0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.11 % Command : tptp2X_and_run_prover9 %d %s 0.11/0.31 % Computer : n025.cluster.edu 0.11/0.31 % Model : x86_64 x86_64 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.31 % Memory : 8042.1875MB 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.31 % CPULimit : 960 0.11/0.31 % DateTime : Thu Jul 2 09:17:38 EDT 2020 0.11/0.32 % CPUTime : 0.39/0.97 ============================== Prover9 =============================== 0.39/0.97 Prover9 (32) version 2009-11A, November 2009. 0.39/0.97 Process 8002 was started by sandbox2 on n025.cluster.edu, 0.39/0.97 Thu Jul 2 09:17:38 2020 0.39/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_7846_n025.cluster.edu". 0.39/0.97 ============================== end of head =========================== 0.39/0.97 0.39/0.97 ============================== INPUT ================================= 0.39/0.97 0.39/0.97 % Reading from file /tmp/Prover9_7846_n025.cluster.edu 0.39/0.97 0.39/0.97 set(prolog_style_variables). 0.39/0.97 set(auto2). 0.39/0.97 % set(auto2) -> set(auto). 0.39/0.97 % set(auto) -> set(auto_inference). 0.39/0.97 % set(auto) -> set(auto_setup). 0.39/0.97 % set(auto_setup) -> set(predicate_elim). 0.39/0.97 % set(auto_setup) -> assign(eq_defs, unfold). 0.39/0.97 % set(auto) -> set(auto_limits). 0.39/0.97 % set(auto_limits) -> assign(max_weight, "100.000"). 0.39/0.97 % set(auto_limits) -> assign(sos_limit, 20000). 0.39/0.97 % set(auto) -> set(auto_denials). 0.39/0.97 % set(auto) -> set(auto_process). 0.39/0.97 % set(auto2) -> assign(new_constants, 1). 0.39/0.97 % set(auto2) -> assign(fold_denial_max, 3). 0.39/0.97 % set(auto2) -> assign(max_weight, "200.000"). 0.39/0.97 % set(auto2) -> assign(max_hours, 1). 0.39/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.39/0.97 % set(auto2) -> assign(max_seconds, 0). 0.39/0.97 % set(auto2) -> assign(max_minutes, 5). 0.39/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.39/0.97 % set(auto2) -> set(sort_initial_sos). 0.39/0.97 % set(auto2) -> assign(sos_limit, -1). 0.39/0.97 % set(auto2) -> assign(lrs_ticks, 3000). 0.39/0.97 % set(auto2) -> assign(max_megs, 400). 0.39/0.97 % set(auto2) -> assign(stats, some). 0.39/0.97 % set(auto2) -> clear(echo_input). 0.39/0.97 % set(auto2) -> set(quiet). 0.39/0.97 % set(auto2) -> clear(print_initial_clauses). 0.39/0.97 % set(auto2) -> clear(print_given). 0.39/0.97 assign(lrs_ticks,-1). 0.39/0.97 assign(sos_limit,10000). 0.39/0.97 assign(order,kbo). 0.39/0.97 set(lex_order_vars). 0.39/0.97 clear(print_given). 0.39/0.97 0.39/0.97 % formulas(sos). % not echoed (12 formulas) 0.39/0.97 0.39/0.97 ============================== end of input ========================== 0.39/0.97 0.39/0.97 % From the command line: assign(max_seconds, 960). 0.39/0.97 0.39/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.39/0.97 0.39/0.97 % Formulas that are not ordinary clauses: 0.39/0.97 1 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 2 (all D all C all B all A ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D))))) # label(f07) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 3 (all B all A B = mult(i(A),mult(A,B))) # label(f10) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 4 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 5 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 6 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 7 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 8 (all C all B all A mult(ld(A,mult(B,A)),ld(A,mult(C,A))) = ld(A,mult(mult(B,C),A))) # label(f09) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 9 (all D all C all B all A rd(mult(mult(mult(A,B),C),D),mult(C,D)) = mult(rd(mult(mult(A,C),D),mult(C,D)),rd(mult(mult(B,C),D),mult(C,D)))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 10 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 11 (all B all A A = mult(mult(A,B),i(B))) # label(f11) # label(axiom) # label(non_clause). [assumption]. 0.39/0.97 12 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 0.39/0.97 0.39/0.97 ============================== end of process non-clausal formulas === 0.39/0.97 0.39/0.97 ============================== PROCESS INITIAL CLAUSES =============== 0.39/0.97 0.39/0.97 ============================== PREDICATE ELIMINATION ================= 89.15/89.53 89.15/89.53 ============================== end predicate elimination ============= 89.15/89.53 89.15/89.53 Auto_denials: 89.15/89.53 % copying label goals to answer in negative clause 89.15/89.53 % copying label goals to answer in negative clause 89.15/89.53 % copying label goals to answer in negative clause 89.15/89.53 % copying label goals to answer in negative clause 89.15/89.53 % assign(max_proofs, 4). % (Horn set with more than one neg. clause) 89.15/89.53 89.15/89.53 Term ordering decisions: 89.15/89.53 89.15/89.53 % Assigning unary symbol i kb_weight 0 and highest precedence (18). 89.15/89.53 Function symbol KB weights: unit=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. mult=1. ld=1. rd=1. i=0. 89.15/89.53 89.15/89.53 ============================== end of process initial clauses ======== 89.15/89.53 89.15/89.53 ============================== CLAUSES FOR SEARCH ==================== 89.15/89.53 89.15/89.53 ============================== end of clauses for search ============= 89.15/89.53 89.15/89.53 ============================== SEARCH ================================ 89.15/89.53 89.15/89.53 % Starting search at 0.01 seconds. 89.15/89.53 89.15/89.53 Low Water (keep): wt=77.000, iters=3366 89.15/89.53 89.15/89.53 Low Water (keep): wt=71.000, iters=3393 89.15/89.53 89.15/89.53 Low Water (keep): wt=68.000, iters=3426 89.15/89.53 89.15/89.53 Low Water (keep): wt=61.000, iters=3406 89.15/89.53 89.15/89.53 Low Water (keep): wt=59.000, iters=3376 89.15/89.53 89.15/89.53 Low Water (keep): wt=57.000, iters=3343 89.15/89.53 89.15/89.53 Low Water (keep): wt=55.000, iters=3420 89.15/89.53 89.15/89.53 Low Water (keep): wt=53.000, iters=3393 89.15/89.53 89.15/89.53 Low Water (keep): wt=52.000, iters=3390 89.15/89.53 89.15/89.53 Low Water (keep): wt=51.000, iters=3344 89.15/89.53 89.15/89.53 Low Water (keep): wt=49.000, iters=3361 89.15/89.53 89.15/89.53 Low Water (keep): wt=48.000, iters=3344 89.15/89.53 89.15/89.53 Low Water (keep): wt=47.000, iters=3371 89.15/89.53 89.15/89.53 Low Water (keep): wt=46.000, iters=3336 89.15/89.53 89.15/89.53 Low Water (keep): wt=45.000, iters=3391 89.15/89.53 89.15/89.53 Low Water (keep): wt=44.000, iters=3349 89.15/89.53 89.15/89.53 Low Water (keep): wt=43.000, iters=3353 89.15/89.53 89.15/89.53 Low Water (keep): wt=42.000, iters=3363 89.15/89.53 89.15/89.53 Low Water (keep): wt=41.000, iters=3485 89.15/89.53 89.15/89.53 Low Water (keep): wt=40.000, iters=3355 89.15/89.53 89.15/89.53 Low Water (keep): wt=39.000, iters=3344 89.15/89.53 89.15/89.53 Low Water (keep): wt=38.000, iters=3340 89.15/89.53 89.15/89.53 Low Water (keep): wt=37.000, iters=3337 89.15/89.53 89.15/89.53 Low Water (keep): wt=36.000, iters=3365 89.15/89.53 89.15/89.53 Low Water (keep): wt=35.000, iters=3360 89.15/89.53 89.15/89.53 Low Water (displace): id=7173, wt=197.000 89.15/89.53 89.15/89.53 Low Water (displace): id=7215, wt=196.000 89.15/89.53 89.15/89.53 Low Water (displace): id=6397, wt=195.000 89.15/89.53 89.15/89.53 Low Water (displace): id=6156, wt=191.000 89.15/89.53 89.15/89.53 Low Water (displace): id=7227, wt=187.000 89.15/89.53 89.15/89.53 Low Water (displace): id=13872, wt=28.000 89.15/89.53 89.15/89.53 Low Water (displace): id=13890, wt=26.000 89.15/89.53 89.15/89.53 Low Water (displace): id=13892, wt=23.000 89.15/89.53 89.15/89.53 Low Water (displace): id=15163, wt=22.000 89.15/89.53 89.15/89.53 Low Water (keep): wt=34.000, iters=3346 89.15/89.53 89.15/89.53 Low Water (keep): wt=33.000, iters=3333 89.15/89.53 89.15/89.53 Low Water (displace): id=19064, wt=21.000 89.15/89.53 89.15/89.53 Low Water (keep): wt=32.000, iters=3339 89.15/89.53 89.15/89.53 Low Water (keep): wt=31.000, iters=3380 89.15/89.53 89.15/89.53 Low Water (keep): wt=30.000, iters=3338 89.15/89.53 89.15/89.53 Low Water (keep): wt=29.000, iters=3336 89.15/89.53 89.15/89.53 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 45 (0.00 of 41.45 sec). 89.15/89.53 89.15/89.53 Low Water (keep): wt=28.000, iters=3346 89.15/89.53 89.15/89.53 ============================== PROOF ================================= 89.15/89.53 % SZS status Theorem 89.15/89.53 % SZS output start Refutation 89.15/89.53 89.15/89.53 % Proof 1 at 87.59 (+ 0.93) seconds: goals. 89.15/89.53 % Length of proof is 271. 89.15/89.53 % Level of proof is 37. 89.15/89.53 % Maximum clause weight is 66.000. 89.15/89.53 % Given clauses 838. 89.15/89.53 89.15/89.53 1 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 2 (all D all C all B all A ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D))))) # label(f07) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 3 (all B all A B = mult(i(A),mult(A,B))) # label(f10) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 5 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 6 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 7 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 8 (all C all B all A mult(ld(A,mult(B,A)),ld(A,mult(C,A))) = ld(A,mult(mult(B,C),A))) # label(f09) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 9 (all D all C all B all A rd(mult(mult(mult(A,B),C),D),mult(C,D)) = mult(rd(mult(mult(A,C),D),mult(C,D)),rd(mult(mult(B,C),D),mult(C,D)))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 10 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 11 (all B all A A = mult(mult(A,B),i(B))) # label(f11) # label(axiom) # label(non_clause). [assumption]. 89.15/89.53 12 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 89.15/89.53 13 mult(A,unit) = A # label(f05) # label(axiom). [clausify(6)]. 89.15/89.53 14 mult(unit,A) = A # label(f06) # label(axiom). [clausify(7)]. 89.15/89.53 15 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(1)]. 89.15/89.53 17 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(5)]. 89.15/89.53 18 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(10)]. 89.15/89.53 19 mult(i(A),mult(A,B)) = B # label(f10) # label(axiom). [clausify(3)]. 89.15/89.53 20 mult(mult(A,B),i(B)) = A # label(f11) # label(axiom). [clausify(11)]. 89.15/89.53 21 ld(A,mult(mult(B,C),A)) = mult(ld(A,mult(B,A)),ld(A,mult(C,A))) # label(f09) # label(axiom). [clausify(8)]. 89.15/89.53 22 mult(ld(A,mult(B,A)),ld(A,mult(C,A))) = ld(A,mult(mult(B,C),A)). [copy(21),flip(a)]. 89.15/89.53 23 ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))) # label(f07) # label(axiom). [clausify(2)]. 89.15/89.53 24 mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))) = ld(mult(A,B),mult(A,mult(B,mult(C,D)))). [copy(23),flip(a)]. 89.15/89.53 25 rd(mult(mult(mult(A,B),C),D),mult(C,D)) = mult(rd(mult(mult(A,C),D),mult(C,D)),rd(mult(mult(B,C),D),mult(C,D))) # label(f08) # label(axiom). [clausify(9)]. 89.15/89.53 26 mult(rd(mult(mult(A,B),C),mult(B,C)),rd(mult(mult(D,B),C),mult(B,C))) = rd(mult(mult(mult(A,D),B),C),mult(B,C)). [copy(25),flip(a)]. 89.15/89.53 28 mult(mult(c6,mult(c4,c5)),c6) != mult(mult(c6,c4),mult(c5,c6)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(12)]. 89.15/89.53 35 rd(A,ld(B,A)) = B. [para(17(a,1),15(a,1,1))]. 89.15/89.53 37 mult(i(A),A) = unit. [para(13(a,1),19(a,1,2))]. 89.15/89.53 39 rd(A,mult(B,A)) = i(B). [para(19(a,1),15(a,1,1))]. 89.15/89.53 41 ld(A,B) = mult(i(A),B). [para(17(a,1),19(a,1,2)),flip(a)]. 89.15/89.53 44 i(i(A)) = A. [back_rewrite(35),rewrite([41(1),39(3)])]. 89.15/89.53 45 mult(mult(i(mult(A,B)),mult(A,mult(B,C))),mult(i(mult(A,B)),mult(A,mult(B,D)))) = mult(i(mult(A,B)),mult(A,mult(B,mult(C,D)))). [back_rewrite(24),rewrite([41(4),41(9),41(16)])]. 89.15/89.53 46 mult(mult(i(A),mult(B,A)),mult(i(A),mult(C,A))) = mult(i(A),mult(mult(B,C),A)). [back_rewrite(22),rewrite([41(2),41(5),41(10)])]. 89.15/89.53 47 mult(A,mult(i(A),B)) = B. [back_rewrite(17),rewrite([41(1)])]. 89.15/89.53 49 mult(A,i(A)) = unit. [para(14(a,1),20(a,1,1))]. 89.15/89.53 51 rd(A,B) = mult(A,i(B)). [para(18(a,1),20(a,1,1)),flip(a)]. 89.15/89.53 52 mult(i(mult(A,B)),A) = i(B). [para(20(a,1),19(a,1,2))]. 89.15/89.53 54 mult(mult(mult(mult(A,B),C),i(mult(B,C))),mult(mult(mult(D,B),C),i(mult(B,C)))) = mult(mult(mult(mult(A,D),B),C),i(mult(B,C))). [back_rewrite(26),rewrite([51(4),51(9),51(16)])]. 89.15/89.53 55 mult(mult(A,i(B)),B) = A. [back_rewrite(18),rewrite([51(1)])]. 89.15/89.53 58 mult(mult(i(A),mult(i(B),mult(mult(B,A),C))),mult(i(A),mult(i(B),mult(mult(B,A),D)))) = mult(i(A),mult(i(B),mult(mult(B,A),mult(C,D)))). [para(19(a,1),45(a,1,1,1,1)),rewrite([19(9),19(16)])]. 89.15/89.53 61 mult(A,mult(i(mult(B,i(A))),mult(B,mult(i(A),C)))) = mult(i(mult(B,i(A))),mult(B,C)). [para(19(a,1),45(a,2,2,2)),rewrite([37(5),13(5),52(4),44(2)])]. 89.15/89.53 63 mult(mult(i(A),mult(mult(A,B),mult(i(B),C))),mult(i(A),mult(mult(A,B),mult(i(B),D)))) = mult(i(A),mult(mult(A,B),mult(i(B),mult(C,D)))). [para(20(a,1),45(a,1,1,1,1)),rewrite([20(9),20(16)])]. 89.15/89.53 68 mult(mult(A,mult(i(mult(B,A)),mult(B,C))),A) = mult(A,mult(i(mult(B,A)),mult(B,mult(C,A)))). [para(37(a,1),45(a,1,2,2)),rewrite([52(3),44(2),52(8),44(7),13(7),52(9),44(8)])]. 89.15/89.53 70 mult(i(A),mult(i(mult(B,A)),mult(B,mult(A,C)))) = mult(i(mult(B,A)),mult(B,C)). [para(49(a,1),45(a,1,1,2,2)),rewrite([13(4),52(3),47(12)])]. 89.15/89.53 77 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),mult(i(A),mult(B,mult(mult(i(B),A),D)))) = mult(i(A),mult(B,mult(mult(i(B),A),mult(C,D)))). [para(47(a,1),45(a,1,1,1,1)),rewrite([47(9),47(16)])]. 89.15/89.54 78 mult(mult(i(mult(A,B)),mult(A,C)),mult(i(mult(A,B)),mult(A,mult(B,D)))) = mult(i(mult(A,B)),mult(A,mult(B,mult(mult(i(B),C),D)))). [para(47(a,1),45(a,1,1,2,2))]. 89.15/89.54 79 mult(mult(i(mult(A,B)),mult(A,mult(B,C))),mult(i(mult(A,B)),mult(A,D))) = mult(i(mult(A,B)),mult(A,mult(B,mult(C,mult(i(B),D))))). [para(47(a,1),45(a,1,2,2,2))]. 89.15/89.54 80 i(mult(A,B)) = mult(i(B),i(A)). [para(19(a,1),52(a,1,1,1)),flip(a)]. 89.15/89.54 81 mult(mult(mult(i(A),i(B)),mult(B,mult(A,C))),mult(mult(i(A),i(B)),mult(B,D))) = mult(mult(i(A),i(B)),mult(B,mult(A,mult(C,mult(i(A),D))))). [back_rewrite(79),rewrite([80(2),80(8),80(14)])]. 89.15/89.54 82 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(mult(i(A),i(B)),mult(B,mult(A,D)))) = mult(mult(i(A),i(B)),mult(B,mult(A,mult(mult(i(A),C),D)))). [back_rewrite(78),rewrite([80(2),80(7),80(14)])]. 89.15/89.54 87 mult(i(A),mult(mult(i(A),i(B)),mult(B,mult(A,C)))) = mult(mult(i(A),i(B)),mult(B,C)). [back_rewrite(70),rewrite([80(3),80(10)])]. 89.15/89.54 89 mult(mult(A,mult(mult(i(A),i(B)),mult(B,C))),A) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,A)))). [back_rewrite(68),rewrite([80(2),80(9)])]. 89.15/89.54 93 mult(A,mult(mult(A,i(B)),mult(B,mult(i(A),C)))) = mult(mult(A,i(B)),mult(B,C)). [back_rewrite(61),rewrite([80(3),44(2),80(10),44(9)])]. 89.15/89.54 95 mult(mult(mult(mult(A,B),C),mult(i(C),i(B))),mult(mult(mult(D,B),C),mult(i(C),i(B)))) = mult(mult(mult(mult(A,D),B),C),mult(i(C),i(B))). [back_rewrite(54),rewrite([80(4),80(10),80(18)])]. 89.15/89.54 98 mult(i(A),mult(mult(A,B),A)) = mult(B,A). [para(19(a,1),46(a,1,1)),rewrite([47(4)]),flip(a)]. 89.15/89.54 99 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),mult(mult(i(A),i(B)),A)) = mult(mult(i(A),i(B)),mult(mult(C,i(B)),mult(B,A))). [para(19(a,1),46(a,1,2,2)),rewrite([80(2),80(8),80(13)])]. 89.15/89.54 103 mult(mult(A,B),mult(A,mult(C,i(A)))) = mult(A,mult(mult(mult(B,A),C),i(A))). [para(20(a,1),46(a,1,1,2)),rewrite([44(2),44(3),44(7)])]. 89.15/89.54 104 mult(mult(A,mult(B,i(A))),mult(A,C)) = mult(A,mult(mult(B,mult(C,A)),i(A))). [para(20(a,1),46(a,1,2,2)),rewrite([44(2),44(5),44(7)])]. 89.15/89.54 111 mult(mult(mult(i(A),B),mult(C,mult(i(B),A))),mult(mult(i(A),B),A)) = mult(mult(i(A),B),mult(mult(C,B),mult(i(B),A))). [para(47(a,1),46(a,1,2,2)),rewrite([80(3),44(3),80(9),44(9),80(13),44(13)])]. 89.15/89.54 113 mult(mult(i(A),B),mult(i(A),mult(C,A))) = mult(i(A),mult(mult(mult(B,i(A)),C),A)). [para(55(a,1),46(a,1,1,2))]. 89.15/89.54 114 mult(mult(i(A),mult(B,A)),mult(i(A),C)) = mult(i(A),mult(mult(B,mult(C,i(A))),A)). [para(55(a,1),46(a,1,2,2))]. 89.15/89.54 118 mult(mult(i(A),i(B)),mult(mult(B,A),C)) = C. [para(80(a,1),19(a,1,1))]. 89.15/89.54 119 mult(mult(A,mult(B,C)),mult(i(C),i(B))) = A. [para(80(a,1),20(a,1,2))]. 89.15/89.54 120 mult(mult(i(A),i(B)),mult(B,A)) = unit. [para(80(a,1),37(a,1,1))]. 89.15/89.54 121 mult(mult(A,B),mult(i(B),i(A))) = unit. [para(80(a,1),49(a,1,2))]. 89.15/89.54 122 mult(mult(A,B),mult(mult(i(B),i(A)),C)) = C. [para(80(a,1),47(a,1,2,1))]. 89.15/89.54 123 mult(mult(A,mult(i(B),i(C))),mult(C,B)) = A. [para(80(a,1),55(a,1,1,2))]. 89.15/89.54 125 mult(mult(i(A),B),mult(i(B),A)) = unit. [para(44(a,1),120(a,1,1,2))]. 89.15/89.54 132 mult(mult(mult(mult(i(A),mult(i(B),i(C))),C),B),mult(i(B),mult(i(C),mult(mult(C,B),mult(A,D))))) = mult(i(B),mult(i(C),mult(mult(C,B),D))). [para(58(a,1),19(a,1,2)),rewrite([80(7),80(5),80(3),80(3),44(7),44(8)])]. 89.15/89.54 134 mult(mult(A,mult(mult(i(A),i(B)),mult(B,C))),mult(A,mult(mult(i(A),i(B)),mult(B,D)))) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,D)))). [para(20(a,1),58(a,1,1,2,2,1)),rewrite([44(2),80(2),44(8),80(8),20(12),44(15),80(15),20(19)])]. 89.15/89.54 137 mult(mult(A,mult(i(B),mult(mult(B,i(A)),C))),mult(A,mult(i(B),mult(mult(B,i(A)),D)))) = mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,D)))). [para(44(a,1),58(a,1,1,1)),rewrite([44(8),44(15)])]. 89.15/89.54 138 mult(mult(i(A),i(B)),mult(i(A),mult(i(B),mult(mult(B,A),C)))) = mult(i(A),mult(i(B),C)). [para(49(a,1),58(a,1,1,2,2)),rewrite([13(4),80(15),122(18)])]. 89.15/89.54 141 mult(mult(i(A),mult(i(B),C)),mult(i(A),mult(i(B),mult(mult(B,A),D)))) = mult(i(A),mult(i(B),mult(mult(B,A),mult(mult(mult(i(A),i(B)),C),D)))). [para(47(a,1),58(a,1,1,2,2)),rewrite([80(16)])]. 89.15/89.54 165 mult(mult(A,B),A) = mult(A,mult(B,A)). [para(98(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.54 166 mult(mult(A,B),i(A)) = mult(A,mult(B,i(A))). [para(19(a,1),98(a,1,2,1)),rewrite([44(2)]),flip(a)]. 89.15/89.54 169 mult(mult(i(A),i(B)),mult(B,mult(B,A))) = mult(i(A),mult(B,A)). [para(20(a,1),98(a,1,2,1)),rewrite([80(2)])]. 89.15/89.54 170 mult(mult(i(A),B),A) = mult(i(A),mult(B,A)). [para(47(a,1),98(a,1,2,1)),flip(a)]. 89.15/89.54 176 mult(A,mult(mult(mult(i(A),i(B)),mult(B,C)),A)) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,A)))). [back_rewrite(89),rewrite([165(7)])]. 89.15/89.54 177 mult(mult(c6,c4),mult(c5,c6)) != mult(c6,mult(mult(c4,c5),c6)) # answer(goals). [back_rewrite(28),rewrite([165(7)]),flip(a)]. 89.15/89.54 184 mult(mult(mult(i(A),B),mult(C,mult(i(B),A))),mult(i(A),mult(B,A))) = mult(mult(i(A),B),mult(mult(C,B),mult(i(B),A))). [back_rewrite(111),rewrite([170(9)])]. 89.15/89.54 186 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),mult(i(A),mult(i(B),A))) = mult(mult(i(A),i(B)),mult(mult(C,i(B)),mult(B,A))). [back_rewrite(99),rewrite([170(10)])]. 89.15/89.54 188 mult(mult(i(A),i(B)),mult(B,mult(A,B))) = B. [para(165(a,1),19(a,1,2)),rewrite([80(2)])]. 89.15/89.54 190 mult(mult(A,B),mult(i(B),mult(A,B))) = mult(A,mult(A,B)). [para(20(a,1),165(a,1,1)),flip(a)]. 89.15/89.54 200 mult(mult(i(A),B),mult(mult(i(B),A),C)) = C. [para(44(a,1),118(a,1,1,2))]. 89.15/89.54 206 mult(mult(mult(mult(i(A),B),mult(i(B),i(C))),C),mult(i(C),mult(mult(C,B),mult(i(B),mult(A,D))))) = mult(i(C),mult(mult(C,B),mult(i(B),D))). [para(63(a,1),19(a,1,2)),rewrite([80(7),80(5),80(3),44(3),80(4),44(8)])]. 89.15/89.54 208 mult(mult(i(A),mult(mult(A,B),C)),mult(i(A),mult(mult(A,B),mult(i(B),D)))) = mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),D)))). [para(19(a,1),63(a,1,1,2,2))]. 89.15/89.54 210 mult(A,mult(i(B),mult(mult(B,A),mult(i(A),C)))) = mult(i(B),mult(mult(B,A),C)). [para(19(a,1),63(a,2,2,2)),rewrite([37(4),13(4),19(3)])]. 89.15/89.54 227 mult(mult(i(A),B),mult(i(B),mult(mult(A,mult(mult(A,C),i(B))),B))) = mult(A,mult(mult(i(A),B),mult(i(B),mult(mult(A,mult(C,i(B))),B)))). [para(165(a,1),63(a,1,1,2)),rewrite([80(3),44(3),47(7),200(6),80(3),44(3),170(5),114(8),80(13),44(13),170(15),114(19)]),flip(a)]. 89.15/89.54 234 mult(mult(A,mult(i(B),C)),mult(i(C),B)) = A. [para(44(a,1),119(a,1,2,2))]. 89.15/89.54 253 mult(mult(A,mult(i(B),i(A))),mult(mult(A,mult(B,i(A))),C)) = C. [para(166(a,1),118(a,1,2,1)),rewrite([44(2),80(2)])]. 89.15/89.54 279 mult(mult(A,mult(B,C)),mult(A,mult(B,mult(mult(i(B),i(A)),D)))) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(mult(mult(A,B),C),D)))). [para(118(a,1),77(a,1,1,2,2)),rewrite([44(2),44(4),44(11)])]. 89.15/89.54 280 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),mult(A,mult(B,D))) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,mult(mult(A,B),D))))). [para(118(a,1),77(a,1,2,2,2)),rewrite([44(2),44(8),44(11)])]. 89.15/89.54 289 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,C)))) = mult(B,mult(i(A),mult(B,mult(mult(i(B),A),C)))). [para(166(a,1),77(a,1,1,2,2)),rewrite([44(4),47(5),19(3),44(12)]),flip(a)]. 89.15/89.54 290 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),B) = mult(i(A),mult(B,mult(mult(i(B),A),mult(C,B)))). [para(166(a,1),77(a,1,2,2,2)),rewrite([44(10),47(11),19(9),44(12)])]. 89.15/89.54 293 mult(mult(i(A),B),mult(i(B),mult(A,B))) = B. [para(170(a,1),19(a,1,2)),rewrite([80(3),44(3)])]. 89.15/89.54 297 mult(mult(i(A),mult(i(B),A)),mult(mult(i(A),mult(B,A)),C)) = C. [para(170(a,1),118(a,1,2,1)),rewrite([80(4),44(4)])]. 89.15/89.54 303 mult(mult(i(A),mult(B,A)),mult(i(B),A)) = mult(mult(i(A),B),mult(A,mult(i(B),A))). [para(170(a,1),166(a,1,1)),rewrite([80(6),44(6),80(11),44(11)])]. 89.15/89.54 334 mult(mult(A,i(B)),mult(B,mult(A,C))) = mult(A,mult(mult(A,i(B)),mult(B,C))). [para(19(a,1),81(a,2,2,2)),rewrite([44(2),37(4),13(4),55(3),44(2),44(7),44(9)]),flip(a)]. 89.15/89.54 387 mult(A,mult(mult(i(A),i(B)),mult(B,mult(mult(A,B),mult(i(B),C))))) = mult(mult(A,B),mult(A,mult(mult(i(A),i(B)),C))). [para(188(a,1),81(a,1,1,2)),rewrite([80(5),44(3),44(3),19(3),80(6),44(4),44(4),19(4),80(12),44(10),44(10),19(10)]),flip(a)]. 89.15/89.54 428 mult(mult(i(A),B),mult(mult(A,B),mult(i(B),A))) = mult(i(A),mult(mult(B,A),A)). [para(293(a,1),165(a,2,2)),rewrite([303(6),184(10),170(11)])]. 89.15/89.54 439 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(mult(i(C),i(B)),mult(B,mult(C,mult(mult(i(C),A),D))))) = mult(mult(i(C),i(B)),mult(B,mult(C,D))). [para(82(a,1),19(a,1,2)),rewrite([80(6),80(2),80(7),44(5),44(5)])]. 89.15/89.54 444 mult(mult(mult(A,i(B)),mult(B,C)),A) = mult(mult(A,i(B)),mult(B,mult(C,A))). [para(37(a,1),82(a,1,2,2,2)),rewrite([44(2),44(6),13(8),55(7),44(7),44(10),165(10),19(11)])]. 89.15/89.54 461 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),i(A))))) = mult(i(A),mult(mult(mult(A,B),C),i(A))). [para(121(a,1),82(a,1,2,2)),rewrite([44(2),80(2),47(4),44(6),80(6),47(8),13(7),165(6),44(8),80(8),47(10),44(11)]),flip(a)]. 89.15/89.54 474 mult(mult(mult(i(A),mult(mult(i(B),i(C)),i(D))),D),mult(mult(i(A),mult(mult(i(B),i(C)),i(D))),mult(mult(D,mult(C,B)),mult(A,E)))) = mult(mult(i(A),mult(mult(i(B),i(C)),i(D))),mult(mult(D,mult(C,B)),mult(A,mult(mult(i(A),mult(i(B),i(C))),E)))). [para(119(a,1),82(a,1,1,2)),rewrite([80(4),80(3),80(12),80(11),80(25),80(24)])]. 89.15/89.54 480 mult(mult(mult(i(A),mult(mult(B,C),i(D))),D),mult(mult(i(A),mult(mult(B,C),i(D))),mult(mult(D,mult(i(C),i(B))),mult(A,E)))) = mult(mult(i(A),mult(mult(B,C),i(D))),mult(mult(D,mult(i(C),i(B))),mult(A,mult(mult(i(A),mult(B,C)),E)))). [para(123(a,1),82(a,1,1,2)),rewrite([80(6),80(5),44(3),44(3),80(12),80(11),44(9),44(9),80(25),80(24),44(22),44(22)])]. 89.15/89.54 750 mult(mult(i(A),i(B)),mult(B,mult(A,C))) = mult(A,mult(mult(i(A),i(B)),mult(B,C))). [para(87(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.54 755 mult(mult(A,i(B)),mult(B,A)) = mult(A,A). [para(37(a,1),87(a,1,2,2,2)),rewrite([44(2),44(2),13(4),55(3),44(3)]),flip(a)]. 