0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.02/0.23 % Computer : n012.star.cs.uiowa.edu 0.02/0.23 % Model : x86_64 x86_64 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.23 % Memory : 32218.625MB 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.23 % CPULimit : 300 0.02/0.23 % DateTime : Sat Jul 14 06:02:39 CDT 2018 0.02/0.23 % CPUTime : 0.06/0.43 ============================== Prover9 =============================== 0.06/0.43 Prover9 (32) version 2009-11A, November 2009. 0.06/0.43 Process 33723 was started by sandbox on n012.star.cs.uiowa.edu, 0.06/0.43 Sat Jul 14 06:02:40 2018 0.06/0.43 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_33691_n012.star.cs.uiowa.edu". 0.06/0.43 ============================== end of head =========================== 0.06/0.43 0.06/0.43 ============================== INPUT ================================= 0.06/0.43 0.06/0.43 % Reading from file /tmp/Prover9_33691_n012.star.cs.uiowa.edu 0.06/0.43 0.06/0.43 set(prolog_style_variables). 0.06/0.43 set(auto2). 0.06/0.43 % set(auto2) -> set(auto). 0.06/0.43 % set(auto) -> set(auto_inference). 0.06/0.43 % set(auto) -> set(auto_setup). 0.06/0.43 % set(auto_setup) -> set(predicate_elim). 0.06/0.43 % set(auto_setup) -> assign(eq_defs, unfold). 0.06/0.43 % set(auto) -> set(auto_limits). 0.06/0.43 % set(auto_limits) -> assign(max_weight, "100.000"). 0.06/0.43 % set(auto_limits) -> assign(sos_limit, 20000). 0.06/0.43 % set(auto) -> set(auto_denials). 0.06/0.43 % set(auto) -> set(auto_process). 0.06/0.43 % set(auto2) -> assign(new_constants, 1). 0.06/0.43 % set(auto2) -> assign(fold_denial_max, 3). 0.06/0.43 % set(auto2) -> assign(max_weight, "200.000"). 0.06/0.43 % set(auto2) -> assign(max_hours, 1). 0.06/0.43 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.06/0.43 % set(auto2) -> assign(max_seconds, 0). 0.06/0.43 % set(auto2) -> assign(max_minutes, 5). 0.06/0.43 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.06/0.43 % set(auto2) -> set(sort_initial_sos). 0.06/0.43 % set(auto2) -> assign(sos_limit, -1). 0.06/0.43 % set(auto2) -> assign(lrs_ticks, 3000). 0.06/0.43 % set(auto2) -> assign(max_megs, 400). 0.06/0.43 % set(auto2) -> assign(stats, some). 0.06/0.43 % set(auto2) -> clear(echo_input). 0.06/0.43 % set(auto2) -> set(quiet). 0.06/0.43 % set(auto2) -> clear(print_initial_clauses). 0.06/0.43 % set(auto2) -> clear(print_given). 0.06/0.43 assign(lrs_ticks,-1). 0.06/0.43 assign(sos_limit,10000). 0.06/0.43 assign(order,kbo). 0.06/0.43 set(lex_order_vars). 0.06/0.43 clear(print_given). 0.06/0.43 0.06/0.43 % formulas(sos). % not echoed (21 formulas) 0.06/0.43 0.06/0.43 ============================== end of input ========================== 0.06/0.43 0.06/0.43 % From the command line: assign(max_seconds, 300). 0.06/0.43 0.06/0.43 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.06/0.43 0.06/0.43 % Formulas that are not ordinary clauses: 0.06/0.43 1 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 2 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 6 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 8 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 9 (all A all B all C multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C))) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 10 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 11 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 13 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.43 14 (all X0 one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 15 (all X0 all X1 antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))) # label(domain2) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 16 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 17 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 18 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 19 (all X0 one = addition(antidomain(antidomain(X0)),antidomain(X0))) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 20 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 21 -(all X0 all X1 all X2 addition(domain(multiplication(X0,domain(X1))),domain(multiplication(X0,domain(X2)))) = domain(multiplication(X0,addition(domain(X1),domain(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 117.00/117.24 117.00/117.24 ============================== end of process non-clausal formulas === 117.00/117.24 117.00/117.24 ============================== PROCESS INITIAL CLAUSES =============== 117.00/117.24 117.00/117.24 ============================== PREDICATE ELIMINATION ================= 117.00/117.24 22 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(11)]. 117.00/117.24 23 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(11)]. 117.00/117.24 117.00/117.24 ============================== end predicate elimination ============= 117.00/117.24 117.00/117.24 Auto_denials: 117.00/117.24 % copying label goals to answer in negative clause 117.00/117.24 117.00/117.24 Term ordering decisions: 117.00/117.24 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. antidomain=1. coantidomain=1. codomain=1. domain=1. 117.00/117.24 117.00/117.24 ============================== end of process initial clauses ======== 117.00/117.24 117.00/117.24 ============================== CLAUSES FOR SEARCH ==================== 117.00/117.24 117.00/117.24 ============================== end of clauses for search ============= 117.00/117.24 117.00/117.24 ============================== SEARCH ================================ 117.00/117.24 117.00/117.24 % Starting search at 0.01 seconds. 117.00/117.24 117.00/117.24 Low Water (keep): wt=41.000, iters=3359 117.00/117.24 117.00/117.24 Low Water (keep): wt=36.000, iters=3336 117.00/117.24 117.00/117.24 Low Water (keep): wt=35.000, iters=3361 117.00/117.24 117.00/117.24 Low Water (keep): wt=33.000, iters=3433 117.00/117.24 117.00/117.24 Low Water (keep): wt=32.000, iters=3364 117.00/117.24 117.00/117.24 Low Water (keep): wt=31.000, iters=3441 117.00/117.24 117.00/117.24 Low Water (keep): wt=30.000, iters=3335 117.00/117.24 117.00/117.24 Low Water (keep): wt=29.000, iters=3354 117.00/117.24 117.00/117.24 Low Water (keep): wt=28.000, iters=3356 117.00/117.24 117.00/117.24 Low Water (keep): wt=27.000, iters=3343 117.00/117.24 117.00/117.24 Low Water (keep): wt=26.000, iters=3356 117.00/117.24 117.00/117.24 Low Water (keep): wt=25.000, iters=3339 117.00/117.24 117.00/117.24 Low Water (keep): wt=24.000, iters=3339 117.00/117.24 117.00/117.24 Low Water (keep): wt=23.000, iters=3377 117.00/117.24 117.00/117.24 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 2.39 sec). 