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
%------------------------------------------------------------------------------