% 44863 [para:44856.1.2,44447.1.2.1,demod:44546] equal(and(a,or(t2,X)),and(a,or(b,X))).
% 44882 [para:44819.1.2,44448.1.2.2] equal(or(and(X,Y),and(Z,Y)),and(or(and(X,Y),Z),Y)).
% 44887 [para:44749.1.1,44442.1.1] equal(not(t3),and(b,not(t3))).
% 44897 [para:44757.1.1,44442.1.1] equal(not(t5),and(t4,not(t5))).
% 44899 [para:44757.1.1,44447.1.2.1,demod:44458] equal(and(not(t5),or(t4,X)),not(t5)).
% 44901 [para:44757.1.1,44462.1.1.1,demod:44453,44513,44461,44572] equal(t6,xor(t5,t4)).
% 44906 [para:44634.1.2,44519.1.2.2] equal(ll1,or(t2,a)).
% 44907 [para:44638.1.2,44519.1.2.2] equal(ll1,or(t3,b)).
% 44908 [para:44642.1.2,44519.1.2.2] equal(ll1,or(t4,t2)).
% 44909 [para:44646.1.2,44519.1.2.2] equal(ll1,or(t5,t4)).
% 44910 [para:44492.1.1,44519.1.2.2,demod:44443] equal(ll1,or(cin,or(t1,carry_def))).
% 44911 [para:44650.1.2,44519.1.2.2] equal(ll1,or(t6,t4)).
% 44912 [para:44660.1.2,44519.1.2.2] equal(ll1,or(t7,t5)).
% 44914 [para:44668.1.2,44519.1.2.2] equal(ll1,or(carry,t1)).
% 44917 [para:44686.1.2,44519.1.2.2] equal(ll1,or(t3,t1)).
% 44918 [para:44706.1.2,44519.1.2.2] equal(ll1,or(t4,t3)).
% 44921 [para:44726.1.2,44519.1.2.2] equal(ll1,or(t7,cin)).
% 44922 [para:44730.1.2,44519.1.2.2] equal(ll1,or(sum,t7)).
% 44923 [para:44734.1.2,44519.1.2.2] equal(ll1,or(carry,t5)).
% 44927 [para:44901.1.2,44712.1.1.2] equal(xor(t5,t6),t4).
% 44933 [para:44906.1.2,44441.1.1] equal(ll1,or(a,t2)).
% 44951 [para:44819.1.2,44520.1.2.2] equal(ll1,or(not(and(X,Y)),Y)).
% 44953 [para:44909.1.2,44443.1.1.1,demod:44491] equal(ll1,or(t5,or(t4,X))).
% 44958 [para:44911.1.2,44448.1.2.1,demod:44494] equal(or(t6,and(t4,X)),or(t6,X)).
% 44960 [para:44912.1.2,44441.1.1] equal(ll1,or(t5,t7)).
% 44962 [para:44912.1.2,44448.1.2.1,demod:44494] equal(or(t7,and(t5,X)),or(t7,X)).
% 44968 [para:44914.1.2,44441.1.1] equal(ll1,or(t1,carry)).
% 45033 [para:44908.1.2,44521.1.1.2,demod:44456] equal(ll1,or(t2,or(X,t4))).
% 45054 [para:44917.1.2,44441.1.1] equal(ll1,or(t1,t3)).
% 45059 [para:44918.1.2,44441.1.1] equal(ll1,or(t3,t4)).
% 45063 [para:44918.1.2,44521.1.1.2,demod:44456] equal(ll1,or(t3,or(X,t4))).
% 45072 [para:44911.1.2,44523.1.1.2,demod:44456] equal(ll1,or(t6,or(X,t4))).
% 45075 [para:44914.1.2,44523.1.1.2,demod:44456] equal(ll1,or(carry,or(X,t1))).
% 45096 [para:44921.1.2,44448.1.2.1,demod:44494] equal(or(t7,and(cin,X)),or(t7,X)).
% 45097 [para:44921.1.2,44448.1.2.2,demod:44446] equal(or(t7,and(X,cin)),or(t7,X)).
% 45100 [para:44922.1.2,44441.1.1] equal(ll1,or(t7,sum)).
% 45106 [para:44923.1.2,44441.1.1] equal(ll1,or(t5,carry)).
% 45113 [para:44524.1.1,44447.1.2.2,demod:44447,44824] equal(and(X,or(Y,and(Z,X))),and(X,or(Y,Z))).
% 45115 [para:44509.1.2,44524.1.1.2.2,demod:44509,44846] equal(and(t1,not(t2)),not(t2)).
% 45120 [para:44851.1.2,44524.1.1.2.2,demod:44851,44825] equal(and(t2,not(t1)),not(t1)).
% 45125 [para:44927.1.1,44463.1.1] equal(t4,xor(t6,t5)).