117.00/117.24 117.00/117.24 Low Water (keep): wt=22.000, iters=3340 117.00/117.24 117.00/117.24 Low Water (keep): wt=21.000, iters=3337 117.00/117.24 117.00/117.24 Low Water (keep): wt=20.000, iters=3333 117.00/117.24 117.00/117.24 Low Water (displace): id=6778, wt=49.000 117.00/117.24 117.00/117.24 Low Water (displace): id=5278, wt=48.000 117.00/117.24 117.00/117.24 Low Water (displace): id=7640, wt=47.000 117.00/117.24 117.00/117.24 Low Water (displace): id=8866, wt=46.000 117.00/117.24 117.00/117.24 Low Water (displace): id=8602, wt=45.000 117.00/117.24 117.00/117.24 Low Water (displace): id=7050, wt=44.000 117.00/117.24 117.00/117.24 Low Water (displace): id=15146, wt=19.000 117.00/117.24 117.00/117.24 Low Water (displace): id=15229, wt=16.000 117.00/117.24 117.00/117.24 Low Water (displace): id=15232, wt=14.000 117.00/117.24 117.00/117.24 Low Water (keep): wt=19.000, iters=3347 117.00/117.24 117.00/117.24 Low Water (keep): wt=17.000, iters=3850 117.00/117.24 117.00/117.24 Low Water (displace): id=22651, wt=13.000 117.00/117.24 117.00/117.24 Low Water (displace): id=22831, wt=12.000 117.00/117.24 117.00/117.24 Low Water (keep): wt=16.000, iters=3335 117.00/117.24 117.00/117.24 ============================== PROOF ================================= 117.00/117.24 % SZS status Theorem 117.00/117.24 % SZS output start Refutation 117.00/117.24 117.00/117.24 % Proof 1 at 114.39 (+ 2.42) seconds: goals. 117.00/117.24 % Length of proof is 313. 117.00/117.24 % Level of proof is 42. 117.00/117.24 % Maximum clause weight is 27.000. 117.00/117.24 % Given clauses 3242. 117.00/117.24 117.00/117.24 1 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 2 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 6 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 8 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 9 (all A all B all C multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C))) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 10 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 13 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 14 (all X0 one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 15 (all X0 all X1 antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))) # label(domain2) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 16 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 18 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 19 (all X0 one = addition(antidomain(antidomain(X0)),antidomain(X0))) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 20 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 117.00/117.24 21 -(all X0 all X1 all X2 addition(domain(multiplication(X0,domain(X1))),domain(multiplication(X0,domain(X2)))) = domain(multiplication(X0,addition(domain(X1),domain(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 117.00/117.24 24 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(4)]. 117.00/117.24 25 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(5)]. 117.00/117.24 26 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(6)]. 117.00/117.24 27 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(7)]. 117.00/117.24 28 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(8)]. 117.00/117.24 29 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(12)]. 117.00/117.24 30 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(16)]. 117.00/117.24 32 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(18)]. 117.00/117.24 33 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(20)]. 117.00/117.24 34 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(3)]. 117.00/117.24 35 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(14)]. 117.00/117.24 36 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(35),rewrite([34(4)])]. 117.00/117.24 37 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(19)]. 117.00/117.24 38 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(37),rewrite([34(4)])]. 117.00/117.24 39 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(9)]. 117.00/117.24 40 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(10)]. 117.00/117.24 41 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(40),rewrite([34(2)]),flip(a)]. 117.00/117.24 42 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom). [clausify(1)]. 117.00/117.24 43 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom). [clausify(2)]. 117.00/117.24 44 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(13)]. 117.00/117.24 45 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(44),flip(a)]. 117.00/117.24 46 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(15)]. 117.00/117.24 47 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(46),flip(a)]. 117.00/117.24 48 domain(multiplication(c1,addition(domain(c2),domain(c3)))) != addition(domain(multiplication(c1,domain(c2))),domain(multiplication(c1,domain(c3)))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(21)]. 117.00/117.24 49 addition(antidomain(antidomain(multiplication(c1,antidomain(antidomain(c2))))),antidomain(antidomain(multiplication(c1,antidomain(antidomain(c3)))))) != antidomain(antidomain(multiplication(c1,addition(antidomain(antidomain(c2)),antidomain(antidomain(c3)))))) # answer(goals). [copy(48),rewrite([33(3),33(6),33(10),33(14),33(17),33(21),33(24)]),flip(a)]. 117.00/117.24 50 coantidomain(one) = zero. [para(30(a,1),24(a,1)),flip(a)]. 117.00/117.24 51 antidomain(one) = zero. [para(32(a,1),25(a,1)),flip(a)]. 117.00/117.24 52 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(39(a,1),30(a,1))]. 117.00/117.24 53 multiplication(A,multiplication(coantidomain(A),B)) = zero. [para(30(a,1),39(a,1,1)),rewrite([26(2)]),flip(a)]. 117.00/117.24 54 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(32(a,1),39(a,1,1)),rewrite([26(2)]),flip(a)]. 117.00/117.24 55 addition(A,addition(A,B)) = addition(A,B). [para(41(a,1),29(a,1)),rewrite([34(1),34(2),41(2,R),29(1),34(3)])]. 117.00/117.24 56 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)). [para(25(a,1),42(a,1,1)),rewrite([34(4)])]. 117.00/117.24 57 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(27(a,1),42(a,2,2)),rewrite([28(3),34(3)])]. 117.00/117.24 58 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(30(a,1),42(a,1,1)),rewrite([57(3),34(3)]),flip(a)]. 117.00/117.24 59 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(32(a,1),42(a,1,1)),rewrite([57(4)]),flip(a)]. 117.00/117.24 60 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A). [para(24(a,1),43(a,1,1)),rewrite([34(4)])]. 117.00/117.24 61 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(30(a,1),43(a,1,1)),rewrite([57(4),34(3)]),flip(a)]. 117.00/117.24 62 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(32(a,1),43(a,1,1)),rewrite([57(3),34(3)]),flip(a)]. 117.00/117.24 63 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(39(a,1),43(a,1,1)),rewrite([34(6)])]. 117.00/117.24 66 addition(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(25(a,1),45(a,1,1,1)),rewrite([25(5),25(9)])]. 