TSTP Solution File: GRP764-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP764-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 6.83s 7.17s
% Output : Refutation 6.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP764-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 15:14:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 6.83/7.17 ============================== Prover9 ===============================
% 6.83/7.17 Prover9 (32) version 2009-11A, November 2009.
% 6.83/7.17 Process 797 was started by sandbox on n012.cluster.edu,
% 6.83/7.17 Mon Jun 13 15:14:41 2022
% 6.83/7.17 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_612_n012.cluster.edu".
% 6.83/7.17 ============================== end of head ===========================
% 6.83/7.17
% 6.83/7.17 ============================== INPUT =================================
% 6.83/7.17
% 6.83/7.17 % Reading from file /tmp/Prover9_612_n012.cluster.edu
% 6.83/7.17
% 6.83/7.17 set(prolog_style_variables).
% 6.83/7.17 set(auto2).
% 6.83/7.17 % set(auto2) -> set(auto).
% 6.83/7.17 % set(auto) -> set(auto_inference).
% 6.83/7.17 % set(auto) -> set(auto_setup).
% 6.83/7.17 % set(auto_setup) -> set(predicate_elim).
% 6.83/7.17 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.83/7.17 % set(auto) -> set(auto_limits).
% 6.83/7.17 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.83/7.17 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.83/7.17 % set(auto) -> set(auto_denials).
% 6.83/7.17 % set(auto) -> set(auto_process).
% 6.83/7.17 % set(auto2) -> assign(new_constants, 1).
% 6.83/7.17 % set(auto2) -> assign(fold_denial_max, 3).
% 6.83/7.17 % set(auto2) -> assign(max_weight, "200.000").
% 6.83/7.17 % set(auto2) -> assign(max_hours, 1).
% 6.83/7.17 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.83/7.17 % set(auto2) -> assign(max_seconds, 0).
% 6.83/7.17 % set(auto2) -> assign(max_minutes, 5).
% 6.83/7.17 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.83/7.17 % set(auto2) -> set(sort_initial_sos).
% 6.83/7.17 % set(auto2) -> assign(sos_limit, -1).
% 6.83/7.17 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.83/7.17 % set(auto2) -> assign(max_megs, 400).
% 6.83/7.17 % set(auto2) -> assign(stats, some).
% 6.83/7.17 % set(auto2) -> clear(echo_input).
% 6.83/7.17 % set(auto2) -> set(quiet).
% 6.83/7.17 % set(auto2) -> clear(print_initial_clauses).
% 6.83/7.17 % set(auto2) -> clear(print_given).
% 6.83/7.17 assign(lrs_ticks,-1).
% 6.83/7.17 assign(sos_limit,10000).
% 6.83/7.17 assign(order,kbo).
% 6.83/7.17 set(lex_order_vars).
% 6.83/7.17 clear(print_given).
% 6.83/7.17
% 6.83/7.17 % formulas(sos). % not echoed (13 formulas)
% 6.83/7.17
% 6.83/7.17 ============================== end of input ==========================
% 6.83/7.17
% 6.83/7.17 % From the command line: assign(max_seconds, 300).
% 6.83/7.17
% 6.83/7.17 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.83/7.17
% 6.83/7.17 % Formulas that are not ordinary clauses:
% 6.83/7.17
% 6.83/7.17 ============================== end of process non-clausal formulas ===
% 6.83/7.17
% 6.83/7.17 ============================== PROCESS INITIAL CLAUSES ===============
% 6.83/7.17
% 6.83/7.17 ============================== PREDICATE ELIMINATION =================
% 6.83/7.17
% 6.83/7.17 ============================== end predicate elimination =============
% 6.83/7.17
% 6.83/7.17 Auto_denials:
% 6.83/7.17 % copying label goals to answer in negative clause
% 6.83/7.17
% 6.83/7.17 Term ordering decisions:
% 6.83/7.17 Function symbol KB weights: one=1. x0=1. x1=1. product=1. quotient=1. difference=1. i=1. j=1. eta=1.
% 6.83/7.17
% 6.83/7.17 ============================== end of process initial clauses ========
% 6.83/7.17
% 6.83/7.17 ============================== CLAUSES FOR SEARCH ====================
% 6.83/7.17
% 6.83/7.17 ============================== end of clauses for search =============
% 6.83/7.17
% 6.83/7.17 ============================== SEARCH ================================
% 6.83/7.17
% 6.83/7.17 % Starting search at 0.01 seconds.
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=75.000, iters=3360
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=71.000, iters=3338
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=65.000, iters=3355
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=63.000, iters=3350
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=59.000, iters=3406
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=55.000, iters=3411
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=51.000, iters=3340
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=49.000, iters=3364
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=47.000, iters=3368
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=45.000, iters=3350
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=43.000, iters=3337
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=41.000, iters=3336
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=39.000, iters=3333
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=37.000, iters=3344
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=35.000, iters=3333
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=33.000, iters=3352
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=31.000, iters=3337
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=29.000, iters=3349
% 6.83/7.17
% 6.83/7.17 Low Water (displace): id=2849, wt=151.000
% 6.83/7.17
% 6.83/7.17 Low Water (displace): id=5047, wt=139.000
% 6.83/7.17
% 6.83/7.17 Low Water (displace): id=4203, wt=135.000
% 6.83/7.17
% 6.83/7.17 Low Water (displace): id=15521, wt=23.000
% 6.83/7.17
% 6.83/7.17 Low Water (displace): id=15527, wt=21.000
% 6.83/7.17
% 6.83/7.17 Low Water (displace): id=15697, wt=19.000
% 6.83/7.17
% 6.83/7.17 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 122 (0.00 of 3.36 sec).
% 6.83/7.17
% 6.83/7.17 Low Water (keep): wt=27.000, iters=3333
% 6.83/7.17
% 6.83/7.17 ============================== PROOF =================================
% 6.83/7.17 % SZS status Unsatisfiable
% 6.83/7.17 % SZS output start Refutation
% 6.83/7.17
% 6.83/7.17 % Proof 1 at 6.05 (+ 0.16) seconds: goals.
% 6.83/7.17 % Length of proof is 343.
% 6.83/7.17 % Level of proof is 39.
% 6.83/7.17 % Maximum clause weight is 39.000.
% 6.83/7.17 % Given clauses 707.
% 6.83/7.17
% 6.83/7.17 1 product(A,one) = A # label(sos01) # label(axiom). [assumption].
% 6.83/7.17 2 product(one,A) = A # label(sos02) # label(axiom). [assumption].
% 6.83/7.17 3 i(A) = difference(A,one) # label(sos09) # label(axiom). [assumption].
% 6.83/7.17 4 j(A) = quotient(one,A) # label(sos10) # label(axiom). [assumption].
% 6.83/7.17 5 product(A,difference(A,B)) = B # label(sos03) # label(axiom). [assumption].
% 6.83/7.17 6 difference(A,product(A,B)) = B # label(sos04) # label(axiom). [assumption].
% 6.83/7.17 7 quotient(product(A,B),B) = A # label(sos05) # label(axiom). [assumption].
% 6.83/7.17 8 product(quotient(A,B),B) = A # label(sos06) # label(axiom). [assumption].
% 6.83/7.17 9 eta(A) = product(i(A),A) # label(sos12) # label(axiom). [assumption].
% 6.83/7.17 10 eta(A) = product(difference(A,one),A). [copy(9),rewrite([3(2)])].
% 6.83/7.17 11 product(i(A),A) = product(A,j(A)) # label(sos11) # label(axiom). [assumption].
% 6.83/7.17 12 product(difference(A,one),A) = product(A,quotient(one,A)). [copy(11),rewrite([3(1),4(4)])].
% 6.83/7.17 13 difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) # label(sos07) # label(axiom). [assumption].
% 6.83/7.17 14 difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) # label(sos08) # label(axiom). [assumption].
% 6.83/7.17 15 product(x0,product(eta(x0),x1)) != product(j(j(x0)),x1) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 6.83/7.17 16 product(x0,product(product(x0,quotient(one,x0)),x1)) != product(quotient(one,quotient(one,x0)),x1) # answer(goals). [copy(15),rewrite([10(3),12(6),4(11),4(13)])].
% 6.83/7.17 18 difference(one,A) = A. [para(5(a,1),2(a,1)),flip(a)].
% 6.83/7.17 19 difference(A,A) = one. [para(1(a,1),6(a,1,2))].
% 6.83/7.17 20 quotient(A,one) = A. [para(1(a,1),7(a,1,1))].
% 6.83/7.17 21 quotient(A,A) = one. [para(2(a,1),7(a,1,1))].
% 6.83/7.17 22 quotient(A,difference(B,A)) = B. [para(5(a,1),7(a,1,1))].
% 6.83/7.17 23 difference(quotient(A,B),A) = B. [para(8(a,1),6(a,1,2))].
% 6.83/7.18 24 difference(difference(A,one),product(A,quotient(one,A))) = A. [para(12(a,1),6(a,1,2))].
% 6.83/7.18 25 quotient(product(A,quotient(one,A)),A) = difference(A,one). [para(12(a,1),7(a,1,1))].
% 6.83/7.18 26 product(A,quotient(product(B,product(C,A)),A)) = product(product(A,B),C). [para(13(a,1),5(a,1,2))].
% 6.83/7.18 27 quotient(product(difference(A,B),product(C,A)),A) = difference(A,product(B,C)). [para(5(a,1),13(a,1,2,1)),flip(a)].
% 6.83/7.18 28 quotient(product(A,product(difference(product(B,A),C),B)),B) = difference(B,C). [para(5(a,1),13(a,1,2)),flip(a)].
% 6.83/7.18 29 quotient(product(A,product(B,quotient(C,A))),quotient(C,A)) = difference(quotient(C,A),product(C,B)). [para(8(a,1),13(a,1,2,1)),flip(a)].
% 6.83/7.18 30 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),13(a,1,2,1))].
