TSTP Solution File: GRP186-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP186-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 11:18:02 EDT 2022
% Result : Unsatisfiable 8.08s 8.37s
% Output : Refutation 8.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP186-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 05:45:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.35/3.65 ============================== Prover9 ===============================
% 3.35/3.65 Prover9 (32) version 2009-11A, November 2009.
% 3.35/3.65 Process 28193 was started by sandbox2 on n010.cluster.edu,
% 3.35/3.65 Tue Jun 14 05:45:25 2022
% 3.35/3.65 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28040_n010.cluster.edu".
% 3.35/3.65 ============================== end of head ===========================
% 3.35/3.65
% 3.35/3.65 ============================== INPUT =================================
% 3.35/3.65
% 3.35/3.65 % Reading from file /tmp/Prover9_28040_n010.cluster.edu
% 3.35/3.65
% 3.35/3.65 set(prolog_style_variables).
% 3.35/3.65 set(auto2).
% 3.35/3.65 % set(auto2) -> set(auto).
% 3.35/3.65 % set(auto) -> set(auto_inference).
% 3.35/3.65 % set(auto) -> set(auto_setup).
% 3.35/3.65 % set(auto_setup) -> set(predicate_elim).
% 3.35/3.65 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.35/3.65 % set(auto) -> set(auto_limits).
% 3.35/3.65 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.35/3.65 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.35/3.65 % set(auto) -> set(auto_denials).
% 3.35/3.65 % set(auto) -> set(auto_process).
% 3.35/3.65 % set(auto2) -> assign(new_constants, 1).
% 3.35/3.65 % set(auto2) -> assign(fold_denial_max, 3).
% 3.35/3.65 % set(auto2) -> assign(max_weight, "200.000").
% 3.35/3.65 % set(auto2) -> assign(max_hours, 1).
% 3.35/3.65 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.35/3.65 % set(auto2) -> assign(max_seconds, 0).
% 3.35/3.65 % set(auto2) -> assign(max_minutes, 5).
% 3.35/3.65 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.35/3.65 % set(auto2) -> set(sort_initial_sos).
% 3.35/3.65 % set(auto2) -> assign(sos_limit, -1).
% 3.35/3.65 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.35/3.65 % set(auto2) -> assign(max_megs, 400).
% 3.35/3.65 % set(auto2) -> assign(stats, some).
% 3.35/3.65 % set(auto2) -> clear(echo_input).
% 3.35/3.65 % set(auto2) -> set(quiet).
% 3.35/3.65 % set(auto2) -> clear(print_initial_clauses).
% 3.35/3.65 % set(auto2) -> clear(print_given).
% 3.35/3.65 assign(lrs_ticks,-1).
% 3.35/3.65 assign(sos_limit,10000).
% 3.35/3.65 assign(order,kbo).
% 3.35/3.65 set(lex_order_vars).
% 3.35/3.65 clear(print_given).
% 3.35/3.65
% 3.35/3.65 % formulas(sos). % not echoed (16 formulas)
% 3.35/3.65
% 3.35/3.65 ============================== end of input ==========================
% 3.35/3.65
% 3.35/3.65 % From the command line: assign(max_seconds, 300).
% 3.35/3.65
% 3.35/3.65 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.35/3.65
% 3.35/3.65 % Formulas that are not ordinary clauses:
% 3.35/3.65
% 3.35/3.65 ============================== end of process non-clausal formulas ===
% 3.35/3.65
% 3.35/3.65 ============================== PROCESS INITIAL CLAUSES ===============
% 3.35/3.65
% 3.35/3.65 ============================== PREDICATE ELIMINATION =================
% 3.35/3.65
% 3.35/3.65 ============================== end predicate elimination =============
% 3.35/3.65
% 3.35/3.65 Auto_denials:
% 3.35/3.65 % copying label prove_p23 to answer in negative clause
% 3.35/3.65
% 3.35/3.65 Term ordering decisions:
% 3.35/3.65
% 3.35/3.65 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 3.35/3.65 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 3.35/3.65
% 3.35/3.65 ============================== end of process initial clauses ========
% 3.35/3.65
% 3.35/3.65 ============================== CLAUSES FOR SEARCH ====================
% 3.35/3.65
% 3.35/3.65 ============================== end of clauses for search =============
% 3.35/3.65
% 3.35/3.65 ============================== SEARCH ================================
% 3.35/3.65
% 3.35/3.65 % Starting search at 0.01 seconds.