117.00/117.24 70 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(32(a,1),45(a,1,1,1))]. 117.00/117.24 71 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(39(a,1),45(a,1,1,1))]. 117.00/117.24 75 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(30(a,1),47(a,1,1,1))]. 117.00/117.24 78 addition(antidomain(multiplication(A,multiplication(B,C))),antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C)))))) = antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C))))). [para(39(a,1),47(a,1,1,1)),rewrite([39(7),39(13)])]. 117.00/117.24 79 addition(zero,coantidomain(zero)) = one. [para(50(a,1),36(a,1,1)),rewrite([50(3)])]. 117.00/117.24 80 addition(zero,antidomain(zero)) = one. [para(51(a,1),38(a,1,1)),rewrite([51(3)])]. 117.00/117.24 83 multiplication(A,coantidomain(zero)) = A. [para(79(a,1),42(a,2,2)),rewrite([28(2),57(5),25(5)])]. 117.00/117.24 87 multiplication(A,antidomain(zero)) = A. [para(80(a,1),42(a,2,2)),rewrite([28(2),57(5),25(5)])]. 117.00/117.24 96 coantidomain(zero) = one. [para(83(a,1),24(a,1)),flip(a)]. 117.00/117.24 99 addition(one,coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [back_rewrite(70),rewrite([96(2)])]. 117.00/117.24 102 antidomain(zero) = one. [para(87(a,1),24(a,1)),flip(a)]. 117.00/117.24 106 addition(one,antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [back_rewrite(75),rewrite([102(2)])]. 117.00/117.24 108 multiplication(addition(A,B),multiplication(coantidomain(B),C)) = multiplication(A,multiplication(coantidomain(B),C)). [para(53(a,1),43(a,1,1)),rewrite([57(5),34(4)]),flip(a)]. 117.00/117.24 111 addition(one,antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))))) = antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))). [para(53(a,1),47(a,1,1,1)),rewrite([102(2)])]. 117.00/117.24 112 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(39(a,1),54(a,1,2))]. 117.00/117.24 113 multiplication(antidomain(A),addition(B,multiplication(A,C))) = multiplication(antidomain(A),B). [para(54(a,1),42(a,1,1)),rewrite([57(4),34(5)]),flip(a)]. 117.00/117.24 116 addition(one,antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))). [para(54(a,1),47(a,1,1,1)),rewrite([102(2)])]. 117.00/117.24 117 addition(one,coantidomain(A)) = one. [para(36(a,1),55(a,1,2)),rewrite([34(3),36(7)])]. 117.00/117.24 118 addition(one,antidomain(A)) = one. [para(38(a,1),55(a,1,2)),rewrite([34(3),38(7)])]. 117.00/117.24 122 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(99),rewrite([117(7)]),flip(a)]. 117.00/117.24 124 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [back_rewrite(116),rewrite([118(8)]),flip(a)]. 117.00/117.24 125 antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))) = one. [back_rewrite(111),rewrite([118(8)]),flip(a)]. 117.00/117.24 126 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(106),rewrite([118(7)]),flip(a)]. 117.00/117.24 129 addition(A,multiplication(A,coantidomain(B))) = A. [para(117(a,1),42(a,2,2)),rewrite([25(2),25(5)])]. 117.00/117.24 130 addition(A,multiplication(coantidomain(B),A)) = A. [para(117(a,1),43(a,2,1)),rewrite([24(2),24(5)])]. 117.00/117.24 131 addition(A,multiplication(A,antidomain(B))) = A. [para(118(a,1),42(a,2,2)),rewrite([25(2),25(5)])]. 117.00/117.24 132 addition(A,multiplication(antidomain(B),A)) = A. [para(118(a,1),43(a,2,1)),rewrite([24(2),24(5)])]. 117.00/117.24 148 addition(A,addition(B,multiplication(A,coantidomain(C)))) = addition(A,B). [para(129(a,1),41(a,2,2)),rewrite([34(3),34(5)])]. 117.00/117.24 161 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(36(a,1),58(a,1,2)),rewrite([25(3)]),flip(a)]. 117.00/117.24 164 multiplication(A,addition(B,addition(C,coantidomain(A)))) = multiplication(A,addition(B,C)). [para(58(a,1),42(a,1,1)),rewrite([42(3),34(5),41(5,R),34(4)]),flip(a)]. 117.00/117.24 165 addition(multiplication(A,B),multiplication(C,addition(B,coantidomain(A)))) = multiplication(addition(A,C),addition(B,coantidomain(A))). [para(58(a,1),43(a,1,1))]. 117.00/117.24 167 multiplication(coantidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(45(a,1),58(a,1,2)),rewrite([30(8),39(7)]),flip(a)]. 117.00/117.24 170 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(161(a,1),42(a,1,1)),rewrite([56(4),34(7)]),flip(a)]. 117.00/117.24 175 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(122(a,1),30(a,1,2)),rewrite([25(6)])]. 117.00/117.24 179 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(175(a,1),43(a,1,1)),rewrite([57(3),34(5)]),flip(a)]. 117.00/117.24 181 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(126(a,1),32(a,1,1)),rewrite([24(6)])]. 117.00/117.24 184 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(36(a,1),59(a,1,2)),rewrite([25(4)]),flip(a)]. 117.00/117.24 189 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(43(a,1),59(a,1,2))]. 117.00/117.24 191 multiplication(antidomain(A),multiplication(coantidomain(B),A)) = zero. [para(130(a,1),59(a,1,2)),rewrite([32(2)]),flip(a)]. 117.00/117.24 193 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(132(a,1),59(a,1,2)),rewrite([32(2)]),flip(a)]. 117.00/117.24 195 multiplication(A,multiplication(B,antidomain(antidomain(coantidomain(multiplication(A,B)))))) = zero. [para(181(a,1),39(a,1)),flip(a)]. 117.00/117.24 196 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(181(a,1),42(a,1,1)),rewrite([57(3),34(5)]),flip(a)]. 117.00/117.24 207 multiplication(addition(A,antidomain(B)),multiplication(coantidomain(C),B)) = multiplication(A,multiplication(coantidomain(C),B)). [para(191(a,1),43(a,1,1)),rewrite([57(5),34(5)]),flip(a)]. 117.00/117.24 221 addition(coantidomain(addition(A,multiplication(B,A))),coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A))) = coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A)). [para(60(a,2),45(a,1,1,1))]. 117.00/117.24 228 multiplication(addition(A,one),A) = multiplication(A,addition(A,one)). [para(60(a,1),56(a,1))]. 117.00/117.24 230 addition(A,addition(coantidomain(B),multiplication(B,A))) = multiplication(addition(B,one),addition(A,coantidomain(B))). [para(58(a,1),60(a,1,2)),rewrite([34(4),41(4),34(3),41(4,R),34(3)])]. 117.00/117.24 235 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(193(a,1),43(a,1,1)),rewrite([57(5),34(5)]),flip(a)]. 117.00/117.24 239 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(59(a,1),193(a,1,2))]. 117.00/117.24 250 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(38(a,1),62(a,1,1)),rewrite([24(3)]),flip(a)]. 117.00/117.24 255 multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = zero. [para(47(a,1),62(a,1,1)),rewrite([32(8)]),flip(a)]. 117.00/117.24 257 addition(A,addition(antidomain(B),multiplication(A,B))) = multiplication(addition(A,antidomain(B)),addition(B,one)). [para(62(a,1),56(a,1,2)),rewrite([34(4),41(4),34(3),41(4,R),34(3)])]. 117.00/117.24 258 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(34(a,1),61(a,1,1))]. 