89.15/89.54 772 mult(mult(A,mult(mult(i(A),i(B)),i(C))),mult(mult(C,mult(B,A)),i(B))) = mult(A,mult(mult(A,mult(mult(i(A),i(B)),i(C))),C)). [para(119(a,1),87(a,1,2,2)),rewrite([44(2),44(2),80(3),80(2),44(10),80(11),80(10)]),flip(a)]. 89.15/89.54 775 mult(mult(mult(i(A),i(B)),mult(B,C)),A) = mult(mult(i(A),i(B)),mult(B,mult(C,A))). [para(87(a,1),166(a,1,1)),rewrite([44(7),750(13),44(15),165(14),176(14),19(15)])]. 89.15/89.54 796 mult(mult(mult(i(A),B),i(C)),mult(C,mult(i(A),mult(B,A)))) = mult(mult(i(A),B),mult(mult(mult(i(A),B),i(C)),mult(C,A))). [para(293(a,1),87(a,1,2,2,2)),rewrite([80(3),44(3),80(5),44(5),80(12),44(12)]),flip(a)]. 89.15/89.54 884 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(C,mult(mult(i(C),i(B)),mult(B,mult(mult(i(C),A),D))))) = mult(C,mult(mult(i(C),i(B)),mult(B,D))). [back_rewrite(439),rewrite([750(14),750(21)])]. 89.15/89.54 907 mult(mult(A,i(B)),mult(B,B)) = mult(A,B). [para(755(a,1),19(a,1,2)),rewrite([80(3),44(2)])]. 89.15/89.54 908 mult(mult(A,mult(B,A)),B) = mult(mult(A,B),mult(A,B)). [para(19(a,1),755(a,1,2)),rewrite([44(3),165(2)])]. 89.15/89.54 910 mult(mult(A,B),mult(A,B)) = mult(A,mult(B,mult(A,B))). [para(20(a,1),755(a,1,1)),flip(a)]. 89.15/89.54 912 mult(mult(A,B),mult(i(B),A)) = mult(A,A). [para(44(a,1),755(a,1,1,2))]. 89.15/89.54 913 mult(mult(A,mult(A,i(B))),B) = mult(A,A). [para(55(a,1),755(a,1,2)),rewrite([80(3),44(2)])]. 89.15/89.54 917 mult(mult(A,B),mult(i(B),i(B))) = mult(A,i(B)). [para(755(a,1),122(a,1,2))]. 89.15/89.54 930 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [back_rewrite(908),rewrite([910(6)])]. 89.15/89.54 931 mult(mult(i(A),B),mult(A,A)) = mult(i(A),mult(mult(B,A),A)). [back_rewrite(428),rewrite([912(6)])]. 89.15/89.54 956 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),907(a,1,1)),flip(a)]. 89.15/89.54 990 mult(mult(i(A),B),mult(A,A)) = mult(i(A),mult(B,mult(A,A))). [back_rewrite(931),rewrite([956(7)])]. 89.15/89.54 1007 mult(mult(A,mult(B,B)),i(B)) = mult(A,B). [para(956(a,1),20(a,1,1))]. 89.15/89.54 1021 mult(mult(A,mult(B,mult(C,mult(B,C)))),mult(i(C),i(B))) = mult(A,mult(B,C)). [para(956(a,1),119(a,1,1)),rewrite([910(3)])]. 89.15/89.54 1183 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(913(a,1),55(a,1,1)),rewrite([44(4)])]. 89.15/89.54 1191 mult(mult(A,mult(A,B)),B) = mult(A,mult(A,mult(B,B))). [para(913(a,1),907(a,1,1)),rewrite([1183(3),44(5)]),flip(a)]. 89.15/89.54 1272 mult(mult(A,mult(A,mult(B,B))),i(B)) = mult(A,mult(A,B)). [para(1183(a,1),1007(a,1,1)),rewrite([1183(7)])]. 89.15/89.54 1282 mult(mult(A,i(B)),mult(B,mult(i(A),C))) = mult(i(A),mult(mult(A,i(B)),mult(B,C))). [para(93(a,1),19(a,1,2)),flip(a)]. 89.15/89.54 1461 mult(mult(A,mult(B,mult(A,B))),C) = mult(mult(A,B),mult(mult(A,B),C)). [para(910(a,1),1183(a,1,1))]. 89.15/89.54 1479 mult(mult(mult(mult(A,B),C),mult(i(C),i(B))),B) = mult(mult(mult(A,C),mult(i(C),i(B))),mult(B,B)). [para(49(a,1),95(a,1,2,1)),rewrite([80(3),80(7),80(9),44(7),44(7),20(8),80(9),80(11),44(9),44(9),20(10),14(8),956(7),80(11),80(15),80(17),44(15),44(15),20(16)]),flip(a)]. 89.15/89.54 1692 mult(mult(A,mult(B,A)),i(B)) = mult(mult(A,B),mult(A,i(B))). [para(930(a,1),917(a,1,1)),rewrite([1461(7),917(6)]),flip(a)]. 89.15/89.54 1820 mult(A,mult(mult(mult(B,A),mult(C,A)),i(A))) = mult(mult(A,B),mult(A,C)). [para(20(a,1),103(a,1,2,2)),flip(a)]. 89.15/89.54 1823 mult(mult(A,mult(i(B),i(A))),mult(i(C),i(A))) = mult(A,mult(mult(i(B),mult(i(A),i(C))),i(A))). [para(103(a,1),80(a,1,1)),rewrite([80(6),80(5),44(2),80(3),80(3),166(8),80(12),80(11),44(10),166(12),80(14)]),flip(a)]. 89.15/89.54 1914 mult(mult(i(A),B),mult(A,B)) = mult(i(A),mult(B,mult(A,B))). [para(19(a,1),1191(a,1,1,2)),rewrite([910(9),19(10)])]. 89.15/89.54 2046 mult(mult(i(A),i(B)),mult(B,mult(i(C),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),i(C)),i(B))). [para(104(a,1),80(a,1,1)),rewrite([80(6),80(5),44(2),80(3),80(2),166(8),80(10),80(15),80(14),44(13),166(15)]),flip(a)]. 89.15/89.54 2481 mult(mult(A,B),mult(i(B),mult(i(A),C))) = mult(i(B),mult(i(A),mult(mult(A,B),C))). [para(37(a,1),132(a,1,1,1,1)),rewrite([14(2),122(9)])]. 89.15/89.54 2513 mult(mult(i(A),B),mult(i(B),mult(A,C))) = mult(i(B),mult(A,mult(mult(i(A),B),C))). [para(200(a,1),132(a,1,2,2,2)),rewrite([80(3),44(3),44(5),125(5),14(3),44(5),44(9)])]. 89.15/89.54 2748 mult(i(A),mult(B,mult(mult(i(B),i(A)),mult(A,C)))) = mult(B,mult(mult(i(B),i(A)),C)). [para(49(a,1),134(a,1,1,2,2)),rewrite([13(5),47(4),47(14)])]. 89.15/89.54 3229 mult(mult(i(A),mult(B,mult(A,B))),mult(i(B),i(A))) = mult(i(A),B). [para(19(a,1),1272(a,2,2)),rewrite([910(5),19(6),80(6)])]. 89.15/89.54 3231 mult(mult(A,mult(B,mult(i(A),B))),mult(i(B),A)) = mult(A,B). [para(47(a,1),1272(a,2,2)),rewrite([910(5),47(6),80(7),44(7)])]. 89.15/89.54 3234 mult(mult(mult(i(A),i(B)),mult(C,mult(mult(B,A),C))),mult(i(C),mult(i(A),i(B)))) = mult(mult(i(A),i(B)),C). [para(118(a,1),1272(a,2,2)),rewrite([910(11),118(12),80(10),80(10)])]. 89.15/89.54 3332 mult(mult(A,mult(i(B),mult(mult(B,i(A)),C))),B) = mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,B)))). [para(165(a,1),137(a,1,2,2,2)),rewrite([19(11),47(9)])]. 89.15/89.54 3343 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),B) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,B)))). [para(170(a,1),137(a,1,2,2,2)),rewrite([44(2),44(8),47(11),47(9),44(9)])]. 89.15/89.54 3636 mult(mult(A,B),mult(A,mult(B,C))) = mult(A,mult(B,mult(mult(A,B),C))). [para(118(a,1),138(a,1,2,2,2)),rewrite([44(2),44(2),44(3),44(3),44(6),44(6)])]. 89.15/89.54 3653 mult(mult(A,i(B)),mult(A,B)) = mult(A,mult(i(B),mult(A,B))). [para(755(a,1),138(a,1,2,2,2)),rewrite([44(2),44(4),19(5),44(6)])]. 89.15/89.54 4077 mult(mult(A,mult(B,C)),mult(A,B)) = mult(A,mult(B,mult(C,mult(A,B)))). [para(120(a,1),141(a,1,2,2,2)),rewrite([44(2),44(2),44(4),44(4),13(4),44(6),44(6),44(9),44(9),165(11),118(12)])]. 89.15/89.54 7517 mult(mult(mult(i(A),i(B)),i(C)),mult(C,mult(C,mult(B,A)))) = mult(mult(i(A),i(B)),mult(C,mult(B,A))). [para(80(a,1),169(a,1,1,1)),rewrite([80(11)])]. 89.15/89.54 7532 mult(mult(i(A),i(B)),mult(A,mult(B,A))) = mult(i(A),mult(mult(i(B),mult(A,B)),A)). [para(169(a,1),103(a,2,2,1)),rewrite([44(8),165(7),165(6),19(8),44(12)])]. 89.15/89.54 7537 mult(mult(i(A),i(B)),mult(B,mult(mult(C,mult(A,B)),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),mult(C,mult(A,B))),i(B))). [para(104(a,1),169(a,1,2,2)),rewrite([80(2),80(7),80(6),44(5),166(7),2046(8),103(17),55(11),103(15),55(8),7517(9),80(11),104(17)]),flip(a)]. 89.15/89.54 7974 mult(mult(i(A),mult(B,A)),B) = mult(i(A),mult(B,mult(A,B))). [para(3231(a,1),169(a,1,2,2)),rewrite([80(3),44(3),80(7),80(6),80(5),44(5),165(6),1692(8),200(9),4077(9),1914(7),750(10),47(8),7532(6),47(7),80(7),44(7),3231(13),1914(8)])]. 89.15/89.54 8045 mult(mult(A,B),mult(B,A)) = mult(A,mult(B,mult(B,A))). [para(20(a,1),3653(a,1,2)),rewrite([44(3),956(2),165(3),1183(2),44(6),20(7)]),flip(a)]. 89.15/89.54 8411 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),C) = mult(mult(i(A),i(B)),mult(C,mult(mult(B,A),C))). [para(119(a,1),8045(a,1,2)),rewrite([119(18),165(13)])]. 89.15/89.54 10106 mult(mult(i(A),i(B)),mult(B,mult(mult(C,mult(mult(A,B),C)),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),mult(C,mult(mult(A,B),C))),i(B))). [para(103(a,1),7974(a,2,2,2)),rewrite([80(2),104(8),7537(9),103(13),55(9),8411(7),80(12),103(22),55(16)]),flip(a)]. 89.15/89.54 11706 mult(mult(i(A),i(B)),mult(mult(mult(mult(B,A),C),i(B)),mult(B,A))) = mult(mult(C,mult(B,A)),mult(i(A),mult(i(B),A))). [para(165(a,1),186(a,1,1,2)),rewrite([118(8)]),flip(a)]. 89.15/89.54 12180 mult(mult(mult(A,B),mult(i(B),i(C))),C) = mult(i(C),mult(mult(C,B),mult(i(B),A))). [para(37(a,1),206(a,1,2,2,2,2)),rewrite([44(2),13(11),20(10),37(8),13(8)])]. 89.15/89.54 12223 mult(mult(mult(A,B),mult(i(B),i(C))),mult(C,C)) = mult(i(C),mult(mult(C,B),mult(i(B),mult(A,C)))). [back_rewrite(1479),rewrite([12180(7)]),flip(a)]. 89.15/89.54 12433 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),mult(A,B))))) = mult(mult(i(A),mult(mult(A,B),C)),mult(A,B)). [para(190(a,1),208(a,1,2,2)),rewrite([19(8)]),flip(a)]. 89.15/89.54 12848 mult(i(A),mult(mult(i(B),i(A)),mult(A,mult(mult(B,mult(C,A)),i(A))))) = mult(mult(i(B),i(A)),mult(mult(A,mult(B,i(A))),C)). [para(166(a,1),210(a,1,2,2,1)),rewrite([80(3),44(9),104(9),80(13),166(17)])]. 89.15/89.54 12849 mult(A,mult(mult(i(B),A),mult(i(A),mult(mult(B,mult(C,i(A))),A)))) = mult(mult(i(B),A),mult(mult(i(A),mult(B,A)),C)). [para(170(a,1),210(a,1,2,2,1)),rewrite([80(3),44(3),114(8),80(13),44(13),170(15)])]. 89.15/89.54 16806 mult(mult(i(A),i(B)),mult(B,mult(C,i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),C),i(B))). [para(103(a,1),3229(a,1,1,2,2)),rewrite([80(2),103(12),55(6),10106(10),80(14),80(13),44(12),166(14),80(16),1823(18),103(19),55(10),3234(13),80(9)]),flip(a)]. 89.15/89.54 16813 mult(mult(i(A),i(B)),mult(mult(B,mult(A,i(B))),C)) = mult(mult(i(B),i(A)),mult(A,C)). [back_rewrite(12848),rewrite([16806(10),444(9),20(7),19(8)]),flip(a)]. 89.15/89.54 16882 mult(A,mult(mult(i(A),i(B)),mult(B,mult(mult(B,A),C)))) = mult(B,mult(A,C)). [para(3636(a,1),19(a,1,2)),rewrite([80(2),750(8)])]. 89.15/89.54 16898 mult(mult(A,mult(B,C)),mult(mult(i(C),i(B)),mult(A,D))) = mult(A,mult(mult(A,mult(B,C)),mult(mult(i(C),i(B)),D))). [para(119(a,1),3636(a,1,1)),rewrite([119(19)]),flip(a)]. 89.15/89.54 17253 mult(mult(mult(A,B),mult(i(B),C)),A) = mult(mult(A,B),mult(i(B),mult(C,A))). [para(20(a,1),4077(a,1,2)),rewrite([20(10)])]. 89.15/89.54 17254 mult(A,mult(B,mult(mult(i(B),C),mult(A,B)))) = mult(mult(A,C),mult(A,B)). [para(47(a,1),4077(a,1,1,2)),flip(a)]. 89.15/89.54 17364 mult(mult(A,B),mult(mult(C,mult(A,B)),i(B))) = mult(A,mult(B,mult(C,A))). [para(4077(a,1),210(a,2,2)),rewrite([80(6),16898(10),55(8),19(8),19(12)])]. 89.15/89.54 18133 mult(mult(A,mult(B,C)),mult(i(B),i(A))) = mult(A,mult(B,mult(C,mult(i(B),i(A))))). [para(166(a,1),279(a,2,2,2,2)),rewrite([80(7),910(9),47(10),47(8),80(12),118(16)])]. 89.15/89.54 19242 mult(mult(mult(A,B),mult(C,B)),i(B)) = mult(i(B),mult(mult(B,A),mult(B,C))). [para(1820(a,1),19(a,1,2)),flip(a)]. 89.15/89.54 19267 mult(i(A),mult(mult(mult(A,B),mult(A,C)),A)) = mult(mult(B,A),mult(C,A)). [para(1820(a,1),104(a,2,2,1)),rewrite([44(3),19(3),47(6),44(9)]),flip(a)]. 89.15/89.54 19320 mult(mult(mult(A,B),mult(A,C)),A) = mult(A,mult(mult(B,A),mult(C,A))). [para(1820(a,1),227(a,2,2,2,2,1)),rewrite([37(2),166(8),19242(7),47(8),165(7),19(8),14(6),37(6),19267(11),14(9)])]. 89.15/89.54 19460 mult(A,mult(mult(i(A),mult(B,A)),mult(C,A))) = mult(mult(B,mult(A,C)),A). [para(47(a,1),19320(a,1,1,1)),rewrite([170(6)]),flip(a)]. 89.15/89.54 19461 mult(A,mult(mult(B,A),mult(i(A),mult(C,A)))) = mult(mult(mult(A,B),C),A). [para(47(a,1),19320(a,1,1,2)),rewrite([170(7)]),flip(a)]. 89.15/89.54 19554 mult(mult(i(A),B),mult(mult(i(B),mult(A,B)),C)) = mult(mult(B,i(A)),mult(A,C)). [back_rewrite(12849),rewrite([19461(10),444(7),55(5)]),flip(a)]. 89.15/89.54 20678 mult(mult(A,B),mult(i(B),mult(mult(B,C),A))) = mult(mult(mult(A,B),C),A). [para(20(a,1),17254(a,1,2,2,2)),rewrite([44(4),20(11)])]. 89.15/89.54 20692 mult(mult(mult(i(A),B),C),mult(i(A),mult(B,A))) = mult(mult(i(A),B),mult(mult(mult(C,i(A)),B),A)). [para(170(a,1),17254(a,1,2,2,2)),rewrite([113(8),47(9),170(13)]),flip(a)]. 89.15/89.54 20883 mult(mult(A,B),mult(i(B),mult(C,mult(A,B)))) = mult(A,mult(mult(C,A),B)). [para(20(a,1),17364(a,1,1)),rewrite([20(3),44(3)]),flip(a)]. 89.15/89.54 20892 mult(mult(A,B),mult(mult(mult(A,B),mult(C,mult(A,B))),i(B))) = mult(A,mult(B,mult(mult(mult(A,B),C),A))). [para(165(a,1),17364(a,1,2,1))]. 89.15/89.54 20992 mult(mult(mult(mult(A,B),C),A),B) = mult(mult(A,B),mult(mult(C,A),B)). [para(17364(a,1),227(a,2,2,2,2,1)),rewrite([80(2),170(4),20892(13),113(13),20(5),19(8),165(6),19(7),80(7),170(9),113(16),20(10),19(11),165(9),19(10)])]. 89.15/89.54 21042 mult(mult(i(A),mult(mult(A,B),C)),mult(A,B)) = mult(mult(mult(B,C),A),B). [back_rewrite(12433),rewrite([20883(8),19(6)]),flip(a)]. 89.15/89.54 21243 mult(mult(mult(A,B),i(C)),mult(C,A)) = mult(A,mult(mult(B,i(C)),mult(C,A))). [para(19(a,1),20992(a,1,1,1,1)),rewrite([19(8)])]. 89.15/89.54 21247 mult(mult(A,B),mult(mult(mult(mult(i(B),i(A)),C),A),B)) = mult(mult(C,A),B). [para(47(a,1),20992(a,1,1,1)),rewrite([80(5)]),flip(a)]. 89.15/89.54 21954 mult(mult(i(A),mult(B,A)),mult(C,A)) = mult(i(A),mult(mult(B,mult(A,C)),A)). [para(19460(a,1),19(a,1,2)),flip(a)]. 89.15/89.54 21961 mult(mult(mult(A,i(B)),mult(B,C)),B) = mult(B,mult(mult(i(B),A),mult(C,B))). [para(55(a,1),19460(a,1,2,1,2)),flip(a)]. 89.15/89.54 21962 mult(mult(A,mult(B,mult(C,i(B)))),B) = mult(B,mult(mult(i(B),mult(A,B)),C)). [para(55(a,1),19460(a,1,2,2)),flip(a)]. 89.15/89.54 22108 mult(mult(A,mult(B,C)),mult(A,C)) = mult(A,mult(mult(B,mult(C,A)),C)). [para(19460(a,1),4077(a,2,2)),rewrite([47(4)])]. 89.15/89.54 22737 mult(mult(A,B),mult(i(B),mult(C,B))) = mult(i(B),mult(mult(mult(B,A),C),B)). [para(19461(a,1),19(a,1,2)),flip(a)]. 89.15/89.54 22745 mult(mult(mult(A,B),mult(C,i(A))),A) = mult(A,mult(mult(B,A),mult(i(A),C))). [para(55(a,1),19461(a,1,2,2,2)),flip(a)]. 89.15/89.54 22879 mult(A,mult(B,mult(mult(i(B),i(A)),mult(mult(mult(B,A),C),B)))) = mult(B,mult(A,mult(C,B))). [para(19461(a,1),280(a,2,2,2,2)),rewrite([170(4),47(5),47(3),47(4)]),flip(a)]. 89.15/89.54 23009 mult(mult(i(A),i(B)),mult(mult(mult(B,A),C),B)) = mult(i(A),mult(mult(A,C),B)). [para(20678(a,1),19(a,1,2)),rewrite([80(2)])]. 89.15/89.54 23259 mult(i(A),mult(mult(A,B),mult(C,mult(A,B)))) = mult(B,mult(mult(C,A),B)). [para(20883(a,1),210(a,1,2,2)),rewrite([19(5)]),flip(a)]. 89.15/89.54 23280 mult(mult(A,B),mult(mult(i(B),C),mult(A,B))) = mult(mult(A,mult(C,A)),B). [para(20883(a,1),279(a,1,2)),rewrite([44(6),80(6),47(8),37(6),14(6),165(6),44(10),80(10),47(12),20(12),2481(15),23259(14),165(9),19(12)])]. 89.15/89.54 23384 mult(mult(mult(mult(A,B),C),i(A)),mult(A,B)) = mult(mult(A,mult(B,C)),B). [para(19(a,1),21042(a,1,1,2,1)),rewrite([44(2),19(5)]),flip(a)]. 89.15/89.54 23496 mult(mult(A,mult(B,C)),mult(i(C),mult(i(B),C))) = mult(mult(i(C),i(B)),mult(mult(B,mult(C,A)),C)). [back_rewrite(11706),rewrite([23384(9)]),flip(a)]. 89.15/89.54 23671 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))). [para(23259(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.54 23779 mult(A,mult(B,mult(mult(mult(i(B),C),A),B))) = mult(mult(A,mult(C,A)),B). [back_rewrite(23280),rewrite([23671(6)])]. 89.15/89.54 23903 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,mult(C,mult(i(B),A)))))) = mult(B,mult(mult(C,i(B)),A)). [para(23671(a,1),289(a,2,2,2,2)),rewrite([47(18),19(16)])]. 89.15/89.54 23932 mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,B)))) = mult(mult(C,i(A)),mult(A,B)). [para(47(a,1),23384(a,1,1,1)),rewrite([80(6),3343(11)]),flip(a)]. 89.15/89.54 23938 mult(i(A),mult(B,mult(mult(i(B),A),mult(C,B)))) = mult(mult(C,A),mult(i(A),B)). [para(200(a,1),23384(a,1,1,1)),rewrite([44(2),290(11)]),flip(a)]. 89.15/89.54 23944 mult(mult(mult(mult(A,B),C),i(A)),mult(A,mult(B,mult(A,B)))) = mult(mult(mult(A,mult(B,C)),B),mult(A,B)). [para(23384(a,1),956(a,1,1)),rewrite([910(12)]),flip(a)]. 89.15/89.54 23949 mult(mult(i(A),mult(mult(A,B),C)),mult(B,A)) = mult(i(A),mult(mult(mult(A,mult(B,C)),B),A)). [para(23384(a,1),103(a,2,2,1)),rewrite([44(8),165(7),19(8),44(12)])]. 89.15/89.54 24005 mult(mult(A,mult(mult(B,C),A)),B) = mult(A,mult(B,mult(mult(C,A),B))). [para(20678(a,1),23384(a,1,1,1)),rewrite([20(5),165(4),23671(4),47(9)]),flip(a)]. 89.15/89.54 24015 mult(mult(mult(mult(A,B),C),i(B)),mult(B,A)) = mult(A,mult(B,mult(C,A))). [back_rewrite(22879),rewrite([23932(9)])]. 89.15/89.54 24027 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),B) = mult(mult(C,A),mult(i(A),B)). [back_rewrite(290),rewrite([23938(14)])]. 89.15/89.54 24032 mult(mult(A,mult(B,A)),mult(B,C)) = mult(A,mult(mult(B,mult(A,B)),C)). [para(20(a,1),24005(a,1,1,2,1)),rewrite([23671(10),23779(10)])]. 89.15/89.54 24279 mult(A,mult(mult(B,mult(A,B)),mult(i(B),C))) = mult(mult(A,mult(B,A)),C). [para(47(a,1),24032(a,1,2)),flip(a)]. 89.15/89.54 24669 mult(i(A),mult(mult(mult(A,mult(B,C)),B),A)) = mult(B,mult(mult(C,B),A)). [para(20(a,1),24015(a,1,1,1,1)),rewrite([44(3),22737(6),20883(12)])]. 89.15/89.54 24697 mult(A,mult(mult(mult(mult(mult(B,A),C),i(A)),i(B)),mult(B,A))) = mult(A,mult(B,mult(A,C))). [para(103(a,1),24015(a,1,1,1)),rewrite([21243(9),165(13),55(12)])]. 89.15/89.54 24769 mult(mult(A,mult(mult(A,B),C)),mult(A,B)) = mult(A,mult(mult(A,mult(B,mult(C,A))),B)). [para(24015(a,1),22108(a,2,2,1)),rewrite([55(5)])]. 89.15/89.54 24782 mult(mult(i(A),mult(mult(A,B),C)),mult(B,A)) = mult(B,mult(mult(C,B),A)). [back_rewrite(23949),rewrite([24669(12)])]. 89.15/89.54 24944 mult(mult(mult(A,mult(B,C)),B),A) = mult(A,mult(B,mult(mult(C,B),A))). [para(24669(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.54 25031 mult(A,mult(B,mult(mult(i(B),mult(C,B)),A))) = mult(mult(mult(A,C),B),A). [para(47(a,1),24944(a,1,1,1,2)),rewrite([170(6)]),flip(a)]. 89.15/89.54 25035 mult(mult(A,mult(mult(i(A),mult(B,A)),C)),B) = mult(B,mult(A,mult(C,B))). [para(55(a,1),24944(a,2,2,2,1)),rewrite([21962(5)])]. 89.15/89.54 25333 mult(mult(A,B),mult(i(B),mult(C,A))) = mult(A,mult(mult(C,i(B)),mult(B,A))). [para(47(a,1),25031(a,1,2,2,1,2)),rewrite([80(5),44(5),170(5),19554(7),17253(10)]),flip(a)]. 89.15/89.54 25401 mult(mult(A,B),mult(i(B),mult(C,mult(B,A)))) = mult(mult(mult(A,C),B),A). [para(25031(a,1),17364(a,2)),rewrite([21954(6),165(8),20(7)])]. 89.15/89.54 25404 mult(mult(A,B),mult(mult(C,mult(B,A)),i(A))) = mult(mult(A,mult(B,C)),B). [para(23384(a,1),25031(a,2)),rewrite([44(4),104(7),19(8)])]. 89.15/89.54 25413 mult(A,mult(B,mult(mult(C,mult(A,B)),i(B)))) = mult(mult(mult(A,B),C),A). [back_rewrite(20678),rewrite([25333(6),166(3),104(5)])]. 89.15/89.54 25414 mult(mult(mult(A,B),mult(i(B),C)),A) = mult(A,mult(mult(C,i(B)),mult(B,A))). [back_rewrite(17253),rewrite([25333(10)])]. 89.15/89.54 25417 mult(mult(mult(A,B),mult(i(B),i(C))),mult(C,C)) = mult(mult(A,i(B)),mult(B,C)). [back_rewrite(12223),rewrite([25333(13),19(14)])]. 89.15/89.54 25516 mult(mult(i(A),i(B)),mult(mult(mult(B,C),A),B)) = mult(i(A),mult(C,mult(A,B))). [para(25401(a,1),19(a,1,2)),rewrite([80(2)])]. 89.15/89.54 25524 mult(mult(mult(A,mult(B,mult(i(A),i(C)))),C),A) = mult(mult(A,C),mult(i(C),B)). [para(55(a,1),25401(a,1,2,2)),rewrite([80(6)]),flip(a)]. 89.15/89.54 25608 mult(mult(mult(mult(A,B),C),B),A) = mult(mult(A,B),mult(mult(C,B),A)). [para(24782(a,1),25401(a,1,2,2)),rewrite([19(6),47(9)]),flip(a)]. 89.15/89.54 25707 mult(mult(A,mult(B,mult(i(A),i(C)))),C) = mult(mult(A,C),mult(i(C),mult(B,i(A)))). [para(17364(a,1),387(a,2,2,2)),rewrite([44(11),22737(12),47(13),23009(11),47(9),47(14)])]. 89.15/89.54 25711 mult(A,mult(mult(mult(B,i(A)),i(C)),mult(C,A))) = mult(mult(A,C),mult(i(C),B)). [back_rewrite(25524),rewrite([25707(6),25414(7)])]. 89.15/89.54 25712 mult(mult(A,B),mult(i(B),mult(mult(B,A),C))) = mult(A,mult(B,mult(A,C))). [back_rewrite(24697),rewrite([25711(9)])]. 89.15/89.54 25925 mult(mult(i(A),i(B)),mult(mult(B,mult(A,C)),A)) = mult(mult(C,mult(A,B)),i(B)). [para(25404(a,1),19(a,1,2)),rewrite([80(2)])]. 89.15/89.54 25935 mult(mult(mult(A,mult(B,C)),B),mult(A,B)) = mult(A,mult(B,mult(mult(C,mult(B,A)),B))). [para(25404(a,1),165(a,1,1)),rewrite([23671(13),55(10)])]. 89.15/89.54 25997 mult(mult(A,mult(B,C)),mult(B,A)) = mult(A,mult(B,mult(C,mult(B,A)))). [para(25404(a,1),24015(a,1,1,1)),rewrite([20(5),55(9)])]. 89.15/89.54 26004 mult(mult(A,mult(B,C)),mult(i(C),mult(i(B),C))) = mult(mult(A,mult(C,B)),i(B)). [back_rewrite(23496),rewrite([25925(14)])]. 89.15/89.54 26005 mult(mult(mult(mult(A,B),C),i(A)),mult(A,mult(B,mult(A,B)))) = mult(A,mult(B,mult(mult(C,mult(B,A)),B))). [back_rewrite(23944),rewrite([25935(13)])]. 89.15/89.54 26017 mult(A,mult(B,mult(mult(i(B),C),mult(B,A)))) = mult(mult(A,C),mult(B,A)). [para(47(a,1),25997(a,1,1,2)),flip(a)]. 89.15/89.54 26149 mult(mult(i(A),B),mult(mult(mult(C,i(A)),B),A)) = mult(i(A),mult(mult(B,mult(C,mult(i(A),B))),A)). [para(25413(a,1),114(a,1)),rewrite([165(5),20(4),20692(7),165(13),20(12),44(13),20(14)])]. 89.15/89.54 26166 mult(i(A),mult(mult(A,B),mult(mult(C,A),B))) = mult(B,mult(i(A),mult(mult(A,C),mult(A,B)))). [para(25413(a,1),210(a,1,2,2)),rewrite([20(4),20(11),44(11)]),flip(a)]. 89.15/89.54 26191 mult(A,mult(mult(B,mult(mult(C,mult(A,B)),A)),i(A))) = mult(mult(A,B),mult(mult(C,A),B)). [para(25413(a,1),23384(a,2,1)),rewrite([17364(6),166(5),104(7),22108(4),20992(11)])]. 89.15/89.54 26198 mult(mult(A,B),mult(mult(C,B),A)) = mult(A,mult(B,mult(C,mult(B,A)))). [para(25413(a,1),25035(a,1,1)),rewrite([47(4),25608(4),47(8),80(10),80(8),44(11),170(10),26004(11),55(9)])]. 89.15/89.54 26210 mult(mult(mult(i(A),B),C),mult(i(A),mult(B,A))) = mult(i(A),mult(mult(B,mult(C,mult(i(A),B))),A)). [back_rewrite(20692),rewrite([26149(14)])]. 89.15/89.54 26298 mult(A,mult(B,mult(mult(C,i(B)),mult(B,A)))) = mult(mult(A,B),mult(C,A)). [para(55(a,1),26198(a,1,2,1)),flip(a)]. 89.15/89.54 26524 mult(i(A),mult(mult(A,B),mult(mult(B,A),C))) = mult(B,mult(B,mult(A,C))). [para(25712(a,1),210(a,1,2,2)),rewrite([19(5)]),flip(a)]. 89.15/89.54 26546 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,C)))) = mult(mult(B,i(A)),mult(A,C)). [para(289(a,2),25712(a,2)),rewrite([44(4),200(8)]),flip(a)]. 89.15/89.54 26623 mult(mult(A,i(B)),mult(B,mult(C,mult(i(A),B)))) = mult(A,mult(mult(C,i(A)),B)). [back_rewrite(23903),rewrite([26546(10)])]. 89.15/89.54 26819 mult(A,mult(mult(B,i(A)),mult(mult(mult(A,i(B)),C),B))) = mult(mult(A,C),B). [para(55(a,1),26017(a,1,2,2,2)),rewrite([80(5),44(4),55(12)])]. 89.15/89.54 27452 mult(mult(mult(i(A),i(B)),mult(B,mult(C,i(A)))),mult(A,A)) = mult(mult(i(A),i(B)),mult(B,mult(C,A))). [para(444(a,1),907(a,1,1)),rewrite([775(15)])]. 89.15/89.54 27475 mult(mult(A,i(B)),mult(B,mult(C,A))) = mult(A,mult(mult(C,B),mult(i(B),A))). [para(444(a,1),25413(a,2)),rewrite([44(7),22745(6),19(7)]),flip(a)]. 89.15/89.54 27484 mult(mult(i(A),i(B)),mult(B,mult(C,A))) = mult(i(A),mult(mult(C,i(B)),mult(B,A))). [back_rewrite(27452),rewrite([27475(7),990(9),25417(8)]),flip(a)]. 89.15/89.54 27605 mult(mult(A,B),mult(mult(B,A),C)) = mult(A,mult(B,mult(B,mult(A,C)))). [para(26524(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.54 27613 mult(A,mult(A,mult(B,mult(mult(i(B),i(A)),C)))) = mult(i(B),mult(mult(B,A),C)). [para(47(a,1),26524(a,1,2,2)),rewrite([80(6)]),flip(a)]. 89.15/89.54 27654 mult(A,mult(A,mult(mult(i(A),i(B)),mult(B,C)))) = mult(mult(A,B),mult(i(B),C)). [para(253(a,1),26524(a,1,2,2)),rewrite([80(4),44(2),44(2),55(5),16813(12)]),flip(a)]. 89.15/89.54 27656 mult(i(A),mult(i(A),mult(mult(A,i(B)),mult(B,C)))) = mult(mult(i(A),B),mult(i(B),C)). [para(297(a,1),26524(a,1,2,2)),rewrite([80(3),44(3),20(6),19554(14)]),flip(a)]. 89.15/89.54 28573 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(C,mult(B,A)),i(A))))) = mult(i(A),mult(mult(A,C),B)). [para(25401(a,1),461(a,2,2,1)),rewrite([47(8),20(16)])]. 89.15/89.54 28774 mult(i(A),mult(mult(A,i(B)),mult(B,C))) = mult(A,mult(mult(i(A),B),mult(i(B),C))). [para(24279(a,1),474(a,2,2,2)),rewrite([44(2),44(3),37(2),14(3),55(3),44(2),44(3),37(2),14(3),37(4),13(4),44(5),1282(8),1282(7),27656(8),44(8),44(9),37(8),14(9),37(10),13(10),44(11),49(11),13(11),1282(12)]),flip(a)]. 89.15/89.54 28782 mult(mult(A,i(B)),mult(B,mult(i(A),C))) = mult(A,mult(mult(i(A),B),mult(i(B),C))). [back_rewrite(1282),rewrite([28774(12)])]. 89.15/89.54 28980 mult(i(A),mult(mult(A,B),mult(i(B),C))) = mult(A,mult(mult(i(A),i(B)),mult(B,C))). [para(24279(a,1),480(a,2,2,2)),rewrite([49(3),14(4),55(4),49(4),14(5),44(6),49(6),13(6),44(6),750(8),750(7),27654(8),49(9),14(10),44(11),49(11),13(11),37(11),13(11),750(12)])]. 