============================== Prover9 =============================== Prover9 (32) version 2009-11A, November 2009. Process 5127 was started by mccune on cleo, Tue Nov 3 09:45:16 2009 The command was "/home/mccune/LADR/bin/prover9 -f ba-4basis.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file ba-4basis.in assign(max_seconds,30). assign(new_constants,1). formulas(sos). x v (y v z) = y v (x v z) # label(AJ). x ^ y = (x' v y')' # label(DM). x v x' = y v y' # label(ONE). (x v y') ^ (x v y) = x # label(CUT). end_of_list. formulas(goals). x'' = x # answer(CC). x v (x ^ y) = x # answer(B1). x ^ (y v z) = (x ^ y) v (x ^ z) # answer(DIST1). x v (y ^ (x v z)) = x v (z ^ (x v y)) # answer(MOD). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 x'' = x # answer(CC) # label(non_clause) # label(goal). [goal]. 2 x v (x ^ y) = x # answer(B1) # label(non_clause) # label(goal). [goal]. 3 x ^ (y v z) = (x ^ y) v (x ^ z) # answer(DIST1) # label(non_clause) # label(goal). [goal]. 4 x v (y ^ (x v z)) = x v (z ^ (x v y)) # answer(MOD) # label(non_clause) # label(goal). [goal]. ============================== end of process non-clausal formulas === ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). x v (y v z) = y v (x v z) # label(AJ). [assumption]. x ^ y = (x' v y')' # label(DM). [assumption]. x v x' = y v y' # label(ONE). [assumption]. (x v y') ^ (x v y) = x # label(CUT). [assumption]. c1'' != c1 # answer(CC). [deny(1)]. c2 v (c2 ^ c3) != c2 # answer(B1). [deny(2)]. (c4 ^ c5) v (c4 ^ c6) != c4 ^ (c5 v c6) # answer(DIST1). [deny(3)]. c7 v (c9 ^ (c7 v c8)) != c7 v (c8 ^ (c7 v c9)) # answer(MOD). [deny(4)]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination ============= Auto_denials: % assign(max_proofs, 4). % (Horn set with more than one neg. clause) Term ordering decisions: Predicate symbol precedence: predicate_order([ = ]). Function symbol precedence: function_order([ c1, c2, c3, c4, c5, c6, c7, c8, c9, v, ^, ' ]). After inverse_order: (no changes). Unfolding symbols: ^/2. Auto_inference settings: % set(paramodulation). % (positive equality literals) Auto_process settings: (no changes). kept: 5 x v (y v z) = y v (x v z) # label(AJ). [assumption]. kept: 6 x ^ y = (x' v y')' # label(DM). [assumption]. kept: 7 x v x' = y v y' # label(ONE). [assumption]. 8 (x v y') ^ (x v y) = x # label(CUT). [assumption]. kept: 9 ((x v y')' v (x v y)')' = x. [copy(8),rewrite([6(4)])]. kept: 10 c1'' != c1 # answer(CC). [deny(1)]. 11 c2 v (c2 ^ c3) != c2 # answer(B1). [deny(2)]. kept: 12 c2 v (c2' v c3')' != c2 # answer(B1). [copy(11),rewrite([6(4)])]. 13 (c4 ^ c5) v (c4 ^ c6) != c4 ^ (c5 v c6) # answer(DIST1). [deny(3)]. kept: 14 (c4' v (c5 v c6)')' != (c4' v c5')' v (c4' v c6')' # answer(DIST1). [copy(13),rewrite([6(3),6(9),6(18)]),flip(a)]. 15 c7 v (c9 ^ (c7 v c8)) != c7 v (c8 ^ (c7 v c9)) # answer(MOD). [deny(4)]. kept: 16 c7 v (c8' v (c7 v c9)')' != c7 v (c9' v (c7 v c8)')' # answer(MOD). [copy(15),rewrite([6(6),6(16)]),flip(a)]. NOTE: New constant: x v x' = c_0. [new_symbol(7)]. NOTE: New Function symbol precedence: function_order([ c1, c2, c3, c4, c5, c6, c7, c8, c9, c_0, v, ^, ' ]). kept: 17 x v x' = c_0. [new_symbol(7)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 5 x v (y v z) = y v (x v z) # label(AJ). [assumption]. 6 x ^ y = (x' v y')' # label(DM). [assumption]. 9 ((x v y')' v (x v y)')' = x. [copy(8),rewrite([6(4)])]. 10 c1'' != c1 # answer(CC). [deny(1)]. 12 c2 v (c2' v c3')' != c2 # answer(B1). [copy(11),rewrite([6(4)])]. 14 (c4' v (c5 v c6)')' != (c4' v c5')' v (c4' v c6')' # answer(DIST1). [copy(13),rewrite([6(3),6(9),6(18)]),flip(a)]. 16 c7 v (c8' v (c7 v c9)')' != c7 v (c9' v (c7 v c8)')' # answer(MOD). [copy(15),rewrite([6(6),6(16)]),flip(a)]. 17 x v x' = c_0. [new_symbol(7)]. end_of_list. formulas(demodulators). 5 x v (y v z) = y v (x v z) # label(AJ). [assumption]. % (lex-dep) 6 x ^ y = (x' v y')' # label(DM). [assumption]. 9 ((x v y')' v (x v y)')' = x. [copy(8),rewrite([6(4)])]. 17 x v x' = c_0. [new_symbol(7)]. end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.01 seconds. given #1 (I,wt=11): 5 x v (y v z) = y v (x v z) # label(AJ). [assumption]. given #2 (I,wt=10): 6 x ^ y = (x' v y')' # label(DM). [assumption]. given #3 (I,wt=13): 9 ((x v y')' v (x v y)')' = x. [copy(8),rewrite([6(4)])]. given #4 (I,wt=5): 10 c1'' != c1 # answer(CC). [deny(1)]. given #5 (I,wt=10): 12 c2 v (c2' v c3')' != c2 # answer(B1). [copy(11),rewrite([6(4)])]. given #6 (I,wt=22): 14 (c4' v (c5 v c6)')' != (c4' v c5')' v (c4' v c6')' # answer(DIST1). [copy(13),rewrite([6(3),6(9),6(18)]),flip(a)]. given #7 (I,wt=21): 16 c7 v (c8' v (c7 v c9)')' != c7 v (c9' v (c7 v c8)')' # answer(MOD). [copy(15),rewrite([6(6),6(16)]),flip(a)]. given #8 (I,wt=6): 17 x v x' = c_0. [new_symbol(7)]. given #9 (A,wt=15): 18 x v (y v (z v u)) = z v (x v (y v u)). [para(5(a,1),5(a,1,2))]. given #10 (T,wt=10): 23 x v (y v x') = y v c_0. [para(17(a,1),5(a,1,2)),flip(a)]. given #11 (T,wt=10): 24 (c_0' v (x v x)')' = x. [para(17(a,1),9(a,1,1,1,1))]. given #12 (T,wt=11): 49 (c_0' v (x v x)') v x = c_0. [para(24(a,1),17(a,1,2))]. given #13 (T,wt=12): 25 ((x v x'')' v c_0')' = x. [para(17(a,1),9(a,1,1,2,1))]. given #14 (A,wt=17): 19 ((x v (y v z)')' v (y v (x v z))')' = x. [para(5(a,1),9(a,1,1,2,1))]. given #15 (T,wt=13): 47 (x v (c_0' v (x v x))')' = c_0'. [para(24(a,1),9(a,1,1,1))]. given #16 (T,wt=13): 68 ((x v x'')' v c_0') v x = c_0. [para(25(a,1),17(a,1,2))]. given #17 (T,wt=13): 85 (x v (x v (c_0' v x))')' = c_0'. [para(24(a,1),19(a,1,1,1))]. given #18 (T,wt=14): 26 ((x v y')' v (x v y)') v x = c_0. [para(9(a,1),17(a,1,2))]. given #19 (A,wt=21): 20 ((x v y)' v (x v ((y v z')' v (y v z)'))')' = x. [para(9(a,1),9(a,1,1,1,1,2))]. given #20 (T,wt=14): 33 x v (y v (z v x')) = y v (z v c_0). [para(17(a,1),18(a,1,2,2)),flip(a)]. given #21 (T,wt=14): 97 (x v (c_0' v (x v x))') v c_0' = c_0. [para(47(a,1),17(a,1,2))]. given #22 (T,wt=11): 256 x v (c_0' v (x v x))' = c_0. [back_rewrite(243),rewrite([248(10),24(8)]),flip(a)]. given #23 (T,wt=11): 260 x v (x v (c_0' v x))' = c_0. [para(5(a,1),256(a,1,2,1))]. given #24 (A,wt=19): 21 (x v (x v ((x v y')' v y))')' = (x v y')'. [para(9(a,1),9(a,1,1,1)),rewrite([5(5)])]. given #25 (T,wt=12): 266 (c_0' v (x v x)) v c_0 = x v c_0. [para(256(a,1),23(a,1,2))]. given #26 (T,wt=12): 267 c_0'' v (c_0'' v c_0)' = c_0. [para(23(a,1),256(a,1,2,1))]. given #27 (T,wt=12): 277 (x v (c_0' v x)) v c_0 = x v c_0. [para(260(a,1),23(a,1,2))]. given #28 (T,wt=13): 322 (c_0'' v c_0) v c_0 = c_0'' v c_0. [para(23(a,1),266(a,1,1))]. given #29 (A,wt=21): 22 (((x v y')' v (x v y)'')' v x)' = (x v y')'. [para(9(a,1),9(a,1,1,2))]. given #30 (T,wt=15): 28 x v (y v (z v u)) = z v (y v (x v u)). [para(18(a,1),5(a,1))]. given #31 (T,wt=15): 30 x v (y v (z v u)) = x v (z v (y v u)). [para(18(a,2),5(a,1))]. given #32 (T,wt=15): 48 ((c_0' v (x v x)'')' v x)' = c_0'. [para(24(a,1),9(a,1,1,2))]. given #33 (T,wt=15): 52 (c_0' v (x v x)') v (y v x) = y v c_0. [para(24(a,1),23(a,1,2,2))]. given #34 (A,wt=19): 27 x v (y v (z v (u v w))) = z v (x v (u v (y v w))). [para(18(a,1),5(a,1,2))]. given #35 (T,wt=15): 63 (c_0' v (x' v x')') v c_0 = x v c_0. [para(49(a,1),23(a,1,2)),flip(a)]. given #36 (T,wt=15): 95 (c_0' v (x v (c_0' v (x v x)))')' = x. [para(47(a,1),9(a,1,1,1))]. given #37 (T,wt=15): 106 (c_0' v (c_0' v (x v (x v x)))')' = x. [para(47(a,1),19(a,1,1,1))]. given #38 (T,wt=15): 126 (c_0' v (x v (x v (c_0' v x)))')' = x. [para(85(a,1),9(a,1,1,1))]. given #39 (A,wt=19): 29 x v (y v (z v (u v w))) = u v (x v (y v (z v w))). [para(18(a,2),5(a,1,2))]. given #40 (T,wt=15): 258 x v (y v (c_0' v (x v x))') = y v c_0. [para(256(a,1),5(a,1,2)),flip(a)]. given #41 (T,wt=15): 273 x v (y v (x v (c_0' v x))') = y v c_0. [para(260(a,1),5(a,1,2)),flip(a)]. given #42 (T,wt=16): 42 ((x v (y v x')')' v (y v c_0)')' = x. [para(23(a,1),9(a,1,1,2,1))]. given #43 (T,wt=16): 45 (c_0' v (x v ((x v y) v y))')' = x v y. [para(5(a,1),24(a,1,1,2,1))]. given #44 (A,wt=21): 31 ((x v (y v (z v u))')' v (z v (x v (y v u)))')' = x. [para(18(a,1),9(a,1,1,2,1))]. given #45 (T,wt=9): 963 c_0'' v c_0 = c_0''. [para(322(a,1),45(a,1,1,2,1,2,1)),rewrite([322(14),5(13),322(12),330(14),322(10)]),flip(a)]. given #46 (T,wt=13): 999 c_0'' v (x v c_0) = x v c_0''. [back_rewrite(339),rewrite([963(5),963(11)])]. given #47 (T,wt=14): 1083 c_0' v (c_0'' v (x v c_0)) = x v c_0. [para(999(a,2),23(a,1,2))]. given #48 (T,wt=14): 1137 c_0'' v (x v (c_0' v c_0)) = x v c_0. [para(1083(a,1),18(a,2))]. given #49 (A,wt=21): 32 ((x v (y v (z v u))')' v (y v (z v (x v u)))')' = x. [para(18(a,2),9(a,1,1,2,1))]. given #50 (T,wt=15): 1078 (c_0' v (c_0 v c_0)') v c_0'' = c_0''. [para(963(a,1),52(a,1,2)),rewrite([963(16)])]. given #51 (T,wt=12): 1263 (c_0' v c_0''')'' = c_0'. [para(1078(a,1),42(a,1,1,1,1,2,1)),rewrite([49(17),955(11)])]. given #52 (T,wt=10): 1266 (c_0' v c_0''')' = c_0. [para(1263(a,1),17(a,1,2)),rewrite([955(11)])]. given #53 (T,wt=11): 1272 (c_0' v c_0''') v c_0 = c_0. [para(1266(a,1),17(a,1,2))]. given #54 (A,wt=23): 34 x v (y v (z v (u v (w v v5)))) = u v (x v (y v (w v (z v v5)))). [para(18(a,1),18(a,1,2,2))]. given #55 (T,wt=15): 1100 (c_0'' v (x v c_0))' = (x v c_0'')'. [para(999(a,2),21(a,2,1)),rewrite([21(12)]),flip(a)]. given #56 (T,wt=15): 1271 ((c_0' v c_0'''')' v c_0)' = c_0'. [para(1266(a,1),9(a,1,1,2))]. given #57 (T,wt=15): 1273 (c_0' v c_0''') v (x v c_0) = x v c_0. [para(1266(a,1),23(a,1,2,2))]. given #58 (T,wt=15): 1284 (c_0''' v (c_0' v c_0)')' = c_0''. [para(1266(a,1),42(a,1,1,1,1,2)),rewrite([963(5)])]. given #59 (A,wt=19): 35 x v (y v (z v (u v w))) = u v (x v (z v (y v w))). [para(18(a,1),18(a,1,2))]. given #60 (T,wt=15): 1291 (c_0' v c_0''') v c_0'' = c_0''. [para(1272(a,1),999(a,1,2)),rewrite([963(5)]),flip(a)]. given #61 (T,wt=16): 152 ((c_0' v (x v x)'')' v x) v c_0' = c_0. [para(24(a,1),26(a,1,1,2))]. given #62 (T,wt=13): 1707 (c_0' v (x v x)'')' v x = c_0. [para(152(a,1),9(a,1,1,1,1)),rewrite([651(12),24(8)]),flip(a)]. given #63 (T,wt=13): 1719 (c_0' v (c_0' v c_0')'')' = c_0. [para(152(a,1),45(a,1,1,2,1,2)),rewrite([463(18),1707(25)])]. given #64 (A,wt=23): 36 x v (y v (z v (u v (w v v5)))) = z v (x v (w v (y v (u v v5)))). [para(18(a,1),18(a,2,2,2))]. given #65 (T,wt=14): 1787 (c_0' v (c_0' v c_0')'') v c_0 = c_0. [para(1719(a,1),17(a,1,2))]. given #66 (T,wt=16): 165 (c_0' v (x v (c_0' v (x v x)))') v x = c_0. [para(47(a,1),26(a,1,1,1))]. given #67 (T,wt=16): 169 (c_0' v (x v (x v (c_0' v x)))') v x = c_0. [para(85(a,1),26(a,1,1,1))]. given #68 (T,wt=16): 687 (c_0' v (c_0' v (x v (x v x)))') v x = c_0. [para(106(a,1),17(a,1,2))]. given #69 (A,wt=19): 37 x v (y v (z v (u v w))) = z v (u v (x v (y v w))). [para(18(a,1),18(a,2,2))]. given #70 (T,wt=16): 869 (c_0' v (x v x)) v (y v c_0) = x v (y v c_0). [para(258(a,1),33(a,1,2))]. given #71 (T,wt=8): 2387 c_0 v (c_0' v c_0) = c_0. [para(869(a,1),45(a,1,1,2,1,2)),rewrite([5(10),5(9),126(13),5(7)]),flip(a)]. given #72 (T,wt=7): 2426 c_0'' = c_0 v c_0. [para(2387(a,1),52(a,1,2)),rewrite([5(11),1157(15)])]. given #73 (T,wt=9): 2431 (c_0 v c_0) v c_0 = c_0 v c_0. [para(2387(a,1),1137(a,1,2)),rewrite([2426(3)])]. given #74 (A,wt=23): 38 x v (y v (z v (u v (w v v5)))) = w v (x v (y v (z v (u v v5)))). [para(18(a,2),18(a,1,2,2))]. given #75 (T,wt=12): 2416 c_0 v (x v (c_0' v c_0)) = x v c_0. [para(2387(a,1),5(a,1,2)),flip(a)]. given #76 (T,wt=12): 2419 c_0' v (x v (c_0 v c_0)) = x v c_0. [para(2387(a,1),18(a,1,2)),flip(a)]. given #77 (T,wt=12): 2420 c_0 v (c_0' v (x v c_0)) = x v c_0. [para(2387(a,1),18(a,2,2))]. given #78 (T,wt=12): 2493 ((c_0 v (c_0 v c_0))' v c_0')' = c_0. [back_rewrite(1519),rewrite([2426(5),1707(11),2426(4),2426(15),1707(21)])]. given #79 (A,wt=19): 39 x v (y v (z v (u v w))) = y v (x v (u v (z v w))). [para(18(a,2),18(a,1,2))]. given #80 (T,wt=13): 2492 ((c_0 v (c_0 v c_0))' v c_0') v c_0 = c_0. [back_rewrite(1521),rewrite([2426(5),2426(14),1707(20),2426(13),5(21),1707(20)])]. given #81 (T,wt=13): 2582 (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0). [back_rewrite(1119),rewrite([2426(3),2426(16),5(17),63(16)])]. given #82 (T,wt=13): 2592 (c_0 v (x v c_0))' = (x v (c_0 v c_0))'. [back_rewrite(1100),rewrite([2426(3),2582(6),2426(8)])]. given #83 (T,wt=14): 2417 ((c_0 v (c_0' v c_0)')' v c_0')' = c_0. [para(2387(a,1),9(a,1,1,2,1))]. given #84 (A,wt=23): 40 x v (y v (z v (u v (w v v5)))) = z v (x v (u v (w v (y v v5)))). [para(18(a,2),18(a,2,2,2))]. given #85 (T,wt=14): 2514 (x v (c_0 v c_0)) v (c_0 v (x v c_0))' = c_0. [back_rewrite(1491),rewrite([2426(3),2426(7),2496(11)])]. given #86 (T,wt=14): 2564 (c_0 v c_0) v (x v (c_0' v c_0)) = x v c_0. [back_rewrite(1137),rewrite([2426(3)])]. given #87 (T,wt=14): 2649 (c_0 v (x v c_0)) v (x v (c_0 v c_0))' = c_0. [back_rewrite(2515),rewrite([2582(6)])]. given #88 (T,wt=14): 2667 (c_0' v (c_0 v (c_0 v c_0))')' = c_0 v c_0. [para(2431(a,1),45(a,1,1,2,1,2,1)),rewrite([2431(10),5(9),2431(8),2431(15)])]. given #89 (A,wt=19): 41 x v (y v (z v (u v w))) = u v (y v (x v (z v w))). [para(18(a,2),18(a,2,2)),flip(a)]. given #90 (T,wt=14): 3381 (c_0 v c_0) v (c_0' v (x v c_0)) = x v c_0. [para(5(a,1),2564(a,1,2))]. given #91 (T,wt=15): 2422 ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0. [para(2387(a,1),26(a,1,1,2,1))]. given #92 (T,wt=15): 2525 ((c_0 v c_0)' v (c_0' v c_0)')' = c_0 v c_0. [back_rewrite(1284),rewrite([2426(3),2426(14)])]. given #93 (T,wt=15): 2601 ((c_0 v (x v c_0))' v (x v c_0')')' = x. [back_rewrite(1082),rewrite([2426(3),2582(6)])]. given #94 (A,wt=18): 43 ((x v y')' v (x v y)') v (z v x) = z v c_0. [para(9(a,1),23(a,1,2,2))]. given #95 (T,wt=11): 3579 c_0' v (c_0' v c_0')' = c_0. [para(49(a,1),2601(a,1,1,2,1)),rewrite([63(12),2493(10)]),flip(a)]. given #96 (T,wt=12): 3838 (c_0' v c_0') v c_0 = c_0' v c_0. [para(3579(a,1),23(a,1,2))]. given #97 (T,wt=14): 3588 (c_0' v x')' v (c_0' v x)' = c_0. [para(26(a,1),2601(a,1,1,2,1)),rewrite([149(13),2493(10)]),flip(a)]. given #98 (T,wt=15): 2656 (c_0 v (x v c_0)) v c_0 = (x v (c_0 v c_0)) v c_0. [back_rewrite(2497),rewrite([2582(6)])]. given #99 (A,wt=18): 44 x v (y v (z v (u v x'))) = y v (z v (u v c_0)). [para(23(a,1),18(a,1,2,2)),flip(a)]. given #100 (T,wt=15): 2661 ((x v (c_0 v c_0))' v (x v c_0')')' = x. [para(2426(a,1),9(a,1,1,1,1,2))]. given #101 (T,wt=15): 3836 c_0' v (x v (c_0' v c_0')') = x v c_0. [para(3579(a,1),5(a,1,2)),flip(a)]. given #102 (T,wt=15): 3890 (c_0' v x')' v c_0 = (c_0' v x) v c_0. [para(3588(a,1),23(a,1,2)),flip(a)]. given #103 (T,wt=9): 4237 c_0' v (c_0' v c_0) = c_0. [back_rewrite(3947),rewrite([4145(21),5(20),4117(19)])]. given #104 (A,wt=18): 46 ((x v y)' v (x v (c_0' v (y v y)'))')' = x. [para(24(a,1),9(a,1,1,1,1,2))]. given #105 (T,wt=5): 4395 c_0 v c_0 = c_0. [back_rewrite(2422),rewrite([4273(5),4379(5),17(4),4316(7)])]. given #106 (T,wt=5): 4530 c_0'' = c_0. [back_rewrite(2426),rewrite([4395(6)])]. given #107 (T,wt=6): 4447 c_0' v c_0 = c_0. [back_rewrite(4273),rewrite([4395(7)])]. given #108 (T,wt=8): 4444 (c_0' v c_0')' = c_0. [back_rewrite(4286),rewrite([4395(9)])]. given #109 (A,wt=22): 50 (c_0' v (x v (y v ((y v (x v z)) v z)))')' = y v (x v z). [para(18(a,1),24(a,1,1,2,1)),rewrite([5(6)])]. given #110 (T,wt=9): 4398 c_0 v (x v c_0) = x v c_0. [back_rewrite(2416),rewrite([4273(5),4395(4)])]. given #111 (T,wt=9): 4442 (c_0' v c_0') v c_0 = c_0. [back_rewrite(4316),rewrite([4395(10)])]. given #112 (T,wt=10): 4414 c_0' v (x v c_0) = x v c_0. [back_rewrite(3087),rewrite([4395(6),4395(5),4395(8),4109(8)])]. given #113 (T,wt=11): 4712 x v ((x v c_0) v c_0) = x v c_0. [para(869(a,1),50(a,1,1,2,1,2,2)),rewrite([5(11),4527(12),5(10),4523(13),5(9),4527(10)]),flip(a)]. given #114 (A,wt=22): 51 (c_0' v (x v (y v ((x v (y v z)) v z)))')' = x v (y v z). [para(18(a,2),24(a,1,1,2,1))]. given #115 (T,wt=12): 4736 (c_0' v (x v c_0)')' = x v c_0. [para(3588(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite([3887(16),4712(7),3588(17)])]. given #116 (T,wt=12): 4856 ((x v c_0)' v c_0')' = x v c_0. [para(4736(a,1),42(a,1,1,1,1,2)),rewrite([5(5),4712(5),4447(7)])]. given #117 (T,wt=13): 4397 c_0 v (x v (y v c_0)) = x v (y v c_0). [back_rewrite(2418),rewrite([4273(5),4395(4)])]. given #118 (T,wt=13): 4518 ((x v c_0)' v (x v c_0')')' = x. [back_rewrite(2661),rewrite([4395(3)])]. given #119 (A,wt=17): 53 x v ((c_0' v (x v ((x v y) v y))') v y) = c_0. [para(49(a,1),5(a,1)),rewrite([5(6)]),flip(a)]. given #120 (T,wt=13): 4549 (c_0' v c_0') v (x v c_0) = x v c_0. [back_rewrite(4109),rewrite([4414(13)])]. given #121 (T,wt=13): 4742 x v ((c_0' v (x v c_0)') v c_0) = c_0. [para(4398(a,1),52(a,1,2)),rewrite([5(7),4712(7),5(9),4395(12)])]. given #122 (T,wt=7): 5022 (x v c_0) v c_0 = c_0. [back_rewrite(4988),rewrite([4999(12)])]. ============================== PROOF ================================= % Proof 1 at 1.32 (+ 0.02) seconds: CC. % Length of proof is 129. % Level of proof is 37. % Maximum clause weight is 39.000. % Given clauses 122. 1 x'' = x # answer(CC) # label(non_clause) # label(goal). [goal]. 5 x v (y v z) = y v (x v z) # label(AJ). [assumption]. 6 x ^ y = (x' v y')' # label(DM). [assumption]. 7 x v x' = y v y' # label(ONE). [assumption]. 8 (x v y') ^ (x v y) = x # label(CUT). [assumption]. 9 ((x v y')' v (x v y)')' = x. [copy(8),rewrite([6(4)])]. 10 c1'' != c1 # answer(CC). [deny(1)]. 17 x v x' = c_0. [new_symbol(7)]. 18 x v (y v (z v u)) = z v (x v (y v u)). [para(5(a,1),5(a,1,2))]. 19 ((x v (y v z)')' v (y v (x v z))')' = x. [para(5(a,1),9(a,1,1,2,1))]. 21 (x v (x v ((x v y')' v y))')' = (x v y')'. [para(9(a,1),9(a,1,1,1)),rewrite([5(5)])]. 22 (((x v y')' v (x v y)'')' v x)' = (x v y')'. [para(9(a,1),9(a,1,1,2))]. 23 x v (y v x') = y v c_0. [para(17(a,1),5(a,1,2)),flip(a)]. 24 (c_0' v (x v x)')' = x. [para(17(a,1),9(a,1,1,1,1))]. 25 ((x v x'')' v c_0')' = x. [para(17(a,1),9(a,1,1,2,1))]. 26 ((x v y')' v (x v y)') v x = c_0. [para(9(a,1),17(a,1,2))]. 29 x v (y v (z v (u v w))) = u v (x v (y v (z v w))). [para(18(a,2),5(a,1,2))]. 31 ((x v (y v (z v u))')' v (z v (x v (y v u)))')' = x. [para(18(a,1),9(a,1,1,2,1))]. 33 x v (y v (z v x')) = y v (z v c_0). [para(17(a,1),18(a,1,2,2)),flip(a)]. 42 ((x v (y v x')')' v (y v c_0)')' = x. [para(23(a,1),9(a,1,1,2,1))]. 44 x v (y v (z v (u v x'))) = y v (z v (u v c_0)). [para(23(a,1),18(a,1,2,2)),flip(a)]. 45 (c_0' v (x v ((x v y) v y))')' = x v y. [para(5(a,1),24(a,1,1,2,1))]. 47 (x v (c_0' v (x v x))')' = c_0'. [para(24(a,1),9(a,1,1,1))]. 48 ((c_0' v (x v x)'')' v x)' = c_0'. [para(24(a,1),9(a,1,1,2))]. 49 (c_0' v (x v x)') v x = c_0. [para(24(a,1),17(a,1,2))]. 50 (c_0' v (x v (y v ((y v (x v z)) v z)))')' = y v (x v z). [para(18(a,1),24(a,1,1,2,1)),rewrite([5(6)])]. 52 (c_0' v (x v x)') v (y v x) = y v c_0. [para(24(a,1),23(a,1,2,2))]. 53 x v ((c_0' v (x v ((x v y) v y))') v y) = c_0. [para(49(a,1),5(a,1)),rewrite([5(6)]),flip(a)]. 63 (c_0' v (x' v x')') v c_0 = x v c_0. [para(49(a,1),23(a,1,2)),flip(a)]. 65 (x v ((x v x'')' v c_0)')' = (x v x'')'. [para(25(a,1),9(a,1,1,1))]. 68 ((x v x'')' v c_0') v x = c_0. [para(25(a,1),17(a,1,2))]. 85 (x v (x v (c_0' v x))')' = c_0'. [para(24(a,1),19(a,1,1,1))]. 95 (c_0' v (x v (c_0' v (x v x)))')' = x. [para(47(a,1),9(a,1,1,1))]. 97 (x v (c_0' v (x v x))') v c_0' = c_0. [para(47(a,1),17(a,1,2))]. 126 (c_0' v (x v (x v (c_0' v x)))')' = x. [para(85(a,1),9(a,1,1,1))]. 149 ((x' v y')' v (x' v y)') v c_0 = x v c_0. [para(26(a,1),23(a,1,2)),flip(a)]. 152 ((c_0' v (x v x)'')' v x) v c_0' = c_0. [para(24(a,1),26(a,1,1,2))]. 165 (c_0' v (x v (c_0' v (x v x)))') v x = c_0. [para(47(a,1),26(a,1,1,1))]. 169 (c_0' v (x v (x v (c_0' v x)))') v x = c_0. [para(85(a,1),26(a,1,1,1))]. 243 (c_0' v ((x v (c_0' v (x v x))') v c_0)')' = x v (c_0' v (x v x))'. [para(97(a,1),9(a,1,1,1,1))]. 248 (x v (c_0' v (x v x))') v c_0 = c_0 v c_0. [para(97(a,1),23(a,1,2)),flip(a)]. 256 x v (c_0' v (x v x))' = c_0. [back_rewrite(243),rewrite([248(10),24(8)]),flip(a)]. 258 x v (y v (c_0' v (x v x))') = y v c_0. [para(256(a,1),5(a,1,2)),flip(a)]. 266 (c_0' v (x v x)) v c_0 = x v c_0. [para(256(a,1),23(a,1,2))]. 267 c_0'' v (c_0'' v c_0)' = c_0. [para(23(a,1),256(a,1,2,1))]. 322 (c_0'' v c_0) v c_0 = c_0'' v c_0. [para(23(a,1),266(a,1,1))]. 330 (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''. [para(267(a,1),9(a,1,1,1,1))]. 339 (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0). [para(267(a,1),33(a,1,2,2))]. 651 ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0. [para(48(a,1),63(a,1,1,2,1,1)),rewrite([48(13),63(11)]),flip(a)]. 672 (c_0' v (x v ((x v c_0'') v ((x v c_0'') v c_0)))')' = x v c_0''. [para(33(a,1),95(a,1,1,2,1,2)),rewrite([5(13),5(14)])]. 712 (c_0' v (x v (x v (c_0' v x)))') v (y v x) = y v c_0. [para(126(a,1),23(a,1,2,2))]. 869 (c_0' v (x v x)) v (y v c_0) = x v (y v c_0). [para(258(a,1),33(a,1,2))]. 955 (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'. [para(68(a,1),45(a,1,1,2,1,2)),rewrite([65(15)]),flip(a)]. 963 c_0'' v c_0 = c_0''. [para(322(a,1),45(a,1,1,2,1,2,1)),rewrite([322(14),5(13),322(12),330(14),322(10)]),flip(a)]. 999 c_0'' v (x v c_0) = x v c_0''. [back_rewrite(339),rewrite([963(5),963(11)])]. 1028 ((x v (y v (z v (u v x')))')' v (z v (y v (u v c_0)))')' = x. [para(33(a,1),31(a,1,1,2,1,2))]. 1078 (c_0' v (c_0 v c_0)') v c_0'' = c_0''. [para(963(a,1),52(a,1,2)),rewrite([963(16)])]. 1082 ((c_0'' v (x v c_0))' v (x v c_0')')' = x. [para(999(a,2),9(a,1,1,1,1))]. 1083 c_0' v (c_0'' v (x v c_0)) = x v c_0. [para(999(a,2),23(a,1,2))]. 1119 c_0'' v (x v c_0) = (c_0' v (x' v x')') v c_0''. [para(63(a,1),999(a,1,2))]. 1136 c_0' v (c_0'' v (x v (y v c_0))) = x v (y v c_0). [para(1083(a,1),18(a,2,2))]. 1137 c_0'' v (x v (c_0' v c_0)) = x v c_0. [para(1083(a,1),18(a,2))]. 1157 (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0''. [para(49(a,1),1137(a,1,2)),rewrite([963(5),5(14)]),flip(a)]. 1263 (c_0' v c_0''')'' = c_0'. [para(1078(a,1),42(a,1,1,1,1,2,1)),rewrite([49(17),955(11)])]. 1266 (c_0' v c_0''')' = c_0. [para(1263(a,1),17(a,1,2)),rewrite([955(11)])]. 1271 ((c_0' v c_0'''')' v c_0)' = c_0'. [para(1266(a,1),9(a,1,1,2))]. 1284 (c_0''' v (c_0' v c_0)')' = c_0''. [para(1266(a,1),42(a,1,1,1,1,2)),rewrite([963(5)])]. 1519 ((((c_0' v c_0'''')' v c_0) v c_0'')' v c_0')' = (c_0' v c_0'''')' v c_0. [para(1271(a,1),25(a,1,1,1,1,2,1))]. 1546 ((c_0''' v (c_0' v c_0)'')' v c_0'')' = c_0'''. [para(1284(a,1),9(a,1,1,2))]. 1707 (c_0' v (x v x)'')' v x = c_0. [para(152(a,1),9(a,1,1,1,1)),rewrite([651(12),24(8)]),flip(a)]. 2115 ((x v c_0')' v ((c_0' v (y v (y v (c_0' v y)))') v (x v y))')' = x. [para(169(a,1),19(a,1,1,1,1,2,1))]. 2387 c_0 v (c_0' v c_0) = c_0. [para(869(a,1),45(a,1,1,2,1,2)),rewrite([5(10),5(9),126(13),5(7)]),flip(a)]. 2416 c_0 v (x v (c_0' v c_0)) = x v c_0. [para(2387(a,1),5(a,1,2)),flip(a)]. 2422 ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0. [para(2387(a,1),26(a,1,1,2,1))]. 2426 c_0'' = c_0 v c_0. [para(2387(a,1),52(a,1,2)),rewrite([5(11),1157(15)])]. 2428 c_0 v (x v (y v (z v (c_0' v c_0)))) = x v (y v (z v c_0)). [para(2387(a,1),29(a,1,2,2,2)),flip(a)]. 2488 (c_0 v (((c_0 v c_0)' v (c_0' v c_0)'')' v c_0))' = (c_0 v c_0)'. [back_rewrite(1546),rewrite([2426(3),2426(15),5(16),2426(20)])]. 2493 ((c_0 v (c_0 v c_0))' v c_0')' = c_0. [back_rewrite(1519),rewrite([2426(5),1707(11),2426(4),2426(15),1707(21)])]. 2544 (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0 v c_0. [back_rewrite(1157),rewrite([2426(18)])]. 2565 (c_0 v c_0) v (c_0' v (x v (y v c_0))) = x v (y v c_0). [back_rewrite(1136),rewrite([2426(5),5(10)])]. 2582 (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0). [back_rewrite(1119),rewrite([2426(3),2426(16),5(17),63(16)])]. 2601 ((c_0 v (x v c_0))' v (x v c_0')')' = x. [back_rewrite(1082),rewrite([2426(3),2582(6)])]. 2619 (c_0' v (x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))')' = x v (c_0 v c_0). [back_rewrite(672),rewrite([2426(5),2426(9),2426(20)])]. 3579 c_0' v (c_0' v c_0')' = c_0. [para(49(a,1),2601(a,1,1,2,1)),rewrite([63(12),2493(10)]),flip(a)]. 3588 (c_0' v x')' v (c_0' v x)' = c_0. [para(26(a,1),2601(a,1,1,2,1)),rewrite([149(13),2493(10)]),flip(a)]. 3836 c_0' v (x v (c_0' v c_0')') = x v c_0. [para(3579(a,1),5(a,1,2)),flip(a)]. 3838 (c_0' v c_0') v c_0 = c_0' v c_0. [para(3579(a,1),23(a,1,2))]. 3847 (c_0' v ((c_0' v c_0')' v ((c_0' v c_0')' v c_0))') v (c_0' v c_0')' = c_0. [para(3579(a,1),169(a,1,1,2,1,2,2))]. 3887 (c_0' v x')' v (y v (z v (c_0' v x)')) = y v (z v c_0). [para(3588(a,1),18(a,1,2,2)),flip(a)]. 3890 (c_0' v x')' v c_0 = (c_0' v x) v c_0. [para(3588(a,1),23(a,1,2)),flip(a)]. 3947 (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v (c_0' v c_0')' = c_0. [back_rewrite(3847),rewrite([3890(16),5(15),3890(14)])]. 4047 (((x v (y v (z v (u v x')))')' v (y v (z v (u v c_0)))'')' v x)' = (x v (y v (z v (u v x')))')'. [para(44(a,1),22(a,1,1,1,1,2,1,1))]. 4117 (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v c_0 = c_0' v c_0. [para(165(a,1),3836(a,1,2)),rewrite([3836(28),3890(20),5(19),3890(18)]),flip(a)]. 4145 (c_0' v c_0')' = c_0' v c_0. [para(3890(a,1),21(a,1,1,2,1,2)),rewrite([45(14)]),flip(a)]. 4237 c_0' v (c_0' v c_0) = c_0. [back_rewrite(3947),rewrite([4145(21),5(20),4117(19)])]. 4273 c_0' v c_0 = c_0 v c_0. [para(4237(a,1),52(a,1,2)),rewrite([5(11),2544(15)]),flip(a)]. 4274 c_0 v (c_0 v c_0) = c_0. [para(52(a,2),4237(a,1,2)),rewrite([5(11),49(10),4273(6),5(6),4273(5)])]. 4316 (c_0' v c_0') v c_0 = c_0 v c_0. [back_rewrite(3838),rewrite([4273(11)])]. 4379 (c_0 v c_0)' = c_0'. [back_rewrite(2488),rewrite([4273(9),17(11),4273(5),4274(5)]),flip(a)]. 4392 c_0 v (x v (y v (z v (c_0 v c_0)))) = x v (y v (z v c_0)). [back_rewrite(2428),rewrite([4273(5)])]. 4395 c_0 v c_0 = c_0. [back_rewrite(2422),rewrite([4273(5),4379(5),17(4),4316(7)])]. 4398 c_0 v (x v c_0) = x v c_0. [back_rewrite(2416),rewrite([4273(5),4395(4)])]. 4431 c_0 v (x v (y v (z v c_0))) = x v (y v (z v c_0)). [back_rewrite(4392),rewrite([4395(4)])]. 4447 c_0' v c_0 = c_0. [back_rewrite(4273),rewrite([4395(7)])]. 4523 (c_0' v (x v ((x v c_0) v ((x v c_0) v c_0)))')' = x v c_0. [back_rewrite(2619),rewrite([4395(5),4395(7),4395(16)])]. 4527 c_0' v (x v (y v c_0)) = x v (y v c_0). [back_rewrite(2565),rewrite([4395(3),4431(8)])]. 4530 c_0'' = c_0. [back_rewrite(2426),rewrite([4395(6)])]. 4712 x v ((x v c_0) v c_0) = x v c_0. [para(869(a,1),50(a,1,1,2,1,2,2)),rewrite([5(11),4527(12),5(10),4523(13),5(9),4527(10)]),flip(a)]. 4736 (c_0' v (x v c_0)')' = x v c_0. [para(3588(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite([3887(16),4712(7),3588(17)])]. 4742 x v ((c_0' v (x v c_0)') v c_0) = c_0. [para(4398(a,1),52(a,1,2)),rewrite([5(7),4712(7),5(9),4395(12)])]. 4747 x v (y v ((x v c_0) v c_0)) = y v (x v c_0). [para(4712(a,1),5(a,1,2)),flip(a)]. 4856 ((x v c_0)' v c_0')' = x v c_0. [para(4736(a,1),42(a,1,1,1,1,2)),rewrite([5(5),4712(5),4447(7)])]. 4869 ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x. [para(4856(a,1),19(a,1,1,1,1,2))]. 4879 ((x v c_0)' v ((x v c_0) v ((x v c_0)' v c_0))')' = x v c_0. [para(4856(a,1),21(a,1,1,2,1,2,1)),rewrite([5(11),4856(21)])]. 4887 ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0. [para(4856(a,1),42(a,1,1,1,1,2)),rewrite([4398(4)])]. 4988 x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0. [para(4712(a,1),53(a,1,2,1,2,1,2,1)),rewrite([4747(10),5(7),4712(7),5(11)])]. 4999 x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0. [para(4742(a,1),5(a,1,2)),flip(a)]. 5007 (((x v ((c_0' v (x v c_0)') v c_0)')' v c_0)' v x)' = (x v ((c_0' v (x v c_0)') v c_0)')'. [para(4742(a,1),22(a,1,1,1,1,2,1,1)),rewrite([4530(14)])]. 5022 (x v c_0) v c_0 = c_0. [back_rewrite(4988),rewrite([4999(12)])]. 5040 (x v c_0) v (y v c_0) = y v c_0. [para(5022(a,1),5(a,1,2)),flip(a)]. 5056 x v c_0 = c_0. [back_rewrite(4879),rewrite([5040(11),4887(11)]),flip(a)]. 5060 (c_0' v x)' = (x v c_0')'. [back_rewrite(5007),rewrite([5056(4),5056(7),5056(6),5056(8),5056(11)])]. 5089 (c_0' v (c_0' v (x v c_0'))')' = x. [back_rewrite(4869),rewrite([5056(2),5056(2),5056(4)])]. 5186 (x v (y v (z v (u v x')))')' = (c_0' v x)'. [back_rewrite(4047),rewrite([5056(9),5056(9),5056(9),4530(10),5056(9)]),flip(a)]. 5637 (c_0' v (c_0' v x)')' = x. [back_rewrite(1028),rewrite([5186(7),5056(6),5056(6),5056(6),5060(8,R)])]. 5717 (c_0' v (x v (x v (c_0' v x)))') v (y v x) = c_0. [back_rewrite(712),rewrite([5056(13)])]. 5887 x v c_0' = x. [back_rewrite(5089),rewrite([5637(11)])]. 5917 x'' = x. [back_rewrite(2115),rewrite([5887(3),5717(12),5887(4)])]. 5918 $F # answer(CC). [resolve(5917,a,10,a)]. ============================== end of proof ========================== ============================== PROOF ================================= % Proof 2 at 1.41 (+ 0.02) seconds: B1. % Length of proof is 154. % Level of proof is 41. % Maximum clause weight is 86.000. % Given clauses 122. 2 x v (x ^ y) = x # answer(B1) # label(non_clause) # label(goal). [goal]. 5 x v (y v z) = y v (x v z) # label(AJ). [assumption]. 6 x ^ y = (x' v y')' # label(DM). [assumption]. 7 x v x' = y v y' # label(ONE). [assumption]. 8 (x v y') ^ (x v y) = x # label(CUT). [assumption]. 9 ((x v y')' v (x v y)')' = x. [copy(8),rewrite([6(4)])]. 11 c2 v (c2 ^ c3) != c2 # answer(B1). [deny(2)]. 12 c2 v (c2' v c3')' != c2 # answer(B1). [copy(11),rewrite([6(4)])]. 17 x v x' = c_0. [new_symbol(7)]. 18 x v (y v (z v u)) = z v (x v (y v u)). [para(5(a,1),5(a,1,2))]. 19 ((x v (y v z)')' v (y v (x v z))')' = x. [para(5(a,1),9(a,1,1,2,1))]. 20 ((x v y)' v (x v ((y v z')' v (y v z)'))')' = x. [para(9(a,1),9(a,1,1,1,1,2))]. 21 (x v (x v ((x v y')' v y))')' = (x v y')'. [para(9(a,1),9(a,1,1,1)),rewrite([5(5)])]. 22 (((x v y')' v (x v y)'')' v x)' = (x v y')'. [para(9(a,1),9(a,1,1,2))]. 23 x v (y v x') = y v c_0. [para(17(a,1),5(a,1,2)),flip(a)]. 24 (c_0' v (x v x)')' = x. [para(17(a,1),9(a,1,1,1,1))]. 25 ((x v x'')' v c_0')' = x. [para(17(a,1),9(a,1,1,2,1))]. 26 ((x v y')' v (x v y)') v x = c_0. [para(9(a,1),17(a,1,2))]. 27 x v (y v (z v (u v w))) = z v (x v (u v (y v w))). [para(18(a,1),5(a,1,2))]. 29 x v (y v (z v (u v w))) = u v (x v (y v (z v w))). [para(18(a,2),5(a,1,2))]. 31 ((x v (y v (z v u))')' v (z v (x v (y v u)))')' = x. [para(18(a,1),9(a,1,1,2,1))]. 33 x v (y v (z v x')) = y v (z v c_0). [para(17(a,1),18(a,1,2,2)),flip(a)]. 42 ((x v (y v x')')' v (y v c_0)')' = x. [para(23(a,1),9(a,1,1,2,1))]. 44 x v (y v (z v (u v x'))) = y v (z v (u v c_0)). [para(23(a,1),18(a,1,2,2)),flip(a)]. 45 (c_0' v (x v ((x v y) v y))')' = x v y. [para(5(a,1),24(a,1,1,2,1))]. 46 ((x v y)' v (x v (c_0' v (y v y)'))')' = x. [para(24(a,1),9(a,1,1,1,1,2))]. 47 (x v (c_0' v (x v x))')' = c_0'. [para(24(a,1),9(a,1,1,1))]. 48 ((c_0' v (x v x)'')' v x)' = c_0'. [para(24(a,1),9(a,1,1,2))]. 49 (c_0' v (x v x)') v x = c_0. [para(24(a,1),17(a,1,2))]. 50 (c_0' v (x v (y v ((y v (x v z)) v z)))')' = y v (x v z). [para(18(a,1),24(a,1,1,2,1)),rewrite([5(6)])]. 52 (c_0' v (x v x)') v (y v x) = y v c_0. [para(24(a,1),23(a,1,2,2))]. 53 x v ((c_0' v (x v ((x v y) v y))') v y) = c_0. [para(49(a,1),5(a,1)),rewrite([5(6)]),flip(a)]. 63 (c_0' v (x' v x')') v c_0 = x v c_0. [para(49(a,1),23(a,1,2)),flip(a)]. 65 (x v ((x v x'')' v c_0)')' = (x v x'')'. [para(25(a,1),9(a,1,1,1))]. 66 (((x v x'')' v c_0'')' v x)' = (x v x'')'. [para(25(a,1),9(a,1,1,2))]. 68 ((x v x'')' v c_0') v x = c_0. [para(25(a,1),17(a,1,2))]. 85 (x v (x v (c_0' v x))')' = c_0'. [para(24(a,1),19(a,1,1,1))]. 95 (c_0' v (x v (c_0' v (x v x)))')' = x. [para(47(a,1),9(a,1,1,1))]. 97 (x v (c_0' v (x v x))') v c_0' = c_0. [para(47(a,1),17(a,1,2))]. 