============================== Prover9 =============================== Prover9 (32) version 22-May-2007, May 2007. Process 28426 was started by mccune on cleo, Tue May 22 15:17:08 2007 The command was "/home/mccune/bin/prover9 -f dist-long-short.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file dist-long-short.in assign(max_seconds,300). assign(order,kbo). set(lex_order_vars). formulas(sos). f(x,x,y) = x # label(majority). f(x,y,z) = f(z,x,y) # label(2a). f(x,y,z) = f(x,z,y) # label(2b). f(f(x,w,y),w,z) = f(x,w,f(y,w,z)) # label(associativity). f(f(x,y,z),u,w) = f(f(x,u,w),f(y,u,w),f(z,u,w)) # label(dist_long). end_of_list. formulas(goals). f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)) # answer(dist_short). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)) # answer(dist_short) # 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). f(x,x,y) = x # label(majority). [assumption]. f(x,y,z) = f(z,x,y) # label(2a). [assumption]. f(x,y,z) = f(x,z,y) # label(2b). [assumption]. f(f(x,y,z),y,u) = f(x,y,f(z,y,u)) # label(associativity). [assumption]. f(f(x,y,z),u,v) = f(f(x,u,v),f(y,u,v),f(z,u,v)) # label(dist_long). [assumption]. f(f(c1,c2,c3),c4,c5) != f(c1,f(c2,c4,c5),f(c3,c4,c5)) # answer(dist_short). [deny(1)]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination ============= Auto_denials: (no changes). Term ordering decisions: Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. f=1. Predicate symbol precedence: predicate_order([ = ]). Function symbol precedence: function_order([ c1, c2, c3, c4, c5, f ]). Skipping inverse_order, because term ordering is KBO. Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(paramodulation) -> set(back_demod). Auto_process settings: (no changes). ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 2 f(x,x,y) = x # label(majority). [assumption]. 3 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. 4 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. 6 f(x,y,f(x,z,u)) = f(x,z,f(x,y,u)). [copy(5),rewrite([3(2),3(2),3(3,R),4(3)]),rewrite([3(1,R),4(1),4(3),3(4,R),4(4)])]. 8 f(f(x,y,z),f(y,z,u),f(y,z,v)) = f(y,z,f(x,u,v)). [copy(7),rewrite([3(2),3(2)]),flip(a),rewrite([3(2),3(2),3(3),3(3)])]. 10 f(c1,f(c2,c4,c5),f(c3,c4,c5)) != f(c4,c5,f(c1,c2,c3)) # answer(dist_short). [copy(9),rewrite([3(7),3(7)]),flip(a)]. end_of_list. formulas(demodulators). 2 f(x,x,y) = x # label(majority). [assumption]. 3 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. % (lex-dep) 4 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. % (lex-dep) 8 f(f(x,y,z),f(y,z,u),f(y,z,v)) = f(y,z,f(x,u,v)). [copy(7),rewrite([3(2),3(2)]),flip(a),rewrite([3(2),3(2),3(3),3(3)])]. end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.00 seconds. given #1 (I,wt=6): 2 f(x,x,y) = x # label(majority). [assumption]. given #2 (I,wt=9): 3 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. given #3 (I,wt=9): 4 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. given #4 (I,wt=15): 6 f(x,y,f(x,z,u)) = f(x,z,f(x,y,u)). [copy(5),rewrite([3(2),3(2),3(3,R),4(3)]),rewrite([3(1,R),4(1),4(3),3(4,R),4(4)])]. given #5 (I,wt=21): 8 f(f(x,y,z),f(y,z,u),f(y,z,v)) = f(y,z,f(x,u,v)). [copy(7),rewrite([3(2),3(2)]),flip(a),rewrite([3(2),3(2),3(3),3(3)])]. given #6 (I,wt=18): 10 f(c1,f(c2,c4,c5),f(c3,c4,c5)) != f(c4,c5,f(c1,c2,c3)) # answer(dist_short). [copy(9),rewrite([3(7),3(7)]),flip(a)]. given #7 (A,wt=6): 11 f(x,y,y) = y. [para(3(a,1),2(a,1))]. given #8 (T,wt=12): 28 f(x,y,f(x,z,y)) = f(x,z,y). [para(11(a,1),6(a,1,3)),flip(a)]. given #9 (T,wt=12): 29 f(x,y,f(x,y,z)) = f(x,y,z). [para(11(a,1),6(a,1)),rewrite([4(3),28(3)]),flip(a)]. given #10 (T,wt=15): 12 f(x,y,f(z,x,u)) = f(z,x,f(x,y,u)). [para(6(a,1),3(a,2)),rewrite([4(2),3(3,R),4(3)]),flip(a)]. given #11 (T,wt=15): 13 f(x,y,f(x,z,u)) = f(x,u,f(x,y,z)). [para(3(a,1),6(a,1,3)),rewrite([3(1,R),4(1)])]. given #12 (A,wt=21): 14 f(x,y,f(x,z,f(x,u,v))) = f(x,u,f(x,y,f(x,z,v))). [para(6(a,1),6(a,1,3))]. given #13 (T,wt=15): 38 f(x,y,f(z,y,u)) = f(z,y,f(x,y,u)). [para(12(a,1),3(a,2)),rewrite([4(2),3(3,R),4(3)])]. given #14 (T,wt=15): 50 f(x,y,f(z,x,u)) = f(z,x,f(x,u,y)). [para(13(a,1),3(a,2)),rewrite([4(2),3(3,R),4(3)]),flip(a)]. given #15 (T,wt=15): 51 f(x,y,f(x,z,u)) = f(x,u,f(x,z,y)). [para(13(a,1),4(a,2)),rewrite([4(2),4(3)])]. given #16 (T,wt=18): 30 f(x,f(y,x,z),f(u,y,x)) = f(y,x,f(u,x,z)). [para(11(a,1),8(a,1,2)),rewrite([3(3,R)])]. given #17 (A,wt=21): 16 f(f(x,y,z),f(x,y,u),f(x,y,v)) = f(x,y,f(u,v,z)). [para(8(a,1),3(a,1)),rewrite([3(4),3(4)]),flip(a)]. given #18 (T,wt=15): 187 f(x,y,f(x,z,f(y,z,u))) = f(x,y,z). [back_rewrite(135),rewrite([3(1,R),4(1),3(2,R),4(2),183(4),3(1,R),4(1),3(4,R),4(4)])]. given #19 (T,wt=15): 189 f(x,y,f(y,z,f(x,z,u))) = f(x,y,z). [para(187(a,1),3(a,2)),rewrite([4(3),3(4,R),4(4)])]. given #20 (T,wt=15): 190 f(x,y,f(x,z,f(z,y,u))) = f(x,z,y). [para(187(a,1),4(a,2)),rewrite([3(1,R),4(1),4(3),4(4)])]. given #21 (T,wt=15): 200 f(x,f(y,z,u),f(x,y,z)) = f(x,y,z). [para(187(a,1),13(a,1)),flip(a)]. given #22 (A,wt=21): 17 f(f(x,y,z),f(x,z,u),f(x,z,v)) = f(x,z,f(y,u,v)). [para(3(a,1),8(a,1,1)),rewrite([3(2,R),4(2),3(3,R),4(3),3(6,R),4(6)])]. given #23 (T,wt=15): 204 f(x,y,f(z,x,u)) = f(x,u,f(z,x,y)). [para(50(a,2),187(a,2)),rewrite([4(3),198(5)])]. given #24 (T,wt=15): 226 f(x,y,f(z,x,f(z,y,u))) = f(z,x,y). [para(189(a,1),187(a,2)),rewrite([4(5),198(7)])]. given #25 (T,wt=15): 236 f(x,f(y,z,u),f(y,z,x)) = f(y,z,x). [para(200(a,1),3(a,2)),rewrite([3(2),3(2),3(3),3(4),3(4)])]. given #26 (T,wt=15): 237 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(3(a,1),200(a,1,2))]. given #27 (A,wt=33): 18 f(f(x,y,z),f(y,z,u),f(v,f(y,z,w),f(x,y,z))) = f(v,f(x,y,z),f(y,z,f(x,u,w))). [para(8(a,1),6(a,1,3)),rewrite([3(4,R),4(4),3(9,R)]),flip(a)]. given #28 (T,wt=12): 365 f(x,y,f(z,x,y)) = f(z,x,y). [para(237(a,1),2(a,1)),rewrite([3(2),3(2)])]. given #29 (T,wt=15): 238 f(x,f(y,z,u),f(x,y,u)) = f(x,y,u). [para(3(a,2),200(a,1,2)),rewrite([4(2),4(4)])]. given #30 (T,wt=15): 239 f(x,f(x,y,z),f(y,z,u)) = f(x,y,z). [para(200(a,1),4(a,1)),flip(a)]. given #31 (T,wt=15): 320 f(x,y,f(z,u,x)) = f(z,x,f(u,x,y)). [para(204(a,1),3(a,2)),rewrite([4(2),3(3)]),flip(a)]. given #32 (A,wt=33): 19 f(f(x,y,f(x,z,u)),f(z,v,f(x,y,u)),f(z,w,f(x,y,u))) = f(z,f(x,y,u),f(x,v,w)). [para(6(a,1),8(a,1,1)),rewrite([4(4),4(6)])]. given #33 (T,wt=15): 330 f(x,y,f(z,y,f(x,z,u))) = f(x,z,y). [para(226(a,1),3(a,2)),rewrite([3(1,R),4(1),4(3),3(4)])]. given #34 (T,wt=15): 343 f(x,f(y,z,u),f(y,x,z)) = f(y,x,z). [para(226(a,1),204(a,1)),flip(a)]. given #35 (T,wt=15): 345 f(x,y,f(z,u,x)) = f(u,x,f(z,x,y)). [para(204(a,1),226(a,2)),rewrite([4(3),3(4,R),4(4),233(5),3(3)]),flip(a)]. given #36 (T,wt=15): 346 f(x,y,f(z,y,f(z,x,u))) = f(z,x,y). [para(226(a,1),226(a,2)),rewrite([3(1,R),4(1),3(3,R),4(3),4(5),3(6,R),4(6),233(7),3(4)])]. given #37 (A,wt=27): 20 f(f(x,y,z),f(y,u,f(y,z,v)),f(y,z,w)) = f(y,z,f(x,w,f(y,u,v))). [para(6(a,1),8(a,1,2)),rewrite([4(7)])]. given #38 (T,wt=15): 347 f(x,f(y,z,x),f(y,z,u)) = f(y,z,x). [para(236(a,1),4(a,1)),flip(a)]. given #39 (T,wt=15): 366 f(x,f(y,z,u),f(z,u,x)) = f(z,u,x). [para(237(a,1),3(a,2)),rewrite([3(2),3(2),3(3),3(4),3(4)])]. given #40 (T,wt=15): 368 f(x,y,f(x,z,f(y,u,z))) = f(x,y,z). [para(237(a,1),6(a,2)),rewrite([3(1,R),4(1),4(2)])]. given #41 (T,wt=15): 373 f(x,y,f(x,z,f(u,y,z))) = f(x,y,z). [para(237(a,1),8(a,2)),rewrite([2(2),4(2),4(4),83(5),11(3)])]. given #42 (A,wt=27): 21 f(f(x,y,z),f(y,z,u),f(y,v,f(y,z,w))) = f(y,z,f(x,u,f(y,v,w))). [para(6(a,1),8(a,1,3))]. given #43 (T,wt=15): 399 f(x,f(x,y,z),f(u,y,z)) = f(x,y,z). [para(189(a,1),237(a,1,3)),rewrite([4(5),315(5),3(2),3(2),189(6)])]. given #44 (T,wt=15): 547 f(x,f(y,z,u),f(y,u,x)) = f(y,u,x). [para(238(a,1),3(a,2)),rewrite([3(2),3(2),3(3),3(4),3(4)])]. given #45 (T,wt=15): 617 f(x,y,f(z,u,y)) = f(z,y,f(x,u,y)). [para(320(a,1),3(a,2)),rewrite([4(2),3(3)])]. given #46 (T,wt=15): 774 f(x,f(y,x,z),f(y,z,u)) = f(y,x,z). [para(365(a,1),19(a,1,2)),rewrite([29(2),2(5)]),flip(a)]. given #47 (A,wt=21): 22 f(x,y,f(z,u,f(z,v,w))) = f(x,y,f(z,v,f(z,u,w))). [para(6(a,1),8(a,2,3)),rewrite([8(5)])]. given #48 (T,wt=15): 830 f(x,y,f(z,u,y)) = f(u,y,f(x,z,y)). [para(345(a,1),3(a,2)),rewrite([4(2),3(3)])]. given #49 (T,wt=15): 837 f(x,y,f(z,u,y)) = f(u,y,f(z,x,y)). [para(345(a,1),226(a,2)),rewrite([4(3),3(4,R),4(4),631(5),3(3)])]. given #50 (T,wt=15): 1063 f(x,y,f(x,z,f(z,u,y))) = f(x,z,y). [para(373(a,1),4(a,2)),rewrite([3(1),4(3),4(4)])]. given #51 (T,wt=15): 1205 f(x,f(y,z,x),f(u,y,z)) = f(y,z,x). [para(399(a,1),236(a,1,3)),rewrite([3(2),3(2),4(3),3(4),3(4),4(5),846(5),854(4),3(2),3(2)]),flip(a)]. given #52 (A,wt=45): 23 f(f(x,y,f(z,u,v)),f(w,f(x,y,u),f(x,y,v)),f(v6,f(x,y,u),f(x,y,v))) = f(f(x,y,u),f(x,y,v),f(w,v6,f(x,y,z))). [para(8(a,1),8(a,1,1)),rewrite([3(5),3(8),3(12),3(12),3(13),3(13)])]. given #53 (T,wt=15): 1246 f(x,f(y,x,z),f(u,y,z)) = f(y,x,z). [para(343(a,1),617(a,1,3)),rewrite([11(3),178(6),3(4,R),4(4),820(5),3(3,R),4(3)]),flip(a)]. given #54 (T,wt=18): 31 f(x,f(y,z,x),f(z,x,u)) = f(z,x,f(y,x,u)). [para(11(a,1),8(a,1,3)),rewrite([3(3),4(4)])]. given #55 (T,wt=15): 1651 f(x,y,f(y,z,f(x,u,z))) = f(x,y,z). [para(31(a,1),23(a,2)),rewrite([36(3),11(1),29(4),11(4),29(6),2(6),2(4),83(5),29(5),125(5),4(3)]),flip(a)]. given #56 (T,wt=15): 1674 