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 : n065.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 05:50:54 CDT 2018 0.03/0.23 % CPUTime : 0.06/0.49 ============================== Prover9 =============================== 0.06/0.49 Prover9 (32) version 2009-11A, November 2009. 0.06/0.49 Process 12072 was started by sandbox on n065.star.cs.uiowa.edu, 0.06/0.49 Sat Jul 14 05:50:55 2018 0.06/0.49 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12040_n065.star.cs.uiowa.edu". 0.06/0.49 ============================== end of head =========================== 0.06/0.49 0.06/0.49 ============================== INPUT ================================= 0.06/0.49 0.06/0.49 % Reading from file /tmp/Prover9_12040_n065.star.cs.uiowa.edu 0.06/0.49 0.06/0.49 set(prolog_style_variables). 0.06/0.49 set(auto2). 0.06/0.49 % set(auto2) -> set(auto). 0.06/0.49 % set(auto) -> set(auto_inference). 0.06/0.49 % set(auto) -> set(auto_setup). 0.06/0.49 % set(auto_setup) -> set(predicate_elim). 0.06/0.49 % set(auto_setup) -> assign(eq_defs, unfold). 0.06/0.49 % set(auto) -> set(auto_limits). 0.06/0.49 % set(auto_limits) -> assign(max_weight, "100.000"). 0.06/0.49 % set(auto_limits) -> assign(sos_limit, 20000). 0.06/0.49 % set(auto) -> set(auto_denials). 0.06/0.49 % set(auto) -> set(auto_process). 0.06/0.49 % set(auto2) -> assign(new_constants, 1). 0.06/0.49 % set(auto2) -> assign(fold_denial_max, 3). 0.06/0.49 % set(auto2) -> assign(max_weight, "200.000"). 0.06/0.49 % set(auto2) -> assign(max_hours, 1). 0.06/0.49 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.06/0.49 % set(auto2) -> assign(max_seconds, 0). 0.06/0.49 % set(auto2) -> assign(max_minutes, 5). 0.06/0.49 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.06/0.49 % set(auto2) -> set(sort_initial_sos). 0.06/0.49 % set(auto2) -> assign(sos_limit, -1). 0.06/0.49 % set(auto2) -> assign(lrs_ticks, 3000). 0.06/0.49 % set(auto2) -> assign(max_megs, 400). 0.06/0.49 % set(auto2) -> assign(stats, some). 0.06/0.49 % set(auto2) -> clear(echo_input). 0.06/0.49 % set(auto2) -> set(quiet). 0.06/0.49 % set(auto2) -> clear(print_initial_clauses). 0.06/0.49 % set(auto2) -> clear(print_given). 0.06/0.49 assign(lrs_ticks,-1). 0.06/0.49 assign(sos_limit,10000). 0.06/0.49 assign(order,kbo). 0.06/0.49 set(lex_order_vars). 0.06/0.49 clear(print_given). 0.06/0.49 0.06/0.49 % formulas(sos). % not echoed (27 formulas) 0.06/0.49 0.06/0.49 ============================== end of input ========================== 0.06/0.49 0.06/0.49 % From the command line: assign(max_seconds, 300). 0.06/0.49 0.06/0.49 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.06/0.49 0.06/0.49 % Formulas that are not ordinary clauses: 0.06/0.49 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]. 0.06/0.49 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]. 0.06/0.49 3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 6 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 8 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 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]. 0.06/0.49 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]. 0.06/0.49 11 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.06/0.49 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]. 0.06/0.49 14 (all X0 one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 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]. 3.89/4.16 16 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 17 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 18 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 19 (all X0 one = addition(antidomain(antidomain(X0)),antidomain(X0))) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 20 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 21 (all X0 all X1 codomain(multiplication(codomain(X1),X0)) = backward_diamond(X0,X1)) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 22 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 23 (all X0 all X1 c(backward_diamond(X0,c(X1))) = backward_box(X0,X1)) # label(backward_box) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 24 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 25 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 26 (all X0 antidomain(domain(X0)) = c(X0)) # label(complement) # label(axiom) # label(non_clause). [assumption]. 3.89/4.16 27 -(all X0 all X1 all X2 (zero = multiplication(forward_diamond(X0,domain(X1)),domain(X2)) -> zero = multiplication(domain(X1),backward_diamond(X0,domain(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 3.89/4.16 3.89/4.16 ============================== end of process non-clausal formulas === 3.89/4.16 3.89/4.16 ============================== PROCESS INITIAL CLAUSES =============== 3.89/4.16 3.89/4.16 ============================== PREDICATE ELIMINATION ================= 3.89/4.16 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(11)]. 3.89/4.16 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(11)]. 