TSTP Solution File: GRP187-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP187-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 11:18:03 EDT 2022
% Result : Unsatisfiable 30.78s 31.05s
% Output : Refutation 30.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP187-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 06:48:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 5.26/5.52 ============================== Prover9 ===============================
% 5.26/5.52 Prover9 (32) version 2009-11A, November 2009.
% 5.26/5.52 Process 581 was started by sandbox on n021.cluster.edu,
% 5.26/5.52 Tue Jun 14 06:48:28 2022
% 5.26/5.52 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_407_n021.cluster.edu".
% 5.26/5.52 ============================== end of head ===========================
% 5.26/5.52
% 5.26/5.52 ============================== INPUT =================================
% 5.26/5.52
% 5.26/5.52 % Reading from file /tmp/Prover9_407_n021.cluster.edu
% 5.26/5.52
% 5.26/5.52 set(prolog_style_variables).
% 5.26/5.52 set(auto2).
% 5.26/5.52 % set(auto2) -> set(auto).
% 5.26/5.52 % set(auto) -> set(auto_inference).
% 5.26/5.52 % set(auto) -> set(auto_setup).
% 5.26/5.52 % set(auto_setup) -> set(predicate_elim).
% 5.26/5.52 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.26/5.52 % set(auto) -> set(auto_limits).
% 5.26/5.52 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.26/5.52 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.26/5.52 % set(auto) -> set(auto_denials).
% 5.26/5.52 % set(auto) -> set(auto_process).
% 5.26/5.52 % set(auto2) -> assign(new_constants, 1).
% 5.26/5.52 % set(auto2) -> assign(fold_denial_max, 3).
% 5.26/5.52 % set(auto2) -> assign(max_weight, "200.000").
% 5.26/5.52 % set(auto2) -> assign(max_hours, 1).
% 5.26/5.52 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.26/5.52 % set(auto2) -> assign(max_seconds, 0).
% 5.26/5.52 % set(auto2) -> assign(max_minutes, 5).
% 5.26/5.52 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.26/5.52 % set(auto2) -> set(sort_initial_sos).
% 5.26/5.52 % set(auto2) -> assign(sos_limit, -1).
% 5.26/5.52 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.26/5.52 % set(auto2) -> assign(max_megs, 400).
% 5.26/5.52 % set(auto2) -> assign(stats, some).
% 5.26/5.52 % set(auto2) -> clear(echo_input).
% 5.26/5.52 % set(auto2) -> set(quiet).
% 5.26/5.52 % set(auto2) -> clear(print_initial_clauses).
% 5.26/5.52 % set(auto2) -> clear(print_given).
% 5.26/5.52 assign(lrs_ticks,-1).
% 5.26/5.52 assign(sos_limit,10000).
% 5.26/5.52 assign(order,kbo).
% 5.26/5.52 set(lex_order_vars).
% 5.26/5.52 clear(print_given).
% 5.26/5.52
% 5.26/5.52 % formulas(sos). % not echoed (17 formulas)
% 5.26/5.52
% 5.26/5.52 ============================== end of input ==========================
% 5.26/5.52
% 5.26/5.52 % From the command line: assign(max_seconds, 300).
% 5.26/5.52
% 5.26/5.52 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.26/5.52
% 5.26/5.52 % Formulas that are not ordinary clauses:
% 5.26/5.52
% 5.26/5.52 ============================== end of process non-clausal formulas ===
% 5.26/5.52
% 5.26/5.52 ============================== PROCESS INITIAL CLAUSES ===============
% 5.26/5.52
% 5.26/5.52 ============================== PREDICATE ELIMINATION =================
% 5.26/5.52
% 5.26/5.52 ============================== end predicate elimination =============
% 5.26/5.52
% 5.26/5.52 Auto_denials:
% 5.26/5.52 % copying label prove_p33 to answer in negative clause
% 5.26/5.52
% 5.26/5.52 Term ordering decisions:
% 5.26/5.52
% 5.26/5.52 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 5.26/5.52 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. least_upper_bound=1. greatest_lower_bound=1. inverse=0.
% 5.26/5.52
% 5.26/5.52 ============================== end of process initial clauses ========
% 5.26/5.52
% 5.26/5.52 ============================== CLAUSES FOR SEARCH ====================
% 5.26/5.52
% 5.26/5.52 ============================== end of clauses for search =============
% 5.26/5.52
% 5.26/5.52 ============================== SEARCH ================================
% 5.26/5.52
% 5.26/5.52 % Starting search at 0.01 seconds.
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=35.000, iters=3409
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=29.000, iters=3348
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=28.000, iters=3356
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=27.000, iters=3361
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=26.000, iters=3358
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=25.000, iters=3400
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=24.000, iters=3340
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=23.000, iters=3356
% 5.26/5.52
% 5.26/5.52 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 1.16 sec).
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=22.000, iters=3341
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=21.000, iters=3346
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=20.000, iters=3385
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=19.000, iters=3355
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=18.000, iters=3338
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=6337, wt=43.000
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=6338, wt=39.000
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=6128, wt=38.000
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=6636, wt=37.000
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=6358, wt=36.000
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=13005, wt=17.000
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=13006, wt=16.000
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=13206, wt=15.000
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=13412, wt=14.000
% 5.26/5.52
% 5.26/5.52 Low Water (keep): wt=17.000, iters=3335
% 5.26/5.52
% 5.26/5.52 Low Water (displace): id=15216, wt=13.000
% 30.78/31.05
% 30.78/31.05 Low Water (keep): wt=16.000, iters=3333
% 30.78/31.05
% 30.78/31.05 Low Water (displace): id=18036, wt=12.000
% 30.78/31.05
% 30.78/31.05 Low Water (keep): wt=15.000, iters=3338
% 30.78/31.05
% 30.78/31.05 ============================== PROOF =================================
% 30.78/31.05 % SZS status Unsatisfiable
% 30.78/31.05 % SZS output start Refutation
% 30.78/31.05
% 30.78/31.05 % Proof 1 at 29.29 (+ 0.74) seconds: prove_p33.
% 30.78/31.05 % Length of proof is 510.
% 30.78/31.05 % Level of proof is 46.
% 30.78/31.05 % Maximum clause weight is 21.000.
% 30.78/31.05 % Given clauses 3490.
% 30.78/31.05
% 30.78/31.05 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 30.78/31.05 2 least_upper_bound(A,A) = A # label(idempotence_of_lub) # label(axiom). [assumption].
% 30.78/31.05 3 greatest_lower_bound(A,A) = A # label(idempotence_of_gld) # label(axiom). [assumption].
% 30.78/31.05 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 30.78/31.05 5 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 30.78/31.05 6 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 30.78/31.05 7 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 30.78/31.05 8 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 30.78/31.05 9 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 30.78/31.05 10 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C) # label(associativity_of_glb) # label(axiom). [assumption].
% 30.78/31.05 11 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(10),rewrite([5(4)])].
% 30.78/31.05 12 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C) # label(associativity_of_lub) # label(axiom). [assumption].
% 30.78/31.05 13 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(12),rewrite([6(4)])].
% 30.78/31.05 14 greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b))) = identity # label(p33_1) # label(hypothesis). [assumption].
% 30.78/31.05 15 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 30.78/31.05 16 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(15),flip(a)].
% 30.78/31.05 17 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 30.78/31.05 18 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(17),flip(a)].
% 30.78/31.05 19 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 30.78/31.05 20 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(19),flip(a)].
% 30.78/31.05 21 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 30.78/31.05 22 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(21),flip(a)].
% 30.78/31.05 23 multiply(a,b) != multiply(b,a) # label(prove_p33) # label(negated_conjecture) # answer(prove_p33). [assumption].
% 30.78/31.05 24 multiply(b,a) != multiply(a,b) # answer(prove_p33). [copy(23),flip(a)].
% 30.78/31.05 25 multiply(b,a) = c_0. [new_symbol(24)].
% 30.78/31.05 26 multiply(a,b) != c_0 # answer(prove_p33). [back_rewrite(24),rewrite([25(3)]),flip(a)].
% 30.78/31.05 27 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),9(a,1,1)),rewrite([1(2)]),flip(a)].
% 30.78/31.05 28 greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B). [para(11(a,1),3(a,1)),rewrite([5(1),5(2),11(2,R),3(1),5(3)])].
% 30.78/31.05 29 greatest_lower_bound(A,greatest_lower_bound(B,least_upper_bound(A,C))) = greatest_lower_bound(A,B). [para(8(a,1),11(a,2,2)),rewrite([5(2),5(4)])].
% 30.78/31.05 30 least_upper_bound(A,least_upper_bound(A,B)) = least_upper_bound(A,B). [para(13(a,1),2(a,1)),rewrite([6(1),6(2),13(2,R),2(1),6(3)])].
% 30.78/31.05 31 least_upper_bound(A,least_upper_bound(B,greatest_lower_bound(A,C))) = least_upper_bound(A,B). [para(7(a,1),13(a,2,2)),rewrite([6(2),6(4)])].
% 30.78/31.05 33 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(4(a,1),16(a,1,1))].
% 30.78/31.05 34 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(4(a,1),18(a,1,1))].
% 30.78/31.05 35 least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A). [para(1(a,1),20(a,1,1)),rewrite([6(4)])].
% 30.78/31.05 36 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(4(a,1),20(a,1,1)),rewrite([6(5)])].
% 30.78/31.05 37 least_upper_bound(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(least_upper_bound(D,multiply(A,B)),C). [para(9(a,1),20(a,1,1)),rewrite([6(6)])].
% 30.78/31.05 38 least_upper_bound(multiply(A,B),multiply(C,multiply(D,B))) = multiply(least_upper_bound(A,multiply(C,D)),B). [para(9(a,1),20(a,1,2))].
% 30.78/31.05 39 greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(B,identity),A). [para(1(a,1),22(a,1,1)),rewrite([5(4)])].
% 30.78/31.05 40 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(4(a,1),22(a,1,1)),rewrite([5(5)])].
% 30.78/31.05 41 greatest_lower_bound(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(greatest_lower_bound(D,multiply(A,B)),C). [para(9(a,1),22(a,1,1)),rewrite([5(6)])].
% 30.78/31.05 42 greatest_lower_bound(multiply(A,B),multiply(C,multiply(D,B))) = multiply(greatest_lower_bound(A,multiply(C,D)),B). [para(9(a,1),22(a,1,2))].
% 30.78/31.05 43 multiply(b,multiply(a,A)) = multiply(c_0,A). [para(25(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 44 least_upper_bound(c_0,multiply(b,A)) = multiply(b,least_upper_bound(A,a)). [para(25(a,1),16(a,1,1)),rewrite([6(7)])].
% 30.78/31.05 45 greatest_lower_bound(c_0,multiply(b,A)) = multiply(b,greatest_lower_bound(A,a)). [para(25(a,1),18(a,1,1)),rewrite([5(7)])].
% 30.78/31.05 46 least_upper_bound(c_0,multiply(A,a)) = multiply(least_upper_bound(A,b),a). [para(25(a,1),20(a,1,1)),rewrite([6(6)])].
% 30.78/31.05 47 greatest_lower_bound(c_0,multiply(A,a)) = multiply(greatest_lower_bound(A,b),a). [para(25(a,1),22(a,1,1)),rewrite([5(6)])].
% 30.78/31.05 49 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),27(a,1,2))].
% 30.78/31.05 51 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(27(a,1),16(a,1,1)),rewrite([6(6)]),flip(a)].
% 30.78/31.05 52 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(27(a,1),18(a,1,1)),rewrite([5(6)]),flip(a)].
% 30.78/31.05 53 least_upper_bound(A,multiply(B,multiply(C,A))) = multiply(least_upper_bound(B,inverse(C)),multiply(C,A)). [para(27(a,1),20(a,1,1)),rewrite([6(5)])].
% 30.78/31.05 54 greatest_lower_bound(A,multiply(B,multiply(C,A))) = multiply(greatest_lower_bound(B,inverse(C)),multiply(C,A)). [para(27(a,1),22(a,1,1)),rewrite([5(5)])].
% 30.78/31.05 55 multiply(inverse(b),c_0) = a. [para(25(a,1),27(a,1,2))].
% 30.78/31.05 56 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(27(a,1),27(a,1,2))].
% 30.78/31.05 57 multiply(A,identity) = A. [back_rewrite(49),rewrite([56(4)])].
% 30.78/31.05 58 inverse(identity) = identity. [para(57(a,1),4(a,1))].
% 30.78/31.05 59 least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(B,identity)). [para(57(a,1),16(a,1,1)),rewrite([6(4)])].
% 30.78/31.05 60 greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(B,identity)). [para(57(a,1),18(a,1,1)),rewrite([5(4)])].
% 30.78/31.05 61 multiply(inverse(b),multiply(c_0,A)) = multiply(a,A). [para(55(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 62 least_upper_bound(a,multiply(inverse(b),A)) = multiply(inverse(b),least_upper_bound(A,c_0)). [para(55(a,1),16(a,1,1)),rewrite([6(9)])].
% 30.78/31.05 63 greatest_lower_bound(a,multiply(inverse(b),A)) = multiply(inverse(b),greatest_lower_bound(A,c_0)). [para(55(a,1),18(a,1,1)),rewrite([5(9)])].
% 30.78/31.05 65 greatest_lower_bound(a,multiply(A,c_0)) = multiply(greatest_lower_bound(A,inverse(b)),c_0). [para(55(a,1),22(a,1,1)),rewrite([5(7)])].
% 30.78/31.05 68 greatest_lower_bound(b,least_upper_bound(a,inverse(a))) = greatest_lower_bound(identity,b). [para(14(a,1),29(a,1,2)),rewrite([5(3)]),flip(a)].
% 30.78/31.05 70 greatest_lower_bound(multiply(A,B),greatest_lower_bound(multiply(A,C),least_upper_bound(D,multiply(A,B)))) = multiply(A,greatest_lower_bound(B,C)). [para(18(a,1),29(a,2)),rewrite([6(4)])].
% 30.78/31.05 71 greatest_lower_bound(multiply(A,B),greatest_lower_bound(multiply(C,B),least_upper_bound(D,multiply(A,B)))) = multiply(greatest_lower_bound(A,C),B). [para(22(a,1),29(a,2)),rewrite([6(4)])].
% 30.78/31.05 77 greatest_lower_bound(multiply(c_0,A),multiply(b,B)) = multiply(b,greatest_lower_bound(B,multiply(a,A))). [para(43(a,1),18(a,1,1)),rewrite([5(9)])].
% 30.78/31.05 79 multiply(A,inverse(A)) = identity. [para(56(a,1),4(a,1))].
% 30.78/31.05 84 multiply(A,multiply(inverse(A),B)) = B. [para(56(a,1),27(a,1))].
% 30.78/31.05 85 inverse(inverse(A)) = A. [para(56(a,1),57(a,1)),rewrite([57(2)]),flip(a)].