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=37.000, iters=3366
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=36.000, iters=3360
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=35.000, iters=3385
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=32.000, iters=3422
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=31.000, iters=3394
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=30.000, iters=3334
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=29.000, iters=3483
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=28.000, iters=3393
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=27.000, iters=3365
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=26.000, iters=3338
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=25.000, iters=3360
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=24.000, iters=3336
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=23.000, iters=3350
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=22.000, iters=3337
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=21.000, iters=3333
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=20.000, iters=3341
% 3.35/3.65
% 3.35/3.65 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 2.11 sec).
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=19.000, iters=3340
% 3.35/3.65
% 3.35/3.65 Low Water (keep): wt=18.000, iters=3341
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=5290, wt=43.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=5752, wt=41.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=6153, wt=40.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=5694, wt=39.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=5693, wt=38.000
% 3.35/3.65
% 3.35/3.65 Low Water (displace): id=6243, wt=37.000
% 8.08/8.37
% 8.08/8.37 Low Water (displace): id=12573, wt=17.000
% 8.08/8.37
% 8.08/8.37 Low Water (displace): id=12656, wt=16.000
% 8.08/8.37
% 8.08/8.37 Low Water (displace): id=13160, wt=15.000
% 8.08/8.37
% 8.08/8.37 Low Water (keep): wt=17.000, iters=3345
% 8.08/8.37
% 8.08/8.37 Low Water (displace): id=13353, wt=14.000
% 8.08/8.37
% 8.08/8.37 Low Water (displace): id=15119, wt=13.000
% 8.08/8.37
% 8.08/8.37 ============================== PROOF =================================
% 8.08/8.37 % SZS status Unsatisfiable
% 8.08/8.37 % SZS output start Refutation
% 8.08/8.37
% 8.08/8.37 % Proof 1 at 7.17 (+ 0.24) seconds: prove_p23.
% 8.08/8.37 % Length of proof is 112.
% 8.08/8.37 % Level of proof is 15.
% 8.08/8.37 % Maximum clause weight is 19.000.
% 8.08/8.37 % Given clauses 1022.
% 8.08/8.37
% 8.08/8.37 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 8.08/8.37 2 least_upper_bound(A,A) = A # label(idempotence_of_lub) # label(axiom). [assumption].
% 8.08/8.37 3 greatest_lower_bound(A,A) = A # label(idempotence_of_gld) # label(axiom). [assumption].
% 8.08/8.37 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 8.08/8.37 5 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 8.08/8.37 6 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 8.08/8.37 7 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 8.08/8.37 8 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 8.08/8.37 9 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 8.08/8.37 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].
% 8.08/8.37 11 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(10),rewrite([5(4)])].
% 8.08/8.37 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].
% 8.08/8.37 13 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(12),rewrite([6(4)])].
% 8.08/8.37 14 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 8.08/8.37 15 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(14),flip(a)].
% 8.08/8.37 16 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 8.08/8.37 17 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(16),flip(a)].
% 8.08/8.37 18 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 8.08/8.37 19 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(18),flip(a)].
% 8.08/8.37 20 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 8.08/8.37 21 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(20),flip(a)].
% 8.08/8.37 22 least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) # label(prove_p23) # label(negated_conjecture) # answer(prove_p23). [assumption].
% 8.08/8.37 23 least_upper_bound(identity,multiply(a,b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) # answer(prove_p23). [copy(22),rewrite([6(5)])].
% 8.08/8.37 24 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),9(a,1,1)),rewrite([1(2)]),flip(a)].
% 8.08/8.37 25 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)])].
% 8.08/8.37 28 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)])].
% 8.08/8.37 29 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(4(a,1),15(a,1,1))].
