0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.23 % Computer : n145.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 05:50:10 CDT 2018 0.03/0.23 % CPUTime : 0.06/0.44 ============================== Prover9 =============================== 0.06/0.44 Prover9 (32) version 2009-11A, November 2009. 0.06/0.44 Process 23547 was started by sandbox on n145.star.cs.uiowa.edu, 0.06/0.44 Sat Jul 14 05:50:10 2018 0.06/0.44 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23515_n145.star.cs.uiowa.edu". 0.06/0.44 ============================== end of head =========================== 0.06/0.44 0.06/0.44 ============================== INPUT ================================= 0.06/0.44 0.06/0.44 % Reading from file /tmp/Prover9_23515_n145.star.cs.uiowa.edu 0.06/0.44 0.06/0.44 set(prolog_style_variables). 0.06/0.44 set(auto2). 0.06/0.44 % set(auto2) -> set(auto). 0.06/0.44 % set(auto) -> set(auto_inference). 0.06/0.44 % set(auto) -> set(auto_setup). 0.06/0.44 % set(auto_setup) -> set(predicate_elim). 0.06/0.44 % set(auto_setup) -> assign(eq_defs, unfold). 0.06/0.44 % set(auto) -> set(auto_limits). 0.06/0.44 % set(auto_limits) -> assign(max_weight, "100.000"). 0.06/0.44 % set(auto_limits) -> assign(sos_limit, 20000). 0.06/0.44 % set(auto) -> set(auto_denials). 0.06/0.44 % set(auto) -> set(auto_process). 0.06/0.44 % set(auto2) -> assign(new_constants, 1). 0.06/0.44 % set(auto2) -> assign(fold_denial_max, 3). 0.06/0.44 % set(auto2) -> assign(max_weight, "200.000"). 0.06/0.44 % set(auto2) -> assign(max_hours, 1). 0.06/0.44 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.06/0.44 % set(auto2) -> assign(max_seconds, 0). 0.06/0.44 % set(auto2) -> assign(max_minutes, 5). 0.06/0.44 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.06/0.44 % set(auto2) -> set(sort_initial_sos). 0.06/0.44 % set(auto2) -> assign(sos_limit, -1). 0.06/0.44 % set(auto2) -> assign(lrs_ticks, 3000). 0.06/0.44 % set(auto2) -> assign(max_megs, 400). 0.06/0.44 % set(auto2) -> assign(stats, some). 0.06/0.44 % set(auto2) -> clear(echo_input). 0.06/0.44 % set(auto2) -> set(quiet). 0.06/0.44 % set(auto2) -> clear(print_initial_clauses). 0.06/0.44 % set(auto2) -> clear(print_given). 0.06/0.44 assign(lrs_ticks,-1). 0.06/0.44 assign(sos_limit,10000). 0.06/0.44 assign(order,kbo). 0.06/0.44 set(lex_order_vars). 0.06/0.44 clear(print_given). 0.06/0.44 0.06/0.44 % formulas(sos). % not echoed (27 formulas) 0.06/0.44 0.06/0.44 ============================== end of input ========================== 0.06/0.44 0.06/0.44 % From the command line: assign(max_seconds, 300). 0.06/0.44 0.06/0.44 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.06/0.44 0.06/0.44 % Formulas that are not ordinary clauses: 0.06/0.44 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]. 0.06/0.44 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]. 0.06/0.44 3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 6 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 8 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 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]. 0.06/0.44 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]. 0.06/0.44 11 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 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]. 0.06/0.44 14 (all X0 one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 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]. 3.90/4.11 16 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 17 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 18 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 19 (all X0 one = addition(antidomain(antidomain(X0)),antidomain(X0))) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 20 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 21 (all X0 all X1 codomain(multiplication(codomain(X1),X0)) = backward_diamond(X0,X1)) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 22 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 23 (all X0 all X1 c(backward_diamond(X0,c(X1))) = backward_box(X0,X1)) # label(backward_box) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 24 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 25 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 26 (all X0 antidomain(domain(X0)) = c(X0)) # label(complement) # label(axiom) # label(non_clause). [assumption]. 3.90/4.11 27 -(all X0 all X1 all X2 (zero = multiplication(domain(X1),backward_diamond(X0,domain(X2))) -> zero = multiplication(forward_diamond(X0,domain(X1)),domain(X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 3.90/4.11 3.90/4.11 ============================== end of process non-clausal formulas === 3.90/4.11 3.90/4.11 ============================== PROCESS INITIAL CLAUSES =============== 3.90/4.11 3.90/4.11 ============================== PREDICATE ELIMINATION ================= 3.90/4.11 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(11)]. 3.90/4.11 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(11)]. 3.90/4.11 3.90/4.11 ============================== end predicate elimination ============= 3.90/4.11 3.90/4.11 Auto_denials: 3.90/4.11 % copying label goals to answer in negative clause 3.90/4.11 3.90/4.11 Term ordering decisions: 3.90/4.11 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. backward_diamond=1. forward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. domain=1. c=1. codomain=1. 3.90/4.11 3.90/4.11 ============================== end of process initial clauses ======== 3.90/4.11 3.90/4.11 ============================== CLAUSES FOR SEARCH ==================== 3.90/4.11 3.90/4.11 ============================== end of clauses for search ============= 3.90/4.11 3.90/4.11 ============================== SEARCH ================================ 3.90/4.11 3.90/4.11 % Starting search at 0.01 seconds. 