TSTP Solution File: RNG035-7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG035-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 : Mon Jul 18 20:39:15 EDT 2022
% Result : Unsatisfiable 54.76s 55.05s
% Output : Refutation 54.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : RNG035-7 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 20:30:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.51/4.83 ============================== Prover9 ===============================
% 4.51/4.83 Prover9 (32) version 2009-11A, November 2009.
% 4.51/4.83 Process 9328 was started by sandbox2 on n026.cluster.edu,
% 4.51/4.83 Mon May 30 20:30:41 2022
% 4.51/4.83 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9172_n026.cluster.edu".
% 4.51/4.83 ============================== end of head ===========================
% 4.51/4.83
% 4.51/4.83 ============================== INPUT =================================
% 4.51/4.83
% 4.51/4.83 % Reading from file /tmp/Prover9_9172_n026.cluster.edu
% 4.51/4.83
% 4.51/4.83 set(prolog_style_variables).
% 4.51/4.83 set(auto2).
% 4.51/4.83 % set(auto2) -> set(auto).
% 4.51/4.83 % set(auto) -> set(auto_inference).
% 4.51/4.83 % set(auto) -> set(auto_setup).
% 4.51/4.83 % set(auto_setup) -> set(predicate_elim).
% 4.51/4.83 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.51/4.83 % set(auto) -> set(auto_limits).
% 4.51/4.83 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.51/4.83 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.51/4.83 % set(auto) -> set(auto_denials).
% 4.51/4.83 % set(auto) -> set(auto_process).
% 4.51/4.83 % set(auto2) -> assign(new_constants, 1).
% 4.51/4.83 % set(auto2) -> assign(fold_denial_max, 3).
% 4.51/4.83 % set(auto2) -> assign(max_weight, "200.000").
% 4.51/4.83 % set(auto2) -> assign(max_hours, 1).
% 4.51/4.83 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.51/4.83 % set(auto2) -> assign(max_seconds, 0).
% 4.51/4.83 % set(auto2) -> assign(max_minutes, 5).
% 4.51/4.83 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.51/4.83 % set(auto2) -> set(sort_initial_sos).
% 4.51/4.83 % set(auto2) -> assign(sos_limit, -1).
% 4.51/4.83 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.51/4.83 % set(auto2) -> assign(max_megs, 400).
% 4.51/4.83 % set(auto2) -> assign(stats, some).
% 4.51/4.83 % set(auto2) -> clear(echo_input).
% 4.51/4.83 % set(auto2) -> set(quiet).
% 4.51/4.83 % set(auto2) -> clear(print_initial_clauses).
% 4.51/4.83 % set(auto2) -> clear(print_given).
% 4.51/4.83 assign(lrs_ticks,-1).
% 4.51/4.83 assign(sos_limit,10000).
% 4.51/4.83 assign(order,kbo).
% 4.51/4.83 set(lex_order_vars).
% 4.51/4.83 clear(print_given).
% 4.51/4.83
% 4.51/4.83 % formulas(sos). % not echoed (12 formulas)
% 4.51/4.83
% 4.51/4.83 ============================== end of input ==========================
% 4.51/4.83
% 4.51/4.83 % From the command line: assign(max_seconds, 300).
% 4.51/4.83
% 4.51/4.83 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.51/4.83
% 4.51/4.83 % Formulas that are not ordinary clauses:
% 4.51/4.83
% 4.51/4.83 ============================== end of process non-clausal formulas ===
% 4.51/4.83
% 4.51/4.83 ============================== PROCESS INITIAL CLAUSES ===============
% 4.51/4.83
% 4.51/4.83 ============================== PREDICATE ELIMINATION =================
% 4.51/4.83
% 4.51/4.83 ============================== end predicate elimination =============
% 4.51/4.83
% 4.51/4.83 Auto_denials:
% 4.51/4.83 % copying label prove_commutativity to answer in negative clause
% 4.51/4.83
% 4.51/4.83 Term ordering decisions:
% 4.51/4.83
% 4.51/4.83 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (8).
% 4.51/4.83 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. add=1. multiply=1. additive_inverse=0.
% 4.51/4.83
% 4.51/4.83 ============================== end of process initial clauses ========
% 4.51/4.83
% 4.51/4.83 ============================== CLAUSES FOR SEARCH ====================
% 4.51/4.83
% 4.51/4.83 ============================== end of clauses for search =============
% 4.51/4.83
% 4.51/4.83 ============================== SEARCH ================================
% 4.51/4.83
% 4.51/4.83 % Starting search at 0.01 seconds.
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=81.000, iters=3357
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=71.000, iters=3370
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=69.000, iters=3343
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=61.000, iters=3333
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=59.000, iters=3333
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=55.000, iters=3357
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=54.000, iters=3381
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=52.000, iters=3334
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=51.000, iters=3379
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=50.000, iters=3384
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=49.000, iters=3411
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=47.000, iters=3367
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=46.000, iters=3390
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=45.000, iters=3398
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=43.000, iters=3341
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=41.000, iters=3356
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=39.000, iters=3356
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=37.000, iters=3351
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=35.000, iters=3339
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=33.000, iters=3342
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=32.000, iters=3336
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=31.000, iters=3346
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=30.000, iters=3357
% 4.51/4.83
% 4.51/4.83 Low Water (keep): wt=29.000, iters=3340
% 4.51/4.83
% 4.51/4.83 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 88 (0.00 of 3.74 sec).
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=28.000, iters=3338
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=27.000, iters=3345
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=6066, wt=187.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=2901, wt=177.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=6221, wt=165.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=5895, wt=163.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=6058, wt=151.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=6295, wt=143.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=6282, wt=139.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=5668, wt=137.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=2472, wt=135.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=5035, wt=133.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=5844, wt=129.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=6038, wt=125.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=5293, wt=123.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=6079, wt=119.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=6284, wt=117.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=13334, wt=24.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=13538, wt=20.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=13539, wt=19.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=13542, wt=18.000
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=26.000, iters=3334
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=25.000, iters=3333
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=24.000, iters=3488
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=23.000, iters=3335
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=23813, wt=17.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=23824, wt=16.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=23834, wt=15.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=24208, wt=14.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=24220, wt=13.000
% 54.76/55.05
% 54.76/55.05 Low Water (displace): id=24307, wt=12.000
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=22.000, iters=3341
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=21.000, iters=3345
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=20.000, iters=3339
% 54.76/55.05
% 54.76/55.05 Low Water (keep): wt=19.000, iters=3338
% 54.76/55.05
% 54.76/55.05 ============================== PROOF =================================
% 54.76/55.05 % SZS status Unsatisfiable
% 54.76/55.05 % SZS output start Refutation
% 54.76/55.05
% 54.76/55.05 % Proof 1 at 53.22 (+ 0.79) seconds: prove_commutativity.
% 54.76/55.05 % Length of proof is 602.
% 54.76/55.05 % Level of proof is 69.
% 54.76/55.05 % Maximum clause weight is 46.000.
% 54.76/55.05 % Given clauses 2576.
% 54.76/55.05
% 54.76/55.05 2 add(A,additive_identity) = A # label(right_additive_identity) # label(axiom). [assumption].
% 54.76/55.05 3 multiply(a,b) = c # label(a_times_b_is_c) # label(negated_conjecture). [assumption].
% 54.76/55.05 4 c = multiply(a,b). [copy(3),flip(a)].
% 54.76/55.05 6 add(A,additive_inverse(A)) = additive_identity # label(right_additive_inverse) # label(axiom). [assumption].
% 54.76/55.05 7 add(A,B) = add(B,A) # label(commutativity_for_addition) # label(axiom). [assumption].
% 54.76/55.05 8 multiply(A,multiply(A,multiply(A,A))) = A # label(x_fourthed_is_x) # label(hypothesis). [assumption].
% 54.76/55.05 9 add(A,add(B,C)) = add(add(A,B),C) # label(associativity_for_addition) # label(axiom). [assumption].
% 54.76/55.05 10 add(A,add(B,C)) = add(C,add(A,B)). [copy(9),rewrite([7(4)])].
% 54.76/55.05 11 multiply(A,multiply(B,C)) = multiply(multiply(A,B),C) # label(associativity_for_multiplication) # label(axiom). [assumption].
% 54.76/55.05 12 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [copy(11),flip(a)].
% 54.76/55.05 13 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distribute1) # label(axiom). [assumption].
% 54.76/55.05 14 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(13),flip(a)].
% 54.76/55.05 15 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distribute2) # label(axiom). [assumption].
% 54.76/55.05 16 add(multiply(A,B),multiply(C,B)) = multiply(add(A,C),B). [copy(15),flip(a)].
% 54.76/55.05 17 multiply(b,a) != c # label(prove_commutativity) # label(negated_conjecture) # answer(prove_commutativity). [assumption].
% 54.76/55.05 18 multiply(b,a) != multiply(a,b) # answer(prove_commutativity). [copy(17),rewrite([4(4)])].
% 54.76/55.05 19 multiply(b,a) = c_0. [new_symbol(18)].
% 54.76/55.05 20 multiply(a,b) != c_0 # answer(prove_commutativity). [back_rewrite(18),rewrite([19(3)]),flip(a)].
% 54.76/55.05 21 add(A,add(B,additive_inverse(A))) = B. [para(6(a,1),10(a,2,2)),rewrite([7(2),2(5)])].
% 54.76/55.05 22 multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))))) = multiply(A,B). [para(12(a,1),8(a,1,2,2)),rewrite([12(6),12(7)])].
% 54.76/55.05 23 multiply(A,multiply(A,multiply(A,multiply(A,B)))) = multiply(A,B). [para(8(a,1),12(a,1,1)),rewrite([12(4),12(3)]),flip(a)].
% 54.76/55.05 24 multiply(A,add(B,multiply(A,multiply(A,A)))) = add(A,multiply(A,B)). [para(8(a,1),14(a,1,1)),rewrite([7(5)]),flip(a)].
% 54.76/55.05 25 multiply(add(A,B),multiply(A,multiply(A,A))) = add(A,multiply(B,multiply(A,multiply(A,A)))). [para(8(a,1),16(a,1,1)),flip(a)].
% 54.76/55.05 26 multiply(add(A,B),multiply(B,multiply(B,B))) = add(B,multiply(A,multiply(B,multiply(B,B)))). [para(8(a,1),16(a,1,2)),rewrite([7(4)]),flip(a)].
% 54.76/55.05 27 add(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(add(D,multiply(A,B)),C). [para(12(a,1),16(a,1,1)),rewrite([7(6)])].
% 54.76/55.05 28 add(multiply(A,B),multiply(C,multiply(D,B))) = multiply(add(A,multiply(C,D)),B). [para(12(a,1),16(a,1,2))].
% 54.76/55.05 29 multiply(add(A,A),B) = multiply(A,add(B,B)). [para(16(a,1),14(a,1))].
% 54.76/55.05 30 multiply(b,multiply(a,A)) = multiply(c_0,A). [para(19(a,1),12(a,1,1)),flip(a)].
% 54.76/55.05 31 multiply(b,add(A,a)) = add(c_0,multiply(b,A)). [para(19(a,1),14(a,1,1)),rewrite([7(7)]),flip(a)].
% 54.76/55.05 32 multiply(add(A,b),a) = add(c_0,multiply(A,a)). [para(19(a,1),16(a,1,1)),rewrite([7(6)]),flip(a)].
% 54.76/55.05 33 add(A,add(B,add(C,additive_inverse(A)))) = add(B,C). [para(21(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),7(5)])].
% 54.76/55.05 34 multiply(c_0,multiply(a,multiply(a,a))) = c_0. [para(8(a,1),30(a,1,2)),rewrite([19(3)]),flip(a)].
% 54.76/55.05 35 multiply(b,add(A,multiply(a,B))) = add(multiply(c_0,B),multiply(b,A)). [para(30(a,1),14(a,1,1)),rewrite([7(9)]),flip(a)].
% 54.76/55.05 36 multiply(add(c_0,multiply(A,a)),B) = multiply(add(A,b),multiply(a,B)). [para(30(a,1),16(a,1,1)),rewrite([28(6),7(7)])].
% 54.76/55.05 37 multiply(c_0,multiply(a,multiply(a,multiply(a,A)))) = multiply(c_0,A). [para(34(a,1),12(a,1,1)),rewrite([12(9),12(8)]),flip(a)].
% 54.76/55.05 38 multiply(c_0,add(A,multiply(a,multiply(a,a)))) = add(c_0,multiply(c_0,A)). [para(34(a,1),14(a,1,1)),rewrite([7(11)]),flip(a)].
% 54.76/55.05 39 multiply(add(A,c_0),multiply(a,multiply(a,a))) = add(c_0,multiply(A,multiply(a,multiply(a,a)))). [para(34(a,1),16(a,1,1)),rewrite([7(10)]),flip(a)].
% 54.76/55.05 40 multiply(additive_identity,add(A,A)) = multiply(additive_identity,A). [para(2(a,1),29(a,1,1)),flip(a)].
% 54.76/55.05 47 multiply(add(A,A),add(B,C)) = multiply(A,add(B,add(B,add(C,C)))). [para(10(a,1),29(a,2,2)),rewrite([7(5),10(6,R),7(5),10(5,R)])].
% 54.76/55.05 48 multiply(add(A,A),multiply(B,C)) = multiply(A,multiply(add(B,B),C)). [para(29(a,1),12(a,1,1)),rewrite([12(3)]),flip(a)].
% 54.76/55.05 50 multiply(add(A,A),multiply(B,C)) = multiply(A,multiply(B,add(C,C))). [para(29(a,1),12(a,2)),rewrite([12(3),14(6)])].
% 54.76/55.05 53 multiply(A,add(B,add(B,C))) = add(multiply(add(A,A),B),multiply(A,C)). [para(29(a,2),14(a,1,1)),rewrite([7(6),10(6),7(5)]),flip(a)].
% 54.76/55.05 54 multiply(A,add(B,add(C,C))) = add(multiply(A,B),multiply(add(A,A),C)). [para(29(a,2),14(a,1,2)),flip(a)].
% 54.76/55.05 55 multiply(add(A,add(A,B)),C) = add(multiply(A,add(C,C)),multiply(B,C)). [para(29(a,1),16(a,1,1)),rewrite([7(6),10(6),7(5)]),flip(a)].
% 54.76/55.05 56 multiply(add(A,add(B,B)),C) = add(multiply(A,C),multiply(B,add(C,C))). [para(29(a,1),16(a,1,2)),flip(a)].
% 54.76/55.05 59 multiply(c_0,add(A,A)) = multiply(b,multiply(add(a,a),A)). [para(29(a,2),30(a,1,2)),flip(a)].
% 54.76/55.05 63 multiply(additive_identity,add(A,add(A,B))) = multiply(additive_identity,add(A,B)). [para(40(a,1),14(a,1,1)),rewrite([14(5),7(6),10(6),7(5)]),flip(a)].
% 54.76/55.05 67 multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,multiply(B,C)))))))) = multiply(A,multiply(B,C)). [para(22(a,1),12(a,1,1)),rewrite([12(2),12(9),12(8),12(7),12(6),12(5),12(4)]),flip(a)].
% 54.76/55.05 68 multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,C))))))))))) = multiply(A,multiply(B,C)). [para(22(a,1),12(a,1)),rewrite([12(2),12(6),12(8),12(10)]),flip(a)].
% 54.76/55.05 69 multiply(A,add(B,multiply(C,multiply(A,multiply(C,multiply(A,multiply(C,multiply(A,C)))))))) = multiply(A,add(C,B)). [para(22(a,1),14(a,1,1)),rewrite([14(3),7(9)]),flip(a)].
% 54.76/55.05 70 add(multiply(A,B),multiply(C,multiply(B,multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B)))))))) = multiply(add(A,C),multiply(B,multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))))). [para(22(a,1),16(a,1,1))].
% 54.76/55.05 72 multiply(a,multiply(c_0,multiply(c_0,multiply(c_0,b)))) = multiply(a,b). [para(30(a,1),22(a,1,2,2,2,2,2)),rewrite([30(10),30(10)])].
% 54.76/55.05 73 multiply(A,multiply(B,multiply(add(A,A),multiply(B,multiply(add(A,A),multiply(B,multiply(add(A,A),add(B,B)))))))) = multiply(add(A,A),B). [para(22(a,1),29(a,1)),rewrite([14(21),14(19),14(16),14(14),14(11),14(9)]),flip(a)].
% 54.76/55.05 74 multiply(add(A,A),multiply(B,multiply(add(A,A),multiply(B,multiply(add(A,A),multiply(B,multiply(A,add(B,B)))))))) = multiply(add(A,A),B). [para(29(a,1),22(a,1,2,2,2,2,2,2))].
% 54.76/55.05 87 multiply(add(c_0,multiply(b,A)),B) = multiply(b,multiply(add(A,a),B)). [para(31(a,1),12(a,1,1))].
% 54.76/55.05 89 multiply(b,add(A,add(B,a))) = add(c_0,multiply(b,add(A,B))). [para(31(a,1),14(a,1,2)),rewrite([10(7,R),14(6),7(3)]),flip(a)].
% 54.76/55.05 91 add(c_0,add(multiply(b,A),multiply(B,add(A,a)))) = multiply(add(B,b),add(A,a)). [para(31(a,1),16(a,1,2)),rewrite([10(8),7(7),10(8,R),7(7)])].
% 54.76/55.05 95 multiply(add(b,multiply(A,B)),a) = add(c_0,multiply(A,multiply(B,a))). [para(12(a,1),32(a,2,2)),rewrite([7(3)])].
% 54.76/55.05 98 add(add(c_0,multiply(A,a)),multiply(B,a)) = multiply(add(A,add(B,b)),a). [para(32(a,1),16(a,1,1)),rewrite([7(10),10(10,R),7(9)])].
% 54.76/55.05 99 multiply(add(A,add(B,b)),a) = add(c_0,multiply(add(A,B),a)). [para(32(a,1),16(a,1,2)),rewrite([10(7,R),16(6),7(2)]),flip(a)].
% 54.76/55.05 102 add(add(c_0,multiply(A,a)),multiply(B,a)) = add(c_0,multiply(add(A,B),a)). [back_rewrite(98),rewrite([99(12)])].
% 54.76/55.05 103 add(A,add(B,add(C,add(D,additive_inverse(A))))) = add(B,add(C,D)). [para(33(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),10(3,R),7(2),10(7),7(6),10(7,R),7(6)])].
% 54.76/55.05 104 multiply(A,add(B,multiply(A,multiply(A,multiply(A,C))))) = multiply(A,add(C,B)). [para(23(a,1),14(a,1,1)),rewrite([14(3),7(6)]),flip(a)].
% 54.76/55.05 106 multiply(b,multiply(b,multiply(b,c_0))) = c_0. [para(19(a,1),23(a,1,2,2,2)),rewrite([19(10)])].
% 54.76/55.05 107 multiply(b,multiply(b,multiply(b,multiply(c_0,A)))) = multiply(c_0,A). [para(30(a,1),23(a,1,2,2,2)),rewrite([30(12)])].
% 54.76/55.05 114 multiply(b,multiply(b,multiply(b,add(c_0,multiply(b,A))))) = add(c_0,multiply(b,A)). [para(31(a,1),23(a,1,2,2,2)),rewrite([31(14)])].