% 45127 [para:44927.1.1,44837.1.2.2] equal(t5,xor(t6,t4)).
% 45133 [para:44485.1.2,44525.1.2.2,demod:44485] equal(not(t7),and(t5,not(t7))).
% 45143 [para:44933.1.2,44448.1.2.1,demod:44494] equal(or(a,and(t2,X)),or(a,X)).
% 45157 [para:44526.1.2,44442.1.1,demod:44444] equal(ll0,and(not(X),and(Y,X))).
% 45195 [para:44481.1.2,44528.1.2.2,demod:44479] equal(ll0,and(a,not(t3))).
% 45212 [para:45195.1.2,44442.1.1] equal(ll0,and(not(t3),a)).
% 45220 [para:45212.1.2,44462.1.1.1,demod:44490] equal(and(t3,not(a)),xor(t3,a)).
% 45226 [para:44510.1.2,44529.1.2.2,demod:45195] equal(and(not(t2),b),ll0).
% 45239 [para:44509.1.2,44530.1.2.2,demod:45212] equal(ll0,and(b,not(t2))).
% 45250 [para:45226.1.1,44462.1.1.1,demod:44490] equal(and(t2,not(b)),xor(t2,b)).
% 45258 [para:44765.1.1,44462.1.1.1,demod:45127,44461,44572] equal(not(and(t6,t4)),t5).
% 45259 [para:45258.1.1,44453.1.1.1] equal(not(t5),and(t6,t4)).
% 45272 [para:45259.1.2,44442.1.1] equal(not(t5),and(t4,t6)).
% 45278 [para:45259.1.2,44524.1.1.2.2,demod:45259,44897] equal(and(t6,not(t5)),not(t5)).
% 45295 [para:44514.1.2,44532.1.2.2,demod:44479] equal(ll0,and(t4,not(t7))).
% 45303 [para:45295.1.2,44442.1.1] equal(ll0,and(not(t7),t4)).
% 45323 [para:44777.1.1,44462.1.1.1,demod:44461,44572] equal(not(and(carry,t1)),xor(carry,t1)).
% 45324 [para:44485.1.2,44533.1.2.2,demod:45295] equal(and(not(t6),cin),ll0).
% 45329 [para:44516.1.2,44533.1.2.2] equal(and(not(t6),t1),and(t4,not(carry))).
% 45337 [para:45324.1.1,44442.1.1] equal(ll0,and(cin,not(t6))).
% 45347 [para:44781.1.1,44462.1.1.1,demod:44453,44510,44461,44572] equal(t3,xor(t1,b)).
% 45350 [para:45347.1.2,44712.1.1.2] equal(xor(t1,t3),b).
% 45351 [para:45347.1.2,44837.1.2.2] equal(t1,xor(b,t3)).
% 45364 [para:45337.1.2,44534.1.2.2,demod:44457,44460] equal(not(or(t7,t6)),ll0).
% 45365 [para:45350.1.1,44463.1.1] equal(b,xor(t3,t1)).
% 45371 [para:45364.1.1,44453.1.1.1,demod:44454] equal(ll1,or(t7,t6)).
% 45384 [para:45371.1.2,44441.1.1] equal(ll1,or(t6,t7)).
% 45394 [para:44788.1.1,44462.1.1.1,demod:44840,44461,45120] equal(not(and(t2,t1)),a).
% 45395 [para:45394.1.1,44453.1.1.1] equal(not(a),and(t2,t1)).
% 45413 [para:45395.1.2,44442.1.1] equal(not(a),and(t1,t2)).
% 45426 [para:45413.1.2,44530.1.2.2] equal(and(not(t3),t2),and(b,not(a))).
% 45520 [para:44792.1.1,44462.1.1.1,demod:45365,44461,44572] equal(not(and(t3,t1)),b).
% 45522 [para:45520.1.1,44453.1.1.1] equal(not(b),and(t3,t1)).
% 45526 [para:45522.1.2,44442.1.1] equal(not(b),and(t1,t3)).
% 45531 [para:45522.1.2,44541.1.2.1] equal(t3,or(not(b),t3)).
% 45535 [para:45522.1.2,44531.1.2.2,demod:45250] equal(and(not(t4),t1),xor(t2,b)).
% 45541 [para:45526.1.2,44529.1.2.2] equal(and(not(t2),t3),and(a,not(b))).
% 45551 [para:45531.1.2,44459.1.1.2] equal(and(not(b),t3),not(b)).
% 45580 [para:44800.1.1,44462.1.1.1,demod:44453,44485,44461,44572] equal(t7,xor(t5,cin)).
% 45584 [para:45580.1.2,44712.1.1.2] equal(xor(t5,t7),cin).