117.00/117.24 259 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(36(a,1),61(a,1,1)),rewrite([24(5)]),flip(a)]. 117.00/117.24 260 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(38(a,1),61(a,1,1)),rewrite([24(5)]),flip(a)]. 117.00/117.24 270 multiplication(A,coantidomain(addition(A,B))) = zero. [para(55(a,1),61(a,1,1)),rewrite([30(4)]),flip(a)]. 117.00/117.24 273 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(250(a,1),39(a,1,1)),flip(a)]. 117.00/117.24 275 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(250(a,1),43(a,1,1)),rewrite([60(4),34(6)]),flip(a)]. 117.00/117.24 279 coantidomain(addition(A,one)) = zero. [para(270(a,1),24(a,1)),rewrite([34(3)]),flip(a)]. 117.00/117.24 289 antidomain(multiplication(A,antidomain(antidomain(coantidomain(addition(A,B)))))) = one. [para(270(a,1),47(a,1,1,1)),rewrite([102(2),118(8)]),flip(a)]. 117.00/117.24 290 multiplication(A,coantidomain(multiplication(A,addition(B,one)))) = zero. [para(56(a,1),270(a,1,2,1))]. 117.00/117.24 295 addition(coantidomain(A),coantidomain(addition(A,multiplication(B,A)))) = coantidomain(A). [back_rewrite(221),rewrite([279(6),96(5),24(5),34(5),279(8),96(7),24(7)])]. 117.00/117.24 296 addition(coantidomain(A),coantidomain(multiplication(addition(B,one),A))) = coantidomain(A). [para(279(a,1),45(a,1,2,1,1,1)),rewrite([96(6),24(6),34(6),279(9),96(8),24(8)])]. 117.00/117.24 301 multiplication(addition(antidomain(A),multiplication(B,C)),A) = multiplication(B,multiplication(C,A)). [para(32(a,1),63(a,1,2)),rewrite([34(4),57(4)]),flip(a)]. 117.00/117.24 432 antidomain(addition(A,one)) = zero. [para(32(a,1),290(a,1,2,1)),rewrite([96(5),25(5)])]. 117.00/117.24 443 addition(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(A). [para(432(a,1),47(a,1,2,1,2,1)),rewrite([102(6),25(6),34(6),432(9),102(8),25(8)])]. 117.00/117.24 469 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one. [para(30(a,1),71(a,1,1,1,2)),rewrite([28(2),96(2),117(8)]),flip(a)]. 117.00/117.24 470 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B)) = one. [para(32(a,1),71(a,1,1,1,2)),rewrite([28(2),96(2),117(8)]),flip(a)]. 117.00/117.24 471 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(32(a,1),71(a,1,1,1)),rewrite([96(2),117(9)]),flip(a)]. 117.00/117.24 496 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [para(193(a,1),71(a,1,1,1)),rewrite([96(2),117(9)]),flip(a)]. 117.00/117.24 515 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(124(a,1),32(a,1,1)),rewrite([24(7)])]. 117.00/117.24 523 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(515(a,1),42(a,1,1)),rewrite([57(4),34(7)]),flip(a)]. 117.00/117.24 532 multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))) = zero. [para(125(a,1),32(a,1,1)),rewrite([24(7)])]. 117.00/117.24 541 multiplication(addition(A,B),antidomain(antidomain(multiplication(coantidomain(B),C)))) = multiplication(A,antidomain(antidomain(multiplication(coantidomain(B),C)))). [para(532(a,1),43(a,1,1)),rewrite([57(7),34(6)]),flip(a)]. 117.00/117.24 680 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(184(a,1),132(a,1,2)),rewrite([34(5)])]. 117.00/117.24 748 addition(multiplication(addition(A,one),B),multiplication(A,addition(A,one))) = multiplication(addition(A,one),addition(A,B)). [para(228(a,1),42(a,1,2)),rewrite([34(10)])]. 117.00/117.24 781 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(34(a,1),239(a,1,1,1))]. 117.00/117.24 876 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(38(a,1),258(a,1,1)),rewrite([24(4)]),flip(a)]. 117.00/117.24 879 multiplication(A,multiplication(addition(B,C),coantidomain(multiplication(A,B)))) = multiplication(A,multiplication(C,coantidomain(multiplication(A,B)))). [para(42(a,1),258(a,1,1)),rewrite([39(5),39(9)])]. 117.00/117.24 884 multiplication(A,multiplication(antidomain(B),coantidomain(A))) = zero. [para(131(a,1),258(a,1,1)),rewrite([30(2),39(5)]),flip(a)]. 117.00/117.24 940 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [para(884(a,1),71(a,1,1,1)),rewrite([96(2),117(9)]),flip(a)]. 117.00/117.24 1052 multiplication(A,antidomain(antidomain(coantidomain(addition(A,B))))) = zero. [para(289(a,1),32(a,1,1)),rewrite([24(7)])]. 117.00/117.24 1108 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [para(469(a,1),30(a,1,2)),rewrite([25(7)])]. 117.00/117.24 1122 multiplication(coantidomain(coantidomain(addition(A,multiplication(B,A)))),coantidomain(A)) = zero. [para(60(a,2),1108(a,1,1,1,1))]. 117.00/117.24 1131 multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [para(470(a,1),30(a,1,2)),rewrite([25(7)])]. 117.00/117.24 1144 multiplication(antidomain(antidomain(A)),addition(B,antidomain(A))) = multiplication(antidomain(antidomain(A)),B). [para(250(a,1),113(a,1,2,2))]. 117.00/117.24 1186 multiplication(antidomain(addition(A,B)),A) = zero. [para(55(a,1),781(a,1,1,1)),rewrite([273(6)])]. 117.00/117.24 2567 addition(one,addition(antidomain(A),coantidomain(B))) = one. [para(118(a,1),148(a,2)),rewrite([24(5)])]. 117.00/117.24 2779 multiplication(coantidomain(coantidomain(A)),antidomain(antidomain(coantidomain(addition(A,B))))) = zero. [para(1052(a,1),167(a,1,2,2,1)),rewrite([96(8),25(8)])]. 117.00/117.24 2901 multiplication(coantidomain(antidomain(A)),A) = A. [para(36(a,1),179(a,1,1)),rewrite([24(2)]),flip(a)]. 117.00/117.24 2941 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(2901(a,1),131(a,1,2)),rewrite([34(5)])]. 117.00/117.24 2952 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(coantidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [para(2901(a,1),78(a,1,2,1)),rewrite([34(13),2901(22)])]. 117.00/117.24 2955 multiplication(antidomain(multiplication(A,coantidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(2901(a,1),112(a,1,2,2))]. 117.00/117.24 3374 multiplication(A,addition(coantidomain(A),coantidomain(coantidomain(coantidomain(B))))) = multiplication(A,coantidomain(coantidomain(coantidomain(B)))). [para(66(a,1),164(a,2,2)),rewrite([34(6),41(7,R),34(6),66(6)])]. 117.00/117.24 3473 addition(multiplication(coantidomain(A),B),multiplication(coantidomain(coantidomain(A)),addition(B,one))) = addition(B,coantidomain(coantidomain(A))). [para(36(a,1),165(a,2,1)),rewrite([170(8),24(13)])]. 117.00/117.24 3729 multiplication(coantidomain(coantidomain(A)),multiplication(B,antidomain(antidomain(coantidomain(multiplication(A,B)))))) = zero. [para(195(a,1),167(a,1,2,2,1)),rewrite([96(9),25(9)])]. 117.00/117.24 3750 multiplication(A,antidomain(coantidomain(A))) = A. [para(38(a,1),196(a,1,2)),rewrite([25(2)]),flip(a)]. 117.00/117.24 3780 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(3750(a,1),39(a,1,1)),flip(a)]. 117.00/117.24 3781 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(3750(a,1),39(a,1)),flip(a)]. 