% 54.76/55.05 116 multiply(b,add(A,multiply(b,multiply(b,c_0)))) = add(c_0,multiply(b,A)). [para(106(a,1),14(a,1,1)),rewrite([7(11)]),flip(a)].
% 54.76/55.05 118 multiply(c_0,add(A,multiply(a,multiply(a,multiply(a,B))))) = multiply(c_0,add(B,A)). [para(37(a,1),14(a,1,1)),rewrite([14(5),7(11)]),flip(a)].
% 54.76/55.05 122 multiply(c_0,add(A,add(A,add(B,B)))) = multiply(b,multiply(add(a,a),add(A,B))). [para(10(a,1),59(a,1,2)),rewrite([7(2),7(3),10(3,R),7(10)])].
% 54.76/55.05 134 multiply(b,multiply(add(a,a),A)) = multiply(add(c_0,c_0),A). [para(59(a,1),29(a,2)),flip(a)].
% 54.76/55.05 143 multiply(c_0,add(A,add(A,add(B,B)))) = multiply(add(c_0,c_0),add(A,B)). [back_rewrite(122),rewrite([134(12)])].
% 54.76/55.05 155 multiply(A,multiply(A,multiply(A,add(A,A)))) = add(A,A). [para(8(a,1),24(a,2,2)),rewrite([14(5),14(3)])].
% 54.76/55.05 156 multiply(A,multiply(add(B,multiply(A,multiply(A,A))),C)) = multiply(add(A,multiply(A,B)),C). [para(24(a,1),12(a,1,1)),flip(a)].
% 54.76/55.05 157 multiply(A,multiply(B,add(C,multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B)))))))) = multiply(A,add(B,multiply(B,C))). [para(24(a,1),12(a,1)),rewrite([12(3),14(4),12(7),12(8)]),flip(a)].
% 54.76/55.05 158 multiply(A,add(B,add(C,multiply(A,multiply(A,A))))) = add(add(A,multiply(A,B)),multiply(A,C)). [para(24(a,1),14(a,1,1)),rewrite([7(8),10(8,R),7(7)]),flip(a)].
% 54.76/55.05 159 add(add(A,multiply(A,B)),multiply(A,C)) = add(A,multiply(A,add(B,C))). [para(24(a,1),14(a,1,2)),rewrite([10(4,R),14(3),7(1),158(8)]),flip(a)].
% 54.76/55.05 160 multiply(A,multiply(A,add(B,multiply(A,A)))) = add(A,multiply(A,multiply(A,B))). [para(14(a,1),24(a,1,2))].
% 54.76/55.05 162 multiply(A,multiply(add(A,B),multiply(A,A))) = add(A,multiply(A,multiply(B,multiply(A,A)))). [para(16(a,1),24(a,1,2)),rewrite([7(1)])].
% 54.76/55.05 171 multiply(b,multiply(b,multiply(b,add(b,c_0)))) = add(b,c_0). [para(106(a,1),24(a,2,2)),rewrite([7(12),14(12),14(9)])].
% 54.76/55.05 174 multiply(A,add(B,multiply(A,multiply(A,add(A,A))))) = add(A,add(A,multiply(A,B))). [para(24(a,1),24(a,2,2)),rewrite([7(6),10(6,R),14(5),14(3)])].
% 54.76/55.05 176 multiply(additive_identity,additive_identity) = multiply(additive_identity,A). [para(6(a,1),63(a,1,2,2)),rewrite([2(3),6(5)]),flip(a)].
% 54.76/55.05 181 multiply(additive_identity,additive_identity) = additive_identity. [para(176(a,1),8(a,1,2,2)),rewrite([176(5,R),176(5,R)])].
% 54.76/55.05 183 multiply(additive_identity,A) = additive_identity. [para(176(a,2),12(a,1,1)),rewrite([181(3),176(5,R),181(5)])].
% 54.76/55.05 185 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(176(a,2),16(a,1,1)),rewrite([183(3),7(5),2(5)])].
% 54.76/55.05 186 add(additive_identity,c_0) = c_0. [para(19(a,1),185(a,1,2)),rewrite([19(6)])].
% 54.76/55.05 187 add(additive_identity,add(c_0,multiply(b,A))) = add(c_0,multiply(b,A)). [para(31(a,1),185(a,1,2)),rewrite([31(10)])].
% 54.76/55.05 189 add(A,multiply(A,additive_identity)) = A. [para(185(a,1),24(a,1,2)),rewrite([8(3)]),flip(a)].
% 54.76/55.05 190 add(A,multiply(additive_inverse(A),multiply(A,multiply(A,A)))) = additive_identity. [para(6(a,1),25(a,1,1)),rewrite([183(4)]),flip(a)].
% 54.76/55.05 210 add(A,add(B,multiply(A,additive_identity))) = add(A,B). [para(189(a,1),10(a,2,2)),rewrite([7(3),7(5)])].
% 54.76/55.05 218 add(additive_inverse(A),multiply(A,multiply(additive_inverse(A),multiply(additive_inverse(A),additive_inverse(A))))) = additive_identity. [para(6(a,1),26(a,1,1)),rewrite([183(7)]),flip(a)].
% 54.76/55.05 221 add(A,add(multiply(B,multiply(A,multiply(A,A))),multiply(add(B,A),C))) = multiply(add(B,A),add(C,multiply(A,multiply(A,A)))). [para(26(a,1),14(a,1,2)),rewrite([10(7,R)])].
% 54.76/55.05 234 add(A,add(B,multiply(additive_inverse(A),multiply(A,multiply(A,A))))) = B. [para(190(a,1),10(a,2,2)),rewrite([7(5),2(8)])].
% 54.76/55.05 237 multiply(A,additive_identity) = additive_identity. [para(190(a,1),210(a,2)),rewrite([7(7),234(8)])].
% 54.76/55.05 239 multiply(a,multiply(c_0,multiply(c_0,multiply(c_0,multiply(b,A))))) = multiply(a,multiply(b,A)). [para(72(a,1),12(a,1,1)),rewrite([12(4),12(13),12(12),12(11)]),flip(a)].
% 54.76/55.05 240 multiply(a,add(A,multiply(c_0,multiply(c_0,multiply(c_0,b))))) = multiply(a,add(A,b)). [para(72(a,1),14(a,1,1)),rewrite([14(6),7(3),7(13)]),flip(a)].
% 54.76/55.05 247 multiply(add(A,multiply(B,C)),multiply(C,multiply(C,C))) = add(multiply(B,C),multiply(A,multiply(C,multiply(C,C)))). [para(8(a,1),27(a,1,1,2)),flip(a)].
% 54.76/55.05 249 add(multiply(A,multiply(B,multiply(C,D))),multiply(E,D)) = multiply(add(E,multiply(A,multiply(B,C))),D). [para(12(a,1),27(a,1,1,2))].
% 54.76/55.05 250 add(multiply(A,multiply(B,C)),multiply(D,multiply(E,C))) = multiply(add(multiply(D,E),multiply(A,B)),C). [para(12(a,1),27(a,1,2))].
% 54.76/55.05 251 multiply(add(A,multiply(A,B)),C) = multiply(A,add(C,multiply(B,C))). [para(27(a,1),14(a,1)),rewrite([7(5)])].
% 54.76/55.05 254 add(multiply(c_0,A),multiply(B,multiply(C,multiply(a,A)))) = multiply(add(b,multiply(B,C)),multiply(a,A)). [para(30(a,1),27(a,1,2)),rewrite([7(7)])].
% 54.76/55.05 262 add(multiply(A,multiply(add(B,B),C)),multiply(D,add(C,C))) = multiply(add(D,multiply(A,B)),add(C,C)). [para(29(a,2),27(a,1,1,2))].
% 54.76/55.05 270 multiply(add(add(A,b),multiply(B,C)),a) = add(c_0,multiply(add(A,multiply(B,C)),a)). [para(32(a,1),27(a,1,2)),rewrite([10(8,R),28(7)]),flip(a)].
% 54.76/55.05 276 multiply(add(b,multiply(A,B)),multiply(b,multiply(b,c_0))) = add(c_0,multiply(A,multiply(B,multiply(b,multiply(b,c_0))))). [para(106(a,1),27(a,1,2)),rewrite([7(9)]),flip(a)].
% 54.76/55.05 278 multiply(add(A,multiply(c_0,a)),multiply(a,multiply(a,B))) = multiply(add(b,multiply(A,a)),multiply(a,B)). [para(37(a,1),27(a,1,1)),rewrite([254(8)]),flip(a)].
% 54.76/55.05 290 multiply(add(A,multiply(a,c_0)),multiply(c_0,multiply(c_0,b))) = add(multiply(a,b),multiply(A,multiply(c_0,multiply(c_0,b)))). [para(72(a,1),27(a,1,1)),flip(a)].
% 54.76/55.05 309 add(add(A,A),multiply(A,B)) = add(A,add(A,multiply(A,B))). [para(155(a,1),14(a,1,1)),rewrite([7(7),174(8)])].
% 54.76/55.05 310 add(add(A,A),multiply(B,multiply(A,multiply(A,add(A,A))))) = multiply(add(A,B),multiply(A,multiply(A,add(A,A)))). [para(155(a,1),16(a,1,1))].
% 54.76/55.05 312 multiply(c_0,multiply(a,multiply(a,add(a,a)))) = add(c_0,c_0). [para(155(a,1),30(a,1,2)),rewrite([31(5),19(4)]),flip(a)].
% 54.76/55.05 319 multiply(add(A,multiply(B,B)),multiply(B,add(B,B))) = add(add(B,B),multiply(A,multiply(B,add(B,B)))). [para(155(a,1),27(a,1,1)),flip(a)].
% 54.76/55.05 324 multiply(b,multiply(b,multiply(b,multiply(add(b,c_0),A)))) = multiply(add(b,c_0),A). [para(171(a,1),12(a,1,1)),rewrite([12(13),12(12)]),flip(a)].
% 54.76/55.05 325 multiply(b,add(A,multiply(b,multiply(b,add(b,c_0))))) = add(add(b,c_0),multiply(b,A)). [para(171(a,1),14(a,1,1)),rewrite([7(15)]),flip(a)].
% 54.76/55.05 326 add(add(b,c_0),multiply(b,A)) = add(b,add(c_0,multiply(b,A))). [para(171(a,1),14(a,1,2)),rewrite([10(6),7(5),10(6,R),7(5),325(16)]),flip(a)].
% 54.76/55.05 333 multiply(b,add(A,multiply(b,multiply(b,add(b,c_0))))) = add(b,add(c_0,multiply(b,A))). [back_rewrite(325),rewrite([326(16)])].
% 54.76/55.05 334 add(multiply(A,B),multiply(C,multiply(B,multiply(B,B)))) = multiply(add(A,multiply(C,multiply(B,B))),B). [para(8(a,1),28(a,1,2,2)),rewrite([249(5),247(9)]),flip(a)].
% 54.76/55.05 335 add(multiply(A,B),multiply(C,multiply(D,multiply(E,B)))) = multiply(add(A,multiply(C,multiply(D,E))),B). [para(12(a,1),28(a,1,2,2))].
% 54.76/55.05 336 multiply(add(c_0,multiply(A,multiply(B,a))),C) = multiply(add(b,multiply(A,B)),multiply(a,C)). [para(30(a,1),28(a,1,1)),rewrite([335(7)])].
% 54.76/55.05 347 multiply(add(A,multiply(B,C)),multiply(C,multiply(C,multiply(C,D)))) = multiply(add(B,multiply(A,multiply(C,C))),multiply(C,D)). [para(23(a,1),28(a,1,2,2)),rewrite([249(7)]),flip(a)].
% 54.76/55.05 348 multiply(add(A,multiply(B,B)),multiply(B,multiply(B,C))) = multiply(add(B,multiply(A,multiply(B,B))),C). [para(23(a,1),28(a,1,2)),rewrite([7(5),335(5)]),flip(a)].
% 54.76/55.05 365 multiply(add(A,multiply(B,C)),multiply(C,multiply(C,C))) = multiply(add(B,multiply(A,multiply(C,C))),C). [back_rewrite(247),rewrite([334(10)])].
% 54.76/55.05 366 multiply(add(A,multiply(a,c_0)),multiply(c_0,multiply(c_0,b))) = multiply(add(a,multiply(A,multiply(c_0,c_0))),b). [back_rewrite(290),rewrite([335(20)])].
% 54.76/55.05 370 add(additive_identity,add(c_0,multiply(c_0,A))) = add(c_0,multiply(c_0,A)). [para(30(a,1),187(a,1,2,2)),rewrite([30(11)])].
% 54.76/55.05 387 multiply(add(multiply(c_0,A),multiply(b,B)),C) = multiply(b,multiply(add(B,multiply(a,A)),C)). [para(35(a,1),12(a,1,1))].
% 54.76/55.05 414 multiply(add(b,b),multiply(a,A)) = multiply(add(c_0,c_0),A). [para(19(a,1),36(a,1,1,2)),flip(a)].
% 54.76/55.05 420 multiply(add(A,multiply(c_0,multiply(a,a))),multiply(a,B)) = multiply(add(A,b),multiply(a,B)). [para(23(a,1),36(a,2,2)),rewrite([347(11)])].
% 54.76/55.05 422 multiply(add(additive_identity,b),multiply(a,A)) = multiply(c_0,A). [para(183(a,1),36(a,1,1,2)),rewrite([7(3),186(3)]),flip(a)].
% 54.76/55.05 437 multiply(add(additive_identity,b),add(a,a)) = add(c_0,c_0). [para(155(a,1),422(a,1,2)),rewrite([312(16)])].
% 54.76/55.05 441 multiply(add(additive_identity,add(additive_identity,add(b,b))),a) = add(c_0,c_0). [para(437(a,1),29(a,2)),rewrite([10(7),7(6),10(7,R),7(6),10(6,R)])].
% 54.76/55.05 463 multiply(c_0,multiply(add(A,a),multiply(a,a))) = add(c_0,multiply(c_0,multiply(A,multiply(a,a)))). [para(16(a,1),38(a,1,2))].
% 54.76/55.05 472 multiply(add(A,add(additive_identity,add(additive_identity,add(b,b)))),a) = add(add(c_0,c_0),multiply(A,a)). [para(441(a,1),16(a,1,1)),rewrite([7(14)]),flip(a)].
% 54.76/55.05 473 add(add(c_0,c_0),multiply(A,a)) = add(c_0,add(c_0,multiply(A,a))). [para(441(a,1),16(a,1,2)),rewrite([10(6),7(5),472(16)]),flip(a)].
% 54.76/55.05 484 add(A,multiply(add(additive_inverse(A),multiply(B,C)),multiply(A,multiply(A,A)))) = multiply(B,multiply(C,multiply(A,multiply(A,A)))). [para(27(a,1),234(a,1,2))].
% 54.76/55.05 634 multiply(add(add(A,c_0),multiply(B,C)),multiply(a,multiply(a,a))) = add(c_0,multiply(add(A,multiply(B,C)),multiply(a,multiply(a,a)))). [para(39(a,1),27(a,1,2)),rewrite([10(16,R),28(15)]),flip(a)].
% 54.76/55.05 732 multiply(b,multiply(add(additive_identity,a),A)) = multiply(c_0,A). [para(237(a,1),87(a,1,1,2)),rewrite([7(3),186(3)]),flip(a)].
% 54.76/55.05 760 multiply(c_0,multiply(add(additive_identity,a),multiply(add(additive_identity,a),add(additive_identity,add(additive_identity,add(a,a)))))) = multiply(b,add(additive_identity,add(additive_identity,add(a,a)))). [para(155(a,1),732(a,1,2)),rewrite([10(8),7(7),10(8,R),7(7),10(7,R),10(23),7(22),10(23,R),7(22),10(22,R)]),flip(a)].
% 54.76/55.05 764 multiply(add(b,b),multiply(add(additive_identity,a),A)) = multiply(c_0,add(A,A)). [para(732(a,1),50(a,2))].
% 54.76/55.05 782 multiply(b,add(A,add(B,add(C,a)))) = add(c_0,multiply(b,add(A,add(B,C)))). [para(10(a,1),89(a,2,2,2)),rewrite([7(4),10(4),7(3),10(4,R),7(3),10(10),7(9),10(10,R),7(9)])].
% 54.76/55.05 805 multiply(c_0,multiply(add(additive_identity,a),multiply(add(additive_identity,a),add(additive_identity,add(additive_identity,add(a,a)))))) = add(c_0,c_0). [back_rewrite(760),rewrite([782(26),89(25),2(23),237(22),7(21),186(21)])].
% 54.76/55.05 862 multiply(add(b,c_0),a) = add(c_0,multiply(c_0,a)). [para(19(a,1),95(a,1,1,2)),rewrite([30(11)])].
% 54.76/55.05 871 multiply(add(b,add(c_0,c_0)),a) = add(c_0,multiply(c_0,add(a,a))). [para(134(a,1),95(a,2,2)),rewrite([31(6),19(5),29(13)])].
% 54.76/55.05 899 add(c_0,add(c_0,multiply(add(A,A),a))) = multiply(add(A,b),add(a,a)). [para(99(a,1),29(a,1)),rewrite([7(4),99(6)])].
% 54.76/55.05 954 multiply(b,multiply(add(b,multiply(A,B)),multiply(b,c_0))) = add(c_0,multiply(b,multiply(A,multiply(B,multiply(b,c_0))))). [para(27(a,1),116(a,1,2))].
% 54.76/55.05 989 multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),additive_inverse(a)) = additive_identity. [para(218(a,1),35(a,1,2)),rewrite([237(3),7(16),335(16)]),flip(a)].
% 54.76/55.05 1016 multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),multiply(additive_inverse(a),A)) = additive_identity. [para(989(a,1),12(a,1,1)),rewrite([183(2)]),flip(a)].
% 54.76/55.05 1017 multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),add(A,additive_inverse(a))) = multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),A). [para(989(a,1),14(a,1,1)),rewrite([185(12),7(22)]),flip(a)].
% 54.76/55.05 1019 multiply(add(A,multiply(B,add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))))),additive_inverse(a)) = multiply(A,additive_inverse(a)). [para(989(a,1),27(a,1,1,2)),rewrite([237(2),185(5)]),flip(a)].
% 54.76/55.05 1033 multiply(add(A,multiply(A,B)),multiply(C,D)) = multiply(A,multiply(add(C,multiply(B,C)),D)). [para(251(a,1),12(a,1,1)),rewrite([12(4)]),flip(a)].
% 54.76/55.05 1121 multiply(add(A,multiply(A,multiply(B,C))),multiply(B,D)) = multiply(A,multiply(B,add(D,multiply(C,multiply(B,D))))). [para(28(a,1),251(a,1,1)),rewrite([12(2),12(5),12(8),12(10)])].
% 54.76/55.05 1136 multiply(add(b,c_0),multiply(a,A)) = multiply(c_0,add(A,multiply(a,A))). [para(251(a,1),36(a,1)),rewrite([7(8)]),flip(a)].