% 8.08/8.37 30 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(4(a,1),17(a,1,1))].
% 8.08/8.37 31 least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A). [para(1(a,1),19(a,1,1)),rewrite([6(4)])].
% 8.08/8.37 32 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(4(a,1),19(a,1,1)),rewrite([6(5)])].
% 8.08/8.37 35 greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(B,identity),A). [para(1(a,1),21(a,1,1)),rewrite([5(4)])].
% 8.08/8.37 36 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(4(a,1),21(a,1,1)),rewrite([5(5)])].
% 8.08/8.37 37 greatest_lower_bound(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(greatest_lower_bound(D,multiply(A,B)),C). [para(9(a,1),21(a,1,1)),rewrite([5(6)])].
% 8.08/8.37 40 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),24(a,1,2))].
% 8.08/8.37 42 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(24(a,1),15(a,1,1)),rewrite([6(6)]),flip(a)].
% 8.08/8.37 43 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(24(a,1),17(a,1,1)),rewrite([5(6)]),flip(a)].
% 8.08/8.37 46 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(24(a,1),24(a,1,2))].
% 8.08/8.37 47 multiply(A,identity) = A. [back_rewrite(40),rewrite([46(4)])].
% 8.08/8.37 49 least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(B,identity)). [para(47(a,1),15(a,1,1)),rewrite([6(4)])].
% 8.08/8.37 50 greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(B,identity)). [para(47(a,1),17(a,1,1)),rewrite([5(4)])].
% 8.08/8.37 54 multiply(A,inverse(A)) = identity. [para(46(a,1),4(a,1))].
% 8.08/8.37 60 inverse(inverse(A)) = A. [para(46(a,1),47(a,1)),rewrite([47(2)]),flip(a)].
% 8.08/8.37 61 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(54(a,1),9(a,1)),flip(a)].
% 8.08/8.37 62 least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))). [para(54(a,1),15(a,1,1)),rewrite([6(5)])].
% 8.08/8.37 79 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(61(a,1),24(a,1,2)),rewrite([47(3)]),flip(a)].
% 8.08/8.37 87 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(79(a,1),24(a,1,2)),flip(a)].
% 8.08/8.37 88 multiply(least_upper_bound(inverse(A),identity),A) = least_upper_bound(A,identity). [para(4(a,1),31(a,1,2)),flip(a)].
% 8.08/8.37 89 greatest_lower_bound(A,multiply(least_upper_bound(B,identity),A)) = A. [para(31(a,1),8(a,1,2))].
% 8.08/8.37 104 multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(B,multiply(A,B))) = B. [para(31(a,2),24(a,1,2))].
% 8.08/8.37 108 multiply(least_upper_bound(A,identity),inverse(A)) = least_upper_bound(inverse(A),identity). [para(54(a,1),31(a,1,2)),flip(a)].
% 8.08/8.37 112 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(29(a,1),8(a,1,2))].
% 8.08/8.37 126 multiply(inverse(A),least_upper_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [para(47(a,1),29(a,1,2)),flip(a)].
% 8.08/8.37 129 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(28(a,1),29(a,2,2))].
% 8.08/8.37 134 greatest_lower_bound(identity,least_upper_bound(A,identity)) = identity. [para(47(a,1),89(a,1,2))].
% 8.08/8.37 137 greatest_lower_bound(A,multiply(A,least_upper_bound(B,identity))) = A. [para(134(a,1),17(a,2,2)),rewrite([47(2),47(6)])].
% 8.08/8.37 139 greatest_lower_bound(A,greatest_lower_bound(B,multiply(A,least_upper_bound(C,identity)))) = greatest_lower_bound(A,B). [para(137(a,1),11(a,2,2)),rewrite([5(4),5(6)])].
% 8.08/8.37 150 multiply(inverse(least_upper_bound(inverse(A),identity)),least_upper_bound(A,identity)) = A. [para(88(a,1),24(a,1,2))].
% 8.08/8.37 168 multiply(inverse(A),greatest_lower_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)). [para(47(a,1),30(a,1,2)),flip(a)].
