TSTP Solution File: KLE109+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : KLE109+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 02:22:16 EDT 2022
% Result : Theorem 73.03s 73.35s
% Output : Refutation 73.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE109+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 11:19:50 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.68/0.97 ============================== Prover9 ===============================
% 0.68/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.68/0.97 Process 12229 was started by sandbox2 on n014.cluster.edu,
% 0.68/0.97 Thu Jun 16 11:19:51 2022
% 0.68/0.97 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12059_n014.cluster.edu".
% 0.68/0.97 ============================== end of head ===========================
% 0.68/0.97
% 0.68/0.97 ============================== INPUT =================================
% 0.68/0.97
% 0.68/0.97 % Reading from file /tmp/Prover9_12059_n014.cluster.edu
% 0.68/0.97
% 0.68/0.97 set(prolog_style_variables).
% 0.68/0.97 set(auto2).
% 0.68/0.97 % set(auto2) -> set(auto).
% 0.68/0.97 % set(auto) -> set(auto_inference).
% 0.68/0.97 % set(auto) -> set(auto_setup).
% 0.68/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.68/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/0.97 % set(auto) -> set(auto_limits).
% 0.68/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/0.97 % set(auto) -> set(auto_denials).
% 0.68/0.97 % set(auto) -> set(auto_process).
% 0.68/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.68/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.68/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.68/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.68/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.68/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.68/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.68/0.97 % set(auto2) -> assign(stats, some).
% 0.68/0.97 % set(auto2) -> clear(echo_input).
% 0.68/0.97 % set(auto2) -> set(quiet).
% 0.68/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.68/0.97 % set(auto2) -> clear(print_given).
% 0.68/0.97 assign(lrs_ticks,-1).
% 0.68/0.97 assign(sos_limit,10000).
% 0.68/0.97 assign(order,kbo).
% 0.68/0.97 set(lex_order_vars).
% 0.68/0.97 clear(print_given).
% 0.68/0.97
% 0.68/0.97 % formulas(sos). % not echoed (27 formulas)
% 0.68/0.97
% 0.68/0.97 ============================== end of input ==========================
% 0.68/0.97
% 0.68/0.97 % From the command line: assign(max_seconds, 300).
% 0.68/0.97
% 0.68/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/0.97
% 0.68/0.97 % Formulas that are not ordinary clauses:
% 0.68/0.97 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 2 (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].
% 0.68/0.97 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 12 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 0.68/0.97 14 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 18 (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].
% 5.00/5.27 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 22 (all X0 all X1 domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1))) # label(domain_difference) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 25 (all X0 all X1 forward_box(X0,X1) = c(forward_diamond(X0,c(X1)))) # label(forward_box) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 5.00/5.27 27 -(all X0 all X1 addition(forward_diamond(X0,backward_box(X0,domain(X1))),domain(X1)) = domain(X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.00/5.27
% 5.00/5.27 ============================== end of process non-clausal formulas ===
% 5.00/5.27
% 5.00/5.27 ============================== PROCESS INITIAL CLAUSES ===============
% 5.00/5.27
% 5.00/5.27 ============================== PREDICATE ELIMINATION =================
% 5.00/5.27 28 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(12)].
% 5.00/5.27 29 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom). [clausify(12)].
% 5.00/5.27
% 5.00/5.27 ============================== end predicate elimination =============
% 5.00/5.27
% 5.00/5.27 Auto_denials:
% 5.00/5.27 % copying label goals to answer in negative clause
% 5.00/5.27
% 5.00/5.27 Term ordering decisions:
% 5.00/5.27 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. backward_diamond=1. forward_diamond=1. backward_box=1. domain_difference=1. forward_box=1. antidomain=1. coantidomain=1. c=1. domain=1. codomain=1.
% 5.00/5.27
% 5.00/5.27 ============================== end of process initial clauses ========
% 5.00/5.27
% 5.00/5.27 ============================== CLAUSES FOR SEARCH ====================
% 5.00/5.27
% 5.00/5.27 ============================== end of clauses for search =============
% 5.00/5.27
% 5.00/5.27 ============================== SEARCH ================================
% 5.00/5.27
% 5.00/5.27 % Starting search at 0.01 seconds.
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=36.000, iters=3371
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=33.000, iters=3334
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=32.000, iters=3363
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=31.000, iters=3361
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=30.000, iters=3341
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=29.000, iters=3400
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=28.000, iters=3336
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=27.000, iters=3356
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=26.000, iters=3342
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=25.000, iters=3336
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=21.000, iters=4360
% 5.00/5.27
% 5.00/5.27 Low Water (keep): wt=20.000, iters=3982
% 5.00/5.27
% 5.00/5.27 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 1.80 sec).
% 5.00/5.27
% 5.00/5.27 Low Water (displace): id=6269, wt=49.000
% 5.00/5.27
% 5.00/5.27 Low Water (displace): id=3691, wt=48.000
% 5.00/5.27
% 5.00/5.27 Low Water (displace): id=6917, wt=47.000
% 5.00/5.27
% 5.00/5.27 Low Water (displace): id=4653, wt=46.000
% 5.00/5.27
% 5.00/5.27 Low Water (displace): id=6918, wt=45.000
% 5.00/5.27
% 5.00/5.27 Low Water (displace): id=5879, wt=44.000
% 5.00/5.27
% 5.00/5.27 Low Water (displace): id=4321, wt=43.000
% 5.00/5.27
% 5.00/5.27 Low Water (displace): id=15505, wt=19.000
% 73.03/73.35
% 73.03/73.35 Low Water (displace): id=15513, wt=18.000
% 73.03/73.35
% 73.03/73.35 Low Water (displace): id=15514, wt=17.000
% 73.03/73.35
% 73.03/73.35 Low Water (displace): id=15539, wt=15.000
% 73.03/73.35
% 73.03/73.35 Low Water (displace): id=15971, wt=14.000
% 73.03/73.35
% 73.03/73.35 Low Water (keep): wt=19.000, iters=3338
% 73.03/73.35
% 73.03/73.35 Low Water (displace): id=16592, wt=13.000
% 73.03/73.35
% 73.03/73.35 Low Water (keep): wt=18.000, iters=3338
% 73.03/73.35
% 73.03/73.35 Low Water (displace): id=22341, wt=12.000
% 73.03/73.35
% 73.03/73.35 Low Water (keep): wt=17.000, iters=3341
% 73.03/73.35
% 73.03/73.35 Low Water (keep): wt=16.000, iters=3340
% 73.03/73.35
% 73.03/73.35 ============================== PROOF =================================
% 73.03/73.35 % SZS status Theorem
% 73.03/73.35 % SZS output start Refutation
% 73.03/73.35
% 73.03/73.35 % Proof 1 at 70.02 (+ 2.38) seconds: goals.
% 73.03/73.35 % Length of proof is 337.
% 73.03/73.35 % Level of proof is 40.
% 73.03/73.35 % Maximum clause weight is 29.000.
% 73.03/73.35 % Given clauses 3057.
% 73.03/73.35
% 73.03/73.35 1 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 2 (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].
% 73.03/73.35 3 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 4 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 5 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 6 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 8 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 9 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 10 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 11 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 13 (all X0 multiplication(antidomain(X0),X0) = zero) # label(domain1) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 14 (all X0 all X1 addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1))))) # label(domain2) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 15 (all X0 addition(antidomain(antidomain(X0)),antidomain(X0)) = one) # label(domain3) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 16 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 17 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 18 (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].
% 73.03/73.35 19 (all X0 addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one) # label(codomain3) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 20 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 21 (all X0 c(X0) = antidomain(domain(X0))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 23 (all X0 all X1 forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1)))) # label(forward_diamond) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 24 (all X0 all X1 backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0))) # label(backward_diamond) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 26 (all X0 all X1 backward_box(X0,X1) = c(backward_diamond(X0,c(X1)))) # label(backward_box) # label(axiom) # label(non_clause). [assumption].
