TSTP Solution File: GRP765-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP765-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 8.83s 9.10s
% Output : Refutation 8.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP765-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 07:27:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 7.24/7.52 ============================== Prover9 ===============================
% 7.24/7.52 Prover9 (32) version 2009-11A, November 2009.
% 7.24/7.52 Process 23401 was started by sandbox on n007.cluster.edu,
% 7.24/7.52 Tue Jun 14 07:27:25 2022
% 7.24/7.52 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23248_n007.cluster.edu".
% 7.24/7.52 ============================== end of head ===========================
% 7.24/7.52
% 7.24/7.52 ============================== INPUT =================================
% 7.24/7.52
% 7.24/7.52 % Reading from file /tmp/Prover9_23248_n007.cluster.edu
% 7.24/7.52
% 7.24/7.52 set(prolog_style_variables).
% 7.24/7.52 set(auto2).
% 7.24/7.52 % set(auto2) -> set(auto).
% 7.24/7.52 % set(auto) -> set(auto_inference).
% 7.24/7.52 % set(auto) -> set(auto_setup).
% 7.24/7.52 % set(auto_setup) -> set(predicate_elim).
% 7.24/7.52 % set(auto_setup) -> assign(eq_defs, unfold).
% 7.24/7.52 % set(auto) -> set(auto_limits).
% 7.24/7.52 % set(auto_limits) -> assign(max_weight, "100.000").
% 7.24/7.52 % set(auto_limits) -> assign(sos_limit, 20000).
% 7.24/7.52 % set(auto) -> set(auto_denials).
% 7.24/7.52 % set(auto) -> set(auto_process).
% 7.24/7.52 % set(auto2) -> assign(new_constants, 1).
% 7.24/7.52 % set(auto2) -> assign(fold_denial_max, 3).
% 7.24/7.52 % set(auto2) -> assign(max_weight, "200.000").
% 7.24/7.52 % set(auto2) -> assign(max_hours, 1).
% 7.24/7.52 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 7.24/7.52 % set(auto2) -> assign(max_seconds, 0).
% 7.24/7.52 % set(auto2) -> assign(max_minutes, 5).
% 7.24/7.52 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 7.24/7.52 % set(auto2) -> set(sort_initial_sos).
% 7.24/7.52 % set(auto2) -> assign(sos_limit, -1).
% 7.24/7.52 % set(auto2) -> assign(lrs_ticks, 3000).
% 7.24/7.52 % set(auto2) -> assign(max_megs, 400).
% 7.24/7.52 % set(auto2) -> assign(stats, some).
% 7.24/7.52 % set(auto2) -> clear(echo_input).
% 7.24/7.52 % set(auto2) -> set(quiet).
% 7.24/7.52 % set(auto2) -> clear(print_initial_clauses).
% 7.24/7.52 % set(auto2) -> clear(print_given).
% 7.24/7.52 assign(lrs_ticks,-1).
% 7.24/7.52 assign(sos_limit,10000).
% 7.24/7.52 assign(order,kbo).
% 7.24/7.52 set(lex_order_vars).
% 7.24/7.52 clear(print_given).
% 7.24/7.52
% 7.24/7.52 % formulas(sos). % not echoed (13 formulas)
% 7.24/7.52
% 7.24/7.52 ============================== end of input ==========================
% 7.24/7.52
% 7.24/7.52 % From the command line: assign(max_seconds, 300).
% 7.24/7.52
% 7.24/7.52 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 7.24/7.52
% 7.24/7.52 % Formulas that are not ordinary clauses:
% 7.24/7.52
% 7.24/7.52 ============================== end of process non-clausal formulas ===
% 7.24/7.52
% 7.24/7.52 ============================== PROCESS INITIAL CLAUSES ===============
% 7.24/7.52
% 7.24/7.52 ============================== PREDICATE ELIMINATION =================
% 7.24/7.52
% 7.24/7.52 ============================== end predicate elimination =============
% 7.24/7.52
% 7.24/7.52 Auto_denials:
% 7.24/7.52 % copying label goals to answer in negative clause
% 7.24/7.52
% 7.24/7.52 Term ordering decisions:
% 7.24/7.52 Function symbol KB weights: one=1. x0=1. x1=1. product=1. quotient=1. difference=1. i=1. j=1. eta=1.