% 8.08/8.37 189 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(32(a,1),8(a,1,2))].
% 8.08/8.37 207 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(32(a,2),24(a,1,2))].
% 8.08/8.37 266 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(60(a,1),189(a,1,2,1,2))].
% 8.08/8.37 272 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(A))) = identity. [para(6(a,1),266(a,1,2,1))].
% 8.08/8.37 273 greatest_lower_bound(identity,multiply(A,inverse(greatest_lower_bound(A,B)))) = identity. [para(7(a,1),266(a,1,2,1))].
% 8.08/8.37 303 greatest_lower_bound(identity,multiply(least_upper_bound(A,least_upper_bound(B,C)),inverse(C))) = identity. [para(13(a,2),272(a,1,2,1))].
% 8.08/8.37 308 greatest_lower_bound(identity,multiply(A,multiply(B,inverse(greatest_lower_bound(C,multiply(A,B)))))) = identity. [para(9(a,1),273(a,1,2)),rewrite([5(3)])].
% 8.08/8.37 322 multiply(greatest_lower_bound(inverse(A),identity),A) = greatest_lower_bound(A,identity). [para(4(a,1),35(a,1,2)),flip(a)].
% 8.08/8.37 340 multiply(greatest_lower_bound(A,identity),inverse(A)) = greatest_lower_bound(inverse(A),identity). [para(54(a,1),35(a,1,2)),flip(a)].
% 8.08/8.37 366 multiply(greatest_lower_bound(identity,inverse(A)),A) = greatest_lower_bound(A,identity). [para(5(a,1),322(a,1,1))].
% 8.08/8.37 384 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(36(a,1),7(a,1,2))].
% 8.08/8.37 396 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(36(a,2),17(a,2)),rewrite([17(9)])].
% 8.08/8.37 401 multiply(inverse(greatest_lower_bound(A,inverse(B))),greatest_lower_bound(identity,multiply(A,B))) = B. [para(36(a,2),24(a,1,2))].
% 8.08/8.37 407 greatest_lower_bound(identity,least_upper_bound(A,multiply(B,A))) = multiply(greatest_lower_bound(least_upper_bound(B,identity),inverse(A)),A). [para(31(a,2),36(a,1,2))].
% 8.08/8.37 433 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(60(a,1),384(a,1,2,1,2))].
% 8.08/8.37 459 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),A)) = identity. [para(112(a,1),433(a,1,2,1)),rewrite([87(6),60(6),1(6)])].
% 8.08/8.37 476 multiply(greatest_lower_bound(A,multiply(B,C)),inverse(C)) = greatest_lower_bound(B,multiply(A,inverse(C))). [para(54(a,1),37(a,1,1,2)),rewrite([47(2)]),flip(a)].
% 8.08/8.37 550 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),B)) = identity. [para(6(a,1),459(a,1,2,1,1))].
% 8.08/8.37 599 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(433(a,1),42(a,1,2)),rewrite([47(4),47(7)]),flip(a)].
% 8.08/8.37 646 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(266(a,1),43(a,1,2)),rewrite([47(4),47(7)]),flip(a)].
% 8.08/8.37 761 multiply(A,least_upper_bound(inverse(A),identity)) = least_upper_bound(A,identity). [para(54(a,1),49(a,1,2)),flip(a)].
% 8.08/8.37 783 least_upper_bound(greatest_lower_bound(A,identity),greatest_lower_bound(inverse(A),identity)) = multiply(greatest_lower_bound(inverse(A),identity),least_upper_bound(A,identity)). [para(322(a,1),49(a,1,2)),rewrite([6(6)])].
% 8.08/8.37 786 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(366(a,1),49(a,1,2)),rewrite([6(6)])].
% 8.08/8.37 814 greatest_lower_bound(least_upper_bound(A,identity),least_upper_bound(inverse(A),identity)) = multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)). [para(761(a,1),35(a,1,2)),rewrite([5(6)])].
% 8.08/8.37 927 multiply(A,greatest_lower_bound(inverse(A),identity)) = greatest_lower_bound(A,identity). [para(54(a,1),50(a,1,2)),flip(a)].