% 73.03/73.35 27 -(all X0 all X1 addition(forward_diamond(X0,backward_box(X0,domain(X1))),domain(X1)) = domain(X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 73.03/73.35 30 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(3)].
% 73.03/73.35 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(4)].
% 73.03/73.35 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(6)].
% 73.03/73.35 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(7)].
% 73.03/73.35 34 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(10)].
% 73.03/73.35 35 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(11)].
% 73.03/73.35 36 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom). [clausify(13)].
% 73.03/73.35 37 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom). [clausify(16)].
% 73.03/73.35 38 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom). [clausify(17)].
% 73.03/73.35 39 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom). [clausify(20)].
% 73.03/73.35 40 c(A) = antidomain(domain(A)) # label(complement) # label(axiom). [clausify(21)].
% 73.03/73.35 41 c(A) = antidomain(antidomain(antidomain(A))). [copy(40),rewrite([37(2)])].
% 73.03/73.35 42 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(1)].
% 73.03/73.35 43 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom). [clausify(15)].
% 73.03/73.35 44 addition(antidomain(A),antidomain(antidomain(A))) = one. [copy(43),rewrite([42(4)])].
% 73.03/73.35 45 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom). [clausify(19)].
% 73.03/73.35 46 addition(coantidomain(A),coantidomain(coantidomain(A))) = one. [copy(45),rewrite([42(4)])].
% 73.03/73.35 49 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom). [clausify(23)].
% 73.03/73.35 50 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))). [copy(49),rewrite([37(2),37(5)])].
% 73.03/73.36 51 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom). [clausify(24)].
% 73.03/73.36 52 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))). [copy(51),rewrite([39(2),39(5)])].
% 73.03/73.36 55 backward_box(A,B) = c(backward_diamond(A,c(B))) # label(backward_box) # label(axiom). [clausify(26)].
% 73.03/73.36 56 backward_box(A,B) = antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(B))))),A)))))). [copy(55),rewrite([41(2),52(5),41(10)])].
% 73.03/73.36 57 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(2)].
% 73.03/73.36 58 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(57),rewrite([42(2)]),flip(a)].
% 73.03/73.36 59 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom). [clausify(5)].
% 73.03/73.36 60 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(8)].
% 73.03/73.36 61 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(60),flip(a)].
% 73.03/73.36 62 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(9)].
% 73.03/73.36 63 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(62),flip(a)].
% 73.03/73.36 64 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom). [clausify(14)].
% 73.03/73.36 65 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))). [copy(64),flip(a)].
% 73.03/73.36 66 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom). [clausify(18)].
% 73.03/73.36 67 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)). [copy(66),flip(a)].
% 73.03/73.36 68 domain(c2) != addition(forward_diamond(c1,backward_box(c1,domain(c2))),domain(c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(27)].
% 73.03/73.36 69 addition(antidomain(antidomain(c2)),antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(antidomain(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))),c1)))))))))))) != antidomain(antidomain(c2)) # answer(goals). [copy(68),rewrite([37(2),37(7),56(9),50(20),37(26),42(28)]),flip(a)].
% 73.03/73.36 70 antidomain(one) = zero. [para(36(a,1),32(a,1)),flip(a)].
% 73.03/73.36 71 coantidomain(one) = zero. [para(38(a,1),33(a,1)),flip(a)].
% 73.03/73.36 72 addition(A,addition(A,B)) = addition(A,B). [para(58(a,1),31(a,1)),rewrite([42(1),42(2),58(2,R),31(1),42(3)])].
% 73.03/73.36 73 multiplication(antidomain(A),multiplication(A,B)) = zero. [para(36(a,1),59(a,1,1)),rewrite([35(2)]),flip(a)].
% 73.03/73.36 74 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(59(a,1),38(a,1))].
% 73.03/73.36 75 multiplication(A,multiplication(coantidomain(A),B)) = zero. [para(38(a,1),59(a,1,1)),rewrite([35(2)]),flip(a)].
% 73.03/73.36 76 addition(zero,multiplication(A,B)) = multiplication(A,B). [para(30(a,1),61(a,2,2)),rewrite([34(3),42(3)])].
% 73.03/73.36 77 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),61(a,1,1)),rewrite([42(4)]),flip(a)].
% 73.03/73.36 78 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B). [para(36(a,1),61(a,1,1)),rewrite([76(4)]),flip(a)].
% 73.03/73.36 79 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B). [para(38(a,1),61(a,1,1)),rewrite([76(3),42(3)]),flip(a)].
% 73.03/73.36 80 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)). [para(33(a,1),63(a,1,1)),rewrite([42(4)]),flip(a)].
% 73.03/73.36 81 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B). [para(36(a,1),63(a,1,1)),rewrite([76(3),42(3)]),flip(a)].
% 73.03/73.36 82 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)). [para(38(a,1),63(a,1,1)),rewrite([76(4),42(3)]),flip(a)].
% 73.03/73.36 83 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)])].
% 73.03/73.36 90 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))). [para(38(a,1),65(a,1,1,1))].
% 73.03/73.36 91 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),65(a,1,1,1)),rewrite([59(7),59(13)])].
% 73.03/73.36 95 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)). [para(36(a,1),67(a,1,1,1))].
% 73.03/73.36 98 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),67(a,1,1,1))].
% 73.03/73.36 99 addition(zero,antidomain(zero)) = one. [para(70(a,1),44(a,1,1)),rewrite([70(3)])].
% 73.03/73.36 100 addition(zero,coantidomain(zero)) = one. [para(71(a,1),46(a,1,1)),rewrite([71(3)])].
% 73.03/73.36 103 multiplication(A,antidomain(zero)) = A. [para(99(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 73.03/73.36 107 multiplication(A,coantidomain(zero)) = A. [para(100(a,1),61(a,2,2)),rewrite([34(2),76(5),32(5)])].
% 73.03/73.36 109 addition(one,antidomain(A)) = one. [para(44(a,1),72(a,1,2)),rewrite([42(3),44(7)])].
% 73.03/73.36 110 addition(one,coantidomain(A)) = one. [para(46(a,1),72(a,1,2)),rewrite([42(3),46(7)])].
% 73.03/73.36 111 antidomain(zero) = one. [para(103(a,1),33(a,1)),flip(a)].
% 73.03/73.36 112 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one. [back_rewrite(90),rewrite([111(2),109(7)]),flip(a)].
% 73.03/73.36 114 coantidomain(zero) = one. [para(107(a,1),33(a,1)),flip(a)].
% 73.03/73.36 116 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one. [back_rewrite(95),rewrite([114(2),110(7)]),flip(a)].
% 73.03/73.36 117 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero. [para(59(a,1),73(a,1,2))].
% 73.03/73.36 120 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one. [para(73(a,1),65(a,1,1,1)),rewrite([111(2),109(8)]),flip(a)].
% 73.03/73.36 122 addition(A,multiplication(A,antidomain(B))) = A. [para(109(a,1),61(a,2,2)),rewrite([32(2),32(5)])].
% 73.03/73.36 123 addition(A,multiplication(antidomain(B),A)) = A. [para(109(a,1),63(a,2,1)),rewrite([33(2),33(5)])].
% 73.03/73.36 124 addition(A,multiplication(A,coantidomain(B))) = A. [para(110(a,1),61(a,2,2)),rewrite([32(2),32(5)])].
% 73.03/73.36 125 addition(A,multiplication(coantidomain(B),A)) = A. [para(110(a,1),63(a,2,1)),rewrite([33(2),33(5)])].
% 73.03/73.36 127 multiplication(A,addition(B,multiplication(coantidomain(A),C))) = multiplication(A,B). [para(75(a,1),61(a,1,1)),rewrite([76(3),42(4)]),flip(a)].
% 73.03/73.36 128 multiplication(addition(A,B),multiplication(coantidomain(B),C)) = multiplication(A,multiplication(coantidomain(B),C)). [para(75(a,1),63(a,1,1)),rewrite([76(5),42(4)]),flip(a)].
% 73.03/73.36 129 antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))) = one. [para(75(a,1),65(a,1,1,1)),rewrite([111(2),109(8)]),flip(a)].