% 7.24/7.52
% 7.24/7.52 ============================== end of process initial clauses ========
% 7.24/7.52
% 7.24/7.52 ============================== CLAUSES FOR SEARCH ====================
% 7.24/7.52
% 7.24/7.52 ============================== end of clauses for search =============
% 7.24/7.52
% 7.24/7.52 ============================== SEARCH ================================
% 7.24/7.52
% 7.24/7.52 % Starting search at 0.01 seconds.
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=75.000, iters=3360
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=71.000, iters=3338
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=65.000, iters=3355
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=63.000, iters=3350
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=59.000, iters=3406
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=55.000, iters=3411
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=51.000, iters=3340
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=49.000, iters=3364
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=47.000, iters=3368
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=45.000, iters=3350
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=43.000, iters=3337
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=41.000, iters=3336
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=39.000, iters=3333
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=37.000, iters=3344
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=35.000, iters=3333
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=33.000, iters=3352
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=31.000, iters=3337
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=29.000, iters=3349
% 7.24/7.52
% 7.24/7.52 Low Water (displace): id=2849, wt=151.000
% 7.24/7.52
% 7.24/7.52 Low Water (displace): id=5047, wt=139.000
% 7.24/7.52
% 7.24/7.52 Low Water (displace): id=4203, wt=135.000
% 7.24/7.52
% 7.24/7.52 Low Water (displace): id=15521, wt=23.000
% 7.24/7.52
% 7.24/7.52 Low Water (displace): id=15527, wt=21.000
% 7.24/7.52
% 7.24/7.52 Low Water (displace): id=15697, wt=19.000
% 7.24/7.52
% 7.24/7.52 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 122 (0.00 of 3.40 sec).
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=27.000, iters=3333
% 7.24/7.52
% 7.24/7.52 Low Water (keep): wt=25.000, iters=3336
% 8.83/9.10
% 8.83/9.10 Low Water (displace): id=22479, wt=17.000
% 8.83/9.10
% 8.83/9.10 ============================== PROOF =================================
% 8.83/9.10 % SZS status Unsatisfiable
% 8.83/9.10 % SZS output start Refutation
% 8.83/9.10
% 8.83/9.10 % Proof 1 at 7.95 (+ 0.18) seconds: goals.
% 8.83/9.10 % Length of proof is 214.
% 8.83/9.10 % Level of proof is 39.
% 8.83/9.10 % Maximum clause weight is 39.000.
% 8.83/9.10 % Given clauses 802.
% 8.83/9.10
% 8.83/9.10 1 product(A,one) = A # label(sos01) # label(axiom). [assumption].
% 8.83/9.10 2 product(one,A) = A # label(sos02) # label(axiom). [assumption].
% 8.83/9.10 3 i(A) = difference(A,one) # label(sos09) # label(axiom). [assumption].
% 8.83/9.10 4 j(A) = quotient(one,A) # label(sos10) # label(axiom). [assumption].
% 8.83/9.10 5 product(A,difference(A,B)) = B # label(sos03) # label(axiom). [assumption].
% 8.83/9.10 6 difference(A,product(A,B)) = B # label(sos04) # label(axiom). [assumption].
% 8.83/9.10 7 quotient(product(A,B),B) = A # label(sos05) # label(axiom). [assumption].
% 8.83/9.10 8 product(quotient(A,B),B) = A # label(sos06) # label(axiom). [assumption].
% 8.83/9.10 9 eta(A) = product(i(A),A) # label(sos12) # label(axiom). [assumption].
% 8.83/9.10 10 eta(A) = product(difference(A,one),A). [copy(9),rewrite([3(2)])].
% 8.83/9.10 11 product(i(A),A) = product(A,j(A)) # label(sos11) # label(axiom). [assumption].
% 8.83/9.10 12 product(difference(A,one),A) = product(A,quotient(one,A)). [copy(11),rewrite([3(1),4(4)])].