f(x,y,f(z,x,f(z,u,y))) = f(z,x,y). [para(1651(a,1),16(a,2)),rewrite([11(3),3(4),3(4),1634(4),29(3)])]. given #57 (A,wt=45): 24 f(f(x,f(y,z,u),f(z,u,v)),f(z,u,f(y,v,w)),f(v6,f(y,z,u),f(z,u,v))) = f(f(y,z,u),f(z,u,v),f(x,v6,f(z,u,w))). [para(8(a,1),8(a,1,2)),rewrite([3(8),4(13)])]. given #58 (T,wt=18): 36 f(x,y,f(z,u,f(x,y,v))) = f(x,y,f(z,v,u)). [para(28(a,1),8(a,1,2)),rewrite([4(2),8(4),4(3),4(4)]),flip(a)]. given #59 (T,wt=18): 41 f(x,f(x,y,z),f(u,x,y)) = f(u,x,f(x,y,z)). [para(12(a,1),8(a,2)),rewrite([3(2),2(2),3(3,R)])]. given #60 (T,wt=18): 165 f(x,y,f(z,u,f(x,v,y))) = f(x,y,f(v,z,u)). [para(28(a,1),16(a,1,1)),rewrite([17(4)]),flip(a)]. given #61 (T,wt=18): 212 f(x,y,f(y,z,f(x,u,f(x,z,v)))) = f(x,y,z). [para(6(a,1),189(a,1,3,3))]. given #62 (A,wt=45): 25 f(f(x,f(y,z,u),f(z,u,v)),f(w,f(y,z,u),f(z,u,v)),f(z,u,f(y,v,v6))) = f(f(y,z,u),f(z,u,v),f(x,w,f(z,u,v6))). [para(8(a,1),8(a,1,3)),rewrite([3(6)])]. given #63 (T,wt=18): 219 f(x,y,f(y,z,f(z,u,f(x,z,v)))) = f(x,y,z). [para(12(a,2),189(a,1,3,3))]. given #64 (T,wt=18): 249 f(x,f(y,z,f(z,u,v)),f(x,z,u)) = f(x,z,u). [para(12(a,1),200(a,1,2))]. given #65 (T,wt=18): 261 f(x,f(y,z,f(z,u,v)),f(x,z,v)) = f(x,z,v). [para(50(a,1),200(a,1,2))]. given #66 (T,wt=18): 288 f(x,f(y,z,x),f(y,x,u)) = f(y,x,f(z,x,u)). [para(11(a,1),17(a,1,3)),rewrite([3(3),4(4)])]. given #67 (A,wt=27): 26 f(x,y,f(f(z,u,v),f(z,u,w),f(v6,z,u))) = f(x,y,f(z,u,f(v6,v,w))). [para(8(a,1),8(a,2,3)),rewrite([3(2),3(2),16(7)])]. given #68 (T,wt=18): 351 f(f(x,y,z),f(x,z,u),f(x,y,z)) = f(x,y,z). [para(28(a,1),236(a,1,3)),rewrite([28(6)])]. given #69 (T,wt=15): 2850 f(x,f(y,z,u),f(x,y,z)) = f(x,y,z). [para(236(a,1),351(a,1,3)),rewrite([3(2),3(4),4(5),3(6),3(7),1498(7),3(2,R),4(2),36(4),2156(4),187(3),3(3)]),flip(a)]. given #70 (T,wt=15): 2866 f(x,f(y,z,u),f(x,y,u)) = f(x,y,u). [para(547(a,1),351(a,1,3)),rewrite([3(2),3(4),4(5),3(6),3(7),1498(7),3(2,R),4(2),36(4),573(4),3(3)]),flip(a)]. given #71 (T,wt=18): 394 f(x,f(y,z,f(u,v,y)),f(x,v,y)) = f(x,v,y). [para(237(a,1),187(a,2)),rewrite([3(5),183(6),381(6)])]. given #72 (A,wt=21): 39 f(x,y,f(z,u,f(x,z,v))) = f(x,z,f(x,y,f(z,u,v))). [para(12(a,2),6(a,1,3))]. given #73 (T,wt=18): 401 f(x,y,f(x,z,f(z,u,f(v,y,z)))) = f(x,y,z). [para(237(a,1),200(a,1,3)),rewrite([3(3),4(5),183(5),237(7)])]. given #74 (T,wt=18): 405 f(x,y,f(x,z,f(u,z,f(v,y,z)))) = f(x,y,z). [para(237(a,1),237(a,1,3)),rewrite([4(5),183(5),3(2,R),4(2),237(7)])]. given #75 (T,wt=18): 541 f(x,y,f(z,u,f(v,x,y))) = f(x,y,f(v,z,u)). [para(365(a,1),16(a,1,1)),rewrite([8(4)]),flip(a)]. given #76 (T,wt=18): 568 f(x,f(y,z,f(u,v,y)),f(x,u,y)) = f(x,u,y). [para(238(a,1),187(a,2)),rewrite([3(5),183(6),556(6)])]. given #77 (A,wt=33): 40 f(f(x,y,f(y,z,u)),f(z,v,f(x,y,u)),f(z,w,f(x,y,u))) = f(z,f(x,y,u),f(y,v,w)). [para(12(a,1),8(a,1,1)),rewrite([4(4),4(6)])]. given #78 (T,wt=18): 573 f(x,y,f(x,z,f(z,u,f(y,v,z)))) = f(x,y,z). [para(238(a,1),200(a,1,3)),rewrite([3(3),4(5),183(5),238(7)])]. given #79 (T,wt=18): 578 f(x,y,f(x,z,f(u,z,f(y,v,z)))) = f(x,y,z). [para(238(a,1),237(a,1,3)),rewrite([4(5),183(5),3(2,R),4(2),238(7)])]. given #80 (T,wt=18): 660 f(x,y,f(x,z,f(y,u,f(y,v,z)))) = f(x,y,z). [back_rewrite(252),rewrite([646(4)])]. given #81 (T,wt=18): 854 f(x,f(y,z,x),f(y,u,f(v,y,z))) = f(y,z,x). [back_rewrite(822),rewrite([846(5)])]. given #82 (A,wt=27): 43 f(f(x,y,z),f(z,u,f(y,z,v)),f(y,z,w)) = f(y,z,f(x,w,f(z,u,v))). [para(12(a,2),8(a,1,2)),rewrite([4(7)])]. given #83 (T,wt=18): 1220 f(x,f(y,z,x),f(y,u,f(y,v,z))) = f(y,z,x). [para(547(a,1),343(a,1,3)),rewrite([4(3),4(5),846(5),547(7)])]. given #84 (T,wt=18): 1314 f(x,y,f(y,z,f(u,z,f(x,z,v)))) = f(x,y,z). [para(343(a,1),830(a,1,3)),rewrite([11(3),1234(6)]),flip(a)]. given #85 (T,wt=18): 1692 f(x,y,f(y,z,f(z,u,f(x,v,z)))) = f(x,y,z). [para(1674(a,1),347(a,1,2)),rewrite([3(5,R),1186(5),1674(7)])]. given #86 (T,wt=18): 2260 f(x,y,f(x,z,f(y,u,f(z,y,v)))) = f(x,z,y). [para(212(a,1),3(a,2)),rewrite([3(1,R),4(1),4(4),3(5),3(5)])]. given #87 (A,wt=27): 44 f(f(x,y,z),f(y,z,u),f(z,v,f(y,z,w))) = f(y,z,f(x,u,f(z,v,w))). [para(12(a,2),8(a,1,3))]. given #88 (T,wt=18): 2273 f(x,y,f(z,x,f(z,u,f(z,y,v)))) = f(z,x,y). [para(212(a,1),16(a,2)),rewrite([11(4),3(5),3(5),1634(5),29(4)])]. given #89 (T,wt=18): 2337 f(x,y,f(z,f(u,y,z),f(x,u,z))) = f(x,y,z). [para(11(a,1),25(a,2)),rewrite([3(1,R),4(1),29(3),2153(3),29(2),3(3,R),4(3),29(5),288(5),4(6),36(7),11(5),3(6),157(6),29(6)])]. given #90 (T,wt=18): 2480 f(x,y,f(x,z,f(z,u,f(z,y,v)))) = f(x,z,y). [para(219(a,1),3(a,2)),rewrite([3(1,R),4(1),4(4),3(5),3(5)])]. given #91 (T,wt=18): 2491 f(x,y,f(z,f(x,z,u),f(y,z,v))) = f(x,y,z). [para(50(a,2),219(a,1,3))]. given #92 (A,wt=21): 45 f(x,y,f(z,u,f(v,z,w))) = f(x,y,f(v,z,f(z,u,w))). [para(12(a,2),8(a,2,3)),rewrite([8(5)]),flip(a)]. given #93 (T,wt=18): 2493 f(x,y,f(z,x,f(y,u,f(z,y,v)))) = f(z,x,y). [para(219(a,1),16(a,2)),rewrite([11(4),3(5),3(5),1634(5),29(4)])]. given #94 (T,wt=18): 2540 f(x,f(y,z,f(z,u,v)),f(z,u,x)) = f(z,u,x). [para(249(a,1),3(a,2)),rewrite([3(3),3(3),3(4),3(5),3(5)])]. given #95 (T,wt=15): 4872 f(x,y,f(x,z,f(u,z,y))) = f(x,z,y). [para(2540(a,1),617(a,1,3)),rewrite([11(3),3(4,R),4(4),360(7),3(5,R),4(5),3810(6),3(2),3(3,R),4(3)]),flip(a)]. given #96 (T,wt=18): 2644 f(x,f(y,z,f(z,u,v)),f(z,v,x)) = f(z,v,x). [para(261(a,1),3(a,2)),rewrite([3(3),3(3),3(4),3(5),3(5)])]. given #97 (A,wt=33): 47 f(f(x,y,z),f(y,z,u),f(v,f(x,y,z),f(y,z,w))) = f(v,f(x,y,z),f(y,z,f(x,u,w))). [para(8(a,1),12(a,2,3))]. given #98 (T,wt=18): 2648 f(x,y,f(x,z,f(u,y,f(y,v,z)))) = f(x,y,z). [para(261(a,1),8(a,2)),rewrite([2(3),4(3),4(6),2153(7),28(6)])]. given #99 (T,wt=18): 2884 f(x,f(y,z,f(y,u,v)),f(x,y,u)) = f(x,y,u). [para(249(a,1),351(a,1,1)),rewrite([4(3),3(5,R),4(5),1498(8),3(3,R),4(3),36(5),4(3),2312(5),2(1),11(1),3(3,R),4(3)]),flip(a)]. given #100 (T,wt=18): 2895 f(x,f(y,z,f(y,u,v)),f(x,y,v)) = f(x,y,v). [para(13(a,2),2850(a,1,2))]. given #101 (T,wt=18): 2900 f(x,y,f(x,z,f(y,u,f(v,y,z)))) = f(x,y,z). [para(237(a,1),2850(a,1,3)),rewrite([3(3),4(5),2153(5),165(4),237(7)])]. given #102 (A,wt=21): 49 f(x,y,f(z,u,f(x,u,v))) = f(x,u,f(x,y,f(z,u,v))). [para(12(a,1),12(a,1,3)),rewrite([3(1,R),4(1),3(6,R),4(6)])]. given #103 (T,wt=18): 2924 f(x,f(y,z,f(u,y,v)),f(x,u,y)) = f(x,u,y). [para(394(a,1),3(a,1)),rewrite([3(3),3(3),3(5,R)]),flip(a)]. given #104 (T,wt=18): 2925 f(x,f(y,z,f(y,u,v)),f(y,v,x)) = f(y,v,x). [para(394(a,1),3(a,2)),rewrite([3(1),3(3),4(3),3(4),3(5),4(5)])]. given #105 (T,wt=18): 2926 f(x,f(y,z,f(u,v,z)),f(x,v,z)) = f(x,v,z). [para(3(a,2),394(a,1,2)),rewrite([4(2)])]. given #106 (T,wt=18): 2935 f(x,y,f(x,z,f(z,u,f(z,v,y)))) = f(x,z,y). [para(394(a,1),8(a,2)),rewrite([3(1),2(3),3(1),4(3),3(4),4(6),2153(7),28(6),4(5)])]. given #107 (A,wt=21): 52 f(x,y,f(x,z,f(x,u,v))) = f(x,u,f(x,y,f(x,v,z))). [para(13(a,1),6(a,2,3)),flip(a)]. given #108 (T,wt=18): 3274 f(x,y,f(z,f(y,z,u),f(x,z,v))) = f(x,y,z). [para(50(a,2),401(a,1,3)),rewrite([3(1),3(1)])]. given #109 (T,wt=18): 3393 f(x,f(y,z,f(y,u,v)),f(y,u,x)) = f(y,u,x). [para(568(a,1),3(a,2)),rewrite([3(1),3(3),4(3),3(4),3(5),4(5)])]. given #110 (T,wt=18): 3394 f(x,f(y,z,f(u,v,z)),f(x,u,z)) = f(x,u,z). [para(3(a,2),568(a,1,2)),rewrite([4(2)])]. given #111 (T,wt=18): 4138 f(x,y,f(z,f(x,z,y),f(u,z,y))) = f(x,z,y). [para(1220(a,1),38(a,1,3)),rewrite([11(3),4(4),3810(7),3(3)]),flip(a)]. given #112 (A,wt=21): 53 f(x,y,f(x,z,f(x,u,v))) = f(x,v,f(x,y,f(x,z,u))). [para(13(a,2),6(a,1,3))]. given #113 (T,wt=18): 4152 f(x,y,f(z,x,f(u,y,f(z,y,v)))) = f(z,x,y). [para(1314(a,1),16(a,2)),rewrite([11(4),3(5),3(5),1634(5),29(4)])]. given #114 (T,wt=18): 4366 f(x,y,f(z,y,f(z,u,f(x,z,v)))) = f(x,z,y). [para(2273(a,1),3(a,2)),rewrite([3(1,R),4(1),4(4),3(5)])]. given #115 (T,wt=18): 4375 f(x,f(y,z,f(y,u,v)),f(y,x,u)) = f(y,x,u). [para(2273(a,1),204(a,1)),flip(a)]. given #116 (T,wt=18): 4449 f(x,y,f(z,f(y,u,z),f(x,u,z))) = f(x,y,z). [para(3(a,1),2337(a,1,3)),rewrite([3(2,R),4(2),3(3,R)])]. given #117 (A,wt=21): 55 f(x,y,f(z,u,f(z,v,w))) = f(x,y,f(z,w,f(z,u,v))). [para(13(a,1),8(a,2,3)),rewrite([8(5)])]. given #118 (T,wt=18): 4520 f(x,y,f(z,f(x,u,z),f(y,u,z))) = f(x,y,z). [para(2337(a,1),165(a,2)),rewrite([3(1,R),4(1),4(3),36(5),3(3,R)])]. given #119 (T,wt=18): 4578 f(x,y,f(z,u,f(z,v,f(x,z,y)))) = f(x,z,y). [para(2491(a,1),4(a,2)),rewrite([3(2,R),4(2),3532(3),4(4),4(5)])]. given #120 (T,wt=18): 4797 f(x,y,f(z,y,f(x,u,f(x,z,v)))) = f(x,z,y). [para(2493(a,1),3(a,2)),rewrite([3(1,R),4(1),4(4),3(5)])]. given #121 (T,wt=18): 4804 f(x,f(y,z,f(u,y,v)),f(u,x,y)) = f(u,x,y). [para(2493(a,1),204(a,1)),flip(a)]. given #122 (A,wt=33): 56 f(f(x,y,f(x,z,u)),f(u,v,f(x,y,z)),f(u,w,f(x,y,z))) = f(u,f(x,y,z),f(x,v,w)). [para(13(a,2),8(a,1,1)),rewrite([4(4),4(6)])]. given #123 (T,wt=18): 4864 f(x,y,f(z,y,f(z,u,f(z,x,v)))) = f(z,x,y). [para(2540(a,1),345(a,1)),rewrite([3(3,R),4(3)]),flip(a)]. given #124 (T,wt=18): 4898 f(x,f(y,z,f(z,u,v)),f(z,x,u)) = f(z,x,u). [para(2540(a,1),40(a,2)),rewrite([2(9),3(7),3456(7),4(5)])]. given #125 (T,wt=18): 4955 f(x,f(y,z,f(y,u,v)),f(y,x,v)) = f(y,x,v). [para(2644(a,1),8(a,2)),rewrite([3(2,R),4(2),3(5,R),4(5),4(6),3(8,R),4(8),3(9),2(9),3(7),3532(7),29(7),4(5)])]. given #126 (T,wt=18): 4971 f(x,f(y,z,f(z,u,v)),f(z,x,v)) = f(z,x,v). [para(2644(a,1),40(a,2)),rewrite([2(9),3(7),3456(7),4(5)])]. given #127 (A,wt=21): 60 f(x,f(y,z,u),f(x,v,y)) = f(x,v,f(y,z,f(x,y,u))). [para(12(a,2),13(a,1,3)),flip(a)]. given #128 (T,wt=18): 5241 f(x,y,f(x,z,f(u,y,f(z,y,v)))) = f(x,z,y). [para(2648(a,1),4(a,2)),rewrite([3(1),4(4),4(5)])]. given #129 (T,wt=18): 5588 f(x,y,f(x,z,f(u,z,f(z,v,y)))) = f(x,z,y). [para(2926(a,1),8(a,2)),rewrite([3(1),2(3),3(1),4(3),3(4),4(6),2153(7),28(6),4(5)])]. given #130 (T,wt=18): 5835 f(x,f(y,z,f(u,y,v)),f(x,y,v)) = f(x,y,v). [back_rewrite(1988),rewrite([5691(6)])]. given #131 (T,wt=18): 5946 f(x,y,f(x,z,f(u,z,f(z,y,v)))) = f(x,z,y). [para(3394(a,1),8(a,2)),rewrite([3(1),2(3),3(1),4(3),3(4),4(6),2153(7),28(6),4(5)])]. given #132 (A,wt=21): 62 f(x,y,f(z,x,f(x,u,v))) = f(z,x,f(x,u,f(x,y,v))). [para(14(a,1),3(a,2)),rewrite([4(3),3(5,R),4(5)]),flip(a)]. given #133 (T,wt=18): 6205 f(x,y,f(z,y,f(x,u,f(z,x,v)))) = f(z,x,y). [para(4366(a,1),38(a,1)),flip(a)]. given #134 (T,wt=18): 6487 f(x,y,f(z,f(x,y,z),f(z,u,v))) = f(x,y,z). [para(13(a,1),4578(a,1,3)),rewrite([4(1),4(5)])]. given #135 (T,wt=18): 6500 f(x,y,f(z,u,f(z,v,f(z,x,y)))) = f(z,x,y). [para(4578(a,1),236(a,2)),rewrite([3(1,R),4(1),3(5,R),4(5),6494(9),3(6),6499(6),3(5,R),4(5)])]. given #136 (T,wt=18): 6938 f(x,y,f(z,x,f(z,u,f(z,v,y)))) = f(z,x,y). [para(4955(a,1),8(a,2)),rewrite([3(6),2(6),4(6),3(7,R),2153(7),365(6)])]. given #137 (A,wt=21): 63 f(x,y,f(y,z,f(y,u,v))) = f(y,z,f(y,u,f(x,y,v))). [para(14(a,2),3(a,2)),rewrite([4(3),3(4,R),4(4)])]. given #138 (T,wt=18): 6941 f(x,y,f(z,u,f(z,x,f(z,v,y)))) = f(z,x,y). [para(4955(a,1),19(a,2)),rewrite([2(6),3(7,R),2153(7),1687(6),3(4,R),4(4),365(4)])]. given #139 (T,wt=18): 6960 f(x,y,f(z,u,f(x,u,f(u,v,y)))) = f(x,u,y). [para(28(a,1),4971(a,1,3)),rewrite([3(1),3(4),4(5),2153(5),5448(5),4(1),3(5),3(6,R),4(6),29(6)])]. given #140 (T,wt=18): 6964 f(x,y,f(z,u,f(u,x,f(u,v,y)))) = f(u,x,y). [para(4971(a,1),40(a,2)),rewrite([2(6),3(7,R),2153(7),4921(6),3(4,R),4(4),365(4)])]. given #141 (T,wt=18): 7398 f(x,y,f(z,u,f(x,z,f(z,v,y)))) = f(x,z,y). [back_rewrite(3828),rewrite([7352(9)])]. given #142 (A,wt=27): 64 f(x,y,f(x,z,f(x,u,f(x,v,w)))) = f(x,u,f(x,y,f(x,v,f(x,z,w)))). [para(14(a,1),6(a,1,3))]. given #143 (T,wt=18): 7410 f(x,f(y,z,f(u,z,v)),f(x,z,v)) = f(x,z,v). [para(3(a,2),5835(a,1,2)),rewrite([4(2)])]. given #144 (T,wt=21): 65 f(x,y,f(x,z,f(x,u,v))) = f(x,u,f(x,z,f(x,y,v))). [para(14(a,1),6(a,1))]. given #145 (T,wt=21): 86 f(x,y,f(x,z,f(x,u,v))) = f(x,u,f(x,v,f(x,y,z))). [para(13(a,1),14(a,2,3))]. given #146 (T,wt=21): 96 f(x,y,f(z,u,f(y,z,v))) = f(y,z,f(x,y,f(z,u,v))). [para(6(a,1),38(a,1,3)),rewrite([3(1,R),4(1),3(6,R),4(6)])]. given #147 (A,wt=27): 66 f(x,y,f(x,z,f(x,u,f(x,v,w)))) = f(x,v,f(x,y,f(x,z,f(x,u,w)))). [para(14(a,2),6(a,1,3))]. given #148 (T,wt=18): 9095 f(x,f(y,x,z),f(u,x,z)) = f(y,x,f(u,x,z)). [para(366(a,1),96(a,2,3)),rewrite([3(3),4(3),541(4),3(2,R),4(2),3365(4),3(2),2(2),4(2),3(4),3(5,R)]),flip(a)]. given #149 (T,wt=21): 97 f(x,y,f(z,u,f(z,x,v))) = f(z,x,f(x,y,f(z,u,v))). [para(6(a,1),38(a,2,3)),rewrite([3(2,R),4(2),3(6,R),4(6)]),flip(a)]. given #150 (T,wt=21): 102 f(x,y,f(z,u,f(y,u,v))) = f(y,u,f(x,y,f(z,u,v))). [para(12(a,1),38(a,1,3)),rewrite([3(1,R),4(1),3(6,R),4(6)])]. given #151 (T,wt=18): 10024 f(x,f(y,z,x),f(u,z,x)) = f(y,x,f(u,z,x)). [para(366(a,1),102(a,2,3)),rewrite([3(3),4(3),541(4),3(2,R),4(2),3365(4),11(2),4(2),3(4),3(5,R)]),flip(a)]. given #152 (A,wt=45): 67 f(f(x,y,f(x,z,f(x,u,v))),f(z,w,f(x,u,f(x,y,v))),f(z,v6,f(x,u,f(x,y,v)))) = f(z,f(x,u,f(x,y,v)),f(x,w,v6)). [para(14(a,1),8(a,1,1)),rewrite([4(6),4(9)])]. given #153 (T,wt=18): 10032 f(x,f(y,z,x),f(z,u,x)) = f(y,x,f(z,u,x)). [para(547(a,1),102(a,2,3)),rewrite([3(3),4(3),165(4),3(2,R),4(2),2174(4),11(2),4(2),3(4),3(5,R)]),flip(a)]. given #154 (T,wt=21): 103 f(x,f(y,z,u),f(x,v,z)) = f(x,v,f(y,z,f(x,z,u))). [para(38(a,1),13(a,1,3)),flip(a)]. given #155 (T,wt=21): 104 f(x,y,f(z,u,f(z,x,v))) = f(z,x,f(x,y,f(z,v,u))). [para(13(a,1),38(a,2,3)),rewrite([3(2,R),4(2),3(6,R),4(6)]),flip(a)]. given #156 (T,wt=21): 110 f(x,y,f(z,u,f(x,z,v))) = f(x,z,f(x,y,f(z,v,u))). [para(50(a,2),6(a,2,3)),flip(a)]. given #157 (A,wt=27): 69 f(x,y,f(z,u,f(z,v,f(z,w,v6)))) = f(x,y,f(z,w,f(z,u,f(z,v,v6)))). [para(14(a,1),8(a,2,3)),rewrite([8(6)])]. given #158 (T,wt=21): 112 f(x,y,f(z,u,f(v,z,w))) = f(x,y,f(v,z,f(z,w,u))). [para(50(a,2),8(a,2,3)),rewrite([8(5)]),flip(a)]. given #159 (T,wt=21): 117 f(x,y,f(y,z,f(y,u,v))) = f(y,z,f(y,v,f(x,y,u))). [para(50(a,2),38(a,2,3)),rewrite([3(2,R),4(2),3(6,R),4(6)])]. Low Water (keep, True_semantics): wt=93 given #160 (T,wt=21): 118 f(x,f(y,z,u),f(x,z,v)) = f(x,v,f(y,z,f(x,z,u))). [para(38(a,1),50(a,2,3)),rewrite([3(2),3(2),3(6,R),4(6)])]. given #161 (T,wt=21): 120 f(x,y,f(x,z,f(x,u,v))) = f(x,v,f(x,y,f(x,u,z))). [para(6(a,1),51(a,2,3)),rewrite([83(3),4(1),4(4)])]. given #162 (A,wt=45): 70 f(f(x,y,f(x,z,f(x,u,v))),f(u,w,f(x,y,f(x,z,v))),f(u,v6,f(x,y,f(x,z,v)))) = f(u,f(x,y,f(x,z,v)),f(x,w,v6)). [para(14(a,2),8(a,1,1)),rewrite([4(6),4(9)])]. given #163 (T,wt=21): 121 f(x,y,f(x,z,f(x,u,v))) = f(x,v,f(x,u,f(x,y,z))). [para(13(a,1),51(a,2,3)),rewrite([83(3),4(1),4(4)])]. given #164 (T,wt=21): 170 f(x,y,f(z,u,f(z,v,w))) = f(x,y,f(z,w,f(z,v,u))). [para(13(a,1),16(a,2,3)),rewrite([3(5,R),16(5),3(2),4(4)])]. given #165 (T,wt=21): 194 f(x,y,f(z,u,f(x,v,f(y,v,w)))) = f(x,y,f(z,v,u)). [para(187(a,1),8(a,1,2)),rewrite([8(4),4(5)]),flip(a)]. given #166 (T,wt=21): 215 f(x,y,f(z,u,f(y,v,f(x,v,w)))) = f(x,y,f(z,v,u)). [para(189(a,1),8(a,1,2)),rewrite([8(4),4(5)]),flip(a)]. given #167 (A,wt=33): 71 f(f(x,y,z),f(y,u,f(y,v,f(y,z,w))),f(y,z,v6)) = f(y,z,f(x,v6,f(y,u,f(y,v,w)))). [para(14(a,2),8(a,1,2)),rewrite([4(9)])]. Low Water (keep, True_semantics): wt=81 given #168 (T,wt=18): 13185 f(x,y,f(z,u,f(v,z,f(x,z,y)))) = f(x,z,y). [para(237(a,1),215(a,2)),rewrite([3(4,R),10998(4),8727(6)])]. given #169 (T,wt=18): 13201 f(x,y,f(z,f(x,z,u),f(y,v,z))) = f(x,y,z). [para(368(a,1),215(a,2)),rewrite([4924(5)])]. given #170 (T,wt=21): 220 f(x,f(y,z,f(x,z,u)),f(x,v,y)) = f(x,v,f(x,y,z)). [para(189(a,1),13(a,1,3)),flip(a)]. Low Water (keep, True_semantics): wt=75 Low Water (keep, True_semantics): wt=72 given #171 (T,wt=21): 222 f(x,y,f(y,z,f(x,u,f(x,v,f(x,z,w))))) = f(x,y,z). [para(14(a,2),189(a,1,3,3))]. Low Water (keep, True_semantics): wt=69 given #172 (A,wt=33): 72 f(f(x,y,z),f(y,z,u),f(y,v,f(y,w,f(y,z,v6)))) = f(y,z,f(x,u,f(y,v,f(y,w,v6)))). [para(14(a,2),8(a,1,3))]. given #173 (T,wt=21): 235 f(x,y,f(z,u,f(x,v,f(v,y,w)))) = f(x,y,f(v,z,u)). [para(190(a,1),16(a,1,1)),rewrite([17(4)]),flip(a)]. given #174 (T,wt=21): 271 f(x,y,f(x,f(z,u,v),f(y,z,u))) = f(x,y,f(z,u,v)). [para(200(a,1),187(a,1,3,3))]. given #175 (T,wt=18): 14575 f(x,y,f(z,f(x,y,z),f(u,v,w))) = f(x,y,z). [para(271(a,1),6487(a,1,3))]. given #176 (T,wt=18): 14655 f(x,y,f(z,f(x,z,y),f(u,v,w))) = f(x,z,y). [para(14575(a,1),3(a,2)),rewrite([3(1),3(1),4(4),3(5),3(5)])]. given #177 (A,wt=24): 76 f(x,y,f(x,z,f(x,u,f(x,v,y)))) = f(x,z,f(x,u,f(x,v,y))). [para(28(a,1),14(a,1,3,3)),flip(a)]. given #178 (T,wt=21): 273 f(x,y,f(y,f(z,u,v),f(x,z,u))) = f(x,y,f(z,u,v)). [para(200(a,1),189(a,1,3,3))]. given #179 (T,wt=18): 15086 f(x,y,f(z,f(y,z,u),f(x,v,z))) = f(x,y,z). [para(6960(a,1),273(a,2)),rewrite([3(1),4(5),845(5),36(5),4(5)])]. given #180 (T,wt=21): 275 f(x,f(y,z,u),f(x,v,f(y,z,v))) = f(x,v,f(y,z,u)). [para(200(a,1),190(a,1,3,3)),rewrite([3(2),3(2)])]. given #181 (T,wt=18): 15286 f(x,f(y,z,u),f(v,y,z)) = f(y,z,f(v,u,x)). [para(275(a,1),24(a,2)),rewrite([2(4),47(7),4(3),29(3),5051(4),3(5,R)]),flip(a)]. given #182 (A,wt=27): 78 f(x,y,f(z,u,f(x,z,f(z,v,w)))) = f(x,z,f(x,y,f(z,v,f(z,u,w)))). [para(14(a,1),12(a,1,3)),rewrite([3(2,R),4(2),3(8,R),4(8)])]. given #183 (T,wt=18): 15475 f(x,f(y,z,u),f(z,u,v)) = f(z,u,f(x,y,v)). [back_rewrite(9737),rewrite([15228(5),15286(3),3(1)]),flip(a)]. ============================== PROOF ================================= % Proof 1 at 76.52 (+ 0.08) seconds: dist_short. % Length of proof is 90. % Level of proof is 16. % Maximum clause weight is 54. % Given clauses 183. 1 f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)) # answer(dist_short) # label(non_clause) # label(goal). [goal]. 2 f(x,x,y) = x # label(majority). [assumption]. 3 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. 4 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. 5 f(f(x,y,z),y,u) = f(x,y,f(z,y,u)) # label(associativity). [assumption]. 6 f(x,y,f(x,z,u)) = f(x,z,f(x,y,u)). [copy(5),rewrite([3(2),3(2),3(3,R),4(3)]),rewrite([3(1,R),4(1),4(3),3(4,R),4(4)])]. 7 f(f(x,y,z),u,v) = f(f(x,u,v),f(y,u,v),f(z,u,v)) # label(dist_long). [assumption]. 8 f(f(x,y,z),f(y,z,u),f(y,z,v)) = f(y,z,f(x,u,v)). [copy(7),rewrite([3(2),3(2)]),flip(a),rewrite([3(2),3(2),3(3),3(3)])]. 9 f(f(c1,c2,c3),c4,c5) != f(c1,f(c2,c4,c5),f(c3,c4,c5)) # answer(dist_short). [deny(1)]. 10 f(c1,f(c2,c4,c5),f(c3,c4,c5)) != f(c4,c5,f(c1,c2,c3)) # answer(dist_short). [copy(9),rewrite([3(7),3(7)]),flip(a)]. 11 f(x,y,y) = y. [para(3(a,1),2(a,1))]. 12 f(x,y,f(z,x,u)) = f(z,x,f(x,y,u)). [para(6(a,1),3(a,2)),rewrite([4(2),3(3,R),4(3)]),flip(a)]. 13 f(x,y,f(x,z,u)) = f(x,u,f(x,y,z)). [para(3(a,1),6(a,1,3)),rewrite([3(1,R),4(1)])]. 14 f(x,y,f(x,z,f(x,u,v))) = f(x,u,f(x,y,f(x,z,v))). [para(6(a,1),6(a,1,3))]. 16 f(f(x,y,z),f(x,y,u),f(x,y,v)) = f(x,y,f(u,v,z)). [para(8(a,1),3(a,1)),rewrite([3(4),3(4)]),flip(a)]. 17 f(f(x,y,z),f(x,z,u),f(x,z,v)) = f(x,z,f(y,u,v)). [para(3(a,1),8(a,1,1)),rewrite([3(2,R),4(2),3(3,R),4(3),3(6,R),4(6)])]. 