% 54.76/55.05 1186 multiply(add(c_0,add(add(b,c_0),multiply(c_0,a))),A) = multiply(add(b,c_0),add(A,multiply(a,A))). [para(862(a,1),251(a,1,1,2)),rewrite([10(9,R),7(8)])].
% 54.76/55.05 1203 multiply(A,add(additive_identity,additive_inverse(a))) = multiply(A,additive_inverse(a)). [para(989(a,1),251(a,2,2,2)),rewrite([1019(14),7(7)]),flip(a)].
% 54.76/55.05 1212 multiply(A,add(B,add(additive_identity,additive_inverse(a)))) = multiply(A,add(B,additive_inverse(a))). [para(1203(a,1),14(a,1,1)),rewrite([14(5),7(3),7(9)]),flip(a)].
% 54.76/55.05 1493 add(add(b,c_0),multiply(c_0,A)) = add(b,add(c_0,multiply(c_0,A))). [para(30(a,1),326(a,1,2)),rewrite([30(12)])].
% 54.76/55.05 1511 multiply(add(b,add(c_0,add(c_0,multiply(c_0,a)))),A) = multiply(add(b,c_0),add(A,multiply(a,A))). [back_rewrite(1186),rewrite([1493(8),10(9,R),7(8)])].
% 54.76/55.05 1585 add(c_0,add(c_0,multiply(A,add(a,a)))) = multiply(add(A,b),add(a,a)). [para(29(a,1),473(a,2,2,2)),rewrite([473(7),899(7)]),flip(a)].
% 54.76/55.05 1607 multiply(add(b,b),add(additive_identity,a)) = add(c_0,c_0). [para(8(a,1),764(a,1,2)),rewrite([14(31),14(26),10(21),7(20),10(21,R),7(20),10(20,R),805(24)])].
% 54.76/55.05 1628 add(multiply(c_0,add(A,A)),multiply(B,A)) = multiply(add(B,add(c_0,c_0)),A). [para(764(a,1),27(a,1,1)),rewrite([1607(12)])].
% 54.76/55.05 1695 multiply(add(A,add(b,add(c_0,c_0))),a) = add(c_0,multiply(add(A,add(c_0,c_0)),a)). [para(871(a,1),16(a,1,2)),rewrite([10(10,R),1628(9)]),flip(a)].
% 54.76/55.05 1719 add(multiply(A,additive_inverse(B)),multiply(add(A,A),B)) = multiply(A,B). [para(6(a,1),53(a,1,2,2)),rewrite([2(2),7(6)]),flip(a)].
% 54.76/55.05 1877 add(multiply(b,additive_inverse(multiply(a,A))),multiply(add(c_0,c_0),A)) = multiply(c_0,A). [para(30(a,1),1719(a,2)),rewrite([414(11)])].
% 54.76/55.05 1915 add(multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),additive_inverse(additive_inverse(a))),multiply(add(b,add(b,multiply(c_0,multiply(additive_inverse(a),add(additive_inverse(a),additive_inverse(a)))))),additive_inverse(a))) = additive_identity. [para(989(a,1),1719(a,2)),rewrite([10(32),7(31),10(32,R),7(31),10(31,R),14(30),14(27)])].
% 54.76/55.05 1953 add(multiply(A,B),multiply(add(A,A),additive_inverse(B))) = multiply(A,additive_inverse(B)). [para(21(a,1),54(a,1,2)),flip(a)].
% 54.76/55.05 2143 add(multiply(additive_inverse(A),B),multiply(A,add(B,B))) = multiply(A,B). [para(6(a,1),55(a,1,1,2)),rewrite([2(2),7(6)]),flip(a)].
% 54.76/55.05 2389 add(multiply(A,B),multiply(additive_inverse(A),add(B,B))) = multiply(additive_inverse(A),B). [para(21(a,1),56(a,1,1)),flip(a)].
% 54.76/55.05 2580 multiply(additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))),additive_inverse(a)) = additive_identity. [para(989(a,1),2143(a,2)),rewrite([1017(28),989(25),7(15),185(15)])].
% 54.76/55.05 2977 add(multiply(c_0,add(A,multiply(a,A))),multiply(add(b,c_0),B)) = multiply(add(b,c_0),add(B,multiply(a,A))). [para(1136(a,1),14(a,1,1)),rewrite([7(16)])].
% 54.76/55.05 2997 multiply(add(b,c_0),multiply(add(b,c_0),multiply(add(b,c_0),multiply(c_0,add(A,multiply(a,A)))))) = multiply(add(b,c_0),multiply(a,A)). [para(1136(a,1),23(a,1,2,2,2))].
% 54.76/55.05 3029 multiply(c_0,add(add(A,multiply(B,A)),multiply(a,add(A,multiply(B,A))))) = multiply(add(b,c_0),multiply(add(a,multiply(a,B)),A)). [para(251(a,2),1136(a,1,2)),flip(a)].
% 54.76/55.05 3098 add(c_0,multiply(b,add(A,additive_inverse(a)))) = multiply(b,A). [para(1212(a,1),31(a,2,2)),rewrite([7(8),33(8),2(3)]),flip(a)].
% 54.76/55.05 3158 multiply(A,add(B,multiply(C,multiply(A,multiply(C,multiply(A,multiply(C,multiply(A,multiply(C,D))))))))) = multiply(A,add(B,multiply(C,D))). [para(67(a,1),14(a,1,1)),rewrite([14(4),7(2),7(11)]),flip(a)].
% 54.76/55.05 3161 multiply(c_0,multiply(A,multiply(a,multiply(A,multiply(a,multiply(A,multiply(a,multiply(A,B)))))))) = multiply(c_0,multiply(A,B)). [para(67(a,1),30(a,1,2)),rewrite([30(5)]),flip(a)].
% 54.76/55.05 3320 add(c_0,add(multiply(c_0,A),multiply(b,additive_inverse(a)))) = multiply(c_0,A). [para(30(a,1),3098(a,2)),rewrite([7(7),35(8)])].
% 54.76/55.05 3335 add(c_0,multiply(b,add(additive_inverse(a),multiply(A,B)))) = multiply(b,multiply(A,B)). [para(67(a,1),3098(a,2)),rewrite([7(15),3158(16)])].
% 54.76/55.05 3523 add(c_0,add(multiply(b,additive_inverse(a)),multiply(c_0,A))) = multiply(c_0,A). [para(7(a,1),3320(a,1,2))].
% 54.76/55.05 3532 multiply(c_0,add(A,add(A,B))) = add(c_0,add(multiply(b,additive_inverse(a)),add(multiply(add(c_0,c_0),A),multiply(c_0,B)))). [para(53(a,1),3320(a,1,2,1)),rewrite([7(13)]),flip(a)].
% 54.76/55.05 4410 add(add(c_0,multiply(c_0,multiply(additive_inverse(a),multiply(additive_inverse(a),a)))),multiply(add(b,add(b,multiply(c_0,multiply(additive_inverse(a),add(additive_inverse(a),additive_inverse(a)))))),additive_inverse(a))) = additive_identity. [para(989(a,1),1953(a,2)),rewrite([95(11),12(9),10(30),7(29),10(30,R),7(29),10(29,R),14(28),14(25)])].
% 54.76/55.05 4496 add(multiply(A,add(B,C)),multiply(additive_inverse(A),add(B,add(B,add(C,C))))) = multiply(additive_inverse(A),add(B,C)). [para(10(a,1),2389(a,1,2,2)),rewrite([7(5),10(6,R),7(5),10(5,R)])].
% 54.76/55.05 4504 multiply(additive_inverse(A),add(B,B)) = multiply(add(additive_inverse(A),additive_inverse(A)),B). [para(29(a,2),2389(a,2)),rewrite([10(6),7(5),4496(8)])].
% 54.76/55.05 4663 add(add(A,A),multiply(add(A,A),B)) = add(A,add(A,multiply(add(A,A),B))). [para(73(a,1),309(a,1,2)),rewrite([73(15)])].
% 54.76/55.05 4839 multiply(additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))),add(A,additive_inverse(a))) = multiply(additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))),A). [para(2580(a,1),14(a,1,1)),rewrite([185(13),7(24)]),flip(a)].
% 54.76/55.05 4850 multiply(additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))),a) = additive_identity. [para(2580(a,1),1953(a,2)),rewrite([29(36),4839(28),2580(25),7(14),185(14)])].
% 54.76/55.05 4854 multiply(additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))),add(A,a)) = multiply(additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))),A). [para(4850(a,1),14(a,1,1)),rewrite([185(13),7(23)]),flip(a)].
% 54.76/55.05 4866 add(c_0,multiply(c_0,multiply(additive_inverse(a),multiply(additive_inverse(a),a)))) = additive_identity. [para(4850(a,1),2389(a,2)),rewrite([95(11),12(9),4854(25),4850(23),7(13),370(13)])].
% 54.76/55.05 4894 multiply(add(b,add(b,multiply(c_0,multiply(additive_inverse(a),add(additive_inverse(a),additive_inverse(a)))))),additive_inverse(a)) = additive_identity. [back_rewrite(4410),rewrite([4866(11),185(19)])].
% 54.76/55.05 4896 multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),additive_inverse(additive_inverse(a))) = additive_identity. [back_rewrite(1915),rewrite([4894(30),7(15),185(15)])].
% 54.76/55.05 5701 multiply(add(A,multiply(B,add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))))),additive_inverse(additive_inverse(a))) = multiply(A,additive_inverse(additive_inverse(a))). [para(4896(a,1),27(a,1,1,2)),rewrite([237(2),185(6)]),flip(a)].
% 54.76/55.05 5704 multiply(A,add(additive_identity,additive_inverse(additive_inverse(a)))) = multiply(A,additive_inverse(additive_inverse(a))). [para(4896(a,1),251(a,2,2,2)),rewrite([5701(15),7(9)]),flip(a)].
% 54.76/55.05 5737 multiply(b,additive_inverse(additive_inverse(a))) = c_0. [para(5704(a,1),3098(a,2)),rewrite([7(10),21(10),237(4),7(3),186(3)]),flip(a)].
% 54.76/55.05 5747 multiply(b,multiply(additive_inverse(additive_inverse(a)),A)) = multiply(c_0,A). [para(5737(a,1),12(a,1,1)),flip(a)].
% 54.76/55.05 6643 add(c_0,add(multiply(b,add(A,additive_inverse(a))),multiply(B,A))) = multiply(add(B,b),A). [para(1212(a,1),91(a,1,2,1)),rewrite([7(13),33(13),2(8),7(18),33(18),2(13)])].
% 54.76/55.05 6666 multiply(additive_inverse(a),add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))) = additive_identity. [para(1016(a,1),22(a,1,2,2,2,2,2)),rewrite([237(26),237(24),237(15),237(13),237(4)]),flip(a)].
% 54.76/55.05 6687 multiply(add(A,additive_inverse(a)),add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))) = multiply(A,add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))). [para(6666(a,1),16(a,1,1)),rewrite([185(12),7(13)]),flip(a)].
% 54.76/55.05 6695 multiply(additive_inverse(a),additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))))) = additive_identity. [para(6666(a,1),1719(a,2)),rewrite([6687(28),6666(25),7(15),185(15)])].
% 54.76/55.05 6704 multiply(add(A,additive_inverse(a)),additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))))) = multiply(A,additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))))). [para(6695(a,1),16(a,1,1)),rewrite([185(13),7(14)]),flip(a)].
% 54.76/55.05 6718 multiply(a,additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))))) = additive_identity. [para(6695(a,1),2389(a,2)),rewrite([29(36,R),6704(28),6695(25),7(14),185(14)])].
% 54.76/55.05 6883 multiply(a,add(A,additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))))) = multiply(a,A). [para(6718(a,1),14(a,1,1)),rewrite([185(4),7(14)]),flip(a)].
% 54.76/55.05 6884 multiply(add(A,a),additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))))) = multiply(A,additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))))). [para(6718(a,1),16(a,1,1)),rewrite([185(13),7(13)]),flip(a)].
% 54.76/55.05 6886 add(additive_identity,a) = a. [para(6718(a,1),24(a,2,2)),rewrite([7(17),6883(18),8(7),7(4)]),flip(a)].
% 54.76/55.05 6897 multiply(a,add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))) = additive_identity. [para(6718(a,1),1953(a,2)),rewrite([6884(25),6718(23),7(13),185(13)])].
% 54.76/55.05 6929 multiply(a,add(A,add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))))) = multiply(a,A). [para(6897(a,1),14(a,1,1)),rewrite([185(4),7(13)]),flip(a)].
% 54.76/55.05 6931 multiply(c_0,add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))) = additive_identity. [para(6897(a,1),30(a,1,2)),rewrite([237(3)]),flip(a)].
% 54.76/55.05 6983 multiply(c_0,multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),A)) = additive_identity. [para(6931(a,1),12(a,1,1)),rewrite([183(2)]),flip(a)].
% 54.76/55.05 7114 multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),c_0) = additive_identity. [para(6983(a,1),22(a,1,2,2,2,2,2)),rewrite([237(31),237(22),237(21),237(12),237(11)]),flip(a)].
% 54.76/55.05 7127 multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),multiply(c_0,A)) = additive_identity. [para(6983(a,1),67(a,1,2,2,2,2,2)),rewrite([237(31),237(22),237(21),237(12),237(11)]),flip(a)].
% 54.76/55.05 7128 multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),multiply(A,c_0)) = additive_identity. [para(6983(a,1),68(a,1,2,2,2,2,2,2,2,2)),rewrite([237(31),237(31),237(22),237(21),237(21),237(12),237(11),237(11)]),flip(a)].
% 54.76/55.05 7129 multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),add(A,c_0)) = multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),A). [para(6983(a,1),69(a,1,2,2,2,2,2,2)),rewrite([237(31),237(22),237(21),237(12),2(11),7(21)]),flip(a)].
% 54.76/55.05 7142 multiply(additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))),c_0) = additive_identity. [para(7114(a,1),2143(a,2)),rewrite([7129(25),7114(23),7(14),185(14)])].
% 54.76/55.05 7248 multiply(additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))),multiply(c_0,A)) = additive_identity. [para(7142(a,1),12(a,1,1)),rewrite([183(2)]),flip(a)].
% 54.76/55.05 7280 add(multiply(add(b,c_0),add(a,a)),multiply(A,a)) = add(c_0,add(c_0,multiply(add(A,add(c_0,c_0)),a))). [para(871(a,1),102(a,1,1,2)),rewrite([1585(9),7(3),7(17),1695(19)])].
% 54.76/55.05 7350 multiply(A,multiply(add(B,multiply(A,multiply(A,multiply(A,C)))),D)) = multiply(A,multiply(add(C,B),D)). [para(104(a,1),12(a,1,1)),rewrite([12(3)]),flip(a)].
% 54.76/55.05 7861 multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),add(A,multiply(c_0,B))) = multiply(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a)))),A). [para(7127(a,1),14(a,1,1)),rewrite([185(12),7(22)]),flip(a)].
% 54.76/55.05 8502 multiply(add(A,A),multiply(c_0,B)) = multiply(A,add(multiply(b,additive_inverse(multiply(a,B))),add(multiply(b,additive_inverse(multiply(a,B))),multiply(add(c_0,c_0),add(B,B))))). [para(1877(a,1),47(a,1,2)),rewrite([14(23)])].
% 54.76/55.05 8523 add(multiply(add(c_0,c_0),add(A,B)),multiply(b,additive_inverse(multiply(a,add(A,multiply(add(c_0,c_0),multiply(add(c_0,c_0),multiply(add(c_0,c_0),B)))))))) = multiply(c_0,add(A,multiply(add(c_0,c_0),multiply(add(c_0,c_0),multiply(add(c_0,c_0),B))))). [para(104(a,1),1877(a,1,2)),rewrite([7(22),7(24)])].
% 54.76/55.05 8534 multiply(c_0,multiply(additive_inverse(a),multiply(additive_inverse(a),additive_inverse(a)))) = c_0. [para(190(a,1),3335(a,1,2,2)),rewrite([237(4),7(3),186(3),5747(15)]),flip(a)].
% 54.76/55.05 8610 add(multiply(additive_inverse(c_0),multiply(additive_inverse(a),multiply(additive_inverse(a),additive_inverse(a)))),multiply(c_0,multiply(additive_inverse(a),multiply(additive_inverse(a),add(additive_inverse(a),additive_inverse(a)))))) = c_0. [para(8534(a,1),2143(a,2)),rewrite([14(29),14(25)])].
% 54.76/55.05 9363 multiply(c_0,add(multiply(A,B),add(multiply(A,B),multiply(C,multiply(D,add(B,B)))))) = multiply(add(c_0,c_0),multiply(add(A,multiply(C,D)),B)). [para(28(a,1),143(a,2,2)),rewrite([14(8),14(6)])].
% 54.76/55.05 9744 multiply(b,multiply(b,multiply(b,multiply(add(b,multiply(c_0,A)),B)))) = multiply(add(b,multiply(c_0,A)),B). [para(107(a,1),156(a,2,1,2)),rewrite([7(13),14(13),14(10),12(10),12(9)])].
% 54.76/55.05 10024 multiply(additive_inverse(add(b,multiply(c_0,multiply(additive_inverse(a),additive_inverse(a))))),add(c_0,multiply(c_0,A))) = additive_identity. [para(7142(a,1),157(a,1,2,2,2,2,2,2,2)),rewrite([237(35),237(34),237(24),237(23),2(13),7248(13)]),flip(a)].
% 54.76/55.05 10206 add(multiply(add(b,c_0),add(a,a)),multiply(add(c_0,c_0),A)) = add(c_0,add(c_0,multiply(add(c_0,c_0),add(A,a)))). [para(473(a,1),159(a,1,1)),rewrite([29(7),1585(9),7(3),7(20),4663(22)])].
% 54.76/55.05 10336 multiply(A,multiply(A,multiply(A,add(A,B)))) = add(A,multiply(A,multiply(A,multiply(A,B)))). [para(14(a,1),160(a,1,2,2)),rewrite([7(1)])].
% 54.76/55.05 10338 multiply(A,multiply(A,multiply(add(A,B),A))) = add(A,multiply(A,multiply(A,multiply(B,A)))). [para(16(a,1),160(a,1,2,2)),rewrite([7(1)])].
% 54.76/55.05 10355 add(A,add(A,multiply(A,multiply(add(A,add(A,add(A,A))),B)))) = add(A,add(A,multiply(add(A,A),multiply(add(A,A),B)))). [para(48(a,1),160(a,2,2)),rewrite([160(8),4663(6),10(10),7(9),309(13)]),flip(a)].
% 54.76/55.05 10386 multiply(A,multiply(A,add(multiply(A,A),multiply(B,C)))) = add(A,multiply(A,multiply(A,multiply(B,C)))). [para(67(a,1),160(a,2,2,2)),rewrite([7(9),3158(10)])].
% 54.76/55.05 10585 add(A,multiply(A,multiply(additive_inverse(A),multiply(A,A)))) = additive_identity. [para(6(a,1),162(a,1,2,1)),rewrite([183(3),237(2)]),flip(a)].
% 54.76/55.05 10673 add(A,add(B,multiply(A,multiply(additive_inverse(A),multiply(A,A))))) = B. [para(10585(a,1),10(a,2,2)),rewrite([7(5),2(8)])].