% 45586 [para:44540.1.1,44442.1.1,demod:44541] equal(X,and(or(Y,X),X)).
% 45626 [para:44804.1.1,44462.1.1.1,demod:45125,44461,45278] equal(not(and(t6,t5)),t4).
% 45628 [para:45626.1.1,44453.1.1.1] equal(not(t4),and(t6,t5)).
% 45630 [para:45628.1.2,44442.1.1] equal(not(t4),and(t5,t6)).
% 45687 [para:44960.1.2,44544.1.1.2,demod:44446] equal(not(t5),and(not(t5),t7)).
% 45689 [para:44968.1.2,44544.1.1.2,demod:44446] equal(not(t1),and(not(t1),carry)).
% 45691 [para:45059.1.2,44544.1.1.2,demod:44446] equal(not(t3),and(not(t3),t4)).
% 45694 [para:45100.1.2,44544.1.1.2,demod:44446] equal(not(t7),and(not(t7),sum)).
% 45695 [para:45106.1.2,44544.1.1.2,demod:44446] equal(not(t5),and(not(t5),carry)).
% 45696 [para:45371.1.2,44544.1.1.2,demod:44446] equal(not(t7),and(not(t7),t6)).
% 45697 [para:45384.1.2,44544.1.1.2,demod:44446] equal(not(t6),and(not(t6),t7)).
% 45710 [para:44545.1.1,44537.1.1.2] equal(and(X,and(not(Y),Z)),and(or(Z,Y),and(X,not(Y)))).
% 45724 [para:44442.1.1,44546.1.2.2,demod:44863] equal(and(a,or(t2,X)),or(not(t1),and(X,a))).
% 45761 [para:44887.1.2,44462.1.1.2,demod:45351,44461,45551] equal(not(and(b,t3)),t1).
% 45762 [para:45761.1.1,44453.1.1.1] equal(not(t1),and(b,t3)).
% 45771 [para:45762.1.2,44442.1.1] equal(not(t1),and(t3,b)).
% 45773 [para:45762.1.2,44447.1.2.1,demod:44581] equal(and(b,or(t3,X)),and(b,or(a,X))).
% 45783 [para:45771.1.2,44531.1.2.2,demod:45120] equal(and(not(t4),b),not(t1)).
% 45832 [para:44953.1.2,44448.1.2.1,demod:44494] equal(or(t5,and(or(t4,X),Y)),or(t5,Y)).
% 45900 [para:45395.1.2,44553.1.2.1,demod:44461,44446,45054] equal(t2,not(and(a,t4))).
% 45906 [para:45900.1.2,44453.1.1.1] equal(not(t2),and(a,t4)).
% 46065 [para:45075.1.2,44545.1.1.2,demod:44446] equal(not(or(X,t1)),and(not(or(X,t1)),carry)).
% 46111 [para:45628.1.2,44560.1.2.2,demod:44461,44446,44912] equal(t6,not(and(sum,t4))).
% 46112 [para:46111.1.2,44453.1.1.1] equal(not(t6),and(sum,t4)).
% 46114 [para:46112.1.2,44442.1.1] equal(not(t6),and(t4,sum)).
% 46240 [para:45115.1.1,44530.1.2.2,demod:45239,44460] equal(not(or(t3,t2)),ll0).
% 46241 [para:46240.1.1,44453.1.1.1,demod:44454] equal(ll1,or(t3,t2)).
% 46249 [para:46241.1.2,44544.1.1.2,demod:45426,44446] equal(not(t3),and(b,not(a))).
% 46250 [para:46241.1.2,44545.1.1.2,demod:45541,44446] equal(not(t2),and(a,not(b))).
% 46254 [para:44442.1.1,44565.1.2.2] equal(and(X,or(Y,Z)),or(and(Y,X),and(Z,X))).
% 46438 [para:45133.1.2,44462.1.1.2,demod:45584,44461,45687] equal(not(and(t5,t7)),cin).
% 46440 [para:46438.1.1,44453.1.1.1] equal(not(cin),and(t5,t7)).
% 46466 [para:46440.1.2,44533.1.2.2,demod:45697] equal(not(t6),and(t4,not(cin))).
% 46497 [para:44460.1.2,44570.1.1.2] equal(or(X,not(or(X,Y))),or(X,not(Y))).
% 46499 [para:45212.1.2,44570.1.1.2,demod:44445] equal(t3,or(t3,a)).
% 46500 [para:45226.1.1,44570.1.1.2,demod:44445] equal(t2,or(t2,b)).
% 46501 [para:45303.1.2,44570.1.1.2,demod:44445] equal(t7,or(t7,t4)).
% 46502 [para:45324.1.1,44570.1.1.2,demod:44445] equal(t6,or(t6,cin)).
% 46510 [para:46499.1.2,45586.1.2.1] equal(a,and(t3,a)).