108 (c_0' v (((x' v x''')' v c_0') v x)')' = (x' v x''')' v c_0'. [para(68(a,1),9(a,1,1,1,1))]. 126 (c_0' v (x v (x v (c_0' v x)))')' = x. [para(85(a,1),9(a,1,1,1))]. 149 ((x' v y')' v (x' v y)') v c_0 = x v c_0. [para(26(a,1),23(a,1,2)),flip(a)]. 152 ((c_0' v (x v x)'')' v x) v c_0' = c_0. [para(24(a,1),26(a,1,1,2))]. 165 (c_0' v (x v (c_0' v (x v x)))') v x = c_0. [para(47(a,1),26(a,1,1,1))]. 169 (c_0' v (x v (x v (c_0' v x)))') v x = c_0. [para(85(a,1),26(a,1,1,1))]. 243 (c_0' v ((x v (c_0' v (x v x))') v c_0)')' = x v (c_0' v (x v x))'. [para(97(a,1),9(a,1,1,1,1))]. 248 (x v (c_0' v (x v x))') v c_0 = c_0 v c_0. [para(97(a,1),23(a,1,2)),flip(a)]. 256 x v (c_0' v (x v x))' = c_0. [back_rewrite(243),rewrite([248(10),24(8)]),flip(a)]. 258 x v (y v (c_0' v (x v x))') = y v c_0. [para(256(a,1),5(a,1,2)),flip(a)]. 266 (c_0' v (x v x)) v c_0 = x v c_0. [para(256(a,1),23(a,1,2))]. 267 c_0'' v (c_0'' v c_0)' = c_0. [para(23(a,1),256(a,1,2,1))]. 322 (c_0'' v c_0) v c_0 = c_0'' v c_0. [para(23(a,1),266(a,1,1))]. 330 (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''. [para(267(a,1),9(a,1,1,1,1))]. 339 (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0). [para(267(a,1),33(a,1,2,2))]. 523 (((x v c_0')' v ((c_0' v (y v y)') v (x v y))'')' v x)' = (x v c_0')'. [para(52(a,2),22(a,1,1,1,1,2,1,1))]. 651 ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0. [para(48(a,1),63(a,1,1,2,1,1)),rewrite([48(13),63(11)]),flip(a)]. 672 (c_0' v (x v ((x v c_0'') v ((x v c_0'') v c_0)))')' = x v c_0''. [para(33(a,1),95(a,1,1,2,1,2)),rewrite([5(13),5(14)])]. 682 (c_0' v (c_0' v (x v ((x v y) v ((x v y) v y))))')' = x v y. [para(27(a,2),95(a,1,1,2,1))]. 712 (c_0' v (x v (x v (c_0' v x)))') v (y v x) = y v c_0. [para(126(a,1),23(a,1,2,2))]. 869 (c_0' v (x v x)) v (y v c_0) = x v (y v c_0). [para(258(a,1),33(a,1,2))]. 935 ((x v (x' v y')')' v (((x' v y')' v (x' v y)'')' v c_0)')' = x. [para(22(a,1),42(a,1,1,1,1,2))]. 955 (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'. [para(68(a,1),45(a,1,1,2,1,2)),rewrite([65(15)]),flip(a)]. 963 c_0'' v c_0 = c_0''. [para(322(a,1),45(a,1,1,2,1,2,1)),rewrite([322(14),5(13),322(12),330(14),322(10)]),flip(a)]. 999 c_0'' v (x v c_0) = x v c_0''. [back_rewrite(339),rewrite([963(5),963(11)])]. 1028 ((x v (y v (z v (u v x')))')' v (z v (y v (u v c_0)))')' = x. [para(33(a,1),31(a,1,1,2,1,2))]. 1078 (c_0' v (c_0 v c_0)') v c_0'' = c_0''. [para(963(a,1),52(a,1,2)),rewrite([963(16)])]. 1082 ((c_0'' v (x v c_0))' v (x v c_0')')' = x. [para(999(a,2),9(a,1,1,1,1))]. 1083 c_0' v (c_0'' v (x v c_0)) = x v c_0. [para(999(a,2),23(a,1,2))]. 1119 c_0'' v (x v c_0) = (c_0' v (x' v x')') v c_0''. [para(63(a,1),999(a,1,2))]. 1136 c_0' v (c_0'' v (x v (y v c_0))) = x v (y v c_0). [para(1083(a,1),18(a,2,2))]. 1137 c_0'' v (x v (c_0' v c_0)) = x v c_0. [para(1083(a,1),18(a,2))]. 1157 (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0''. [para(49(a,1),1137(a,1,2)),rewrite([963(5),5(14)]),flip(a)]. 1263 (c_0' v c_0''')'' = c_0'. [para(1078(a,1),42(a,1,1,1,1,2,1)),rewrite([49(17),955(11)])]. 1266 (c_0' v c_0''')' = c_0. [para(1263(a,1),17(a,1,2)),rewrite([955(11)])]. 1271 ((c_0' v c_0'''')' v c_0)' = c_0'. [para(1266(a,1),9(a,1,1,2))]. 1284 (c_0''' v (c_0' v c_0)')' = c_0''. [para(1266(a,1),42(a,1,1,1,1,2)),rewrite([963(5)])]. 1519 ((((c_0' v c_0'''')' v c_0) v c_0'')' v c_0')' = (c_0' v c_0'''')' v c_0. [para(1271(a,1),25(a,1,1,1,1,2,1))]. 1546 ((c_0''' v (c_0' v c_0)'')' v c_0'')' = c_0'''. [para(1284(a,1),9(a,1,1,2))]. 1707 (c_0' v (x v x)'')' v x = c_0. [para(152(a,1),9(a,1,1,1,1)),rewrite([651(12),24(8)]),flip(a)]. 2028 (((c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))') v x)' v c_0')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'. [para(165(a,1),20(a,1,1,2,1)),rewrite([5(23),5(25),5(24),5(56),5(58),5(57)])]. 2115 ((x v c_0')' v ((c_0' v (y v (y v (c_0' v y)))') v (x v y))')' = x. [para(169(a,1),19(a,1,1,1,1,2,1))]. 2387 c_0 v (c_0' v c_0) = c_0. [para(869(a,1),45(a,1,1,2,1,2)),rewrite([5(10),5(9),126(13),5(7)]),flip(a)]. 2416 c_0 v (x v (c_0' v c_0)) = x v c_0. [para(2387(a,1),5(a,1,2)),flip(a)]. 2422 ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0. [para(2387(a,1),26(a,1,1,2,1))]. 2426 c_0'' = c_0 v c_0. [para(2387(a,1),52(a,1,2)),rewrite([5(11),1157(15)])]. 2428 c_0 v (x v (y v (z v (c_0' v c_0)))) = x v (y v (z v c_0)). [para(2387(a,1),29(a,1,2,2,2)),flip(a)]. 2488 (c_0 v (((c_0 v c_0)' v (c_0' v c_0)'')' v c_0))' = (c_0 v c_0)'. [back_rewrite(1546),rewrite([2426(3),2426(15),5(16),2426(20)])]. 2493 ((c_0 v (c_0 v c_0))' v c_0')' = c_0. [back_rewrite(1519),rewrite([2426(5),1707(11),2426(4),2426(15),1707(21)])]. 2544 (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0 v c_0. [back_rewrite(1157),rewrite([2426(18)])]. 2565 (c_0 v c_0) v (c_0' v (x v (y v c_0))) = x v (y v c_0). [back_rewrite(1136),rewrite([2426(5),5(10)])]. 2582 (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0). [back_rewrite(1119),rewrite([2426(3),2426(16),5(17),63(16)])]. 2601 ((c_0 v (x v c_0))' v (x v c_0')')' = x. [back_rewrite(1082),rewrite([2426(3),2582(6)])]. 2619 (c_0' v (x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))')' = x v (c_0 v c_0). [back_rewrite(672),rewrite([2426(5),2426(9),2426(20)])]. 2634 ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'. [back_rewrite(66),rewrite([2426(7),5(8)])]. 3579 c_0' v (c_0' v c_0')' = c_0. [para(49(a,1),2601(a,1,1,2,1)),rewrite([63(12),2493(10)]),flip(a)]. 3588 (c_0' v x')' v (c_0' v x)' = c_0. [para(26(a,1),2601(a,1,1,2,1)),rewrite([149(13),2493(10)]),flip(a)]. 3836 c_0' v (x v (c_0' v c_0')') = x v c_0. [para(3579(a,1),5(a,1,2)),flip(a)]. 3838 (c_0' v c_0') v c_0 = c_0' v c_0. [para(3579(a,1),23(a,1,2))]. 3847 (c_0' v ((c_0' v c_0')' v ((c_0' v c_0')' v c_0))') v (c_0' v c_0')' = c_0. [para(3579(a,1),169(a,1,1,2,1,2,2))]. 3887 (c_0' v x')' v (y v (z v (c_0' v x)')) = y v (z v c_0). [para(3588(a,1),18(a,1,2,2)),flip(a)]. 3890 (c_0' v x')' v c_0 = (c_0' v x) v c_0. [para(3588(a,1),23(a,1,2)),flip(a)]. 3947 (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v (c_0' v c_0')' = c_0. [back_rewrite(3847),rewrite([3890(16),5(15),3890(14)])]. 4047 (((x v (y v (z v (u v x')))')' v (y v (z v (u v c_0)))'')' v x)' = (x v (y v (z v (u v x')))')'. [para(44(a,1),22(a,1,1,1,1,2,1,1))]. 4117 (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v c_0 = c_0' v c_0. [para(165(a,1),3836(a,1,2)),rewrite([3836(28),3890(20),5(19),3890(18)]),flip(a)]. 4145 (c_0' v c_0')' = c_0' v c_0. [para(3890(a,1),21(a,1,1,2,1,2)),rewrite([45(14)]),flip(a)]. 4237 c_0' v (c_0' v c_0) = c_0. [back_rewrite(3947),rewrite([4145(21),5(20),4117(19)])]. 4273 c_0' v c_0 = c_0 v c_0. [para(4237(a,1),52(a,1,2)),rewrite([5(11),2544(15)]),flip(a)]. 4274 c_0 v (c_0 v c_0) = c_0. [para(52(a,2),4237(a,1,2)),rewrite([5(11),49(10),4273(6),5(6),4273(5)])]. 4316 (c_0' v c_0') v c_0 = c_0 v c_0. [back_rewrite(3838),rewrite([4273(11)])]. 4379 (c_0 v c_0)' = c_0'. [back_rewrite(2488),rewrite([4273(9),17(11),4273(5),4274(5)]),flip(a)]. 4392 c_0 v (x v (y v (z v (c_0 v c_0)))) = x v (y v (z v c_0)). [back_rewrite(2428),rewrite([4273(5)])]. 4395 c_0 v c_0 = c_0. [back_rewrite(2422),rewrite([4273(5),4379(5),17(4),4316(7)])]. 4398 c_0 v (x v c_0) = x v c_0. [back_rewrite(2416),rewrite([4273(5),4395(4)])]. 4431 c_0 v (x v (y v (z v c_0))) = x v (y v (z v c_0)). [back_rewrite(4392),rewrite([4395(4)])]. 4447 c_0' v c_0 = c_0. [back_rewrite(4273),rewrite([4395(7)])]. 4523 (c_0' v (x v ((x v c_0) v ((x v c_0) v c_0)))')' = x v c_0. [back_rewrite(2619),rewrite([4395(5),4395(7),4395(16)])]. 4527 c_0' v (x v (y v c_0)) = x v (y v c_0). [back_rewrite(2565),rewrite([4395(3),4431(8)])]. 4530 c_0'' = c_0. [back_rewrite(2426),rewrite([4395(6)])]. 4536 (((x v x'')' v c_0)' v x)' = (x v x'')'. [back_rewrite(2634),rewrite([4398(8)])]. 4630 (((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)' v c_0')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'. [para(165(a,1),46(a,1,1,2,1)),rewrite([5(20),5(22),5(21),5(50),5(52),5(51)])]. 4712 x v ((x v c_0) v c_0) = x v c_0. [para(869(a,1),50(a,1,1,2,1,2,2)),rewrite([5(11),4527(12),5(10),4523(13),5(9),4527(10)]),flip(a)]. 4736 (c_0' v (x v c_0)')' = x v c_0. [para(3588(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite([3887(16),4712(7),3588(17)])]. 4742 x v ((c_0' v (x v c_0)') v c_0) = c_0. [para(4398(a,1),52(a,1,2)),rewrite([5(7),4712(7),5(9),4395(12)])]. 4747 x v (y v ((x v c_0) v c_0)) = y v (x v c_0). [para(4712(a,1),5(a,1,2)),flip(a)]. 4856 ((x v c_0)' v c_0')' = x v c_0. [para(4736(a,1),42(a,1,1,1,1,2)),rewrite([5(5),4712(5),4447(7)])]. 4869 ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x. [para(4856(a,1),19(a,1,1,1,1,2))]. 4879 ((x v c_0)' v ((x v c_0) v ((x v c_0)' v c_0))')' = x v c_0. [para(4856(a,1),21(a,1,1,2,1,2,1)),rewrite([5(11),4856(21)])]. 4887 ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0. [para(4856(a,1),42(a,1,1,1,1,2)),rewrite([4398(4)])]. 4988 x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0. [para(4712(a,1),53(a,1,2,1,2,1,2,1)),rewrite([4747(10),5(7),4712(7),5(11)])]. 4999 x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0. [para(4742(a,1),5(a,1,2)),flip(a)]. 5007 (((x v ((c_0' v (x v c_0)') v c_0)')' v c_0)' v x)' = (x v ((c_0' v (x v c_0)') v c_0)')'. [para(4742(a,1),22(a,1,1,1,1,2,1,1)),rewrite([4530(14)])]. 5022 (x v c_0) v c_0 = c_0. [back_rewrite(4988),rewrite([4999(12)])]. 5040 (x v c_0) v (y v c_0) = y v c_0. [para(5022(a,1),5(a,1,2)),flip(a)]. 5056 x v c_0 = c_0. [back_rewrite(4879),rewrite([5040(11),4887(11)]),flip(a)]. 5060 (c_0' v x)' = (x v c_0')'. [back_rewrite(5007),rewrite([5056(4),5056(7),5056(6),5056(8),5056(11)])]. 5089 (c_0' v (c_0' v (x v c_0'))')' = x. [back_rewrite(4869),rewrite([5056(2),5056(2),5056(4)])]. 5139 (x v x'')' = (c_0' v x)'. [back_rewrite(4536),rewrite([5056(6)]),flip(a)]. 5186 (x v (y v (z v (u v x')))')' = (c_0' v x)'. [back_rewrite(4047),rewrite([5056(9),5056(9),5056(9),4530(10),5056(9)]),flip(a)]. 5637 (c_0' v (c_0' v x)')' = x. [back_rewrite(1028),rewrite([5186(7),5056(6),5056(6),5056(6),5060(8,R)])]. 5654 (c_0' v (x v (x' v y')')')' = x. [back_rewrite(935),rewrite([5056(18),5060(10,R)])]. 5717 (c_0' v (x v (x v (c_0' v x)))') v (y v x) = c_0. [back_rewrite(712),rewrite([5056(13)])]. 5779 (c_0' v (x v x)') v (y v x) = c_0. [back_rewrite(52),rewrite([5056(9)])]. 5793 (c_0' v ((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'. [back_rewrite(4630),rewrite([5060(30,R)])]. 5810 (c_0' v ((c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))') v x)')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'. [back_rewrite(2028),rewrite([5060(33,R)])]. 5880 (c_0' v (((c_0' v x')' v c_0') v x)')' = (c_0' v x')' v c_0'. [back_rewrite(108),rewrite([5139(8),5139(20)])]. 5887 x v c_0' = x. [back_rewrite(5089),rewrite([5637(11)])]. 5910 x v ((x v y) v ((x v y) v y)) = x v y. [back_rewrite(682),rewrite([5637(13)])]. 5917 x'' = x. [back_rewrite(2115),rewrite([5887(3),5717(12),5887(4)])]. 5926 (c_0' v x)' = x'. [back_rewrite(523),rewrite([5887(3),5779(8),5917(4),5056(3),5887(7)])]. 5935 x v x = x. [back_rewrite(5880),rewrite([5926(7),5917(4),5887(5),5926(6),5917(3),5926(6),5917(3),5887(4)])]. 6061 (c_0' v x) v x = c_0' v x. [back_rewrite(5810),rewrite([5910(26),5926(14),9(11),5926(9),5917(6),5910(28),5926(16),9(13)])]. 6063 c_0' v x = x. [back_rewrite(5793),rewrite([5935(11),5935(15),5935(17),6061(18),5935(17),5926(15),5926(12),5926(9),5917(6),6061(6),5926(6),5926(5),5917(2),5935(9),5935(13),5935(15),6061(16),5935(15),5926(13),5926(10),5926(7),5917(4)]),flip(a)]. 6086 x v (x' v y')' = x. [back_rewrite(5654),rewrite([6063(9),5917(7)])]. 6087 $F # answer(B1). [resolve(6086,a,12,a)]. ============================== end of proof ========================== % Redundant proof: 6377 $F # answer(CC). [back_rewrite(10),rewrite([5917(3)]),xx(a)]. % Redundant proof: 6483 $F # answer(B1). [back_rewrite(12),rewrite([6086(8)]),xx(a)]. % Disable descendants (x means already disabled): 11x 12x 10x given #123 (T,wt=5): 5056 x v c_0 = c_0. [back_rewrite(4879),rewrite([5040(11),4887(11)]),flip(a)]. given #124 (A,wt=25): 71 ((x v y)' v (x v ((y v (z v u)')' v (z v (y v u))'))')' = x. [para(19(a,1),9(a,1,1,1,1,2))]. given #125 (T,wt=5): 5917 x'' = x. [back_rewrite(2115),rewrite([5887(3),5717(12),5887(4)])]. given #126 (T,wt=5): 5935 x v x = x. [back_rewrite(5880),rewrite([5926(7),5917(4),5887(5),5926(6),5917(3),5926(6),5917(3),5887(4)])]. given #127 (T,wt=5): 6005 c_0 v x = c_0. [back_rewrite(5167),rewrite([5887(5),5917(4),5926(4),5929(2),5887(4)])]. given #128 (T,wt=6): 5887 x v c_0' = x. [back_rewrite(5089),rewrite([5637(11)])]. % Operation v is commutative; C redundancy checks enabled. given #129 (A,wt=25): 76 ((x v (y v (z v (u v w)))')' v (z v (x v (u v (y v w))))')' = x. [para(18(a,1),19(a,1,1,1,1,2,1))]. given #130 (T,wt=6): 6063 c_0' v x = x. [back_rewrite(5793),rewrite([5935(11),5935(15),5935(17),6061(18),5935(17),5926(15),5926(12),5926(9),5917(6),6061(6),5926(6),5926(5),5917(2),5935(9),5935(13),5935(15),6061(16),5935(15),5926(13),5926(10),5926(7),5917(4)]),flip(a)]. given #131 (T,wt=7): 6642 x v y = y v x. [para(5887(a,1),5(a,1,2)),rewrite([5887(4)])]. given #132 (T,wt=8): 5783 x v (y v x') = c_0. [back_rewrite(23),rewrite([5056(5)])]. given #133 (T,wt=8): 6781 x v (x' v y) = c_0. [back_rewrite(6269),rewrite([6642(9),6587(9),6642(8),6667(8),6642(10),6580(10),6643(3)])]. given #134 (A,wt=25): 77 ((x v (y v (z v (u v w)))')' v (y v (u v (x v (z v w))))')' = x. [para(18(a,1),19(a,1,1,2,1,2))]. given #135 (T,wt=9): 6587 x v (y v x')' = x. [back_rewrite(6077),rewrite([6578(10)])]. given #136 (T,wt=9): 6604 x v (y v x) = y v x. [para(5935(a,1),5(a,1,2)),flip(a)]. given #137 (T,wt=9): 6836 x v (x v y) = x v y. [back_rewrite(6078),rewrite([6642(2)])]. given #138 (T,wt=9): 7273 x v (x' v y)' = x. [para(6642(a,1),6587(a,1,2,1))]. given #139 (A,wt=21): 78 ((x v (y v (z v u))')' v (z v (y v (x v u)))')' = x. [para(18(a,1),19(a,1,1,2,1))]. given #140 (T,wt=10): 5782 x v (y v (z v x')) = c_0. [back_rewrite(33),rewrite([5056(6),5056(6)])]. given #141 (T,wt=10): 5966 x' v (y v x)' = x'. [back_rewrite(5773),rewrite([5926(6),5887(6),5926(9),5917(6),5926(8),5887(8)])]. given #142 (T,wt=8): 7406 (x v y) v y' = c_0. [para(5966(a,1),5783(a,1,2))]. given #143 (T,wt=8): 7434 (x v y) v x' = c_0. [para(6642(a,1),7406(a,1,1))]. given #144 (A,wt=25): 79 ((x v (y v (z v (u v w)))')' v (u v (x v (y v (z v w))))')' = x. [para(18(a,2),19(a,1,1,1,1,2,1))]. given #145 (T,wt=10): 5967 x' v (y v (z v x)) = c_0. [back_rewrite(5750),rewrite([5926(4),5887(4)])]. given #146 (T,wt=10): 6869 x v (y v (x v y)') = c_0. [back_rewrite(5934),rewrite([6642(3)])]. given #147 (T,wt=10): 7173 x v (y v (x' v z)) = c_0. [para(6781(a,1),5(a,1,2)),rewrite([5056(2)]),flip(a)]. given #148 (T,wt=10): 7175 x' v (y v (x v z)) = c_0. [para(6781(a,1),18(a,1,2)),rewrite([5056(2)]),flip(a)]. given #149 (A,wt=25): 80 ((x v (y v (z v (u v w)))')' v (y v (z v (u v (x v w))))')' = x. [para(18(a,2),19(a,1,1,2,1,2))]. given #150 (T,wt=10): 7326 x' v (x v y)' = x'. [para(5917(a,1),7273(a,1,2,1,1))]. given #151 (T,wt=10): 7378 x v ((y v x') v z) = c_0. [para(6642(a,1),5782(a,1,2))]. given #152 (T,wt=10): 7379 x v ((x' v y) v z) = c_0. [para(7273(a,1),5782(a,1,2,2)),rewrite([6643(4)])]. given #153 (T,wt=10): 7407 (x v y) v (z v y') = c_0. [para(5966(a,1),5782(a,1,2,2))]. given #154 (A,wt=25): 92 ((x v y)' v ((y v (z v u)')' v (x v (z v (y v u))'))')' = x. [para(19(a,1),19(a,1,1,1,1,2))]. given #155 (T,wt=10): 7435 (x v y) v (z v x') = c_0. [para(7434(a,1),5(a,1,2)),rewrite([5056(2)]),flip(a)]. given #156 (T,wt=10): 7436 (x v (y v z)) v y' = c_0. [para(5(a,1),7434(a,1,1))]. given #157 (T,wt=10): 7541 (x v (y v z)) v z' = c_0. [para(5967(a,1),6642(a,1)),flip(a)]. given #158 (T,wt=10): 7542 x' v ((y v x) v z) = c_0. [para(6642(a,1),5967(a,1,2))]. given #159 (A,wt=23): 420 x v (y v (z v (u v (w v v5)))) = w v (x v (y v (u v (z v v5)))). [para(28(a,1),18(a,1,2,2))]. given #160 (T,wt=10): 7575 x' v ((x v y) v z) = c_0. [para(6642(a,1),7175(a,1,2))]. given #161 (T,wt=10): 7668 (x v y) v (y' v z) = c_0. [para(5966(a,1),7378(a,1,2,1))]. given #162 (T,wt=10): 7669 (x v y) v (x' v z) = c_0. [para(7326(a,1),7378(a,1,2,1))]. given #163 (T,wt=10): 7839 ((x v y) v z) v y' = c_0. [para(5966(a,1),7435(a,1,2))]. given #164 (A,wt=23): 421 x v (y v (z v (u v (w v v5)))) = z v (x v (w v (u v (y v v5)))). [para(28(a,1),18(a,2,2,2))]. given #165 (T,wt=10): 7840 ((x v y) v z) v x' = c_0. [para(7326(a,1),7435(a,1,2))]. given #166 (T,wt=11): 6586 x v (y v (z v x'))' = x. [back_rewrite(6079),rewrite([6578(12)])]. given #167 (T,wt=11): 6643 x v (y v z) = z v (x v y). [para(5887(a,1),18(a,1,2,2)),rewrite([5887(5)])]. % Operation v is associative-commutative; CAC redundancy checks enabled. % back CAC tautology: 6643 x v (y v z) = z v (x v y). [para(5887(a,1),18(a,1,2,2)),rewrite([5887(5)])]. % back CAC tautology: 421 x v (y v (z v (u v (w v v5)))) = z v (x v (w v (u v (y v v5)))). [para(28(a,1),18(a,2,2,2))]. % back CAC tautology: 420 x v (y v (z v (u v (w v v5)))) = w v (x v (y v (u v (z v v5)))). [para(28(a,1),18(a,1,2,2))]. % back CAC tautology: 41 x v (y v (z v (u v w))) = u v (y v (x v (z v w))). [para(18(a,2),18(a,2,2)),flip(a)]. % back CAC tautology: 40 x v (y v (z v (u v (w v v5)))) = z v (x v (u v (w v (y v v5)))). [para(18(a,2),18(a,2,2,2))]. % back CAC tautology: 39 x v (y v (z v (u v w))) = y v (x v (u v (z v w))). [para(18(a,2),18(a,1,2))]. % back CAC tautology: 38 x v (y v (z v (u v (w v v5)))) = w v (x v (y v (z v (u v v5)))). [para(18(a,2),18(a,1,2,2))]. % back CAC tautology: 37 x v (y v (z v (u v w))) = z v (u v (x v (y v w))). [para(18(a,1),18(a,2,2))]. % back CAC tautology: 36 x v (y v (z v (u v (w v v5)))) = z v (x v (w v (y v (u v v5)))). [para(18(a,1),18(a,2,2,2))]. % back CAC tautology: 35 x v (y v (z v (u v w))) = u v (x v (z v (y v w))). [para(18(a,1),18(a,1,2))]. % back CAC tautology: 34 x v (y v (z v (u v (w v v5)))) = u v (x v (y v (w v (z v v5)))). [para(18(a,1),18(a,1,2,2))]. % back CAC tautology: 29 x v (y v (z v (u v w))) = u v (x v (y v (z v w))). [para(18(a,2),5(a,1,2))]. % back CAC tautology: 27 x v (y v (z v (u v w))) = z v (x v (u v (y v w))). [para(18(a,1),5(a,1,2))]. % back CAC tautology: 30 x v (y v (z v u)) = x v (z v (y v u)). [para(18(a,2),5(a,1))]. % back CAC tautology: 28 x v (y v (z v u)) = z v (y v (x v u)). [para(18(a,1),5(a,1))]. % back CAC tautology: 18 x v (y v (z v u)) = z v (x v (y v u)). [para(5(a,1),5(a,1,2))]. % back CAC tautology: 8510 x v (y v (z v (u v w))) = w v (y v (z v (x v u))). [para(6643(a,2),41(a,2,2,2)),flip(a)]. % back CAC tautology: 8509 x v (y v (z v (u v (w v v5)))) = u v (y v (x v (w v (v5 v z)))). [para(6643(a,2),41(a,2,2,2,2))]. % back CAC tautology: 8507 x v (y v (z v (u v w))) = z v (y v (x v (w v u))). [para(6643(a,2),41(a,1,2,2))]. % back CAC tautology: 8506 x v (y v (z v (u v (w v v5)))) = v5 v (y v (x v (z v (u v w)))). [para(6643(a,2),41(a,1,2,2,2))]. % back CAC tautology: 8503 x v (y v (z v (u v w))) = u v (y v (w v (x v z))). [para(6643(a,1),41(a,2,2,2))]. % back CAC tautology: 8502 x v (y v (z v (u v (w v v5)))) = u v (y v (x v (v5 v (z v w)))). [para(6643(a,1),41(a,2,2,2,2))]. % back CAC tautology: 8499 x v (y v (z v (u v w))) = w v (y v (x v (u v z))). [para(6643(a,1),41(a,1,2,2))]. % back CAC tautology: 8498 x v (y v (z v (u v (w v v5)))) = w v (y v (x v (z v (v5 v u)))). [para(6643(a,1),41(a,1,2,2,2))]. % back CAC tautology: 8491 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (u v (w v (v5 v (v6 v y))))). [para(6643(a,2),40(a,2,2,2,2,2))]. % back CAC tautology: 8487 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (u v (v6 v (y v (w v v5))))). [para(6643(a,2),40(a,1,2,2,2,2))]. % back CAC tautology: 8483 x v (y v (z v (u v (w v v5)))) = z v (x v (u v (v5 v (w v y)))). [para(6643(a,1),40(a,2,2,2,2))]. % back CAC tautology: 8482 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (u v (w v (v6 v (y v v5))))). [para(6643(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 8478 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (u v (v5 v (y v (v6 v w))))). [para(6643(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 8474 x v (y v (z v (u v w))) = y v (x v (z v (w v u))). [para(6643(a,2),39(a,1,2,2))]. % back CAC tautology: 8473 x v (y v (z v (u v (w v v5)))) = y v (x v (v5 v (z v (u v w)))). [para(6643(a,2),39(a,1,2,2,2))]. % back CAC tautology: 8470 x v (y v (z v (u v w))) = y v (x v (w v (u v z))). [para(6643(a,1),39(a,1,2,2))]. % back CAC tautology: 8469 x v (y v (z v (u v (w v v5)))) = y v (x v (w v (z v (v5 v u)))). [para(6643(a,1),39(a,1,2,2,2))]. % back CAC tautology: 8461 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (y v (z v (v5 v (v6 v u))))). [para(6643(a,2),38(a,2,2,2,2,2))]. % back CAC tautology: 8458 x v (y v (z v (u v (w v (v5 v v6))))) = v6 v (x v (y v (z v (u v (w v v5))))). [para(6643(a,2),38(a,1,2,2,2,2))]. % back CAC tautology: 8454 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (y v (z v (v6 v (u v v5))))). [para(6643(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 8450 x v (y v (z v (u v (w v v5)))) = v5 v (x v (y v (z v (w v u)))). [para(6643(a,1),38(a,1,2,2,2))]. % back CAC tautology: 8449 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (y v (z v (u v (v6 v w))))). [para(6643(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 8445 x v (y v (z v (u v w))) = w v (z v (x v (y v u))). [para(6643(a,2),37(a,1,2,2))]. % back CAC tautology: 8444 x v (y v (z v (u v (w v v5)))) = z v (v5 v (x v (y v (u v w)))). [para(6643(a,2),37(a,1,2,2,2))]. % back CAC tautology: 8441 x v (y v (z v (u v w))) = u v (w v (x v (y v z))). [para(6643(a,1),37(a,1,2,2))]. % back CAC tautology: 8440 x v (y v (z v (u v (w v v5)))) = z v (w v (x v (y v (v5 v u)))). [para(6643(a,1),37(a,1,2,2,2))]. % back CAC tautology: 8432 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (w v (y v (v5 v (v6 v u))))). [para(6643(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 8428 x v (y v (z v (u v (w v v5)))) = z v (x v (u v (y v (v5 v w)))). [para(6643(a,2),36(a,1,2,2,2))]. % back CAC tautology: 8427 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (v6 v (y v (u v (w v v5))))). [para(6643(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 8423 x v (y v (z v (u v (w v v5)))) = z v (x v (w v (v5 v (y v u)))). [para(6643(a,1),36(a,2,2,2,2))]. % back CAC tautology: 8422 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (w v (y v (v6 v (u v v5))))). [para(6643(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 8418 x v (y v (z v (u v (w v v5)))) = z v (x v (v5 v (y v (w v u)))). [para(6643(a,1),36(a,1,2,2,2))]. % back CAC tautology: 8417 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (v5 v (y v (u v (v6 v w))))). [para(6643(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 8412 x v (y v (z v (u v (w v v5)))) = u v (x v (z v (w v (v5 v y)))). [para(6643(a,2),35(a,2,2,2,2))]. % back CAC tautology: 8410 x v (y v (z v (u v (w v v5)))) = v5 v (x v (z v (y v (u v w)))). [para(6643(a,2),35(a,1,2,2,2))]. % back CAC tautology: 8407 x v (y v (z v (u v w))) = u v (x v (w v (z v y))). [para(6643(a,1),35(a,2,2,2))]. % back CAC tautology: 8406 x v (y v (z v (u v (w v v5)))) = u v (x v (z v (v5 v (y v w)))). [para(6643(a,1),35(a,2,2,2,2))]. % back CAC tautology: 8403 x v (y v (z v (u v w))) = w v (x v (u v (y v z))). [para(6643(a,1),35(a,1,2,2))]. % back CAC tautology: 8402 x v (y v (z v (u v (w v v5)))) = w v (x v (z v (y v (v5 v u)))). [para(6643(a,1),35(a,1,2,2,2))]. % back CAC tautology: 8394 x v (y v (z v (u v (w v v5)))) = u v (x v (y v (z v (v5 v w)))). [para(6643(a,2),34(a,2,2,2,2))]. % back CAC tautology: 8393 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (y v (w v (v5 v (v6 v z))))). [para(6643(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 8389 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (y v (v6 v (z v (w v v5))))). [para(6643(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 8385 x v (y v (z v (u v (w v v5)))) = u v (x v (y v (v5 v (w v z)))). [para(6643(a,1),34(a,2,2,2,2))]. % back CAC tautology: 8384 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (y v (w v (v6 v (z v v5))))). [para(6643(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 8380 x v (y v (z v (u v (w v v5)))) = w v (x v (y v (v5 v (z v u)))). [para(6643(a,1),34(a,1,2,2,2))]. % back CAC tautology: 8379 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (y v (v5 v (z v (v6 v w))))). [para(6643(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 8368 x v (y v (z v (u v w))) = z v (x v (y v (w v u))). [para(6643(a,2),27(a,2,2,2))]. % back CAC tautology: 8363 x v (y v (z v (u v w))) = u v (x v (w v (y v z))). [para(6643(a,1),27(a,1,2,2))]. % back CAC tautology: 8361 x v (y v (z v (u v w))) = x v (w v (y v (z v u))). [para(6643(a,2),30(a,1,2,2))]. % back CAC tautology: 8360 x v (y v (z v u)) = x v (u v (z v y)). [para(6643(a,1),30(a,1,2))]. % back CAC tautology: 8359 x v (y v (z v (u v w))) = x v (u v (y v (w v z))). [para(6643(a,1),30(a,1,2,2))]. % back CAC tautology: 8356 x v (y v (z v u)) = u v (z v (x v y)). [para(6643(a,1),28(a,1,2))]. % back CAC tautology: 8328 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v5 v (v8 v (y v (v7 v (v6 v v9)))))))). [para(421(a,2),421(a,2,2,2,2,2))]. % back CAC tautology: 8327 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (v6 v (z v (y v (v5 v (u v v7)))))). [para(421(a,2),421(a,1,2,2))]. % back CAC tautology: 8326 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v6 v (u v (y v (w v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,2),421(a,1,2,2,2,2))]. % back CAC tautology: 8325 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v5 v (u v (v7 v (v6 v (y v v8))))))). [para(421(a,1),421(a,2,2,2,2))]. % back CAC tautology: 8324 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v6 v (y v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8323 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (w v (y v (u v (v6 v (v5 v v8))))))). [para(421(a,1),421(a,1,2,2,2))]. % back CAC tautology: 8322 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (u v (y v (v8 v (w v (v7 v (v6 v v9)))))))). [para(421(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8317 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (w v (x v (z v (y v (u v v6))))). [para(420(a,2),421(a,2,2)),flip(a)]. % back CAC tautology: 8316 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v5 v (v6 v (v8 v (v7 v (y v v9)))))))). [para(420(a,2),421(a,2,2,2,2,2))]. % back CAC tautology: 8315 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (u v (z v (y v (v5 v (w v v7)))))). [para(420(a,2),421(a,1,2,2))]. % back CAC tautology: 8314 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v8 v (u v (y v (w v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,2),421(a,1,2,2,2,2))]. % back CAC tautology: 8313 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (w v (u v (v5 v (y v v7)))))). [para(420(a,1),421(a,2,2,2))]. % back CAC tautology: 8312 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v7 v (u v (y v (v6 v (v5 v v8))))))). [para(420(a,1),421(a,2,2,2,2))]. % back CAC tautology: 8311 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v8 v (y v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8310 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v6 v (w v (y v (v5 v (z v v7)))))). [para(420(a,1),421(a,1,2,2))]. % back CAC tautology: 8309 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (w v (y v (v7 v (v6 v (u v v8))))))). [para(420(a,1),421(a,1,2,2,2))]. % back CAC tautology: 8308 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (u v (y v (v6 v (v8 v (v7 v (w v v9)))))))). [para(420(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8307 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (u v (v6 v (y v (v5 v (z v v7)))))). [para(421(a,2),420(a,2,2,2))]. % back CAC tautology: 8306 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v5 v (v8 v (z v (v7 v (v6 v v9)))))))). [para(421(a,2),420(a,2,2,2,2,2))]. % back CAC tautology: 8305 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v6 v (x v (y v (u v (z v (w v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,2),420(a,1,2,2,2,2))]. % back CAC tautology: 8304 x v (y v (z v (u v (w v (v5 v v6))))) = w v (u v (x v (v5 v (z v (y v v6))))). [para(421(a,1),420(a,2,2))]. % back CAC tautology: 8303 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v5 v (u v (v7 v (v6 v (z v v8))))))). [para(421(a,1),420(a,2,2,2,2))]. % back CAC tautology: 8302 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v6 v (z v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 8301 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (w v (z v (u v (v6 v (v5 v v8))))))). [para(421(a,1),420(a,1,2,2,2))]. % back CAC tautology: 8300 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (u v (z v (v8 v (w v (v7 v (v6 v v9)))))))). [para(421(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 8277 x v (y v (z v (u v (w v v5)))) = z v (x v (w v (u v (v5 v y)))). [para(6642(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8273 x v (y v (z v (u v (w v v5)))) = z v (x v (v5 v (u v (y v w)))). [para(6642(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8270 x v (y v (z v (u v w))) = z v (x v (w v (u v y))). [para(5887(a,1),421(a,1,2,2,2,2)),rewrite([5887(7)])]. % back CAC tautology: 8267 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v6 v (v5 v (v7 v (y v v8))))))). [para(41(a,2),421(a,2,2,2,2,2))]. % back CAC tautology: 8266 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (u v (y v (v5 v (w v (v6 v v8))))))). [para(41(a,2),421(a,1,2,2,2,2))]. % back CAC tautology: 8265 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v7 v (v5 v (y v (v6 v v8))))))). [para(41(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8264 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v6 v (u v (y v (v5 v (v7 v (w v v8))))))). [para(41(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8263 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (z v (x v (v6 v (v5 v (u v v7)))))). [para(421(a,2),41(a,2,2,2)),flip(a)]. % back CAC tautology: 8262 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (w v (v7 v (z v (v6 v (v5 v v8))))))). [para(421(a,2),41(a,2,2,2,2))]. % back CAC tautology: 8261 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (u v (x v (y v (w v (z v v6))))). [para(421(a,2),41(a,1,2))]. % back CAC tautology: 8260 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (y v (x v (z v (u v (v7 v (v6 v (w v v8))))))). [para(421(a,2),41(a,1,2,2,2))]. % back CAC tautology: 8259 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (v5 v (z v (v7 v (v6 v (w v v8))))))). [para(421(a,1),41(a,2,2,2,2))]. % back CAC tautology: 8258 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (y v (x v (u v (z v (v5 v (w v v7)))))). [para(421(a,1),41(a,1,2,2))]. % back CAC tautology: 8257 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (y v (x v (z v (v7 v (u v (v6 v (v5 v v8))))))). [para(421(a,1),41(a,1,2,2,2))]. % back CAC tautology: 8256 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v5 v (v8 v (y v (v6 v (v7 v v9)))))))). [para(40(a,2),421(a,2,2,2,2,2))]. % back CAC tautology: 8255 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (v5 v (z v (y v (v6 v (u v v7)))))). [para(40(a,2),421(a,1,2,2))]. % back CAC tautology: 8254 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v6 v (u v (y v (w v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,2),421(a,1,2,2,2,2))]. % back CAC tautology: 8253 