TSTP Solution File: GRP766-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP766-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 : Sat Jul 16 11:20:58 EDT 2022
% Result : Unsatisfiable 39.01s 39.32s
% Output : Refutation 39.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP766-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n008.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 Jun 13 21:54:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 39.01/39.32 ============================== Prover9 ===============================
% 39.01/39.32 Prover9 (32) version 2009-11A, November 2009.
% 39.01/39.32 Process 19119 was started by sandbox on n008.cluster.edu,
% 39.01/39.32 Mon Jun 13 21:54:53 2022
% 39.01/39.32 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18965_n008.cluster.edu".
% 39.01/39.32 ============================== end of head ===========================
% 39.01/39.32
% 39.01/39.32 ============================== INPUT =================================
% 39.01/39.32
% 39.01/39.32 % Reading from file /tmp/Prover9_18965_n008.cluster.edu
% 39.01/39.32
% 39.01/39.32 set(prolog_style_variables).
% 39.01/39.32 set(auto2).
% 39.01/39.32 % set(auto2) -> set(auto).
% 39.01/39.32 % set(auto) -> set(auto_inference).
% 39.01/39.32 % set(auto) -> set(auto_setup).
% 39.01/39.32 % set(auto_setup) -> set(predicate_elim).
% 39.01/39.32 % set(auto_setup) -> assign(eq_defs, unfold).
% 39.01/39.32 % set(auto) -> set(auto_limits).
% 39.01/39.32 % set(auto_limits) -> assign(max_weight, "100.000").
% 39.01/39.32 % set(auto_limits) -> assign(sos_limit, 20000).
% 39.01/39.32 % set(auto) -> set(auto_denials).
% 39.01/39.32 % set(auto) -> set(auto_process).
% 39.01/39.32 % set(auto2) -> assign(new_constants, 1).
% 39.01/39.32 % set(auto2) -> assign(fold_denial_max, 3).
% 39.01/39.32 % set(auto2) -> assign(max_weight, "200.000").
% 39.01/39.32 % set(auto2) -> assign(max_hours, 1).
% 39.01/39.32 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 39.01/39.32 % set(auto2) -> assign(max_seconds, 0).
% 39.01/39.32 % set(auto2) -> assign(max_minutes, 5).
% 39.01/39.32 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 39.01/39.32 % set(auto2) -> set(sort_initial_sos).
% 39.01/39.32 % set(auto2) -> assign(sos_limit, -1).
% 39.01/39.32 % set(auto2) -> assign(lrs_ticks, 3000).
% 39.01/39.32 % set(auto2) -> assign(max_megs, 400).
% 39.01/39.32 % set(auto2) -> assign(stats, some).
% 39.01/39.32 % set(auto2) -> clear(echo_input).
% 39.01/39.32 % set(auto2) -> set(quiet).
% 39.01/39.32 % set(auto2) -> clear(print_initial_clauses).
% 39.01/39.32 % set(auto2) -> clear(print_given).
% 39.01/39.32 assign(lrs_ticks,-1).
% 39.01/39.32 assign(sos_limit,10000).
% 39.01/39.32 assign(order,kbo).
% 39.01/39.32 set(lex_order_vars).
% 39.01/39.32 clear(print_given).
% 39.01/39.32
% 39.01/39.32 % formulas(sos). % not echoed (20 formulas)
% 39.01/39.32
% 39.01/39.32 ============================== end of input ==========================
% 39.01/39.32
% 39.01/39.32 % From the command line: assign(max_seconds, 300).
% 39.01/39.32
% 39.01/39.32 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 39.01/39.32
% 39.01/39.32 % Formulas that are not ordinary clauses:
% 39.01/39.32
% 39.01/39.32 ============================== end of process non-clausal formulas ===
% 39.01/39.32
% 39.01/39.32 ============================== PROCESS INITIAL CLAUSES ===============
% 39.01/39.32
% 39.01/39.32 ============================== PREDICATE ELIMINATION =================
% 39.01/39.32
% 39.01/39.32 ============================== end predicate elimination =============
% 39.01/39.32
% 39.01/39.32 Auto_denials:
% 39.01/39.32 % copying label goals to answer in negative clause
% 39.01/39.32
% 39.01/39.32 Term ordering decisions:
% 39.01/39.32 Function symbol KB weights: one=1. x0=1. x1=1. x2=1. product=1. quotient=1. difference=1. t=1. eta=1. i=1. j=1. l=1.
% 39.01/39.32
% 39.01/39.32 ============================== end of process initial clauses ========
% 39.01/39.32
% 39.01/39.32 ============================== CLAUSES FOR SEARCH ====================
% 39.01/39.32
% 39.01/39.32 ============================== end of clauses for search =============
% 39.01/39.32
% 39.01/39.32 ============================== SEARCH ================================
% 39.01/39.32
% 39.01/39.32 % Starting search at 0.01 seconds.
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=71.000, iters=3348
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=59.000, iters=3335
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=55.000, iters=3446
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=49.000, iters=3406
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=47.000, iters=3340
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=41.000, iters=3335
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=39.000, iters=3341
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=37.000, iters=3335
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=35.000, iters=3348
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=33.000, iters=3338
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=31.000, iters=3340
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=29.000, iters=3333
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=27.000, iters=3339
% 39.01/39.32
% 39.01/39.32 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 87 (0.00 of 2.63 sec).
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=25.000, iters=3333
% 39.01/39.32
% 39.01/39.32 Low Water (displace): id=1744, wt=139.000
% 39.01/39.32
% 39.01/39.32 Low Water (displace): id=17786, wt=23.000
% 39.01/39.32
% 39.01/39.32 Low Water (displace): id=17825, wt=21.000
% 39.01/39.32
% 39.01/39.32 Low Water (displace): id=17993, wt=19.000
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=23.000, iters=3336
% 39.01/39.32
% 39.01/39.32 Low Water (displace): id=26571, wt=17.000
% 39.01/39.32
% 39.01/39.32 Low Water (keep): wt=21.000, iters=3334
% 39.01/39.32
% 39.01/39.32 Low Water (displace): id=33454, wt=15.000
% 39.01/39.32
% 39.01/39.32 ============================== PROOF =================================
% 39.01/39.32 % SZS status Unsatisfiable
% 39.01/39.32 % SZS output start Refutation
% 39.01/39.32
% 39.01/39.32 % Proof 1 at 37.36 (+ 0.98) seconds: goals.
% 39.01/39.32 % Length of proof is 444.
% 39.01/39.32 % Level of proof is 45.
% 39.01/39.32 % Maximum clause weight is 43.000.
% 39.01/39.32 % Given clauses 1889.
% 39.01/39.32
% 39.01/39.32 1 product(A,one) = A # label(sos01) # label(axiom). [assumption].
% 39.01/39.32 2 product(one,A) = A # label(sos02) # label(axiom). [assumption].
% 39.01/39.32 3 i(A) = difference(A,one) # label(sos09) # label(axiom). [assumption].
% 39.01/39.32 4 j(A) = quotient(one,A) # label(sos10) # label(axiom). [assumption].
% 39.01/39.32 5 product(A,difference(A,B)) = B # label(sos03) # label(axiom). [assumption].
% 39.01/39.32 6 difference(A,product(A,B)) = B # label(sos04) # label(axiom). [assumption].
% 39.01/39.32 7 quotient(product(A,B),B) = A # label(sos05) # label(axiom). [assumption].
% 39.01/39.32 8 product(quotient(A,B),B) = A # label(sos06) # label(axiom). [assumption].
% 39.01/39.32 9 eta(A) = product(i(A),A) # label(sos12) # label(axiom). [assumption].
% 39.01/39.32 10 eta(A) = product(difference(A,one),A). [copy(9),rewrite([3(2)])].
% 39.01/39.32 11 product(i(A),A) = product(A,j(A)) # label(sos11) # label(axiom). [assumption].
% 39.01/39.32 12 product(difference(A,one),A) = product(A,quotient(one,A)). [copy(11),rewrite([3(1),4(4)])].
% 39.01/39.32 13 t(A,B) = quotient(product(A,B),A) # label(sos18) # label(axiom). [assumption].
% 39.01/39.32 14 product(i(i(A)),B) = product(eta(A),product(A,B)) # label(sos15) # label(axiom). [assumption].
% 39.01/39.32 15 product(product(A,quotient(one,A)),product(A,B)) = product(difference(difference(A,one),one),B). [copy(14),rewrite([3(1),3(3),10(6),12(8)]),flip(a)].
% 39.01/39.32 16 product(A,product(eta(A),B)) = product(j(j(A)),B) # label(sos16) # label(axiom). [assumption].
% 39.01/39.32 17 product(A,product(product(A,quotient(one,A)),B)) = product(quotient(one,quotient(one,A)),B). [copy(16),rewrite([10(1),12(3),4(6),4(8)])].
% 39.01/39.32 18 product(A,product(B,eta(A))) = product(product(A,B),eta(A)) # label(sos17) # label(axiom). [assumption].
% 39.01/39.32 19 product(product(A,B),product(A,quotient(one,A))) = product(A,product(B,product(A,quotient(one,A)))). [copy(18),rewrite([10(1),12(3),10(7),12(9)]),flip(a)].
% 39.01/39.32 21 difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) # label(sos07) # label(axiom). [assumption].
% 39.01/39.32 24 t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) # label(sos19) # label(axiom). [assumption].
% 39.01/39.32 25 product(quotient(product(product(A,quotient(one,A)),B),product(A,quotient(one,A))),quotient(product(product(A,quotient(one,A)),C),product(A,quotient(one,A)))) = quotient(product(product(A,quotient(one,A)),product(B,C)),product(A,quotient(one,A))). [copy(24),rewrite([10(1),12(3),13(5),10(10),12(12),13(13),10(18),12(20),13(21)]),flip(a)].
% 39.01/39.32 26 difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) # label(sos08) # label(axiom). [assumption].
% 39.01/39.32 27 product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 39.01/39.32 28 product(product(product(x0,quotient(one,x0)),x1),x2) != product(product(x0,quotient(one,x0)),product(x1,x2)) # answer(goals). [copy(27),rewrite([10(2),12(5),10(11),12(14)]),flip(a)].
% 39.01/39.32 32 difference(one,A) = A. [para(5(a,1),2(a,1)),flip(a)].
% 39.01/39.32 33 difference(A,A) = one. [para(1(a,1),6(a,1,2))].
% 39.01/39.32 34 quotient(A,one) = A. [para(1(a,1),7(a,1,1))].
% 39.01/39.32 35 quotient(A,A) = one. [para(2(a,1),7(a,1,1))].
% 39.01/39.32 36 quotient(A,difference(B,A)) = B. [para(5(a,1),7(a,1,1))].
% 39.01/39.32 37 difference(quotient(A,B),A) = B. [para(8(a,1),6(a,1,2))].
% 39.01/39.32 38 difference(difference(A,one),product(A,quotient(one,A))) = A. [para(12(a,1),6(a,1,2))].
% 39.01/39.32 39 quotient(product(A,quotient(one,A)),A) = difference(A,one). [para(12(a,1),7(a,1,1))].
% 39.01/39.32 40 product(product(A,quotient(one,A)),A) = difference(difference(A,one),one). [para(1(a,1),15(a,1,2)),rewrite([1(10)])].
% 39.01/39.32 41 product(difference(difference(A,one),one),difference(A,B)) = product(product(A,quotient(one,A)),B). [para(5(a,1),15(a,1,2)),flip(a)].
% 39.01/39.32 42 difference(product(A,quotient(one,A)),product(difference(difference(A,one),one),B)) = product(A,B). [para(15(a,1),6(a,1,2))].
% 39.01/39.32 43 quotient(product(difference(difference(A,one),one),B),product(A,B)) = product(A,quotient(one,A)). [para(15(a,1),7(a,1,1))].
% 39.01/39.32 44 product(product(quotient(A,B),quotient(one,quotient(A,B))),A) = product(difference(difference(quotient(A,B),one),one),B). [para(8(a,1),15(a,1,2))].
% 39.01/39.32 45 product(A,product(quotient(one,A),product(A,quotient(one,A)))) = product(difference(difference(difference(A,one),one),one),A). [para(12(a,1),15(a,1,2)),rewrite([36(6),12(3),19(7)])].
% 39.01/39.32 47 product(A,product(A,quotient(one,A))) = quotient(one,quotient(one,A)). [para(1(a,1),17(a,1,2)),rewrite([1(10)])].
% 39.01/39.32 48 product(quotient(one,quotient(one,A)),difference(product(A,quotient(one,A)),B)) = product(A,B). [para(5(a,1),17(a,1,2)),flip(a)].
% 39.01/39.32 49 difference(A,product(quotient(one,quotient(one,A)),B)) = product(product(A,quotient(one,A)),B). [para(17(a,1),6(a,1,2))].
% 39.01/39.32 51 product(difference(difference(A,one),one),product(product(A,quotient(one,A)),B)) = product(product(A,quotient(one,A)),product(quotient(one,quotient(one,A)),B)). [para(17(a,1),15(a,1,2)),flip(a)].
% 39.01/39.32 52 product(product(A,quotient(one,A)),product(quotient(one,quotient(one,A)),B)) = product(A,B). [para(17(a,1),15(a,2)),rewrite([36(13),12(10),36(9),12(6),17(8),36(16),36(13)])].
% 39.01/39.32 55 product(difference(difference(A,one),one),product(product(A,quotient(one,A)),B)) = product(A,B). [back_rewrite(51),rewrite([52(18)])].