18 f(f(x,y,z),f(y,z,u),f(v,f(y,z,w),f(x,y,z))) = f(v,f(x,y,z),f(y,z,f(x,u,w))). [para(8(a,1),6(a,1,3)),rewrite([3(4,R),4(4),3(9,R)]),flip(a)]. 21 f(f(x,y,z),f(y,z,u),f(y,v,f(y,z,w))) = f(y,z,f(x,u,f(y,v,w))). [para(6(a,1),8(a,1,3))]. 23 f(f(x,y,f(z,u,v)),f(w,f(x,y,u),f(x,y,v)),f(v6,f(x,y,u),f(x,y,v))) = f(f(x,y,u),f(x,y,v),f(w,v6,f(x,y,z))). [para(8(a,1),8(a,1,1)),rewrite([3(5),3(8),3(12),3(12),3(13),3(13)])]. 24 f(f(x,f(y,z,u),f(z,u,v)),f(z,u,f(y,v,w)),f(v6,f(y,z,u),f(z,u,v))) = f(f(y,z,u),f(z,u,v),f(x,v6,f(z,u,w))). [para(8(a,1),8(a,1,2)),rewrite([3(8),4(13)])]. 28 f(x,y,f(x,z,y)) = f(x,z,y). [para(11(a,1),6(a,1,3)),flip(a)]. 29 f(x,y,f(x,y,z)) = f(x,y,z). [para(11(a,1),6(a,1)),rewrite([4(3),28(3)]),flip(a)]. 30 f(x,f(y,x,z),f(u,y,x)) = f(y,x,f(u,x,z)). [para(11(a,1),8(a,1,2)),rewrite([3(3,R)])]. 31 f(x,f(y,z,x),f(z,x,u)) = f(z,x,f(y,x,u)). [para(11(a,1),8(a,1,3)),rewrite([3(3),4(4)])]. 35 f(f(x,y,z),f(z,u,f(x,y,z)),f(z,v,f(x,y,z))) = f(z,f(x,y,z),f(x,u,v)). [para(28(a,1),8(a,1,1)),rewrite([4(3),4(5)])]. 36 f(x,y,f(z,u,f(x,y,v))) = f(x,y,f(z,v,u)). [para(28(a,1),8(a,1,2)),rewrite([4(2),8(4),4(3),4(4)]),flip(a)]. 38 f(x,y,f(z,y,u)) = f(z,y,f(x,y,u)). [para(12(a,1),3(a,2)),rewrite([4(2),3(3,R),4(3)])]. 40 f(f(x,y,f(y,z,u)),f(z,v,f(x,y,u)),f(z,w,f(x,y,u))) = f(z,f(x,y,u),f(y,v,w)). [para(12(a,1),8(a,1,1)),rewrite([4(4),4(6)])]. 41 f(x,f(x,y,z),f(u,x,y)) = f(u,x,f(x,y,z)). [para(12(a,1),8(a,2)),rewrite([3(2),2(2),3(3,R)])]. 47 f(f(x,y,z),f(y,z,u),f(v,f(x,y,z),f(y,z,w))) = f(v,f(x,y,z),f(y,z,f(x,u,w))). [para(8(a,1),12(a,2,3))]. 50 f(x,y,f(z,x,u)) = f(z,x,f(x,u,y)). [para(13(a,1),3(a,2)),rewrite([4(2),3(3,R),4(3)]),flip(a)]. 83 f(x,f(x,y,z),f(x,u,v)) = f(x,y,f(x,u,f(x,v,z))). [para(14(a,1),13(a,1)),flip(a)]. 96 f(x,y,f(z,u,f(y,z,v))) = f(y,z,f(x,y,f(z,u,v))). [para(6(a,1),38(a,1,3)),rewrite([3(1,R),4(1),3(6,R),4(6)])]. 125 f(x,f(y,x,z),f(y,x,u)) = f(y,x,f(x,u,z)). [para(30(a,1),3(a,1)),rewrite([3(1,R),4(1),3(3),3(3),3(5,R)]),flip(a)]. 135 f(x,f(y,x,z),f(y,u,f(y,x,z))) = f(y,x,z). [para(29(a,1),30(a,1,3)),rewrite([4(3),3(5),2(5),4(4)]),flip(a)]. 140 f(f(x,y,z),f(x,u,f(x,y,z)),f(x,y,f(x,z,v))) = f(x,f(x,y,z),f(u,v,f(x,y,z))). [para(12(a,2),30(a,1,3)),rewrite([4(3),3(4),3(4),3(9)])]. 157 f(f(x,y,z),f(x,u,f(x,y,v)),f(x,y,w)) = f(x,y,f(z,w,f(x,u,v))). [para(6(a,1),16(a,1,2)),rewrite([3(7),4(7)])]. 165 f(x,y,f(z,u,f(x,v,y))) = f(x,y,f(v,z,u)). [para(28(a,1),16(a,1,1)),rewrite([17(4)]),flip(a)]. 183 f(x,f(x,y,z),f(u,v,f(x,y,z))) = f(x,y,f(x,z,f(z,u,v))). [back_rewrite(140),rewrite([157(6),4(2),125(3)]),flip(a)]. 187 f(x,y,f(x,z,f(y,z,u))) = f(x,y,z). [back_rewrite(135),rewrite([3(1,R),4(1),3(2,R),4(2),183(4),3(1,R),4(1),3(4,R),4(4)])]. 189 f(x,y,f(y,z,f(x,z,u))) = f(x,y,z). [para(187(a,1),3(a,2)),rewrite([4(3),3(4,R),4(4)])]. 190 f(x,y,f(x,z,f(z,y,u))) = f(x,z,y). [para(187(a,1),4(a,2)),rewrite([3(1,R),4(1),4(3),4(4)])]. 198 f(x,y,f(x,f(y,z,u),f(y,v,f(y,z,u)))) = f(y,z,f(x,y,u)). [para(12(a,2),187(a,2)),rewrite([4(3)])]. 200 f(x,f(y,z,u),f(x,y,z)) = f(x,y,z). [para(187(a,1),13(a,1)),flip(a)]. 204 f(x,y,f(z,x,u)) = f(x,u,f(z,x,y)). [para(50(a,2),187(a,2)),rewrite([4(3),198(5)])]. 226 f(x,y,f(z,x,f(z,y,u))) = f(z,x,y). [para(189(a,1),187(a,2)),rewrite([4(5),198(7)])]. 233 f(x,f(y,z,u),f(x,z,f(z,v,f(y,z,u)))) = f(y,z,f(x,z,u)). [para(38(a,1),190(a,2)),rewrite([4(3)])]. 236 f(x,f(y,z,u),f(y,z,x)) = f(y,z,x). [para(200(a,1),3(a,2)),rewrite([3(2),3(2),3(3),3(4),3(4)])]. 237 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(3(a,1),200(a,1,2))]. 252 f(x,f(y,z,f(y,u,v)),f(x,y,v)) = f(x,y,v). [para(13(a,2),200(a,1,2))]. 275 f(x,f(y,z,u),f(x,v,f(y,z,v))) = f(x,v,f(y,z,u)). [para(200(a,1),190(a,1,3,3)),rewrite([3(2),3(2)])]. 295 f(f(x,y,f(x,z,u)),f(x,v,f(x,y,z)),f(x,w,f(x,y,z))) = f(x,f(x,y,z),f(u,v,w)). [para(13(a,2),17(a,1,1)),rewrite([4(4),4(6)])]. 320 f(x,y,f(z,u,x)) = f(z,x,f(u,x,y)). [para(204(a,1),3(a,2)),rewrite([4(2),3(3)]),flip(a)]. 343 f(x,f(y,z,u),f(y,x,z)) = f(y,x,z). [para(226(a,1),204(a,1)),flip(a)]. 345 f(x,y,f(z,u,x)) = f(u,x,f(z,x,y)). [para(204(a,1),226(a,2)),rewrite([4(3),3(4,R),4(4),233(5),3(3)]),flip(a)]. 360 f(x,f(y,z,x),f(u,v,f(y,z,w))) = f(x,f(y,z,x),f(y,u,v)). [para(236(a,1),17(a,1,1)),rewrite([4(3),4(5),35(6),3(6),3(6)]),flip(a)]. 365 f(x,y,f(z,x,y)) = f(z,x,y). [para(237(a,1),2(a,1)),rewrite([3(2),3(2)])]. 366 f(x,f(y,z,u),f(z,u,x)) = f(z,u,x). [para(237(a,1),3(a,2)),rewrite([3(2),3(2),3(3),3(4),3(4)])]. 373 f(x,y,f(x,z,f(u,y,z))) = f(x,y,z). [para(237(a,1),8(a,2)),rewrite([2(2),4(2),4(4),83(5),11(3)])]. 418 f(f(x,y,z),f(y,z,u),f(x,y,f(y,z,v))) = f(y,z,f(y,f(x,y,z),f(x,u,v))). [para(6(a,1),18(a,2)),rewrite([41(5)])]. 