% 46518 [para:46500.1.2,45586.1.2.1] equal(b,and(t2,b)).
% 46527 [para:46501.1.2,45033.1.2.2] equal(ll1,or(t2,t7)).
% 46528 [para:46501.1.2,45063.1.2.2] equal(ll1,or(t3,t7)).
% 46536 [para:46502.1.2,45586.1.2.1] equal(cin,and(t6,cin)).
% 46551 [para:46510.1.2,44531.1.2.2,demod:44851] equal(and(not(t4),a),not(t1)).
% 46564 [para:46518.1.2,44552.1.2.2,demod:44446,44907] equal(t2,or(not(t4),b)).
% 46569 [para:44483.1.2,44572.1.1.2,demod:44453,44484,44461] equal(t6,or(not(t4),cin)).
% 46595 [para:45906.1.2,44572.1.1.2,demod:44453,44856,44461] equal(t1,or(not(a),t4)).
% 46597 [para:46114.1.2,44572.1.1.2,demod:44453,45272,44461] equal(t5,or(not(t4),sum)).
% 46657 [para:46536.1.2,44560.1.2.2,demod:44446,44921] equal(t6,or(not(sum),cin)).
% 46839 [para:46564.1.2,44542.1.1.2] equal(and(t4,t2),and(t4,b)).
% 46954 [para:46595.1.2,44540.1.1.2,demod:44541] equal(and(t4,t1),t4).
% 46955 [para:46595.1.2,45586.1.2.1] equal(t4,and(t1,t4)).
% 46958 [para:46595.1.2,45072.1.2.2] equal(ll1,or(t6,t1)).
% 46964 [para:46954.1.1,44569.1.2.2] equal(t1,or(t1,t4)).
% 46965 [para:46954.1.1,44819.1.2.1] equal(t1,or(t4,t1)).
% 46970 [para:46954.1.1,44572.1.1.2,demod:44478] equal(ll1,or(not(t4),t1)).
% 46972 [para:46955.1.2,44527.1.2.2] equal(ll0,and(not(t1),t4)).
% 46973 [para:46955.1.2,44530.1.2.2,demod:45691] equal(not(t3),and(b,t4)).
% 46974 [para:46955.1.2,44562.1.2.2,demod:44446,44909] equal(t1,or(not(carry),t4)).
% 46987 [para:46958.1.2,44441.1.1] equal(ll1,or(t1,t6)).
% 46993 [para:46958.1.2,44544.1.1.2,demod:45329,44446] equal(not(t6),and(t4,not(carry))).
% 46994 [para:46958.1.2,44545.1.1.2,demod:44446] equal(not(t1),and(not(t1),t6)).
% 47022 [para:46597.1.2,45586.1.2.1] equal(sum,and(t5,sum)).
% 47114 [para:46657.1.2,44542.1.1.2] equal(and(sum,t6),and(sum,cin)).
% 47144 [para:46970.1.2,44441.1.1] equal(ll1,or(t1,not(t4))).
% 47152 [para:46973.1.2,44442.1.1,demod:46839] equal(not(t3),and(t4,t2)).
% 47186 [para:46972.1.2,44442.1.1] equal(ll0,and(t4,not(t1))).
% 47190 [para:46972.1.2,44462.1.1.1,demod:44490] equal(and(t1,not(t4)),xor(t1,t4)).
% 47200 [para:46974.1.2,44542.1.1.2] equal(and(carry,t1),and(carry,t4)).
% 47201 [para:46974.1.2,44545.1.1.2,demod:44460,45535] equal(xor(t2,b),not(or(t4,carry))).
% 47299 [para:47186.1.2,44462.1.1.2,demod:44445,45535] equal(xor(t2,b),xor(t4,t1)).
% 47354 [para:45395.1.2,44589.1.2.2,demod:45220,45535] equal(xor(t2,b),xor(t3,a)).
% 47403 [para:46510.1.2,44591.1.2.1,demod:44446,44933] equal(t3,or(a,not(t4))).
% 47550 [para:44466.1.1,44604.1.2.2,demod:46497,44460,44477] equal(or(cin,not(t1)),or(cin,carry_def)).
% 47617 [para:45689.1.2,44569.1.2.2] equal(carry,or(carry,not(t1))).
% 47618 [para:45689.1.2,44819.1.2.1] equal(carry,or(not(t1),carry)).
% 47625 [para:47617.1.2,44448.1.2.2,demod:44569,44568] equal(or(carry,and(X,not(t1))),carry).
% 47642 [para:45630.1.2,44615.1.2.2,demod:45696] equal(not(t7),and(cin,not(t4))).
% 47647 [para:47022.1.2,44615.1.2.2,demod:45694] equal(not(t7),and(cin,sum)).