% 8.83/9.10 13 difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) # label(sos07) # label(axiom). [assumption].
% 8.83/9.10 14 difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) # label(sos08) # label(axiom). [assumption].
% 8.83/9.10 15 product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 8.83/9.10 16 product(product(x0,quotient(one,x0)),product(x0,x1)) != product(difference(difference(x0,one),one),x1) # answer(goals). [copy(15),rewrite([3(2),3(4),10(9),12(12)]),flip(a)].
% 8.83/9.10 18 difference(one,A) = A. [para(5(a,1),2(a,1)),flip(a)].
% 8.83/9.10 19 difference(A,A) = one. [para(1(a,1),6(a,1,2))].
% 8.83/9.10 20 quotient(A,one) = A. [para(1(a,1),7(a,1,1))].
% 8.83/9.10 21 quotient(A,A) = one. [para(2(a,1),7(a,1,1))].
% 8.83/9.10 22 quotient(A,difference(B,A)) = B. [para(5(a,1),7(a,1,1))].
% 8.83/9.10 23 difference(quotient(A,B),A) = B. [para(8(a,1),6(a,1,2))].
% 8.83/9.10 24 difference(difference(A,one),product(A,quotient(one,A))) = A. [para(12(a,1),6(a,1,2))].
% 8.83/9.10 25 quotient(product(A,quotient(one,A)),A) = difference(A,one). [para(12(a,1),7(a,1,1))].
% 8.83/9.10 26 product(A,quotient(product(B,product(C,A)),A)) = product(product(A,B),C). [para(13(a,1),5(a,1,2))].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 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))].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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))].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 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))].
% 8.83/9.10 51 product(difference(A,product(B,C)),A) = product(difference(A,B),product(C,A)). [para(27(a,1),8(a,1,1))].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 58 difference(product(A,B),A) = quotient(difference(B,A),A). [para(1(a,1),33(a,1,2)),rewrite([2(4)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 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))].
% 8.83/9.10 66 quotient(product(A,B),quotient(difference(C,product(B,A)),A)) = product(A,C). [para(33(a,1),22(a,1,2))].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 73 quotient(difference(difference(A,B),A),A) = difference(B,A). [para(5(a,1),58(a,1,1)),flip(a)].
% 8.83/9.10 76 quotient(A,quotient(difference(B,A),A)) = product(A,B). [para(58(a,1),22(a,1,2))].
% 8.83/9.10 79 difference(difference(A,B),A) = product(difference(B,A),A). [para(73(a,1),8(a,1,1)),flip(a)].
% 8.83/9.10 85 quotient(A,quotient(B,A)) = product(A,quotient(A,B)). [para(23(a,1),76(a,1,2,1))].
% 8.83/9.10 86 difference(product(quotient(one,A),difference(A,one)),one) = product(A,A). [back_rewrite(67),rewrite([85(10),20(9)])].
% 8.83/9.10 92 product(difference(A,B),product(difference(B,A),A)) = A. [para(79(a,1),5(a,1,2))].
% 8.83/9.10 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)])].
% 8.83/9.10 95 quotient(A,product(difference(B,A),A)) = difference(A,B). [para(79(a,1),22(a,1,2))].
% 8.83/9.10 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)])].
% 8.83/9.10 101 product(A,quotient(A,product(B,A))) = quotient(A,B). [para(7(a,1),85(a,1,2)),flip(a)].
% 8.83/9.10 105 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)])].
% 8.83/9.10 111 product(difference(A,one),product(A,A)) = A. [para(18(a,1),92(a,1,2,1))].
% 8.83/9.10 121 quotient(A,product(A,A)) = difference(A,one). [para(111(a,1),7(a,1,1))].
% 8.83/9.10 123 product(A,product(quotient(one,A),quotient(one,A))) = quotient(one,A). [para(23(a,1),111(a,1,1))].
% 8.83/9.10 134 quotient(product(A,A),difference(A,one)) = product(product(A,A),A). [para(121(a,1),85(a,1,2)),rewrite([7(7)])].