% 6.83/7.18 32 difference(A,product(B,product(difference(B,A),C))) = quotient(quotient(product(C,A),difference(B,A)),B). [para(5(a,1),14(a,1,1)),rewrite([5(6)])].
% 6.83/7.18 33 difference(product(A,B),product(A,C)) = quotient(difference(B,product(C,A)),A). [para(5(a,1),14(a,1,2,2)),rewrite([27(7)])].
% 6.83/7.18 34 difference(A,product(quotient(A,B),product(B,C))) = quotient(quotient(product(C,A),B),quotient(A,B)). [para(8(a,1),14(a,1,1)),rewrite([8(6)])].
% 6.83/7.18 39 product(quotient(one,A),quotient(one,quotient(one,A))) = product(A,quotient(one,A)). [para(23(a,1),12(a,1,1)),flip(a)].
% 6.83/7.18 40 difference(difference(difference(A,one),one),product(A,quotient(one,A))) = difference(A,one). [para(22(a,1),24(a,1,2,2)),rewrite([12(7)])].
% 6.83/7.18 41 quotient(product(A,quotient(one,A)),difference(A,one)) = difference(difference(A,one),one). [para(22(a,1),25(a,1,1,2)),rewrite([12(3)])].
% 6.83/7.18 42 product(difference(A,B),quotient(product(C,B),difference(A,B))) = product(product(difference(A,B),C),A). [para(5(a,1),26(a,1,2,1,2))].
% 6.83/7.18 43 product(product(A,B),quotient(C,A)) = product(A,quotient(product(B,C),A)). [para(8(a,1),26(a,1,2,1,2)),flip(a)].
% 6.83/7.18 44 product(product(A,quotient(B,product(C,A))),C) = product(A,quotient(B,A)). [para(8(a,1),26(a,1,2,1)),flip(a)].
% 6.83/7.18 50 quotient(product(difference(difference(A,B),C),B),difference(A,B)) = difference(difference(A,B),product(C,A)). [para(5(a,1),27(a,1,1,2))].
% 6.83/7.18 51 product(difference(A,product(B,C)),A) = product(difference(A,B),product(C,A)). [para(27(a,1),8(a,1,1))].
% 6.83/7.18 52 difference(A,product(B,quotient(C,A))) = quotient(product(difference(A,B),C),A). [para(8(a,1),27(a,1,1,2)),flip(a)].
% 6.83/7.18 56 product(A,product(difference(product(B,A),C),B)) = product(difference(B,C),B). [para(28(a,1),8(a,1,1)),flip(a)].
% 6.83/7.18 58 difference(product(A,B),A) = quotient(difference(B,A),A). [para(1(a,1),33(a,1,2)),rewrite([2(4)])].
% 6.83/7.18 59 quotient(difference(difference(A,B),product(C,A)),A) = difference(B,product(A,C)). [para(5(a,1),33(a,1,1)),flip(a)].
% 6.83/7.18 61 quotient(quotient(product(difference(A,B),C),A),quotient(C,A)) = difference(C,product(quotient(C,A),B)). [para(8(a,1),33(a,1,1)),rewrite([52(6)]),flip(a)].
% 6.83/7.18 63 difference(product(A,quotient(one,A)),product(difference(A,one),B)) = quotient(difference(A,product(B,difference(A,one))),difference(A,one)). [para(12(a,1),33(a,1,1))].
% 6.83/7.18 66 quotient(product(A,B),quotient(difference(C,product(B,A)),A)) = product(A,C). [para(33(a,1),22(a,1,2))].
% 6.83/7.18 67 difference(product(quotient(one,A),difference(A,one)),one) = quotient(A,quotient(one,A)). [para(24(a,1),33(a,2,1)),rewrite([8(8)])].
% 6.83/7.18 69 difference(product(A,B),product(product(A,C),D)) = quotient(difference(B,product(C,product(D,A))),A). [para(26(a,1),33(a,1,2)),rewrite([8(8)])].
% 6.83/7.18 73 quotient(difference(difference(A,B),A),A) = difference(B,A). [para(5(a,1),58(a,1,1)),flip(a)].
% 6.83/7.18 75 difference(product(A,quotient(one,A)),difference(A,one)) = quotient(difference(A,difference(A,one)),difference(A,one)). [para(12(a,1),58(a,1,1))].
% 6.83/7.18 76 quotient(A,quotient(difference(B,A),A)) = product(A,B). [para(58(a,1),22(a,1,2))].
% 6.83/7.18 79 difference(difference(A,B),A) = product(difference(B,A),A). [para(73(a,1),8(a,1,1)),flip(a)].
% 6.83/7.18 85 quotient(A,quotient(B,A)) = product(A,quotient(A,B)). [para(23(a,1),76(a,1,2,1))].
% 6.83/7.18 86 difference(product(quotient(one,A),difference(A,one)),one) = product(A,A). [back_rewrite(67),rewrite([85(10),20(9)])].
% 6.83/7.18 92 product(difference(A,B),product(difference(B,A),A)) = A. [para(79(a,1),5(a,1,2))].
% 6.83/7.18 93 difference(quotient(difference(A,B),B),product(B,A)) = product(A,product(B,A)). [para(6(a,1),79(a,2,1)),rewrite([58(2)])].
% 6.83/7.18 95 quotient(A,product(difference(B,A),A)) = difference(A,B). [para(79(a,1),22(a,1,2))].
% 6.83/7.18 97 difference(quotient(difference(A,difference(A,one)),difference(A,one)),product(A,quotient(one,A))) = product(A,product(A,quotient(one,A))). [para(24(a,1),79(a,2,1)),rewrite([75(6)])].
% 6.83/7.18 99 difference(quotient(difference(A,product(B,C)),C),product(C,A)) = product(quotient(difference(B,product(A,C)),C),product(C,A)). [para(33(a,1),79(a,1,1)),rewrite([33(8)])].
% 6.83/7.18 101 product(A,quotient(A,product(B,A))) = quotient(A,B). [para(7(a,1),85(a,1,2)),flip(a)].
% 6.83/7.18 105 quotient(product(quotient(A,B),product(C,product(B,quotient(B,A)))),product(B,quotient(B,A))) = quotient(difference(quotient(B,A),product(C,B)),B). [para(85(a,1),29(a,1,1,2,2)),rewrite([85(7),85(10),33(12)])].
% 6.83/7.18 111 product(difference(A,one),product(A,A)) = A. [para(18(a,1),92(a,1,2,1))].
% 6.83/7.18 121 quotient(A,product(A,A)) = difference(A,one). [para(111(a,1),7(a,1,1))].
% 6.83/7.18 123 product(A,product(quotient(one,A),quotient(one,A))) = quotient(one,A). [para(23(a,1),111(a,1,1))].
% 6.83/7.18 134 quotient(product(A,A),difference(A,one)) = product(product(A,A),A). [para(121(a,1),85(a,1,2)),rewrite([7(7)])].
% 6.83/7.18 137 difference(A,quotient(A,B)) = quotient(A,product(B,A)). [para(23(a,1),95(a,1,2,1)),flip(a)].
% 6.83/7.18 140 quotient(product(A,B),product(quotient(difference(C,product(B,A)),A),product(A,B))) = quotient(difference(B,product(C,A)),A). [para(33(a,1),95(a,1,2,1)),rewrite([33(10)])].
% 6.83/7.18 146 quotient(quotient(A,B),quotient(A,product(B,A))) = A. [para(101(a,1),7(a,1,1))].
% 6.83/7.18 147 quotient(product(quotient(A,product(B,A)),product(C,A)),A) = difference(A,product(quotient(A,B),C)). [para(101(a,1),13(a,1,2,1)),flip(a)].
% 6.83/7.18 163 quotient(product(A,product(product(quotient(difference(A,B),B),C),B)),B) = quotient(quotient(product(C,B),quotient(difference(A,B),B)),product(B,A)). [para(32(a,1),13(a,1)),rewrite([58(3),58(8)]),flip(a)].
% 6.83/7.18 165 quotient(quotient(A,difference(B,one)),B) = product(B,product(difference(B,one),A)). [para(32(a,1),18(a,1)),rewrite([1(2)])].
% 6.83/7.18 186 product(quotient(one,A),difference(A,one)) = quotient(one,product(A,A)). [para(86(a,1),22(a,1,2)),flip(a)].
% 6.83/7.18 190 product(quotient(one,A),quotient(one,A)) = difference(A,quotient(one,A)). [para(123(a,1),6(a,1,2)),flip(a)].
% 6.83/7.18 194 product(product(product(A,A),A),difference(A,one)) = product(A,A). [para(134(a,1),8(a,1,1))].
% 6.83/7.18 197 product(A,quotient(quotient(product(B,A),C),quotient(A,C))) = product(quotient(A,C),product(C,B)). [para(34(a,1),5(a,1,2))].
% 6.83/7.18 200 quotient(quotient(A,B),quotient(one,B)) = product(quotient(one,B),product(B,A)). [para(34(a,1),18(a,1)),rewrite([1(2)])].
% 6.83/7.18 208 quotient(product(quotient(A,B),product(product(quotient(B,A),C),A)),A) = quotient(quotient(product(C,A),quotient(B,A)),product(A,quotient(A,B))). [para(85(a,1),34(a,1,2,1)),rewrite([13(6),85(11)])].
% 6.83/7.18 224 difference(quotient(one,A),quotient(one,product(A,A))) = difference(A,one). [para(186(a,1),6(a,1,2))].
% 6.83/7.18 225 quotient(quotient(one,product(A,A)),difference(A,one)) = quotient(one,A). [para(186(a,1),7(a,1,1))].
% 6.83/7.18 226 quotient(product(difference(A,one),product(B,quotient(one,A))),quotient(one,A)) = difference(quotient(one,A),product(quotient(one,product(A,A)),B)). [para(186(a,1),13(a,1,2,1)),flip(a)].