3.89/4.16 3.89/4.16 ============================== end predicate elimination ============= 3.89/4.16 3.89/4.16 Auto_denials: 3.89/4.16 % copying label goals to answer in negative clause 3.89/4.16 3.89/4.16 Term ordering decisions: 3.89/4.16 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. c3=1. multiplication=1. addition=1. forward_diamond=1. backward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. domain=1. c=1. codomain=1. 3.89/4.16 3.89/4.16 ============================== end of process initial clauses ======== 3.89/4.16 3.89/4.16 ============================== CLAUSES FOR SEARCH ==================== 3.89/4.16 3.89/4.16 ============================== end of clauses for search ============= 3.89/4.16 3.89/4.16 ============================== SEARCH ================================ 3.89/4.16 3.89/4.16 % Starting search at 0.01 seconds. 3.89/4.16 3.89/4.16 Low Water (keep): wt=41.000, iters=3333 3.89/4.16 3.89/4.16 Low Water (keep): wt=40.000, iters=3343 3.89/4.16 3.89/4.16 Low Water (keep): wt=39.000, iters=3337 3.89/4.16 3.89/4.16 Low Water (keep): wt=38.000, iters=3366 3.89/4.16 3.89/4.16 Low Water (keep): wt=36.000, iters=3365 3.89/4.16 3.89/4.16 Low Water (keep): wt=35.000, iters=3366 3.89/4.16 3.89/4.16 Low Water (keep): wt=34.000, iters=3339 3.89/4.16 3.89/4.16 Low Water (keep): wt=33.000, iters=3341 3.89/4.16 3.89/4.16 Low Water (keep): wt=32.000, iters=3350 3.89/4.16 3.89/4.16 Low Water (keep): wt=31.000, iters=3418 3.89/4.16 3.89/4.16 Low Water (keep): wt=30.000, iters=3365 3.89/4.16 3.89/4.16 Low Water (keep): wt=29.000, iters=3347 3.89/4.16 3.89/4.16 Low Water (keep): wt=28.000, iters=3336 3.89/4.16 3.89/4.16 Low Water (keep): wt=27.000, iters=3343 3.89/4.16 3.89/4.16 Low Water (keep): wt=26.000, iters=3333 3.89/4.16 3.89/4.16 Low Water (keep): wt=25.000, iters=3356 3.89/4.16 3.89/4.16 Low Water (keep): wt=24.000, iters=3375 3.89/4.16 3.89/4.16 Low Water (keep): wt=23.000, iters=3348 3.89/4.16 3.89/4.16 Low Water (keep): wt=22.000, iters=3356 3.89/4.16 3.89/4.16 Low Water (displace): id=6213, wt=54.000 3.89/4.16 3.89/4.16 Low Water (displace): id=4337, wt=50.000 86.59/86.86 86.59/86.86 Low Water (displace): id=6467, wt=48.000 86.59/86.86 86.59/86.86 Low Water (displace): id=8190, wt=46.000 86.59/86.86 86.59/86.86 Low Water (displace): id=8243, wt=44.000 86.59/86.86 86.59/86.86 Low Water (displace): id=8192, wt=43.000 86.59/86.86 86.59/86.86 Low Water (displace): id=8210, wt=42.000 86.59/86.86 86.59/86.86 Low Water (displace): id=14292, wt=17.000 86.59/86.86 86.59/86.86 Low Water (displace): id=14885, wt=16.000 86.59/86.86 86.59/86.86 Low Water (displace): id=14913, wt=15.000 86.59/86.86 86.59/86.86 Low Water (keep): wt=21.000, iters=3341 86.59/86.86 86.59/86.86 Low Water (keep): wt=20.000, iters=3352 86.59/86.86 86.59/86.86 Low Water (keep): wt=19.000, iters=3334 86.59/86.86 86.59/86.86 Low Water (displace): id=20885, wt=14.000 86.59/86.86 86.59/86.86 Low Water (displace): id=23066, wt=13.000 86.59/86.86 86.59/86.86 Low Water (keep): wt=18.000, iters=3341 86.59/86.86 86.59/86.86 Low Water (keep): wt=17.000, iters=3350 86.59/86.86 86.59/86.86 Low Water (keep): wt=16.000, iters=3333 86.59/86.86 86.59/86.86 Low Water (keep): wt=15.000, iters=4327 86.59/86.86 86.59/86.86 ============================== PROOF ================================= 86.59/86.86 % SZS status Theorem 86.59/86.86 % SZS output start Refutation 86.59/86.86 86.59/86.86 % Proof 1 at 84.71 (+ 1.65) seconds: goals. 86.59/86.86 % Length of proof is 259. 86.59/86.86 % Level of proof is 34. 86.59/86.86 % Maximum clause weight is 29.000. 86.59/86.86 % Given clauses 2708. 86.59/86.86 86.59/86.86 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]. 86.59/86.86 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]. 86.59/86.86 3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 6 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 8 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 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]. 86.59/86.86 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]. 86.59/86.86 12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 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]. 86.59/86.86 14 (all X0 one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))) # label(codomain3) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 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]. 86.59/86.86 16 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 17 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 18 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 19 (all X0 one = addition(antidomain(antidomain(X0)),antidomain(X0))) # label(domain3) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 20 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 21 (all X0 all X1 codomain(multiplication(codomain(X1),X0)) = backward_diamond(X0,X1)) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 24 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 25 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption]. 86.59/86.86 27 -(all X0 all X1 all X2 (zero = multiplication(forward_diamond(X0,domain(X1)),domain(X2)) -> zero = multiplication(domain(X1),backward_diamond(X0,domain(X2))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 86.59/86.86 30 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(4)]. 