% 47650 [para:47647.1.2,44442.1.1,demod:47114] equal(not(t7),and(sum,t6)).
% 47760 [para:45695.1.2,44819.1.2.1] equal(carry,or(not(t5),carry)).
% 47882 [para:45783.1.1,44570.1.1.2] equal(or(t4,not(t1)),or(t4,b)).
% 47902 [para:45630.1.2,44624.1.2.2,demod:45323,47200,44461,44446,46987] equal(t5,xor(carry,t1)).
% 47910 [para:47902.1.2,44712.1.1.2] equal(xor(carry,t5),t1).
% 47913 [para:47910.1.1,44463.1.1] equal(t1,xor(t5,carry)).
% 47923 [para:45630.1.2,44625.1.2.1,demod:44461,44446,46958] equal(t5,not(and(t4,carry))).
% 47927 [para:47923.1.2,44453.1.1.1] equal(not(t5),and(t4,carry)).
% 47936 [para:47927.1.2,44572.1.1.2,demod:44453,44484,44461] equal(t6,or(not(t4),carry)).
% 47959 [para:47936.1.2,45586.1.2.1] equal(carry,and(t6,carry)).
% 47980 [para:47959.1.2,44605.1.1.2.2] equal(or(t6,and(X,carry)),t6).
% 48061 [para:46249.1.2,44442.1.1] equal(not(t3),and(not(a),b)).
% 48070 [para:46249.1.2,44571.1.1.2] equal(or(a,not(t3)),or(a,b)).
% 48091 [para:44632.1.2,44592.1.2.2,demod:44592] equal(and(not(t5),and(or(t4,X),Y)),and(not(t5),Y)).
% 48100 [para:46250.1.2,44462.1.1.2,demod:44453,44511,44461,48061] equal(t4,xor(a,b)).
% 48105 [para:46250.1.2,44571.1.1.2] equal(or(b,not(t2)),or(b,a)).
% 48108 [para:48100.1.2,44712.1.1.2] equal(xor(a,t4),b).
% 48111 [para:48108.1.1,44463.1.1] equal(b,xor(t4,a)).
% 48113 [para:48108.1.1,44837.1.2.2] equal(a,xor(t4,b)).
% 48152 [para:46466.1.2,44442.1.1] equal(not(t6),and(not(cin),t4)).
% 48285 [para:46551.1.1,44570.1.1.2,demod:47882] equal(or(t4,b),or(t4,a)).
% 48340 [para:46569.1.2,44643.1.2.2] equal(or(t2,cin),or(t2,t6)).
% 48342 [para:47936.1.2,44643.1.2.2] equal(or(t2,carry),or(t2,t6)).
% 48525 [para:46993.1.2,44537.1.1.2] equal(and(X,not(t6)),and(not(carry),and(X,t4))).
% 48539 [para:46994.1.2,44819.1.2.1] equal(t6,or(not(t1),t6)).
% 48626 [para:44654.1.1,44450.1.1.2,demod:44460,45710] equal(and(X,not(or(Y,X))),ll0).
% 48639 [para:46564.1.2,44654.1.1.1] equal(not(t2),and(t4,not(b))).
% 48642 [para:46974.1.2,44654.1.1.1] equal(not(t1),and(carry,not(t4))).
% 48661 [para:44655.1.1,44449.1.1.2,demod:44461,44573,44443] equal(or(X,not(and(Y,X))),ll1).
% 48682 [para:47403.1.2,44655.1.1.1] equal(not(t3),and(not(a),t4)).
% 48692 [para:47642.1.2,44462.1.1.2,demod:44453,44486,44461,48152] equal(sum,xor(cin,t4)).
% 48739 [para:46972.1.2,44657.1.2.2,demod:44457] equal(and(not(or(X,t1)),t4),ll0).
% 49112 [para:44460.1.2,44671.1.1.2] equal(or(t1,not(or(X,carry))),t1).
% 49125 [para:48639.1.2,44571.1.1.2,demod:48105] equal(or(b,a),or(b,t4)).
% 49136 [para:48642.1.2,44571.1.1.2,demod:47882] equal(or(t4,b),or(t4,carry)).
% 49163 [para:48682.1.2,44570.1.1.2,demod:48070] equal(or(a,b),or(a,t4)).
% 49207 [para:44704.1.1,44463.1.1,demod:48692,48100,44464] equal(sum_def,sum).
% 49210 [para:49207.1.2,44476.1.1,cut:44440] -equal(carry,carry_def).
% 49235 [para:49207.1.2,46597.1.2.2] equal(t5,or(not(t4),sum_def)).
% 49240 [para:49207.1.2,46657.1.2.1.1] equal(t6,or(not(sum_def),cin)).
% 49252 [para:49207.1.2,47647.1.2.2] equal(not(t7),and(cin,sum_def)).