% 39.01/39.32 56 product(A,product(difference(A,B),product(A,quotient(one,A)))) = product(B,product(A,quotient(one,A))). [para(5(a,1),19(a,1,1)),flip(a)].
% 39.01/39.32 57 quotient(difference(difference(A,one),one),A) = product(A,quotient(one,A)). [para(19(a,1),6(a,1,2)),rewrite([26(7),15(5),7(6)])].
% 39.01/39.32 58 quotient(product(A,product(B,product(A,quotient(one,A)))),product(A,quotient(one,A))) = product(A,B). [para(19(a,1),7(a,1,1))].
% 39.01/39.32 59 product(quotient(A,B),product(B,product(quotient(A,B),quotient(one,quotient(A,B))))) = product(A,product(quotient(A,B),quotient(one,quotient(A,B)))). [para(8(a,1),19(a,1,1)),flip(a)].
% 39.01/39.32 60 product(difference(difference(difference(A,one),one),one),A) = product(difference(A,one),quotient(one,quotient(one,A))). [para(12(a,1),19(a,1,1)),rewrite([36(9),12(6),19(7),45(7),36(15),12(12),47(13)])].
% 39.01/39.32 61 product(product(product(A,B),quotient(one,product(A,B))),product(A,product(B,product(A,quotient(one,A))))) = product(difference(difference(product(A,B),one),one),product(A,quotient(one,A))). [para(19(a,1),15(a,1,2))].
% 39.01/39.32 62 product(difference(difference(A,one),one),quotient(one,A)) = product(difference(A,one),quotient(one,quotient(one,A))). [para(19(a,1),15(a,1)),rewrite([45(7),60(7)]),flip(a)].
% 39.01/39.32 66 product(A,product(quotient(one,A),product(A,quotient(one,A)))) = product(difference(A,one),quotient(one,quotient(one,A))). [back_rewrite(45),rewrite([60(14)])].
% 39.01/39.32 67 product(A,quotient(product(B,product(C,A)),A)) = product(product(A,B),C). [para(21(a,1),5(a,1,2))].
% 39.01/39.32 68 quotient(product(difference(A,B),product(C,A)),A) = difference(A,product(B,C)). [para(5(a,1),21(a,1,2,1)),flip(a)].
% 39.01/39.32 69 quotient(product(A,product(difference(product(B,A),C),B)),B) = difference(B,C). [para(5(a,1),21(a,1,2)),flip(a)].
% 39.01/39.32 70 quotient(product(A,product(B,quotient(C,A))),quotient(C,A)) = difference(quotient(C,A),product(C,B)). [para(8(a,1),21(a,1,2,1)),flip(a)].
% 39.01/39.32 71 difference(difference(A,one),product(product(A,quotient(one,A)),B)) = quotient(product(A,product(B,difference(A,one))),difference(A,one)). [para(12(a,1),21(a,1,2,1))].
% 39.01/39.32 73 quotient(product(quotient(one,A),product(product(A,B),A)),A) = difference(A,product(difference(difference(A,one),one),B)). [para(15(a,1),21(a,1,2)),flip(a)].
% 39.01/39.32 74 quotient(product(product(product(A,quotient(one,A)),B),product(C,A)),A) = difference(A,product(product(quotient(one,quotient(one,A)),B),C)). [para(17(a,1),21(a,1,2,1)),flip(a)].
% 39.01/39.32 77 quotient(product(A,difference(difference(B,one),one)),B) = product(A,product(B,quotient(one,B))). [para(19(a,1),21(a,1,2)),rewrite([6(6),40(8)]),flip(a)].
% 39.01/39.32 78 quotient(product(product(A,quotient(one,A)),product(difference(product(A,quotient(one,A)),B),C)),product(A,quotient(one,A))) = product(quotient(B,product(A,quotient(one,A))),quotient(product(product(A,quotient(one,A)),C),product(A,quotient(one,A)))). [para(5(a,1),25(a,1,1,1)),flip(a)].
% 39.01/39.32 79 quotient(product(product(A,quotient(one,A)),product(B,difference(product(A,quotient(one,A)),C))),product(A,quotient(one,A))) = product(quotient(product(product(A,quotient(one,A)),B),product(A,quotient(one,A))),quotient(C,product(A,quotient(one,A)))). [para(5(a,1),25(a,1,2,1)),flip(a)].
% 39.01/39.32 98 difference(A,product(B,product(difference(B,A),C))) = quotient(quotient(product(C,A),difference(B,A)),B). [para(5(a,1),26(a,1,1)),rewrite([5(6)])].
% 39.01/39.32 99 difference(product(A,B),product(A,C)) = quotient(difference(B,product(C,A)),A). [para(5(a,1),26(a,1,2,2)),rewrite([68(7)])].
% 39.01/39.32 100 difference(A,product(quotient(A,B),product(B,C))) = quotient(quotient(product(C,A),B),quotient(A,B)). [para(8(a,1),26(a,1,1)),rewrite([8(6)])].
% 39.01/39.32 105 difference(product(quotient(one,quotient(one,A)),B),product(A,product(product(product(A,quotient(one,A)),B),C))) = quotient(quotient(product(C,product(quotient(one,quotient(one,A)),B)),product(product(A,quotient(one,A)),B)),A). [para(17(a,1),26(a,1,1)),rewrite([17(17)])].
% 39.01/39.32 124 product(product(A,quotient(one,A)),product(difference(A,one),B)) = product(difference(difference(difference(A,one),one),one),B). [para(36(a,1),15(a,1,1,2)),rewrite([12(3)])].
% 39.01/39.32 125 product(difference(A,one),product(product(A,quotient(one,A)),B)) = product(quotient(one,A),B). [para(36(a,1),17(a,1,2,1,2)),rewrite([12(5),36(12)])].
% 39.01/39.32 128 product(quotient(one,A),quotient(one,quotient(one,A))) = product(A,quotient(one,A)). [para(37(a,1),12(a,1,1)),flip(a)].
% 39.01/39.32 129 product(product(A,quotient(one,A)),product(quotient(one,A),B)) = product(difference(A,one),B). [para(37(a,1),15(a,2,1,1)),rewrite([128(7)])].
% 39.01/39.32 131 quotient(product(product(A,quotient(one,A)),product(quotient(one,product(A,quotient(one,A))),B)),product(A,quotient(one,A))) = product(difference(product(A,quotient(one,A)),one),quotient(product(product(A,quotient(one,A)),B),product(A,quotient(one,A)))). [para(39(a,1),25(a,1,1)),flip(a)].
% 39.01/39.32 134 difference(product(A,quotient(one,A)),difference(difference(A,one),one)) = A. [para(40(a,1),6(a,1,2))].
% 39.01/39.32 136 product(quotient(one,quotient(one,A)),A) = product(A,difference(difference(A,one),one)). [para(40(a,1),17(a,1,2)),flip(a)].
% 39.01/39.32 138 quotient(product(quotient(one,A),product(A,A)),A) = difference(A,difference(difference(A,one),one)). [para(40(a,1),21(a,1,2)),flip(a)].
% 39.01/39.32 143 product(product(A,quotient(one,A)),difference(A,one)) = difference(difference(difference(A,one),one),one). [para(36(a,1),40(a,1,1,2)),rewrite([12(3)])].
% 39.01/39.32 144 product(product(A,quotient(one,A)),quotient(one,A)) = difference(A,one). [para(37(a,1),40(a,2,1)),rewrite([128(7)])].
% 39.01/39.32 145 difference(A,quotient(one,quotient(one,A))) = product(A,quotient(one,A)). [para(47(a,1),6(a,1,2))].
% 39.01/39.32 146 quotient(quotient(one,quotient(one,A)),product(A,quotient(one,A))) = A. [para(47(a,1),7(a,1,1))].
% 39.01/39.32 147 product(difference(difference(A,one),one),product(A,quotient(one,A))) = product(product(A,quotient(one,A)),quotient(one,quotient(one,A))). [para(47(a,1),15(a,1,2)),flip(a)].
% 39.01/39.32 148 product(product(A,quotient(one,A)),quotient(one,quotient(one,A))) = A. [para(47(a,1),15(a,2)),rewrite([36(13),12(10),36(9),12(6),47(7),36(15),36(12)])].
% 39.01/39.32 153 quotient(quotient(one,quotient(one,A)),quotient(one,A)) = difference(quotient(one,A),A). [para(47(a,1),21(a,2,1)),rewrite([8(5),2(4)]),flip(a)].
% 39.01/39.32 156 product(difference(A,one),product(A,quotient(one,A))) = quotient(one,A). [para(36(a,1),47(a,1,2,2)),rewrite([12(5),36(11)])].
% 39.01/39.32 157 product(difference(difference(A,one),one),product(A,quotient(one,A))) = A. [back_rewrite(147),rewrite([148(16)])].
% 39.01/39.32 162 difference(difference(difference(A,one),one),product(product(A,quotient(one,A)),B)) = difference(A,B). [para(41(a,1),6(a,1,2))].
% 39.01/39.32 164 product(difference(difference(difference(difference(A,one),one),one),one),difference(A,B)) = product(product(A,quotient(one,A)),product(product(A,quotient(one,A)),B)). [para(41(a,1),15(a,1,2)),rewrite([36(10),12(7),36(6),12(3)]),flip(a)].
% 39.01/39.32 165 product(difference(difference(A,one),one),product(difference(A,B),product(A,quotient(one,A)))) = product(product(product(A,quotient(one,A)),B),product(A,quotient(one,A))). [para(41(a,1),19(a,1,1)),rewrite([36(14),12(11),36(10),12(7),36(23),12(20),36(19),12(16)]),flip(a)].
% 39.01/39.32 166 quotient(product(difference(A,B),product(C,difference(difference(A,one),one))),difference(difference(A,one),one)) = difference(difference(difference(A,one),one),product(product(product(A,quotient(one,A)),B),C)). [para(41(a,1),21(a,1,2,1)),flip(a)].
% 39.01/39.32 168 product(difference(A,one),difference(quotient(one,A),B)) = product(product(A,quotient(one,A)),B). [para(37(a,1),41(a,1,1,1)),rewrite([128(13)])].
% 39.01/39.32 169 quotient(difference(A,one),quotient(one,A)) = product(A,quotient(one,A)). [para(37(a,1),57(a,1,1,1)),rewrite([128(12)])].
% 39.01/39.32 174 difference(A,difference(A,one)) = quotient(quotient(one,A),A). [para(144(a,1),21(a,1,2)),rewrite([8(8),1(7)])].
% 39.01/39.32 175 product(quotient(difference(A,one),product(A,quotient(one,A))),quotient(product(product(A,quotient(one,A)),B),product(A,quotient(one,A)))) = quotient(product(difference(A,one),B),product(A,quotient(one,A))). [para(144(a,1),25(a,1,1,1)),rewrite([129(22)])].
% 39.01/39.32 177 product(A,quotient(quotient(one,A),A)) = difference(A,one). [para(174(a,1),5(a,1,2))].
% 39.01/39.32 180 product(A,difference(difference(difference(A,one),one),B)) = difference(product(A,quotient(one,A)),B). [para(5(a,1),42(a,1,2)),flip(a)].
% 39.01/39.32 182 quotient(difference(quotient(one,A),product(B,A)),A) = product(quotient(one,quotient(one,A)),B). [para(17(a,1),42(a,1,2)),rewrite([36(10),36(7),99(5),36(15),12(12),36(11),12(8),17(10)])].
% 39.01/39.32 183 difference(product(A,quotient(one,A)),product(difference(difference(difference(A,one),one),one),B)) = product(difference(A,one),B). [para(36(a,1),42(a,1,1,2)),rewrite([12(3)])].
% 39.01/39.32 190 product(quotient(one,quotient(one,A)),quotient(quotient(one,product(A,quotient(one,A))),product(A,quotient(one,A)))) = product(A,difference(product(A,quotient(one,A)),one)). [para(177(a,1),17(a,1,2)),flip(a)].
% 39.01/39.32 191 product(A,product(quotient(quotient(one,A),A),product(A,quotient(one,A)))) = quotient(one,A). [para(177(a,1),19(a,1,1)),rewrite([156(6)]),flip(a)].
% 39.01/39.32 199 difference(difference(A,one),quotient(one,A)) = product(A,quotient(one,A)). [para(36(a,1),145(a,1,2,2)),rewrite([36(11),12(8)])].
% 39.01/39.32 203 quotient(product(A,B),product(quotient(one,quotient(one,A)),B)) = product(A,quotient(one,A)). [para(17(a,1),43(a,1,1)),rewrite([36(7),36(4),36(11),12(8),36(7),12(4),17(6)])].
% 39.01/39.32 213 product(quotient(one,quotient(one,A)),quotient(one,quotient(one,A))) = product(A,A). [para(148(a,1),17(a,1,2)),flip(a)].
% 39.01/39.32 215 quotient(product(quotient(one,quotient(one,A)),product(B,product(A,quotient(one,A)))),product(A,quotient(one,A))) = product(quotient(one,quotient(one,A)),B). [para(148(a,1),21(a,1,2,1)),rewrite([99(5),182(5)]),flip(a)].
% 39.01/39.32 221 product(difference(A,one),product(difference(A,one),quotient(one,quotient(one,A)))) = product(quotient(one,A),product(A,quotient(one,A))). [para(156(a,1),19(a,1,1)),rewrite([36(8),12(5),36(17),12(14),19(15),66(15)]),flip(a)].