86.59/86.86 31 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(5)]. 86.59/86.86 32 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(6)]. 86.59/86.86 33 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(7)]. 86.59/86.86 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(8)]. 86.59/86.86 35 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(12)]. 86.59/86.86 36 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(16)]. 86.59/86.86 37 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(17)]. 86.59/86.86 38 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(18)]. 86.59/86.86 39 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(20)]. 86.59/86.86 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(3)]. 86.59/86.86 43 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(14)]. 86.59/86.86 44 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(43),rewrite([42(4)])]. 86.59/86.86 45 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(19)]. 86.59/86.86 46 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(45),rewrite([42(4)])]. 86.59/86.86 47 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(21)]. 86.59/86.86 48 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(47),rewrite([37(2),37(5)])]. 86.59/86.86 53 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(24)]. 86.59/86.86 54 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(53),rewrite([39(2),39(5)])]. 86.59/86.86 55 domain_difference(A,B) = multiplication(domain(A),antidomain(B)) # label(domain_difference) # label(axiom). [clausify(25)]. 86.59/86.86 56 domain_difference(A,B) = multiplication(antidomain(antidomain(A)),antidomain(B)). [copy(55),rewrite([39(2)])]. 86.59/86.86 57 multiplication(forward_diamond(c1,domain(c2)),domain(c3)) = zero # label(goals) # label(negated_conjecture). [clausify(27)]. 86.59/86.86 58 zero = multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))). [copy(57),rewrite([39(3),54(5),39(11)]),flip(a)]. 86.59/86.86 59 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(9)]. 86.59/86.86 60 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(10)]. 86.59/86.86 61 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(60),rewrite([42(2)]),flip(a)]. 86.59/86.86 62 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom). [clausify(1)]. 86.59/86.86 63 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom). [clausify(2)]. 86.59/86.86 64 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(13)]. 86.59/86.86 65 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(64),flip(a)]. 86.59/86.86 66 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(15)]. 86.59/86.86 67 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(66),flip(a)]. 86.59/86.86 68 multiplication(domain(c2),backward_diamond(c1,domain(c3))) != zero # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)]. 86.59/86.86 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(2),39(6),48(8),58(14)]),flip(a)]. 86.59/86.86 71 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))) = multiplication(antidomain(A),A). [back_rewrite(38),rewrite([58(3)]),flip(a)]. 86.59/86.86 72 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))) = multiplication(A,coantidomain(A)). [back_rewrite(36),rewrite([58(3)]),flip(a)]. 86.59/86.86 73 multiplication(A,multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3)))) = multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))). [back_rewrite(34),rewrite([58(1),58(15)])]. 86.59/86.86 74 addition(A,multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3)))) = A. [back_rewrite(33),rewrite([58(1)])]. 86.59/86.86 75 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),multiplication(antidomain(antidomain(c3)),A)) = multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))). [back_rewrite(32),rewrite([58(1),59(14),58(15)])]. 86.59/86.86 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)])]. 86.59/86.86 77 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)). [para(31(a,1),62(a,1,1)),rewrite([42(4)])]. 86.59/86.86 78 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A). [para(30(a,1),63(a,1,1)),rewrite([42(4)])]. 86.59/86.86 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))]. 86.59/86.86 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)])]. 86.59/86.86 87 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),antidomain(antidomain(c3))) = antidomain(one). [para(71(a,2),31(a,1))]. 86.59/86.86 89 multiplication(antidomain(A),A) = antidomain(one). [para(71(a,1),56(a,2)),rewrite([56(10),87(13)]),flip(a)]. 86.59/86.86 90 multiplication(antidomain(one),A) = antidomain(one). [para(71(a,1),59(a,1,1)),rewrite([89(2),75(17),87(16)])]. 86.59/86.86 91 multiplication(antidomain(A),multiplication(A,B)) = antidomain(one). [para(71(a,2),59(a,1,1)),rewrite([87(13),90(3)]),flip(a)]. 86.59/86.86 93 addition(antidomain(one),multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(A,B)). [para(71(a,2),62(a,1,1)),rewrite([87(13)])]. 86.59/86.86 95 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)])]. 86.59/86.86 97 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)])]. 