% 73.03/73.36 135 multiplication(addition(A,B),multiplication(C,coantidomain(multiplication(B,C)))) = multiplication(A,multiplication(C,coantidomain(multiplication(B,C)))). [para(74(a,1),63(a,1,1)),rewrite([76(6),42(5)]),flip(a)].
% 73.03/73.36 141 addition(A,addition(B,multiplication(A,coantidomain(C)))) = addition(A,B). [para(124(a,1),58(a,2,2)),rewrite([42(3),42(5)])].
% 73.03/73.36 147 multiplication(addition(A,multiplication(A,B)),C) = multiplication(A,multiplication(addition(B,one),C)). [para(77(a,1),59(a,1,1))].
% 73.03/73.36 149 addition(addition(A,multiplication(A,B)),multiplication(A,C)) = multiplication(A,addition(B,addition(C,one))). [para(77(a,1),61(a,1,1)),rewrite([42(7),58(7,R),42(6)])].
% 73.03/73.36 151 addition(addition(A,multiplication(A,B)),multiplication(C,addition(B,one))) = multiplication(addition(A,C),addition(B,one)). [para(77(a,1),63(a,1,1))].
% 73.03/73.36 155 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,antidomain(antidomain(addition(B,one)))))) = antidomain(multiplication(A,antidomain(antidomain(addition(B,one))))). [para(77(a,1),65(a,1,1,1))].
% 73.03/73.36 159 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero. [para(112(a,1),36(a,1,1)),rewrite([33(6)])].
% 73.03/73.36 164 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B). [para(159(a,1),61(a,1,1)),rewrite([76(3),42(5)]),flip(a)].
% 73.03/73.36 170 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)). [para(46(a,1),78(a,1,2)),rewrite([32(4)]),flip(a)].
% 73.03/73.36 173 addition(multiplication(antidomain(A),B),multiplication(C,addition(A,B))) = multiplication(addition(C,antidomain(A)),addition(A,B)). [para(78(a,1),63(a,1,1)),rewrite([42(7)])].
% 73.03/73.36 174 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)). [para(63(a,1),78(a,1,2))].
% 73.03/73.36 178 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero. [para(123(a,1),78(a,1,2)),rewrite([36(2)]),flip(a)].
% 73.03/73.36 179 multiplication(antidomain(A),multiplication(coantidomain(B),A)) = zero. [para(125(a,1),78(a,1,2)),rewrite([36(2)]),flip(a)].
% 73.03/73.36 191 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A). [para(46(a,1),79(a,1,2)),rewrite([32(3)]),flip(a)].
% 73.03/73.36 194 multiplication(A,addition(B,addition(C,coantidomain(A)))) = multiplication(A,addition(B,C)). [para(79(a,1),61(a,1,1)),rewrite([61(3),42(5),58(5,R),42(4)]),flip(a)].
% 73.03/73.36 198 multiplication(coantidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [para(67(a,1),79(a,1,2)),rewrite([38(8),59(7)]),flip(a)].
% 73.03/73.36 200 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)). [para(191(a,1),61(a,1,1)),rewrite([77(4,R),42(7)]),flip(a)].
% 73.03/73.36 205 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero. [para(116(a,1),38(a,1,2)),rewrite([32(6)])].
% 73.03/73.36 209 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [para(205(a,1),63(a,1,1)),rewrite([76(3),42(5)]),flip(a)].
% 73.03/73.36 213 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)). [para(178(a,1),63(a,1,1)),rewrite([76(5),42(5)]),flip(a)].
% 73.03/73.36 216 multiplication(antidomain(addition(A,B)),multiplication(antidomain(A),B)) = zero. [para(78(a,1),178(a,1,2))].
% 73.03/73.36 229 addition(coantidomain(addition(A,multiplication(B,A))),coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A))) = coantidomain(multiplication(coantidomain(coantidomain(addition(B,one))),A)). [para(80(a,1),67(a,1,1,1))].
% 73.03/73.36 239 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))). [para(79(a,1),80(a,2,2)),rewrite([42(9),58(9),42(8),58(9,R),42(8)])].
% 73.03/73.36 240 multiplication(antidomain(A),multiplication(coantidomain(B),multiplication(A,C))) = zero. [para(179(a,1),59(a,1,1)),rewrite([35(2),59(5)]),flip(a)].
% 73.03/73.36 242 multiplication(addition(A,antidomain(B)),multiplication(coantidomain(C),B)) = multiplication(A,multiplication(coantidomain(C),B)). [para(179(a,1),63(a,1,1)),rewrite([76(5),42(5)]),flip(a)].
% 73.03/73.36 256 multiplication(antidomain(A),antidomain(A)) = antidomain(A). [para(44(a,1),81(a,1,1)),rewrite([33(3)]),flip(a)].
% 73.03/73.36 258 multiplication(addition(A,addition(B,antidomain(C))),C) = multiplication(addition(A,B),C). [para(81(a,1),63(a,1,1)),rewrite([63(3),42(5),58(5,R),42(4)]),flip(a)].
% 73.03/73.36 260 multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = zero. [para(65(a,1),81(a,1,1)),rewrite([36(8)]),flip(a)].
% 73.03/73.36 263 multiplication(addition(A,antidomain(B)),addition(B,one)) = addition(A,addition(antidomain(B),multiplication(A,B))). [para(81(a,1),77(a,2,2)),rewrite([42(9),58(9),42(8),58(9,R),42(8)])].
% 73.03/73.36 264 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)). [para(42(a,1),82(a,1,1))].
% 73.03/73.36 265 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))). [para(44(a,1),82(a,1,1)),rewrite([33(5)]),flip(a)].
% 73.03/73.36 266 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))). [para(46(a,1),82(a,1,1)),rewrite([33(5)]),flip(a)].
% 73.03/73.36 270 multiplication(A,multiplication(addition(B,C),coantidomain(multiplication(A,C)))) = multiplication(A,multiplication(B,coantidomain(multiplication(A,C)))). [para(61(a,1),82(a,1,1)),rewrite([59(5),59(9)])].
% 73.03/73.36 275 multiplication(A,coantidomain(addition(A,B))) = zero. [para(72(a,1),82(a,1,1)),rewrite([38(4)]),flip(a)].
% 73.03/73.36 279 multiplication(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),B). [para(256(a,1),59(a,1,1)),flip(a)].
% 73.03/73.36 280 multiplication(antidomain(A),addition(B,antidomain(A))) = multiplication(antidomain(A),addition(B,one)). [para(256(a,1),61(a,1,1)),rewrite([77(4,R),42(7)]),flip(a)].
% 73.03/73.36 281 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)). [para(256(a,1),63(a,1,1)),rewrite([80(4,R),42(6)]),flip(a)].
% 73.03/73.36 285 coantidomain(addition(A,one)) = zero. [para(275(a,1),33(a,1)),rewrite([42(3)]),flip(a)].
% 73.03/73.36 295 coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B)))) = one. [para(275(a,1),67(a,1,1,1)),rewrite([114(2),110(8)]),flip(a)].
% 73.03/73.36 297 multiplication(A,coantidomain(multiplication(A,addition(B,one)))) = zero. [para(77(a,2),275(a,1,2,1))].
% 73.03/73.36 302 addition(coantidomain(A),coantidomain(addition(A,multiplication(B,A)))) = coantidomain(A). [back_rewrite(229),rewrite([285(6),114(5),33(5),42(5),285(8),114(7),33(7)])].
% 73.03/73.36 307 multiplication(addition(antidomain(A),multiplication(B,C)),A) = multiplication(B,multiplication(C,A)). [para(36(a,1),83(a,1,2)),rewrite([42(4),76(4)]),flip(a)].
% 73.03/73.36 336 multiplication(addition(A,multiplication(B,coantidomain(C))),coantidomain(C)) = multiplication(addition(B,A),coantidomain(C)). [para(191(a,1),83(a,1,1,2)),rewrite([63(5)]),flip(a)].
