Prooof out3b2-221

x + (x + (x + x)')' = g(x).   x + (x + (x + (x + g(x)))') = h(x). % Problem 221

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

% Proof 1 at 168.64 (+ 0.75) seconds: Winker2b.
% Length of proof is 31.
% Level of proof is 10.
% Maximum clause weight is 34.
% Given clauses 1407.

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 + x)')' = g(x).  [assumption].
10 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)])].
28 x + (y + (x + (x + (x + g(x)))')) = y + h(x).  [para(10(a,1),7(a,2,2)),rewrite([17(7),7(6)])].
29 (h(x)' + (x + (x + (x + (x + g(x)))')')')' = x.  [para(10(a,1),8(a,1,1,1,1))].
31 x + (y + (x + (x + x)')') = y + g(x).  [para(9(a,1),17(a,1,2)),flip(a)].
52 (x + (x + (y + (x + y')'))')' = (x + y')'.  [para(8(a,1),19(a,1,1,2)),rewrite([6(5),7(5),6(7)])].
92 (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)])].
188 x + (x + (y + (x + (x + g(x)))')) = y + h(x).  [para(28(a,1),7(a,2)),rewrite([17(7),7(6)])].
249 ((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)])].
410 ((x + y)' + (x + (x + (y' + (x + y)')))')' = x.  [para(23(a,1),8(a,1,1,2)),rewrite([6(10)])].
553 (x + (h(x) + (x + (x + (x + (x + g(x)))')')')')' = (x + (x + (x + (x + g(x)))')')'.  [para(29(a,1),19(a,1,1,2)),rewrite([6(10),6(12)])].
1458 (x + (x + (x + g(x)))')' = (x + (x + x)')'.  [para(31(a,1),52(a,1,1,2,1)),rewrite([6(3),17(3),6(2)])].
1565 (x + (h(x) + g(x)')')' = g(x)'.  [back_rewrite(553),rewrite([1458(7),9(6),1458(13),9(12)])].
14842 (x + (x + (h(x) + g(x)')'))' = (x + (x + g(x)))'.  [para(188(a,1),92(a,1,1,2,2,1)),rewrite([6(4)])].
14922 ((x + (x + g(x)))' + (h(x) + g(x)')')' = x.  [para(14842(a,1),410(a,1,1,1)),rewrite([1565(11),14842(14),188(13),6(8)])].
15031 (x + (x + (x + (g(x) + (h(x) + g(x)')')))')' = (h(x) + g(x)')'.  [para(14922(a,1),19(a,1,1,2)),rewrite([6(9),7(9),7(8),6(11)])].
22847 ((x + (x + x)')' + (x + (x + (x + (h(x) + g(x)')')))')' = x.  [para(1458(a,1),249(a,1,1,1)),rewrite([188(13),6(8)])].
24456 (x + (x + x)')' = (h(x) + g(x)')'.  [para(22847(a,1),8(a,1,1,2)),rewrite([6(13),7(13),7(12),7(11),31(11),6(7),6(11),15031(12)]),flip(a)].
25312 x + (h(x) + g(x)')' = g(x).  [back_rewrite(9),rewrite([24456(4)])].
25379 (x + (x + g(x)))' = (x + g(x))'.  [back_rewrite(14842),rewrite([25312(6)]),flip(a)].
25380 $F # answer(Winker2b).  [resolve(25379,a,12,a)].

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