86.59/86.86 102 multiplication(antidomain(antidomain(c2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) != antidomain(one) # answer(goals). [para(71(a,1),69(a,1)),rewrite([89(2)]),flip(a)]. 86.59/86.86 104 addition(A,antidomain(one)) = A. [back_rewrite(74),rewrite([87(13)])]. 86.59/86.86 105 multiplication(A,antidomain(one)) = antidomain(one). [back_rewrite(73),rewrite([87(13),87(16)])]. 86.59/86.86 106 multiplication(A,coantidomain(A)) = antidomain(one). [back_rewrite(72),rewrite([87(13)]),flip(a)]. 86.59/86.86 108 addition(one,coantidomain(A)) = one. [para(44(a,1),76(a,1,2)),rewrite([42(3),44(7)])]. 86.59/86.86 109 addition(one,antidomain(A)) = one. [para(46(a,1),76(a,1,2)),rewrite([42(3),46(7)])]. 86.59/86.86 110 addition(antidomain(one),multiplication(A,B)) = multiplication(A,B). [para(104(a,1),62(a,2,2)),rewrite([105(4),42(4)])]. 86.59/86.86 111 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [back_rewrite(95),rewrite([110(4)]),flip(a)]. 86.59/86.86 113 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [back_rewrite(93),rewrite([110(5)]),flip(a)]. 86.59/86.86 115 addition(A,multiplication(A,coantidomain(B))) = A. [para(108(a,1),62(a,2,2)),rewrite([31(2),31(5)])]. 86.59/86.86 116 addition(A,multiplication(coantidomain(B),A)) = A. [para(108(a,1),63(a,2,1)),rewrite([30(2),30(5)])]. 86.59/86.86 117 addition(A,multiplication(A,antidomain(B))) = A. [para(109(a,1),62(a,2,2)),rewrite([31(2),31(5)])]. 86.59/86.86 118 addition(A,multiplication(antidomain(B),A)) = A. [para(109(a,1),63(a,2,1)),rewrite([30(2),30(5)])]. 86.59/86.86 134 coantidomain(one) = antidomain(one). [para(106(a,1),30(a,1)),flip(a)]. 86.59/86.86 135 multiplication(A,multiplication(coantidomain(A),B)) = antidomain(one). [para(106(a,1),59(a,1,1)),rewrite([90(3)]),flip(a)]. 86.59/86.86 137 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(106(a,1),62(a,1,1)),rewrite([110(4),42(3)]),flip(a)]. 86.59/86.86 138 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)]. 86.59/86.86 141 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))]. 86.59/86.86 152 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))]. 86.59/86.86 158 addition(antidomain(one),coantidomain(antidomain(one))) = one. [para(134(a,1),44(a,1,1)),rewrite([134(4)])]. 86.59/86.86 160 addition(antidomain(one),antidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(89(a,1),115(a,1,2)),rewrite([42(5)])]. 86.59/86.86 181 addition(antidomain(one),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(106(a,1),118(a,1,2)),rewrite([42(5)])]. 86.59/86.86 182 coantidomain(antidomain(one)) = one. [back_rewrite(158),rewrite([181(6)])]. 86.59/86.86 184 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(97),rewrite([182(3),108(7)]),flip(a)]. 86.59/86.86 186 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = antidomain(one). [para(59(a,1),91(a,1,2))]. 86.59/86.86 198 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))]. 86.59/86.86 222 multiplication(coantidomain(coantidomain(antidomain(A))),A) = antidomain(one). [para(184(a,1),106(a,1,2)),rewrite([31(6)])]. 86.59/86.86 231 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)]. 86.59/86.86 237 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(46(a,1),111(a,1,1)),rewrite([30(3)]),flip(a)]. 86.59/86.86 253 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B)) = one. [para(89(a,1),83(a,1,1,1,2)),rewrite([105(3),182(3),108(8)]),flip(a)]. 86.59/86.86 254 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(89(a,1),83(a,1,1,1)),rewrite([182(3),108(9)]),flip(a)]. 86.59/86.86 255 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)]. 86.59/86.86 267 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(237(a,1),59(a,1,1)),flip(a)]. 86.59/86.86 269 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)]. 86.59/86.86 279 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)]. 86.59/86.86 284 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)])]. 86.59/86.86 290 multiplication(coantidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = antidomain(one). [para(83(a,1),137(a,1,2)),rewrite([106(10),59(10)]),flip(a)]. 86.59/86.86 302 antidomain(antidomain(one)) = one. [para(134(a,1),160(a,1,2,1)),rewrite([46(6),134(3)]),flip(a)]. 86.59/86.86 305 antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))) = one. [back_rewrite(198),rewrite([302(3),109(8)]),flip(a)]. 86.59/86.86 307 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(141),rewrite([302(3),109(7)]),flip(a)]. 86.59/86.86 313 multiplication(A,antidomain(antidomain(coantidomain(A)))) = antidomain(one). [para(307(a,1),89(a,1,1)),rewrite([30(6)])]. 86.59/86.86 324 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)]. 86.59/86.86 339 multiplication(antidomain(multiplication(A,multiplication(B,C))),multiplication(A,multiplication(B,antidomain(antidomain(C))))) = antidomain(one). [para(86(a,1),111(a,1,1)),rewrite([89(10)]),flip(a)]. 86.59/86.86 359 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(44(a,1),113(a,1,2)),rewrite([31(4)]),flip(a)]. 86.59/86.86 363 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))]. 