% 39.01/39.32 223 difference(difference(difference(A,one),one),A) = product(A,quotient(one,A)). [para(157(a,1),6(a,1,2))].
% 39.01/39.32 224 quotient(A,product(A,quotient(one,A))) = difference(difference(A,one),one). [para(157(a,1),7(a,1,1))].
% 39.01/39.32 253 quotient(difference(A,one),product(A,quotient(one,A))) = difference(difference(difference(A,one),one),one). [para(36(a,1),224(a,1,2,2)),rewrite([12(5)])].
% 39.01/39.32 255 product(difference(difference(difference(A,one),one),one),quotient(product(product(A,quotient(one,A)),B),product(A,quotient(one,A)))) = quotient(product(difference(A,one),B),product(A,quotient(one,A))). [back_rewrite(175),rewrite([253(6)])].
% 39.01/39.32 257 product(product(A,B),quotient(C,A)) = product(A,quotient(product(B,C),A)). [para(8(a,1),67(a,1,2,1,2)),flip(a)].
% 39.01/39.32 258 product(product(A,quotient(B,product(C,A))),C) = product(A,quotient(B,A)). [para(8(a,1),67(a,1,2,1)),flip(a)].
% 39.01/39.32 262 product(product(A,product(B,quotient(one,B))),B) = product(A,difference(difference(B,one),one)). [para(15(a,1),67(a,1,2,1)),rewrite([7(6)]),flip(a)].
% 39.01/39.32 283 product(product(quotient(one,A),difference(A,one)),A) = quotient(one,A). [para(156(a,1),67(a,1,2,1)),rewrite([35(7),1(4)]),flip(a)].
% 39.01/39.32 295 product(A,difference(product(A,quotient(one,A)),B)) = product(difference(difference(A,one),one),B). [para(48(a,1),15(a,1,2)),rewrite([128(11),128(7),15(5),37(11),37(9)]),flip(a)].
% 39.01/39.32 296 product(quotient(one,quotient(one,A)),product(difference(product(A,quotient(one,A)),B),product(A,quotient(one,A)))) = product(A,product(B,product(A,quotient(one,A)))). [para(48(a,1),19(a,1,1)),rewrite([128(12),128(8),19(5),128(24),128(20)]),flip(a)].
% 39.01/39.32 301 product(quotient(one,quotient(one,A)),quotient(quotient(one,product(A,quotient(one,A))),product(A,quotient(one,A)))) = difference(difference(A,one),one). [back_rewrite(190),rewrite([295(20),1(20)])].
% 39.01/39.32 303 product(quotient(one,A),difference(A,one)) = quotient(quotient(one,A),A). [para(283(a,1),7(a,1,1)),flip(a)].
% 39.01/39.32 307 quotient(quotient(quotient(one,A),A),difference(A,one)) = quotient(one,A). [para(303(a,1),7(a,1,1))].
% 39.01/39.32 308 product(A,quotient(product(quotient(one,A),quotient(one,A)),A)) = product(difference(A,one),difference(A,one)). [para(303(a,1),15(a,1,2)),rewrite([128(7),257(7),37(11)])].
% 39.01/39.32 309 product(A,difference(difference(A,one),one)) = difference(quotient(one,A),A). [para(303(a,1),17(a,2)),rewrite([37(7),40(4),153(12)])].
% 39.01/39.32 310 product(quotient(quotient(one,A),A),product(A,quotient(one,A))) = product(quotient(one,A),quotient(one,A)). [para(303(a,1),19(a,1,1)),rewrite([128(10),128(18),156(15)])].
% 39.01/39.32 312 difference(quotient(one,A),A) = quotient(A,difference(A,one)). [para(36(a,1),303(a,1,1)),rewrite([309(5),36(7)])].
% 39.01/39.32 319 product(quotient(one,quotient(one,A)),A) = quotient(A,difference(A,one)). [back_rewrite(136),rewrite([309(10),312(8)])].
% 39.01/39.32 320 product(A,product(quotient(one,A),quotient(one,A))) = quotient(one,A). [back_rewrite(191),rewrite([310(7)])].
% 39.01/39.32 322 quotient(quotient(one,quotient(one,A)),quotient(one,A)) = quotient(A,difference(A,one)). [back_rewrite(153),rewrite([312(10)])].
% 39.01/39.32 323 product(quotient(one,A),quotient(A,difference(A,one))) = A. [para(312(a,1),5(a,1,2))].
% 39.01/39.32 327 product(quotient(one,A),product(quotient(A,difference(A,one)),product(A,quotient(one,A)))) = quotient(one,quotient(one,A)). [para(323(a,1),19(a,1,1)),rewrite([128(7),47(4),128(16)]),flip(a)].
% 39.01/39.32 337 product(difference(A,one),difference(A,one)) = difference(A,quotient(one,A)). [para(177(a,1),49(a,1,2)),rewrite([37(6),322(17),37(12),257(10),308(10)]),flip(a)].
% 39.01/39.32 338 difference(product(A,quotient(one,A)),one) = difference(A,difference(difference(A,one),one)). [para(177(a,1),49(a,2)),rewrite([301(14)]),flip(a)].
% 39.01/39.32 372 quotient(product(product(A,quotient(one,A)),product(quotient(one,product(A,quotient(one,A))),B)),product(A,quotient(one,A))) = product(difference(A,difference(difference(A,one),one)),quotient(product(product(A,quotient(one,A)),B),product(A,quotient(one,A)))). [back_rewrite(131),rewrite([338(19)])].
% 39.01/39.32 377 quotient(quotient(A,difference(A,one)),A) = quotient(one,quotient(one,A)). [para(37(a,1),307(a,1,2)),rewrite([322(7)])].
% 39.01/39.32 379 product(quotient(A,difference(A,one)),product(A,quotient(one,A))) = product(A,A). [para(319(a,1),19(a,1,1)),rewrite([128(14),128(10),128(22),128(18),47(15),213(16)])].
% 39.01/39.32 386 product(quotient(one,A),product(A,A)) = quotient(one,quotient(one,A)). [back_rewrite(327),rewrite([379(9)])].
% 39.01/39.32 387 difference(A,difference(difference(A,one),one)) = quotient(quotient(one,quotient(one,A)),A). [back_rewrite(138),rewrite([386(4)]),flip(a)].
% 39.01/39.32 389 quotient(product(product(A,quotient(one,A)),product(quotient(one,product(A,quotient(one,A))),B)),product(A,quotient(one,A))) = product(quotient(quotient(one,quotient(one,A)),A),quotient(product(product(A,quotient(one,A)),B),product(A,quotient(one,A)))). [back_rewrite(372),rewrite([387(19)])].
% 39.01/39.32 419 difference(product(A,quotient(one,A)),one) = quotient(quotient(one,quotient(one,A)),A). [back_rewrite(338),rewrite([387(10)])].
% 39.01/39.32 425 product(quotient(one,A),quotient(one,A)) = difference(A,quotient(one,A)). [para(320(a,1),6(a,1,2)),flip(a)].
% 39.01/39.32 433 difference(quotient(one,A),quotient(one,quotient(one,A))) = product(A,A). [back_rewrite(213),rewrite([425(9)])].
% 39.01/39.32 454 product(product(A,quotient(one,A)),product(quotient(one,quotient(one,quotient(one,quotient(one,A)))),B)) = product(quotient(one,quotient(one,A)),B). [para(17(a,1),52(a,1,2)),rewrite([128(24),128(20),17(18)])].
% 39.01/39.32 469 product(A,quotient(product(B,product(C,quotient(one,quotient(one,A)))),quotient(one,quotient(one,A)))) = product(product(A,quotient(one,A)),product(product(quotient(one,quotient(one,A)),B),C)). [para(67(a,1),52(a,1,2)),flip(a)].
% 39.01/39.32 485 product(difference(A,quotient(one,A)),product(A,quotient(one,A))) = product(difference(A,one),quotient(one,A)). [para(337(a,1),19(a,1,1)),rewrite([36(9),12(6),36(17),12(14),156(15)])].
% 39.01/39.32 522 quotient(product(product(A,A),product(B,quotient(one,A))),quotient(one,A)) = difference(quotient(one,A),product(quotient(one,quotient(one,A)),B)). [para(386(a,1),21(a,1,2,1)),flip(a)].
% 39.01/39.32 530 product(product(A,quotient(one,A)),difference(A,quotient(one,A))) = difference(A,quotient(one,quotient(one,quotient(one,A)))). [para(386(a,1),49(a,1,2)),rewrite([425(15)]),flip(a)].
% 39.01/39.32 531 product(product(A,quotient(one,A)),quotient(one,quotient(one,quotient(one,A)))) = quotient(one,A). [para(386(a,1),52(a,1,2)),rewrite([425(15),5(14)])].
% 39.01/39.32 537 difference(A,quotient(one,quotient(one,quotient(one,A)))) = product(difference(A,one),quotient(one,A)). [para(425(a,1),15(a,1,2)),rewrite([128(7),530(7),37(11)])].
% 39.01/39.32 546 product(product(A,quotient(one,A)),difference(A,quotient(one,A))) = product(difference(A,one),quotient(one,A)). [back_rewrite(530),rewrite([537(14)])].
% 39.01/39.32 578 difference(difference(difference(A,one),one),product(A,B)) = product(product(A,quotient(one,A)),B). [para(55(a,1),6(a,1,2))].
% 39.01/39.32 586 product(difference(difference(difference(A,one),one),one),product(product(A,quotient(one,A)),B)) = product(difference(A,one),B). [para(36(a,1),55(a,1,2,1,2)),rewrite([12(9)])].
% 39.01/39.32 598 product(difference(difference(A,one),one),product(A,B)) = product(A,product(quotient(one,quotient(one,A)),B)). [para(52(a,1),55(a,1,2))].
% 39.01/39.32 605 product(difference(A,product(B,C)),A) = product(difference(A,B),product(C,A)). [para(68(a,1),8(a,1,1))].
% 39.01/39.32 606 difference(A,product(B,quotient(C,A))) = quotient(product(difference(A,B),C),A). [para(8(a,1),68(a,1,1,2)),flip(a)].
% 39.01/39.32 617 difference(A,product(B,product(A,quotient(one,A)))) = product(difference(A,B),product(A,quotient(one,A))). [para(40(a,1),68(a,1,1,2)),rewrite([77(7)]),flip(a)].
% 39.01/39.32 621 quotient(product(difference(quotient(one,quotient(one,A)),B),A),quotient(one,quotient(one,A))) = difference(quotient(one,quotient(one,A)),product(B,product(A,quotient(one,A)))). [para(148(a,1),68(a,1,1,2))].
% 39.01/39.32 639 product(A,product(difference(product(B,A),C),B)) = product(difference(B,C),B). [para(69(a,1),8(a,1,1)),flip(a)].
% 39.01/39.32 645 product(quotient(one,quotient(one,A)),difference(A,B)) = difference(product(A,quotient(one,A)),B). [para(148(a,1),69(a,1,1,2,1,1)),rewrite([215(14)])].
% 39.01/39.32 650 quotient(A,quotient(one,A)) = product(A,A). [para(433(a,1),69(a,2)),rewrite([639(12),433(7),257(4),1(2),35(1),1(2)])].
% 39.01/39.32 655 product(product(product(A,quotient(one,A)),B),product(A,quotient(one,A))) = product(product(A,quotient(one,A)),product(B,product(A,quotient(one,A)))). [para(56(a,1),15(a,1,2)),rewrite([165(18)]),flip(a)].
% 39.01/39.32 666 product(A,product(difference(difference(difference(A,one),one),B),product(A,quotient(one,A)))) = difference(product(A,quotient(one,A)),product(B,product(A,quotient(one,A)))). [para(56(a,1),42(a,1,2)),rewrite([36(13),12(10),36(9),12(6),36(23),12(20),36(19),12(16)]),flip(a)].
% 39.01/39.32 678 difference(A,quotient(one,A)) = quotient(difference(A,one),A). [para(36(a,1),650(a,1,2)),rewrite([337(8)]),flip(a)].
% 39.01/39.32 679 difference(product(A,A),A) = quotient(one,A). [para(650(a,1),37(a,1,1))].
% 39.01/39.32 684 product(A,quotient(quotient(quotient(one,A),A),A)) = product(difference(A,one),quotient(one,A)). [back_rewrite(546),rewrite([678(6),257(7),303(5)])].
% 39.01/39.32 697 product(quotient(difference(A,one),A),product(A,quotient(one,A))) = product(difference(A,one),quotient(one,A)). [back_rewrite(485),rewrite([678(3)])].
% 39.01/39.32 704 product(quotient(one,A),quotient(one,A)) = quotient(difference(A,one),A). [back_rewrite(425),rewrite([678(8)])].
% 39.01/39.32 706 product(difference(A,one),difference(A,one)) = quotient(difference(A,one),A). [back_rewrite(337),rewrite([678(8)])].
% 39.01/39.32 707 difference(product(difference(A,one),quotient(one,quotient(one,A))),product(A,quotient(one,A))) = quotient(one,product(A,quotient(one,A))). [para(15(a,1),679(a,1,1)),rewrite([62(7)])].
% 39.01/39.32 712 product(A,quotient(difference(A,one),A)) = quotient(one,A). [para(678(a,1),5(a,1,2))].