% 8.83/9.10 137 difference(A,quotient(A,B)) = quotient(A,product(B,A)). [para(23(a,1),95(a,1,2,1)),flip(a)].
% 8.83/9.10 140 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)])].
% 8.83/9.10 146 quotient(quotient(A,B),quotient(A,product(B,A))) = A. [para(101(a,1),7(a,1,1))].
% 8.83/9.10 165 quotient(quotient(A,difference(B,one)),B) = product(B,product(difference(B,one),A)). [para(32(a,1),18(a,1)),rewrite([1(2)])].
% 8.83/9.10 186 product(quotient(one,A),difference(A,one)) = quotient(one,product(A,A)). [para(86(a,1),22(a,1,2)),flip(a)].
% 8.83/9.10 190 product(quotient(one,A),quotient(one,A)) = difference(A,quotient(one,A)). [para(123(a,1),6(a,1,2)),flip(a)].
% 8.83/9.10 194 product(product(product(A,A),A),difference(A,one)) = product(A,A). [para(134(a,1),8(a,1,1))].
% 8.83/9.10 200 quotient(quotient(A,B),quotient(one,B)) = product(quotient(one,B),product(B,A)). [para(34(a,1),18(a,1)),rewrite([1(2)])].
% 8.83/9.10 224 difference(quotient(one,A),quotient(one,product(A,A))) = difference(A,one). [para(186(a,1),6(a,1,2))].
% 8.83/9.10 227 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)].
% 8.83/9.10 228 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)].
% 8.83/9.10 234 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)])].
% 8.83/9.10 235 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))].
% 8.83/9.10 238 difference(quotient(one,A),difference(A,quotient(one,A))) = quotient(one,A). [para(190(a,1),6(a,1,2))].
% 8.83/9.10 310 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))].
% 8.83/9.10 314 product(A,quotient(product(difference(A,B),C),A)) = product(B,quotient(C,A)). [para(5(a,1),43(a,1,1)),flip(a)].
% 8.83/9.10 317 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))].
% 8.83/9.10 347 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))].
% 8.83/9.10 384 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)])].
% 8.83/9.10 410 quotient(product(A,quotient(B,A)),C) = product(A,quotient(B,product(C,A))). [para(44(a,1),7(a,1,1))].
% 8.83/9.10 445 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)])].
% 8.83/9.10 452 product(A,quotient(one,product(A,A))) = difference(A,one). [back_rewrite(25),rewrite([410(4)])].
% 8.83/9.10 453 difference(difference(A,one),product(A,quotient(quotient(one,A),A))) = one. [back_rewrite(234),rewrite([452(11),21(12)])].
% 8.83/9.10 474 difference(A,difference(A,one)) = quotient(one,product(A,A)). [para(452(a,1),6(a,1,2))].
% 8.83/9.10 475 quotient(difference(A,one),quotient(one,product(A,A))) = A. [para(452(a,1),7(a,1,1))].
% 8.83/9.10 520 quotient(difference(A,one),quotient(one,A)) = product(A,quotient(one,A)). [back_rewrite(235),rewrite([475(8),12(3)]),flip(a)].
% 8.83/9.10 524 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)].
% 8.83/9.10 529 quotient(one,difference(A,quotient(one,A))) = difference(quotient(one,A),A). [back_rewrite(228),rewrite([524(10)])].
% 8.83/9.10 532 product(A,quotient(quotient(one,A),A)) = difference(A,one). [para(453(a,1),5(a,1,2)),rewrite([1(4)]),flip(a)].
% 8.83/9.10 573 quotient(quotient(one,A),A) = quotient(one,product(A,A)). [para(532(a,1),6(a,1,2)),rewrite([474(3)]),flip(a)].
% 8.83/9.10 574 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)])].
% 8.83/9.10 580 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)].
% 8.83/9.10 581 difference(quotient(one,product(A,A)),quotient(one,A)) = A. [para(573(a,1),23(a,1,1))].
% 8.83/9.10 592 quotient(one,product(difference(A,one),difference(A,one))) = quotient(A,difference(A,one)). [back_rewrite(227),rewrite([580(12)])].