86.59/86.86 367 multiplication(antidomain(A),multiplication(coantidomain(B),A)) = antidomain(one). [para(116(a,1),113(a,1,2)),rewrite([89(2)]),flip(a)]. 86.59/86.86 371 multiplication(antidomain(A),multiplication(antidomain(B),A)) = antidomain(one). [para(118(a,1),113(a,1,2)),rewrite([89(2)]),flip(a)]. 86.59/86.86 377 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)]. 86.59/86.86 384 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)]. 86.59/86.86 392 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2))))))),addition(antidomain(antidomain(c3)),antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(c2)))))))) = antidomain(one). [para(87(a,1),113(a,2)),rewrite([42(21)])]. 86.59/86.86 395 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)]. 86.59/86.86 402 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)]. 86.59/86.86 406 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = antidomain(one). [para(113(a,1),371(a,1,2))]. 86.59/86.86 418 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),138(a,1,1))]. 86.59/86.86 419 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(44(a,1),138(a,1,1)),rewrite([30(5)]),flip(a)]. 86.59/86.86 420 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(46(a,1),138(a,1,1)),rewrite([30(5)]),flip(a)]. 86.59/86.86 429 multiplication(A,coantidomain(addition(A,B))) = antidomain(one). [para(76(a,1),138(a,1,1)),rewrite([106(4)]),flip(a)]. 86.59/86.86 444 coantidomain(addition(A,one)) = antidomain(one). [para(429(a,1),30(a,1)),rewrite([42(4)]),flip(a)]. 86.59/86.86 456 multiplication(A,coantidomain(multiplication(A,addition(B,one)))) = antidomain(one). [para(77(a,1),429(a,1,2,1))]. 86.59/86.86 467 addition(coantidomain(A),coantidomain(addition(A,multiplication(B,A)))) = coantidomain(A). [back_rewrite(152),rewrite([444(6),182(6),30(5),42(5),444(8),182(8),30(7)])]. 86.59/86.86 540 multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B) = antidomain(one). [para(253(a,1),106(a,1,2)),rewrite([31(7)])]. 86.59/86.86 561 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = antidomain(one). [para(255(a,1),106(a,1,2)),rewrite([31(7)])]. 86.59/86.86 571 multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))) = antidomain(one). [para(305(a,1),89(a,1,1)),rewrite([30(7)])]. 86.59/86.86 727 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)])]. 86.59/86.86 734 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(46(a,1),418(a,1,1)),rewrite([30(4)]),flip(a)]. 86.59/86.86 737 multiplication(A,multiplication(addition(B,C),coantidomain(multiplication(A,B)))) = multiplication(A,multiplication(C,coantidomain(multiplication(A,B)))). [para(62(a,1),418(a,1,1)),rewrite([59(5),59(9)])]. 86.59/86.86 955 antidomain(addition(A,one)) = antidomain(one). [para(89(a,1),456(a,1,2,1)),rewrite([182(6),31(5)])]. 86.59/86.86 966 addition(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(A). [para(955(a,1),67(a,1,2,1,2,1)),rewrite([302(7),31(6),42(6),955(9),302(9),31(8)])]. 86.59/86.86 1169 multiplication(A,addition(B,antidomain(antidomain(multiplication(coantidomain(A),C))))) = multiplication(A,B). [para(571(a,1),62(a,1,1)),rewrite([110(4),42(6)]),flip(a)]. 86.59/86.86 2003 multiplication(coantidomain(antidomain(A)),A) = A. [para(44(a,1),231(a,1,1)),rewrite([30(2)]),flip(a)]. 86.59/86.86 2083 multiplication(coantidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B). [para(2003(a,1),59(a,1,1)),flip(a)]. 86.59/86.86 2091 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(2003(a,1),117(a,1,2)),rewrite([42(5)])]. 86.59/86.86 2100 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(2003(a,1),86(a,1,2,1)),rewrite([42(13),2003(22)])]. 86.59/86.86 2490 multiplication(A,antidomain(coantidomain(A))) = A. [para(46(a,1),324(a,1,2)),rewrite([31(2)]),flip(a)]. 86.59/86.86 2558 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2490(a,1),59(a,1,1)),flip(a)]. 86.59/86.86 2559 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2490(a,1),59(a,1)),flip(a)]. 86.59/86.86 2566 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2490(a,1),116(a,1,2)),rewrite([42(5)])]. 86.59/86.86 2601 multiplication(A,coantidomain(coantidomain(A))) = A. [para(359(a,1),2558(a,1,2)),rewrite([2490(3)]),flip(a)]. 86.59/86.86 2634 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(419),rewrite([2601(5)]),flip(a)]. 86.59/86.86 2669 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2634(a,1),727(a,1,2)),rewrite([42(5),2566(5),2634(6)])]. 86.59/86.86 2887 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2669(a,1),734(a,1,1,1)),rewrite([2669(5),359(5),2669(5)]),flip(a)]. 86.59/86.86 2889 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2669(a,1),734(a,2,1)),rewrite([2887(2),2887(6),734(9),2887(6)])]. 86.59/86.86 2898 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2634(a,1),2669(a,1,1,1)),rewrite([2887(2),2887(5)]),flip(a)]. 86.59/86.86 2899 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2634(a,1),2669(a,2)),rewrite([2887(2),2898(3),2889(4)])]. 86.59/86.86 3158 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = antidomain(one). [back_rewrite(561),rewrite([2887(3)])]. 86.59/86.86 3162 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),B) = antidomain(one). [back_rewrite(540),rewrite([2887(4)])]. 