89.15/89.54 28981 mult(mult(mult(A,mult(B,C)),B),mult(i(B),i(C))) = mult(i(C),mult(mult(C,A),B)). [back_rewrite(28573),rewrite([28980(10),27475(9),47(10)])]. 89.15/89.54 29104 mult(A,mult(B,mult(i(A),mult(mult(A,C),B)))) = mult(mult(A,mult(B,C)),B). [para(23384(a,1),1021(a,2)),rewrite([26005(8),18133(9),28981(7)])]. 89.15/89.54 29147 mult(mult(A,i(B)),mult(B,mult(mult(A,C),B))) = mult(A,mult(B,mult(mult(i(B),A),mult(C,B)))). [para(29104(a,1),334(a,2,2)),rewrite([80(5),44(4),26819(10),21961(11)])]. 89.15/89.54 29833 mult(A,mult(mult(i(A),i(B)),mult(mult(C,B),A))) = mult(i(B),mult(C,mult(B,A))). [para(25031(a,1),750(a,1,2)),rewrite([25516(7),29147(13),47(14)]),flip(a)]. 89.15/89.54 29980 mult(A,mult(A,mult(mult(i(A),B),mult(i(B),C)))) = mult(mult(A,i(B)),mult(B,C)). [para(234(a,1),772(a,1,2,1)),rewrite([44(3),80(6),80(5),44(5),200(7),44(4),44(7),80(10),80(9),44(9),200(11),28782(10)]),flip(a)]. 89.15/89.54 30581 mult(mult(mult(i(A),B),i(C)),mult(C,A)) = mult(C,mult(mult(mult(i(C),i(A)),B),A)). [para(796(a,1),750(a,1,2)),rewrite([80(6),44(3),80(4),44(4),19(5),200(12),80(12),44(9),80(10),44(10),19(11),26210(16),22737(17),26623(15),165(13),19(14)])]. 89.15/89.54 31859 mult(i(A),mult(i(B),mult(mult(B,A),C))) = mult(A,mult(B,mult(mult(i(B),i(A)),C))). [para(3636(a,1),884(a,1,1)),rewrite([44(3),44(4),37(3),14(3),19(3),44(2),44(3),80(3),44(6),55(5),44(5),80(5),55(7),2481(8),28980(7),2748(8),44(8),44(9),80(9),44(12),55(11),2481(12)]),flip(a)]. 89.15/89.55 31862 mult(i(A),mult(B,mult(mult(i(B),A),C))) = mult(A,mult(i(B),mult(mult(B,i(A)),C))). [para(27605(a,1),884(a,1,2,2,2)),rewrite([80(4),44(3),55(7),170(5),55(4),80(6),44(5),19(6),19(10),47(8),2513(6),80(10),44(9),19(10)])]. 89.15/89.55 31878 mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,B)))) = mult(mult(C,A),mult(i(A),B)). [back_rewrite(24027),rewrite([31862(6),3332(7)])]. 89.15/89.55 32140 mult(A,mult(B,mult(i(A),mult(mult(A,C),mult(A,B))))) = mult(mult(A,B),mult(mult(C,A),B)). [para(29104(a,1),16882(a,1,2,2)),rewrite([24769(8),27484(9),166(6),104(8),22108(5),26191(8),47(7)]),flip(a)]. 89.15/89.55 32918 mult(mult(mult(mult(i(A),i(B)),C),B),A) = mult(mult(i(A),i(B)),mult(mult(C,B),A)). [para(21247(a,1),19(a,1,2)),rewrite([80(2)]),flip(a)]. 89.15/89.55 32947 mult(mult(mult(mult(A,B),C),i(B)),mult(B,C)) = mult(mult(A,mult(B,C)),C). [para(21247(a,1),23384(a,1,1,1)),rewrite([32918(12),29833(13),47(11)])]. 89.15/89.55 32999 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),mult(mult(B,A),C)) = mult(mult(mult(C,B),A),C). [para(118(a,1),32947(a,1,1,1)),rewrite([44(2),25333(6),166(3),104(5),25413(6),31859(9)]),flip(a)]. 89.15/89.55 33945 mult(A,mult(mult(i(A),mult(mult(A,B),C)),C)) = mult(mult(A,mult(B,C)),C). [para(22737(a,1),23384(a,1,1,1)),rewrite([30581(9),23009(7),47(10)])]. 89.15/89.55 33981 mult(i(A),mult(mult(A,B),mult(mult(C,A),B))) = mult(mult(mult(B,C),A),B). [para(118(a,1),33945(a,1,2,1,2)),rewrite([44(3),31859(12),32999(15)])]. 89.15/89.55 34102 mult(A,mult(i(B),mult(mult(B,C),mult(B,A)))) = mult(mult(mult(A,C),B),A). [back_rewrite(26166),rewrite([33981(6)]),flip(a)]. 89.15/89.55 34110 mult(mult(A,B),mult(mult(C,A),B)) = mult(A,mult(mult(mult(B,C),A),B)). [back_rewrite(32140),rewrite([34102(6)]),flip(a)]. 89.15/89.55 34141 mult(i(A),mult(mult(A,B),mult(C,A))) = mult(mult(B,C),A). [para(34110(a,1),19(a,1,2)),rewrite([80(2),27484(8),20(5)])]. 89.15/89.55 34233 mult(mult(A,B),mult(i(B),C)) = mult(B,mult(mult(i(B),A),C)). [back_rewrite(31878),rewrite([34141(6)]),flip(a)]. 89.15/89.55 34433 mult(mult(A,i(B)),mult(B,C)) = mult(i(B),mult(mult(B,A),C)). [back_rewrite(29980),rewrite([34233(5),27613(7)]),flip(a)]. 89.15/89.55 34546 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [back_rewrite(26298),rewrite([34433(4),47(5)]),flip(a)]. 89.15/89.55 34547 $F # answer(goals). [resolve(34546,a,177,a)]. 89.15/89.55 89.15/89.55 % SZS output end Refutation 89.15/89.55 ============================== end of proof ========================== 89.15/89.55 89.15/89.55 ============================== PROOF ================================= 89.15/89.55 % SZS status Theorem 89.15/89.55 % SZS output start Refutation 89.15/89.55 89.15/89.55 % Proof 2 at 87.60 (+ 0.93) seconds: goals. 89.15/89.55 % Length of proof is 270. 89.15/89.55 % Level of proof is 37. 89.15/89.55 % Maximum clause weight is 66.000. 89.15/89.55 % Given clauses 838. 89.15/89.55 89.15/89.55 1 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 2 (all D all C all B all A ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D))))) # label(f07) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 3 (all B all A B = mult(i(A),mult(A,B))) # label(f10) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 5 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 6 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 7 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 8 (all C all B all A mult(ld(A,mult(B,A)),ld(A,mult(C,A))) = ld(A,mult(mult(B,C),A))) # label(f09) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 9 (all D all C all B all A rd(mult(mult(mult(A,B),C),D),mult(C,D)) = mult(rd(mult(mult(A,C),D),mult(C,D)),rd(mult(mult(B,C),D),mult(C,D)))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 10 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 11 (all B all A A = mult(mult(A,B),i(B))) # label(f11) # label(axiom) # label(non_clause). [assumption]. 89.15/89.55 12 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 89.15/89.55 13 mult(A,unit) = A # label(f05) # label(axiom). [clausify(6)]. 89.15/89.55 14 mult(unit,A) = A # label(f06) # label(axiom). [clausify(7)]. 89.15/89.55 15 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(1)]. 89.15/89.55 17 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(5)]. 89.15/89.55 18 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(10)]. 89.15/89.55 19 mult(i(A),mult(A,B)) = B # label(f10) # label(axiom). [clausify(3)]. 89.15/89.55 20 mult(mult(A,B),i(B)) = A # label(f11) # label(axiom). [clausify(11)]. 89.15/89.55 21 ld(A,mult(mult(B,C),A)) = mult(ld(A,mult(B,A)),ld(A,mult(C,A))) # label(f09) # label(axiom). [clausify(8)]. 89.15/89.55 22 mult(ld(A,mult(B,A)),ld(A,mult(C,A))) = ld(A,mult(mult(B,C),A)). [copy(21),flip(a)]. 89.15/89.55 23 ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))) # label(f07) # label(axiom). [clausify(2)]. 89.15/89.55 24 mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))) = ld(mult(A,B),mult(A,mult(B,mult(C,D)))). [copy(23),flip(a)]. 89.15/89.55 25 rd(mult(mult(mult(A,B),C),D),mult(C,D)) = mult(rd(mult(mult(A,C),D),mult(C,D)),rd(mult(mult(B,C),D),mult(C,D))) # label(f08) # label(axiom). [clausify(9)]. 89.15/89.55 26 mult(rd(mult(mult(A,B),C),mult(B,C)),rd(mult(mult(D,B),C),mult(B,C))) = rd(mult(mult(mult(A,D),B),C),mult(B,C)). [copy(25),flip(a)]. 89.15/89.55 29 mult(mult(c9,c7),mult(c8,c9)) != mult(c9,mult(mult(c7,c8),c9)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(12)]. 89.15/89.55 35 rd(A,ld(B,A)) = B. [para(17(a,1),15(a,1,1))]. 89.15/89.55 37 mult(i(A),A) = unit. [para(13(a,1),19(a,1,2))]. 89.15/89.55 39 rd(A,mult(B,A)) = i(B). [para(19(a,1),15(a,1,1))]. 89.15/89.55 41 ld(A,B) = mult(i(A),B). [para(17(a,1),19(a,1,2)),flip(a)]. 89.15/89.55 44 i(i(A)) = A. [back_rewrite(35),rewrite([41(1),39(3)])]. 89.15/89.55 45 mult(mult(i(mult(A,B)),mult(A,mult(B,C))),mult(i(mult(A,B)),mult(A,mult(B,D)))) = mult(i(mult(A,B)),mult(A,mult(B,mult(C,D)))). [back_rewrite(24),rewrite([41(4),41(9),41(16)])]. 89.15/89.55 46 mult(mult(i(A),mult(B,A)),mult(i(A),mult(C,A))) = mult(i(A),mult(mult(B,C),A)). [back_rewrite(22),rewrite([41(2),41(5),41(10)])]. 89.15/89.55 47 mult(A,mult(i(A),B)) = B. [back_rewrite(17),rewrite([41(1)])]. 89.15/89.55 49 mult(A,i(A)) = unit. [para(14(a,1),20(a,1,1))]. 89.15/89.55 51 rd(A,B) = mult(A,i(B)). [para(18(a,1),20(a,1,1)),flip(a)]. 89.15/89.55 52 mult(i(mult(A,B)),A) = i(B). [para(20(a,1),19(a,1,2))]. 89.15/89.55 54 mult(mult(mult(mult(A,B),C),i(mult(B,C))),mult(mult(mult(D,B),C),i(mult(B,C)))) = mult(mult(mult(mult(A,D),B),C),i(mult(B,C))). [back_rewrite(26),rewrite([51(4),51(9),51(16)])]. 89.15/89.55 55 mult(mult(A,i(B)),B) = A. [back_rewrite(18),rewrite([51(1)])]. 89.15/89.55 58 mult(mult(i(A),mult(i(B),mult(mult(B,A),C))),mult(i(A),mult(i(B),mult(mult(B,A),D)))) = mult(i(A),mult(i(B),mult(mult(B,A),mult(C,D)))). [para(19(a,1),45(a,1,1,1,1)),rewrite([19(9),19(16)])]. 89.15/89.55 61 mult(A,mult(i(mult(B,i(A))),mult(B,mult(i(A),C)))) = mult(i(mult(B,i(A))),mult(B,C)). [para(19(a,1),45(a,2,2,2)),rewrite([37(5),13(5),52(4),44(2)])]. 89.15/89.55 63 mult(mult(i(A),mult(mult(A,B),mult(i(B),C))),mult(i(A),mult(mult(A,B),mult(i(B),D)))) = mult(i(A),mult(mult(A,B),mult(i(B),mult(C,D)))). [para(20(a,1),45(a,1,1,1,1)),rewrite([20(9),20(16)])]. 89.15/89.55 68 mult(mult(A,mult(i(mult(B,A)),mult(B,C))),A) = mult(A,mult(i(mult(B,A)),mult(B,mult(C,A)))). [para(37(a,1),45(a,1,2,2)),rewrite([52(3),44(2),52(8),44(7),13(7),52(9),44(8)])]. 89.15/89.55 70 mult(i(A),mult(i(mult(B,A)),mult(B,mult(A,C)))) = mult(i(mult(B,A)),mult(B,C)). [para(49(a,1),45(a,1,1,2,2)),rewrite([13(4),52(3),47(12)])]. 89.15/89.55 77 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),mult(i(A),mult(B,mult(mult(i(B),A),D)))) = mult(i(A),mult(B,mult(mult(i(B),A),mult(C,D)))). [para(47(a,1),45(a,1,1,1,1)),rewrite([47(9),47(16)])]. 89.15/89.55 78 mult(mult(i(mult(A,B)),mult(A,C)),mult(i(mult(A,B)),mult(A,mult(B,D)))) = mult(i(mult(A,B)),mult(A,mult(B,mult(mult(i(B),C),D)))). [para(47(a,1),45(a,1,1,2,2))]. 89.15/89.55 79 mult(mult(i(mult(A,B)),mult(A,mult(B,C))),mult(i(mult(A,B)),mult(A,D))) = mult(i(mult(A,B)),mult(A,mult(B,mult(C,mult(i(B),D))))). [para(47(a,1),45(a,1,2,2,2))]. 89.15/89.55 80 i(mult(A,B)) = mult(i(B),i(A)). [para(19(a,1),52(a,1,1,1)),flip(a)]. 89.15/89.55 81 mult(mult(mult(i(A),i(B)),mult(B,mult(A,C))),mult(mult(i(A),i(B)),mult(B,D))) = mult(mult(i(A),i(B)),mult(B,mult(A,mult(C,mult(i(A),D))))). [back_rewrite(79),rewrite([80(2),80(8),80(14)])]. 89.15/89.55 82 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(mult(i(A),i(B)),mult(B,mult(A,D)))) = mult(mult(i(A),i(B)),mult(B,mult(A,mult(mult(i(A),C),D)))). [back_rewrite(78),rewrite([80(2),80(7),80(14)])]. 89.15/89.55 87 mult(i(A),mult(mult(i(A),i(B)),mult(B,mult(A,C)))) = mult(mult(i(A),i(B)),mult(B,C)). [back_rewrite(70),rewrite([80(3),80(10)])]. 89.15/89.55 89 mult(mult(A,mult(mult(i(A),i(B)),mult(B,C))),A) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,A)))). [back_rewrite(68),rewrite([80(2),80(9)])]. 89.15/89.55 93 mult(A,mult(mult(A,i(B)),mult(B,mult(i(A),C)))) = mult(mult(A,i(B)),mult(B,C)). [back_rewrite(61),rewrite([80(3),44(2),80(10),44(9)])]. 89.15/89.55 95 mult(mult(mult(mult(A,B),C),mult(i(C),i(B))),mult(mult(mult(D,B),C),mult(i(C),i(B)))) = mult(mult(mult(mult(A,D),B),C),mult(i(C),i(B))). [back_rewrite(54),rewrite([80(4),80(10),80(18)])]. 89.15/89.55 98 mult(i(A),mult(mult(A,B),A)) = mult(B,A). [para(19(a,1),46(a,1,1)),rewrite([47(4)]),flip(a)]. 89.15/89.55 99 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),mult(mult(i(A),i(B)),A)) = mult(mult(i(A),i(B)),mult(mult(C,i(B)),mult(B,A))). [para(19(a,1),46(a,1,2,2)),rewrite([80(2),80(8),80(13)])]. 89.15/89.55 103 mult(mult(A,B),mult(A,mult(C,i(A)))) = mult(A,mult(mult(mult(B,A),C),i(A))). [para(20(a,1),46(a,1,1,2)),rewrite([44(2),44(3),44(7)])]. 89.15/89.55 104 mult(mult(A,mult(B,i(A))),mult(A,C)) = mult(A,mult(mult(B,mult(C,A)),i(A))). [para(20(a,1),46(a,1,2,2)),rewrite([44(2),44(5),44(7)])]. 89.15/89.55 111 mult(mult(mult(i(A),B),mult(C,mult(i(B),A))),mult(mult(i(A),B),A)) = mult(mult(i(A),B),mult(mult(C,B),mult(i(B),A))). [para(47(a,1),46(a,1,2,2)),rewrite([80(3),44(3),80(9),44(9),80(13),44(13)])]. 89.15/89.55 113 mult(mult(i(A),B),mult(i(A),mult(C,A))) = mult(i(A),mult(mult(mult(B,i(A)),C),A)). [para(55(a,1),46(a,1,1,2))]. 89.15/89.55 114 mult(mult(i(A),mult(B,A)),mult(i(A),C)) = mult(i(A),mult(mult(B,mult(C,i(A))),A)). [para(55(a,1),46(a,1,2,2))]. 89.15/89.55 118 mult(mult(i(A),i(B)),mult(mult(B,A),C)) = C. [para(80(a,1),19(a,1,1))]. 89.15/89.55 119 mult(mult(A,mult(B,C)),mult(i(C),i(B))) = A. [para(80(a,1),20(a,1,2))]. 89.15/89.55 120 mult(mult(i(A),i(B)),mult(B,A)) = unit. [para(80(a,1),37(a,1,1))]. 89.15/89.55 121 mult(mult(A,B),mult(i(B),i(A))) = unit. [para(80(a,1),49(a,1,2))]. 89.15/89.55 122 mult(mult(A,B),mult(mult(i(B),i(A)),C)) = C. [para(80(a,1),47(a,1,2,1))]. 89.15/89.55 123 mult(mult(A,mult(i(B),i(C))),mult(C,B)) = A. [para(80(a,1),55(a,1,1,2))]. 89.15/89.55 125 mult(mult(i(A),B),mult(i(B),A)) = unit. [para(44(a,1),120(a,1,1,2))]. 89.15/89.55 132 mult(mult(mult(mult(i(A),mult(i(B),i(C))),C),B),mult(i(B),mult(i(C),mult(mult(C,B),mult(A,D))))) = mult(i(B),mult(i(C),mult(mult(C,B),D))). [para(58(a,1),19(a,1,2)),rewrite([80(7),80(5),80(3),80(3),44(7),44(8)])]. 89.15/89.55 134 mult(mult(A,mult(mult(i(A),i(B)),mult(B,C))),mult(A,mult(mult(i(A),i(B)),mult(B,D)))) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,D)))). [para(20(a,1),58(a,1,1,2,2,1)),rewrite([44(2),80(2),44(8),80(8),20(12),44(15),80(15),20(19)])]. 89.15/89.55 137 mult(mult(A,mult(i(B),mult(mult(B,i(A)),C))),mult(A,mult(i(B),mult(mult(B,i(A)),D)))) = mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,D)))). [para(44(a,1),58(a,1,1,1)),rewrite([44(8),44(15)])]. 89.15/89.55 138 mult(mult(i(A),i(B)),mult(i(A),mult(i(B),mult(mult(B,A),C)))) = mult(i(A),mult(i(B),C)). [para(49(a,1),58(a,1,1,2,2)),rewrite([13(4),80(15),122(18)])]. 89.15/89.55 141 mult(mult(i(A),mult(i(B),C)),mult(i(A),mult(i(B),mult(mult(B,A),D)))) = mult(i(A),mult(i(B),mult(mult(B,A),mult(mult(mult(i(A),i(B)),C),D)))). [para(47(a,1),58(a,1,1,2,2)),rewrite([80(16)])]. 89.15/89.55 165 mult(mult(A,B),A) = mult(A,mult(B,A)). [para(98(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.55 166 mult(mult(A,B),i(A)) = mult(A,mult(B,i(A))). [para(19(a,1),98(a,1,2,1)),rewrite([44(2)]),flip(a)]. 89.15/89.55 169 mult(mult(i(A),i(B)),mult(B,mult(B,A))) = mult(i(A),mult(B,A)). [para(20(a,1),98(a,1,2,1)),rewrite([80(2)])]. 89.15/89.55 170 mult(mult(i(A),B),A) = mult(i(A),mult(B,A)). [para(47(a,1),98(a,1,2,1)),flip(a)]. 89.15/89.55 176 mult(A,mult(mult(mult(i(A),i(B)),mult(B,C)),A)) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,A)))). [back_rewrite(89),rewrite([165(7)])]. 89.15/89.55 184 mult(mult(mult(i(A),B),mult(C,mult(i(B),A))),mult(i(A),mult(B,A))) = mult(mult(i(A),B),mult(mult(C,B),mult(i(B),A))). [back_rewrite(111),rewrite([170(9)])]. 89.15/89.55 186 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),mult(i(A),mult(i(B),A))) = mult(mult(i(A),i(B)),mult(mult(C,i(B)),mult(B,A))). [back_rewrite(99),rewrite([170(10)])]. 89.15/89.55 188 mult(mult(i(A),i(B)),mult(B,mult(A,B))) = B. [para(165(a,1),19(a,1,2)),rewrite([80(2)])]. 89.15/89.55 190 mult(mult(A,B),mult(i(B),mult(A,B))) = mult(A,mult(A,B)). [para(20(a,1),165(a,1,1)),flip(a)]. 89.15/89.55 200 mult(mult(i(A),B),mult(mult(i(B),A),C)) = C. [para(44(a,1),118(a,1,1,2))]. 89.15/89.55 206 mult(mult(mult(mult(i(A),B),mult(i(B),i(C))),C),mult(i(C),mult(mult(C,B),mult(i(B),mult(A,D))))) = mult(i(C),mult(mult(C,B),mult(i(B),D))). [para(63(a,1),19(a,1,2)),rewrite([80(7),80(5),80(3),44(3),80(4),44(8)])]. 89.15/89.55 208 mult(mult(i(A),mult(mult(A,B),C)),mult(i(A),mult(mult(A,B),mult(i(B),D)))) = mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),D)))). [para(19(a,1),63(a,1,1,2,2))]. 89.15/89.55 210 mult(A,mult(i(B),mult(mult(B,A),mult(i(A),C)))) = mult(i(B),mult(mult(B,A),C)). [para(19(a,1),63(a,2,2,2)),rewrite([37(4),13(4),19(3)])]. 89.15/89.55 227 mult(mult(i(A),B),mult(i(B),mult(mult(A,mult(mult(A,C),i(B))),B))) = mult(A,mult(mult(i(A),B),mult(i(B),mult(mult(A,mult(C,i(B))),B)))). [para(165(a,1),63(a,1,1,2)),rewrite([80(3),44(3),47(7),200(6),80(3),44(3),170(5),114(8),80(13),44(13),170(15),114(19)]),flip(a)]. 89.15/89.55 234 mult(mult(A,mult(i(B),C)),mult(i(C),B)) = A. [para(44(a,1),119(a,1,2,2))]. 89.15/89.55 253 mult(mult(A,mult(i(B),i(A))),mult(mult(A,mult(B,i(A))),C)) = C. [para(166(a,1),118(a,1,2,1)),rewrite([44(2),80(2)])]. 89.15/89.55 279 mult(mult(A,mult(B,C)),mult(A,mult(B,mult(mult(i(B),i(A)),D)))) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(mult(mult(A,B),C),D)))). [para(118(a,1),77(a,1,1,2,2)),rewrite([44(2),44(4),44(11)])]. 89.15/89.55 280 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),mult(A,mult(B,D))) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,mult(mult(A,B),D))))). [para(118(a,1),77(a,1,2,2,2)),rewrite([44(2),44(8),44(11)])]. 89.15/89.55 289 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,C)))) = mult(B,mult(i(A),mult(B,mult(mult(i(B),A),C)))). [para(166(a,1),77(a,1,1,2,2)),rewrite([44(4),47(5),19(3),44(12)]),flip(a)]. 89.15/89.55 290 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),B) = mult(i(A),mult(B,mult(mult(i(B),A),mult(C,B)))). [para(166(a,1),77(a,1,2,2,2)),rewrite([44(10),47(11),19(9),44(12)])]. 89.15/89.55 293 mult(mult(i(A),B),mult(i(B),mult(A,B))) = B. [para(170(a,1),19(a,1,2)),rewrite([80(3),44(3)])]. 89.15/89.55 297 mult(mult(i(A),mult(i(B),A)),mult(mult(i(A),mult(B,A)),C)) = C. [para(170(a,1),118(a,1,2,1)),rewrite([80(4),44(4)])]. 89.15/89.55 303 mult(mult(i(A),mult(B,A)),mult(i(B),A)) = mult(mult(i(A),B),mult(A,mult(i(B),A))). [para(170(a,1),166(a,1,1)),rewrite([80(6),44(6),80(11),44(11)])]. 89.15/89.55 334 mult(mult(A,i(B)),mult(B,mult(A,C))) = mult(A,mult(mult(A,i(B)),mult(B,C))). [para(19(a,1),81(a,2,2,2)),rewrite([44(2),37(4),13(4),55(3),44(2),44(7),44(9)]),flip(a)]. 89.15/89.55 387 mult(A,mult(mult(i(A),i(B)),mult(B,mult(mult(A,B),mult(i(B),C))))) = mult(mult(A,B),mult(A,mult(mult(i(A),i(B)),C))). [para(188(a,1),81(a,1,1,2)),rewrite([80(5),44(3),44(3),19(3),80(6),44(4),44(4),19(4),80(12),44(10),44(10),19(10)]),flip(a)]. 89.15/89.55 428 mult(mult(i(A),B),mult(mult(A,B),mult(i(B),A))) = mult(i(A),mult(mult(B,A),A)). [para(293(a,1),165(a,2,2)),rewrite([303(6),184(10),170(11)])]. 89.15/89.55 439 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(mult(i(C),i(B)),mult(B,mult(C,mult(mult(i(C),A),D))))) = mult(mult(i(C),i(B)),mult(B,mult(C,D))). [para(82(a,1),19(a,1,2)),rewrite([80(6),80(2),80(7),44(5),44(5)])]. 89.15/89.55 444 mult(mult(mult(A,i(B)),mult(B,C)),A) = mult(mult(A,i(B)),mult(B,mult(C,A))). [para(37(a,1),82(a,1,2,2,2)),rewrite([44(2),44(6),13(8),55(7),44(7),44(10),165(10),19(11)])]. 89.15/89.55 461 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),i(A))))) = mult(i(A),mult(mult(mult(A,B),C),i(A))). [para(121(a,1),82(a,1,2,2)),rewrite([44(2),80(2),47(4),44(6),80(6),47(8),13(7),165(6),44(8),80(8),47(10),44(11)]),flip(a)]. 89.15/89.55 474 mult(mult(mult(i(A),mult(mult(i(B),i(C)),i(D))),D),mult(mult(i(A),mult(mult(i(B),i(C)),i(D))),mult(mult(D,mult(C,B)),mult(A,E)))) = mult(mult(i(A),mult(mult(i(B),i(C)),i(D))),mult(mult(D,mult(C,B)),mult(A,mult(mult(i(A),mult(i(B),i(C))),E)))). [para(119(a,1),82(a,1,1,2)),rewrite([80(4),80(3),80(12),80(11),80(25),80(24)])]. 89.15/89.55 480 mult(mult(mult(i(A),mult(mult(B,C),i(D))),D),mult(mult(i(A),mult(mult(B,C),i(D))),mult(mult(D,mult(i(C),i(B))),mult(A,E)))) = mult(mult(i(A),mult(mult(B,C),i(D))),mult(mult(D,mult(i(C),i(B))),mult(A,mult(mult(i(A),mult(B,C)),E)))). [para(123(a,1),82(a,1,1,2)),rewrite([80(6),80(5),44(3),44(3),80(12),80(11),44(9),44(9),80(25),80(24),44(22),44(22)])]. 89.15/89.55 750 mult(mult(i(A),i(B)),mult(B,mult(A,C))) = mult(A,mult(mult(i(A),i(B)),mult(B,C))). [para(87(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.55 755 mult(mult(A,i(B)),mult(B,A)) = mult(A,A). [para(37(a,1),87(a,1,2,2,2)),rewrite([44(2),44(2),13(4),55(3),44(3)]),flip(a)]. 89.15/89.55 772 mult(mult(A,mult(mult(i(A),i(B)),i(C))),mult(mult(C,mult(B,A)),i(B))) = mult(A,mult(mult(A,mult(mult(i(A),i(B)),i(C))),C)). [para(119(a,1),87(a,1,2,2)),rewrite([44(2),44(2),80(3),80(2),44(10),80(11),80(10)]),flip(a)]. 89.15/89.55 775 mult(mult(mult(i(A),i(B)),mult(B,C)),A) = mult(mult(i(A),i(B)),mult(B,mult(C,A))). [para(87(a,1),166(a,1,1)),rewrite([44(7),750(13),44(15),165(14),176(14),19(15)])]. 89.15/89.55 796 mult(mult(mult(i(A),B),i(C)),mult(C,mult(i(A),mult(B,A)))) = mult(mult(i(A),B),mult(mult(mult(i(A),B),i(C)),mult(C,A))). [para(293(a,1),87(a,1,2,2,2)),rewrite([80(3),44(3),80(5),44(5),80(12),44(12)]),flip(a)]. 89.15/89.55 884 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(C,mult(mult(i(C),i(B)),mult(B,mult(mult(i(C),A),D))))) = mult(C,mult(mult(i(C),i(B)),mult(B,D))). [back_rewrite(439),rewrite([750(14),750(21)])]. 89.15/89.55 907 mult(mult(A,i(B)),mult(B,B)) = mult(A,B). [para(755(a,1),19(a,1,2)),rewrite([80(3),44(2)])]. 89.15/89.55 908 mult(mult(A,mult(B,A)),B) = mult(mult(A,B),mult(A,B)). [para(19(a,1),755(a,1,2)),rewrite([44(3),165(2)])]. 89.15/89.55 910 mult(mult(A,B),mult(A,B)) = mult(A,mult(B,mult(A,B))). [para(20(a,1),755(a,1,1)),flip(a)]. 89.15/89.55 912 mult(mult(A,B),mult(i(B),A)) = mult(A,A). [para(44(a,1),755(a,1,1,2))]. 89.15/89.55 913 mult(mult(A,mult(A,i(B))),B) = mult(A,A). [para(55(a,1),755(a,1,2)),rewrite([80(3),44(2)])]. 89.15/89.55 917 mult(mult(A,B),mult(i(B),i(B))) = mult(A,i(B)). [para(755(a,1),122(a,1,2))]. 89.15/89.55 930 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [back_rewrite(908),rewrite([910(6)])]. 89.15/89.55 931 mult(mult(i(A),B),mult(A,A)) = mult(i(A),mult(mult(B,A),A)). [back_rewrite(428),rewrite([912(6)])]. 89.15/89.55 956 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),907(a,1,1)),flip(a)]. 89.15/89.55 990 mult(mult(i(A),B),mult(A,A)) = mult(i(A),mult(B,mult(A,A))). [back_rewrite(931),rewrite([956(7)])]. 89.15/89.55 1007 mult(mult(A,mult(B,B)),i(B)) = mult(A,B). [para(956(a,1),20(a,1,1))]. 89.15/89.55 1021 mult(mult(A,mult(B,mult(C,mult(B,C)))),mult(i(C),i(B))) = mult(A,mult(B,C)). [para(956(a,1),119(a,1,1)),rewrite([910(3)])]. 89.15/89.55 1183 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(913(a,1),55(a,1,1)),rewrite([44(4)])]. 89.15/89.55 1191 mult(mult(A,mult(A,B)),B) = mult(A,mult(A,mult(B,B))). [para(913(a,1),907(a,1,1)),rewrite([1183(3),44(5)]),flip(a)]. 89.15/89.55 1272 mult(mult(A,mult(A,mult(B,B))),i(B)) = mult(A,mult(A,B)). [para(1183(a,1),1007(a,1,1)),rewrite([1183(7)])]. 89.15/89.55 1282 mult(mult(A,i(B)),mult(B,mult(i(A),C))) = mult(i(A),mult(mult(A,i(B)),mult(B,C))). [para(93(a,1),19(a,1,2)),flip(a)]. 89.15/89.55 1461 mult(mult(A,mult(B,mult(A,B))),C) = mult(mult(A,B),mult(mult(A,B),C)). [para(910(a,1),1183(a,1,1))]. 89.15/89.55 1479 mult(mult(mult(mult(A,B),C),mult(i(C),i(B))),B) = mult(mult(mult(A,C),mult(i(C),i(B))),mult(B,B)). [para(49(a,1),95(a,1,2,1)),rewrite([80(3),80(7),80(9),44(7),44(7),20(8),80(9),80(11),44(9),44(9),20(10),14(8),956(7),80(11),80(15),80(17),44(15),44(15),20(16)]),flip(a)]. 89.15/89.55 1692 mult(mult(A,mult(B,A)),i(B)) = mult(mult(A,B),mult(A,i(B))). [para(930(a,1),917(a,1,1)),rewrite([1461(7),917(6)]),flip(a)]. 89.15/89.55 1820 mult(A,mult(mult(mult(B,A),mult(C,A)),i(A))) = mult(mult(A,B),mult(A,C)). [para(20(a,1),103(a,1,2,2)),flip(a)]. 89.15/89.55 1823 mult(mult(A,mult(i(B),i(A))),mult(i(C),i(A))) = mult(A,mult(mult(i(B),mult(i(A),i(C))),i(A))). [para(103(a,1),80(a,1,1)),rewrite([80(6),80(5),44(2),80(3),80(3),166(8),80(12),80(11),44(10),166(12),80(14)]),flip(a)]. 89.15/89.55 1914 mult(mult(i(A),B),mult(A,B)) = mult(i(A),mult(B,mult(A,B))). [para(19(a,1),1191(a,1,1,2)),rewrite([910(9),19(10)])]. 89.15/89.55 2046 mult(mult(i(A),i(B)),mult(B,mult(i(C),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),i(C)),i(B))). [para(104(a,1),80(a,1,1)),rewrite([80(6),80(5),44(2),80(3),80(2),166(8),80(10),80(15),80(14),44(13),166(15)]),flip(a)]. 89.15/89.55 2481 mult(mult(A,B),mult(i(B),mult(i(A),C))) = mult(i(B),mult(i(A),mult(mult(A,B),C))). [para(37(a,1),132(a,1,1,1,1)),rewrite([14(2),122(9)])]. 89.15/89.55 2513 mult(mult(i(A),B),mult(i(B),mult(A,C))) = mult(i(B),mult(A,mult(mult(i(A),B),C))). [para(200(a,1),132(a,1,2,2,2)),rewrite([80(3),44(3),44(5),125(5),14(3),44(5),44(9)])]. 89.15/89.55 2748 mult(i(A),mult(B,mult(mult(i(B),i(A)),mult(A,C)))) = mult(B,mult(mult(i(B),i(A)),C)). [para(49(a,1),134(a,1,1,2,2)),rewrite([13(5),47(4),47(14)])]. 