% 54.76/55.05 10675 multiply(A,add(B,multiply(additive_inverse(A),multiply(A,multiply(A,B))))) = additive_identity. [para(10585(a,1),16(a,2,1)),rewrite([12(6),12(5),12(4),14(7),183(8)])].
% 54.76/55.05 10687 add(c_0,multiply(b,multiply(additive_inverse(b),multiply(b,c_0)))) = additive_identity. [para(10585(a,1),95(a,1,1)),rewrite([183(3),12(11),12(10),19(9)]),flip(a)].
% 54.76/55.05 10701 add(A,multiply(A,multiply(A,multiply(additive_inverse(A),A)))) = additive_identity. [para(10585(a,1),162(a,1,2,1)),rewrite([183(3),237(2),12(7),12(6),12(5),8(5)]),flip(a)].
% 54.76/55.05 10718 multiply(b,multiply(add(a,multiply(additive_inverse(b),multiply(b,c_0))),A)) = additive_identity. [para(10687(a,1),87(a,1,1)),rewrite([183(2),7(10)]),flip(a)].
% 54.76/55.05 10729 add(A,add(B,multiply(A,multiply(A,multiply(additive_inverse(A),A))))) = B. [para(10701(a,1),10(a,2,2)),rewrite([7(5),2(8)])].
% 54.76/55.05 10731 multiply(A,add(B,multiply(A,multiply(additive_inverse(A),multiply(A,B))))) = additive_identity. [para(10701(a,1),16(a,2,1)),rewrite([12(6),12(5),12(4),14(7),183(8)])].
% 54.76/55.05 10742 add(c_0,multiply(b,multiply(b,multiply(additive_inverse(b),c_0)))) = additive_identity. [para(10701(a,1),95(a,1,1)),rewrite([183(3),12(11),12(10),19(9)]),flip(a)].
% 54.76/55.05 10788 multiply(b,multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),A)) = additive_identity. [para(10742(a,1),87(a,1,1)),rewrite([183(2),7(10)]),flip(a)].
% 54.76/55.05 12815 multiply(a,multiply(c_0,add(A,multiply(c_0,multiply(c_0,b))))) = multiply(a,add(b,multiply(c_0,A))). [para(14(a,1),240(a,1,2)),rewrite([7(15)])].
% 54.76/55.05 13153 multiply(add(a,add(a,multiply(additive_inverse(b),multiply(b,add(c_0,c_0))))),b) = additive_identity. [para(10718(a,1),74(a,1,2,2,2,2,2)),rewrite([10(17),7(16),10(17,R),7(16),10(16,R),14(15),14(11),10(30),7(29),10(30,R),7(29),10(29,R),14(28),14(24),10(43),7(42),10(43,R),7(42),10(42,R),14(41),14(37),237(40),237(28),237(27),237(15),237(14),10(18),7(17),10(18,R),7(17),10(17,R),14(16),14(12)]),flip(a)].
% 54.76/55.05 13313 multiply(b,multiply(b,multiply(additive_inverse(b),multiply(b,additive_inverse(a))))) = c_0. [para(10731(a,1),3335(a,1,2)),rewrite([7(3),186(3)]),flip(a)].
% 54.76/55.05 13349 multiply(b,multiply(additive_inverse(b),multiply(b,additive_inverse(a)))) = multiply(b,multiply(b,c_0)). [para(13313(a,1),23(a,1,2,2)),flip(a)].
% 54.76/55.05 13393 multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),b) = additive_identity. [para(10788(a,1),22(a,1,2,2,2,2,2)),rewrite([237(28),237(20),237(19),237(11),237(10)]),flip(a)].
% 54.76/55.05 13402 multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),multiply(b,A)) = additive_identity. [para(10788(a,1),67(a,1,2,2,2,2,2)),rewrite([237(28),237(20),237(19),237(11),237(10)]),flip(a)].
% 54.76/55.05 13431 multiply(add(A,add(a,multiply(b,multiply(additive_inverse(b),c_0)))),b) = multiply(A,b). [para(13393(a,1),16(a,1,1)),rewrite([185(4),7(11)]),flip(a)].
% 54.76/55.05 13473 multiply(add(A,multiply(B,multiply(B,B))),B) = add(B,multiply(A,B)). [para(8(a,1),249(a,1,1)),flip(a)].
% 54.76/55.05 13711 add(multiply(A,multiply(B,C)),multiply(D,multiply(E,multiply(F,C)))) = multiply(add(multiply(D,multiply(E,F)),multiply(A,B)),C). [para(12(a,1),250(a,1,2,2))].
% 54.76/55.05 13727 multiply(add(multiply(b,b),multiply(A,B)),multiply(b,c_0)) = add(c_0,multiply(A,multiply(B,multiply(b,c_0)))). [para(106(a,1),250(a,1,2)),rewrite([7(7)]),flip(a)].
% 54.76/55.05 14985 multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),add(A,multiply(b,B))) = multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),A). [para(13402(a,1),14(a,1,1)),rewrite([185(11),7(20)]),flip(a)].
% 54.76/55.05 14987 multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),c_0) = additive_identity. [para(19(a,1),13402(a,1,2))].
% 54.76/55.05 14988 multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),multiply(c_0,A)) = additive_identity. [para(30(a,1),13402(a,1,2))].
% 54.76/55.05 15047 multiply(add(A,add(a,multiply(b,multiply(additive_inverse(b),c_0)))),c_0) = multiply(A,c_0). [para(14987(a,1),16(a,1,1)),rewrite([185(4),7(11)]),flip(a)].
% 54.76/55.05 15434 multiply(c_0,multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),A)) = additive_identity. [para(14988(a,1),67(a,1,2,2,2,2,2)),rewrite([237(21),237(20),237(12),237(11),237(3)]),flip(a)].
% 54.76/55.05 15435 multiply(c_0,multiply(A,add(a,multiply(b,multiply(additive_inverse(b),c_0))))) = additive_identity. [para(14988(a,1),68(a,1,2,2,2,2,2,2,2,2)),rewrite([237(21),237(21),237(20),237(12),237(12),237(11),237(3),237(3)]),flip(a)].
% 54.76/55.05 15436 multiply(c_0,add(A,add(a,multiply(b,multiply(additive_inverse(b),c_0))))) = multiply(c_0,A). [para(14988(a,1),69(a,1,2,2,2,2,2,2)),rewrite([237(21),237(20),237(12),237(11),2(3),7(12)]),flip(a)].
% 54.76/55.05 15590 multiply(add(b,c_0),multiply(b,multiply(b,c_0))) = add(c_0,multiply(c_0,multiply(b,multiply(b,c_0)))). [para(19(a,1),276(a,1,1,2)),rewrite([30(19)])].
% 54.76/55.05 15688 multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),multiply(A,c_0)) = additive_identity. [para(15434(a,1),68(a,1,2,2,2,2,2,2,2,2)),rewrite([237(28),237(28),237(20),237(19),237(19),237(11),237(10),237(10)]),flip(a)].
% 54.76/55.05 15704 multiply(c_0,multiply(A,multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),B))) = additive_identity. [para(15435(a,1),12(a,1,1)),rewrite([183(2),12(12)]),flip(a)].
% 54.76/55.05 15824 multiply(add(a,multiply(b,multiply(additive_inverse(b),c_0))),multiply(A,multiply(B,c_0))) = additive_identity. [para(12(a,1),15688(a,1,2))].
% 54.76/55.05 16584 add(A,add(A,multiply(A,multiply(A,multiply(A,additive_inverse(A)))))) = A. [para(13473(a,1),1719(a,1,2)),rewrite([12(4),12(3),12(7),12(6),8(7),7(6),309(6),12(9),12(8),8(9)])].
% 54.76/55.05 16625 add(A,multiply(A,multiply(A,multiply(A,additive_inverse(A))))) = additive_identity. [para(16584(a,1),26(a,1,1)),rewrite([7350(18),7(2),6(2),183(13),237(2),7350(24),7(8),6(8),183(19),237(8),7(8),10(8,R),7(7),185(7)]),flip(a)].
% 54.76/55.05 16628 add(additive_identity,add(additive_inverse(A),additive_inverse(A))) = add(additive_inverse(A),additive_inverse(A)). [para(4504(a,2),16584(a,1,2,2,2,2)),rewrite([29(23,R),16625(23),7(5)])].
% 54.76/55.05 16629 add(A,add(B,multiply(A,multiply(A,multiply(A,additive_inverse(A)))))) = B. [para(16625(a,1),10(a,2,2)),rewrite([7(5),2(8)])].
% 54.76/55.05 16631 multiply(A,add(B,multiply(A,multiply(A,multiply(additive_inverse(A),B))))) = additive_identity. [para(16625(a,1),16(a,2,1)),rewrite([12(6),12(5),12(4),14(7),183(8)])].
% 54.76/55.05 16636 add(A,add(A,multiply(add(A,A),multiply(add(A,A),multiply(add(A,A),additive_inverse(add(A,A))))))) = additive_identity. [para(48(a,1),16625(a,1,2)),rewrite([10(4),7(3),309(11),10355(11)])].
% 54.76/55.05 16682 add(additive_identity,additive_inverse(A)) = additive_inverse(A). [para(16628(a,1),33(a,1,2)),rewrite([21(4)]),flip(a)].
% 54.76/55.05 16693 add(A,add(additive_identity,add(additive_inverse(A),additive_inverse(B)))) = additive_inverse(B). [para(16682(a,1),33(a,2)),rewrite([7(4)])].
% 54.76/55.05 16696 additive_inverse(additive_inverse(A)) = A. [para(6(a,1),16693(a,1,2,2)),rewrite([2(3),2(2)]),flip(a)].
% 54.76/55.05 16697 add(A,add(additive_inverse(A),additive_inverse(B))) = additive_inverse(B). [para(10(a,1),16693(a,1,2)),rewrite([16682(4),7(3)])].
% 54.76/55.05 16726 add(A,add(B,add(additive_inverse(A),additive_inverse(C)))) = add(B,additive_inverse(C)). [para(16697(a,1),10(a,2,2)),rewrite([7(4)])].
% 54.76/55.05 16819 multiply(c_0,multiply(c_0,multiply(c_0,additive_inverse(c_0)))) = multiply(b,additive_inverse(a)). [para(16629(a,1),3523(a,1)),flip(a)].
% 54.76/55.05 16827 multiply(c_0,multiply(b,additive_inverse(a))) = multiply(c_0,additive_inverse(c_0)). [para(16819(a,1),23(a,1,2))].
% 54.76/55.06 16858 multiply(c_0,multiply(b,multiply(additive_inverse(a),A))) = multiply(c_0,multiply(additive_inverse(c_0),A)). [para(16827(a,1),12(a,1,1)),rewrite([12(5),12(11)]),flip(a)].
% 54.76/55.06 16950 multiply(b,multiply(b,multiply(b,multiply(additive_inverse(b),additive_inverse(a))))) = c_0. [para(16631(a,1),3335(a,1,2)),rewrite([7(3),186(3)]),flip(a)].
% 54.76/55.06 16954 multiply(A,add(B,multiply(A,multiply(additive_inverse(A),multiply(additive_inverse(A),B))))) = additive_identity. [para(10675(a,1),16631(a,1,2,2,2,2)),rewrite([16696(2),237(8),237(8),7(8),10(8,R),7(7),185(7)])].
% 54.76/55.06 16965 multiply(b,add(A,multiply(additive_inverse(b),additive_inverse(a)))) = multiply(b,add(A,c_0)). [para(16950(a,1),104(a,1,2,2)),rewrite([7(11)]),flip(a)].
% 54.76/55.06 17062 multiply(A,add(additive_inverse(B),add(additive_inverse(C),additive_inverse(C)))) = add(multiply(A,B),multiply(add(A,A),add(additive_inverse(B),additive_inverse(C)))). [para(16726(a,1),54(a,1,2)),rewrite([7(5),10(5,R)])].
% 54.76/55.06 17064 multiply(add(additive_inverse(A),add(additive_inverse(B),additive_inverse(B))),C) = add(multiply(A,C),multiply(add(additive_inverse(A),additive_inverse(B)),add(C,C))). [para(16726(a,1),56(a,1,1)),rewrite([7(5),10(5,R)])].
% 54.76/55.06 17580 add(c_0,add(c_0,multiply(A,multiply(b,multiply(b,add(c_0,c_0)))))) = multiply(add(A,b),multiply(b,multiply(b,add(c_0,c_0)))). [para(310(a,1),270(a,1,1)),rewrite([7(2),12(12),12(11),12(10),29(9),31(9),19(8),95(23),12(21),12(20),29(19),31(19),19(18)]),flip(a)].
% 54.76/55.06 18067 multiply(c_0,multiply(additive_inverse(c_0),multiply(additive_inverse(a),multiply(additive_inverse(a),additive_inverse(a))))) = multiply(c_0,additive_inverse(c_0)). [para(8(a,1),16858(a,1,2,2)),rewrite([16827(6)]),flip(a)].
% 54.76/55.06 18159 add(c_0,multiply(b,multiply(additive_inverse(b),multiply(additive_inverse(b),c_0)))) = additive_identity. [para(16954(a,1),114(a,1,2,2)),rewrite([237(4),237(3)]),flip(a)].
% 54.76/55.06 18161 multiply(b,multiply(b,multiply(additive_inverse(b),multiply(additive_inverse(b),additive_inverse(a))))) = c_0. [para(16954(a,1),3335(a,1,2)),rewrite([7(3),186(3)]),flip(a)].
% 54.76/55.06 18185 add(multiply(b,multiply(additive_inverse(b),multiply(additive_inverse(b),multiply(add(c_0,c_0),A)))),multiply(c_0,add(A,A))) = additive_identity. [para(18159(a,1),262(a,2,1)),rewrite([14(16),14(12),12(11),12(10),183(19)])].
% 54.76/55.06 18194 multiply(b,add(c_0,c_0)) = additive_identity. [para(18161(a,1),16631(a,1,2,2)),rewrite([7(8),16965(9)])].
% 54.76/55.06 18205 add(c_0,c_0) = additive_identity. [back_rewrite(17580),rewrite([18194(8),237(5),237(4),7(4),186(4),18194(11),237(8),237(7)])].
% 54.76/55.06 18250 multiply(a,add(b,b)) = additive_identity. [back_rewrite(13153),rewrite([18205(8),237(7),237(6),7(4),6886(4),29(5)])].
% 54.76/55.06 18277 multiply(c_0,add(A,A)) = additive_identity. [back_rewrite(18185),rewrite([18205(8),183(7),237(7),237(5),237(3),185(5)])].
% 54.76/55.06 18489 multiply(add(b,c_0),add(a,a)) = additive_identity. [back_rewrite(10206),rewrite([18205(10),183(9),7(9),185(9),18205(12),183(13),7(11),186(11),18205(10)])].
% 54.76/55.06 18537 multiply(c_0,add(multiply(A,B),add(multiply(A,B),multiply(C,multiply(D,add(B,B)))))) = additive_identity. [back_rewrite(9363),rewrite([18205(12),183(14)])].
% 54.76/55.06 18577 multiply(b,additive_inverse(multiply(a,A))) = multiply(c_0,A). [back_rewrite(8523),rewrite([18205(3),183(3),18205(6),18205(7),18205(8),183(7),237(7),237(6),2(5),185(7),18205(9),18205(10),18205(11),183(10),237(10),237(9),2(8)])].
% 54.76/55.06 18584 multiply(add(A,A),multiply(c_0,B)) = additive_identity. [back_rewrite(8502),rewrite([18577(9),18577(11),18205(11),183(11),7(10),185(10),14(9),18277(7),237(6)])].
% 54.76/55.06 18598 add(c_0,add(c_0,multiply(A,a))) = multiply(A,a). [back_rewrite(7280),rewrite([18489(7),185(4),18205(7),2(6)]),flip(a)].
% 54.76/55.06 18665 multiply(c_0,add(A,add(A,B))) = multiply(c_0,B). [back_rewrite(3532),rewrite([18205(12),183(11),185(13),3523(13)])].
% 54.76/55.06 18945 multiply(add(b,c_0),add(A,multiply(a,A))) = multiply(add(b,multiply(c_0,a)),A). [back_rewrite(1511),rewrite([18598(8)]),flip(a)].
% 54.76/55.06 19008 multiply(c_0,multiply(A,multiply(B,add(C,C)))) = additive_identity. [back_rewrite(18537),rewrite([18665(9)])].
% 54.76/55.06 19102 multiply(additive_inverse(c_0),multiply(additive_inverse(a),multiply(additive_inverse(a),additive_inverse(a)))) = c_0. [back_rewrite(8610),rewrite([19008(24),7(13),185(13)])].
% 54.76/55.06 19119 multiply(c_0,additive_inverse(c_0)) = multiply(c_0,c_0). [back_rewrite(18067),rewrite([19102(12)]),flip(a)].
% 54.76/55.06 19173 multiply(b,additive_inverse(a)) = c_0. [back_rewrite(16819),rewrite([19119(6),8(7)]),flip(a)].
% 54.76/55.06 19216 multiply(b,multiply(additive_inverse(b),c_0)) = multiply(b,multiply(b,c_0)). [back_rewrite(13349),rewrite([19173(7)])].
% 54.76/55.06 19570 multiply(add(a,multiply(b,multiply(b,c_0))),multiply(A,multiply(B,c_0))) = additive_identity. [back_rewrite(15824),rewrite([19216(7)])].
% 54.76/55.06 19592 multiply(c_0,multiply(A,multiply(add(a,multiply(b,multiply(b,c_0))),B))) = additive_identity. [back_rewrite(15704),rewrite([19216(8)])].
% 54.76/55.06 19661 multiply(c_0,add(A,add(a,multiply(b,multiply(b,c_0))))) = multiply(c_0,A). [back_rewrite(15436),rewrite([19216(8)])].
% 54.76/55.06 19663 multiply(c_0,multiply(add(a,multiply(b,multiply(b,c_0))),A)) = additive_identity. [back_rewrite(15434),rewrite([19216(8)])].
% 54.76/55.06 19724 multiply(add(A,add(a,multiply(b,multiply(b,c_0)))),c_0) = multiply(A,c_0). [back_rewrite(15047),rewrite([19216(7)])].
% 54.76/55.06 19746 multiply(add(a,multiply(b,multiply(b,c_0))),add(A,multiply(b,B))) = multiply(add(a,multiply(b,multiply(b,c_0))),A). [back_rewrite(14985),rewrite([19216(7),19216(18)])].
% 54.76/55.06 19771 multiply(add(A,add(a,multiply(b,multiply(b,c_0)))),b) = multiply(A,b). [back_rewrite(13431),rewrite([19216(7)])].
% 54.76/55.06 19788 multiply(add(A,A),multiply(B,c_0)) = additive_identity. [para(18205(a,1),50(a,2,2,2)),rewrite([237(6),237(6)])].
% 54.76/55.06 19792 multiply(c_0,additive_inverse(A)) = multiply(c_0,A). [para(18205(a,1),1719(a,1,2,1)),rewrite([183(5),7(5),185(5)])].
