Prooof out3b2-127

(x + (x + x)')' = g(x).   x + (x + (x + (x + (x + g(x))))') = h(x). % Problem 127

============================== PROOF =================================

% Proof 1 at 49.32 (+ 0.26) seconds: Winker2b.
% Length of proof is 29.
% Level of proof is 9.
% Maximum clause weight is 34.
% Given clauses 687.

2 (exists a exists b (a + b)' = b') # answer(Winker2b) # label(non_clause) # label(goal).  [goal].
6 x + y = y + x # label(Commutativity).  [assumption].
7 (x + y) + z = x + (y + z) # label(Associativity).  [assumption].
8 ((x + y)' + (x + y')')' = x # label(Robbins).  [assumption].
9 (x + (x + x)')' = g(x).  [assumption].
10 x + (x + (x + (x + (x + g(x))))') = h(x).  [assumption].
12 (x + y)' != y' # answer(Winker2b).  [deny(2)].
17 x + (y + z) = y + (x + z).  [para(6(a,1),7(a,1,1)),rewrite([7(2)])].
19 ((x + y)' + (y' + x)')' = x.  [para(6(a,1),8(a,1,1,2,1))].
20 ((x + (y + z))' + (x + (y + z'))')' = x + y.  [para(7(a,1),8(a,1,1,1,1)),rewrite([7(6)])].
22 ((x + y)' + (x + ((y + z)' + (y + z')'))')' = x.  [para(8(a,1),8(a,1,1,2,1,2)),rewrite([6(11)])].
23 (x + (x + (y' + (x + y)'))')' = (x + y)'.  [para(8(a,1),8(a,1,1,2)),rewrite([6(5),7(5),6(7)])].
26 (g(x) + (x + (x + x))')' = x.  [para(9(a,1),8(a,1,1,2)),rewrite([6(5)])].
28 x + (y + (x + (x + (x + (x + g(x))))')) = y + h(x).  [para(10(a,1),7(a,2,2)),rewrite([17(8),7(7)])].
29 (h(x)' + (x + (x + (x + (x + (x + g(x))))')')')' = x.  [para(10(a,1),8(a,1,1,1,1))].
33 (x + (x + (x + (x + g(x))))')' = g(x).  [para(26(a,1),8(a,1,1,2)),rewrite([17(4),17(3),6(2),6(6)])].
34 (h(x)' + (x + g(x))')' = x.  [back_rewrite(29),rewrite([33(9)])].
69 (x + (h(x) + (x + g(x))')')' = (x + g(x))'.  [para(34(a,1),19(a,1,1,2)),rewrite([6(5),6(7)])].
81 (x + (y + (x + (y + (z' + (x + (y + z))')))'))' = (x + (y + z))'.  [para(20(a,1),8(a,1,1,2)),rewrite([6(7),7(7),7(6),6(10),7(10)])].
268 ((x + (y + (z + u))')' + (x + (y + (z + (y + (z + (u' + (y + (z + u))')))')))')' = x.  [para(20(a,1),22(a,1,1,2,1,2,2)),rewrite([6(12),7(12),7(11),6(15),7(15)])].
364 ((x + y)' + (x + (x + (y' + (x + y)')))')' = x.  [para(23(a,1),8(a,1,1,2)),rewrite([6(10)])].
680 x + (x + (y + (x + (x + (x + g(x))))')) = y + h(x).  [para(28(a,1),7(a,2)),rewrite([17(8),7(7)])].
10432 (x + (x + (h(x) + (x + g(x))')'))' = (x + (x + (x + g(x))))'.  [para(680(a,1),81(a,1,1,2,2,1)),rewrite([6(5)])].
17891 ((x + (x + (x + g(x))))' + (h(x) + (x + g(x))')')' = x.  [para(10432(a,1),364(a,1,1,1)),rewrite([69(13),10432(17),680(16),6(10)])].
17918 (x + (x + (x + (x + (g(x) + (h(x) + (x + g(x))')'))))')' = (h(x) + (x + g(x))')'.  [para(17891(a,1),19(a,1,1,2)),rewrite([6(11),7(11),7(10),7(9),6(13)])].
20947 (g(x) + (x + (x + (x + (h(x) + (x + g(x))')')))')' = x.  [para(33(a,1),268(a,1,1,1)),rewrite([680(12),6(6)])].
20951 (h(x) + (x + g(x))')' = g(x).  [para(20947(a,1),8(a,1,1,2)),rewrite([17(11),17(10),17(9),6(13),17918(14)])].
21146 (x + (x + (x + g(x))))' = (x + (x + g(x)))'.  [back_rewrite(10432),rewrite([20951(6)]),flip(a)].
21147 $F # answer(Winker2b).  [resolve(21146,a,12,a)].

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