% 30.78/31.05 87 least_upper_bound(multiply(A,B),least_upper_bound(multiply(A,C),greatest_lower_bound(D,multiply(A,B)))) = multiply(A,least_upper_bound(B,C)). [para(16(a,1),31(a,2)),rewrite([5(4)])].
% 30.78/31.05 89 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(79(a,1),9(a,1)),flip(a)].
% 30.78/31.05 90 least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))). [para(79(a,1),16(a,1,1)),rewrite([6(5)])].
% 30.78/31.05 91 greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(B,inverse(A))). [para(79(a,1),18(a,1,1)),rewrite([5(5)])].
% 30.78/31.05 92 least_upper_bound(identity,multiply(A,inverse(B))) = multiply(least_upper_bound(A,B),inverse(B)). [para(79(a,1),20(a,1,1)),rewrite([6(5)])].
% 30.78/31.05 93 greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(A,B),inverse(B)). [para(79(a,1),22(a,1,1)),rewrite([5(5)])].
% 30.78/31.05 94 multiply(c_0,inverse(a)) = b. [para(79(a,1),43(a,1,2)),rewrite([57(3)]),flip(a)].
% 30.78/31.05 95 multiply(c_0,multiply(inverse(a),A)) = multiply(b,A). [para(94(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 97 greatest_lower_bound(b,multiply(c_0,A)) = multiply(c_0,greatest_lower_bound(A,inverse(a))). [para(94(a,1),18(a,1,1)),rewrite([5(8)])].
% 30.78/31.05 98 least_upper_bound(b,multiply(A,inverse(a))) = multiply(least_upper_bound(A,c_0),inverse(a)). [para(94(a,1),20(a,1,1)),rewrite([6(7)])].
% 30.78/31.05 100 multiply(inverse(c_0),b) = inverse(a). [para(94(a,1),27(a,1,2))].
% 30.78/31.05 105 greatest_lower_bound(inverse(a),multiply(A,b)) = multiply(greatest_lower_bound(A,inverse(c_0)),b). [para(100(a,1),22(a,1,1)),rewrite([5(8)])].
% 30.78/31.05 110 multiply(A,least_upper_bound(B,multiply(inverse(A),C))) = least_upper_bound(C,multiply(A,B)). [para(84(a,1),16(a,1,1)),rewrite([6(5)]),flip(a)].
% 30.78/31.05 111 multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))) = greatest_lower_bound(C,multiply(A,B)). [para(84(a,1),18(a,1,1)),rewrite([5(5)]),flip(a)].
% 30.78/31.05 112 least_upper_bound(A,multiply(B,multiply(inverse(C),A))) = multiply(least_upper_bound(B,C),multiply(inverse(C),A)). [para(84(a,1),20(a,1,1)),rewrite([6(5)])].
% 30.78/31.05 118 multiply(a,inverse(c_0)) = inverse(b). [para(79(a,1),61(a,1,2)),rewrite([57(4)]),flip(a)].
% 30.78/31.05 119 multiply(a,multiply(inverse(c_0),A)) = multiply(inverse(b),A). [para(84(a,1),61(a,1,2)),flip(a)].
% 30.78/31.05 120 least_upper_bound(inverse(b),multiply(a,A)) = multiply(a,least_upper_bound(A,inverse(c_0))). [para(118(a,1),16(a,1,1)),rewrite([6(9)])].
% 30.78/31.05 124 multiply(inverse(a),inverse(b)) = inverse(c_0). [para(118(a,1),27(a,1,2))].
% 30.78/31.05 130 least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity. [para(7(a,1),33(a,2,2)),rewrite([4(7)])].
% 30.78/31.05 131 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(33(a,1),8(a,1,2))].
% 30.78/31.05 132 multiply(least_upper_bound(identity,multiply(inverse(A),B)),C) = multiply(inverse(A),multiply(least_upper_bound(A,B),C)). [para(33(a,2),9(a,1,1))].
% 30.78/31.05 135 least_upper_bound(A,multiply(A,multiply(inverse(B),C))) = multiply(A,multiply(inverse(B),least_upper_bound(B,C))). [para(33(a,1),16(a,2,2)),rewrite([57(2)])].
% 30.78/31.05 146 multiply(inverse(A),least_upper_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [para(57(a,1),33(a,1,2)),flip(a)].
% 30.78/31.05 147 multiply(inverse(b),least_upper_bound(b,c_0)) = least_upper_bound(identity,a). [para(55(a,1),33(a,1,2)),flip(a)].
% 30.78/31.05 150 least_upper_bound(identity,multiply(inverse(A),least_upper_bound(B,greatest_lower_bound(A,C)))) = multiply(inverse(A),least_upper_bound(A,B)). [para(31(a,1),33(a,2,2))].
% 30.78/31.05 154 greatest_lower_bound(identity,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b). [para(68(a,1),29(a,1,2)),rewrite([11(5,R),5(4)])].
% 30.78/31.05 158 least_upper_bound(identity,greatest_lower_bound(a,b)) = identity. [para(154(a,1),7(a,1,2))].
% 30.78/31.05 160 greatest_lower_bound(A,multiply(greatest_lower_bound(a,b),A)) = multiply(greatest_lower_bound(a,b),A). [para(154(a,1),22(a,2,1)),rewrite([1(2)])].
% 30.78/31.05 163 least_upper_bound(A,multiply(greatest_lower_bound(a,b),A)) = A. [para(158(a,1),20(a,2,1)),rewrite([1(2),1(7)])].
% 30.78/31.05 165 multiply(greatest_lower_bound(identity,multiply(inverse(A),B)),C) = multiply(inverse(A),multiply(greatest_lower_bound(A,B),C)). [para(34(a,2),9(a,1,1))].
% 30.78/31.05 166 multiply(A,greatest_lower_bound(identity,multiply(inverse(B),C))) = multiply(A,multiply(inverse(B),greatest_lower_bound(B,C))). [para(34(a,2),9(a,2,2)),rewrite([9(4)]),flip(a)].
% 30.78/31.05 174 least_upper_bound(greatest_lower_bound(identity,multiply(inverse(A),B)),multiply(C,greatest_lower_bound(A,B))) = multiply(least_upper_bound(C,inverse(A)),greatest_lower_bound(A,B)). [para(34(a,2),20(a,1,1)),rewrite([6(9)])].
% 30.78/31.05 175 least_upper_bound(multiply(A,greatest_lower_bound(B,C)),greatest_lower_bound(identity,multiply(inverse(B),C))) = multiply(least_upper_bound(A,inverse(B)),greatest_lower_bound(B,C)). [para(34(a,2),20(a,1,2))].
% 30.78/31.05 180 multiply(inverse(A),greatest_lower_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)). [para(57(a,1),34(a,1,2)),flip(a)].
% 30.78/31.05 181 multiply(inverse(b),greatest_lower_bound(b,c_0)) = greatest_lower_bound(identity,a). [para(55(a,1),34(a,1,2)),flip(a)].
% 30.78/31.05 184 greatest_lower_bound(identity,multiply(inverse(A),greatest_lower_bound(B,least_upper_bound(A,C)))) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(29(a,1),34(a,2,2))].
% 30.78/31.05 185 multiply(inverse(c_0),greatest_lower_bound(b,c_0)) = greatest_lower_bound(identity,inverse(a)). [para(100(a,1),34(a,1,2)),rewrite([5(9)]),flip(a)].
% 30.78/31.05 186 multiply(inverse(a),greatest_lower_bound(a,inverse(b))) = greatest_lower_bound(identity,inverse(c_0)). [para(124(a,1),34(a,1,2)),flip(a)].
% 30.78/31.05 191 least_upper_bound(A,least_upper_bound(B,multiply(greatest_lower_bound(a,b),A))) = least_upper_bound(A,B). [para(163(a,1),13(a,2,2)),rewrite([6(5),6(7)])].
% 30.78/31.05 200 multiply(least_upper_bound(inverse(A),identity),A) = least_upper_bound(A,identity). [para(4(a,1),35(a,1,2)),flip(a)].
% 30.78/31.05 206 least_upper_bound(A,least_upper_bound(B,multiply(C,A))) = least_upper_bound(B,multiply(least_upper_bound(C,identity),A)). [para(35(a,1),13(a,2,2)),rewrite([6(2)])].
% 30.78/31.05 211 greatest_lower_bound(multiply(least_upper_bound(A,identity),B),least_upper_bound(C,multiply(A,C))) = multiply(least_upper_bound(A,identity),greatest_lower_bound(B,C)). [para(35(a,2),18(a,1,2))].
% 30.78/31.05 216 multiply(least_upper_bound(identity,b),a) = least_upper_bound(a,c_0). [para(25(a,1),35(a,1,2)),rewrite([6(6)]),flip(a)].
% 30.78/31.05 219 multiply(least_upper_bound(identity,inverse(b)),c_0) = least_upper_bound(a,c_0). [para(55(a,1),35(a,1,2)),rewrite([6(3),6(7)]),flip(a)].
% 30.78/31.05 223 multiply(least_upper_bound(A,identity),inverse(A)) = least_upper_bound(inverse(A),identity). [para(79(a,1),35(a,1,2)),flip(a)].
% 30.78/31.05 224 multiply(least_upper_bound(identity,c_0),inverse(a)) = least_upper_bound(b,inverse(a)). [para(94(a,1),35(a,1,2)),rewrite([6(4),6(7)]),flip(a)].
% 30.78/31.05 225 multiply(least_upper_bound(identity,inverse(c_0)),b) = least_upper_bound(b,inverse(a)). [para(100(a,1),35(a,1,2)),rewrite([6(8)]),flip(a)].
% 30.78/31.05 228 multiply(least_upper_bound(identity,a),inverse(c_0)) = least_upper_bound(inverse(b),inverse(c_0)). [para(118(a,1),35(a,1,2)),rewrite([6(5),6(8)]),flip(a)].
% 30.78/31.05 241 greatest_lower_bound(least_upper_bound(a,c_0),multiply(least_upper_bound(identity,b),A)) = multiply(least_upper_bound(identity,b),greatest_lower_bound(A,a)). [para(216(a,1),18(a,1,1)),rewrite([5(13)])].
% 30.78/31.05 248 multiply(least_upper_bound(identity,inverse(A)),A) = least_upper_bound(A,identity). [para(1(a,1),36(a,1,2)),rewrite([6(2)]),flip(a)].
% 30.78/31.05 249 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(36(a,1),8(a,1,2))].
% 30.78/31.05 255 least_upper_bound(A,multiply(A,multiply(B,C))) = multiply(A,multiply(least_upper_bound(B,inverse(C)),C)). [para(36(a,1),16(a,2,2)),rewrite([57(2)])].
% 30.78/31.05 258 multiply(least_upper_bound(A,inverse(least_upper_bound(B,C))),least_upper_bound(B,C)) = least_upper_bound(identity,multiply(A,least_upper_bound(B,C))). [para(36(a,2),16(a,2)),rewrite([16(9)])].
% 30.78/31.05 261 multiply(least_upper_bound(A,inverse(greatest_lower_bound(B,C))),greatest_lower_bound(B,C)) = least_upper_bound(identity,multiply(A,greatest_lower_bound(B,C))). [para(36(a,2),18(a,2)),rewrite([18(9)])].
% 30.78/31.05 266 multiply(least_upper_bound(b,inverse(a)),a) = least_upper_bound(identity,c_0). [para(25(a,1),36(a,1,2)),flip(a)].
% 30.78/31.05 267 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(36(a,2),27(a,1,2))].
% 30.78/31.05 268 multiply(least_upper_bound(inverse(b),inverse(c_0)),c_0) = least_upper_bound(identity,a). [para(55(a,1),36(a,1,2)),flip(a)].
% 30.78/31.05 270 least_upper_bound(identity,least_upper_bound(multiply(A,B),greatest_lower_bound(C,identity))) = multiply(least_upper_bound(A,inverse(B)),B). [para(36(a,1),31(a,2)),rewrite([5(4)])].
% 30.78/31.05 271 multiply(least_upper_bound(a,c_0),inverse(a)) = least_upper_bound(identity,b). [para(94(a,1),36(a,1,2)),rewrite([85(7),6(6)]),flip(a)].
% 30.78/31.05 273 multiply(least_upper_bound(a,c_0),inverse(c_0)) = least_upper_bound(identity,inverse(b)). [para(118(a,1),36(a,1,2)),rewrite([85(8)]),flip(a)].
% 30.78/31.05 274 multiply(least_upper_bound(b,inverse(a)),inverse(b)) = least_upper_bound(identity,inverse(c_0)). [para(124(a,1),36(a,1,2)),rewrite([85(9),6(8)]),flip(a)].
% 30.78/31.05 275 multiply(least_upper_bound(inverse(A),inverse(B)),B) = multiply(inverse(A),least_upper_bound(A,B)). [para(36(a,1),33(a,1))].
% 30.78/31.05 278 least_upper_bound(A,least_upper_bound(identity,multiply(B,A))) = multiply(least_upper_bound(B,least_upper_bound(inverse(A),identity)),A). [para(36(a,2),35(a,1,2)),rewrite([6(8),13(8,R)])].
% 30.78/31.05 288 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(89(a,1),27(a,1,2)),rewrite([57(3)]),flip(a)].
% 30.78/31.05 300 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(288(a,1),27(a,1,2)),flip(a)].
% 30.78/31.05 301 multiply(least_upper_bound(A,B),inverse(least_upper_bound(identity,multiply(inverse(A),B)))) = A. [para(33(a,2),288(a,1,2,1)),rewrite([85(9)])].
% 30.78/31.05 302 multiply(greatest_lower_bound(A,B),inverse(greatest_lower_bound(identity,multiply(inverse(A),B)))) = A. [para(34(a,2),288(a,1,2,1)),rewrite([85(9)])].
% 30.78/31.05 304 multiply(a,inverse(least_upper_bound(a,c_0))) = inverse(least_upper_bound(identity,b)). [para(216(a,1),288(a,1,2,1))].
% 30.78/31.05 313 least_upper_bound(identity,multiply(b,A)) = multiply(least_upper_bound(inverse(A),b),A). [para(95(a,1),36(a,1,2)),rewrite([300(9),85(9),46(9),9(13),84(12)])].
% 30.78/31.05 314 multiply(least_upper_bound(A,multiply(B,inverse(C))),C) = least_upper_bound(B,multiply(A,C)). [para(4(a,1),37(a,1,1,2)),rewrite([57(2)]),flip(a)].
% 30.78/31.05 321 least_upper_bound(c_0,multiply(A,multiply(B,a))) = multiply(least_upper_bound(b,multiply(A,B)),a). [para(25(a,1),37(a,1,2)),rewrite([6(5)])].
% 30.78/31.05 322 multiply(least_upper_bound(A,multiply(B,inverse(C))),multiply(C,D)) = multiply(least_upper_bound(B,multiply(A,C)),D). [para(27(a,1),37(a,1,1,2)),rewrite([38(4)]),flip(a)].
