TSTP Solution File: KLE108-10 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : KLE108-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n025.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   : Timeout 288.54s 288.83s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem  : KLE108-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Thu Jun 16 08:46:11 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 5.20/5.51  ============================== Prover9 ===============================
% 5.20/5.51  Prover9 (32) version 2009-11A, November 2009.
% 5.20/5.51  Process 19516 was started by sandbox on n025.cluster.edu,
% 5.20/5.51  Thu Jun 16 08:46:12 2022
% 5.20/5.51  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19363_n025.cluster.edu".
% 5.20/5.51  ============================== end of head ===========================
% 5.20/5.51  
% 5.20/5.51  ============================== INPUT =================================
% 5.20/5.51  
% 5.20/5.51  % Reading from file /tmp/Prover9_19363_n025.cluster.edu
% 5.20/5.51  
% 5.20/5.51  set(prolog_style_variables).
% 5.20/5.51  set(auto2).
% 5.20/5.51      % set(auto2) -> set(auto).
% 5.20/5.51      % set(auto) -> set(auto_inference).
% 5.20/5.51      % set(auto) -> set(auto_setup).
% 5.20/5.51      % set(auto_setup) -> set(predicate_elim).
% 5.20/5.51      % set(auto_setup) -> assign(eq_defs, unfold).
% 5.20/5.51      % set(auto) -> set(auto_limits).
% 5.20/5.51      % set(auto_limits) -> assign(max_weight, "100.000").
% 5.20/5.51      % set(auto_limits) -> assign(sos_limit, 20000).
% 5.20/5.51      % set(auto) -> set(auto_denials).
% 5.20/5.51      % set(auto) -> set(auto_process).
% 5.20/5.51      % set(auto2) -> assign(new_constants, 1).
% 5.20/5.51      % set(auto2) -> assign(fold_denial_max, 3).
% 5.20/5.51      % set(auto2) -> assign(max_weight, "200.000").
% 5.20/5.51      % set(auto2) -> assign(max_hours, 1).
% 5.20/5.51      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.20/5.51      % set(auto2) -> assign(max_seconds, 0).
% 5.20/5.51      % set(auto2) -> assign(max_minutes, 5).
% 5.20/5.51      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.20/5.51      % set(auto2) -> set(sort_initial_sos).
% 5.20/5.51      % set(auto2) -> assign(sos_limit, -1).
% 5.20/5.51      % set(auto2) -> assign(lrs_ticks, 3000).
% 5.20/5.51      % set(auto2) -> assign(max_megs, 400).
% 5.20/5.51      % set(auto2) -> assign(stats, some).
% 5.20/5.51      % set(auto2) -> clear(echo_input).
% 5.20/5.51      % set(auto2) -> set(quiet).
% 5.20/5.51      % set(auto2) -> clear(print_initial_clauses).
% 5.20/5.51      % set(auto2) -> clear(print_given).
% 5.20/5.51  assign(lrs_ticks,-1).
% 5.20/5.51  assign(sos_limit,10000).
% 5.20/5.51  assign(order,kbo).
% 5.20/5.51  set(lex_order_vars).
% 5.20/5.51  clear(print_given).
% 5.20/5.51  
% 5.20/5.51  % formulas(sos).  % not echoed (31 formulas)
% 5.20/5.51  
% 5.20/5.51  ============================== end of input ==========================
% 5.20/5.51  
% 5.20/5.51  % From the command line: assign(max_seconds, 300).
% 5.20/5.51  
% 5.20/5.51  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.20/5.51  
% 5.20/5.51  % Formulas that are not ordinary clauses:
% 5.20/5.51  
% 5.20/5.51  ============================== end of process non-clausal formulas ===
% 5.20/5.51  
% 5.20/5.51  ============================== PROCESS INITIAL CLAUSES ===============
% 5.20/5.51  
% 5.20/5.51  ============================== PREDICATE ELIMINATION =================
% 5.20/5.51  
% 5.20/5.51  ============================== end predicate elimination =============
% 5.20/5.51  
% 5.20/5.51  Auto_denials:
% 5.20/5.51    % copying label goals_1 to answer in negative clause
% 5.20/5.51  
% 5.20/5.51  Term ordering decisions:
% 5.20/5.51  Function symbol KB weights:  zero=1. one=1. true=1. sK1_goals_X2=1. sK3_goals_X0=1. sK2_goals_X1=1. multiplication=1. addition=1. forward_box=1. backward_diamond=1. forward_diamond=1. leq=1. backward_box=1. domain_difference=1. antidomain=1. coantidomain=1. domain=1. c=1. codomain=1. ifeq=1. ifeq2=1.
% 5.20/5.51  
% 5.20/5.51  ============================== end of process initial clauses ========
% 5.20/5.51  
% 5.20/5.51  ============================== CLAUSES FOR SEARCH ====================
% 5.20/5.51  
% 5.20/5.51  ============================== end of clauses for search =============
% 5.20/5.51  
% 5.20/5.51  ============================== SEARCH ================================
% 5.20/5.51  
% 5.20/5.51  % Starting search at 0.01 seconds.
% 5.20/5.51  
% 5.20/5.51  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 36 (0.00 of 1.07 sec).
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=55.000, iters=3368
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=47.000, iters=3362
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=46.000, iters=3360
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=43.000, iters=3348
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=42.000, iters=3340
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=38.000, iters=3375
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=37.000, iters=3457
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=36.000, iters=3452
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=35.000, iters=3406
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=33.000, iters=3341
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=31.000, iters=3393
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=30.000, iters=3337
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=29.000, iters=3336
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=28.000, iters=3361
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=27.000, iters=3415
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=26.000, iters=3363
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=25.000, iters=3490
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=23.000, iters=3333
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=19.000, iters=3708
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=18.000, iters=3346
% 5.20/5.51  
% 5.20/5.51  Low Water (keep): wt=17.000, iters=3337
% 288.54/288.83  
% 288.54/288.83  Low Water (displace): id=5244, wt=52.000
% 288.54/288.83  
% 288.54/288.83  Low Water (displace): id=4160, wt=51.000
% 288.54/288.83  
% 288.54/288.83  Low Water (displace): id=16825, wt=16.000
% 288.54/288.83  
% 288.54/288.83  Low Water (displace): id=16826, wt=15.000
% 288.54/288.83  
% 288.54/288.83  Low Water (displace): id=16846, wt=14.000
% 288.54/288.83  
% 288.54/288.83  Low Water (displace): id=18126, wt=13.000
% 288.54/288.83  
% 288.54/288.83  Low Water (keep): wt=16.000, iters=3345
% 288.54/288.83  
% 288.54/288.83  Low Water (displace): id=21068, wt=12.000
% 288.54/288.83  
% 288.54/288.83  Low Water (keep): wt=15.000, iters=3358
% 288.54/288.83  
% 288.54/288.83  ============================== PROOF =================================
% 288.54/288.83  % SZS status Unsatisfiable
% 288.54/288.83  % SZS output start Refutation
% 288.54/288.83  
% 288.54/288.83  % Proof 1 at 276.74 (+ 11.03) seconds: goals_1.
% 288.54/288.83  % Length of proof is 310.
% 288.54/288.83  % Level of proof is 32.
% 288.54/288.83  % Maximum clause weight is 37.000.
% 288.54/288.83  % Given clauses 8517.
% 288.54/288.83  
% 288.54/288.83  1 addition(A,zero) = A # label(additive_identity) # label(axiom).  [assumption].
% 288.54/288.83  2 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [assumption].
% 288.54/288.83  3 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [assumption].
% 288.54/288.83  4 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [assumption].
% 288.54/288.83  5 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom).  [assumption].
% 288.54/288.83  6 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [assumption].
% 288.54/288.83  7 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom).  [assumption].
% 288.54/288.83  8 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom).  [assumption].
% 288.54/288.83  9 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom).  [assumption].
% 288.54/288.83  10 codomain(A) = coantidomain(coantidomain(A)) # label(codomain4) # label(axiom).  [assumption].
% 288.54/288.83  11 c(A) = antidomain(domain(A)) # label(complement) # label(axiom).  [assumption].
% 288.54/288.83  12 c(A) = antidomain(antidomain(antidomain(A))).  [copy(11),rewrite([8(2)])].
% 288.54/288.83  13 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom).  [assumption].
% 288.54/288.83  14 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom).  [assumption].
% 288.54/288.83  15 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [assumption].
% 288.54/288.83  16 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom).  [assumption].