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v5 v (u v (v6 v (v7 v (y v v8))))))). [para(40(a,1),421(a,2,2,2,2))]. % back CAC tautology: 8252 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v6 v (y v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8251 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (w v (y v (u v (v5 v (v6 v v8))))))). [para(40(a,1),421(a,1,2,2,2))]. % back CAC tautology: 8250 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (u v (y v (v8 v (w v (v6 v (v7 v v9)))))))). [para(40(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8249 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v5 v (v8 v (y v (v7 v (v6 v v9)))))))). [para(421(a,2),40(a,2,2,2,2,2))]. % back CAC tautology: 8248 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (v5 v (w v (u v (z v v6))))). [para(421(a,2),40(a,1,2))]. % back CAC tautology: 8247 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v6 v (y v (w v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,2),40(a,1,2,2,2,2))]. % back CAC tautology: 8246 x v (y v (z v (u v (w v (v5 v v6))))) = z v (w v (x v (v5 v (y v (u v v6))))). [para(421(a,1),40(a,2,2))]. % back CAC tautology: 8245 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v5 v (w v (v7 v (v6 v (y v v8))))))). [para(421(a,1),40(a,2,2,2,2))]. % back CAC tautology: 8244 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v6 v (y v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 8243 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v5 v (y v (v8 v (w v (v7 v (v6 v v9)))))))). [para(421(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 8242 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v5 v (y v (v7 v (v6 v v8))))))). [para(39(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8241 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (u v (y v (w v (v7 v (v6 v v8))))))). [para(39(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8240 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (v5 v (z v (u v (v7 v (v6 v (w v v8))))))). [para(421(a,2),39(a,1,2,2,2))]. % back CAC tautology: 8239 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (w v (z v (v7 v (u v (v6 v (v5 v v8))))))). [para(421(a,1),39(a,1,2,2,2))]. % back CAC tautology: 8238 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (u v (x v (z v (y v (w v v6))))). [para(38(a,2),421(a,2,2)),flip(a)]. % back CAC tautology: 8237 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v5 v (v6 v (v7 v (v8 v (y v v9)))))))). [para(38(a,2),421(a,2,2,2,2,2))]. % back CAC tautology: 8236 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (u v (z v (y v (w v (v5 v v7)))))). [para(38(a,2),421(a,1,2,2))]. % back CAC tautology: 8235 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v8 v (u v (y v (w v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,2),421(a,1,2,2,2,2))]. % back CAC tautology: 8234 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (w v (u v (y v (v5 v v7)))))). [para(38(a,1),421(a,2,2,2))]. % back CAC tautology: 8233 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v7 v (u v (y v (v5 v (v6 v v8))))))). [para(38(a,1),421(a,2,2,2,2))]. % back CAC tautology: 8232 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v8 v (y v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8231 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v5 v (w v (y v (v6 v (z v v7)))))). [para(38(a,1),421(a,1,2,2))]. % back CAC tautology: 8230 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (w v (y v (v6 v (v7 v (u v v8))))))). [para(38(a,1),421(a,1,2,2,2))]. % back CAC tautology: 8229 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (u v (y v (v6 v (v7 v (v8 v (w v v9)))))))). [para(38(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8228 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (v6 v (y v (v5 v (u v v7)))))). [para(421(a,2),38(a,2,2,2))]. % back CAC tautology: 8227 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v5 v (v8 v (u v (v7 v (v6 v v9)))))))). [para(421(a,2),38(a,2,2,2,2,2))]. % back CAC tautology: 8226 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v6 v (x v (y v (z v (u v (w v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,2),38(a,1,2,2,2,2))]. % back CAC tautology: 8225 x v (y v (z v (u v (w v (v5 v v6))))) = w v (z v (x v (v5 v (u v (y v v6))))). [para(421(a,1),38(a,2,2))]. % back CAC tautology: 8224 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v6 v (u v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 8223 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (z v (w v (u v (v6 v (v5 v v8))))))). [para(421(a,1),38(a,1,2,2,2))]. % back CAC tautology: 8222 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (z v (u v (v8 v (w v (v7 v (v6 v v9)))))))). [para(421(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 8221 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (v5 v (v6 v (u v (y v v7)))))). [para(37(a,1),421(a,2,2,2,2))]. % back CAC tautology: 8220 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v6 v (v7 v (y v (v5 v v8))))))). [para(37(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8219 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (v5 v (y v (u v (w v v7)))))). [para(37(a,1),421(a,1,2,2,2))]. % back CAC tautology: 8218 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v6 v (u v (y v (v7 v (w v (v5 v v8))))))). [para(37(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8217 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (z v (x v (y v (v6 v (v5 v (u v v7)))))). [para(421(a,2),37(a,1,2,2))]. % back CAC tautology: 8216 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (v5 v (x v (y v (u v (v7 v (v6 v (w v v8))))))). [para(421(a,2),37(a,1,2,2,2))]. % back CAC tautology: 8215 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (v6 v (x v (y v (z v (v5 v (w v v7)))))). [para(421(a,1),37(a,1,2,2))]. % back CAC tautology: 8214 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (w v (x v (y v (v7 v (u v (v6 v (v5 v v8))))))). [para(421(a,1),37(a,1,2,2,2))]. % back CAC tautology: 8213 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v5 v (v7 v (y v (v8 v (v6 v v9)))))))). [para(36(a,2),421(a,2,2,2,2,2))]. % back CAC tautology: 8212 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (v6 v (z v (y v (u v (v5 v v7)))))). [para(36(a,2),421(a,1,2,2))]. % back CAC tautology: 8211 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v6 v (u v (y v (w v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,2),421(a,1,2,2,2,2))]. % back CAC tautology: 8210 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v5 v (u v (v7 v (y v (v6 v v8))))))). [para(36(a,1),421(a,2,2,2,2))]. % back CAC tautology: 8209 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v6 v (y v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8208 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v6 v (w v (y v (u v (v7 v (v5 v v8))))))). [para(36(a,1),421(a,1,2,2,2))]. % back CAC tautology: 8207 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (u v (y v (v7 v (w v (v8 v (v6 v v9)))))))). [para(36(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8206 x v (y v (z v (u v (w v (v5 v v6))))) = u v (v5 v (x v (w v (y v (z v v6))))). [para(421(a,2),36(a,2,2)),flip(a)]. % back CAC tautology: 8205 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v5 v (v8 v (u v (v7 v (v6 v v9)))))))). [para(421(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 8204 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v6 v (y v (u v (w v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 8203 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v6 v (u v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 8202 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (y v (w v (u v (v6 v (v5 v v8))))))). [para(421(a,1),36(a,1,2,2,2))]. % back CAC tautology: 8201 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (y v (u v (v8 v (w v (v7 v (v6 v v9)))))))). [para(421(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 8200 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (v6 v (u v (v5 v (y v v7)))))). [para(35(a,1),421(a,2,2,2,2))]. % back CAC tautology: 8199 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v7 v (y v (v6 v (v5 v v8))))))). [para(35(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8198 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (u v (y v (v7 v (v6 v (w v v8))))))). [para(35(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8197 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (w v (v7 v (y v (v6 v (v5 v v8))))))). [para(421(a,2),35(a,2,2,2,2))]. % back CAC tautology: 8196 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (z v (y v (u v (v7 v (v6 v (w v v8))))))). [para(421(a,2),35(a,1,2,2,2))]. % back CAC tautology: 8195 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (v5 v (y v (v7 v (v6 v (w v v8))))))). [para(421(a,1),35(a,2,2,2,2))]. % back CAC tautology: 8194 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (z v (y v (v7 v (u v (v6 v (v5 v v8))))))). [para(421(a,1),35(a,1,2,2,2))]. % back CAC tautology: 8193 x v (y v (z v (u v (w v (v5 v v6))))) = w v (v5 v (x v (z v (y v (u v v6))))). [para(34(a,2),421(a,2,2)),flip(a)]. % back CAC tautology: 8192 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v5 v (v6 v (v8 v (y v (v7 v v9)))))))). [para(34(a,2),421(a,2,2,2,2,2))]. % back CAC tautology: 8191 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (u v (z v (y v (v6 v (w v v7)))))). [para(34(a,2),421(a,1,2,2))]. % back CAC tautology: 8190 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v7 v (u v (y v (w v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,2),421(a,1,2,2,2,2))]. % back CAC tautology: 8189 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v5 v (w v (u v (v6 v (y v v7)))))). [para(34(a,1),421(a,2,2,2))]. % back CAC tautology: 8188 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v6 v (u v (y v (v7 v (v5 v v8))))))). [para(34(a,1),421(a,2,2,2,2))]. % back CAC tautology: 8187 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (u v (v7 v (y v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,1),421(a,2,2,2,2,2))]. % back CAC tautology: 8186 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v6 v (w v (y v (z v (v5 v v7)))))). [para(34(a,1),421(a,1,2,2))]. % back CAC tautology: 8185 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (w v (y v (v7 v (u v (v6 v v8))))))). [para(34(a,1),421(a,1,2,2,2))]. % back CAC tautology: 8184 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (u v (y v (v6 v (v8 v (w v (v7 v v9)))))))). [para(34(a,1),421(a,1,2,2,2,2))]. % back CAC tautology: 8183 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v5 v (v8 v (z v (v7 v (v6 v v9)))))))). [para(421(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 8182 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (v6 v (w v (v5 v (u v v7)))))). [para(421(a,2),34(a,1,2,2))]. % back CAC tautology: 8181 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v6 v (z v (w v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 8180 x v (y v (z v (u v (w v (v5 v v6))))) = u v (w v (x v (v5 v (z v (y v v6))))). [para(421(a,1),34(a,2,2))]. % back CAC tautology: 8179 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (y v (v6 v (v5 v (w v v7)))))). [para(421(a,1),34(a,2,2,2))]. % back CAC tautology: 8178 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v5 v (w v (v7 v (v6 v (z v v8))))))). [para(421(a,1),34(a,2,2,2,2))]. % back CAC tautology: 8177 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v6 v (z v (v8 v (v7 v (v5 v v9)))))))). [para(421(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 8176 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v5 v (z v (v8 v (w v (v7 v (v6 v v9)))))))). [para(421(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 8175 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (w v (y v (z v (v6 v (v5 v (u v v7)))))). [para(421(a,2),30(a,1,2,2))]. % back CAC tautology: 8174 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (u v (y v (v6 v (z v (v5 v (w v v7)))))). [para(421(a,1),30(a,1,2,2))]. % back CAC tautology: 8098 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (w v (z v (x v (u v v6))))). [para(420(a,2),420(a,2,2)),flip(a)]. % back CAC tautology: 8097 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (u v (z v (v6 v (v5 v (y v v7)))))). [para(420(a,2),420(a,2,2,2))]. % back CAC tautology: 8096 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v5 v (v6 v (v8 v (v7 v (z v v9)))))))). [para(420(a,2),420(a,2,2,2,2,2))]. % back CAC tautology: 8095 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v8 v (x v (y v (u v (z v (w v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,2),420(a,1,2,2,2,2))]. % back CAC tautology: 8094 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (v6 v (y v (u v (v5 v (z v v7)))))). [para(420(a,1),420(a,2,2,2))]. % back CAC tautology: 8093 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v7 v (u v (z v (v6 v (v5 v v8))))))). [para(420(a,1),420(a,2,2,2,2))]. % back CAC tautology: 8092 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v8 v (z v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 8091 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (w v (u v (v5 v (z v v7)))))). [para(420(a,1),420(a,1,2,2))]. % back CAC tautology: 8090 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (w v (z v (v7 v (v6 v (u v v8))))))). [para(420(a,1),420(a,1,2,2,2))]. % back CAC tautology: 8089 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (u v (z v (v6 v (v8 v (v7 v (w v v9)))))))). [para(420(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 8064 x v (y v (z v (u v (w v v5)))) = w v (x v (y v (u v (v5 v z)))). [para(6642(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 8060 x v (y v (z v (u v (w v v5)))) = v5 v (x v (y v (u v (z v w)))). [para(6642(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 8057 x v (y v (z v (u v w))) = w v (x v (y v (u v z))). [para(5887(a,1),420(a,1,2,2,2,2)),rewrite([5887(7)])]. % back CAC tautology: 8054 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v6 v (v5 v (v7 v (z v v8))))))). [para(41(a,2),420(a,2,2,2,2,2))]. % back CAC tautology: 8053 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (u v (z v (v5 v (w v (v6 v v8))))))). [para(41(a,2),420(a,1,2,2,2,2))]. % back CAC tautology: 8052 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (v5 v (u v (y v (z v v6))))). [para(41(a,1),420(a,2,2,2))]. % back CAC tautology: 8051 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v7 v (v5 v (z v (v6 v v8))))))). [para(41(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 8050 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (x v (y v (u v (z v (v5 v (v7 v (w v v8))))))). [para(41(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 8049 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (y v (z v (x v (u v (v5 v (w v v7)))))). [para(420(a,2),41(a,2,2,2)),flip(a)]. % back CAC tautology: 8048 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (w v (v5 v (v7 v (v6 v (z v v8))))))). [para(420(a,2),41(a,2,2,2,2))]. % back CAC tautology: 8047 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (y v (x v (v6 v (u v (v5 v (w v v7)))))). [para(420(a,2),41(a,1,2,2))]. % back CAC tautology: 8046 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (y v (x v (z v (u v (w v (v6 v (v5 v v8))))))). [para(420(a,2),41(a,1,2,2,2))]. % back CAC tautology: 8045 x v (y v (z v (u v (w v (v5 v v6))))) = u v (v5 v (y v (x v (w v (z v v6))))). [para(420(a,1),41(a,2,2))]. % back CAC tautology: 8044 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (v6 v (x v (z v (v5 v (w v v7)))))). [para(420(a,1),41(a,2,2,2))]. % back CAC tautology: 8043 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (v7 v (z v (w v (v6 v (v5 v v8))))))). [para(420(a,1),41(a,2,2,2,2))]. % back CAC tautology: 8042 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (z v (x v (u v (w v (y v v6))))). [para(420(a,1),41(a,1,2))]. % back CAC tautology: 8041 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (x v (u v (v6 v (v5 v (z v v7)))))). [para(420(a,1),41(a,1,2,2))]. % back CAC tautology: 8040 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (y v (x v (z v (v5 v (v7 v (v6 v (u v v8))))))). [para(420(a,1),41(a,1,2,2,2))]. % back CAC tautology: 8039 x v (y v (z v (u v (w v (v5 v v6))))) = w v (y v (v5 v (x v (u v (z v v6))))). [para(40(a,2),420(a,2,2))]. % back CAC tautology: 8038 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (u v (v6 v (y v (z v (v5 v v7)))))). [para(40(a,2),420(a,2,2,2))]. % back CAC tautology: 8037 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v5 v (v8 v (z v (v6 v (v7 v v9)))))))). [para(40(a,2),420(a,2,2,2,2,2))]. % back CAC tautology: 8036 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (u v (w v (y v (z v v6))))). [para(40(a,2),420(a,1,2))]. % back CAC tautology: 8035 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v6 v (x v (y v (u v (z v (w v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,2),420(a,1,2,2,2,2))]. % back CAC tautology: 8034 x v (y v (z v (u v (w v (v5 v v6))))) = w v (u v (x v (z v (v5 v (y v v6))))). [para(40(a,1),420(a,2,2))]. % back CAC tautology: 8033 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v5 v (u v (v6 v (v7 v (z v v8))))))). [para(40(a,1),420(a,2,2,2,2))]. % back CAC tautology: 8032 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v6 v (z v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 8031 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (w v (z v (u v (v5 v (v6 v v8))))))). [para(40(a,1),420(a,1,2,2,2))]. % back CAC tautology: 8030 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (u v (z v (v8 v (w v (v6 v (v7 v v9)))))))). [para(40(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 8029 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (w v (x v (y v (z v (u v v6))))). [para(420(a,2),40(a,2,2)),flip(a)]. % back CAC tautology: 8028 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (y v (v5 v (v7 v (v6 v (w v v8))))))). [para(420(a,2),40(a,2,2,2,2))]. % back CAC tautology: 8027 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v5 v (v6 v (v8 v (v7 v (y v v9)))))))). [para(420(a,2),40(a,2,2,2,2,2))]. % back CAC tautology: 8026 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (z v (u v (y v (v5 v (w v v7)))))). [para(420(a,2),40(a,1,2,2))]. % back CAC tautology: 8025 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (u v (y v (w v (v6 v (v5 v v8))))))). [para(420(a,2),40(a,1,2,2,2))]. % back CAC tautology: 8024 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v8 v (y v (w v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,2),40(a,1,2,2,2,2))]. % back CAC tautology: 8023 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (u v (w v (v5 v (y v v7)))))). [para(420(a,1),40(a,2,2,2))]. % back CAC tautology: 8022 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v7 v (w v (y v (v6 v (v5 v v8))))))). [para(420(a,1),40(a,2,2,2,2))]. % back CAC tautology: 8021 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v8 v (y v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 8020 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (v5 v (w v (z v (y v v6))))). [para(420(a,1),40(a,1,2))]. % back CAC tautology: 8019 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (w v (v6 v (y v (v5 v (z v v7)))))). [para(420(a,1),40(a,1,2,2))]. % back CAC tautology: 8018 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v5 v (y v (v7 v (v6 v (u v v8))))))). [para(420(a,1),40(a,1,2,2,2))]. % back CAC tautology: 8017 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v5 v (y v (v6 v (v8 v (v7 v (w v v9)))))))). [para(420(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 8016 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v5 v (z v (v7 v (v6 v v8))))))). [para(39(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 8015 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (u v (z v (w v (v7 v (v6 v v8))))))). [para(39(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 8014 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (z v (v6 v (u v (v5 v (w v v7)))))). [para(420(a,2),39(a,1,2,2))]. % back CAC tautology: 8013 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (v7 v (z v (u v (w v (v6 v (v5 v v8))))))). [para(420(a,2),39(a,1,2,2,2))]. % back CAC tautology: 8012 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (v6 v (u v (z v (v5 v (w v v7)))))). [para(420(a,1),39(a,1,2,2)),flip(a)]. % back CAC tautology: 8011 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (w v (z v (v5 v (v7 v (v6 v (u v v8))))))). [para(420(a,1),39(a,1,2,2,2))]. % back CAC tautology: 8010 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (u v (z v (x v (w v v6))))). [para(38(a,2),420(a,2,2)),flip(a)]. % back CAC tautology: 8009 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (u v (z v (v5 v (v6 v (y v v7)))))). [para(38(a,2),420(a,2,2,2))]. % back CAC tautology: 8008 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v5 v (v6 v (v7 v (v8 v (z v v9)))))))). [para(38(a,2),420(a,2,2,2,2,2))]. % back CAC tautology: 8007 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v8 v (x v (y v (u v (z v (w v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,2),420(a,1,2,2,2,2))]. % back CAC tautology: 8006 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (v6 v (y v (u v (z v (v5 v v7)))))). [para(38(a,1),420(a,2,2,2))]. % back CAC tautology: 8005 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v7 v (u v (z v (v5 v (v6 v v8))))))). [para(38(a,1),420(a,2,2,2,2))]. % back CAC tautology: 8004 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v8 v (z v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 8003 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (y v (w v (u v (v6 v (z v v7)))))). [para(38(a,1),420(a,1,2,2))]. % back CAC tautology: 8002 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (w v (z v (v6 v (v7 v (u v v8))))))). [para(38(a,1),420(a,1,2,2,2))]. % back CAC tautology: 8001 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (u v (z v (v6 v (v7 v (v8 v (w v v9)))))))). [para(38(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 8000 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (z v (w v (x v (u v v6))))). [para(420(a,2),38(a,2,2)),flip(a)]. % back CAC tautology: 7999 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (u v (v6 v (v5 v (y v v7)))))). [para(420(a,2),38(a,2,2,2))]. % back CAC tautology: 7998 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v5 v (v6 v (v8 v (v7 v (u v v9)))))))). [para(420(a,2),38(a,2,2,2,2,2))]. % back CAC tautology: 7997 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (z v (v7 v (w v (v6 v (v5 v v8))))))). [para(420(a,2),38(a,1,2,2,2))]. % back CAC tautology: 7996 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v8 v (x v (y v (z v (u v (w v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,2),38(a,1,2,2,2,2))]. % back CAC tautology: 7995 x v (y v (z v (u v (w v (v5 v v6))))) = w v (v5 v (x v (y v (u v (z v v6))))). [para(420(a,1),38(a,2,2))]. % back CAC tautology: 7994 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (v6 v (y v (z v (v5 v (u v v7)))))). [para(420(a,1),38(a,2,2,2))]. % back CAC tautology: 7993 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v7 v (z v (u v (v6 v (v5 v v8))))))). [para(420(a,1),38(a,2,2,2,2))]. % back CAC tautology: 7992 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v8 v (u v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 7991 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (u v (w v (v5 v (z v v7)))))). [para(420(a,1),38(a,1,2,2))]. % back CAC tautology: 7990 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (z v (w v (v7 v (v6 v (u v v8))))))). [para(420(a,1),38(a,1,2,2,2))]. % back CAC tautology: 7989 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (z v (u v (v6 v (v8 v (v7 v (w v v9)))))))). [para(420(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 7988 x v (y v (z v (u v (w v v5)))) = w v (u v (z v (x v (y v v5)))). [para(37(a,1),420(a,2,2))]. % back CAC tautology: 7987 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (v5 v (v6 v (u v (z v v7)))))). [para(37(a,1),420(a,2,2,2,2))]. % back CAC tautology: 7986 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v6 v (v7 v (z v (v5 v v8))))))). [para(37(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 7985 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (v5 v (z v (u v (w v v7)))))). [para(37(a,1),420(a,1,2,2,2))]. % back CAC tautology: 7984 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (x v (y v (u v (z v (v7 v (w v (v5 v v8))))))). [para(37(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 7983 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (z v (x v (y v (u v (v5 v (w v v7)))))). [para(420(a,2),37(a,1,2,2))]. % back CAC tautology: 7982 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (v7 v (x v (y v (u v (w v (v6 v (v5 v v8))))))). [para(420(a,2),37(a,1,2,2,2))]. % back CAC tautology: 7981 x v (y v (z v (u v (w v v5)))) = w v (u v (y v (z v (x v v5)))). [para(420(a,1),37(a,1))]. % back CAC tautology: 7980 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (w v (x v (y v (v6 v (v5 v (z v v7)))))). [para(420(a,1),37(a,1,2,2))]. % back CAC tautology: 7979 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (w v (x v (y v (v5 v (v7 v (v6 v (u v v8))))))). [para(420(a,1),37(a,1,2,2,2))]. % back CAC tautology: 7978 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (u v (v5 v (y v (v6 v (z v v7)))))). [para(36(a,2),420(a,2,2,2))]. % back CAC tautology: 7977 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v5 v (v7 v (z v (v8 v (v6 v v9)))))))). [para(36(a,2),420(a,2,2,2,2,2))]. % back CAC tautology: 7976 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v6 v (x v (y v (u v (z v (w v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,2),420(a,1,2,2,2,2))]. % back CAC tautology: 7975 x v (y v (z v (u v (w v (v5 v v6))))) = w v (u v (x v (v5 v (y v (z v v6))))). [para(36(a,1),420(a,2,2))]. % back CAC tautology: 7974 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v5 v (u v (v7 v (z v (v6 v v8))))))). [para(36(a,1),420(a,2,2,2,2))]. % back CAC tautology: 7973 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v6 v (z v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 7972 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (x v (y v (w v (z v (u v (v7 v (v5 v v8))))))). [para(36(a,1),420(a,1,2,2,2))]. % back CAC tautology: 7971 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (u v (z v (v7 v (w v (v8 v (v6 v v9)))))))). [para(36(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 7970 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (z v (x v (w v (y v (u v v6))))). [para(420(a,2),36(a,2,2)),flip(a)]. % back CAC tautology: 7969 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v5 v (v7 v (v6 v (y v v8))))))). [para(420(a,2),36(a,2,2,2,2))]. % back CAC tautology: 7968 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v5 v (v6 v (v8 v (v7 v (u v v9)))))))). [para(420(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 7967 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (w v (v5 v (z v (u v v6))))). [para(420(a,2),36(a,1,2))]. % back CAC tautology: 7966 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (u v (y v (z v (v5 v (w v v7)))))). [para(420(a,2),36(a,1,2,2))]. % back CAC tautology: 7965 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (y v (v7 v (w v (v6 v (v5 v v8))))))). [para(420(a,2),36(a,1,2,2,2))]. % back CAC tautology: 7964 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v8 v (y v (u v (w v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 7963 x v (y v (z v (u v (w v (v5 v v6))))) = z v (v5 v (x v (w v (u v (y v v6))))). [para(420(a,1),36(a,2,2))]. % back CAC tautology: 7962 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (w v (y v (v5 v (u v v7)))))). [para(420(a,1),36(a,2,2,2))]. % back CAC tautology: 7961 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v7 v (y v (u v (v6 v (v5 v v8))))))). [para(420(a,1),36(a,2,2,2,2))]. % back CAC tautology: 7960 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v8 v (u v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 7959 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (y v (w v (v7 v (v6 v (u v v8))))))). [para(420(a,1),36(a,1,2,2,2))]. % back CAC tautology: 7958 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (y v (u v (v6 v (v8 v (v7 v (w v v9)))))))). [para(420(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 7957 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (u v (v5 v (z v (y v v6))))). [para(35(a,2),420(a,2,2,2))]. % back CAC tautology: 7956 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v5 v (v7 v (v6 v (z v v8))))))). [para(35(a,2),420(a,2,2,2,2,2))]. % back CAC tautology: 7955 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v7 v (z v (v6 v (v5 v v8))))))). [para(35(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 7954 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (w v (z v (v5 v (u v v7)))))). [para(35(a,1),420(a,1,2,2,2))]. % back CAC tautology: 7953 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (u v (z v (v7 v (v6 v (w v v8))))))). [para(35(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 7952 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (z v (y v (x v (w v (u v v6))))). [para(420(a,2),35(a,2,2)),flip(a)]. % back CAC tautology: 7951 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (w v (v5 v (v7 v (v6 v (y v v8))))))). [para(420(a,2),35(a,2,2,2,2))]. % back CAC tautology: 7950 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (z v (y v (u v (w v (v6 v (v5 v v8))))))). [para(420(a,2),35(a,1,2,2,2))]. % back CAC tautology: 7949 x v (y v (z v (u v (w v (v5 v v6))))) = u v (v5 v (x v (z v (w v (y v v6))))). [para(420(a,1),35(a,2,2))]. % back CAC tautology: 7948 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v6 v (z v (y v (v5 v (w v v7)))))). [para(420(a,1),35(a,2,2,2))]. % back CAC tautology: 7947 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (v7 v (y v (w v (v6 v (v5 v v8))))))). [para(420(a,1),35(a,2,2,2,2))]. % back CAC tautology: 7946 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (u v (z v (w v (y v v6))))). [para(420(a,1),35(a,1,2))]. % back CAC tautology: 7945 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (u v (y v (v6 v (v5 v (z v v7)))))). [para(420(a,1),35(a,1,2,2))]. % back CAC tautology: 7944 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (z v (y v (v5 v (v7 v (v6 v (u v v8))))))). [para(420(a,1),35(a,1,2,2,2))]. % back CAC tautology: 7943 x v (y v (z v (u v (w v (v5 v v6))))) = w v (y v (v5 v (z v (x v (u v v6))))). [para(34(a,2),420(a,2,2)),flip(a)]. % back CAC tautology: 7942 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (u v (z v (v6 v (y v (v5 v v7)))))). [para(34(a,2),420(a,2,2,2))]. % back CAC tautology: 7941 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v5 v (v6 v (v8 v (z v (v7 v v9)))))))). [para(34(a,2),420(a,2,2,2,2,2))]. % back CAC tautology: 7940 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (w v (z v (y v (u v v6))))). [para(34(a,2),420(a,1,2))]. % back CAC tautology: 7939 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v7 v (x v (y v (u v (z v (w v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,2),420(a,1,2,2,2,2))]. % back CAC tautology: 7938 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (v5 v (y v (u v (v6 v (z v v7)))))). [para(34(a,1),420(a,2,2,2))]. % back CAC tautology: 