% 39.01/39.32 718 product(quotient(one,A),product(A,quotient(one,A))) = product(A,product(difference(A,one),quotient(one,A))). [para(678(a,1),56(a,1,2,1)),rewrite([697(7)]),flip(a)].
% 39.01/39.32 720 product(difference(A,one),product(difference(A,one),quotient(one,quotient(one,A)))) = product(A,product(difference(A,one),quotient(one,A))). [back_rewrite(221),rewrite([718(16)])].
% 39.01/39.32 721 product(A,product(A,product(difference(A,one),quotient(one,A)))) = product(difference(A,one),quotient(one,quotient(one,A))). [back_rewrite(66),rewrite([718(6)])].
% 39.01/39.32 722 product(A,product(difference(A,one),quotient(one,A))) = quotient(one,quotient(one,quotient(one,A))). [para(712(a,1),17(a,2)),rewrite([37(9),650(10),704(8),257(7),303(5),684(5)])].
% 39.01/39.32 734 product(difference(A,one),quotient(one,quotient(one,A))) = product(A,quotient(one,quotient(one,quotient(one,A)))). [back_rewrite(721),rewrite([722(6)]),flip(a)].
% 39.01/39.32 735 product(difference(A,one),product(A,quotient(one,quotient(one,quotient(one,A))))) = quotient(one,quotient(one,quotient(one,A))). [back_rewrite(720),rewrite([734(9),722(16)])].
% 39.01/39.32 737 product(quotient(one,A),product(A,quotient(one,A))) = quotient(one,quotient(one,quotient(one,A))). [back_rewrite(718),rewrite([722(12)])].
% 39.01/39.32 738 quotient(quotient(one,quotient(one,A)),A) = quotient(one,product(A,quotient(one,A))). [back_rewrite(707),rewrite([734(7),99(11),8(9),37(8)])].
% 39.01/39.32 765 difference(product(A,quotient(one,A)),one) = quotient(one,product(A,quotient(one,A))). [back_rewrite(419),rewrite([738(10)])].
% 39.01/39.32 770 quotient(product(product(A,quotient(one,A)),product(quotient(one,product(A,quotient(one,A))),B)),product(A,quotient(one,A))) = product(quotient(one,product(A,quotient(one,A))),quotient(product(product(A,quotient(one,A)),B),product(A,quotient(one,A)))). [back_rewrite(389),rewrite([738(19)])].
% 39.01/39.32 771 difference(A,difference(difference(A,one),one)) = quotient(one,product(A,quotient(one,A))). [back_rewrite(387),rewrite([738(10)])].
% 39.01/39.32 774 quotient(product(A,B),product(A,quotient(one,A))) = product(A,quotient(B,product(A,quotient(one,A)))). [para(8(a,1),58(a,1,1,2))].
% 39.01/39.32 779 quotient(quotient(one,quotient(one,quotient(one,A))),product(A,quotient(one,A))) = quotient(one,A). [para(156(a,1),58(a,2)),rewrite([36(11),12(8),19(9),737(8),735(10),36(12),12(9)])].
% 39.01/39.32 835 difference(product(A,B),A) = quotient(difference(B,A),A). [para(1(a,1),99(a,1,2)),rewrite([2(4)])].
% 39.01/39.32 836 quotient(difference(difference(A,B),product(C,A)),A) = difference(B,product(A,C)). [para(5(a,1),99(a,1,1)),flip(a)].
% 39.01/39.32 853 quotient(product(A,B),quotient(difference(C,product(B,A)),A)) = product(A,C). [para(99(a,1),36(a,1,2))].
% 39.01/39.32 854 difference(quotient(quotient(one,A),A),one) = product(A,A). [para(38(a,1),99(a,2,1)),rewrite([303(5),8(6),650(8)])].
% 39.01/39.32 862 difference(product(A,B),difference(A,one)) = quotient(difference(B,quotient(one,A)),A). [para(177(a,1),99(a,1,2)),rewrite([8(8)])].
% 39.01/39.32 864 quotient(difference(quotient(one,quotient(one,A)),product(B,product(A,quotient(one,A)))),product(A,quotient(one,A))) = quotient(product(quotient(one,A),product(B,A)),A). [para(148(a,1),99(a,1,1)),rewrite([21(5)]),flip(a)].
% 39.01/39.32 866 quotient(difference(product(A,quotient(one,A)),product(B,difference(A,one))),difference(A,one)) = difference(quotient(one,A),product(difference(A,one),B)). [para(156(a,1),99(a,1,1)),flip(a)].
% 39.01/39.32 893 quotient(difference(product(A,A),product(B,quotient(one,A))),quotient(one,A)) = difference(quotient(one,quotient(one,A)),product(quotient(one,A),B)). [para(386(a,1),99(a,1,1)),flip(a)].
% 39.01/39.32 905 difference(product(A,B),quotient(one,A)) = quotient(difference(B,difference(A,one)),A). [para(712(a,1),99(a,1,2)),rewrite([8(8)])].
% 39.01/39.32 923 quotient(difference(difference(A,B),A),A) = difference(B,A). [para(5(a,1),835(a,1,1)),flip(a)].
% 39.01/39.32 930 quotient(A,quotient(difference(B,A),A)) = product(A,B). [para(835(a,1),36(a,1,2))].
% 39.01/39.32 932 difference(quotient(one,quotient(one,A)),A) = quotient(one,product(A,quotient(one,A))). [para(47(a,1),835(a,1,1)),rewrite([835(9),312(8),377(9),738(10)])].
% 39.01/39.32 935 quotient(one,product(A,quotient(one,A))) = quotient(A,difference(difference(A,one),one)). [para(134(a,1),835(a,2,1)),rewrite([598(8),8(7),1(2),771(5)])].
% 39.01/39.32 938 difference(quotient(one,A),difference(A,one)) = quotient(quotient(one,A),difference(A,one)). [para(156(a,1),835(a,1,1)),rewrite([862(11),33(10)])].
% 39.01/39.32 944 quotient(difference(product(quotient(one,quotient(one,A)),B),product(A,quotient(one,A))),product(A,quotient(one,A))) = quotient(difference(B,one),A). [para(52(a,1),835(a,1,1)),rewrite([99(5),8(3)]),flip(a)].
% 39.01/39.32 983 product(quotient(quotient(one,A),A),quotient(one,quotient(quotient(one,A),A))) = one. [para(854(a,1),12(a,1,1)),rewrite([257(5),39(4),5(3)]),flip(a)].
% 39.01/39.32 984 product(difference(product(A,A),one),B) = product(quotient(quotient(one,A),A),B). [para(854(a,1),15(a,2,1,1)),rewrite([983(9),2(6)]),flip(a)].
% 39.01/39.32 985 quotient(quotient(one,A),A) = quotient(one,product(A,A)). [para(854(a,1),36(a,1,2)),flip(a)].
% 39.01/39.32 990 product(product(A,A),quotient(one,product(A,A))) = one. [para(854(a,1),43(a,1,1,1,1)),rewrite([984(4),985(3),985(7),35(9),985(4),985(8),128(10)]),flip(a)].
% 39.01/39.32 991 quotient(one,quotient(one,product(A,A))) = product(A,A). [para(854(a,1),156(a,1,1)),rewrite([985(4),985(8),128(10),990(6),1(3),985(5)]),flip(a)].
% 39.01/39.32 992 product(quotient(one,product(A,A)),A) = quotient(one,A). [para(854(a,1),44(a,2,1,1)),rewrite([985(3),985(7),991(8),8(5),2(4),984(6),985(5)]),flip(a)].
% 39.01/39.32 1035 product(A,quotient(one,product(A,A))) = difference(A,one). [back_rewrite(177),rewrite([985(3)])].
% 39.01/39.32 1042 difference(difference(A,B),A) = product(difference(B,A),A). [para(923(a,1),8(a,1,1)),flip(a)].
% 39.01/39.32 1054 quotient(A,quotient(B,A)) = product(A,quotient(A,B)). [para(37(a,1),930(a,1,2,1))].
% 39.01/39.32 1080 difference(quotient(A,product(B,quotient(one,B))),product(A,quotient(one,quotient(one,B)))) = B. [para(52(a,1),70(a,1,1)),rewrite([7(10)]),flip(a)].
% 39.01/39.32 1132 quotient(product(A,product(product(quotient(one,quotient(one,A)),B),difference(A,one))),difference(A,one)) = difference(difference(A,one),product(A,B)). [para(52(a,1),71(a,1,2)),flip(a)].
% 39.01/39.32 1137 quotient(quotient(one,A),difference(A,one)) = quotient(one,product(A,quotient(one,A))). [para(706(a,1),71(a,2,1,2)),rewrite([143(8),771(9),36(7),12(4),712(9)]),flip(a)].
% 39.01/39.32 1142 difference(quotient(one,A),difference(A,one)) = quotient(one,product(A,quotient(one,A))). [back_rewrite(938),rewrite([1137(10)])].
% 39.01/39.32 1154 product(difference(A,B),product(difference(B,A),A)) = A. [para(1042(a,1),5(a,1,2))].
% 39.01/39.32 1155 difference(quotient(difference(A,B),B),product(B,A)) = product(A,product(B,A)). [para(6(a,1),1042(a,2,1)),rewrite([835(2)])].
% 39.01/39.32 1157 quotient(A,product(difference(B,A),A)) = difference(A,B). [para(1042(a,1),36(a,1,2))].
% 39.01/39.32 1158 product(difference(A,quotient(A,B)),quotient(A,B)) = difference(B,quotient(A,B)). [para(37(a,1),1042(a,1,1)),flip(a)].
% 39.01/39.32 1162 product(quotient(one,product(A,quotient(one,A))),A) = quotient(one,quotient(one,A)). [para(145(a,1),1042(a,1,1)),rewrite([835(4),312(3),377(4),932(9)]),flip(a)].
% 39.01/39.32 1163 product(quotient(one,product(A,quotient(one,A))),difference(A,one)) = quotient(one,A). [para(199(a,1),1042(a,1,1)),rewrite([862(6),33(5),1142(7)]),flip(a)].
% 39.01/39.32 1165 product(quotient(one,product(A,quotient(one,A))),difference(difference(A,one),one)) = A. [para(223(a,1),1042(a,1,1)),rewrite([134(8),771(5)]),flip(a)].
% 39.01/39.32 1221 product(A,quotient(A,product(B,A))) = quotient(A,B). [para(7(a,1),1054(a,1,2)),flip(a)].
% 39.01/39.32 1249 product(quotient(difference(A,B),B),product(A,product(B,A))) = product(B,A). [para(6(a,1),1154(a,1,2,1)),rewrite([835(2)])].
% 39.01/39.32 1271 quotient(product(A,B),product(B,product(A,B))) = quotient(difference(B,A),A). [para(6(a,1),1157(a,1,2,1)),rewrite([835(6)])].
% 39.01/39.32 1273 difference(A,quotient(A,B)) = quotient(A,product(B,A)). [para(37(a,1),1157(a,1,2,1)),flip(a)].
% 39.01/39.32 1289 product(quotient(A,product(B,A)),quotient(A,B)) = difference(B,quotient(A,B)). [back_rewrite(1158),rewrite([1273(2)])].
% 39.01/39.32 1294 quotient(product(A,product(product(difference(A,one),B),difference(A,one))),difference(A,one)) = difference(difference(A,one),product(difference(difference(difference(A,one),one),one),B)). [para(36(a,1),73(a,1,1,1))].
% 39.01/39.32 1336 product(A,quotient(product(A,quotient(one,A)),product(B,product(A,quotient(one,A))))) = product(difference(difference(A,one),one),quotient(product(A,quotient(one,A)),B)). [para(1221(a,1),55(a,1,2)),flip(a)].
% 39.01/39.32 1634 quotient(product(product(A,quotient(one,A)),B),product(A,quotient(one,A))) = product(product(A,quotient(one,A)),quotient(B,product(A,quotient(one,A)))). [para(5(a,1),79(a,1,1,2)),rewrite([19(15),737(14),774(19),779(18)])].
% 39.01/39.32 1637 product(product(A,quotient(one,A)),quotient(product(B,difference(product(A,quotient(one,A)),product(C,product(A,quotient(one,A))))),product(A,quotient(one,A)))) = product(product(product(A,quotient(one,A)),quotient(B,product(A,quotient(one,A)))),C). [para(7(a,1),79(a,2,2)),rewrite([1634(17),1634(25)])].
% 39.01/39.32 1638 product(product(A,quotient(one,A)),product(quotient(B,product(A,quotient(one,A))),C)) = product(product(A,quotient(one,A)),product(B,difference(product(A,quotient(one,A)),C))). [para(79(a,1),8(a,1,1)),rewrite([1634(8),257(13),655(17),8(16)])].
% 39.01/39.32 1641 product(product(A,quotient(one,A)),quotient(product(quotient(B,product(A,quotient(one,A))),C),product(A,quotient(one,A)))) = product(product(A,quotient(one,A)),quotient(product(B,difference(product(A,quotient(one,A)),C)),product(A,quotient(one,A)))). [para(79(a,1),13(a,2)),rewrite([13(9),1634(13),1634(21),257(26)]),flip(a)].
% 39.01/39.32 1731 product(quotient(one,product(A,quotient(one,A))),product(product(A,quotient(one,A)),quotient(B,product(A,quotient(one,A))))) = quotient(B,product(A,quotient(one,A))). [back_rewrite(770),rewrite([1638(10),2(9),5(8),1634(17)]),flip(a)].