% 8.83/9.10 632 product(difference(A,one),product(A,quotient(one,A))) = quotient(one,A). [para(581(a,1),92(a,1,2,1)),rewrite([224(6)])].
% 8.83/9.10 634 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)].
% 8.83/9.10 713 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)])].
% 8.83/9.10 723 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))].
% 8.83/9.10 742 quotient(difference(difference(A,one),B),difference(A,one)) = difference(difference(A,one),product(B,A)). [para(1(a,1),50(a,1,1))].
% 8.83/9.10 788 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)].
% 8.83/9.10 789 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)])].
% 8.83/9.10 797 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))].
% 8.83/9.10 809 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)])].
% 8.83/9.10 830 product(difference(difference(A,one),one),product(A,quotient(one,A))) = A. [back_rewrite(797),rewrite([809(4),85(10),713(9)])].
% 8.83/9.10 832 product(difference(A,one),product(B,A)) = product(difference(A,B),A). [para(2(a,1),51(a,1,1,2)),flip(a)].
% 8.83/9.10 834 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)].
% 8.83/9.10 908 quotient(product(difference(A,one),B),A) = difference(A,quotient(B,A)). [para(2(a,1),52(a,1,2)),flip(a)].
% 8.83/9.10 911 quotient(product(A,quotient(B,C)),quotient(product(difference(C,A),B),C)) = C. [para(52(a,1),22(a,1,2))].
% 8.83/9.10 966 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)])].
% 8.83/9.10 968 quotient(product(quotient(one,A),product(A,A)),A) = quotient(A,difference(difference(A,one),one)). [back_rewrite(788),rewrite([966(10)])].
% 8.83/9.10 1141 product(difference(A,quotient(B,A)),A) = product(difference(A,one),B). [para(8(a,1),832(a,1,2)),flip(a)].
% 8.83/9.10 1194 difference(A,product(difference(B,C),B)) = product(difference(product(B,A),C),B). [para(56(a,1),6(a,1,2))].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 1256 difference(A,quotient(one,A)) = quotient(difference(A,one),A). [para(1(a,1),908(a,1,1)),flip(a)].
% 8.83/9.10 1257 difference(A,quotient(difference(difference(A,one),B),A)) = quotient(B,A). [para(5(a,1),908(a,1,1)),flip(a)].
% 8.83/9.10 1334 quotient(one,quotient(difference(A,one),A)) = difference(quotient(one,A),A). [back_rewrite(529),rewrite([1256(4)])].
% 8.83/9.10 1350 difference(quotient(one,A),quotient(difference(A,one),A)) = quotient(one,A). [back_rewrite(238),rewrite([1256(5)])].
% 8.83/9.10 1354 product(A,quotient(difference(A,one),A)) = quotient(one,A). [para(1256(a,1),5(a,1,2))].
% 8.83/9.10 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)])].
% 8.83/9.10 1385 product(quotient(A,difference(difference(A,one),one)),A) = quotient(one,quotient(one,A)). [back_rewrite(1243),rewrite([1366(10)])].
% 8.83/9.10 1388 quotient(quotient(one,quotient(one,A)),A) = quotient(A,difference(difference(A,one),one)). [back_rewrite(968),rewrite([1366(4)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 1422 quotient(difference(difference(A,one),product(B,difference(difference(A,one),one))),difference(difference(A,one),one)) = difference(product(A,quotient(one,A)),product(difference(difference(A,one),one),B)). [para(40(a,1),59(a,1,1,1))].
% 8.83/9.10 1464 quotient(difference(difference(A,one),B),difference(A,one)) = product(product(A,B),A). [back_rewrite(742),rewrite([1403(10),18(9)])].
% 8.83/9.10 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)])].
% 8.83/9.10 1585 quotient(difference(difference(A,one),B),A) = product(A,quotient(B,A)). [para(1257(a,1),5(a,1,2)),flip(a)].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 1690 quotient(product(A,B),quotient(C,A)) = product(A,quotient(product(B,A),C)). [para(23(a,1),66(a,1,2,1))].