3.90/4.11 3.90/4.11 Low Water (keep): wt=46.000, iters=3400 3.90/4.11 3.90/4.11 Low Water (keep): wt=43.000, iters=3396 3.90/4.11 3.90/4.11 Low Water (keep): wt=41.000, iters=3352 3.90/4.11 3.90/4.11 Low Water (keep): wt=38.000, iters=3356 3.90/4.11 3.90/4.11 Low Water (keep): wt=36.000, iters=3355 3.90/4.11 3.90/4.11 Low Water (keep): wt=35.000, iters=3359 3.90/4.11 3.90/4.11 Low Water (keep): wt=33.000, iters=3333 3.90/4.11 3.90/4.11 Low Water (keep): wt=32.000, iters=3344 3.90/4.11 3.90/4.11 Low Water (keep): wt=31.000, iters=3413 3.90/4.11 3.90/4.11 Low Water (keep): wt=30.000, iters=3361 3.90/4.11 3.90/4.11 Low Water (keep): wt=29.000, iters=3343 3.90/4.11 3.90/4.11 Low Water (keep): wt=28.000, iters=3333 3.90/4.11 3.90/4.11 Low Water (keep): wt=27.000, iters=3340 3.90/4.11 3.90/4.11 Low Water (keep): wt=26.000, iters=3354 3.90/4.11 3.90/4.11 Low Water (keep): wt=25.000, iters=3354 3.90/4.11 3.90/4.11 Low Water (keep): wt=24.000, iters=3372 3.90/4.11 3.90/4.11 Low Water (keep): wt=23.000, iters=3346 3.90/4.11 3.90/4.11 Low Water (keep): wt=22.000, iters=3356 3.90/4.11 3.90/4.11 Low Water (displace): id=6213, wt=54.000 3.90/4.11 3.90/4.11 Low Water (displace): id=4160, wt=50.000 3.90/4.11 3.90/4.11 Low Water (displace): id=6467, wt=48.000 39.66/39.95 39.66/39.95 Low Water (displace): id=8190, wt=46.000 39.66/39.95 39.66/39.95 Low Water (displace): id=8243, wt=44.000 39.66/39.95 39.66/39.95 Low Water (displace): id=8192, wt=43.000 39.66/39.95 39.66/39.95 Low Water (displace): id=8210, wt=42.000 39.66/39.95 39.66/39.95 Low Water (displace): id=14312, wt=17.000 39.66/39.95 39.66/39.95 Low Water (displace): id=14892, wt=16.000 39.66/39.95 39.66/39.95 Low Water (displace): id=14920, wt=15.000 39.66/39.95 39.66/39.95 Low Water (keep): wt=21.000, iters=3338 39.66/39.95 39.66/39.95 Low Water (keep): wt=19.000, iters=4213 39.66/39.95 39.66/39.95 Low Water (displace): id=20938, wt=14.000 39.66/39.95 39.66/39.95 Low Water (displace): id=24118, wt=13.000 39.66/39.95 39.66/39.95 Low Water (keep): wt=18.000, iters=3337 39.66/39.95 39.66/39.95 Low Water (keep): wt=17.000, iters=3336 39.66/39.95 39.66/39.95 Low Water (keep): wt=16.000, iters=4494 39.66/39.95 39.66/39.95 ============================== PROOF ================================= 39.66/39.95 % SZS status Theorem 39.66/39.95 % SZS output start Refutation 39.66/39.95 39.66/39.95 % Proof 1 at 38.72 (+ 0.79) seconds: goals. 39.66/39.95 % Length of proof is 306. 39.66/39.95 % Level of proof is 39. 39.66/39.95 % Maximum clause weight is 29.000. 39.66/39.95 % Given clauses 1703. 39.66/39.95 39.66/39.95 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]. 39.66/39.95 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]. 39.66/39.95 3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 6 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 8 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 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]. 39.66/39.95 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]. 39.66/39.95 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 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]. 39.66/39.95 14 (all X0 one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 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]. 39.66/39.95 16 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 17 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 18 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 19 (all X0 one = addition(antidomain(antidomain(X0)),antidomain(X0))) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 20 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 21 (all X0 all X1 codomain(multiplication(codomain(X1),X0)) = backward_diamond(X0,X1)) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 24 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption]. 39.66/39.95 27 -(all X0 all X1 all X2 (zero = multiplication(domain(X1),backward_diamond(X0,domain(X2))) -> zero = multiplication(forward_diamond(X0,domain(X1)),domain(X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 39.66/39.95 30 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(4)]. 39.66/39.95 31 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(5)]. 39.66/39.95 32 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(6)]. 39.66/39.95 33 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(7)]. 39.66/39.95 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(8)]. 39.66/39.95 35 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(12)]. 39.66/39.95 36 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(16)]. 39.66/39.95 37 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(17)]. 39.66/39.95 38 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(18)]. 39.66/39.95 39 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(20)]. 39.66/39.95 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(3)]. 39.66/39.95 43 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(14)]. 39.66/39.95 44 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(43),rewrite([42(4)])]. 39.66/39.95 45 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(19)]. 39.66/39.95 46 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(45),rewrite([42(4)])]. 39.66/39.95 47 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(21)]. 39.66/39.95 48 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(47),rewrite([37(2),37(5)])]. 39.66/39.95 53 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(24)]. 39.66/39.95 54 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(53),rewrite([39(2),39(5)])]. 39.66/39.95 57 multiplication(domain(c2),backward_diamond(c1,domain(c3))) = zero # label(goals) # label(negated_conjecture). [clausify(27)]. 39.66/39.95 58 zero = multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))). [copy(57),rewrite([39(2),39(6),48(8)]),flip(a)]. 39.66/39.95 59 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(9)]. 39.66/39.95 60 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(10)]. 39.66/39.95 61 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(60),rewrite([42(2)]),flip(a)]. 39.66/39.95 62 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom). [clausify(1)]. 39.66/39.95 63 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom). [clausify(2)]. 39.66/39.95 64 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(13)]. 39.66/39.95 65 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(64),flip(a)]. 39.66/39.95 66 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(15)]. 39.66/39.95 67 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(66),flip(a)]. 39.66/39.95 68 multiplication(forward_diamond(c1,domain(c2)),domain(c3)) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)]. 39.66/39.95 69 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))) != multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) # answer(goals). [copy(68),rewrite([39(3),54(5),39(11),58(14)])]. 39.66/39.95 71 multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) = multiplication(antidomain(A),A). [back_rewrite(38),rewrite([58(3)]),flip(a)]. 