117.00/117.24 3787 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(3750(a,1),130(a,1,2)),rewrite([34(5)])]. 117.00/117.24 3981 multiplication(A,coantidomain(coantidomain(A))) = A. [para(184(a,1),3780(a,1,2)),rewrite([3750(3)]),flip(a)]. 117.00/117.24 4027 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(259),rewrite([3981(5)]),flip(a)]. 117.00/117.24 4056 multiplication(A,addition(coantidomain(A),coantidomain(B))) = multiplication(A,coantidomain(B)). [back_rewrite(3374),rewrite([4027(4),4027(7)])]. 117.00/117.24 4082 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(4027(a,1),680(a,1,2)),rewrite([34(5),3787(5),4027(6)])]. 117.00/117.24 4099 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(4082(a,1),38(a,1,1)),rewrite([4082(4)])]. 117.00/117.24 4104 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(4082(a,1),876(a,1,1,1)),rewrite([4082(5),184(5),4082(5)]),flip(a)]. 117.00/117.24 4106 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(4082(a,1),876(a,2,1)),rewrite([4104(2),4104(6),876(9),4104(6)])]. 117.00/117.24 4115 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(4027(a,1),4082(a,1,1,1)),rewrite([4104(2),4104(5)]),flip(a)]. 117.00/117.24 4116 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(4027(a,1),4082(a,2)),rewrite([4104(2),4115(3),4106(4)])]. 117.00/117.24 4162 multiplication(antidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [back_rewrite(3729),rewrite([4104(2),4116(6)])]. 117.00/117.24 4181 addition(multiplication(coantidomain(A),B),multiplication(antidomain(coantidomain(A)),addition(B,one))) = addition(B,antidomain(coantidomain(A))). [back_rewrite(3473),rewrite([4104(4),4104(10)])]. 117.00/117.24 4332 multiplication(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [back_rewrite(2779),rewrite([4104(2),4116(6)])]. 117.00/117.24 4557 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [back_rewrite(1131),rewrite([4104(4)])]. 117.00/117.24 4565 multiplication(antidomain(coantidomain(addition(A,multiplication(B,A)))),coantidomain(A)) = zero. [back_rewrite(1122),rewrite([4104(4)])]. 117.00/117.24 4572 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [back_rewrite(1108),rewrite([4104(3)])]. 117.00/117.24 4594 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [back_rewrite(940),rewrite([4104(4)])]. 117.00/117.24 4632 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [back_rewrite(496),rewrite([4104(5)])]. 117.00/117.24 4646 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(471),rewrite([4104(5)])]. 117.00/117.24 4869 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),antidomain(coantidomain(B))) = zero. [para(4116(a,1),4557(a,1,1,1,1,2))]. 117.00/117.24 5039 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(38(a,1),189(a,1,2,1)),rewrite([24(5)]),flip(a)]. 117.00/117.24 5140 multiplication(antidomain(multiplication(coantidomain(A),B)),multiplication(antidomain(coantidomain(A)),B)) = multiplication(antidomain(multiplication(coantidomain(A),B)),B). [para(4099(a,1),189(a,1,2,1)),rewrite([24(5)]),flip(a)]. 117.00/117.24 5493 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),antidomain(antidomain(B))) = zero. [para(4557(a,1),255(a,1,1,1)),rewrite([102(2),24(9)])]. 117.00/117.24 5510 coantidomain(antidomain(antidomain(A))) = antidomain(A). [para(260(a,1),56(a,1,2)),rewrite([2941(5),34(9),117(9),25(6)])]. 117.00/117.24 5522 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(5510(a,1),4104(a,1,1)),rewrite([5510(5)])]. 117.00/117.24 5523 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(5510(a,1),4104(a,2,1)),rewrite([5522(3),5522(4)])]. 117.00/117.24 5524 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(5510(a,1),4116(a,2)),rewrite([5522(3),5523(4)])]. 117.00/117.24 5692 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [back_rewrite(2955),rewrite([5522(2)])]. 117.00/117.24 5693 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [back_rewrite(2952),rewrite([5522(9)])]. 117.00/117.24 5797 multiplication(antidomain(A),multiplication(coantidomain(B),antidomain(A))) = multiplication(coantidomain(B),antidomain(A)). [para(38(a,1),207(a,1,1)),rewrite([24(5)]),flip(a)]. 117.00/117.24 6178 multiplication(coantidomain(addition(A,multiplication(B,A))),coantidomain(A)) = coantidomain(addition(A,multiplication(B,A))). [para(295(a,1),170(a,1,2)),rewrite([34(11),117(11),25(10)])]. 117.00/117.24 6196 multiplication(coantidomain(multiplication(addition(A,one),B)),coantidomain(B)) = coantidomain(multiplication(addition(A,one),B)). [para(296(a,1),170(a,1,2)),rewrite([34(13),117(13),25(12)])]. 117.00/117.24 8573 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(38(a,1),235(a,1,1)),rewrite([24(5)]),flip(a)]. 117.00/117.24 9735 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A)) = zero. [para(4594(a,1),30(a,1,2)),rewrite([25(8)])]. 117.00/117.24 9758 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A)) = zero. [para(4116(a,1),9735(a,1,1,1,1,2))]. 117.00/117.24 9772 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(addition(A,B))) = zero. [para(61(a,1),9758(a,1,1,1,1))]. 117.00/117.24 9788 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = zero. [para(4632(a,1),30(a,1,2)),rewrite([25(8)])]. 117.00/117.24 9869 multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A) = zero. [para(4116(a,1),9788(a,1,1,1,1,2))]. 117.00/117.24 10066 multiplication(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(multiplication(A,addition(B,one))). [para(443(a,1),275(a,1,1)),rewrite([34(9),118(9),24(12)])]. 117.00/117.24 10906 multiplication(addition(antidomain(A),antidomain(B)),A) = multiplication(antidomain(B),A). [para(250(a,1),301(a,1,1,2)),rewrite([273(8)])]. 117.00/117.24 13522 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero. [para(4646(a,1),30(a,1,2)),rewrite([25(8)])]. 117.00/117.24 17182 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(38(a,1),523(a,1,2)),rewrite([25(3)]),flip(a)]. 117.00/117.24 17183 antidomain(multiplication(A,addition(B,one))) = antidomain(A). [back_rewrite(10066),rewrite([17182(6)]),flip(a)]. 117.00/117.24 17217 antidomain(addition(A,multiplication(A,B))) = antidomain(A). [para(56(a,2),17183(a,1,1))]. 117.00/117.24 17320 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17182(a,1),132(a,1,2)),rewrite([34(4)])]. 117.00/117.24 17330 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(17182(a,1),3780(a,1,2)),rewrite([3750(3)]),flip(a)]. 117.00/117.24 17337 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(17182(a,1),230(a,1,2,2)),rewrite([5522(4),34(6),38(6),34(4),118(4),34(4),118(4),5522(6),34(7),24(8)]),flip(a)]. 117.00/117.24 17352 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17182(a,1),3781(a,1,2,2,1,1)),rewrite([5522(5),5524(6),8573(6),17182(8)])]. 117.00/117.24 17409 addition(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(multiplication(antidomain(antidomain(A)),B)). [para(17330(a,1),132(a,1,2)),rewrite([5522(2),34(6),5522(8)])]. 