% 6.83/7.18 227 quotient(one,product(difference(A,one),difference(A,one))) = product(A,difference(difference(A,one),one)). [para(22(a,1),186(a,1,1)),flip(a)].
% 6.83/7.18 228 quotient(one,difference(A,quotient(one,A))) = product(quotient(one,quotient(one,A)),A). [para(23(a,1),186(a,1,2)),rewrite([190(11)]),flip(a)].
% 6.83/7.18 234 difference(difference(A,one),product(A,quotient(quotient(one,A),A))) = quotient(product(A,quotient(one,product(A,A))),difference(A,one)). [para(186(a,1),30(a,2,1,2)),rewrite([43(8),1(6)])].
% 6.83/7.18 235 product(difference(A,one),quotient(difference(A,one),quotient(one,product(A,A)))) = quotient(difference(A,one),quotient(one,A)). [para(186(a,1),101(a,1,2,2))].
% 6.83/7.18 238 difference(quotient(one,A),difference(A,quotient(one,A))) = quotient(one,A). [para(190(a,1),6(a,1,2))].
% 6.83/7.18 240 product(quotient(one,A),quotient(product(B,difference(A,quotient(one,A))),quotient(one,A))) = product(product(quotient(one,A),B),quotient(one,A)). [para(190(a,1),26(a,1,2,1,2))].
% 6.83/7.18 273 product(difference(quotient(one,product(A,A)),quotient(one,A)),quotient(one,A)) = difference(difference(A,one),quotient(one,A)). [para(224(a,1),79(a,1,1)),flip(a)].
% 6.83/7.18 292 difference(quotient(one,A),product(A,quotient(one,A))) = quotient(one,quotient(one,A)). [para(39(a,1),6(a,1,2))].
% 6.83/7.18 307 difference(product(quotient(one,A),difference(difference(A,one),one)),one) = quotient(difference(A,one),quotient(one,A)). [para(40(a,1),33(a,2,1)),rewrite([8(10)])].
% 6.83/7.18 310 quotient(product(A,quotient(one,A)),product(difference(A,one),product(A,quotient(one,A)))) = difference(product(A,quotient(one,A)),difference(difference(A,one),one)). [para(40(a,1),95(a,1,2,1))].
% 6.83/7.18 314 product(A,quotient(product(difference(A,B),C),A)) = product(B,quotient(C,A)). [para(5(a,1),43(a,1,1)),flip(a)].
% 6.83/7.18 317 product(product(A,quotient(one,A)),quotient(B,difference(A,one))) = product(difference(A,one),quotient(product(A,B),difference(A,one))). [para(12(a,1),43(a,1,1))].
% 6.83/7.18 347 product(difference(A,one),quotient(B,difference(A,one))) = product(product(difference(A,one),B),A). [para(1(a,1),42(a,1,2,1))].
% 6.83/7.18 384 product(product(A,quotient(one,A)),quotient(B,difference(A,one))) = product(product(difference(A,one),product(A,B)),A). [back_rewrite(317),rewrite([347(14)])].
% 6.83/7.18 410 quotient(product(A,quotient(B,A)),C) = product(A,quotient(B,product(C,A))). [para(44(a,1),7(a,1,1))].
% 6.83/7.18 416 product(product(A,product(B,quotient(C,product(product(D,A),B)))),D) = product(A,product(B,quotient(C,product(A,B)))). [para(44(a,1),26(a,1,2,1)),rewrite([410(3)]),flip(a)].
% 6.83/7.18 445 product(A,quotient(one,product(product(difference(A,one),product(A,quotient(one,A))),A))) = difference(product(A,quotient(one,A)),difference(difference(A,one),one)). [back_rewrite(310),rewrite([410(10)])].
% 6.83/7.18 451 product(A,quotient(one,product(A,quotient(one,A)))) = difference(difference(A,one),one). [back_rewrite(41),rewrite([410(6),12(4)])].
% 6.83/7.18 452 product(A,quotient(one,product(A,A))) = difference(A,one). [back_rewrite(25),rewrite([410(4)])].
% 6.83/7.18 453 difference(difference(A,one),product(A,quotient(quotient(one,A),A))) = one. [back_rewrite(234),rewrite([452(11),21(12)])].
% 6.83/7.18 474 difference(A,difference(A,one)) = quotient(one,product(A,A)). [para(452(a,1),6(a,1,2))].
% 6.83/7.18 475 quotient(difference(A,one),quotient(one,product(A,A))) = A. [para(452(a,1),7(a,1,1))].
% 6.83/7.18 482 quotient(difference(A,product(quotient(one,product(B,B)),B)),B) = difference(product(B,A),difference(B,one)). [para(452(a,1),33(a,1,2)),flip(a)].
% 6.83/7.18 517 product(A,product(A,quotient(one,A))) = quotient(one,quotient(one,A)). [back_rewrite(97),rewrite([474(3),225(6),292(6)]),flip(a)].
% 6.83/7.18 520 quotient(difference(A,one),quotient(one,A)) = product(A,quotient(one,A)). [back_rewrite(235),rewrite([475(8),12(3)]),flip(a)].
% 6.83/7.18 523 difference(product(quotient(one,A),difference(difference(A,one),one)),one) = product(A,quotient(one,A)). [back_rewrite(307),rewrite([520(14)])].
% 6.83/7.18 524 product(quotient(one,quotient(one,A)),A) = difference(quotient(one,A),A). [para(23(a,1),474(a,1,2)),rewrite([190(9),228(8)]),flip(a)].
% 6.83/7.18 529 quotient(one,difference(A,quotient(one,A))) = difference(quotient(one,A),A). [back_rewrite(228),rewrite([524(10)])].
% 6.83/7.18 532 product(A,quotient(quotient(one,A),A)) = difference(A,one). [para(453(a,1),5(a,1,2)),rewrite([1(4)]),flip(a)].
% 6.83/7.18 573 quotient(quotient(one,A),A) = quotient(one,product(A,A)). [para(532(a,1),6(a,1,2)),rewrite([474(3)]),flip(a)].
% 6.83/7.18 574 product(product(A,quotient(one,A)),A) = difference(difference(A,one),one). [para(22(a,1),532(a,1,2,1)),rewrite([347(6),12(3)])].
% 6.83/7.18 575 quotient(one,quotient(one,product(A,A))) = product(A,A). [para(532(a,1),29(a,1,1,2)),rewrite([5(3),573(4),573(8),8(11),23(10)])].
% 6.83/7.18 579 product(quotient(one,product(A,A)),A) = quotient(one,A). [para(573(a,1),8(a,1,1))].
% 6.83/7.18 580 product(A,difference(difference(A,one),one)) = quotient(A,difference(A,one)). [para(22(a,1),573(a,1,1)),rewrite([227(10)]),flip(a)].
% 6.83/7.18 581 difference(quotient(one,product(A,A)),quotient(one,A)) = A. [para(573(a,1),23(a,1,1))].
% 6.83/7.18 586 difference(quotient(one,A),product(quotient(one,product(A,A)),product(A,B))) = quotient(quotient(product(B,quotient(one,A)),A),quotient(one,product(A,A))). [para(573(a,1),34(a,1,2,1)),rewrite([573(15)])].
% 6.83/7.18 590 difference(product(A,B),difference(A,one)) = quotient(difference(B,quotient(one,A)),A). [back_rewrite(482),rewrite([579(4)]),flip(a)].
% 6.83/7.18 592 quotient(one,product(difference(A,one),difference(A,one))) = quotient(A,difference(A,one)). [back_rewrite(227),rewrite([580(12)])].
% 6.83/7.18 596 difference(difference(A,one),quotient(one,A)) = product(A,quotient(one,A)). [back_rewrite(273),rewrite([581(6)]),flip(a)].
% 6.83/7.18 609 quotient(one,difference(quotient(one,A),A)) = difference(A,quotient(one,A)). [para(190(a,1),575(a,1,2,2)),rewrite([529(6),190(10)])].
% 6.83/7.18 632 product(difference(A,one),product(A,quotient(one,A))) = quotient(one,A). [para(581(a,1),92(a,1,2,1)),rewrite([224(6)])].
% 6.83/7.18 634 difference(product(A,quotient(one,A)),difference(difference(A,one),one)) = A. [back_rewrite(445),rewrite([632(7),8(4),21(3),1(2)]),flip(a)].
% 6.83/7.18 687 quotient(product(product(A,quotient(one,A)),product(B,A)),A) = difference(A,product(quotient(one,quotient(one,A)),B)). [para(517(a,1),13(a,1,2,1)),flip(a)].
% 6.83/7.18 700 product(quotient(one,A),product(A,quotient(one,A))) = quotient(one,quotient(one,quotient(one,A))). [para(39(a,1),517(a,1,2))].
% 6.83/7.18 713 quotient(difference(difference(A,one),one),A) = product(A,quotient(one,A)). [para(22(a,1),520(a,1,2)),rewrite([22(11),12(8)])].
% 6.83/7.18 714 quotient(A,quotient(one,quotient(one,A))) = product(A,quotient(one,A)). [para(23(a,1),520(a,1,1)),rewrite([39(12)])].
% 6.83/7.18 723 quotient(product(difference(A,B),difference(quotient(one,A),A)),A) = difference(A,product(B,quotient(one,quotient(one,A)))). [para(524(a,1),27(a,1,1,2))].
% 6.83/7.18 742 quotient(difference(difference(A,one),B),difference(A,one)) = difference(difference(A,one),product(B,A)). [para(1(a,1),50(a,1,1))].
% 6.83/7.18 788 quotient(product(quotient(one,A),product(A,A)),A) = difference(A,difference(difference(A,one),one)). [para(574(a,1),13(a,1,2)),flip(a)].
% 6.83/7.18 789 product(product(A,quotient(one,A)),difference(A,one)) = difference(difference(difference(A,one),one),one). [para(22(a,1),574(a,1,1,2)),rewrite([12(3)])].
% 6.83/7.18 797 quotient(quotient(A,product(A,quotient(one,A))),quotient(A,difference(difference(A,one),one))) = A. [para(574(a,1),146(a,1,2,2))].