39.66/39.95 72 multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) = multiplication(A,coantidomain(A)). [back_rewrite(36),rewrite([58(3)]),flip(a)]. 39.66/39.95 73 multiplication(A,multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1))))) = multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))). [back_rewrite(34),rewrite([58(1),58(15)])]. 39.66/39.95 74 addition(A,multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1))))) = A. [back_rewrite(33),rewrite([58(1)])]. 39.66/39.95 75 multiplication(antidomain(antidomain(c2)),multiplication(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1))),A)) = multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))). [back_rewrite(32),rewrite([58(1),59(14),58(15)])]. 39.66/39.95 76 addition(A,addition(A,B)) = addition(A,B). [para(61(a,1),35(a,1)),rewrite([42(1),42(2),61(2,R),35(1),42(3)])]. 39.66/39.95 77 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)). [para(31(a,1),62(a,1,1)),rewrite([42(4)])]. 39.66/39.95 78 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A). [para(30(a,1),63(a,1,1)),rewrite([42(4)])]. 39.66/39.95 79 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C). [para(59(a,1),63(a,1,1)),rewrite([42(6)])]. 39.66/39.95 83 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)). [para(59(a,1),65(a,1,1,1))]. 39.66/39.95 84 addition(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))). [para(30(a,1),67(a,1,1,1)),rewrite([30(5),30(9)])]. 39.66/39.95 86 addition(antidomain(multiplication(A,multiplication(B,C))),antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C)))))) = antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C))))). [para(59(a,1),67(a,1,1,1)),rewrite([59(7),59(13)])]. 39.66/39.95 87 multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) = antidomain(one). [para(71(a,2),31(a,1))]. 39.66/39.95 90 multiplication(antidomain(A),A) = antidomain(one). [para(71(a,1),58(a,2)),rewrite([58(1),87(13)]),flip(a)]. 39.66/39.95 91 multiplication(antidomain(one),A) = antidomain(one). [para(71(a,1),59(a,1,1)),rewrite([90(2),75(17),87(16)])]. 39.66/39.95 92 multiplication(antidomain(A),multiplication(A,B)) = antidomain(one). [para(71(a,2),59(a,1,1)),rewrite([87(13),91(3)]),flip(a)]. 39.66/39.95 93 multiplication(antidomain(antidomain(c2)),addition(A,coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1))))) = addition(antidomain(one),multiplication(antidomain(antidomain(c2)),A)). [para(71(a,1),62(a,1,1)),rewrite([90(2),42(20)]),flip(a)]. 39.66/39.95 94 addition(antidomain(one),multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(A,B)). [para(71(a,2),62(a,1,1)),rewrite([87(13)])]. 39.66/39.95 96 addition(antidomain(one),multiplication(A,B)) = multiplication(addition(A,antidomain(B)),B). [para(71(a,2),63(a,1,1)),rewrite([87(13),42(6)])]. 39.66/39.95 98 addition(coantidomain(antidomain(one)),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(71(a,2),65(a,1,1,1)),rewrite([87(13)])]. 39.66/39.95 102 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))) != antidomain(one) # answer(goals). [para(71(a,1),69(a,2)),rewrite([90(15)])]. 39.66/39.95 104 addition(A,antidomain(one)) = A. [back_rewrite(74),rewrite([87(13)])]. 39.66/39.95 105 multiplication(A,antidomain(one)) = antidomain(one). [back_rewrite(73),rewrite([87(13),87(16)])]. 39.66/39.95 106 multiplication(A,coantidomain(A)) = antidomain(one). [back_rewrite(72),rewrite([87(13)]),flip(a)]. 39.66/39.95 108 addition(one,coantidomain(A)) = one. [para(44(a,1),76(a,1,2)),rewrite([42(3),44(7)])]. 39.66/39.95 109 addition(one,antidomain(A)) = one. [para(46(a,1),76(a,1,2)),rewrite([42(3),46(7)])]. 39.66/39.95 110 addition(antidomain(one),multiplication(A,B)) = multiplication(A,B). [para(104(a,1),62(a,2,2)),rewrite([105(4),42(4)])]. 39.66/39.95 111 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [back_rewrite(96),rewrite([110(4)]),flip(a)]. 39.66/39.95 113 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [back_rewrite(94),rewrite([110(5)]),flip(a)]. 39.66/39.95 114 multiplication(antidomain(antidomain(c2)),addition(A,coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1))))) = multiplication(antidomain(antidomain(c2)),A). [back_rewrite(93),rewrite([110(21)])]. 39.66/39.95 115 addition(A,multiplication(A,coantidomain(B))) = A. [para(108(a,1),62(a,2,2)),rewrite([31(2),31(5)])]. 39.66/39.95 116 addition(A,multiplication(coantidomain(B),A)) = A. [para(108(a,1),63(a,2,1)),rewrite([30(2),30(5)])]. 39.66/39.95 117 addition(A,multiplication(A,antidomain(B))) = A. [para(109(a,1),62(a,2,2)),rewrite([31(2),31(5)])]. 39.66/39.95 118 addition(A,multiplication(antidomain(B),A)) = A. [para(109(a,1),63(a,2,1)),rewrite([30(2),30(5)])]. 39.66/39.95 134 coantidomain(one) = antidomain(one). [para(106(a,1),30(a,1)),flip(a)]. 39.66/39.95 135 multiplication(A,multiplication(coantidomain(A),B)) = antidomain(one). [para(106(a,1),59(a,1,1)),rewrite([91(3)]),flip(a)]. 39.66/39.95 136 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = antidomain(one). [para(106(a,1),59(a,1)),flip(a)]. 39.66/39.95 137 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(106(a,1),62(a,1,1)),rewrite([110(4),42(3)]),flip(a)]. 39.66/39.95 138 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(106(a,1),63(a,1,1)),rewrite([110(5),42(3)]),flip(a)]. 39.66/39.95 141 addition(antidomain(antidomain(one)),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(106(a,1),67(a,1,1,1))]. 39.66/39.95 152 addition(coantidomain(addition(A,multiplication(B,A))),coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A))) = coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A)). [para(78(a,2),65(a,1,1,1))]. 39.66/39.95 155 multiplication(addition(A,one),A) = multiplication(A,addition(A,one)). [para(78(a,1),77(a,1))]. 39.66/39.95 158 addition(antidomain(one),coantidomain(antidomain(one))) = one. [para(134(a,1),44(a,1,1)),rewrite([134(4)])]. 39.66/39.95 160 addition(antidomain(one),antidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(90(a,1),115(a,1,2)),rewrite([42(5)])]. 39.66/39.95 174 multiplication(addition(antidomain(A),multiplication(B,C)),A) = multiplication(B,multiplication(C,A)). [para(90(a,1),79(a,1,2)),rewrite([42(5),110(5)]),flip(a)]. 39.66/39.95 181 addition(antidomain(one),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(106(a,1),118(a,1,2)),rewrite([42(5)])]. 39.66/39.95 182 coantidomain(antidomain(one)) = one. [back_rewrite(158),rewrite([181(6)])]. 