% 288.54/288.83  17 addition(antidomain(A),antidomain(antidomain(A))) = one.  [copy(16),rewrite([15(4)])].
% 288.54/288.83  18 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom).  [assumption].
% 288.54/288.83  19 addition(coantidomain(A),coantidomain(coantidomain(A))) = one.  [copy(18),rewrite([15(4)])].
% 288.54/288.83  22 forward_diamond(A,B) = domain(multiplication(A,domain(B))) # label(forward_diamond) # label(axiom).  [assumption].
% 288.54/288.83  23 forward_diamond(A,B) = antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))).  [copy(22),rewrite([8(2),8(5)])].
% 288.54/288.83  24 backward_diamond(A,B) = codomain(multiplication(codomain(B),A)) # label(backward_diamond) # label(axiom).  [assumption].
% 288.54/288.83  25 backward_diamond(A,B) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(B)),A))).  [copy(24),rewrite([10(2),10(5)])].
% 288.54/288.83  26 forward_box(A,B) = c(forward_diamond(A,c(B))) # label(forward_box) # label(axiom).  [assumption].
% 288.54/288.83  27 forward_box(A,B) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(A,antidomain(antidomain(antidomain(antidomain(antidomain(B))))))))))).  [copy(26),rewrite([12(2),23(5),12(10)])].
% 288.54/288.83  30 addition(A,addition(B,C)) = addition(addition(A,B),C) # label(additive_associativity) # label(axiom).  [assumption].
% 288.54/288.83  31 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(30),rewrite([15(4)])].
% 288.54/288.83  32 multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) # label(multiplicative_associativity) # label(axiom).  [assumption].
% 288.54/288.83  33 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)).  [copy(32),flip(a)].
% 288.54/288.83  34 ifeq(leq(A,B),true,addition(A,B),B) = B # label(order_1) # label(axiom).  [assumption].
% 288.54/288.83  35 ifeq2(addition(A,B),B,leq(A,B),true) = true # label(order) # label(axiom).  [assumption].
% 288.54/288.83  36 addition(domain(sK2_goals_X1),forward_box(sK3_goals_X0,domain(sK1_goals_X2))) = forward_box(sK3_goals_X0,domain(sK1_goals_X2)) # label(goals) # label(negated_conjecture).  [assumption].
% 288.54/288.83  37 addition(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2)))))))))))))) = antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))))))))).  [copy(36),rewrite([8(2),8(6),27(8),8(22),27(24)])].
% 288.54/288.83  38 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom).  [assumption].
% 288.54/288.83  39 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)).  [copy(38),flip(a)].
% 288.54/288.83  40 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom).  [assumption].
% 288.54/288.83  41 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B).  [copy(40),flip(a)].
% 288.54/288.83  42 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))) # label(domain2) # label(axiom).  [assumption].
% 288.54/288.83  43 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)) # label(codomain2) # label(axiom).  [assumption].
% 288.54/288.83  44 addition(backward_diamond(sK3_goals_X0,domain(sK2_goals_X1)),domain(sK1_goals_X2)) != domain(sK1_goals_X2) # label(goals_1) # label(negated_conjecture) # answer(goals_1).  [assumption].
% 288.54/288.83  45 addition(antidomain(antidomain(sK1_goals_X2)),coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(sK2_goals_X1)))),sK3_goals_X0)))) != antidomain(antidomain(sK1_goals_X2)) # answer(goals_1).  [copy(44),rewrite([8(3),25(5),8(11),15(13),8(15)])].
% 288.54/288.83  46 antidomain(one) = zero.  [para(7(a,1),3(a,1)),flip(a)].
% 288.54/288.83  47 coantidomain(one) = zero.  [para(9(a,1),4(a,1)),flip(a)].
% 288.54/288.83  48 addition(A,addition(A,B)) = addition(A,B).  [para(31(a,1),2(a,1)),rewrite([15(1),15(2),31(2,R),2(1),15(3)])].
% 288.54/288.83  49 multiplication(antidomain(A),multiplication(A,B)) = zero.  [para(7(a,1),33(a,1,1)),rewrite([6(2)]),flip(a)].
% 288.54/288.83  50 multiplication(A,multiplication(B,coantidomain(multiplication(A,B)))) = zero.  [para(33(a,1),9(a,1))].
% 288.54/288.83  51 multiplication(A,multiplication(coantidomain(A),B)) = zero.  [para(9(a,1),33(a,1,1)),rewrite([6(2)]),flip(a)].
% 288.54/288.83  58 ifeq2(addition(A,B),A,leq(B,A),true) = true.  [para(15(a,1),35(a,1,1))].
% 288.54/288.83  62 ifeq2(addition(A,addition(B,C)),addition(A,B),leq(C,addition(A,B)),true) = true.  [para(31(a,2),35(a,1,1))].
% 288.54/288.83  65 addition(zero,multiplication(A,B)) = multiplication(A,B).  [para(1(a,1),39(a,2,2)),rewrite([5(3),15(3)])].
% 288.54/288.83  66 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)).  [para(3(a,1),39(a,1,1)),rewrite([15(4)]),flip(a)].
% 288.54/288.83  67 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B).  [para(7(a,1),39(a,1,1)),rewrite([65(4)]),flip(a)].
% 288.54/288.83  68 multiplication(A,addition(B,coantidomain(A))) = multiplication(A,B).  [para(9(a,1),39(a,1,1)),rewrite([65(3),15(3)]),flip(a)].
% 288.54/288.83  69 ifeq(leq(multiplication(A,B),multiplication(A,C)),true,multiplication(A,addition(B,C)),multiplication(A,C)) = multiplication(A,C).  [para(39(a,1),34(a,1,3))].
% 288.54/288.83  71 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)).  [para(4(a,1),41(a,1,1)),rewrite([15(4)]),flip(a)].
% 288.54/288.83  72 multiplication(addition(A,antidomain(B)),B) = multiplication(A,B).  [para(7(a,1),41(a,1,1)),rewrite([65(3),15(3)]),flip(a)].
% 288.54/288.83  73 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)).  [para(9(a,1),41(a,1,1)),rewrite([65(4),15(3)]),flip(a)].
% 288.54/288.83  74 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C).  [para(33(a,1),41(a,1,1)),rewrite([15(6)])].
% 288.54/288.83  76 ifeq(leq(multiplication(A,B),multiplication(C,B)),true,multiplication(addition(A,C),B),multiplication(C,B)) = multiplication(C,B).  [para(41(a,1),34(a,1,3))].
% 288.54/288.83  79 addition(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))).  [para(4(a,1),42(a,1,1,1)),rewrite([4(5),4(9)])].
% 288.54/288.83  81 addition(antidomain(zero),antidomain(multiplication(antidomain(A),antidomain(antidomain(A))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))).  [para(7(a,1),42(a,1,1,1))].
% 288.54/288.83  83 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))).  [para(9(a,1),42(a,1,1,1))].
% 288.54/288.83  90 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)).  [para(7(a,1),43(a,1,1,1))].
% 288.54/288.83  93 addition(coantidomain(multiplication(A,multiplication(B,C))),coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C))) = coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),C)).  [para(33(a,1),43(a,1,1,1))].
% 288.54/288.83  96 addition(zero,antidomain(zero)) = one.  [para(46(a,1),17(a,1,1)),rewrite([46(3)])].
% 288.54/288.83  97 addition(zero,coantidomain(zero)) = one.  [para(47(a,1),19(a,1,1)),rewrite([47(3)])].
% 288.54/288.83  102 multiplication(A,antidomain(zero)) = A.  [para(96(a,1),39(a,2,2)),rewrite([5(2),65(5),3(5)])].
% 288.54/288.83  107 addition(one,antidomain(A)) = one.  [para(17(a,1),48(a,1,2)),rewrite([15(3),17(7)])].
% 288.54/288.83  108 addition(one,coantidomain(A)) = one.  [para(19(a,1),48(a,1,2)),rewrite([15(3),19(7)])].
% 288.54/288.83  110 leq(A,addition(A,B)) = true.  [para(48(a,1),35(a,1,1)),rewrite([13(6)])].
% 288.54/288.83  114 multiplication(A,coantidomain(zero)) = A.  [para(97(a,1),39(a,2,2)),rewrite([5(2),65(5),3(5)])].
% 288.54/288.83  116 antidomain(zero) = one.  [para(102(a,1),4(a,1)),flip(a)].