117.00/117.24 17444 antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [back_rewrite(5693),rewrite([17409(13)])]. 117.00/117.24 17554 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17352(a,1),39(a,1,1)),flip(a)]. 117.00/117.24 17583 multiplication(antidomain(multiplication(coantidomain(A),B)),B) = multiplication(antidomain(coantidomain(A)),B). [back_rewrite(5140),rewrite([17554(7)]),flip(a)]. 117.00/117.24 17584 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(5039),rewrite([17554(7)]),flip(a)]. 117.00/117.24 18846 multiplication(antidomain(antidomain(A)),multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(193(a,1),17584(a,1,1,1)),rewrite([102(2),24(4)]),flip(a)]. 117.00/117.24 18850 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(1186(a,1),17584(a,1,1,1)),rewrite([102(2),24(2)]),flip(a)]. 117.00/117.24 18858 multiplication(coantidomain(A),coantidomain(addition(A,B))) = coantidomain(addition(A,B)). [para(4332(a,1),17584(a,1,1,1)),rewrite([102(2),24(4),4116(5)]),flip(a)]. 117.00/117.24 18859 multiplication(coantidomain(multiplication(A,antidomain(B))),B) = B. [para(4557(a,1),17584(a,1,1,1)),rewrite([102(2),24(2),4116(5)]),flip(a)]. 117.00/117.24 18860 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(4572(a,1),17584(a,1,1,1)),rewrite([102(2),24(3),4116(5)]),flip(a)]. 117.00/117.24 18877 multiplication(coantidomain(A),multiplication(B,coantidomain(multiplication(A,B)))) = multiplication(B,coantidomain(multiplication(A,B))). [para(4162(a,1),17584(a,1,1,1)),rewrite([102(2),24(5),4116(6)]),flip(a)]. 117.00/117.24 18882 coantidomain(addition(A,multiplication(B,A))) = coantidomain(A). [para(4565(a,1),17584(a,1,1,1)),rewrite([102(2),24(3),4116(6),6178(6)]),flip(a)]. 117.00/117.24 18888 multiplication(coantidomain(multiplication(A,coantidomain(B))),coantidomain(A)) = coantidomain(A). [para(9758(a,1),17584(a,1,1,1)),rewrite([102(2),24(3),4116(6)]),flip(a)]. 117.00/117.24 18889 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A. [para(9788(a,1),17584(a,1,1,1)),rewrite([102(2),24(2),4116(6)]),flip(a)]. 117.00/117.24 18890 multiplication(coantidomain(multiplication(antidomain(A),coantidomain(B))),A) = A. [para(9869(a,1),17584(a,1,1,1)),rewrite([102(2),24(2),4116(6)]),flip(a)]. 117.00/117.24 18891 multiplication(coantidomain(multiplication(A,coantidomain(B))),antidomain(coantidomain(B))) = antidomain(coantidomain(B)). [para(4869(a,1),17584(a,1,1,1)),rewrite([102(2),24(4),4116(7)]),flip(a)]. 117.00/117.24 18894 multiplication(coantidomain(multiplication(A,antidomain(B))),antidomain(antidomain(B))) = antidomain(antidomain(B)). [para(5493(a,1),17584(a,1,1,1)),rewrite([102(2),24(4),4116(7)]),flip(a)]. 117.00/117.24 18897 multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)) = multiplication(A,B). [para(5692(a,1),17584(a,1,1,1)),rewrite([102(2),24(3)]),flip(a)]. 117.00/117.24 18913 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(13522(a,1),17584(a,1,1,1)),rewrite([102(2),24(2),4116(6)]),flip(a)]. 117.00/117.24 18949 coantidomain(multiplication(addition(A,one),B)) = coantidomain(B). [back_rewrite(6196),rewrite([18860(6)]),flip(a)]. 117.00/117.24 18952 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [back_rewrite(17444),rewrite([18897(7)]),flip(a)]. 117.00/117.24 18986 antidomain(antidomain(multiplication(c1,addition(antidomain(antidomain(c2)),antidomain(antidomain(c3)))))) != addition(antidomain(antidomain(multiplication(c1,c2))),antidomain(antidomain(multiplication(c1,c3)))) # answer(goals). [back_rewrite(49),rewrite([18952(6),18952(11)]),flip(a)]. 117.00/117.24 18987 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(34(a,1),18850(a,1,1,1,1))]. 117.00/117.24 19004 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(18850(a,1),17352(a,1,1,1)),rewrite([5524(5),5524(8)])]. 117.00/117.24 19041 addition(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = one. [para(18859(a,1),17337(a,1,2,1)),rewrite([4116(5),34(5)])]. 117.00/117.24 19042 multiplication(antidomain(A),antidomain(coantidomain(multiplication(B,antidomain(A))))) = antidomain(coantidomain(multiplication(B,antidomain(A)))). [para(18859(a,1),17352(a,1,1,1))]. 117.00/117.24 19085 coantidomain(addition(A,multiplication(B,multiplication(C,A)))) = coantidomain(A). [para(39(a,1),18882(a,1,1,2))]. 117.00/117.24 19105 coantidomain(addition(A,antidomain(multiplication(coantidomain(A),B)))) = antidomain(antidomain(multiplication(coantidomain(A),B))). [para(17330(a,1),18882(a,1,1,2)),rewrite([34(4),5522(9)])]. 117.00/117.24 19164 addition(antidomain(A),antidomain(addition(B,A))) = antidomain(A). [para(18987(a,1),17320(a,1,2,1)),rewrite([5524(4),34(4),18987(8)])]. 117.00/117.24 19170 addition(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(multiplication(B,A)). [para(18860(a,1),56(a,1,2)),rewrite([34(4),34(9),117(9),25(8)])]. 117.00/117.24 19180 addition(antidomain(coantidomain(A)),coantidomain(multiplication(B,A))) = one. [para(18860(a,1),257(a,1,2,2)),rewrite([34(6),4099(6),34(4),117(4),34(6),34(9),117(9),25(8)]),flip(a)]. 117.00/117.24 19189 coantidomain(addition(A,coantidomain(multiplication(B,A)))) = zero. [para(18860(a,1),9772(a,1,1,1,1)),rewrite([4104(2),4116(3),34(4),18858(6)])]. 117.00/117.24 19207 coantidomain(addition(A,coantidomain(A))) = zero. [para(24(a,1),19189(a,1,1,2,1))]. 117.00/117.24 19247 multiplication(A,coantidomain(multiplication(addition(B,coantidomain(B)),A))) = zero. [para(19207(a,1),4162(a,1,1,1)),rewrite([102(2),24(7)])]. 117.00/117.24 19336 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(18889(a,1),17330(a,1,2,1)),rewrite([39(5),8573(5)])]. 117.00/117.24 19339 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),antidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))). [para(18889(a,1),17352(a,1,1,1))]. 117.00/117.24 19528 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))). [para(18890(a,1),17182(a,1,2,1)),rewrite([19336(7)])]. 117.00/117.24 19529 multiplication(antidomain(A),coantidomain(B)) = multiplication(coantidomain(B),antidomain(A)). [para(18890(a,1),17330(a,1,2,1)),rewrite([39(5),5797(5)]),flip(a)]. 117.00/117.24 19556 multiplication(antidomain(antidomain(A)),coantidomain(multiplication(B,antidomain(A)))) = antidomain(antidomain(A)). [back_rewrite(18894),rewrite([19529(6,R)])]. 117.00/117.24 19557 multiplication(antidomain(coantidomain(A)),coantidomain(multiplication(B,coantidomain(A)))) = antidomain(coantidomain(A)). [back_rewrite(18891),rewrite([19529(6,R)])]. 117.00/117.24 19730 addition(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = one. [para(4116(a,1),19041(a,1,1)),rewrite([4116(4)])]. 117.00/117.24 19756 addition(antidomain(A),antidomain(multiplication(coantidomain(B),A))) = antidomain(multiplication(coantidomain(B),A)). [para(130(a,1),19164(a,1,2,1)),rewrite([34(5)])]. 