39.66/39.95 184 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(98),rewrite([182(3),108(7)]),flip(a)]. 39.66/39.95 186 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = antidomain(one). [para(59(a,1),92(a,1,2))]. 39.66/39.95 198 addition(antidomain(antidomain(one)),antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))))) = antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))). [para(135(a,1),67(a,1,1,1))]. 39.66/39.95 222 multiplication(coantidomain(coantidomain(antidomain(A))),A) = antidomain(one). [para(184(a,1),106(a,1,2)),rewrite([31(6)])]. 39.66/39.95 231 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(222(a,1),63(a,1,1)),rewrite([110(4),42(5)]),flip(a)]. 39.66/39.95 237 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(46(a,1),111(a,1,1)),rewrite([30(3)]),flip(a)]. 39.66/39.95 243 multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = antidomain(one). [para(67(a,1),111(a,1,1)),rewrite([90(8)]),flip(a)]. 39.66/39.95 244 addition(A,addition(antidomain(B),multiplication(A,B))) = multiplication(addition(A,antidomain(B)),addition(B,one)). [para(111(a,1),77(a,1,2)),rewrite([42(4),61(4),42(3),61(4,R),42(3)])]. 39.66/39.95 253 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B)) = one. [para(90(a,1),83(a,1,1,1,2)),rewrite([105(3),182(3),108(8)]),flip(a)]. 39.66/39.95 254 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(90(a,1),83(a,1,1,1)),rewrite([182(3),108(9)]),flip(a)]. 39.66/39.95 255 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one. [para(106(a,1),83(a,1,1,1,2)),rewrite([105(3),182(3),108(8)]),flip(a)]. 39.66/39.95 267 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(237(a,1),59(a,1,1)),flip(a)]. 39.66/39.95 269 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(237(a,1),63(a,1,1)),rewrite([78(4),42(6)]),flip(a)]. 39.66/39.95 276 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(44(a,1),137(a,1,2)),rewrite([31(3)]),flip(a)]. 39.66/39.95 279 multiplication(A,addition(B,addition(C,coantidomain(A)))) = multiplication(A,addition(B,C)). [para(137(a,1),62(a,1,1)),rewrite([62(3),42(5),61(5,R),42(4)]),flip(a)]. 39.66/39.95 284 addition(A,addition(coantidomain(B),multiplication(B,A))) = multiplication(addition(B,one),addition(A,coantidomain(B))). [para(137(a,1),78(a,1,2)),rewrite([42(4),61(4),42(3),61(4,R),42(3)])]. 39.66/39.95 291 multiplication(coantidomain(A),multiplication(coantidomain(A),B)) = multiplication(coantidomain(A),B). [para(276(a,1),59(a,1,1)),flip(a)]. 39.66/39.95 292 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(276(a,1),62(a,1,1)),rewrite([77(4),42(7)]),flip(a)]. 39.66/39.95 302 antidomain(antidomain(one)) = one. [para(134(a,1),160(a,1,2,1)),rewrite([46(6),134(3)]),flip(a)]. 39.66/39.95 305 antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))) = one. [back_rewrite(198),rewrite([302(3),109(8)]),flip(a)]. 39.66/39.95 307 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(141),rewrite([302(3),109(7)]),flip(a)]. 39.66/39.95 310 multiplication(antidomain(A),antidomain(antidomain(A))) = antidomain(one). [para(84(a,1),111(a,1,1)),rewrite([90(6)]),flip(a)]. 39.66/39.95 313 multiplication(A,antidomain(antidomain(coantidomain(A)))) = antidomain(one). [para(307(a,1),90(a,1,1)),rewrite([30(6)])]. 39.66/39.95 316 multiplication(addition(A,antidomain(B)),antidomain(antidomain(B))) = multiplication(A,antidomain(antidomain(B))). [para(310(a,1),63(a,1,1)),rewrite([110(6),42(5)]),flip(a)]. 39.66/39.95 324 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(313(a,1),62(a,1,1)),rewrite([110(4),42(5)]),flip(a)]. 39.66/39.95 359 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(44(a,1),113(a,1,2)),rewrite([31(4)]),flip(a)]. 39.66/39.95 363 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(63(a,1),113(a,1,2))]. 39.66/39.95 367 multiplication(antidomain(A),multiplication(coantidomain(B),A)) = antidomain(one). [para(116(a,1),113(a,1,2)),rewrite([90(2)]),flip(a)]. 39.66/39.95 371 multiplication(antidomain(A),multiplication(antidomain(B),A)) = antidomain(one). [para(118(a,1),113(a,1,2)),rewrite([90(2)]),flip(a)]. 39.66/39.95 377 multiplication(addition(A,antidomain(B)),multiplication(coantidomain(C),B)) = multiplication(A,multiplication(coantidomain(C),B)). [para(367(a,1),63(a,1,1)),rewrite([110(6),42(5)]),flip(a)]. 39.66/39.95 384 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [para(367(a,1),83(a,1,1,1)),rewrite([182(3),108(9)]),flip(a)]. 39.66/39.95 394 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(371(a,1),63(a,1,1)),rewrite([110(6),42(5)]),flip(a)]. 39.66/39.95 401 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [para(371(a,1),83(a,1,1,1)),rewrite([182(3),108(9)]),flip(a)]. 39.66/39.95 405 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = antidomain(one). [para(113(a,1),371(a,1,2))]. 39.66/39.95 417 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),138(a,1,1))]. 39.66/39.95 418 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(44(a,1),138(a,1,1)),rewrite([30(5)]),flip(a)]. 39.66/39.95 419 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(46(a,1),138(a,1,1)),rewrite([30(5)]),flip(a)]. 39.66/39.95 428 multiplication(A,coantidomain(addition(A,B))) = antidomain(one). [para(76(a,1),138(a,1,1)),rewrite([106(4)]),flip(a)]. 39.66/39.95 443 coantidomain(addition(A,one)) = antidomain(one). [para(428(a,1),30(a,1)),rewrite([42(4)]),flip(a)]. 39.66/39.95 451 multiplication(A,multiplication(B,coantidomain(multiplication(addition(A,C),B)))) = antidomain(one). [para(63(a,1),428(a,1,2,1)),rewrite([59(5)])]. 39.66/39.95 452 coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B)))) = one. [para(428(a,1),65(a,1,1,1)),rewrite([182(3),108(8)]),flip(a)]. 39.66/39.95 455 multiplication(A,coantidomain(multiplication(A,addition(B,one)))) = antidomain(one). [para(77(a,1),428(a,1,2,1))]. 39.66/39.95 466 addition(coantidomain(A),coantidomain(addition(A,multiplication(B,A)))) = coantidomain(A). [back_rewrite(152),rewrite([443(6),182(6),30(5),42(5),443(8),182(8),30(7)])]. 39.66/39.95 475 addition(coantidomain(A),coantidomain(multiplication(addition(B,one),A))) = coantidomain(A). [para(443(a,1),65(a,1,2,1,1,1)),rewrite([182(7),30(6),42(6),443(9),182(9),30(8)])]. 39.66/39.95 480 addition(multiplication(addition(A,one),B),multiplication(A,addition(A,one))) = multiplication(addition(A,one),addition(A,B)). [para(155(a,1),62(a,1,2)),rewrite([42(10)])]. 39.66/39.95 540 multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B) = antidomain(one). [para(253(a,1),106(a,1,2)),rewrite([31(7)])]. 