% 49257 [para:49207.1.2,47650.1.2.1] equal(not(t7),and(sum_def,t6)).
% 49573 [para:49235.1.2,44643.1.2.2] equal(or(t2,sum_def),or(t2,t5)).
% 49677 [para:49240.1.2,44542.1.1.2,demod:49257] equal(not(t7),and(sum_def,cin)).
% 49818 [para:49252.1.2,44447.1.2.1,demod:44616] equal(and(cin,or(sum_def,X)),and(cin,or(t5,X))).
% 49892 [para:44923.1.2,44696.1.1.2.1,demod:47910,44716,44445,44455] equal(and(carry,t5),not(t1)).
% 49893 [para:45106.1.2,44696.1.1.2.1,demod:47913,44716,44445,44455] equal(and(t5,carry),not(t1)).
% 49968 [para:46499.1.2,44696.1.1.2.1,demod:47354,44716,49163,48070,46510] equal(or(a,t4),not(xor(t2,b))).
% 49969 [para:46500.1.2,44696.1.1.2.1,demod:49968,44716,49125,48105,46518] equal(or(b,t4),or(a,t4)).
% 49981 [para:46954.1.1,44696.1.1.1,demod:49969,49968,47299,44716,49136,47882,46965] equal(or(t4,carry),or(b,t4)).
% 49982 [para:46955.1.2,44696.1.1.1,demod:44716,49136,47882,46964] equal(or(t4,carry),not(xor(t1,t4))).
% 49991 [para:47144.1.2,44696.1.1.2.1,demod:47201,49982,44717,44716,44445,44455,47190] equal(xor(t1,t4),xor(t2,b)).
% 50116 [para:49892.1.1,44447.1.2.1] equal(and(carry,or(t5,X)),or(not(t1),and(carry,X))).
% 50384 [para:46569.1.2,44707.1.2.2] equal(or(t3,cin),or(t3,t6)).
% 50386 [para:47936.1.2,44707.1.2.2] equal(or(t3,carry),or(t3,t6)).
% 50524 [para:44910.1.2,44441.1.1,demod:44443] equal(ll1,or(t1,or(carry_def,cin))).
% 50757 [para:48285.1.2,45586.1.2.1,demod:49136] equal(a,and(or(t4,carry),a)).
% 50822 [para:49125.1.1,44568.1.2.1,demod:49981,44606,44477] equal(b,and(or(t4,carry),b)).
% 50913 [para:49573.1.2,44441.1.1] equal(or(t2,sum_def),or(t5,t2)).
% 51061 [para:50524.1.2,44523.1.1] equal(ll1,or(carry_def,or(t1,cin))).
% 51144 [para:50757.1.2,44458.1.1.2,demod:44443] equal(or(t4,or(carry,a)),or(t4,carry)).
% 51156 [para:50757.1.2,44696.1.1.1,demod:45347,48111,44464,49991,47201,51144,44443] equal(or(a,xor(t1,t4)),t3).
% 51207 [para:50822.1.2,44458.1.1.2,demod:44443] equal(or(t4,or(carry,b)),or(t4,carry)).
% 51219 [para:50822.1.2,44696.1.1.1,demod:44829,48113,44464,49991,47201,51207,44443] equal(or(b,xor(t1,t4)),t2).
% 51364 [para:47618.1.2,44739.1.2.2,demod:48342,44863] equal(and(a,or(t2,t6)),and(a,carry)).
% 51365 [para:48539.1.2,44739.1.2.2,demod:51364,44863] equal(and(a,carry),and(a,t6)).
% 51381 [para:51061.1.2,44544.1.1.2,demod:44446] equal(not(carry_def),and(not(carry_def),or(t1,cin))).
% 51471 [para:51156.1.1,44545.1.1.2,demod:50757,49982] equal(and(or(t4,carry),t3),a).
% 51531 [para:51219.1.1,44545.1.1.2,demod:50822,49982] equal(and(or(t4,carry),t2),b).
% 51625 [para:51365.1.1,44442.1.1] equal(and(a,t6),and(carry,a)).
% 51647 [para:44441.1.1,51471.1.1.1] equal(and(or(carry,t4),t3),a).
% 51689 [para:44441.1.1,51531.1.1.1] equal(and(or(carry,t4),t2),b).
% 51714 [para:51625.1.1,44442.1.1] equal(and(carry,a),and(t6,a)).
% 51730 [para:51647.1.1,44632.1.2.2,demod:51714] equal(and(carry,t3),and(t6,a)).
% 51747 [para:51689.1.1,44632.1.2.2] equal(and(carry,t2),and(carry,b)).
% 51784 [para:51730.1.1,44442.1.1] equal(and(t6,a),and(t3,carry)).