% 8.83/9.10 1743 product(A,product(difference(A,one),difference(A,one))) = quotient(one,A). [para(22(a,1),1366(a,1,1)),rewrite([22(11)])].
% 8.83/9.10 1924 difference(product(A,quotient(B,A)),difference(difference(A,one),B)) = A. [para(1585(a,1),23(a,1,1))].
% 8.83/9.10 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)].
% 8.83/9.10 1987 difference(quotient(one,A),A) = quotient(A,difference(A,one)). [back_rewrite(592),rewrite([1976(6),1334(5)])].
% 8.83/9.10 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)])].
% 8.83/9.10 2083 product(quotient(one,quotient(one,A)),A) = quotient(A,difference(A,one)). [back_rewrite(524),rewrite([1987(8)])].
% 8.83/9.10 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)].
% 8.83/9.10 2530 difference(quotient(one,A),product(A,A)) = product(A,product(A,A)). [para(19(a,1),93(a,1,1,1))].
% 8.83/9.10 2564 quotient(product(A,product(A,A)),A) = quotient(A,difference(A,one)). [back_rewrite(1672),rewrite([2530(4)])].
% 8.83/9.10 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)].
% 8.83/9.10 3457 product(product(A,product(difference(A,one),B)),A) = quotient(B,difference(A,one)). [para(165(a,1),8(a,1,1))].
% 8.83/9.10 3593 product(A,quotient(difference(A,B),A)) = product(B,quotient(one,A)). [para(1(a,1),314(a,1,2,1))].
% 8.83/9.10 3690 quotient(product(A,quotient(one,B)),quotient(difference(B,A),B)) = B. [para(3593(a,1),7(a,1,1))].
% 8.83/9.10 3764 quotient(A,quotient(difference(B,quotient(A,quotient(one,B))),B)) = B. [para(8(a,1),3690(a,1,1))].
% 8.83/9.10 3917 quotient(difference(A,quotient(B,quotient(one,A))),A) = difference(A,B). [para(3764(a,1),23(a,1,1)),flip(a)].
% 8.83/9.10 3924 difference(A,quotient(B,quotient(one,A))) = product(difference(A,B),A). [para(3917(a,1),8(a,1,1)),flip(a)].
% 8.83/9.10 3937 product(A,product(difference(A,B),A)) = quotient(B,quotient(one,A)). [para(3924(a,1),5(a,1,2))].
% 8.83/9.10 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)])].
% 8.83/9.10 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))].
% 8.83/9.10 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)].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 4676 quotient(product(difference(A,B),A),product(C,A)) = difference(A,quotient(B,C)). [para(834(a,1),7(a,1,1))].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 6156 product(product(product(A,B),A),difference(A,one)) = difference(difference(A,one),B). [para(1464(a,1),8(a,1,1))].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 9622 product(A,product(product(B,A),difference(A,one))) = difference(quotient(one,A),B). [back_rewrite(4128),rewrite([9460(4)])].
% 8.83/9.10 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)])].
% 8.83/9.10 9736 difference(product(A,quotient(one,A)),product(difference(difference(A,one),one),B)) = product(product(A,product(B,difference(difference(A,one),one))),difference(A,one)). [back_rewrite(1422),rewrite([9671(13),22(4)]),flip(a)].
% 8.83/9.10 10259 product(A,quotient(product(B,A),product(A,quotient(one,A)))) = quotient(product(A,B),difference(A,one)). [para(12(a,1),4252(a,1,2,2))].
% 8.83/9.10 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)].
% 8.83/9.10 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))].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 13979 product(product(product(quotient(A,quotient(one,B)),B),B),difference(B,one)) = product(product(A,B),difference(difference(B,one),one)). [para(11554(a,1),9460(a,2,1)),rewrite([22(8)])].
% 8.83/9.10 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)].
% 8.83/9.10 14582 product(A,product(difference(A,B),product(A,quotient(one,A)))) = product(quotient(B,A),quotient(one,quotient(one,A))). [para(12688(a,1),3593(a,1,2,1)),rewrite([1690(9),20(8),4021(8),832(7),51(5),12(4)])].