7937 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v6 v (u v (z v (v7 v (v5 v v8))))))). [para(34(a,1),420(a,2,2,2,2))]. % back CAC tautology: 7936 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (u v (v7 v (z v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,1),420(a,2,2,2,2,2))]. % back CAC tautology: 7935 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (w v (u v (z v (v5 v v7)))))). [para(34(a,1),420(a,1,2,2))]. % back CAC tautology: 7934 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (w v (z v (v7 v (u v (v6 v v8))))))). [para(34(a,1),420(a,1,2,2,2))]. % back CAC tautology: 7933 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (u v (z v (v6 v (v8 v (w v (v7 v v9)))))))). [para(34(a,1),420(a,1,2,2,2,2))]. % back CAC tautology: 7932 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (w v (x v (z v (u v v6))))). [para(420(a,2),34(a,2,2)),flip(a)]. % back CAC tautology: 7931 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (w v (z v (v6 v (v5 v (y v v7)))))). [para(420(a,2),34(a,2,2,2))]. % back CAC tautology: 7930 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (z v (v5 v (v7 v (v6 v (w v v8))))))). [para(420(a,2),34(a,2,2,2,2))]. % back CAC tautology: 7929 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v5 v (v6 v (v8 v (v7 v (z v v9)))))))). [para(420(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 7928 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (u v (v6 v (v5 v (w v v7)))))). [para(420(a,2),34(a,1,2,2))]. % back CAC tautology: 7927 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (u v (z v (w v (v6 v (v5 v v8))))))). [para(420(a,2),34(a,1,2,2,2))]. % back CAC tautology: 7926 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v8 v (z v (w v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 7925 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v6 v (y v (w v (v5 v (z v v7)))))). [para(420(a,1),34(a,2,2,2))]. % back CAC tautology: 7924 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v7 v (w v (z v (v6 v (v5 v v8))))))). [para(420(a,1),34(a,2,2,2,2))]. % back CAC tautology: 7923 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v8 v (z v (v5 v (v7 v (v6 v v9)))))))). [para(420(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 7922 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (z v (w v (u v (y v v6))))). [para(420(a,1),34(a,1,2))]. % back CAC tautology: 7921 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (v6 v (u v (v5 v (z v v7)))))). [para(420(a,1),34(a,1,2,2))]. % back CAC tautology: 7920 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v5 v (z v (v7 v (v6 v (u v v8))))))). [para(420(a,1),34(a,1,2,2,2))]. % back CAC tautology: 7919 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v5 v (z v (v6 v (v8 v (v7 v (w v v9)))))))). [para(420(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 7918 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (v6 v (u v (v5 v (w v v7)))))). [para(420(a,2),29(a,1,2,2))]. % back CAC tautology: 7917 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v6 v (y v (z v (v5 v (w v v7)))))). [para(420(a,1),29(a,2,2,2))]. % back CAC tautology: 7916 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (w v (v6 v (v5 v (u v v7)))))). [para(420(a,2),27(a,2,2,2))]. % back CAC tautology: 7915 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (w v (y v (v6 v (v5 v (z v v7)))))). [para(420(a,1),27(a,1,2,2))]. % back CAC tautology: 7914 x v (y v (z v (u v (w v (v5 v v6))))) = x v (y v (v5 v (z v (w v (u v v6))))). [para(420(a,2),30(a,1,2))]. % back CAC tautology: 7913 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (v6 v (y v (z v (u v (v5 v (w v v7)))))). [para(420(a,2),30(a,1,2,2))]. % back CAC tautology: 7912 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (u v (y v (w v (v6 v (v5 v (z v v7)))))). [para(420(a,1),30(a,1,2,2))]. % back CAC tautology: 7911 x v (y v (z v (u v (w v (v5 v v6))))) = u v (z v (x v (v5 v (w v (y v v6))))). [para(420(a,1),28(a,1,2))]. % back CAC tautology: 7169 x v (y v (z v (u v w))) = u v (y v (x v (w v z))). [para(6642(a,1),41(a,2,2,2,2))]. % back CAC tautology: 7165 x v (y v (z v (u v w))) = w v (y v (x v (z v u))). [para(6642(a,1),41(a,1,2,2,2))]. % back CAC tautology: 7160 x v (y v (z v (u v (w v v5)))) = z v (x v (u v (w v (v5 v y)))). [para(6642(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 7155 x v (y v (z v (u v (w v v5)))) = z v (x v (u v (v5 v (y v w)))). [para(6642(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 7151 x v (y v (z v (u v w))) = y v (x v (w v (z v u))). [para(6642(a,1),39(a,1,2,2,2))]. % back CAC tautology: 7146 x v (y v (z v (u v (w v v5)))) = w v (x v (y v (z v (v5 v u)))). [para(6642(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 7141 x v (y v (z v (u v (w v v5)))) = v5 v (x v (y v (z v (u v w)))). [para(6642(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 7137 x v (y v (z v (u v w))) = z v (w v (x v (y v u))). [para(6642(a,1),37(a,1,2,2,2))]. % back CAC tautology: 7132 x v (y v (z v (u v (w v v5)))) = z v (x v (w v (y v (v5 v u)))). [para(6642(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 7127 x v (y v (z v (u v (w v v5)))) = z v (x v (v5 v (y v (u v w)))). [para(6642(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 7123 x v (y v (z v (u v w))) = u v (x v (z v (w v y))). [para(6642(a,1),35(a,2,2,2,2))]. % back CAC tautology: 7119 x v (y v (z v (u v w))) = w v (x v (z v (y v u))). [para(6642(a,1),35(a,1,2,2,2))]. % back CAC tautology: 7114 x v (y v (z v (u v (w v v5)))) = u v (x v (y v (w v (v5 v z)))). [para(6642(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 7109 x v (y v (z v (u v (w v v5)))) = u v (x v (y v (v5 v (z v w)))). [para(6642(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 7094 x v (y v (z v u)) = x v (u v (y v z)). [para(6642(a,1),30(a,1,2,2))]. % back CAC tautology: 6654 x v (y v (z v u)) = u v (y v (x v z)). [para(5887(a,1),41(a,1,2,2,2)),rewrite([5887(6)])]. % back CAC tautology: 6653 x v (y v (z v (u v w))) = z v (x v (u v (w v y))). [para(5887(a,1),40(a,1,2,2,2,2)),rewrite([5887(7)])]. % back CAC tautology: 6652 x v (y v (z v u)) = y v (x v (u v z)). [para(5887(a,1),39(a,1,2,2,2)),rewrite([5887(6)])]. % back CAC tautology: 6651 x v (y v (z v (u v w))) = w v (x v (y v (z v u))). [para(5887(a,1),38(a,1,2,2,2,2)),rewrite([5887(7)])]. % back CAC tautology: 6650 x v (y v (z v u)) = z v (u v (x v y)). [para(5887(a,1),37(a,1,2,2,2)),rewrite([5887(6)])]. % back CAC tautology: 6649 x v (y v (z v (u v w))) = z v (x v (w v (y v u))). [para(5887(a,1),36(a,1,2,2,2,2)),rewrite([5887(7)])]. % back CAC tautology: 6648 x v (y v (z v u)) = u v (x v (z v y)). [para(5887(a,1),35(a,1,2,2,2)),rewrite([5887(6)])]. % back CAC tautology: 6647 x v (y v (z v (u v w))) = u v (x v (y v (w v z))). [para(5887(a,1),34(a,1,2,2,2,2)),rewrite([5887(7)])]. % back CAC tautology: 6646 x v (y v (z v u)) = u v (x v (y v z)). [para(5887(a,1),29(a,1,2,2,2)),rewrite([5887(6)])]. % back CAC tautology: 6645 x v (y v (z v u)) = z v (x v (u v y)). [para(5887(a,1),27(a,1,2,2,2)),rewrite([5887(6)])]. % back CAC tautology: 6644 x v (y v z) = z v (y v x). [para(5887(a,1),28(a,1,2,2)),rewrite([5887(5)])]. % back CAC tautology: 4727 x v (y v (z v (u v (w v (v5 v v6))))) = x v (v5 v (u v (y v (z v (w v v6))))). [para(40(a,2),50(a,2,2)),rewrite([5(13),5(12),5(11),5(10),4690(18)]),flip(a)]. % back CAC tautology: 4724 x v (y v (z v (u v (w v (v5 v v6))))) = x v (v5 v (z v (y v (w v (u v v6))))). [para(40(a,1),50(a,2,2)),rewrite([5(13),5(12),5(11),5(10),4690(18)])]. % back CAC tautology: 4718 x v (y v (z v (u v (w v (v5 v v6))))) = x v (u v (v5 v (y v (w v (z v v6))))). [para(38(a,2),50(a,2,2)),rewrite([5(13),5(12),5(11),5(10),4690(18)])]. % back CAC tautology: 4716 x v (y v (z v (u v (w v (v5 v v6))))) = x v (v5 v (z v (u v (y v (w v v6))))). [para(38(a,1),50(a,2,2)),rewrite([5(13),5(12),5(11),5(10),4690(18)]),flip(a)]. % back CAC tautology: 4703 x v (y v (z v (u v (w v (v5 v v6))))) = x v (v5 v (z v (w v (u v (y v v6))))). [para(36(a,1),50(a,2,2)),rewrite([5(13),5(12),5(11),5(10),4690(18)])]. % back CAC tautology: 4693 x v (y v (z v (u v (w v (v5 v v6))))) = x v (v5 v (w v (y v (u v (z v v6))))). [para(34(a,2),50(a,2,2)),rewrite([5(13),5(12),5(11),5(10),4690(18)]),flip(a)]. % back CAC tautology: 3560 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (v5 v (w v (v6 v (z v v7)))))). [para(41(a,2),41(a,2,2,2,2))]. % back CAC tautology: 3559 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (y v (x v (z v (w v (u v (v5 v v7)))))). [para(41(a,2),41(a,1,2,2,2))]. % back CAC tautology: 3558 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (v6 v (w v (z v (v5 v v7)))))). [para(41(a,1),41(a,2,2,2,2))]. % back CAC tautology: 3557 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (y v (x v (z v (w v (v6 v (u v v7)))))). [para(41(a,1),41(a,1,2,2,2))]. % back CAC tautology: 3556 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (z v (x v (v5 v (v6 v (u v v7)))))). [para(40(a,2),41(a,2,2,2)),flip(a)]. % back CAC tautology: 3555 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (w v (v7 v (z v (v5 v (v6 v v8))))))). [para(40(a,2),41(a,2,2,2,2))]. % back CAC tautology: 3554 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (y v (x v (z v (u v (v6 v (v7 v (w v v8))))))). [para(40(a,2),41(a,1,2,2,2))]. % back CAC tautology: 3553 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (v5 v (z v (v6 v (v7 v (w v v8))))))). [para(40(a,1),41(a,2,2,2,2))]. % back CAC tautology: 3552 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (y v (x v (u v (z v (w v (v5 v v7)))))). [para(40(a,1),41(a,1,2,2))]. % back CAC tautology: 3551 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (y v (x v (z v (v7 v (u v (v5 v (v6 v v8))))))). [para(40(a,1),41(a,1,2,2,2))]. % back CAC tautology: 3550 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v6 v (v5 v (v7 v (y v v8))))))). [para(41(a,2),40(a,2,2,2,2,2))]. % back CAC tautology: 3549 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v7 v (y v (v5 v (w v (v6 v v8))))))). [para(41(a,2),40(a,1,2,2,2,2))]. % back CAC tautology: 3548 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v7 v (v5 v (y v (v6 v v8))))))). [para(41(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 3547 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v6 v (y v (v5 v (v7 v (w v v8))))))). [para(41(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 3543 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (w v (z v (v6 v (v5 v v7)))))). [para(39(a,1),41(a,2,2,2,2))]. % back CAC tautology: 3542 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (x v (z v (u v (v6 v (v5 v v7)))))). [para(39(a,1),41(a,1,2,2,2))]. % back CAC tautology: 3541 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (v6 v (z v (w v (u v (v5 v v7)))))). [para(41(a,2),39(a,1,2,2,2))]. % back CAC tautology: 3540 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (v5 v (z v (w v (v6 v (u v v7)))))). [para(41(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3539 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (y v (z v (x v (u v (w v (v5 v v7)))))). [para(38(a,2),41(a,2,2,2)),flip(a)]. % back CAC tautology: 3538 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (w v (v5 v (v6 v (v7 v (z v v8))))))). [para(38(a,2),41(a,2,2,2,2))]. % back CAC tautology: 3537 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (y v (x v (v6 v (u v (w v (v5 v v7)))))). [para(38(a,2),41(a,1,2,2))]. % back CAC tautology: 3536 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (y v (x v (z v (u v (w v (v5 v (v6 v v8))))))). [para(38(a,2),41(a,1,2,2,2))]. % back CAC tautology: 3535 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (v6 v (x v (z v (w v (v5 v v7)))))). [para(38(a,1),41(a,2,2,2))]. % back CAC tautology: 3534 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (v7 v (z v (w v (v5 v (v6 v v8))))))). [para(38(a,1),41(a,2,2,2,2))]. % back CAC tautology: 3533 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (x v (u v (v5 v (v6 v (z v v7)))))). [para(38(a,1),41(a,1,2,2))]. % back CAC tautology: 3532 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (y v (x v (z v (v5 v (v6 v (v7 v (u v v8))))))). [para(38(a,1),41(a,1,2,2,2))]. % back CAC tautology: 3531 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v6 v (v5 v (v7 v (u v v8))))))). [para(41(a,2),38(a,2,2,2,2,2))]. % back CAC tautology: 3530 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (z v (u v (v5 v (w v (v6 v v8))))))). [para(41(a,2),38(a,1,2,2,2,2))]. % back CAC tautology: 3529 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v7 v (v5 v (u v (v6 v v8))))))). [para(41(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 3528 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (x v (y v (z v (u v (v5 v (v7 v (w v v8))))))). [para(41(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 3523 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (v5 v (v6 v (z v (w v v7)))))). [para(37(a,1),41(a,2,2,2,2))]. % back CAC tautology: 3522 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (x v (w v (z v (u v v6))))). [para(37(a,1),41(a,1,2,2))]. % back CAC tautology: 3521 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (y v (x v (z v (v6 v (u v (w v v7)))))). [para(37(a,1),41(a,1,2,2,2))]. % back CAC tautology: 3520 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (v6 v (x v (y v (w v (u v (v5 v v7)))))). [para(41(a,2),37(a,1,2,2,2))]. % back CAC tautology: 3519 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (v5 v (x v (y v (w v (v6 v (u v v7)))))). [para(41(a,1),37(a,1,2,2,2))]. % back CAC tautology: 3502 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (z v (x v (v6 v (u v (v5 v v7)))))). [para(36(a,2),41(a,2,2,2)),flip(a)]. % back CAC tautology: 3501 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (w v (v6 v (z v (v7 v (v5 v v8))))))). [para(36(a,2),41(a,2,2,2,2))]. % back CAC tautology: 3500 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (y v (x v (z v (u v (v7 v (w v (v6 v v8))))))). [para(36(a,2),41(a,1,2,2,2))]. % back CAC tautology: 3499 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (v5 v (z v (v7 v (w v (v6 v v8))))))). [para(36(a,1),41(a,2,2,2,2))]. % back CAC tautology: 3498 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (y v (x v (u v (z v (v6 v (w v v7)))))). [para(36(a,1),41(a,1,2,2))]. % back CAC tautology: 3497 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (y v (x v (z v (v6 v (u v (v7 v (v5 v v8))))))). [para(36(a,1),41(a,1,2,2,2))]. % back CAC tautology: 3496 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v6 v (v5 v (v7 v (u v v8))))))). [para(41(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 3495 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (y v (u v (v5 v (w v (v6 v v8))))))). [para(41(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 3494 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v7 v (v5 v (u v (v6 v v8))))))). [para(41(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 3493 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v6 v (y v (u v (v5 v (v7 v (w v v8))))))). [para(41(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 3487 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (z v (x v (w v (u v v6))))). [para(35(a,2),41(a,2,2,2)),flip(a)]. % back CAC tautology: 3486 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (w v (v6 v (v5 v (z v v7)))))). [para(35(a,2),41(a,2,2,2,2))]. % back CAC tautology: 3485 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (y v (x v (z v (u v (v5 v (w v v7)))))). [para(35(a,2),41(a,1,2,2,2))]. % back CAC tautology: 3484 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (v6 v (z v (v5 v (w v v7)))))). [para(35(a,1),41(a,2,2,2,2))]. % back CAC tautology: 3483 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (x v (u v (w v (z v v6))))). [para(35(a,1),41(a,1,2,2))]. % back CAC tautology: 3482 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (x v (z v (v6 v (v5 v (u v v7)))))). [para(35(a,1),41(a,1,2,2,2))]. % back CAC tautology: 3481 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (v5 v (w v (v6 v (y v v7)))))). [para(41(a,2),35(a,2,2,2,2))]. % back CAC tautology: 3480 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (z v (y v (w v (u v (v5 v v7)))))). [para(41(a,2),35(a,1,2,2,2))]. % back CAC tautology: 3479 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (v6 v (w v (y v (v5 v v7)))))). [para(41(a,1),35(a,2,2,2,2))]. % back CAC tautology: 3478 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (z v (y v (w v (v6 v (u v v7)))))). [para(41(a,1),35(a,1,2,2,2))]. % back CAC tautology: 3477 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (y v (z v (x v (u v (v6 v (w v v7)))))). [para(34(a,2),41(a,2,2,2)),flip(a)]. % back CAC tautology: 3476 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (w v (v5 v (v7 v (z v (v6 v v8))))))). [para(34(a,2),41(a,2,2,2,2))]. % back CAC tautology: 3475 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (y v (x v (v5 v (u v (v6 v (w v v7)))))). [para(34(a,2),41(a,1,2,2))]. % back CAC tautology: 3474 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (y v (x v (z v (u v (w v (v7 v (v5 v v8))))))). [para(34(a,2),41(a,1,2,2,2))]. % back CAC tautology: 3473 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (v5 v (x v (z v (v6 v (w v v7)))))). [para(34(a,1),41(a,2,2,2))]. % back CAC tautology: 3472 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (y v (x v (v6 v (z v (w v (v7 v (v5 v v8))))))). [para(34(a,1),41(a,2,2,2,2))]. % back CAC tautology: 3471 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (x v (u v (v6 v (z v (v5 v v7)))))). [para(34(a,1),41(a,1,2,2))]. % back CAC tautology: 3470 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (y v (x v (z v (v5 v (v7 v (u v (v6 v v8))))))). [para(34(a,1),41(a,1,2,2,2))]. % back CAC tautology: 3469 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v6 v (v5 v (v7 v (z v v8))))))). [para(41(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 3468 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v7 v (z v (v5 v (w v (v6 v v8))))))). [para(41(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 3467 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v7 v (v5 v (z v (v6 v v8))))))). [para(41(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 3466 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v6 v (z v (v5 v (v7 v (w v v8))))))). [para(41(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 3438 x v (y v (z v (u v (w v (v5 v v6))))) = x v (v5 v (y v (u v (z v (w v v6))))). [para(41(a,2),30(a,1,2,2))]. % back CAC tautology: 3437 x v (y v (z v (u v (w v (v5 v v6))))) = x v (w v (y v (u v (v5 v (z v v6))))). [para(41(a,1),30(a,1,2,2))]. % back CAC tautology: 3436 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (x v (u v (z v (w v v6))))). [para(41(a,2),28(a,1,2,2))]. % back CAC tautology: 3435 x v (y v (z v (u v (w v (v5 v v6))))) = w v (y v (x v (u v (v5 v (z v v6))))). [para(41(a,1),28(a,1,2,2))]. % back CAC tautology: 3370 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (v6 v (u v (y v (v5 v v7)))))). [para(40(a,2),40(a,2,2,2))]. % back CAC tautology: 3369 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v5 v (v8 v (y v (v6 v (v7 v v9)))))))). [para(40(a,2),40(a,2,2,2,2,2))]. % back CAC tautology: 3368 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (u v (y v (v6 v (v7 v (w v v8))))))). [para(40(a,2),40(a,1,2,2,2))]. % back CAC tautology: 3367 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v6 v (y v (w v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,2),40(a,1,2,2,2,2))]. % back CAC tautology: 3366 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v5 v (w v (v6 v (v7 v (y v v8))))))). [para(40(a,1),40(a,2,2,2,2))]. % back CAC tautology: 3365 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v6 v (y v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 3364 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v5 v (y v (v8 v (w v (v6 v (v7 v v9)))))))). [para(40(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 3360 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v5 v (y v (v7 v (v6 v v8))))))). [para(39(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 3359 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v5 v (y v (w v (v7 v (v6 v v8))))))). [para(39(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 3358 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (v5 v (z v (u v (v6 v (v7 v (w v v8))))))). [para(40(a,2),39(a,1,2,2,2))]. % back CAC tautology: 3357 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (w v (z v (v7 v (u v (v5 v (v6 v v8))))))). [para(40(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3356 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (u v (x v (y v (z v (w v v6))))). [para(38(a,2),40(a,2,2)),flip(a)]. % back CAC tautology: 3355 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v5 v (v6 v (v7 v (v8 v (y v v9)))))))). [para(38(a,2),40(a,2,2,2,2,2))]. % back CAC tautology: 3354 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (z v (u v (y v (w v (v5 v v7)))))). [para(38(a,2),40(a,1,2,2))]. % back CAC tautology: 3353 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (u v (y v (w v (v5 v (v6 v v8))))))). [para(38(a,2),40(a,1,2,2,2))]. % back CAC tautology: 3352 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v8 v (y v (w v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,2),40(a,1,2,2,2,2))]. % back CAC tautology: 3351 x v (y v (z v (u v (w v (v5 v v6))))) = z v (v5 v (x v (u v (w v (y v v6))))). [para(38(a,1),40(a,2,2))]. % back CAC tautology: 3350 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (u v (w v (y v (v5 v v7)))))). [para(38(a,1),40(a,2,2,2))]. % back CAC tautology: 3349 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v7 v (w v (y v (v5 v (v6 v v8))))))). [para(38(a,1),40(a,2,2,2,2))]. % back CAC tautology: 3348 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v8 v (y v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 3347 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v5 v (y v (v6 v (v7 v (v8 v (w v v9)))))))). [para(38(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 3346 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v7 v (z v (v5 v (v6 v v8))))))). [para(40(a,2),38(a,2,2,2,2))]. % back CAC tautology: 3345 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v5 v (v8 v (u v (v6 v (v7 v v9)))))))). [para(40(a,2),38(a,2,2,2,2,2))]. % back CAC tautology: 3344 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (y v (w v (z v (v6 v (u v v7)))))). [para(40(a,2),38(a,1,2,2))]. % back CAC tautology: 3343 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v6 v (x v (y v (z v (u v (w v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,2),38(a,1,2,2,2,2))]. % back CAC tautology: 3342 x v (y v (z v (u v (w v (v5 v v6))))) = w v (z v (x v (u v (v5 v (y v v6))))). [para(40(a,1),38(a,2,2))]. % back CAC tautology: 3341 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v6 v (u v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 3340 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (z v (w v (u v (v5 v (v6 v v8))))))). [para(40(a,1),38(a,1,2,2,2))]. % back CAC tautology: 3339 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (z v (u v (v8 v (w v (v6 v (v7 v v9)))))))). [para(40(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 3331 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (v5 v (v6 v (w v (y v v7)))))). [para(37(a,1),40(a,2,2,2,2))]. % back CAC tautology: 3330 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v6 v (v7 v (y v (v5 v v8))))))). [para(37(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 3329 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v5 v (v6 v (y v (u v (w v v7)))))). [para(37(a,1),40(a,1,2,2,2))]. % back CAC tautology: 3328 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v6 v (y v (v7 v (w v (v5 v v8))))))). [para(37(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 3327 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (z v (x v (y v (v5 v (v6 v (u v v7)))))). [para(40(a,2),37(a,1,2,2))]. % back CAC tautology: 3326 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (v5 v (x v (y v (u v (v6 v (v7 v (w v v8))))))). [para(40(a,2),37(a,1,2,2,2))]. % back CAC tautology: 3325 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (v6 v (x v (y v (z v (w v (v5 v v7)))))). [para(40(a,1),37(a,1,2,2))]. % back CAC tautology: 3324 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (w v (x v (y v (v7 v (u v (v5 v (v6 v v8))))))). [para(40(a,1),37(a,1,2,2,2))]. % back CAC tautology: 3292 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (v5 v (u v (v6 v (y v v7)))))). [para(36(a,2),40(a,2,2,2))]. % back CAC tautology: 3291 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v5 v (v7 v (y v (v8 v (v6 v v9)))))))). [para(36(a,2),40(a,2,2,2,2,2))]. % back CAC tautology: 3290 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (v6 v (y v (u v (v5 v v7)))))). [para(36(a,2),40(a,1,2,2))]. % back CAC tautology: 3289 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (u v (y v (v7 v (w v (v6 v v8))))))). [para(36(a,2),40(a,1,2,2,2))]. % back CAC tautology: 3288 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v6 v (y v (w v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,2),40(a,1,2,2,2,2))]. % back CAC tautology: 3287 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v5 v (w v (v7 v (y v (v6 v v8))))))). [para(36(a,1),40(a,2,2,2,2))]. % back CAC tautology: 3286 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v6 v (y v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 3285 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v5 v (y v (v7 v (w v (v8 v (v6 v v9)))))))). [para(36(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 3284 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v7 v (y v (v5 v (v6 v v8))))))). [para(40(a,2),36(a,2,2,2,2))]. % back CAC tautology: 3283 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v5 v (v8 v (u v (v6 v (v7 v v9)))))))). [para(40(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 3282 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (y v (v5 v (v6 v (v7 v (w v v8))))))). [para(40(a,2),36(a,1,2,2,2))]. % back CAC tautology: 3281 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v6 v (y v (u v (w v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 3280 x v (y v (z v (u v (w v v5)))) = w v (z v (y v (u v (x v v5)))). [para(40(a,1),36(a,2))]. % back CAC tautology: 3279 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v5 v (y v (v6 v (v7 v (u v v8))))))). [para(40(a,1),36(a,2,2,2,2))]. % back CAC tautology: 3278 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v6 v (u v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 3277 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (y v (w v (u v (v5 v (v6 v v8))))))). [para(40(a,1),36(a,1,2,2,2))]. % back CAC tautology: 3276 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (y v (u v (v8 v (w v (v6 v (v7 v v9)))))))). [para(40(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 3265 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v5 v (v7 v (v6 v (y v v8))))))). [para(35(a,2),40(a,2,2,2,2,2))]. % back CAC tautology: 3264 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (u v (y v (v5 v (w v v7)))))). [para(35(a,2),40(a,1,2,2,2))]. % back CAC tautology: 3263 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v7 v (y v (w v (v6 v (v5 v v8))))))). [para(35(a,2),40(a,1,2,2,2,2))]. % back CAC tautology: 3262 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (v6 v (w v (v5 v (y v v7)))))). [para(35(a,1),40(a,2,2,2,2))]. % back CAC tautology: 3261 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v7 v (y v (v6 v (v5 v v8))))))). [para(35(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 3260 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (v5 v (w v (y v (z v v6))))). [para(35(a,1),40(a,1,2,2))]. % back CAC tautology: 3259 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v5 v (y v (v7 v (v6 v (w v v8))))))). [para(35(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 3258 x v (y v (z v (u v (w v (v5 v v6))))) = u v (w v (y v (x v (v5 v (z v v6))))). [para(40(a,2),35(a,2,2)),flip(a)]. % back CAC tautology: 3257 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (w v (v7 v (y v (v5 v (v6 v v8))))))). [para(40(a,2),35(a,2,2,2,2))]. % back CAC tautology: 3256 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (z v (y v (u v (v6 v (v7 v (w v v8))))))). [para(40(a,2),35(a,1,2,2,2))]. % back CAC tautology: 3255 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (v5 v (y v (v6 v (v7 v (w v v8))))))). [para(40(a,1),35(a,2,2,2,2))]. % back CAC tautology: 3254 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (z v (y v (v7 v (u v (v5 v (v6 v v8))))))). [para(40(a,1),35(a,1,2,2,2))]. % back CAC tautology: 3253 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v5 v (v6 v (v8 v (y v (v7 v v9)))))))). [para(34(a,2),40(a,2,2,2,2,2))]. % back CAC tautology: 3252 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (z v (u v (y v (v6 v (w v v7)))))). [para(34(a,2),40(a,1,2,2))]. % back CAC tautology: 3251 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v6 v (u v (y v (w v (v7 v (v5 v v8))))))). [para(34(a,2),40(a,1,2,2,2))]. % back CAC tautology: 3250 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v7 v (y v (w v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,2),40(a,1,2,2,2,2))]. % back CAC tautology: 3249 x v (y v (z v (u v (w v (v5 v v6))))) = z v (y v (x v (u v (v5 v (w v v6))))). [para(34(a,1),40(a,2,2))]. % back CAC tautology: 3248 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v5 v (u v (w v (v6 v (y v v7)))))). [para(34(a,1),40(a,2,2,2))]. % back CAC tautology: 3247 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v6 v (w v (y v (v7 v (v5 v v8))))))). [para(34(a,1),40(a,2,2,2,2))]. % back CAC tautology: 3246 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (w v (v7 v (y v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,1),40(a,2,2,2,2,2))]. % back CAC tautology: 3245 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (u v (v5 v (y v (v6 v (v8 v (w v (v7 v v9)))))))). [para(34(a,1),40(a,1,2,2,2,2))]. % back CAC tautology: 3244 x v (y v (z v (u v (w v (v5 v v6))))) = u v (y v (v5 v (x v (w v (z v v6))))). [para(40(a,2),34(a,2,2))]. % back CAC tautology: 3243 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (w v (v6 v (y v (z v (v5 v v7)))))). [para(40(a,2),34(a,2,2,2))]. % back CAC tautology: 3242 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v5 v (v8 v (z v (v6 v (v7 v v9)))))))). [para(40(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 3241 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (u v (z v (v6 v (v7 v (w v v8))))))). [para(40(a,2),34(a,1,2,2,2))]. % back CAC tautology: 3240 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v6 v (z v (w v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 3239 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v5 v (w v (v6 v (v7 v (z v v8))))))). [para(40(a,1),34(a,2,2,2,2))]. % back CAC tautology: 3238 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v6 v (z v (v7 v (v8 v (v5 v v9)))))))). [para(40(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 3237 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v5 v (z v (v8 v (w v (v6 v (v7 v v9)))))))). [para(40(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 3212 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (v6 