% 54.76/55.06 19795 multiply(additive_inverse(A),c_0) = multiply(A,c_0). [para(18205(a,1),2143(a,1,2,2)),rewrite([237(5),7(5),185(5)])].
% 54.76/55.06 19900 multiply(b,add(A,additive_inverse(a))) = add(c_0,multiply(b,A)). [para(19173(a,1),14(a,1,1)),rewrite([7(8)]),flip(a)].
% 54.76/55.06 19936 add(c_0,add(add(c_0,multiply(b,A)),multiply(B,A))) = multiply(add(B,b),A). [back_rewrite(6643),rewrite([19900(6)])].
% 54.76/55.06 19958 multiply(add(A,A),multiply(a,b)) = additive_identity. [para(18250(a,1),50(a,2,2)),rewrite([237(7)])].
% 54.76/55.06 20101 multiply(c_0,multiply(additive_inverse(A),B)) = multiply(c_0,multiply(A,B)). [para(19792(a,1),12(a,1,1)),rewrite([12(3)]),flip(a)].
% 54.76/55.06 20213 multiply(additive_inverse(add(b,multiply(c_0,multiply(a,additive_inverse(a))))),add(c_0,multiply(c_0,A))) = additive_identity. [back_rewrite(10024),rewrite([20101(8)])].
% 54.76/55.06 20285 multiply(add(b,multiply(c_0,multiply(a,additive_inverse(a)))),add(A,multiply(c_0,B))) = multiply(add(b,multiply(c_0,multiply(a,additive_inverse(a)))),A). [back_rewrite(7861),rewrite([20101(8),20101(20)])].
% 54.76/55.06 20326 multiply(add(b,multiply(c_0,multiply(a,additive_inverse(a)))),multiply(A,c_0)) = additive_identity. [back_rewrite(7128),rewrite([20101(8)])].
% 54.76/55.06 20355 multiply(a,add(A,add(b,multiply(c_0,multiply(a,additive_inverse(a)))))) = multiply(a,A). [back_rewrite(6929),rewrite([20101(9)])].
% 54.76/55.06 20421 multiply(additive_inverse(A),multiply(c_0,B)) = multiply(A,multiply(c_0,B)). [para(19795(a,1),12(a,1,1)),rewrite([12(3)]),flip(a)].
% 54.76/55.06 20435 multiply(additive_inverse(A),add(c_0,multiply(c_0,B))) = multiply(A,add(c_0,multiply(c_0,B))). [para(19795(a,1),157(a,1,2,2,2,2,2,2,2)),rewrite([20421(10),20421(11),20421(13),157(12)]),flip(a)].
% 54.76/55.06 20438 multiply(add(A,multiply(B,multiply(C,additive_inverse(D)))),c_0) = multiply(add(A,multiply(B,multiply(C,D))),c_0). [para(19795(a,1),249(a,1,1,2,2)),rewrite([249(7)]),flip(a)].
% 54.76/55.06 20534 multiply(add(b,multiply(c_0,multiply(a,a))),c_0) = additive_identity. [back_rewrite(20213),rewrite([20435(14),20285(13),20438(10)])].
% 54.76/55.06 20961 multiply(A,additive_inverse(multiply(c_0,B))) = multiply(A,multiply(c_0,B)). [para(18584(a,1),1719(a,1,2)),rewrite([7(6),185(6)])].
% 54.76/55.06 21169 multiply(A,additive_inverse(multiply(B,c_0))) = multiply(A,multiply(B,c_0)). [para(19788(a,1),1719(a,1,2)),rewrite([7(6),185(6)])].
% 54.76/55.06 21188 multiply(A,additive_inverse(multiply(a,b))) = multiply(A,multiply(a,b)). [para(19958(a,1),1719(a,1,2)),rewrite([7(7),185(7)])].
% 54.76/55.06 22105 multiply(A,multiply(A,multiply(A,add(B,multiply(A,B))))) = multiply(add(A,multiply(A,multiply(A,A))),B). [para(348(a,1),251(a,1)),rewrite([14(10),14(8)]),flip(a)].
% 54.76/55.06 22663 multiply(c_0,multiply(add(A,add(A,B)),C)) = multiply(c_0,multiply(B,C)). [para(16(a,1),18665(a,1,2,2)),rewrite([16(5)])].
% 54.76/55.06 23006 multiply(add(A,add(b,multiply(c_0,multiply(a,a)))),c_0) = multiply(A,c_0). [para(20534(a,1),16(a,1,1)),rewrite([185(4),7(10)]),flip(a)].
% 54.76/55.06 23251 multiply(add(A,multiply(B,multiply(C,multiply(C,C)))),C) = multiply(add(B,A),C). [para(16(a,1),365(a,1,1)),rewrite([12(5),8(4),12(5)]),flip(a)].
% 54.76/55.06 23886 multiply(b,multiply(add(A,multiply(a,A)),B)) = multiply(add(b,c_0),multiply(A,B)). [para(16(a,1),387(a,1,1)),rewrite([7(3),12(5)]),flip(a)].
% 54.76/55.06 24827 additive_inverse(multiply(c_0,A)) = multiply(c_0,A). [para(20961(a,1),8(a,1,2,2)),rewrite([20421(12),12(11),20421(12),12(11),20421(12),12(11),22(11)]),flip(a)].
% 54.76/55.06 24922 multiply(A,add(B,additive_inverse(multiply(C,c_0)))) = multiply(A,add(B,multiply(C,c_0))). [para(21169(a,1),14(a,1,1)),rewrite([14(5),7(3),7(8)]),flip(a)].
% 54.76/55.06 24929 multiply(additive_inverse(A),multiply(B,c_0)) = multiply(A,multiply(B,c_0)). [para(21169(a,1),2143(a,1,1)),rewrite([24922(12),7(10),6(10),237(6),7(6),185(6),21169(8)])].
% 54.76/55.06 24937 add(additive_inverse(multiply(A,c_0)),additive_inverse(multiply(A,c_0))) = additive_identity. [para(21169(a,1),319(a,1,1,2)),rewrite([24929(6),12(5),24922(17),7(15),6(15),237(11),237(8),24922(19),7(17),6(17),237(13),237(10),7(10),16628(10)]),flip(a)].
% 54.76/55.06 24983 additive_inverse(multiply(A,c_0)) = multiply(A,c_0). [para(24937(a,1),21(a,1,2)),rewrite([7(4),185(4)]),flip(a)].
% 54.76/55.06 24998 multiply(A,add(B,additive_inverse(multiply(a,b)))) = multiply(A,add(B,multiply(a,b))). [para(21188(a,1),14(a,1,1)),rewrite([14(6),7(4),7(10)]),flip(a)].
% 54.76/55.06 25004 multiply(additive_inverse(A),multiply(a,b)) = multiply(A,multiply(a,b)). [para(21188(a,1),2143(a,1,1)),rewrite([24998(15),7(13),6(13),237(7),7(7),185(7),21188(10)])].
% 54.76/55.06 25016 add(additive_inverse(multiply(a,b)),additive_inverse(multiply(a,b))) = additive_identity. [para(21188(a,1),319(a,1,1,2)),rewrite([25004(8),12(7),30(6),24998(20),7(18),6(18),237(12),237(8),24998(24),7(22),6(22),237(16),237(12),7(12),16628(12)]),flip(a)].
% 54.76/55.06 25046 additive_inverse(multiply(a,b)) = multiply(a,b). [para(25016(a,1),21(a,1,2)),rewrite([7(5),185(5)]),flip(a)].
% 54.76/55.06 25253 multiply(c_0,multiply(add(A,multiply(a,a)),multiply(a,B))) = multiply(add(b,multiply(c_0,A)),multiply(a,B)). [para(14(a,1),420(a,1,1)),rewrite([12(9),7(13)])].
% 54.76/55.06 26719 multiply(additive_inverse(A),multiply(additive_inverse(A),multiply(additive_inverse(A),A))) = A. [para(16625(a,1),484(a,1,2,1)),rewrite([183(4),2(2),16696(5),12(8),12(7),8(6)]),flip(a)].
% 54.76/55.06 29924 multiply(A,multiply(A,multiply(A,additive_inverse(A)))) = additive_inverse(A). [para(16696(a,1),26719(a,1,1)),rewrite([16696(2),16696(2)])].
% 54.76/55.06 29928 add(A,add(A,additive_inverse(add(A,A)))) = additive_identity. [back_rewrite(16636),rewrite([29924(8)])].
% 54.76/55.06 29939 add(additive_inverse(A),additive_inverse(add(additive_inverse(A),additive_inverse(A)))) = A. [para(29928(a,1),16726(a,1,2)),rewrite([2(2)]),flip(a)].
% 54.76/55.06 29941 multiply(A,multiply(A,multiply(A,multiply(additive_inverse(A),B)))) = multiply(additive_inverse(A),B). [para(29924(a,1),12(a,1,1)),rewrite([12(6),12(5)]),flip(a)].
% 54.76/55.06 29942 multiply(A,add(B,multiply(A,multiply(A,additive_inverse(A))))) = add(additive_inverse(A),multiply(A,B)). [para(29924(a,1),14(a,1,1)),rewrite([7(7)]),flip(a)].
% 54.76/55.06 29950 add(A,add(additive_inverse(A),multiply(A,B))) = multiply(A,B). [para(29924(a,1),159(a,1,1,2)),rewrite([6(2),185(3),7(5),29942(6)]),flip(a)].
% 54.76/55.06 30021 add(add(A,B),additive_inverse(C)) = add(A,add(B,additive_inverse(C))). [para(29939(a,1),103(a,1,2,2,2)),rewrite([7(4),10(5,R),7(4),10(6,R),33(6)])].
% 54.76/55.06 31389 multiply(A,multiply(additive_inverse(A),multiply(A,A))) = additive_inverse(A). [para(29950(a,1),10673(a,1))].
% 54.76/55.06 31390 multiply(A,multiply(A,multiply(additive_inverse(A),A))) = additive_inverse(A). [para(29950(a,1),10729(a,1))].
% 54.76/55.06 31414 add(A,multiply(A,multiply(A,multiply(additive_inverse(A),additive_inverse(A))))) = additive_identity. [para(31389(a,1),16631(a,1,2,2,2,2)),rewrite([16696(2),16696(6),7(7),14(7),10386(7)])].
% 54.76/55.06 31424 multiply(c_0,multiply(a,additive_inverse(a))) = multiply(c_0,multiply(a,a)). [para(31390(a,1),37(a,1,2,2)),rewrite([20101(12)])].
% 54.76/55.06 31471 multiply(a,add(A,add(b,multiply(c_0,multiply(a,a))))) = multiply(a,A). [back_rewrite(20355),rewrite([31424(8)])].
% 54.76/55.06 31480 multiply(add(b,multiply(c_0,multiply(a,a))),multiply(A,c_0)) = additive_identity. [back_rewrite(20326),rewrite([31424(7)])].
% 54.76/55.06 32349 multiply(c_0,multiply(b,multiply(b,multiply(c_0,multiply(a,a))))) = c_0. [para(19663(a,1),463(a,2,2)),rewrite([7(10),22663(15),12(10),12(9),7(14),186(14)])].
% 54.76/55.06 35046 add(add(A,B),multiply(c_0,C)) = add(A,add(B,multiply(c_0,C))). [para(24827(a,1),30021(a,1,2)),rewrite([24827(7)])].
% 54.76/55.06 35047 add(add(A,B),multiply(C,c_0)) = add(A,add(B,multiply(C,c_0))). [para(24983(a,1),30021(a,1,2)),rewrite([24983(7)])].
% 54.76/55.06 35048 add(add(A,B),multiply(a,b)) = add(A,add(B,multiply(a,b))). [para(25046(a,1),30021(a,1,2)),rewrite([25046(9)])].
% 54.76/55.06 36159 add(A,add(B,multiply(A,multiply(A,multiply(additive_inverse(A),additive_inverse(A)))))) = B. [para(31414(a,1),10(a,2,2)),rewrite([7(6),2(9)])].
% 54.76/55.06 36163 add(A,multiply(additive_inverse(A),multiply(additive_inverse(A),multiply(A,A)))) = additive_identity. [para(31414(a,1),162(a,1,2,1)),rewrite([183(3),237(2),12(8),12(7),12(6),29941(9)]),flip(a)].
% 54.76/55.06 36168 multiply(additive_inverse(A),multiply(additive_inverse(A),multiply(A,A))) = A. [para(31414(a,1),484(a,1,2,1)),rewrite([183(4),2(2),16696(4),16696(4),12(7),12(6),8(5)]),flip(a)].
% 54.76/55.06 36172 add(A,A) = additive_identity. [back_rewrite(36163),rewrite([36168(5)])].
% 54.76/55.06 36193 multiply(additive_inverse(A),B) = multiply(A,B). [back_rewrite(17064),rewrite([36172(4),2(3),36172(7),237(8),7(5),185(5)])].
% 54.76/55.06 36194 multiply(A,additive_inverse(B)) = multiply(A,B). [back_rewrite(17062),rewrite([36172(4),2(3),36172(4),183(8),7(5),185(5)])].
% 54.76/55.06 36307 add(A,add(A,B)) = B. [back_rewrite(36159),rewrite([36194(3),36193(2),8(3),7(1)])].
% 54.76/55.06 36700 multiply(add(b,add(multiply(a,c_0),multiply(c_0,multiply(a,a)))),multiply(c_0,multiply(c_0,b))) = multiply(a,b). [para(31480(a,1),366(a,2,1,2)),rewrite([7(11),10(11,R),7(10),7(20),6886(20)])].
% 54.76/55.06 36859 add(c_0,multiply(c_0,multiply(b,multiply(b,c_0)))) = add(c_0,multiply(c_0,a)). [para(32349(a,1),95(a,1,1,2)),rewrite([862(5),12(18),12(17),12(16),12(15),34(16)]),flip(a)].
% 54.76/55.06 36867 multiply(a,multiply(b,multiply(b,multiply(c_0,multiply(a,a))))) = multiply(a,multiply(c_0,multiply(c_0,c_0))). [para(32349(a,1),239(a,1,2,2,2)),flip(a)].
% 54.76/55.06 36900 multiply(add(b,c_0),multiply(b,multiply(b,c_0))) = add(c_0,multiply(c_0,a)). [back_rewrite(15590),rewrite([36859(18)])].
% 54.76/55.06 37129 add(multiply(b,multiply(b,c_0)),multiply(a,multiply(b,multiply(b,multiply(c_0,multiply(b,multiply(b,multiply(c_0,multiply(b,multiply(b,c_0)))))))))) = additive_identity. [para(19570(a,1),221(a,1,2,2)),rewrite([12(22),12(21),12(23),12(22),7(26),185(26),12(51),12(50),12(52),12(51),19746(54),19570(36)])].
% 54.76/55.06 37247 multiply(c_0,add(a,multiply(a,multiply(c_0,multiply(c_0,c_0))))) = additive_identity. [para(162(a,1),19592(a,1,2)),rewrite([12(12),12(11),36867(13)])].
% 54.76/55.06 37339 multiply(c_0,multiply(add(a,multiply(a,multiply(c_0,multiply(c_0,c_0)))),A)) = additive_identity. [para(37247(a,1),12(a,1,1)),rewrite([183(2)]),flip(a)].
% 54.76/55.06 37563 multiply(c_0,multiply(b,multiply(b,c_0))) = multiply(c_0,a). [para(36307(a,1),19661(a,1,2))].
% 54.76/55.06 37566 add(multiply(b,multiply(b,c_0)),multiply(a,multiply(b,multiply(b,multiply(c_0,multiply(b,multiply(b,multiply(c_0,a)))))))) = additive_identity. [back_rewrite(37129),rewrite([37563(18)])].
% 54.76/55.06 37615 multiply(c_0,multiply(b,multiply(b,multiply(c_0,A)))) = multiply(c_0,multiply(a,A)). [para(37563(a,1),12(a,1,1)),rewrite([12(4),12(11),12(10)]),flip(a)].
% 54.76/55.06 37616 multiply(c_0,add(A,multiply(b,multiply(b,c_0)))) = multiply(c_0,add(A,a)). [para(37563(a,1),14(a,1,1)),rewrite([14(6),7(3),7(11)]),flip(a)].
% 54.76/55.06 37628 multiply(c_0,multiply(b,multiply(b,add(c_0,multiply(c_0,A))))) = multiply(c_0,add(a,multiply(a,A))). [para(37563(a,1),157(a,1,2,2,2,2,2,2,2)),rewrite([12(22),12(21),37615(23),12(20),12(19),37615(21),12(19),12(18),37615(20),157(16),12(18),12(17),14(19),14(16)]),flip(a)].
% 54.76/55.06 37632 multiply(a,multiply(c_0,multiply(c_0,multiply(c_0,a)))) = multiply(a,multiply(b,multiply(b,c_0))). [para(37563(a,1),239(a,1,2,2,2))].
% 54.76/55.06 37677 multiply(add(multiply(b,b),multiply(a,multiply(c_0,c_0))),c_0) = additive_identity. [back_rewrite(37566),rewrite([37615(17),36867(16),13711(13),7(9)])].
% 54.76/55.06 37682 multiply(add(multiply(b,b),multiply(a,multiply(c_0,c_0))),multiply(c_0,A)) = additive_identity. [para(37677(a,1),12(a,1,1)),rewrite([183(2)]),flip(a)].
% 54.76/55.06 37929 multiply(b,multiply(b,multiply(c_0,c_0))) = multiply(a,c_0). [para(36307(a,1),19724(a,1,1)),rewrite([12(7),12(6)])].
% 54.76/55.06 37931 multiply(b,multiply(b,multiply(c_0,multiply(c_0,A)))) = multiply(a,multiply(c_0,A)). [para(37929(a,1),12(a,1,1)),rewrite([12(4),12(11),12(10)]),flip(a)].
% 54.76/55.06 37932 multiply(b,add(A,multiply(b,multiply(c_0,c_0)))) = add(multiply(a,c_0),multiply(b,A)). [para(37929(a,1),14(a,1,1)),rewrite([7(13)]),flip(a)].
% 54.76/55.06 37938 multiply(b,multiply(b,multiply(add(b,c_0),c_0))) = add(c_0,multiply(a,c_0)). [para(37929(a,1),116(a,2,2)),rewrite([7(12),14(12),16(9)])].
% 54.76/55.06 38032 multiply(b,multiply(b,multiply(c_0,b))) = multiply(a,b). [para(36307(a,1),19771(a,1,1)),rewrite([12(7),12(6)])].
% 54.76/55.06 38033 multiply(b,multiply(b,multiply(c_0,multiply(b,A)))) = multiply(a,multiply(b,A)). [para(38032(a,1),12(a,1,1)),rewrite([12(4),12(11),12(10)]),flip(a)].
% 54.76/55.06 38034 multiply(b,add(A,multiply(b,multiply(c_0,b)))) = add(multiply(a,b),multiply(b,A)). [para(38032(a,1),14(a,1,1)),rewrite([7(13)]),flip(a)].
% 54.76/55.06 38052 multiply(a,multiply(c_0,multiply(c_0,multiply(c_0,multiply(a,b))))) = multiply(a,multiply(a,b)). [para(38032(a,1),239(a,1,2,2,2,2)),rewrite([38032(19)])].