% 6.83/7.18 809 quotient(A,product(A,quotient(one,A))) = difference(difference(A,one),one). [para(580(a,1),6(a,1,2)),rewrite([137(4),12(3)])].
% 6.83/7.18 811 quotient(product(difference(difference(A,one),one),product(B,A)),A) = difference(A,product(quotient(A,difference(A,one)),B)). [para(580(a,1),13(a,1,2,1)),flip(a)].
% 6.83/7.18 830 product(difference(difference(A,one),one),product(A,quotient(one,A))) = A. [back_rewrite(797),rewrite([809(4),85(10),713(9)])].
% 6.83/7.18 832 product(difference(A,one),product(B,A)) = product(difference(A,B),A). [para(2(a,1),51(a,1,1,2)),flip(a)].
% 6.83/7.18 833 product(difference(A,B),product(difference(B,C),A)) = product(difference(A,C),A). [para(5(a,1),51(a,1,1,2)),flip(a)].
% 6.83/7.18 834 product(difference(A,quotient(B,C)),product(C,A)) = product(difference(A,B),A). [para(8(a,1),51(a,1,1,2)),flip(a)].
% 6.83/7.18 904 difference(difference(difference(A,one),one),A) = product(A,quotient(one,A)). [para(22(a,1),596(a,1,2)),rewrite([22(11),12(8)])].
% 6.83/7.18 908 quotient(product(difference(A,one),B),A) = difference(A,quotient(B,A)). [para(2(a,1),52(a,1,2)),flip(a)].
% 6.83/7.18 911 quotient(product(A,quotient(B,C)),quotient(product(difference(C,A),B),C)) = C. [para(52(a,1),22(a,1,2))].
% 6.83/7.18 966 difference(A,difference(difference(A,one),one)) = quotient(A,difference(difference(A,one),one)). [para(634(a,1),58(a,2,1)),rewrite([830(8)])].
% 6.83/7.18 968 quotient(product(quotient(one,A),product(A,A)),A) = quotient(A,difference(difference(A,one),one)). [back_rewrite(788),rewrite([966(10)])].
% 6.83/7.18 1012 quotient(product(quotient(one,quotient(one,A)),product(B,product(A,quotient(one,A)))),product(A,quotient(one,A))) = quotient(difference(quotient(one,A),product(B,A)),A). [para(714(a,1),29(a,1,1,2,2)),rewrite([714(14),714(18),33(18)])].
% 6.83/7.18 1140 quotient(product(difference(A,B),A),product(B,A)) = difference(A,one). [para(832(a,1),7(a,1,1))].
% 6.83/7.18 1141 product(difference(A,quotient(B,A)),A) = product(difference(A,one),B). [para(8(a,1),832(a,1,2)),flip(a)].
% 6.83/7.18 1194 difference(A,product(difference(B,C),B)) = product(difference(product(B,A),C),B). [para(56(a,1),6(a,1,2))].
% 6.83/7.18 1196 product(difference(quotient(A,B),C),quotient(A,B)) = product(B,product(difference(A,C),quotient(A,B))). [para(8(a,1),56(a,1,2,1,1)),flip(a)].
% 6.83/7.18 1243 product(quotient(A,difference(difference(A,one),one)),A) = product(quotient(one,A),product(A,A)). [para(634(a,1),56(a,1,2,1)),rewrite([966(9)]),flip(a)].
% 6.83/7.18 1256 difference(A,quotient(one,A)) = quotient(difference(A,one),A). [para(1(a,1),908(a,1,1)),flip(a)].
% 6.83/7.18 1257 difference(A,quotient(difference(difference(A,one),B),A)) = quotient(B,A). [para(5(a,1),908(a,1,1)),flip(a)].
% 6.83/7.18 1259 difference(quotient(one,A),quotient(B,quotient(one,A))) = quotient(product(A,B),quotient(one,A)). [para(23(a,1),908(a,1,1,1)),flip(a)].
% 6.83/7.18 1330 quotient(one,difference(quotient(one,A),A)) = quotient(difference(A,one),A). [back_rewrite(609),rewrite([1256(8)])].
% 6.83/7.18 1334 quotient(one,quotient(difference(A,one),A)) = difference(quotient(one,A),A). [back_rewrite(529),rewrite([1256(4)])].
% 6.83/7.18 1348 product(quotient(one,A),quotient(product(B,quotient(difference(A,one),A)),quotient(one,A))) = product(product(quotient(one,A),B),quotient(one,A)). [back_rewrite(240),rewrite([1256(5)])].
% 6.83/7.18 1350 difference(quotient(one,A),quotient(difference(A,one),A)) = quotient(one,A). [back_rewrite(238),rewrite([1256(5)])].
% 6.83/7.18 1351 product(quotient(one,A),quotient(one,A)) = quotient(difference(A,one),A). [back_rewrite(190),rewrite([1256(8)])].
% 6.83/7.18 1354 product(A,quotient(difference(A,one),A)) = quotient(one,A). [para(1256(a,1),5(a,1,2))].
% 6.83/7.18 1355 quotient(quotient(one,A),quotient(difference(A,one),A)) = A. [para(1256(a,1),22(a,1,2))].
% 6.83/7.18 1366 product(quotient(one,A),product(A,A)) = quotient(one,quotient(one,A)). [para(23(a,1),1354(a,1,2,1)),rewrite([85(5),20(4)])].
% 6.83/7.18 1385 product(quotient(A,difference(difference(A,one),one)),A) = quotient(one,quotient(one,A)). [back_rewrite(1243),rewrite([1366(10)])].
% 6.83/7.18 1388 quotient(quotient(one,quotient(one,A)),A) = quotient(A,difference(difference(A,one),one)). [back_rewrite(968),rewrite([1366(4)])].
% 6.83/7.18 1401 quotient(quotient(one,quotient(one,A)),product(A,A)) = quotient(one,A). [para(23(a,1),1355(a,1,2,1)),rewrite([85(7),20(6)])].
% 6.83/7.18 1402 quotient(difference(difference(difference(A,B),C),B),difference(A,B)) = product(difference(product(A,C),B),A). [para(5(a,1),59(a,1,1,2)),rewrite([1194(8)])].
% 6.83/7.18 1403 difference(difference(A,B),product(C,A)) = product(difference(B,product(A,C)),A). [para(59(a,1),8(a,1,1)),flip(a)].
% 6.83/7.18 1404 difference(A,product(B,quotient(C,B))) = quotient(difference(difference(B,A),C),B). [para(8(a,1),59(a,1,1,2)),flip(a)].
% 6.83/7.18 1407 quotient(difference(difference(A,B),one),A) = product(difference(product(A,B),one),A). [para(12(a,1),59(a,2,2)),rewrite([5(6),1402(8),1404(8)]),flip(a)].
% 6.83/7.18 1464 quotient(difference(difference(A,one),B),difference(A,one)) = product(product(A,B),A). [back_rewrite(742),rewrite([1403(10),18(9)])].
% 6.83/7.18 1466 quotient(product(difference(difference(A,B),C),B),difference(A,B)) = product(difference(B,product(A,C)),A). [back_rewrite(50),rewrite([1403(8)])].
% 6.83/7.18 1509 quotient(product(A,B),product(product(B,A),B)) = difference(B,one). [para(6(a,1),1140(a,1,1,1))].
% 6.83/7.18 1532 quotient(product(difference(A,B),C),product(product(B,quotient(C,A)),A)) = difference(A,one). [para(52(a,1),1140(a,1,1,1)),rewrite([8(4)])].
% 6.83/7.18 1533 difference(product(A,quotient(one,A)),one) = quotient(quotient(one,A),difference(A,one)). [para(632(a,1),1140(a,1,2)),rewrite([590(6),19(5),700(6),1388(9),23(6)]),flip(a)].
% 6.83/7.18 1534 quotient(quotient(one,A),difference(A,one)) = quotient(A,difference(difference(A,one),one)). [para(634(a,1),1140(a,1,1,1)),rewrite([517(4),830(12),1388(5),1533(10)]),flip(a)].
% 6.83/7.18 1547 difference(product(A,quotient(one,A)),one) = quotient(A,difference(difference(A,one),one)). [back_rewrite(1533),rewrite([1534(10)])].
% 6.83/7.18 1585 quotient(difference(difference(A,one),B),A) = product(A,quotient(B,A)). [para(1257(a,1),5(a,1,2)),flip(a)].
% 6.83/7.18 1672 quotient(difference(quotient(one,A),product(A,A)),A) = quotient(A,difference(A,one)). [para(194(a,1),63(a,2,1,2)),rewrite([832(8),6(5),33(5),6(7)])].
% 6.83/7.18 1684 difference(quotient(one,quotient(one,A)),product(A,A)) = quotient(one,quotient(one,A)). [para(23(a,1),1350(a,1,2,1)),rewrite([85(7),20(6)])].
% 6.83/7.18 1690 quotient(product(A,B),quotient(C,A)) = product(A,quotient(product(B,A),C)). [para(23(a,1),66(a,1,2,1))].
% 6.83/7.18 1720 difference(quotient(one,A),quotient(B,quotient(one,A))) = product(A,product(B,A)). [back_rewrite(1259),rewrite([1690(10),20(9)])].
% 6.83/7.18 1743 product(A,product(difference(A,one),difference(A,one))) = quotient(one,A). [para(22(a,1),1366(a,1,1)),rewrite([22(11)])].
% 6.83/7.18 1749 quotient(quotient(product(A,product(A,A)),A),A) = quotient(product(A,A),quotient(one,quotient(one,A))). [para(1366(a,1),137(a,2,2)),rewrite([1690(5),20(4),33(4),13(3)])].
% 6.83/7.18 1903 quotient(product(quotient(A,product(B,B)),B),product(B,quotient(A,B))) = difference(B,one). [para(44(a,1),1509(a,1,2))].