% 39.01/39.32 1741 quotient(product(difference(A,one),B),product(A,quotient(one,A))) = product(difference(A,one),quotient(B,product(A,quotient(one,A)))). [back_rewrite(255),rewrite([1634(14),586(15)]),flip(a)].
% 39.01/39.32 1754 product(quotient(A,product(B,quotient(one,B))),product(product(B,quotient(one,B)),quotient(C,product(B,quotient(one,B))))) = product(product(B,quotient(one,B)),quotient(product(difference(product(B,quotient(one,B)),A),C),product(B,quotient(one,B)))). [back_rewrite(78),rewrite([1634(13),1634(25)]),flip(a)].
% 39.01/39.32 1760 product(product(A,quotient(one,A)),quotient(difference(product(A,quotient(one,A)),B),product(A,quotient(one,A)))) = quotient(B,product(A,quotient(one,A))). [back_rewrite(1731),rewrite([1754(14),765(8),1641(14),2(9)])].
% 39.01/39.32 1800 quotient(quotient(A,difference(B,one)),B) = product(B,product(difference(B,one),A)). [para(98(a,1),32(a,1)),rewrite([1(2)])].
% 39.01/39.32 1835 quotient(quotient(product(quotient(difference(A,B),product(C,difference(A,B))),B),difference(A,B)),A) = difference(B,product(A,quotient(difference(A,B),C))). [para(1221(a,1),98(a,1,2,2)),flip(a)].
% 39.01/39.32 1899 quotient(quotient(product(product(product(A,quotient(one,A)),B),C),A),quotient(C,A)) = difference(C,product(quotient(C,A),product(quotient(one,quotient(one,A)),B))). [para(17(a,1),100(a,1,2,2)),flip(a)].
% 39.01/39.32 1902 quotient(quotient(A,B),quotient(one,B)) = product(quotient(one,B),product(B,A)). [para(100(a,1),32(a,1)),rewrite([1(2)])].
% 39.01/39.32 2177 product(quotient(one,A),product(difference(quotient(one,A),B),product(A,quotient(one,A)))) = product(B,product(A,quotient(one,A))). [para(128(a,1),56(a,1,2,2)),rewrite([128(17)])].
% 39.01/39.32 2237 product(A,quotient(product(difference(A,B),C),A)) = product(B,quotient(C,A)). [para(5(a,1),257(a,1,1)),flip(a)].
% 39.01/39.32 2243 product(A,product(A,quotient(product(quotient(one,A),B),A))) = product(quotient(one,quotient(one,A)),quotient(B,A)). [para(257(a,1),17(a,1,2))].
% 39.01/39.32 2253 product(difference(A,one),quotient(product(product(A,quotient(one,A)),B),difference(A,one))) = product(quotient(one,A),quotient(B,difference(A,one))). [para(156(a,1),257(a,1,1)),flip(a)].
% 39.01/39.32 2259 quotient(product(product(A,quotient(one,A)),B),A) = product(A,quotient(product(quotient(one,A),B),A)). [para(257(a,1),49(a,2)),rewrite([606(7),145(5)])].
% 39.01/39.32 2355 quotient(product(A,quotient(B,A)),C) = product(A,quotient(B,product(C,A))). [para(258(a,1),7(a,1,1))].
% 39.01/39.32 2454 product(A,product(quotient(one,quotient(one,A)),quotient(one,product(B,A)))) = product(A,product(A,quotient(one,product(B,difference(difference(A,one),one))))). [back_rewrite(1336),rewrite([2355(8),262(6),2355(17),598(18)]),flip(a)].
% 39.01/39.32 2541 product(difference(A,one),product(B,A)) = product(difference(A,B),A). [para(2(a,1),605(a,1,1,2)),flip(a)].
% 39.01/39.32 2542 product(difference(A,B),product(difference(B,C),A)) = product(difference(A,C),A). [para(5(a,1),605(a,1,1,2)),flip(a)].
% 39.01/39.32 2543 product(difference(A,quotient(B,C)),product(C,A)) = product(difference(A,B),A). [para(8(a,1),605(a,1,1,2)),flip(a)].
% 39.01/39.32 2562 product(product(product(A,quotient(one,A)),B),difference(difference(A,one),one)) = product(product(A,quotient(one,A)),product(B,difference(difference(A,one),one))). [para(223(a,1),605(a,2,1)),rewrite([578(6)])].
% 39.01/39.32 2622 product(quotient(quotient(product(A,B),C),quotient(B,C)),B) = product(quotient(B,product(C,B)),product(product(C,A),B)). [para(100(a,1),605(a,1,1)),rewrite([1273(7)])].
% 39.01/39.32 2694 difference(difference(A,one),product(difference(A,B),A)) = product(B,A). [para(2541(a,1),6(a,1,2))].
% 39.01/39.32 2695 quotient(product(difference(A,B),A),product(B,A)) = difference(A,one). [para(2541(a,1),7(a,1,1))].
% 39.01/39.32 2696 product(difference(A,quotient(B,A)),A) = product(difference(A,one),B). [para(8(a,1),2541(a,1,2)),flip(a)].
% 39.01/39.32 2702 product(difference(quotient(one,A),B),quotient(one,A)) = product(A,product(B,quotient(one,A))). [para(37(a,1),2541(a,1,1)),flip(a)].
% 39.01/39.32 2732 quotient(product(A,product(product(difference(A,B),A),difference(A,one))),difference(A,one)) = difference(difference(A,one),product(difference(difference(difference(A,one),one),one),product(B,A))). [para(2541(a,1),73(a,1,1,2,1)),rewrite([36(4)])].
% 39.01/39.32 2764 difference(difference(A,one),product(B,A)) = product(product(A,B),A). [para(6(a,1),2694(a,1,2,1))].
% 39.01/39.32 2766 difference(difference(A,one),product(B,product(C,A))) = product(product(product(A,B),C),A). [para(21(a,1),2694(a,1,2,1)),rewrite([8(6)])].
% 39.01/39.32 2768 difference(quotient(one,product(A,quotient(one,A))),product(A,product(B,product(A,quotient(one,A))))) = product(product(difference(difference(A,one),one),B),product(A,quotient(one,A))). [para(42(a,1),2694(a,1,2,1)),rewrite([765(5),19(10)])].
% 39.01/39.32 2781 difference(difference(A,one),difference(A,B)) = product(product(B,A),difference(A,one)). [para(2694(a,1),605(a,1,1)),rewrite([5(11),1(10)]),flip(a)].
% 39.01/39.32 2783 quotient(product(A,product(product(difference(A,B),A),difference(A,one))),difference(A,one)) = product(product(quotient(one,product(A,quotient(one,A))),B),A). [back_rewrite(2732),rewrite([2766(20),180(16),765(14)])].
% 39.01/39.32 2796 quotient(product(A,B),product(product(B,A),B)) = difference(B,one). [para(6(a,1),2695(a,1,1,1))].
% 39.01/39.32 2833 quotient(product(difference(A,one),B),A) = difference(A,quotient(B,A)). [para(2696(a,1),7(a,1,1))].
% 39.01/39.32 2836 product(product(difference(difference(A,one),one),quotient(B,product(A,quotient(one,A)))),product(A,quotient(one,A))) = product(A,product(quotient(one,product(A,quotient(one,A))),B)). [para(2696(a,1),19(a,2,2)),rewrite([295(9),765(18)])].
% 39.01/39.32 2849 quotient(difference(A,product(difference(B,one),C)),B) = difference(product(B,A),quotient(C,B)). [para(2696(a,1),99(a,2,1,2)),rewrite([5(4)]),flip(a)].
% 39.01/39.32 2935 product(product(difference(A,B),A),difference(A,B)) = difference(difference(difference(A,B),one),B). [para(5(a,1),2764(a,1,2)),flip(a)].
% 39.01/39.32 2936 product(product(A,quotient(B,A)),A) = difference(difference(A,one),B). [para(8(a,1),2764(a,1,2)),flip(a)].
% 39.01/39.32 2940 product(product(quotient(one,A),B),quotient(one,A)) = quotient(difference(A,B),A). [para(37(a,1),2764(a,1,1)),rewrite([606(4),1(3)]),flip(a)].
% 39.01/39.32 2954 quotient(difference(difference(A,one),B),difference(A,one)) = product(product(A,B),A). [para(2764(a,1),68(a,2)),rewrite([5(6),1(5)])].
% 39.01/39.32 2965 quotient(product(product(A,quotient(one,A)),B),difference(A,one)) = product(product(A,product(quotient(one,A),B)),A). [para(2764(a,1),74(a,2)),rewrite([36(6),12(3),5(7),1(6),36(12)])].
% 39.01/39.32 2978 product(product(product(A,B),A),difference(A,one)) = difference(difference(A,one),B). [para(2764(a,1),605(a,1,1)),rewrite([5(11),1(10)])].
% 39.01/39.32 2995 product(quotient(one,A),quotient(B,difference(A,one))) = product(product(quotient(one,A),B),A). [back_rewrite(2253),rewrite([2965(9),2541(8),6(5)]),flip(a)].
% 39.01/39.32 3011 quotient(product(A,quotient(one,B)),quotient(difference(B,A),B)) = B. [para(37(a,1),2796(a,2)),rewrite([2940(9)])].
% 39.01/39.32 3153 difference(product(A,quotient(B,A)),difference(difference(A,one),B)) = A. [para(2936(a,1),6(a,1,2))].
% 39.01/39.32 3154 quotient(difference(difference(A,one),B),A) = product(A,quotient(B,A)). [para(2936(a,1),7(a,1,1))].
% 39.01/39.32 3175 quotient(product(A,product(B,difference(A,one))),difference(A,one)) = product(product(quotient(one,quotient(one,A)),quotient(B,A)),A). [para(71(a,1),2936(a,2)),rewrite([2259(5),2243(6)]),flip(a)].
% 39.01/39.32 3189 difference(quotient(one,product(A,quotient(one,A))),B) = product(product(A,quotient(one,A)),B). [para(2936(a,1),77(a,2)),rewrite([2562(13),1638(13),3153(11),2259(6),67(6),765(9)]),flip(a)].
% 39.01/39.32 3208 product(product(quotient(one,product(A,quotient(one,A))),B),A) = product(difference(product(A,quotient(one,A)),B),A). [back_rewrite(2783),rewrite([3175(9),7(7),645(6)]),flip(a)].
% 39.01/39.32 3213 difference(difference(A,one),product(difference(difference(difference(A,one),one),one),B)) = product(difference(product(A,quotient(one,A)),quotient(B,A)),A). [back_rewrite(1294),rewrite([3175(10),2833(8),645(7)]),flip(a)].
% 39.01/39.32 3219 product(product(quotient(one,quotient(one,A)),quotient(product(quotient(one,quotient(one,A)),B),A)),A) = difference(difference(A,one),product(A,B)). [back_rewrite(1132),rewrite([3175(12)])].
% 39.01/39.32 3225 difference(difference(A,one),product(product(A,quotient(one,A)),B)) = product(product(quotient(one,quotient(one,A)),quotient(B,A)),A). [back_rewrite(71),rewrite([3175(14)])].
% 39.01/39.32 3229 product(product(difference(difference(A,one),one),B),product(A,quotient(one,A))) = product(difference(difference(A,one),one),product(B,product(A,quotient(one,A)))). [back_rewrite(2768),rewrite([3189(11),15(9)]),flip(a)].
% 39.01/39.32 3233 product(A,product(quotient(one,product(A,quotient(one,A))),B)) = product(difference(difference(A,one),one),B). [back_rewrite(2836),rewrite([3229(13),8(12)]),flip(a)].
% 39.01/39.32 3239 product(A,quotient(difference(A,B),A)) = product(B,quotient(one,A)). [para(3011(a,1),8(a,1,1))].
% 39.01/39.32 3240 quotient(A,quotient(difference(B,quotient(A,quotient(one,B))),B)) = B. [para(8(a,1),3011(a,1,1))].
% 39.01/39.32 3248 product(A,product(quotient(difference(A,B),A),product(A,quotient(one,A)))) = product(product(B,quotient(one,A)),product(A,quotient(one,A))). [para(3011(a,1),59(a,1,1)),rewrite([3011(8),3011(9),3011(16),3011(17)])].
% 39.01/39.32 3274 product(A,quotient(one,product(B,quotient(one,B)))) = quotient(A,product(B,quotient(one,B))). [back_rewrite(1760),rewrite([3239(12)])].
% 39.01/39.32 3309 product(quotient(one,A),quotient(B,quotient(one,A))) = quotient(difference(A,B),quotient(one,A)). [para(37(a,1),3154(a,1,1,1)),flip(a)].
% 39.01/39.32 3564 difference(product(A,quotient(one,A)),product(B,difference(A,one))) = product(A,product(product(difference(A,one),B),difference(A,one))). [para(3239(a,1),42(a,1,2)),rewrite([36(9),2954(17)])].
% 39.01/39.32 3576 difference(product(A,B),product(C,quotient(one,A))) = quotient(difference(B,difference(A,C)),A). [para(3239(a,1),99(a,1,2)),rewrite([8(8)])].
% 39.01/39.32 3608 product(product(A,quotient(one,B)),B) = product(product(A,B),difference(B,one)). [para(3239(a,1),2764(a,2,1)),rewrite([8(5),2781(4)]),flip(a)].
% 39.01/39.32 3615 quotient(product(product(A,B),difference(B,one)),B) = product(A,quotient(one,B)). [para(3239(a,1),3154(a,2)),rewrite([2781(4)])].