% 54.76/55.06 38826 multiply(c_0,multiply(a,multiply(a,c_0))) = multiply(b,c_0). [para(36307(a,1),23006(a,1,1)),rewrite([12(7),12(6)])].
% 54.76/55.06 38831 multiply(c_0,multiply(a,multiply(a,multiply(c_0,A)))) = multiply(b,multiply(c_0,A)). [para(38826(a,1),12(a,1,1)),rewrite([12(4),12(11),12(10)]),flip(a)].
% 54.76/55.06 38832 multiply(c_0,add(A,multiply(a,multiply(a,c_0)))) = add(multiply(b,c_0),multiply(c_0,A)). [para(38826(a,1),14(a,1,1)),rewrite([7(13)]),flip(a)].
% 54.76/55.06 38852 multiply(add(A,multiply(c_0,multiply(a,a))),c_0) = multiply(add(A,b),c_0). [para(38826(a,1),249(a,1,1)),rewrite([16(6),7(2)]),flip(a)].
% 54.76/55.06 39291 multiply(a,multiply(c_0,multiply(a,a))) = multiply(a,b). [para(36307(a,1),31471(a,1,2))].
% 54.76/55.06 39292 multiply(a,multiply(c_0,multiply(a,multiply(a,A)))) = multiply(a,multiply(b,A)). [para(39291(a,1),12(a,1,1)),rewrite([12(4),12(11),12(10)]),flip(a)].
% 54.76/55.06 39293 multiply(a,add(A,multiply(c_0,multiply(a,a)))) = multiply(a,add(A,b)). [para(39291(a,1),14(a,1,1)),rewrite([14(6),7(3),7(11)]),flip(a)].
% 54.76/55.06 39295 multiply(c_0,multiply(c_0,multiply(a,a))) = multiply(c_0,b). [para(39291(a,1),30(a,1,2)),rewrite([30(5)]),flip(a)].
% 54.76/55.06 39305 multiply(c_0,add(A,multiply(c_0,multiply(a,a)))) = multiply(c_0,add(A,b)). [para(39291(a,1),118(a,1,2,2,2,2)),rewrite([118(10),7(3),7(11)]),flip(a)].
% 54.76/55.06 39351 multiply(c_0,multiply(c_0,multiply(c_0,b))) = multiply(c_0,multiply(a,a)). [para(39295(a,1),23(a,1,2,2))].
% 54.76/55.06 39358 multiply(c_0,add(A,multiply(c_0,multiply(c_0,b)))) = multiply(c_0,add(A,multiply(a,a))). [para(39295(a,1),104(a,1,2,2,2)),rewrite([7(13)])].
% 54.76/55.06 39418 multiply(a,multiply(c_0,add(A,multiply(a,a)))) = multiply(a,add(b,multiply(c_0,A))). [back_rewrite(12815),rewrite([39358(9)])].
% 54.76/55.06 39424 multiply(c_0,multiply(c_0,multiply(c_0,add(b,c_0)))) = add(c_0,multiply(c_0,multiply(a,a))). [para(39351(a,1),24(a,2,2)),rewrite([14(12),14(9)])].
% 54.76/55.06 39431 multiply(c_0,multiply(c_0,multiply(c_0,multiply(add(b,c_0),A)))) = multiply(add(b,multiply(c_0,a)),multiply(a,A)). [para(39351(a,1),156(a,2,1,2)),rewrite([14(12),14(9),12(9),12(8),336(18)])].
% 54.76/55.06 40551 add(add(A,B),multiply(C,multiply(D,c_0))) = add(A,add(B,multiply(C,multiply(D,c_0)))). [para(12(a,1),35047(a,1,2)),rewrite([12(8)])].
% 54.76/55.06 40706 add(additive_identity,add(multiply(A,B),multiply(a,b))) = add(multiply(A,B),multiply(a,b)). [para(185(a,1),35048(a,1,1)),flip(a)].
% 54.76/55.06 40944 multiply(c_0,multiply(a,multiply(c_0,multiply(c_0,b)))) = c_0. [para(37339(a,1),463(a,2,2)),rewrite([7(12),36307(12),12(12),12(11),12(10),39295(10),7(12),186(12)])].
% 54.76/55.06 40955 multiply(add(A,multiply(c_0,a)),multiply(c_0,multiply(c_0,b))) = add(c_0,multiply(A,multiply(c_0,multiply(c_0,b)))). [para(40944(a,1),27(a,1,1)),flip(a)].
% 54.76/55.06 41083 multiply(c_0,multiply(a,multiply(c_0,multiply(c_0,c_0)))) = multiply(c_0,a). [para(8(a,1),37615(a,1,2,2,2)),rewrite([37563(7)]),flip(a)].
% 54.76/55.06 41192 multiply(b,multiply(c_0,multiply(c_0,b))) = multiply(c_0,a). [para(40944(a,1),37615(a,1,2,2,2)),rewrite([37563(7),38831(14)]),flip(a)].
% 54.76/55.06 41210 multiply(b,multiply(c_0,multiply(c_0,multiply(b,A)))) = multiply(c_0,multiply(a,A)). [para(41192(a,1),12(a,1,1)),rewrite([12(4),12(11),12(10)]),flip(a)].
% 54.76/55.06 41213 multiply(b,multiply(b,multiply(c_0,a))) = multiply(c_0,multiply(c_0,b)). [para(41192(a,1),107(a,1,2,2))].
% 54.76/55.06 41367 multiply(b,multiply(c_0,multiply(c_0,c_0))) = multiply(c_0,multiply(a,a)). [para(41083(a,1),37615(a,1,2,2,2)),rewrite([41213(8),39351(7),38831(16)]),flip(a)].
% 54.76/55.06 41384 multiply(b,multiply(b,multiply(c_0,multiply(a,A)))) = multiply(c_0,multiply(c_0,multiply(b,A))). [para(41213(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 41490 multiply(b,multiply(c_0,multiply(b,multiply(c_0,multiply(b,multiply(c_0,b)))))) = multiply(c_0,multiply(a,a)). [para(41367(a,1),67(a,1,2,2,2,2,2,2)),rewrite([39295(12),41367(20)])].
% 54.76/55.06 41599 multiply(c_0,multiply(b,add(A,multiply(b,c_0)))) = multiply(c_0,add(a,multiply(b,A))). [para(14(a,1),37616(a,1,2)),rewrite([7(13)])].
% 54.76/55.06 41692 add(c_0,multiply(a,multiply(c_0,multiply(c_0,multiply(b,c_0))))) = additive_identity. [para(38826(a,1),37682(a,1,2)),rewrite([13727(13),12(9)])].
% 54.76/55.06 41845 multiply(a,multiply(c_0,multiply(c_0,multiply(b,c_0)))) = c_0. [para(41692(a,1),634(a,2,2,1)),rewrite([36172(3),185(11),12(15),12(14),12(13),12(12),34(11),183(17),7(12),186(12)])].
% 54.76/55.06 41850 multiply(a,add(A,multiply(c_0,multiply(c_0,multiply(b,c_0))))) = add(c_0,multiply(a,A)). [para(41845(a,1),14(a,1,1)),rewrite([7(13)]),flip(a)].
% 54.76/55.06 41852 multiply(a,multiply(a,multiply(a,c_0))) = c_0. [para(41845(a,1),23(a,1,2,2,2)),rewrite([41845(16)])].
% 54.76/55.06 41859 multiply(a,multiply(c_0,multiply(a,multiply(c_0,multiply(a,multiply(c_0,c_0)))))) = c_0. [para(41845(a,1),67(a,1,2,2,2,2,2,2)),rewrite([41845(22)])].
% 54.76/55.06 41860 multiply(a,add(A,multiply(a,multiply(a,c_0)))) = add(c_0,multiply(a,A)). [para(41845(a,1),104(a,1,2,2,2,2)),rewrite([7(17),41850(18)])].
% 54.76/55.06 41906 multiply(a,multiply(a,multiply(a,multiply(c_0,A)))) = multiply(c_0,A). [para(41852(a,1),12(a,1,1)),rewrite([12(9),12(8)]),flip(a)].
% 54.76/55.06 41928 multiply(a,add(A,multiply(a,multiply(a,multiply(c_0,B))))) = add(multiply(c_0,B),multiply(a,A)). [para(41906(a,1),14(a,1,1)),rewrite([7(13)]),flip(a)].
% 54.76/55.06 41932 multiply(add(A,multiply(a,a)),multiply(a,multiply(c_0,B))) = multiply(add(c_0,multiply(A,multiply(a,c_0))),B). [para(41906(a,1),27(a,1,1)),rewrite([335(8)]),flip(a)].
% 54.76/55.06 41949 multiply(add(A,multiply(a,multiply(a,a))),multiply(c_0,B)) = multiply(add(c_0,multiply(A,c_0)),B). [para(41906(a,1),249(a,1,1)),rewrite([28(6)]),flip(a)].
% 54.76/55.06 41973 multiply(a,multiply(a,multiply(a,b))) = multiply(c_0,multiply(a,a)). [para(39291(a,1),41906(a,1,2,2))].
% 54.76/55.06 41974 multiply(c_0,multiply(c_0,multiply(b,c_0))) = multiply(a,multiply(a,c_0)). [para(41845(a,1),41906(a,1,2,2)),flip(a)].
% 54.76/55.06 42084 multiply(a,add(A,multiply(a,multiply(a,b)))) = add(multiply(c_0,multiply(a,a)),multiply(a,A)). [para(41973(a,1),14(a,1,1)),rewrite([7(15)]),flip(a)].
% 54.76/55.06 42086 multiply(c_0,multiply(a,multiply(a,b))) = multiply(b,multiply(c_0,multiply(a,a))). [para(41973(a,1),30(a,1,2)),flip(a)].
% 54.76/55.06 42090 add(multiply(A,multiply(a,b)),multiply(c_0,multiply(a,a))) = multiply(add(A,multiply(a,a)),multiply(a,b)). [para(41973(a,1),28(a,1,2))].
% 54.76/55.06 42092 multiply(add(b,multiply(c_0,a)),multiply(a,b)) = multiply(add(b,c_0),multiply(c_0,multiply(a,a))). [para(41973(a,1),1136(a,1,2)),rewrite([41973(22),42090(21),25253(20)]),flip(a)].
% 54.76/55.06 42099 multiply(add(A,multiply(a,multiply(a,a))),b) = add(multiply(c_0,multiply(a,a)),multiply(A,b)). [para(41973(a,1),249(a,1,1)),flip(a)].
% 54.76/55.06 42144 multiply(c_0,add(A,multiply(c_0,multiply(b,c_0)))) = add(multiply(a,multiply(a,c_0)),multiply(c_0,A)). [para(41974(a,1),14(a,1,1)),rewrite([7(15)]),flip(a)].
% 54.76/55.06 42146 multiply(c_0,multiply(c_0,multiply(add(b,c_0),c_0))) = add(c_0,multiply(a,multiply(a,c_0))). [para(41974(a,1),24(a,2,2)),rewrite([14(12),16(9)])].
% 54.76/55.06 42214 multiply(a,multiply(c_0,multiply(c_0,c_0))) = multiply(b,multiply(b,c_0)). [para(8(a,1),37931(a,1,2,2)),flip(a)].
% 54.76/55.06 42217 multiply(a,multiply(c_0,multiply(c_0,multiply(c_0,A)))) = multiply(b,multiply(b,multiply(c_0,A))). [para(23(a,1),37931(a,1,2,2)),flip(a)].
% 54.76/55.06 42289 multiply(b,multiply(c_0,a)) = multiply(a,multiply(c_0,b)). [para(39295(a,1),37931(a,1,2,2,2)),rewrite([41192(8),39295(13)])].
% 54.76/55.06 42290 multiply(a,multiply(c_0,multiply(c_0,b))) = multiply(c_0,multiply(c_0,c_0)). [para(39351(a,1),37931(a,1,2,2)),rewrite([41384(9),19(5)]),flip(a)].
% 54.76/55.06 42291 multiply(b,multiply(c_0,multiply(a,a))) = multiply(a,multiply(c_0,c_0)). [para(41367(a,1),37931(a,1,2))].
% 54.76/55.06 42363 multiply(c_0,multiply(c_0,multiply(b,b))) = multiply(a,multiply(a,b)). [back_rewrite(38052),rewrite([42217(11),41384(9)])].
% 54.76/55.06 42364 multiply(a,multiply(b,multiply(b,c_0))) = multiply(c_0,multiply(c_0,b)). [back_rewrite(37632),rewrite([42217(9),42289(6),30(7)]),flip(a)].
% 54.76/55.06 42413 multiply(c_0,multiply(a,multiply(a,b))) = multiply(a,multiply(c_0,c_0)). [back_rewrite(42086),rewrite([42291(14)])].
% 54.76/55.06 42519 multiply(b,multiply(c_0,multiply(a,A))) = multiply(a,multiply(c_0,multiply(b,A))). [para(42289(a,1),12(a,1,1)),rewrite([12(6),12(5),12(11)]),flip(a)].
% 54.76/55.06 42520 add(multiply(a,multiply(c_0,b)),multiply(b,A)) = multiply(b,add(A,multiply(c_0,a))). [para(42289(a,1),14(a,1,1)),rewrite([7(13)])].
% 54.76/55.06 42541 add(multiply(a,multiply(c_0,b)),multiply(A,multiply(B,a))) = multiply(add(multiply(A,B),multiply(b,c_0)),a). [para(42289(a,1),250(a,1,1))].
% 54.76/55.06 42670 multiply(a,multiply(c_0,multiply(c_0,multiply(b,A)))) = multiply(c_0,multiply(c_0,multiply(c_0,A))). [para(42290(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 42754 multiply(c_0,multiply(a,multiply(c_0,c_0))) = multiply(c_0,multiply(b,b)). [para(42363(a,1),23(a,1,2,2)),rewrite([42413(8)])].
% 54.76/55.06 42838 multiply(a,multiply(c_0,multiply(a,multiply(c_0,multiply(b,b))))) = c_0. [back_rewrite(41859),rewrite([42754(10)])].
% 54.76/55.06 42903 multiply(a,multiply(b,multiply(b,multiply(c_0,A)))) = multiply(c_0,multiply(c_0,multiply(b,A))). [para(42364(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 43023 multiply(c_0,multiply(a,multiply(a,multiply(b,A)))) = multiply(a,multiply(c_0,multiply(c_0,A))). [para(42413(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 43031 multiply(b,add(A,multiply(c_0,multiply(a,a)))) = add(multiply(a,multiply(c_0,c_0)),multiply(b,A)). [para(42413(a,1),35(a,2,1)),rewrite([41973(8)])].
% 54.76/55.06 43091 multiply(a,multiply(a,multiply(c_0,c_0))) = multiply(a,multiply(b,b)). [para(42413(a,1),37931(a,1,2,2,2)),rewrite([42754(9),38033(9),42413(13)]),flip(a)].
% 54.76/55.06 43106 multiply(c_0,multiply(a,multiply(c_0,multiply(c_0,A)))) = multiply(c_0,multiply(b,multiply(b,A))). [para(42754(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 43199 multiply(c_0,multiply(a,multiply(c_0,multiply(b,b)))) = multiply(a,multiply(a,c_0)). [para(42838(a,1),41906(a,1,2,2)),flip(a)].
% 54.76/55.06 43400 multiply(a,add(A,multiply(a,multiply(c_0,c_0)))) = multiply(a,add(A,multiply(b,b))). [para(43091(a,1),14(a,1,1)),rewrite([14(8),7(5),7(13)]),flip(a)].
% 54.76/55.06 43460 multiply(a,multiply(a,multiply(b,b))) = multiply(c_0,c_0). [para(43091(a,1),41906(a,1,2))].
% 54.76/55.06 43462 multiply(a,multiply(a,multiply(b,multiply(b,A)))) = multiply(c_0,multiply(c_0,A)). [para(43460(a,1),12(a,1,1)),rewrite([12(4),12(11),12(10)]),flip(a)].
% 54.76/55.06 43465 multiply(c_0,multiply(a,multiply(b,b))) = multiply(b,multiply(c_0,c_0)). [para(43460(a,1),30(a,1,2)),flip(a)].
% 54.76/55.06 43511 multiply(c_0,multiply(a,multiply(b,multiply(b,A)))) = multiply(b,multiply(c_0,multiply(c_0,A))). [para(43465(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 43726 add(multiply(c_0,b),multiply(a,multiply(b,multiply(c_0,multiply(b,multiply(c_0,b)))))) = multiply(add(b,c_0),multiply(c_0,multiply(a,a))). [para(38033(a,1),70(a,1,2)),rewrite([7(18),41490(31)])].
% 54.76/55.06 44030 multiply(c_0,multiply(add(A,multiply(a,a)),c_0)) = multiply(add(b,multiply(c_0,A)),c_0). [para(14(a,1),38852(a,1,1)),rewrite([12(8),7(12)])].
% 54.76/55.06 44098 multiply(a,multiply(b,multiply(b,b))) = multiply(b,multiply(b,c_0)). [para(43460(a,1),39292(a,1,2,2)),rewrite([42214(7)]),flip(a)].
% 54.76/55.06 44169 multiply(c_0,multiply(b,multiply(b,b))) = c_0. [para(44098(a,1),30(a,1,2)),rewrite([106(7)]),flip(a)].
% 54.76/55.06 44177 multiply(c_0,multiply(b,multiply(b,add(b,c_0)))) = add(c_0,multiply(c_0,a)). [para(44098(a,1),1136(a,1,2)),rewrite([36900(9),44098(18),14(17),14(14)]),flip(a)].
% 54.76/55.06 44178 multiply(c_0,add(A,multiply(b,multiply(b,b)))) = add(c_0,multiply(c_0,A)). [para(44098(a,1),118(a,1,2,2,2,2)),rewrite([42364(9),42290(8),24(8),7(11)]),flip(a)].
% 54.76/55.06 44222 multiply(c_0,multiply(b,multiply(b,multiply(b,A)))) = multiply(c_0,A). [para(44169(a,1),12(a,1,1)),rewrite([12(9),12(8)]),flip(a)].
% 54.76/55.06 44257 multiply(c_0,multiply(b,multiply(b,add(c_0,multiply(b,A))))) = multiply(c_0,add(A,a)). [para(31(a,1),44222(a,1,2,2,2))].
% 54.76/55.06 44639 multiply(b,add(A,multiply(c_0,multiply(c_0,multiply(b,B))))) = add(multiply(c_0,multiply(a,B)),multiply(b,A)). [para(41210(a,1),14(a,1,1)),rewrite([7(15)]),flip(a)].
% 54.76/55.06 44694 multiply(c_0,multiply(a,multiply(b,c_0))) = multiply(b,multiply(c_0,multiply(c_0,a))). [para(37563(a,1),41210(a,1,2,2)),flip(a)].
% 54.76/55.06 44768 multiply(b,multiply(add(b,c_0),multiply(b,c_0))) = add(c_0,multiply(b,multiply(c_0,multiply(b,c_0)))). [para(19(a,1),954(a,1,2,1,2)),rewrite([30(18)])].