% 73.03/73.36 440 antidomain(addition(A,one)) = zero. [para(36(a,1),297(a,1,2,1)),rewrite([114(5),32(5)])].
% 73.03/73.36 450 addition(antidomain(A),antidomain(addition(A,multiplication(A,B)))) = antidomain(A). [back_rewrite(155),rewrite([440(6),111(5),32(5),42(5),440(8),111(7),32(7)])].
% 73.03/73.36 451 addition(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(A). [para(440(a,1),65(a,1,2,1,2,1)),rewrite([111(6),32(6),42(6),440(9),111(8),32(8)])].
% 73.03/73.36 482 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,addition(B,multiplication(B,C))))) = antidomain(multiplication(A,B)). [para(77(a,1),91(a,1,1,1,2)),rewrite([440(7),111(6),32(6),42(7),440(10),111(9),32(9)])].
% 73.03/73.36 517 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero. [para(120(a,1),36(a,1,1)),rewrite([33(7)])].
% 73.03/73.36 525 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B). [para(517(a,1),61(a,1,1)),rewrite([76(4),42(7)]),flip(a)].
% 73.03/73.36 534 multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))) = zero. [para(129(a,1),36(a,1,1)),rewrite([33(7)])].
% 73.03/73.36 543 multiplication(addition(A,B),antidomain(antidomain(multiplication(coantidomain(B),C)))) = multiplication(A,antidomain(antidomain(multiplication(coantidomain(B),C)))). [para(534(a,1),63(a,1,1)),rewrite([76(7),42(6)]),flip(a)].
% 73.03/73.36 567 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B)) = one. [para(36(a,1),98(a,1,1,1,2)),rewrite([34(2),114(2),110(8)]),flip(a)].
% 73.03/73.36 568 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [para(36(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 73.03/73.36 569 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one. [para(38(a,1),98(a,1,1,1,2)),rewrite([34(2),114(2),110(8)]),flip(a)].
% 73.03/73.36 589 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [para(178(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 73.03/73.36 594 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [para(179(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 73.03/73.36 656 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)). [para(170(a,1),123(a,1,2)),rewrite([42(5)])].
% 73.03/73.36 754 multiplication(antidomain(addition(A,B)),multiplication(antidomain(B),A)) = zero. [para(42(a,1),216(a,1,1,1))].
% 73.03/73.36 822 multiplication(antidomain(A),addition(B,multiplication(coantidomain(C),multiplication(A,D)))) = multiplication(antidomain(A),B). [para(240(a,1),61(a,1,1)),rewrite([76(4),42(7)]),flip(a)].
% 73.03/73.36 853 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(44(a,1),264(a,1,1)),rewrite([33(4)]),flip(a)].
% 73.03/73.36 857 multiplication(addition(A,B),multiplication(C,coantidomain(multiplication(A,C)))) = multiplication(B,multiplication(C,coantidomain(multiplication(A,C)))). [para(63(a,1),264(a,1,1)),rewrite([59(5),59(9)])].
% 73.03/73.36 859 multiplication(A,multiplication(antidomain(B),coantidomain(A))) = zero. [para(122(a,1),264(a,1,1)),rewrite([38(2),59(5)]),flip(a)].
% 73.03/73.36 861 multiplication(A,multiplication(coantidomain(B),coantidomain(A))) = zero. [para(124(a,1),264(a,1,1)),rewrite([38(2),59(5)]),flip(a)].
% 73.03/73.36 885 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [para(859(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 73.03/73.36 890 multiplication(A,addition(B,addition(C,multiplication(coantidomain(A),D)))) = multiplication(A,addition(B,C)). [para(127(a,1),61(a,1,1)),rewrite([61(3),42(6),58(6,R),42(5)]),flip(a)].
% 73.03/73.36 930 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [para(861(a,1),98(a,1,1,1)),rewrite([114(2),110(9)]),flip(a)].
% 73.03/73.36 959 multiplication(addition(A,B),multiplication(coantidomain(A),C)) = multiplication(B,multiplication(coantidomain(A),C)). [para(42(a,1),128(a,1,1))].
% 73.03/73.36 1036 multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [para(295(a,1),38(a,1,2)),rewrite([32(7)])].
% 73.03/73.36 1099 multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [para(567(a,1),38(a,1,2)),rewrite([32(7)])].
% 73.03/73.36 1114 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [para(569(a,1),38(a,1,2)),rewrite([32(7)])].
% 73.03/73.36 1128 multiplication(coantidomain(coantidomain(addition(A,multiplication(B,A)))),coantidomain(A)) = zero. [para(80(a,1),1114(a,1,1,1,1))].
% 73.03/73.36 1186 multiplication(antidomain(addition(A,B)),A) = zero. [para(72(a,1),754(a,1,1,1)),rewrite([279(6)])].
% 73.03/73.36 1225 multiplication(antidomain(A),multiplication(B,coantidomain(multiplication(antidomain(antidomain(A)),B)))) = multiplication(B,coantidomain(multiplication(antidomain(antidomain(A)),B))). [para(44(a,1),135(a,1,1)),rewrite([33(7)]),flip(a)].
% 73.03/73.36 1425 addition(one,addition(coantidomain(A),coantidomain(B))) = one. [para(110(a,1),141(a,2)),rewrite([33(5)])].
% 73.03/73.36 1442 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)). [para(853(a,1),124(a,1,2))].
% 73.03/73.36 2298 addition(A,addition(B,multiplication(addition(A,B),C))) = multiplication(addition(A,B),addition(C,one)). [para(77(a,1),151(a,1,2)),rewrite([58(5,R),58(4,R),63(3),58(4,R),42(3)])].
% 73.03/73.36 2387 multiplication(A,antidomain(coantidomain(A))) = A. [para(44(a,1),164(a,1,2)),rewrite([32(2)]),flip(a)].
% 73.03/73.36 2409 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B). [para(2387(a,1),59(a,1,1)),flip(a)].
% 73.03/73.36 2410 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B). [para(2387(a,1),59(a,1)),flip(a)].
% 73.03/73.36 2411 multiplication(A,addition(B,antidomain(coantidomain(A)))) = addition(A,multiplication(A,B)). [para(2387(a,1),61(a,1,1)),rewrite([42(5)]),flip(a)].
% 73.03/73.36 2417 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))). [para(2387(a,1),125(a,1,2)),rewrite([42(5)])].
% 73.03/73.36 2516 multiplication(A,coantidomain(coantidomain(A))) = A. [para(170(a,1),2409(a,1,2)),rewrite([2387(3)]),flip(a)].
% 73.03/73.36 2549 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A). [back_rewrite(266),rewrite([2516(5)]),flip(a)].
% 73.03/73.36 2578 antidomain(coantidomain(coantidomain(A))) = coantidomain(A). [para(2549(a,1),656(a,1,2)),rewrite([42(5),2417(5),2549(6)])].
% 73.03/73.36 2593 addition(antidomain(antidomain(c2)),antidomain(antidomain(multiplication(c1,antidomain(antidomain(antidomain(antidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))),c1)))))))))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(69),rewrite([2578(17)])].
% 73.03/73.36 2680 addition(coantidomain(A),antidomain(coantidomain(A))) = one. [para(2578(a,1),44(a,1,1)),rewrite([2578(4)])].
% 73.03/73.36 2686 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)). [para(2578(a,1),853(a,1,1,1)),rewrite([2578(5),170(5),2578(5)]),flip(a)].
% 73.03/73.36 2688 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)). [para(2578(a,1),853(a,2,1)),rewrite([2686(2),2686(6),853(9),2686(6)])].
% 73.03/73.36 2695 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))). [para(2549(a,1),2578(a,1,1,1)),rewrite([2686(2),2686(5)]),flip(a)].
% 73.03/73.36 2696 antidomain(antidomain(coantidomain(A))) = coantidomain(A). [para(2549(a,1),2578(a,2)),rewrite([2686(2),2695(3),2688(4)])].
% 73.03/73.36 2709 addition(antidomain(antidomain(c2)),antidomain(antidomain(multiplication(c1,coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))))),c1)))))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(2593),rewrite([2686(12),2696(17),2696(17)])].