89.15/89.55 3229 mult(mult(i(A),mult(B,mult(A,B))),mult(i(B),i(A))) = mult(i(A),B). [para(19(a,1),1272(a,2,2)),rewrite([910(5),19(6),80(6)])]. 89.15/89.55 3231 mult(mult(A,mult(B,mult(i(A),B))),mult(i(B),A)) = mult(A,B). [para(47(a,1),1272(a,2,2)),rewrite([910(5),47(6),80(7),44(7)])]. 89.15/89.55 3234 mult(mult(mult(i(A),i(B)),mult(C,mult(mult(B,A),C))),mult(i(C),mult(i(A),i(B)))) = mult(mult(i(A),i(B)),C). [para(118(a,1),1272(a,2,2)),rewrite([910(11),118(12),80(10),80(10)])]. 89.15/89.55 3332 mult(mult(A,mult(i(B),mult(mult(B,i(A)),C))),B) = mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,B)))). [para(165(a,1),137(a,1,2,2,2)),rewrite([19(11),47(9)])]. 89.15/89.55 3343 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),B) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,B)))). [para(170(a,1),137(a,1,2,2,2)),rewrite([44(2),44(8),47(11),47(9),44(9)])]. 89.15/89.55 3636 mult(mult(A,B),mult(A,mult(B,C))) = mult(A,mult(B,mult(mult(A,B),C))). [para(118(a,1),138(a,1,2,2,2)),rewrite([44(2),44(2),44(3),44(3),44(6),44(6)])]. 89.15/89.55 3653 mult(mult(A,i(B)),mult(A,B)) = mult(A,mult(i(B),mult(A,B))). [para(755(a,1),138(a,1,2,2,2)),rewrite([44(2),44(4),19(5),44(6)])]. 89.15/89.55 4077 mult(mult(A,mult(B,C)),mult(A,B)) = mult(A,mult(B,mult(C,mult(A,B)))). [para(120(a,1),141(a,1,2,2,2)),rewrite([44(2),44(2),44(4),44(4),13(4),44(6),44(6),44(9),44(9),165(11),118(12)])]. 89.15/89.55 7517 mult(mult(mult(i(A),i(B)),i(C)),mult(C,mult(C,mult(B,A)))) = mult(mult(i(A),i(B)),mult(C,mult(B,A))). [para(80(a,1),169(a,1,1,1)),rewrite([80(11)])]. 89.15/89.55 7532 mult(mult(i(A),i(B)),mult(A,mult(B,A))) = mult(i(A),mult(mult(i(B),mult(A,B)),A)). [para(169(a,1),103(a,2,2,1)),rewrite([44(8),165(7),165(6),19(8),44(12)])]. 89.15/89.55 7537 mult(mult(i(A),i(B)),mult(B,mult(mult(C,mult(A,B)),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),mult(C,mult(A,B))),i(B))). [para(104(a,1),169(a,1,2,2)),rewrite([80(2),80(7),80(6),44(5),166(7),2046(8),103(17),55(11),103(15),55(8),7517(9),80(11),104(17)]),flip(a)]. 89.15/89.55 7974 mult(mult(i(A),mult(B,A)),B) = mult(i(A),mult(B,mult(A,B))). [para(3231(a,1),169(a,1,2,2)),rewrite([80(3),44(3),80(7),80(6),80(5),44(5),165(6),1692(8),200(9),4077(9),1914(7),750(10),47(8),7532(6),47(7),80(7),44(7),3231(13),1914(8)])]. 89.15/89.55 8045 mult(mult(A,B),mult(B,A)) = mult(A,mult(B,mult(B,A))). [para(20(a,1),3653(a,1,2)),rewrite([44(3),956(2),165(3),1183(2),44(6),20(7)]),flip(a)]. 89.15/89.55 8411 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),C) = mult(mult(i(A),i(B)),mult(C,mult(mult(B,A),C))). [para(119(a,1),8045(a,1,2)),rewrite([119(18),165(13)])]. 89.15/89.55 10106 mult(mult(i(A),i(B)),mult(B,mult(mult(C,mult(mult(A,B),C)),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),mult(C,mult(mult(A,B),C))),i(B))). [para(103(a,1),7974(a,2,2,2)),rewrite([80(2),104(8),7537(9),103(13),55(9),8411(7),80(12),103(22),55(16)]),flip(a)]. 89.15/89.55 11706 mult(mult(i(A),i(B)),mult(mult(mult(mult(B,A),C),i(B)),mult(B,A))) = mult(mult(C,mult(B,A)),mult(i(A),mult(i(B),A))). [para(165(a,1),186(a,1,1,2)),rewrite([118(8)]),flip(a)]. 89.15/89.55 12180 mult(mult(mult(A,B),mult(i(B),i(C))),C) = mult(i(C),mult(mult(C,B),mult(i(B),A))). [para(37(a,1),206(a,1,2,2,2,2)),rewrite([44(2),13(11),20(10),37(8),13(8)])]. 89.15/89.55 12223 mult(mult(mult(A,B),mult(i(B),i(C))),mult(C,C)) = mult(i(C),mult(mult(C,B),mult(i(B),mult(A,C)))). [back_rewrite(1479),rewrite([12180(7)]),flip(a)]. 89.15/89.55 12433 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),mult(A,B))))) = mult(mult(i(A),mult(mult(A,B),C)),mult(A,B)). [para(190(a,1),208(a,1,2,2)),rewrite([19(8)]),flip(a)]. 89.15/89.55 12848 mult(i(A),mult(mult(i(B),i(A)),mult(A,mult(mult(B,mult(C,A)),i(A))))) = mult(mult(i(B),i(A)),mult(mult(A,mult(B,i(A))),C)). [para(166(a,1),210(a,1,2,2,1)),rewrite([80(3),44(9),104(9),80(13),166(17)])]. 89.15/89.55 12849 mult(A,mult(mult(i(B),A),mult(i(A),mult(mult(B,mult(C,i(A))),A)))) = mult(mult(i(B),A),mult(mult(i(A),mult(B,A)),C)). [para(170(a,1),210(a,1,2,2,1)),rewrite([80(3),44(3),114(8),80(13),44(13),170(15)])]. 89.15/89.55 16806 mult(mult(i(A),i(B)),mult(B,mult(C,i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),C),i(B))). [para(103(a,1),3229(a,1,1,2,2)),rewrite([80(2),103(12),55(6),10106(10),80(14),80(13),44(12),166(14),80(16),1823(18),103(19),55(10),3234(13),80(9)]),flip(a)]. 89.15/89.55 16813 mult(mult(i(A),i(B)),mult(mult(B,mult(A,i(B))),C)) = mult(mult(i(B),i(A)),mult(A,C)). [back_rewrite(12848),rewrite([16806(10),444(9),20(7),19(8)]),flip(a)]. 89.15/89.55 16882 mult(A,mult(mult(i(A),i(B)),mult(B,mult(mult(B,A),C)))) = mult(B,mult(A,C)). [para(3636(a,1),19(a,1,2)),rewrite([80(2),750(8)])]. 89.15/89.55 16898 mult(mult(A,mult(B,C)),mult(mult(i(C),i(B)),mult(A,D))) = mult(A,mult(mult(A,mult(B,C)),mult(mult(i(C),i(B)),D))). [para(119(a,1),3636(a,1,1)),rewrite([119(19)]),flip(a)]. 89.15/89.55 17253 mult(mult(mult(A,B),mult(i(B),C)),A) = mult(mult(A,B),mult(i(B),mult(C,A))). [para(20(a,1),4077(a,1,2)),rewrite([20(10)])]. 89.15/89.55 17254 mult(A,mult(B,mult(mult(i(B),C),mult(A,B)))) = mult(mult(A,C),mult(A,B)). [para(47(a,1),4077(a,1,1,2)),flip(a)]. 89.15/89.55 17364 mult(mult(A,B),mult(mult(C,mult(A,B)),i(B))) = mult(A,mult(B,mult(C,A))). [para(4077(a,1),210(a,2,2)),rewrite([80(6),16898(10),55(8),19(8),19(12)])]. 89.15/89.55 18133 mult(mult(A,mult(B,C)),mult(i(B),i(A))) = mult(A,mult(B,mult(C,mult(i(B),i(A))))). [para(166(a,1),279(a,2,2,2,2)),rewrite([80(7),910(9),47(10),47(8),80(12),118(16)])]. 89.15/89.55 19242 mult(mult(mult(A,B),mult(C,B)),i(B)) = mult(i(B),mult(mult(B,A),mult(B,C))). [para(1820(a,1),19(a,1,2)),flip(a)]. 89.15/89.55 19267 mult(i(A),mult(mult(mult(A,B),mult(A,C)),A)) = mult(mult(B,A),mult(C,A)). [para(1820(a,1),104(a,2,2,1)),rewrite([44(3),19(3),47(6),44(9)]),flip(a)]. 89.15/89.55 19320 mult(mult(mult(A,B),mult(A,C)),A) = mult(A,mult(mult(B,A),mult(C,A))). [para(1820(a,1),227(a,2,2,2,2,1)),rewrite([37(2),166(8),19242(7),47(8),165(7),19(8),14(6),37(6),19267(11),14(9)])]. 89.15/89.55 19460 mult(A,mult(mult(i(A),mult(B,A)),mult(C,A))) = mult(mult(B,mult(A,C)),A). [para(47(a,1),19320(a,1,1,1)),rewrite([170(6)]),flip(a)]. 89.15/89.55 19461 mult(A,mult(mult(B,A),mult(i(A),mult(C,A)))) = mult(mult(mult(A,B),C),A). [para(47(a,1),19320(a,1,1,2)),rewrite([170(7)]),flip(a)]. 89.15/89.55 19554 mult(mult(i(A),B),mult(mult(i(B),mult(A,B)),C)) = mult(mult(B,i(A)),mult(A,C)). [back_rewrite(12849),rewrite([19461(10),444(7),55(5)]),flip(a)]. 89.15/89.55 20678 mult(mult(A,B),mult(i(B),mult(mult(B,C),A))) = mult(mult(mult(A,B),C),A). [para(20(a,1),17254(a,1,2,2,2)),rewrite([44(4),20(11)])]. 89.15/89.55 20692 mult(mult(mult(i(A),B),C),mult(i(A),mult(B,A))) = mult(mult(i(A),B),mult(mult(mult(C,i(A)),B),A)). [para(170(a,1),17254(a,1,2,2,2)),rewrite([113(8),47(9),170(13)]),flip(a)]. 89.15/89.55 20883 mult(mult(A,B),mult(i(B),mult(C,mult(A,B)))) = mult(A,mult(mult(C,A),B)). [para(20(a,1),17364(a,1,1)),rewrite([20(3),44(3)]),flip(a)]. 89.15/89.55 20892 mult(mult(A,B),mult(mult(mult(A,B),mult(C,mult(A,B))),i(B))) = mult(A,mult(B,mult(mult(mult(A,B),C),A))). [para(165(a,1),17364(a,1,2,1))]. 89.15/89.55 20992 mult(mult(mult(mult(A,B),C),A),B) = mult(mult(A,B),mult(mult(C,A),B)). [para(17364(a,1),227(a,2,2,2,2,1)),rewrite([80(2),170(4),20892(13),113(13),20(5),19(8),165(6),19(7),80(7),170(9),113(16),20(10),19(11),165(9),19(10)])]. 89.15/89.55 21042 mult(mult(i(A),mult(mult(A,B),C)),mult(A,B)) = mult(mult(mult(B,C),A),B). [back_rewrite(12433),rewrite([20883(8),19(6)]),flip(a)]. 89.15/89.55 21243 mult(mult(mult(A,B),i(C)),mult(C,A)) = mult(A,mult(mult(B,i(C)),mult(C,A))). [para(19(a,1),20992(a,1,1,1,1)),rewrite([19(8)])]. 89.15/89.55 21247 mult(mult(A,B),mult(mult(mult(mult(i(B),i(A)),C),A),B)) = mult(mult(C,A),B). [para(47(a,1),20992(a,1,1,1)),rewrite([80(5)]),flip(a)]. 89.15/89.55 21954 mult(mult(i(A),mult(B,A)),mult(C,A)) = mult(i(A),mult(mult(B,mult(A,C)),A)). [para(19460(a,1),19(a,1,2)),flip(a)]. 89.15/89.55 21961 mult(mult(mult(A,i(B)),mult(B,C)),B) = mult(B,mult(mult(i(B),A),mult(C,B))). [para(55(a,1),19460(a,1,2,1,2)),flip(a)]. 89.15/89.55 21962 mult(mult(A,mult(B,mult(C,i(B)))),B) = mult(B,mult(mult(i(B),mult(A,B)),C)). [para(55(a,1),19460(a,1,2,2)),flip(a)]. 89.15/89.55 22108 mult(mult(A,mult(B,C)),mult(A,C)) = mult(A,mult(mult(B,mult(C,A)),C)). [para(19460(a,1),4077(a,2,2)),rewrite([47(4)])]. 89.15/89.55 22737 mult(mult(A,B),mult(i(B),mult(C,B))) = mult(i(B),mult(mult(mult(B,A),C),B)). [para(19461(a,1),19(a,1,2)),flip(a)]. 89.15/89.55 22745 mult(mult(mult(A,B),mult(C,i(A))),A) = mult(A,mult(mult(B,A),mult(i(A),C))). [para(55(a,1),19461(a,1,2,2,2)),flip(a)]. 89.15/89.55 22879 mult(A,mult(B,mult(mult(i(B),i(A)),mult(mult(mult(B,A),C),B)))) = mult(B,mult(A,mult(C,B))). [para(19461(a,1),280(a,2,2,2,2)),rewrite([170(4),47(5),47(3),47(4)]),flip(a)]. 89.15/89.55 23009 mult(mult(i(A),i(B)),mult(mult(mult(B,A),C),B)) = mult(i(A),mult(mult(A,C),B)). [para(20678(a,1),19(a,1,2)),rewrite([80(2)])]. 89.15/89.55 23259 mult(i(A),mult(mult(A,B),mult(C,mult(A,B)))) = mult(B,mult(mult(C,A),B)). [para(20883(a,1),210(a,1,2,2)),rewrite([19(5)]),flip(a)]. 89.15/89.55 23280 mult(mult(A,B),mult(mult(i(B),C),mult(A,B))) = mult(mult(A,mult(C,A)),B). [para(20883(a,1),279(a,1,2)),rewrite([44(6),80(6),47(8),37(6),14(6),165(6),44(10),80(10),47(12),20(12),2481(15),23259(14),165(9),19(12)])]. 89.15/89.55 23384 mult(mult(mult(mult(A,B),C),i(A)),mult(A,B)) = mult(mult(A,mult(B,C)),B). [para(19(a,1),21042(a,1,1,2,1)),rewrite([44(2),19(5)]),flip(a)]. 89.15/89.55 23496 mult(mult(A,mult(B,C)),mult(i(C),mult(i(B),C))) = mult(mult(i(C),i(B)),mult(mult(B,mult(C,A)),C)). [back_rewrite(11706),rewrite([23384(9)]),flip(a)]. 89.15/89.55 23671 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))). [para(23259(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.55 23779 mult(A,mult(B,mult(mult(mult(i(B),C),A),B))) = mult(mult(A,mult(C,A)),B). [back_rewrite(23280),rewrite([23671(6)])]. 89.15/89.55 23903 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,mult(C,mult(i(B),A)))))) = mult(B,mult(mult(C,i(B)),A)). [para(23671(a,1),289(a,2,2,2,2)),rewrite([47(18),19(16)])]. 89.15/89.55 23932 mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,B)))) = mult(mult(C,i(A)),mult(A,B)). [para(47(a,1),23384(a,1,1,1)),rewrite([80(6),3343(11)]),flip(a)]. 89.15/89.55 23938 mult(i(A),mult(B,mult(mult(i(B),A),mult(C,B)))) = mult(mult(C,A),mult(i(A),B)). [para(200(a,1),23384(a,1,1,1)),rewrite([44(2),290(11)]),flip(a)]. 89.15/89.55 23944 mult(mult(mult(mult(A,B),C),i(A)),mult(A,mult(B,mult(A,B)))) = mult(mult(mult(A,mult(B,C)),B),mult(A,B)). [para(23384(a,1),956(a,1,1)),rewrite([910(12)]),flip(a)]. 89.15/89.55 23949 mult(mult(i(A),mult(mult(A,B),C)),mult(B,A)) = mult(i(A),mult(mult(mult(A,mult(B,C)),B),A)). [para(23384(a,1),103(a,2,2,1)),rewrite([44(8),165(7),19(8),44(12)])]. 89.15/89.55 24005 mult(mult(A,mult(mult(B,C),A)),B) = mult(A,mult(B,mult(mult(C,A),B))). [para(20678(a,1),23384(a,1,1,1)),rewrite([20(5),165(4),23671(4),47(9)]),flip(a)]. 89.15/89.55 24015 mult(mult(mult(mult(A,B),C),i(B)),mult(B,A)) = mult(A,mult(B,mult(C,A))). [back_rewrite(22879),rewrite([23932(9)])]. 89.15/89.55 24027 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),B) = mult(mult(C,A),mult(i(A),B)). [back_rewrite(290),rewrite([23938(14)])]. 89.15/89.55 24032 mult(mult(A,mult(B,A)),mult(B,C)) = mult(A,mult(mult(B,mult(A,B)),C)). [para(20(a,1),24005(a,1,1,2,1)),rewrite([23671(10),23779(10)])]. 89.15/89.55 24279 mult(A,mult(mult(B,mult(A,B)),mult(i(B),C))) = mult(mult(A,mult(B,A)),C). [para(47(a,1),24032(a,1,2)),flip(a)]. 89.15/89.55 24669 mult(i(A),mult(mult(mult(A,mult(B,C)),B),A)) = mult(B,mult(mult(C,B),A)). [para(20(a,1),24015(a,1,1,1,1)),rewrite([44(3),22737(6),20883(12)])]. 89.15/89.55 24697 mult(A,mult(mult(mult(mult(mult(B,A),C),i(A)),i(B)),mult(B,A))) = mult(A,mult(B,mult(A,C))). [para(103(a,1),24015(a,1,1,1)),rewrite([21243(9),165(13),55(12)])]. 89.15/89.55 24769 mult(mult(A,mult(mult(A,B),C)),mult(A,B)) = mult(A,mult(mult(A,mult(B,mult(C,A))),B)). [para(24015(a,1),22108(a,2,2,1)),rewrite([55(5)])]. 89.15/89.55 24782 mult(mult(i(A),mult(mult(A,B),C)),mult(B,A)) = mult(B,mult(mult(C,B),A)). [back_rewrite(23949),rewrite([24669(12)])]. 89.15/89.55 24944 mult(mult(mult(A,mult(B,C)),B),A) = mult(A,mult(B,mult(mult(C,B),A))). [para(24669(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.55 25031 mult(A,mult(B,mult(mult(i(B),mult(C,B)),A))) = mult(mult(mult(A,C),B),A). [para(47(a,1),24944(a,1,1,1,2)),rewrite([170(6)]),flip(a)]. 89.15/89.55 25035 mult(mult(A,mult(mult(i(A),mult(B,A)),C)),B) = mult(B,mult(A,mult(C,B))). [para(55(a,1),24944(a,2,2,2,1)),rewrite([21962(5)])]. 89.15/89.55 25333 mult(mult(A,B),mult(i(B),mult(C,A))) = mult(A,mult(mult(C,i(B)),mult(B,A))). [para(47(a,1),25031(a,1,2,2,1,2)),rewrite([80(5),44(5),170(5),19554(7),17253(10)]),flip(a)]. 89.15/89.55 25401 mult(mult(A,B),mult(i(B),mult(C,mult(B,A)))) = mult(mult(mult(A,C),B),A). [para(25031(a,1),17364(a,2)),rewrite([21954(6),165(8),20(7)])]. 89.15/89.55 25404 mult(mult(A,B),mult(mult(C,mult(B,A)),i(A))) = mult(mult(A,mult(B,C)),B). [para(23384(a,1),25031(a,2)),rewrite([44(4),104(7),19(8)])]. 89.15/89.55 25413 mult(A,mult(B,mult(mult(C,mult(A,B)),i(B)))) = mult(mult(mult(A,B),C),A). [back_rewrite(20678),rewrite([25333(6),166(3),104(5)])]. 89.15/89.55 25414 mult(mult(mult(A,B),mult(i(B),C)),A) = mult(A,mult(mult(C,i(B)),mult(B,A))). [back_rewrite(17253),rewrite([25333(10)])]. 89.15/89.55 25417 mult(mult(mult(A,B),mult(i(B),i(C))),mult(C,C)) = mult(mult(A,i(B)),mult(B,C)). [back_rewrite(12223),rewrite([25333(13),19(14)])]. 89.15/89.55 25516 mult(mult(i(A),i(B)),mult(mult(mult(B,C),A),B)) = mult(i(A),mult(C,mult(A,B))). [para(25401(a,1),19(a,1,2)),rewrite([80(2)])]. 89.15/89.55 25524 mult(mult(mult(A,mult(B,mult(i(A),i(C)))),C),A) = mult(mult(A,C),mult(i(C),B)). [para(55(a,1),25401(a,1,2,2)),rewrite([80(6)]),flip(a)]. 89.15/89.55 25608 mult(mult(mult(mult(A,B),C),B),A) = mult(mult(A,B),mult(mult(C,B),A)). [para(24782(a,1),25401(a,1,2,2)),rewrite([19(6),47(9)]),flip(a)]. 89.15/89.55 25707 mult(mult(A,mult(B,mult(i(A),i(C)))),C) = mult(mult(A,C),mult(i(C),mult(B,i(A)))). [para(17364(a,1),387(a,2,2,2)),rewrite([44(11),22737(12),47(13),23009(11),47(9),47(14)])]. 89.15/89.55 25711 mult(A,mult(mult(mult(B,i(A)),i(C)),mult(C,A))) = mult(mult(A,C),mult(i(C),B)). [back_rewrite(25524),rewrite([25707(6),25414(7)])]. 89.15/89.55 25712 mult(mult(A,B),mult(i(B),mult(mult(B,A),C))) = mult(A,mult(B,mult(A,C))). [back_rewrite(24697),rewrite([25711(9)])]. 89.15/89.55 25925 mult(mult(i(A),i(B)),mult(mult(B,mult(A,C)),A)) = mult(mult(C,mult(A,B)),i(B)). [para(25404(a,1),19(a,1,2)),rewrite([80(2)])]. 89.15/89.55 25935 mult(mult(mult(A,mult(B,C)),B),mult(A,B)) = mult(A,mult(B,mult(mult(C,mult(B,A)),B))). [para(25404(a,1),165(a,1,1)),rewrite([23671(13),55(10)])]. 89.15/89.55 25997 mult(mult(A,mult(B,C)),mult(B,A)) = mult(A,mult(B,mult(C,mult(B,A)))). [para(25404(a,1),24015(a,1,1,1)),rewrite([20(5),55(9)])]. 89.15/89.55 26004 mult(mult(A,mult(B,C)),mult(i(C),mult(i(B),C))) = mult(mult(A,mult(C,B)),i(B)). [back_rewrite(23496),rewrite([25925(14)])]. 89.15/89.55 26005 mult(mult(mult(mult(A,B),C),i(A)),mult(A,mult(B,mult(A,B)))) = mult(A,mult(B,mult(mult(C,mult(B,A)),B))). [back_rewrite(23944),rewrite([25935(13)])]. 89.15/89.55 26017 mult(A,mult(B,mult(mult(i(B),C),mult(B,A)))) = mult(mult(A,C),mult(B,A)). [para(47(a,1),25997(a,1,1,2)),flip(a)]. 89.15/89.55 26149 mult(mult(i(A),B),mult(mult(mult(C,i(A)),B),A)) = mult(i(A),mult(mult(B,mult(C,mult(i(A),B))),A)). [para(25413(a,1),114(a,1)),rewrite([165(5),20(4),20692(7),165(13),20(12),44(13),20(14)])]. 89.15/89.55 26166 mult(i(A),mult(mult(A,B),mult(mult(C,A),B))) = mult(B,mult(i(A),mult(mult(A,C),mult(A,B)))). [para(25413(a,1),210(a,1,2,2)),rewrite([20(4),20(11),44(11)]),flip(a)]. 89.15/89.55 26191 mult(A,mult(mult(B,mult(mult(C,mult(A,B)),A)),i(A))) = mult(mult(A,B),mult(mult(C,A),B)). [para(25413(a,1),23384(a,2,1)),rewrite([17364(6),166(5),104(7),22108(4),20992(11)])]. 89.15/89.55 26198 mult(mult(A,B),mult(mult(C,B),A)) = mult(A,mult(B,mult(C,mult(B,A)))). [para(25413(a,1),25035(a,1,1)),rewrite([47(4),25608(4),47(8),80(10),80(8),44(11),170(10),26004(11),55(9)])]. 89.15/89.55 26210 mult(mult(mult(i(A),B),C),mult(i(A),mult(B,A))) = mult(i(A),mult(mult(B,mult(C,mult(i(A),B))),A)). [back_rewrite(20692),rewrite([26149(14)])]. 89.15/89.55 26298 mult(A,mult(B,mult(mult(C,i(B)),mult(B,A)))) = mult(mult(A,B),mult(C,A)). [para(55(a,1),26198(a,1,2,1)),flip(a)]. 89.15/89.55 26524 mult(i(A),mult(mult(A,B),mult(mult(B,A),C))) = mult(B,mult(B,mult(A,C))). [para(25712(a,1),210(a,1,2,2)),rewrite([19(5)]),flip(a)]. 89.15/89.55 26546 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,C)))) = mult(mult(B,i(A)),mult(A,C)). [para(289(a,2),25712(a,2)),rewrite([44(4),200(8)]),flip(a)]. 89.15/89.55 26623 mult(mult(A,i(B)),mult(B,mult(C,mult(i(A),B)))) = mult(A,mult(mult(C,i(A)),B)). [back_rewrite(23903),rewrite([26546(10)])]. 89.15/89.55 26819 mult(A,mult(mult(B,i(A)),mult(mult(mult(A,i(B)),C),B))) = mult(mult(A,C),B). [para(55(a,1),26017(a,1,2,2,2)),rewrite([80(5),44(4),55(12)])]. 89.15/89.55 27452 mult(mult(mult(i(A),i(B)),mult(B,mult(C,i(A)))),mult(A,A)) = mult(mult(i(A),i(B)),mult(B,mult(C,A))). [para(444(a,1),907(a,1,1)),rewrite([775(15)])]. 89.15/89.55 27475 mult(mult(A,i(B)),mult(B,mult(C,A))) = mult(A,mult(mult(C,B),mult(i(B),A))). [para(444(a,1),25413(a,2)),rewrite([44(7),22745(6),19(7)]),flip(a)]. 89.15/89.55 27484 mult(mult(i(A),i(B)),mult(B,mult(C,A))) = mult(i(A),mult(mult(C,i(B)),mult(B,A))). [back_rewrite(27452),rewrite([27475(7),990(9),25417(8)]),flip(a)]. 89.15/89.55 27605 mult(mult(A,B),mult(mult(B,A),C)) = mult(A,mult(B,mult(B,mult(A,C)))). [para(26524(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.15/89.55 27613 mult(A,mult(A,mult(B,mult(mult(i(B),i(A)),C)))) = mult(i(B),mult(mult(B,A),C)). [para(47(a,1),26524(a,1,2,2)),rewrite([80(6)]),flip(a)]. 89.15/89.55 27654 mult(A,mult(A,mult(mult(i(A),i(B)),mult(B,C)))) = mult(mult(A,B),mult(i(B),C)). [para(253(a,1),26524(a,1,2,2)),rewrite([80(4),44(2),44(2),55(5),16813(12)]),flip(a)]. 89.15/89.55 27656 mult(i(A),mult(i(A),mult(mult(A,i(B)),mult(B,C)))) = mult(mult(i(A),B),mult(i(B),C)). [para(297(a,1),26524(a,1,2,2)),rewrite([80(3),44(3),20(6),19554(14)]),flip(a)]. 89.15/89.55 28573 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(C,mult(B,A)),i(A))))) = mult(i(A),mult(mult(A,C),B)). [para(25401(a,1),461(a,2,2,1)),rewrite([47(8),20(16)])]. 89.15/89.55 28774 mult(i(A),mult(mult(A,i(B)),mult(B,C))) = mult(A,mult(mult(i(A),B),mult(i(B),C))). [para(24279(a,1),474(a,2,2,2)),rewrite([44(2),44(3),37(2),14(3),55(3),44(2),44(3),37(2),14(3),37(4),13(4),44(5),1282(8),1282(7),27656(8),44(8),44(9),37(8),14(9),37(10),13(10),44(11),49(11),13(11),1282(12)]),flip(a)]. 89.15/89.55 28782 mult(mult(A,i(B)),mult(B,mult(i(A),C))) = mult(A,mult(mult(i(A),B),mult(i(B),C))). [back_rewrite(1282),rewrite([28774(12)])]. 89.15/89.55 28980 mult(i(A),mult(mult(A,B),mult(i(B),C))) = mult(A,mult(mult(i(A),i(B)),mult(B,C))). [para(24279(a,1),480(a,2,2,2)),rewrite([49(3),14(4),55(4),49(4),14(5),44(6),49(6),13(6),44(6),750(8),750(7),27654(8),49(9),14(10),44(11),49(11),13(11),37(11),13(11),750(12)])]. 89.15/89.55 28981 mult(mult(mult(A,mult(B,C)),B),mult(i(B),i(C))) = mult(i(C),mult(mult(C,A),B)). [back_rewrite(28573),rewrite([28980(10),27475(9),47(10)])]. 89.15/89.55 29104 mult(A,mult(B,mult(i(A),mult(mult(A,C),B)))) = mult(mult(A,mult(B,C)),B). [para(23384(a,1),1021(a,2)),rewrite([26005(8),18133(9),28981(7)])]. 89.15/89.55 29147 mult(mult(A,i(B)),mult(B,mult(mult(A,C),B))) = mult(A,mult(B,mult(mult(i(B),A),mult(C,B)))). [para(29104(a,1),334(a,2,2)),rewrite([80(5),44(4),26819(10),21961(11)])]. 89.15/89.55 29833 mult(A,mult(mult(i(A),i(B)),mult(mult(C,B),A))) = mult(i(B),mult(C,mult(B,A))). [para(25031(a,1),750(a,1,2)),rewrite([25516(7),29147(13),47(14)]),flip(a)]. 89.15/89.55 29980 mult(A,mult(A,mult(mult(i(A),B),mult(i(B),C)))) = mult(mult(A,i(B)),mult(B,C)). [para(234(a,1),772(a,1,2,1)),rewrite([44(3),80(6),80(5),44(5),200(7),44(4),44(7),80(10),80(9),44(9),200(11),28782(10)]),flip(a)]. 89.15/89.55 30581 mult(mult(mult(i(A),B),i(C)),mult(C,A)) = mult(C,mult(mult(mult(i(C),i(A)),B),A)). [para(796(a,1),750(a,1,2)),rewrite([80(6),44(3),80(4),44(4),19(5),200(12),80(12),44(9),80(10),44(10),19(11),26210(16),22737(17),26623(15),165(13),19(14)])]. 89.15/89.55 31859 mult(i(A),mult(i(B),mult(mult(B,A),C))) = mult(A,mult(B,mult(mult(i(B),i(A)),C))). [para(3636(a,1),884(a,1,1)),rewrite([44(3),44(4),37(3),14(3),19(3),44(2),44(3),80(3),44(6),55(5),44(5),80(5),55(7),2481(8),28980(7),2748(8),44(8),44(9),80(9),44(12),55(11),2481(12)]),flip(a)]. 89.15/89.55 31862 mult(i(A),mult(B,mult(mult(i(B),A),C))) = mult(A,mult(i(B),mult(mult(B,i(A)),C))). [para(27605(a,1),884(a,1,2,2,2)),rewrite([80(4),44(3),55(7),170(5),55(4),80(6),44(5),19(6),19(10),47(8),2513(6),80(10),44(9),19(10)])]. 89.15/89.55 31878 mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,B)))) = mult(mult(C,A),mult(i(A),B)). [back_rewrite(24027),rewrite([31862(6),3332(7)])]. 89.15/89.59 32140 mult(A,mult(B,mult(i(A),mult(mult(A,C),mult(A,B))))) = mult(mult(A,B),mult(mult(C,A),B)). [para(29104(a,1),16882(a,1,2,2)),rewrite([24769(8),27484(9),166(6),104(8),22108(5),26191(8),47(7)]),flip(a)]. 89.15/89.59 32918 mult(mult(mult(mult(i(A),i(B)),C),B),A) = mult(mult(i(A),i(B)),mult(mult(C,B),A)). [para(21247(a,1),19(a,1,2)),rewrite([80(2)]),flip(a)]. 89.15/89.59 32947 mult(mult(mult(mult(A,B),C),i(B)),mult(B,C)) = mult(mult(A,mult(B,C)),C). [para(21247(a,1),23384(a,1,1,1)),rewrite([32918(12),29833(13),47(11)])]. 89.15/89.59 32999 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),mult(mult(B,A),C)) = mult(mult(mult(C,B),A),C). [para(118(a,1),32947(a,1,1,1)),rewrite([44(2),25333(6),166(3),104(5),25413(6),31859(9)]),flip(a)]. 89.15/89.59 33945 mult(A,mult(mult(i(A),mult(mult(A,B),C)),C)) = mult(mult(A,mult(B,C)),C). [para(22737(a,1),23384(a,1,1,1)),rewrite([30581(9),23009(7),47(10)])]. 89.15/89.59 33981 mult(i(A),mult(mult(A,B),mult(mult(C,A),B))) = mult(mult(mult(B,C),A),B). [para(118(a,1),33945(a,1,2,1,2)),rewrite([44(3),31859(12),32999(15)])]. 89.15/89.59 34102 mult(A,mult(i(B),mult(mult(B,C),mult(B,A)))) = mult(mult(mult(A,C),B),A). [back_rewrite(26166),rewrite([33981(6)]),flip(a)]. 89.15/89.59 34110 mult(mult(A,B),mult(mult(C,A),B)) = mult(A,mult(mult(mult(B,C),A),B)). [back_rewrite(32140),rewrite([34102(6)]),flip(a)]. 89.15/89.59 34141 mult(i(A),mult(mult(A,B),mult(C,A))) = mult(mult(B,C),A). [para(34110(a,1),19(a,1,2)),rewrite([80(2),27484(8),20(5)])]. 89.15/89.59 34233 mult(mult(A,B),mult(i(B),C)) = mult(B,mult(mult(i(B),A),C)). [back_rewrite(31878),rewrite([34141(6)]),flip(a)]. 89.15/89.59 34433 mult(mult(A,i(B)),mult(B,C)) = mult(i(B),mult(mult(B,A),C)). [back_rewrite(29980),rewrite([34233(5),27613(7)]),flip(a)]. 89.15/89.59 34546 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [back_rewrite(26298),rewrite([34433(4),47(5)]),flip(a)]. 89.15/89.59 34548 $F # answer(goals). [resolve(34546,a,29,a)]. 89.15/89.59 89.15/89.59 % SZS output end Refutation 89.15/89.59 ============================== end of proof ========================== 89.15/89.59 89.15/89.59 ============================== PROOF ================================= 89.15/89.59 % SZS status Theorem 89.15/89.59 % SZS output start Refutation 89.15/89.59 89.15/89.59 % Proof 3 at 87.64 (+ 0.93) seconds: goals. 89.15/89.59 % Length of proof is 264. 89.15/89.59 % Level of proof is 36. 89.15/89.59 % Maximum clause weight is 62.000. 89.15/89.59 % Given clauses 838. 