v (w v (y v (v5 v v7)))))). [para(29(a,1),40(a,2,2,2,2))]. % back CAC tautology: 3203 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (v5 v (w v (v6 v (y v v7)))))). [para(27(a,1),40(a,2,2,2,2))]. % back CAC tautology: 3202 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v7 v (y v (v5 v (v6 v v8))))))). [para(40(a,2),27(a,2,2,2,2))]. % back CAC tautology: 3201 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v5 v (y v (v6 v (v7 v (w v v8))))))). [para(40(a,1),27(a,2,2,2,2))]. % back CAC tautology: 3188 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (w v (y v (z v (v5 v (v6 v (u v v7)))))). [para(40(a,2),30(a,1,2,2))]. % back CAC tautology: 3187 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (u v (y v (v6 v (z v (w v (v5 v v7)))))). [para(40(a,1),30(a,1,2,2))]. % back CAC tautology: 3186 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (x v (z v (v5 v (v6 v (u v v7)))))). [para(40(a,2),28(a,1,2,2))]. % back CAC tautology: 3185 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (v6 v (z v (w v (v5 v v7)))))). [para(40(a,1),28(a,1,2,2))]. % back CAC tautology: 3067 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (w v (z v (u v (v6 v (v5 v v7)))))). [para(39(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3066 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (z v (v6 v (u v (w v (v5 v v7)))))). [para(38(a,2),39(a,1,2,2))]. % back CAC tautology: 3065 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (v7 v (z v (u v (w v (v5 v (v6 v v8))))))). [para(38(a,2),39(a,1,2,2,2))]. % back CAC tautology: 3064 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (v6 v (u v (z v (w v (v5 v v7)))))). [para(38(a,1),39(a,1,2,2)),flip(a)]. % back CAC tautology: 3063 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (w v (z v (v5 v (v6 v (v7 v (u v v8))))))). [para(38(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3062 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v5 v (u v (v7 v (v6 v v8))))))). [para(39(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 3061 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (z v (u v (w v (v7 v (v6 v v8))))))). [para(39(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 3058 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (v5 v (z v (v6 v (u v (w v v7)))))). [para(37(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3057 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (w v (x v (y v (u v (v6 v (v5 v v7)))))). [para(39(a,1),37(a,1,2,2,2))]. % back CAC tautology: 3049 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (v5 v (z v (u v (v7 v (w v (v6 v v8))))))). [para(36(a,2),39(a,1,2,2,2))]. % back CAC tautology: 3048 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (w v (z v (v6 v (u v (v7 v (v5 v v8))))))). [para(36(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3047 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (u v (y v (v6 v (v5 v v7)))))). [para(39(a,1),36(a,2,2,2,2))]. % back CAC tautology: 3046 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v5 v (u v (v7 v (v6 v v8))))))). [para(39(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 3045 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (y v (w v (v6 v (v5 v v7)))))). [para(39(a,1),36(a,1,2,2,2))]. % back CAC tautology: 3044 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (y v (u v (w v (v7 v (v6 v v8))))))). [para(39(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 3041 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (v6 v (z v (u v (v5 v (w v v7)))))). [para(35(a,2),39(a,1,2,2,2))]. % back CAC tautology: 3040 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (v5 v (u v (w v (z v v6))))). [para(35(a,1),39(a,1,2,2))]. % back CAC tautology: 3039 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (w v (z v (v6 v (v5 v (u v v7)))))). [para(35(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3038 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (w v (y v (v6 v (v5 v v7)))))). [para(39(a,1),35(a,2,2,2,2))]. % back CAC tautology: 3037 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (y v (u v (v6 v (v5 v v7)))))). [para(39(a,1),35(a,1,2,2,2))]. % back CAC tautology: 3036 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (z v (v5 v (u v (v6 v (w v v7)))))). [para(34(a,2),39(a,1,2,2))]. % back CAC tautology: 3035 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (v6 v (z v (u v (w v (v7 v (v5 v v8))))))). [para(34(a,2),39(a,1,2,2,2))]. % back CAC tautology: 3034 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (v5 v (u v (z v (v6 v (w v v7)))))). [para(34(a,1),39(a,1,2,2)),flip(a)]. % back CAC tautology: 3033 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = y v (x v (w v (z v (v5 v (v7 v (u v (v6 v v8))))))). [para(34(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3032 x v (y v (z v (u v (w v v5)))) = x v (u v (w v (y v (z v v5)))). [para(39(a,1),34(a,2))]. % back CAC tautology: 3031 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (z v (w v (v6 v (v5 v v7)))))). [para(39(a,1),34(a,2,2,2,2))]. % back CAC tautology: 3030 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v5 v (z v (v7 v (v6 v v8))))))). [para(39(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 3029 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (u v (z v (v6 v (v5 v v7)))))). [para(39(a,1),34(a,1,2,2,2))]. % back CAC tautology: 3028 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v5 v (z v (w v (v7 v (v6 v v8))))))). [para(39(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 3020 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (v6 v (z v (u v (w v (v5 v v7)))))). [para(29(a,2),39(a,1,2,2,2))]. % back CAC tautology: 3019 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (w v (z v (v5 v (v6 v (u v v7)))))). [para(29(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3017 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (v5 v (z v (u v (v6 v (w v v7)))))). [para(27(a,2),39(a,1,2,2,2))]. % back CAC tautology: 3016 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = y v (x v (w v (z v (v6 v (u v (v5 v v7)))))). [para(27(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3015 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (w v (y v (v6 v (v5 v v7)))))). [para(39(a,1),27(a,2,2,2,2))]. % back CAC tautology: 3011 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (u v (z v (v5 v (w v v6))))). [para(30(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3010 x v (y v (z v (u v (w v (v5 v v6))))) = x v (u v (y v (z v (v5 v (w v v6))))). [para(39(a,1),30(a,1,2,2))]. % back CAC tautology: 3009 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (v5 v (z v (w v (u v v6))))). [para(28(a,1),39(a,1,2,2,2))]. % back CAC tautology: 3008 x v (y v (z v (u v (w v (v5 v v6))))) = u v (y v (x v (z v (v5 v (w v v6))))). [para(39(a,1),28(a,1,2,2))]. % back CAC tautology: 2939 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (z v (u v (x v (w v v6))))). [para(38(a,2),38(a,2,2)),flip(a)]. % back CAC tautology: 2938 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (u v (v5 v (v6 v (y v v7)))))). [para(38(a,2),38(a,2,2,2))]. % back CAC tautology: 2937 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v5 v (v6 v (v7 v (z v v8))))))). [para(38(a,2),38(a,2,2,2,2))]. % back CAC tautology: 2936 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v5 v (v6 v (v7 v (v8 v (u v v9)))))))). [para(38(a,2),38(a,2,2,2,2,2))]. % back CAC tautology: 2935 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (z v (v7 v (w v (v5 v (v6 v v8))))))). [para(38(a,2),38(a,1,2,2,2))]. % back CAC tautology: 2934 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v8 v (x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,2),38(a,1,2,2,2,2))]. % back CAC tautology: 2933 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v7 v (z v (u v (v5 v (v6 v v8))))))). [para(38(a,1),38(a,2,2,2,2))]. % back CAC tautology: 2932 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v8 v (u v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 2931 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (z v (u v (w v (y v v6))))). [para(38(a,1),38(a,1,2))]. % back CAC tautology: 2930 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (y v (u v (w v (v6 v (z v v7)))))). [para(38(a,1),38(a,1,2,2))]. % back CAC tautology: 2929 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (z v (w v (v6 v (v7 v (u v v8))))))). [para(38(a,1),38(a,1,2,2,2))]. % back CAC tautology: 2928 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (z v (u v (v6 v (v7 v (v8 v (w v v9)))))))). [para(38(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 2918 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (u v (v5 v (y v (z v v6))))). [para(37(a,1),38(a,2,2,2))]. % back CAC tautology: 2917 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (v5 v (v6 v (z v (u v v7)))))). [para(37(a,1),38(a,2,2,2,2))]. % back CAC tautology: 2916 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v6 v (v7 v (u v (v5 v v8))))))). [para(37(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 2915 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (z v (v5 v (u v (w v v7)))))). [para(37(a,1),38(a,1,2,2,2))]. % back CAC tautology: 2914 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (x v (y v (z v (u v (v7 v (w v (v5 v v8))))))). [para(37(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 2913 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (z v (x v (y v (u v (w v (v5 v v7)))))). [para(38(a,2),37(a,1,2,2))]. % back CAC tautology: 2912 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (v7 v (x v (y v (u v (w v (v5 v (v6 v v8))))))). [para(38(a,2),37(a,1,2,2,2))]. % back CAC tautology: 2911 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (w v (x v (y v (v5 v (v6 v (z v v7)))))). [para(38(a,1),37(a,1,2,2))]. % back CAC tautology: 2910 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (w v (x v (y v (v5 v (v6 v (v7 v (u v v8))))))). [para(38(a,1),37(a,1,2,2,2))]. % back CAC tautology: 2872 x v (y v (z v (u v (w v (v5 v v6))))) = w v (y v (u v (x v (v5 v (z v v6))))). [para(36(a,2),38(a,2,2))]. % back CAC tautology: 2871 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (v5 v (y v (v6 v (u v v7)))))). [para(36(a,2),38(a,2,2,2))]. % back CAC tautology: 2870 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v6 v (z v (v7 v (v5 v v8))))))). [para(36(a,2),38(a,2,2,2,2))]. % back CAC tautology: 2869 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v5 v (v7 v (u v (v8 v (v6 v v9)))))))). [para(36(a,2),38(a,2,2,2,2,2))]. % back CAC tautology: 2868 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (w v (z v (u v (v5 v v7)))))). [para(36(a,2),38(a,1,2,2))]. % back CAC tautology: 2867 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v6 v (x v (y v (z v (u v (w v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,2),38(a,1,2,2,2,2))]. % back CAC tautology: 2866 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v6 v (u v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 2865 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (z v (w v (y v (u v v6))))). [para(36(a,1),38(a,1,2))]. % back CAC tautology: 2864 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (x v (y v (z v (w v (u v (v7 v (v5 v v8))))))). [para(36(a,1),38(a,1,2,2,2))]. % back CAC tautology: 2863 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (z v (u v (v7 v (w v (v8 v (v6 v v9)))))))). [para(36(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 2862 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (z v (x v (u v (y v (w v v6))))). [para(38(a,2),36(a,2,2)),flip(a)]. % back CAC tautology: 2861 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v5 v (v6 v (v7 v (y v v8))))))). [para(38(a,2),36(a,2,2,2,2))]. % back CAC tautology: 2860 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v5 v (v6 v (v7 v (v8 v (u v v9)))))))). [para(38(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 2859 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (u v (y v (z v (w v (v5 v v7)))))). [para(38(a,2),36(a,1,2,2))]. % back CAC tautology: 2858 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (y v (v7 v (w v (v5 v (v6 v v8))))))). [para(38(a,2),36(a,1,2,2,2))]. % back CAC tautology: 2857 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v8 v (y v (u v (w v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 2856 x v (y v (z v (u v (w v (v5 v v6))))) = z v (v5 v (x v (w v (y v (u v v6))))). [para(38(a,1),36(a,2,2))]. % back CAC tautology: 2855 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (w v (y v (u v (v5 v v7)))))). [para(38(a,1),36(a,2,2,2))]. % back CAC tautology: 2854 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v7 v (y v (u v (v5 v (v6 v v8))))))). [para(38(a,1),36(a,2,2,2,2))]. % back CAC tautology: 2853 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v8 v (u v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 2852 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (y v (w v (v6 v (v7 v (u v v8))))))). [para(38(a,1),36(a,1,2,2,2))]. % back CAC tautology: 2851 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (y v (u v (v6 v (v7 v (v8 v (w v v9)))))))). [para(38(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 2839 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (u v (v6 v (v5 v (z v v7)))))). [para(35(a,2),38(a,2,2,2,2))]. % back CAC tautology: 2838 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v5 v (v7 v (v6 v (u v v8))))))). [para(35(a,2),38(a,2,2,2,2,2))]. % back CAC tautology: 2837 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (z v (u v (w v (v6 v (v5 v v8))))))). [para(35(a,2),38(a,1,2,2,2,2))]. % back CAC tautology: 2836 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (v5 v (y v (u v (z v v6))))). [para(35(a,1),38(a,2,2,2))]. % back CAC tautology: 2835 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v7 v (u v (v6 v (v5 v v8))))))). [para(35(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 2834 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (z v (w v (v5 v (u v v7)))))). [para(35(a,1),38(a,1,2,2,2))]. % back CAC tautology: 2833 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (z v (u v (v7 v (v6 v (w v v8))))))). [para(35(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 2832 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (z v (y v (x v (u v (w v v6))))). [para(38(a,2),35(a,2,2)),flip(a)]. % back CAC tautology: 2831 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (w v (v5 v (v6 v (v7 v (y v v8))))))). [para(38(a,2),35(a,2,2,2,2))]. % back CAC tautology: 2830 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (z v (y v (u v (w v (v5 v (v6 v v8))))))). [para(38(a,2),35(a,1,2,2,2))]. % back CAC tautology: 2829 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v6 v (z v (y v (w v (v5 v v7)))))). [para(38(a,1),35(a,2,2,2))]. % back CAC tautology: 2828 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (v7 v (y v (w v (v5 v (v6 v v8))))))). [para(38(a,1),35(a,2,2,2,2))]. % back CAC tautology: 2827 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (u v (z v (v5 v (y v v6))))). [para(38(a,1),35(a,1,2))]. % back CAC tautology: 2826 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (u v (y v (v5 v (v6 v (z v v7)))))). [para(38(a,1),35(a,1,2,2))]. % back CAC tautology: 2825 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (z v (y v (v5 v (v6 v (v7 v (u v v8))))))). [para(38(a,1),35(a,1,2,2,2))]. % back CAC tautology: 2824 x v (y v (z v (u v (w v (v5 v v6))))) = w v (y v (z v (v5 v (x v (u v v6))))). [para(34(a,2),38(a,2,2))]. % back CAC tautology: 2823 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (u v (v6 v (y v (v5 v v7)))))). [para(34(a,2),38(a,2,2,2))]. % back CAC tautology: 2822 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (u v (v5 v (v7 v (z v (v6 v v8))))))). [para(34(a,2),38(a,2,2,2,2))]. % back CAC tautology: 2821 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v5 v (v6 v (v8 v (u v (v7 v v9)))))))). [para(34(a,2),38(a,2,2,2,2,2))]. % back CAC tautology: 2820 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v7 v (x v (y v (z v (u v (w v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,2),38(a,1,2,2,2,2))]. % back CAC tautology: 2819 x v (y v (z v (u v (w v (v5 v v6))))) = w v (u v (x v (y v (v5 v (z v v6))))). [para(34(a,1),38(a,2,2))]. % back CAC tautology: 2818 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (v5 v (y v (z v (v6 v (u v v7)))))). [para(34(a,1),38(a,2,2,2))]. % back CAC tautology: 2817 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = w v (x v (y v (z v (v7 v (u v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 2816 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (u v (w v (z v (v5 v v7)))))). [para(34(a,1),38(a,1,2,2))]. % back CAC tautology: 2815 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (z v (w v (v7 v (u v (v6 v v8))))))). [para(34(a,1),38(a,1,2,2,2))]. % back CAC tautology: 2814 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = v5 v (x v (y v (z v (u v (v6 v (v8 v (w v (v7 v v9)))))))). [para(34(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 2813 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (u v (x v (z v (w v v6))))). [para(38(a,2),34(a,2,2)),flip(a)]. % back CAC tautology: 2812 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (w v (z v (v5 v (v6 v (y v v7)))))). [para(38(a,2),34(a,2,2,2))]. % back CAC tautology: 2811 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (z v (v5 v (v6 v (v7 v (w v v8))))))). [para(38(a,2),34(a,2,2,2,2))]. % back CAC tautology: 2810 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v5 v (v6 v (v7 v (v8 v (z v v9)))))))). [para(38(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 2809 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (u v (z v (w v (v5 v (v6 v v8))))))). [para(38(a,2),34(a,1,2,2,2))]. % back CAC tautology: 2808 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v8 v (z v (w v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 2807 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v7 v (w v (z v (v5 v (v6 v v8))))))). [para(38(a,1),34(a,2,2,2,2))]. % back CAC tautology: 2806 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v8 v (z v (v5 v (v6 v (v7 v v9)))))))). [para(38(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 2805 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (z v (v5 v (u v (y v v6))))). [para(38(a,1),34(a,1,2))]. % back CAC tautology: 2804 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (v5 v (u v (v6 v (z v v7)))))). [para(38(a,1),34(a,1,2,2))]. % back CAC tautology: 2803 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v5 v (z v (v6 v (v7 v (u v v8))))))). [para(38(a,1),34(a,1,2,2,2))]. % back CAC tautology: 2802 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v5 v (z v (v6 v (v7 v (v8 v (w v v9)))))))). [para(38(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 2772 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v7 v (u v (v5 v (v6 v v8))))))). [para(29(a,1),38(a,2,2,2,2,2))]. % back CAC tautology: 2771 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (y v (z v (w v (v6 v (u v v7)))))). [para(29(a,1),38(a,1,2,2,2))]. % back CAC tautology: 2770 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (z v (u v (v6 v (v7 v (w v v8))))))). [para(29(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 2769 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (z v (x v (u v (w v v6))))). [para(38(a,2),29(a,2,2)),flip(a)]. % back CAC tautology: 2768 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (v6 v (u v (w v (v5 v v7)))))). [para(38(a,2),29(a,1,2,2))]. % back CAC tautology: 2767 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v7 v (x v (y v (z v (u v (w v (v5 v (v6 v v8))))))). [para(38(a,2),29(a,1,2,2,2))]. % back CAC tautology: 2766 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v6 v (y v (z v (w v (v5 v v7)))))). [para(38(a,1),29(a,2,2,2))]. % back CAC tautology: 2765 x v (y v (z v (u v (w v v5)))) = w v (y v (z v (u v (x v v5)))). [para(38(a,1),29(a,1))]. % back CAC tautology: 2764 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (z v (u v (v5 v (y v v6))))). [para(38(a,1),29(a,1,2))]. % back CAC tautology: 2763 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (u v (v5 v (v6 v (z v v7)))))). [para(38(a,1),29(a,1,2,2))]. % back CAC tautology: 2762 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v5 v (v6 v (v7 v (u v v8))))))). [para(38(a,1),29(a,1,2,2,2))]. % back CAC tautology: 2752 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (z v (v5 v (y v (u v v6))))). [para(27(a,2),38(a,2,2,2))]. % back CAC tautology: 2751 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (z v (w v (u v (v5 v v7)))))). [para(27(a,1),38(a,1,2,2,2))]. % back CAC tautology: 2750 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (w v (v5 v (v6 v (u v v7)))))). [para(38(a,2),27(a,2,2,2))]. % back CAC tautology: 2749 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v5 v (v6 v (v7 v (y v v8))))))). [para(38(a,2),27(a,2,2,2,2))]. % back CAC tautology: 2748 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (u v (y v (w v (v5 v v7)))))). [para(38(a,1),27(a,2,2,2))]. % back CAC tautology: 2747 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v7 v (y v (w v (v5 v (v6 v v8))))))). [para(38(a,1),27(a,2,2,2,2))]. % back CAC tautology: 2746 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (w v (y v (v5 v (v6 v (z v v7)))))). [para(38(a,1),27(a,1,2,2))]. % back CAC tautology: 2732 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (z v (u v (v6 v (v5 v v7)))))). [para(30(a,1),38(a,1,2,2,2,2))]. % back CAC tautology: 2731 x v (y v (z v (u v (w v (v5 v v6))))) = x v (y v (v5 v (z v (u v (w v v6))))). [para(38(a,2),30(a,1,2))]. % back CAC tautology: 2730 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (v6 v (y v (z v (u v (w v (v5 v v7)))))). [para(38(a,2),30(a,1,2,2))]. % back CAC tautology: 2729 x v (y v (z v (u v (w v (v5 v v6))))) = x v (v5 v (z v (y v (u v (w v v6))))). [para(38(a,1),30(a,1,2)),flip(a)]. % back CAC tautology: 2728 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (u v (y v (w v (v5 v (v6 v (z v v7)))))). [para(38(a,1),30(a,1,2,2))]. % back CAC tautology: 2727 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (y v (x v (z v (u v (w v (v5 v v7)))))). [para(38(a,2),28(a,1,2,2))]. % back CAC tautology: 2726 x v (y v (z v (u v (w v (v5 v v6))))) = u v (z v (x v (w v (v5 v (y v v6))))). [para(38(a,1),28(a,1,2))]. % back CAC tautology: 2725 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (w v (v5 v (v6 v (z v v7)))))). [para(38(a,1),28(a,1,2,2))]. % back CAC tautology: 2668 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (v5 v (z v (u v (w v v6))))). [para(38(a,2),18(a,1,2))]. % back CAC tautology: 2349 x v (y v (z v (u v (w v (v5 v v6))))) = w v (v5 v (x v (y v (z v (u v v6))))). [para(37(a,1),37(a,1,2,2))]. % back CAC tautology: 2348 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (v5 v (x v (y v (v6 v (u v (w v v7)))))). [para(37(a,1),37(a,1,2,2,2))]. % back CAC tautology: 2336 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (z v (x v (y v (v6 v (u v (v5 v v7)))))). [para(36(a,2),37(a,1,2,2))]. % back CAC tautology: 2335 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (v5 v (x v (y v (u v (v7 v (w v (v6 v v8))))))). [para(36(a,2),37(a,1,2,2,2))]. % back CAC tautology: 2334 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (v5 v (x v (y v (z v (v6 v (w v v7)))))). [para(36(a,1),37(a,1,2,2))]. % back CAC tautology: 2333 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (w v (x v (y v (v6 v (u v (v7 v (v5 v v8))))))). [para(36(a,1),37(a,1,2,2,2))]. % back CAC tautology: 2332 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (v5 v (v6 v (y v (u v v7)))))). [para(37(a,1),36(a,2,2,2,2))]. % back CAC tautology: 2331 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v6 v (v7 v (u v (v5 v v8))))))). [para(37(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 2330 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (y v (v5 v (u v (w v v7)))))). [para(37(a,1),36(a,1,2,2,2))]. % back CAC tautology: 2329 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v6 v (y v (u v (v7 v (w v (v5 v v8))))))). [para(37(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 2325 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (z v (x v (y v (w v (u v v6))))). [para(35(a,2),37(a,1,2,2))]. % back CAC tautology: 2324 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (v6 v (x v (y v (u v (v5 v (w v v7)))))). [para(35(a,2),37(a,1,2,2,2))]. % back CAC tautology: 2323 x v (y v (z v (u v (w v (v5 v v6))))) = u v (v5 v (x v (y v (w v (z v v6))))). [para(35(a,1),37(a,1,2,2))]. % back CAC tautology: 2322 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (w v (x v (y v (v6 v (v5 v (u v v7)))))). [para(35(a,1),37(a,1,2,2,2))]. % back CAC tautology: 2321 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (v5 v (v6 v (y v (w v v7)))))). [para(37(a,1),35(a,2,2,2,2))]. % back CAC tautology: 2320 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (z v (y v (v6 v (u v (w v v7)))))). [para(37(a,1),35(a,1,2,2,2))]. % back CAC tautology: 2319 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (z v (x v (y v (u v (v6 v (w v v7)))))). [para(34(a,2),37(a,1,2,2))]. % back CAC tautology: 2318 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (v6 v (x v (y v (u v (w v (v7 v (v5 v v8))))))). [para(34(a,2),37(a,1,2,2,2))]. % back CAC tautology: 2317 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (w v (x v (y v (v6 v (z v (v5 v v7)))))). [para(34(a,1),37(a,1,2,2))]. % back CAC tautology: 2316 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (w v (x v (y v (v5 v (v7 v (u v (v6 v v8))))))). [para(34(a,1),37(a,1,2,2,2))]. % back CAC tautology: 2315 x v (y v (z v (u v (w v v5)))) = u v (w v (z v (x v (y v v5)))). [para(37(a,1),34(a,2,2))]. % back CAC tautology: 2314 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (v5 v (v6 v (w v (z v v7)))))). [para(37(a,1),34(a,2,2,2,2))]. % back CAC tautology: 2313 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v6 v (v7 v (z v (v5 v v8))))))). [para(37(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 2312 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (y v (v6 v (z v (u v (w v v7)))))). [para(37(a,1),34(a,1,2,2,2))]. % back CAC tautology: 2311 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v6 v (z v (v7 v (w v (v5 v v8))))))). [para(37(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 2294 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (z v (x v (y v (u v (w v v6))))). [para(29(a,2),37(a,1,2,2))]. % back CAC tautology: 2293 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (v6 v (x v (y v (u v (w v (v5 v v7)))))). [para(29(a,2),37(a,1,2,2,2))]. % back CAC tautology: 2292 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (w v (x v (y v (v5 v (v6 v (u v v7)))))). [para(29(a,1),37(a,1,2,2,2))]. % back CAC tautology: 2291 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (v5 v (v6 v (z v (w v v7)))))). [para(37(a,1),29(a,2,2,2,2))]. % back CAC tautology: 2290 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (y v (z v (v6 v (u v (w v v7)))))). [para(37(a,1),29(a,1,2,2,2))]. % back CAC tautology: 2286 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (v5 v (x v (y v (u v (v6 v (w v v7)))))). [para(27(a,2),37(a,1,2,2,2))]. % back CAC tautology: 2285 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (w v (x v (y v (v6 v (u v (v5 v v7)))))). [para(27(a,1),37(a,1,2,2,2))]. % back CAC tautology: 2284 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (v5 v (v6 v (y v (w v v7)))))). [para(37(a,1),27(a,2,2,2,2))]. % back CAC tautology: 2283 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v5 v (y v (v6 v (u v (w v v7)))))). [para(37(a,1),27(a,1,2,2,2))]. % back CAC tautology: 2278 x v (y v (z v (u v (w v (v5 v v6))))) = z v (u v (x v (y v (v5 v (w v v6))))). [para(30(a,1),37(a,1,2,2,2))]. % back CAC tautology: 2277 x v (y v (z v (u v (w v (v5 v v6))))) = x v (w v (y v (v5 v (z v (u v v6))))). [para(37(a,1),30(a,1,2,2))]. % back CAC tautology: 2276 x v (y v (z v (u v (w v (v5 v v6))))) = z v (v5 v (x v (y v (w v (u v v6))))). [para(28(a,1),37(a,1,2,2,2))]. % back CAC tautology: 2275 x v (y v (z v (u v (w v (v5 v v6))))) = w v (y v (x v (v5 v (z v (u v v6))))). [para(37(a,1),28(a,1,2,2))]. % back CAC tautology: 2002 x v (y v (z v (u v (w v (v5 v v6))))) = u v (v5 v (x v (z v (y v (w v v6))))). [para(36(a,2),36(a,2,2)),flip(a)]. % back CAC tautology: 2001 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (v5 v (w v (v6 v (u v v7)))))). [para(36(a,2),36(a,2,2,2))]. % back CAC tautology: 2000 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v6 v (y v (v7 v (v5 v v8))))))). [para(36(a,2),36(a,2,2,2,2))]. % back CAC tautology: 1999 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v5 v (v7 v (u v (v8 v (v6 v v9)))))))). [para(36(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 1998 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (z v (u v (v5 v (w v v6))))). [para(36(a,2),36(a,1,2))]. % back CAC tautology: 1997 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (v6 v (y v (z v (u v (v5 v v7)))))). [para(36(a,2),36(a,1,2,2))]. % back CAC tautology: 1996 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (y v (v5 v (v7 v (w v (v6 v v8))))))). [para(36(a,2),36(a,1,2,2,2))]. % back CAC tautology: 1995 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v6 v (y v (u v (w v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 1994 x v (y v (z v (u v (w v v5)))) = w v (z v (u v (x v (y v v5)))). [para(36(a,1),36(a,2))]. % back CAC tautology: 1993 x v (y v (z v (u v (w v (v5 v v6))))) = z v (y v (x v (v5 v (w v (u v v6))))). [para(36(a,1),36(a,2,2))]. % back CAC tautology: 1992 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v5 v (y v (v7 v (u v (v6 v v8))))))). [para(36(a,1),36(a,2,2,2,2))]. % back CAC tautology: 1991 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v6 v (u v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 1990 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (v5 v (z v (y v (u v v6))))). [para(36(a,1),36(a,1,2))]. % back CAC tautology: 1989 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (y v (v5 v (v6 v (w v v7)))))). [para(36(a,1),36(a,1,2,2))]. % back CAC tautology: 1988 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v6 v (y v (w v (u v (v7 v (v5 v v8))))))). [para(36(a,1),36(a,1,2,2,2))]. % back CAC tautology: 1987 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (y v (u v (v7 v (w v (v8 v (v6 v v9)))))))). [para(36(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 1976 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (u v (v6 v (v5 v (y v v7)))))). [para(35(a,2),36(a,2,2,2,2))]. % back CAC tautology: 1975 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v5 v (v7 v (v6 v (u v v8))))))). [para(35(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 1974 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (w v (y v (z v (u v v6))))). [para(35(a,2),36(a,1,2,2))]. % back CAC tautology: 1973 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (y v (v6 v (v5 v (w v v7)))))). [para(35(a,2),36(a,1,2,2,2))]. % back CAC tautology: 1972 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (y v (u v (w v (v6 v (v5 v v8))))))). [para(35(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 1971 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (v5 v (w v (u v (y v