% 73.03/73.36 2921 multiplication(antidomain(coantidomain(addition(A,multiplication(B,A)))),coantidomain(A)) = zero. [back_rewrite(1128),rewrite([2686(4)])].
% 73.03/73.36 2928 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero. [back_rewrite(1114),rewrite([2686(3)])].
% 73.03/73.36 2941 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero. [back_rewrite(1099),rewrite([2686(4)])].
% 73.03/73.36 2961 multiplication(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero. [back_rewrite(1036),rewrite([2686(2)])].
% 73.03/73.36 2966 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one. [back_rewrite(930),rewrite([2686(4)])].
% 73.03/73.36 2969 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one. [back_rewrite(885),rewrite([2686(4)])].
% 73.03/73.36 3011 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one. [back_rewrite(594),rewrite([2686(5)])].
% 73.03/73.36 3016 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one. [back_rewrite(589),rewrite([2686(5)])].
% 73.03/73.36 3027 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one. [back_rewrite(568),rewrite([2686(5)])].
% 73.03/73.36 3046 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B). [back_rewrite(209),rewrite([2686(3)])].
% 73.03/73.36 3050 multiplication(antidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero. [back_rewrite(198),rewrite([2686(2)])].
% 73.03/73.36 3053 backward_diamond(A,B) = antidomain(coantidomain(multiplication(antidomain(coantidomain(B)),A))). [back_rewrite(52),rewrite([2686(3),2686(6)])].
% 73.03/73.36 3337 addition(multiplication(antidomain(antidomain(A)),B),multiplication(antidomain(A),addition(B,one))) = addition(B,antidomain(A)). [para(44(a,1),173(a,2,1)),rewrite([42(6),280(7),42(11),33(12)])].
% 73.03/73.36 3372 multiplication(A,multiplication(addition(coantidomain(A),antidomain(B)),addition(B,C))) = multiplication(A,multiplication(antidomain(B),C)). [para(173(a,1),127(a,1,2))].
% 73.03/73.36 3465 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B). [para(44(a,1),174(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 73.03/73.36 3558 multiplication(antidomain(multiplication(coantidomain(A),B)),multiplication(antidomain(coantidomain(A)),B)) = multiplication(antidomain(multiplication(coantidomain(A),B)),B). [para(2680(a,1),174(a,1,2,1)),rewrite([33(5)]),flip(a)].
% 73.03/73.36 3937 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),antidomain(antidomain(B))) = zero. [para(2941(a,1),260(a,1,1,1)),rewrite([111(2),33(9)])].
% 73.03/73.36 3959 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = antidomain(A). [para(265(a,1),124(a,1,2))].
% 73.03/73.36 4466 multiplication(A,addition(coantidomain(A),coantidomain(B))) = multiplication(A,coantidomain(B)). [para(302(a,1),194(a,2,2)),rewrite([42(6),58(7,R),42(6),302(6)])].
% 73.03/73.36 4541 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,multiplication(addition(B,one),addition(C,one))))) = antidomain(addition(A,multiplication(A,B))). [para(147(a,1),450(a,1,2,1,2)),rewrite([149(10),42(8),2298(9)])].
% 73.03/73.36 4932 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)). [para(1442(a,1),200(a,1,2)),rewrite([42(11),109(11),32(9)])].
% 73.03/73.36 4937 multiplication(coantidomain(antidomain(antidomain(A))),antidomain(A)) = coantidomain(antidomain(antidomain(A))). [para(3959(a,1),200(a,1,2)),rewrite([42(11),109(11),32(10)])].
% 73.03/73.36 4939 multiplication(coantidomain(addition(A,multiplication(B,A))),coantidomain(A)) = coantidomain(addition(A,multiplication(B,A))). [para(302(a,1),200(a,1,2)),rewrite([42(11),110(11),32(10)])].
% 73.03/73.36 5151 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)). [para(44(a,1),213(a,1,1)),rewrite([33(5)]),flip(a)].
% 73.03/73.36 7571 addition(antidomain(antidomain(A)),antidomain(coantidomain(antidomain(A)))) = one. [para(4932(a,1),239(a,2,2,2)),rewrite([42(4),110(4),2686(6),33(8),2686(11),42(14),2680(14),42(10),109(10)])].
% 73.03/73.36 7899 multiplication(antidomain(A),multiplication(coantidomain(B),antidomain(A))) = multiplication(coantidomain(B),antidomain(A)). [para(44(a,1),242(a,1,1)),rewrite([33(5)]),flip(a)].
% 73.03/73.36 8566 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A)) = zero. [para(2966(a,1),38(a,1,2)),rewrite([32(8)])].
% 73.03/73.36 8581 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(addition(A,B))) = zero. [para(82(a,1),8566(a,1,1,1,1))].
% 73.03/73.36 8595 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A)) = zero. [para(2969(a,1),38(a,1,2)),rewrite([32(8)])].
% 73.03/73.36 8724 multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A) = zero. [para(3011(a,1),38(a,1,2)),rewrite([32(8)])].
% 73.03/73.36 8965 multiplication(A,multiplication(antidomain(antidomain(B)),coantidomain(multiplication(A,antidomain(coantidomain(antidomain(B))))))) = multiplication(A,coantidomain(multiplication(A,antidomain(coantidomain(antidomain(B)))))). [para(7571(a,1),270(a,1,2,1)),rewrite([33(7)]),flip(a)].
% 73.03/73.36 9112 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = zero. [para(3016(a,1),38(a,1,2)),rewrite([32(8)])].
% 73.03/73.36 9145 multiplication(coantidomain(antidomain(A)),A) = A. [para(2680(a,1),3046(a,1,1)),rewrite([33(2)]),flip(a)].
% 73.03/73.36 9155 multiplication(antidomain(antidomain(A)),A) = A. [para(7571(a,1),3046(a,1,1)),rewrite([33(2)]),flip(a)].
% 73.03/73.36 9159 coantidomain(antidomain(antidomain(A))) = antidomain(A). [back_rewrite(4937),rewrite([9145(5)]),flip(a)].
% 73.03/73.36 9171 addition(antidomain(antidomain(c2)),antidomain(antidomain(multiplication(c1,coantidomain(multiplication(antidomain(antidomain(antidomain(antidomain(antidomain(c2))))),c1)))))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(2709),rewrite([9159(11)])].
% 73.03/73.36 9209 multiplication(antidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B). [para(9155(a,1),59(a,1,1)),flip(a)].
% 73.03/73.36 9219 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero. [para(9155(a,1),117(a,1,2,2))].
% 73.03/73.36 9251 coantidomain(antidomain(A)) = antidomain(antidomain(A)). [para(9159(a,1),2686(a,1,1)),rewrite([9159(5)])].
% 73.03/73.36 9252 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)). [para(9159(a,1),2686(a,2,1)),rewrite([9251(3),9251(4)])].
% 73.03/73.36 9253 antidomain(antidomain(antidomain(A))) = antidomain(A). [para(9159(a,1),2696(a,2)),rewrite([9251(3),9252(4)])].
% 73.03/73.36 9269 multiplication(A,multiplication(antidomain(antidomain(B)),coantidomain(multiplication(A,antidomain(B))))) = multiplication(A,coantidomain(multiplication(A,antidomain(B)))). [back_rewrite(8965),rewrite([9251(4),9253(5),9251(9),9253(10)])].
% 73.03/73.36 9408 addition(antidomain(antidomain(c2)),antidomain(antidomain(multiplication(c1,coantidomain(multiplication(antidomain(c2),c1)))))) != antidomain(antidomain(c2)) # answer(goals). [back_rewrite(9171),rewrite([9253(8),9253(8)])].
% 73.03/73.36 9475 multiplication(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(multiplication(A,addition(B,one))). [para(451(a,1),281(a,1,1)),rewrite([42(9),109(9),33(12)])].