117.00/117.24 19757 addition(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(multiplication(antidomain(B),A)). [para(132(a,1),19164(a,1,2,1)),rewrite([34(5)])]. 117.00/117.24 19774 multiplication(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(A). [para(19180(a,1),59(a,1,2)),rewrite([4116(3),25(3),4116(4)]),flip(a)]. 117.00/117.24 19849 multiplication(coantidomain(A),antidomain(coantidomain(multiplication(B,coantidomain(A))))) = antidomain(coantidomain(multiplication(B,coantidomain(A)))). [para(19730(a,1),61(a,1,1)),rewrite([4104(5),24(6),4104(9)]),flip(a)]. 117.00/117.24 19851 multiplication(A,coantidomain(multiplication(B,coantidomain(A)))) = A. [para(19730(a,1),4056(a,1,2)),rewrite([25(2)]),flip(a)]. 117.00/117.24 20150 addition(antidomain(A),coantidomain(multiplication(antidomain(multiplication(B,A)),B))) = one. [para(18913(a,1),17337(a,1,2,1)),rewrite([4116(6),34(6)])]. 117.00/117.24 20456 coantidomain(addition(antidomain(coantidomain(A)),multiplication(B,A))) = coantidomain(A). [para(3750(a,1),19085(a,1,1,2,2)),rewrite([5522(8),4116(8)])]. 117.00/117.24 20667 coantidomain(multiplication(addition(A,coantidomain(A)),B)) = coantidomain(B). [para(19247(a,1),18913(a,1,1,1,1,1)),rewrite([102(2),24(2),19774(6)]),flip(a)]. 117.00/117.24 20675 coantidomain(multiplication(antidomain(coantidomain(A)),B)) = coantidomain(multiplication(A,B)). [para(108(a,1),20667(a,1,1)),rewrite([4104(2),3780(4),4104(4)]),flip(a)]. 117.00/117.24 20697 coantidomain(multiplication(A,antidomain(antidomain(multiplication(antidomain(coantidomain(A)),B))))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [para(541(a,1),20667(a,1,1)),rewrite([4104(2),4104(9),5522(13),5524(13)])]. 117.00/117.24 20925 antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))) = multiplication(antidomain(A),antidomain(B)). [para(19336(a,1),3781(a,1,2,2,1,1)),rewrite([19336(5),19042(8),19339(7)])]. 117.00/117.24 21070 multiplication(coantidomain(A),coantidomain(B)) = multiplication(coantidomain(B),coantidomain(A)). [para(4116(a,1),19529(a,1,1)),rewrite([4116(7)])]. 117.00/117.24 21094 antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))) = multiplication(coantidomain(B),antidomain(A)). [para(19529(a,1),3781(a,2)),rewrite([19849(8),19528(7)])]. 117.00/117.24 21095 multiplication(A,antidomain(coantidomain(multiplication(A,coantidomain(B))))) = multiplication(A,coantidomain(B)). [para(19529(a,2),3781(a,1,2)),rewrite([19529(6),19849(6)])]. 117.00/117.24 21107 multiplication(A,antidomain(multiplication(antidomain(B),coantidomain(A)))) = A. [para(19529(a,2),17330(a,1,2,1))]. 117.00/117.24 21109 antidomain(multiplication(antidomain(A),coantidomain(B))) = antidomain(multiplication(coantidomain(B),antidomain(A))). [para(19529(a,1),17320(a,1,2,1)),rewrite([19756(7)]),flip(a)]. 117.00/117.24 21129 multiplication(coantidomain(A),antidomain(multiplication(coantidomain(B),coantidomain(A)))) = multiplication(coantidomain(A),antidomain(coantidomain(B))). [para(19529(a,1),17583(a,2)),rewrite([19529(6)])]. 117.00/117.24 21133 multiplication(A,coantidomain(multiplication(coantidomain(A),antidomain(B)))) = A. [para(19529(a,1),19851(a,1,2,1))]. 117.00/117.24 21154 multiplication(coantidomain(A),coantidomain(multiplication(A,coantidomain(B)))) = coantidomain(A). [back_rewrite(18888),rewrite([21070(5)])]. 117.00/117.24 21180 coantidomain(addition(A,antidomain(multiplication(antidomain(B),coantidomain(A))))) = antidomain(antidomain(multiplication(antidomain(B),coantidomain(A)))). [para(21107(a,1),18882(a,1,1,2)),rewrite([34(5),5522(11)])]. 117.00/117.24 21186 multiplication(A,coantidomain(multiplication(coantidomain(A),coantidomain(B)))) = A. [para(4116(a,1),21133(a,1,2,1,2))]. 117.00/117.24 21212 antidomain(coantidomain(multiplication(coantidomain(A),coantidomain(B)))) = multiplication(coantidomain(A),coantidomain(B)). [para(21186(a,1),19774(a,1,2,1)),rewrite([4104(5),19529(7),21095(7),4104(8)]),flip(a)]. 117.00/117.24 21685 multiplication(antidomain(coantidomain(A)),coantidomain(addition(B,A))) = zero. [para(748(a,1),4332(a,1,2,1)),rewrite([18949(4),18949(7)])]. 117.00/117.24 21705 multiplication(coantidomain(A),coantidomain(addition(B,A))) = coantidomain(addition(B,A)). [para(21685(a,1),17584(a,1,1,1)),rewrite([102(2),24(4),4116(5)]),flip(a)]. 117.00/117.24 21741 antidomain(antidomain(multiplication(coantidomain(A),coantidomain(B)))) = multiplication(coantidomain(A),coantidomain(B)). [para(21186(a,1),20456(a,1,1,2)),rewrite([4104(5),21212(5),34(5),19105(6),4104(10),21212(10)])]. 117.00/117.24 21794 coantidomain(multiplication(coantidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,coantidomain(A))). [para(19529(a,1),20675(a,1,1))]. 117.00/117.24 22042 multiplication(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = multiplication(coantidomain(B),coantidomain(A)). [para(17583(a,1),21154(a,1,2,1)),rewrite([5522(5),21741(5),20675(8),39(7),18877(7),5522(10),21741(10)])]. 117.00/117.24 23093 addition(antidomain(coantidomain(A)),coantidomain(multiplication(B,coantidomain(A)))) = coantidomain(multiplication(B,coantidomain(A))). [para(61(a,1),19170(a,1,2,1)),rewrite([4104(2),34(7),258(9)])]. 117.00/117.24 24302 addition(coantidomain(A),antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = one. [para(52(a,1),20150(a,1,2,1,1,1)),rewrite([102(6),24(6),34(6)])]. 117.00/117.24 24713 multiplication(A,coantidomain(multiplication(A,antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [para(38(a,1),879(a,1,2,1)),rewrite([24(5),19556(10)])]. 117.00/117.24 24714 multiplication(A,coantidomain(multiplication(A,coantidomain(B)))) = multiplication(A,antidomain(coantidomain(B))). [para(4099(a,1),879(a,1,2,1)),rewrite([24(5),19557(10)])]. 117.00/117.24 26581 addition(coantidomain(addition(A,B)),antidomain(multiplication(coantidomain(A),coantidomain(B)))) = one. [para(61(a,1),24302(a,1,2,1,2,1)),rewrite([22042(7)])]. 117.00/117.24 28801 antidomain(addition(antidomain(antidomain(A)),multiplication(antidomain(B),A))) = antidomain(A). [para(18846(a,1),17217(a,1,1,2)),rewrite([5524(9)])]. 117.00/117.24 28826 antidomain(antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(21133(a,1),28801(a,1,1,2)),rewrite([5522(2),19336(4),20925(6),18952(5),34(5),19757(5),5522(6),19336(8),20925(10)])]. 117.00/117.24 28827 antidomain(antidomain(multiplication(coantidomain(A),B))) = multiplication(coantidomain(A),antidomain(antidomain(B))). [para(21186(a,1),28801(a,1,1,2)),rewrite([5522(2),21094(6),18952(5),34(5),19756(5),5522(6),21094(10)])]. 117.00/117.24 28839 coantidomain(addition(A,antidomain(multiplication(antidomain(B),coantidomain(A))))) = multiplication(antidomain(B),coantidomain(A)). [back_rewrite(21180),rewrite([28826(11),4116(10)])]. 