% 51798 [para:51747.1.2,44442.1.1] equal(and(carry,t2),and(b,carry)).
% 51854 [para:51798.1.2,44581.1.2.2,demod:50913,50116,50386,45773] equal(and(b,or(t3,t6)),and(carry,or(t2,sum_def))).
% 52421 [para:47618.1.2,44779.1.2.2,demod:51798,51854,50386,45773] equal(and(carry,or(t2,sum_def)),and(carry,t2)).
% 52422 [para:48539.1.2,44779.1.2.2,demod:52421,51854,45773] equal(and(carry,t2),and(b,t6)).
% 52423 [para:52422.1.2,44442.1.1] equal(and(carry,t2),and(t6,b)).
% 52424 [para:52423.1.1,44442.1.1] equal(and(t6,b),and(t2,carry)).
% 52515 [para:44784.1.1,44532.1.2.2,demod:44899,44532,48091,49981,49125] equal(and(not(t5),carry_def),not(t5)).
% 52522 [para:44784.1.1,44616.1.2.2,demod:44446,44953,44616,49818,45832,49981,49125] equal(and(cin,or(sum_def,carry_def)),cin).
% 52529 [para:52515.1.1,44819.1.2.1] equal(carry_def,or(not(t5),carry_def)).
% 52536 [para:52515.1.1,44680.1.1.1,demod:44453] equal(t5,or(t5,not(carry_def))).
% 52568 [para:52529.1.2,44654.1.1.1] equal(not(carry_def),and(t5,not(carry_def))).
% 52635 [para:52568.1.2,44615.1.2.2,demod:44460] equal(not(or(t7,carry_def)),and(cin,not(carry_def))).
% 52639 [para:52522.1.1,44442.1.1] equal(cin,and(or(sum_def,carry_def),cin)).
% 52956 [para:47760.1.2,44798.1.2.2] equal(and(cin,or(t4,carry)),and(cin,carry)).
% 53010 [para:44460.1.2,47625.1.1.2] equal(or(carry,not(or(X,t1))),carry).
% 53460 [para:48739.1.1,44447.1.2.1,demod:44490] equal(and(not(or(X,t1)),or(t4,Y)),and(not(or(X,t1)),Y)).
% 53466 [para:44466.1.1,44821.1.2.2,demod:52956,53010,44443,44460,44477,49981,49969,49163] equal(and(cin,carry),and(cin,carry_def)).
% 53488 [para:53466.1.1,44442.1.1] equal(and(cin,carry_def),and(carry,cin)).
% 53490 [para:53488.1.1,44442.1.1] equal(and(carry,cin),and(carry_def,cin)).
% 53838 [para:44492.1.1,44835.1.2.2,demod:44541,53490,53488,53466,52956,49981,49969,49163] equal(or(and(carry_def,cin),not(or(cin,t1))),carry_def).
% 54031 [para:52639.1.2,44854.1.1.2,demod:49677] equal(or(carry_def,cin),or(carry_def,not(t7))).
% 54611 [para:44466.1.1,44882.1.2.1,demod:53838,46065,53460,44460,44477,53490,53488,53466,52956,49981,49969,49163] equal(carry_def,and(carry_def,or(t4,carry))).
% 54635 [para:54611.1.2,48661.1.1.2.1,demod:44443] equal(or(t4,or(carry,not(carry_def))),ll1).
% 55646 [para:47152.1.2,44958.1.1.2] equal(or(t6,not(t3)),or(t6,t2)).
% 55648 [para:46839.1.2,44958.1.1.2,demod:55646,47152] equal(or(t6,t2),or(t6,b)).
% 55676 [para:55648.1.2,44448.1.2.2,demod:44448] equal(or(t6,and(X,b)),or(t6,and(X,t2))).
% 55733 [para:49893.1.1,44962.1.1.2] equal(or(t7,not(t1)),or(t7,carry)).
% 57702 [para:47550.1.1,44441.1.1] equal(or(cin,carry_def),or(not(t1),cin)).
% 59133 [para:54031.1.2,44544.1.1.2,demod:44460,44544] equal(and(not(carry_def),cin),not(or(carry_def,t7))).
% 59179 [para:54635.1.1,44545.1.1.2,demod:48525,44446,44444,44655] equal(and(not(carry),carry_def),and(carry_def,not(t6))).
% 59881 [para:55733.1.1,44441.1.1] equal(or(t7,carry),or(not(t1),t7)).
% 59985 [para:57702.1.2,44739.1.2.2,demod:51784,51714,51625,51365,51364,48340,44863] equal(and(t3,carry),and(a,or(cin,carry_def))).
% 59987 [para:57702.1.2,44779.1.2.2,demod:52424,52423,52421,51854,50384,45773] equal(and(t2,carry),and(b,or(cin,carry_def))).