% 39.01/39.32 3618 product(difference(product(A,quotient(one,A)),quotient(B,A)),A) = difference(quotient(one,A),product(difference(A,one),B)). [back_rewrite(866),rewrite([3564(7),3175(10),2833(8),645(7)])].
% 39.01/39.32 3629 difference(quotient(one,quotient(one,A)),product(quotient(one,A),B)) = product(quotient(one,A),difference(A,B)). [back_rewrite(893),rewrite([3576(5),1902(6),5(5)]),flip(a)].
% 39.01/39.32 3631 difference(difference(A,one),product(difference(difference(difference(A,one),one),one),B)) = difference(quotient(one,A),product(difference(A,one),B)). [back_rewrite(3213),rewrite([3618(16)])].
% 39.01/39.32 3634 quotient(difference(A,quotient(B,quotient(one,A))),A) = difference(A,B). [para(3240(a,1),37(a,1,1)),flip(a)].
% 39.01/39.32 3639 difference(A,quotient(B,quotient(one,A))) = product(difference(A,B),A). [para(3634(a,1),8(a,1,1)),flip(a)].
% 39.01/39.32 3650 product(A,product(difference(A,B),A)) = quotient(B,quotient(one,A)). [para(3639(a,1),5(a,1,2))].
% 39.01/39.32 3652 product(difference(difference(A,one),B),difference(A,one)) = difference(difference(A,one),quotient(B,A)). [para(36(a,1),3639(a,1,2,2)),flip(a)].
% 39.01/39.32 3687 product(product(A,quotient(one,A)),difference(difference(difference(A,one),one),one)) = difference(difference(difference(difference(difference(A,one),one),one),one),one). [para(124(a,1),61(a,1,2)),rewrite([143(6),143(13),36(14),12(11),36(10),12(7),36(6),12(3),3274(18),35(16),1(11),143(16),3274(29),35(27),1(22)])].
% 39.01/39.32 3700 quotient(product(quotient(one,A),product(product(quotient(one,A),B),A)),A) = difference(A,product(difference(A,one),B)). [para(124(a,1),74(a,2,2)),rewrite([531(10),37(8),37(14),37(12)])].
% 39.01/39.32 3706 difference(A,product(difference(difference(A,one),one),B)) = difference(product(A,quotient(one,A)),B). [para(124(a,1),105(a,1,2,2)),rewrite([3274(10),146(8),765(5),37(7),765(5),3233(7),765(11),3274(22),146(20),3208(13),3274(20),35(18),34(13),7(12)])].
% 39.01/39.32 3717 difference(quotient(one,A),product(difference(A,one),B)) = difference(product(A,quotient(one,A)),B). [back_rewrite(3631),rewrite([3706(10),36(6),12(3)]),flip(a)].
% 39.01/39.32 3744 product(difference(product(A,quotient(one,A)),quotient(B,A)),A) = difference(product(A,quotient(one,A)),B). [back_rewrite(3618),rewrite([3717(12)])].
% 39.01/39.32 3746 quotient(product(A,B),quotient(one,A)) = product(A,product(B,A)). [para(6(a,1),3650(a,1,2,1)),flip(a)].
% 39.01/39.32 3749 quotient(product(product(A,B),C),quotient(one,A)) = product(A,product(B,product(C,A))). [para(21(a,1),3650(a,1,2,1)),rewrite([8(4)]),flip(a)].
% 39.01/39.32 3750 product(quotient(A,B),product(B,quotient(A,B))) = quotient(A,quotient(one,quotient(A,B))). [para(37(a,1),3650(a,1,2,1))].
% 39.01/39.32 3757 quotient(A,quotient(one,product(B,quotient(one,B)))) = product(A,product(B,quotient(one,B))). [para(3650(a,1),49(a,2)),rewrite([296(13),6(6)]),flip(a)].
% 39.01/39.32 3773 product(A,product(product(B,A),difference(A,one))) = difference(quotient(one,A),B). [para(70(a,1),3650(a,2)),rewrite([6(5),3608(4),2(9)])].
% 39.01/39.32 3804 product(A,product(difference(A,B),product(C,A))) = quotient(product(B,C),quotient(one,A)). [para(605(a,1),3650(a,1,2))].
% 39.01/39.32 3807 product(quotient(one,A),product(A,B)) = product(A,product(difference(A,one),B)). [para(2696(a,1),3650(a,1,2)),rewrite([1902(8)]),flip(a)].
% 39.01/39.32 3826 difference(quotient(one,A),product(quotient(one,quotient(one,A)),B)) = product(A,difference(quotient(one,A),B)). [back_rewrite(522),rewrite([3749(8),3608(4),3773(5)]),flip(a)].
% 39.01/39.32 3831 quotient(product(A,B),quotient(one,quotient(one,B))) = product(A,product(B,quotient(one,B))). [back_rewrite(2177),rewrite([3804(10)])].
% 39.01/39.32 3870 difference(quotient(one,quotient(one,A)),product(B,product(A,quotient(one,A)))) = product(difference(quotient(one,quotient(one,A)),B),product(A,quotient(one,A))). [back_rewrite(621),rewrite([3831(11)]),flip(a)].
% 39.01/39.32 3883 quotient(product(quotient(one,A),product(B,A)),A) = difference(quotient(one,quotient(one,A)),B). [back_rewrite(864),rewrite([3870(9),7(13)]),flip(a)].
% 39.01/39.32 3891 difference(A,product(difference(A,one),B)) = product(quotient(one,A),difference(A,B)). [back_rewrite(3700),rewrite([3883(8),3629(8)]),flip(a)].
% 39.01/39.32 3933 product(difference(A,one),product(B,difference(A,one))) = difference(A,quotient(B,A)). [para(36(a,1),3746(a,1,2)),rewrite([2833(4)]),flip(a)].
% 39.01/39.32 3983 difference(A,product(quotient(B,A),quotient(one,quotient(B,A)))) = quotient(product(difference(A,difference(quotient(B,A),one)),B),A). [para(12(a,1),606(a,1,2))].
% 39.01/39.32 4012 difference(A,product(difference(quotient(B,A),C),product(D,quotient(B,A)))) = quotient(product(difference(A,difference(quotient(B,A),product(C,D))),B),A). [para(605(a,1),606(a,1,2))].
% 39.01/39.32 4038 product(difference(A,one),product(difference(difference(A,one),one),B)) = product(A,product(difference(A,one),B)). [para(15(a,1),125(a,1,2)),rewrite([3807(12)])].
% 39.01/39.32 4041 product(product(A,difference(B,one)),product(B,quotient(one,B))) = product(A,quotient(one,B)). [para(125(a,1),67(a,1,2,1)),rewrite([7(4)]),flip(a)].
% 39.01/39.32 4071 product(A,product(difference(A,one),product(B,quotient(one,A)))) = quotient(B,quotient(one,quotient(one,A))). [para(3650(a,1),125(a,2)),rewrite([2702(11),15(10),4038(11)])].
% 39.01/39.32 4159 difference(A,product(difference(B,C),B)) = product(difference(product(B,A),C),B). [para(639(a,1),6(a,1,2))].
% 39.01/39.32 4161 product(difference(quotient(A,B),C),quotient(A,B)) = product(B,product(difference(A,C),quotient(A,B))). [para(8(a,1),639(a,1,2,1,1)),flip(a)].
% 39.01/39.32 4175 product(difference(product(A,quotient(one,A)),B),A) = product(quotient(one,A),product(product(A,B),A)). [para(42(a,1),639(a,1,2,1)),rewrite([3706(11)]),flip(a)].
% 39.01/39.32 4243 product(A,product(difference(difference(difference(A,one),B),C),product(A,quotient(B,A)))) = product(difference(product(A,quotient(B,A)),C),product(A,quotient(B,A))). [para(2936(a,1),639(a,1,2,1,1))].
% 39.01/39.32 4265 product(quotient(one,A),difference(difference(A,one),B)) = difference(product(A,quotient(one,A)),B). [back_rewrite(3744),rewrite([4175(6),2936(5)])].
% 39.01/39.32 4282 difference(product(A,quotient(one,A)),product(B,product(A,quotient(one,A)))) = product(difference(product(A,quotient(one,A)),B),product(A,quotient(one,A))). [back_rewrite(666),rewrite([4243(10)]),flip(a)].
% 39.01/39.32 4288 product(product(product(A,quotient(one,A)),quotient(B,product(A,quotient(one,A)))),C) = product(product(product(A,quotient(one,A)),B),difference(product(A,quotient(one,A)),C)). [back_rewrite(1637),rewrite([4282(11),67(17)]),flip(a)].
% 39.01/39.32 4404 quotient(difference(product(A,quotient(one,A)),B),B) = quotient(one,product(A,quotient(one,A))). [para(765(a,1),2796(a,2)),rewrite([655(12),1271(13)])].
% 39.01/39.32 4411 product(product(A,product(B,quotient(one,B))),quotient(one,B)) = product(A,difference(B,one)). [para(129(a,1),67(a,1,2,1)),rewrite([7(4)]),flip(a)].
% 39.01/39.32 4412 product(A,product(quotient(one,A),difference(A,B))) = product(difference(A,one),B). [para(129(a,1),67(a,2)),rewrite([3883(8),3629(8)])].
% 39.01/39.32 4461 quotient(difference(difference(difference(A,B),C),B),difference(A,B)) = product(difference(product(A,C),B),A). [para(5(a,1),836(a,1,1,2)),rewrite([4159(8)])].
% 39.01/39.32 4462 difference(difference(A,B),product(C,A)) = product(difference(B,product(A,C)),A). [para(836(a,1),8(a,1,1)),flip(a)].
% 39.01/39.32 4463 difference(A,product(B,quotient(C,B))) = quotient(difference(difference(B,A),C),B). [para(8(a,1),836(a,1,1,2)),flip(a)].
% 39.01/39.32 4466 quotient(difference(difference(A,B),one),A) = product(difference(product(A,B),one),A). [para(12(a,1),836(a,2,2)),rewrite([5(6),4461(8),4463(8)]),flip(a)].
% 39.01/39.32 4511 difference(A,product(difference(B,C),product(D,B))) = product(difference(product(B,A),product(C,D)),B). [para(605(a,1),836(a,2,2)),rewrite([5(6),4461(8)]),flip(a)].
% 39.01/39.32 4534 quotient(product(difference(A,difference(quotient(B,A),one)),B),A) = product(difference(B,one),quotient(B,A)). [back_rewrite(3983),rewrite([4463(6),4466(6),8(2)]),flip(a)].
% 39.01/39.32 4563 quotient(quotient(difference(product(product(A,quotient(one,A)),B),one),A),product(A,quotient(one,A))) = quotient(difference(B,one),A). [back_rewrite(944),rewrite([4463(9),49(6)])].
% 39.01/39.32 4572 quotient(product(difference(A,difference(quotient(B,A),product(C,D))),B),A) = product(difference(B,product(C,D)),quotient(B,A)). [back_rewrite(4012),rewrite([4511(6),8(2)]),flip(a)].
% 39.01/39.32 4583 quotient(product(A,B),quotient(C,A)) = product(A,quotient(product(B,A),C)). [para(37(a,1),853(a,1,2,1))].
% 39.01/39.32 4720 difference(difference(A,one),product(B,product(A,quotient(one,A)))) = product(difference(difference(A,one),B),product(A,quotient(one,A))). [para(143(a,1),68(a,1,1,2)),rewrite([77(13),36(9),12(6)]),flip(a)].
% 39.01/39.32 4724 quotient(product(difference(difference(difference(A,one),one),one),product(B,A)),A) = difference(A,product(quotient(one,product(A,quotient(one,A))),B)). [para(143(a,1),74(a,1,1,1)),rewrite([645(16),765(14)])].
% 39.01/39.32 4813 product(A,quotient(B,difference(difference(B,one),one))) = quotient(A,product(B,quotient(one,B))). [para(935(a,1),3239(a,2,2)),rewrite([3239(12),3274(6)]),flip(a)].
% 39.01/39.32 4958 difference(A,difference(product(A,quotient(one,A)),B)) = difference(difference(difference(A,one),one),B). [para(5(a,1),162(a,1,2)),flip(a)].
% 39.01/39.32 4959 product(product(quotient(one,quotient(one,A)),quotient(B,A)),A) = difference(quotient(one,A),B). [para(37(a,1),162(a,1,1,1)),rewrite([3309(9),169(7),3225(7)])].
% 39.01/39.32 4962 difference(difference(difference(A,one),one),quotient(one,product(A,quotient(one,A)))) = difference(A,quotient(one,product(A,quotient(one,quotient(one,quotient(one,A)))))). [para(1035(a,1),162(a,1,2)),rewrite([765(9),19(18),3750(17)])].
% 39.01/39.32 4973 quotient(difference(A,B),difference(A,one)) = product(product(quotient(one,A),B),A). [para(162(a,1),3154(a,1,1)),rewrite([2965(13),2541(12),6(9)])].
% 39.01/39.32 4975 difference(A,quotient(difference(product(A,quotient(one,A)),B),product(A,quotient(one,A)))) = difference(difference(difference(A,one),one),quotient(B,product(A,quotient(one,A)))). [para(3239(a,1),162(a,1,2)),rewrite([3274(10)]),flip(a)].