% 30.78/31.05 329 multiply(least_upper_bound(A,multiply(B,C)),inverse(C)) = least_upper_bound(B,multiply(A,inverse(C))). [para(79(a,1),37(a,1,1,2)),rewrite([57(2)]),flip(a)].
% 30.78/31.05 331 least_upper_bound(multiply(A,b),multiply(B,inverse(a))) = multiply(least_upper_bound(B,multiply(A,c_0)),inverse(a)). [para(94(a,1),37(a,1,1,2))].
% 30.78/31.05 335 multiply(least_upper_bound(A,multiply(B,C)),multiply(inverse(C),D)) = multiply(least_upper_bound(B,multiply(A,inverse(C))),D). [para(84(a,1),37(a,1,1,2)),rewrite([38(5)]),flip(a)].
% 30.78/31.05 366 least_upper_bound(identity,multiply(A,greatest_lower_bound(B,inverse(A)))) = identity. [para(85(a,1),130(a,1,2,1)),rewrite([5(3)])].
% 30.78/31.05 397 greatest_lower_bound(identity,multiply(A,least_upper_bound(B,inverse(A)))) = identity. [para(85(a,1),131(a,1,2,1)),rewrite([6(3)])].
% 30.78/31.05 405 multiply(b,least_upper_bound(identity,a)) = least_upper_bound(b,c_0). [para(147(a,1),27(a,1,2)),rewrite([85(3)])].
% 30.78/31.05 406 least_upper_bound(identity,least_upper_bound(a,least_upper_bound(b,c_0))) = multiply(least_upper_bound(identity,inverse(b)),least_upper_bound(b,c_0)). [para(147(a,1),35(a,1,2)),rewrite([6(7),13(7),6(6),13(6),6(5),13(6,R),6(5),13(7,R),6(6),13(6),6(5),13(6,R),6(5),6(11)])].
% 30.78/31.05 415 greatest_lower_bound(least_upper_bound(b,c_0),multiply(A,least_upper_bound(identity,a))) = multiply(greatest_lower_bound(A,b),least_upper_bound(identity,a)). [para(405(a,1),22(a,1,1)),rewrite([5(10)])].
% 30.78/31.05 416 multiply(least_upper_bound(identity,inverse(b)),least_upper_bound(b,c_0)) = multiply(least_upper_bound(identity,b),least_upper_bound(identity,a)). [para(405(a,1),35(a,1,2)),rewrite([13(7),6(6),13(6),6(5),13(6,R),6(5),13(7,R),6(6),13(6),6(5),13(6,R),6(5),406(7),6(11)])].
% 30.78/31.05 419 least_upper_bound(identity,least_upper_bound(a,least_upper_bound(b,c_0))) = multiply(least_upper_bound(identity,b),least_upper_bound(identity,a)). [back_rewrite(406),rewrite([416(15)])].
% 30.78/31.05 420 multiply(greatest_lower_bound(inverse(A),identity),A) = greatest_lower_bound(A,identity). [para(4(a,1),39(a,1,2)),flip(a)].
% 30.78/31.05 435 multiply(greatest_lower_bound(identity,b),a) = greatest_lower_bound(a,c_0). [para(25(a,1),39(a,1,2)),rewrite([5(6)]),flip(a)].
% 30.78/31.05 436 multiply(inverse(greatest_lower_bound(A,identity)),greatest_lower_bound(B,multiply(A,B))) = B. [para(39(a,2),27(a,1,2))].
% 30.78/31.05 438 multiply(greatest_lower_bound(identity,inverse(b)),c_0) = greatest_lower_bound(a,c_0). [para(55(a,1),39(a,1,2)),rewrite([5(3),5(7)]),flip(a)].
% 30.78/31.05 441 multiply(greatest_lower_bound(A,identity),inverse(A)) = greatest_lower_bound(inverse(A),identity). [para(79(a,1),39(a,1,2)),flip(a)].
% 30.78/31.05 442 multiply(greatest_lower_bound(identity,c_0),inverse(a)) = greatest_lower_bound(b,inverse(a)). [para(94(a,1),39(a,1,2)),rewrite([5(4),5(7)]),flip(a)].
% 30.78/31.05 449 greatest_lower_bound(identity,multiply(inverse(A),multiply(B,A))) = multiply(inverse(A),multiply(greatest_lower_bound(B,identity),A)). [para(39(a,1),34(a,2,2))].
% 30.78/31.05 452 greatest_lower_bound(A,least_upper_bound(identity,multiply(B,A))) = multiply(greatest_lower_bound(identity,least_upper_bound(B,inverse(A))),A). [para(36(a,2),39(a,1,2)),rewrite([5(8)])].
% 30.78/31.05 467 multiply(inverse(greatest_lower_bound(identity,b)),greatest_lower_bound(a,c_0)) = a. [para(435(a,1),27(a,1,2))].
% 30.78/31.05 482 multiply(b,greatest_lower_bound(identity,a)) = greatest_lower_bound(b,c_0). [para(181(a,1),27(a,1,2)),rewrite([85(3)])].
% 30.78/31.05 496 least_upper_bound(greatest_lower_bound(b,c_0),multiply(A,multiply(B,greatest_lower_bound(identity,a)))) = multiply(least_upper_bound(b,multiply(A,B)),greatest_lower_bound(identity,a)). [para(482(a,1),37(a,1,2)),rewrite([6(9)])].
% 30.78/31.05 497 multiply(greatest_lower_bound(identity,b),greatest_lower_bound(identity,a)) = greatest_lower_bound(a,greatest_lower_bound(b,c_0)). [para(482(a,1),39(a,1,2)),rewrite([11(7),5(6),11(6),5(5),11(6,R),5(5),154(6),11(5),5(4),11(5,R),5(4),5(8)]),flip(a)].
% 30.78/31.05 499 multiply(greatest_lower_bound(identity,inverse(A)),A) = greatest_lower_bound(A,identity). [para(1(a,1),40(a,1,2)),rewrite([5(2)]),flip(a)].
% 30.78/31.05 500 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(40(a,1),7(a,1,2))].
% 30.78/31.05 512 multiply(greatest_lower_bound(A,inverse(greatest_lower_bound(B,C))),greatest_lower_bound(B,C)) = greatest_lower_bound(identity,multiply(A,greatest_lower_bound(B,C))). [para(40(a,2),18(a,2)),rewrite([18(9)])].
% 30.78/31.05 517 multiply(greatest_lower_bound(b,inverse(a)),a) = greatest_lower_bound(identity,c_0). [para(25(a,1),40(a,1,2)),flip(a)].
% 30.78/31.05 518 multiply(inverse(greatest_lower_bound(A,inverse(B))),greatest_lower_bound(identity,multiply(A,B))) = B. [para(40(a,2),27(a,1,2))].
% 30.78/31.05 523 multiply(greatest_lower_bound(a,c_0),inverse(a)) = greatest_lower_bound(identity,b). [para(94(a,1),40(a,1,2)),rewrite([85(7),5(6)]),flip(a)].
% 30.78/31.05 524 multiply(greatest_lower_bound(inverse(b),inverse(c_0)),b) = greatest_lower_bound(identity,inverse(a)). [para(100(a,1),40(a,1,2)),rewrite([5(9)]),flip(a)].
% 30.78/31.05 527 multiply(greatest_lower_bound(a,c_0),inverse(c_0)) = greatest_lower_bound(identity,inverse(b)). [para(118(a,1),40(a,1,2)),rewrite([85(8)]),flip(a)].
% 30.78/31.05 529 multiply(greatest_lower_bound(inverse(A),inverse(B)),B) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(40(a,1),34(a,1))].
% 30.78/31.05 536 greatest_lower_bound(identity,multiply(b,A)) = multiply(greatest_lower_bound(inverse(A),b),A). [para(95(a,1),40(a,1,2)),rewrite([300(9),85(9),47(9),9(13),84(12)])].
% 30.78/31.05 547 multiply(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))),a) = greatest_lower_bound(identity,greatest_lower_bound(a,c_0)). [para(435(a,1),40(a,1,2)),rewrite([5(11),11(11),5(10),11(11,R),5(10)]),flip(a)].
% 30.78/31.05 566 multiply(inverse(least_upper_bound(identity,inverse(b))),least_upper_bound(a,c_0)) = c_0. [para(219(a,1),27(a,1,2))].
% 30.78/31.05 567 multiply(least_upper_bound(identity,least_upper_bound(inverse(b),inverse(c_0))),c_0) = least_upper_bound(identity,least_upper_bound(a,c_0)). [para(219(a,1),36(a,1,2)),rewrite([6(12),13(12),6(11),13(12,R),6(11)]),flip(a)].
% 30.78/31.05 582 multiply(greatest_lower_bound(A,multiply(B,inverse(C))),C) = greatest_lower_bound(B,multiply(A,C)). [para(4(a,1),41(a,1,1,2)),rewrite([57(2)]),flip(a)].
% 30.78/31.05 590 multiply(greatest_lower_bound(A,multiply(B,inverse(C))),multiply(C,D)) = multiply(greatest_lower_bound(B,multiply(A,C)),D). [para(27(a,1),41(a,1,1,2)),rewrite([42(4)]),flip(a)].
% 30.78/31.05 659 greatest_lower_bound(A,multiply(A,multiply(least_upper_bound(B,inverse(C)),C))) = A. [para(249(a,1),18(a,2,2)),rewrite([57(2),57(7)])].
% 30.78/31.05 662 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(85(a,1),249(a,1,2,1,2))].
% 30.78/31.05 663 multiply(least_upper_bound(b,inverse(a)),multiply(a,A)) = multiply(least_upper_bound(identity,c_0),A). [para(266(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 703 multiply(least_upper_bound(a,c_0),multiply(inverse(a),A)) = multiply(least_upper_bound(identity,b),A). [para(271(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 710 multiply(inverse(least_upper_bound(a,c_0)),least_upper_bound(identity,b)) = inverse(a). [para(271(a,1),27(a,1,2))].
% 30.78/31.05 715 multiply(greatest_lower_bound(identity,least_upper_bound(a,c_0)),inverse(a)) = greatest_lower_bound(inverse(a),least_upper_bound(identity,b)). [para(271(a,1),39(a,1,2)),rewrite([5(11)]),flip(a)].
% 30.78/31.05 728 multiply(inverse(greatest_lower_bound(b,c_0)),b) = inverse(greatest_lower_bound(identity,a)). [para(181(a,1),300(a,1,1)),rewrite([85(11)]),flip(a)].
% 30.78/31.05 735 greatest_lower_bound(identity,multiply(least_upper_bound(inverse(A),multiply(B,C)),A)) = identity. [para(300(a,1),249(a,1,2,1,2)),rewrite([322(7)])].
% 30.78/31.05 745 multiply(b,least_upper_bound(a,inverse(b))) = least_upper_bound(identity,c_0). [para(79(a,1),44(a,1,2)),rewrite([6(3),6(8)]),flip(a)].
% 30.78/31.05 747 multiply(least_upper_bound(identity,b),c_0) = multiply(b,least_upper_bound(a,c_0)). [para(44(a,1),35(a,1)),rewrite([6(4),6(8)]),flip(a)].
% 30.78/31.05 762 least_upper_bound(greatest_lower_bound(A,identity),multiply(greatest_lower_bound(inverse(A),identity),B)) = multiply(greatest_lower_bound(inverse(A),identity),least_upper_bound(A,B)). [para(420(a,1),16(a,1,1))].
% 30.78/31.05 781 multiply(b,greatest_lower_bound(a,inverse(b))) = greatest_lower_bound(identity,c_0). [para(79(a,1),45(a,1,2)),rewrite([5(3),5(8)]),flip(a)].
% 30.78/31.05 822 multiply(inverse(greatest_lower_bound(identity,inverse(b))),greatest_lower_bound(a,c_0)) = c_0. [para(438(a,1),27(a,1,2))].
% 30.78/31.05 842 multiply(inverse(greatest_lower_bound(a,c_0)),greatest_lower_bound(identity,b)) = inverse(a). [para(467(a,1),300(a,1,1)),rewrite([85(11)]),flip(a)].
% 30.78/31.05 872 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(85(a,1),500(a,1,2,1,2))].
% 30.78/31.05 908 least_upper_bound(inverse(A),greatest_lower_bound(B,inverse(A))) = inverse(A). [para(366(a,1),51(a,1,2)),rewrite([57(3),57(6),6(5)]),flip(a)].
% 30.78/31.05 916 least_upper_bound(A,inverse(greatest_lower_bound(B,inverse(A)))) = inverse(greatest_lower_bound(B,inverse(A))). [para(500(a,1),51(a,1,2)),rewrite([57(5),57(8)]),flip(a)].
% 30.78/31.05 918 multiply(greatest_lower_bound(b,inverse(a)),multiply(a,A)) = multiply(greatest_lower_bound(identity,c_0),A). [para(517(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 937 multiply(greatest_lower_bound(a,c_0),multiply(inverse(a),A)) = multiply(greatest_lower_bound(identity,b),A). [para(523(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 987 greatest_lower_bound(A,inverse(least_upper_bound(B,inverse(A)))) = inverse(least_upper_bound(B,inverse(A))). [para(249(a,1),52(a,1,2)),rewrite([57(5),57(8)]),flip(a)].
% 30.78/31.05 992 greatest_lower_bound(inverse(A),least_upper_bound(B,inverse(A))) = inverse(A). [para(397(a,1),52(a,1,2)),rewrite([57(3),57(6),5(5)]),flip(a)].
% 30.78/31.05 996 multiply(inverse(A),multiply(greatest_lower_bound(A,b),a)) = multiply(greatest_lower_bound(inverse(A),inverse(b)),c_0). [para(47(a,1),52(a,1,2)),rewrite([65(11)])].
% 30.78/31.05 1004 greatest_lower_bound(greatest_lower_bound(A,multiply(B,C)),multiply(B,D)) = multiply(B,greatest_lower_bound(D,greatest_lower_bound(C,multiply(inverse(B),A)))). [para(52(a,1),52(a,1,2,2)),rewrite([85(2),85(9)]),flip(a)].
% 30.78/31.05 1005 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(A))) = identity. [para(6(a,1),662(a,1,2,1))].
% 30.78/31.05 1006 greatest_lower_bound(identity,multiply(A,inverse(greatest_lower_bound(A,B)))) = identity. [para(7(a,1),662(a,1,2,1))].
% 30.78/31.05 1016 greatest_lower_bound(identity,inverse(greatest_lower_bound(a,b))) = identity. [para(158(a,1),662(a,1,2,1)),rewrite([1(7)])].
% 30.78/31.05 1018 greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),A)) = identity. [para(130(a,1),662(a,1,2,1)),rewrite([300(6),85(6),1(6)])].
% 30.78/31.05 1030 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(662(a,1),52(a,1,2)),rewrite([57(4),57(7)]),flip(a)].