89.15/89.59 89.15/89.59 1 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 2 (all D all C all B all A ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D))))) # label(f07) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 3 (all B all A B = mult(i(A),mult(A,B))) # label(f10) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 5 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 6 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 7 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 8 (all C all B all A mult(ld(A,mult(B,A)),ld(A,mult(C,A))) = ld(A,mult(mult(B,C),A))) # label(f09) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 9 (all D all C all B all A rd(mult(mult(mult(A,B),C),D),mult(C,D)) = mult(rd(mult(mult(A,C),D),mult(C,D)),rd(mult(mult(B,C),D),mult(C,D)))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 10 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 11 (all B all A A = mult(mult(A,B),i(B))) # label(f11) # label(axiom) # label(non_clause). [assumption]. 89.15/89.59 12 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 89.15/89.59 13 mult(A,unit) = A # label(f05) # label(axiom). [clausify(6)]. 89.15/89.59 14 mult(unit,A) = A # label(f06) # label(axiom). [clausify(7)]. 89.15/89.59 15 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(1)]. 89.15/89.59 17 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(5)]. 89.15/89.59 18 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(10)]. 89.15/89.59 19 mult(i(A),mult(A,B)) = B # label(f10) # label(axiom). [clausify(3)]. 89.15/89.59 20 mult(mult(A,B),i(B)) = A # label(f11) # label(axiom). [clausify(11)]. 89.15/89.59 21 ld(A,mult(mult(B,C),A)) = mult(ld(A,mult(B,A)),ld(A,mult(C,A))) # label(f09) # label(axiom). [clausify(8)]. 89.15/89.59 22 mult(ld(A,mult(B,A)),ld(A,mult(C,A))) = ld(A,mult(mult(B,C),A)). [copy(21),flip(a)]. 89.15/89.59 23 ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))) # label(f07) # label(axiom). [clausify(2)]. 89.15/89.59 24 mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))) = ld(mult(A,B),mult(A,mult(B,mult(C,D)))). [copy(23),flip(a)]. 89.15/89.59 25 rd(mult(mult(mult(A,B),C),D),mult(C,D)) = mult(rd(mult(mult(A,C),D),mult(C,D)),rd(mult(mult(B,C),D),mult(C,D))) # label(f08) # label(axiom). [clausify(9)]. 89.15/89.59 26 mult(rd(mult(mult(A,B),C),mult(B,C)),rd(mult(mult(D,B),C),mult(B,C))) = rd(mult(mult(mult(A,D),B),C),mult(B,C)). [copy(25),flip(a)]. 89.15/89.59 30 mult(mult(mult(c10,c12),c11),c12) != mult(c10,mult(c12,mult(c11,c12))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(12)]. 89.15/89.59 35 rd(A,ld(B,A)) = B. [para(17(a,1),15(a,1,1))]. 89.15/89.59 37 mult(i(A),A) = unit. [para(13(a,1),19(a,1,2))]. 89.15/89.59 39 rd(A,mult(B,A)) = i(B). [para(19(a,1),15(a,1,1))]. 89.15/89.59 41 ld(A,B) = mult(i(A),B). [para(17(a,1),19(a,1,2)),flip(a)]. 89.15/89.59 44 i(i(A)) = A. [back_rewrite(35),rewrite([41(1),39(3)])]. 89.15/89.59 45 mult(mult(i(mult(A,B)),mult(A,mult(B,C))),mult(i(mult(A,B)),mult(A,mult(B,D)))) = mult(i(mult(A,B)),mult(A,mult(B,mult(C,D)))). [back_rewrite(24),rewrite([41(4),41(9),41(16)])]. 89.15/89.59 46 mult(mult(i(A),mult(B,A)),mult(i(A),mult(C,A))) = mult(i(A),mult(mult(B,C),A)). [back_rewrite(22),rewrite([41(2),41(5),41(10)])]. 89.15/89.59 47 mult(A,mult(i(A),B)) = B. [back_rewrite(17),rewrite([41(1)])]. 89.15/89.59 49 mult(A,i(A)) = unit. [para(14(a,1),20(a,1,1))]. 89.15/89.59 51 rd(A,B) = mult(A,i(B)). [para(18(a,1),20(a,1,1)),flip(a)]. 89.15/89.59 52 mult(i(mult(A,B)),A) = i(B). [para(20(a,1),19(a,1,2))]. 89.15/89.59 54 mult(mult(mult(mult(A,B),C),i(mult(B,C))),mult(mult(mult(D,B),C),i(mult(B,C)))) = mult(mult(mult(mult(A,D),B),C),i(mult(B,C))). [back_rewrite(26),rewrite([51(4),51(9),51(16)])]. 89.15/89.59 55 mult(mult(A,i(B)),B) = A. [back_rewrite(18),rewrite([51(1)])]. 89.15/89.59 58 mult(mult(i(A),mult(i(B),mult(mult(B,A),C))),mult(i(A),mult(i(B),mult(mult(B,A),D)))) = mult(i(A),mult(i(B),mult(mult(B,A),mult(C,D)))). [para(19(a,1),45(a,1,1,1,1)),rewrite([19(9),19(16)])]. 89.15/89.59 63 mult(mult(i(A),mult(mult(A,B),mult(i(B),C))),mult(i(A),mult(mult(A,B),mult(i(B),D)))) = mult(i(A),mult(mult(A,B),mult(i(B),mult(C,D)))). [para(20(a,1),45(a,1,1,1,1)),rewrite([20(9),20(16)])]. 89.15/89.59 68 mult(mult(A,mult(i(mult(B,A)),mult(B,C))),A) = mult(A,mult(i(mult(B,A)),mult(B,mult(C,A)))). [para(37(a,1),45(a,1,2,2)),rewrite([52(3),44(2),52(8),44(7),13(7),52(9),44(8)])]. 89.15/89.59 70 mult(i(A),mult(i(mult(B,A)),mult(B,mult(A,C)))) = mult(i(mult(B,A)),mult(B,C)). [para(49(a,1),45(a,1,1,2,2)),rewrite([13(4),52(3),47(12)])]. 89.15/89.59 77 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),mult(i(A),mult(B,mult(mult(i(B),A),D)))) = mult(i(A),mult(B,mult(mult(i(B),A),mult(C,D)))). [para(47(a,1),45(a,1,1,1,1)),rewrite([47(9),47(16)])]. 89.15/89.59 78 mult(mult(i(mult(A,B)),mult(A,C)),mult(i(mult(A,B)),mult(A,mult(B,D)))) = mult(i(mult(A,B)),mult(A,mult(B,mult(mult(i(B),C),D)))). [para(47(a,1),45(a,1,1,2,2))]. 89.15/89.59 79 mult(mult(i(mult(A,B)),mult(A,mult(B,C))),mult(i(mult(A,B)),mult(A,D))) = mult(i(mult(A,B)),mult(A,mult(B,mult(C,mult(i(B),D))))). [para(47(a,1),45(a,1,2,2,2))]. 89.15/89.59 80 i(mult(A,B)) = mult(i(B),i(A)). [para(19(a,1),52(a,1,1,1)),flip(a)]. 89.15/89.59 81 mult(mult(mult(i(A),i(B)),mult(B,mult(A,C))),mult(mult(i(A),i(B)),mult(B,D))) = mult(mult(i(A),i(B)),mult(B,mult(A,mult(C,mult(i(A),D))))). [back_rewrite(79),rewrite([80(2),80(8),80(14)])]. 89.15/89.59 82 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(mult(i(A),i(B)),mult(B,mult(A,D)))) = mult(mult(i(A),i(B)),mult(B,mult(A,mult(mult(i(A),C),D)))). [back_rewrite(78),rewrite([80(2),80(7),80(14)])]. 89.15/89.59 87 mult(i(A),mult(mult(i(A),i(B)),mult(B,mult(A,C)))) = mult(mult(i(A),i(B)),mult(B,C)). [back_rewrite(70),rewrite([80(3),80(10)])]. 89.15/89.59 89 mult(mult(A,mult(mult(i(A),i(B)),mult(B,C))),A) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,A)))). [back_rewrite(68),rewrite([80(2),80(9)])]. 89.15/89.59 95 mult(mult(mult(mult(A,B),C),mult(i(C),i(B))),mult(mult(mult(D,B),C),mult(i(C),i(B)))) = mult(mult(mult(mult(A,D),B),C),mult(i(C),i(B))). [back_rewrite(54),rewrite([80(4),80(10),80(18)])]. 89.15/89.59 98 mult(i(A),mult(mult(A,B),A)) = mult(B,A). [para(19(a,1),46(a,1,1)),rewrite([47(4)]),flip(a)]. 89.15/89.59 99 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),mult(mult(i(A),i(B)),A)) = mult(mult(i(A),i(B)),mult(mult(C,i(B)),mult(B,A))). [para(19(a,1),46(a,1,2,2)),rewrite([80(2),80(8),80(13)])]. 89.15/89.59 103 mult(mult(A,B),mult(A,mult(C,i(A)))) = mult(A,mult(mult(mult(B,A),C),i(A))). [para(20(a,1),46(a,1,1,2)),rewrite([44(2),44(3),44(7)])]. 89.15/89.59 104 mult(mult(A,mult(B,i(A))),mult(A,C)) = mult(A,mult(mult(B,mult(C,A)),i(A))). [para(20(a,1),46(a,1,2,2)),rewrite([44(2),44(5),44(7)])]. 89.15/89.59 111 mult(mult(mult(i(A),B),mult(C,mult(i(B),A))),mult(mult(i(A),B),A)) = mult(mult(i(A),B),mult(mult(C,B),mult(i(B),A))). [para(47(a,1),46(a,1,2,2)),rewrite([80(3),44(3),80(9),44(9),80(13),44(13)])]. 89.24/89.59 113 mult(mult(i(A),B),mult(i(A),mult(C,A))) = mult(i(A),mult(mult(mult(B,i(A)),C),A)). [para(55(a,1),46(a,1,1,2))]. 89.24/89.59 114 mult(mult(i(A),mult(B,A)),mult(i(A),C)) = mult(i(A),mult(mult(B,mult(C,i(A))),A)). [para(55(a,1),46(a,1,2,2))]. 89.24/89.59 118 mult(mult(i(A),i(B)),mult(mult(B,A),C)) = C. [para(80(a,1),19(a,1,1))]. 89.24/89.59 119 mult(mult(A,mult(B,C)),mult(i(C),i(B))) = A. [para(80(a,1),20(a,1,2))]. 89.24/89.59 120 mult(mult(i(A),i(B)),mult(B,A)) = unit. [para(80(a,1),37(a,1,1))]. 89.24/89.59 121 mult(mult(A,B),mult(i(B),i(A))) = unit. [para(80(a,1),49(a,1,2))]. 89.24/89.59 122 mult(mult(A,B),mult(mult(i(B),i(A)),C)) = C. [para(80(a,1),47(a,1,2,1))]. 89.24/89.59 123 mult(mult(A,mult(i(B),i(C))),mult(C,B)) = A. [para(80(a,1),55(a,1,1,2))]. 89.24/89.59 132 mult(mult(mult(mult(i(A),mult(i(B),i(C))),C),B),mult(i(B),mult(i(C),mult(mult(C,B),mult(A,D))))) = mult(i(B),mult(i(C),mult(mult(C,B),D))). [para(58(a,1),19(a,1,2)),rewrite([80(7),80(5),80(3),80(3),44(7),44(8)])]. 89.24/89.59 134 mult(mult(A,mult(mult(i(A),i(B)),mult(B,C))),mult(A,mult(mult(i(A),i(B)),mult(B,D)))) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,D)))). [para(20(a,1),58(a,1,1,2,2,1)),rewrite([44(2),80(2),44(8),80(8),20(12),44(15),80(15),20(19)])]. 89.24/89.59 137 mult(mult(A,mult(i(B),mult(mult(B,i(A)),C))),mult(A,mult(i(B),mult(mult(B,i(A)),D)))) = mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,D)))). [para(44(a,1),58(a,1,1,1)),rewrite([44(8),44(15)])]. 89.24/89.59 138 mult(mult(i(A),i(B)),mult(i(A),mult(i(B),mult(mult(B,A),C)))) = mult(i(A),mult(i(B),C)). [para(49(a,1),58(a,1,1,2,2)),rewrite([13(4),80(15),122(18)])]. 89.24/89.59 141 mult(mult(i(A),mult(i(B),C)),mult(i(A),mult(i(B),mult(mult(B,A),D)))) = mult(i(A),mult(i(B),mult(mult(B,A),mult(mult(mult(i(A),i(B)),C),D)))). [para(47(a,1),58(a,1,1,2,2)),rewrite([80(16)])]. 89.24/89.59 165 mult(mult(A,B),A) = mult(A,mult(B,A)). [para(98(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.24/89.59 166 mult(mult(A,B),i(A)) = mult(A,mult(B,i(A))). [para(19(a,1),98(a,1,2,1)),rewrite([44(2)]),flip(a)]. 89.24/89.59 169 mult(mult(i(A),i(B)),mult(B,mult(B,A))) = mult(i(A),mult(B,A)). [para(20(a,1),98(a,1,2,1)),rewrite([80(2)])]. 89.24/89.59 170 mult(mult(i(A),B),A) = mult(i(A),mult(B,A)). [para(47(a,1),98(a,1,2,1)),flip(a)]. 89.24/89.59 176 mult(A,mult(mult(mult(i(A),i(B)),mult(B,C)),A)) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,A)))). [back_rewrite(89),rewrite([165(7)])]. 89.24/89.59 184 mult(mult(mult(i(A),B),mult(C,mult(i(B),A))),mult(i(A),mult(B,A))) = mult(mult(i(A),B),mult(mult(C,B),mult(i(B),A))). [back_rewrite(111),rewrite([170(9)])]. 89.24/89.59 186 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),mult(i(A),mult(i(B),A))) = mult(mult(i(A),i(B)),mult(mult(C,i(B)),mult(B,A))). [back_rewrite(99),rewrite([170(10)])]. 89.24/89.59 188 mult(mult(i(A),i(B)),mult(B,mult(A,B))) = B. [para(165(a,1),19(a,1,2)),rewrite([80(2)])]. 89.24/89.59 190 mult(mult(A,B),mult(i(B),mult(A,B))) = mult(A,mult(A,B)). [para(20(a,1),165(a,1,1)),flip(a)]. 89.24/89.59 200 mult(mult(i(A),B),mult(mult(i(B),A),C)) = C. [para(44(a,1),118(a,1,1,2))]. 89.24/89.59 206 mult(mult(mult(mult(i(A),B),mult(i(B),i(C))),C),mult(i(C),mult(mult(C,B),mult(i(B),mult(A,D))))) = mult(i(C),mult(mult(C,B),mult(i(B),D))). [para(63(a,1),19(a,1,2)),rewrite([80(7),80(5),80(3),44(3),80(4),44(8)])]. 89.24/89.59 208 mult(mult(i(A),mult(mult(A,B),C)),mult(i(A),mult(mult(A,B),mult(i(B),D)))) = mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),D)))). [para(19(a,1),63(a,1,1,2,2))]. 89.24/89.59 210 mult(A,mult(i(B),mult(mult(B,A),mult(i(A),C)))) = mult(i(B),mult(mult(B,A),C)). [para(19(a,1),63(a,2,2,2)),rewrite([37(4),13(4),19(3)])]. 89.24/89.59 227 mult(mult(i(A),B),mult(i(B),mult(mult(A,mult(mult(A,C),i(B))),B))) = mult(A,mult(mult(i(A),B),mult(i(B),mult(mult(A,mult(C,i(B))),B)))). [para(165(a,1),63(a,1,1,2)),rewrite([80(3),44(3),47(7),200(6),80(3),44(3),170(5),114(8),80(13),44(13),170(15),114(19)]),flip(a)]. 89.24/89.59 253 mult(mult(A,mult(i(B),i(A))),mult(mult(A,mult(B,i(A))),C)) = C. [para(166(a,1),118(a,1,2,1)),rewrite([44(2),80(2)])]. 89.24/89.59 279 mult(mult(A,mult(B,C)),mult(A,mult(B,mult(mult(i(B),i(A)),D)))) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(mult(mult(A,B),C),D)))). [para(118(a,1),77(a,1,1,2,2)),rewrite([44(2),44(4),44(11)])]. 89.24/89.59 280 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),mult(A,mult(B,D))) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,mult(mult(A,B),D))))). [para(118(a,1),77(a,1,2,2,2)),rewrite([44(2),44(8),44(11)])]. 89.24/89.59 289 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,C)))) = mult(B,mult(i(A),mult(B,mult(mult(i(B),A),C)))). [para(166(a,1),77(a,1,1,2,2)),rewrite([44(4),47(5),19(3),44(12)]),flip(a)]. 89.24/89.59 293 mult(mult(i(A),B),mult(i(B),mult(A,B))) = B. [para(170(a,1),19(a,1,2)),rewrite([80(3),44(3)])]. 89.24/89.59 303 mult(mult(i(A),mult(B,A)),mult(i(B),A)) = mult(mult(i(A),B),mult(A,mult(i(B),A))). [para(170(a,1),166(a,1,1)),rewrite([80(6),44(6),80(11),44(11)])]. 89.24/89.59 334 mult(mult(A,i(B)),mult(B,mult(A,C))) = mult(A,mult(mult(A,i(B)),mult(B,C))). [para(19(a,1),81(a,2,2,2)),rewrite([44(2),37(4),13(4),55(3),44(2),44(7),44(9)]),flip(a)]. 89.24/89.59 387 mult(A,mult(mult(i(A),i(B)),mult(B,mult(mult(A,B),mult(i(B),C))))) = mult(mult(A,B),mult(A,mult(mult(i(A),i(B)),C))). [para(188(a,1),81(a,1,1,2)),rewrite([80(5),44(3),44(3),19(3),80(6),44(4),44(4),19(4),80(12),44(10),44(10),19(10)]),flip(a)]. 89.24/89.59 428 mult(mult(i(A),B),mult(mult(A,B),mult(i(B),A))) = mult(i(A),mult(mult(B,A),A)). [para(293(a,1),165(a,2,2)),rewrite([303(6),184(10),170(11)])]. 89.24/89.59 439 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(mult(i(C),i(B)),mult(B,mult(C,mult(mult(i(C),A),D))))) = mult(mult(i(C),i(B)),mult(B,mult(C,D))). [para(82(a,1),19(a,1,2)),rewrite([80(6),80(2),80(7),44(5),44(5)])]. 89.24/89.59 444 mult(mult(mult(A,i(B)),mult(B,C)),A) = mult(mult(A,i(B)),mult(B,mult(C,A))). [para(37(a,1),82(a,1,2,2,2)),rewrite([44(2),44(6),13(8),55(7),44(7),44(10),165(10),19(11)])]. 89.24/89.59 461 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),i(A))))) = mult(i(A),mult(mult(mult(A,B),C),i(A))). [para(121(a,1),82(a,1,2,2)),rewrite([44(2),80(2),47(4),44(6),80(6),47(8),13(7),165(6),44(8),80(8),47(10),44(11)]),flip(a)]. 89.24/89.59 480 mult(mult(mult(i(A),mult(mult(B,C),i(D))),D),mult(mult(i(A),mult(mult(B,C),i(D))),mult(mult(D,mult(i(C),i(B))),mult(A,E)))) = mult(mult(i(A),mult(mult(B,C),i(D))),mult(mult(D,mult(i(C),i(B))),mult(A,mult(mult(i(A),mult(B,C)),E)))). [para(123(a,1),82(a,1,1,2)),rewrite([80(6),80(5),44(3),44(3),80(12),80(11),44(9),44(9),80(25),80(24),44(22),44(22)])]. 89.24/89.59 750 mult(mult(i(A),i(B)),mult(B,mult(A,C))) = mult(A,mult(mult(i(A),i(B)),mult(B,C))). [para(87(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.24/89.59 755 mult(mult(A,i(B)),mult(B,A)) = mult(A,A). [para(37(a,1),87(a,1,2,2,2)),rewrite([44(2),44(2),13(4),55(3),44(3)]),flip(a)]. 89.24/89.59 775 mult(mult(mult(i(A),i(B)),mult(B,C)),A) = mult(mult(i(A),i(B)),mult(B,mult(C,A))). [para(87(a,1),166(a,1,1)),rewrite([44(7),750(13),44(15),165(14),176(14),19(15)])]. 89.24/89.59 796 mult(mult(mult(i(A),B),i(C)),mult(C,mult(i(A),mult(B,A)))) = mult(mult(i(A),B),mult(mult(mult(i(A),B),i(C)),mult(C,A))). [para(293(a,1),87(a,1,2,2,2)),rewrite([80(3),44(3),80(5),44(5),80(12),44(12)]),flip(a)]. 89.24/89.59 884 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(C,mult(mult(i(C),i(B)),mult(B,mult(mult(i(C),A),D))))) = mult(C,mult(mult(i(C),i(B)),mult(B,D))). [back_rewrite(439),rewrite([750(14),750(21)])]. 89.24/89.59 907 mult(mult(A,i(B)),mult(B,B)) = mult(A,B). [para(755(a,1),19(a,1,2)),rewrite([80(3),44(2)])]. 89.24/89.59 908 mult(mult(A,mult(B,A)),B) = mult(mult(A,B),mult(A,B)). [para(19(a,1),755(a,1,2)),rewrite([44(3),165(2)])]. 89.24/89.59 910 mult(mult(A,B),mult(A,B)) = mult(A,mult(B,mult(A,B))). [para(20(a,1),755(a,1,1)),flip(a)]. 89.24/89.59 912 mult(mult(A,B),mult(i(B),A)) = mult(A,A). [para(44(a,1),755(a,1,1,2))]. 89.24/89.59 913 mult(mult(A,mult(A,i(B))),B) = mult(A,A). [para(55(a,1),755(a,1,2)),rewrite([80(3),44(2)])]. 89.24/89.59 917 mult(mult(A,B),mult(i(B),i(B))) = mult(A,i(B)). [para(755(a,1),122(a,1,2))]. 89.24/89.59 930 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [back_rewrite(908),rewrite([910(6)])]. 89.24/89.59 931 mult(mult(i(A),B),mult(A,A)) = mult(i(A),mult(mult(B,A),A)). [back_rewrite(428),rewrite([912(6)])]. 89.24/89.59 956 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),907(a,1,1)),flip(a)]. 89.24/89.59 990 mult(mult(i(A),B),mult(A,A)) = mult(i(A),mult(B,mult(A,A))). [back_rewrite(931),rewrite([956(7)])]. 89.24/89.59 1007 mult(mult(A,mult(B,B)),i(B)) = mult(A,B). [para(956(a,1),20(a,1,1))]. 89.24/89.59 1021 mult(mult(A,mult(B,mult(C,mult(B,C)))),mult(i(C),i(B))) = mult(A,mult(B,C)). [para(956(a,1),119(a,1,1)),rewrite([910(3)])]. 89.24/89.59 1183 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(913(a,1),55(a,1,1)),rewrite([44(4)])]. 89.24/89.59 1191 mult(mult(A,mult(A,B)),B) = mult(A,mult(A,mult(B,B))). [para(913(a,1),907(a,1,1)),rewrite([1183(3),44(5)]),flip(a)]. 89.24/89.59 1272 mult(mult(A,mult(A,mult(B,B))),i(B)) = mult(A,mult(A,B)). [para(1183(a,1),1007(a,1,1)),rewrite([1183(7)])]. 89.24/89.59 1461 mult(mult(A,mult(B,mult(A,B))),C) = mult(mult(A,B),mult(mult(A,B),C)). [para(910(a,1),1183(a,1,1))]. 89.24/89.59 1479 mult(mult(mult(mult(A,B),C),mult(i(C),i(B))),B) = mult(mult(mult(A,C),mult(i(C),i(B))),mult(B,B)). [para(49(a,1),95(a,1,2,1)),rewrite([80(3),80(7),80(9),44(7),44(7),20(8),80(9),80(11),44(9),44(9),20(10),14(8),956(7),80(11),80(15),80(17),44(15),44(15),20(16)]),flip(a)]. 89.24/89.59 1692 mult(mult(A,mult(B,A)),i(B)) = mult(mult(A,B),mult(A,i(B))). [para(930(a,1),917(a,1,1)),rewrite([1461(7),917(6)]),flip(a)]. 89.24/89.59 1820 mult(A,mult(mult(mult(B,A),mult(C,A)),i(A))) = mult(mult(A,B),mult(A,C)). [para(20(a,1),103(a,1,2,2)),flip(a)]. 89.24/89.59 1823 mult(mult(A,mult(i(B),i(A))),mult(i(C),i(A))) = mult(A,mult(mult(i(B),mult(i(A),i(C))),i(A))). [para(103(a,1),80(a,1,1)),rewrite([80(6),80(5),44(2),80(3),80(3),166(8),80(12),80(11),44(10),166(12),80(14)]),flip(a)]. 89.24/89.59 1914 mult(mult(i(A),B),mult(A,B)) = mult(i(A),mult(B,mult(A,B))). [para(19(a,1),1191(a,1,1,2)),rewrite([910(9),19(10)])]. 89.24/89.59 2046 mult(mult(i(A),i(B)),mult(B,mult(i(C),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),i(C)),i(B))). [para(104(a,1),80(a,1,1)),rewrite([80(6),80(5),44(2),80(3),80(2),166(8),80(10),80(15),80(14),44(13),166(15)]),flip(a)]. 89.24/89.59 2481 mult(mult(A,B),mult(i(B),mult(i(A),C))) = mult(i(B),mult(i(A),mult(mult(A,B),C))). [para(37(a,1),132(a,1,1,1,1)),rewrite([14(2),122(9)])]. 89.24/89.59 2748 mult(i(A),mult(B,mult(mult(i(B),i(A)),mult(A,C)))) = mult(B,mult(mult(i(B),i(A)),C)). [para(49(a,1),134(a,1,1,2,2)),rewrite([13(5),47(4),47(14)])]. 89.24/89.59 3229 mult(mult(i(A),mult(B,mult(A,B))),mult(i(B),i(A))) = mult(i(A),B). [para(19(a,1),1272(a,2,2)),rewrite([910(5),19(6),80(6)])]. 89.24/89.59 3231 mult(mult(A,mult(B,mult(i(A),B))),mult(i(B),A)) = mult(A,B). [para(47(a,1),1272(a,2,2)),rewrite([910(5),47(6),80(7),44(7)])]. 89.24/89.59 3234 mult(mult(mult(i(A),i(B)),mult(C,mult(mult(B,A),C))),mult(i(C),mult(i(A),i(B)))) = mult(mult(i(A),i(B)),C). [para(118(a,1),1272(a,2,2)),rewrite([910(11),118(12),80(10),80(10)])]. 89.24/89.59 3343 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),B) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,B)))). [para(170(a,1),137(a,1,2,2,2)),rewrite([44(2),44(8),47(11),47(9),44(9)])]. 89.24/89.59 3636 mult(mult(A,B),mult(A,mult(B,C))) = mult(A,mult(B,mult(mult(A,B),C))). [para(118(a,1),138(a,1,2,2,2)),rewrite([44(2),44(2),44(3),44(3),44(6),44(6)])]. 89.24/89.59 3653 mult(mult(A,i(B)),mult(A,B)) = mult(A,mult(i(B),mult(A,B))). [para(755(a,1),138(a,1,2,2,2)),rewrite([44(2),44(4),19(5),44(6)])]. 89.24/89.59 4077 mult(mult(A,mult(B,C)),mult(A,B)) = mult(A,mult(B,mult(C,mult(A,B)))). [para(120(a,1),141(a,1,2,2,2)),rewrite([44(2),44(2),44(4),44(4),13(4),44(6),44(6),44(9),44(9),165(11),118(12)])]. 89.24/89.59 7517 mult(mult(mult(i(A),i(B)),i(C)),mult(C,mult(C,mult(B,A)))) = mult(mult(i(A),i(B)),mult(C,mult(B,A))). [para(80(a,1),169(a,1,1,1)),rewrite([80(11)])]. 89.24/89.60 7532 mult(mult(i(A),i(B)),mult(A,mult(B,A))) = mult(i(A),mult(mult(i(B),mult(A,B)),A)). [para(169(a,1),103(a,2,2,1)),rewrite([44(8),165(7),165(6),19(8),44(12)])]. 89.24/89.60 7537 mult(mult(i(A),i(B)),mult(B,mult(mult(C,mult(A,B)),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),mult(C,mult(A,B))),i(B))). [para(104(a,1),169(a,1,2,2)),rewrite([80(2),80(7),80(6),44(5),166(7),2046(8),103(17),55(11),103(15),55(8),7517(9),80(11),104(17)]),flip(a)]. 89.24/89.60 7974 mult(mult(i(A),mult(B,A)),B) = mult(i(A),mult(B,mult(A,B))). [para(3231(a,1),169(a,1,2,2)),rewrite([80(3),44(3),80(7),80(6),80(5),44(5),165(6),1692(8),200(9),4077(9),1914(7),750(10),47(8),7532(6),47(7),80(7),44(7),3231(13),1914(8)])]. 89.24/89.60 8045 mult(mult(A,B),mult(B,A)) = mult(A,mult(B,mult(B,A))). [para(20(a,1),3653(a,1,2)),rewrite([44(3),956(2),165(3),1183(2),44(6),20(7)]),flip(a)]. 89.24/89.60 8411 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),C) = mult(mult(i(A),i(B)),mult(C,mult(mult(B,A),C))). [para(119(a,1),8045(a,1,2)),rewrite([119(18),165(13)])]. 89.24/89.60 10106 mult(mult(i(A),i(B)),mult(B,mult(mult(C,mult(mult(A,B),C)),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),mult(C,mult(mult(A,B),C))),i(B))). [para(103(a,1),7974(a,2,2,2)),rewrite([80(2),104(8),7537(9),103(13),55(9),8411(7),80(12),103(22),55(16)]),flip(a)]. 89.24/89.60 11706 mult(mult(i(A),i(B)),mult(mult(mult(mult(B,A),C),i(B)),mult(B,A))) = mult(mult(C,mult(B,A)),mult(i(A),mult(i(B),A))). [para(165(a,1),186(a,1,1,2)),rewrite([118(8)]),flip(a)]. 89.24/89.60 12180 mult(mult(mult(A,B),mult(i(B),i(C))),C) = mult(i(C),mult(mult(C,B),mult(i(B),A))). [para(37(a,1),206(a,1,2,2,2,2)),rewrite([44(2),13(11),20(10),37(8),13(8)])]. 89.24/89.60 12223 mult(mult(mult(A,B),mult(i(B),i(C))),mult(C,C)) = mult(i(C),mult(mult(C,B),mult(i(B),mult(A,C)))). [back_rewrite(1479),rewrite([12180(7)]),flip(a)]. 89.24/89.60 12433 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),mult(A,B))))) = mult(mult(i(A),mult(mult(A,B),C)),mult(A,B)). [para(190(a,1),208(a,1,2,2)),rewrite([19(8)]),flip(a)]. 89.24/89.60 12848 mult(i(A),mult(mult(i(B),i(A)),mult(A,mult(mult(B,mult(C,A)),i(A))))) = mult(mult(i(B),i(A)),mult(mult(A,mult(B,i(A))),C)). [para(166(a,1),210(a,1,2,2,1)),rewrite([80(3),44(9),104(9),80(13),166(17)])]. 89.24/89.60 12849 mult(A,mult(mult(i(B),A),mult(i(A),mult(mult(B,mult(C,i(A))),A)))) = mult(mult(i(B),A),mult(mult(i(A),mult(B,A)),C)). [para(170(a,1),210(a,1,2,2,1)),rewrite([80(3),44(3),114(8),80(13),44(13),170(15)])]. 89.24/89.60 16806 mult(mult(i(A),i(B)),mult(B,mult(C,i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),C),i(B))). [para(103(a,1),3229(a,1,1,2,2)),rewrite([80(2),103(12),55(6),10106(10),80(14),80(13),44(12),166(14),80(16),1823(18),103(19),55(10),3234(13),80(9)]),flip(a)]. 89.24/89.60 16813 mult(mult(i(A),i(B)),mult(mult(B,mult(A,i(B))),C)) = mult(mult(i(B),i(A)),mult(A,C)). [back_rewrite(12848),rewrite([16806(10),444(9),20(7),19(8)]),flip(a)]. 89.24/89.60 16882 mult(A,mult(mult(i(A),i(B)),mult(B,mult(mult(B,A),C)))) = mult(B,mult(A,C)). [para(3636(a,1),19(a,1,2)),rewrite([80(2),750(8)])]. 89.24/89.60 16898 mult(mult(A,mult(B,C)),mult(mult(i(C),i(B)),mult(A,D))) = mult(A,mult(mult(A,mult(B,C)),mult(mult(i(C),i(B)),D))). [para(119(a,1),3636(a,1,1)),rewrite([119(19)]),flip(a)]. 89.24/89.60 17253 mult(mult(mult(A,B),mult(i(B),C)),A) = mult(mult(A,B),mult(i(B),mult(C,A))). [para(20(a,1),4077(a,1,2)),rewrite([20(10)])]. 89.24/89.60 17254 mult(A,mult(B,mult(mult(i(B),C),mult(A,B)))) = mult(mult(A,C),mult(A,B)). [para(47(a,1),4077(a,1,1,2)),flip(a)]. 89.24/89.60 17364 mult(mult(A,B),mult(mult(C,mult(A,B)),i(B))) = mult(A,mult(B,mult(C,A))). [para(4077(a,1),210(a,2,2)),rewrite([80(6),16898(10),55(8),19(8),19(12)])]. 89.24/89.60 18133 mult(mult(A,mult(B,C)),mult(i(B),i(A))) = mult(A,mult(B,mult(C,mult(i(B),i(A))))). [para(166(a,1),279(a,2,2,2,2)),rewrite([80(7),910(9),47(10),47(8),80(12),118(16)])]. 89.24/89.60 19242 mult(mult(mult(A,B),mult(C,B)),i(B)) = mult(i(B),mult(mult(B,A),mult(B,C))). [para(1820(a,1),19(a,1,2)),flip(a)]. 89.24/89.60 19267 mult(i(A),mult(mult(mult(A,B),mult(A,C)),A)) = mult(mult(B,A),mult(C,A)). [para(1820(a,1),104(a,2,2,1)),rewrite([44(3),19(3),47(6),44(9)]),flip(a)]. 89.24/89.60 19320 mult(mult(mult(A,B),mult(A,C)),A) = mult(A,mult(mult(B,A),mult(C,A))). [para(1820(a,1),227(a,2,2,2,2,1)),rewrite([37(2),166(8),19242(7),47(8),165(7),19(8),14(6),37(6),19267(11),14(9)])]. 89.24/89.60 19460 mult(A,mult(mult(i(A),mult(B,A)),mult(C,A))) = mult(mult(B,mult(A,C)),A). [para(47(a,1),19320(a,1,1,1)),rewrite([170(6)]),flip(a)]. 89.24/89.60 19461 mult(A,mult(mult(B,A),mult(i(A),mult(C,A)))) = mult(mult(mult(A,B),C),A). [para(47(a,1),19320(a,1,1,2)),rewrite([170(7)]),flip(a)]. 