% 39.01/39.32 4994 difference(difference(A,one),product(A,B)) = product(A,difference(quotient(one,A),B)). [back_rewrite(3219),rewrite([4959(12),3826(8)]),flip(a)].
% 39.01/39.32 5052 product(product(quotient(one,quotient(one,A)),B),product(A,B)) = difference(quotient(difference(B,one),A),product(A,B)). [para(52(a,1),1155(a,1,2)),rewrite([4463(9),49(6),4563(11),52(19)]),flip(a)].
% 39.01/39.32 5099 quotient(product(A,quotient(one,quotient(one,B))),B) = quotient(A,product(B,quotient(one,B))). [para(1162(a,1),21(a,2,1,2)),rewrite([3274(7),774(5),6(6)]),flip(a)].
% 39.01/39.32 5100 difference(A,quotient(B,product(A,quotient(one,A)))) = quotient(difference(A,B),product(A,quotient(one,A))). [para(1162(a,1),68(a,1,1,2)),rewrite([5099(7),3274(11)]),flip(a)].
% 39.01/39.32 5118 difference(difference(difference(A,one),one),quotient(B,product(A,quotient(one,A)))) = quotient(difference(difference(difference(A,one),one),B),product(A,quotient(one,A))). [back_rewrite(4975),rewrite([5100(9),4958(5)]),flip(a)].
% 39.01/39.32 5121 difference(A,quotient(one,product(A,quotient(one,quotient(one,quotient(one,A)))))) = quotient(difference(difference(difference(A,one),one),one),product(A,quotient(one,A))). [back_rewrite(4962),rewrite([5118(10)]),flip(a)].
% 39.01/39.32 5149 quotient(product(A,quotient(one,B)),difference(B,one)) = quotient(A,product(B,quotient(one,B))). [para(1163(a,1),21(a,2,1,2)),rewrite([3274(11),1741(9),6(10)]),flip(a)].
% 39.01/39.32 5171 difference(A,product(quotient(one,product(A,quotient(one,A))),B)) = difference(difference(difference(A,one),one),B). [para(1165(a,1),99(a,1,1)),rewrite([3274(17),5118(16),3757(22),8(20)])].
% 39.01/39.32 5184 quotient(product(difference(difference(difference(A,one),one),one),product(B,A)),A) = difference(difference(difference(A,one),one),B). [back_rewrite(4724),rewrite([5171(16)])].
% 39.01/39.32 5349 quotient(difference(difference(difference(A,one),one),one),product(A,quotient(one,A))) = difference(difference(difference(difference(difference(A,one),one),one),one),one). [para(1142(a,1),164(a,1,2)),rewrite([37(4),3274(12),3309(17),169(15),3309(20),169(18),143(19),3687(20)])].
% 39.01/39.32 5378 difference(A,quotient(one,product(A,quotient(one,quotient(one,quotient(one,A)))))) = difference(difference(difference(difference(difference(A,one),one),one),one),one). [back_rewrite(5121),rewrite([5349(20)])].
% 39.01/39.32 5490 difference(difference(difference(A,one),one),product(quotient(one,product(A,quotient(one,A))),B)) = difference(difference(difference(difference(difference(A,one),one),one),one),B). [para(1035(a,1),166(a,2,2,1)),rewrite([19(8),3750(7),5378(10),5184(21),765(18)]),flip(a)].
% 39.01/39.32 6193 product(A,product(difference(A,one),product(B,difference(difference(difference(A,one),one),one)))) = quotient(product(B,product(A,quotient(one,A))),A). [para(77(a,1),1800(a,1,1)),rewrite([36(6),12(3)]),flip(a)].
% 39.01/39.32 6197 product(product(A,B),product(A,product(difference(A,one),C))) = product(A,quotient(product(B,quotient(C,difference(A,one))),A)). [para(1800(a,1),257(a,1,2))].
% 39.01/39.32 6245 product(quotient(one,quotient(one,A)),quotient(B,A)) = quotient(difference(quotient(one,A),B),A). [para(8(a,1),182(a,1,1,2)),flip(a)].
% 39.01/39.32 6404 product(A,quotient(difference(difference(B,A),C),B)) = product(B,quotient(C,B)). [para(5(a,1),2237(a,1,2,1)),flip(a)].
% 39.01/39.32 6405 product(quotient(A,B),quotient(one,quotient(A,B))) = product(B,product(difference(A,one),quotient(A,B))). [para(12(a,1),2237(a,2)),rewrite([4534(6)]),flip(a)].
% 39.01/39.32 6445 product(difference(quotient(A,B),C),product(D,quotient(A,B))) = product(B,product(difference(A,product(C,D)),quotient(A,B))). [para(605(a,1),2237(a,2)),rewrite([4572(6)]),flip(a)].
% 39.01/39.32 6668 product(difference(A,B),quotient(B,product(C,difference(A,B)))) = quotient(product(difference(A,B),A),C). [para(36(a,1),2355(a,1,1,2)),flip(a)].
% 39.01/39.32 6760 product(A,product(quotient(B,A),product(A,quotient(one,A)))) = product(A,quotient(B,quotient(one,quotient(one,A)))). [para(1162(a,1),2355(a,2,2,2)),rewrite([3757(8),19(6)])].
% 39.01/39.32 6796 product(product(A,quotient(one,B)),product(B,quotient(one,B))) = product(B,quotient(difference(B,A),quotient(one,quotient(one,B)))). [back_rewrite(3248),rewrite([6760(7)]),flip(a)].
% 39.01/39.32 6807 difference(product(A,quotient(one,A)),difference(difference(A,one),quotient(B,A))) = product(A,product(B,difference(A,one))). [para(2542(a,1),42(a,1,2)),rewrite([3652(9),32(10)])].
% 39.01/39.32 6899 quotient(product(difference(A,B),A),product(C,A)) = difference(A,quotient(B,C)). [para(2543(a,1),7(a,1,1))].
% 39.01/39.32 7127 product(A,product(product(B,difference(A,one)),difference(difference(A,one),one))) = difference(product(A,quotient(one,A)),difference(difference(A,one),B)). [para(2781(a,1),180(a,1,2))].
% 39.01/39.32 7375 quotient(difference(product(product(A,quotient(one,A)),B),one),A) = product(quotient(difference(B,one),A),product(A,quotient(one,A))). [para(203(a,1),1289(a,1,2)),rewrite([5052(8),36(7),203(19),4463(16),49(13)]),flip(a)].
% 39.01/39.32 7400 quotient(product(product(A,B),quotient(one,B)),B) = product(A,difference(B,one)). [para(56(a,1),2940(a,1,1)),rewrite([6405(7),33(3),2(4),4411(7),6405(13),33(9),2(10),6445(10),32(6),6(9)]),flip(a)].
% 39.01/39.32 7460 quotient(product(A,B),product(B,quotient(one,B))) = product(A,difference(difference(B,one),one)). [para(56(a,1),2954(a,2,1)),rewrite([4720(8),2781(4),4041(8),5149(7),262(10)])].
% 39.01/39.32 7473 product(product(A,difference(B,one)),difference(difference(B,one),one)) = product(product(A,B),difference(B,one)). [para(2954(a,1),2936(a,1,1,2)),rewrite([2541(5),6(2),2781(12)]),flip(a)].
% 39.01/39.32 7483 difference(product(A,quotient(one,A)),difference(difference(A,one),B)) = difference(quotient(one,A),B). [back_rewrite(7127),rewrite([7473(8),3773(5)]),flip(a)].
% 39.01/39.32 7486 difference(quotient(one,A),quotient(B,A)) = product(A,product(B,difference(A,one))). [back_rewrite(6807),rewrite([7483(8)])].
% 39.01/39.32 7498 product(product(A,difference(difference(B,one),one)),difference(B,one)) = product(product(A,B),quotient(one,B)). [para(56(a,1),2978(a,1,1,1)),rewrite([262(5),4720(16),2781(12),4041(16)])].
% 39.01/39.32 7764 quotient(product(A,difference(B,one)),B) = product(quotient(A,B),quotient(one,B)). [para(8(a,1),3615(a,1,1,1))].
% 39.01/39.32 7918 difference(product(A,quotient(one,A)),difference(difference(difference(A,one),one),B)) = difference(A,B). [para(3773(a,1),183(a,1,2)),rewrite([36(11),7473(27),7473(23),7473(19),3933(16),7(11)])].
% 39.01/39.32 8029 quotient(product(A,product(difference(A,one),B)),product(A,B)) = quotient(one,A). [para(3807(a,1),7(a,1,1))].
% 39.01/39.32 8030 product(difference(A,one),product(A,B)) = product(A,product(quotient(one,A),B)). [para(3807(a,1),15(a,1,2)),rewrite([6405(7),33(3),2(4),6197(8),2995(6),7(5),37(8)]),flip(a)].
% 39.01/39.32 8472 product(quotient(one,A),difference(A,difference(difference(A,one),B))) = difference(A,B). [para(5(a,1),3891(a,1,2)),flip(a)].
% 39.01/39.32 8504 product(quotient(one,product(A,quotient(one,A))),difference(product(A,quotient(one,A)),B)) = product(A,difference(difference(difference(difference(difference(A,one),one),one),one),B)). [para(3891(a,1),180(a,2)),rewrite([765(9),5490(11)]),flip(a)].
% 39.01/39.32 8666 product(quotient(difference(difference(A,one),B),B),difference(A,quotient(B,A))) = product(B,difference(A,one)). [para(3933(a,1),1249(a,1,2))].
% 39.01/39.32 8671 product(difference(A,one),product(B,difference(difference(difference(A,one),one),one))) = difference(A,quotient(B,difference(difference(A,one),one))). [para(3933(a,1),183(a,1,2)),rewrite([7918(14)]),flip(a)].
% 39.01/39.32 8685 quotient(product(A,product(B,quotient(one,B))),B) = quotient(A,difference(difference(B,one),one)). [back_rewrite(6193),rewrite([8671(10),5(7)]),flip(a)].
% 39.01/39.32 9037 product(quotient(one,product(A,quotient(one,A))),B) = difference(product(A,quotient(one,A)),B). [para(4412(a,1),41(a,2)),rewrite([8504(14),6(15),180(14),36(10),12(7),36(6),12(3),765(9)]),flip(a)].
% 39.01/39.32 9283 difference(difference(A,B),product(difference(A,C),D)) = product(difference(B,product(C,quotient(D,A))),A). [para(2237(a,1),4462(a,2,1,2)),rewrite([8(5)])].
% 39.01/39.32 9657 product(product(difference(product(A,B),one),A),A) = difference(difference(A,B),one). [para(4466(a,1),8(a,1,1))].
% 39.01/39.32 9667 product(difference(product(A,product(quotient(one,quotient(one,A)),B)),one),A) = product(quotient(difference(B,one),A),product(A,quotient(one,A))). [para(49(a,1),4466(a,1,1,1)),rewrite([7375(7)]),flip(a)].
% 39.01/39.32 9749 product(A,quotient(product(difference(A,B),A),C)) = quotient(B,quotient(C,A)). [para(5(a,1),4583(a,1,1)),flip(a)].
% 39.01/39.32 9752 product(A,product(A,quotient(one,product(B,A)))) = quotient(one,quotient(B,A)). [para(12(a,1),4583(a,2,2,1)),rewrite([5(3),2355(7)]),flip(a)].
% 39.01/39.32 9791 quotient(difference(A,one),quotient(B,A)) = product(A,quotient(quotient(one,A),B)). [para(992(a,1),4583(a,2,2,1)),rewrite([1035(4)])].
% 39.01/39.32 10493 product(product(A,difference(B,one)),B) = product(product(A,B),quotient(one,B)). [para(262(a,1),2781(a,2,1)),rewrite([617(7),9283(8),2355(5),1035(5),32(5),7498(12)])].
% 39.01/39.32 10524 product(quotient(A,quotient(one,quotient(one,B))),B) = quotient(A,product(B,quotient(one,B))). [para(3650(a,1),4973(a,2,1)),rewrite([4161(6),32(2),6(5),5149(6)]),flip(a)].
% 39.01/39.32 10911 product(quotient(A,B),quotient(C,quotient(A,B))) = product(A,quotient(difference(B,C),quotient(A,B))). [para(37(a,1),6404(a,1,2,1,1)),flip(a)].
% 39.01/39.32 11401 product(A,quotient(one,product(product(B,A),A))) = difference(A,quotient(one,B)). [para(12(a,1),6899(a,1,1)),rewrite([2355(5)])].
% 39.01/39.32 11406 product(A,quotient(one,product(product(B,A),quotient(one,A)))) = difference(difference(A,one),quotient(one,B)). [para(41(a,1),6899(a,1,1)),rewrite([1(5),2355(7),10493(5)])].
% 39.01/39.32 11420 difference(A,quotient(quotient(one,A),B)) = quotient(difference(A,one),product(B,A)). [para(678(a,1),6899(a,1,1,1)),rewrite([8(4)]),flip(a)].
% 39.01/39.32 11466 difference(product(A,quotient(one,A)),quotient(one,B)) = quotient(one,product(B,product(A,quotient(one,A)))). [para(765(a,1),6899(a,1,1,1)),rewrite([8(9)]),flip(a)].
% 39.01/39.32 11819 quotient(product(A,quotient(one,B)),B) = product(quotient(A,B),difference(B,one)). [para(8(a,1),7400(a,1,1,1))].