39.66/39.95 542 multiplication(antidomain(antidomain(c2)),coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1))) = antidomain(antidomain(c2)). [para(44(a,1),114(a,1,2)),rewrite([31(5)]),flip(a)]. 39.66/39.96 557 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = antidomain(one). [para(255(a,1),106(a,1,2)),rewrite([31(7)])]. 39.66/39.96 567 multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))) = antidomain(one). [para(305(a,1),90(a,1,1)),rewrite([30(7)])]. 39.66/39.96 721 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(359(a,1),78(a,1,2)),rewrite([42(5),42(9),109(9),30(9)])]. 39.66/39.96 729 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(46(a,1),417(a,1,1)),rewrite([30(4)]),flip(a)]. 39.66/39.96 732 multiplication(A,multiplication(addition(B,C),coantidomain(multiplication(A,B)))) = multiplication(A,multiplication(C,coantidomain(multiplication(A,B)))). [para(62(a,1),417(a,1,1)),rewrite([59(5),59(9)])]. 39.66/39.96 737 multiplication(A,multiplication(antidomain(B),coantidomain(A))) = antidomain(one). [para(117(a,1),417(a,1,1)),rewrite([106(2),59(6)]),flip(a)]. 39.66/39.96 782 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [para(737(a,1),83(a,1,1,1)),rewrite([182(3),108(9)]),flip(a)]. 39.66/39.96 890 multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B))) = antidomain(one). [para(452(a,1),106(a,1,2)),rewrite([31(7)])]. 39.66/39.96 948 antidomain(addition(A,one)) = antidomain(one). [para(90(a,1),455(a,1,2,1)),rewrite([182(6),31(5)])]. 39.66/39.96 959 addition(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(A). [para(948(a,1),67(a,1,2,1,2,1)),rewrite([302(7),31(6),42(6),948(9),302(9),31(8)])]. 39.66/39.96 1161 multiplication(A,addition(B,antidomain(antidomain(multiplication(coantidomain(A),C))))) = multiplication(A,B). [para(567(a,1),62(a,1,1)),rewrite([110(4),42(6)]),flip(a)]. 39.66/39.96 1992 multiplication(coantidomain(antidomain(A)),A) = A. [para(44(a,1),231(a,1,1)),rewrite([30(2)]),flip(a)]. 39.66/39.96 2072 multiplication(coantidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B). [para(1992(a,1),59(a,1,1)),flip(a)]. 39.66/39.96 2080 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(1992(a,1),117(a,1,2)),rewrite([42(5)])]. 39.66/39.96 2089 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(1992(a,1),86(a,1,2,1)),rewrite([42(13),1992(22)])]. 39.66/39.96 2479 multiplication(A,antidomain(coantidomain(A))) = A. [para(46(a,1),324(a,1,2)),rewrite([31(2)]),flip(a)]. 39.66/39.96 2548 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2479(a,1),59(a,1,1)),flip(a)]. 39.66/39.96 2549 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2479(a,1),59(a,1)),flip(a)]. 39.66/39.96 2556 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2479(a,1),116(a,1,2)),rewrite([42(5)])]. 39.66/39.96 2591 multiplication(A,coantidomain(coantidomain(A))) = A. [para(359(a,1),2548(a,1,2)),rewrite([2479(3)]),flip(a)]. 39.66/39.96 2624 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(418),rewrite([2591(5)]),flip(a)]. 39.66/39.96 2659 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2624(a,1),721(a,1,2)),rewrite([42(5),2556(5),2624(6)])]. 39.66/39.96 2875 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2659(a,1),46(a,1,1)),rewrite([2659(4)])]. 39.66/39.96 2880 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2659(a,1),729(a,1,1,1)),rewrite([2659(5),359(5),2659(5)]),flip(a)]. 39.66/39.96 2882 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2659(a,1),729(a,2,1)),rewrite([2880(2),2880(6),729(9),2880(6)])]. 39.66/39.96 2891 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2624(a,1),2659(a,1,1,1)),rewrite([2880(2),2880(5)]),flip(a)]. 39.66/39.96 2892 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2624(a,1),2659(a,2)),rewrite([2880(2),2891(3),2882(4)])]. 39.66/39.96 3142 multiplication(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = antidomain(one). [back_rewrite(890),rewrite([2880(2)])]. 39.66/39.96 3149 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [back_rewrite(782),rewrite([2880(4)])]. 39.66/39.96 3172 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = antidomain(one). [back_rewrite(557),rewrite([2880(3)])]. 39.66/39.96 3184 multiplication(antidomain(antidomain(c2)),coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(c3)))),c1))) = antidomain(antidomain(c2)). [back_rewrite(542),rewrite([2880(8)])]. 39.66/39.96 3186 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),B) = antidomain(one). [back_rewrite(540),rewrite([2880(4)])]. 39.66/39.96 3209 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [back_rewrite(401),rewrite([2880(5)])]. 39.66/39.96 3215 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [back_rewrite(384),rewrite([2880(5)])]. 39.66/39.96 3230 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(254),rewrite([2880(5)])]. 39.66/39.96 3240 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(antidomain(coantidomain(A)),B))) = coantidomain(multiplication(antidomain(coantidomain(A)),B)). [back_rewrite(65),rewrite([2880(4),2880(9)])]. 39.66/39.96 4064 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = antidomain(one). [para(42(a,1),405(a,1,1,1))]. 39.66/39.96 4068 multiplication(antidomain(addition(A,B)),addition(C,multiplication(antidomain(A),B))) = multiplication(antidomain(addition(A,B)),C). [para(405(a,1),62(a,1,1)),rewrite([110(6),42(8)]),flip(a)]. 39.66/39.96 4072 addition(antidomain(one),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(405(a,1),77(a,1,2)),rewrite([42(5),42(11),4068(12),31(9)])]. 39.66/39.96 4136 coantidomain(antidomain(antidomain(A))) = antidomain(A). [para(419(a,1),77(a,1,2)),rewrite([2080(5),42(9),108(9),31(6)])]. 39.66/39.96 4161 multiplication(antidomain(antidomain(c2)),coantidomain(multiplication(antidomain(antidomain(c3)),c1))) = antidomain(antidomain(c2)). [back_rewrite(3184),rewrite([4136(7)])]. 39.66/39.96 4276 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(4136(a,1),2880(a,1,1)),rewrite([4136(5)])]. 39.66/39.96 4277 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(4136(a,1),2880(a,2,1)),rewrite([4276(3),4276(4)])]. 39.66/39.96 4278 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(4136(a,1),2892(a,2)),rewrite([4276(3),4277(4)])]. 39.66/39.96 4349 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(2089),rewrite([4276(9)])]. 