89.24/89.60 19554 mult(mult(i(A),B),mult(mult(i(B),mult(A,B)),C)) = mult(mult(B,i(A)),mult(A,C)). [back_rewrite(12849),rewrite([19461(10),444(7),55(5)]),flip(a)]. 89.24/89.60 20675 mult(i(A),mult(mult(A,B),mult(A,C))) = mult(C,mult(mult(i(C),B),mult(A,C))). [para(17254(a,1),19(a,1,2))]. 89.24/89.60 20678 mult(mult(A,B),mult(i(B),mult(mult(B,C),A))) = mult(mult(mult(A,B),C),A). [para(20(a,1),17254(a,1,2,2,2)),rewrite([44(4),20(11)])]. 89.24/89.60 20692 mult(mult(mult(i(A),B),C),mult(i(A),mult(B,A))) = mult(mult(i(A),B),mult(mult(mult(C,i(A)),B),A)). [para(170(a,1),17254(a,1,2,2,2)),rewrite([113(8),47(9),170(13)]),flip(a)]. 89.24/89.60 20883 mult(mult(A,B),mult(i(B),mult(C,mult(A,B)))) = mult(A,mult(mult(C,A),B)). [para(20(a,1),17364(a,1,1)),rewrite([20(3),44(3)]),flip(a)]. 89.24/89.60 20892 mult(mult(A,B),mult(mult(mult(A,B),mult(C,mult(A,B))),i(B))) = mult(A,mult(B,mult(mult(mult(A,B),C),A))). [para(165(a,1),17364(a,1,2,1))]. 89.24/89.60 20992 mult(mult(mult(mult(A,B),C),A),B) = mult(mult(A,B),mult(mult(C,A),B)). [para(17364(a,1),227(a,2,2,2,2,1)),rewrite([80(2),170(4),20892(13),113(13),20(5),19(8),165(6),19(7),80(7),170(9),113(16),20(10),19(11),165(9),19(10)])]. 89.24/89.60 21042 mult(mult(i(A),mult(mult(A,B),C)),mult(A,B)) = mult(mult(mult(B,C),A),B). [back_rewrite(12433),rewrite([20883(8),19(6)]),flip(a)]. 89.24/89.60 21243 mult(mult(mult(A,B),i(C)),mult(C,A)) = mult(A,mult(mult(B,i(C)),mult(C,A))). [para(19(a,1),20992(a,1,1,1,1)),rewrite([19(8)])]. 89.24/89.60 21247 mult(mult(A,B),mult(mult(mult(mult(i(B),i(A)),C),A),B)) = mult(mult(C,A),B). [para(47(a,1),20992(a,1,1,1)),rewrite([80(5)]),flip(a)]. 89.24/89.60 21954 mult(mult(i(A),mult(B,A)),mult(C,A)) = mult(i(A),mult(mult(B,mult(A,C)),A)). [para(19460(a,1),19(a,1,2)),flip(a)]. 89.24/89.60 21961 mult(mult(mult(A,i(B)),mult(B,C)),B) = mult(B,mult(mult(i(B),A),mult(C,B))). [para(55(a,1),19460(a,1,2,1,2)),flip(a)]. 89.24/89.60 21962 mult(mult(A,mult(B,mult(C,i(B)))),B) = mult(B,mult(mult(i(B),mult(A,B)),C)). [para(55(a,1),19460(a,1,2,2)),flip(a)]. 89.24/89.60 22108 mult(mult(A,mult(B,C)),mult(A,C)) = mult(A,mult(mult(B,mult(C,A)),C)). [para(19460(a,1),4077(a,2,2)),rewrite([47(4)])]. 89.24/89.60 22737 mult(mult(A,B),mult(i(B),mult(C,B))) = mult(i(B),mult(mult(mult(B,A),C),B)). [para(19461(a,1),19(a,1,2)),flip(a)]. 89.24/89.60 22741 mult(mult(mult(i(A),B),mult(C,A)),i(A)) = mult(i(A),mult(mult(B,i(A)),mult(A,C))). [para(20(a,1),19461(a,1,2,2,2)),rewrite([44(5)]),flip(a)]. 89.24/89.60 22745 mult(mult(mult(A,B),mult(C,i(A))),A) = mult(A,mult(mult(B,A),mult(i(A),C))). [para(55(a,1),19461(a,1,2,2,2)),flip(a)]. 89.24/89.60 22879 mult(A,mult(B,mult(mult(i(B),i(A)),mult(mult(mult(B,A),C),B)))) = mult(B,mult(A,mult(C,B))). [para(19461(a,1),280(a,2,2,2,2)),rewrite([170(4),47(5),47(3),47(4)]),flip(a)]. 89.24/89.60 23009 mult(mult(i(A),i(B)),mult(mult(mult(B,A),C),B)) = mult(i(A),mult(mult(A,C),B)). [para(20678(a,1),19(a,1,2)),rewrite([80(2)])]. 89.24/89.60 23259 mult(i(A),mult(mult(A,B),mult(C,mult(A,B)))) = mult(B,mult(mult(C,A),B)). [para(20883(a,1),210(a,1,2,2)),rewrite([19(5)]),flip(a)]. 89.24/89.60 23280 mult(mult(A,B),mult(mult(i(B),C),mult(A,B))) = mult(mult(A,mult(C,A)),B). [para(20883(a,1),279(a,1,2)),rewrite([44(6),80(6),47(8),37(6),14(6),165(6),44(10),80(10),47(12),20(12),2481(15),23259(14),165(9),19(12)])]. 89.24/89.60 23384 mult(mult(mult(mult(A,B),C),i(A)),mult(A,B)) = mult(mult(A,mult(B,C)),B). [para(19(a,1),21042(a,1,1,2,1)),rewrite([44(2),19(5)]),flip(a)]. 89.24/89.60 23496 mult(mult(A,mult(B,C)),mult(i(C),mult(i(B),C))) = mult(mult(i(C),i(B)),mult(mult(B,mult(C,A)),C)). [back_rewrite(11706),rewrite([23384(9)]),flip(a)]. 89.24/89.60 23671 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))). [para(23259(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.24/89.60 23700 mult(mult(A,mult(B,mult(mult(C,A),B))),i(B)) = mult(A,mult(mult(B,C),A)). [para(104(a,1),23259(a,1,2,2)),rewrite([103(8),23671(5),19(9),165(10),55(9)])]. 89.24/89.60 23779 mult(A,mult(B,mult(mult(mult(i(B),C),A),B))) = mult(mult(A,mult(C,A)),B). [back_rewrite(23280),rewrite([23671(6)])]. 89.24/89.60 23903 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,mult(C,mult(i(B),A)))))) = mult(B,mult(mult(C,i(B)),A)). [para(23671(a,1),289(a,2,2,2,2)),rewrite([47(18),19(16)])]. 89.24/89.60 23932 mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,B)))) = mult(mult(C,i(A)),mult(A,B)). [para(47(a,1),23384(a,1,1,1)),rewrite([80(6),3343(11)]),flip(a)]. 89.24/89.60 23944 mult(mult(mult(mult(A,B),C),i(A)),mult(A,mult(B,mult(A,B)))) = mult(mult(mult(A,mult(B,C)),B),mult(A,B)). [para(23384(a,1),956(a,1,1)),rewrite([910(12)]),flip(a)]. 89.24/89.60 23949 mult(mult(i(A),mult(mult(A,B),C)),mult(B,A)) = mult(i(A),mult(mult(mult(A,mult(B,C)),B),A)). [para(23384(a,1),103(a,2,2,1)),rewrite([44(8),165(7),19(8),44(12)])]. 89.24/89.60 24005 mult(mult(A,mult(mult(B,C),A)),B) = mult(A,mult(B,mult(mult(C,A),B))). [para(20678(a,1),23384(a,1,1,1)),rewrite([20(5),165(4),23671(4),47(9)]),flip(a)]. 89.24/89.60 24015 mult(mult(mult(mult(A,B),C),i(B)),mult(B,A)) = mult(A,mult(B,mult(C,A))). [back_rewrite(22879),rewrite([23932(9)])]. 89.24/89.60 24031 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [para(19(a,1),24005(a,2,2,2,1)),rewrite([23671(6),55(3)])]. 89.24/89.60 24032 mult(mult(A,mult(B,A)),mult(B,C)) = mult(A,mult(mult(B,mult(A,B)),C)). [para(20(a,1),24005(a,1,1,2,1)),rewrite([23671(10),23779(10)])]. 89.24/89.60 24134 mult(mult(A,mult(B,i(C))),mult(C,B)) = mult(mult(A,i(C)),mult(C,mult(B,B))). [para(19(a,1),24031(a,2,2,2)),rewrite([166(4),19(5),956(9)])]. 89.24/89.60 24143 mult(mult(A,mult(B,mult(B,i(C)))),C) = mult(mult(A,i(C)),mult(C,mult(B,B))). [para(55(a,1),24031(a,2,2,2)),rewrite([23671(6),166(4),19(5),24134(10)])]. 89.24/89.60 24279 mult(A,mult(mult(B,mult(A,B)),mult(i(B),C))) = mult(mult(A,mult(B,A)),C). [para(47(a,1),24032(a,1,2)),flip(a)]. 89.24/89.60 24669 mult(i(A),mult(mult(mult(A,mult(B,C)),B),A)) = mult(B,mult(mult(C,B),A)). [para(20(a,1),24015(a,1,1,1,1)),rewrite([44(3),22737(6),20883(12)])]. 89.24/89.60 24697 mult(A,mult(mult(mult(mult(mult(B,A),C),i(A)),i(B)),mult(B,A))) = mult(A,mult(B,mult(A,C))). [para(103(a,1),24015(a,1,1,1)),rewrite([21243(9),165(13),55(12)])]. 89.24/89.60 24769 mult(mult(A,mult(mult(A,B),C)),mult(A,B)) = mult(A,mult(mult(A,mult(B,mult(C,A))),B)). [para(24015(a,1),22108(a,2,2,1)),rewrite([55(5)])]. 89.24/89.60 24782 mult(mult(i(A),mult(mult(A,B),C)),mult(B,A)) = mult(B,mult(mult(C,B),A)). [back_rewrite(23949),rewrite([24669(12)])]. 89.24/89.60 24944 mult(mult(mult(A,mult(B,C)),B),A) = mult(A,mult(B,mult(mult(C,B),A))). [para(24669(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.24/89.60 25031 mult(A,mult(B,mult(mult(i(B),mult(C,B)),A))) = mult(mult(mult(A,C),B),A). [para(47(a,1),24944(a,1,1,1,2)),rewrite([170(6)]),flip(a)]. 89.24/89.60 25333 mult(mult(A,B),mult(i(B),mult(C,A))) = mult(A,mult(mult(C,i(B)),mult(B,A))). [para(47(a,1),25031(a,1,2,2,1,2)),rewrite([80(5),44(5),170(5),19554(7),17253(10)]),flip(a)]. 89.24/89.60 25334 mult(mult(mult(A,mult(B,i(C))),C),A) = mult(A,mult(C,mult(mult(i(C),B),A))). [para(55(a,1),25031(a,1,2,2,1,2)),flip(a)]. 89.24/89.60 25401 mult(mult(A,B),mult(i(B),mult(C,mult(B,A)))) = mult(mult(mult(A,C),B),A). [para(25031(a,1),17364(a,2)),rewrite([21954(6),165(8),20(7)])]. 89.24/89.60 25404 mult(mult(A,B),mult(mult(C,mult(B,A)),i(A))) = mult(mult(A,mult(B,C)),B). [para(23384(a,1),25031(a,2)),rewrite([44(4),104(7),19(8)])]. 89.24/89.60 25413 mult(A,mult(B,mult(mult(C,mult(A,B)),i(B)))) = mult(mult(mult(A,B),C),A). [back_rewrite(20678),rewrite([25333(6),166(3),104(5)])]. 89.24/89.60 25414 mult(mult(mult(A,B),mult(i(B),C)),A) = mult(A,mult(mult(C,i(B)),mult(B,A))). [back_rewrite(17253),rewrite([25333(10)])]. 89.24/89.60 25417 mult(mult(mult(A,B),mult(i(B),i(C))),mult(C,C)) = mult(mult(A,i(B)),mult(B,C)). [back_rewrite(12223),rewrite([25333(13),19(14)])]. 89.24/89.60 25516 mult(mult(i(A),i(B)),mult(mult(mult(B,C),A),B)) = mult(i(A),mult(C,mult(A,B))). [para(25401(a,1),19(a,1,2)),rewrite([80(2)])]. 89.24/89.60 25524 mult(mult(mult(A,mult(B,mult(i(A),i(C)))),C),A) = mult(mult(A,C),mult(i(C),B)). [para(55(a,1),25401(a,1,2,2)),rewrite([80(6)]),flip(a)]. 89.24/89.60 25608 mult(mult(mult(mult(A,B),C),B),A) = mult(mult(A,B),mult(mult(C,B),A)). [para(24782(a,1),25401(a,1,2,2)),rewrite([19(6),47(9)]),flip(a)]. 89.24/89.60 25647 mult(mult(A,B),mult(C,mult(C,A))) = mult(A,mult(mult(B,mult(C,C)),A)). [para(913(a,1),25608(a,2,2,1)),rewrite([24143(6),20(3),165(4),1183(7)]),flip(a)]. 89.24/89.60 25707 mult(mult(A,mult(B,mult(i(A),i(C)))),C) = mult(mult(A,C),mult(i(C),mult(B,i(A)))). [para(17364(a,1),387(a,2,2,2)),rewrite([44(11),22737(12),47(13),23009(11),47(9),47(14)])]. 89.24/89.60 25711 mult(A,mult(mult(mult(B,i(A)),i(C)),mult(C,A))) = mult(mult(A,C),mult(i(C),B)). [back_rewrite(25524),rewrite([25707(6),25414(7)])]. 89.24/89.60 25712 mult(mult(A,B),mult(i(B),mult(mult(B,A),C))) = mult(A,mult(B,mult(A,C))). [back_rewrite(24697),rewrite([25711(9)])]. 89.24/89.60 25717 mult(mult(A,mult(B,mult(B,A))),C) = mult(A,mult(B,mult(B,mult(A,C)))). [para(20(a,1),25647(a,1,1)),rewrite([23671(11),23779(11),1183(6)]),flip(a)]. 89.24/89.60 25855 mult(i(A),mult(mult(B,A),mult(mult(B,A),mult(i(A),C)))) = mult(mult(i(A),mult(B,mult(A,B))),C). [para(20(a,1),25717(a,1,1,2,2)),rewrite([165(3)]),flip(a)]. 89.24/89.60 25925 mult(mult(i(A),i(B)),mult(mult(B,mult(A,C)),A)) = mult(mult(C,mult(A,B)),i(B)). [para(25404(a,1),19(a,1,2)),rewrite([80(2)])]. 89.24/89.60 25935 mult(mult(mult(A,mult(B,C)),B),mult(A,B)) = mult(A,mult(B,mult(mult(C,mult(B,A)),B))). [para(25404(a,1),165(a,1,1)),rewrite([23671(13),55(10)])]. 89.24/89.60 25997 mult(mult(A,mult(B,C)),mult(B,A)) = mult(A,mult(B,mult(C,mult(B,A)))). [para(25404(a,1),24015(a,1,1,1)),rewrite([20(5),55(9)])]. 89.24/89.60 26004 mult(mult(A,mult(B,C)),mult(i(C),mult(i(B),C))) = mult(mult(A,mult(C,B)),i(B)). [back_rewrite(23496),rewrite([25925(14)])]. 89.24/89.60 26005 mult(mult(mult(mult(A,B),C),i(A)),mult(A,mult(B,mult(A,B)))) = mult(A,mult(B,mult(mult(C,mult(B,A)),B))). [back_rewrite(23944),rewrite([25935(13)])]. 89.24/89.60 26017 mult(A,mult(B,mult(mult(i(B),C),mult(B,A)))) = mult(mult(A,C),mult(B,A)). [para(47(a,1),25997(a,1,1,2)),flip(a)]. 89.24/89.60 26118 mult(mult(mult(A,B),mult(mult(A,B),C)),A) = mult(A,mult(B,mult(A,mult(mult(B,C),A)))). [para(165(a,1),25413(a,1,2,2,1)),rewrite([23671(4),23700(6)]),flip(a)]. 89.24/89.60 26149 mult(mult(i(A),B),mult(mult(mult(C,i(A)),B),A)) = mult(i(A),mult(mult(B,mult(C,mult(i(A),B))),A)). [para(25413(a,1),114(a,1)),rewrite([165(5),20(4),20692(7),165(13),20(12),44(13),20(14)])]. 89.24/89.60 26166 mult(i(A),mult(mult(A,B),mult(mult(C,A),B))) = mult(B,mult(i(A),mult(mult(A,C),mult(A,B)))). [para(25413(a,1),210(a,1,2,2)),rewrite([20(4),20(11),44(11)]),flip(a)]. 89.24/89.60 26191 mult(A,mult(mult(B,mult(mult(C,mult(A,B)),A)),i(A))) = mult(mult(A,B),mult(mult(C,A),B)). [para(25413(a,1),23384(a,2,1)),rewrite([17364(6),166(5),104(7),22108(4),20992(11)])]. 89.24/89.60 26210 mult(mult(mult(i(A),B),C),mult(i(A),mult(B,A))) = mult(i(A),mult(mult(B,mult(C,mult(i(A),B))),A)). [back_rewrite(20692),rewrite([26149(14)])]. 89.24/89.60 26524 mult(i(A),mult(mult(A,B),mult(mult(B,A),C))) = mult(B,mult(B,mult(A,C))). [para(25712(a,1),210(a,1,2,2)),rewrite([19(5)]),flip(a)]. 89.24/89.60 26546 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,C)))) = mult(mult(B,i(A)),mult(A,C)). [para(289(a,2),25712(a,2)),rewrite([44(4),200(8)]),flip(a)]. 89.24/89.60 26623 mult(mult(A,i(B)),mult(B,mult(C,mult(i(A),B)))) = mult(A,mult(mult(C,i(A)),B)). [back_rewrite(23903),rewrite([26546(10)])]. 89.24/89.60 26814 mult(mult(A,B),mult(i(A),mult(mult(A,C),B))) = mult(mult(mult(A,B),C),B). [para(19(a,1),26017(a,1,2,2,2)),rewrite([44(4),19(11)])]. 89.24/89.60 26819 mult(A,mult(mult(B,i(A)),mult(mult(mult(A,i(B)),C),B))) = mult(mult(A,C),B). [para(55(a,1),26017(a,1,2,2,2)),rewrite([80(5),44(4),55(12)])]. 89.24/89.60 27452 mult(mult(mult(i(A),i(B)),mult(B,mult(C,i(A)))),mult(A,A)) = mult(mult(i(A),i(B)),mult(B,mult(C,A))). [para(444(a,1),907(a,1,1)),rewrite([775(15)])]. 89.24/89.60 27475 mult(mult(A,i(B)),mult(B,mult(C,A))) = mult(A,mult(mult(C,B),mult(i(B),A))). [para(444(a,1),25413(a,2)),rewrite([44(7),22745(6),19(7)]),flip(a)]. 89.24/89.60 27484 mult(mult(i(A),i(B)),mult(B,mult(C,A))) = mult(i(A),mult(mult(C,i(B)),mult(B,A))). [back_rewrite(27452),rewrite([27475(7),990(9),25417(8)]),flip(a)]. 89.24/89.60 27610 mult(mult(A,B),mult(mult(A,B),mult(i(B),C))) = mult(B,mult(mult(i(B),mult(A,B)),mult(A,C))). [para(20(a,1),26524(a,1,2,2,1)),rewrite([44(2)]),flip(a)]. 89.24/89.60 27654 mult(A,mult(A,mult(mult(i(A),i(B)),mult(B,C)))) = mult(mult(A,B),mult(i(B),C)). [para(253(a,1),26524(a,1,2,2)),rewrite([80(4),44(2),44(2),55(5),16813(12)]),flip(a)]. 89.24/89.60 27701 mult(mult(i(A),mult(B,mult(A,B))),C) = mult(mult(i(A),mult(B,A)),mult(B,C)). [back_rewrite(25855),rewrite([27610(7),19(8)]),flip(a)]. 89.24/89.60 28573 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(C,mult(B,A)),i(A))))) = mult(i(A),mult(mult(A,C),B)). [para(25401(a,1),461(a,2,2,1)),rewrite([47(8),20(16)])]. 89.24/89.60 28980 mult(i(A),mult(mult(A,B),mult(i(B),C))) = mult(A,mult(mult(i(A),i(B)),mult(B,C))). [para(24279(a,1),480(a,2,2,2)),rewrite([49(3),14(4),55(4),49(4),14(5),44(6),49(6),13(6),44(6),750(8),750(7),27654(8),49(9),14(10),44(11),49(11),13(11),37(11),13(11),750(12)])]. 89.24/89.60 28981 mult(mult(mult(A,mult(B,C)),B),mult(i(B),i(C))) = mult(i(C),mult(mult(C,A),B)). [back_rewrite(28573),rewrite([28980(10),27475(9),47(10)])]. 89.24/89.60 29104 mult(A,mult(B,mult(i(A),mult(mult(A,C),B)))) = mult(mult(A,mult(B,C)),B). [para(23384(a,1),1021(a,2)),rewrite([26005(8),18133(9),28981(7)])]. 89.24/89.60 29147 mult(mult(A,i(B)),mult(B,mult(mult(A,C),B))) = mult(A,mult(B,mult(mult(i(B),A),mult(C,B)))). [para(29104(a,1),334(a,2,2)),rewrite([80(5),44(4),26819(10),21961(11)])]. 89.24/89.60 29833 mult(A,mult(mult(i(A),i(B)),mult(mult(C,B),A))) = mult(i(B),mult(C,mult(B,A))). [para(25031(a,1),750(a,1,2)),rewrite([25516(7),29147(13),47(14)]),flip(a)]. 89.24/89.60 30581 mult(mult(mult(i(A),B),i(C)),mult(C,A)) = mult(C,mult(mult(mult(i(C),i(A)),B),A)). [para(796(a,1),750(a,1,2)),rewrite([80(6),44(3),80(4),44(4),19(5),200(12),80(12),44(9),80(10),44(10),19(11),26210(16),22737(17),26623(15),165(13),19(14)])]. 89.24/89.60 31859 mult(i(A),mult(i(B),mult(mult(B,A),C))) = mult(A,mult(B,mult(mult(i(B),i(A)),C))). [para(3636(a,1),884(a,1,1)),rewrite([44(3),44(4),37(3),14(3),19(3),44(2),44(3),80(3),44(6),55(5),44(5),80(5),55(7),2481(8),28980(7),2748(8),44(8),44(9),80(9),44(12),55(11),2481(12)]),flip(a)]. 89.24/89.60 32140 mult(A,mult(B,mult(i(A),mult(mult(A,C),mult(A,B))))) = mult(mult(A,B),mult(mult(C,A),B)). [para(29104(a,1),16882(a,1,2,2)),rewrite([24769(8),27484(9),166(6),104(8),22108(5),26191(8),47(7)]),flip(a)]. 89.24/89.60 32516 mult(mult(A,B),mult(mult(mult(i(B),i(A)),C),B)) = mult(A,mult(mult(i(A),C),B)). [para(19(a,1),20675(a,1,2,2)),rewrite([44(2),80(7),19(12)]),flip(a)]. 89.24/89.60 32918 mult(mult(mult(mult(i(A),i(B)),C),B),A) = mult(mult(i(A),i(B)),mult(mult(C,B),A)). [para(21247(a,1),19(a,1,2)),rewrite([80(2)]),flip(a)]. 89.24/89.60 32919 mult(A,mult(mult(mult(i(A),B),mult(A,C)),i(C))) = mult(mult(B,mult(A,C)),i(C)). [para(20(a,1),21247(a,1,1)),rewrite([44(2),80(2),47(4)])]. 89.24/89.60 32947 mult(mult(mult(mult(A,B),C),i(B)),mult(B,C)) = mult(mult(A,mult(B,C)),C). [para(21247(a,1),23384(a,1,1,1)),rewrite([32918(12),29833(13),47(11)])]. 89.24/89.60 32956 mult(A,mult(B,mult(mult(i(B),mult(i(A),C)),A))) = mult(B,mult(mult(i(B),C),A)). [para(26814(a,1),21247(a,1,2,1,1)),rewrite([55(8),32516(7),44(6),25334(11)]),flip(a)]. 89.24/89.60 32999 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),mult(mult(B,A),C)) = mult(mult(mult(C,B),A),C). [para(118(a,1),32947(a,1,1,1)),rewrite([44(2),25333(6),166(3),104(5),25413(6),31859(9)]),flip(a)]. 89.24/89.60 33562 mult(A,mult(mult(i(A),mult(B,A)),mult(mult(C,mult(A,B)),i(B)))) = mult(mult(mult(B,A),C),A). [para(25413(a,1),21962(a,2)),rewrite([47(4),80(6),80(4),44(7),170(6),26004(7),21962(9),47(13)])]. 89.24/89.60 33945 mult(A,mult(mult(i(A),mult(mult(A,B),C)),C)) = mult(mult(A,mult(B,C)),C). [para(22737(a,1),23384(a,1,1,1)),rewrite([30581(9),23009(7),47(10)])]. 89.24/89.60 33949 mult(mult(i(A),mult(B,A)),mult(B,mult(C,A))) = mult(i(A),mult(B,mult(A,mult(mult(B,C),A)))). [para(22737(a,1),25717(a,2,2,2)),rewrite([20(5),165(3),27701(6),22737(14),26118(13),19(14)])]. 89.24/89.60 33981 mult(i(A),mult(mult(A,B),mult(mult(C,A),B))) = mult(mult(mult(B,C),A),B). [para(118(a,1),33945(a,1,2,1,2)),rewrite([44(3),31859(12),32999(15)])]. 89.24/89.60 34102 mult(A,mult(i(B),mult(mult(B,C),mult(B,A)))) = mult(mult(mult(A,C),B),A). [back_rewrite(26166),rewrite([33981(6)]),flip(a)]. 89.24/89.60 34110 mult(mult(A,B),mult(mult(C,A),B)) = mult(A,mult(mult(mult(B,C),A),B)). [back_rewrite(32140),rewrite([34102(6)]),flip(a)]. 89.24/89.60 34145 mult(A,mult(mult(B,mult(A,C)),i(C))) = mult(A,mult(C,mult(mult(i(C),B),A))). [para(20(a,1),34110(a,1,1)),rewrite([22741(12),25401(13),25334(10)])]. 89.24/89.60 34242 mult(mult(A,mult(B,C)),i(C)) = mult(C,mult(mult(i(C),A),B)). [back_rewrite(32919),rewrite([34145(7),32956(7)]),flip(a)]. 89.47/89.85 34599 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [back_rewrite(33562),rewrite([34242(7),33949(8),47(4),47(6)]),flip(a)]. 89.47/89.85 34600 $F # answer(goals). [resolve(34599,a,30,a)]. 89.47/89.85 89.47/89.85 % SZS output end Refutation 89.47/89.85 ============================== end of proof ========================== 89.47/89.85 89.47/89.85 ============================== PROOF ================================= 89.47/89.85 % SZS status Theorem 89.47/89.85 % SZS output start Refutation 89.47/89.85 89.47/89.85 % Proof 4 at 87.90 (+ 0.93) seconds: goals. 89.47/89.85 % Length of proof is 330. 89.47/89.85 % Level of proof is 39. 89.47/89.85 % Maximum clause weight is 66.000. 89.47/89.85 % Given clauses 838. 89.47/89.85 89.47/89.85 1 (all B all A A = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 2 (all D all C all B all A ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D))))) # label(f07) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 3 (all B all A B = mult(i(A),mult(A,B))) # label(f10) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 5 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 6 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 7 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 8 (all C all B all A mult(ld(A,mult(B,A)),ld(A,mult(C,A))) = ld(A,mult(mult(B,C),A))) # label(f09) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 9 (all D all C all B all A rd(mult(mult(mult(A,B),C),D),mult(C,D)) = mult(rd(mult(mult(A,C),D),mult(C,D)),rd(mult(mult(B,C),D),mult(C,D)))) # label(f08) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 10 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 11 (all B all A A = mult(mult(A,B),i(B))) # label(f11) # label(axiom) # label(non_clause). [assumption]. 89.47/89.85 12 -((all X0 all X1 all X2 mult(mult(mult(X2,X0),X2),X1) = mult(X2,mult(X0,mult(X2,X1)))) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11))) | (all X3 all X4 all X5 mult(mult(mult(X3,X5),X4),X5) = mult(X3,mult(X5,mult(X4,X5))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 89.47/89.85 13 mult(A,unit) = A # label(f05) # label(axiom). [clausify(6)]. 89.47/89.85 14 mult(unit,A) = A # label(f06) # label(axiom). [clausify(7)]. 89.47/89.85 15 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(1)]. 89.47/89.85 17 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(5)]. 89.47/89.85 18 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(10)]. 89.47/89.85 19 mult(i(A),mult(A,B)) = B # label(f10) # label(axiom). [clausify(3)]. 89.47/89.85 20 mult(mult(A,B),i(B)) = A # label(f11) # label(axiom). [clausify(11)]. 89.47/89.85 21 ld(A,mult(mult(B,C),A)) = mult(ld(A,mult(B,A)),ld(A,mult(C,A))) # label(f09) # label(axiom). [clausify(8)]. 89.47/89.85 22 mult(ld(A,mult(B,A)),ld(A,mult(C,A))) = ld(A,mult(mult(B,C),A)). [copy(21),flip(a)]. 89.47/89.85 23 ld(mult(A,B),mult(A,mult(B,mult(C,D)))) = mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))) # label(f07) # label(axiom). [clausify(2)]. 89.47/89.85 24 mult(ld(mult(A,B),mult(A,mult(B,C))),ld(mult(A,B),mult(A,mult(B,D)))) = ld(mult(A,B),mult(A,mult(B,mult(C,D)))). [copy(23),flip(a)]. 89.47/89.85 25 rd(mult(mult(mult(A,B),C),D),mult(C,D)) = mult(rd(mult(mult(A,C),D),mult(C,D)),rd(mult(mult(B,C),D),mult(C,D))) # label(f08) # label(axiom). [clausify(9)]. 89.47/89.85 26 mult(rd(mult(mult(A,B),C),mult(B,C)),rd(mult(mult(D,B),C),mult(B,C))) = rd(mult(mult(mult(A,D),B),C),mult(B,C)). [copy(25),flip(a)]. 89.47/89.85 27 mult(mult(mult(c3,c1),c3),c2) != mult(c3,mult(c1,mult(c3,c2))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(12)]. 89.47/89.85 35 rd(A,ld(B,A)) = B. [para(17(a,1),15(a,1,1))]. 89.47/89.85 37 mult(i(A),A) = unit. [para(13(a,1),19(a,1,2))]. 89.47/89.85 39 rd(A,mult(B,A)) = i(B). [para(19(a,1),15(a,1,1))]. 89.47/89.85 41 ld(A,B) = mult(i(A),B). [para(17(a,1),19(a,1,2)),flip(a)]. 89.47/89.85 44 i(i(A)) = A. [back_rewrite(35),rewrite([41(1),39(3)])]. 89.47/89.85 45 mult(mult(i(mult(A,B)),mult(A,mult(B,C))),mult(i(mult(A,B)),mult(A,mult(B,D)))) = mult(i(mult(A,B)),mult(A,mult(B,mult(C,D)))). [back_rewrite(24),rewrite([41(4),41(9),41(16)])]. 89.47/89.85 46 mult(mult(i(A),mult(B,A)),mult(i(A),mult(C,A))) = mult(i(A),mult(mult(B,C),A)). [back_rewrite(22),rewrite([41(2),41(5),41(10)])]. 89.47/89.85 47 mult(A,mult(i(A),B)) = B. [back_rewrite(17),rewrite([41(1)])]. 89.47/89.85 49 mult(A,i(A)) = unit. [para(14(a,1),20(a,1,1))]. 89.47/89.85 51 rd(A,B) = mult(A,i(B)). [para(18(a,1),20(a,1,1)),flip(a)]. 89.47/89.85 52 mult(i(mult(A,B)),A) = i(B). [para(20(a,1),19(a,1,2))]. 89.47/89.85 54 mult(mult(mult(mult(A,B),C),i(mult(B,C))),mult(mult(mult(D,B),C),i(mult(B,C)))) = mult(mult(mult(mult(A,D),B),C),i(mult(B,C))). [back_rewrite(26),rewrite([51(4),51(9),51(16)])]. 89.47/89.85 55 mult(mult(A,i(B)),B) = A. [back_rewrite(18),rewrite([51(1)])]. 89.47/89.85 58 mult(mult(i(A),mult(i(B),mult(mult(B,A),C))),mult(i(A),mult(i(B),mult(mult(B,A),D)))) = mult(i(A),mult(i(B),mult(mult(B,A),mult(C,D)))). [para(19(a,1),45(a,1,1,1,1)),rewrite([19(9),19(16)])]. 89.47/89.85 61 mult(A,mult(i(mult(B,i(A))),mult(B,mult(i(A),C)))) = mult(i(mult(B,i(A))),mult(B,C)). [para(19(a,1),45(a,2,2,2)),rewrite([37(5),13(5),52(4),44(2)])]. 89.47/89.85 63 mult(mult(i(A),mult(mult(A,B),mult(i(B),C))),mult(i(A),mult(mult(A,B),mult(i(B),D)))) = mult(i(A),mult(mult(A,B),mult(i(B),mult(C,D)))). [para(20(a,1),45(a,1,1,1,1)),rewrite([20(9),20(16)])]. 89.47/89.85 68 mult(mult(A,mult(i(mult(B,A)),mult(B,C))),A) = mult(A,mult(i(mult(B,A)),mult(B,mult(C,A)))). [para(37(a,1),45(a,1,2,2)),rewrite([52(3),44(2),52(8),44(7),13(7),52(9),44(8)])]. 89.47/89.85 70 mult(i(A),mult(i(mult(B,A)),mult(B,mult(A,C)))) = mult(i(mult(B,A)),mult(B,C)). [para(49(a,1),45(a,1,1,2,2)),rewrite([13(4),52(3),47(12)])]. 89.47/89.85 77 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),mult(i(A),mult(B,mult(mult(i(B),A),D)))) = mult(i(A),mult(B,mult(mult(i(B),A),mult(C,D)))). [para(47(a,1),45(a,1,1,1,1)),rewrite([47(9),47(16)])]. 89.47/89.85 78 mult(mult(i(mult(A,B)),mult(A,C)),mult(i(mult(A,B)),mult(A,mult(B,D)))) = mult(i(mult(A,B)),mult(A,mult(B,mult(mult(i(B),C),D)))). [para(47(a,1),45(a,1,1,2,2))]. 89.47/89.85 79 mult(mult(i(mult(A,B)),mult(A,mult(B,C))),mult(i(mult(A,B)),mult(A,D))) = mult(i(mult(A,B)),mult(A,mult(B,mult(C,mult(i(B),D))))). [para(47(a,1),45(a,1,2,2,2))]. 89.47/89.85 80 i(mult(A,B)) = mult(i(B),i(A)). [para(19(a,1),52(a,1,1,1)),flip(a)]. 89.47/89.85 81 mult(mult(mult(i(A),i(B)),mult(B,mult(A,C))),mult(mult(i(A),i(B)),mult(B,D))) = mult(mult(i(A),i(B)),mult(B,mult(A,mult(C,mult(i(A),D))))). [back_rewrite(79),rewrite([80(2),80(8),80(14)])]. 