% 6.83/7.18 1923 product(product(A,quotient(B,A)),A) = difference(difference(A,one),B). [para(1585(a,1),8(a,1,1))].
% 6.83/7.18 1924 difference(product(A,quotient(B,A)),difference(difference(A,one),B)) = A. [para(1585(a,1),23(a,1,1))].
% 6.83/7.18 1925 product(quotient(one,A),quotient(B,quotient(one,A))) = quotient(difference(A,B),quotient(one,A)). [para(23(a,1),1585(a,1,1,1)),flip(a)].
% 6.83/7.18 1949 product(quotient(one,A),product(A,product(difference(A,B),difference(A,one)))) = product(product(quotient(one,A),B),quotient(one,A)). [back_rewrite(1348),rewrite([1925(10),52(5),200(8)])].
% 6.83/7.18 1976 product(difference(A,one),difference(A,one)) = quotient(difference(A,one),A). [para(1743(a,1),6(a,1,2)),rewrite([1256(3)]),flip(a)].
% 6.83/7.18 1987 difference(quotient(one,A),A) = quotient(A,difference(A,one)). [back_rewrite(592),rewrite([1976(6),1334(5)])].
% 6.83/7.18 2009 quotient(one,quotient(A,difference(A,one))) = quotient(difference(A,one),A). [back_rewrite(1330),rewrite([1987(4)])].
% 6.83/7.18 2077 quotient(product(difference(A,B),quotient(A,difference(A,one))),A) = difference(A,product(B,quotient(one,quotient(one,A)))). [back_rewrite(723),rewrite([1987(4)])].
% 6.83/7.18 2083 product(quotient(one,quotient(one,A)),A) = quotient(A,difference(A,one)). [back_rewrite(524),rewrite([1987(8)])].
% 6.83/7.18 2143 quotient(difference(quotient(one,A),product(B,product(C,quotient(one,A)))),quotient(one,A)) = difference(quotient(difference(A,one),A),product(product(quotient(one,A),B),C)). [para(1351(a,1),69(a,1,1)),flip(a)].
% 6.83/7.18 2150 product(quotient(one,A),quotient(A,difference(A,one))) = A. [para(1987(a,1),5(a,1,2))].
% 6.83/7.18 2155 difference(A,product(quotient(one,A),product(quotient(A,difference(A,one)),B))) = quotient(quotient(product(B,A),quotient(A,difference(A,one))),quotient(one,A)). [para(1987(a,1),32(a,1,2,2,1)),rewrite([1987(12)])].
% 6.83/7.18 2362 product(difference(A,difference(difference(A,one),B)),A) = product(quotient(B,A),product(A,A)). [para(1924(a,1),56(a,1,2,1)),flip(a)].
% 6.83/7.18 2530 difference(quotient(one,A),product(A,A)) = product(A,product(A,A)). [para(19(a,1),93(a,1,1,1))].
% 6.83/7.18 2564 quotient(product(A,product(A,A)),A) = quotient(A,difference(A,one)). [back_rewrite(1672),rewrite([2530(4)])].
% 6.83/7.18 2567 quotient(product(A,A),quotient(one,quotient(one,A))) = quotient(one,quotient(one,A)). [back_rewrite(1749),rewrite([2564(3),165(4),12(3),517(4)]),flip(a)].
% 6.83/7.18 2658 product(quotient(A,difference(A,one)),product(A,quotient(one,A))) = product(A,A). [para(2530(a,1),51(a,1,1)),rewrite([43(5),1(3),7(2),1987(4)]),flip(a)].
% 6.83/7.18 3456 product(A,product(difference(A,one),product(B,difference(A,one)))) = quotient(B,A). [para(7(a,1),165(a,1,1)),flip(a)].
% 6.83/7.18 3457 product(product(A,product(difference(A,one),B)),A) = quotient(B,difference(A,one)). [para(165(a,1),8(a,1,1))].
% 6.83/7.18 3593 product(A,quotient(difference(A,B),A)) = product(B,quotient(one,A)). [para(1(a,1),314(a,1,2,1))].
% 6.83/7.18 3690 quotient(product(A,quotient(one,B)),quotient(difference(B,A),B)) = B. [para(3593(a,1),7(a,1,1))].
% 6.83/7.18 3764 quotient(A,quotient(difference(B,quotient(A,quotient(one,B))),B)) = B. [para(8(a,1),3690(a,1,1))].
% 6.83/7.18 3917 quotient(difference(A,quotient(B,quotient(one,A))),A) = difference(A,B). [para(3764(a,1),23(a,1,1)),flip(a)].
% 6.83/7.18 3924 difference(A,quotient(B,quotient(one,A))) = product(difference(A,B),A). [para(3917(a,1),8(a,1,1)),flip(a)].
% 6.83/7.18 3934 quotient(difference(A,difference(quotient(one,A),B)),A) = product(B,quotient(one,A)). [para(3917(a,1),3917(a,1,1,2)),rewrite([3924(13),1196(11),18(7),6(10)])].
% 6.83/7.18 3937 product(A,product(difference(A,B),A)) = quotient(B,quotient(one,A)). [para(3924(a,1),5(a,1,2))].
% 6.83/7.18 3956 difference(A,product(quotient(one,A),B)) = product(difference(A,one),difference(A,B)). [para(61(a,1),3924(a,1,2)),rewrite([18(5),1(7),1141(8)])].
% 6.83/7.18 3980 quotient(quotient(product(A,B),quotient(B,difference(B,one))),quotient(one,B)) = product(difference(B,one),difference(B,product(quotient(B,difference(B,one)),A))). [back_rewrite(2155),rewrite([3956(8)]),flip(a)].
% 6.83/7.18 3986 product(A,quotient(quotient(B,quotient(one,A)),A)) = product(product(A,A),difference(A,B)). [para(3937(a,1),26(a,1,2,1))].
% 6.83/7.18 4015 product(A,product(difference(A,B),product(C,A))) = quotient(product(B,C),quotient(one,A)). [para(51(a,1),3937(a,1,2))].
% 6.83/7.18 4021 product(quotient(one,A),product(A,B)) = product(A,product(difference(A,one),B)). [para(1141(a,1),3937(a,1,2)),rewrite([200(8)]),flip(a)].
% 6.83/7.18 4024 product(A,product(difference(A,one),difference(A,B))) = product(quotient(one,A),B). [para(61(a,1),3937(a,2)),rewrite([1(3),1141(4),18(10)])].
% 6.83/7.18 4107 product(product(quotient(one,A),B),quotient(one,A)) = quotient(difference(A,B),A). [back_rewrite(1949),rewrite([4021(8),3456(8)]),flip(a)].
% 6.83/7.18 4111 quotient(quotient(A,B),quotient(one,B)) = product(B,product(difference(B,one),A)). [back_rewrite(200),rewrite([4021(8)])].
% 6.83/7.18 4128 product(A,product(product(B,quotient(one,A)),A)) = difference(quotient(one,A),B). [para(1(a,1),105(a,2,1,2)),rewrite([20(2),2(4),2(8),1690(7),20(6),20(10)])].
% 6.83/7.18 4186 product(A,product(difference(A,one),difference(quotient(one,A),B))) = product(quotient(one,quotient(one,A)),B). [para(1401(a,1),105(a,1,1,2,2,2)),rewrite([2567(6),8(11),1(6),1401(15),8(12),20(7),1401(11),52(13),1(10),4111(16),23(11),4021(12)]),flip(a)].
% 6.91/7.18 4252 product(A,quotient(product(B,A),product(C,A))) = quotient(product(A,B),C). [para(7(a,1),410(a,1,1,2)),flip(a)].
% 6.91/7.18 4292 product(quotient(one,A),difference(difference(A,one),one)) = quotient(A,difference(difference(A,one),one)). [para(809(a,1),410(a,2,2)),rewrite([85(5),20(4),4021(4),12(3),517(4),1388(5)]),flip(a)].
% 6.91/7.18 4343 product(A,quotient(difference(A,B),product(C,A))) = quotient(product(B,quotient(one,A)),C). [para(3593(a,1),410(a,1,1)),flip(a)].
% 6.91/7.18 4357 difference(quotient(A,difference(difference(A,one),one)),one) = product(A,quotient(one,A)). [back_rewrite(523),rewrite([4292(7)])].
% 6.91/7.18 4362 quotient(one,product(A,quotient(one,A))) = quotient(A,difference(difference(A,one),one)). [para(451(a,1),6(a,1,2)),rewrite([966(5)]),flip(a)].
% 6.91/7.18 4370 quotient(difference(quotient(one,product(A,quotient(one,A))),product(B,A)),A) = difference(difference(difference(A,one),one),product(A,B)). [para(451(a,1),33(a,1,1)),flip(a)].
% 6.91/7.18 4633 product(quotient(A,difference(difference(A,one),one)),product(A,quotient(one,A))) = one. [para(632(a,1),833(a,1,2)),rewrite([58(4),1987(3),165(4),12(3),517(4),8(7),1547(6)]),flip(a)].
% 6.91/7.18 4676 quotient(product(difference(A,B),A),product(C,A)) = difference(A,quotient(B,C)). [para(834(a,1),7(a,1,1))].
% 6.91/7.18 4857 quotient(product(A,B),product(difference(C,product(B,A)),B)) = difference(B,C). [para(22(a,1),911(a,1,1,2)),rewrite([1466(6)])].
% 6.91/7.18 5444 product(product(A,B),quotient(A,difference(difference(A,one),one))) = product(A,quotient(product(B,quotient(one,quotient(one,A))),A)). [para(1385(a,1),26(a,1,2,1,2)),flip(a)].
% 6.91/7.18 5458 quotient(one,quotient(A,difference(difference(A,one),one))) = product(A,quotient(one,A)). [para(1385(a,1),61(a,2,2)),rewrite([904(5),1923(4),21(9),3924(12),12(10)])].