39.66/39.96 4357 multiplication(antidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B). [back_rewrite(2072),rewrite([4276(2)])]. 39.66/39.96 4358 multiplication(antidomain(antidomain(A)),A) = A. [back_rewrite(1992),rewrite([4276(2)])]. 39.66/39.96 4367 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(c2))))),antidomain(antidomain(c3))) != antidomain(one) # answer(goals). [back_rewrite(102),rewrite([4278(5)])]. 39.66/39.96 4372 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),antidomain(antidomain(B))) = antidomain(one). [para(4276(a,1),3172(a,1,2))]. 39.66/39.96 4384 multiplication(addition(antidomain(A),coantidomain(B)),A) = multiplication(coantidomain(B),A). [para(276(a,1),174(a,1,1,2)),rewrite([291(8)])]. 39.66/39.96 5033 multiplication(antidomain(multiplication(A,B)),addition(C,multiplication(A,multiplication(B,D)))) = multiplication(antidomain(multiplication(A,B)),C). [para(186(a,1),62(a,1,1)),rewrite([110(6),42(8)]),flip(a)]. 39.66/39.96 5035 addition(antidomain(one),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(186(a,1),77(a,1,2)),rewrite([42(5),42(11),5033(12),31(9)])]. 39.66/39.96 5092 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = antidomain(one). [para(4358(a,1),186(a,1,2,2))]. 39.66/39.96 5524 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A)) = antidomain(one). [para(3149(a,1),106(a,1,2)),rewrite([31(8)])]. 39.66/39.96 5553 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = antidomain(one). [para(3209(a,1),106(a,1,2)),rewrite([31(8)])]. 39.66/39.96 5560 multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A) = antidomain(one). [para(3215(a,1),106(a,1,2)),rewrite([31(8)])]. 39.66/39.96 5915 multiplication(antidomain(addition(A,B)),A) = antidomain(one). [para(76(a,1),4064(a,1,1,1)),rewrite([267(6)])]. 39.66/39.96 5960 multiplication(antidomain(multiplication(A,addition(B,C))),multiplication(A,B)) = antidomain(one). [para(62(a,1),5915(a,1,1,1))]. 39.66/39.96 5965 multiplication(antidomain(multiplication(A,addition(B,one))),A) = antidomain(one). [para(77(a,1),5915(a,1,1,1))]. 39.66/39.96 6522 multiplication(antidomain(multiplication(A,addition(B,one))),addition(A,C)) = multiplication(antidomain(multiplication(A,addition(B,one))),C). [para(5965(a,1),62(a,1,1)),rewrite([110(8)]),flip(a)]. 39.66/39.96 6870 antidomain(addition(A,multiplication(A,B))) = antidomain(multiplication(A,addition(B,one))). [para(77(a,1),4072(a,1,2,1)),rewrite([5035(7)]),flip(a)]. 39.66/39.96 8456 multiplication(A,coantidomain(multiplication(addition(A,B),antidomain(coantidomain(A))))) = antidomain(one). [para(451(a,1),2548(a,1)),flip(a)]. 39.66/39.96 9270 multiplication(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(multiplication(A,addition(B,one))). [para(959(a,1),269(a,1,1)),rewrite([42(9),109(9),30(12)])]. 39.66/39.96 9651 multiplication(A,addition(coantidomain(A),coantidomain(B))) = multiplication(A,coantidomain(B)). [para(466(a,1),279(a,2,2)),rewrite([42(6),61(7,R),42(6),466(6)])]. 39.66/39.96 10670 multiplication(coantidomain(multiplication(addition(A,one),B)),coantidomain(B)) = coantidomain(multiplication(addition(A,one),B)). [para(475(a,1),292(a,1,2)),rewrite([42(13),108(13),31(12)])]. 39.66/39.96 11010 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = antidomain(one). [para(3230(a,1),106(a,1,2)),rewrite([31(8)])]. 39.66/39.96 11732 multiplication(antidomain(multiplication(A,addition(B,C))),addition(D,multiplication(A,B))) = multiplication(antidomain(multiplication(A,addition(B,C))),D). [para(5960(a,1),62(a,1,1)),rewrite([110(7),42(9)]),flip(a)]. 39.66/39.96 12840 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(46(a,1),363(a,1,2,1)),rewrite([30(5)]),flip(a)]. 39.66/39.96 13185 multiplication(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,addition(B,one)))) = antidomain(addition(A,multiplication(A,B))). [para(6870(a,1),237(a,1,2))]. 39.66/39.96 13187 multiplication(antidomain(addition(A,multiplication(A,B))),C) = multiplication(antidomain(multiplication(A,addition(B,one))),C). [para(6870(a,1),113(a,1,1)),rewrite([42(7),61(7,R),42(6),6522(8),11732(7)]),flip(a)]. 39.66/39.96 14243 multiplication(antidomain(A),multiplication(coantidomain(B),antidomain(A))) = multiplication(coantidomain(B),antidomain(A)). [para(46(a,1),377(a,1,1)),rewrite([30(5)]),flip(a)]. 39.66/39.96 14593 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(46(a,1),394(a,1,1)),rewrite([30(5)]),flip(a)]. 39.66/39.96 15958 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(46(a,1),1161(a,1,2)),rewrite([31(2)]),flip(a)]. 39.66/39.96 15976 addition(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(multiplication(antidomain(antidomain(A)),B)). [para(15958(a,1),118(a,1,2)),rewrite([4276(2),42(6),4276(8)])]. 39.66/39.96 15977 multiplication(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(A). [para(15958(a,1),113(a,2)),rewrite([4276(3),113(7)])]. 39.66/39.96 16005 antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [back_rewrite(4349),rewrite([15976(13)])]. 39.66/39.96 16063 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(4357(a,1),15977(a,1,2,1))]. 39.66/39.96 16074 antidomain(multiplication(A,addition(B,one))) = antidomain(A). [back_rewrite(9270),rewrite([16063(6)]),flip(a)]. 39.66/39.96 16105 multiplication(antidomain(addition(A,multiplication(A,B))),C) = multiplication(antidomain(A),C). [back_rewrite(13187),rewrite([16074(8)])]. 39.66/39.96 16106 antidomain(addition(A,multiplication(A,B))) = antidomain(A). [back_rewrite(13185),rewrite([16074(7),16105(5),237(3)]),flip(a)]. 39.66/39.96 16209 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(16063(a,1),78(a,1,2)),rewrite([42(4),42(7),109(7),30(8)])]. 39.66/39.96 16225 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(16063(a,1),284(a,1,2,2)),rewrite([4276(4),42(6),46(6),42(4),109(4),42(4),109(4),4276(6),42(7),30(8)]),flip(a)]. 39.66/39.96 16226 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(16063(a,1),2549(a,1,2,2,1,1)),rewrite([4276(5),4278(6),14593(6),16063(8)])]. 39.66/39.96 16321 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(16226(a,1),59(a,1,1)),flip(a)]. 39.66/39.96 16360 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(12840),rewrite([16321(7)]),flip(a)]. 39.66/39.96 17397 multiplication(antidomain(antidomain(A)),multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(371(a,1),16360(a,1,1,1)),rewrite([302(3),30(4)]),flip(a)]. 