% 8.83/9.10 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)].
% 8.83/9.10 16473 quotient(product(A,difference(B,one)),quotient(one,B)) = product(quotient(A,B),quotient(one,quotient(one,B))). [para(12(a,1),4015(a,1,2,2)),rewrite([14582(6)]),flip(a)].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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))].
% 8.83/9.10 19086 quotient(product(A,quotient(one,quotient(one,B))),B) = quotient(A,product(B,quotient(one,B))). [back_rewrite(11877),rewrite([19062(12)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 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)].
% 8.83/9.10 19817 quotient(product(A,quotient(one,B)),difference(B,one)) = quotient(A,product(B,quotient(one,B))). [back_rewrite(12810),rewrite([19757(12)])].
% 8.83/9.10 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)])].
% 8.83/9.10 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)].
% 8.83/9.10 20004 quotient(quotient(product(A,quotient(one,B)),B),difference(B,one)) = quotient(A,B). [para(7(a,1),19871(a,1,1)),flip(a)].
% 8.83/9.10 20087 quotient(product(A,quotient(one,B)),B) = product(quotient(A,B),difference(B,one)). [para(20004(a,1),8(a,1,1)),flip(a)].
% 8.83/9.10 20244 product(product(quotient(A,B),difference(B,one)),B) = product(A,quotient(one,B)). [para(20087(a,1),8(a,1,1))].
% 8.83/9.10 20280 product(product(A,quotient(one,quotient(one,B))),B) = product(product(A,B),difference(difference(B,one),one)). [para(20087(a,1),11554(a,1,1,1)),rewrite([23(7),13979(8)]),flip(a)].
% 8.83/9.10 20439 product(product(A,difference(B,one)),B) = product(product(A,B),quotient(one,B)). [para(7(a,1),20244(a,1,1,1))].
% 8.83/9.10 20820 quotient(product(A,B),product(B,quotient(one,B))) = product(A,difference(difference(B,one),one)). [para(20439(a,1),6174(a,1,1)),rewrite([19817(7),16473(11),20280(12),8(7)])].
% 8.83/9.10 20863 product(A,product(B,difference(difference(A,one),one))) = quotient(product(A,B),difference(A,one)). [back_rewrite(10259),rewrite([20820(5)])].
% 8.83/9.10 20881 difference(product(A,quotient(one,A)),product(difference(difference(A,one),one),B)) = product(A,B). [back_rewrite(9736),rewrite([20863(15),8(16)])].
% 8.83/9.10 23156 product(product(A,quotient(one,A)),product(A,B)) = product(difference(difference(A,one),one),B). [para(20881(a,1),5(a,1,2))].
% 8.83/9.10 23157 $F # answer(goals). [resolve(23156,a,16,a)].
% 8.83/9.10
% 8.83/9.10 % SZS output end Refutation
% 8.83/9.10 ============================== end of proof ==========================
% 8.83/9.10
% 8.83/9.10 ============================== STATISTICS ============================
% 8.83/9.10
% 8.83/9.10 Given=802. Generated=308495. Kept=23153. proofs=1.
% 8.83/9.10 Usable=540. Sos=9999. Demods=10433. Limbo=0, Disabled=12626. Hints=0.
% 8.83/9.10 Megabytes=28.58.
% 8.83/9.10 User_CPU=7.95, System_CPU=0.18, Wall_clock=8.
% 8.83/9.10
% 8.83/9.10 ============================== end of statistics =====================
% 8.83/9.10
% 8.83/9.10 ============================== end of search =========================
% 8.83/9.10
% 8.83/9.10 THEOREM PROVED
% 8.83/9.10 % SZS status Unsatisfiable
% 8.83/9.10
% 8.83/9.10 Exiting with 1 proof.
% 8.83/9.10
% 8.83/9.10 Process 23401 exit (max_proofs) Tue Jun 14 07:27:33 2022
% 8.83/9.10 Prover9 interrupted
%------------------------------------------------------------------------------