% 8.08/8.37 933 multiply(least_upper_bound(inverse(A),identity),greatest_lower_bound(A,identity)) = multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)). [para(88(a,1),50(a,1,2)),rewrite([5(6),814(6)]),flip(a)].
% 8.08/8.37 978 multiply(least_upper_bound(A,identity),greatest_lower_bound(inverse(A),identity)) = multiply(greatest_lower_bound(inverse(A),identity),least_upper_bound(A,identity)). [para(927(a,1),31(a,1,2)),rewrite([6(6),783(6)]),flip(a)].
% 8.08/8.37 1028 multiply(greatest_lower_bound(inverse(A),identity),least_upper_bound(A,identity)) = multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)). [para(108(a,1),50(a,1,2)),rewrite([814(6),978(12)]),flip(a)].
% 8.08/8.37 1030 least_upper_bound(greatest_lower_bound(A,identity),greatest_lower_bound(inverse(A),identity)) = multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)). [back_rewrite(783),rewrite([1028(12)])].
% 8.08/8.37 1126 least_upper_bound(A,inverse(least_upper_bound(inverse(A),identity))) = A. [para(150(a,1),49(a,1,2)),rewrite([6(5),6(13),13(13,R),2(12),150(12)])].
% 8.08/8.37 1130 multiply(inverse(greatest_lower_bound(A,identity)),A) = inverse(greatest_lower_bound(identity,inverse(A))). [para(168(a,1),87(a,1,1)),rewrite([60(9)]),flip(a)].
% 8.08/8.37 1230 multiply(A,inverse(greatest_lower_bound(A,identity))) = inverse(greatest_lower_bound(inverse(A),identity)). [para(340(a,1),87(a,1,1)),rewrite([60(6)]),flip(a)].
% 8.08/8.37 1259 multiply(greatest_lower_bound(A,B),least_upper_bound(C,inverse(greatest_lower_bound(A,B)))) = least_upper_bound(identity,multiply(greatest_lower_bound(A,B),C)). [para(62(a,2),21(a,2)),rewrite([21(9)])].
% 8.08/8.37 1611 multiply(inverse(least_upper_bound(A,identity)),multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity))) = greatest_lower_bound(inverse(A),identity). [para(927(a,1),104(a,1,2,2)),rewrite([6(9),1030(9)])].
% 8.08/8.37 2841 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),least_upper_bound(inverse(B),identity))) = identity. [para(1126(a,1),303(a,1,2,1,2)),rewrite([60(7)])].
% 8.08/8.37 5025 greatest_lower_bound(inverse(greatest_lower_bound(A,identity)),inverse(greatest_lower_bound(identity,inverse(A)))) = identity. [para(1130(a,1),50(a,1,2)),rewrite([4(14)])].
% 8.08/8.37 5237 multiply(A,multiply(B,inverse(greatest_lower_bound(identity,multiply(A,B))))) = inverse(greatest_lower_bound(identity,multiply(inverse(B),inverse(A)))). [para(1230(a,1),9(a,1)),rewrite([87(2),5(5),5(9)]),flip(a)].
% 8.08/8.37 6400 greatest_lower_bound(A,multiply(greatest_lower_bound(A,B),least_upper_bound(C,identity))) = greatest_lower_bound(A,multiply(B,least_upper_bound(C,identity))). [para(21(a,1),139(a,1,2)),rewrite([5(1)])].
% 8.08/8.37 9540 least_upper_bound(identity,multiply(greatest_lower_bound(A,identity),least_upper_bound(B,identity))) = least_upper_bound(identity,multiply(greatest_lower_bound(A,identity),B)). [para(5025(a,1),129(a,1,2,2,2)),rewrite([60(5),60(11),6(13),1259(14)])].
% 8.08/8.37 11218 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(433(a,1),207(a,1,2)),rewrite([60(3),6(2),47(5)])].
% 8.08/8.37 11219 inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(B,A)))) = A. [para(550(a,1),207(a,1,2)),rewrite([6(4),47(7)])].