39.66/39.96 17399 multiplication(antidomain(antidomain(A)),coantidomain(addition(B,antidomain(A)))) = coantidomain(addition(B,antidomain(A))). [para(428(a,1),16360(a,1,1,1)),rewrite([302(3),42(3),30(5),42(7)]),flip(a)]. 39.66/39.96 17405 multiplication(coantidomain(A),coantidomain(addition(A,B))) = coantidomain(addition(A,B)). [para(3142(a,1),16360(a,1,1,1)),rewrite([302(3),30(4),2892(5)]),flip(a)]. 39.66/39.96 17406 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(3172(a,1),16360(a,1,1,1)),rewrite([302(3),30(3),2892(5)]),flip(a)]. 39.66/39.96 17407 multiplication(coantidomain(multiplication(A,antidomain(B))),B) = B. [para(3186(a,1),16360(a,1,1,1)),rewrite([302(3),30(2),2892(5)]),flip(a)]. 39.66/39.96 17415 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(5915(a,1),16360(a,1,1,1)),rewrite([302(3),30(2)]),flip(a)]. 39.66/39.96 17420 multiplication(coantidomain(multiplication(A,antidomain(B))),coantidomain(A)) = coantidomain(A). [para(5524(a,1),16360(a,1,1,1)),rewrite([302(3),30(3),2892(6)]),flip(a)]. 39.66/39.96 17423 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A. [para(5553(a,1),16360(a,1,1,1)),rewrite([302(3),30(2),2892(6)]),flip(a)]. 39.66/39.96 17424 multiplication(coantidomain(multiplication(antidomain(A),coantidomain(B))),A) = A. [para(5560(a,1),16360(a,1,1,1)),rewrite([302(3),30(2),2892(6)]),flip(a)]. 39.66/39.96 17443 multiplication(coantidomain(multiplication(A,antidomain(B))),antidomain(antidomain(B))) = antidomain(antidomain(B)). [para(4372(a,1),16360(a,1,1,1)),rewrite([302(3),30(4),2892(7)]),flip(a)]. 39.66/39.96 17448 multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)) = multiplication(A,B). [para(5092(a,1),16360(a,1,1,1)),rewrite([302(3),30(3)]),flip(a)]. 39.66/39.96 17473 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(11010(a,1),16360(a,1,1,1)),rewrite([302(3),30(2),2892(6)]),flip(a)]. 39.66/39.96 17494 coantidomain(multiplication(addition(A,one),B)) = coantidomain(B). [back_rewrite(10670),rewrite([17406(6)]),flip(a)]. 39.66/39.96 17498 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [back_rewrite(16005),rewrite([17448(7)]),flip(a)]. 39.66/39.96 17557 multiplication(antidomain(antidomain(multiplication(c1,c2))),antidomain(antidomain(c3))) != antidomain(one) # answer(goals). [back_rewrite(4367),rewrite([17498(6)])]. 39.66/39.96 17584 addition(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = one. [para(17407(a,1),16225(a,1,2,1)),rewrite([2892(5),42(5)])]. 39.66/39.96 17585 multiplication(antidomain(A),antidomain(coantidomain(multiplication(B,antidomain(A))))) = antidomain(coantidomain(multiplication(B,antidomain(A)))). [para(17407(a,1),16226(a,1,1,1))]. 39.66/39.96 17593 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(42(a,1),17415(a,1,1,1,1))]. 39.66/39.96 17615 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(17415(a,1),16226(a,1,1,1)),rewrite([4278(5),4278(8)])]. 39.66/39.96 17789 addition(antidomain(A),antidomain(addition(B,A))) = antidomain(A). [para(17593(a,1),16209(a,1,2,1)),rewrite([4278(4),42(4),17593(8)])]. 39.66/39.96 17796 addition(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(multiplication(B,A)). [para(17406(a,1),77(a,1,2)),rewrite([42(4),42(9),108(9),31(8)])]. 39.66/39.96 17860 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(17423(a,1),15958(a,1,2,1)),rewrite([59(5),14593(5)])]. 39.66/39.96 17863 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),antidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))). [para(17423(a,1),16063(a,1,2,1)),rewrite([17860(7)])]. 39.66/39.96 17885 multiplication(antidomain(antidomain(c3)),antidomain(antidomain(multiplication(c1,c2)))) != antidomain(one) # answer(goals). [back_rewrite(17557),rewrite([17860(9)])]. 39.66/39.96 18057 multiplication(antidomain(A),coantidomain(B)) = multiplication(coantidomain(B),antidomain(A)). [para(17424(a,1),15958(a,1,2,1)),rewrite([59(5),14243(5)]),flip(a)]. 39.66/39.96 18060 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))). [para(17424(a,1),16063(a,1,2,1)),rewrite([17860(7)])]. 39.66/39.96 18082 multiplication(antidomain(antidomain(A)),coantidomain(multiplication(B,antidomain(A)))) = antidomain(antidomain(A)). [back_rewrite(17443),rewrite([18057(6,R)])]. 39.66/39.96 18121 addition(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = one. [para(2892(a,1),17584(a,1,1)),rewrite([2892(4)])]. 39.66/39.96 18252 addition(antidomain(A),antidomain(multiplication(coantidomain(B),A))) = antidomain(multiplication(coantidomain(B),A)). [para(116(a,1),17789(a,1,2,1)),rewrite([42(5)])]. 39.66/39.96 18253 addition(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(multiplication(antidomain(B),A)). [para(118(a,1),17789(a,1,2,1)),rewrite([42(5)])]. 39.66/39.96 18318 multiplication(coantidomain(A),antidomain(coantidomain(multiplication(B,coantidomain(A))))) = antidomain(coantidomain(multiplication(B,coantidomain(A)))). [para(18121(a,1),138(a,1,1)),rewrite([2880(5),30(6),2880(9)]),flip(a)]. 39.66/39.96 18322 multiplication(A,coantidomain(multiplication(B,coantidomain(A)))) = A. [para(18121(a,1),9651(a,1,2)),rewrite([31(2)]),flip(a)]. 39.66/39.96 18338 multiplication(coantidomain(A),coantidomain(multiplication(B,antidomain(coantidomain(A))))) = coantidomain(A). [para(18322(a,1),291(a,1,2)),rewrite([276(3),2880(4)]),flip(a)]. 39.66/39.96 18435 addition(antidomain(coantidomain(A)),coantidomain(multiplication(A,antidomain(B)))) = one. [para(17420(a,1),244(a,1,2,2)),rewrite([42(7),2875(7),42(5),108(5),42(7),42(10),108(10),31(9)]),flip(a)]. 39.66/39.96 18667 coantidomain(multiplication(addition(A,B),antidomain(coantidomain(A)))) = coantidomain(A). [para(8456(a,1),17473(a,1,1,1,1,1)),rewrite([302(3),30(2),18338(7)]),flip(a)]. 39.66/39.96 18683 addition(antidomain(A),coantidomain(multiplication(antidomain(multiplication(B,A)),B))) = one. [para(17473(a,1),16225(a,1,2,1)),rewrite([2892(6),42(6)])]. 39.66/39.96 18923 antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))) = multiplication(antidomain(A),antidomain(B)). [para(17860(a,1),2549(a,1,2,2,1,1)),rewrite([17860(5),17585(8),17863(7)])]. 39.66/39.96 18939 multiplication(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(A). [para(17860(a,1),15977(a,1,2,1)),rewrite([17498(6)])]. 39.66/39.96 18952 multiplication(coantidomain(multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B)))),B) = B. [para(17860(a,1),17473(a,1,1,1))]. 39.66/39.96 19117 antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))) = multiplication(coantidomain(B),antidomain(A)). [para(18057(a,1),2549(a,2)),rewrite([18318(8),18060(7)])]. 