% 39.01/39.32 11857 product(quotient(A,B),product(B,quotient(one,B))) = quotient(A,quotient(one,quotient(one,B))). [para(7486(a,1),56(a,1,2,1)),rewrite([10911(13),9791(12),34(11),2(11),19(10),4041(9),3807(7),4071(7),10911(13),9791(12),34(11),2(11)]),flip(a)].
% 39.01/39.32 11888 product(difference(product(A,product(quotient(one,quotient(one,A)),B)),one),A) = quotient(difference(B,one),quotient(one,quotient(one,A))). [back_rewrite(9667),rewrite([11857(16)])].
% 39.01/39.32 12040 quotient(A,product(product(B,quotient(one,B)),A)) = quotient(one,product(B,quotient(one,B))). [para(765(a,1),8029(a,1,1,2,1)),rewrite([9037(9),5(8)])].
% 39.01/39.32 12285 difference(quotient(one,A),difference(A,B)) = difference(A,difference(difference(A,one),B)). [para(8472(a,1),6(a,1,2))].
% 39.01/39.32 12712 difference(difference(A,difference(A,B)),one) = product(product(difference(B,one),A),A). [para(5(a,1),9657(a,1,1,1,1)),flip(a)].
% 39.01/39.32 12720 difference(product(product(A,quotient(one,A)),B),one) = quotient(difference(B,one),product(A,quotient(one,A))). [para(49(a,1),9657(a,2,1)),rewrite([11888(9),10524(8)]),flip(a)].
% 39.01/39.32 12874 quotient(one,quotient(A,product(B,quotient(one,B)))) = product(product(B,quotient(one,B)),quotient(one,A)). [para(765(a,1),9749(a,1,2,1,1)),rewrite([8(12)]),flip(a)].
% 39.01/39.32 12876 product(product(A,quotient(one,A)),quotient(B,quotient(C,quotient(one,A)))) = product(difference(A,one),quotient(product(A,product(B,quotient(one,A))),C)). [para(9749(a,1),129(a,1,2)),rewrite([4161(16),32(12)])].
% 39.01/39.32 12929 product(A,product(A,quotient(one,product(B,difference(difference(A,one),one))))) = product(product(A,quotient(one,A)),quotient(one,quotient(B,A))). [para(9752(a,1),15(a,1,2)),rewrite([598(16),2454(16)]),flip(a)].
% 39.01/39.32 12930 product(product(A,quotient(one,A)),quotient(one,quotient(B,A))) = quotient(one,quotient(B,difference(difference(A,one),one))). [para(9752(a,1),15(a,2)),rewrite([6668(15),12(10),36(9),12(6),2355(7),9752(8)])].
% 39.01/39.32 13020 product(A,product(A,quotient(one,product(B,difference(difference(A,one),one))))) = quotient(one,quotient(B,difference(difference(A,one),one))). [back_rewrite(12929),rewrite([12930(16)])].
% 39.01/39.32 13762 product(A,quotient(one,product(product(product(B,A),A),difference(A,one)))) = difference(A,quotient(one,product(B,difference(A,one)))). [para(10493(a,1),11401(a,1,2,2,1)),rewrite([3608(6)])].
% 39.01/39.32 13805 product(product(A,quotient(one,A)),quotient(quotient(one,quotient(one,A)),B)) = product(difference(A,one),quotient(A,product(B,quotient(one,A)))). [para(11420(a,1),168(a,1,2)),rewrite([37(6)]),flip(a)].
% 39.01/39.32 13895 product(quotient(quotient(A,quotient(one,B)),B),difference(B,one)) = quotient(A,B). [para(8(a,1),11819(a,1,1)),flip(a)].
% 39.01/39.32 14063 product(difference(A,difference(difference(A,one),B)),quotient(one,A)) = product(A,product(difference(A,B),quotient(one,A))). [para(12285(a,1),2541(a,2,1)),rewrite([37(4)]),flip(a)].
% 39.01/39.32 14339 quotient(one,product(product(difference(A,one),B),B)) = difference(B,difference(B,A)). [para(12712(a,1),36(a,1,2))].
% 39.01/39.32 14791 quotient(quotient(A,quotient(one,B)),B) = quotient(quotient(A,B),difference(B,one)). [para(13895(a,1),7(a,1,1)),flip(a)].
% 39.01/39.32 14817 quotient(one,product(difference(product(A,quotient(one,A)),B),B)) = difference(B,product(difference(product(A,B),one),A)). [para(765(a,1),14339(a,1,2,1,1)),rewrite([9037(7),4463(11),4466(11)])].
% 39.01/39.32 14947 quotient(quotient(A,B),product(B,quotient(one,B))) = quotient(A,difference(difference(B,one),one)). [para(77(a,1),14791(a,1,1)),rewrite([10911(7),9791(6),34(5),2(5),8685(5),37(9),7764(9),5149(12)]),flip(a)].
% 39.01/39.32 15023 product(A,quotient(difference(A,B),quotient(one,quotient(one,A)))) = product(B,quotient(one,quotient(one,quotient(one,A)))). [para(3239(a,1),454(a,2)),rewrite([6245(22),12285(15),37(13),12285(11),37(9),12285(7),12876(13),14063(9),34(10),8030(9),3807(8),4071(8)])].
% 39.01/39.32 15031 product(product(A,quotient(one,B)),product(B,quotient(one,B))) = product(A,quotient(one,quotient(one,quotient(one,B)))). [back_rewrite(6796),rewrite([15023(14)])].
% 39.01/39.32 15155 product(quotient(one,quotient(one,A)),quotient(one,product(B,A))) = product(A,quotient(one,product(B,difference(difference(A,one),one)))). [para(1273(a,1),645(a,2)),rewrite([2355(8),6(9),2355(16),262(14)])].
% 39.01/39.32 15750 difference(product(A,quotient(difference(A,one),product(B,quotient(one,B)))),quotient(quotient(one,quotient(one,B)),A)) = quotient(B,A). [para(1080(a,1),2849(a,1,1)),flip(a)].
% 39.01/39.32 15989 difference(quotient(difference(A,one),product(B,quotient(one,B))),A) = product(product(product(B,quotient(one,B)),A),A). [para(3189(a,1),2935(a,1,1,1)),rewrite([3274(10),1634(8),3189(14),4288(13),6(12),3189(11),12720(11)]),flip(a)].
% 39.01/39.32 16021 quotient(difference(product(A,quotient(one,A)),B),product(quotient(B,product(A,quotient(one,A))),B)) = difference(B,one). [para(3274(a,1),2796(a,1,2,1)),rewrite([9037(6)])].
% 39.01/39.32 16243 difference(A,quotient(one,quotient(B,difference(difference(A,one),one)))) = product(A,quotient(one,product(B,difference(difference(A,one),one)))). [para(1273(a,1),3706(a,2)),rewrite([2355(8),598(9),15155(8),13020(9),2355(16),262(14)])].
% 39.01/39.32 16655 product(A,quotient(one,product(product(B,A),difference(A,one)))) = difference(quotient(one,A),quotient(one,B)). [para(4041(a,1),1273(a,2,2)),rewrite([2355(10),10493(8),11406(10),7483(9),2355(12),3608(10)]),flip(a)].
% 39.01/39.32 16665 product(product(A,quotient(one,A)),quotient(one,product(B,quotient(one,quotient(one,quotient(one,A)))))) = quotient(one,product(B,quotient(one,A))). [para(4041(a,1),11401(a,1,2,2,1)),rewrite([15031(11),11466(22),4041(21)])].
% 39.01/39.32 16667 difference(quotient(one,A),quotient(one,product(B,A))) = difference(A,quotient(one,product(B,difference(A,one)))). [back_rewrite(13762),rewrite([16655(8)])].
% 39.01/39.32 16748 product(quotient(one,A),quotient(one,product(B,difference(A,one)))) = product(A,quotient(one,product(B,difference(difference(A,one),one)))). [para(1273(a,1),4265(a,2)),rewrite([2355(8),4994(9),16667(8),5(9),2355(16),262(14)])].
% 39.01/39.32 23708 product(quotient(A,product(B,quotient(one,B))),C) = product(A,difference(product(B,quotient(one,B)),C)). [para(1638(a,1),6(a,1,2)),rewrite([6(13)]),flip(a)].
% 39.01/39.32 23710 quotient(difference(product(A,quotient(one,A)),B),product(B,difference(product(A,quotient(one,A)),B))) = difference(B,one). [back_rewrite(16021),rewrite([23708(9)])].
% 39.01/39.32 24074 product(A,quotient(difference(A,one),product(B,quotient(one,B)))) = quotient(one,product(B,quotient(one,B))). [para(12040(a,1),8666(a,1,2,2)),rewrite([12720(6),15989(7),7(6),905(14),765(9),257(15),5(10),985(12),19(11),3750(10),16665(13),12720(11)]),flip(a)].
% 39.01/39.32 24097 product(difference(A,one),quotient(A,product(B,quotient(one,A)))) = quotient(A,B). [back_rewrite(15750),rewrite([24074(7),3189(11),13805(9)])].
% 39.01/39.32 24279 product(A,product(product(B,quotient(one,A)),quotient(quotient(one,product(B,quotient(one,A))),A))) = product(B,quotient(one,B)). [para(24097(a,1),2542(a,1,2)),rewrite([37(5),257(5),8(3),12(14),10911(14),9791(13)]),flip(a)].
% 39.01/39.32 24308 product(difference(A,one),difference(difference(quotient(A,product(B,quotient(one,A))),one),one)) = quotient(A,difference(difference(B,one),one)). [para(24097(a,1),7460(a,1,1)),rewrite([10911(12),9791(11),24279(12),14947(5)]),flip(a)].
% 39.01/39.32 24615 product(difference(product(A,B),one),difference(difference(A,one),one)) = difference(B,one). [para(4404(a,1),1835(a,2,2,2)),rewrite([23710(10),12(3),2355(8),14817(7),5(6),7460(8),3274(17),35(15)])].
% 39.01/39.32 24676 product(difference(A,one),difference(difference(B,one),one)) = difference(difference(B,A),one). [para(5(a,1),24615(a,1,1,1))].
% 39.01/39.32 24739 difference(product(A,quotient(one,B)),one) = quotient(B,difference(difference(A,one),one)). [back_rewrite(24308),rewrite([24676(11),37(5)])].
% 39.01/39.32 25072 quotient(one,quotient(A,difference(difference(B,one),one))) = product(B,quotient(one,A)). [para(24739(a,1),36(a,1,2))].
% 39.01/39.32 25082 product(A,quotient(one,product(B,difference(difference(A,one),one)))) = quotient(one,B). [back_rewrite(16243),rewrite([25072(7),6(4)]),flip(a)].
% 39.01/39.32 25093 product(quotient(one,A),quotient(one,product(B,difference(A,one)))) = quotient(one,B). [back_rewrite(16748),rewrite([25082(16)])].
% 39.01/39.32 25417 product(product(A,quotient(one,A)),quotient(one,B)) = product(A,quotient(one,product(B,A))). [para(25093(a,1),15(a,1,2)),rewrite([10911(7),9791(6),34(5),2(5),37(10),6668(14),12(9),2355(10)])].
% 39.01/39.32 25453 quotient(one,quotient(A,product(B,quotient(one,B)))) = product(B,quotient(one,product(A,B))). [back_rewrite(12874),rewrite([25417(12)])].
% 39.01/39.32 25651 quotient(quotient(product(A,B),product(C,quotient(one,C))),quotient(B,product(C,quotient(one,C)))) = A. [para(935(a,1),1899(a,1,1,1,1,1,2)),rewrite([4813(9),35(7),2(2),3757(21),2(19),23708(19),6(18),6(12)])].
% 39.01/39.32 35672 quotient(product(A,product(B,product(C,quotient(one,C)))),product(C,quotient(one,C))) = product(A,B). [para(12040(a,1),2622(a,2,1)),rewrite([25651(10),23708(12),21(11),2(12)]),flip(a)].
% 39.01/39.32 36286 product(product(product(A,quotient(one,A)),B),C) = product(product(A,quotient(one,A)),product(B,C)). [para(25453(a,1),469(a,1,2,1,2,2)),rewrite([2(6),3757(15),2(13),35672(12),3274(14),35(12),3757(13),2(11),2(12)]),flip(a)].
% 39.01/39.32 36287 $F # answer(goals). [resolve(36286,a,28,a)].
% 39.01/39.32
% 39.01/39.32 % SZS output end Refutation
% 39.01/39.32 ============================== end of proof ==========================
% 39.01/39.32
% 39.01/39.32 ============================== STATISTICS ============================
% 39.01/39.32
% 39.01/39.32 Given=1889. Generated=1796758. Kept=36278. proofs=1.
% 39.01/39.32 Usable=1303. Sos=9978. Demods=11057. Limbo=2, Disabled=25014. Hints=0.
% 39.01/39.32 Megabytes=33.24.
% 39.01/39.32 User_CPU=37.37, System_CPU=0.99, Wall_clock=38.
% 39.01/39.32
% 39.01/39.32 ============================== end of statistics =====================
% 39.01/39.32
% 39.01/39.32 ============================== end of search =========================
% 39.01/39.32
% 39.01/39.32 THEOREM PROVED
% 39.01/39.32 % SZS status Unsatisfiable
% 39.01/39.32
% 39.01/39.32 Exiting with 1 proof.
% 39.01/39.32
% 39.01/39.32 Process 19119 exit (max_proofs) Mon Jun 13 21:55:31 2022
% 39.01/39.32 Prover9 interrupted
%------------------------------------------------------------------------------