89.47/89.85 82 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(mult(i(A),i(B)),mult(B,mult(A,D)))) = mult(mult(i(A),i(B)),mult(B,mult(A,mult(mult(i(A),C),D)))). [back_rewrite(78),rewrite([80(2),80(7),80(14)])]. 89.47/89.85 87 mult(i(A),mult(mult(i(A),i(B)),mult(B,mult(A,C)))) = mult(mult(i(A),i(B)),mult(B,C)). [back_rewrite(70),rewrite([80(3),80(10)])]. 89.47/89.85 89 mult(mult(A,mult(mult(i(A),i(B)),mult(B,C))),A) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,A)))). [back_rewrite(68),rewrite([80(2),80(9)])]. 89.47/89.85 93 mult(A,mult(mult(A,i(B)),mult(B,mult(i(A),C)))) = mult(mult(A,i(B)),mult(B,C)). [back_rewrite(61),rewrite([80(3),44(2),80(10),44(9)])]. 89.47/89.85 95 mult(mult(mult(mult(A,B),C),mult(i(C),i(B))),mult(mult(mult(D,B),C),mult(i(C),i(B)))) = mult(mult(mult(mult(A,D),B),C),mult(i(C),i(B))). [back_rewrite(54),rewrite([80(4),80(10),80(18)])]. 89.47/89.85 98 mult(i(A),mult(mult(A,B),A)) = mult(B,A). [para(19(a,1),46(a,1,1)),rewrite([47(4)]),flip(a)]. 89.47/89.85 99 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),mult(mult(i(A),i(B)),A)) = mult(mult(i(A),i(B)),mult(mult(C,i(B)),mult(B,A))). [para(19(a,1),46(a,1,2,2)),rewrite([80(2),80(8),80(13)])]. 89.47/89.85 103 mult(mult(A,B),mult(A,mult(C,i(A)))) = mult(A,mult(mult(mult(B,A),C),i(A))). [para(20(a,1),46(a,1,1,2)),rewrite([44(2),44(3),44(7)])]. 89.47/89.85 104 mult(mult(A,mult(B,i(A))),mult(A,C)) = mult(A,mult(mult(B,mult(C,A)),i(A))). [para(20(a,1),46(a,1,2,2)),rewrite([44(2),44(5),44(7)])]. 89.47/89.85 111 mult(mult(mult(i(A),B),mult(C,mult(i(B),A))),mult(mult(i(A),B),A)) = mult(mult(i(A),B),mult(mult(C,B),mult(i(B),A))). [para(47(a,1),46(a,1,2,2)),rewrite([80(3),44(3),80(9),44(9),80(13),44(13)])]. 89.47/89.85 113 mult(mult(i(A),B),mult(i(A),mult(C,A))) = mult(i(A),mult(mult(mult(B,i(A)),C),A)). [para(55(a,1),46(a,1,1,2))]. 89.47/89.85 114 mult(mult(i(A),mult(B,A)),mult(i(A),C)) = mult(i(A),mult(mult(B,mult(C,i(A))),A)). [para(55(a,1),46(a,1,2,2))]. 89.47/89.85 118 mult(mult(i(A),i(B)),mult(mult(B,A),C)) = C. [para(80(a,1),19(a,1,1))]. 89.47/89.85 119 mult(mult(A,mult(B,C)),mult(i(C),i(B))) = A. [para(80(a,1),20(a,1,2))]. 89.47/89.85 120 mult(mult(i(A),i(B)),mult(B,A)) = unit. [para(80(a,1),37(a,1,1))]. 89.47/89.85 121 mult(mult(A,B),mult(i(B),i(A))) = unit. [para(80(a,1),49(a,1,2))]. 89.47/89.85 122 mult(mult(A,B),mult(mult(i(B),i(A)),C)) = C. [para(80(a,1),47(a,1,2,1))]. 89.47/89.85 123 mult(mult(A,mult(i(B),i(C))),mult(C,B)) = A. [para(80(a,1),55(a,1,1,2))]. 89.47/89.85 125 mult(mult(i(A),B),mult(i(B),A)) = unit. [para(44(a,1),120(a,1,1,2))]. 89.47/89.85 132 mult(mult(mult(mult(i(A),mult(i(B),i(C))),C),B),mult(i(B),mult(i(C),mult(mult(C,B),mult(A,D))))) = mult(i(B),mult(i(C),mult(mult(C,B),D))). [para(58(a,1),19(a,1,2)),rewrite([80(7),80(5),80(3),80(3),44(7),44(8)])]. 89.47/89.85 134 mult(mult(A,mult(mult(i(A),i(B)),mult(B,C))),mult(A,mult(mult(i(A),i(B)),mult(B,D)))) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,D)))). [para(20(a,1),58(a,1,1,2,2,1)),rewrite([44(2),80(2),44(8),80(8),20(12),44(15),80(15),20(19)])]. 89.47/89.85 137 mult(mult(A,mult(i(B),mult(mult(B,i(A)),C))),mult(A,mult(i(B),mult(mult(B,i(A)),D)))) = mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,D)))). [para(44(a,1),58(a,1,1,1)),rewrite([44(8),44(15)])]. 89.47/89.85 138 mult(mult(i(A),i(B)),mult(i(A),mult(i(B),mult(mult(B,A),C)))) = mult(i(A),mult(i(B),C)). [para(49(a,1),58(a,1,1,2,2)),rewrite([13(4),80(15),122(18)])]. 89.47/89.85 141 mult(mult(i(A),mult(i(B),C)),mult(i(A),mult(i(B),mult(mult(B,A),D)))) = mult(i(A),mult(i(B),mult(mult(B,A),mult(mult(mult(i(A),i(B)),C),D)))). [para(47(a,1),58(a,1,1,2,2)),rewrite([80(16)])]. 89.47/89.85 165 mult(mult(A,B),A) = mult(A,mult(B,A)). [para(98(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.47/89.85 166 mult(mult(A,B),i(A)) = mult(A,mult(B,i(A))). [para(19(a,1),98(a,1,2,1)),rewrite([44(2)]),flip(a)]. 89.47/89.85 169 mult(mult(i(A),i(B)),mult(B,mult(B,A))) = mult(i(A),mult(B,A)). [para(20(a,1),98(a,1,2,1)),rewrite([80(2)])]. 89.47/89.85 170 mult(mult(i(A),B),A) = mult(i(A),mult(B,A)). [para(47(a,1),98(a,1,2,1)),flip(a)]. 89.47/89.85 176 mult(A,mult(mult(mult(i(A),i(B)),mult(B,C)),A)) = mult(A,mult(mult(i(A),i(B)),mult(B,mult(C,A)))). [back_rewrite(89),rewrite([165(7)])]. 89.47/89.85 178 mult(mult(c3,mult(c1,c3)),c2) != mult(c3,mult(c1,mult(c3,c2))) # answer(goals). [back_rewrite(27),rewrite([165(5)])]. 89.47/89.85 184 mult(mult(mult(i(A),B),mult(C,mult(i(B),A))),mult(i(A),mult(B,A))) = mult(mult(i(A),B),mult(mult(C,B),mult(i(B),A))). [back_rewrite(111),rewrite([170(9)])]. 89.47/89.85 186 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),mult(i(A),mult(i(B),A))) = mult(mult(i(A),i(B)),mult(mult(C,i(B)),mult(B,A))). [back_rewrite(99),rewrite([170(10)])]. 89.47/89.85 188 mult(mult(i(A),i(B)),mult(B,mult(A,B))) = B. [para(165(a,1),19(a,1,2)),rewrite([80(2)])]. 89.47/89.85 190 mult(mult(A,B),mult(i(B),mult(A,B))) = mult(A,mult(A,B)). [para(20(a,1),165(a,1,1)),flip(a)]. 89.47/89.85 200 mult(mult(i(A),B),mult(mult(i(B),A),C)) = C. [para(44(a,1),118(a,1,1,2))]. 89.47/89.85 206 mult(mult(mult(mult(i(A),B),mult(i(B),i(C))),C),mult(i(C),mult(mult(C,B),mult(i(B),mult(A,D))))) = mult(i(C),mult(mult(C,B),mult(i(B),D))). [para(63(a,1),19(a,1,2)),rewrite([80(7),80(5),80(3),44(3),80(4),44(8)])]. 89.47/89.85 208 mult(mult(i(A),mult(mult(A,B),C)),mult(i(A),mult(mult(A,B),mult(i(B),D)))) = mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),D)))). [para(19(a,1),63(a,1,1,2,2))]. 89.47/89.85 210 mult(A,mult(i(B),mult(mult(B,A),mult(i(A),C)))) = mult(i(B),mult(mult(B,A),C)). [para(19(a,1),63(a,2,2,2)),rewrite([37(4),13(4),19(3)])]. 89.47/89.85 226 mult(mult(mult(i(A),i(B)),mult(mult(B,mult(A,B)),mult(i(B),C))),mult(mult(i(A),i(B)),mult(mult(B,mult(A,B)),mult(i(B),D)))) = mult(mult(i(A),i(B)),mult(mult(B,mult(A,B)),mult(i(B),mult(C,D)))). [para(165(a,1),63(a,1,1,2,1)),rewrite([80(2),80(11),165(14),80(21),165(24)])]. 89.47/89.85 227 mult(mult(i(A),B),mult(i(B),mult(mult(A,mult(mult(A,C),i(B))),B))) = mult(A,mult(mult(i(A),B),mult(i(B),mult(mult(A,mult(C,i(B))),B)))). [para(165(a,1),63(a,1,1,2)),rewrite([80(3),44(3),47(7),200(6),80(3),44(3),170(5),114(8),80(13),44(13),170(15),114(19)]),flip(a)]. 89.47/89.85 234 mult(mult(A,mult(i(B),C)),mult(i(C),B)) = A. [para(44(a,1),119(a,1,2,2))]. 89.47/89.85 253 mult(mult(A,mult(i(B),i(A))),mult(mult(A,mult(B,i(A))),C)) = C. [para(166(a,1),118(a,1,2,1)),rewrite([44(2),80(2)])]. 89.47/89.86 256 mult(mult(A,mult(B,i(A))),mult(mult(A,mult(i(B),i(A))),C)) = C. [para(166(a,1),122(a,1,1)),rewrite([44(5),80(5)])]. 89.47/89.86 279 mult(mult(A,mult(B,C)),mult(A,mult(B,mult(mult(i(B),i(A)),D)))) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(mult(mult(A,B),C),D)))). [para(118(a,1),77(a,1,1,2,2)),rewrite([44(2),44(4),44(11)])]. 89.47/89.86 280 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),mult(A,mult(B,D))) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,mult(mult(A,B),D))))). [para(118(a,1),77(a,1,2,2,2)),rewrite([44(2),44(8),44(11)])]. 89.47/89.86 289 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,C)))) = mult(B,mult(i(A),mult(B,mult(mult(i(B),A),C)))). [para(166(a,1),77(a,1,1,2,2)),rewrite([44(4),47(5),19(3),44(12)]),flip(a)]. 89.47/89.86 290 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),B) = mult(i(A),mult(B,mult(mult(i(B),A),mult(C,B)))). [para(166(a,1),77(a,1,2,2,2)),rewrite([44(10),47(11),19(9),44(12)])]. 89.47/89.86 293 mult(mult(i(A),B),mult(i(B),mult(A,B))) = B. [para(170(a,1),19(a,1,2)),rewrite([80(3),44(3)])]. 89.47/89.86 297 mult(mult(i(A),mult(i(B),A)),mult(mult(i(A),mult(B,A)),C)) = C. [para(170(a,1),118(a,1,2,1)),rewrite([80(4),44(4)])]. 89.47/89.86 303 mult(mult(i(A),mult(B,A)),mult(i(B),A)) = mult(mult(i(A),B),mult(A,mult(i(B),A))). [para(170(a,1),166(a,1,1)),rewrite([80(6),44(6),80(11),44(11)])]. 89.47/89.86 334 mult(mult(A,i(B)),mult(B,mult(A,C))) = mult(A,mult(mult(A,i(B)),mult(B,C))). [para(19(a,1),81(a,2,2,2)),rewrite([44(2),37(4),13(4),55(3),44(2),44(7),44(9)]),flip(a)]. 89.47/89.86 387 mult(A,mult(mult(i(A),i(B)),mult(B,mult(mult(A,B),mult(i(B),C))))) = mult(mult(A,B),mult(A,mult(mult(i(A),i(B)),C))). [para(188(a,1),81(a,1,1,2)),rewrite([80(5),44(3),44(3),19(3),80(6),44(4),44(4),19(4),80(12),44(10),44(10),19(10)]),flip(a)]. 89.47/89.86 428 mult(mult(i(A),B),mult(mult(A,B),mult(i(B),A))) = mult(i(A),mult(mult(B,A),A)). [para(293(a,1),165(a,2,2)),rewrite([303(6),184(10),170(11)])]. 89.47/89.86 439 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(mult(i(C),i(B)),mult(B,mult(C,mult(mult(i(C),A),D))))) = mult(mult(i(C),i(B)),mult(B,mult(C,D))). [para(82(a,1),19(a,1,2)),rewrite([80(6),80(2),80(7),44(5),44(5)])]. 89.47/89.86 444 mult(mult(mult(A,i(B)),mult(B,C)),A) = mult(mult(A,i(B)),mult(B,mult(C,A))). [para(37(a,1),82(a,1,2,2,2)),rewrite([44(2),44(6),13(8),55(7),44(7),44(10),165(10),19(11)])]. 89.47/89.86 461 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),i(A))))) = mult(i(A),mult(mult(mult(A,B),C),i(A))). [para(121(a,1),82(a,1,2,2)),rewrite([44(2),80(2),47(4),44(6),80(6),47(8),13(7),165(6),44(8),80(8),47(10),44(11)]),flip(a)]. 89.47/89.86 474 mult(mult(mult(i(A),mult(mult(i(B),i(C)),i(D))),D),mult(mult(i(A),mult(mult(i(B),i(C)),i(D))),mult(mult(D,mult(C,B)),mult(A,E)))) = mult(mult(i(A),mult(mult(i(B),i(C)),i(D))),mult(mult(D,mult(C,B)),mult(A,mult(mult(i(A),mult(i(B),i(C))),E)))). [para(119(a,1),82(a,1,1,2)),rewrite([80(4),80(3),80(12),80(11),80(25),80(24)])]. 89.47/89.86 480 mult(mult(mult(i(A),mult(mult(B,C),i(D))),D),mult(mult(i(A),mult(mult(B,C),i(D))),mult(mult(D,mult(i(C),i(B))),mult(A,E)))) = mult(mult(i(A),mult(mult(B,C),i(D))),mult(mult(D,mult(i(C),i(B))),mult(A,mult(mult(i(A),mult(B,C)),E)))). [para(123(a,1),82(a,1,1,2)),rewrite([80(6),80(5),44(3),44(3),80(12),80(11),44(9),44(9),80(25),80(24),44(22),44(22)])]. 89.47/89.86 750 mult(mult(i(A),i(B)),mult(B,mult(A,C))) = mult(A,mult(mult(i(A),i(B)),mult(B,C))). [para(87(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.47/89.86 755 mult(mult(A,i(B)),mult(B,A)) = mult(A,A). [para(37(a,1),87(a,1,2,2,2)),rewrite([44(2),44(2),13(4),55(3),44(3)]),flip(a)]. 89.47/89.86 772 mult(mult(A,mult(mult(i(A),i(B)),i(C))),mult(mult(C,mult(B,A)),i(B))) = mult(A,mult(mult(A,mult(mult(i(A),i(B)),i(C))),C)). [para(119(a,1),87(a,1,2,2)),rewrite([44(2),44(2),80(3),80(2),44(10),80(11),80(10)]),flip(a)]. 89.47/89.86 775 mult(mult(mult(i(A),i(B)),mult(B,C)),A) = mult(mult(i(A),i(B)),mult(B,mult(C,A))). [para(87(a,1),166(a,1,1)),rewrite([44(7),750(13),44(15),165(14),176(14),19(15)])]. 89.47/89.86 796 mult(mult(mult(i(A),B),i(C)),mult(C,mult(i(A),mult(B,A)))) = mult(mult(i(A),B),mult(mult(mult(i(A),B),i(C)),mult(C,A))). [para(293(a,1),87(a,1,2,2,2)),rewrite([80(3),44(3),80(5),44(5),80(12),44(12)]),flip(a)]. 89.47/89.86 884 mult(mult(mult(i(A),i(B)),mult(B,C)),mult(C,mult(mult(i(C),i(B)),mult(B,mult(mult(i(C),A),D))))) = mult(C,mult(mult(i(C),i(B)),mult(B,D))). [back_rewrite(439),rewrite([750(14),750(21)])]. 89.47/89.86 907 mult(mult(A,i(B)),mult(B,B)) = mult(A,B). [para(755(a,1),19(a,1,2)),rewrite([80(3),44(2)])]. 89.47/89.86 908 mult(mult(A,mult(B,A)),B) = mult(mult(A,B),mult(A,B)). [para(19(a,1),755(a,1,2)),rewrite([44(3),165(2)])]. 89.47/89.86 910 mult(mult(A,B),mult(A,B)) = mult(A,mult(B,mult(A,B))). [para(20(a,1),755(a,1,1)),flip(a)]. 89.47/89.86 912 mult(mult(A,B),mult(i(B),A)) = mult(A,A). [para(44(a,1),755(a,1,1,2))]. 89.47/89.86 913 mult(mult(A,mult(A,i(B))),B) = mult(A,A). [para(55(a,1),755(a,1,2)),rewrite([80(3),44(2)])]. 89.47/89.86 917 mult(mult(A,B),mult(i(B),i(B))) = mult(A,i(B)). [para(755(a,1),122(a,1,2))]. 89.47/89.86 930 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [back_rewrite(908),rewrite([910(6)])]. 89.47/89.86 931 mult(mult(i(A),B),mult(A,A)) = mult(i(A),mult(mult(B,A),A)). [back_rewrite(428),rewrite([912(6)])]. 89.47/89.86 956 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),907(a,1,1)),flip(a)]. 89.47/89.86 990 mult(mult(i(A),B),mult(A,A)) = mult(i(A),mult(B,mult(A,A))). [back_rewrite(931),rewrite([956(7)])]. 89.47/89.86 1007 mult(mult(A,mult(B,B)),i(B)) = mult(A,B). [para(956(a,1),20(a,1,1))]. 89.47/89.86 1008 mult(mult(A,mult(i(B),i(B))),B) = mult(A,i(B)). [para(956(a,1),55(a,1,1))]. 89.47/89.86 1021 mult(mult(A,mult(B,mult(C,mult(B,C)))),mult(i(C),i(B))) = mult(A,mult(B,C)). [para(956(a,1),119(a,1,1)),rewrite([910(3)])]. 89.47/89.86 1183 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(913(a,1),55(a,1,1)),rewrite([44(4)])]. 89.47/89.86 1191 mult(mult(A,mult(A,B)),B) = mult(A,mult(A,mult(B,B))). [para(913(a,1),907(a,1,1)),rewrite([1183(3),44(5)]),flip(a)]. 89.47/89.86 1272 mult(mult(A,mult(A,mult(B,B))),i(B)) = mult(A,mult(A,B)). [para(1183(a,1),1007(a,1,1)),rewrite([1183(7)])]. 89.47/89.86 1282 mult(mult(A,i(B)),mult(B,mult(i(A),C))) = mult(i(A),mult(mult(A,i(B)),mult(B,C))). [para(93(a,1),19(a,1,2)),flip(a)]. 89.47/89.86 1461 mult(mult(A,mult(B,mult(A,B))),C) = mult(mult(A,B),mult(mult(A,B),C)). [para(910(a,1),1183(a,1,1))]. 89.47/89.86 1479 mult(mult(mult(mult(A,B),C),mult(i(C),i(B))),B) = mult(mult(mult(A,C),mult(i(C),i(B))),mult(B,B)). [para(49(a,1),95(a,1,2,1)),rewrite([80(3),80(7),80(9),44(7),44(7),20(8),80(9),80(11),44(9),44(9),20(10),14(8),956(7),80(11),80(15),80(17),44(15),44(15),20(16)]),flip(a)]. 89.47/89.86 1692 mult(mult(A,mult(B,A)),i(B)) = mult(mult(A,B),mult(A,i(B))). [para(930(a,1),917(a,1,1)),rewrite([1461(7),917(6)]),flip(a)]. 89.47/89.86 1820 mult(A,mult(mult(mult(B,A),mult(C,A)),i(A))) = mult(mult(A,B),mult(A,C)). [para(20(a,1),103(a,1,2,2)),flip(a)]. 89.47/89.86 1823 mult(mult(A,mult(i(B),i(A))),mult(i(C),i(A))) = mult(A,mult(mult(i(B),mult(i(A),i(C))),i(A))). [para(103(a,1),80(a,1,1)),rewrite([80(6),80(5),44(2),80(3),80(3),166(8),80(12),80(11),44(10),166(12),80(14)]),flip(a)]. 89.47/89.86 1914 mult(mult(i(A),B),mult(A,B)) = mult(i(A),mult(B,mult(A,B))). [para(19(a,1),1191(a,1,1,2)),rewrite([910(9),19(10)])]. 89.47/89.86 2046 mult(mult(i(A),i(B)),mult(B,mult(i(C),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),i(C)),i(B))). [para(104(a,1),80(a,1,1)),rewrite([80(6),80(5),44(2),80(3),80(2),166(8),80(10),80(15),80(14),44(13),166(15)]),flip(a)]. 89.47/89.86 2481 mult(mult(A,B),mult(i(B),mult(i(A),C))) = mult(i(B),mult(i(A),mult(mult(A,B),C))). [para(37(a,1),132(a,1,1,1,1)),rewrite([14(2),122(9)])]. 89.47/89.86 2513 mult(mult(i(A),B),mult(i(B),mult(A,C))) = mult(i(B),mult(A,mult(mult(i(A),B),C))). [para(200(a,1),132(a,1,2,2,2)),rewrite([80(3),44(3),44(5),125(5),14(3),44(5),44(9)])]. 89.47/89.86 2748 mult(i(A),mult(B,mult(mult(i(B),i(A)),mult(A,C)))) = mult(B,mult(mult(i(B),i(A)),C)). [para(49(a,1),134(a,1,1,2,2)),rewrite([13(5),47(4),47(14)])]. 89.47/89.86 3229 mult(mult(i(A),mult(B,mult(A,B))),mult(i(B),i(A))) = mult(i(A),B). [para(19(a,1),1272(a,2,2)),rewrite([910(5),19(6),80(6)])]. 89.47/89.86 3231 mult(mult(A,mult(B,mult(i(A),B))),mult(i(B),A)) = mult(A,B). [para(47(a,1),1272(a,2,2)),rewrite([910(5),47(6),80(7),44(7)])]. 89.47/89.86 3234 mult(mult(mult(i(A),i(B)),mult(C,mult(mult(B,A),C))),mult(i(C),mult(i(A),i(B)))) = mult(mult(i(A),i(B)),C). [para(118(a,1),1272(a,2,2)),rewrite([910(11),118(12),80(10),80(10)])]. 89.47/89.86 3332 mult(mult(A,mult(i(B),mult(mult(B,i(A)),C))),B) = mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,B)))). [para(165(a,1),137(a,1,2,2,2)),rewrite([19(11),47(9)])]. 89.47/89.86 3343 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),B) = mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,B)))). [para(170(a,1),137(a,1,2,2,2)),rewrite([44(2),44(8),47(11),47(9),44(9)])]. 89.47/89.86 3636 mult(mult(A,B),mult(A,mult(B,C))) = mult(A,mult(B,mult(mult(A,B),C))). [para(118(a,1),138(a,1,2,2,2)),rewrite([44(2),44(2),44(3),44(3),44(6),44(6)])]. 89.47/89.86 3653 mult(mult(A,i(B)),mult(A,B)) = mult(A,mult(i(B),mult(A,B))). [para(755(a,1),138(a,1,2,2,2)),rewrite([44(2),44(4),19(5),44(6)])]. 89.47/89.86 4077 mult(mult(A,mult(B,C)),mult(A,B)) = mult(A,mult(B,mult(C,mult(A,B)))). [para(120(a,1),141(a,1,2,2,2)),rewrite([44(2),44(2),44(4),44(4),13(4),44(6),44(6),44(9),44(9),165(11),118(12)])]. 89.47/89.86 7517 mult(mult(mult(i(A),i(B)),i(C)),mult(C,mult(C,mult(B,A)))) = mult(mult(i(A),i(B)),mult(C,mult(B,A))). [para(80(a,1),169(a,1,1,1)),rewrite([80(11)])]. 89.47/89.86 7532 mult(mult(i(A),i(B)),mult(A,mult(B,A))) = mult(i(A),mult(mult(i(B),mult(A,B)),A)). [para(169(a,1),103(a,2,2,1)),rewrite([44(8),165(7),165(6),19(8),44(12)])]. 89.47/89.86 7537 mult(mult(i(A),i(B)),mult(B,mult(mult(C,mult(A,B)),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),mult(C,mult(A,B))),i(B))). [para(104(a,1),169(a,1,2,2)),rewrite([80(2),80(7),80(6),44(5),166(7),2046(8),103(17),55(11),103(15),55(8),7517(9),80(11),104(17)]),flip(a)]. 89.47/89.86 7974 mult(mult(i(A),mult(B,A)),B) = mult(i(A),mult(B,mult(A,B))). [para(3231(a,1),169(a,1,2,2)),rewrite([80(3),44(3),80(7),80(6),80(5),44(5),165(6),1692(8),200(9),4077(9),1914(7),750(10),47(8),7532(6),47(7),80(7),44(7),3231(13),1914(8)])]. 89.47/89.86 8045 mult(mult(A,B),mult(B,A)) = mult(A,mult(B,mult(B,A))). [para(20(a,1),3653(a,1,2)),rewrite([44(3),956(2),165(3),1183(2),44(6),20(7)]),flip(a)]. 89.47/89.86 8411 mult(mult(mult(i(A),i(B)),mult(C,mult(B,A))),C) = mult(mult(i(A),i(B)),mult(C,mult(mult(B,A),C))). [para(119(a,1),8045(a,1,2)),rewrite([119(18),165(13)])]. 89.47/89.86 10106 mult(mult(i(A),i(B)),mult(B,mult(mult(C,mult(mult(A,B),C)),i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),mult(C,mult(mult(A,B),C))),i(B))). [para(103(a,1),7974(a,2,2,2)),rewrite([80(2),104(8),7537(9),103(13),55(9),8411(7),80(12),103(22),55(16)]),flip(a)]. 89.47/89.86 10872 mult(mult(i(A),B),mult(mult(mult(mult(i(B),A),C),B),mult(i(B),A))) = mult(mult(C,mult(i(B),A)),mult(i(A),mult(B,A))). [para(165(a,1),184(a,1,1,2)),rewrite([200(9)]),flip(a)]. 89.47/89.86 11706 mult(mult(i(A),i(B)),mult(mult(mult(mult(B,A),C),i(B)),mult(B,A))) = mult(mult(C,mult(B,A)),mult(i(A),mult(i(B),A))). [para(165(a,1),186(a,1,1,2)),rewrite([118(8)]),flip(a)]. 89.47/89.86 12180 mult(mult(mult(A,B),mult(i(B),i(C))),C) = mult(i(C),mult(mult(C,B),mult(i(B),A))). [para(37(a,1),206(a,1,2,2,2,2)),rewrite([44(2),13(11),20(10),37(8),13(8)])]. 89.47/89.86 12223 mult(mult(mult(A,B),mult(i(B),i(C))),mult(C,C)) = mult(i(C),mult(mult(C,B),mult(i(B),mult(A,C)))). [back_rewrite(1479),rewrite([12180(7)]),flip(a)]. 89.47/89.86 12406 mult(mult(i(A),mult(mult(A,B),C)),B) = mult(i(A),mult(mult(A,B),mult(C,B))). [para(37(a,1),208(a,1,2,2,2)),rewrite([13(8),19(7),165(10),19(11)])]. 89.47/89.86 12433 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(B,C),mult(A,B))))) = mult(mult(i(A),mult(mult(A,B),C)),mult(A,B)). [para(190(a,1),208(a,1,2,2)),rewrite([19(8)]),flip(a)]. 89.47/89.86 12848 mult(i(A),mult(mult(i(B),i(A)),mult(A,mult(mult(B,mult(C,A)),i(A))))) = mult(mult(i(B),i(A)),mult(mult(A,mult(B,i(A))),C)). [para(166(a,1),210(a,1,2,2,1)),rewrite([80(3),44(9),104(9),80(13),166(17)])]. 89.47/89.86 12849 mult(A,mult(mult(i(B),A),mult(i(A),mult(mult(B,mult(C,i(A))),A)))) = mult(mult(i(B),A),mult(mult(i(A),mult(B,A)),C)). [para(170(a,1),210(a,1,2,2,1)),rewrite([80(3),44(3),114(8),80(13),44(13),170(15)])]. 89.47/89.86 16806 mult(mult(i(A),i(B)),mult(B,mult(C,i(B)))) = mult(B,mult(mult(mult(i(B),i(A)),C),i(B))). [para(103(a,1),3229(a,1,1,2,2)),rewrite([80(2),103(12),55(6),10106(10),80(14),80(13),44(12),166(14),80(16),1823(18),103(19),55(10),3234(13),80(9)]),flip(a)]. 89.47/89.86 16813 mult(mult(i(A),i(B)),mult(mult(B,mult(A,i(B))),C)) = mult(mult(i(B),i(A)),mult(A,C)). [back_rewrite(12848),rewrite([16806(10),444(9),20(7),19(8)]),flip(a)]. 89.47/89.86 16882 mult(A,mult(mult(i(A),i(B)),mult(B,mult(mult(B,A),C)))) = mult(B,mult(A,C)). [para(3636(a,1),19(a,1,2)),rewrite([80(2),750(8)])]. 89.47/89.86 16898 mult(mult(A,mult(B,C)),mult(mult(i(C),i(B)),mult(A,D))) = mult(A,mult(mult(A,mult(B,C)),mult(mult(i(C),i(B)),D))). [para(119(a,1),3636(a,1,1)),rewrite([119(19)]),flip(a)]. 89.47/89.86 17253 mult(mult(mult(A,B),mult(i(B),C)),A) = mult(mult(A,B),mult(i(B),mult(C,A))). [para(20(a,1),4077(a,1,2)),rewrite([20(10)])]. 89.47/89.86 17254 mult(A,mult(B,mult(mult(i(B),C),mult(A,B)))) = mult(mult(A,C),mult(A,B)). [para(47(a,1),4077(a,1,1,2)),flip(a)]. 89.47/89.86 17364 mult(mult(A,B),mult(mult(C,mult(A,B)),i(B))) = mult(A,mult(B,mult(C,A))). [para(4077(a,1),210(a,2,2)),rewrite([80(6),16898(10),55(8),19(8),19(12)])]. 89.47/89.86 18133 mult(mult(A,mult(B,C)),mult(i(B),i(A))) = mult(A,mult(B,mult(C,mult(i(B),i(A))))). [para(166(a,1),279(a,2,2,2,2)),rewrite([80(7),910(9),47(10),47(8),80(12),118(16)])]. 89.47/89.86 19242 mult(mult(mult(A,B),mult(C,B)),i(B)) = mult(i(B),mult(mult(B,A),mult(B,C))). [para(1820(a,1),19(a,1,2)),flip(a)]. 89.47/89.86 19267 mult(i(A),mult(mult(mult(A,B),mult(A,C)),A)) = mult(mult(B,A),mult(C,A)). [para(1820(a,1),104(a,2,2,1)),rewrite([44(3),19(3),47(6),44(9)]),flip(a)]. 89.47/89.86 19320 mult(mult(mult(A,B),mult(A,C)),A) = mult(A,mult(mult(B,A),mult(C,A))). [para(1820(a,1),227(a,2,2,2,2,1)),rewrite([37(2),166(8),19242(7),47(8),165(7),19(8),14(6),37(6),19267(11),14(9)])]. 89.47/89.86 19460 mult(A,mult(mult(i(A),mult(B,A)),mult(C,A))) = mult(mult(B,mult(A,C)),A). [para(47(a,1),19320(a,1,1,1)),rewrite([170(6)]),flip(a)]. 89.47/89.86 19461 mult(A,mult(mult(B,A),mult(i(A),mult(C,A)))) = mult(mult(mult(A,B),C),A). [para(47(a,1),19320(a,1,1,2)),rewrite([170(7)]),flip(a)]. 89.47/89.86 19554 mult(mult(i(A),B),mult(mult(i(B),mult(A,B)),C)) = mult(mult(B,i(A)),mult(A,C)). [back_rewrite(12849),rewrite([19461(10),444(7),55(5)]),flip(a)]. 89.47/89.86 20675 mult(i(A),mult(mult(A,B),mult(A,C))) = mult(C,mult(mult(i(C),B),mult(A,C))). [para(17254(a,1),19(a,1,2))]. 89.47/89.86 20678 mult(mult(A,B),mult(i(B),mult(mult(B,C),A))) = mult(mult(mult(A,B),C),A). [para(20(a,1),17254(a,1,2,2,2)),rewrite([44(4),20(11)])]. 89.47/89.86 20692 mult(mult(mult(i(A),B),C),mult(i(A),mult(B,A))) = mult(mult(i(A),B),mult(mult(mult(C,i(A)),B),A)). [para(170(a,1),17254(a,1,2,2,2)),rewrite([113(8),47(9),170(13)]),flip(a)]. 89.47/89.86 20883 mult(mult(A,B),mult(i(B),mult(C,mult(A,B)))) = mult(A,mult(mult(C,A),B)). [para(20(a,1),17364(a,1,1)),rewrite([20(3),44(3)]),flip(a)]. 89.47/89.86 20885 mult(A,mult(mult(i(A),B),mult(C,A))) = mult(B,mult(mult(C,B),mult(i(B),A))). [para(47(a,1),17364(a,1,1)),rewrite([47(3),80(4),44(4)]),flip(a)]. 89.47/89.86 20892 mult(mult(A,B),mult(mult(mult(A,B),mult(C,mult(A,B))),i(B))) = mult(A,mult(B,mult(mult(mult(A,B),C),A))). [para(165(a,1),17364(a,1,2,1))]. 89.47/89.86 20992 mult(mult(mult(mult(A,B),C),A),B) = mult(mult(A,B),mult(mult(C,A),B)). [para(17364(a,1),227(a,2,2,2,2,1)),rewrite([80(2),170(4),20892(13),113(13),20(5),19(8),165(6),19(7),80(7),170(9),113(16),20(10),19(11),165(9),19(10)])]. 89.47/89.86 21042 mult(mult(i(A),mult(mult(A,B),C)),mult(A,B)) = mult(mult(mult(B,C),A),B). [back_rewrite(12433),rewrite([20883(8),19(6)]),flip(a)]. 89.47/89.86 21243 mult(mult(mult(A,B),i(C)),mult(C,A)) = mult(A,mult(mult(B,i(C)),mult(C,A))). [para(19(a,1),20992(a,1,1,1,1)),rewrite([19(8)])]. 89.47/89.86 21245 mult(mult(mult(A,B),mult(A,C)),i(C)) = mult(A,mult(mult(B,mult(A,C)),i(C))). [para(20(a,1),20992(a,1,1,1,1)),rewrite([20(8)])]. 89.47/89.86 21247 mult(mult(A,B),mult(mult(mult(mult(i(B),i(A)),C),A),B)) = mult(mult(C,A),B). [para(47(a,1),20992(a,1,1,1)),rewrite([80(5)]),flip(a)]. 89.47/89.86 21954 mult(mult(i(A),mult(B,A)),mult(C,A)) = mult(i(A),mult(mult(B,mult(A,C)),A)). [para(19460(a,1),19(a,1,2)),flip(a)]. 89.47/89.86 21961 mult(mult(mult(A,i(B)),mult(B,C)),B) = mult(B,mult(mult(i(B),A),mult(C,B))). [para(55(a,1),19460(a,1,2,1,2)),flip(a)]. 89.47/89.86 21962 mult(mult(A,mult(B,mult(C,i(B)))),B) = mult(B,mult(mult(i(B),mult(A,B)),C)). [para(55(a,1),19460(a,1,2,2)),flip(a)]. 89.47/89.86 22108 mult(mult(A,mult(B,C)),mult(A,C)) = mult(A,mult(mult(B,mult(C,A)),C)). [para(19460(a,1),4077(a,2,2)),rewrite([47(4)])]. 89.47/89.86 22200 mult(mult(A,mult(mult(B,mult(C,A)),C)),mult(i(C),i(A))) = mult(A,mult(B,C)). [para(22108(a,1),20(a,1,1)),rewrite([80(6)])]. 