% 288.54/288.83  117 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one.  [back_rewrite(83),rewrite([116(2),107(7)]),flip(a)].
% 288.54/288.83  118 antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))) = one.  [back_rewrite(81),rewrite([116(2),107(7)]),flip(a)].
% 288.54/288.83  119 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero.  [para(33(a,1),49(a,1,2))].
% 288.54/288.83  122 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one.  [para(49(a,1),42(a,1,1,1)),rewrite([116(2),107(8)]),flip(a)].
% 288.54/288.83  126 addition(A,multiplication(A,antidomain(B))) = A.  [para(107(a,1),39(a,2,2)),rewrite([3(2),3(5)])].
% 288.54/288.83  127 addition(A,multiplication(antidomain(B),A)) = A.  [para(107(a,1),41(a,2,1)),rewrite([4(2),4(5)])].
% 288.54/288.83  130 addition(A,multiplication(A,coantidomain(B))) = A.  [para(108(a,1),39(a,2,2)),rewrite([3(2),3(5)])].
% 288.54/288.83  131 addition(A,multiplication(coantidomain(B),A)) = A.  [para(108(a,1),41(a,2,1)),rewrite([4(2),4(5)])].
% 288.54/288.83  132 coantidomain(zero) = one.  [para(114(a,1),4(a,1)),flip(a)].
% 288.54/288.83  135 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one.  [back_rewrite(90),rewrite([132(2),108(7)]),flip(a)].
% 288.54/288.83  140 antidomain(multiplication(A,antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B))))))) = one.  [para(50(a,1),42(a,1,1,1)),rewrite([116(2),107(9)]),flip(a)].
% 288.54/288.83  144 leq(multiplication(A,B),multiplication(A,addition(B,C))) = true.  [para(39(a,1),110(a,1,2))].
% 288.54/288.83  147 multiplication(addition(A,B),multiplication(coantidomain(B),C)) = multiplication(A,multiplication(coantidomain(B),C)).  [para(51(a,1),41(a,1,1)),rewrite([65(5),15(4)]),flip(a)].
% 288.54/288.83  148 antidomain(multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B))))) = one.  [para(51(a,1),42(a,1,1,1)),rewrite([116(2),107(8)]),flip(a)].
% 288.54/288.83  151 addition(A,addition(B,multiplication(A,antidomain(C)))) = addition(A,B).  [para(126(a,1),31(a,2,2)),rewrite([15(3),15(5)])].
% 288.54/288.83  156 ifeq(leq(A,multiplication(antidomain(B),A)),true,A,multiplication(antidomain(B),A)) = multiplication(antidomain(B),A).  [para(127(a,1),34(a,1,3))].
% 288.54/288.83  167 leq(zero,multiplication(A,B)) = true.  [para(65(a,1),35(a,1,1)),rewrite([13(7)])].
% 288.54/288.83  168 leq(zero,A) = true.  [para(3(a,1),167(a,1,2))].
% 288.54/288.83  169 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero.  [para(117(a,1),7(a,1,1)),rewrite([4(6)])].
% 288.54/288.83  174 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B).  [para(169(a,1),39(a,1,1)),rewrite([65(3),15(5)]),flip(a)].
% 288.54/288.83  177 multiplication(antidomain(A),antidomain(antidomain(A))) = zero.  [para(118(a,1),7(a,1,1)),rewrite([4(6)])].
% 288.54/288.83  181 multiplication(addition(A,antidomain(B)),antidomain(antidomain(B))) = multiplication(A,antidomain(antidomain(B))).  [para(177(a,1),41(a,1,1)),rewrite([65(5),15(5)]),flip(a)].
% 288.54/288.83  183 addition(zero,antidomain(A)) = antidomain(A).  [para(177(a,1),126(a,1,2)),rewrite([15(3)])].
% 288.54/288.83  196 leq(multiplication(A,coantidomain(B)),A) = true.  [para(130(a,1),58(a,1,1)),rewrite([13(5)])].
% 288.54/288.83  197 leq(multiplication(coantidomain(A),B),B) = true.  [para(131(a,1),58(a,1,1)),rewrite([13(5)])].
% 288.54/288.83  207 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero.  [para(135(a,1),9(a,1,2)),rewrite([3(6)])].
% 288.54/288.83  211 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B).  [para(207(a,1),41(a,1,1)),rewrite([65(3),15(5)]),flip(a)].
% 288.54/288.83  213 multiplication(coantidomain(A),coantidomain(A)) = coantidomain(A).  [para(19(a,1),68(a,1,2)),rewrite([3(3)]),flip(a)].
% 288.54/288.83  220 multiplication(coantidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero.  [para(43(a,1),68(a,1,2)),rewrite([9(8),33(7)]),flip(a)].
% 288.54/288.83  223 multiplication(coantidomain(A),multiplication(coantidomain(A),B)) = multiplication(coantidomain(A),B).  [para(213(a,1),33(a,1,1)),flip(a)].
% 288.54/288.83  224 multiplication(coantidomain(A),addition(B,coantidomain(A))) = multiplication(coantidomain(A),addition(B,one)).  [para(213(a,1),39(a,1,1)),rewrite([66(4,R),15(7)]),flip(a)].
% 288.54/288.83  267 leq(multiplication(A,antidomain(B)),addition(C,A)) = true.  [para(126(a,1),62(a,1,1,2)),rewrite([13(8)])].
% 288.54/288.83  268 leq(multiplication(antidomain(A),B),addition(C,B)) = true.  [para(127(a,1),62(a,1,1,2)),rewrite([13(8)])].
% 288.54/288.83  271 multiplication(antidomain(A),antidomain(A)) = antidomain(A).  [para(17(a,1),72(a,1,1)),rewrite([4(3)]),flip(a)].
% 288.54/288.83  275 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(addition(A,antidomain(antidomain(antidomain(B)))),B))) = antidomain(multiplication(A,antidomain(antidomain(B)))).  [para(72(a,1),42(a,1,2,1)),rewrite([15(11),72(18)])].
% 288.54/288.83  276 multiplication(antidomain(multiplication(A,B)),multiplication(A,antidomain(antidomain(B)))) = zero.  [para(42(a,1),72(a,1,1)),rewrite([7(8)]),flip(a)].
% 288.54/288.83  283 multiplication(addition(A,antidomain(B)),antidomain(B)) = multiplication(addition(A,one),antidomain(B)).  [para(271(a,1),41(a,1,1)),rewrite([71(4,R),15(6)]),flip(a)].
% 288.54/288.83  316 leq(multiplication(antidomain(A),multiplication(B,antidomain(C))),B) = true.  [para(127(a,1),267(a,1,2)),rewrite([33(4)])].
% 288.54/288.83  322 addition(A,multiplication(B,addition(C,one))) = addition(B,addition(A,multiplication(B,C))).  [para(66(a,2),31(a,2,2)),rewrite([15(2)]),flip(a)].
% 288.54/288.83  333 addition(antidomain(addition(A,multiplication(A,B))),antidomain(multiplication(A,antidomain(antidomain(addition(B,one)))))) = antidomain(multiplication(A,antidomain(antidomain(addition(B,one))))).  [para(66(a,1),42(a,1,1,1))].
% 288.54/288.83  337 leq(A,multiplication(A,addition(B,one))) = true.  [para(66(a,2),110(a,1,2))].
% 288.54/288.83  353 leq(antidomain(addition(A,one)),zero) = true.  [para(7(a,1),337(a,1,2))].
% 288.54/288.83  358 antidomain(addition(A,one)) = zero.  [para(353(a,1),34(a,1,1)),rewrite([15(7),183(7),14(7)])].
% 288.54/288.83  359 addition(antidomain(A),antidomain(addition(A,multiplication(A,B)))) = antidomain(A).  [back_rewrite(333),rewrite([358(6),116(5),3(5),15(5),358(8),116(7),3(7)])].
% 288.54/288.83  360 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)).  [para(19(a,1),67(a,1,2)),rewrite([3(4)]),flip(a)].
% 288.54/288.83  364 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)).  [para(41(a,1),67(a,1,2))].
% 288.54/288.83  366 addition(addition(A,B),multiplication(antidomain(A),B)) = addition(A,B).  [para(67(a,1),127(a,1,2))].
% 288.54/288.83  367 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero.  [para(127(a,1),67(a,1,2)),rewrite([7(2)]),flip(a)].