% 30.78/31.05 1032 greatest_lower_bound(A,multiply(inverse(greatest_lower_bound(a,b)),A)) = A. [para(1016(a,1),22(a,2,1)),rewrite([1(2),1(8)])].
% 30.78/31.05 1044 multiply(inverse(b),least_upper_bound(identity,c_0)) = least_upper_bound(a,inverse(b)). [para(745(a,1),27(a,1,2))].
% 30.78/31.05 1045 least_upper_bound(identity,least_upper_bound(a,least_upper_bound(c_0,inverse(b)))) = multiply(least_upper_bound(identity,b),least_upper_bound(a,inverse(b))). [para(745(a,1),35(a,1,2)),rewrite([6(8),13(8),6(7),13(7,R),6(6),13(8,R),6(7),13(7),6(6),13(7,R),6(6),6(11)])].
% 30.78/31.05 1074 least_upper_bound(A,multiply(c_0,A)) = multiply(least_upper_bound(identity,c_0),A). [para(43(a,1),53(a,1,2)),rewrite([663(10)])].
% 30.78/31.05 1075 least_upper_bound(A,multiply(a,A)) = multiply(least_upper_bound(inverse(b),inverse(c_0)),multiply(c_0,A)). [para(61(a,1),53(a,1,2))].
% 30.78/31.05 1089 least_upper_bound(A,multiply(b,A)) = multiply(least_upper_bound(identity,b),A). [para(95(a,1),53(a,1,2)),rewrite([85(7),6(6),703(10)])].
% 30.78/31.05 1122 multiply(least_upper_bound(A,inverse(greatest_lower_bound(identity,inverse(b)))),greatest_lower_bound(a,c_0)) = least_upper_bound(c_0,multiply(A,greatest_lower_bound(a,c_0))). [para(438(a,1),53(a,1,2,2)),rewrite([438(18)]),flip(a)].
% 30.78/31.05 1143 multiply(inverse(b),greatest_lower_bound(identity,c_0)) = greatest_lower_bound(a,inverse(b)). [para(781(a,1),27(a,1,2))].
% 30.78/31.05 1144 least_upper_bound(greatest_lower_bound(identity,c_0),greatest_lower_bound(a,inverse(b))) = multiply(least_upper_bound(identity,b),greatest_lower_bound(a,inverse(b))). [para(781(a,1),35(a,1,2)),rewrite([6(8),6(11)])].
% 30.78/31.05 1153 multiply(inverse(greatest_lower_bound(a,inverse(b))),inverse(b)) = inverse(greatest_lower_bound(identity,c_0)). [para(781(a,1),300(a,1,1)),flip(a)].
% 30.78/31.05 1189 greatest_lower_bound(A,multiply(c_0,A)) = multiply(greatest_lower_bound(identity,c_0),A). [para(43(a,1),54(a,1,2)),rewrite([918(10)])].
% 30.78/31.05 1204 greatest_lower_bound(A,multiply(b,A)) = multiply(greatest_lower_bound(identity,b),A). [para(95(a,1),54(a,1,2)),rewrite([85(7),5(6),937(10)])].
% 30.78/31.05 1221 multiply(greatest_lower_bound(A,inverse(least_upper_bound(identity,inverse(b)))),least_upper_bound(a,c_0)) = greatest_lower_bound(c_0,multiply(A,least_upper_bound(a,c_0))). [para(219(a,1),54(a,1,2,2)),rewrite([219(18)]),flip(a)].
% 30.78/31.05 1263 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(A))) = identity. [para(5(a,1),872(a,1,2,1))].
% 30.78/31.05 1264 least_upper_bound(identity,multiply(A,inverse(least_upper_bound(A,B)))) = identity. [para(8(a,1),872(a,1,2,1))].
% 30.78/31.05 1268 least_upper_bound(A,multiply(A,multiply(greatest_lower_bound(B,C),inverse(C)))) = A. [para(872(a,1),16(a,2,2)),rewrite([57(2),57(7)])].
% 30.78/31.05 1279 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),A)) = identity. [para(131(a,1),872(a,1,2,1)),rewrite([300(6),85(6),1(6)])].
% 30.78/31.05 1287 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(872(a,1),51(a,1,2)),rewrite([57(4),57(7)]),flip(a)].
% 30.78/31.05 1314 multiply(A,least_upper_bound(inverse(A),identity)) = least_upper_bound(A,identity). [para(79(a,1),59(a,1,2)),flip(a)].
% 30.78/31.05 1316 multiply(inverse(c_0),least_upper_bound(identity,b)) = least_upper_bound(inverse(a),inverse(c_0)). [para(100(a,1),59(a,1,2)),rewrite([6(5),6(10)]),flip(a)].
% 30.78/31.05 1318 multiply(a,least_upper_bound(identity,inverse(c_0))) = least_upper_bound(a,inverse(b)). [para(118(a,1),59(a,1,2)),rewrite([6(9)]),flip(a)].
% 30.78/31.05 1319 multiply(inverse(a),least_upper_bound(identity,inverse(b))) = least_upper_bound(inverse(a),inverse(c_0)). [para(124(a,1),59(a,1,2)),rewrite([6(11)]),flip(a)].
% 30.78/31.05 1352 multiply(least_upper_bound(a,c_0),least_upper_bound(identity,inverse(a))) = multiply(least_upper_bound(identity,b),least_upper_bound(identity,a)). [para(271(a,1),59(a,1,2)),rewrite([6(7),13(7),6(6),13(6,R),6(5),13(7,R),6(6),13(6),6(5),13(6,R),6(5),419(7),6(14)]),flip(a)].
% 30.78/31.05 1359 least_upper_bound(greatest_lower_bound(A,identity),greatest_lower_bound(identity,inverse(A))) = multiply(greatest_lower_bound(identity,inverse(A)),least_upper_bound(A,identity)). [para(499(a,1),59(a,1,2)),rewrite([6(6)])].
% 30.78/31.05 1401 multiply(A,greatest_lower_bound(inverse(A),identity)) = greatest_lower_bound(A,identity). [para(79(a,1),60(a,1,2)),flip(a)].
% 30.78/31.05 1402 multiply(c_0,greatest_lower_bound(identity,inverse(a))) = greatest_lower_bound(b,c_0). [para(94(a,1),60(a,1,2)),rewrite([5(3),5(8)]),flip(a)].
% 30.78/31.05 1405 multiply(a,greatest_lower_bound(identity,inverse(c_0))) = greatest_lower_bound(a,inverse(b)). [para(118(a,1),60(a,1,2)),rewrite([5(9)]),flip(a)].
% 30.78/31.05 1406 multiply(inverse(a),greatest_lower_bound(identity,inverse(b))) = greatest_lower_bound(inverse(a),inverse(c_0)). [para(124(a,1),60(a,1,2)),rewrite([5(11)]),flip(a)].
% 30.78/31.05 1424 multiply(inverse(b),greatest_lower_bound(identity,greatest_lower_bound(b,c_0))) = greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))). [para(181(a,1),60(a,1,2)),rewrite([11(6),5(5),11(6,R),5(5),5(13)]),flip(a)].
% 30.78/31.05 1428 greatest_lower_bound(least_upper_bound(identity,inverse(b)),least_upper_bound(a,c_0)) = multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(identity,c_0)). [para(219(a,1),60(a,1,2)),rewrite([5(15)])].
% 30.78/31.05 1433 greatest_lower_bound(least_upper_bound(A,identity),least_upper_bound(identity,inverse(A))) = multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(A,identity)). [para(248(a,1),60(a,1,2)),rewrite([5(6)])].
% 30.78/31.05 1444 multiply(greatest_lower_bound(b,c_0),a) = multiply(c_0,greatest_lower_bound(identity,a)). [para(60(a,1),47(a,1)),rewrite([5(4),5(8)]),flip(a)].
% 30.78/31.05 1459 multiply(greatest_lower_bound(A,inverse(B)),multiply(B,A)) = multiply(A,greatest_lower_bound(identity,multiply(B,A))). [para(60(a,1),54(a,1)),rewrite([5(3)]),flip(a)].
% 30.78/31.05 1465 greatest_lower_bound(identity,multiply(least_upper_bound(A,least_upper_bound(B,C)),inverse(B))) = identity. [para(13(a,1),1005(a,1,2,1))].
% 30.78/31.05 1482 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(A,B))) = inverse(A). [para(1006(a,1),52(a,1,2)),rewrite([57(3),57(6),5(5)]),flip(a)].
% 30.78/31.05 1483 greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),B)) = identity. [para(5(a,1),1018(a,1,2,1,1))].
% 30.78/31.05 1485 greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(A,greatest_lower_bound(B,C))),C)) = identity. [para(11(a,2),1018(a,1,2,1,1))].
% 30.78/31.05 1503 multiply(inverse(b),greatest_lower_bound(c_0,least_upper_bound(A,c_0))) = a. [para(62(a,1),8(a,1,2)),rewrite([63(7),5(6)])].
% 30.78/31.05 1592 least_upper_bound(inverse(A),inverse(greatest_lower_bound(A,B))) = inverse(greatest_lower_bound(A,B)). [para(1263(a,1),51(a,1,2)),rewrite([57(4),57(7)]),flip(a)].
% 30.78/31.05 1617 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),B)) = identity. [para(6(a,1),1279(a,1,2,1,1))].
% 30.78/31.05 1641 multiply(greatest_lower_bound(inverse(b),least_upper_bound(identity,inverse(c_0))),c_0) = greatest_lower_bound(a,least_upper_bound(identity,c_0)). [para(200(a,1),65(a,1,2)),rewrite([6(4),6(9),5(12)]),flip(a)].
% 30.78/31.05 1651 multiply(A,least_upper_bound(identity,inverse(A))) = least_upper_bound(A,identity). [para(6(a,1),1314(a,1,2))].
% 30.78/31.05 1659 least_upper_bound(identity,least_upper_bound(inverse(A),identity)) = least_upper_bound(identity,inverse(A)). [para(1314(a,1),33(a,1,2)),rewrite([85(8),30(9),146(9)])].
% 30.78/31.05 1661 multiply(c_0,least_upper_bound(inverse(a),inverse(c_0))) = least_upper_bound(identity,b). [para(1314(a,1),95(a,2)),rewrite([6(7),1319(8),6(10)])].
% 30.78/31.05 1710 multiply(A,greatest_lower_bound(identity,inverse(A))) = greatest_lower_bound(A,identity). [para(5(a,1),1401(a,1,2))].
% 30.78/31.05 1718 greatest_lower_bound(identity,greatest_lower_bound(inverse(A),identity)) = greatest_lower_bound(identity,inverse(A)). [para(1401(a,1),34(a,1,2)),rewrite([85(8),28(9),180(9)])].
% 30.78/31.05 1729 multiply(b,least_upper_bound(a,greatest_lower_bound(identity,inverse(b)))) = least_upper_bound(c_0,greatest_lower_bound(identity,b)). [para(1401(a,1),44(a,1,2)),rewrite([5(4),5(10),6(12)]),flip(a)].
% 30.78/31.05 1749 multiply(inverse(greatest_lower_bound(identity,inverse(a))),inverse(c_0)) = inverse(greatest_lower_bound(b,c_0)). [para(1402(a,1),300(a,1,1)),flip(a)].
% 30.78/31.05 1763 greatest_lower_bound(A,inverse(greatest_lower_bound(B,inverse(A)))) = A. [para(85(a,1),1482(a,1,1)),rewrite([5(2),85(6)])].
% 30.78/31.05 1764 greatest_lower_bound(inverse(b),inverse(greatest_lower_bound(identity,b))) = inverse(b). [para(68(a,1),1482(a,1,2,1))].
% 30.78/31.05 1784 multiply(greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))),A) = identity. [para(1483(a,1),40(a,1)),rewrite([5(5)]),flip(a)].
% 30.78/31.05 1793 greatest_lower_bound(c_0,least_upper_bound(A,c_0)) = c_0. [para(1503(a,1),27(a,1,2)),rewrite([85(3),25(3)]),flip(a)].
% 30.78/31.05 1807 multiply(inverse(A),greatest_lower_bound(B,greatest_lower_bound(C,least_upper_bound(A,B)))) = multiply(inverse(A),greatest_lower_bound(B,C)). [para(33(a,1),70(a,1,2,2)),rewrite([18(8),18(7)])].
% 30.78/31.05 1918 greatest_lower_bound(least_upper_bound(A,multiply(B,C)),multiply(greatest_lower_bound(B,D),C)) = multiply(greatest_lower_bound(B,D),C). [para(71(a,1),11(a,1)),rewrite([22(7)]),flip(a)].
% 30.78/31.05 2054 multiply(A,multiply(least_upper_bound(identity,inverse(A)),B)) = multiply(least_upper_bound(A,identity),B). [para(1651(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 2065 multiply(inverse(least_upper_bound(identity,inverse(A))),inverse(A)) = inverse(least_upper_bound(A,identity)). [para(1651(a,1),300(a,1,1)),flip(a)].
% 30.78/31.05 2074 multiply(greatest_lower_bound(identity,inverse(A)),least_upper_bound(A,identity)) = multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,inverse(A))). [para(1710(a,1),35(a,1,2)),rewrite([6(6),1359(6)])].
% 30.78/31.05 2088 least_upper_bound(greatest_lower_bound(A,identity),greatest_lower_bound(identity,inverse(A))) = multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,inverse(A))). [back_rewrite(1359),rewrite([2074(12)])].
% 30.78/31.05 2163 multiply(a,least_upper_bound(inverse(a),inverse(c_0))) = least_upper_bound(identity,inverse(b)). [para(1314(a,1),119(a,2)),rewrite([85(6),6(6),1316(7),6(11)])].
% 30.78/31.05 2210 multiply(b,greatest_lower_bound(A,multiply(a,multiply(B,A)))) = multiply(c_0,multiply(greatest_lower_bound(B,inverse(a)),A)). [para(77(a,1),41(a,1)),rewrite([97(10),9(12)])].
% 30.78/31.05 2264 multiply(inverse(c_0),greatest_lower_bound(identity,greatest_lower_bound(b,c_0))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(c_0))). [para(185(a,1),60(a,1,2)),rewrite([11(7),5(6),11(7,R),5(6),5(14)]),flip(a)].
% 30.78/31.05 2333 multiply(inverse(b),inverse(least_upper_bound(identity,inverse(c_0)))) = inverse(least_upper_bound(b,inverse(a))). [para(225(a,1),300(a,1,1)),flip(a)].
% 30.78/31.05 2350 multiply(least_upper_bound(inverse(b),inverse(c_0)),multiply(c_0,A)) = multiply(least_upper_bound(identity,a),A). [para(268(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 2360 multiply(greatest_lower_bound(identity,least_upper_bound(inverse(b),inverse(c_0))),c_0) = greatest_lower_bound(c_0,least_upper_bound(identity,a)). [para(268(a,1),39(a,1,2)),rewrite([5(12)]),flip(a)].