% 60502 [para:59881.1.2,44740.1.2.1,demod:44446,46527,45724] equal(a,and(or(t7,carry),a)).
% 60503 [para:59881.1.2,44779.1.2.2,demod:44446,46528,45773] equal(b,and(b,or(t7,carry))).
% 61097 [para:53466.1.1,45096.1.1.2,demod:45097,53490,53488] equal(or(t7,carry_def),or(t7,carry)).
% 61127 [para:61097.1.2,49112.1.1.2.1,demod:52635] equal(or(t1,and(cin,not(carry_def))),t1).
% 61161 [para:61097.1.2,60502.1.2.1] equal(a,and(or(t7,carry_def),a)).
% 61162 [para:61097.1.2,60503.1.2.2] equal(b,and(b,or(t7,carry_def))).
% 61214 [para:44441.1.1,61161.1.2.1] equal(a,and(or(carry_def,t7),a)).
% 61249 [para:44441.1.1,61162.1.2.2] equal(b,and(b,or(carry_def,t7))).
% 61301 [para:61214.1.2,44527.1.2.2,demod:44444,59133] equal(ll0,and(not(carry_def),and(cin,a))).
% 61351 [para:61249.1.2,45157.1.2.2,demod:44444,59133] equal(ll0,and(not(carry_def),and(cin,b))).
% 61623 [para:61127.1.1,45113.1.1.2,demod:51381] equal(and(not(carry_def),t1),not(carry_def)).
% 61624 [para:61623.1.1,44442.1.1] equal(not(carry_def),and(t1,not(carry_def))).
% 61761 [para:61624.1.2,44562.1.2.2,demod:44461,44487,52536] equal(not(carry),not(and(carry,carry_def))).
% 61795 [para:61761.1.2,44951.1.2.1] equal(ll1,or(not(carry),carry_def)).
% 61863 [para:61795.1.2,44696.1.1.2.1,demod:44453,44445,44455,59179] equal(and(carry_def,not(t6)),xor(carry,carry_def)).
% 62461 [para:61301.1.2,44570.1.1.2,demod:44445] equal(carry_def,or(carry_def,and(cin,a))).
% 62466 [para:62461.1.2,44441.1.1] equal(carry_def,or(and(cin,a),carry_def)).
% 62501 [para:62466.1.2,44882.1.2.1,demod:59985,46254] equal(and(t3,carry),and(carry_def,a)).
% 62578 [para:62501.1.1,45157.1.2.2] equal(ll0,and(not(carry),and(carry_def,a))).
% 63028 [para:61351.1.2,44570.1.1.2,demod:44445] equal(carry_def,or(carry_def,and(cin,b))).
% 63033 [para:63028.1.2,44441.1.1] equal(carry_def,or(and(cin,b),carry_def)).
% 63068 [para:63033.1.2,44882.1.2.1,demod:59987,46254] equal(and(t2,carry),and(carry_def,b)).
% 63139 [para:63068.1.1,47980.1.1.2,demod:55676] equal(or(t6,and(carry_def,t2)),t6).
% 63187 [para:44442.1.1,63139.1.1.2] equal(or(t6,and(t2,carry_def)),t6).
% 63277 [para:63187.1.1,48626.1.1.2.1,demod:61863,44444] equal(and(t2,xor(carry,carry_def)),ll0).
% 63311 [para:63277.1.1,45143.1.1.2,demod:44445] equal(a,or(a,xor(carry,carry_def))).
% 63378 [para:63311.1.2,45586.1.2.1] equal(xor(carry,carry_def),and(a,xor(carry,carry_def))).
% 65901 [para:62578.1.2,44537.1.1,demod:63378,61863,59179] equal(ll0,xor(carry,carry_def)).
% 65907 [para:65901.1.2,44712.1.1.2,demod:44691,cut:49210] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% using first neg lit preferred strategy
% not using sos strategy
% using unit paramodulation strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% clause length limited to 3
% clause depth limited to 4
% seconds given: 30
%
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 7853
% derived clauses: 943313
% kept clauses: 65714
% kept size sum: 266692
% kept mid-nuclei: 2
% kept new demods: 63410
% forw unit-subs: 760883
% forw double-subs: 0
% forw overdouble-subs: 0
% backward subs: 21
% fast unit cutoff: 4
% full unit cutoff: 0
% dbl unit cutoff: 0
% real runtime : 40.95
% process. runtime: 40.41
% specific non-discr-tree subsumption statistics:
% tried: 0
% length fails: 0
% strength fails: 0
% predlist fails: 0
% aux str. fails: 0
% by-lit fails: 0
% full subs tried: 0
% full subs fail: 0
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/HWV/HWV003-2+eq_r.in")
%
%------------------------------------------------------------------------------