v6))))). [para(35(a,1),36(a,2,2,2))]. % back CAC tautology: 1970 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (v6 v (y v (v5 v (u v v7)))))). [para(35(a,1),36(a,2,2,2,2))]. % back CAC tautology: 1969 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v7 v (u v (v6 v (v5 v v8))))))). [para(35(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 1968 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (y v (w v (v5 v (u v v7)))))). [para(35(a,1),36(a,1,2,2,2))]. % back CAC tautology: 1967 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (y v (u v (v7 v (v6 v (w v v8))))))). [para(35(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 1966 x v (y v (z v (u v (w v (v5 v v6))))) = u v (v5 v (y v (x v (z v (w v v6))))). [para(36(a,2),35(a,2,2)),flip(a)]. % back CAC tautology: 1965 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (w v (v6 v (y v (v7 v (v5 v v8))))))). [para(36(a,2),35(a,2,2,2,2))]. % back CAC tautology: 1964 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (z v (y v (u v (v7 v (w v (v6 v v8))))))). [para(36(a,2),35(a,1,2,2,2))]. % back CAC tautology: 1963 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (v5 v (y v (v7 v (w v (v6 v v8))))))). [para(36(a,1),35(a,2,2,2,2))]. % back CAC tautology: 1962 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (z v (y v (v6 v (u v (v7 v (v5 v v8))))))). [para(36(a,1),35(a,1,2,2,2))]. % back CAC tautology: 1961 x v (y v (z v (u v (w v (v5 v v6))))) = w v (z v (x v (v5 v (y v (u v v6))))). [para(34(a,2),36(a,2,2)),flip(a)]. % back CAC tautology: 1960 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (u v (v6 v (w v (v5 v v7)))))). [para(34(a,2),36(a,2,2,2))]. % back CAC tautology: 1959 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (u v (v5 v (v7 v (y v (v6 v v8))))))). [para(34(a,2),36(a,2,2,2,2))]. % back CAC tautology: 1958 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v5 v (v6 v (v8 v (u v (v7 v v9)))))))). [para(34(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 1957 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (v5 v (w v (z v (u v v6))))). [para(34(a,2),36(a,1,2))]. % back CAC tautology: 1956 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (u v (y v (z v (v6 v (w v v7)))))). [para(34(a,2),36(a,1,2,2))]. % back CAC tautology: 1955 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (y v (v6 v (w v (v7 v (v5 v v8))))))). [para(34(a,2),36(a,1,2,2,2))]. % back CAC tautology: 1954 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v7 v (y v (u v (w v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 1953 x v (y v (z v (u v (w v (v5 v v6))))) = z v (v5 v (x v (y v (u v (w v v6))))). [para(34(a,1),36(a,2,2)),flip(a)]. % back CAC tautology: 1952 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v5 v (w v (y v (v6 v (u v v7)))))). [para(34(a,1),36(a,2,2,2))]. % back CAC tautology: 1951 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (v6 v (y v (u v (v7 v (v5 v v8))))))). [para(34(a,1),36(a,2,2,2,2))]. % back CAC tautology: 1950 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (w v (y v (v7 v (u v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 1949 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v6 v (y v (w v (z v (v5 v v7)))))). [para(34(a,1),36(a,1,2,2))]. % back CAC tautology: 1948 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (y v (w v (v7 v (u v (v6 v v8))))))). [para(34(a,1),36(a,1,2,2,2))]. % back CAC tautology: 1947 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = z v (x v (v5 v (y v (u v (v6 v (v8 v (w v (v7 v v9)))))))). [para(34(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 1946 x v (y v (z v (u v (w v v5)))) = x v (w v (u v (z v (y v v5)))). [para(36(a,2),34(a,2))]. % back CAC tautology: 1945 x v (y v (z v (u v (w v (v5 v v6))))) = u v (y v (z v (x v (v5 v (w v v6))))). [para(36(a,2),34(a,2,2))]. % back CAC tautology: 1944 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (w v (v5 v (y v (v6 v (z v v7)))))). [para(36(a,2),34(a,2,2,2))]. % back CAC tautology: 1943 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (z v (v6 v (w v (v7 v (v5 v v8))))))). [para(36(a,2),34(a,2,2,2,2))]. % back CAC tautology: 1942 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v5 v (v7 v (z v (v8 v (v6 v v9)))))))). [para(36(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 1941 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (v6 v (w v (u v (v5 v v7)))))). [para(36(a,2),34(a,1,2,2))]. % back CAC tautology: 1940 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (u v (z v (v7 v (w v (v6 v v8))))))). [para(36(a,2),34(a,1,2,2,2))]. % back CAC tautology: 1939 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v6 v (z v (w v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 1938 x v (y v (z v (u v (w v (v5 v v6))))) = u v (w v (x v (v5 v (y v (z v v6))))). [para(36(a,1),34(a,2,2))]. % back CAC tautology: 1937 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (y v (v6 v (w v (v5 v v7)))))). [para(36(a,1),34(a,2,2,2))]. % back CAC tautology: 1936 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v5 v (w v (v7 v (z v (v6 v v8))))))). [para(36(a,1),34(a,2,2,2,2))]. % back CAC tautology: 1935 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v6 v (z v (v8 v (v5 v (v7 v v9)))))))). [para(36(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 1934 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (z v (v5 v (w v (u v v6))))). [para(36(a,1),34(a,1,2))]. % back CAC tautology: 1933 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v6 v (z v (u v (v7 v (v5 v v8))))))). [para(36(a,1),34(a,1,2,2,2))]. % back CAC tautology: 1932 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v5 v (z v (v7 v (w v (v8 v (v6 v v9)))))))). [para(36(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 1910 x v (y v (z v (u v (w v v5)))) = w v (y v (u v (z v (x v v5)))). [para(36(a,1),45(a,2)),rewrite([5(12),5(11),5(10),5(9),1442(16)])]. % back CAC tautology: 1901 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (u v (v5 v (v6 v (y v v7)))))). [para(29(a,2),36(a,2,2,2,2))]. % back CAC tautology: 1900 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v5 v (v6 v (v7 v (u v v8))))))). [para(29(a,2),36(a,2,2,2,2,2))]. % back CAC tautology: 1899 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (y v (v6 v (w v (v5 v v7)))))). [para(29(a,2),36(a,1,2,2,2))]. % back CAC tautology: 1898 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v7 v (y v (u v (w v (v5 v (v6 v v8))))))). [para(29(a,2),36(a,1,2,2,2,2))]. % back CAC tautology: 1897 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (v5 v (w v (y v (u v v6))))). [para(29(a,1),36(a,2,2,2))]. % back CAC tautology: 1896 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (v6 v (y v (u v (v5 v v7)))))). [para(29(a,1),36(a,2,2,2,2))]. % back CAC tautology: 1895 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v7 v (u v (v5 v (v6 v v8))))))). [para(29(a,1),36(a,2,2,2,2,2))]. % back CAC tautology: 1894 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v5 v (y v (w v (v6 v (u v v7)))))). [para(29(a,1),36(a,1,2,2,2))]. % back CAC tautology: 1893 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (y v (u v (v6 v (v7 v (w v v8))))))). [para(29(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 1892 x v (y v (z v (u v (w v (v5 v v6))))) = u v (y v (v5 v (x v (z v (w v v6))))). [para(36(a,2),29(a,2,2)),flip(a)]. % back CAC tautology: 1891 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v5 v (x v (y v (z v (u v (v7 v (w v (v6 v v8))))))). [para(36(a,2),29(a,1,2,2,2))]. % back CAC tautology: 1890 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v6 v (u v (v7 v (v5 v v8))))))). [para(36(a,1),29(a,1,2,2,2))]. % back CAC tautology: 1881 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (v5 v (y v (z v (u v v6))))). [para(27(a,2),36(a,1,2,2))]. % back CAC tautology: 1880 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (y v (v5 v (v6 v (w v v7)))))). [para(27(a,2),36(a,1,2,2,2))]. % back CAC tautology: 1879 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (v5 v (y v (v6 v (u v v7)))))). [para(27(a,1),36(a,2,2,2,2))]. % back CAC tautology: 1878 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (y v (w v (u v (v5 v v7)))))). [para(27(a,1),36(a,1,2,2,2))]. % back CAC tautology: 1877 x v (y v (z v (u v (w v (v5 v v6))))) = u v (v5 v (x v (y v (z v (w v v6))))). [para(36(a,2),27(a,2,2)),flip(a)]. % back CAC tautology: 1876 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v6 v (y v (v7 v (v5 v v8))))))). [para(36(a,2),27(a,2,2,2,2))]. % back CAC tautology: 1875 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (v5 v (u v (z v (w v v6))))). [para(36(a,2),27(a,1,2))]. % back CAC tautology: 1874 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v5 v (y v (u v (v7 v (w v (v6 v v8))))))). [para(36(a,2),27(a,1,2,2,2))]. % back CAC tautology: 1873 x v (y v (z v (u v (w v (v5 v v6))))) = z v (y v (x v (v5 v (u v (w v v6))))). [para(36(a,1),27(a,2,2))]. % back CAC tautology: 1872 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (u v (v6 v (y v (v5 v v7)))))). [para(36(a,1),27(a,2,2,2))]. % back CAC tautology: 1871 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v5 v (y v (v7 v (w v (v6 v v8))))))). [para(36(a,1),27(a,2,2,2,2))]. % back CAC tautology: 1870 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v6 v (u v (v7 v (v5 v v8))))))). [para(36(a,1),27(a,1,2,2,2))]. % back CAC tautology: 1858 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (y v (u v (v6 v (v5 v v7)))))). [para(30(a,1),36(a,1,2,2,2,2))]. % back CAC tautology: 1857 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (w v (y v (z v (v6 v (u v (v5 v v7)))))). [para(36(a,2),30(a,1,2,2))]. % back CAC tautology: 1856 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (u v (y v (v5 v (z v (v6 v (w v v7)))))). [para(36(a,1),30(a,1,2,2))]. % back CAC tautology: 1855 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (w v (v5 v (u v (y v v6))))). [para(28(a,1),36(a,2,2,2,2))]. % back CAC tautology: 1854 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (y v (x v (z v (v6 v (u v (v5 v v7)))))). [para(36(a,2),28(a,1,2,2))]. % back CAC tautology: 1853 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (v5 v (z v (v6 v (w v v7)))))). [para(36(a,1),28(a,1,2,2))]. % back CAC tautology: 1691 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (w v (v6 v (v5 v (y v v7)))))). [para(35(a,2),35(a,2,2,2,2))]. % back CAC tautology: 1690 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (z v (y v (u v (v5 v (w v v7)))))). [para(35(a,2),35(a,1,2,2,2))]. % back CAC tautology: 1689 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (v5 v (z v (w v (y v v6))))). [para(35(a,1),35(a,2,2,2))]. % back CAC tautology: 1688 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (v6 v (y v (v5 v (w v v7)))))). [para(35(a,1),35(a,2,2,2,2))]. % back CAC tautology: 1687 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (u v (y v (w v (z v v6))))). [para(35(a,1),35(a,1,2,2))]. % back CAC tautology: 1686 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (y v (v6 v (v5 v (u v v7)))))). [para(35(a,1),35(a,1,2,2,2))]. % back CAC tautology: 1685 x v (y v (z v (u v (w v (v5 v v6))))) = w v (z v (y v (x v (v5 v (u v v6))))). [para(34(a,2),35(a,2,2)),flip(a)]. % back CAC tautology: 1684 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (w v (v5 v (v7 v (y v (v6 v v8))))))). [para(34(a,2),35(a,2,2,2,2))]. % back CAC tautology: 1683 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (x v (z v (y v (u v (w v (v7 v (v5 v v8))))))). [para(34(a,2),35(a,1,2,2,2))]. % back CAC tautology: 1682 x v (y v (z v (u v (w v (v5 v v6))))) = u v (w v (x v (z v (v5 v (y v v6))))). [para(34(a,1),35(a,2,2))]. % back CAC tautology: 1681 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v5 v (z v (y v (v6 v (w v v7)))))). [para(34(a,1),35(a,2,2,2))]. % back CAC tautology: 1680 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (z v (v6 v (y v (w v (v7 v (v5 v v8))))))). [para(34(a,1),35(a,2,2,2,2))]. % back CAC tautology: 1679 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (u v (z v (y v (w v v6))))). [para(34(a,1),35(a,1,2))]. % back CAC tautology: 1678 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (u v (y v (v6 v (z v (v5 v v7)))))). [para(34(a,1),35(a,1,2,2))]. % back CAC tautology: 1677 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (z v (y v (v5 v (v7 v (u v (v6 v v8))))))). [para(34(a,1),35(a,1,2,2,2))]. % back CAC tautology: 1676 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (w v (v5 v (z v (y v v6))))). [para(35(a,2),34(a,2,2,2))]. % back CAC tautology: 1675 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (z v (v6 v (v5 v (w v v7)))))). [para(35(a,2),34(a,2,2,2,2))]. % back CAC tautology: 1674 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v5 v (v7 v (v6 v (z v v8))))))). [para(35(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 1673 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (u v (z v (v5 v (w v v7)))))). [para(35(a,2),34(a,1,2,2,2))]. % back CAC tautology: 1672 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v7 v (z v (w v (v6 v (v5 v v8))))))). [para(35(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 1671 x v (y v (z v (u v (w v v5)))) = w v (u v (y v (x v (z v v5)))). [para(35(a,1),34(a,2))]. % back CAC tautology: 1670 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (v6 v (w v (v5 v (z v v7)))))). [para(35(a,1),34(a,2,2,2,2))]. % back CAC tautology: 1669 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v7 v (z v (v6 v (v5 v v8))))))). [para(35(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 1668 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (y v (w v (u v (z v v6))))). [para(35(a,1),34(a,1,2,2))]. % back CAC tautology: 1667 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (v6 v (z v (v5 v (u v v7)))))). [para(35(a,1),34(a,1,2,2,2))]. % back CAC tautology: 1666 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v5 v (z v (v7 v (v6 v (w v v8))))))). [para(35(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 1639 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (w v (v5 v (v6 v (y v v7)))))). [para(29(a,2),35(a,2,2,2,2))]. % back CAC tautology: 1638 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (z v (y v (u v (w v (v5 v v7)))))). [para(29(a,2),35(a,1,2,2,2))]. % back CAC tautology: 1637 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (v6 v (y v (w v (v5 v v7)))))). [para(29(a,1),35(a,2,2,2,2))]. % back CAC tautology: 1636 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (u v (y v (v5 v (z v v6))))). [para(29(a,1),35(a,1,2,2))]. % back CAC tautology: 1635 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (y v (v5 v (v6 v (u v v7)))))). [para(29(a,1),35(a,1,2,2,2))]. % back CAC tautology: 1634 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (z v (u v (v5 v (w v v7)))))). [para(35(a,2),29(a,1,2,2,2))]. % back CAC tautology: 1633 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (y v (u v (w v (z v v6))))). [para(35(a,1),29(a,1,2,2))]. % back CAC tautology: 1632 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (z v (v6 v (v5 v (u v v7)))))). [para(35(a,1),29(a,1,2,2,2))]. % back CAC tautology: 1625 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (v5 v (y v (v6 v (w v v7)))))). [para(27(a,1),35(a,2,2,2,2))]. % back CAC tautology: 1624 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (u v (y v (z v (w v v6))))). [para(27(a,1),35(a,1,2,2))]. % back CAC tautology: 1623 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (z v (y v (v6 v (u v (v5 v v7)))))). [para(27(a,1),35(a,1,2,2,2))]. % back CAC tautology: 1622 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (w v (v6 v (v5 v (y v v7)))))). [para(35(a,2),27(a,2,2,2,2))]. % back CAC tautology: 1621 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (y v (u v (v5 v (w v v7)))))). [para(35(a,2),27(a,1,2,2,2))]. % back CAC tautology: 1620 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (v5 v (u v (w v (y v v6))))). [para(35(a,1),27(a,2,2,2))]. % back CAC tautology: 1619 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (v6 v (y v (v5 v (w v v7)))))). [para(35(a,1),27(a,2,2,2,2))]. % back CAC tautology: 1618 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (y v (v6 v (v5 v (u v v7)))))). [para(35(a,1),27(a,1,2,2,2))]. % back CAC tautology: 1607 x v (y v (z v (u v (w v (v5 v v6))))) = x v (v5 v (y v (z v (w v (u v v6))))). [para(35(a,2),30(a,1,2,2))]. % back CAC tautology: 1606 x v (y v (z v (u v (w v v5)))) = x v (w v (z v (u v (y v v5)))). [para(35(a,1),30(a,1,2))]. % back CAC tautology: 1605 x v (y v (z v (u v (w v (v5 v v6))))) = x v (u v (y v (v5 v (w v (z v v6))))). [para(35(a,1),30(a,1,2,2))]. % back CAC tautology: 1604 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (z v (v5 v (w v (y v v6))))). [para(28(a,1),35(a,2,2,2,2))]. % back CAC tautology: 1603 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (z v (y v (w v (u v v6))))). [para(28(a,1),35(a,1,2,2,2))]. % back CAC tautology: 1602 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (x v (z v (w v (u v v6))))). [para(35(a,2),28(a,1,2,2))]. % back CAC tautology: 1601 x v (y v (z v (u v (w v v5)))) = w v (z v (x v (u v (y v v5)))). [para(35(a,1),28(a,1,2))]. % back CAC tautology: 1600 x v (y v (z v (u v (w v (v5 v v6))))) = u v (y v (x v (v5 v (w v (z v v6))))). [para(35(a,1),28(a,1,2,2))]. % back CAC tautology: 1485 x v (y v (z v (u v (w v (v5 v v6))))) = w v (y v (v5 v (x v (z v (u v v6))))). [para(34(a,2),34(a,2,2)),flip(a)]. % back CAC tautology: 1484 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (w v (z v (v6 v (y v (v5 v v7)))))). [para(34(a,2),34(a,2,2,2))]. % back CAC tautology: 1483 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (z v (v5 v (v7 v (w v (v6 v v8))))))). [para(34(a,2),34(a,2,2,2,2))]. % back CAC tautology: 1482 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v5 v (v6 v (v8 v (z v (v7 v v9)))))))). [para(34(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 1481 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (w v (v5 v (y v (u v v6))))). [para(34(a,2),34(a,1,2))]. % back CAC tautology: 1480 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (u v (v5 v (v6 v (w v v7)))))). [para(34(a,2),34(a,1,2,2))]. % back CAC tautology: 1479 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (x v (y v (u v (z v (w v (v7 v (v5 v v8))))))). [para(34(a,2),34(a,1,2,2,2))]. % back CAC tautology: 1478 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v7 v (z v (w v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 1477 x v (y v (z v (u v (w v (v5 v v6))))) = u v (z v (x v (y v (v5 v (w v v6))))). [para(34(a,1),34(a,2,2))]. % back CAC tautology: 1476 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v5 v (y v (w v (v6 v (z v v7)))))). [para(34(a,1),34(a,2,2,2))]. % back CAC tautology: 1475 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v6 v (w v (z v (v7 v (v5 v v8))))))). [para(34(a,1),34(a,2,2,2,2))]. % back CAC tautology: 1474 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (w v (v7 v (z v (v5 v (v8 v (v6 v v9)))))))). [para(34(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 1473 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (v6 v (u v (z v (v5 v v7)))))). [para(34(a,1),34(a,1,2,2))]. % back CAC tautology: 1472 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (v5 v (z v (v7 v (u v (v6 v v8))))))). [para(34(a,1),34(a,1,2,2,2))]. % back CAC tautology: 1471 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v (v8 v v9)))))))) = u v (x v (y v (v5 v (z v (v6 v (v8 v (w v (v7 v v9)))))))). [para(34(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 1445 x v (y v (z v (u v (w v v5)))) = w v (u v (x v (z v (y v v5)))). [para(34(a,2),45(a,2)),rewrite([5(12),5(11),5(10),5(9),1442(16)]),flip(a)]. % back CAC tautology: 1434 x v (y v (z v (u v (w v v5)))) = w v (y v (u v (x v (z v v5)))). [para(29(a,2),34(a,2,2)),flip(a)]. % back CAC tautology: 1433 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (w v (z v (v5 v (y v v6))))). [para(29(a,2),34(a,2,2,2))]. % back CAC tautology: 1432 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (z v (v5 v (v6 v (w v v7)))))). [para(29(a,2),34(a,2,2,2,2))]. % back CAC tautology: 1431 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v5 v (v6 v (v7 v (z v v8))))))). [para(29(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 1430 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (y v (u v (v5 v (w v v6))))). [para(29(a,2),34(a,1,2,2))]. % back CAC tautology: 1429 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (u v (z v (w v (v5 v v7)))))). [para(29(a,2),34(a,1,2,2,2))]. % back CAC tautology: 1428 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v7 v (z v (w v (v5 v (v6 v v8))))))). [para(29(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 1427 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (v5 v (y v (w v (z v v6))))). [para(29(a,1),34(a,2,2,2))]. % back CAC tautology: 1426 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (v6 v (w v (z v (v5 v v7)))))). [para(29(a,1),34(a,2,2,2,2))]. % back CAC tautology: 1425 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v7 v (z v (v5 v (v6 v v8))))))). [para(29(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 1424 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (y v (v5 v (u v (z v v6))))). [para(29(a,1),34(a,1,2,2))]. % back CAC tautology: 1423 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (v5 v (z v (v6 v (u v v7)))))). [para(29(a,1),34(a,1,2,2,2))]. % back CAC tautology: 1422 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v5 v (z v (v6 v (v7 v (w v v8))))))). [para(29(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 1421 x v (y v (z v (u v (w v v5)))) = x v (y v (w v (u v (z v v5)))). [para(34(a,2),29(a,2))]. % back CAC tautology: 1420 x v (y v (z v (u v (w v (v5 v v6))))) = w v (y v (z v (x v (v5 v (u v v6))))). [para(34(a,2),29(a,2,2)),flip(a)]. % back CAC tautology: 1419 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (z v (w v (v6 v (y v (v5 v v7)))))). [para(34(a,2),29(a,2,2,2))]. % back CAC tautology: 1418 x v (y v (z v (u v (w v v5)))) = w v (u v (x v (y v (z v v5)))). [para(34(a,2),29(a,1))]. % back CAC tautology: 1417 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (v5 v (u v (v6 v (w v v7)))))). [para(34(a,2),29(a,1,2,2))]. % back CAC tautology: 1416 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = v6 v (x v (y v (z v (u v (w v (v7 v (v5 v v8))))))). [para(34(a,2),29(a,1,2,2,2))]. % back CAC tautology: 1415 x v (y v (z v (u v (w v (v5 v v6))))) = u v (w v (x v (y v (v5 v (z v v6))))). [para(34(a,1),29(a,2,2))]. % back CAC tautology: 1414 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (v5 v (y v (z v (v6 v (w v v7)))))). [para(34(a,1),29(a,2,2,2))]. % back CAC tautology: 1413 x v (y v (z v (u v (w v v5)))) = x v (y v (z v (w v (u v v5)))). [para(34(a,1),29(a,1))]. % back CAC tautology: 1412 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (z v (u v (y v (w v v6))))). [para(34(a,1),29(a,1,2))]. % back CAC tautology: 1411 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (u v (v6 v (z v (v5 v v7)))))). [para(34(a,1),29(a,1,2,2))]. % back CAC tautology: 1410 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = w v (x v (y v (z v (v5 v (v7 v (u v (v6 v v8))))))). [para(34(a,1),29(a,1,2,2,2))]. % back CAC tautology: 1400 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (w v (v5 v (y v (z v v6))))). [para(27(a,2),34(a,2,2,2))]. % back CAC tautology: 1399 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (z v (v6 v (w v (v5 v v7)))))). [para(27(a,2),34(a,2,2,2,2))]. % back CAC tautology: 1398 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v5 v (v7 v (z v (v6 v v8))))))). [para(27(a,2),34(a,2,2,2,2,2))]. % back CAC tautology: 1397 x v (y v (z v (u v (w v v5)))) = w v (x v (u v (z v (y v v5)))). [para(27(a,2),34(a,1,2))]. % back CAC tautology: 1396 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (y v (v5 v (w v (u v v6))))). [para(27(a,2),34(a,1,2,2))]. % back CAC tautology: 1395 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (y v (u v (z v (v6 v (w v v7)))))). [para(27(a,2),34(a,1,2,2,2))]. % back CAC tautology: 1394 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v6 v (z v (w v (v7 v (v5 v v8))))))). [para(27(a,2),34(a,1,2,2,2,2))]. % back CAC tautology: 1393 x v (y v (z v (u v (w v v5)))) = u v (w v (x v (z v (y v v5)))). [para(27(a,1),34(a,2,2))]. % back CAC tautology: 1392 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (z v (y v (v5 v (w v v6))))). [para(27(a,1),34(a,2,2,2))]. % back CAC tautology: 1391 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (v5 v (w v (v6 v (z v v7)))))). [para(27(a,1),34(a,2,2,2,2))]. % back CAC tautology: 1390 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (w v (v6 v (z v (v7 v (v5 v v8))))))). [para(27(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 1389 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (v6 v (z v (u v (v5 v v7)))))). [para(27(a,1),34(a,1,2,2,2))]. % back CAC tautology: 1388 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = u v (x v (y v (v5 v (z v (v7 v (w v (v6 v v8))))))). [para(27(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 1387 x v (y v (z v (u v (w v v5)))) = x v (w v (u v (y v (z v v5)))). [para(34(a,2),27(a,2)),flip(a)]. % back CAC tautology: 1386 x v (y v (z v (u v (w v (v5 v v6))))) = w v (z v (x v (y v (v5 v (u v v6))))). [para(34(a,2),27(a,2,2)),flip(a)]. % back CAC tautology: 1385 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (y v (w v (v6 v (u v (v5 v v7)))))). [para(34(a,2),27(a,2,2,2))]. % back CAC tautology: 1384 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (w v (v5 v (v7 v (y v (v6 v v8))))))). [para(34(a,2),27(a,2,2,2,2))]. % back CAC tautology: 1383 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (z v (v5 v (u v (w v v6))))). [para(34(a,2),27(a,1,2)),flip(a)]. % back CAC tautology: 1382 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (z v (y v (u v (v6 v (w v v7)))))). [para(34(a,2),27(a,1,2,2))]. % back CAC tautology: 1381 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (v6 v (y v (u v (w v (v7 v (v5 v v8))))))). [para(34(a,2),27(a,1,2,2,2))]. % back CAC tautology: 1380 x v (y v (z v (u v (w v (v5 v v6))))) = z v (v5 v (x v (u v (y v (w v v6))))). [para(34(a,1),27(a,2,2)),flip(a)]. % back CAC tautology: 1379 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v5 v (u v (y v (v6 v (w v v7)))))). [para(34(a,1),27(a,2,2,2))]. % back CAC tautology: 1378 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (u v (v6 v (y v (w v (v7 v (v5 v v8))))))). [para(34(a,1),27(a,2,2,2,2))]. % back CAC tautology: 1377 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (v5 v (z v (y v (w v v6))))). [para(34(a,1),27(a,1,2))]. % back CAC tautology: 1376 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (w v (y v (v6 v (z v (v5 v v7)))))). [para(34(a,1),27(a,1,2,2))]. % back CAC tautology: 1375 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v v8))))))) = z v (x v (w v (y v (v5 v (v7 v (u v (v6 v v8))))))). [para(34(a,1),27(a,1,2,2,2))]. % back CAC tautology: 1358 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (w v (z v (v6 v (v5 v v7)))))). [para(30(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 1357 x v (y v (z v (u v (w v (v5 v v6))))) = x v (y v (w v (z v (v5 v (u v v6))))). [para(34(a,2),30(a,1,2))]. % back CAC tautology: 1356 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (v5 v (y v (z v (u v (v6 v (w v v7)))))). [para(34(a,2),30(a,1,2,2))]. % back CAC tautology: 1355 x v (y v (z v (u v (w v (v5 v v6))))) = x v (w v (z v (y v (v5 v (u v v6))))). [para(34(a,1),30(a,1,2)),flip(a)]. % back CAC tautology: 1354 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = x v (u v (y v (w v (v6 v (z v (v5 v v7)))))). [para(34(a,1),30(a,1,2,2))]. % back CAC tautology: 1353 x v (y v (z v (u v (w v v5)))) = u v (w v (y v (x v (z v v5)))). [para(28(a,1),34(a,2,2))]. % back CAC tautology: 1352 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (w v (v6 v (v5 v (z v v7)))))). [para(28(a,1),34(a,2,2,2,2,2))]. % back CAC tautology: 1351 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (y v (w v (z v (u v v6))))). [para(28(a,1),34(a,1,2,2,2))]. % back CAC tautology: 1350 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (v6 v (z v (v5 v (w v v7)))))). [para(28(a,1),34(a,1,2,2,2,2))]. % back CAC tautology: 1349 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (y v (x v (z v (u v (v6 v (w v v7)))))). [para(34(a,2),28(a,1,2,2))]. % back CAC tautology: 1348 x v (y v (z v (u v (w v v5)))) = w v (z v (y v (x v (u v v5)))). [para(34(a,1),28(a,1))]. % back CAC tautology: 1347 x v (y v (z v (u v (w v (v5 v v6))))) = u v (z v (x v (v5 v (y v (w v v6))))). [para(34(a,1),28(a,1,2))]. % back CAC tautology: 1346 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (y v (x v (w v (v6 v (z v (v5 v v7)))))). [para(34(a,1),28(a,1,2,2))]. % back CAC tautology: 1295 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (y v (v5 v (z v (u v v6))))). [para(18(a,1),34(a,1,2,2,2))]. % back CAC tautology: 1294 x v (y v (z v (u v (w v (v5 v v6))))) = y v (x v (w v (z v (v5 v (u v v6))))). [para(34(a,2),18(a,1,2))]. % back CAC tautology: 1293 x v (y v (z v (u v (w v (v5 v v6))))) = z v (w v (x v (y v (v5 v (u v v6))))). [para(34(a,1),18(a,2,2))]. % back CAC tautology: 859 x v (y v (z v (u v (w v v5)))) = w v (y v (z v (x v (u v v5)))). [para(29(a,2),29(a,2,2)),flip(a)]. % back CAC tautology: 858 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (z v (w v (v5 v (y v v6))))). [para(29(a,2),29(a,2,2,2))]. % back CAC tautology: 857 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (w v (v5 v (v6 v (z v v7)))))). [para(29(a,2),29(a,2,2,2,2))]. % back CAC tautology: 856 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v6 v (x v (y v (z v (u v (w v (v5 v v7)))))). [para(29(a,2),29(a,1,2,2,2))]. % back CAC tautology: 855 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (v6 v (z v (w v (v5 v v7)))))). [para(29(a,1),29(a,2,2,2,2))]. % back CAC tautology: 854 x v (y v (z v (u v (w v v5)))) = w v (x v (z v (u v (y v v5)))). [para(29(a,1),29(a,1,2))]. % back CAC tautology: 853 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (y v (u v (v5 v (z v v6))))). [para(29(a,1),29(a,1,2,2))]. % back CAC tautology: 852 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (z v (v5 v (v6 v (u v v7)))))). [para(29(a,1),29(a,1,2,2,2))]. % back CAC tautology: 842 x v (y v (z v (u v (w v v5)))) = u v (y v (w v (x v (z v v5)))). [para(27(a,2),29(a,2,2))]. % back CAC tautology: 841 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (z v (v5 v (y v (w v v6))))). [para(27(a,2),29(a,2,2,2))]. % back CAC tautology: 840 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (w v (v6 v (z v (v5 v v7)))))). [para(27(a,2),29(a,2,2,2,2))]. % back CAC tautology: 839 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = v5 v (x v (y v (z v (u v (v6 v (w v v7)))))). [para(27(a,2),29(a,1,2,2,2))]. % back CAC tautology: 838 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = u v (x v (y v (v5 v (z v (v6 v (w v v7)))))). [para(27(a,1),29(a,2,2,2,2))]. % back CAC tautology: 837 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (y v (u v (z v (w v v6))))). [para(27(a,1),29(a,1,2,2))]. % back CAC tautology: 836 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = w v (x v (y v (z v (v6 v (u v (v5 v v7)))))). [para(27(a,1),29(a,1,2,2,2))]. % back