86.59/86.86 3171 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [back_rewrite(402),rewrite([2887(5)])]. 86.59/86.86 3175 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [back_rewrite(384),rewrite([2887(5)])]. 86.59/86.86 3180 multiplication(antidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = antidomain(one). [back_rewrite(290),rewrite([2887(3)])]. 86.59/86.86 3190 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(254),rewrite([2887(5)])]. 86.59/86.86 3197 multiplication(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(c3)))),c1)))) != antidomain(one) # answer(goals). [back_rewrite(102),rewrite([2887(8),2887(12)])]. 86.59/86.86 3198 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(antidomain(coantidomain(A)),B))) = coantidomain(multiplication(antidomain(coantidomain(A)),B)). [back_rewrite(65),rewrite([2887(4),2887(9)])]. 86.59/86.86 4038 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = antidomain(one). [para(42(a,1),406(a,1,1,1))]. 86.59/86.86 4042 multiplication(antidomain(addition(A,B)),addition(C,multiplication(antidomain(A),B))) = multiplication(antidomain(addition(A,B)),C). [para(406(a,1),62(a,1,1)),rewrite([110(6),42(8)]),flip(a)]. 86.59/86.86 4046 addition(antidomain(one),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(406(a,1),77(a,1,2)),rewrite([42(5),42(11),4042(12),31(9)])]. 86.59/86.86 4111 coantidomain(antidomain(antidomain(A))) = antidomain(A). [para(420(a,1),77(a,1,2)),rewrite([2091(5),42(9),108(9),31(6)])]. 86.59/86.86 4112 multiplication(antidomain(antidomain(c2)),antidomain(coantidomain(multiplication(antidomain(antidomain(c3)),c1)))) != antidomain(one) # answer(goals). [back_rewrite(3197),rewrite([4111(7)])]. 86.59/86.86 4195 multiplication(antidomain(antidomain(A)),addition(B,antidomain(A))) = multiplication(antidomain(antidomain(A)),B). [para(4111(a,1),137(a,1,2,2))]. 86.59/86.86 4198 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(4111(a,1),2887(a,1,1)),rewrite([4111(5)])]. 86.59/86.86 4199 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(4111(a,1),2887(a,2,1)),rewrite([4198(3),4198(4)])]. 86.59/86.86 4200 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(4111(a,1),2899(a,2)),rewrite([4198(3),4199(4)])]. 86.59/86.86 4201 multiplication(antidomain(antidomain(multiplication(c1,antidomain(antidomain(c2))))),antidomain(antidomain(c3))) = antidomain(one). [back_rewrite(392),rewrite([4200(5),4200(15),4195(18)])]. 86.59/86.86 4273 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(2100),rewrite([4198(9)])]. 86.59/86.86 4281 multiplication(antidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B). [back_rewrite(2083),rewrite([4198(2)])]. 86.59/86.86 4282 multiplication(antidomain(antidomain(A)),A) = A. [back_rewrite(2003),rewrite([4198(2)])]. 86.59/86.86 4372 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),antidomain(antidomain(B))) = antidomain(one). [para(4198(a,1),3158(a,1,2))]. 86.59/86.86 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)]. 86.59/86.86 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)])]. 86.59/86.86 5092 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = antidomain(one). [para(4282(a,1),186(a,1,2,2))]. 86.59/86.86 5553 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = antidomain(one). [para(3171(a,1),106(a,1,2)),rewrite([31(8)])]. 86.59/86.86 5560 multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A) = antidomain(one). [para(3175(a,1),106(a,1,2)),rewrite([31(8)])]. 86.59/86.86 5915 multiplication(antidomain(addition(A,B)),A) = antidomain(one). [para(76(a,1),4038(a,1,1,1)),rewrite([267(6)])]. 86.59/86.86 5960 multiplication(antidomain(multiplication(A,addition(B,C))),multiplication(A,B)) = antidomain(one). [para(62(a,1),5915(a,1,1,1))]. 86.59/86.86 5965 multiplication(antidomain(multiplication(A,addition(B,one))),A) = antidomain(one). [para(77(a,1),5915(a,1,1,1))]. 86.59/86.86 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)]. 86.59/86.86 6870 antidomain(addition(A,multiplication(A,B))) = antidomain(multiplication(A,addition(B,one))). [para(77(a,1),4046(a,1,2,1)),rewrite([5035(7)]),flip(a)]. 86.59/86.86 9264 multiplication(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(multiplication(A,addition(B,one))). [para(966(a,1),269(a,1,1)),rewrite([42(9),109(9),30(12)])]. 86.59/86.86 9645 multiplication(A,addition(coantidomain(A),coantidomain(B))) = multiplication(A,coantidomain(B)). [para(467(a,1),279(a,2,2)),rewrite([42(6),61(7,R),42(6),467(6)])]. 86.59/86.86 11004 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = antidomain(one). [para(3190(a,1),106(a,1,2)),rewrite([31(8)])]. 86.59/86.86 11725 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)]. 86.59/86.86 12833 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)]. 86.59/86.86 13178 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))]. 86.59/86.86 13180 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),11725(7)]),flip(a)]. 86.59/86.86 14236 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)]. 86.59/86.86 14586 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(46(a,1),395(a,1,1)),rewrite([30(5)]),flip(a)]. 