% 8.08/8.37 11246 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(11218(a,1),646(a,1,2)),rewrite([5(4),11218(7)])].
% 8.08/8.37 11252 greatest_lower_bound(A,least_upper_bound(B,A)) = A. [para(11219(a,1),646(a,1,2)),rewrite([60(3),5(2),11219(7)])].
% 8.08/8.37 11293 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(11246(a,1),599(a,1,2,1)),rewrite([60(3),60(3),6(2),11246(6),60(4)])].
% 8.08/8.37 12441 inverse(greatest_lower_bound(least_upper_bound(A,B),inverse(least_upper_bound(inverse(B),identity)))) = least_upper_bound(inverse(B),identity). [para(2841(a,1),401(a,1,2)),rewrite([47(9)])].
% 8.08/8.37 14856 multiply(A,inverse(greatest_lower_bound(B,multiply(C,A)))) = inverse(greatest_lower_bound(C,multiply(B,inverse(A)))). [para(308(a,1),401(a,1,2)),rewrite([87(5),60(4),476(4),25(4),47(6)]),flip(a)].
% 8.08/8.37 14870 inverse(greatest_lower_bound(identity,multiply(inverse(A),inverse(B)))) = multiply(B,inverse(greatest_lower_bound(B,inverse(A)))). [back_rewrite(5237),rewrite([14856(5),1(3)]),flip(a)].
% 8.08/8.37 17006 greatest_lower_bound(identity,multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity))) = identity. [para(168(a,1),407(a,1,2,2)),rewrite([786(7),6400(8),126(5),8(5),396(11),933(8)]),flip(a)].
% 8.08/8.37 17020 multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)) = identity. [para(17006(a,1),11293(a,1,2)),rewrite([6(8),9540(8),340(5),11293(5)]),flip(a)].
% 8.08/8.37 17024 inverse(least_upper_bound(A,identity)) = greatest_lower_bound(inverse(A),identity). [back_rewrite(1611),rewrite([17020(9),47(5)])].
% 8.08/8.37 17080 inverse(greatest_lower_bound(A,identity)) = least_upper_bound(inverse(A),identity). [back_rewrite(12441),rewrite([17024(5),60(3),11(4),5(3),11252(3),5(2)])].
% 8.08/8.37 17371 inverse(greatest_lower_bound(identity,multiply(A,B))) = least_upper_bound(identity,multiply(inverse(B),inverse(A))). [para(87(a,1),17080(a,2,1)),rewrite([5(3),6(9)])].
% 8.08/8.37 17451 least_upper_bound(identity,multiply(A,B)) = multiply(A,inverse(greatest_lower_bound(A,inverse(B)))). [back_rewrite(14870),rewrite([17371(6),60(3),60(3)])].
% 8.08/8.37 17452 $F # answer(prove_p23). [resolve(17451,a,23,a)].
% 8.08/8.37
% 8.08/8.37 % SZS output end Refutation
% 8.08/8.37 ============================== end of proof ==========================
% 8.08/8.37
% 8.08/8.37 ============================== STATISTICS ============================
% 8.08/8.37
% 8.08/8.37 Given=1022. Generated=364908. Kept=17444. proofs=1.
% 8.08/8.37 Usable=764. Sos=7867. Demods=8017. Limbo=80, Disabled=8748. Hints=0.
% 8.08/8.37 Megabytes=16.33.
% 8.08/8.37 User_CPU=7.17, System_CPU=0.24, Wall_clock=7.
% 8.08/8.37
% 8.08/8.37 ============================== end of statistics =====================
% 8.08/8.37
% 8.08/8.37 ============================== end of search =========================
% 8.08/8.37
% 8.08/8.37 THEOREM PROVED
% 8.08/8.37 % SZS status Unsatisfiable
% 8.08/8.37
% 8.08/8.37 Exiting with 1 proof.
% 8.08/8.37
% 8.08/8.37 Process 28193 exit (max_proofs) Tue Jun 14 05:45:32 2022
% 8.08/8.37 Prover9 interrupted
%------------------------------------------------------------------------------