% 73.03/73.36 10101 multiplication(addition(antidomain(A),antidomain(B)),A) = multiplication(antidomain(B),A). [para(256(a,1),307(a,1,1,2)),rewrite([279(8)])].
% 73.03/73.36 12937 multiplication(addition(coantidomain(A),coantidomain(B)),coantidomain(A)) = coantidomain(A). [para(125(a,1),336(a,1,1)),rewrite([191(3),42(4)]),flip(a)].
% 73.03/73.36 12976 addition(coantidomain(A),addition(coantidomain(B),antidomain(coantidomain(A)))) = one. [para(12937(a,1),263(a,2,2,2)),rewrite([42(6),58(6,R),42(9),110(9),32(8),42(13),2680(13),42(11),1425(11)])].
% 73.03/73.36 12983 addition(antidomain(A),addition(antidomain(antidomain(A)),coantidomain(B))) = one. [para(9251(a,1),12976(a,1,1)),rewrite([9251(5),9253(6),58(6)])].
% 73.03/73.36 12995 addition(antidomain(A),addition(antidomain(antidomain(A)),antidomain(coantidomain(B)))) = one. [para(2686(a,1),12983(a,1,2,2))].
% 73.03/73.36 13058 addition(antidomain(A),addition(antidomain(B),antidomain(antidomain(A)))) = one. [para(9251(a,1),12995(a,1,2,2,1)),rewrite([9253(6),42(5)])].
% 73.03/73.36 13064 multiplication(addition(antidomain(A),antidomain(B)),antidomain(A)) = antidomain(A). [para(13058(a,1),258(a,1,1)),rewrite([33(3)]),flip(a)].
% 73.03/73.36 13080 multiplication(antidomain(antidomain(addition(antidomain(A),antidomain(B)))),antidomain(A)) = antidomain(A). [para(13064(a,1),9209(a,1,2)),rewrite([13064(12)])].
% 73.03/73.36 13346 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero. [para(3027(a,1),38(a,1,2)),rewrite([32(8)])].
% 73.03/73.36 15372 addition(antidomain(antidomain(A)),antidomain(antidomain(addition(antidomain(A),antidomain(B))))) = one. [para(13080(a,1),263(a,2,2,2)),rewrite([42(8),42(11),109(11),32(10),42(17),44(17),42(15),109(15)])].
% 73.03/73.36 16414 multiplication(antidomain(A),antidomain(antidomain(addition(antidomain(A),antidomain(B))))) = antidomain(A). [para(15372(a,1),78(a,1,2)),rewrite([9253(3),32(3),9253(4)]),flip(a)].
% 73.03/73.36 16700 antidomain(multiplication(A,addition(B,one))) = antidomain(addition(A,multiplication(A,B))). [para(77(a,1),482(a,1,1,1)),rewrite([77(9,R),4541(11)]),flip(a)].
% 73.03/73.36 16848 multiplication(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,B)). [para(65(a,1),16414(a,1,2,1,1)),rewrite([9253(8)])].
% 73.03/73.36 17172 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A). [para(44(a,1),525(a,1,2)),rewrite([32(3)]),flip(a)].
% 73.03/73.36 17175 antidomain(multiplication(A,addition(B,one))) = antidomain(A). [back_rewrite(9475),rewrite([17172(6)]),flip(a)].
% 73.03/73.36 17179 antidomain(addition(A,multiplication(A,B))) = antidomain(A). [back_rewrite(16700),rewrite([17175(4)]),flip(a)].
% 73.03/73.36 17300 addition(antidomain(A),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)). [para(17172(a,1),123(a,1,2)),rewrite([42(4)])].
% 73.03/73.36 17309 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A. [para(17172(a,1),2409(a,1,2)),rewrite([2387(3)]),flip(a)].
% 73.03/73.36 17317 addition(antidomain(antidomain(A)),antidomain(multiplication(A,B))) = one. [para(17172(a,1),239(a,2,2,2)),rewrite([42(3),109(3),9251(5),42(6),33(7),9251(9),42(11),44(11),42(9),109(9)])].
% 73.03/73.36 17325 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A). [para(17172(a,1),2410(a,1,2,2,1,1)),rewrite([9251(5),9253(6),5151(6),17172(8)])].
% 73.03/73.36 17449 addition(antidomain(A),antidomain(multiplication(antidomain(A),B))) = one. [para(78(a,1),17317(a,1,2,1)),rewrite([9253(3)])].
% 73.03/73.36 17499 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C). [para(17325(a,1),59(a,1,1)),flip(a)].
% 73.03/73.36 17530 multiplication(antidomain(multiplication(coantidomain(A),B)),B) = multiplication(antidomain(coantidomain(A)),B). [back_rewrite(3558),rewrite([17499(7)]),flip(a)].
% 73.03/73.36 17531 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B). [back_rewrite(3465),rewrite([17499(7)]),flip(a)].
% 73.03/73.36 17555 multiplication(antidomain(multiplication(antidomain(A),B)),A) = A. [para(17449(a,1),10101(a,1,1)),rewrite([33(2)]),flip(a)].
% 73.03/73.36 18509 multiplication(antidomain(antidomain(A)),multiplication(antidomain(B),A)) = multiplication(antidomain(B),A). [para(178(a,1),17531(a,1,1,1)),rewrite([111(2),33(4)]),flip(a)].
% 73.03/73.36 18513 multiplication(antidomain(antidomain(addition(A,B))),A) = A. [para(1186(a,1),17531(a,1,1,1)),rewrite([111(2),33(2)]),flip(a)].
% 73.03/73.36 18521 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B). [para(2928(a,1),17531(a,1,1,1)),rewrite([111(2),33(3),2696(5)]),flip(a)].
% 73.03/73.36 18522 multiplication(coantidomain(multiplication(A,antidomain(B))),B) = B. [para(2941(a,1),17531(a,1,1,1)),rewrite([111(2),33(2),2696(5)]),flip(a)].
% 73.03/73.36 18523 multiplication(coantidomain(A),coantidomain(addition(A,B))) = coantidomain(addition(A,B)). [para(2961(a,1),17531(a,1,1,1)),rewrite([111(2),33(4),2696(5)]),flip(a)].
% 73.03/73.36 18533 coantidomain(addition(A,multiplication(B,A))) = coantidomain(A). [para(2921(a,1),17531(a,1,1,1)),rewrite([111(2),33(3),2696(6),4939(6)]),flip(a)].
% 73.03/73.36 18540 multiplication(coantidomain(multiplication(A,coantidomain(B))),coantidomain(A)) = coantidomain(A). [para(8566(a,1),17531(a,1,1,1)),rewrite([111(2),33(3),2696(6)]),flip(a)].
% 73.03/73.36 18541 multiplication(coantidomain(multiplication(A,antidomain(B))),coantidomain(A)) = coantidomain(A). [para(8595(a,1),17531(a,1,1,1)),rewrite([111(2),33(3),2696(6)]),flip(a)].
% 73.03/73.36 18542 multiplication(coantidomain(multiplication(antidomain(A),coantidomain(B))),A) = A. [para(8724(a,1),17531(a,1,1,1)),rewrite([111(2),33(2),2696(6)]),flip(a)].
% 73.03/73.36 18543 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A. [para(9112(a,1),17531(a,1,1,1)),rewrite([111(2),33(2),2696(6)]),flip(a)].
% 73.03/73.36 18545 multiplication(coantidomain(A),multiplication(B,coantidomain(multiplication(A,B)))) = multiplication(B,coantidomain(multiplication(A,B))). [para(3050(a,1),17531(a,1,1,1)),rewrite([111(2),33(5),2696(6)]),flip(a)].
% 73.03/73.36 18548 multiplication(coantidomain(multiplication(A,antidomain(B))),antidomain(antidomain(B))) = antidomain(antidomain(B)). [para(3937(a,1),17531(a,1,1,1)),rewrite([111(2),33(4),2696(7)]),flip(a)].
% 73.03/73.36 18566 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B. [para(13346(a,1),17531(a,1,1,1)),rewrite([111(2),33(2),2696(6)]),flip(a)].
