============================== Prover9 =============================== Prover9 (32) version November-2006, November 2006. Process 3856 was started by mccune on cleo.thornwood, Wed Nov 22 11:24:11 2006 The command was "/home/mccune/bin/prover9 -f gt.in AN.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file gt.in op(450,infix,@). op(400,infix_right,*). assign(eq_defs,fold). assign(max_weight,25). formulas(sos). (x * y) * z = x * y * z. e * x = x. x' * x = e. x @ y = x' * y' * x * y. end_of_list. % Reading from file AN.in formulas(sos). (x @ y) @ z = u @ (v @ w). end_of_list. formulas(sos). (A @ B) * C != C * (A @ B) # answer(N). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: ============================== end of process non-clausal formulas === ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). (x * y) * z = x * y * z. [assumption]. e * x = x. [assumption]. x' * x = e. [assumption]. x @ y = x' * y' * x * y. [assumption]. (x @ y) @ z = u @ (v @ w). [assumption]. (A @ B) * C != C * (A @ B) # answer(N). [assumption]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination ============= Auto_denials: (no changes). Term ordering decisions: Relation symbol precedence: lex([ = ]). Function symbol precedence: lex([ e, A, B, C, *, @, ' ]). After inverse_order: Function symbol precedence: lex([ e, A, B, C, *, ', @ ]). Folding symbols: @/2. After fold_eq: Function symbol precedence: lex([ e, A, B, C, @, *, ' ]). 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). 1 (x * y) * z = x * y * z. [assumption]. 2 e * x = x. [assumption]. 3 x' * x = e. [assumption]. 5 x' * y' * x * y = x @ y. [copy(4),flip(a)]. 6 (x @ y) @ z = u @ (v @ w). [assumption]. 7 (A @ B) * C != C * (A @ B) # answer(N). [assumption]. end_of_list. formulas(demodulators). 1 (x * y) * z = x * y * z. [assumption]. 2 e * x = x. [assumption]. 3 x' * x = e. [assumption]. 5 x' * y' * x * y = x @ y. [copy(4),flip(a)]. end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.00 seconds. given #1 (I,wt=11): 1 (x * y) * z = x * y * z. [assumption]. given #2 (I,wt=5): 2 e * x = x. [assumption]. given #3 (I,wt=6): 3 x' * x = e. [assumption]. given #4 (I,wt=13): 5 x' * y' * x * y = x @ y. [copy(4),flip(a)]. given #5 (I,wt=11): 6 (x @ y) @ z = u @ (v @ w). [assumption]. given #6 (I,wt=11): 7 (A @ B) * C != C * (A @ B) # answer(N). [assumption]. given #7 (F,wt=5): 11 e @ x = e. [para(2(a,1),5(a,1,2,2)),rewrite(3(4),3(4)),flip(a)]. given #8 (F,wt=5): 19 x @ e = e. [back_rewrite(17),rewrite(18(2)),flip(a)]. given #9 (T,wt=6): 12 x' @ x = e. [para(3(a,1),5(a,1,2,2)),rewrite(8(6)),flip(a)]. given #10 (T,wt=7): 16 x @ (y @ z) = e. [para(11(a,1),6(a,1,1)),rewrite(11(2)),flip(a)]. given #11 (A,wt=8): 8 x' * x * y = y. [para(3(a,1),1(a,1,1)),rewrite(2(2)),flip(a)]. given #12 (F,wt=5): 24 x @ x = e. [para(8(a,1),5(a,1,2)),rewrite(3(2)),flip(a)]. given #13 (F,wt=5): 29 x * e = x. [back_rewrite(22),rewrite(26(4))]. given #14 (T,wt=4): 31 e' = e. [para(29(a,1),3(a,1))]. given #15 (T,wt=7): 18 (x @ y) @ z = e. [para(11(a,1),6(a,2))]. given #16 (A,wt=17): 9 x' * y' * x * y * z = (x @ y) * z. [para(5(a,1),1(a,1,1)),rewrite(1(7),1(6)),flip(a)]. given #17 (F,wt=17): 41 A' * B' * A * B * C != C * (A @ B) # answer(N). [para(9(a,2),7(a,1))]. given #18 (F,wt=9): 26 x'' * y = x * y. [para(8(a,1),8(a,1,2))]. given #19 (T,wt=5): 56 x'' = x. [para(26(a,1),29(a,1)),rewrite(29(2)),flip(a)]. given #20 (T,wt=6): 51 x * x' = e. [para(26(a,1),3(a,1))]. given #21 (A,wt=19): 10 (x * y)' * z' * x * y * z = x * y @ z. [para(1(a,1),5(a,1,2,2))]. given #22 (F,wt=6): 59 x @ x' = e. [para(56(a,1),12(a,1,1))]. given #23 (F,wt=7): 75 x * x @ x = e. [para(10(a,1),10(a,1,2)),rewrite(3(2),31(2),2(4),3(4),11(5))]. given #24 (T,wt=8): 55 x * x' * y = y. [para(26(a,1),8(a,1))]. given #25 (T,wt=10): 60 x * y * (x * y)' = e. [para(51(a,1),1(a,1)),flip(a)]. given #26 (A,wt=12): 20 (x * y)' * x * y * z = z. [para(1(a,1),8(a,1,2))]. given #27 (F,wt=7): 93 x @ x * x = e. [para(20(a,1),5(a,1,2)),rewrite(3(2)),flip(a)]. given #28 (F,wt=9): 84 x * (y * x)' = y'. [para(60(a,1),8(a,1,2)),rewrite(29(3)),flip(a)]. given #29 (T,wt=8): 114 (x @ y)' = y @ x. [para(9(a,2),84(a,1,2,1)),rewrite(113(7),113(5),113(3),113(2),1(5),56(7),1(6),1(5),56(8),1(7),1(6),1(5),5(6),55(4)),flip(a)]. given #30 (T,wt=9): 127 (x @ y) * (y @ x) = e. [back_rewrite(86),rewrite(113(8),113(6),113(4),113(3),1(6),56(8),1(7),1(6),56(9),1(8),1(7),1(6),5(7),55(5))]. given #31 (A,wt=12): 27 x' * y * x = y * (y @ x). [back_rewrite(25),rewrite(26(4)),flip(a)]. given #32 (F,wt=9): 131 x * y @ x = y @ x. [back_rewrite(69),rewrite(113(2),1(5),5(5)),flip(a)]. given #33 (F,wt=9): 155 x @ y * x = x @ y. [back_rewrite(148),rewrite(154(4)),flip(a)]. given #34 (T,wt=8): 184 x' @ y = y @ x. [back_rewrite(180),rewrite(181(3))]. given #35 (T,wt=8): 185 x @ y' = y @ x. [back_rewrite(177),rewrite(181(2)),flip(a)]. given #36 (A,wt=21): 32 x * y' * z' * y * z * u = x * (y @ z) * u. [para(9(a,1),1(a,2,2)),rewrite(1(7))]. given #37 (F,wt=12): 202 (B @ A') * C != C * (A @ B) # answer(N). [para(185(a,2),7(a,1,1))]. given #38 (F,wt=12): 203 C * (B @ A') != (A @ B) * C # answer(N). [para(185(a,2),7(a,2,2)),flip(a)]. given #39 (T,wt=9): 173 x @ x * y = x @ y. [para(131(a,1),114(a,1,1)),rewrite(114(2)),flip(a)]. given #40 (T,wt=9): 181 x * y @ y = x @ y. [para(155(a,1),114(a,1,1)),rewrite(114(2)),flip(a)]. given #41 (A,wt=13): 35 x' * y * x = (x @ y') * y. [para(3(a,1),9(a,1,2,2,2)),rewrite(29(5),26(4))]. given #42 (F,wt=13): 227 (B @ A') * C != C * (B @ A') # answer(N). [para(184(a,2),202(a,2,2)),rewrite(211(11))]. given #43 (F,wt=17): 226 B' * A * B * A' * C != C * (A @ B) # answer(N). [para(9(a,2),202(a,1)),rewrite(56(5))]. given #44 (T,wt=9): 197 x' @ y' = x @ y. [para(184(a,2),184(a,1))]. given #45 (T,wt=9): 211 x' @ y = x @ y'. [para(185(a,1),184(a,1)),flip(a)]. given #46 (A,wt=22): 38 x' * y * x * (y @ z) = (x @ y') * z' * y * z. [para(5(a,1),9(a,1,2,2,2)),rewrite(26(6))]. given #47 (F,wt=18): 206 A' * B' * A * B * C != C * (B @ A') # answer(N). [para(185(a,2),41(a,2,2))]. given #48 (F,wt=18): 253 B' * A * B * A' * C != C * (B @ A') # answer(N). [para(9(a,2),227(a,1)),rewrite(56(5))]. given #49 (T,wt=10): 113 (x * y)' = y' * x'. [para(84(a,1),8(a,1,2)),flip(a)]. given #50 (T,wt=10): 147 x * y @ y' = y @ x. [back_rewrite(74),rewrite(131(5))]. given #51 (A,wt=12): 40 (x' @ y) * x = x * (y @ x). [para(5(a,1),9(a,1,2)),rewrite(26(4)),flip(a)]. given #52 (F,wt=10): 157 x' @ y * x = y @ x. [para(27(a,1),5(a,1,2,2)),rewrite(56(2),113(2),1(6),8(5),55(4)),flip(a)]. given #53 (F,wt=10): 172 x' * y @ x = y @ x. [para(55(a,1),131(a,1,1)),flip(a)]. given #54 (T,wt=10): 175 x' * y * x @ y = e. [para(27(a,2),131(a,1,1)),rewrite(18(6))]. given #55 (T,wt=10): 191 (x @ y) * (x @ y') = e. [para(184(a,1),127(a,1,1))]. given #56 (A,wt=16): 43 x' * y * x * z = y * (y @ x) * z. [para(9(a,1),8(a,1,2)),rewrite(26(5)),flip(a)]. ============================== PROOF ================================= % Proof 1 at 0.04 (+ 0.00) seconds: N. % Length of proof is 43. % Level of proof is 14. % Maximum clause weight is 20. % Given clauses 56. 1 (x * y) * z = x * y * z. [assumption]. 2 e * x = x. [assumption]. 3 x' * x = e. [assumption]. 4 x @ y = x' * y' * x * y. [assumption]. 5 x' * y' * x * y = x @ y. [copy(4),flip(a)]. 6 (x @ y) @ z = u @ (v @ w). [assumption]. 7 (A @ B) * C != C * (A @ B) # answer(N). [assumption]. 8 x' * x * y = y. [para(3(a,1),1(a,1,1)),rewrite(2(2)),flip(a)]. 9 x' * y' * x * y * z = (x @ y) * z. [para(5(a,1),1(a,1,1)),rewrite(1(7),1(6)),flip(a)]. 10 (x * y)' * z' * x * y * z = x * y @ z. [para(1(a,1),5(a,1,2,2))]. 11 e @ x = e. [para(2(a,1),5(a,1,2,2)),rewrite(3(4),3(4)),flip(a)]. 16 x @ (y @ z) = e. [para(11(a,1),6(a,1,1)),rewrite(11(2)),flip(a)]. 22 x'' * e = x. [para(3(a,1),8(a,1,2))]. 26 x'' * y = x * y. [para(8(a,1),8(a,1,2))]. 29 x * e = x. [back_rewrite(22),rewrite(26(4))]. 