% 30.78/31.05 2374 least_upper_bound(A,multiply(a,A)) = multiply(least_upper_bound(identity,a),A). [back_rewrite(1075),rewrite([2350(11)])].
% 30.78/31.05 2406 least_upper_bound(identity,least_upper_bound(a,greatest_lower_bound(A,identity))) = least_upper_bound(identity,a). [para(147(a,1),87(a,2)),rewrite([4(4),55(5),4(6)])].
% 30.78/31.05 2520 multiply(least_upper_bound(a,c_0),greatest_lower_bound(identity,inverse(c_0))) = multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(identity,c_0)). [para(273(a,1),60(a,1,2)),rewrite([5(8),1428(8),5(15)]),flip(a)].
% 30.78/31.05 2539 greatest_lower_bound(identity,inverse(least_upper_bound(identity,b))) = inverse(least_upper_bound(identity,b)). [para(304(a,1),40(a,1,2)),rewrite([85(12),8(11),304(12)])].
% 30.78/31.05 2753 multiply(c_0,least_upper_bound(inverse(c_0),greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(identity,greatest_lower_bound(b,c_0)). [para(1402(a,1),90(a,1,2)),rewrite([6(13)]),flip(a)].
% 30.78/31.05 2800 multiply(least_upper_bound(a,greatest_lower_bound(identity,c_0)),inverse(a)) = least_upper_bound(identity,greatest_lower_bound(b,inverse(a))). [para(442(a,1),36(a,1,2)),rewrite([85(12),6(11)]),flip(a)].
% 30.78/31.05 2886 least_upper_bound(A,greatest_lower_bound(identity,multiply(A,B))) = multiply(A,least_upper_bound(identity,greatest_lower_bound(B,inverse(A)))). [para(91(a,2),59(a,1,2)),rewrite([6(8)])].
% 30.78/31.05 2898 greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,b),inverse(b))) = multiply(greatest_lower_bound(identity,b),inverse(b)). [para(1764(a,1),91(a,2,2))].
% 30.78/31.05 3053 multiply(inverse(least_upper_bound(identity,inverse(b))),multiply(least_upper_bound(identity,b),least_upper_bound(a,inverse(b)))) = least_upper_bound(identity,c_0). [para(566(a,1),33(a,1,2)),rewrite([13(16),6(15),13(15,R),6(14),13(16,R),6(15),13(15,R),6(14),1045(16)]),flip(a)].
% 30.78/31.05 3079 multiply(inverse(least_upper_bound(a,c_0)),multiply(least_upper_bound(identity,b),A)) = multiply(inverse(a),A). [para(710(a,1),9(a,1,1)),flip(a)].
% 30.78/31.05 3095 multiply(greatest_lower_bound(A,greatest_lower_bound(B,C)),inverse(greatest_lower_bound(B,C))) = greatest_lower_bound(identity,multiply(A,inverse(greatest_lower_bound(B,C)))). [para(11(a,1),93(a,2,1)),rewrite([11(7),5(6),11(7,R),5(6)]),flip(a)].
% 30.78/31.05 3105 greatest_lower_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = greatest_lower_bound(identity,multiply(A,inverse(B))). [para(93(a,1),28(a,1,2))].
% 30.78/31.05 3162 multiply(greatest_lower_bound(identity,b),inverse(b)) = greatest_lower_bound(identity,inverse(b)). [back_rewrite(2898),rewrite([3105(8),1(5)]),flip(a)].
% 30.78/31.05 3232 multiply(greatest_lower_bound(b,c_0),inverse(greatest_lower_bound(identity,a))) = b. [para(728(a,1),27(a,1,2)),rewrite([85(5)])].
% 30.78/31.05 3264 multiply(greatest_lower_bound(identity,a),inverse(greatest_lower_bound(b,c_0))) = inverse(b). [para(3232(a,1),300(a,1,1)),rewrite([85(7)]),flip(a)].
% 30.78/31.05 3548 multiply(least_upper_bound(identity,c_0),c_0) = multiply(c_0,least_upper_bound(identity,c_0)). [para(1074(a,1),59(a,1)),rewrite([6(9)])].
% 30.78/31.05 3599 multiply(greatest_lower_bound(inverse(c_0),least_upper_bound(identity,inverse(b))),b) = greatest_lower_bound(inverse(a),least_upper_bound(identity,b)). [para(200(a,1),105(a,1,2)),rewrite([6(5),6(10),5(13)]),flip(a)].
% 30.78/31.05 3645 least_upper_bound(greatest_lower_bound(identity,b),greatest_lower_bound(identity,inverse(b))) = multiply(least_upper_bound(identity,b),greatest_lower_bound(identity,inverse(b))). [para(1401(a,1),1089(a,1,2)),rewrite([5(4),5(7),6(8),5(15)])].
% 30.78/31.05 3671 multiply(least_upper_bound(identity,inverse(b)),greatest_lower_bound(identity,c_0)) = multiply(least_upper_bound(identity,b),greatest_lower_bound(a,inverse(b))). [para(1143(a,1),35(a,1,2)),rewrite([1144(8),6(12)]),flip(a)].
% 30.78/31.05 3683 multiply(least_upper_bound(a,c_0),greatest_lower_bound(identity,inverse(c_0))) = multiply(least_upper_bound(identity,b),greatest_lower_bound(a,inverse(b))). [back_rewrite(2520),rewrite([3671(16)])].
% 30.78/31.05 3724 greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,c_0))) = identity. [para(1189(a,1),1006(a,1,2,2,1)),rewrite([300(6),84(8)])].
% 30.78/31.05 3751 least_upper_bound(identity,inverse(greatest_lower_bound(identity,c_0))) = inverse(greatest_lower_bound(identity,c_0)). [para(3724(a,1),908(a,1,2)),rewrite([6(6)])].
% 30.78/31.05 3809 greatest_lower_bound(least_upper_bound(identity,b),least_upper_bound(identity,inverse(b))) = multiply(greatest_lower_bound(identity,b),least_upper_bound(identity,inverse(b))). [para(1314(a,1),1204(a,1,2)),rewrite([6(4),6(7),5(8),6(15)])].
% 30.78/31.05 3987 multiply(inverse(least_upper_bound(identity,inverse(c_0))),inverse(a)) = inverse(least_upper_bound(a,inverse(b))). [para(1318(a,1),300(a,1,1)),flip(a)].
% 30.78/31.05 4046 multiply(A,greatest_lower_bound(B,greatest_lower_bound(C,multiply(inverse(A),D)))) = greatest_lower_bound(D,multiply(A,greatest_lower_bound(B,C))). [para(111(a,1),18(a,1,2)),rewrite([11(4,R),18(3),5(1)]),flip(a)].
% 30.78/31.05 4063 greatest_lower_bound(greatest_lower_bound(A,B),multiply(inverse(C),D)) = greatest_lower_bound(A,greatest_lower_bound(B,multiply(inverse(C),D))). [para(111(a,1),52(a,2,2)),rewrite([85(3),1004(5),11(5,R),5(4),4046(6),52(5),11(8,R),5(7)])].
% 30.78/31.05 4093 greatest_lower_bound(greatest_lower_bound(A,B),multiply(C,D)) = greatest_lower_bound(A,greatest_lower_bound(B,multiply(C,D))). [para(111(a,1),111(a,2,2)),rewrite([4063(6),18(5),111(5),11(6,R),5(5)])].
% 30.78/31.05 4215 multiply(inverse(greatest_lower_bound(identity,inverse(c_0))),inverse(a)) = inverse(greatest_lower_bound(a,inverse(b))). [para(1405(a,1),300(a,1,1)),flip(a)].
% 30.78/31.05 4275 least_upper_bound(a,multiply(c_0,greatest_lower_bound(identity,a))) = multiply(least_upper_bound(identity,greatest_lower_bound(b,c_0)),a). [para(1444(a,1),35(a,1,2)),rewrite([6(12)])].
% 30.78/31.05 4543 least_upper_bound(identity,inverse(least_upper_bound(identity,inverse(A)))) = identity. [para(1659(a,1),1264(a,1,2,2,1)),rewrite([1(7)])].
% 30.78/31.05 4553 greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(A)))) = inverse(least_upper_bound(identity,inverse(A))). [para(4543(a,1),992(a,1,2)),rewrite([5(6)])].
% 30.78/31.05 4559 multiply(inverse(b),least_upper_bound(identity,b)) = least_upper_bound(identity,inverse(b)). [para(1661(a,1),61(a,1,2)),rewrite([2163(13)])].
% 30.78/31.05 4568 multiply(inverse(least_upper_bound(inverse(a),inverse(c_0))),inverse(c_0)) = inverse(least_upper_bound(identity,b)). [para(1661(a,1),300(a,1,1)),flip(a)].
% 30.78/31.05 4584 greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,inverse(A)))) = identity. [para(1718(a,1),1006(a,1,2,2,1)),rewrite([1(7)])].
% 30.78/31.05 4592 multiply(a,least_upper_bound(inverse(c_0),greatest_lower_bound(identity,inverse(a)))) = least_upper_bound(inverse(b),greatest_lower_bound(identity,a)). [para(1401(a,1),120(a,1,2)),rewrite([5(5),5(11),6(14)]),flip(a)].
% 30.78/31.05 4600 greatest_lower_bound(A,multiply(A,inverse(greatest_lower_bound(identity,inverse(B))))) = A. [para(4584(a,1),18(a,2,2)),rewrite([57(2),57(8)])].
% 30.78/31.05 4604 least_upper_bound(identity,inverse(greatest_lower_bound(identity,inverse(A)))) = inverse(greatest_lower_bound(identity,inverse(A))). [para(4584(a,1),908(a,1,2)),rewrite([6(6)])].
% 30.78/31.05 4900 multiply(least_upper_bound(identity,a),a) = multiply(a,least_upper_bound(identity,a)). [para(2374(a,1),59(a,1)),rewrite([6(9)])].
% 30.78/31.05 5088 multiply(greatest_lower_bound(identity,b),least_upper_bound(identity,inverse(b))) = multiply(least_upper_bound(identity,b),greatest_lower_bound(identity,inverse(b))). [para(3162(a,1),59(a,1,2)),rewrite([3645(8),6(15)]),flip(a)].
% 30.78/31.05 5093 greatest_lower_bound(least_upper_bound(identity,b),least_upper_bound(identity,inverse(b))) = multiply(least_upper_bound(identity,b),greatest_lower_bound(identity,inverse(b))). [back_rewrite(3809),rewrite([5088(16)])].
% 30.78/31.05 5222 greatest_lower_bound(identity,multiply(a,inverse(greatest_lower_bound(b,c_0)))) = greatest_lower_bound(identity,inverse(b)). [para(3264(a,1),40(a,1,2)),rewrite([85(12),11(11),5(10),11(10),5(9),11(10,R),5(9),154(10),11(9),5(8),11(9,R),5(8),3095(14)]),flip(a)].
% 30.78/31.05 5438 multiply(greatest_lower_bound(identity,c_0),least_upper_bound(identity,c_0)) = multiply(least_upper_bound(identity,c_0),greatest_lower_bound(identity,c_0)). [para(3548(a,1),60(a,1,2)),rewrite([39(9),5(3),5(13)])].
% 30.78/31.05 5594 least_upper_bound(A,multiply(A,a)) = multiply(A,least_upper_bound(identity,a)). [para(55(a,1),135(a,1,2,2)),rewrite([147(9)])].
% 30.78/31.05 5672 least_upper_bound(A,multiply(A,c_0)) = multiply(A,least_upper_bound(identity,c_0)). [para(566(a,1),135(a,1,2,2)),rewrite([13(16),6(15),13(15,R),6(14),13(16,R),6(15),13(15,R),6(14),1045(16),3053(17)])].
% 30.78/31.05 6189 multiply(greatest_lower_bound(identity,inverse(b)),least_upper_bound(identity,b)) = multiply(least_upper_bound(identity,b),greatest_lower_bound(identity,inverse(b))). [para(4559(a,1),39(a,1,2)),rewrite([5093(8),5(12)]),flip(a)].
% 30.78/31.05 6208 greatest_lower_bound(A,multiply(A,least_upper_bound(identity,b))) = A. [para(2539(a,1),4600(a,1,2,2,1)),rewrite([85(5)])].
% 30.78/31.05 6386 multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)) = multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)). [para(4900(a,1),60(a,1,2)),rewrite([39(9),5(3),5(13)])].
% 30.78/31.05 7196 multiply(inverse(greatest_lower_bound(identity,least_upper_bound(b,inverse(a)))),greatest_lower_bound(a,least_upper_bound(identity,c_0))) = a. [para(266(a,1),436(a,1,2,2)),rewrite([5(6)])].
% 30.78/31.05 7206 multiply(inverse(greatest_lower_bound(A,identity)),multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(A,identity))) = least_upper_bound(identity,inverse(A)). [para(1651(a,1),436(a,1,2,2)),rewrite([5(9),1433(9)])].
% 30.78/31.05 7325 multiply(inverse(greatest_lower_bound(identity,multiply(inverse(A),B))),multiply(inverse(A),greatest_lower_bound(A,B))) = identity. [para(166(a,1),4(a,1))].
% 30.78/31.05 7709 least_upper_bound(identity,multiply(least_upper_bound(A,inverse(B)),greatest_lower_bound(B,C))) = least_upper_bound(identity,multiply(A,greatest_lower_bound(B,C))). [para(36(a,2),174(a,1,2)),rewrite([13(9,R),175(8),6(11),13(11,R),6(10),1592(10),261(11)])].
% 30.78/31.05 8504 least_upper_bound(c_0,multiply(greatest_lower_bound(a,b),least_upper_bound(identity,c_0))) = least_upper_bound(c_0,greatest_lower_bound(a,b)). [para(5672(a,1),191(a,1,2))].
% 30.78/31.05 8576 multiply(least_upper_bound(c_0,greatest_lower_bound(a,b)),inverse(a)) = multiply(b,least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b)))). [para(536(a,2),98(a,1,2)),rewrite([2886(8),85(12),6(14)]),flip(a)].
% 30.78/31.05 8960 greatest_lower_bound(identity,multiply(least_upper_bound(inverse(A),a),A)) = identity. [para(55(a,1),735(a,1,2,1,2))].
% 30.78/31.05 9589 greatest_lower_bound(A,least_upper_bound(B,multiply(least_upper_bound(C,identity),A))) = A. [para(206(a,1),8(a,1,2))].
% 30.78/31.05 9880 greatest_lower_bound(A,multiply(least_upper_bound(B,identity),greatest_lower_bound(A,C))) = greatest_lower_bound(A,multiply(least_upper_bound(B,identity),C)). [para(211(a,1),29(a,1,2)),rewrite([5(3)])].
% 30.78/31.05 10694 multiply(inverse(least_upper_bound(identity,b)),c_0) = inverse(least_upper_bound(inverse(a),inverse(c_0))). [para(1316(a,1),300(a,1,1)),rewrite([85(13)]),flip(a)].