% 54.76/55.06 44823 multiply(a,multiply(add(A,multiply(a,multiply(a,c_0))),B)) = multiply(add(c_0,multiply(a,A)),B). [para(41860(a,1),12(a,1,1)),flip(a)].
% 54.76/55.06 45035 multiply(a,multiply(c_0,multiply(c_0,a))) = multiply(b,c_0). [para(34(a,1),42519(a,1,2)),rewrite([30(10)]),flip(a)].
% 54.76/55.06 45036 multiply(a,multiply(c_0,multiply(c_0,multiply(a,A)))) = multiply(b,multiply(c_0,A)). [para(37(a,1),42519(a,1,2)),rewrite([30(12)]),flip(a)].
% 54.76/55.06 45089 multiply(a,multiply(c_0,multiply(b,multiply(c_0,c_0)))) = multiply(b,multiply(c_0,multiply(b,b))). [para(42754(a,1),42519(a,1,2)),flip(a)].
% 54.76/55.06 45097 multiply(a,add(A,multiply(c_0,multiply(c_0,a)))) = add(multiply(b,c_0),multiply(a,A)). [para(45035(a,1),14(a,1,1)),rewrite([7(13)]),flip(a)].
% 54.76/55.06 45099 multiply(c_0,multiply(c_0,multiply(c_0,a))) = multiply(b,multiply(b,c_0)). [para(45035(a,1),30(a,1,2)),flip(a)].
% 54.76/55.06 45132 multiply(a,multiply(a,multiply(b,c_0))) = multiply(c_0,multiply(c_0,a)). [para(45035(a,1),41906(a,1,2,2))].
% 54.76/55.06 45133 multiply(a,multiply(c_0,multiply(b,multiply(c_0,multiply(c_0,a))))) = multiply(b,multiply(c_0,multiply(b,c_0))). [para(45035(a,1),42519(a,1,2,2)),flip(a)].
% 54.76/55.06 45156 multiply(c_0,multiply(c_0,multiply(c_0,multiply(a,A)))) = multiply(b,multiply(b,multiply(c_0,A))). [para(45099(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 45185 multiply(a,multiply(a,multiply(b,multiply(c_0,A)))) = multiply(c_0,multiply(c_0,multiply(a,A))). [para(45132(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 45374 multiply(a,multiply(a,multiply(c_0,multiply(a,b)))) = multiply(b,c_0). [para(43199(a,1),43462(a,2,2)),rewrite([30(12),42363(10),30(9),38826(16)])].
% 54.76/55.06 45404 multiply(c_0,multiply(a,b)) = multiply(a,multiply(b,c_0)). [para(45374(a,1),41906(a,1,2)),flip(a)].
% 54.76/55.06 45410 multiply(c_0,multiply(a,multiply(b,A))) = multiply(a,multiply(b,multiply(c_0,A))). [para(45404(a,1),12(a,1,1)),rewrite([12(6),12(5),12(11)]),flip(a)].
% 54.76/55.06 45478 multiply(a,multiply(c_0,multiply(b,b))) = multiply(c_0,multiply(b,c_0)). [para(45404(a,1),42519(a,1,2)),rewrite([30(7)]),flip(a)].
% 54.76/55.06 45486 multiply(b,multiply(c_0,multiply(c_0,a))) = multiply(a,multiply(b,multiply(c_0,c_0))). [back_rewrite(44694),rewrite([45410(7)]),flip(a)].
% 54.76/55.06 45490 multiply(a,multiply(b,multiply(c_0,multiply(b,A)))) = multiply(b,multiply(c_0,multiply(c_0,A))). [back_rewrite(43511),rewrite([45410(8)])].
% 54.76/55.06 45491 multiply(a,multiply(b,multiply(c_0,b))) = multiply(b,multiply(c_0,c_0)). [back_rewrite(43465),rewrite([45410(7)])].
% 54.76/55.06 45508 multiply(b,multiply(c_0,multiply(b,c_0))) = multiply(a,multiply(a,b)). [back_rewrite(45133),rewrite([45486(9),45410(10),41367(9),39291(8)]),flip(a)].
% 54.76/55.06 45511 multiply(add(b,c_0),multiply(c_0,multiply(a,a))) = add(multiply(c_0,b),multiply(a,multiply(c_0,c_0))). [back_rewrite(43726),rewrite([45490(14),39351(11),42519(10),19(8)]),flip(a)].
% 54.76/55.06 45525 multiply(b,multiply(add(b,c_0),multiply(b,c_0))) = add(c_0,multiply(a,multiply(a,b))). [back_rewrite(44768),rewrite([45508(17)])].
% 54.76/55.06 45527 multiply(add(b,multiply(c_0,a)),multiply(a,b)) = add(multiply(c_0,b),multiply(a,multiply(c_0,c_0))). [back_rewrite(42092),rewrite([45511(18)])].
% 54.76/55.06 45595 multiply(add(b,c_0),multiply(add(A,multiply(a,A)),B)) = multiply(add(b,multiply(c_0,a)),multiply(A,B)). [para(862(a,1),1033(a,1,1,2)),rewrite([10(9,R),7(8),35046(8),10(9,R),7(8),36307(8)]),flip(a)].
% 54.76/55.06 46063 multiply(a,multiply(c_0,multiply(b,multiply(b,A)))) = multiply(c_0,multiply(b,multiply(c_0,A))). [para(45478(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 46075 multiply(add(b,c_0),multiply(c_0,multiply(b,c_0))) = multiply(c_0,multiply(c_0,multiply(b,add(b,c_0)))). [para(45478(a,1),1136(a,1,2)),rewrite([45478(22),14(21),14(18)])].
% 54.76/55.06 46119 multiply(c_0,multiply(b,multiply(c_0,b))) = multiply(a,c_0). [para(45491(a,1),30(a,1,2)),rewrite([37929(7)]),flip(a)].
% 54.76/55.06 46178 multiply(c_0,multiply(b,multiply(c_0,multiply(b,A)))) = multiply(a,multiply(c_0,A)). [para(46119(a,1),12(a,1,1)),rewrite([12(4),12(11),12(10)]),flip(a)].
% 54.76/55.06 46179 multiply(c_0,add(A,multiply(b,multiply(c_0,b)))) = add(multiply(a,c_0),multiply(c_0,A)). [para(46119(a,1),14(a,1,1)),rewrite([7(13)]),flip(a)].
% 54.76/55.06 46220 multiply(c_0,multiply(a,multiply(c_0,b))) = multiply(a,multiply(c_0,multiply(b,c_0))). [para(46119(a,1),41210(a,1,2,2)),rewrite([42519(7)]),flip(a)].
% 54.76/55.06 46221 multiply(a,multiply(a,multiply(c_0,b))) = multiply(c_0,multiply(a,c_0)). [para(46119(a,1),43462(a,2,2)),rewrite([38032(10),30(7)])].
% 54.76/55.06 46470 multiply(b,multiply(c_0,multiply(b,multiply(c_0,A)))) = multiply(a,multiply(a,multiply(b,A))). [para(45508(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 46511 multiply(a,multiply(a,multiply(c_0,multiply(b,A)))) = multiply(c_0,multiply(a,multiply(c_0,A))). [para(46221(a,1),12(a,1,1)),rewrite([12(6),12(5),12(13),12(12)]),flip(a)].
% 54.76/55.06 46519 add(multiply(A,multiply(c_0,b)),multiply(c_0,multiply(a,c_0))) = multiply(add(A,multiply(a,a)),multiply(c_0,b)). [para(46221(a,1),28(a,1,2))].
% 54.76/55.06 46527 multiply(add(A,multiply(a,multiply(a,c_0))),b) = add(multiply(c_0,multiply(a,c_0)),multiply(A,b)). [para(46221(a,1),249(a,1,1)),flip(a)].
% 54.76/55.06 46561 multiply(a,multiply(c_0,multiply(a,c_0))) = multiply(c_0,b). [para(46221(a,1),41906(a,1,2))].
% 54.76/55.06 46562 multiply(c_0,multiply(c_0,multiply(a,c_0))) = multiply(b,multiply(c_0,b)). [para(46221(a,1),38831(a,1,2))].
% 54.76/55.06 46572 multiply(a,add(A,multiply(c_0,multiply(a,c_0)))) = add(multiply(c_0,b),multiply(a,A)). [para(46561(a,1),14(a,1,1)),rewrite([7(13)]),flip(a)].
% 54.76/55.06 46579 multiply(c_0,multiply(c_0,add(b,multiply(a,c_0)))) = multiply(add(b,c_0),multiply(c_0,b)). [para(46561(a,1),1136(a,1,2)),rewrite([46561(20),7(17),14(17)]),flip(a)].
% 54.76/55.06 47040 multiply(b,multiply(c_0,multiply(c_0,add(b,c_0)))) = multiply(c_0,add(a,multiply(a,a))). [para(44177(a,1),37615(a,1,2,2,2)),rewrite([37628(11),45410(18),45490(18)]),flip(a)].
% 54.76/55.06 47043 multiply(c_0,multiply(b,multiply(c_0,add(b,c_0)))) = multiply(a,add(c_0,multiply(c_0,a))). [para(44177(a,1),42519(a,2,2)),rewrite([45410(10),30(11)])].
% 54.76/55.06 47044 multiply(a,multiply(a,multiply(b,add(b,c_0)))) = multiply(c_0,add(c_0,multiply(c_0,a))). [para(44177(a,1),43462(a,2,2)),rewrite([10336(12),106(11)])].
% 54.76/55.06 47089 multiply(c_0,multiply(add(b,c_0),multiply(b,b))) = add(c_0,multiply(a,multiply(a,b))). [para(42363(a,1),44178(a,2,2)),rewrite([7(12),16(12)])].
% 54.76/55.06 47093 multiply(c_0,multiply(b,multiply(add(b,c_0),b))) = add(c_0,multiply(a,c_0)). [para(46119(a,1),44178(a,2,2)),rewrite([7(12),14(12),16(9)])].
% 54.76/55.06 47222 multiply(add(A,multiply(c_0,a)),multiply(a,multiply(b,multiply(c_0,B)))) = multiply(add(b,multiply(A,a)),multiply(b,multiply(c_0,B))). [para(45036(a,1),278(a,1,2,2)),rewrite([45036(23)])].
% 54.76/55.06 47223 multiply(add(A,multiply(B,multiply(a,a))),multiply(b,multiply(c_0,C))) = multiply(add(B,multiply(A,a)),multiply(c_0,multiply(c_0,multiply(a,C)))). [para(45036(a,1),347(a,1,2,2,2)),rewrite([45185(11),45036(23)]),flip(a)].
% 54.76/55.06 47226 multiply(c_0,multiply(b,multiply(c_0,c_0))) = multiply(a,multiply(c_0,a)). [para(45132(a,1),45036(a,1,2,2,2)),rewrite([45099(9),37563(8),45410(13),30(14)]),flip(a)].
% 54.76/55.06 47237 multiply(b,multiply(c_0,multiply(b,b))) = multiply(a,multiply(a,multiply(c_0,a))). [back_rewrite(45089),rewrite([47226(8)]),flip(a)].
% 54.76/55.06 47241 multiply(c_0,add(A,multiply(b,multiply(c_0,c_0)))) = add(multiply(a,multiply(c_0,a)),multiply(c_0,A)). [para(47226(a,1),14(a,1,1)),rewrite([7(15)]),flip(a)].
% 54.76/55.06 47307 multiply(a,multiply(b,multiply(add(b,c_0),multiply(a,A)))) = multiply(c_0,multiply(a,multiply(add(b,c_0),A))). [para(1136(a,2),45410(a,2,2,2)),rewrite([35(7),7(7),16(7)]),flip(a)].
% 54.76/55.06 47919 multiply(c_0,multiply(b,multiply(c_0,multiply(add(b,c_0),A)))) = multiply(a,multiply(add(b,c_0),multiply(a,A))). [para(1136(a,2),46178(a,2,2)),rewrite([35(8),7(8),16(8)])].
% 54.76/55.06 47950 add(multiply(A,multiply(c_0,b)),multiply(a,multiply(c_0,multiply(b,c_0)))) = multiply(add(A,multiply(c_0,a)),multiply(c_0,b)). [para(46220(a,1),28(a,1,2))].
% 54.76/55.06 48251 multiply(c_0,multiply(a,add(b,multiply(a,b)))) = multiply(a,multiply(add(b,c_0),c_0)). [para(47093(a,1),45410(a,2,2,2)),rewrite([10338(11),38032(10),35(17),7(17),16(17)])].
% 54.76/55.06 48253 multiply(a,multiply(c_0,multiply(add(b,c_0),b))) = multiply(c_0,multiply(add(b,c_0),c_0)). [para(47093(a,1),46178(a,1,2,2)),rewrite([35(8),7(8),16(8)]),flip(a)].
% 54.76/55.06 49243 multiply(add(b,c_0),multiply(c_0,multiply(c_0,add(b,c_0)))) = add(c_0,multiply(c_0,a)). [para(42290(a,1),18945(a,1,2,2)),rewrite([14(14),14(11),40955(22),41192(19)])].
% 54.76/55.06 49569 multiply(c_0,multiply(c_0,multiply(b,add(b,c_0)))) = multiply(a,multiply(a,add(b,c_0))). [para(41974(a,1),19936(a,1,2,2)),rewrite([45508(9),7(14),10(14),7(13),10(14,R),7(13),14(13),14(10),36307(11),7(10),46075(16)]),flip(a)].
% 54.76/55.06 49588 multiply(add(b,c_0),multiply(b,multiply(c_0,b))) = multiply(a,add(b,c_0)). [para(46119(a,1),19936(a,1,2,2)),rewrite([38032(9),7(10),10(10),7(9),10(10,R),7(9),14(9),36307(9),7(8)]),flip(a)].
% 54.76/55.06 49591 multiply(add(b,multiply(c_0,a)),multiply(c_0,b)) = multiply(add(b,c_0),multiply(c_0,multiply(a,c_0))). [para(46562(a,1),19936(a,1,2,2)),rewrite([42519(9),7(16),10(16,R),7(15),47950(15),36307(13),7(12)])].
% 54.76/55.06 49671 multiply(add(b,c_0),multiply(add(b,c_0),multiply(add(b,c_0),multiply(a,add(b,c_0))))) = multiply(a,add(b,c_0)). [para(49588(a,1),23(a,1,2,2,2)),rewrite([49588(26)])].
% 54.76/55.06 49677 multiply(b,multiply(b,multiply(c_0,add(b,c_0)))) = multiply(a,add(b,c_0)). [para(49588(a,1),324(a,1,2,2,2)),rewrite([30(9),49588(18)])].
% 54.76/55.06 49697 multiply(b,multiply(b,multiply(add(b,c_0),add(b,c_0)))) = add(b,add(c_0,multiply(a,add(b,c_0)))). [para(49677(a,1),333(a,2,2,2)),rewrite([7(16),14(16),16(13)])].
% 54.76/55.06 49702 multiply(a,multiply(c_0,multiply(a,add(b,c_0)))) = multiply(c_0,add(b,multiply(c_0,a))). [para(49677(a,1),42519(a,2,2,2)),rewrite([45410(12),47040(11),39418(10),30(9)]),flip(a)].
% 54.76/55.06 49703 multiply(c_0,multiply(a,add(c_0,multiply(c_0,a)))) = multiply(a,multiply(a,multiply(c_0,add(b,c_0)))). [para(49677(a,1),43462(a,1,2,2,2)),rewrite([30(9),47043(19)]),flip(a)].
% 54.76/55.06 49704 multiply(c_0,multiply(a,multiply(a,add(b,c_0)))) = multiply(a,multiply(c_0,add(c_0,multiply(c_0,a)))). [para(49677(a,1),45410(a,1,2,2)),rewrite([47043(20),30(19)])].
% 54.76/55.06 49779 multiply(add(b,multiply(c_0,a)),multiply(b,multiply(c_0,c_0))) = multiply(a,add(b,c_0)). [para(49588(a,1),23251(a,2)),rewrite([12(18),12(17),38032(16),45404(13),30(14),12(13),12(12),45508(11),42413(10),30(9),41367(8),47223(13),45404(11),45410(12),47222(13)])].
% 54.76/55.06 49825 multiply(add(b,c_0),multiply(c_0,multiply(a,c_0))) = multiply(b,multiply(c_0,add(b,multiply(a,c_0)))). [para(46221(a,1),23886(a,2,2)),rewrite([41932(12),46527(10),7(10),14(10)]),flip(a)].
% 54.76/55.06 49837 multiply(add(b,multiply(c_0,a)),multiply(c_0,b)) = multiply(b,multiply(c_0,add(b,multiply(a,c_0)))). [back_rewrite(49591),rewrite([49825(18)])].
% 54.76/55.06 50573 multiply(b,multiply(add(b,c_0),multiply(c_0,c_0))) = add(multiply(a,c_0),multiply(c_0,multiply(a,a))). [para(41367(a,1),37932(a,2,2)),rewrite([7(12),16(12)])].
% 54.76/55.06 50679 multiply(b,multiply(add(b,c_0),multiply(c_0,b))) = add(multiply(a,b),multiply(c_0,a)). [para(41192(a,1),38034(a,2,2)),rewrite([7(12),16(12)])].
% 54.76/55.06 50776 multiply(c_0,multiply(a,add(A,multiply(a,c_0)))) = add(multiply(b,c_0),multiply(c_0,multiply(a,A))). [para(14(a,1),38832(a,1,2))].
% 54.76/55.06 50805 multiply(a,multiply(c_0,add(c_0,multiply(c_0,a)))) = multiply(add(b,multiply(a,c_0)),c_0). [para(42413(a,1),38832(a,2,2)),rewrite([14(12),14(9),49704(9),28(18)])].
% 54.76/55.06 50828 multiply(c_0,multiply(a,multiply(a,add(b,c_0)))) = multiply(add(b,multiply(a,c_0)),c_0). [back_rewrite(49704),rewrite([50805(18)])].
% 54.76/55.06 51066 multiply(b,multiply(add(b,multiply(a,c_0)),c_0)) = multiply(a,multiply(c_0,multiply(c_0,add(b,c_0)))). [para(39424(a,1),37931(a,1,2,2)),rewrite([43031(10),7(10),28(10)])].
% 54.76/55.06 51141 multiply(add(b,multiply(a,c_0)),multiply(b,A)) = multiply(b,multiply(add(b,multiply(c_0,a)),A)). [para(37929(a,1),1121(a,1,1,2)),rewrite([12(16),44639(18),7(16),28(16)])].
% 54.76/55.06 51420 add(additive_identity,add(multiply(a,b),multiply(A,B))) = add(multiply(A,B),multiply(a,b)). [para(7(a,1),40706(a,1,2))].
% 54.76/55.06 51482 multiply(c_0,multiply(b,multiply(b,add(A,c_0)))) = multiply(c_0,add(a,multiply(b,multiply(b,A)))). [para(14(a,1),41599(a,1,2,2))].
% 54.76/55.06 51642 multiply(c_0,add(A,multiply(c_0,multiply(add(b,c_0),multiply(c_0,A))))) = multiply(a,multiply(a,multiply(c_0,A))). [para(42146(a,1),251(a,1,1,2)),rewrite([36307(9),12(6),12(5),12(15),12(14)]),flip(a)].