39.66/39.96 19177 multiplication(A,coantidomain(multiplication(coantidomain(A),antidomain(B)))) = A. [para(18057(a,1),18322(a,1,2,1))]. 39.66/39.96 19183 antidomain(multiplication(antidomain(antidomain(A)),coantidomain(B))) = antidomain(multiplication(coantidomain(B),A)). [para(18057(a,2),17498(a,1,1))]. 39.66/39.96 19233 multiplication(A,coantidomain(multiplication(coantidomain(A),coantidomain(B)))) = A. [para(2892(a,1),19177(a,1,2,1,2))]. 39.66/39.96 19471 addition(coantidomain(A),antidomain(coantidomain(addition(A,B)))) = one. [para(18667(a,1),18435(a,1,2)),rewrite([42(5)])]. 39.66/39.96 19492 addition(coantidomain(A),antidomain(coantidomain(addition(B,A)))) = one. [para(480(a,1),19471(a,1,2,1,1)),rewrite([17494(4),17494(6)])]. 39.66/39.96 20410 coantidomain(multiplication(antidomain(coantidomain(A)),B)) = coantidomain(multiplication(A,B)). [para(2548(a,1),17796(a,1,2,1)),rewrite([42(7),3240(7),2548(8)])]. 39.66/39.96 20510 coantidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [para(17860(a,1),20410(a,1,1))]. 39.66/39.96 20850 addition(coantidomain(A),antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = one. [para(136(a,1),18683(a,1,2,1,1,1)),rewrite([302(7),30(6),42(6)])]. 39.66/39.96 21597 multiplication(A,coantidomain(multiplication(A,antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [para(46(a,1),732(a,1,2,1)),rewrite([30(5),18082(10)])]. 39.66/39.96 22317 addition(coantidomain(addition(A,antidomain(B))),antidomain(multiplication(coantidomain(multiplication(A,antidomain(antidomain(B)))),B))) = one. [para(316(a,1),20850(a,1,2,1,2,1)),rewrite([19183(11)])]. 39.66/39.96 24744 antidomain(addition(antidomain(antidomain(A)),multiplication(antidomain(B),A))) = antidomain(A). [para(17397(a,1),16106(a,1,1,2)),rewrite([4278(9)])]. 39.66/39.96 24768 antidomain(antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(19177(a,1),24744(a,1,1,2)),rewrite([4276(2),17860(4),18923(6),17498(5),42(5),18253(5),4276(6),17860(8),18923(10)])]. 39.66/39.96 24769 antidomain(antidomain(multiplication(coantidomain(A),B))) = multiplication(coantidomain(A),antidomain(antidomain(B))). [para(19233(a,1),24744(a,1,1,2)),rewrite([4276(2),19117(6),17498(5),42(5),18252(5),4276(6),19117(10)])]. 39.66/39.96 27115 coantidomain(multiplication(antidomain(A),antidomain(B))) = antidomain(multiplication(antidomain(A),antidomain(B))). [para(18923(a,1),2892(a,1,1)),flip(a)]. 39.66/39.96 27212 antidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [back_rewrite(20510),rewrite([27115(5)])]. 39.66/39.96 27213 multiplication(antidomain(multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B)))),B) = B. [back_rewrite(18952),rewrite([27115(6)])]. 39.66/39.96 27462 coantidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [para(2880(a,1),19183(a,1,1,2)),rewrite([27212(6),2880(6)])]. 39.66/39.96 27494 addition(antidomain(multiplication(coantidomain(A),B)),coantidomain(addition(A,antidomain(B)))) = one. [back_rewrite(22317),rewrite([27462(7),16360(8),2892(6),42(7)])]. 39.66/39.96 28524 multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B))) = multiplication(A,antidomain(B)). [para(4278(a,1),21597(a,2,2)),rewrite([27462(4)])]. 39.66/39.96 29661 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(B)). [para(27213(a,1),16063(a,1,2,1)),rewrite([24768(7),24768(5),17498(6),59(7),17860(6),18939(6),24768(10),24768(8),17498(9)]),flip(a)]. 39.66/39.96 29791 multiplication(coantidomain(A),antidomain(antidomain(B))) = coantidomain(addition(A,antidomain(B))). [para(27494(a,1),113(a,1,2)),rewrite([24769(4),31(6),24769(8),59(12),17399(11),17405(9)])]. 39.66/39.96 29871 multiplication(antidomain(antidomain(A)),antidomain(antidomain(B))) = coantidomain(addition(antidomain(A),antidomain(B))). [para(4276(a,1),29791(a,1,1))]. 39.66/39.96 29884 multiplication(antidomain(antidomain(A)),coantidomain(B)) = coantidomain(addition(B,antidomain(A))). [para(29791(a,1),18057(a,2))]. 39.66/39.96 29977 coantidomain(addition(antidomain(c3),antidomain(multiplication(c1,c2)))) != antidomain(one) # answer(goals). [back_rewrite(17885),rewrite([29871(9)])]. 39.66/39.96 29996 coantidomain(addition(antidomain(c2),multiplication(antidomain(antidomain(c3)),c1))) = antidomain(antidomain(c2)). [back_rewrite(4161),rewrite([29884(10),42(8)])]. 39.66/39.96 30571 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)). [para(17615(a,1),28524(a,2)),rewrite([4276(3),4278(4),113(4),29661(5)])]. 39.66/39.96 30619 coantidomain(addition(antidomain(A),antidomain(B))) = antidomain(addition(antidomain(A),antidomain(B))). [back_rewrite(29871),rewrite([30571(5)]),flip(a)]. 39.66/39.96 30858 antidomain(addition(antidomain(c3),antidomain(multiplication(c1,c2)))) != antidomain(one) # answer(goals). [back_rewrite(29977),rewrite([30619(8)])]. 39.66/39.96 32177 addition(antidomain(c2),coantidomain(multiplication(antidomain(antidomain(c3)),c1))) = one. [para(29996(a,1),19492(a,1,2,1)),rewrite([4278(10),42(9)])]. 39.66/39.96 32393 multiplication(coantidomain(multiplication(antidomain(antidomain(c3)),c1)),c2) = c2. [para(32177(a,1),4384(a,1,1)),rewrite([30(3)]),flip(a)]. 39.66/39.96 32473 multiplication(antidomain(antidomain(c3)),multiplication(c1,c2)) = antidomain(one). [para(32393(a,1),135(a,1,2)),rewrite([59(7)])]. 39.66/39.96 32577 antidomain(addition(antidomain(c3),antidomain(multiplication(c1,c2)))) = antidomain(one). [para(32473(a,1),243(a,1,1,1)),rewrite([302(3),30571(10),30(10)])]. 39.66/39.96 32578 $F # answer(goals). [resolve(32577,a,30858,a)]. 39.66/39.96 39.66/39.96 % SZS output end Refutation 39.66/39.96 ============================== end of proof ========================== 39.66/39.96 39.66/39.96 ============================== STATISTICS ============================ 39.66/39.96 39.66/39.96 Given=1703. Generated=1436722. Kept=32535. proofs=1. 39.66/39.96 Usable=1036. Sos=8423. Demods=9029. Limbo=5, Disabled=23099. Hints=0. 39.66/39.96 Megabytes=26.65. 39.66/39.96 User_CPU=38.72, System_CPU=0.80, Wall_clock=39. 39.66/39.96 39.66/39.96 ============================== end of statistics ===================== 39.66/39.96 39.66/39.96 ============================== end of search ========================= 39.66/39.96 39.66/39.96 THEOREM PROVED 39.66/39.96 % SZS status Theorem 39.66/39.96 39.66/39.96 Exiting with 1 proof. 39.66/39.96 39.66/39.96 Process 23547 exit (max_proofs) Sat Jul 14 05:50:49 2018 39.66/39.96 Prover9 interrupted 39.77/39.97 EOF