% 6.91/7.18 5685 difference(difference(A,B),quotient(one,A)) = product(difference(B,difference(A,one)),A). [para(452(a,1),1403(a,2,1,2)),rewrite([579(5)])].
% 6.91/7.18 5704 difference(quotient(difference(A,one),A),product(B,A)) = product(difference(quotient(one,A),product(A,B)),A). [para(1256(a,1),1403(a,1,1))].
% 6.91/7.18 6156 product(product(product(A,B),A),difference(A,one)) = difference(difference(A,one),B). [para(1464(a,1),8(a,1,1))].
% 6.91/7.18 6174 quotient(product(A,B),difference(B,one)) = product(quotient(A,quotient(one,B)),B). [para(3937(a,1),1464(a,2,1)),rewrite([1194(5),5(3),18(2)])].
% 6.91/7.18 6258 product(product(A,quotient(one,A)),quotient(one,product(A,quotient(one,A)))) = one. [para(1547(a,1),12(a,1,1)),rewrite([4633(9)]),flip(a)].
% 6.91/7.18 6605 product(quotient(A,difference(difference(A,one),one)),product(A,A)) = quotient(A,difference(A,one)). [para(1684(a,1),99(a,2,1,1)),rewrite([2083(5),137(4),12(3),809(4),1407(5),1(2),12(3),33(5),2530(4),2564(3),1388(8)]),flip(a)].
% 6.91/7.18 6719 quotient(product(A,A),quotient(A,difference(A,one))) = product(A,quotient(one,A)). [para(1684(a,1),140(a,1,2,1,1)),rewrite([1388(6),6605(8),2083(10),137(9),12(8),809(9),1407(10),1(7),12(8)])].
% 6.91/7.18 6725 product(A,quotient(product(difference(A,B),A),C)) = quotient(B,quotient(C,A)). [para(5(a,1),1690(a,1,1)),flip(a)].
% 6.91/7.18 6824 quotient(product(A,quotient(B,C)),quotient(D,C)) = product(C,quotient(product(difference(C,A),B),D)). [para(314(a,1),1690(a,1,1)),rewrite([8(8)])].
% 6.91/7.18 6854 quotient(product(A,B),quotient(A,difference(difference(A,one),one))) = product(A,quotient(product(B,A),quotient(one,quotient(one,A)))). [para(1388(a,1),1690(a,1,2))].
% 6.91/7.18 7031 product(difference(A,one),product(B,difference(A,one))) = difference(A,quotient(B,A)). [para(22(a,1),1720(a,1,1)),rewrite([22(4)]),flip(a)].
% 6.91/7.18 7044 difference(quotient(one,A),product(A,B)) = product(A,difference(difference(A,one),B)). [para(1923(a,1),1720(a,2,2)),rewrite([1690(7),8(4),20(4)])].
% 6.91/7.18 7075 difference(quotient(difference(A,one),A),product(B,A)) = product(product(A,difference(difference(A,one),B)),A). [back_rewrite(5704),rewrite([7044(9)])].
% 6.91/7.18 8008 difference(quotient(difference(quotient(A,difference(A,one)),product(B,product(A,quotient(one,A)))),product(A,quotient(one,A))),product(A,A)) = product(quotient(difference(B,product(A,A)),product(A,quotient(one,A))),product(A,A)). [para(2658(a,1),99(a,2,1,1,2)),rewrite([384(19),832(16),19(13),2(14),384(27),832(24),19(21),2(22)])].
% 6.91/7.18 8024 quotient(difference(quotient(A,difference(A,one)),product(B,product(A,quotient(one,A)))),product(A,quotient(one,A))) = quotient(product(A,A),product(quotient(difference(B,product(A,A)),product(A,quotient(one,A))),product(A,A))). [para(2658(a,1),140(a,1,2,1,1,2)),rewrite([384(7),832(4),19(1),2(2),384(14),832(11),19(8),2(9)]),flip(a)].
% 6.91/7.18 8801 quotient(product(difference(A,one),product(A,quotient(B,A))),quotient(one,A)) = quotient(quotient(product(B,quotient(one,A)),A),quotient(one,product(A,A))). [para(186(a,1),163(a,2,2)),rewrite([5685(7),18(6),12(5),7(8),43(6),1(4),5685(16),18(15),12(14),7(17)])].
% 6.91/7.18 8818 quotient(quotient(product(A,difference(B,one)),B),quotient(difference(B,one),B)) = quotient(difference(B,quotient(product(B,A),B)),difference(B,one)). [para(1976(a,1),163(a,2,2)),rewrite([19(7),22(6),7031(7),19(14),22(13)]),flip(a)].
% 6.91/7.18 8821 quotient(quotient(product(A,quotient(one,quotient(one,B))),quotient(one,B)),quotient(B,difference(B,one))) = product(quotient(one,B),product(quotient(B,difference(B,one)),difference(B,A))). [para(2083(a,1),163(a,2,2)),rewrite([3924(5),12(3),410(8),2083(6),2009(5),3593(4),2(4),43(8),1(4),1925(6),6824(10),1987(5),20(9),3924(18),12(16),410(21),2083(19),2009(18),3593(17),2(17)]),flip(a)].
% 6.91/7.18 9282 difference(A,difference(quotient(one,A),B)) = product(product(B,quotient(one,A)),A). [para(3934(a,1),8(a,1,1)),flip(a)].
% 6.91/7.18 9356 difference(A,quotient(B,quotient(one,quotient(one,A)))) = product(difference(A,one),product(B,quotient(one,A))). [para(3937(a,1),3956(a,1,2)),rewrite([1196(14),18(10),6(13)])].
% 6.91/7.18 9460 product(product(A,quotient(one,B)),B) = product(product(A,B),difference(B,one)). [para(4021(a,1),26(a,1,2,1)),rewrite([26(6)]),flip(a)].
% 6.91/7.18 9550 difference(A,difference(quotient(one,A),B)) = product(product(B,A),difference(A,one)). [back_rewrite(9282),rewrite([9460(8)])].
% 6.91/7.18 9622 product(A,product(product(B,A),difference(A,one))) = difference(quotient(one,A),B). [back_rewrite(4128),rewrite([9460(4)])].
% 6.91/7.18 9671 quotient(difference(A,B),difference(A,one)) = product(product(quotient(one,A),B),A). [para(4024(a,1),1464(a,2,1)),rewrite([6(7)])].
% 6.91/7.18 9683 difference(A,product(quotient(one,quotient(one,A)),B)) = product(difference(A,one),difference(quotient(one,A),B)). [para(4024(a,1),3956(a,1,2)),rewrite([23(12),6(13)])].
% 6.91/7.18 9690 quotient(quotient(product(A,difference(B,one)),B),quotient(difference(B,one),B)) = product(product(quotient(one,B),quotient(product(B,A),B)),B). [back_rewrite(8818),rewrite([9671(14)])].
% 6.91/7.18 9748 quotient(product(product(A,quotient(one,A)),product(B,A)),A) = product(difference(A,one),difference(quotient(one,A),B)). [back_rewrite(687),rewrite([9683(12)])].
% 6.91/7.18 10257 difference(A,quotient(product(A,B),C)) = quotient(product(B,A),product(C,A)). [para(4252(a,1),6(a,1,2))].
% 6.91/7.18 10294 product(A,quotient(product(B,A),quotient(A,difference(A,one)))) = quotient(product(A,B),quotient(one,quotient(one,A))). [para(2083(a,1),4252(a,1,2,2))].
% 6.91/7.18 10490 quotient(product(product(A,quotient(one,A)),product(B,quotient(A,difference(difference(A,one),one)))),quotient(A,difference(difference(A,one),one))) = difference(quotient(A,difference(difference(A,one),one)),B). [para(4357(a,1),27(a,1,1,1)),rewrite([2(23)])].
% 6.91/7.18 10573 quotient(product(product(A,quotient(one,A)),B),quotient(A,difference(difference(A,one),one))) = product(product(A,quotient(one,A)),product(B,product(A,quotient(one,A)))). [para(4362(a,1),1690(a,1,2)),rewrite([20(19)])].
% 6.91/7.18 10612 product(product(A,quotient(one,A)),product(product(B,quotient(A,difference(difference(A,one),one))),product(A,quotient(one,A)))) = difference(quotient(A,difference(difference(A,one),one)),B). [back_rewrite(10490),rewrite([10573(16)])].
% 6.91/7.18 10862 quotient(product(product(A,quotient(one,A)),product(B,product(A,quotient(one,A)))),product(A,quotient(one,A))) = quotient(product(A,difference(quotient(one,quotient(one,A)),product(B,A))),A). [para(4633(a,1),147(a,1,1,1,2)),rewrite([20(5),6854(24),8(18),69(24),9683(23),23(16)])].
% 6.91/7.18 10871 difference(A,quotient(B,quotient(C,A))) = quotient(product(difference(A,B),A),C). [para(8(a,1),4676(a,1,2)),flip(a)].
% 6.91/7.18 10910 quotient(product(difference(A,one),B),product(C,A)) = difference(A,quotient(quotient(B,A),C)). [para(1141(a,1),4676(a,1,1))].
% 6.91/7.18 11191 quotient(product(A,A),product(difference(B,product(A,A)),quotient(A,difference(A,one)))) = difference(quotient(A,difference(A,one)),B). [para(2658(a,1),4857(a,1,2,1,2)),rewrite([384(7),832(4),19(1),2(2)])].
% 6.91/7.18 11554 product(product(quotient(A,quotient(one,B)),B),difference(B,one)) = product(A,B). [para(3937(a,1),6156(a,1,1,1)),rewrite([1194(12),5(10),18(9)])].
% 6.91/7.18 11651 difference(difference(A,one),quotient(B,quotient(one,A))) = product(difference(difference(A,one),one),product(B,A)). [para(6174(a,1),1141(a,1,1,2)),rewrite([1403(7),18(6),6156(8)])].