% 30.78/31.05 10798 greatest_lower_bound(identity,least_upper_bound(A,least_upper_bound(identity,a))) = identity. [para(2406(a,1),1465(a,1,2,1,2)),rewrite([58(7),57(7)])].
% 30.78/31.05 10812 greatest_lower_bound(identity,least_upper_bound(A,multiply(least_upper_bound(inverse(B),b),B))) = identity. [para(313(a,1),1465(a,1,2,1,2)),rewrite([58(8),57(8)])].
% 30.78/31.05 10830 least_upper_bound(A,multiply(A,inverse(least_upper_bound(B,least_upper_bound(identity,a))))) = A. [para(10798(a,1),1268(a,1,2,2,1)),rewrite([1(7)])].
% 30.78/31.05 10890 multiply(greatest_lower_bound(identity,b),least_upper_bound(a,c_0)) = multiply(least_upper_bound(identity,b),greatest_lower_bound(a,c_0)). [para(747(a,1),241(a,1,2)),rewrite([39(9),5(3),5(13)])].
% 30.78/31.05 10894 multiply(greatest_lower_bound(identity,multiply(inverse(a),A)),B) = multiply(inverse(a),multiply(greatest_lower_bound(A,a),B)). [para(241(a,1),165(a,2,2,1)),rewrite([3079(10),9(17),3079(18)])].
% 30.78/31.05 11419 least_upper_bound(A,multiply(A,b)) = multiply(A,least_upper_bound(identity,b)). [para(94(a,1),255(a,1,2,2)),rewrite([85(7),6(6),271(9)])].
% 30.78/31.05 11531 least_upper_bound(least_upper_bound(A,B),inverse(C)) = least_upper_bound(A,least_upper_bound(B,inverse(C))). [para(258(a,1),132(a,2,2)),rewrite([314(8),1(4),13(3),6(2),13(3,R),6(2),51(9),57(7)]),flip(a)].
% 30.78/31.05 11637 greatest_lower_bound(b,multiply(least_upper_bound(A,identity),least_upper_bound(identity,b))) = b. [para(11419(a,1),9589(a,1,2))].
% 30.78/31.05 11811 multiply(greatest_lower_bound(inverse(least_upper_bound(identity,b)),multiply(inverse(b),least_upper_bound(A,identity))),least_upper_bound(identity,b)) = identity. [para(11637(a,1),1784(a,1,1,2,1)),rewrite([300(7),5(11),590(18)])].
% 30.78/31.05 11820 greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(A,B)),least_upper_bound(B,C))) = identity. [para(8(a,1),1485(a,1,2,1,1,2))].
% 30.78/31.05 11858 greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(A,c_0)),least_upper_bound(B,c_0))) = identity. [para(1793(a,1),1485(a,1,2,1,1,2))].
% 30.78/31.05 12183 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(872(a,1),267(a,1,2)),rewrite([85(3),6(2),57(5)])].
% 30.78/31.05 12184 inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(B,A)))) = A. [para(1617(a,1),267(a,1,2)),rewrite([6(4),57(7)])].
% 30.78/31.05 12191 multiply(inverse(least_upper_bound(identity,inverse(a))),least_upper_bound(identity,a)) = a. [para(5594(a,1),267(a,1,2)),rewrite([1(10)])].
% 30.78/31.05 12192 multiply(inverse(least_upper_bound(identity,inverse(c_0))),least_upper_bound(identity,c_0)) = c_0. [para(5672(a,1),267(a,1,2)),rewrite([1(10)])].
% 30.78/31.05 12223 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(12183(a,1),1030(a,1,2)),rewrite([5(4),12183(7)])].
% 30.78/31.05 12238 greatest_lower_bound(A,least_upper_bound(B,A)) = A. [para(12184(a,1),1030(a,1,2)),rewrite([85(3),5(2),12184(7)])].
% 30.78/31.05 12279 greatest_lower_bound(inverse(greatest_lower_bound(inverse(A),identity)),inverse(greatest_lower_bound(identity,inverse(A)))) = inverse(greatest_lower_bound(inverse(A),identity)). [para(1718(a,1),12223(a,1,2,1))].
% 30.78/31.05 12291 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(12223(a,1),1287(a,1,2,1)),rewrite([85(3),85(3),6(2),12223(6),85(4)])].
% 30.78/31.05 12365 least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,inverse(A)),greatest_lower_bound(B,identity))) = identity. [para(180(a,1),270(a,1,2,1)),rewrite([1592(13),4(14)])].
% 30.78/31.05 12368 least_upper_bound(identity,least_upper_bound(greatest_lower_bound(b,inverse(a)),greatest_lower_bound(A,identity))) = least_upper_bound(identity,greatest_lower_bound(b,inverse(a))). [para(442(a,1),270(a,1,2,1)),rewrite([85(15),6(14),2800(17)])].
% 30.78/31.05 12537 least_upper_bound(identity,multiply(least_upper_bound(identity,b),greatest_lower_bound(a,inverse(b)))) = least_upper_bound(identity,greatest_lower_bound(a,inverse(b))). [para(1143(a,1),278(a,1,2,2)),rewrite([13(10,R),6(9),1144(9),6(18),3751(18),261(21),1143(17)])].
% 30.78/31.05 12698 multiply(least_upper_bound(A,multiply(A,B)),inverse(least_upper_bound(B,identity))) = A. [para(27(a,1),301(a,1,2,1,2)),rewrite([6(4)])].
% 30.78/31.05 12769 multiply(greatest_lower_bound(A,multiply(A,B)),inverse(greatest_lower_bound(B,identity))) = A. [para(27(a,1),302(a,1,2,1,2)),rewrite([5(4)])].
% 30.78/31.05 12770 multiply(greatest_lower_bound(A,identity),inverse(greatest_lower_bound(identity,inverse(A)))) = A. [para(57(a,1),302(a,1,2,1,2))].
% 30.78/31.05 12789 multiply(greatest_lower_bound(a,greatest_lower_bound(b,c_0)),inverse(greatest_lower_bound(identity,inverse(a)))) = greatest_lower_bound(a,c_0). [para(842(a,1),302(a,1,2,1,2)),rewrite([5(7),11(7),5(6),11(6,R),5(5),154(6),11(5),5(4),11(5,R),5(4)])].
% 30.78/31.05 12791 multiply(greatest_lower_bound(b,least_upper_bound(identity,c_0)),inverse(greatest_lower_bound(identity,least_upper_bound(a,inverse(b))))) = b. [para(1044(a,1),302(a,1,2,1,2))].
% 30.78/31.05 12795 greatest_lower_bound(a,inverse(greatest_lower_bound(identity,multiply(inverse(a),b)))) = a. [para(302(a,1),160(a,1,2)),rewrite([5(9),302(20)])].
% 30.78/31.05 12925 least_upper_bound(identity,multiply(greatest_lower_bound(inverse(a),inverse(b)),c_0)) = identity. [para(12795(a,1),366(a,1,2,2)),rewrite([10894(9),5(6),996(9)])].
% 30.78/31.05 12935 least_upper_bound(c_0,inverse(greatest_lower_bound(inverse(a),inverse(b)))) = inverse(greatest_lower_bound(inverse(a),inverse(b))). [para(12925(a,1),51(a,1,2)),rewrite([57(8),57(15)]),flip(a)].
% 30.78/31.05 12942 inverse(least_upper_bound(inverse(c_0),greatest_lower_bound(inverse(a),inverse(b)))) = c_0. [para(12925(a,1),267(a,1,2)),rewrite([6(8),57(11)])].
% 30.78/31.05 12946 least_upper_bound(inverse(c_0),greatest_lower_bound(inverse(a),inverse(b))) = inverse(c_0). [para(12942(a,1),85(a,1,1)),flip(a)].
% 30.78/31.05 12948 greatest_lower_bound(c_0,inverse(greatest_lower_bound(inverse(a),inverse(b)))) = c_0. [para(12942(a,1),1030(a,1,2)),rewrite([5(8),12946(16),85(11)])].
% 30.78/31.05 12953 greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),inverse(c_0))) = greatest_lower_bound(inverse(a),inverse(b)). [para(12948(a,1),1763(a,1,2,1)),rewrite([5(8),11(8),5(7),11(8,R),5(7)])].
% 30.78/31.05 16098 greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,b))) = multiply(a,greatest_lower_bound(inverse(a),least_upper_bound(identity,b))). [para(271(a,1),449(a,1,2,2)),rewrite([85(4),85(10),5(13),715(16)])].
% 30.78/31.05 16187 greatest_lower_bound(least_upper_bound(A,identity),inverse(greatest_lower_bound(identity,inverse(A)))) = inverse(greatest_lower_bound(identity,inverse(A))). [para(12770(a,1),452(a,1,2,2)),rewrite([6(6),5(7),85(15),2088(14),9880(15),223(12),12238(12),1(13)])].
% 30.78/31.05 16987 greatest_lower_bound(identity,least_upper_bound(A,least_upper_bound(identity,least_upper_bound(a,b)))) = identity. [para(10830(a,1),10812(a,1,2)),rewrite([85(7),6(7),13(7,R),6(6),13(6),6(5),13(6,R),6(5)])].
% 30.78/31.05 16991 least_upper_bound(identity,inverse(least_upper_bound(A,least_upper_bound(identity,least_upper_bound(a,b))))) = identity. [para(16987(a,1),872(a,1,2,1)),rewrite([1(10)])].
% 30.78/31.05 17649 greatest_lower_bound(greatest_lower_bound(A,B),least_upper_bound(B,C)) = greatest_lower_bound(A,B). [para(11820(a,1),302(a,1,2,1)),rewrite([58(5),57(5)])].
% 30.78/31.05 17774 greatest_lower_bound(A,least_upper_bound(B,multiply(A,least_upper_bound(identity,b)))) = A. [para(6208(a,1),17649(a,1,1)),rewrite([6(5),6208(11)])].
% 30.78/31.05 18085 greatest_lower_bound(A,multiply(least_upper_bound(A,B),least_upper_bound(identity,b))) = A. [para(20(a,1),17774(a,1,2)),rewrite([6(1)])].
% 30.78/31.05 19028 greatest_lower_bound(greatest_lower_bound(A,B),inverse(C)) = greatest_lower_bound(A,greatest_lower_bound(B,inverse(C))). [para(512(a,1),165(a,2,2)),rewrite([582(8),1(4),11(3),5(2),11(3,R),5(2),52(9),57(7)]),flip(a)].
% 30.78/31.05 19264 inverse(greatest_lower_bound(least_upper_bound(A,identity),inverse(least_upper_bound(identity,b)))) = least_upper_bound(identity,b). [para(18085(a,1),518(a,1,2)),rewrite([6(2),57(10)])].
% 30.78/31.05 19486 multiply(inverse(greatest_lower_bound(inverse(A),inverse(B))),multiply(inverse(A),greatest_lower_bound(A,B))) = B. [para(529(a,1),27(a,1,2))].
% 30.78/31.05 19936 greatest_lower_bound(greatest_lower_bound(A,c_0),least_upper_bound(B,c_0)) = greatest_lower_bound(A,c_0). [para(11858(a,1),302(a,1,2,1)),rewrite([58(7),57(7)])].
% 30.78/31.05 19944 least_upper_bound(least_upper_bound(A,c_0),greatest_lower_bound(B,c_0)) = least_upper_bound(A,c_0). [para(19936(a,1),12291(a,1,2))].
% 30.78/31.05 20749 multiply(A,inverse(greatest_lower_bound(identity,multiply(B,A)))) = inverse(greatest_lower_bound(B,inverse(A))). [para(518(a,1),12769(a,1,1,2)),rewrite([5(4),1763(4),5(5),28(5)])].
% 30.78/31.05 22492 least_upper_bound(identity,inverse(least_upper_bound(identity,least_upper_bound(a,b)))) = identity. [para(2(a,1),16991(a,1,2,1))].
% 30.78/31.05 22500 greatest_lower_bound(A,multiply(A,least_upper_bound(identity,least_upper_bound(a,b)))) = A. [para(22492(a,1),659(a,1,2,2,1)),rewrite([1(7)])].
% 30.78/31.05 22504 greatest_lower_bound(A,least_upper_bound(B,multiply(A,least_upper_bound(identity,least_upper_bound(a,b))))) = A. [para(22500(a,1),17649(a,1,1)),rewrite([6(7),22500(15)])].
% 30.78/31.05 25441 least_upper_bound(c_0,multiply(least_upper_bound(identity,b),greatest_lower_bound(a,c_0))) = c_0. [para(1089(a,2),1122(a,2,2)),rewrite([11531(9),916(8),4604(7),822(9),35(11),6(5)]),flip(a)].
% 30.78/31.05 25692 greatest_lower_bound(c_0,multiply(least_upper_bound(identity,b),greatest_lower_bound(a,c_0))) = c_0. [para(1204(a,2),1221(a,2,2)),rewrite([19028(9),987(8),4553(7),566(9),39(11),5(5),10890(9)]),flip(a)].
% 30.78/31.05 25698 multiply(least_upper_bound(identity,b),greatest_lower_bound(a,c_0)) = c_0. [para(25692(a,1),12291(a,1,2)),rewrite([6(9),25441(9)]),flip(a)].
% 30.78/31.05 25703 inverse(least_upper_bound(inverse(a),inverse(c_0))) = greatest_lower_bound(a,c_0). [para(25698(a,1),27(a,1,2)),rewrite([10694(6)])].
% 30.78/31.05 25711 inverse(least_upper_bound(identity,b)) = greatest_lower_bound(identity,inverse(b)). [back_rewrite(4568),rewrite([25703(6),527(6)]),flip(a)].
% 30.78/31.05 25730 inverse(greatest_lower_bound(identity,inverse(b))) = least_upper_bound(identity,b). [back_rewrite(19264),rewrite([25711(6),11(7),5(6),12238(6),5(4)])].
% 30.78/31.05 25741 multiply(least_upper_bound(identity,b),greatest_lower_bound(identity,inverse(b))) = identity. [back_rewrite(11811),rewrite([25711(4),4093(10),60(9),5(7),12238(7),57(5),6189(8)])].
% 30.78/31.05 25796 multiply(greatest_lower_bound(identity,b),least_upper_bound(identity,inverse(b))) = identity. [back_rewrite(5088),rewrite([25741(16)])].
% 30.78/31.06 25866 greatest_lower_bound(identity,multiply(least_upper_bound(identity,least_upper_bound(a,b)),greatest_lower_bound(identity,inverse(b)))) = identity. [para(25730(a,1),8960(a,1,2,1,1)),rewrite([6(6),13(6,R),6(5)])].
% 30.78/31.06 27649 greatest_lower_bound(identity,multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(A,identity))) = identity. [para(1433(a,1),29(a,1,2)),rewrite([12238(12)])].