% 288.54/288.83  368 multiplication(antidomain(A),multiplication(coantidomain(B),A)) = zero.  [para(131(a,1),67(a,1,2)),rewrite([7(2)]),flip(a)].
% 288.54/288.83  369 addition(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(A).  [para(358(a,1),42(a,1,2,1,2,1)),rewrite([116(6),3(6),15(6),358(9),116(8),3(8)])].
% 288.54/288.84  379 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)).  [para(367(a,1),41(a,1,1)),rewrite([65(5),15(5)]),flip(a)].
% 288.54/288.84  386 multiplication(addition(A,antidomain(B)),multiplication(coantidomain(C),B)) = multiplication(A,multiplication(coantidomain(C),B)).  [para(368(a,1),41(a,1,1)),rewrite([65(5),15(5)]),flip(a)].
% 288.54/288.84  391 ifeq(leq(multiplication(antidomain(addition(A,B)),A),multiplication(antidomain(addition(A,B)),B)),true,zero,multiplication(antidomain(addition(A,B)),B)) = multiplication(antidomain(addition(A,B)),B).  [para(7(a,1),69(a,1,3))].
% 288.54/288.84  392 ifeq(leq(multiplication(A,antidomain(B)),multiplication(A,antidomain(antidomain(B)))),true,A,multiplication(A,antidomain(antidomain(B)))) = multiplication(A,antidomain(antidomain(B))).  [para(17(a,1),69(a,1,3,2)),rewrite([3(9)])].
% 288.54/288.84  414 leq(multiplication(antidomain(A),B),addition(B,C)) = true.  [para(15(a,1),268(a,1,2))].
% 288.54/288.84  519 multiplication(addition(A,one),addition(B,coantidomain(A))) = addition(B,addition(coantidomain(A),multiplication(A,B))).  [para(68(a,1),71(a,2,2)),rewrite([15(9),31(9),15(8),31(9,R),15(8)])].
% 288.54/288.84  560 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)).  [para(15(a,1),73(a,1,1))].
% 288.54/288.84  562 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))).  [para(19(a,1),73(a,1,1)),rewrite([4(5)]),flip(a)].
% 288.54/288.84  572 multiplication(A,coantidomain(addition(A,B))) = zero.  [para(48(a,1),73(a,1,1)),rewrite([9(4)]),flip(a)].
% 288.54/288.84  589 antidomain(multiplication(A,antidomain(antidomain(coantidomain(addition(A,B)))))) = one.  [para(572(a,1),42(a,1,1,1)),rewrite([116(2),107(8)]),flip(a)].
% 288.54/288.84  590 coantidomain(multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B)))) = one.  [para(572(a,1),43(a,1,1,1)),rewrite([132(2),108(8)]),flip(a)].
% 288.54/288.84  602 leq(multiplication(antidomain(A),B),multiplication(B,addition(C,one))) = true.  [para(66(a,2),414(a,1,2))].
% 288.54/288.84  612 multiplication(addition(antidomain(A),multiplication(B,C)),A) = multiplication(B,multiplication(C,A)).  [para(7(a,1),74(a,1,2)),rewrite([15(4),65(4)]),flip(a)].
% 288.54/288.84  774 multiplication(A,coantidomain(addition(B,A))) = zero.  [para(9(a,1),76(a,1,3)),rewrite([572(3),168(5),14(7)]),flip(a)].
% 288.54/288.84  775 ifeq(leq(multiplication(antidomain(A),B),multiplication(antidomain(antidomain(A)),B)),true,B,multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(antidomain(A)),B).  [para(17(a,1),76(a,1,3,1)),rewrite([4(9)])].
% 288.54/288.84  782 ifeq(leq(multiplication(A,antidomain(antidomain(coantidomain(addition(A,B))))),multiplication(B,antidomain(antidomain(coantidomain(addition(A,B)))))),true,zero,multiplication(B,antidomain(antidomain(coantidomain(addition(A,B)))))) = multiplication(B,antidomain(antidomain(coantidomain(addition(A,B))))).  [para(169(a,1),76(a,1,3))].
% 288.54/288.84  804 multiplication(A,multiplication(antidomain(B),coantidomain(A))) = zero.  [para(126(a,1),774(a,1,2,1)),rewrite([33(4)])].
% 288.54/288.84  805 multiplication(A,multiplication(coantidomain(B),coantidomain(A))) = zero.  [para(130(a,1),774(a,1,2,1)),rewrite([33(4)])].
% 288.54/288.84  811 multiplication(addition(A,B),multiplication(antidomain(C),coantidomain(B))) = multiplication(A,multiplication(antidomain(C),coantidomain(B))).  [para(804(a,1),41(a,1,1)),rewrite([65(6),15(5)]),flip(a)].
% 288.54/288.84  822 multiplication(addition(A,B),multiplication(coantidomain(C),coantidomain(B))) = multiplication(A,multiplication(coantidomain(C),coantidomain(B))).  [para(805(a,1),41(a,1,1)),rewrite([65(6),15(5)]),flip(a)].
% 288.54/288.84  886 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero.  [para(122(a,1),7(a,1,1)),rewrite([4(7)])].
% 288.54/288.84  898 multiplication(antidomain(A),antidomain(antidomain(addition(A,multiplication(A,B))))) = zero.  [para(66(a,1),886(a,1,2,1,1))].
% 288.54/288.84  978 leq(multiplication(antidomain(addition(A,B)),A),zero) = true.  [para(7(a,1),144(a,1,2))].
% 288.54/288.84  992 multiplication(antidomain(addition(A,B)),A) = zero.  [para(978(a,1),34(a,1,1)),rewrite([15(7),65(7),14(7)])].
% 288.54/288.84  1005 multiplication(antidomain(addition(A,B)),B) = zero.  [back_rewrite(391),rewrite([992(3),168(5),14(7)]),flip(a)].
% 288.54/288.84  1014 antidomain(multiplication(antidomain(addition(A,B)),antidomain(antidomain(A)))) = one.  [para(992(a,1),42(a,1,1,1)),rewrite([116(2),107(8)]),flip(a)].
% 288.54/288.84  1034 multiplication(antidomain(multiplication(addition(A,B),C)),multiplication(B,C)) = zero.  [para(41(a,1),1005(a,1,1,1))].
% 288.54/288.84  1157 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B)) = one.  [para(7(a,1),93(a,1,1,1,2)),rewrite([5(2),132(2),108(8)]),flip(a)].
% 288.54/288.84  1158 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one.  [para(7(a,1),93(a,1,1,1)),rewrite([132(2),108(9)]),flip(a)].
% 288.54/288.84  1159 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B))) = one.  [para(9(a,1),93(a,1,1,1,2)),rewrite([5(2),132(2),108(8)]),flip(a)].
% 288.54/288.84  1172 multiplication(coantidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = zero.  [para(93(a,1),68(a,1,2)),rewrite([9(10),33(9)]),flip(a)].
% 288.54/288.84  1191 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one.  [para(367(a,1),93(a,1,1,1)),rewrite([132(2),108(9)]),flip(a)].
% 288.54/288.84  1193 coantidomain(multiplication(coantidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one.  [para(368(a,1),93(a,1,1,1)),rewrite([132(2),108(9)]),flip(a)].
% 288.54/288.84  1286 multiplication(A,antidomain(antidomain(multiplication(coantidomain(A),B)))) = zero.  [para(148(a,1),7(a,1,1)),rewrite([4(7)])].
% 288.54/288.84  1450 addition(A,multiplication(antidomain(B),multiplication(A,antidomain(C)))) = A.  [para(316(a,1),34(a,1,1)),rewrite([15(7),14(8)])].
% 288.54/288.84  1531 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)).  [para(360(a,1),127(a,1,2)),rewrite([15(5)])].
% 288.54/288.84  1741 multiplication(A,antidomain(antidomain(multiplication(B,coantidomain(multiplication(A,B)))))) = zero.  [para(140(a,1),7(a,1,1)),rewrite([4(8)])].
% 288.54/288.84  1912 addition(one,addition(antidomain(A),antidomain(B))) = one.  [para(107(a,1),151(a,2)),rewrite([4(5)])].
% 288.54/288.84  2029 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)).  [para(17(a,1),560(a,1,1)),rewrite([4(4)]),flip(a)].
% 288.54/288.84  2032 multiplication(A,multiplication(addition(B,C),coantidomain(multiplication(A,B)))) = multiplication(A,multiplication(C,coantidomain(multiplication(A,B)))).  [para(39(a,1),560(a,1,1)),rewrite([33(5),33(9)])].