% 6.91/7.18 11665 product(product(quotient(A,B),product(B,B)),B) = product(A,quotient(B,difference(B,one))). [para(6174(a,1),314(a,1,2)),rewrite([832(10),10871(7),2362(5),20(5)])].
% 6.91/7.18 11717 quotient(difference(quotient(one,product(A,quotient(one,A))),product(B,product(A,quotient(one,A)))),product(A,quotient(one,A))) = product(product(A,quotient(one,A)),B). [para(6258(a,1),33(a,1,1)),rewrite([18(6)]),flip(a)].
% 6.91/7.18 11783 quotient(product(difference(quotient(A,difference(A,one)),B),product(A,A)),quotient(A,difference(A,one))) = difference(quotient(A,difference(A,one)),product(B,product(A,quotient(one,A)))). [para(6719(a,1),52(a,1,2,2)),flip(a)].
% 6.91/7.18 11784 quotient(difference(quotient(A,difference(A,one)),product(B,product(A,quotient(one,A)))),product(A,quotient(one,A))) = difference(A,quotient(difference(A,product(B,A)),A)). [para(6719(a,1),61(a,1,2)),rewrite([11783(10),6719(18),69(18),3956(17),908(18)])].
% 6.91/7.18 11789 quotient(product(A,A),product(quotient(difference(B,product(A,A)),product(A,quotient(one,A))),product(A,A))) = difference(A,quotient(difference(A,product(B,A)),A)). [back_rewrite(8024),rewrite([11784(12)]),flip(a)].
% 6.91/7.18 11791 product(quotient(difference(A,product(B,B)),product(B,quotient(one,B))),product(B,B)) = product(difference(A,product(B,B)),quotient(B,difference(B,one))). [back_rewrite(8008),rewrite([11784(12),1403(6),99(5),11665(6)]),flip(a)].
% 6.91/7.18 11793 difference(A,quotient(difference(A,product(B,A)),A)) = difference(quotient(A,difference(A,one)),B). [back_rewrite(11789),rewrite([11791(9),11191(8)]),flip(a)].
% 6.91/7.18 11877 product(quotient(A,difference(A,one)),difference(A,quotient(difference(A,product(B,quotient(one,quotient(one,A)))),A))) = quotient(B,product(A,quotient(one,A))). [para(6719(a,1),6725(a,2,2)),rewrite([1196(11),10910(13),2077(9)])].
% 6.91/7.18 12268 product(quotient(A,difference(A,one)),product(difference(A,one),B)) = product(quotient(one,A),product(quotient(A,difference(A,one)),B)). [para(6174(a,1),197(a,1,2,1)),rewrite([10294(9),6824(9),1987(5),20(8)]),flip(a)].
% 6.91/7.18 12316 quotient(product(A,difference(B,one)),B) = product(quotient(A,B),quotient(one,B)). [para(7031(a,1),314(a,1,2,1)),rewrite([3593(4),2(10)]),flip(a)].
% 6.91/7.18 12339 product(product(quotient(one,A),quotient(product(A,B),A)),A) = product(A,product(product(quotient(one,A),quotient(B,A)),A)). [back_rewrite(9690),rewrite([12316(4),6824(8),1(4),9671(5)]),flip(a)].
% 6.91/7.18 12571 product(product(A,difference(B,one)),difference(difference(B,one),one)) = product(product(A,B),difference(B,one)). [para(22(a,1),9460(a,1,1,2)),flip(a)].
% 6.91/7.18 12623 product(product(A,quotient(B,difference(difference(B,one),one))),product(B,quotient(one,B))) = product(product(A,product(B,quotient(one,B))),quotient(B,difference(difference(B,one),one))). [para(4357(a,1),9460(a,2,2)),rewrite([5458(7)]),flip(a)].
% 6.91/7.18 12644 product(product(A,quotient(one,A)),product(product(B,product(A,quotient(one,A))),quotient(A,difference(difference(A,one),one)))) = difference(quotient(A,difference(difference(A,one),one)),B). [back_rewrite(10612),rewrite([12623(13)])].
% 6.91/7.18 12688 difference(quotient(one,A),quotient(B,A)) = product(A,product(B,difference(A,one))). [para(8(a,1),9622(a,1,2,1)),flip(a)].
% 6.91/7.18 12691 product(quotient(one,A),product(product(B,A),difference(A,one))) = difference(quotient(one,quotient(one,A)),B). [para(23(a,1),9622(a,1,2,2)),rewrite([9460(6)])].
% 6.91/7.18 12718 difference(quotient(one,product(A,quotient(one,A))),B) = difference(quotient(A,difference(difference(A,one),one)),B). [para(1547(a,1),9622(a,1,2,2)),rewrite([12644(14)]),flip(a)].
% 6.91/7.18 12796 difference(difference(A,one),product(quotient(one,A),B)) = product(difference(difference(A,one),one),difference(A,B)). [para(9671(a,1),1141(a,1,1,2)),rewrite([1403(7),18(6),6156(8)])].
% 6.91/7.18 12810 quotient(product(A,quotient(one,B)),difference(B,one)) = product(quotient(A,quotient(one,quotient(one,B))),B). [para(3937(a,1),9671(a,2,1)),rewrite([1196(6),18(2),6(5)])].
% 6.91/7.18 13041 quotient(product(quotient(A,quotient(one,B)),B),quotient(B,difference(B,one))) = product(difference(B,one),difference(B,product(quotient(B,difference(B,one)),A))). [para(809(a,1),208(a,1,1,1)),rewrite([410(8),452(8),811(10),12268(7),3956(8),410(13),452(13),6174(12),809(16),580(17)]),flip(a)].
% 6.91/7.18 13151 product(quotient(product(A,B),product(B,B)),B) = product(difference(B,one),product(B,A)). [para(10257(a,1),1141(a,1,1))].
% 6.91/7.18 13161 quotient(product(A,B),quotient(B,difference(B,one))) = product(difference(B,one),product(B,quotient(A,B))). [para(2083(a,1),10257(a,2,2)),rewrite([9356(7),43(6),1(4)]),flip(a)].
% 6.91/7.18 13227 quotient(quotient(product(A,B),product(C,B)),difference(B,one)) = product(product(quotient(one,B),quotient(product(B,A),C)),B). [para(10257(a,1),9671(a,1,1))].
% 6.91/7.18 13236 product(difference(A,one),difference(A,product(quotient(A,difference(A,one)),B))) = product(difference(A,one),product(product(A,A),difference(A,B))). [back_rewrite(13041),rewrite([13161(8),3986(7)]),flip(a)].
% 6.91/7.18 13239 quotient(quotient(product(A,quotient(one,B)),B),quotient(one,product(B,B))) = product(difference(B,one),product(product(B,B),difference(B,A))). [back_rewrite(3980),rewrite([13161(5),8801(8),13236(16)])].
% 6.91/7.18 13250 difference(quotient(one,A),product(quotient(one,product(A,A)),product(A,B))) = product(difference(A,one),product(product(A,A),difference(A,B))). [back_rewrite(586),rewrite([13239(16)])].
% 6.91/7.18 13730 product(difference(A,one),product(product(A,A),difference(A,product(B,A)))) = quotient(product(difference(A,one),product(A,B)),quotient(one,A)). [para(1141(a,1),226(a,1,1,2)),rewrite([23(6),1720(18),13250(16)]),flip(a)].
% 6.91/7.18 13977 quotient(product(A,B),difference(difference(B,one),one)) = product(quotient(A,quotient(one,B)),difference(B,one)). [para(11554(a,1),6174(a,1,1)),rewrite([22(14),7(11)])].
% 6.91/7.18 14569 product(difference(A,one),product(B,difference(difference(A,one),one))) = difference(A,quotient(B,difference(A,one))). [para(22(a,1),12688(a,1,1)),flip(a)].
% 6.91/7.18 14994 quotient(product(difference(A,one),B),product(A,quotient(one,A))) = difference(A,quotient(quotient(B,A),difference(A,one))). [para(789(a,1),4252(a,1,2,2)),rewrite([13977(12),22(6),14569(9)]),flip(a)].
% 6.91/7.18 15273 quotient(product(quotient(A,difference(A,one)),B),product(product(A,A),difference(A,B))) = A. [para(1987(a,1),1532(a,1,1,1)),rewrite([43(11),1(9),3986(9),23(12)])].
% 6.91/7.18 15421 product(difference(A,one),product(A,quotient(B,A))) = product(quotient(B,product(A,A)),A). [para(1903(a,1),8(a,1,1))].
% 6.91/7.18 15455 quotient(product(A,B),quotient(B,difference(B,one))) = product(quotient(A,product(B,B)),B). [back_rewrite(13161),rewrite([15421(10)])].
% 6.91/7.18 16265 difference(A,product(quotient(A,difference(A,one)),B)) = product(product(A,A),difference(A,B)). [para(3986(a,1),1585(a,2)),rewrite([11651(6),811(7)])].
% 6.91/7.18 16499 product(quotient(A,difference(A,one)),product(difference(quotient(A,difference(A,one)),B),A)) = product(A,product(product(quotient(one,A),B),A)). [para(2150(a,1),4015(a,1,2,2)),rewrite([2009(17),6824(16),1(12),9671(13)])].
% 6.91/7.18 16501 quotient(product(A,quotient(one,quotient(one,B))),quotient(one,B)) = product(B,product(difference(B,A),quotient(B,difference(B,one)))). [para(2083(a,1),4015(a,1,2,2)),flip(a)].
% 6.91/7.18 16674 product(A,quotient(difference(A,B),product(A,quotient(one,A)))) = product(quotient(B,quotient(one,quotient(one,A))),A). [para(12(a,1),4343(a,1,2,2)),rewrite([12810(12)])].
% 6.91/7.18 17934 product(A,difference(quotient(A,difference(A,one)),B)) = quotient(difference(A,product(B,A)),A). [para(11793(a,1),5(a,1,2))].
% 6.91/7.18 17936 difference(quotient(A,difference(A,one)),quotient(B,A)) = difference(A,quotient(difference(A,B),A)). [para(8(a,1),11793(a,1,2,1,2)),flip(a)].