117.00/117.24 28840 coantidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [back_rewrite(20697),rewrite([28826(5),3780(6)])]. 117.00/117.24 29947 coantidomain(multiplication(antidomain(A),antidomain(B))) = antidomain(multiplication(antidomain(A),antidomain(B))). [para(20925(a,1),4116(a,1,1)),flip(a)]. 117.00/117.24 30002 antidomain(coantidomain(multiplication(A,antidomain(B)))) = multiplication(antidomain(B),antidomain(coantidomain(A))). [para(20675(a,1),20925(a,1,1)),rewrite([19336(8)])]. 117.00/117.24 30114 coantidomain(multiplication(antidomain(A),coantidomain(B))) = antidomain(multiplication(coantidomain(B),antidomain(A))). [para(21094(a,1),4116(a,1,1)),flip(a)]. 117.00/117.24 30115 coantidomain(multiplication(coantidomain(A),antidomain(B))) = antidomain(multiplication(coantidomain(A),antidomain(B))). [para(21094(a,1),5522(a,1,1)),rewrite([30114(8),28827(9),5524(8)])]. 117.00/117.24 30230 antidomain(multiplication(coantidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,coantidomain(A))). [back_rewrite(21794),rewrite([30115(5)])]. 117.00/117.24 30240 antidomain(multiplication(antidomain(coantidomain(A)),coantidomain(B))) = coantidomain(multiplication(A,coantidomain(B))). [para(17583(a,1),21109(a,1,1)),rewrite([21129(11),30230(10)])]. 117.00/117.24 31442 multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B))) = multiplication(A,antidomain(B)). [para(5524(a,1),24713(a,2,2)),rewrite([28840(4)])]. 117.00/117.24 31533 multiplication(coantidomain(A),coantidomain(B)) = coantidomain(addition(A,B)). [para(26581(a,1),1144(a,1,2)),rewrite([28827(5),4116(4),25(5),28827(8),4116(7),39(9),21705(8),18858(7)])]. 117.00/117.24 31592 coantidomain(addition(A,multiplication(B,coantidomain(A)))) = coantidomain(addition(A,B)). [back_rewrite(22042),rewrite([31533(5),21070(7),31533(7)])]. 117.00/117.24 31610 multiplication(antidomain(coantidomain(A)),coantidomain(B)) = coantidomain(addition(B,coantidomain(A))). [para(4104(a,1),31533(a,1,1)),rewrite([34(6)])]. 117.00/117.24 31611 multiplication(coantidomain(A),antidomain(coantidomain(B))) = coantidomain(addition(A,coantidomain(B))). [para(4104(a,1),31533(a,1,2))]. 117.00/117.24 31612 multiplication(antidomain(antidomain(A)),coantidomain(B)) = coantidomain(addition(B,antidomain(A))). [para(5522(a,1),31533(a,1,1)),rewrite([34(6)])]. 117.00/117.24 31662 coantidomain(addition(A,coantidomain(addition(A,B)))) = coantidomain(addition(A,coantidomain(B))). [para(31533(a,1),24714(a,1,2,1)),rewrite([4104(4),31611(5),31611(8)])]. 117.00/117.24 31680 antidomain(coantidomain(addition(A,coantidomain(B)))) = coantidomain(multiplication(B,coantidomain(A))). [back_rewrite(30240),rewrite([31610(4)])]. 117.00/117.24 32068 coantidomain(addition(A,antidomain(antidomain(B)))) = multiplication(antidomain(B),coantidomain(A)). [para(17584(a,1),31592(a,1,1,2)),rewrite([31612(4),31662(5),5522(2),28839(10)])]. 117.00/117.24 32103 multiplication(antidomain(coantidomain(A)),antidomain(coantidomain(B))) = coantidomain(addition(coantidomain(A),coantidomain(B))). [para(4104(a,1),31610(a,1,2)),rewrite([34(8)])]. 117.00/117.24 32834 multiplication(antidomain(A),antidomain(antidomain(addition(A,B)))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(59(a,1),28826(a,1,1,1)),rewrite([28826(4)]),flip(a)]. 117.00/117.24 33019 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(B),antidomain(A)). [para(10906(a,1),30002(a,1,1,1)),rewrite([29947(4),28826(5),5524(4),34(8),32068(9),5522(7),18952(9)]),flip(a)]. 117.00/117.24 33878 multiplication(A,coantidomain(multiplication(B,antidomain(coantidomain(A))))) = multiplication(A,coantidomain(B)). [para(4116(a,1),31442(a,2,2)),rewrite([32103(5),31680(5),4104(2)])]. 117.00/117.24 33903 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)). [para(19004(a,1),31442(a,2)),rewrite([5522(3),5524(4),59(4),33019(5),19336(3)])]. 117.00/117.24 33935 antidomain(addition(A,antidomain(addition(A,antidomain(B))))) = antidomain(addition(A,B)). [para(31442(a,1),28826(a,1,1,1)),rewrite([33903(3),5524(4),5522(5),5524(6),28826(7),33903(7),33903(8)]),flip(a)]. 117.00/117.24 33949 antidomain(addition(A,antidomain(addition(A,B)))) = antidomain(addition(A,antidomain(B))). [back_rewrite(32834),rewrite([33903(5),33903(8)])]. 117.00/117.24 34107 antidomain(addition(A,antidomain(antidomain(B)))) = antidomain(addition(A,B)). [back_rewrite(33935),rewrite([33949(5)])]. 117.00/117.24 34428 antidomain(multiplication(A,addition(B,antidomain(antidomain(C))))) = antidomain(multiplication(A,addition(B,C))). [para(34107(a,1),18952(a,1,1,2,1)),rewrite([18952(5)]),flip(a)]. 117.00/117.24 34467 addition(antidomain(antidomain(multiplication(c1,c2))),antidomain(antidomain(multiplication(c1,c3)))) != antidomain(antidomain(multiplication(c1,addition(c2,c3)))) # answer(goals). [back_rewrite(18986),rewrite([34428(10),34(6),34428(8),34(4)]),flip(a)]. 117.00/117.24 39072 addition(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = addition(antidomain(coantidomain(A)),coantidomain(B)). [para(4056(a,1),4181(a,1,1)),rewrite([31533(3),4104(6),34(10),2567(10),25(6),34(5),4104(7),34(12),55(12)])]. 117.00/117.24 39081 addition(antidomain(coantidomain(A)),coantidomain(B)) = coantidomain(multiplication(B,coantidomain(A))). [para(33878(a,1),4181(a,1,1)),rewrite([31533(3),4104(6),4116(7),34(9),117(9),25(6),34(5),39072(5),4104(6),4116(7),34(10),23093(10)])]. 117.00/117.25 39086 antidomain(multiplication(antidomain(coantidomain(A)),B)) = addition(antidomain(B),coantidomain(A)). [para(5522(a,1),39081(a,1,1,1)),rewrite([5524(3),5522(5),28840(7)]),flip(a)]. 117.00/117.25 39282 addition(antidomain(A),antidomain(antidomain(B))) = antidomain(multiplication(antidomain(B),A)). [para(5522(a,1),39086(a,1,1,1,1)),rewrite([5524(3),5522(6)]),flip(a)]. 117.00/117.25 39397 $F # answer(goals). [back_rewrite(34467),rewrite([39282(11),33903(9),34(7),42(7)]),xx(a)]. 117.00/117.25 117.00/117.25 % SZS output end Refutation 117.00/117.25 ============================== end of proof ========================== 117.00/117.25 117.00/117.25 ============================== STATISTICS ============================ 117.00/117.25 117.00/117.25 Given=3242. Generated=5017132. Kept=39367. proofs=1. 117.00/117.25 Usable=1840. Sos=8096. Demods=9842. Limbo=115, Disabled=29338. Hints=0. 117.00/117.25 Megabytes=29.01. 117.00/117.25 User_CPU=114.39, System_CPU=2.42, Wall_clock=116. 117.00/117.25 117.00/117.25 ============================== end of statistics ===================== 117.00/117.25 117.00/117.25 ============================== end of search ========================= 117.00/117.25 117.00/117.25 THEOREM PROVED 117.00/117.25 % SZS status Theorem 117.00/117.25 117.00/117.25 Exiting with 1 proof. 117.00/117.25 117.00/117.25 Process 33723 exit (max_proofs) Sat Jul 14 06:04:36 2018 117.00/117.25 Prover9 interrupted 117.06/117.25 EOF