% 30.78/31.06 28300 multiply(least_upper_bound(identity,inverse(A)),greatest_lower_bound(A,identity)) = identity. [para(27649(a,1),12291(a,1,2)),rewrite([6(8),7709(8),1(5),12291(4)]),flip(a)].
% 30.78/31.06 28301 inverse(least_upper_bound(identity,inverse(A))) = greatest_lower_bound(A,identity). [para(27649(a,1),1459(a,2,2)),rewrite([19028(7),4553(6),987(5),28300(10),57(6),57(8)])].
% 30.78/31.06 28303 inverse(greatest_lower_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [back_rewrite(7206),rewrite([28300(9),57(5)])].
% 30.78/31.06 28358 multiply(least_upper_bound(identity,c_0),greatest_lower_bound(identity,c_0)) = c_0. [back_rewrite(12192),rewrite([28301(5),5(3),5438(7)])].
% 30.78/31.06 28359 multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) = a. [back_rewrite(12191),rewrite([28301(5),5(3),6386(7)])].
% 30.78/31.06 28382 inverse(least_upper_bound(a,inverse(b))) = greatest_lower_bound(b,inverse(a)). [back_rewrite(3987),rewrite([28301(5),5(3),442(6)]),flip(a)].
% 30.78/31.06 28384 inverse(least_upper_bound(b,inverse(a))) = greatest_lower_bound(a,inverse(b)). [back_rewrite(2333),rewrite([28301(7),5(5),1143(6)]),flip(a)].
% 30.78/31.06 28388 inverse(least_upper_bound(A,identity)) = greatest_lower_bound(inverse(A),identity). [back_rewrite(2065),rewrite([28301(4),441(4)]),flip(a)].
% 30.78/31.06 28395 inverse(greatest_lower_bound(identity,inverse(A))) = least_upper_bound(A,identity). [back_rewrite(12279),rewrite([28303(4),85(3),6(2),16187(7),28303(8),85(7),6(6)])].
% 30.78/31.06 28473 multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)) = a. [back_rewrite(6386),rewrite([28359(14)])].
% 30.78/31.06 28517 multiply(least_upper_bound(A,multiply(A,B)),greatest_lower_bound(inverse(B),identity)) = A. [back_rewrite(12698),rewrite([28388(5)])].
% 30.78/31.06 28558 multiply(greatest_lower_bound(a,greatest_lower_bound(b,c_0)),least_upper_bound(identity,a)) = greatest_lower_bound(a,c_0). [back_rewrite(12789),rewrite([28395(10),6(8)])].
% 30.78/31.06 28573 inverse(greatest_lower_bound(a,inverse(b))) = least_upper_bound(b,inverse(a)). [back_rewrite(4215),rewrite([28395(5),6(3),224(6)]),flip(a)].
% 30.78/31.06 28576 inverse(greatest_lower_bound(b,c_0)) = least_upper_bound(inverse(b),inverse(c_0)). [back_rewrite(1749),rewrite([28395(5),6(3),228(6)]),flip(a)].
% 30.78/31.06 28668 inverse(greatest_lower_bound(identity,c_0)) = least_upper_bound(identity,inverse(c_0)). [back_rewrite(1153),rewrite([28573(5),274(7)]),flip(a)].
% 30.78/31.06 28674 greatest_lower_bound(identity,multiply(a,least_upper_bound(inverse(b),inverse(c_0)))) = greatest_lower_bound(identity,inverse(b)). [back_rewrite(5222),rewrite([28576(6)])].
% 30.78/31.06 28769 inverse(greatest_lower_bound(identity,multiply(A,B))) = least_upper_bound(identity,multiply(inverse(B),inverse(A))). [para(300(a,1),28303(a,2,2)),rewrite([5(3)])].
% 30.78/31.06 28788 inverse(greatest_lower_bound(A,inverse(B))) = least_upper_bound(B,inverse(A)). [back_rewrite(20749),rewrite([28769(4),110(6),57(3),6(2)]),flip(a)].
% 30.78/31.06 28790 multiply(least_upper_bound(inverse(A),inverse(B)),greatest_lower_bound(A,B)) = identity. [back_rewrite(7325),rewrite([28769(5),85(4),335(8),1(4),6(3)])].
% 30.78/31.06 28825 multiply(least_upper_bound(A,B),multiply(inverse(A),greatest_lower_bound(A,B))) = B. [back_rewrite(19486),rewrite([28788(4),85(2),6(1)])].
% 30.78/31.06 28851 least_upper_bound(a,least_upper_bound(b,c_0)) = least_upper_bound(a,b). [back_rewrite(12935),rewrite([28788(7),85(5),6(4),13(5),6(4),13(5,R),6(4),28788(11),85(9),6(8)])].
% 30.78/31.06 28856 multiply(least_upper_bound(identity,b),least_upper_bound(identity,a)) = least_upper_bound(identity,least_upper_bound(a,b)). [back_rewrite(419),rewrite([28851(6)]),flip(a)].
% 30.78/31.06 28857 multiply(least_upper_bound(a,c_0),least_upper_bound(identity,inverse(a))) = least_upper_bound(identity,least_upper_bound(a,b)). [back_rewrite(1352),rewrite([28856(15)])].
% 30.78/31.06 28953 multiply(greatest_lower_bound(a,b),least_upper_bound(identity,a)) = greatest_lower_bound(a,least_upper_bound(b,c_0)). [para(28473(a,1),415(a,1,2)),rewrite([5(5),5(10),11(10),5(9),11(10,R),5(9),154(10)]),flip(a)].
% 30.78/31.06 29040 multiply(greatest_lower_bound(identity,c_0),multiply(least_upper_bound(identity,inverse(c_0)),A)) = A. [para(28668(a,1),84(a,1,2,1))].
% 30.78/31.06 29153 least_upper_bound(identity,least_upper_bound(greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))),greatest_lower_bound(A,identity))) = identity. [para(28382(a,1),12365(a,1,2,1,2))].
% 30.78/31.06 29191 inverse(greatest_lower_bound(identity,least_upper_bound(a,inverse(b)))) = least_upper_bound(identity,greatest_lower_bound(b,inverse(a))). [para(28382(a,1),28303(a,2,2)),rewrite([5(6)])].
% 30.78/31.06 29196 multiply(greatest_lower_bound(b,least_upper_bound(identity,c_0)),least_upper_bound(identity,greatest_lower_bound(b,inverse(a)))) = b. [back_rewrite(12791),rewrite([29191(12)])].
% 30.78/31.06 29243 inverse(greatest_lower_bound(identity,least_upper_bound(b,inverse(a)))) = least_upper_bound(identity,greatest_lower_bound(a,inverse(b))). [para(28384(a,1),28303(a,2,2)),rewrite([5(6)])].
% 30.78/31.06 29245 multiply(least_upper_bound(identity,greatest_lower_bound(a,inverse(b))),greatest_lower_bound(a,least_upper_bound(identity,c_0))) = a. [back_rewrite(7196),rewrite([29243(7)])].
% 30.78/31.06 29325 inverse(least_upper_bound(A,inverse(B))) = greatest_lower_bound(B,inverse(A)). [para(28788(a,1),85(a,1,1))].
% 30.78/31.06 29326 inverse(greatest_lower_bound(A,B)) = least_upper_bound(inverse(A),inverse(B)). [para(85(a,1),28788(a,1,1,2)),rewrite([6(5)])].
% 30.78/31.06 29519 greatest_lower_bound(A,multiply(least_upper_bound(inverse(a),inverse(b)),A)) = A. [back_rewrite(1032),rewrite([29326(4)])].
% 30.78/31.06 29571 inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)). [para(85(a,1),29325(a,1,1,2)),rewrite([5(5)])].
% 30.78/31.06 29812 least_upper_bound(greatest_lower_bound(a,inverse(a)),greatest_lower_bound(b,inverse(b))) = identity. [para(14(a,1),29326(a,1,1)),rewrite([58(2),29571(6),85(6),5(5),29571(10),85(10),5(9)]),flip(a)].
% 30.78/31.06 29898 multiply(least_upper_bound(A,B),greatest_lower_bound(inverse(A),inverse(B))) = identity. [para(29571(a,1),79(a,1,2))].
% 30.78/31.06 29899 multiply(least_upper_bound(A,B),multiply(greatest_lower_bound(inverse(A),inverse(B)),C)) = C. [para(29571(a,1),84(a,1,2,1))].
% 30.78/31.06 30004 least_upper_bound(identity,least_upper_bound(c_0,greatest_lower_bound(a,least_upper_bound(identity,c_0)))) = least_upper_bound(identity,c_0). [para(1641(a,1),278(a,1,2,2)),rewrite([13(9,R),6(8),6(20),6(21),12291(21),248(15),6(12)])].
% 30.78/31.06 30032 multiply(least_upper_bound(identity,multiply(A,inverse(B))),greatest_lower_bound(A,B)) = A. [para(28790(a,1),132(a,2,2)),rewrite([85(3),85(8),57(8)])].
% 30.78/31.06 30193 greatest_lower_bound(b,multiply(inverse(a),least_upper_bound(a,b))) = b. [para(275(a,1),29519(a,1,2))].
% 30.78/31.06 30204 greatest_lower_bound(multiply(a,b),least_upper_bound(a,b)) = multiply(a,b). [para(30193(a,1),52(a,1,2)),rewrite([85(3),85(9),5(10)]),flip(a)].
% 30.78/31.06 30245 least_upper_bound(b,greatest_lower_bound(a,inverse(a))) = least_upper_bound(identity,b). [para(29812(a,1),31(a,1,2)),rewrite([6(3)]),flip(a)].
% 30.78/31.06 30249 least_upper_bound(identity,least_upper_bound(a,b)) = least_upper_bound(a,b). [para(30245(a,1),31(a,1,2)),rewrite([13(5,R),6(4)])].
% 30.78/31.06 30252 least_upper_bound(identity,multiply(inverse(a),least_upper_bound(identity,b))) = multiply(inverse(a),least_upper_bound(a,b)). [para(30245(a,1),150(a,1,2,2))].
% 30.78/31.06 30263 greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a))) = greatest_lower_bound(identity,inverse(b)). [para(30245(a,1),29571(a,1,1)),rewrite([29571(4),58(2),29326(11),85(11),6(10)]),flip(a)].
% 30.78/31.06 30269 multiply(least_upper_bound(a,c_0),least_upper_bound(identity,inverse(a))) = least_upper_bound(a,b). [back_rewrite(28857),rewrite([30249(13)])].
% 30.78/31.06 30270 multiply(least_upper_bound(identity,b),least_upper_bound(identity,a)) = least_upper_bound(a,b). [back_rewrite(28856),rewrite([30249(12)])].
% 30.78/31.06 30273 greatest_lower_bound(identity,multiply(least_upper_bound(a,b),greatest_lower_bound(identity,inverse(b)))) = identity. [back_rewrite(25866),rewrite([30249(6)])].
% 30.78/31.06 30275 greatest_lower_bound(A,least_upper_bound(B,multiply(A,least_upper_bound(a,b)))) = A. [back_rewrite(22504),rewrite([30249(5)])].
% 30.78/31.06 30288 least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))) = identity. [para(30249(a,1),92(a,2,1)),rewrite([29571(6),1(8),29571(14),29898(16)])].
% 30.78/31.06 30289 least_upper_bound(A,multiply(greatest_lower_bound(inverse(a),inverse(b)),A)) = A. [para(30249(a,1),112(a,2,1)),rewrite([29571(5),1(8),29571(14),29899(17)])].
% 30.78/31.06 30305 greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(b))) = greatest_lower_bound(inverse(a),inverse(b)). [para(30249(a,1),29571(a,1,1)),rewrite([29571(4),58(7),29571(10)]),flip(a)].
% 30.78/31.06 30306 multiply(least_upper_bound(c_0,greatest_lower_bound(a,b)),inverse(a)) = b. [back_rewrite(8576),rewrite([30288(16),57(11)])].
% 30.78/31.06 30356 least_upper_bound(c_0,greatest_lower_bound(a,b)) = c_0. [para(30306(a,1),321(a,2,1,2)),rewrite([4(10),57(8),30(7),2(8),25(8)])].
% 30.78/31.06 30359 least_upper_bound(c_0,multiply(greatest_lower_bound(a,b),least_upper_bound(identity,c_0))) = c_0. [back_rewrite(8504),rewrite([30356(14)])].
% 30.78/31.06 30374 greatest_lower_bound(a,greatest_lower_bound(b,c_0)) = greatest_lower_bound(a,b). [para(30356(a,1),12238(a,1,2)),rewrite([5(5),11(5),5(4),11(5,R),5(4)])].
% 30.78/31.06 30386 greatest_lower_bound(a,least_upper_bound(b,c_0)) = greatest_lower_bound(a,c_0). [back_rewrite(28558),rewrite([30374(5),28953(7)])].
% 30.78/31.06 30393 multiply(greatest_lower_bound(identity,b),greatest_lower_bound(identity,a)) = greatest_lower_bound(a,b). [back_rewrite(497),rewrite([30374(12)])].
% 30.78/31.06 30402 multiply(greatest_lower_bound(a,b),least_upper_bound(inverse(b),inverse(c_0))) = greatest_lower_bound(identity,inverse(b)). [para(30374(a,1),93(a,2,1)),rewrite([29326(6),28674(9),29326(11)]),flip(a)].
% 30.78/31.06 30539 least_upper_bound(b,multiply(a,least_upper_bound(identity,b))) = least_upper_bound(a,b). [para(30204(a,1),12291(a,1,2)),rewrite([6(7),13(7),6(6),59(6),6(5)])].
% 30.78/31.06 30547 multiply(greatest_lower_bound(identity,inverse(a)),greatest_lower_bound(identity,inverse(b))) = greatest_lower_bound(inverse(a),inverse(b)). [para(30270(a,1),300(a,1,1)),rewrite([29571(4),29571(9),58(7),29571(13),58(11)]),flip(a)].
% 30.78/31.06 30560 multiply(least_upper_bound(a,b),greatest_lower_bound(identity,a)) = least_upper_bound(a,c_0). [para(30270(a,1),496(a,2,1,2)),rewrite([28359(13),216(8),6(7),19944(7),13(8,R),2(7)]),flip(a)].
% 30.78/31.06 30567 greatest_lower_bound(A,multiply(least_upper_bound(A,B),least_upper_bound(a,b))) = A. [para(20(a,1),30275(a,1,2)),rewrite([6(1)])].
% 30.78/31.06 30595 least_upper_bound(b,multiply(inverse(a),greatest_lower_bound(a,b))) = b. [para(529(a,1),30289(a,1,2))].
% 30.78/31.06 30610 least_upper_bound(multiply(a,b),greatest_lower_bound(a,b)) = multiply(a,b). [para(30595(a,1),51(a,1,2)),rewrite([85(3),85(9),6(10)]),flip(a)].