CAC tautology: 835 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (y v (w v (v5 v (u v v6))))). [para(29(a,2),27(a,2,2,2))]. % back CAC tautology: 834 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (w v (v5 v (v6 v (y v v7)))))). [para(29(a,2),27(a,2,2,2,2))]. % back CAC tautology: 833 x v (y v (z v (u v (w v v5)))) = y v (x v (z v (w v (u v v5)))). [para(29(a,2),27(a,1,2))]. % back CAC tautology: 832 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (z v (y v (u v (w v v6))))). [para(29(a,2),27(a,1,2,2))]. % back CAC tautology: 831 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v6 v (y v (u v (w v (v5 v v7)))))). [para(29(a,2),27(a,1,2,2,2))]. % back CAC tautology: 830 x v (y v (z v (u v (w v v5)))) = z v (w v (x v (u v (y v v5)))). [para(29(a,1),27(a,2,2))]. % back CAC tautology: 829 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (v5 v (u v (y v (w v v6))))). [para(29(a,1),27(a,2,2,2))]. % back CAC tautology: 828 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (v6 v (y v (w v (v5 v v7)))))). [para(29(a,1),27(a,2,2,2,2))]. % back CAC tautology: 827 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (w v (y v (v5 v (z v v6))))). [para(29(a,1),27(a,1,2,2))]. % back CAC tautology: 826 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (y v (v5 v (v6 v (u v v7)))))). [para(29(a,1),27(a,1,2,2,2))]. % back CAC tautology: 811 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (y v (z v (v5 v (w v v6))))). [para(30(a,1),29(a,1,2,2,2))]. % back CAC tautology: 810 x v (y v (z v (u v (w v (v5 v v6))))) = x v (v5 v (y v (z v (u v (w v v6))))). [para(29(a,2),30(a,1,2,2))]. % back CAC tautology: 809 x v (y v (z v (u v (w v (v5 v v6))))) = x v (u v (y v (w v (v5 v (z v v6))))). [para(29(a,1),30(a,1,2,2))]. % back CAC tautology: 808 x v (y v (z v (u v (w v v5)))) = u v (x v (w v (z v (y v v5)))). [para(28(a,1),29(a,2,2,2))]. % back CAC tautology: 807 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (y v (v5 v (w v (z v v6))))). [para(28(a,1),29(a,2,2,2,2))]. % back CAC tautology: 806 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (y v (z v (w v (u v v6))))). [para(28(a,1),29(a,1,2,2,2))]. % back CAC tautology: 805 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (y v (x v (z v (u v (w v v6))))). [para(29(a,2),28(a,1,2,2))]. % back CAC tautology: 804 x v (y v (z v (u v (w v v5)))) = u v (z v (x v (w v (y v v5)))). [para(29(a,1),28(a,1,2))]. % back CAC tautology: 803 x v (y v (z v (u v (w v (v5 v v6))))) = u v (y v (x v (w v (v5 v (z v v6))))). [para(29(a,1),28(a,1,2,2))]. % back CAC tautology: 739 x v (y v (z v (u v (w v (v5 v v6))))) = v5 v (x v (y v (z v (u v (w v v6))))). [para(29(a,2),18(a,1,2,2))]. % back CAC tautology: 738 x v (y v (z v (u v w))) = u v (y v (z v (x v w))). [para(29(a,1),18(a,1))]. % back CAC tautology: 737 x v (y v (z v (u v (w v v5)))) = u v (x v (z v (w v (y v v5)))). [para(29(a,1),18(a,1,2))]. % back CAC tautology: 736 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (y v (w v (v5 v (z v v6))))). [para(29(a,1),18(a,1,2,2))]. % back CAC tautology: 638 x v (y v (z v (u v (w v v5)))) = u v (w v (x v (y v (z v v5)))). [para(27(a,2),27(a,2,2)),flip(a)]. % back CAC tautology: 637 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (y v (v5 v (u v (w v v6))))). [para(27(a,2),27(a,2,2,2))]. % back CAC tautology: 636 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (w v (v6 v (y v (v5 v v7)))))). [para(27(a,2),27(a,2,2,2,2))]. % back CAC tautology: 635 x v (y v (z v (u v (w v v5)))) = y v (x v (w v (u v (z v v5)))). [para(27(a,2),27(a,1,2))]. % back CAC tautology: 634 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (z v (y v (v5 v (u v v6))))). [para(27(a,2),27(a,1,2,2))]. % back CAC tautology: 633 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (v5 v (y v (u v (v6 v (w v v7)))))). [para(27(a,2),27(a,1,2,2,2))]. % back CAC tautology: 632 x v (y v (z v (u v w))) = u v (z v (y v (x v w))). [para(27(a,1),27(a,2))]. % back CAC tautology: 631 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (w v (u v (v5 v (y v v6))))). [para(27(a,1),27(a,2,2,2))]. % back CAC tautology: 630 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (u v (v5 v (y v (v6 v (w v v7)))))). [para(27(a,1),27(a,2,2,2,2))]. % back CAC tautology: 629 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (v5 v (y v (z v (w v v6))))). [para(27(a,1),27(a,1,2,2))]. % back CAC tautology: 628 x v (y v (z v (u v (w v (v5 v (v6 v v7)))))) = z v (x v (w v (y v (v6 v (u v (v5 v v7)))))). [para(27(a,1),27(a,1,2,2,2))]. % back CAC tautology: 613 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (u v (y v (v5 v (w v v6))))). [para(30(a,1),27(a,1,2,2,2))]. % back CAC tautology: 612 x v (y v (z v (u v (w v v5)))) = x v (y v (w v (z v (u v v5)))). [para(27(a,2),30(a,1,2)),flip(a)]. % back CAC tautology: 611 x v (y v (z v (u v (w v (v5 v v6))))) = x v (w v (y v (z v (v5 v (u v v6))))). [para(27(a,2),30(a,1,2,2))]. % back CAC tautology: 610 x v (y v (z v (u v (w v v5)))) = x v (w v (z v (y v (u v v5)))). [para(27(a,1),30(a,1,2))]. % back CAC tautology: 609 x v (y v (z v (u v (w v (v5 v v6))))) = x v (u v (y v (v5 v (z v (w v v6))))). [para(27(a,1),30(a,1,2,2))]. % back CAC tautology: 608 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (u v (v5 v (w v (y v v6))))). [para(28(a,1),27(a,2,2,2,2))]. % back CAC tautology: 607 x v (y v (z v (u v (w v v5)))) = w v (x v (u v (y v (z v v5)))). [para(28(a,1),27(a,1,2,2))]. % back CAC tautology: 606 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (v5 v (y v (w v (u v v6))))). [para(28(a,1),27(a,1,2,2,2))]. % back CAC tautology: 605 x v (y v (z v (u v (w v (v5 v v6))))) = w v (y v (x v (z v (v5 v (u v v6))))). [para(27(a,2),28(a,1,2,2))]. % back CAC tautology: 604 x v (y v (z v (u v (w v v5)))) = w v (z v (x v (y v (u v v5)))). [para(27(a,1),28(a,1,2))]. % back CAC tautology: 603 x v (y v (z v (u v (w v (v5 v v6))))) = u v (y v (x v (v5 v (z v (w v v6))))). [para(27(a,1),28(a,1,2,2))]. % back CAC tautology: 544 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (u v (w v (v5 v (y v v6))))). [para(18(a,2),27(a,2,2,2,2))]. % back CAC tautology: 543 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (v5 v (y v (u v (w v v6))))). [para(18(a,2),27(a,1,2,2,2))]. % back CAC tautology: 542 x v (y v (z v (u v (w v v5)))) = u v (x v (w v (y v (z v v5)))). [para(18(a,1),27(a,1,2,2))]. % back CAC tautology: 541 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (u v (v5 v (y v (w v v6))))). [para(27(a,2),18(a,2,2,2))]. % back CAC tautology: 540 x v (y v (z v (u v (w v v5)))) = y v (x v (w v (z v (u v v5)))). [para(27(a,2),18(a,1,2)),flip(a)]. % back CAC tautology: 539 x v (y v (z v (u v (w v (v5 v v6))))) = w v (x v (y v (z v (v5 v (u v v6))))). [para(27(a,2),18(a,1,2,2))]. % back CAC tautology: 538 x v (y v (z v (u v (w v v5)))) = z v (w v (x v (y v (u v v5)))). [para(27(a,1),18(a,2,2)),flip(a)]. % back CAC tautology: 537 x v (y v (z v (u v (w v (v5 v v6))))) = z v (x v (w v (y v (v5 v (u v v6))))). [para(27(a,1),18(a,2,2,2))]. % back CAC tautology: 536 x v (y v (z v (u v (w v v5)))) = w v (x v (z v (y v (u v v5)))). [para(27(a,1),18(a,1,2))]. % back CAC tautology: 535 x v (y v (z v (u v (w v (v5 v v6))))) = u v (x v (y v (v5 v (z v (w v v6))))). [para(27(a,1),18(a,1,2,2))]. % back CAC tautology: 461 x v (y v (z v (u v (w v v5)))) = x v (z v (y v (w v (u v v5)))). [para(30(a,1),30(a,1,2,2))]. % back CAC tautology: 460 x v (y v (z v (u v (w v v5)))) = x v (w v (y v (u v (z v v5)))). [para(28(a,1),30(a,1,2,2))]. % back CAC tautology: 459 x v (y v (z v (u v (w v v5)))) = z v (y v (x v (w v (u v v5)))). [para(30(a,1),28(a,1,2,2))]. % back CAC tautology: 445 x v (y v (z v (u v w))) = x v (y v (u v (z v w))). [para(18(a,2),30(a,1,2))]. % back CAC tautology: 444 x v (y v (z v (u v (w v v5)))) = x v (w v (y v (z v (u v v5)))). [para(18(a,2),30(a,1,2,2))]. % back CAC tautology: 443 x v (y v (z v (u v w))) = x v (u v (z v (y v w))). [para(18(a,1),30(a,1,2))]. % back CAC tautology: 442 x v (y v (z v (u v (w v v5)))) = x v (u v (y v (w v (z v v5)))). [para(18(a,1),30(a,1,2,2))]. % back CAC tautology: 441 x v (y v (z v (u v (w v v5)))) = z v (x v (y v (w v (u v v5)))). [para(30(a,1),18(a,1,2,2))]. % back CAC tautology: 440 x v (y v (z v (u v w))) = x v (u v (y v (z v w))). [para(5(a,1),30(a,1,2,2))]. % back CAC tautology: 439 x v (y v (z v (u v (w v v5)))) = w v (y v (x v (u v (z v v5)))). [para(28(a,1),28(a,1,2,2))]. % back CAC tautology: 424 x v (y v (z v (u v (w v v5)))) = w v (y v (x v (z v (u v v5)))). [para(18(a,2),28(a,1,2,2))]. % back CAC tautology: 423 x v (y v (z v (u v (w v v5)))) = u v (y v (x v (w v (z v v5)))). [para(18(a,1),28(a,1,2,2))]. % back CAC tautology: 422 x v (y v (z v (u v w))) = u v (z v (x v (y v w))). [para(28(a,1),18(a,2,2)),flip(a)]. given #168 (T,wt=11): 6667 x v (x v y)' = x v y'. [back_rewrite(6581),rewrite([6642(4),6587(4)])]. given #169 (A,wt=25): 426 ((x v (y v (z v (u v w)))')' v (u v (x v (z v (y v w))))')' = x. [para(28(a,1),19(a,1,1,1,1,2,1))]. given #170 (T,wt=8): 8772 x' v (y v x) = c_0. [para(5966(a,1),6667(a,1,2,1)),rewrite([5917(3),6642(2),17(2),5917(5)]),flip(a)]. given #171 (T,wt=11): 7318 x v (y v (x' v z))' = x. [para(5(a,1),7273(a,1,2,1))]. given #172 (T,wt=11): 8516 (x v y) v z = x v (y v z). [para(6643(a,2),6642(a,1)),flip(a)]. given #173 (T,wt=11): 8771 x v (y v x)' = x v y'. [para(6642(a,1),6667(a,1,2,1))]. given #174 (A,wt=25): 427 ((x v (y v (z v (u v w)))')' v (y v (u v (z v (x v w))))')' = x. [para(28(a,1),19(a,1,1,2,1,2))]. given #175 (T,wt=12): 5780 x v (y v (z v (u v x'))) = c_0. [back_rewrite(44),rewrite([5056(7),5056(7),5056(7)])]. given #176 (T,wt=12): 5976 x' v (y v (z v x))' = x'. [back_rewrite(5628),rewrite([5926(6),5887(6),5926(10),5917(7),5926(9),5887(9)])]. given #177 (T,wt=12): 5998 x' v (y v (z v (u v x))) = c_0. [back_rewrite(5340),rewrite([5926(4),5887(4)])]. given #178 (T,wt=12): 7174 x v (y v (z v (x' v u))) = c_0. [para(6781(a,1),18(a,1,2,2)),rewrite([5056(2),5056(2)]),flip(a)]. given #179 (A,wt=25): 447 ((x v (y v (z v (u v w)))')' v (y v (x v (u v (z v w))))')' = x. [para(30(a,1),19(a,1,1,1,1,2,1))]. given #180 (T,wt=12): 7176 x' v (y v (z v (x v u))) = c_0. [para(6781(a,1),27(a,1,2)),rewrite([5056(2)]),flip(a)]. given #181 (T,wt=12): 7656 x' v (y v (x v z))' = x'. [para(5(a,1),7326(a,1,2,1))]. given #182 (T,wt=13): 5933 ((x v y)' v (y' v x)')' = x. [back_rewrite(5882),rewrite([5926(6),5887(6)])]. given #183 (T,wt=13): 6580 (x v y)' v (x v y')' = x'. [para(20(a,1),5917(a,1,1)),rewrite([6578(9)]),flip(a)]. given #184 (A,wt=29): 553 ((x v (y v (z v (u v (w v v5))))')' v (z v (x v (w v (y v (u v v5)))))')' = x. [para(27(a,1),19(a,1,1,1,1,2,1))]. given #185 (T,wt=13): 6585 x v (y v (z v (u v x')))' = x. [back_rewrite(6108),rewrite([6578(14)])]. given #186 (T,wt=13): 6605 x v (y v (z v x)) = y v (z v x). [para(5935(a,1),18(a,1,2,2)),flip(a)]. given #187 (T,wt=13): 6666 x v (y v (x v z)) = y v (x v z). [back_rewrite(6606),rewrite([6642(2),6604(2)])]. given #188 (T,wt=13): 7269 x v (y v (z v x')') = y v x. [para(6587(a,1),5(a,1,2)),flip(a)]. given #189 (A,wt=29): 554 ((x v (y v (z v (u v (w v v5))))')' v (y v (u v (x v (w v (z v v5)))))')' = x. [para(27(a,1),19(a,1,1,2,1,2))]. given #190 (T,wt=13): 7317 x v (y v (x' v z)') = y v x. [para(7273(a,1),5(a,1,2)),flip(a)]. given #191 (T,wt=13): 7321 x v (y v (z v (x' v u)))' = x. [para(18(a,2),7273(a,1,2,1))]. given #192 (T,wt=13): 8823 x v ((y v x')' v z) = x v z. [para(6587(a,1),8516(a,1,1)),flip(a)]. given #193 (T,wt=13): 8825 x v ((x' v y)' v z) = x v z. [para(7273(a,1),8516(a,1,1)),flip(a)]. given #194 (A,wt=25): 555 ((x v (y v (z v (u v w)))')' v (z v (y v (u v (x v w))))')' = x. [para(27(a,1),19(a,1,1,2,1))]. given #195 (T,wt=13): 8852 (x v y)' v (y v x')' = y'. [para(8771(a,1),8771(a,1,2,1)),rewrite([6642(10),5966(10)])]. given #196 (T,wt=13): 8902 (x v y)' v (y' v x)' = x'. [para(5933(a,1),5917(a,1,1)),flip(a)]. Demod_increase_limit: ((y' v ((z v (u v (w v (v5 v (y v v6)))))' v x'))' v (y v (x' v ((y v (u v (w v (v5 v (v6 v z')))))' v ((y v (w v (v5 v (v6 v u'))))' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v ((z v (u v (w v (v5 v (y v v6)))))' v x'))))))))') v ((y v (x' v ((u v (w v (v5 v (v6 v (z' v y')))))' v ((v5 v (v6 v (w' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v z'))))))' v ((w v (v5 v (v6 v (y' v (z v u')))))' v ((v6 v (v5' v ((y v (v6 v v5'))' v ((y v v6')' v (z v u')))))' v ((v5 v (v6 v (y' v (z v (u v w')))))' v ((v6' v (y' v (z v (u v w'))))' v ((v6 v (y' v (z v (u v (w v v5')))))' v ((v6' v (z v (u v (w v (v5 v y')))))' v ((v6 v (z v (u v (w v (v5 v (y v v6)')))))' v ((v5' v (v6' v (y' v (z v (u v (w v (v5 v (y v v6))'))))))' v ((v6 v (w' v (v5' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6)))')))))))' v ((v5 v (v6 v (u' v (w' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6))))'))))))))' v ((u' v (v6' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6))))'))))))' v ((w v (v5 v (v6 v (z' v (u' v ((y v (w v (v5 v (v6 v u'))))' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6)))))')))))))))' v ((v6 v (z' v (v5' v ((y v (w v (v5 v (v6 v u'))))' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6)))))')))))))' v (z' v (v6' v ((y v (w v (v5 v (v6 v u'))))' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6)))))'))))))')))))))))))))))))' v (y' v ((u v (w v (v5 v (v6 v (z' v y')))))' v ((v5 v (v6 v (w' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v z'))))))' v ((w v (v5 v (v6 v (y' v (z v u')))))' v ((v6 v (v5' v ((y v (v6 v v5'))' v ((y v v6')' v (z v u')))))' v ((v5 v (v6 v (y' v (z v (u v w')))))' v ((v6' v (y' v (z v (u v w'))))' v ((v6 v (y' v (z v (u v (w v v5')))))' v ((v6' v (z v (u v (w v (v5 v y')))))' v ((v6 v (z v (u v (w v (v5 v (y v v6)')))))' v ((v5' v (v6' v (y' v (z v (u v (w v (v5 v (y v v6))'))))))' v ((v6 v (w' v (v5' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6)))')))))))' v ((v5 v (v6 v (u' v (w' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6))))'))))))))' v ((u' v (v6' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6))))'))))))' v ((w v (v5 v (v6 v (z' v (u' v ((y v (w v (v5 v (v6 v u'))))' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6)))))')))))))))' v ((v6 v (z' v (v5' v ((y v (w v (v5 v (v6 v u'))))' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6)))))')))))))' v (z' v (v6' v ((y v (w v (v5 v (v6 v u'))))' v ((y v (v5 v (v6 v w')))' v ((y v (v6 v v5'))' v ((y v v6')' v (z v (u v (w v (v5 v (y v v6)))))'))))))'))))))))))))))))') = x. [back_rewrite(2703),rewrite([9756(9),8516(7),8516(6),8516(5),9756(15),8516(13),8516(12),9756(20),8516(18),9756(24),8516(38),8516(37),8516(36),8516(35),9756(42),8516(40),8516(39),8516(38),8516(37),8516(36),9761(42),8827(82),8827(74),8827(67),8827(61),8827(56),6642(54),9761(93),8827(91),8827(84),8827(78),8827(73),7651(69),8516(63),8516(62),8516(61),8516(60),9761(100),8516(99),8516(98),8516(97),9761(135),8898(133),8516(127),8516(126),7660(125),9761(155),8516(154),9761(188),5917(190),8806(218),9761(217),8827(215),8827(209),8827(204),8516(201),8516(200),8516(199),7657(198),9761(224),8516(223),8516(222),9761(251),8898(249),8516(244),7660(243),9761(265),5917(267),8806(288),9761(287),8827(285),8827(280),8516(277),8516(276),7658(275),9761(294),8516(293),9761(314),8898(312),8849(307),7660(306),5917(304),8806(319),9761(318),8827(316),8516(313),7660(312),9761(325),8849(323),5917(325),8806(335),9761(334),7660(332),5917(333),6642(341),8516(341),6642(344),8516(344),8516(343),8516(342),8516(341),6642(346),8516(346),8516(345),8516(344),8516(343),8516(342),8516(341),5(348),5(347),5(346),5(345),5(344),5(343),5(342),5(341),6642(350),8516(350),8516(349),8516(348),8516(347),8516(346),8516(345),8516(344),8516(343),8516(342),8516(341),5(351),5(350),5(349),5(348),5(347),5(346),5(345),5(344),5(343),5(342),5(341),5(353),5(352),5(351),5(350),5(349),5(348),5(347),5(346),5(345),5(344),5(343),5(342),9761(356)])]. Demod_increase_limit (steps=151, size=1087). The most recent kept clause is 9812. From here on, a short message will be printed for each 100 times the limit is hit. ============================== PROOF ================================= % Proof 3 at 3.59 (+ 0.03) seconds: MOD. % Length of proof is 172. % Level of proof is 46. % Maximum clause weight is 86.000. % Given clauses 196. 4 x v (y ^ (x v z)) = x v (z ^ (x v y)) # answer(MOD) # label(non_clause) # label(goal). [goal]. 5 x v (y v z) = y v (x v z) # label(AJ). [assumption]. 6 x ^ y = (x' v y')' # label(DM). [assumption]. 7 x v x' = y v y' # label(ONE). [assumption]. 8 (x v y') ^ (x v y) = x # label(CUT). [assumption]. 9 ((x v y')' v (x v y)')' = x. [copy(8),rewrite([6(4)])]. 15 c7 v (c9 ^ (c7 v c8)) != c7 v (c8 ^ (c7 v c9)) # answer(MOD). [deny(4)]. 16 c7 v (c8' v (c7 v c9)')' != c7 v (c9' v (c7 v c8)')' # answer(MOD). [copy(15),rewrite([6(6),6(16)]),flip(a)]. 17 x v x' = c_0. [new_symbol(7)]. 18 x v (y v (z v u)) = z v (x v (y v u)). [para(5(a,1),5(a,1,2))]. 19 ((x v (y v z)')' v (y v (x v z))')' = x. [para(5(a,1),9(a,1,1,2,1))]. 20 ((x v y)' v (x v ((y v z')' v (y v z)'))')' = x. [para(9(a,1),9(a,1,1,1,1,2))]. 21 (x v (x v ((x v y')' v y))')' = (x v y')'. [para(9(a,1),9(a,1,1,1)),rewrite([5(5)])]. 22 (((x v y')' v (x v y)'')' v x)' = (x v y')'. [para(9(a,1),9(a,1,1,2))]. 23 x v (y v x') = y v c_0. [para(17(a,1),5(a,1,2)),flip(a)]. 24 (c_0' v (x v x)')' = x. [para(17(a,1),9(a,1,1,1,1))]. 25 ((x v x'')' v c_0')' = x. [para(17(a,1),9(a,1,1,2,1))]. 26 ((x v y')' v (x v y)') v x = c_0. [para(9(a,1),17(a,1,2))]. 27 x v (y v (z v (u v w))) = z v (x v (u v (y v w))). [para(18(a,1),5(a,1,2))]. 29 x v (y v (z v (u v w))) = u v (x v (y v (z v w))). [para(18(a,2),5(a,1,2))]. 31 ((x v (y v (z v u))')' v (z v (x v (y v u)))')' = x. [para(18(a,1),9(a,1,1,2,1))]. 33 x v (y v (z v x')) = y v (z v c_0). [para(17(a,1),18(a,1,2,2)),flip(a)]. 42 ((x v (y v x')')' v (y v c_0)')' = x. [para(23(a,1),9(a,1,1,2,1))]. 44 x v (y v (z v (u v x'))) = y v (z v (u v c_0)). [para(23(a,1),18(a,1,2,2)),flip(a)]. 45 (c_0' v (x v ((x v y) v y))')' = x v y. [para(5(a,1),24(a,1,1,2,1))]. 46 ((x v y)' v (x v (c_0' v (y v y)'))')' = x. [para(24(a,1),9(a,1,1,1,1,2))]. 47 (x v (c_0' v (x v x))')' = c_0'. [para(24(a,1),9(a,1,1,1))]. 48 ((c_0' v (x v x)'')' v x)' = c_0'. [para(24(a,1),9(a,1,1,2))]. 49 (c_0' v (x v x)') v x = c_0. [para(24(a,1),17(a,1,2))]. 50 (c_0' v (x v (y v ((y v (x v z)) v z)))')' = y v (x v z). [para(18(a,1),24(a,1,1,2,1)),rewrite([5(6)])]. 52 (c_0' v (x v x)') v (y v x) = y v c_0. [para(24(a,1),23(a,1,2,2))]. 53 x v ((c_0' v (x v ((x v y) v y))') v y) = c_0. [para(49(a,1),5(a,1)),rewrite([5(6)]),flip(a)]. 63 (c_0' v (x' v x')') v c_0 = x v c_0. [para(49(a,1),23(a,1,2)),flip(a)]. 65 (x v ((x v x'')' v c_0)')' = (x v x'')'. [para(25(a,1),9(a,1,1,1))]. 66 (((x v x'')' v c_0'')' v x)' = (x v x'')'. [para(25(a,1),9(a,1,1,2))]. 68 ((x v x'')' v c_0') v x = c_0. [para(25(a,1),17(a,1,2))]. 85 (x v (x v (c_0' v x))')' = c_0'. [para(24(a,1),19(a,1,1,1))]. 91 ((x v y)' v ((y v y'')' v (x v c_0'))')' = x. [para(25(a,1),19(a,1,1,1,1,2))]. 95 (c_0' v (x v (c_0' v (x v x)))')' = x. [para(47(a,1),9(a,1,1,1))]. 97 (x v (c_0' v (x v x))') v c_0' = c_0. [para(47(a,1),17(a,1,2))]. 108 (c_0' v (((x' v x''')' v c_0') v x)')' = (x' v x''')' v c_0'. [para(68(a,1),9(a,1,1,1,1))]. 126 (c_0' v (x v (x v (c_0' v x)))')' = x. [para(85(a,1),9(a,1,1,1))]. 149 ((x' v y')' v (x' v y)') v c_0 = x v c_0. [para(26(a,1),23(a,1,2)),flip(a)]. 152 ((c_0' v (x v x)'')' v x) v c_0' = c_0. [para(24(a,1),26(a,1,1,2))]. 165 (c_0' v (x v (c_0' v (x v x)))') v x = c_0. [para(47(a,1),26(a,1,1,1))]. 169 (c_0' v (x v (x v (c_0' v x)))') v x = c_0. [para(85(a,1),26(a,1,1,1))]. 185 ((x v c_0)' v (y v (((x v y') v z')' v ((x v y') v z)'))')' = y. [para(23(a,1),20(a,1,1,1,1))]. 243 (c_0' v ((x v (c_0' v (x v x))') v c_0)')' = x v (c_0' v (x v x))'. [para(97(a,1),9(a,1,1,1,1))]. 248 (x v (c_0' v (x v x))') v c_0 = c_0 v c_0. [para(97(a,1),23(a,1,2)),flip(a)]. 256 x v (c_0' v (x v x))' = c_0. [back_rewrite(243),rewrite([248(10),24(8)]),flip(a)]. 258 x v (y v (c_0' v (x v x))') = y v c_0. [para(256(a,1),5(a,1,2)),flip(a)]. 266 (c_0' v (x v x)) v c_0 = x v c_0. [para(256(a,1),23(a,1,2))]. 267 c_0'' v (c_0'' v c_0)' = c_0. [para(23(a,1),256(a,1,2,1))]. 322 (c_0'' v c_0) v c_0 = c_0'' v c_0. [para(23(a,1),266(a,1,1))]. 330 (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''. [para(267(a,1),9(a,1,1,1,1))]. 339 (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0). [para(267(a,1),33(a,1,2,2))]. 523 (((x v c_0')' v ((c_0' v (y v y)') v (x v y))'')' v x)' = (x v c_0')'. [para(52(a,2),22(a,1,1,1,1,2,1,1))]. 651 ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0. [para(48(a,1),63(a,1,1,2,1,1)),rewrite([48(13),63(11)]),flip(a)]. 672 (c_0' v (x v ((x v c_0'') v ((x v c_0'') v c_0)))')' = x v c_0''. [para(33(a,1),95(a,1,1,2,1,2)),rewrite([5(13),5(14)])]. 682 (c_0' v (c_0' v (x v ((x v y) v ((x v y) v y))))')' = x v y. [para(27(a,2),95(a,1,1,2,1))]. 712 (c_0' v (x v (x v (c_0' v x)))') v (y v x) = y v c_0. [para(126(a,1),23(a,1,2,2))]. 869 (c_0' v (x v x)) v (y v c_0) = x v (y v c_0). [para(258(a,1),33(a,1,2))]. 955 (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'. [para(68(a,1),45(a,1,1,2,1,2)),rewrite([65(15)]),flip(a)]. 963 c_0'' v c_0 = c_0''. [para(322(a,1),45(a,1,1,2,1,2,1)),rewrite([322(14),5(13),322(12),330(14),322(10)]),flip(a)]. 999 c_0'' v (x v c_0) = x v c_0''. [back_rewrite(339),rewrite([963(5),963(11)])]. 1028 ((x v (y v (z v (u v x')))')' v (z v (y v (u v c_0)))')' = x. [para(33(a,1),31(a,1,1,2,1,2))]. 1078 (c_0' v (c_0 v c_0)') v c_0'' = c_0''. [para(963(a,1),52(a,1,2)),rewrite([963(16)])]. 1082 ((c_0'' v (x v c_0))' v (x v c_0')')' = x. [para(999(a,2),9(a,1,1,1,1))]. 1083 c_0' v (c_0'' v (x v c_0)) = x v c_0. [para(999(a,2),23(a,1,2))]. 1119 c_0'' v (x v c_0) = (c_0' v (x' v x')') v c_0''. [para(63(a,1),999(a,1,2))]. 1136 c_0' v (c_0'' v (x v (y v c_0))) = x v (y v c_0). [para(1083(a,1),18(a,2,2))]. 1137 c_0'' v (x v (c_0' v c_0)) = x v c_0. [para(1083(a,1),18(a,2))]. 1157 (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0''. [para(49(a,1),1137(a,1,2)),rewrite([963(5),5(14)]),flip(a)]. 1263 (c_0' v c_0''')'' = c_0'. [para(1078(a,1),42(a,1,1,1,1,2,1)),rewrite([49(17),955(11)])]. 1266 (c_0' v c_0''')' = c_0. [para(1263(a,1),17(a,1,2)),rewrite([955(11)])]. 1271 ((c_0' v c_0'''')' v c_0)' = c_0'. [para(1266(a,1),9(a,1,1,2))]. 1284 (c_0''' v (c_0' v c_0)')' = c_0''. [para(1266(a,1),42(a,1,1,1,1,2)),rewrite([963(5)])]. 1519 ((((c_0' v c_0'''')' v c_0) v c_0'')' v c_0')' = (c_0' v c_0'''')' v c_0. [para(1271(a,1),25(a,1,1,1,1,2,1))]. 1546 ((c_0''' v (c_0' v c_0)'')' v c_0'')' = c_0'''. [para(1284(a,1),9(a,1,1,2))]. 1707 (c_0' v (x v x)'')' v x = c_0. [para(152(a,1),9(a,1,1,1,1)),rewrite([651(12),24(8)]),flip(a)]. 2028 (((c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))') v x)' v c_0')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'. [para(165(a,1),20(a,1,1,2,1)),rewrite([5(23),5(25),5(24),5(56),5(58),5(57)])]. 2115 ((x v c_0')' v ((c_0' v (y v (y v (c_0' v y)))') v (x v y))')' = x. [para(169(a,1),19(a,1,1,1,1,2,1))]. 2387 c_0 v (c_0' v c_0) = c_0. [para(869(a,1),45(a,1,1,2,1,2)),rewrite([5(10),5(9),126(13),5(7)]),flip(a)]. 2416 c_0 v (x v (c_0' v c_0)) = x v c_0. [para(2387(a,1),5(a,1,2)),flip(a)]. 2422 ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0. [para(2387(a,1),26(a,1,1,2,1))]. 2426 c_0'' = c_0 v c_0. [para(2387(a,1),52(a,1,2)),rewrite([5(11),1157(15)])]. 2428 c_0 v (x v (y v (z v (c_0' v c_0)))) = x v (y v (z v c_0)). [para(2387(a,1),29(a,1,2,2,2)),flip(a)]. 2488 (c_0 v (((c_0 v c_0)' v (c_0' v c_0)'')' v c_0))' = (c_0 v c_0)'. [back_rewrite(1546),rewrite([2426(3),2426(15),5(16),2426(20)])]. 2493 ((c_0 v (c_0 v c_0))' v c_0')' = c_0. [back_rewrite(1519),rewrite([2426(5),1707(11),2426(4),2426(15),1707(21)])]. 2544 (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0 v c_0. [back_rewrite(1157),rewrite([2426(18)])]. 2565 (c_0 v c_0) v (c_0' v (x v (y v c_0))) = x v (y v c_0). [back_rewrite(1136),rewrite([2426(5),5(10)])]. 2582 (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0). [back_rewrite(1119),rewrite([2426(3),2426(16),5(17),63(16)])]. 2601 ((c_0 v (x v c_0))' v (x v c_0')')' = x. [back_rewrite(1082),rewrite([2426(3),2582(6)])]. 2619 (c_0' v (x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))')' = x v (c_0 v c_0). [back_rewrite(672),rewrite([2426(5),2426(9),2426(20)])]. 2634 ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'. [back_rewrite(66),rewrite([2426(7),5(8)])]. 3579 c_0' v (c_0' v c_0')' = c_0. [para(49(a,1),2601(a,1,1,2,1)),rewrite([63(12),2493(10)]),flip(a)]. 3588 (c_0' v x')' v (c_0' v x)' = c_0. [para(26(a,1),2601(a,1,1,2,1)),rewrite([149(13),2493(10)]),flip(a)]. 3836 c_0' v (x v (c_0' v c_0')') = x v c_0. [para(3579(a,1),5(a,1,2)),flip(a)]. 3838 (c_0' v c_0') v c_0 = c_0' v c_0. [para(3579(a,1),23(a,1,2))]. 3847 (c_0' v ((c_0' v c_0')' v ((c_0' v c_0')' v c_0))') v (c_0' v c_0')' = c_0. [para(3579(a,1),169(a,1,1,2,1,2,2))]. 3887 (c_0' v x')' v (y v (z v (c_0' v x)')) = y v (z v c_0). [para(3588(a,1),18(a,1,2,2)),flip(a)]. 3890 (c_0' v x')' v c_0 = (c_0' v x) v c_0. [para(3588(a,1),23(a,1,2)),flip(a)]. 3947 (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v (c_0' v c_0')' = c_0. [back_rewrite(3847),rewrite([3890(16),5(15),3890(14)])]. 4047 (((x v (y v (z v (u v x')))')' v (y v (z v (u v c_0)))'')' v x)' = (x v (y v (z v (u v x')))')'. [para(44(a,1),22(a,1,1,1,1,2,1,1))]. 4117 (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v c_0 = c_0' v c_0. [para(165(a,1),3836(a,1,2)),rewrite([3836(28),3890(20),5(19),3890(18)]),flip(a)]. 4145 (c_0' v c_0')' = c_0' v c_0. [para(3890(a,1),21(a,1,1,2,1,2)),rewrite([45(14)]),flip(a)]. 4237 c_0' v (c_0' v c_0) = c_0. [back_rewrite(3947),rewrite([4145(21),5(20),4117(19)])]. 4273 c_0' v c_0 = c_0 v c_0. [para(4237(a,1),52(a,1,2)),rewrite([5(11),2544(15)]),flip(a)]. 4274 c_0 v (c_0 v c_0) = c_0. [para(52(a,2),4237(a,1,2)),rewrite([5(11),49(10),4273(6),5(6),4273(5)])]. 4316 (c_0' v c_0') v c_0 = c_0 v c_0. [back_rewrite(3838),rewrite([4273(11)])]. 4379 (c_0 v c_0)' = c_0'. [back_rewrite(2488),rewrite([4273(9),17(11),4273(5),4274(5)]),flip(a)]. 4392 c_0 v (x v (y v (z v (c_0 v c_0)))) = x v (y v (z v c_0)). [back_rewrite(2428),rewrite([4273(5)])]. 4395 c_0 v c_0 = c_0. [back_rewrite(2422),rewrite([4273(5),4379(5),17(4),4316(7)])]. 4398 c_0 v (x v c_0) = x v c_0. [back_rewrite(2416),rewrite([4273(5),4395(4)])]. 4431 c_0 v (x v (y v (z v c_0))) = x v (y v (z v c_0)). [back_rewrite(4392),rewrite([4395(4)])]. 4447 c_0' v c_0 = c_0. [back_rewrite(4273),rewrite([4395(7)])]. 4523 (c_0' v (x v ((x v c_0) v ((x v c_0) v c_0)))')' = x v c_0. [back_rewrite(2619),rewrite([4395(5),4395(7),4395(16)])]. 4527 c_0' v (x v (y v c_0)) = x v (y v c_0). [back_rewrite(2565),rewrite([4395(3),4431(8)])]. 4530 c_0'' = c_0. [back_rewrite(2426),rewrite([4395(6)])]. 4536 (((x v x'')' v c_0)' v x)' = (x v x'')'. [back_rewrite(2634),rewrite([4398(8)])]. 4630 (((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)' v c_0')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'. [para(165(a,1),46(a,1,1,2,1)),rewrite([5(20),5(22),5(21),5(50),5(52),5(51)])]. 4712 x v ((x v c_0) v c_0) = x v c_0. [para(869(a,1),50(a,1,1,2,1,2,2)),rewrite([5(11),4527(12),5(10),4523(13),5(9),4527(10)]),flip(a)]. 4736 (c_0' v (x v c_0)')' = x v c_0. [para(3588(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite([3887(16),4712(7),3588(17)])]. 4742 x v ((c_0' v (x v c_0)') v c_0) = c_0. [para(4398(a,1),52(a,1,2)),rewrite([5(7),4712(7),5(9),4395(12)])]. 4747 x v (y v ((x v c_0) v c_0)) = y v (x v c_0). [para(4712(a,1),5(a,1,2)),flip(a)]. 4856 ((x v c_0)' v c_0')' = x v c_0. [para(4736(a,1),42(a,1,1,1,1,2)),rewrite([5(5),4712(5),4447(7)])]. 4869 ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x. [para(4856(a,1),19(a,1,1,1,1,2))]. 4879 ((x v c_0)' v ((x v c_0) v ((x v c_0)' v c_0))')' = x v c_0. [para(4856(a,1),21(a,1,1,2,1,2,1)),rewrite([5(11),4856(21)])]. 4887 ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0. [para(4856(a,1),42(a,1,1,1,1,2)),rewrite([4398(4)])]. 4988 x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0. [para(4712(a,1),53(a,1,2,1,2,1,2,1)),rewrite([4747(10),5(7),4712(7),5(11)])]. 4999 x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0. [para(4742(a,1),5(a,1,2)),flip(a)]. 5007 (((x v ((c_0' v (x v c_0)') v c_0)')' v c_0)' v x)' = (x v ((c_0' v (x v c_0)') v c_0)')'. [para(4742(a,1),22(a,1,1,1,1,2,1,1)),rewrite([4530(14)])]. 5022 (x v c_0) v c_0 = c_0. [back_rewrite(4988),rewrite([4999(12)])]. 5040 (x v c_0) v (y v c_0) = y v c_0. [para(5022(a,1),5(a,1,2)),flip(a)]. 5056 x v c_0 = c_0. [back_rewrite(4879),rewrite([5040(11),4887(11)]),flip(a)]. 5060 (c_0' v x)' = (x v c_0')'. [back_rewrite(5007),rewrite([5056(4),5056(7),5056(6),5056(8),5056(11)])]. 5089 (c_0' v (c_0' v (x v c_0'))')' = x. [back_rewrite(4869),rewrite([5056(2),5056(2),5056(4)])]. 5139 (x v x'')' = (c_0' v x)'. [back_rewrite(4536),rewrite([5056(6)]),flip(a)]. 5186 (x v (y v (z v (u v x')))')' = (c_0' v x)'. [back_rewrite(4047),rewrite([5056(9),5056(9),5056(9),4530(10),5056(9)]),flip(a)]. 5637 (c_0' v (c_0' v x)')' = x. [back_rewrite(1028),rewrite([5186(7),5056(6),5056(6),5056(6),5060(8,R)])]. 5717 (c_0' v (x v (x v (c_0' v x)))') v (y v x) = c_0. [back_rewrite(712),rewrite([5056(13)])]. 5768 (c_0' v (x v (((y v x') v z')' v ((y v x') v z)'))')' = x. [back_rewrite(185),rewrite([5056(2)])]. 5779 (c_0' v (x v x)') v (y v x) = c_0. [back_rewrite(52),rewrite([5056(9)])]. 5793 (c_0' v ((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'. [back_rewrite(4630),rewrite([5060(30,R)])]. 5810 (c_0' v ((c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))') v x)')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'. [back_rewrite(2028),rewrite([5060(33,R)])]. 5880 (c_0' v (((c_0' v x')' v c_0') v x)')' = (c_0' v x')' v c_0'. [back_rewrite(108),rewrite([5139(8),5139(20)])]. 5882 ((x v y)' v ((c_0' v y)' v (x v c_0'))')' = x. [back_rewrite(91),rewrite([5139(6)])]. 5887 x v c_0' = x. [back_rewrite(5089),rewrite([5637(11)])]. 5910 x v ((x v y) v ((x v y) v y)) = x v y. [back_rewrite(682),rewrite([5637(13)])]. 5917 x'' = x. [back_rewrite(2115),rewrite([5887(3),5717(12),5887(4)])]. 5926 (c_0' v x)' = x'. [back_rewrite(523),rewrite([5887(3),5779(8),5917(4),5056(3),5887(7)])]. 5933 ((x v y)' v (y' v x)')' = x. [back_rewrite(5882),rewrite([5926(6),5887(6)])]. 5935 x v x = x. [back_rewrite(5880),rewrite([5926(7),5917(4),5887(5),5926(6),5917(3),5926(6),5917(3),5887(4)])]. 6061 (c_0' v x) v x = c_0' v x. [back_rewrite(5810),rewrite([5910(26),5926(14),9(11),5926(9),5917(6),5910(28),5926(16),9(13)])]. 6063 c_0' v x = x. [back_rewrite(5793),rewrite([5935(11),5935(15),5935(17),6061(18),5935(17),5926(15),5926(12),5926(9),5917(6),6061(6),5926(6),5926(5),5917(2),5935(9),5935(13),5935(15),6061(16),5935(15),5926(13),5926(10),5926(7),5917(4)]),flip(a)]. 6077 x v (((y v x') v z')' v ((y v x') v z)') = x. [back_rewrite(5768),rewrite([6063(15),5917(13)])]. 6578 (x v y')' v (x v y)' = x'. [para(9(a,1),5917(a,1,1)),flip(a)]. 6581 x v (x v ((x v y')' v y))' = x v y'. [para(21(a,1),5917(a,1,1)),rewrite([5917(4)]),flip(a)]. 6587 x v (y v x')' = x. [back_rewrite(6077),rewrite([6578(10)])]. 6642 x v y = y v x. [para(5887(a,1),5(a,1,2)),rewrite([5887(4)])]. 6643 x v (y v z) = z v (x v y). [para(5887(a,1),18(a,1,2,2)),rewrite([5887(5)])]. 6667 x v (x v y)' = x v y'. [back_rewrite(6581),rewrite([6642(4),6587(4)])]. 