% 73.03/73.36 18606 multiplication(antidomain(antidomain(addition(A,B))),B) = B. [para(42(a,1),18513(a,1,1,1,1))].
% 73.03/73.36 18637 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)). [para(18513(a,1),17325(a,1,1,1)),rewrite([9253(5),9253(8)])].
% 73.03/73.36 18685 addition(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = one. [para(18522(a,1),17317(a,1,2,1)),rewrite([2696(5),42(5)])].
% 73.03/73.36 18686 multiplication(antidomain(A),antidomain(coantidomain(multiplication(B,antidomain(A))))) = antidomain(coantidomain(multiplication(B,antidomain(A)))). [para(18522(a,1),17325(a,1,1,1))].
% 73.03/73.36 18732 coantidomain(addition(A,multiplication(B,multiplication(C,A)))) = coantidomain(A). [para(59(a,1),18533(a,1,1,2))].
% 73.03/73.36 18755 coantidomain(addition(A,antidomain(multiplication(coantidomain(A),B)))) = antidomain(antidomain(multiplication(coantidomain(A),B))). [para(17309(a,1),18533(a,1,1,2)),rewrite([42(4),9251(9)])].
% 73.03/73.36 18809 addition(antidomain(A),antidomain(addition(B,A))) = antidomain(A). [para(18606(a,1),17300(a,1,2,1)),rewrite([9253(4),42(4),18606(8)])].
% 73.03/73.36 18828 addition(antidomain(coantidomain(A)),coantidomain(multiplication(B,A))) = one. [para(18521(a,1),263(a,2,2,2)),rewrite([42(5),42(8),110(8),32(7),42(11),2680(11),42(9),110(9)])].
% 73.03/73.36 18833 coantidomain(addition(A,coantidomain(multiplication(B,A)))) = zero. [para(18521(a,1),8581(a,1,1,1,1)),rewrite([2686(2),2696(3),42(4),18523(6)])].
% 73.03/73.36 18853 coantidomain(addition(A,coantidomain(A))) = zero. [para(33(a,1),18833(a,1,1,2,1))].
% 73.03/73.36 18898 multiplication(A,coantidomain(multiplication(addition(B,coantidomain(B)),A))) = zero. [para(18853(a,1),3050(a,1,1,1)),rewrite([111(2),33(7)])].
% 73.03/73.36 18986 multiplication(coantidomain(A),antidomain(B)) = multiplication(antidomain(B),coantidomain(A)). [para(18542(a,1),17309(a,1,2,1)),rewrite([59(5),7899(5)])].
% 73.03/73.36 18989 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))). [para(18542(a,1),17325(a,1,1,1))].
% 73.03/73.36 19018 multiplication(antidomain(antidomain(A)),coantidomain(multiplication(B,antidomain(A)))) = antidomain(antidomain(A)). [back_rewrite(18548),rewrite([18986(6)])].
% 73.03/73.36 19075 multiplication(A,coantidomain(multiplication(A,antidomain(B)))) = multiplication(A,antidomain(antidomain(B))). [back_rewrite(9269),rewrite([19018(6)]),flip(a)].
% 73.03/73.36 19108 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)). [para(18543(a,1),17309(a,1,2,1)),rewrite([59(5),5151(5)])].
% 73.03/73.36 19111 multiplication(antidomain(A),antidomain(coantidomain(multiplication(antidomain(A),antidomain(B))))) = antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))). [para(18543(a,1),17325(a,1,1,1))].
% 73.03/73.36 19402 addition(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = one. [para(2696(a,1),18685(a,1,1)),rewrite([2696(4)])].
% 73.03/73.36 19427 addition(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(multiplication(antidomain(B),A)). [para(123(a,1),18809(a,1,2,1)),rewrite([42(5)])].
% 73.03/73.36 19446 multiplication(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(A). [para(18828(a,1),78(a,1,2)),rewrite([2696(3),32(3),2696(4)]),flip(a)].
% 73.03/73.36 19524 multiplication(coantidomain(A),antidomain(coantidomain(multiplication(B,coantidomain(A))))) = antidomain(coantidomain(multiplication(B,coantidomain(A)))). [para(19402(a,1),82(a,1,1)),rewrite([2686(5),33(6),2686(9)]),flip(a)].
% 73.03/73.36 19526 multiplication(A,coantidomain(multiplication(B,coantidomain(A)))) = A. [para(19402(a,1),4466(a,1,2)),rewrite([32(2)]),flip(a)].
% 73.03/73.36 19662 multiplication(A,multiplication(coantidomain(B),antidomain(coantidomain(A)))) = multiplication(A,coantidomain(B)). [para(18540(a,1),17309(a,1,2,1)),rewrite([59(5)])].
% 73.03/73.36 19820 addition(antidomain(A),coantidomain(multiplication(antidomain(multiplication(B,A)),B))) = one. [para(18566(a,1),17317(a,1,2,1)),rewrite([2696(6),42(6)])].
% 73.03/73.36 20167 coantidomain(addition(antidomain(coantidomain(A)),multiplication(B,A))) = coantidomain(A). [para(2387(a,1),18732(a,1,1,2,2)),rewrite([9251(8),2696(8)])].
% 73.03/73.36 20374 coantidomain(multiplication(addition(A,coantidomain(A)),B)) = coantidomain(B). [para(18898(a,1),18566(a,1,1,1,1,1)),rewrite([111(2),33(2),19446(6)]),flip(a)].
% 73.03/73.36 20380 coantidomain(multiplication(antidomain(coantidomain(A)),B)) = coantidomain(multiplication(A,B)). [para(128(a,1),20374(a,1,1)),rewrite([2686(2),2409(4),2686(4)]),flip(a)].
% 73.03/73.36 20402 coantidomain(multiplication(A,antidomain(antidomain(multiplication(antidomain(coantidomain(A)),B))))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [para(543(a,1),20374(a,1,1)),rewrite([2686(2),2686(9),9251(13),9253(13)])].
% 73.03/73.36 20428 backward_diamond(A,B) = antidomain(coantidomain(multiplication(B,A))). [back_rewrite(3053),rewrite([20380(5)])].
% 73.03/73.36 20634 multiplication(coantidomain(A),coantidomain(B)) = multiplication(coantidomain(B),coantidomain(A)). [para(2696(a,1),18986(a,1,2)),rewrite([2696(6)])].
% 73.03/73.36 20660 antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))) = multiplication(coantidomain(B),antidomain(A)). [para(18986(a,1),2410(a,1,2,2,1,1)),rewrite([18989(8),19524(7)])].
% 73.03/73.36 20661 multiplication(A,antidomain(coantidomain(multiplication(A,coantidomain(B))))) = multiplication(A,coantidomain(B)). [para(18986(a,1),2410(a,1,2)),rewrite([18986(6,R),19524(6)])].
% 73.03/73.36 20721 multiplication(A,coantidomain(multiplication(coantidomain(A),antidomain(B)))) = A. [para(18986(a,2),19526(a,1,2,1))].
% 73.03/73.36 20732 antidomain(coantidomain(multiplication(coantidomain(A),antidomain(B)))) = multiplication(coantidomain(A),antidomain(B)). [para(18986(a,1),20428(a,2,1,1)),rewrite([20428(3),20660(10)])].
% 73.03/73.36 20743 multiplication(coantidomain(A),coantidomain(multiplication(A,antidomain(B)))) = coantidomain(A). [back_rewrite(18541),rewrite([20634(5)])].
% 73.03/73.36 20744 multiplication(coantidomain(A),coantidomain(multiplication(A,coantidomain(B)))) = coantidomain(A). [back_rewrite(18540),rewrite([20634(5)])].
% 73.03/73.36 20811 multiplication(A,coantidomain(multiplication(coantidomain(A),coantidomain(B)))) = A. [para(2696(a,1),20721(a,1,2,1,2))].
% 73.03/73.36 20836 antidomain(coantidomain(multiplication(coantidomain(A),coantidomain(B)))) = multiplication(coantidomain(A),coantidomain(B)). [para(20811(a,1),19446(a,1,2,1)),rewrite([2686(5),18986(7,R),20661(7),2686(8)]),flip(a)].