447 f(x,y,f(x,f(z,x,y),f(z,u,v))) = f(x,f(z,u,v),f(z,x,y)). [para(13(a,1),18(a,2)),rewrite([41(5),418(5),4(7),365(7)])]. 469 f(x,f(y,x,z),f(x,z,f(y,u,v))) = f(x,f(y,u,v),f(y,x,z)). [para(50(a,1),18(a,1,3)),rewrite([29(4),418(5),447(4)]),flip(a)]. 541 f(x,y,f(z,u,f(v,x,y))) = f(x,y,f(v,z,u)). [para(365(a,1),16(a,1,1)),rewrite([8(4)]),flip(a)]. 617 f(x,y,f(z,u,y)) = f(z,y,f(x,u,y)). [para(320(a,1),3(a,2)),rewrite([4(2),3(3)])]. 618 f(x,f(y,z,u),f(y,z,f(y,u,v))) = f(y,z,f(y,u,f(u,x,v))). [para(6(a,1),320(a,1,3)),rewrite([4(2),3(4,R),4(4),3(7),183(8)])]. 620 f(x,f(y,z,u),f(y,v,f(y,z,u))) = f(y,z,f(y,u,f(u,v,x))). [para(12(a,2),320(a,1,3)),rewrite([3(2),3(2),3(4,R),4(4),618(4),4(6)]),flip(a)]. 641 f(x,f(y,z,u),f(y,u,f(z,u,v))) = f(u,f(y,z,u),f(y,x,v)). [para(320(a,1),320(a,1,3)),rewrite([3(4,R),4(4),3(7),360(8)])]. 646 f(x,f(y,z,u),f(x,y,v)) = f(x,y,f(x,v,f(y,z,u))). [back_rewrite(469),rewrite([3(1,R),4(1),83(4),4(2),29(3),3(5,R),4(5)]),flip(a)]. 660 f(x,y,f(x,z,f(y,u,f(y,v,z)))) = f(x,y,z). [back_rewrite(252),rewrite([646(4)])]. 822 f(f(x,y,z),f(y,z,u),f(u,v,f(y,z,u))) = f(y,z,u). [para(237(a,1),343(a,1,3)),rewrite([3(2),3(2),4(3),3(4),3(4),4(5),3(7),3(7),366(8)])]. 846 f(x,f(y,z,u),f(u,v,f(y,z,u))) = f(u,f(y,z,u),f(y,v,x)). [para(320(a,1),345(a,1,3)),rewrite([3(4,R),4(4),641(4),4(6)]),flip(a)]. 854 f(x,f(y,z,x),f(y,u,f(v,y,z))) = f(y,z,x). [back_rewrite(822),rewrite([846(5)])]. 1232 f(x,f(y,z,u),f(v,y,f(y,z,u))) = f(y,z,f(y,u,f(v,u,x))). [para(12(a,2),617(a,1,3)),rewrite([3(2),3(2),618(4),3(1,R),4(1)]),flip(a)]. 1233 f(x,f(y,z,u),f(y,z,f(v,y,u))) = f(y,z,f(y,u,f(v,u,x))). [para(12(a,2),617(a,2,3)),rewrite([3(3,R),4(3),620(4),3(1)]),flip(a)]. 1504 f(x,f(x,y,z),f(u,v,f(x,z,w))) = f(x,f(x,y,z),f(w,u,v)). [para(320(a,2),23(a,1,1)),rewrite([3(1),11(3),3(3),3(3),3(4,R),4(4),11(5),3(5),3(5),3(6,R),4(6),295(7),11(4),3(4),3(4),3(5,R),4(5)]),flip(a)]. 1601 f(f(x,y,f(y,z,u)),f(y,u,f(y,z,v)),f(y,w,f(y,z,u))) = f(y,f(y,z,u),f(x,v,w)). [para(31(a,1),8(a,1,2)),rewrite([3(1),3(3,R),4(3),3(4,R),4(4),3(5),4(6),3(8),3(9,R),4(9),4(10),1504(11),3(9,R),4(9)])]. 1712 f(x,f(x,y,z),f(u,v,f(x,y,w))) = f(x,f(x,y,z),f(u,w,v)). [para(6(a,1),24(a,1,2)),rewrite([2(1),2(5),3(6,R),4(6),1601(7),2(4)]),flip(a)]. 2153 f(x,f(x,y,z),f(u,v,w)) = f(x,y,f(x,z,f(u,v,w))). [para(21(a,1),165(a,1,3)),rewrite([4(2),83(5),4(3),36(3),4(1),29(4),3(5),3(5),1712(8),3(6,R),4(6),1712(7),3(5,R),4(5)]),flip(a)]. 3365 f(x,f(y,z,u),f(z,u,f(x,y,v))) = f(x,f(y,z,u),f(z,u,v)). [para(541(a,1),165(a,1,3)),rewrite([3(2,R),4(2),3(6),3(6)])]. 3895 f(x,f(y,z,f(u,v,w)),f(x,f(y,v6,f(u,v,w)),f(v7,f(y,z,f(u,v,w)),f(y,f(u,v,w),f(z,v,v6))))) = f(x,f(y,z,f(u,v,w)),f(y,v6,f(u,v,w))). [para(40(a,1),854(a,1,3,3)),rewrite([3(5),3(9,R),4(9),3(11,R),4(11),2153(12),3(17)])]. 5051 f(x,f(y,z,u),f(z,u,f(y,v,x))) = f(z,u,f(y,v,x)). [para(366(a,1),47(a,1,3)),rewrite([8(4)]),flip(a)]. 9095 f(x,f(y,x,z),f(u,x,z)) = f(y,x,f(u,x,z)). [para(366(a,1),96(a,2,3)),rewrite([3(3),4(3),541(4),3(2,R),4(2),3365(4),3(2),2(2),4(2),3(4),3(5,R)]),flip(a)]. 9737 f(x,f(y,z,u),f(z,u,f(z,v,f(x,y,v)))) = f(x,f(y,z,u),f(z,u,v)). [para(9095(a,1),373(a,1,3,3)),rewrite([3(2),3(2),3(3),3(3),1232(5),3(2),3(7),3(7)])]. 15228 f(x,f(y,z,u),f(z,v,f(z,w,f(x,y,w)))) = f(x,f(z,v,w),f(y,z,u)). [para(12(a,2),275(a,1,3,3)),rewrite([1233(5),3(2)])]. 15286 f(x,f(y,z,u),f(v,y,z)) = f(y,z,f(v,u,x)). [para(275(a,1),24(a,2)),rewrite([2(4),47(7),4(3),29(3),5051(4),3(5,R)]),flip(a)]. 15475 f(x,f(y,z,u),f(z,u,v)) = f(z,u,f(x,y,v)). [back_rewrite(9737),rewrite([15228(5),15286(3),3(1)]),flip(a)]. 18221 f(x,f(y,z,u),f(y,u,v)) = f(y,u,f(x,z,v)). [para(3(a,2),15286(a,1,2)),rewrite([3(2),4(2),3(4),4(4),3(5,R),4(5)])]. 18605 f(x,f(y,z,f(u,v,w)),f(y,v6,f(u,v,w))) = f(y,f(u,v,w),f(x,z,v6)). [back_rewrite(3895),rewrite([18221(10),3(7,R),4(7),18221(9),18221(8),660(5)]),flip(a)]. 19888 f(x,f(y,z,u),f(v,z,u)) = f(z,u,f(v,x,y)). [para(15475(a,1),15286(a,2)),rewrite([4(2),3(4,R),4(4),18605(5),4(2),3(4)])]. 20207 $F # answer(dist_short). [back_rewrite(10),rewrite([19888(10),3(6),3(6)]),xx(a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=183. Generated=162715. Kept=20202. proofs=1. Usable=110. Sos=8715. Demods=6567. Limbo=319, Disabled=11064. Hints=0. Weight_deleted=617. Literals_deleted=0. Forward_subsumed=141362. Back_subsumed=637. Sos_limit_deleted=533. Sos_displaced=0. Sos_removed=0. New_demodulators=16739 (2 lex), Back_demodulated=10421. Back_unit_deleted=0. Demod_attempts=3381508. Demod_rewrites=1150437. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0. Megabytes=25.02. User_CPU=76.52, System_CPU=0.08, Wall_clock=77. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 1 proof. Process 28426 exit (max_proofs) Tue May 22 15:18:25 2007