89.47/89.86 22737 mult(mult(A,B),mult(i(B),mult(C,B))) = mult(i(B),mult(mult(mult(B,A),C),B)). [para(19461(a,1),19(a,1,2)),flip(a)]. 89.47/89.86 22741 mult(mult(mult(i(A),B),mult(C,A)),i(A)) = mult(i(A),mult(mult(B,i(A)),mult(A,C))). [para(20(a,1),19461(a,1,2,2,2)),rewrite([44(5)]),flip(a)]. 89.47/89.86 22743 mult(mult(A,i(B)),mult(B,mult(C,i(B)))) = mult(B,mult(mult(mult(i(B),A),C),i(B))). [para(19461(a,1),47(a,1,2)),rewrite([44(10)]),flip(a)]. 89.47/89.86 22744 mult(mult(mult(A,mult(B,i(A))),C),A) = mult(A,mult(B,mult(i(A),mult(C,A)))). [para(55(a,1),19461(a,1,2,1)),flip(a)]. 89.47/89.86 22745 mult(mult(mult(A,B),mult(C,i(A))),A) = mult(A,mult(mult(B,A),mult(i(A),C))). [para(55(a,1),19461(a,1,2,2,2)),flip(a)]. 89.47/89.86 22879 mult(A,mult(B,mult(mult(i(B),i(A)),mult(mult(mult(B,A),C),B)))) = mult(B,mult(A,mult(C,B))). [para(19461(a,1),280(a,2,2,2,2)),rewrite([170(4),47(5),47(3),47(4)]),flip(a)]. 89.47/89.86 23009 mult(mult(i(A),i(B)),mult(mult(mult(B,A),C),B)) = mult(i(A),mult(mult(A,C),B)). [para(20678(a,1),19(a,1,2)),rewrite([80(2)])]. 89.47/89.86 23259 mult(i(A),mult(mult(A,B),mult(C,mult(A,B)))) = mult(B,mult(mult(C,A),B)). [para(20883(a,1),210(a,1,2,2)),rewrite([19(5)]),flip(a)]. 89.47/89.86 23280 mult(mult(A,B),mult(mult(i(B),C),mult(A,B))) = mult(mult(A,mult(C,A)),B). [para(20883(a,1),279(a,1,2)),rewrite([44(6),80(6),47(8),37(6),14(6),165(6),44(10),80(10),47(12),20(12),2481(15),23259(14),165(9),19(12)])]. 89.47/89.86 23384 mult(mult(mult(mult(A,B),C),i(A)),mult(A,B)) = mult(mult(A,mult(B,C)),B). [para(19(a,1),21042(a,1,1,2,1)),rewrite([44(2),19(5)]),flip(a)]. 89.47/89.86 23388 mult(mult(mult(mult(i(A),B),C),A),mult(i(A),B)) = mult(mult(i(A),mult(B,C)),B). [para(47(a,1),21042(a,1,1,2,1)),rewrite([47(6)]),flip(a)]. 89.47/89.86 23496 mult(mult(A,mult(B,C)),mult(i(C),mult(i(B),C))) = mult(mult(i(C),i(B)),mult(mult(B,mult(C,A)),C)). [back_rewrite(11706),rewrite([23384(9)]),flip(a)]. 89.47/89.86 23499 mult(mult(A,mult(i(B),C)),mult(i(C),mult(B,C))) = mult(mult(i(C),B),mult(mult(i(B),mult(C,A)),C)). [back_rewrite(10872),rewrite([23388(9)]),flip(a)]. 89.47/89.86 23671 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))). [para(23259(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.47/89.86 23700 mult(mult(A,mult(B,mult(mult(C,A),B))),i(B)) = mult(A,mult(mult(B,C),A)). [para(104(a,1),23259(a,1,2,2)),rewrite([103(8),23671(5),19(9),165(10),55(9)])]. 89.47/89.86 23779 mult(A,mult(B,mult(mult(mult(i(B),C),A),B))) = mult(mult(A,mult(C,A)),B). [back_rewrite(23280),rewrite([23671(6)])]. 89.47/89.86 23903 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,mult(C,mult(i(B),A)))))) = mult(B,mult(mult(C,i(B)),A)). [para(23671(a,1),289(a,2,2,2,2)),rewrite([47(18),19(16)])]. 89.47/89.86 23932 mult(A,mult(B,mult(mult(i(B),i(A)),mult(C,B)))) = mult(mult(C,i(A)),mult(A,B)). [para(47(a,1),23384(a,1,1,1)),rewrite([80(6),3343(11)]),flip(a)]. 89.47/89.86 23938 mult(i(A),mult(B,mult(mult(i(B),A),mult(C,B)))) = mult(mult(C,A),mult(i(A),B)). [para(200(a,1),23384(a,1,1,1)),rewrite([44(2),290(11)]),flip(a)]. 89.47/89.86 23944 mult(mult(mult(mult(A,B),C),i(A)),mult(A,mult(B,mult(A,B)))) = mult(mult(mult(A,mult(B,C)),B),mult(A,B)). [para(23384(a,1),956(a,1,1)),rewrite([910(12)]),flip(a)]. 89.47/89.86 23949 mult(mult(i(A),mult(mult(A,B),C)),mult(B,A)) = mult(i(A),mult(mult(mult(A,mult(B,C)),B),A)). [para(23384(a,1),103(a,2,2,1)),rewrite([44(8),165(7),19(8),44(12)])]. 89.47/89.86 24005 mult(mult(A,mult(mult(B,C),A)),B) = mult(A,mult(B,mult(mult(C,A),B))). [para(20678(a,1),23384(a,1,1,1)),rewrite([20(5),165(4),23671(4),47(9)]),flip(a)]. 89.47/89.86 24015 mult(mult(mult(mult(A,B),C),i(B)),mult(B,A)) = mult(A,mult(B,mult(C,A))). [back_rewrite(22879),rewrite([23932(9)])]. 89.47/89.86 24027 mult(mult(i(A),mult(B,mult(mult(i(B),A),C))),B) = mult(mult(C,A),mult(i(A),B)). [back_rewrite(290),rewrite([23938(14)])]. 89.47/89.86 24031 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [para(19(a,1),24005(a,2,2,2,1)),rewrite([23671(6),55(3)])]. 89.47/89.86 24032 mult(mult(A,mult(B,A)),mult(B,C)) = mult(A,mult(mult(B,mult(A,B)),C)). [para(20(a,1),24005(a,1,1,2,1)),rewrite([23671(10),23779(10)])]. 89.47/89.86 24134 mult(mult(A,mult(B,i(C))),mult(C,B)) = mult(mult(A,i(C)),mult(C,mult(B,B))). [para(19(a,1),24031(a,2,2,2)),rewrite([166(4),19(5),956(9)])]. 89.47/89.86 24143 mult(mult(A,mult(B,mult(B,i(C)))),C) = mult(mult(A,i(C)),mult(C,mult(B,B))). [para(55(a,1),24031(a,2,2,2)),rewrite([23671(6),166(4),19(5),24134(10)])]. 89.47/89.86 24279 mult(A,mult(mult(B,mult(A,B)),mult(i(B),C))) = mult(mult(A,mult(B,A)),C). [para(47(a,1),24032(a,1,2)),flip(a)]. 89.47/89.86 24449 mult(mult(A,mult(B,mult(C,mult(C,B)))),i(B)) = mult(A,mult(mult(B,i(A)),mult(A,mult(C,C)))). [para(913(a,1),23700(a,1,1,2,2,1)),rewrite([1183(2),24143(11)])]. 89.47/89.86 24669 mult(i(A),mult(mult(mult(A,mult(B,C)),B),A)) = mult(B,mult(mult(C,B),A)). [para(20(a,1),24015(a,1,1,1,1)),rewrite([44(3),22737(6),20883(12)])]. 89.47/89.86 24697 mult(A,mult(mult(mult(mult(mult(B,A),C),i(A)),i(B)),mult(B,A))) = mult(A,mult(B,mult(A,C))). [para(103(a,1),24015(a,1,1,1)),rewrite([21243(9),165(13),55(12)])]. 89.47/89.86 24722 mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,A)))) = mult(mult(C,mult(A,i(B))),B). [para(256(a,1),24015(a,1,1,1)),rewrite([80(3),44(2),55(6),22744(12),1282(13),47(11)]),flip(a)]. 89.47/89.86 24769 mult(mult(A,mult(mult(A,B),C)),mult(A,B)) = mult(A,mult(mult(A,mult(B,mult(C,A))),B)). [para(24015(a,1),22108(a,2,2,1)),rewrite([55(5)])]. 89.47/89.86 24782 mult(mult(i(A),mult(mult(A,B),C)),mult(B,A)) = mult(B,mult(mult(C,B),A)). [back_rewrite(23949),rewrite([24669(12)])]. 89.47/89.86 24944 mult(mult(mult(A,mult(B,C)),B),A) = mult(A,mult(B,mult(mult(C,B),A))). [para(24669(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.47/89.86 25031 mult(A,mult(B,mult(mult(i(B),mult(C,B)),A))) = mult(mult(mult(A,C),B),A). [para(47(a,1),24944(a,1,1,1,2)),rewrite([170(6)]),flip(a)]. 89.47/89.86 25035 mult(mult(A,mult(mult(i(A),mult(B,A)),C)),B) = mult(B,mult(A,mult(C,B))). [para(55(a,1),24944(a,2,2,2,1)),rewrite([21962(5)])]. 89.47/89.86 25333 mult(mult(A,B),mult(i(B),mult(C,A))) = mult(A,mult(mult(C,i(B)),mult(B,A))). [para(47(a,1),25031(a,1,2,2,1,2)),rewrite([80(5),44(5),170(5),19554(7),17253(10)]),flip(a)]. 89.47/89.86 25334 mult(mult(mult(A,mult(B,i(C))),C),A) = mult(A,mult(C,mult(mult(i(C),B),A))). [para(55(a,1),25031(a,1,2,2,1,2)),flip(a)]. 89.47/89.86 25401 mult(mult(A,B),mult(i(B),mult(C,mult(B,A)))) = mult(mult(mult(A,C),B),A). [para(25031(a,1),17364(a,2)),rewrite([21954(6),165(8),20(7)])]. 89.47/89.86 25404 mult(mult(A,B),mult(mult(C,mult(B,A)),i(A))) = mult(mult(A,mult(B,C)),B). [para(23384(a,1),25031(a,2)),rewrite([44(4),104(7),19(8)])]. 89.47/89.86 25413 mult(A,mult(B,mult(mult(C,mult(A,B)),i(B)))) = mult(mult(mult(A,B),C),A). [back_rewrite(20678),rewrite([25333(6),166(3),104(5)])]. 89.47/89.86 25414 mult(mult(mult(A,B),mult(i(B),C)),A) = mult(A,mult(mult(C,i(B)),mult(B,A))). [back_rewrite(17253),rewrite([25333(10)])]. 89.47/89.86 25417 mult(mult(mult(A,B),mult(i(B),i(C))),mult(C,C)) = mult(mult(A,i(B)),mult(B,C)). [back_rewrite(12223),rewrite([25333(13),19(14)])]. 89.47/89.86 25516 mult(mult(i(A),i(B)),mult(mult(mult(B,C),A),B)) = mult(i(A),mult(C,mult(A,B))). [para(25401(a,1),19(a,1,2)),rewrite([80(2)])]. 89.47/89.86 25524 mult(mult(mult(A,mult(B,mult(i(A),i(C)))),C),A) = mult(mult(A,C),mult(i(C),B)). [para(55(a,1),25401(a,1,2,2)),rewrite([80(6)]),flip(a)]. 89.47/89.86 25608 mult(mult(mult(mult(A,B),C),B),A) = mult(mult(A,B),mult(mult(C,B),A)). [para(24782(a,1),25401(a,1,2,2)),rewrite([19(6),47(9)]),flip(a)]. 89.47/89.86 25610 mult(mult(mult(A,B),mult(C,A)),i(C)) = mult(A,mult(mult(B,mult(C,A)),i(C))). [para(19(a,1),25608(a,1,1,1,1)),rewrite([19(8)])]. 89.47/89.86 25611 mult(mult(mult(A,B),mult(mult(C,B),A)),i(A)) = mult(mult(mult(A,B),C),B). [para(25608(a,1),20(a,1,1))]. 89.47/89.86 25647 mult(mult(A,B),mult(C,mult(C,A))) = mult(A,mult(mult(B,mult(C,C)),A)). [para(913(a,1),25608(a,2,2,1)),rewrite([24143(6),20(3),165(4),1183(7)]),flip(a)]. 89.47/89.86 25707 mult(mult(A,mult(B,mult(i(A),i(C)))),C) = mult(mult(A,C),mult(i(C),mult(B,i(A)))). [para(17364(a,1),387(a,2,2,2)),rewrite([44(11),22737(12),47(13),23009(11),47(9),47(14)])]. 89.47/89.86 25711 mult(A,mult(mult(mult(B,i(A)),i(C)),mult(C,A))) = mult(mult(A,C),mult(i(C),B)). [back_rewrite(25524),rewrite([25707(6),25414(7)])]. 89.47/89.86 25712 mult(mult(A,B),mult(i(B),mult(mult(B,A),C))) = mult(A,mult(B,mult(A,C))). [back_rewrite(24697),rewrite([25711(9)])]. 89.47/89.86 25717 mult(mult(A,mult(B,mult(B,A))),C) = mult(A,mult(B,mult(B,mult(A,C)))). [para(20(a,1),25647(a,1,1)),rewrite([23671(11),23779(11),1183(6)]),flip(a)]. 89.47/89.86 25854 mult(mult(A,mult(B,mult(B,mult(A,C)))),i(C)) = mult(A,mult(B,mult(B,A))). [para(25717(a,1),20(a,1,1))]. 89.47/89.86 25925 mult(mult(i(A),i(B)),mult(mult(B,mult(A,C)),A)) = mult(mult(C,mult(A,B)),i(B)). [para(25404(a,1),19(a,1,2)),rewrite([80(2)])]. 89.47/89.86 25935 mult(mult(mult(A,mult(B,C)),B),mult(A,B)) = mult(A,mult(B,mult(mult(C,mult(B,A)),B))). [para(25404(a,1),165(a,1,1)),rewrite([23671(13),55(10)])]. 89.47/89.86 25944 mult(mult(i(A),B),mult(mult(i(B),mult(A,C)),A)) = mult(mult(C,mult(A,i(B))),B). [para(25404(a,1),200(a,1,2)),rewrite([44(12)])]. 89.47/89.86 25997 mult(mult(A,mult(B,C)),mult(B,A)) = mult(A,mult(B,mult(C,mult(B,A)))). [para(25404(a,1),24015(a,1,1,1)),rewrite([20(5),55(9)])]. 89.47/89.86 26004 mult(mult(A,mult(B,C)),mult(i(C),mult(i(B),C))) = mult(mult(A,mult(C,B)),i(B)). [back_rewrite(23496),rewrite([25925(14)])]. 89.47/89.86 26005 mult(mult(mult(mult(A,B),C),i(A)),mult(A,mult(B,mult(A,B)))) = mult(A,mult(B,mult(mult(C,mult(B,A)),B))). [back_rewrite(23944),rewrite([25935(13)])]. 89.47/89.86 26007 mult(mult(A,mult(i(B),C)),mult(i(C),mult(B,C))) = mult(mult(A,mult(C,i(B))),B). [back_rewrite(23499),rewrite([25944(14)])]. 89.47/89.86 26017 mult(A,mult(B,mult(mult(i(B),C),mult(B,A)))) = mult(mult(A,C),mult(B,A)). [para(47(a,1),25997(a,1,1,2)),flip(a)]. 89.47/89.86 26106 mult(i(A),mult(mult(mult(A,B),mult(C,B)),A)) = mult(mult(B,C),mult(B,A)). [para(20(a,1),25413(a,1,2,2,1,2)),rewrite([44(5),22737(6),20(9)])]. 89.47/89.86 26149 mult(mult(i(A),B),mult(mult(mult(C,i(A)),B),A)) = mult(i(A),mult(mult(B,mult(C,mult(i(A),B))),A)). [para(25413(a,1),114(a,1)),rewrite([165(5),20(4),20692(7),165(13),20(12),44(13),20(14)])]. 89.47/89.86 26166 mult(i(A),mult(mult(A,B),mult(mult(C,A),B))) = mult(B,mult(i(A),mult(mult(A,C),mult(A,B)))). [para(25413(a,1),210(a,1,2,2)),rewrite([20(4),20(11),44(11)]),flip(a)]. 89.47/89.86 26191 mult(A,mult(mult(B,mult(mult(C,mult(A,B)),A)),i(A))) = mult(mult(A,B),mult(mult(C,A),B)). [para(25413(a,1),23384(a,2,1)),rewrite([17364(6),166(5),104(7),22108(4),20992(11)])]. 89.47/89.86 26198 mult(mult(A,B),mult(mult(C,B),A)) = mult(A,mult(B,mult(C,mult(B,A)))). [para(25413(a,1),25035(a,1,1)),rewrite([47(4),25608(4),47(8),80(10),80(8),44(11),170(10),26004(11),55(9)])]. 89.47/89.86 26210 mult(mult(mult(i(A),B),C),mult(i(A),mult(B,A))) = mult(i(A),mult(mult(B,mult(C,mult(i(A),B))),A)). [back_rewrite(20692),rewrite([26149(14)])]. 89.47/89.86 26263 mult(A,mult(mult(B,mult(C,mult(B,A))),i(A))) = mult(mult(mult(A,B),C),B). [back_rewrite(25611),rewrite([26198(4),166(6)])]. 89.47/89.86 26298 mult(A,mult(B,mult(mult(C,i(B)),mult(B,A)))) = mult(mult(A,B),mult(C,A)). [para(55(a,1),26198(a,1,2,1)),flip(a)]. 89.47/89.86 26524 mult(i(A),mult(mult(A,B),mult(mult(B,A),C))) = mult(B,mult(B,mult(A,C))). [para(25712(a,1),210(a,1,2,2)),rewrite([19(5)]),flip(a)]. 89.47/89.86 26546 mult(i(A),mult(B,mult(mult(i(B),A),mult(B,C)))) = mult(mult(B,i(A)),mult(A,C)). [para(289(a,2),25712(a,2)),rewrite([44(4),200(8)]),flip(a)]. 89.47/89.86 26623 mult(mult(A,i(B)),mult(B,mult(C,mult(i(A),B)))) = mult(A,mult(mult(C,i(A)),B)). [back_rewrite(23903),rewrite([26546(10)])]. 89.47/89.86 26814 mult(mult(A,B),mult(i(A),mult(mult(A,C),B))) = mult(mult(mult(A,B),C),B). [para(19(a,1),26017(a,1,2,2,2)),rewrite([44(4),19(11)])]. 89.47/89.86 26819 mult(A,mult(mult(B,i(A)),mult(mult(mult(A,i(B)),C),B))) = mult(mult(A,C),B). [para(55(a,1),26017(a,1,2,2,2)),rewrite([80(5),44(4),55(12)])]. 89.47/89.86 26944 mult(A,mult(B,mult(mult(C,mult(B,A)),i(A)))) = mult(mult(A,B),mult(C,B)). [para(26106(a,1),104(a,2,2,1)),rewrite([47(4),19(6),21245(8)]),flip(a)]. 89.47/89.86 27050 mult(mult(A,mult(B,mult(A,C))),i(C)) = mult(i(C),mult(mult(mult(C,A),B),A)). [para(26263(a,1),19(a,1,2)),flip(a)]. 89.47/89.86 27052 mult(i(A),mult(mult(mult(A,B),mult(C,mult(A,mult(B,i(A))))),A)) = mult(mult(B,C),mult(A,B)). [para(19(a,1),26263(a,2,1,1)),rewrite([166(5),44(9)])]. 89.47/89.86 27079 mult(mult(mult(A,B),mult(C,C)),B) = mult(A,mult(B,mult(C,mult(C,B)))). [para(1183(a,1),26263(a,1,2,1,2)),rewrite([25854(6)]),flip(a)]. 89.47/89.86 27189 mult(mult(A,mult(B,mult(C,mult(C,B)))),i(B)) = mult(mult(A,B),mult(C,C)). [para(27079(a,1),20(a,1,1))]. 89.47/89.86 27258 mult(A,mult(mult(B,i(A)),mult(A,mult(C,C)))) = mult(mult(A,B),mult(C,C)). [back_rewrite(24449),rewrite([27189(6)]),flip(a)]. 89.47/89.86 27452 mult(mult(mult(i(A),i(B)),mult(B,mult(C,i(A)))),mult(A,A)) = mult(mult(i(A),i(B)),mult(B,mult(C,A))). [para(444(a,1),907(a,1,1)),rewrite([775(15)])]. 89.47/89.86 27475 mult(mult(A,i(B)),mult(B,mult(C,A))) = mult(A,mult(mult(C,B),mult(i(B),A))). [para(444(a,1),25413(a,2)),rewrite([44(7),22745(6),19(7)]),flip(a)]. 89.47/89.86 27484 mult(mult(i(A),i(B)),mult(B,mult(C,A))) = mult(i(A),mult(mult(C,i(B)),mult(B,A))). [back_rewrite(27452),rewrite([27475(7),990(9),25417(8)]),flip(a)]. 89.47/89.86 27519 mult(mult(mult(A,B),mult(C,i(B))),B) = mult(mult(mult(A,B),mult(C,A)),i(A)). [para(26298(a,1),166(a,1,1)),rewrite([27050(12),47(13)]),flip(a)]. 89.47/89.86 27527 mult(mult(A,B),mult(C,mult(A,mult(B,i(A))))) = mult(A,mult(B,mult(mult(C,mult(A,B)),i(A)))). [para(26298(a,1),104(a,1)),rewrite([165(4),55(3),21961(14),165(12),55(11),26017(12),25610(11)])]. 89.47/89.86 27553 mult(mult(A,mult(mult(B,mult(C,A)),i(C))),C) = mult(mult(A,B),mult(C,A)). [back_rewrite(27052),rewrite([27527(7),165(8),19(9)])]. 89.47/89.86 27605 mult(mult(A,B),mult(mult(B,A),C)) = mult(A,mult(B,mult(B,mult(A,C)))). [para(26524(a,1),19(a,1,2)),rewrite([44(2)]),flip(a)]. 89.47/89.86 27613 mult(A,mult(A,mult(B,mult(mult(i(B),i(A)),C)))) = mult(i(B),mult(mult(B,A),C)). [para(47(a,1),26524(a,1,2,2)),rewrite([80(6)]),flip(a)]. 89.47/89.86 27654 mult(A,mult(A,mult(mult(i(A),i(B)),mult(B,C)))) = mult(mult(A,B),mult(i(B),C)). [para(253(a,1),26524(a,1,2,2)),rewrite([80(4),44(2),44(2),55(5),16813(12)]),flip(a)]. 89.47/89.86 27656 mult(i(A),mult(i(A),mult(mult(A,i(B)),mult(B,C)))) = mult(mult(i(A),B),mult(i(B),C)). [para(297(a,1),26524(a,1,2,2)),rewrite([80(3),44(3),20(6),19554(14)]),flip(a)]. 89.47/89.86 28082 mult(A,mult(B,mult(i(A),mult(mult(mult(A,C),B),A)))) = mult(mult(mult(A,B),C),mult(B,A)). [para(26814(a,1),24015(a,1,1,1)),rewrite([20(5),170(9)]),flip(a)]. 89.47/89.86 28161 mult(A,mult(B,mult(mult(B,mult(mult(C,mult(A,B)),i(B))),i(A)))) = mult(mult(A,B),mult(B,C)). [para(104(a,1),26944(a,1,2,2,1)),rewrite([165(14),55(13)])]. 89.47/89.86 28440 mult(mult(A,i(B)),mult(B,mult(C,C))) = mult(i(B),mult(mult(B,A),mult(C,C))). [para(27258(a,1),19(a,1,2)),flip(a)]. 89.47/89.86 28573 mult(i(A),mult(mult(A,B),mult(i(B),mult(mult(C,mult(B,A)),i(A))))) = mult(i(A),mult(mult(A,C),B)). [para(25401(a,1),461(a,2,2,1)),rewrite([47(8),20(16)])]. 89.47/89.86 28774 mult(i(A),mult(mult(A,i(B)),mult(B,C))) = mult(A,mult(mult(i(A),B),mult(i(B),C))). [para(24279(a,1),474(a,2,2,2)),rewrite([44(2),44(3),37(2),14(3),55(3),44(2),44(3),37(2),14(3),37(4),13(4),44(5),1282(8),1282(7),27656(8),44(8),44(9),37(8),14(9),37(10),13(10),44(11),49(11),13(11),1282(12)]),flip(a)]. 89.47/89.86 28782 mult(mult(A,i(B)),mult(B,mult(i(A),C))) = mult(A,mult(mult(i(A),B),mult(i(B),C))). [back_rewrite(1282),rewrite([28774(12)])]. 89.47/89.86 28980 mult(i(A),mult(mult(A,B),mult(i(B),C))) = mult(A,mult(mult(i(A),i(B)),mult(B,C))). [para(24279(a,1),480(a,2,2,2)),rewrite([49(3),14(4),55(4),49(4),14(5),44(6),49(6),13(6),44(6),750(8),750(7),27654(8),49(9),14(10),44(11),49(11),13(11),37(11),13(11),750(12)])]. 89.47/89.86 28981 mult(mult(mult(A,mult(B,C)),B),mult(i(B),i(C))) = mult(i(C),mult(mult(C,A),B)). [back_rewrite(28573),rewrite([28980(10),27475(9),47(10)])]. 89.47/89.86 28995 mult(A,mult(B,mult(mult(i(B),i(A)),mult(A,C)))) = mult(i(B),mult(mult(B,A),C)). [back_rewrite(210),rewrite([28980(6)])]. 89.47/89.86 29104 mult(A,mult(B,mult(i(A),mult(mult(A,C),B)))) = mult(mult(A,mult(B,C)),B). [para(23384(a,1),1021(a,2)),rewrite([26005(8),18133(9),28981(7)])]. 89.47/89.86 29147 mult(mult(A,i(B)),mult(B,mult(mult(A,C),B))) = mult(A,mult(B,mult(mult(i(B),A),mult(C,B)))). [para(29104(a,1),334(a,2,2)),rewrite([80(5),44(4),26819(10),21961(11)])]. 89.47/89.86 29816 mult(mult(mult(A,i(B)),mult(B,C)),i(C)) = mult(C,mult(mult(i(C),i(B)),mult(B,A))). [para(104(a,1),750(a,1,2)),rewrite([80(5),80(4),44(3),166(5),19(6),22743(9),27484(6),165(8),47(9),80(11),80(10),44(9),166(11),19(12),16813(14)])]. 89.47/89.86 29833 mult(A,mult(mult(i(A),i(B)),mult(mult(C,B),A))) = mult(i(B),mult(C,mult(B,A))). [para(25031(a,1),750(a,1,2)),rewrite([25516(7),29147(13),47(14)]),flip(a)]. 89.47/89.86 29980 mult(A,mult(A,mult(mult(i(A),B),mult(i(B),C)))) = mult(mult(A,i(B)),mult(B,C)). [para(234(a,1),772(a,1,2,1)),rewrite([44(3),80(6),80(5),44(5),200(7),44(4),44(7),80(10),80(9),44(9),200(11),28782(10)]),flip(a)]. 89.47/89.86 30581 mult(mult(mult(i(A),B),i(C)),mult(C,A)) = mult(C,mult(mult(mult(i(C),i(A)),B),A)). [para(796(a,1),750(a,1,2)),rewrite([80(6),44(3),80(4),44(4),19(5),200(12),80(12),44(9),80(10),44(10),19(11),26210(16),22737(17),26623(15),165(13),19(14)])]. 89.47/89.86 31280 mult(mult(A,mult(mult(B,mult(C,A)),i(A))),i(C)) = mult(i(C),mult(mult(C,A),B)). [para(12406(a,1),226(a,1,1,2)),rewrite([44(2),80(3),80(2),956(5),44(7),1008(6),44(6),44(9),19(9),1191(7),19(8),28440(6),907(5),19(3),44(2),80(3),80(2),956(5),44(7),1008(6),44(6),166(8),166(7),19(9),44(8),104(8),22743(9),27484(6),165(8),29816(7),19(8),28995(7),44(6),80(7),80(6),956(9),44(11),1008(10),44(10),166(12),166(11),19(13),44(12),104(13),22743(14),27484(11),166(8),104(10),165(13),47(14)]),flip(a)]. 89.47/89.86 31298 mult(A,mult(B,mult(i(A),mult(mult(A,B),C)))) = mult(mult(A,B),mult(B,C)). [back_rewrite(28161),rewrite([31280(7)])]. 89.47/89.86 31332 mult(mult(mult(A,B),C),mult(B,A)) = mult(mult(A,B),mult(C,mult(B,A))). [para(25401(a,1),31298(a,1,2,2,2)),rewrite([28082(7),47(10)])]. 89.47/89.86 31351 mult(mult(A,B),mult(i(C),mult(A,C))) = mult(A,mult(B,mult(i(C),mult(A,C)))). [para(20(a,1),31332(a,1,1,1)),rewrite([20(8)])]. 89.47/89.86 31859 mult(i(A),mult(i(B),mult(mult(B,A),C))) = mult(A,mult(B,mult(mult(i(B),i(A)),C))). [para(3636(a,1),884(a,1,1)),rewrite([44(3),44(4),37(3),14(3),19(3),44(2),44(3),80(3),44(6),55(5),44(5),80(5),55(7),2481(8),28980(7),2748(8),44(8),44(9),80(9),44(12),55(11),2481(12)]),flip(a)]. 89.47/89.86 31862 mult(i(A),mult(B,mult(mult(i(B),A),C))) = mult(A,mult(i(B),mult(mult(B,i(A)),C))). [para(27605(a,1),884(a,1,2,2,2)),rewrite([80(4),44(3),55(7),170(5),55(4),80(6),44(5),19(6),19(10),47(8),2513(6),80(10),44(9),19(10)])]. 89.47/89.86 31878 mult(A,mult(i(B),mult(mult(B,i(A)),mult(C,B)))) = mult(mult(C,A),mult(i(A),B)). [back_rewrite(24027),rewrite([31862(6),3332(7)])]. 89.47/89.86 32140 mult(A,mult(B,mult(i(A),mult(mult(A,C),mult(A,B))))) = mult(mult(A,B),mult(mult(C,A),B)). [para(29104(a,1),16882(a,1,2,2)),rewrite([24769(8),27484(9),166(6),104(8),22108(5),26191(8),47(7)]),flip(a)]. 89.47/89.86 32516 mult(mult(A,B),mult(mult(mult(i(B),i(A)),C),B)) = mult(A,mult(mult(i(A),C),B)). [para(19(a,1),20675(a,1,2,2)),rewrite([44(2),80(7),19(12)]),flip(a)]. 89.47/89.86 32670 mult(mult(mult(A,i(B)),mult(mult(B,C),A)),B) = mult(A,mult(mult(mult(C,A),mult(B,i(A))),A)). [para(20885(a,1),25997(a,1,1)),rewrite([170(8),31351(9),26007(8),170(12),22737(13),113(14),47(15)]),flip(a)]. 89.47/89.86 32918 mult(mult(mult(mult(i(A),i(B)),C),B),A) = mult(mult(i(A),i(B)),mult(mult(C,B),A)). [para(21247(a,1),19(a,1,2)),rewrite([80(2)]),flip(a)]. 89.47/89.86 32919 mult(A,mult(mult(mult(i(A),B),mult(A,C)),i(C))) = mult(mult(B,mult(A,C)),i(C)). [para(20(a,1),21247(a,1,1)),rewrite([44(2),80(2),47(4)])]. 89.47/89.86 32947 mult(mult(mult(mult(A,B),C),i(B)),mult(B,C)) = mult(mult(A,mult(B,C)),C). [para(21247(a,1),23384(a,1,1,1)),rewrite([32918(12),29833(13),47(11)])]. 89.47/89.86 32956 mult(A,mult(B,mult(mult(i(B),mult(i(A),C)),A))) = mult(B,mult(mult(i(B),C),A)). [para(26814(a,1),21247(a,1,2,1,1)),rewrite([55(8),32516(7),44(6),25334(11)]),flip(a)]. 89.47/89.86 32999 mult(mult(A,mult(B,mult(mult(i(B),i(A)),C))),mult(mult(B,A),C)) = mult(mult(mult(C,B),A),C). [para(118(a,1),32947(a,1,1,1)),rewrite([44(2),25333(6),166(3),104(5),25413(6),31859(9)]),flip(a)]. 89.47/89.86 33673 mult(mult(i(A),mult(mult(A,mult(B,C)),C)),i(C)) = mult(i(A),mult(mult(A,B),C)). [para(22200(a,1),27553(a,1,1,2,1)),rewrite([44(5),19(13),28981(14)])]. 89.47/89.86 33945 mult(A,mult(mult(i(A),mult(mult(A,B),C)),C)) = mult(mult(A,mult(B,C)),C). [para(22737(a,1),23384(a,1,1,1)),rewrite([30581(9),23009(7),47(10)])]. 89.47/89.86 33981 mult(i(A),mult(mult(A,B),mult(mult(C,A),B))) = mult(mult(mult(B,C),A),B). [para(118(a,1),33945(a,1,2,1,2)),rewrite([44(3),31859(12),32999(15)])]. 89.47/89.86 34102 mult(A,mult(i(B),mult(mult(B,C),mult(B,A)))) = mult(mult(mult(A,C),B),A). [back_rewrite(26166),rewrite([33981(6)]),flip(a)]. 89.47/89.86 34110 mult(mult(A,B),mult(mult(C,A),B)) = mult(A,mult(mult(mult(B,C),A),B)). [back_rewrite(32140),rewrite([34102(6)]),flip(a)]. 89.47/89.86 34141 mult(i(A),mult(mult(A,B),mult(C,A))) = mult(mult(B,C),A). [para(34110(a,1),19(a,1,2)),rewrite([80(2),27484(8),20(5)])]. 89.47/89.86 34145 mult(A,mult(mult(B,mult(A,C)),i(C))) = mult(A,mult(C,mult(mult(i(C),B),A))). [para(20(a,1),34110(a,1,1)),rewrite([22741(12),25401(13),25334(10)])]. 89.47/89.86 34233 mult(mult(A,B),mult(i(B),C)) = mult(B,mult(mult(i(B),A),C)). [back_rewrite(31878),rewrite([34141(6)]),flip(a)]. 89.47/89.86 34242 mult(mult(A,mult(B,C)),i(C)) = mult(C,mult(mult(i(C),A),B)). [back_rewrite(32919),rewrite([34145(7),32956(7)]),flip(a)]. 89.47/89.87 34433 mult(mult(A,i(B)),mult(B,C)) = mult(i(B),mult(mult(B,A),C)). [back_rewrite(29980),rewrite([34233(5),27613(7)]),flip(a)]. 89.47/89.87 34546 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [back_rewrite(26298),rewrite([34433(4),47(5)]),flip(a)]. 89.47/89.87 34590 mult(mult(A,mult(B,i(C))),C) = mult(i(C),mult(mult(C,A),B)). [back_rewrite(33673),rewrite([34242(7),34433(6),24722(7)])]. 89.47/89.87 34646 mult(i(A),mult(mult(A,mult(B,A)),C)) = mult(B,mult(A,C)). [back_rewrite(27519),rewrite([34590(5),34546(8),166(10),20(9)])]. 89.47/89.87 34745 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [back_rewrite(32670),rewrite([34546(5),19(3),34590(8),34646(8)])]. 89.47/89.87 34746 $F # answer(goals). [resolve(34745,a,178,a)]. 89.47/89.87 89.47/89.87 % SZS output end Refutation 89.47/89.87 ============================== end of proof ========================== 89.47/89.87 89.47/89.87 ============================== STATISTICS ============================ 89.47/89.87 89.47/89.87 Given=838. Generated=1112111. Kept=34727. proofs=4. 89.47/89.87 Usable=469. Sos=8912. Demods=9562. Limbo=372, Disabled=24988. Hints=0. 89.47/89.87 Megabytes=38.70. 89.47/89.87 User_CPU=87.91, System_CPU=0.93, Wall_clock=89. 89.47/89.87 89.47/89.87 ============================== end of statistics ===================== 89.47/89.87 89.47/89.87 ============================== end of search ========================= 89.47/89.87 89.47/89.87 THEOREM PROVED 89.47/89.87 % SZS status Theorem 89.47/89.87 89.47/89.87 Exiting with 4 proofs. 89.47/89.87 89.47/89.87 Process 8002 exit (max_proofs) Thu Jul 2 09:19:07 2020 89.47/89.87 Prover9 interrupted 89.47/89.87 EOF