% 73.03/73.36 20904 antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))) = multiplication(antidomain(A),antidomain(B)). [para(19108(a,1),2410(a,1,2,2,1,1)),rewrite([19108(5),18686(8),19111(7)])].
% 73.03/73.36 20907 multiplication(antidomain(A),addition(antidomain(A),antidomain(B))) = antidomain(A). [para(19108(a,1),2411(a,2,2)),rewrite([9251(4),9253(5),42(4),19108(9),77(10,R),42(9),109(9),32(8)])].
% 73.03/73.36 21424 antidomain(antidomain(multiplication(coantidomain(A),antidomain(B)))) = multiplication(coantidomain(A),antidomain(B)). [para(20721(a,1),20167(a,1,1,2)),rewrite([2686(5),20732(5),42(5),18755(6),2686(10),20732(10)])].
% 73.03/73.36 21425 antidomain(antidomain(multiplication(coantidomain(A),coantidomain(B)))) = multiplication(coantidomain(A),coantidomain(B)). [para(20811(a,1),20167(a,1,1,2)),rewrite([2686(5),20836(5),42(5),18755(6),2686(10),20836(10)])].
% 73.03/73.36 21481 coantidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))). [para(19108(a,1),20380(a,1,1))].
% 73.03/73.36 21565 multiplication(antidomain(A),coantidomain(multiplication(B,antidomain(A)))) = multiplication(coantidomain(B),antidomain(A)). [para(17530(a,1),20743(a,1,2,1)),rewrite([9251(5),21424(5),19108(7),21481(8),59(7),18545(7),9251(10),21424(10)])].
% 73.03/73.36 21574 multiplication(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = multiplication(coantidomain(B),coantidomain(A)). [para(17530(a,1),20744(a,1,2,1)),rewrite([9251(5),21425(5),20380(8),59(7),18545(7),9251(10),21425(10)])].
% 73.03/73.36 21746 multiplication(antidomain(A),addition(antidomain(A),coantidomain(B))) = antidomain(A). [para(2696(a,1),20907(a,1,2,2))].
% 73.03/73.36 21916 addition(antidomain(A),multiplication(antidomain(antidomain(A)),coantidomain(B))) = addition(antidomain(A),coantidomain(B)). [para(21746(a,1),173(a,1,2)),rewrite([42(6),44(10),33(11)])].
% 73.03/73.36 23599 multiplication(A,coantidomain(multiplication(B,antidomain(coantidomain(A))))) = multiplication(A,coantidomain(B)). [para(2409(a,1),857(a,2)),rewrite([21565(8),959(6),19662(5)]),flip(a)].
% 73.03/73.36 23899 addition(coantidomain(A),antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = one. [para(74(a,1),19820(a,1,2,1,1,1)),rewrite([111(6),33(6),42(6)])].
% 73.03/73.36 24114 multiplication(A,addition(coantidomain(A),antidomain(B))) = multiplication(A,antidomain(B)). [para(263(a,2),890(a,1,2)),rewrite([3372(7),32(3)]),flip(a)].
% 73.03/73.36 26749 multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = A. [para(23899(a,1),24114(a,1,2)),rewrite([32(2)]),flip(a)].
% 73.03/73.36 26792 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)). [para(9219(a,1),26749(a,1,2,1,2,1)),rewrite([114(7),32(7),19108(7),16848(7)]),flip(a)].
% 73.03/73.36 27921 multiplication(antidomain(multiplication(A,coantidomain(multiplication(antidomain(antidomain(B)),A)))),B) = B. [para(1225(a,1),17555(a,1,1,1))].
% 73.03/73.36 28284 antidomain(addition(antidomain(antidomain(A)),multiplication(antidomain(B),A))) = antidomain(A). [para(18509(a,1),17179(a,1,1,2)),rewrite([9253(9)])].
% 73.03/73.36 28306 antidomain(antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(antidomain(B))). [para(20721(a,1),28284(a,1,1,2)),rewrite([9251(2),19108(4),20904(6),26792(5),42(5),19427(5),9251(6),19108(8),20904(10)])].
% 73.03/73.36 28309 coantidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(antidomain(coantidomain(A)),B)). [back_rewrite(20402),rewrite([28306(5),2409(6)])].
% 73.03/73.36 28679 multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B))) = multiplication(A,antidomain(B)). [para(9253(a,1),19075(a,2,2)),rewrite([28309(4)])].
% 73.03/73.36 30059 multiplication(coantidomain(A),coantidomain(B)) = coantidomain(addition(A,B)). [para(18523(a,1),23599(a,2)),rewrite([2686(4),2696(5),264(4),21574(5),20634(3)])].
% 73.03/73.36 30152 multiplication(antidomain(antidomain(A)),coantidomain(B)) = coantidomain(addition(B,antidomain(A))). [para(9251(a,1),30059(a,1,1)),rewrite([42(6)])].
% 73.03/73.36 30251 addition(antidomain(A),coantidomain(addition(B,antidomain(A)))) = addition(antidomain(A),coantidomain(B)). [back_rewrite(21916),rewrite([30152(5)])].
% 73.03/73.36 31931 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(B)). [para(28679(a,1),78(a,2)),rewrite([9251(3),9253(4),78(6)])].
% 73.03/73.36 31943 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)). [para(18637(a,1),28679(a,2)),rewrite([9251(3),9253(4),78(4),31931(5)])].
% 73.03/73.36 31944 antidomain(addition(A,multiplication(antidomain(A),B))) = antidomain(addition(A,B)). [para(28679(a,1),822(a,2)),rewrite([9251(3),9253(4),822(9),31943(5),31943(7)])].
% 73.03/73.36 31969 antidomain(addition(A,multiplication(B,coantidomain(multiplication(antidomain(A),B))))) = antidomain(A). [para(27921(a,1),28679(a,2)),rewrite([9253(3),9253(8),9251(11),9253(12),31943(13),31944(12),42(5)])].
% 73.03/73.36 36776 antidomain(multiplication(antidomain(coantidomain(A)),B)) = addition(antidomain(B),coantidomain(A)). [para(23599(a,1),3337(a,1,1)),rewrite([30152(4),9251(7),9253(7),28309(8),42(10),109(10),32(6),42(5),30251(5),9251(6),9253(6),28309(7),42(9),19427(9)]),flip(a)].
% 73.03/73.36 36796 addition(antidomain(A),antidomain(antidomain(B))) = antidomain(multiplication(antidomain(B),A)). [para(9251(a,1),36776(a,1,1,1,1)),rewrite([9253(3),9251(6)]),flip(a)].
% 73.03/73.36 36963 $F # answer(goals). [back_rewrite(9408),rewrite([36796(13),31943(11),42(9),31969(10)]),xx(a)].
% 73.03/73.36
% 73.03/73.36 % SZS output end Refutation
% 73.03/73.36 ============================== end of proof ==========================
% 73.03/73.36
% 73.03/73.36 ============================== STATISTICS ============================
% 73.03/73.36
% 73.03/73.36 Given=3057. Generated=4318123. Kept=36919. proofs=1.
% 73.03/73.36 Usable=1782. Sos=7575. Demods=9337. Limbo=167, Disabled=27423. Hints=0.
% 73.03/73.36 Megabytes=27.20.
% 73.03/73.36 User_CPU=70.02, System_CPU=2.38, Wall_clock=72.
% 73.03/73.36
% 73.03/73.36 ============================== end of statistics =====================
% 73.03/73.36
% 73.03/73.36 ============================== end of search =========================
% 73.03/73.36
% 73.03/73.36 THEOREM PROVED
% 73.03/73.36 % SZS status Theorem
% 73.03/73.36
% 73.03/73.36 Exiting with 1 proof.
% 73.03/73.36
% 73.03/73.36 Process 12229 exit (max_proofs) Thu Jun 16 11:21:03 2022
% 73.03/73.36 Prover9 interrupted
%------------------------------------------------------------------------------