86.59/86.86 15951 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(46(a,1),1169(a,1,2)),rewrite([31(2)]),flip(a)]. 86.59/86.86 15969 addition(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(multiplication(antidomain(antidomain(A)),B)). [para(15951(a,1),118(a,1,2)),rewrite([4198(2),42(6),4198(8)])]. 86.59/86.86 15970 multiplication(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(A). [para(15951(a,1),113(a,2)),rewrite([4198(3),113(7)])]. 86.59/86.86 15998 antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [back_rewrite(4273),rewrite([15969(13)])]. 86.59/86.86 16056 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(4281(a,1),15970(a,1,2,1))]. 86.59/86.86 16067 antidomain(multiplication(A,addition(B,one))) = antidomain(A). [back_rewrite(9264),rewrite([16056(6)]),flip(a)]. 86.59/86.86 16100 multiplication(antidomain(addition(A,multiplication(A,B))),C) = multiplication(antidomain(A),C). [back_rewrite(13180),rewrite([16067(8)])]. 86.59/86.86 16101 antidomain(addition(A,multiplication(A,B))) = antidomain(A). [back_rewrite(13178),rewrite([16067(7),16100(5),237(3)]),flip(a)]. 86.59/86.86 16204 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(16056(a,1),78(a,1,2)),rewrite([42(4),42(7),109(7),30(8)])]. 86.59/86.86 16220 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(16056(a,1),284(a,1,2,2)),rewrite([4198(4),42(6),46(6),42(4),109(4),42(4),109(4),4198(6),42(7),30(8)]),flip(a)]. 86.59/86.86 16221 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(16056(a,1),2559(a,1,2,2,1,1)),rewrite([4198(5),4200(6),14586(6),16056(8)])]. 86.59/86.86 16316 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(16221(a,1),59(a,1,1)),flip(a)]. 86.59/86.86 16355 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(12833),rewrite([16316(7)]),flip(a)]. 86.59/86.86 17394 multiplication(antidomain(antidomain(A)),multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(371(a,1),16355(a,1,1,1)),rewrite([302(3),30(4)]),flip(a)]. 86.59/86.86 17403 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(3158(a,1),16355(a,1,1,1)),rewrite([302(3),30(3),2899(5)]),flip(a)]. 86.59/86.86 17404 multiplication(coantidomain(multiplication(A,antidomain(B))),B) = B. [para(3162(a,1),16355(a,1,1,1)),rewrite([302(3),30(2),2899(5)]),flip(a)]. 86.59/86.86 17412 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(5915(a,1),16355(a,1,1,1)),rewrite([302(3),30(2)]),flip(a)]. 86.59/86.86 17420 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A. [para(5553(a,1),16355(a,1,1,1)),rewrite([302(3),30(2),2899(6)]),flip(a)]. 86.59/86.86 17421 multiplication(coantidomain(multiplication(antidomain(A),coantidomain(B))),A) = A. [para(5560(a,1),16355(a,1,1,1)),rewrite([302(3),30(2),2899(6)]),flip(a)]. 86.59/86.86 17440 multiplication(coantidomain(multiplication(A,antidomain(B))),antidomain(antidomain(B))) = antidomain(antidomain(B)). [para(4372(a,1),16355(a,1,1,1)),rewrite([302(3),30(4),2899(7)]),flip(a)]. 86.59/86.86 17445 multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)) = multiplication(A,B). [para(5092(a,1),16355(a,1,1,1)),rewrite([302(3),30(3)]),flip(a)]. 86.59/86.86 17470 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(11004(a,1),16355(a,1,1,1)),rewrite([302(3),30(2),2899(6)]),flip(a)]. 86.59/86.86 17495 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [back_rewrite(15998),rewrite([17445(7)]),flip(a)]. 86.59/86.86 17565 multiplication(antidomain(antidomain(multiplication(c1,c2))),antidomain(antidomain(c3))) = antidomain(one). [back_rewrite(4201),rewrite([17495(6)])]. 86.59/86.86 17599 addition(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = one. [para(17404(a,1),16220(a,1,2,1)),rewrite([2899(5),42(5)])]. 86.59/86.86 17600 multiplication(antidomain(A),antidomain(coantidomain(multiplication(B,antidomain(A))))) = antidomain(coantidomain(multiplication(B,antidomain(A)))). [para(17404(a,1),16221(a,1,1,1))]. 86.59/86.86 17612 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(42(a,1),17412(a,1,1,1,1))]. 86.59/86.86 17640 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(17412(a,1),16221(a,1,1,1)),rewrite([4200(5),4200(8)])]. 86.59/86.86 17851 addition(antidomain(A),antidomain(addition(B,A))) = antidomain(A). [para(17612(a,1),16204(a,1,2,1)),rewrite([4200(4),42(4),17612(8)])]. 86.59/86.86 17858 addition(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(multiplication(B,A)). [para(17403(a,1),77(a,1,2)),rewrite([42(4),42(9),108(9),31(8)])]. 86.59/86.86 17920 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(17420(a,1),15951(a,1,2,1)),rewrite([59(5),14586(5)])]. 86.59/86.86 17923 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),antidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))). [para(17420(a,1),16056(a,1,2,1)),rewrite([17920(7)])]. 86.59/86.86 17942 multiplication(antidomain(antidomain(c3)),antidomain(antidomain(multiplication(c1,c2)))) = antidomain(one). [back_rewrite(17565),rewrite([17920(9)])]. 86.59/86.86 18123 multiplication(antidomain(A),coantidomain(B)) = multiplication(coantidomain(B),antidomain(A)). [para(17421(a,1),15951(a,1,2,1)),rewrite([59(5),14236(5)]),flip(a)]. 