% 288.54/288.84  2043 multiplication(A,antidomain(antidomain(coantidomain(addition(A,B))))) = zero.  [para(589(a,1),7(a,1,1)),rewrite([4(7)])].
% 288.54/288.84  2056 multiplication(A,antidomain(antidomain(coantidomain(addition(B,A))))) = zero.  [back_rewrite(782),rewrite([2043(5),168(7),14(9)]),flip(a)].
% 288.54/288.84  2086 multiplication(A,multiplication(antidomain(B),antidomain(antidomain(coantidomain(A))))) = zero.  [para(126(a,1),2056(a,1,2,1,1,1)),rewrite([33(6)])].
% 288.54/288.84  2087 multiplication(A,multiplication(coantidomain(B),antidomain(antidomain(coantidomain(A))))) = zero.  [para(130(a,1),2056(a,1,2,1,1,1)),rewrite([33(6)])].
% 288.54/288.84  2118 multiplication(coantidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero.  [para(590(a,1),9(a,1,2)),rewrite([3(7)])].
% 288.54/288.84  2190 ifeq(leq(coantidomain(coantidomain(A)),antidomain(coantidomain(A))),true,coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = antidomain(coantidomain(A)).  [para(360(a,1),156(a,1,1,2)),rewrite([360(13),360(16)])].
% 288.54/288.84  2279 multiplication(antidomain(addition(A,B)),antidomain(antidomain(A))) = zero.  [para(1014(a,1),7(a,1,1)),rewrite([4(7)])].
% 288.54/288.84  2292 multiplication(antidomain(addition(A,B)),antidomain(antidomain(B))) = zero.  [para(15(a,1),2279(a,1,1,1))].
% 288.54/288.84  2323 multiplication(antidomain(A),antidomain(antidomain(multiplication(antidomain(B),A)))) = zero.  [para(127(a,1),2292(a,1,1,1))].
% 288.54/288.84  2528 multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero.  [para(1157(a,1),9(a,1,2)),rewrite([3(7)])].
% 288.54/288.84  2572 multiplication(coantidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero.  [para(1159(a,1),9(a,1,2)),rewrite([3(7)])].
% 288.54/288.84  2724 multiplication(A,antidomain(coantidomain(A))) = A.  [para(17(a,1),174(a,1,2)),rewrite([3(2)]),flip(a)].
% 288.54/288.84  2765 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B).  [para(2724(a,1),33(a,1,1)),flip(a)].
% 288.54/288.84  2768 addition(A,multiplication(B,antidomain(coantidomain(A)))) = multiplication(addition(A,B),antidomain(coantidomain(A))).  [para(2724(a,1),41(a,1,1))].
% 288.54/288.84  2773 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))).  [para(2724(a,1),131(a,1,2)),rewrite([15(5)])].
% 288.54/288.84  2775 leq(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = true.  [para(2724(a,1),197(a,1,1))].
% 288.54/288.84  2944 multiplication(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))).  [para(17(a,1),181(a,1,1)),rewrite([4(5)]),flip(a)].
% 288.54/288.84  2945 multiplication(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(sK1_goals_X2))))))))))))))) = zero.  [para(37(a,1),181(a,1,1)),rewrite([177(32)]),flip(a)].
% 288.54/288.84  2981 addition(antidomain(antidomain(A)),coantidomain(antidomain(A))) = antidomain(antidomain(A)).  [para(2029(a,1),130(a,1,2))].
% 288.54/288.84  3058 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,antidomain(B)))),antidomain(antidomain(coantidomain(A))))) = one.  [para(2086(a,1),93(a,1,1,1)),rewrite([132(2),108(11)]),flip(a)].
% 288.54/288.84  3075 coantidomain(multiplication(coantidomain(coantidomain(multiplication(A,coantidomain(B)))),antidomain(antidomain(coantidomain(A))))) = one.  [para(2087(a,1),93(a,1,1,1)),rewrite([132(2),108(11)]),flip(a)].
% 288.54/288.84  3242 multiplication(A,addition(B,multiplication(antidomain(coantidomain(A)),C))) = multiplication(A,addition(C,B)).  [para(2765(a,1),39(a,1,1)),rewrite([39(3),15(6)]),flip(a)].
% 288.54/288.84  3284 multiplication(A,coantidomain(coantidomain(A))) = A.  [para(360(a,1),2765(a,1,2)),rewrite([2724(3)]),flip(a)].
% 288.54/288.84  3326 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A).  [back_rewrite(562),rewrite([3284(5)]),flip(a)].
% 288.54/288.84  3428 antidomain(coantidomain(coantidomain(A))) = coantidomain(A).  [para(3326(a,1),1531(a,1,2)),rewrite([15(5),2773(5),3326(6)])].
% 288.54/288.84  3430 leq(coantidomain(coantidomain(A)),antidomain(coantidomain(A))) = true.  [para(3326(a,1),2775(a,1,2,1))].
% 288.54/288.84  3448 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)).  [back_rewrite(2190),rewrite([3430(5),14(7)])].
% 288.54/288.84  3458 antidomain(antidomain(coantidomain(A))) = coantidomain(A).  [back_rewrite(3428),rewrite([3448(2)])].
% 288.54/288.84  3510 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A))) = one.  [back_rewrite(3075),rewrite([3448(4),3458(7)])].
% 288.54/288.84  3512 coantidomain(multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A))) = one.  [back_rewrite(3058),rewrite([3448(4),3458(7)])].
% 288.54/288.84  3555 multiplication(antidomain(coantidomain(multiplication(A,B))),coantidomain(B)) = zero.  [back_rewrite(2572),rewrite([3448(3)])].
% 288.54/288.84  3572 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),B) = zero.  [back_rewrite(2528),rewrite([3448(4)])].
% 288.54/288.84  3656 multiplication(antidomain(coantidomain(A)),coantidomain(addition(A,B))) = zero.  [back_rewrite(2118),rewrite([3448(2)])].
% 288.54/288.84  3743 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A)) = one.  [back_rewrite(1193),rewrite([3448(5)])].
% 288.54/288.84  3745 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A)) = one.  [back_rewrite(1191),rewrite([3448(5)])].
% 288.54/288.84  3758 multiplication(antidomain(coantidomain(multiplication(A,B))),multiplication(C,coantidomain(multiplication(A,multiplication(B,C))))) = zero.  [back_rewrite(1172),rewrite([3448(3)])].
% 288.54/288.84  3765 coantidomain(multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B)) = one.  [back_rewrite(1158),rewrite([3448(5)])].
% 288.54/288.84  3800 multiplication(antidomain(coantidomain(A)),multiplication(B,coantidomain(multiplication(A,B)))) = zero.  [back_rewrite(220),rewrite([3448(2)])].
% 288.54/288.84  3801 multiplication(addition(A,antidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B).  [back_rewrite(211),rewrite([3448(3)])].
% 288.54/288.84  3810 addition(antidomain(antidomain(sK1_goals_X2)),antidomain(coantidomain(multiplication(antidomain(coantidomain(antidomain(antidomain(sK2_goals_X1)))),sK3_goals_X0)))) != antidomain(antidomain(sK1_goals_X2)) # answer(goals_1).  [back_rewrite(45),rewrite([3448(8),3448(12)])].
% 288.54/288.84  3812 addition(coantidomain(A),antidomain(coantidomain(A))) = one.  [back_rewrite(19),rewrite([3448(3)])].
% 288.54/288.84  4351 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),antidomain(antidomain(B))) = zero.  [para(3572(a,1),276(a,1,1,1)),rewrite([116(2),4(9)])].
% 288.54/288.84  4767 multiplication(coantidomain(antidomain(A)),antidomain(antidomain(A))) = coantidomain(antidomain(A)).  [para(2981(a,1),224(a,1,2)),rewrite([15(11),107(11),3(9)])].
% 288.54/288.84  5462 addition(multiplication(antidomain(A),B),multiplication(B,addition(C,one))) = multiplication(B,addition(C,one)).  [para(602(a,1),34(a,1,1)),rewrite([14(12)])].
% 288.54/288.84  6424 multiplication(antidomain(A),multiplication(addition(antidomain(B),antidomain(C)),A)) = zero.  [para(1912(a,1),1034(a,1,1,1,1)),rewrite([4(2)])].