% 54.76/55.06 51717 multiply(b,multiply(add(b,multiply(c_0,a)),multiply(b,multiply(b,A)))) = multiply(add(b,multiply(a,c_0)),A). [para(42520(a,1),348(a,1,1)),rewrite([12(12),12(22),12(21),44169(21)])].
% 54.76/55.06 51821 multiply(a,multiply(c_0,add(c_0,multiply(a,c_0)))) = add(multiply(c_0,b),multiply(a,multiply(c_0,c_0))). [para(47093(a,1),42670(a,1,2,2)),rewrite([39431(20),45527(18)])].
% 54.76/55.06 51886 multiply(c_0,multiply(c_0,add(b,multiply(a,b)))) = multiply(a,multiply(b,multiply(add(b,c_0),c_0))). [para(47093(a,1),42903(a,1,2,2,2)),rewrite([35(9),7(9),16(9),10338(20),38032(19)]),flip(a)].
% 54.76/55.06 51899 multiply(c_0,multiply(a,multiply(a,multiply(add(b,c_0),A)))) = multiply(a,multiply(c_0,multiply(add(b,c_0),multiply(a,A)))). [para(1136(a,2),43023(a,2,2,2)),rewrite([35(8),7(8),16(8)])].
% 54.76/55.06 51979 multiply(a,multiply(add(A,multiply(a,c_0)),c_0)) = multiply(a,add(multiply(A,c_0),multiply(b,b))). [para(28(a,1),43400(a,1,2))].
% 54.76/55.06 52147 multiply(c_0,multiply(add(A,multiply(a,a)),multiply(c_0,B))) = multiply(add(b,multiply(c_0,A)),multiply(c_0,B)). [para(44030(a,1),12(a,1,1)),rewrite([12(7),12(15)]),flip(a)].
% 54.76/55.06 52282 multiply(c_0,multiply(b,multiply(add(b,c_0),c_0))) = multiply(add(c_0,multiply(a,c_0)),a). [para(37929(a,1),44257(a,1,2,2,2,2)),rewrite([35(9),7(9),16(9),7(17),47241(18),7(18),28(18)])].
% 54.76/55.06 52286 multiply(c_0,multiply(add(b,c_0),multiply(b,c_0))) = add(multiply(c_0,a),multiply(a,multiply(a,c_0))). [para(45508(a,1),44257(a,1,2,2,2,2)),rewrite([35(11),45404(7),7(11),28(11),23886(10),7(17),42144(18),7(18)])].
% 54.76/55.06 52565 multiply(a,multiply(add(b,c_0),multiply(c_0,a))) = multiply(add(b,multiply(c_0,a)),c_0). [para(46221(a,1),45097(a,2,2)),rewrite([42541(12),7(8),16(8),12(8),28(18)])].
% 54.76/55.06 52609 multiply(c_0,multiply(c_0,add(c_0,multiply(c_0,a)))) = multiply(a,multiply(c_0,multiply(c_0,add(b,c_0)))). [para(39424(a,1),45156(a,2,2,2)),rewrite([43106(13),51482(11),44178(11),43031(19),7(19),28(19),51066(18)])].
% 54.76/55.06 52746 multiply(a,multiply(c_0,multiply(add(b,c_0),multiply(a,c_0)))) = multiply(b,multiply(add(b,c_0),c_0)). [para(42146(a,1),45490(a,2,2,2)),rewrite([47919(13),30(12),38832(21),16(19)])].
% 54.76/55.06 52818 multiply(a,multiply(a,multiply(add(b,multiply(a,b)),c_0))) = add(multiply(b,c_0),multiply(c_0,multiply(c_0,a))). [para(45525(a,1),43462(a,1,2,2,2)),rewrite([35(11),45404(7),7(11),28(11),52286(21),38832(22)])].
% 54.76/55.06 52883 multiply(c_0,multiply(add(b,c_0),multiply(c_0,b))) = add(multiply(a,c_0),multiply(c_0,multiply(a,a))). [para(39351(a,1),46179(a,2,2)),rewrite([7(12),16(12)])].
% 54.76/55.06 52944 multiply(b,multiply(c_0,multiply(add(b,c_0),c_0))) = multiply(a,multiply(a,add(b,multiply(a,b)))). [para(47093(a,1),46470(a,1,2,2,2)),rewrite([35(9),7(9),16(9),10338(20),38032(19)])].
% 54.76/55.06 52953 multiply(b,multiply(b,multiply(c_0,add(b,multiply(a,c_0))))) = multiply(a,add(b,multiply(a,c_0))). [para(45525(a,1),46470(a,2,2,2)),rewrite([52286(12),35(13),42289(12),7(13),46519(13),52147(12),49837(10),42084(21),7(21),39293(22),7(17)])].
% 54.76/55.06 52986 multiply(c_0,multiply(a,multiply(add(c_0,multiply(a,c_0)),a))) = multiply(a,multiply(add(b,c_0),b)). [para(37938(a,1),46511(a,1,2,2,2)),rewrite([51821(10),43400(11),7(8),16(8),52282(18)]),flip(a)].
% 54.76/55.06 52998 multiply(a,multiply(c_0,add(A,multiply(a,c_0)))) = add(multiply(c_0,b),multiply(a,multiply(c_0,A))). [para(14(a,1),46572(a,1,2))].
% 54.76/55.06 53051 multiply(c_0,add(multiply(a,b),multiply(c_0,a))) = multiply(a,multiply(add(b,multiply(a,b)),c_0)). [para(46579(a,1),46063(a,2,2,2)),rewrite([52953(13),50776(10),45404(9),28(10),50679(19)]),flip(a)].
% 54.76/55.06 53113 multiply(add(b,multiply(c_0,add(a,multiply(a,a)))),multiply(c_0,A)) = multiply(c_0,multiply(a,multiply(c_0,A))). [para(47040(a,1),1121(a,1,1,2)),rewrite([12(22),51642(24),30(20)])].
% 54.76/55.06 53168 multiply(b,multiply(c_0,multiply(add(b,multiply(a,b)),c_0))) = multiply(a,add(multiply(a,b),multiply(c_0,a))). [para(47089(a,1),46470(a,1,2,2,2)),rewrite([35(11),45404(7),7(11),28(11),162(22),47237(21),41928(23),7(19)])].
% 54.76/55.06 53446 multiply(c_0,multiply(c_0,multiply(a,multiply(add(b,c_0),c_0)))) = multiply(a,add(b,multiply(a,b))). [para(48251(a,1),42670(a,2,2,2)),rewrite([30(12),51886(11),45410(12),52944(11),22105(12),42099(10),7(10),39293(11),7(6)]),flip(a)].
% 54.76/55.06 53452 multiply(add(b,c_0),multiply(c_0,multiply(add(b,c_0),c_0))) = multiply(c_0,multiply(c_0,multiply(add(b,c_0),add(b,c_0)))). [para(48253(a,1),1136(a,1,2)),rewrite([48253(28),14(27),14(24)])].
% 54.76/55.06 53785 multiply(add(b,c_0),multiply(c_0,multiply(c_0,multiply(add(b,c_0),A)))) = multiply(add(b,c_0),multiply(a,A)). [para(49243(a,1),12(a,1,1)),rewrite([36(6),7(3),12(17),12(16)]),flip(a)].
% 54.76/55.06 54001 multiply(a,multiply(c_0,multiply(a,multiply(add(b,c_0),A)))) = multiply(c_0,multiply(add(b,multiply(c_0,a)),A)). [para(49702(a,1),12(a,1,1)),rewrite([12(8),12(17),12(16)]),flip(a)].
% 54.76/55.06 54527 multiply(a,multiply(c_0,multiply(add(b,c_0),multiply(a,A)))) = multiply(add(b,multiply(a,c_0)),multiply(c_0,A)). [para(50828(a,1),12(a,1,1)),rewrite([12(8),12(17),12(16),51899(18)]),flip(a)].
% 54.76/55.06 54529 multiply(add(b,multiply(a,c_0)),multiply(c_0,c_0)) = multiply(b,multiply(add(b,c_0),c_0)). [back_rewrite(52746),rewrite([54527(11)])].
% 54.76/55.06 54557 add(multiply(a,b),add(multiply(A,B),multiply(a,b))) = multiply(A,B). [para(51420(a,1),35048(a,1,1)),rewrite([7(9),7(19),36307(19),185(12)])].
% 54.76/55.06 54786 multiply(a,multiply(add(b,c_0),multiply(c_0,multiply(a,A)))) = multiply(add(b,multiply(c_0,a)),multiply(c_0,A)). [para(52565(a,1),12(a,1,1)),rewrite([12(8),12(17),12(16)]),flip(a)].
% 54.76/55.06 54809 multiply(c_0,add(A,add(B,multiply(a,add(A,B))))) = multiply(add(b,c_0),multiply(a,add(A,B))). [para(1136(a,1),2977(a,1,2)),rewrite([14(11),10(8,R),10(7,R),14(6),10(6,R),7(5),14(15),7(12)])].
% 54.76/55.06 55058 multiply(c_0,multiply(c_0,multiply(add(b,c_0),add(b,c_0)))) = multiply(a,add(b,c_0)). [para(48253(a,1),2997(a,1,2,2,2,2,2)),rewrite([14(25),14(22),53785(21),49671(17),48253(17),53452(16)]),flip(a)].
% 54.76/55.06 55059 multiply(add(b,c_0),multiply(c_0,multiply(add(b,c_0),c_0))) = multiply(a,add(b,c_0)). [back_rewrite(53452),rewrite([55058(22)])].
% 54.76/55.06 55461 multiply(c_0,multiply(a,multiply(add(c_0,multiply(a,c_0)),A))) = multiply(add(b,multiply(c_0,a)),multiply(c_0,A)). [para(41906(a,1),3029(a,1,2,1,2)),rewrite([7(10),335(10),41906(24),7(19),335(19),44823(19),7(16),16(16),10(14,R),7(13),40551(13),14(12),36307(12),12(9),348(25),41949(23),45595(20)])].
% 54.76/55.06 55467 multiply(add(b,multiply(c_0,a)),multiply(c_0,a)) = multiply(a,multiply(add(b,c_0),b)). [back_rewrite(52986),rewrite([55461(11)])].
% 54.76/55.06 56025 multiply(add(b,c_0),multiply(a,add(b,c_0))) = multiply(add(b,multiply(a,c_0)),c_0). [para(55058(a,1),43106(a,1,2,2)),rewrite([50828(9),49697(19),54809(18)]),flip(a)].
% 54.76/55.06 56034 multiply(add(b,c_0),multiply(c_0,multiply(add(b,c_0),multiply(c_0,A)))) = multiply(a,multiply(add(b,c_0),A)). [para(55059(a,1),12(a,1,1)),rewrite([12(6),12(17),12(16)]),flip(a)].
% 54.76/55.06 56036 multiply(a,multiply(b,add(b,c_0))) = multiply(add(b,c_0),c_0). [para(55059(a,1),22(a,1,2,2,2,2)),rewrite([56034(17),56025(10),51979(9),7(8),14(8)])].
% 54.76/55.06 56042 multiply(c_0,add(c_0,multiply(c_0,a))) = multiply(a,multiply(add(b,c_0),c_0)). [back_rewrite(47044),rewrite([56036(8)]),flip(a)].
% 54.76/55.06 56045 multiply(c_0,multiply(a,multiply(add(b,c_0),c_0))) = multiply(a,multiply(c_0,multiply(c_0,add(b,c_0)))). [back_rewrite(52609),rewrite([56042(8)])].
% 54.76/55.06 56047 multiply(a,add(b,multiply(a,b))) = add(c_0,multiply(c_0,a)). [back_rewrite(53446),rewrite([56045(10),43106(11),51482(9),44178(9)]),flip(a)].
% 54.76/55.06 56057 multiply(a,multiply(b,multiply(add(b,c_0),A))) = multiply(add(b,c_0),multiply(c_0,A)). [para(56036(a,1),12(a,1,1)),rewrite([12(6),12(13)]),flip(a)].
% 54.76/55.06 56059 multiply(c_0,multiply(b,add(b,c_0))) = multiply(b,multiply(add(b,c_0),c_0)). [para(56036(a,1),30(a,1,2)),flip(a)].
% 54.76/55.06 56074 multiply(add(b,c_0),multiply(c_0,b)) = multiply(b,multiply(add(b,c_0),c_0)). [para(56036(a,1),3161(a,1,2,2,2,2,2,2)),rewrite([56057(13),50573(12),39293(13),7(8),30(10),46579(9),56059(14)])].
% 54.76/55.06 56083 multiply(add(b,c_0),multiply(c_0,multiply(a,A))) = multiply(c_0,multiply(a,multiply(add(b,c_0),A))). [back_rewrite(47307),rewrite([56057(10)])].
% 54.76/55.06 56093 multiply(add(c_0,multiply(a,c_0)),a) = multiply(a,multiply(a,add(b,c_0))). [back_rewrite(49569),rewrite([56059(8),52282(9)])].
% 54.76/55.06 56111 add(multiply(a,c_0),multiply(c_0,multiply(a,a))) = multiply(a,multiply(a,add(b,c_0))). [back_rewrite(52883),rewrite([56074(8),52282(9),56093(7)]),flip(a)].
% 54.76/55.06 56113 add(multiply(a,b),multiply(c_0,a)) = add(c_0,multiply(a,c_0)). [back_rewrite(50679),rewrite([56074(8),37938(9)]),flip(a)].
% 54.76/55.06 56120 multiply(add(b,multiply(c_0,a)),multiply(c_0,A)) = multiply(c_0,multiply(add(b,multiply(c_0,a)),A)). [back_rewrite(54786),rewrite([56083(9),54001(10)]),flip(a)].
% 54.76/55.06 56122 multiply(a,multiply(a,multiply(c_0,add(b,c_0)))) = add(multiply(c_0,b),multiply(a,multiply(c_0,c_0))). [back_rewrite(45511),rewrite([56083(9),862(7),49703(9)])].
% 54.76/55.06 56132 multiply(add(b,multiply(a,multiply(a,add(b,c_0)))),multiply(c_0,multiply(c_0,b))) = multiply(a,b). [back_rewrite(36700),rewrite([56111(10)])].
% 54.76/55.06 56134 multiply(b,multiply(c_0,multiply(add(b,multiply(a,b)),c_0))) = multiply(a,add(c_0,multiply(a,c_0))). [back_rewrite(53168),rewrite([56113(19)])].
% 54.76/55.06 56136 multiply(a,multiply(add(b,multiply(a,b)),c_0)) = multiply(c_0,add(c_0,multiply(a,c_0))). [back_rewrite(53051),rewrite([56113(8)]),flip(a)].
% 54.76/55.06 56139 multiply(a,multiply(add(b,c_0),b)) = multiply(c_0,add(b,c_0)). [back_rewrite(55467),rewrite([56120(9),95(8),39305(9),7(4)]),flip(a)].
% 54.76/55.06 56148 multiply(c_0,multiply(a,add(c_0,multiply(c_0,a)))) = add(multiply(c_0,b),multiply(a,multiply(c_0,c_0))). [back_rewrite(49703),rewrite([56122(18)])].
% 54.76/55.06 56155 add(multiply(c_0,b),multiply(a,multiply(c_0,c_0))) = add(multiply(b,c_0),multiply(c_0,multiply(c_0,a))). [back_rewrite(52818),rewrite([56136(10),52998(9)])].
% 54.76/55.06 56167 multiply(c_0,multiply(a,add(c_0,multiply(c_0,a)))) = add(multiply(b,c_0),multiply(c_0,multiply(c_0,a))). [back_rewrite(56148),rewrite([56155(18)])].
% 54.76/55.06 56199 multiply(add(b,multiply(a,b)),c_0) = multiply(c_0,add(b,c_0)). [para(56047(a,1),39292(a,1,2,2,2)),rewrite([56167(10),45097(11),28(9),35(15),7(15),16(15),56139(14)])].
% 54.76/55.06 56206 multiply(add(b,multiply(c_0,a)),multiply(b,A)) = multiply(b,multiply(add(b,multiply(a,c_0)),A)). [para(56047(a,1),23886(a,1,2,1,2)),rewrite([10(12),7(11),10(11,R),7(10),10(12,R),7(11),10(11),7(10),10(11,R),7(10),56113(10),36307(9),45595(18)]),flip(a)].
% 54.76/55.06 56214 multiply(a,add(b,c_0)) = add(c_0,multiply(c_0,a)). [para(56047(a,1),54557(a,1,2,1)),rewrite([7(12),10(12,R),7(11),56113(11),36307(10),14(7),56047(12)])].
% 54.76/55.06 56229 multiply(c_0,add(a,multiply(a,a))) = multiply(a,add(c_0,multiply(a,c_0))). [back_rewrite(56134),rewrite([56199(9),47040(9)])].
% 54.76/55.06 56246 multiply(add(b,multiply(c_0,a)),A) = multiply(add(b,multiply(a,c_0)),A). [back_rewrite(51717),rewrite([56206(11),51141(10),9744(12)])].
% 54.76/55.06 56248 add(c_0,multiply(c_0,a)) = add(c_0,multiply(a,c_0)). [back_rewrite(49779),rewrite([56246(11),51141(11),56246(10),54529(10),37938(9),56214(10)]),flip(a)].
% 54.76/55.06 56249 multiply(add(b,multiply(a,add(c_0,multiply(a,c_0)))),multiply(c_0,multiply(c_0,b))) = multiply(a,b). [back_rewrite(56132),rewrite([56214(7),56248(7)])].
% 54.76/55.06 56319 multiply(add(b,multiply(a,add(c_0,multiply(a,c_0)))),multiply(c_0,A)) = multiply(c_0,multiply(a,multiply(c_0,A))). [back_rewrite(53113),rewrite([56229(8)])].
% 54.76/55.06 56471 multiply(a,b) = c_0. [back_rewrite(56249),rewrite([56319(15),42290(8),8(7)]),flip(a)].
% 54.76/55.06 56472 $F # answer(prove_commutativity). [resolve(56471,a,20,a)].
% 54.76/55.06
% 54.76/55.06 % SZS output end Refutation
% 54.76/55.06 ============================== end of proof ==========================
% 54.76/55.06
% 54.76/55.06 ============================== STATISTICS ============================
% 54.76/55.06
% 54.76/55.06 Given=2576. Generated=1303751. Kept=56465. proofs=1.
% 54.76/55.06 Usable=846. Sos=9589. Demods=9296. Limbo=152, Disabled=45889. Hints=0.
% 54.76/55.06 Megabytes=54.26.
% 54.76/55.06 User_CPU=53.24, System_CPU=0.79, Wall_clock=54.
% 54.76/55.06
% 54.76/55.06 ============================== end of statistics =====================
% 54.76/55.06
% 54.76/55.06 ============================== end of search =========================
% 54.76/55.06
% 54.76/55.06 THEOREM PROVED
% 54.76/55.06 % SZS status Unsatisfiable
% 54.76/55.06
% 54.76/55.06 Exiting with 1 proof.
% 54.76/55.06
% 54.76/55.06 Process 9328 exit (max_proofs) Mon May 30 20:31:35 2022
% 54.76/55.06 Prover9 interrupted
%------------------------------------------------------------------------------