86.59/86.86 18152 multiplication(antidomain(antidomain(A)),coantidomain(multiplication(B,antidomain(A)))) = antidomain(antidomain(A)). [back_rewrite(17440),rewrite([18123(6,R)])]. 86.59/86.86 18219 addition(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = one. [para(2899(a,1),17599(a,1,1)),rewrite([2899(4)])]. 86.59/86.86 18350 addition(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(multiplication(antidomain(B),A)). [para(118(a,1),17851(a,1,2,1)),rewrite([42(5)])]. 86.59/86.86 18419 multiplication(A,coantidomain(multiplication(B,coantidomain(A)))) = A. [para(18219(a,1),9645(a,1,2)),rewrite([31(2)]),flip(a)]. 86.59/86.86 19013 antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))) = multiplication(antidomain(A),antidomain(B)). [para(17920(a,1),2559(a,1,2,2,1,1)),rewrite([17920(5),17600(8),17923(7)])]. 86.59/86.86 19029 multiplication(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(A). [para(17920(a,1),15970(a,1,2,1)),rewrite([17495(6)])]. 86.59/86.86 19042 multiplication(coantidomain(multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B)))),B) = B. [para(17920(a,1),17470(a,1,1,1))]. 86.59/86.86 19266 multiplication(A,coantidomain(multiplication(coantidomain(A),antidomain(B)))) = A. [para(18123(a,1),18419(a,1,2,1))]. 86.59/86.86 19272 antidomain(multiplication(antidomain(antidomain(A)),coantidomain(B))) = antidomain(multiplication(coantidomain(B),A)). [para(18123(a,2),17495(a,1,1))]. 86.59/86.86 20495 coantidomain(multiplication(antidomain(coantidomain(A)),B)) = coantidomain(multiplication(A,B)). [para(2558(a,1),17858(a,1,2,1)),rewrite([42(7),3198(7),2558(8)])]. 86.59/86.86 20595 coantidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [para(17920(a,1),20495(a,1,1))]. 86.59/86.86 20666 antidomain(multiplication(antidomain(antidomain(c3)),multiplication(c1,c2))) = one. [para(17942(a,1),17495(a,1,1)),rewrite([302(3)]),flip(a)]. 86.59/86.86 20670 multiplication(antidomain(antidomain(c3)),multiplication(c1,antidomain(antidomain(c2)))) = antidomain(one). [para(20666(a,1),339(a,1,1)),rewrite([30(11)])]. 86.59/86.86 21603 multiplication(A,coantidomain(multiplication(A,antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [para(46(a,1),737(a,1,2,1)),rewrite([30(5),18152(10)])]. 86.59/86.86 26853 antidomain(addition(antidomain(antidomain(A)),multiplication(antidomain(B),A))) = antidomain(A). [para(17394(a,1),16101(a,1,1,2)),rewrite([4200(9)])]. 86.59/86.86 26872 antidomain(antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(19266(a,1),26853(a,1,1,2)),rewrite([4198(2),17920(4),19013(6),17495(5),42(5),18350(5),4198(6),17920(8),19013(10)])]. 86.59/86.86 29158 coantidomain(multiplication(antidomain(A),antidomain(B))) = antidomain(multiplication(antidomain(A),antidomain(B))). [para(19013(a,1),2899(a,1,1)),flip(a)]. 86.59/86.86 29258 antidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [back_rewrite(20595),rewrite([29158(5)])]. 86.59/86.86 29259 multiplication(antidomain(multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B)))),B) = B. [back_rewrite(19042),rewrite([29158(6)])]. 86.59/86.86 29423 coantidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [para(2887(a,1),19272(a,1,1,2)),rewrite([29258(6),2887(6)])]. 86.59/86.86 35038 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(B)). [para(29259(a,1),16056(a,1,2,1)),rewrite([26872(7),26872(5),17495(6),59(7),17920(6),19029(6),26872(10),26872(8),17495(9)]),flip(a)]. 86.59/86.86 35099 multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B))) = multiplication(A,antidomain(B)). [para(29423(a,1),21603(a,1,2)),rewrite([4200(8)])]. 86.59/86.86 36419 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)). [para(17640(a,1),35099(a,2)),rewrite([4198(3),4200(4),113(4),35038(5)])]. 86.59/86.86 36633 antidomain(addition(antidomain(c2),coantidomain(multiplication(antidomain(antidomain(c3)),c1)))) != antidomain(one) # answer(goals). [back_rewrite(4112),rewrite([36419(11)])]. 86.59/86.86 39395 antidomain(addition(antidomain(c2),coantidomain(multiplication(antidomain(antidomain(c3)),c1)))) = antidomain(one). [para(20670(a,1),3180(a,1,2,2,1)),rewrite([4198(13),302(13),31(12),36419(11),42(9)])]. 86.59/86.86 39396 $F # answer(goals). [resolve(39395,a,36633,a)]. 86.59/86.86 86.59/86.86 % SZS output end Refutation 86.59/86.86 ============================== end of proof ========================== 86.59/86.86 86.59/86.86 ============================== STATISTICS ============================ 86.59/86.86 86.59/86.86 Given=2708. Generated=3175623. Kept=39353. proofs=1. 86.59/86.86 Usable=1718. Sos=7746. Demods=9150. Limbo=9, Disabled=29908. Hints=0. 86.59/86.86 Megabytes=30.32. 86.59/86.86 User_CPU=84.71, System_CPU=1.65, Wall_clock=86. 86.59/86.86 86.59/86.86 ============================== end of statistics ===================== 86.59/86.86 86.59/86.86 ============================== end of search ========================= 86.59/86.86 86.59/86.86 THEOREM PROVED 86.59/86.86 % SZS status Theorem 86.59/86.86 86.59/86.86 Exiting with 1 proof. 86.59/86.86 86.59/86.86 Process 12072 exit (max_proofs) Sat Jul 14 05:52:21 2018 86.59/86.86 Prover9 interrupted 86.59/86.87 EOF