% 288.54/288.84  8860 multiplication(antidomain(A),antidomain(addition(A,multiplication(A,B)))) = antidomain(addition(A,multiplication(A,B))).  [para(359(a,1),283(a,1,1)),rewrite([15(8),107(8),4(10)])].
% 288.54/288.84  8861 multiplication(antidomain(A),antidomain(multiplication(A,addition(B,one)))) = antidomain(multiplication(A,addition(B,one))).  [para(369(a,1),283(a,1,1)),rewrite([15(9),107(9),4(12)])].
% 288.54/288.84  8878 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(addition(A,antidomain(antidomain(antidomain(B)))),B))) = antidomain(multiplication(addition(A,antidomain(antidomain(antidomain(B)))),B)).  [para(275(a,1),283(a,1,1)),rewrite([15(17),107(17),4(19)])].
% 288.54/288.84  8890 antidomain(antidomain(antidomain(A))) = antidomain(A).  [para(2944(a,1),126(a,1,2)),rewrite([79(5)])].
% 288.54/288.84  8891 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(A,B))) = antidomain(multiplication(A,B)).  [back_rewrite(8878),rewrite([8890(7),72(7),8890(10),72(10)])].
% 288.54/288.84  8949 multiplication(antidomain(antidomain(sK2_goals_X1)),antidomain(antidomain(multiplication(sK3_goals_X0,antidomain(sK1_goals_X2))))) = zero.  [back_rewrite(2945),rewrite([8890(8),8890(8),8890(8),8890(10),8890(10)])].
% 288.54/288.84  9183 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(A)) = zero.  [para(3510(a,1),9(a,1,2)),rewrite([3(8)])].
% 288.54/288.84  9193 multiplication(antidomain(coantidomain(multiplication(A,coantidomain(B)))),coantidomain(addition(A,B))) = zero.  [para(73(a,1),9183(a,1,1,1,1))].
% 288.54/288.84  9207 multiplication(antidomain(coantidomain(multiplication(A,antidomain(B)))),coantidomain(A)) = zero.  [para(3512(a,1),9(a,1,2)),rewrite([3(8)])].
% 288.54/288.84  9763 addition(addition(A,B),multiplication(antidomain(A),addition(B,one))) = addition(A,addition(B,antidomain(A))).  [para(366(a,1),322(a,2,2)),rewrite([31(9),15(8),31(9,R),15(8)])].
% 288.54/288.84  10151 multiplication(antidomain(coantidomain(multiplication(antidomain(A),coantidomain(B)))),A) = zero.  [para(3743(a,1),9(a,1,2)),rewrite([3(8)])].
% 288.54/288.84  10456 multiplication(antidomain(coantidomain(multiplication(antidomain(A),antidomain(B)))),A) = zero.  [para(3745(a,1),9(a,1,2)),rewrite([3(8)])].
% 288.54/288.84  10535 multiplication(coantidomain(antidomain(A)),A) = A.  [para(3812(a,1),3801(a,1,1)),rewrite([4(2)]),flip(a)].
% 288.54/288.84  10540 coantidomain(antidomain(A)) = antidomain(antidomain(A)).  [para(4767(a,1),3801(a,2)),rewrite([8890(5),3812(6),4(4)]),flip(a)].
% 288.54/288.84  10541 multiplication(antidomain(antidomain(A)),A) = A.  [back_rewrite(10535),rewrite([10540(2)])].
% 288.54/288.84  10642 addition(antidomain(antidomain(sK1_goals_X2)),antidomain(coantidomain(multiplication(antidomain(antidomain(sK2_goals_X1)),sK3_goals_X0)))) != antidomain(antidomain(sK1_goals_X2)) # answer(goals_1).  [back_rewrite(3810),rewrite([10540(7),8890(7)])].
% 288.54/288.84  10649 multiplication(antidomain(antidomain(A)),multiplication(A,B)) = multiplication(A,B).  [para(10541(a,1),33(a,1,1)),flip(a)].
% 288.54/288.84  10658 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero.  [para(10541(a,1),119(a,1,2,2))].
% 288.54/288.84  12778 addition(zero,addition(antidomain(A),antidomain(B))) = addition(antidomain(A),antidomain(B)).  [para(6424(a,1),1450(a,1,2)),rewrite([15(5)])].
% 288.54/288.84  13287 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B).  [para(17(a,1),364(a,1,2,1)),rewrite([4(5)]),flip(a)].
% 288.54/288.84  13823 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)).  [para(17(a,1),379(a,1,1)),rewrite([4(5)]),flip(a)].
% 288.54/288.84  13970 multiplication(antidomain(A),multiplication(coantidomain(B),antidomain(A))) = multiplication(coantidomain(B),antidomain(A)).  [para(17(a,1),386(a,1,1)),rewrite([4(5)]),flip(a)].
% 288.54/288.84  14070 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A).  [para(886(a,1),392(a,1,1,1)),rewrite([8890(6),168(6),8890(8),14(8),8890(6)]),flip(a)].
% 288.54/288.84  14072 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A.  [para(1286(a,1),392(a,1,1,1)),rewrite([8890(6),168(6),8890(7),14(7),8890(5)]),flip(a)].
% 288.54/288.84  14073 multiplication(antidomain(addition(A,B)),antidomain(A)) = antidomain(addition(A,B)).  [para(2279(a,1),392(a,1,1,1)),rewrite([8890(6),168(6),8890(9),14(9),8890(7)]),flip(a)].
% 288.54/288.84  14074 multiplication(antidomain(addition(A,B)),antidomain(B)) = antidomain(addition(A,B)).  [para(2292(a,1),392(a,1,1,1)),rewrite([8890(6),168(6),8890(9),14(9),8890(7)]),flip(a)].
% 288.54/288.84  14075 multiplication(antidomain(A),antidomain(multiplication(antidomain(B),A))) = antidomain(A).  [para(2323(a,1),392(a,1,1,1)),rewrite([8890(7),168(7),8890(9),14(9),8890(7)]),flip(a)].
% 288.54/288.84  14079 antidomain(addition(A,multiplication(A,B))) = antidomain(A).  [para(898(a,1),392(a,1,1,1)),rewrite([8890(7),8860(6),168(5),8890(9),8860(8),14(7),8890(7),8860(6)]),flip(a)].
% 288.54/288.84  14080 multiplication(A,antidomain(multiplication(B,coantidomain(multiplication(A,B))))) = A.  [para(1741(a,1),392(a,1,1,1)),rewrite([8890(7),168(7),8890(8),14(8),8890(6)]),flip(a)].
% 288.54/288.84  14094 antidomain(multiplication(A,addition(B,one))) = antidomain(A).  [back_rewrite(8861),rewrite([14070(6)]),flip(a)].
% 288.54/288.84  14189 antidomain(addition(antidomain(antidomain(A)),multiplication(A,B))) = antidomain(A).  [para(10649(a,1),14079(a,1,1,2)),rewrite([8890(8)])].
% 288.54/288.84  14602 multiplication(A,antidomain(coantidomain(addition(A,B)))) = A.  [para(572(a,1),14080(a,1,2,1,2,1)),rewrite([132(4),3(4)])].
% 288.54/288.84  14830 antidomain(addition(multiplication(A,B),antidomain(antidomain(A)))) = antidomain(A).  [para(15(a,1),14189(a,1,1))].
% 288.54/288.84  15406 multiplication(antidomain(antidomain(sK2_goals_X1)),multiplication(sK3_goals_X0,antidomain(sK1_goals_X2))) = zero.  [para(8949(a,1),10658(a,1,1,1)),rewrite([116(2),4(10)])].
% 288.54/288.84  15410 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)).  [para(10658(a,1),14080(a,1,2,1,2,1)),rewrite([132(7),3(7),8891(7)]),flip(a)].
% 288.54/288.84  15769 addition(antidomain(A),antidomain(addition(A,B))) = antidomain(A).  [para(14073(a,1),127(a,1,2))].
% 288.54/288.84  15922 multiplication(antidomain(A),antidomain(addition(A,B))) = antidomain(addition(A,B)).  [para(15769(a,1),283(a,1,1)),rewrite([15(7),107(7),4(8)])].
% 288.54/288.84  18622 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A).  [para(14830(a,1),15922(a,1,2)),rewrite([14830(9)])].
% 288.54/288.84  18659 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C).  [para(18622(a,1),33(a,1,1)),flip(a)].
% 288.54/288.84  18677 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B).  [back_rewrite(13287),rewrite([18659(7)]),flip(a)].