43 x' * y * x * z = y * (y @ x) * z. [para(9(a,1),8(a,1,2)),rewrite(26(5)),flip(a)]. 51 x * x' = e. [para(26(a,1),3(a,1))]. 55 x * x' * y = y. [para(26(a,1),8(a,1))]. 56 x'' = x. [para(26(a,1),29(a,1)),rewrite(29(2)),flip(a)]. 60 x * y * (x * y)' = e. [para(51(a,1),1(a,1)),flip(a)]. 69 (x * y)' * y * x = x * y @ x. [para(8(a,1),10(a,1,2))]. 71 x' * (y * x @ y) * x = x @ y * x. [para(9(a,1),10(a,1,2)),rewrite(8(3),8(8))]. 84 x * (y * x)' = y'. [para(60(a,1),8(a,1,2)),rewrite(29(3)),flip(a)]. 86 (x @ y) * z * (x' * y' * x * y * z)' = e. [para(9(a,2),60(a,1,2,2,1))]. 113 (x * y)' = y' * x'. [para(84(a,1),8(a,1,2)),flip(a)]. 114 (x @ y)' = y @ x. [para(9(a,2),84(a,1,2,1)),rewrite(113(7),113(5),113(3),113(2),1(5),56(7),1(6),1(5),56(8),1(7),1(6),1(5),5(6),55(4)),flip(a)]. 127 (x @ y) * (y @ x) = e. [back_rewrite(86),rewrite(113(8),113(6),113(4),113(3),1(6),56(8),1(7),1(6),56(9),1(8),1(7),1(6),5(7),55(5))]. 131 x * y @ x = y @ x. [back_rewrite(69),rewrite(113(2),1(5),5(5)),flip(a)]. 148 x' * (x @ y) * x = x @ y * x. [back_rewrite(71),rewrite(131(3))]. 154 x' * (y @ z) * x = y @ z. [para(127(a,1),9(a,1,2,2,2)),rewrite(114(3),29(4),16(6),2(7))]. 155 x @ y * x = x @ y. [back_rewrite(148),rewrite(154(4)),flip(a)]. 170 x * y @ x' = y @ x'. [para(8(a,1),131(a,1,1)),flip(a)]. 172 x' * y @ x = y @ x. [para(55(a,1),131(a,1,1)),flip(a)]. 177 x * y @ y = y @ x'. [para(8(a,1),155(a,1,2)),rewrite(170(5))]. 180 x' * y @ y = y @ x. [para(55(a,1),155(a,1,2)),rewrite(172(6))]. 181 x * y @ y = x @ y. [para(155(a,1),114(a,1,1)),rewrite(114(2)),flip(a)]. 184 x' @ y = y @ x. [back_rewrite(180),rewrite(181(3))]. 185 x @ y' = y @ x. [back_rewrite(177),rewrite(181(2)),flip(a)]. 202 (B @ A') * C != C * (A @ B) # answer(N). [para(185(a,2),7(a,1,1))]. 211 x' @ y = x @ y'. [para(185(a,1),184(a,1)),flip(a)]. 227 (B @ A') * C != C * (B @ A') # answer(N). [para(184(a,2),202(a,2,2)),rewrite(211(11))]. 367 (x @ y) * z = z * (x @ y). [para(127(a,1),43(a,1,2,2)),rewrite(114(2),29(3),16(4),2(5))]. 368 $F # answer(N). [resolve(367,a,227,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=56. Generated=2019. Kept=366. proofs=1. Usable=46. Sos=189. Demods=138. Limbo=17, Disabled=119. Hints=0. Weight_deleted=124. Literals_deleted=0. Forward_subsumed=1529. Back_subsumed=1. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=227 (1 lex), Back_demodulated=112. Back_unit_deleted=0. Demod_attempts=23388. Demod_rewrites=4623. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0. Megabytes=0.31. User_CPU=0.04, System_CPU=0.00, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 1 proof. Process 3856 exit (max_proofs) Wed Nov 22 11:24:11 2006