% 6.91/7.18 17945 product(difference(quotient(A,difference(A,one)),B),A) = product(difference(A,one),difference(A,product(B,A))). [para(11793(a,1),832(a,2,1)),rewrite([8(6)]),flip(a)].
% 6.91/7.18 18007 product(quotient(one,A),product(quotient(A,difference(A,one)),difference(A,product(B,A)))) = product(A,product(product(quotient(one,A),B),A)). [back_rewrite(16499),rewrite([17945(8),12268(9)])].
% 6.91/7.18 18237 product(quotient(quotient(A,quotient(one,B)),product(B,B)),B) = product(difference(B,one),product(product(B,B),difference(B,A))). [para(3986(a,1),13151(a,2,2)),rewrite([8(5)])].
% 6.91/7.18 18401 quotient(product(quotient(A,difference(A,one)),product(A,B)),product(product(A,A),B)) = A. [para(6(a,1),15273(a,1,2,2))].
% 6.91/7.18 18702 quotient(product(difference(difference(A,one),one),difference(A,product(B,A))),A) = product(product(A,A),difference(quotient(A,difference(A,one)),B)). [para(11793(a,1),16265(a,2,2)),rewrite([52(8),137(4),12(3),809(4)])].
% 6.91/7.18 19062 product(quotient(A,difference(A,one)),difference(A,quotient(difference(A,B),A))) = quotient(B,A). [para(17936(a,1),5(a,1,2))].
% 6.91/7.18 19086 quotient(product(A,quotient(one,quotient(one,B))),B) = quotient(A,product(B,quotient(one,B))). [back_rewrite(11877),rewrite([19062(12)])].
% 6.91/7.18 19096 product(product(A,B),quotient(A,difference(difference(A,one),one))) = product(A,quotient(B,product(A,quotient(one,A)))). [back_rewrite(5444),rewrite([19086(13)])].
% 6.91/7.18 19183 product(A,product(difference(A,B),quotient(A,difference(A,one)))) = product(quotient(B,quotient(one,A)),A). [para(15273(a,1),416(a,1,1,2,2)),rewrite([3937(3),5(11),7(10)]),flip(a)].
% 6.91/7.18 19184 quotient(product(A,quotient(one,quotient(one,B))),quotient(one,B)) = product(quotient(A,quotient(one,B)),B). [back_rewrite(16501),rewrite([19183(14)])].
% 6.91/7.18 19185 product(quotient(one,A),product(quotient(A,difference(A,one)),difference(A,B))) = product(difference(A,one),product(product(A,A),difference(A,B))). [back_rewrite(8821),rewrite([19184(8),15455(8),18237(6)]),flip(a)].
% 6.91/7.18 19187 quotient(product(difference(A,one),product(A,B)),quotient(one,A)) = product(A,product(product(quotient(one,A),B),A)). [back_rewrite(18007),rewrite([19185(9),13730(7)])].
% 6.91/7.18 19238 product(quotient(A,difference(A,one)),product(A,B)) = product(A,product(product(A,A),B)). [para(18401(a,1),8(a,1,1)),flip(a)].
% 6.91/7.18 19694 product(quotient(A,difference(A,one)),quotient(difference(A,B),A)) = quotient(difference(quotient(one,A),B),A). [para(9550(a,1),19062(a,1,2,2,1)),rewrite([12316(8),7(5),52(7),1(6)])].
% 6.91/7.18 19757 product(quotient(A,quotient(one,quotient(one,B))),B) = quotient(A,product(B,quotient(one,B))). [para(22(a,1),19086(a,1,1,2,2)),rewrite([12810(6),22(12),12(9)])].
% 6.91/7.18 19769 product(A,quotient(B,difference(difference(B,one),one))) = quotient(A,product(B,quotient(one,B))). [para(19086(a,1),314(a,1,2)),rewrite([16674(6),19757(6),1388(9)]),flip(a)].
% 6.91/7.18 19778 quotient(product(A,product(difference(A,one),B)),product(A,quotient(one,A))) = quotient(quotient(B,quotient(one,A)),A). [para(3457(a,1),19086(a,1,1)),rewrite([23(6),23(14),4021(12),23(10),4021(8)]),flip(a)].
% 6.91/7.18 19781 quotient(product(quotient(one,quotient(one,A)),B),product(A,quotient(one,A))) = quotient(quotient(difference(quotient(one,A),B),quotient(one,A)),A). [para(4107(a,1),19086(a,1,1)),flip(a)].
% 6.91/7.18 19831 quotient(product(A,B),product(A,quotient(one,A))) = product(A,quotient(B,product(A,quotient(one,A)))). [back_rewrite(19096),rewrite([19769(7)])].
% 6.91/7.18 19849 difference(quotient(A,difference(difference(A,one),one)),B) = product(product(A,quotient(one,A)),B). [back_rewrite(12644),rewrite([19769(13),7(11)]),flip(a)].
% 6.91/7.18 19861 product(A,product(difference(difference(A,one),one),difference(A,B))) = quotient(difference(quotient(one,A),product(B,A)),A). [back_rewrite(1012),rewrite([19781(13),2143(10),7075(8),12796(6),7(9)])].
% 6.91/7.18 19871 quotient(quotient(A,quotient(one,B)),B) = quotient(quotient(A,B),difference(B,one)). [back_rewrite(19778),rewrite([19831(8),14994(7),5(6)]),flip(a)].
% 6.91/7.18 19890 difference(quotient(one,product(A,quotient(one,A))),B) = product(product(A,quotient(one,A)),B). [back_rewrite(12718),rewrite([19849(12)])].
% 6.91/7.18 19950 quotient(product(A,difference(quotient(one,quotient(one,A)),product(B,A))),A) = product(product(A,quotient(one,A)),B). [back_rewrite(11717),rewrite([19890(10),10862(12)])].
% 6.91/7.18 19952 difference(difference(difference(A,one),one),product(A,B)) = product(difference(A,one),difference(quotient(one,A),B)). [back_rewrite(4370),rewrite([19890(7),9748(6)]),flip(a)].
% 6.91/7.18 20005 product(quotient(quotient(A,B),difference(B,one)),B) = quotient(A,quotient(one,B)). [para(19871(a,1),8(a,1,1))].
% 6.91/7.18 20123 quotient(product(A,B),quotient(one,B)) = product(quotient(A,difference(B,one)),B). [para(7(a,1),20005(a,1,1,1)),flip(a)].
% 6.91/7.18 20353 product(product(quotient(A,difference(B,one)),B),quotient(one,B)) = product(A,B). [para(20123(a,1),8(a,1,1))].
% 6.91/7.18 20400 product(product(A,product(product(quotient(one,A),quotient(B,A)),A)),A) = product(A,product(product(quotient(one,A),B),A)). [para(13151(a,1),20123(a,1,1)),rewrite([19187(7),13227(11),12339(11)]),flip(a)].
% 6.91/7.18 20650 product(difference(A,one),product(A,B)) = product(A,product(quotient(one,A),B)). [para(13151(a,1),20353(a,2)),rewrite([13227(6),12339(6),20400(7),43(8),1(6),7(5)]),flip(a)].
% 6.91/7.18 20996 product(difference(difference(A,one),one),difference(A,B)) = product(difference(A,one),difference(quotient(one,A),B)). [para(20650(a,1),6156(a,1,1,1)),rewrite([12571(12),6156(8),12796(6),19952(12)])].
% 6.91/7.18 21002 product(difference(A,one),difference(quotient(one,A),B)) = product(A,difference(quotient(one,quotient(one,A)),B)). [para(9622(a,1),20650(a,1,2)),rewrite([12691(13)])].
% 6.91/7.18 21042 product(A,product(A,difference(quotient(one,quotient(one,A)),B))) = quotient(difference(quotient(one,A),product(B,A)),A). [back_rewrite(19861),rewrite([20996(6),21002(6)])].
% 6.91/7.18 21043 product(product(A,A),difference(quotient(A,difference(A,one)),B)) = product(product(A,quotient(one,A)),B). [back_rewrite(18702),rewrite([20996(7),21002(7),19950(8)]),flip(a)].
% 6.91/7.18 21057 quotient(difference(quotient(one,A),product(B,A)),A) = product(quotient(one,quotient(one,A)),B). [back_rewrite(4186),rewrite([21002(6),21042(7)])].
% 6.91/7.18 21276 product(A,product(product(A,quotient(one,A)),B)) = product(quotient(one,quotient(one,A)),B). [para(17934(a,1),19238(a,1,2)),rewrite([19694(7),21057(5),21043(11)]),flip(a)].
% 6.91/7.18 21277 $F # answer(goals). [resolve(21276,a,16,a)].
% 6.91/7.18
% 6.91/7.18 % SZS output end Refutation
% 6.91/7.18 ============================== end of proof ==========================
% 6.91/7.18
% 6.91/7.18 ============================== STATISTICS ============================
% 6.91/7.18
% 6.91/7.18 Given=707. Generated=235747. Kept=21273. proofs=1.
% 6.91/7.18 Usable=482. Sos=9988. Demods=10376. Limbo=14, Disabled=10801. Hints=0.
% 6.91/7.18 Megabytes=27.64.
% 6.91/7.18 User_CPU=6.05, System_CPU=0.16, Wall_clock=6.
% 6.91/7.18
% 6.91/7.18 ============================== end of statistics =====================
% 6.91/7.18
% 6.91/7.18 ============================== end of search =========================
% 6.91/7.18
% 6.91/7.18 THEOREM PROVED
% 6.91/7.18 % SZS status Unsatisfiable
% 6.91/7.18
% 6.91/7.18 Exiting with 1 proof.
% 6.91/7.18
% 6.91/7.18 Process 797 exit (max_proofs) Mon Jun 13 15:14:47 2022
% 6.91/7.18 Prover9 interrupted
%------------------------------------------------------------------------------