% 288.54/288.84  18751 addition(antidomain(A),antidomain(antidomain(addition(B,A)))) = one.  [para(14074(a,1),519(a,2,2,2)),rewrite([15(4),107(4),10540(5),4(7),10540(9),15(12),17(12),15(8),107(8)])].
% 288.54/288.84  20010 multiplication(addition(antidomain(A),coantidomain(B)),A) = multiplication(coantidomain(B),A).  [para(213(a,1),612(a,1,1,2)),rewrite([223(8)])].
% 288.54/288.84  20269 multiplication(antidomain(coantidomain(multiplication(antidomain(multiplication(A,B)),A))),B) = zero.  [para(3765(a,1),9(a,1,2)),rewrite([3(8)])].
% 288.54/288.84  22483 multiplication(coantidomain(multiplication(A,B)),coantidomain(B)) = coantidomain(B).  [para(3555(a,1),775(a,1,1,1)),rewrite([3458(5),168(6),3458(7),14(8),3458(5)]),flip(a)].
% 288.54/288.84  22485 multiplication(coantidomain(A),coantidomain(addition(A,B))) = coantidomain(addition(A,B)).  [para(3656(a,1),775(a,1,1,1)),rewrite([3458(4),168(6),3458(7),14(9),3458(5)]),flip(a)].
% 288.54/288.84  22488 multiplication(coantidomain(multiplication(A,coantidomain(B))),coantidomain(A)) = coantidomain(A).  [para(9183(a,1),775(a,1,1,1)),rewrite([3458(6),168(7),3458(8),14(9),3458(6)]),flip(a)].
% 288.54/288.84  22489 multiplication(coantidomain(multiplication(A,antidomain(B))),coantidomain(A)) = coantidomain(A).  [para(9207(a,1),775(a,1,1,1)),rewrite([3458(6),168(7),3458(8),14(9),3458(6)]),flip(a)].
% 288.54/288.84  22494 multiplication(coantidomain(multiplication(antidomain(A),coantidomain(B))),A) = A.  [para(10151(a,1),775(a,1,1,1)),rewrite([3458(7),168(7),3458(8),14(8),3458(6)]),flip(a)].
% 288.54/288.84  22495 multiplication(coantidomain(multiplication(antidomain(A),antidomain(B))),A) = A.  [para(10456(a,1),775(a,1,1,1)),rewrite([3458(7),168(7),3458(8),14(8),3458(6)]),flip(a)].
% 288.54/288.84  22497 multiplication(coantidomain(multiplication(A,antidomain(B))),antidomain(antidomain(B))) = antidomain(antidomain(B)).  [para(4351(a,1),775(a,1,1,1)),rewrite([3458(6),168(8),3458(9),14(11),3458(7)]),flip(a)].
% 288.54/288.84  22515 multiplication(coantidomain(multiplication(antidomain(multiplication(A,B)),A)),B) = B.  [para(20269(a,1),775(a,1,1,1)),rewrite([3458(7),168(7),3458(8),14(8),3458(6)]),flip(a)].
% 288.54/288.84  22727 leq(coantidomain(A),coantidomain(multiplication(B,A))) = true.  [para(22483(a,1),196(a,1,1))].
% 288.54/288.84  22746 multiplication(coantidomain(A),antidomain(coantidomain(multiplication(B,A)))) = zero.  [para(22483(a,1),9183(a,1,1,1,1)),rewrite([3448(2),3458(3),3448(4)])].
% 288.54/288.84  22780 coantidomain(addition(A,coantidomain(multiplication(B,A)))) = zero.  [para(22483(a,1),9193(a,1,1,1,1)),rewrite([3448(2),3458(3),15(4),22485(6)])].
% 288.54/288.84  22807 leq(coantidomain(addition(A,B)),coantidomain(A)) = true.  [para(14602(a,1),22727(a,1,2,1)),rewrite([10540(4),3458(4)])].
% 288.54/288.84  22834 coantidomain(addition(A,coantidomain(A))) = zero.  [para(4(a,1),22780(a,1,1,2,1))].
% 288.54/288.84  22873 multiplication(A,coantidomain(multiplication(addition(B,coantidomain(B)),A))) = zero.  [para(22834(a,1),3800(a,1,1,1)),rewrite([116(2),4(7)])].
% 288.54/288.84  22893 leq(coantidomain(addition(A,B)),coantidomain(B)) = true.  [para(15(a,1),22807(a,1,1,1))].
% 288.54/288.84  22944 addition(coantidomain(A),coantidomain(addition(B,A))) = coantidomain(A).  [para(22893(a,1),34(a,1,1)),rewrite([15(6),14(8)])].
% 288.54/288.84  23022 multiplication(coantidomain(A),antidomain(B)) = multiplication(antidomain(B),coantidomain(A)).  [para(22494(a,1),14072(a,1,2,1)),rewrite([33(5),13970(5)])].
% 288.54/288.84  23068 multiplication(antidomain(antidomain(A)),coantidomain(multiplication(B,antidomain(A)))) = antidomain(antidomain(A)).  [back_rewrite(22497),rewrite([23022(6)])].
% 288.54/288.84  23114 multiplication(antidomain(A),antidomain(B)) = multiplication(antidomain(B),antidomain(A)).  [para(22495(a,1),14072(a,1,2,1)),rewrite([33(5),13823(5)])].
% 288.54/288.84  23253 multiplication(coantidomain(A),coantidomain(multiplication(B,A))) = coantidomain(A).  [para(22746(a,1),392(a,1,1,1)),rewrite([3458(6),168(6),3458(8),14(8),3458(6)]),flip(a)].
% 288.54/288.84  23416 addition(coantidomain(A),antidomain(coantidomain(addition(B,A)))) = one.  [para(22944(a,1),18751(a,1,2,1,1)),rewrite([3458(6),15(5)])].
% 288.54/288.84  23560 multiplication(A,multiplication(coantidomain(B),antidomain(coantidomain(A)))) = multiplication(A,coantidomain(B)).  [para(22488(a,1),14072(a,1,2,1)),rewrite([33(5)])].
% 288.54/288.84  23577 multiplication(A,multiplication(antidomain(B),antidomain(coantidomain(A)))) = multiplication(A,antidomain(B)).  [para(22489(a,1),14072(a,1,2,1)),rewrite([33(5)])].
% 288.54/288.84  23850 coantidomain(multiplication(addition(A,coantidomain(A)),B)) = coantidomain(B).  [para(22873(a,1),22515(a,1,1,1,1,1)),rewrite([116(2),4(2),23253(6)]),flip(a)].
% 288.54/288.84  23853 coantidomain(multiplication(antidomain(coantidomain(A)),B)) = coantidomain(multiplication(A,B)).  [para(147(a,1),23850(a,1,1)),rewrite([3448(2),2765(4),3448(4)]),flip(a)].
% 288.54/288.84  23877 coantidomain(multiplication(antidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(A))).  [para(811(a,1),23850(a,1,1)),rewrite([3448(3),23577(5),3448(6)]),flip(a)].
% 288.54/288.84  23878 coantidomain(multiplication(coantidomain(A),antidomain(coantidomain(B)))) = coantidomain(multiplication(B,coantidomain(A))).  [para(822(a,1),23850(a,1,1)),rewrite([3448(3),23560(5),3448(6)]),flip(a)].
% 288.54/288.84  23992 antidomain(multiplication(antidomain(antidomain(A)),coantidomain(B))) = antidomain(multiplication(coantidomain(B),A)).  [para(23022(a,1),15410(a,1,1))].
% 288.54/288.84  24072 multiplication(coantidomain(multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B)))),B) = B.  [para(23114(a,1),22515(a,1,1,1))].
% 288.54/288.84  27057 multiplication(antidomain(antidomain(multiplication(antidomain(A),B))),B) = multiplication(antidomain(A),B).  [para(18677(a,1),18677(a,1,1,1)),rewrite([18677(5),8890(3)]),flip(a)].
% 288.54/288.84  27524 multiplication(A,coantidomain(multiplication(A,antidomain(B)))) = multiplication(A,antidomain(antidomain(B))).  [para(17(a,1),2032(a,1,2,1)),rewrite([4(5),23068(10)])].
% 288.54/288.84  28237 multiplication(coantidomain(multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B)))),B) = B.  [para(23877(a,1),22515(a,1,1))].