7269 x v (y v (z v x')') = y v x. [para(6587(a,1),5(a,1,2)),flip(a)]. 7273 x v (x' v y)' = x. [para(6642(a,1),6587(a,1,2,1))]. 7318 x v (y v (x' v z))' = x. [para(5(a,1),7273(a,1,2,1))]. 8516 (x v y) v z = x v (y v z). [para(6643(a,2),6642(a,1)),flip(a)]. 8771 x v (y v x)' = x v y'. [para(6642(a,1),6667(a,1,2,1))]. 8832 x v ((y v (x' v z))' v u) = x v u. [para(7318(a,1),8516(a,1,1)),flip(a)]. 8848 x v (y v (z v x)') = y v (x v z'). [para(8771(a,1),5(a,1,2)),flip(a)]. 8902 (x v y)' v (y' v x)' = x'. [para(5933(a,1),5917(a,1,1)),flip(a)]. 9756 (x v (y v z)')' = (x v (z v y'))' v (x v z')'. [para(7269(a,1),8902(a,1,2,1)),rewrite([5917(2),6642(4),8848(4),5917(10)]),flip(a)]. 9813 $F # answer(MOD). [back_rewrite(16),rewrite([9756(9),6642(8),8516(8),8832(17),9756(17),6642(16),8516(16),6642(22),8832(25)]),xx(a)]. ============================== end of proof ========================== % Disable descendants (x means already disabled): 15x 16x given #197 (T,wt=13): 8910 (x v y')' v (y v x)' = x'. [para(8771(a,1),6580(a,1,1,1)),rewrite([5917(6),6604(5)])]. given #198 (T,wt=13): 8940 (x v y')' v (z v y) = z v y. [para(6587(a,1),6605(a,1,2,2)),rewrite([6587(9)])]. given #199 (A,wt=20): 5177 x v (y v (z v (u v (w v (v5 v (v6 v (v7 v x'))))))) = c_0. [back_rewrite(4065),rewrite([5056(11),5056(11),5056(11),5056(11),5056(11),5056(11),5056(11)])]. given #200 (F,wt=29): 9814 (c6 v (c4' v c5'))' v (c4' v c6')' != (c4' v c5')' v (c4' v c6')' # answer(DIST1). [back_rewrite(14),rewrite([9756(8),5(7)])]. given #201 (T,wt=13): 8941 (x' v y)' v (z v x) = z v x. [para(7273(a,1),6605(a,1,2,2)),rewrite([7273(9)])]. given #202 (T,wt=13): 9057 (x' v y)' v (y v x)' = y'. [para(5917(a,1),8852(a,1,2,1,2))]. given #203 (T,wt=13): 9058 (x v y)' v (x' v y)' = y'. [para(6642(a,1),8852(a,1,2,1))]. given #204 (T,wt=14): 5765 x v (y v (z v (u v (w v x')))) = c_0. [back_rewrite(229),rewrite([5056(8),5056(8),5056(8),5056(8)])]. given #205 (A,wt=18): 5425 x v (y v (z v (u v (w v (v5 v (v6 v x')))))) = c_0. [back_rewrite(2704),rewrite([5056(10),5056(10),5056(10),5056(10),5056(10),5056(10)])]. given #206 (T,wt=14): 5989 x' v (y v (z v (u v (w v x)))) = c_0. [back_rewrite(5436),rewrite([5926(4),5887(4)])]. given #207 (T,wt=14): 5999 (x v y)' v (z v (x v (u v y))) = c_0. [back_rewrite(5339),rewrite([5926(5),5887(5)])]. given #208 (T,wt=14): 6091 x' v (y v (z v (u v x)))' = x'. [back_rewrite(5622),rewrite([5935(5),6063(6),6063(10),5917(8),5935(9),6063(10)])]. given #209 (T,wt=14): 7177 x v (y v (z v (u v (x' v w)))) = c_0. [para(6781(a,1),29(a,1,2,2,2)),rewrite([5056(2),5056(2),5056(2)]),flip(a)]. given #210 (A,wt=16): 5705 x v (y v (z v (u v (w v (v5 v x'))))) = c_0. [back_rewrite(776),rewrite([5056(9),5056(9),5056(9),5056(9),5056(9)])]. given #211 (T,wt=14): 7178 x' v (y v (z v (u v (x v w)))) = c_0. [para(6781(a,1),34(a,1,2,2)),rewrite([5056(2),5056(2)]),flip(a)]. given #212 (T,wt=14): 7266 x' v (y v (z v (x v u)))' = x'. [para(6781(a,1),77(a,1,1,2,1,2)),rewrite([5056(9),6642(10),6063(10),5917(8)])]. given #213 (T,wt=14): 7380 x' v (y v (z v x)') = y v x'. [para(5966(a,1),5(a,1,2)),flip(a)]. given #214 (T,wt=14): 7563 x v (y v (z v (u v (x v y)'))) = c_0. [para(6869(a,1),37(a,1,2,2)),rewrite([5056(2),5056(2)]),flip(a)]. given #215 (A,wt=16): 5975 (x v y)' v (x v (z v y))' = (x v y)'. [back_rewrite(5642),rewrite([5926(7),5887(7),5926(11),5917(8),5926(11),5887(11)])]. given #216 (T,wt=14): 7655 x' v (y v (x v z)') = y v x'. [para(7326(a,1),5(a,1,2)),flip(a)]. given #217 (T,wt=14): 8522 (x v y)' v (z v (y v (u v x))) = c_0. [para(6643(a,1),5967(a,1,2,2))]. given #218 (T,wt=12): 10176 (x v y)' v (z v (y v x)) = c_0. [para(5935(a,1),8522(a,1,2,2,2))]. given #219 (T,wt=14): 8523 (x v y)' v (z v (x v (y v u))) = c_0. [para(6643(a,2),5967(a,1,2,2))]. given #220 (A,wt=16): 5978 (x v y)' v (z v (u v (x v (w v y)))) = c_0. [back_rewrite(5613),rewrite([5926(5),5887(5)])]. given #221 (T,wt=14): 8528 x v (y v (z v ((x v y)' v u))) = c_0. [para(6643(a,2),7668(a,1,1)),rewrite([8516(6),8516(5)])]. given #222 (T,wt=14): 8826 x' v ((y v x)' v z) = x' v z. [para(5966(a,1),8516(a,1,1)),flip(a)]. given #223 (T,wt=14): 8827 x' v ((x v y)' v z) = x' v z. [para(7326(a,1),8516(a,1,1)),flip(a)]. given #224 (T,wt=14): 8858 x v (y v (z v (u v (y v x)'))) = c_0. [back_rewrite(6698),rewrite([8851(4)])]. given #225 (A,wt=18): 5984 (x v (y v z))' v (u v (y v (w v (x v z)))) = c_0. [back_rewrite(5559),rewrite([5926(6),5887(6)])]. given #226 (T,wt=14): 8942 (x v y)' v (z v y') = z v y'. [para(5966(a,1),6605(a,1,2,2)),rewrite([5966(9)])]. given #227 (T,wt=14): 8943 (x v y)' v (z v x') = z v x'. [para(7326(a,1),6605(a,1,2,2)),rewrite([7326(9)])]. given #228 (T,wt=14): 10064 (x v y)' v (z v (u v (y v x))) = c_0. [para(6642(a,1),5999(a,1,2,2)),rewrite([8516(4)])]. given #229 (T,wt=14): 10177 (x v y)' v (z v (y v (x v u))) = c_0. [para(6642(a,1),8522(a,1,2,2,2))]. given #230 (A,wt=18): 5995 (x v (y v z))' v (u v (x v (y v (w v z)))) = c_0. [back_rewrite(5373),rewrite([5926(6),5887(6)])]. given #231 (T,wt=14): 10221 x v (y v (z v ((y v x)' v u))) = c_0. [para(8528(a,1),5(a,1)),flip(a)]. given #232 (T,wt=15): 6109 x v (y v (z v (u v (w v x'))))' = x. [back_rewrite(5181),rewrite([6063(11),5917(9)])]. given #233 (T,wt=15): 7323 x v (y v (z v (u v (x' v w))))' = x. [para(29(a,2),7273(a,1,2,1))]. given #234 (T,wt=15): 8341 x v (y v (z v (u v x'))') = y v x. [para(6586(a,1),5(a,1,2)),flip(a)]. given #235 (A,wt=20): 6076 (x v (y v z))' v (y v (x v z))' = (x v (y v z))'. [back_rewrite(5784),rewrite([5950(9),6063(8),6063(11),5917(9),5950(14),6063(13)])]. given #236 (T,wt=14): 10603 (x v y)' v (y v x)' = (x v y)'. [para(5887(a,1),6076(a,1,1,1,2)),rewrite([5887(5),5887(8)])]. given #237 (T,wt=15): 8769 x v (y v (x v z)') = y v (x v z'). [para(6667(a,1),5(a,1,2)),flip(a)]. given #238 (T,wt=15): 8770 x v (y v (x v z))' = x v (y v z)'. [para(5(a,1),6667(a,1,2,1))]. given #239 (T,wt=15): 8821 x v (y v (z v (x' v u))') = y v x. [para(7318(a,1),5(a,1,2)),flip(a)]. given #240 (A,wt=17): 6110 x v (y v (z v (u v (w v (v5 v x')))))' = x. [back_rewrite(5179),rewrite([6063(12),5917(10)])]. given #241 (T,wt=15): 8829 x v ((y v (z v x'))' v u) = x v u. [para(6586(a,1),8516(a,1,1)),flip(a)]. given #242 (T,wt=15): 8830 x v ((x v y)' v z) = x v (y' v z). [para(6667(a,1),8516(a,1,1)),rewrite([8516(3)]),flip(a)]. given #243 (T,wt=15): 8832 x v ((y v (x' v z))' v u) = x v u. [para(7318(a,1),8516(a,1,1)),flip(a)]. given #244 (T,wt=15): 8848 x v (y v (z v x)') = y v (x v z'). [para(8771(a,1),5(a,1,2)),flip(a)]. given #245 (A,wt=16): 6387 x' v (y v (z v (u v (w v (v5 v x))))) = c_0. [back_rewrite(5420),rewrite([5935(3),6063(4)])]. given #246 (T,wt=15): 8849 x v ((y v x)' v z) = x v (y' v z). [para(8771(a,1),8516(a,1,1)),rewrite([8516(3)]),flip(a)]. given #247 (T,wt=15): 8851 x v (y v (z v x))' = x v (y v z)'. [para(8516(a,1),8771(a,1,2,1))]. given #248 (T,wt=15): 8944 (x v (y v z'))' v (u v z) = u v z. [para(6586(a,1),6605(a,1,2,2)),rewrite([6586(11)])]. given #249 (T,wt=15): 8946 (x v (y' v z))' v (u v y) = u v y. [para(7318(a,1),6605(a,1,2,2)),rewrite([7318(11)])]. given #250 (A,wt=18): 6408 (x v (y v z))' v (u v (w v (y v (x v z)))) = c_0. [back_rewrite(5077),rewrite([5950(7),6063(6)])]. given #251 (T,wt=15): 10229 (x v y)' v (z v y) = y v (x' v z). [para(8826(a,1),8771(a,1,2,1)),rewrite([8516(7),8771(6),5917(4),5917(9),6642(8),8849(8)])]. given #252 (T,wt=15): 10311 (x v y)' v (z v x) = x v (y' v z). [para(8827(a,1),8771(a,1,2,1)),rewrite([8516(7),8771(6),5917(4),5917(9),6642(8),8830(8)])]. given #253 (T,wt=16): 7179 x v (y v (z v (u v (w v (x' v v5))))) = c_0. [para(6781(a,1),38(a,1,2,2,2,2)),rewrite([5056(2),5056(2),5056(2),5056(2)]),flip(a)]. given #254 (T,wt=16): 7573 x' v (y v (z v (u v (w v (x v v5))))) = c_0. [para(7175(a,1),29(a,1,2,2,2)),rewrite([5056(2),5056(2),5056(2)]),flip(a)]. given #255 (A,wt=17): 6611 x v (y v (z v (u v x))) = y v (z v (u v x)). [para(5935(a,1),29(a,1,2,2,2)),flip(a)]. given #256 (T,wt=16): 7659 x' v (y v (z v (u v (x v w))))' = x'. [para(29(a,2),7326(a,1,2,1))]. given #257 (T,wt=16): 8519 (x v y)' v (y v (z v x))' = (x v y)'. [para(6643(a,1),5966(a,1,2,1))]. given #258 (T,wt=16): 8520 (x v y)' v (x v (y v z))' = (x v y)'. [para(6643(a,2),5966(a,1,2,1))]. given #259 (T,wt=16): 8882 x' v (y v (z v (u v x))') = y v x'. [para(5976(a,1),5(a,1,2)),flip(a)]. given #260 (A,wt=21): 6629 x v (y v (z v (u v (w v x)))) = y v (z v (u v (w v x))). [para(5935(a,1),38(a,1,2,2,2,2)),flip(a)]. given #261 (T,wt=16): 8884 x' v ((y v (z v x))' v u) = x' v u. [para(5976(a,1),8516(a,1,1)),flip(a)]. given #262 (T,wt=16): 8885 x v (y v (z v (u v ((x v y)' v w)))) = c_0. [para(7174(a,1),8516(a,1)),flip(a)]. given #263 (T,wt=16): 8896 (x v y)' v (z v (u v (x v (y v w)))) = c_0. [para(8516(a,1),7176(a,1,2,2,2))]. given #264 (T,wt=16): 8897 x' v (y v (z v (x v u))') = y v x'. [para(7656(a,1),5(a,1,2)),flip(a)]. given #265 (A,wt=21): 6658 x v (y v (z v (u v (x v w)))) = y v (z v (u v (x v w))). [back_rewrite(6630),rewrite([6642(2),6604(2)])]. given #266 (T,wt=16): 8898 x' v ((y v (x v z))' v u) = x' v u. [para(7656(a,1),8516(a,1,1)),flip(a)]. given #267 (T,wt=16): 8948 (x v (y v z))' v (u v z') = u v z'. [para(5976(a,1),6605(a,1,2,2)),rewrite([5976(11)])]. given #268 (T,wt=16): 8949 (x v (y v z))' v (u v y') = u v y'. [para(7656(a,1),6605(a,1,2,2)),rewrite([7656(11)])]. given #269 (T,wt=16): 10056 x' v (y v (z v (u v (w v x))))' = x'. [para(5989(a,1),6667(a,1,2,1)),rewrite([5887(4)]),flip(a)]. given #270 (A,wt=17): 6664 x v (y v (z v (x v u))) = y v (z v (x v u)). [back_rewrite(6612),rewrite([6642(2),6604(2)])]. given #271 (T,wt=16): 10119 (x v y)' v (z v (y v x))' = (x v y)'. [para(6642(a,1),5975(a,1,2,1)),rewrite([8516(4)])]. given #272 (T,wt=16): 10209 (x v y)' v (z v (u v (w v (y v x)))) = c_0. [para(6642(a,1),5978(a,1,2,2,2)),rewrite([8516(4)])]. given #273 (T,wt=16): 10429 x v (y v (z v (u v ((y v x)' v w)))) = c_0. [para(8858(a,1),8516(a,1,1)),rewrite([6005(2),8516(7),8516(6),8516(5)]),flip(a)]. given #274 (T,wt=16): 10634 (x v (y v z))' v (y v x)' = (x v y)'. [para(10603(a,1),8825(a,2)),rewrite([5917(5),8516(4),10633(9)])]. given #275 (A,wt=24): 6933 x v (y v (z v (u v (w v ((x v (y v (z v (u v w))))' v v5))))) = c_0. [back_rewrite(6593),rewrite([6643(7)])]. given #276 (T,wt=16): 10635 (x v (y v z))' v (z v y)' = (z v y)'. [para(10603(a,1),8940(a,1,2)),rewrite([5917(3),10603(11)])]. given #277 (T,wt=16): 11250 (x v (y v z))' v (z v x)' = (z v x)'. [para(8519(a,1),6642(a,1)),flip(a)]. given #278 (T,wt=16): 11251 (x v y)' v (y v (x v z))' = (x v y)'. [para(6642(a,1),8519(a,1,2,1,2))]. given #279 (T,wt=17): 7270 x v (y v (z v (u v x')')) = y v (z v x). [para(6587(a,1),18(a,1,2,2)),flip(a)]. given #280 (A,wt=20): 6942 x v (y v (z v (u v ((y v (x v (z v u)))' v w)))) = c_0. [back_rewrite(6432),rewrite([6643(6)])]. given #281 (T,wt=17): 7320 x v (y v (z v (x' v u)')) = y v (z v x). [para(7273(a,1),18(a,1,2,2)),flip(a)]. given #282 (T,wt=17): 7325 x v (y v (z v (u v (w v (x' v v5)))))' = x. [para(38(a,2),7273(a,1,2,1))]. given #283 (T,wt=17): 8668 x v (y v (z v (u v (w v x')))') = x v y. [back_rewrite(7646),rewrite([8516(7)])]. given #284 (T,wt=17): 8906 (x v y)' v (z v (x v y')') = z v x'. [para(6580(a,1),5(a,1,2)),flip(a)]. given #285 (A,wt=24): 6948 x v (y v (z v (u v (w v ((z v (x v (u v (y v w))))' v v5))))) = c_0. [back_rewrite(6426),rewrite([6643(7)])]. given #286 (T,wt=17): 8908 (x v y)' v ((x v y')' v z) = x' v z. [para(6580(a,1),8516(a,1,1)),flip(a)]. given #287 (T,wt=17): 8938 x v ((y v (z v (u v x')))' v w) = x v w. [para(6585(a,1),8516(a,1,1)),flip(a)]. given #288 (T,wt=17): 8951 (x v (y v (z v u')))' v (w v u) = w v u. [para(6585(a,1),6605(a,1,2,2)),rewrite([6585(13)])]. given #289 (T,wt=17): 8955 x v (y v ((z v x')' v u)) = y v (x v u). [para(7269(a,1),8516(a,1,1)),rewrite([8516(2),8516(7)]),flip(a)]. given #290 (A,wt=20): 6954 x v (y v (z v (u v ((x v (z v (y v u)))' v w)))) = c_0. [back_rewrite(6420),rewrite([6643(6)])]. given #291 (T,wt=17): 8960 (x v y')' v (z v (u v y)) = z v (u v y). [para(7269(a,1),6605(a,1,2,2)),rewrite([8516(7),6664(7),7269(11)])]. given #292 (T,wt=17): 8995 x v (y v ((x' v z)' v u)) = y v (x v u). [para(7317(a,1),8516(a,1,1)),rewrite([8516(2),8516(7)]),flip(a)]. given #293 (T,wt=17): 9000 (x' v y)' v (z v (u v x)) = z v (u v x). [para(7317(a,1),6605(a,1,2,2)),rewrite([8516(7),6664(7),7317(11)])]. given #294 (T,wt=17): 9001 x v (y v (z v (u v (x' v w)))') = y v x. [para(7321(a,1),5(a,1,2)),flip(a)]. given #295 (A,wt=20): 6965 x v (y v (z v (u v ((x v (y v (z v u)))' v w)))) = c_0. [back_rewrite(5993),rewrite([6643(6)])]. given #296 (T,wt=17): 9002 x v ((y v (z v (x' v u)))' v w) = x v w. [para(7321(a,1),8516(a,1,1)),flip(a)]. given #297 (T,wt=17): 9004 (x v (y v (z' v u)))' v (w v z) = w v z. [para(7321(a,1),6605(a,1,2,2)),rewrite([7321(13)])]. given #298 (T,wt=17): 9012 (x v y')' v (z v (y v u)) = z v (y v u). [para(8823(a,1),6605(a,1,2,2)),rewrite([8516(7),6605(6),8823(11)])]. given #299 (T,wt=17): 9020 (x' v y)' v (z v (x v u)) = z v (x v u). [para(8825(a,1),6605(a,1,2,2)),rewrite([8516(7),6605(6),8825(11)])]. given #300 (A,wt=21): 7271 x v (y v (z v (u v (w v x')'))) = y v (z v (u v x)). [para(6587(a,1),29(a,1,2,2,2)),flip(a)]. given #301 (T,wt=17): 9055 (x v y)' v (z v (y v x')') = z v y'. [para(8852(a,1),5(a,1,2)),flip(a)]. given #302 (T,wt=17): 9059 (x v y)' v ((y v x')' v z) = y' v z. [para(8852(a,1),8516(a,1,1)),flip(a)]. given #303 (T,wt=17): 9751 (x v y)' v (z v (y' v x)') = z v x'. [para(8902(a,1),5(a,1,2)),flip(a)]. ============================== PROOF ================================= % Proof 4 at 6.41 (+ 0.05) seconds: DIST1. % Length of proof is 181. % Level of proof is 50. % Maximum clause weight is 86.000. % Given clauses 303. 3 x ^ (y v z) = (x ^ y) v (x ^ z) # answer(DIST1) # label(non_clause) # label(goal). [goal]. 5 x v (y v z) = y v (x v z) # label(AJ). [assumption]. 6 x ^ y = (x' v y')' # label(DM). [assumption]. 7 x v x' = y v y' # label(ONE). [assumption]. 8 (x v y') ^ (x v y) = x # label(CUT). [assumption]. 9 ((x v y')' v (x v y)')' = x. [copy(8),rewrite([6(4)])]. 13 (c4 ^ c5) v (c4 ^ c6) != c4 ^ (c5 v c6) # answer(DIST1). [deny(3)]. 14 (c4' v (c5 v c6)')' != (c4' v c5')' v (c4' v c6')' # answer(DIST1). [copy(13),rewrite([6(3),6(9),6(18)]),flip(a)]. 17 x v x' = c_0. [new_symbol(7)]. 18 x v (y v (z v u)) = z v (x v (y v u)). [para(5(a,1),5(a,1,2))]. 19 ((x v (y v z)')' v (y v (x v z))')' = x. [para(5(a,1),9(a,1,1,2,1))]. 20 ((x v y)' v (x v ((y v z')' v (y v z)'))')' = x. [para(9(a,1),9(a,1,1,1,1,2))]. 21 (x v (x v ((x v y')' v y))')' = (x v y')'. [para(9(a,1),9(a,1,1,1)),rewrite([5(5)])]. 22 (((x v y')' v (x v y)'')' v x)' = (x v y')'. [para(9(a,1),9(a,1,1,2))]. 23 x v (y v x') = y v c_0. [para(17(a,1),5(a,1,2)),flip(a)]. 24 (c_0' v (x v x)')' = x. [para(17(a,1),9(a,1,1,1,1))]. 25 ((x v x'')' v c_0')' = x. [para(17(a,1),9(a,1,1,2,1))]. 26 ((x v y')' v (x v y)') v x = c_0. [para(9(a,1),17(a,1,2))]. 27 x v (y v (z v (u v w))) = z v (x v (u v (y v w))). [para(18(a,1),5(a,1,2))]. 29 x v (y v (z v (u v w))) = u v (x v (y v (z v w))). [para(18(a,2),5(a,1,2))]. 31 ((x v (y v (z v u))')' v (z v (x v (y v u)))')' = x. [para(18(a,1),9(a,1,1,2,1))]. 33 x v (y v (z v x')) = y v (z v c_0). [para(17(a,1),18(a,1,2,2)),flip(a)]. 42 ((x v (y v x')')' v (y v c_0)')' = x. [para(23(a,1),9(a,1,1,2,1))]. 44 x v (y v (z v (u v x'))) = y v (z v (u v c_0)). [para(23(a,1),18(a,1,2,2)),flip(a)]. 45 (c_0' v (x v ((x v y) v y))')' = x v y. [para(5(a,1),24(a,1,1,2,1))]. 46 ((x v y)' v (x v (c_0' v (y v y)'))')' = x. [para(24(a,1),9(a,1,1,1,1,2))]. 47 (x v (c_0' v (x v x))')' = c_0'. [para(24(a,1),9(a,1,1,1))]. 48 ((c_0' v (x v x)'')' v x)' = c_0'. [para(24(a,1),9(a,1,1,2))]. 49 (c_0' v (x v x)') v x = c_0. [para(24(a,1),17(a,1,2))]. 50 (c_0' v (x v (y v ((y v (x v z)) v z)))')' = y v (x v z). [para(18(a,1),24(a,1,1,2,1)),rewrite([5(6)])]. 52 (c_0' v (x v x)') v (y v x) = y v c_0. [para(24(a,1),23(a,1,2,2))]. 53 x v ((c_0' v (x v ((x v y) v y))') v y) = c_0. [para(49(a,1),5(a,1)),rewrite([5(6)]),flip(a)]. 63 (c_0' v (x' v x')') v c_0 = x v c_0. [para(49(a,1),23(a,1,2)),flip(a)]. 65 (x v ((x v x'')' v c_0)')' = (x v x'')'. [para(25(a,1),9(a,1,1,1))]. 66 (((x v x'')' v c_0'')' v x)' = (x v x'')'. [para(25(a,1),9(a,1,1,2))]. 68 ((x v x'')' v c_0') v x = c_0. [para(25(a,1),17(a,1,2))]. 85 (x v (x v (c_0' v x))')' = c_0'. [para(24(a,1),19(a,1,1,1))]. 91 ((x v y)' v ((y v y'')' v (x v c_0'))')' = x. [para(25(a,1),19(a,1,1,1,1,2))]. 95 (c_0' v (x v (c_0' v (x v x)))')' = x. [para(47(a,1),9(a,1,1,1))]. 97 (x v (c_0' v (x v x))') v c_0' = c_0. [para(47(a,1),17(a,1,2))]. 108 (c_0' v (((x' v x''')' v c_0') v x)')' = (x' v x''')' v c_0'. [para(68(a,1),9(a,1,1,1,1))]. 126 (c_0' v (x v (x v (c_0' v x)))')' = x. [para(85(a,1),9(a,1,1,1))]. 149 ((x' v y')' v (x' v y)') v c_0 = x v c_0. [para(26(a,1),23(a,1,2)),flip(a)]. 152 ((c_0' v (x v x)'')' v x) v c_0' = c_0. [para(24(a,1),26(a,1,1,2))]. 165 (c_0' v (x v (c_0' v (x v x)))') v x = c_0. [para(47(a,1),26(a,1,1,1))]. 169 (c_0' v (x v (x v (c_0' v x)))') v x = c_0. [para(85(a,1),26(a,1,1,1))]. 185 ((x v c_0)' v (y v (((x v y') v z')' v ((x v y') v z)'))')' = y. [para(23(a,1),20(a,1,1,1,1))]. 243 (c_0' v ((x v (c_0' v (x v x))') v c_0)')' = x v (c_0' v (x v x))'. [para(97(a,1),9(a,1,1,1,1))]. 248 (x v (c_0' v (x v x))') v c_0 = c_0 v c_0. [para(97(a,1),23(a,1,2)),flip(a)]. 256 x v (c_0' v (x v x))' = c_0. [back_rewrite(243),rewrite([248(10),24(8)]),flip(a)]. 258 x v (y v (c_0' v (x v x))') = y v c_0. [para(256(a,1),5(a,1,2)),flip(a)]. 266 (c_0' v (x v x)) v c_0 = x v c_0. [para(256(a,1),23(a,1,2))]. 267 c_0'' v (c_0'' v c_0)' = c_0. [para(23(a,1),256(a,1,2,1))]. 322 (c_0'' v c_0) v c_0 = c_0'' v c_0. [para(23(a,1),266(a,1,1))]. 330 (c_0' v (c_0'' v (c_0'' v c_0))')' = c_0''. [para(267(a,1),9(a,1,1,1,1))]. 339 (c_0'' v c_0) v (x v c_0) = x v (c_0'' v c_0). [para(267(a,1),33(a,1,2,2))]. 523 (((x v c_0')' v ((c_0' v (y v y)') v (x v y))'')' v x)' = (x v c_0')'. [para(52(a,2),22(a,1,1,1,1,2,1,1))]. 651 ((c_0' v (x v x)'')' v x) v c_0 = c_0 v c_0. [para(48(a,1),63(a,1,1,2,1,1)),rewrite([48(13),63(11)]),flip(a)]. 672 (c_0' v (x v ((x v c_0'') v ((x v c_0'') v c_0)))')' = x v c_0''. [para(33(a,1),95(a,1,1,2,1,2)),rewrite([5(13),5(14)])]. 682 (c_0' v (c_0' v (x v ((x v y) v ((x v y) v y))))')' = x v y. [para(27(a,2),95(a,1,1,2,1))]. 712 (c_0' v (x v (x v (c_0' v x)))') v (y v x) = y v c_0. [para(126(a,1),23(a,1,2,2))]. 869 (c_0' v (x v x)) v (y v c_0) = x v (y v c_0). [para(258(a,1),33(a,1,2))]. 955 (c_0' v c_0''')' v c_0' = (c_0' v c_0''')'. [para(68(a,1),45(a,1,1,2,1,2)),rewrite([65(15)]),flip(a)]. 963 c_0'' v c_0 = c_0''. [para(322(a,1),45(a,1,1,2,1,2,1)),rewrite([322(14),5(13),322(12),330(14),322(10)]),flip(a)]. 999 c_0'' v (x v c_0) = x v c_0''. [back_rewrite(339),rewrite([963(5),963(11)])]. 1012 (((((x v y) v (x v y)'')' v c_0') v (x v (z v y))')' v (z v c_0)')' = ((x v y) v (x v y)'')' v c_0'. [para(68(a,1),31(a,1,1,2,1,2))]. 1028 ((x v (y v (z v (u v x')))')' v (z v (y v (u v c_0)))')' = x. [para(33(a,1),31(a,1,1,2,1,2))]. 1078 (c_0' v (c_0 v c_0)') v c_0'' = c_0''. [para(963(a,1),52(a,1,2)),rewrite([963(16)])]. 1082 ((c_0'' v (x v c_0))' v (x v c_0')')' = x. [para(999(a,2),9(a,1,1,1,1))]. 1083 c_0' v (c_0'' v (x v c_0)) = x v c_0. [para(999(a,2),23(a,1,2))]. 1119 c_0'' v (x v c_0) = (c_0' v (x' v x')') v c_0''. [para(63(a,1),999(a,1,2))]. 1136 c_0' v (c_0'' v (x v (y v c_0))) = x v (y v c_0). [para(1083(a,1),18(a,2,2))]. 1137 c_0'' v (x v (c_0' v c_0)) = x v c_0. [para(1083(a,1),18(a,2))]. 1157 (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0''. [para(49(a,1),1137(a,1,2)),rewrite([963(5),5(14)]),flip(a)]. 1263 (c_0' v c_0''')'' = c_0'. [para(1078(a,1),42(a,1,1,1,1,2,1)),rewrite([49(17),955(11)])]. 1266 (c_0' v c_0''')' = c_0. [para(1263(a,1),17(a,1,2)),rewrite([955(11)])]. 1271 ((c_0' v c_0'''')' v c_0)' = c_0'. [para(1266(a,1),9(a,1,1,2))]. 1284 (c_0''' v (c_0' v c_0)')' = c_0''. [para(1266(a,1),42(a,1,1,1,1,2)),rewrite([963(5)])]. 1519 ((((c_0' v c_0'''')' v c_0) v c_0'')' v c_0')' = (c_0' v c_0'''')' v c_0. [para(1271(a,1),25(a,1,1,1,1,2,1))]. 1546 ((c_0''' v (c_0' v c_0)'')' v c_0'')' = c_0'''. [para(1284(a,1),9(a,1,1,2))]. 1707 (c_0' v (x v x)'')' v x = c_0. [para(152(a,1),9(a,1,1,1,1)),rewrite([651(12),24(8)]),flip(a)]. 2028 (((c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))') v x)' v c_0')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'. [para(165(a,1),20(a,1,1,2,1)),rewrite([5(23),5(25),5(24),5(56),5(58),5(57)])]. 2115 ((x v c_0')' v ((c_0' v (y v (y v (c_0' v y)))') v (x v y))')' = x. [para(169(a,1),19(a,1,1,1,1,2,1))]. 2387 c_0 v (c_0' v c_0) = c_0. [para(869(a,1),45(a,1,1,2,1,2)),rewrite([5(10),5(9),126(13),5(7)]),flip(a)]. 2416 c_0 v (x v (c_0' v c_0)) = x v c_0. [para(2387(a,1),5(a,1,2)),flip(a)]. 2422 ((c_0 v (c_0' v c_0)')' v c_0') v c_0 = c_0. [para(2387(a,1),26(a,1,1,2,1))]. 2426 c_0'' = c_0 v c_0. [para(2387(a,1),52(a,1,2)),rewrite([5(11),1157(15)])]. 2428 c_0 v (x v (y v (z v (c_0' v c_0)))) = x v (y v (z v c_0)). [para(2387(a,1),29(a,1,2,2,2)),flip(a)]. 2488 (c_0 v (((c_0 v c_0)' v (c_0' v c_0)'')' v c_0))' = (c_0 v c_0)'. [back_rewrite(1546),rewrite([2426(3),2426(15),5(16),2426(20)])]. 2493 ((c_0 v (c_0 v c_0))' v c_0')' = c_0. [back_rewrite(1519),rewrite([2426(5),1707(11),2426(4),2426(15),1707(21)])]. 2544 (c_0' v (c_0' v ((c_0' v c_0) v c_0))') v c_0 = c_0 v c_0. [back_rewrite(1157),rewrite([2426(18)])]. 2565 (c_0 v c_0) v (c_0' v (x v (y v c_0))) = x v (y v c_0). [back_rewrite(1136),rewrite([2426(5),5(10)])]. 2582 (c_0 v c_0) v (x v c_0) = c_0 v (x v c_0). [back_rewrite(1119),rewrite([2426(3),2426(16),5(17),63(16)])]. 2601 ((c_0 v (x v c_0))' v (x v c_0')')' = x. [back_rewrite(1082),rewrite([2426(3),2582(6)])]. 2619 (c_0' v (x v ((x v (c_0 v c_0)) v ((x v (c_0 v c_0)) v c_0)))')' = x v (c_0 v c_0). [back_rewrite(672),rewrite([2426(5),2426(9),2426(20)])]. 2634 ((c_0 v ((x v x'')' v c_0))' v x)' = (x v x'')'. [back_rewrite(66),rewrite([2426(7),5(8)])]. 3579 c_0' v (c_0' v c_0')' = c_0. [para(49(a,1),2601(a,1,1,2,1)),rewrite([63(12),2493(10)]),flip(a)]. 3588 (c_0' v x')' v (c_0' v x)' = c_0. [para(26(a,1),2601(a,1,1,2,1)),rewrite([149(13),2493(10)]),flip(a)]. 3836 c_0' v (x v (c_0' v c_0')') = x v c_0. [para(3579(a,1),5(a,1,2)),flip(a)]. 3838 (c_0' v c_0') v c_0 = c_0' v c_0. [para(3579(a,1),23(a,1,2))]. 3847 (c_0' v ((c_0' v c_0')' v ((c_0' v c_0')' v c_0))') v (c_0' v c_0')' = c_0. [para(3579(a,1),169(a,1,1,2,1,2,2))]. 3887 (c_0' v x')' v (y v (z v (c_0' v x)')) = y v (z v c_0). [para(3588(a,1),18(a,1,2,2)),flip(a)]. 3890 (c_0' v x')' v c_0 = (c_0' v x) v c_0. [para(3588(a,1),23(a,1,2)),flip(a)]. 3947 (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v (c_0' v c_0')' = c_0. [back_rewrite(3847),rewrite([3890(16),5(15),3890(14)])]. 4047 (((x v (y v (z v (u v x')))')' v (y v (z v (u v c_0)))'')' v x)' = (x v (y v (z v (u v x')))')'. [para(44(a,1),22(a,1,1,1,1,2,1,1))]. 4117 (c_0' v ((c_0' v c_0) v ((c_0' v c_0) v c_0))') v c_0 = c_0' v c_0. [para(165(a,1),3836(a,1,2)),rewrite([3836(28),3890(20),5(19),3890(18)]),flip(a)]. 4145 (c_0' v c_0')' = c_0' v c_0. [para(3890(a,1),21(a,1,1,2,1,2)),rewrite([45(14)]),flip(a)]. 4237 c_0' v (c_0' v c_0) = c_0. [back_rewrite(3947),rewrite([4145(21),5(20),4117(19)])]. 4273 c_0' v c_0 = c_0 v c_0. [para(4237(a,1),52(a,1,2)),rewrite([5(11),2544(15)]),flip(a)]. 4274 c_0 v (c_0 v c_0) = c_0. [para(52(a,2),4237(a,1,2)),rewrite([5(11),49(10),4273(6),5(6),4273(5)])]. 4316 (c_0' v c_0') v c_0 = c_0 v c_0. [back_rewrite(3838),rewrite([4273(11)])]. 4379 (c_0 v c_0)' = c_0'. [back_rewrite(2488),rewrite([4273(9),17(11),4273(5),4274(5)]),flip(a)]. 4392 c_0 v (x v (y v (z v (c_0 v c_0)))) = x v (y v (z v c_0)). [back_rewrite(2428),rewrite([4273(5)])]. 4395 c_0 v c_0 = c_0. [back_rewrite(2422),rewrite([4273(5),4379(5),17(4),4316(7)])]. 4398 c_0 v (x v c_0) = x v c_0. [back_rewrite(2416),rewrite([4273(5),4395(4)])]. 4431 c_0 v (x v (y v (z v c_0))) = x v (y v (z v c_0)). [back_rewrite(4392),rewrite([4395(4)])]. 4447 c_0' v c_0 = c_0. [back_rewrite(4273),rewrite([4395(7)])]. 4523 (c_0' v (x v ((x v c_0) v ((x v c_0) v c_0)))')' = x v c_0. [back_rewrite(2619),rewrite([4395(5),4395(7),4395(16)])]. 4527 c_0' v (x v (y v c_0)) = x v (y v c_0). [back_rewrite(2565),rewrite([4395(3),4431(8)])]. 4530 c_0'' = c_0. [back_rewrite(2426),rewrite([4395(6)])]. 4536 (((x v x'')' v c_0)' v x)' = (x v x'')'. [back_rewrite(2634),rewrite([4398(8)])]. 4630 (((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)' v c_0')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'. [para(165(a,1),46(a,1,1,2,1)),rewrite([5(20),5(22),5(21),5(50),5(52),5(51)])]. 4712 x v ((x v c_0) v c_0) = x v c_0. [para(869(a,1),50(a,1,1,2,1,2,2)),rewrite([5(11),4527(12),5(10),4523(13),5(9),4527(10)]),flip(a)]. 4736 (c_0' v (x v c_0)')' = x v c_0. [para(3588(a,1),50(a,1,1,2,1,2,2,1,2)),rewrite([3887(16),4712(7),3588(17)])]. 4742 x v ((c_0' v (x v c_0)') v c_0) = c_0. [para(4398(a,1),52(a,1,2)),rewrite([5(7),4712(7),5(9),4395(12)])]. 4747 x v (y v ((x v c_0) v c_0)) = y v (x v c_0). [para(4712(a,1),5(a,1,2)),flip(a)]. 4856 ((x v c_0)' v c_0')' = x v c_0. [para(4736(a,1),42(a,1,1,1,1,2)),rewrite([5(5),4712(5),4447(7)])]. 4869 ((x v (y v c_0))' v ((y v c_0)' v (x v c_0'))')' = x. [para(4856(a,1),19(a,1,1,1,1,2))]. 4879 ((x v c_0)' v ((x v c_0) v ((x v c_0)' v c_0))')' = x v c_0. [para(4856(a,1),21(a,1,1,2,1,2,1)),rewrite([5(11),4856(21)])]. 4887 ((x v c_0)' v ((x v c_0)' v c_0)')' = c_0. [para(4856(a,1),42(a,1,1,1,1,2)),rewrite([4398(4)])]. 4988 x v ((x v c_0) v ((c_0' v (x v c_0)') v c_0)) = c_0. [para(4712(a,1),53(a,1,2,1,2,1,2,1)),rewrite([4747(10),5(7),4712(7),5(11)])]. 4999 x v (y v ((c_0' v (x v c_0)') v c_0)) = y v c_0. [para(4742(a,1),5(a,1,2)),flip(a)]. 5007 (((x v ((c_0' v (x v c_0)') v c_0)')' v c_0)' v x)' = (x v ((c_0' v (x v c_0)') v c_0)')'. [para(4742(a,1),22(a,1,1,1,1,2,1,1)),rewrite([4530(14)])]. 5022 (x v c_0) v c_0 = c_0. [back_rewrite(4988),rewrite([4999(12)])]. 5040 (x v c_0) v (y v c_0) = y v c_0. [para(5022(a,1),5(a,1,2)),flip(a)]. 5056 x v c_0 = c_0. [back_rewrite(4879),rewrite([5040(11),4887(11)]),flip(a)]. 5060 (c_0' v x)' = (x v c_0')'. [back_rewrite(5007),rewrite([5056(4),5056(7),5056(6),5056(8),5056(11)])]. 5089 (c_0' v (c_0' v (x v c_0'))')' = x. [back_rewrite(4869),rewrite([5056(2),5056(2),5056(4)])]. 5139 (x v x'')' = (c_0' v x)'. [back_rewrite(4536),rewrite([5056(6)]),flip(a)]. 5186 (x v (y v (z v (u v x')))')' = (c_0' v x)'. [back_rewrite(4047),rewrite([5056(9),5056(9),5056(9),4530(10),5056(9)]),flip(a)]. 5637 (c_0' v (c_0' v x)')' = x. [back_rewrite(1028),rewrite([5186(7),5056(6),5056(6),5056(6),5060(8,R)])]. 5642 (c_0' v (((c_0' v (x v y))' v c_0') v (x v (z v y))')')' = (c_0' v (x v y))' v c_0'. [back_rewrite(1012),rewrite([5139(6),5056(15),5060(17,R),5139(23)])]. 5717 (c_0' v (x v (x v (c_0' v x)))') v (y v x) = c_0. [back_rewrite(712),rewrite([5056(13)])]. 5768 (c_0' v (x v (((y v x') v z')' v ((y v x') v z)'))')' = x. [back_rewrite(185),rewrite([5056(2)])]. 5779 (c_0' v (x v x)') v (y v x) = c_0. [back_rewrite(52),rewrite([5056(9)])]. 5793 (c_0' v ((c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))') v x)')' = c_0' v (c_0' v (c_0' v ((c_0' v (x v x)') v ((c_0' v (x v x)') v (x v x)'))))'. [back_rewrite(4630),rewrite([5060(30,R)])]. 5810 (c_0' v ((c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))') v x)')' = c_0' v (c_0' v ((x v y')' v (((x v y')' v (x v y)') v (((x v y')' v (x v y)') v (x v y)'))))'. [back_rewrite(2028),rewrite([5060(33,R)])]. 5880 (c_0' v (((c_0' v x')' v c_0') v x)')' = (c_0' v x')' v c_0'. [back_rewrite(108),rewrite([5139(8),5139(20)])]. 5882 ((x v y)' v ((c_0' v y)' v (x v c_0'))')' = x. [back_rewrite(91),rewrite([5139(6)])]. 5887 x v c_0' = x. [back_rewrite(5089),rewrite([5637(11)])]. 5910 x v ((x v y) v ((x v y) v y)) = x v y. [back_rewrite(682),rewrite([5637(13)])]. 5917 x'' = x. [back_rewrite(2115),rewrite([5887(3),5717(12),5887(4)])]. 5926 (c_0' v x)' = x'. [back_rewrite(523),rewrite([5887(3),5779(8),5917(4),5056(3),5887(7)])]. 5933 ((x v y)' v (y' v x)')' = x. [back_rewrite(5882),rewrite([5926(6),5887(6)])]. 5935 x v x = x. [back_rewrite(5880),rewrite([5926(7),5917(4),5887(5),5926(6),5917(3),5926(6),5917(3),5887(4)])]. 5975 (x v y)' v (x v (z v y))' = (x v y)'. [back_rewrite(5642),rewrite([5926(7),5887(7),5926(11),5917(8),5926(11),5887(11)])]. 6061 (c_0' v x) v x = c_0' v x. [back_rewrite(5810),rewrite([5910(26),5926(14),9(11),5926(9),5917(6),5910(28),5926(16),9(13)])]. 6063 c_0' v x = x. [back_rewrite(5793),rewrite([5935(11),5935(15),5935(17),6061(18),5935(17),5926(15),5926(12),5926(9),5917(6),6061(6),5926(6),5926(5),5917(2),5935(9),5935(13),5935(15),6061(16),5935(15),5926(13),5926(10),5926(7),5917(4)]),flip(a)]. 6077 x v (((y v x') v z')' v ((y v x') v z)') = x. [back_rewrite(5768),rewrite([6063(15),5917(13)])]. 6578 (x v y')' v (x v y)' = x'. [para(9(a,1),5917(a,1,1)),flip(a)]. 6581 x v (x v ((x v y')' v y))' = x v y'. [para(21(a,1),5917(a,1,1)),rewrite([5917(4)]),flip(a)]. 6587 x v (y v x')' = x. [back_rewrite(6077),rewrite([6578(10)])]. 6642 x v y = y v x. [para(5887(a,1),5(a,1,2)),rewrite([5887(4)])]. 6643 x v (y v z) = z v (x v y). [para(5887(a,1),18(a,1,2,2)),rewrite([5887(5)])]. 6667 x v (x v y)' = x v y'. [back_rewrite(6581),rewrite([6642(4),6587(4)])]. 7269 x v (y v (z v x')') = y v x. [para(6587(a,1),5(a,1,2)),flip(a)]. 7273 x v (x' v y)' = x. [para(6642(a,1),6587(a,1,2,1))]. 7317 x v (y v (x' v z)') = y v x. [para(7273(a,1),5(a,1,2)),flip(a)]. 8516 (x v y) v z = x v (y v z). [para(6643(a,2),6642(a,1)),flip(a)]. 8771 x v (y v x)' = x v y'. [para(6642(a,1),6667(a,1,2,1))]. 8848 x v (y v (z v x)') = y v (x v z'). [para(8771(a,1),5(a,1,2)),flip(a)]. 8902 (x v y)' v (y' v x)' = x'. [para(5933(a,1),5917(a,1,1)),flip(a)]. 9751 (x v y)' v (z v (y' v x)') = z v x'. [para(8902(a,1),5(a,1,2)),flip(a)]. 9756 (x v (y v z)')' = (x v (z v y'))' v (x v z')'. [para(7269(a,1),8902(a,1,2,1)),rewrite([5917(2),6642(4),8848(4),5917(10)]),flip(a)]. 9814 (c6 v (c4' v c5'))' v (c4' v c6')' != (c4' v c5')' v (c4' v c6')' # answer(DIST1). [back_rewrite(14),rewrite([9756(8),5(7)])]. 10120 (x v y)' v ((x v (z v y))' v (x v z')') = (x v (z v y))' v (x v z')'. [para(7273(a,1),5975(a,1,2,1,2)),rewrite([9756(5),5917(2),6642(10),9756(15),5917(12)])]. 10122 (x v y)' v ((x v (z v y))' v u) = (x v y)' v u. [para(5975(a,1),8516(a,1,1)),flip(a)]. 10142 (x v (y v z))' v (x v y')' = (x v z)' v (x v y')'. [back_rewrite(10120),rewrite([10122(10)]),flip(a)]. 10157 (x v (y v z)')' = (x v y')' v (x v z')'. [back_rewrite(9756),rewrite([10142(12)])]. 12752 (x v (y v z))' v (y v x')' = (y v z)' v (y v x')'. [para(9751(a,1),8902(a,1,2,1)),rewrite([6642(6),8516(6),7317(5),10157(12),5917(9)])]. 12753 $F # answer(DIST1). [resolve(12752,a,9814,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=303. Generated=90008. Kept=12739. proofs=4. Usable=132. Sos=1563. Demods=1580. Limbo=6, Disabled=11045. Hints=0. Kept_by_rule=0, Deleted_by_rule=514. Forward_subsumed=76752. Back_subsumed=181. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=10269 (7 lex), Back_demodulated=9823. Back_unit_deleted=0. Demod_attempts=1783401. Demod_rewrites=296476. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0. Megabytes=12.17. User_CPU=6.41, System_CPU=0.05, Wall_clock=6. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 4 proofs. Process 5127 exit (max_proofs) Tue Nov 3 09:45:22 2009