% 30.78/31.06 30767 least_upper_bound(greatest_lower_bound(identity,c_0),greatest_lower_bound(a,b)) = greatest_lower_bound(identity,c_0). [para(30359(a,1),329(a,1,1)),rewrite([29571(5),58(3),1710(6),5(3),29571(11),58(9),1710(12),5(9),6(10)]),flip(a)].
% 30.78/31.06 30862 multiply(least_upper_bound(a,greatest_lower_bound(identity,b)),least_upper_bound(identity,b)) = least_upper_bound(a,b). [para(30539(a,1),314(a,2)),rewrite([29571(6),58(4),1710(7),5(4)])].
% 30.78/31.06 30864 multiply(least_upper_bound(a,b),greatest_lower_bound(identity,inverse(b))) = least_upper_bound(a,greatest_lower_bound(identity,b)). [para(30539(a,1),329(a,1,1)),rewrite([29571(7),58(5),29571(14),58(12),1710(15),5(12)])].
% 30.78/31.06 30874 greatest_lower_bound(identity,least_upper_bound(a,greatest_lower_bound(identity,b))) = identity. [back_rewrite(30273),rewrite([30864(9)])].
% 30.78/31.06 30880 least_upper_bound(a,greatest_lower_bound(identity,b)) = least_upper_bound(identity,a). [para(30874(a,1),12291(a,1,2)),rewrite([6(7),31(7)]),flip(a)].
% 30.78/31.06 30884 multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)) = least_upper_bound(a,b). [back_rewrite(30862),rewrite([30880(5)])].
% 30.78/31.06 30992 greatest_lower_bound(b,multiply(a,greatest_lower_bound(identity,b))) = greatest_lower_bound(a,b). [para(30610(a,1),12238(a,1,2)),rewrite([5(7),11(7),5(6),60(6),5(5)])].
% 30.78/31.06 31098 greatest_lower_bound(A,greatest_lower_bound(B,least_upper_bound(C,A))) = greatest_lower_bound(A,B). [para(1807(a,1),27(a,1,2)),rewrite([85(2),84(4)]),flip(a)].
% 30.78/31.06 31127 greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))) = greatest_lower_bound(b,inverse(a)). [para(68(a,1),31098(a,1,2)),rewrite([11(6),5(5),11(6,R),5(5),5(10)])].
% 30.78/31.06 31139 least_upper_bound(identity,greatest_lower_bound(b,inverse(a))) = identity. [back_rewrite(29153),rewrite([31127(7),12368(9)])].
% 30.78/31.06 31152 greatest_lower_bound(identity,greatest_lower_bound(a,c_0)) = greatest_lower_bound(identity,c_0). [back_rewrite(547),rewrite([31127(6),517(6)]),flip(a)].
% 30.78/31.06 31153 greatest_lower_bound(b,least_upper_bound(identity,c_0)) = b. [back_rewrite(29196),rewrite([31139(11),57(7)])].
% 30.78/31.06 31182 greatest_lower_bound(b,least_upper_bound(A,least_upper_bound(identity,c_0))) = b. [para(31153(a,1),17649(a,1,1)),rewrite([6(5),31153(11)])].
% 30.78/31.06 31929 greatest_lower_bound(identity,greatest_lower_bound(b,c_0)) = greatest_lower_bound(a,b). [para(30767(a,1),28825(a,1,1)),rewrite([29326(7),58(5),11(14),5(13),11(13,R),5(12),31152(13),11(12,R),5(11),29040(14)])].
% 30.78/31.06 31943 greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(c_0))) = multiply(inverse(c_0),greatest_lower_bound(a,b)). [back_rewrite(2264),rewrite([31929(7)]),flip(a)].
% 30.78/31.06 31945 greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = multiply(inverse(b),greatest_lower_bound(a,b)). [back_rewrite(1424),rewrite([31929(7)]),flip(a)].
% 30.78/31.06 31961 greatest_lower_bound(identity,least_upper_bound(inverse(b),inverse(c_0))) = greatest_lower_bound(identity,inverse(b)). [para(31929(a,1),93(a,2,1)),rewrite([29326(6),1(8),29326(14),30402(16)])].
% 30.78/31.06 31962 least_upper_bound(identity,least_upper_bound(inverse(b),inverse(c_0))) = least_upper_bound(inverse(a),inverse(b)). [para(31929(a,1),29326(a,1,1)),rewrite([29326(4),58(7),29326(10)]),flip(a)].
% 30.78/31.06 31968 greatest_lower_bound(c_0,least_upper_bound(identity,a)) = greatest_lower_bound(a,c_0). [back_rewrite(2360),rewrite([31961(7),438(6)]),flip(a)].
% 30.78/31.06 31971 least_upper_bound(identity,least_upper_bound(a,c_0)) = multiply(least_upper_bound(inverse(a),inverse(b)),c_0). [back_rewrite(567),rewrite([31962(7)]),flip(a)].
% 30.78/31.06 31978 least_upper_bound(inverse(c_0),greatest_lower_bound(identity,inverse(a))) = least_upper_bound(inverse(a),inverse(c_0)). [para(31968(a,1),29326(a,1,1)),rewrite([29326(4),29571(11),58(9)]),flip(a)].
% 30.78/31.06 31980 least_upper_bound(inverse(b),greatest_lower_bound(identity,a)) = least_upper_bound(identity,inverse(b)). [back_rewrite(4592),rewrite([31978(8),2163(7)]),flip(a)].
% 30.78/31.06 31981 least_upper_bound(identity,greatest_lower_bound(b,c_0)) = least_upper_bound(identity,b). [back_rewrite(2753),rewrite([31978(8),1661(7)]),flip(a)].
% 30.78/31.06 31988 least_upper_bound(a,multiply(c_0,greatest_lower_bound(identity,a))) = least_upper_bound(a,c_0). [back_rewrite(4275),rewrite([31981(12),216(12)])].
% 30.78/31.06 32000 least_upper_bound(greatest_lower_bound(identity,inverse(b)),greatest_lower_bound(a,b)) = identity. [para(31980(a,1),762(a,2,2)),rewrite([5(4),85(7),5(7),30393(11),85(11),5(11),25796(16)])].
% 30.78/31.06 32002 least_upper_bound(a,greatest_lower_bound(identity,inverse(b))) = least_upper_bound(identity,a). [para(32000(a,1),31(a,1,2)),rewrite([6(3)]),flip(a)].
% 30.78/31.06 32007 least_upper_bound(c_0,greatest_lower_bound(identity,b)) = least_upper_bound(b,c_0). [back_rewrite(1729),rewrite([32002(7),405(5)]),flip(a)].
% 30.78/31.06 32020 greatest_lower_bound(inverse(c_0),least_upper_bound(identity,inverse(b))) = greatest_lower_bound(inverse(b),inverse(c_0)). [para(32007(a,1),29571(a,1,1)),rewrite([29571(4),29326(11),58(9)]),flip(a)].
% 30.78/31.06 32021 greatest_lower_bound(c_0,multiply(least_upper_bound(b,c_0),least_upper_bound(a,b))) = c_0. [para(32007(a,1),30567(a,1,2,1))].
% 30.78/31.06 32024 greatest_lower_bound(inverse(a),least_upper_bound(identity,b)) = greatest_lower_bound(identity,inverse(a)). [back_rewrite(3599),rewrite([32020(7),524(7)]),flip(a)].
% 30.78/31.06 32027 greatest_lower_bound(identity,multiply(a,least_upper_bound(identity,b))) = greatest_lower_bound(identity,a). [back_rewrite(16098),rewrite([32024(14),1710(13),5(10)])].
% 30.78/31.06 32034 least_upper_bound(identity,multiply(a,least_upper_bound(identity,b))) = least_upper_bound(a,b). [para(32002(a,1),92(a,2,1)),rewrite([29326(7),58(4),85(6),29326(15),58(12),85(14),30884(14)])].
% 30.78/31.06 32049 multiply(least_upper_bound(inverse(a),inverse(b)),c_0) = least_upper_bound(a,b). [para(31988(a,1),329(a,1,1)),rewrite([29326(7),58(5),30269(8),29326(9),58(7),1651(10),6(7),13(8),6(7),13(8,R),6(7),31971(8)]),flip(a)].
% 30.78/31.06 32051 least_upper_bound(identity,least_upper_bound(a,c_0)) = least_upper_bound(a,b). [back_rewrite(31971),rewrite([32049(12)])].
% 30.78/31.06 32061 multiply(inverse(c_0),greatest_lower_bound(a,b)) = greatest_lower_bound(inverse(a),inverse(b)). [para(32051(a,1),29571(a,1,1)),rewrite([29571(4),58(7),29571(10),31943(12)]),flip(a)].
% 30.78/31.06 32062 greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(c_0))) = greatest_lower_bound(inverse(a),inverse(b)). [back_rewrite(31943),rewrite([32061(13)])].
% 30.78/31.06 32064 multiply(c_0,greatest_lower_bound(inverse(a),inverse(b))) = greatest_lower_bound(a,b). [para(25741(a,1),2210(a,1,2,2,2)),rewrite([57(8),5(7),11(7,R),5(6),31945(7),84(8),5(10),32024(10),30547(13)]),flip(a)].
% 30.78/31.06 32073 multiply(greatest_lower_bound(a,b),least_upper_bound(a,b)) = c_0. [para(32021(a,1),582(a,2)),rewrite([29571(8),32064(10),11(7),5(6),30386(6),11(5,R),5(4),30374(5)])].
% 30.78/31.06 32078 greatest_lower_bound(c_0,least_upper_bound(A,multiply(a,least_upper_bound(a,b)))) = c_0. [para(32073(a,1),1918(a,1,2)),rewrite([5(8),32073(15)])].
% 30.78/31.06 32091 multiply(a,least_upper_bound(identity,b)) = least_upper_bound(a,c_0). [para(32027(a,1),28825(a,1,2,2)),rewrite([32034(7),58(5),1(8),30560(7)]),flip(a)].
% 30.78/31.06 32094 multiply(inverse(a),least_upper_bound(a,c_0)) = least_upper_bound(identity,b). [para(32091(a,1),27(a,1,2))].
% 30.78/31.06 32100 multiply(least_upper_bound(a,c_0),greatest_lower_bound(identity,inverse(b))) = a. [para(32091(a,1),28517(a,1,1,2)),rewrite([30(5),29571(7),58(5),5(9),28(9)])].
% 30.78/31.06 32116 least_upper_bound(identity,multiply(inverse(a),c_0)) = least_upper_bound(identity,b). [para(32094(a,1),16(a,2)),rewrite([4(4)])].
% 30.78/31.06 32127 multiply(least_upper_bound(a,c_0),greatest_lower_bound(inverse(a),inverse(b))) = greatest_lower_bound(identity,a). [para(32100(a,1),91(a,1,2)),rewrite([29571(14),11(16),5(15),11(15,R),5(14),30305(15),11(14),5(13),11(14,R),5(13),12953(14)]),flip(a)].
% 30.78/31.06 32147 multiply(least_upper_bound(identity,b),inverse(a)) = multiply(inverse(a),least_upper_bound(identity,b)). [para(32116(a,1),331(a,2,1)),rewrite([1(8),6(7),59(7),6(5)]),flip(a)].
% 30.78/31.06 32189 greatest_lower_bound(c_0,multiply(a,least_upper_bound(A,least_upper_bound(a,b)))) = c_0. [para(16(a,1),32078(a,1,2))].
% 30.78/31.06 32221 multiply(a,greatest_lower_bound(multiply(inverse(a),c_0),least_upper_bound(A,least_upper_bound(a,b)))) = c_0. [para(32189(a,1),111(a,2)),rewrite([5(10)])].
% 30.78/31.06 32442 multiply(inverse(a),multiply(least_upper_bound(a,b),greatest_lower_bound(a,b))) = b. [para(30992(a,1),30032(a,1,2)),rewrite([300(8),29326(6),58(4),2054(10),6(4),32147(7),30252(8),9(10)])].
% 30.78/31.06 32469 greatest_lower_bound(inverse(a),inverse(b)) = greatest_lower_bound(identity,inverse(c_0)). [para(30263(a,1),184(a,1,2,2)),rewrite([1406(8),32062(7),186(12)])].
% 30.78/31.06 32477 multiply(least_upper_bound(identity,b),greatest_lower_bound(a,inverse(b))) = greatest_lower_bound(identity,a). [back_rewrite(32127),rewrite([32469(8),3683(8)])].
% 30.78/31.06 32479 greatest_lower_bound(a,b) = greatest_lower_bound(identity,c_0). [back_rewrite(32064),rewrite([32469(6),1710(6),5(3)]),flip(a)].
% 30.78/31.06 32523 least_upper_bound(identity,greatest_lower_bound(a,inverse(b))) = identity. [back_rewrite(12537),rewrite([32477(9),7(5)]),flip(a)].
% 30.78/31.06 32529 multiply(inverse(a),multiply(least_upper_bound(a,b),greatest_lower_bound(identity,c_0))) = b. [back_rewrite(32442),rewrite([32479(8)])].
% 30.78/31.06 32694 greatest_lower_bound(a,least_upper_bound(identity,c_0)) = a. [back_rewrite(29245),rewrite([32523(6),1(7)])].
% 30.78/31.06 32736 least_upper_bound(a,b) = least_upper_bound(identity,c_0). [back_rewrite(30004),rewrite([32694(7),6(4),32051(5)])].
% 30.78/31.06 32750 multiply(inverse(a),c_0) = b. [back_rewrite(32529),rewrite([32736(5),28358(9)])].
% 30.78/31.06 32778 multiply(a,b) = c_0. [back_rewrite(32221),rewrite([32750(5),32736(5),31182(7)])].
% 30.78/31.06 32779 $F # answer(prove_p33). [resolve(32778,a,26,a)].
% 30.78/31.06
% 30.78/31.06 % SZS output end Refutation
% 30.78/31.06 ============================== end of proof ==========================
% 30.78/31.06
% 30.78/31.06 ============================== STATISTICS ============================
% 30.78/31.06
% 30.78/31.06 Given=3490. Generated=1365035. Kept=32771. proofs=1.
% 30.78/31.06 Usable=1750. Sos=6786. Demods=8065. Limbo=42, Disabled=24209. Hints=0.
% 30.78/31.06 Megabytes=22.85.
% 30.78/31.06 User_CPU=29.30, System_CPU=0.74, Wall_clock=30.
% 30.78/31.06
% 30.78/31.06 ============================== end of statistics =====================
% 30.78/31.06
% 30.78/31.06 ============================== end of search =========================
% 30.78/31.06
% 30.78/31.06 THEOREM PROVED
% 30.78/31.06 % SZS status Unsatisfiable
% 30.78/31.06
% 30.78/31.06 Exiting with 1 proof.
% 30.78/31.06
% 30.78/31.06 Process 581 exit (max_proofs) Tue Jun 14 06:48:58 2022
% 30.78/31.06 Prover9 interrupted
%------------------------------------------------------------------------------