% 288.54/288.84  28238 coantidomain(multiplication(A,antidomain(coantidomain(B)))) = coantidomain(multiplication(B,antidomain(coantidomain(A)))).  [para(23877(a,1),23853(a,1))].
% 288.54/288.84  28276 multiplication(antidomain(A),antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(B)).  [para(24072(a,1),14072(a,1,2,1)),rewrite([33(7),23114(6),14075(6)]),flip(a)].
% 288.54/288.84  28934 multiplication(A,addition(antidomain(antidomain(B)),multiplication(antidomain(B),antidomain(coantidomain(A))))) = A.  [para(17(a,1),3242(a,2,2)),rewrite([23114(6),3(10)])].
% 288.54/288.84  29130 antidomain(antidomain(multiplication(antidomain(A),B))) = multiplication(antidomain(A),antidomain(antidomain(B))).  [para(27057(a,1),392(a,2)),rewrite([15410(5),23114(6),2323(6),15410(6),23114(8),168(9),15410(7),15410(11),23114(13),14(14)])].
% 288.54/288.84  29213 multiplication(antidomain(sK1_goals_X2),antidomain(coantidomain(multiplication(antidomain(antidomain(sK2_goals_X1)),sK3_goals_X0)))) = zero.  [para(15406(a,1),3758(a,1,2,2,1)),rewrite([132(11),3(11),23114(10)])].
% 288.54/288.84  29221 multiplication(antidomain(sK1_goals_X2),coantidomain(multiplication(antidomain(antidomain(sK2_goals_X1)),sK3_goals_X0))) = antidomain(sK1_goals_X2).  [para(29213(a,1),392(a,1,1,1)),rewrite([3458(11),168(11),3458(14),14(14),3458(12)]),flip(a)].
% 288.54/288.84  31098 multiplication(coantidomain(A),coantidomain(multiplication(B,coantidomain(A)))) = multiplication(coantidomain(A),coantidomain(B)).  [para(23878(a,1),27524(a,1,2)),rewrite([3458(9)])].
% 288.54/288.84  31433 multiplication(A,antidomain(multiplication(antidomain(coantidomain(A)),B))) = multiplication(A,antidomain(B)).  [para(28237(a,1),14072(a,1,2,1)),rewrite([33(7),23114(6),14075(6)]),flip(a)].
% 288.54/288.84  31438 multiplication(A,coantidomain(multiplication(B,antidomain(coantidomain(A))))) = multiplication(A,coantidomain(B)).  [para(28238(a,1),27524(a,1,2)),rewrite([3458(8)])].
% 288.54/288.84  31924 coantidomain(multiplication(antidomain(A),antidomain(antidomain(B)))) = antidomain(multiplication(antidomain(A),B)).  [para(29130(a,1),10540(a,1,1)),rewrite([29130(9),15410(10)])].
% 288.54/288.84  33479 multiplication(antidomain(A),antidomain(B)) = antidomain(addition(A,B)).  [para(15922(a,1),31433(a,2)),rewrite([10540(3),8890(4),67(4),28276(5)])].
% 288.54/288.84  33533 antidomain(antidomain(addition(A,antidomain(B)))) = antidomain(multiplication(antidomain(A),B)).  [back_rewrite(31924),rewrite([33479(4),10540(4)])].
% 288.54/288.84  33544 antidomain(antidomain(multiplication(antidomain(A),B))) = antidomain(addition(A,antidomain(B))).  [back_rewrite(29130),rewrite([33479(8)])].
% 288.54/288.84  33546 multiplication(A,addition(antidomain(antidomain(B)),antidomain(addition(B,coantidomain(A))))) = A.  [back_rewrite(28934),rewrite([33479(6)])].
% 288.54/288.84  33597 antidomain(addition(A,antidomain(antidomain(B)))) = antidomain(addition(B,A)).  [para(8890(a,1),33479(a,1,1)),rewrite([33479(3),15(5)]),flip(a)].
% 288.54/288.84  33833 multiplication(A,coantidomain(addition(B,coantidomain(A)))) = multiplication(A,coantidomain(B)).  [para(72(a,1),31438(a,1,2,1)),rewrite([31438(5),3458(5)]),flip(a)].
% 288.54/288.84  33838 multiplication(coantidomain(A),coantidomain(B)) = coantidomain(addition(A,B)).  [para(22485(a,1),31438(a,2)),rewrite([3448(4),3458(5),560(4),31098(5)])].
% 288.54/288.84  33868 multiplication(antidomain(antidomain(A)),coantidomain(B)) = coantidomain(addition(B,antidomain(A))).  [para(10540(a,1),33838(a,1,1)),rewrite([15(6)])].
% 288.54/288.84  33917 antidomain(coantidomain(addition(A,antidomain(B)))) = antidomain(multiplication(coantidomain(A),B)).  [back_rewrite(23992),rewrite([33868(4)])].
% 288.54/288.84  33998 coantidomain(addition(A,antidomain(coantidomain(B)))) = coantidomain(addition(A,B)).  [para(33833(a,1),20010(a,2)),rewrite([3448(2),33917(5),33838(3),15(5),23416(5),3448(3),4(6),33838(7),15(5)])].
% 288.54/288.84  34012 coantidomain(addition(antidomain(A),antidomain(B))) = antidomain(addition(antidomain(A),antidomain(B))).  [para(12778(a,1),33998(a,2,1)),rewrite([33917(6),10540(3),183(6),10540(5),33544(5)]),flip(a)].
% 288.54/288.84  34792 multiplication(A,addition(antidomain(B),antidomain(addition(antidomain(B),coantidomain(A))))) = A.  [para(8890(a,1),33546(a,1,2,1))].
% 288.54/288.84  35251 addition(antidomain(A),antidomain(addition(B,antidomain(A)))) = addition(antidomain(A),antidomain(B)).  [para(34792(a,1),127(a,1,2)),rewrite([10540(4),33597(6),15(7),31(7,R),15(6),15769(6),10540(7),33597(9)]),flip(a)].
% 288.54/288.84  37034 addition(antidomain(A),addition(antidomain(antidomain(A)),antidomain(addition(A,B)))) = one.  [para(15769(a,1),9763(a,1,1)),rewrite([15(7),107(7),3(5),17(4),15(7)]),flip(a)].
% 288.54/288.84  37036 addition(addition(antidomain(A),antidomain(B)),antidomain(multiplication(antidomain(A),B))) = one.  [para(5462(a,1),37034(a,1,2,2,1)),rewrite([33544(7),14094(10),15(8),35251(8),15(6),15(7)])].
% 288.54/288.84  37041 antidomain(multiplication(antidomain(antidomain(A)),B)) = addition(antidomain(A),antidomain(B)).  [para(37036(a,1),2768(a,2,1)),rewrite([34012(10),33533(11),33479(11),41(9),17(7),4(5),15(5),31(5,R),2(4),34012(8),33533(9),4(9)]),flip(a)].
% 288.54/288.84  37052 addition(antidomain(A),antidomain(coantidomain(B))) = antidomain(multiplication(coantidomain(B),A)).  [para(3458(a,1),37041(a,1,1,1)),rewrite([15(7)]),flip(a)].
% 288.54/288.84  37110 $F # answer(goals_1).  [back_rewrite(10642),rewrite([37052(11),23022(9),29221(9)]),xx(a)].
% 288.54/288.84  
% 288.54/288.84  % SZS output end Refutation
% 288.54/288.84  ============================== end of proof ==========================
% 288.54/288.84  
% 288.54/288.84  ============================== STATISTICS ============================
% 288.54/288.84  
% 288.54/288.84  Given=8517. Generated=20066435. Kept=37095. proofs=1.
% 288.54/288.84  Usable=6255. Sos=6758. Demods=12969. Limbo=58, Disabled=24055. Hints=0.
% 288.54/288.84  Megabytes=26.98.
% 288.54/288.84  User_CPU=276.74, System_CPU=11.03, Wall_clock=287.
% 288.54/288.84  
% 288.54/288.84  ============================== end of statistics =====================
% 288.54/288.84  
% 288.54/288.84  ============================== end of search =========================
% 288.54/288.84  
% 288.54/288.84  THEOREM PROVED
% 288.54/288.84  % SZS status Unsatisfiable
% 288.54/288.84  
% 288.54/288.84  Exiting with 1 proof.
% 288.54/288.84  
% 288.54/288.84  Process 19516 exit (max_proofs) Thu Jun 16 08:50:59 2022
% 288.54/288.84  Prover9 interrupted
%------------------------------------------------------------------------------