TSTP Solution File: GRP179-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP179-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 11:17:57 EDT 2022
% Result : Unsatisfiable 7.94s 8.22s
% Output : Refutation 7.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP179-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 09:47:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.19/3.52 ============================== Prover9 ===============================
% 3.19/3.52 Prover9 (32) version 2009-11A, November 2009.
% 3.19/3.52 Process 22488 was started by sandbox on n013.cluster.edu,
% 3.19/3.52 Mon Jun 13 09:47:44 2022
% 3.19/3.52 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22334_n013.cluster.edu".
% 3.19/3.52 ============================== end of head ===========================
% 3.19/3.52
% 3.19/3.52 ============================== INPUT =================================
% 3.19/3.52
% 3.19/3.52 % Reading from file /tmp/Prover9_22334_n013.cluster.edu
% 3.19/3.52
% 3.19/3.52 set(prolog_style_variables).
% 3.19/3.52 set(auto2).
% 3.19/3.52 % set(auto2) -> set(auto).
% 3.19/3.52 % set(auto) -> set(auto_inference).
% 3.19/3.52 % set(auto) -> set(auto_setup).
% 3.19/3.52 % set(auto_setup) -> set(predicate_elim).
% 3.19/3.52 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.19/3.52 % set(auto) -> set(auto_limits).
% 3.19/3.52 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.19/3.52 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.19/3.52 % set(auto) -> set(auto_denials).
% 3.19/3.52 % set(auto) -> set(auto_process).
% 3.19/3.52 % set(auto2) -> assign(new_constants, 1).
% 3.19/3.52 % set(auto2) -> assign(fold_denial_max, 3).
% 3.19/3.52 % set(auto2) -> assign(max_weight, "200.000").
% 3.19/3.52 % set(auto2) -> assign(max_hours, 1).
% 3.19/3.52 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.19/3.52 % set(auto2) -> assign(max_seconds, 0).
% 3.19/3.52 % set(auto2) -> assign(max_minutes, 5).
% 3.19/3.52 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.19/3.52 % set(auto2) -> set(sort_initial_sos).
% 3.19/3.52 % set(auto2) -> assign(sos_limit, -1).
% 3.19/3.52 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.19/3.52 % set(auto2) -> assign(max_megs, 400).
% 3.19/3.52 % set(auto2) -> assign(stats, some).
% 3.19/3.52 % set(auto2) -> clear(echo_input).
% 3.19/3.52 % set(auto2) -> set(quiet).
% 3.19/3.52 % set(auto2) -> clear(print_initial_clauses).
% 3.19/3.52 % set(auto2) -> clear(print_given).
% 3.19/3.52 assign(lrs_ticks,-1).
% 3.19/3.52 assign(sos_limit,10000).
% 3.19/3.52 assign(order,kbo).
% 3.19/3.52 set(lex_order_vars).
% 3.19/3.52 clear(print_given).
% 3.19/3.52
% 3.19/3.52 % formulas(sos). % not echoed (16 formulas)
% 3.19/3.52
% 3.19/3.52 ============================== end of input ==========================
% 3.19/3.52
% 3.19/3.52 % From the command line: assign(max_seconds, 300).
% 3.19/3.52
% 3.19/3.52 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.19/3.52
% 3.19/3.52 % Formulas that are not ordinary clauses:
% 3.19/3.52
% 3.19/3.52 ============================== end of process non-clausal formulas ===
% 3.19/3.52
% 3.19/3.52 ============================== PROCESS INITIAL CLAUSES ===============
% 3.19/3.52
% 3.19/3.52 ============================== PREDICATE ELIMINATION =================
% 3.19/3.52
% 3.19/3.52 ============================== end predicate elimination =============
% 3.19/3.52
% 3.19/3.52 Auto_denials:
% 3.19/3.52 % copying label prove_p10 to answer in negative clause
% 3.19/3.52
% 3.19/3.52 Term ordering decisions:
% 3.19/3.52
% 3.19/3.52 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 3.19/3.52 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 3.19/3.52
% 3.19/3.52 ============================== end of process initial clauses ========
% 3.19/3.52
% 3.19/3.52 ============================== CLAUSES FOR SEARCH ====================
% 3.19/3.52
% 3.19/3.52 ============================== end of clauses for search =============
% 3.19/3.52
% 3.19/3.52 ============================== SEARCH ================================
% 3.19/3.52
% 3.19/3.52 % Starting search at 0.01 seconds.
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=37.000, iters=3366
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=36.000, iters=3360
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=35.000, iters=3385
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=32.000, iters=3422
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=31.000, iters=3394
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=30.000, iters=3334
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=29.000, iters=3483
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=28.000, iters=3393
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=27.000, iters=3365
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=26.000, iters=3338
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=25.000, iters=3360
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=24.000, iters=3336
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=23.000, iters=3350
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=22.000, iters=3337
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=21.000, iters=3333
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=20.000, iters=3341
% 3.19/3.52
% 3.19/3.52 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 1.99 sec).
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=19.000, iters=3340
% 3.19/3.52
% 3.19/3.52 Low Water (keep): wt=18.000, iters=3341
% 3.19/3.52
% 3.19/3.52 Low Water (displace): id=5287, wt=43.000
% 3.19/3.52
% 3.19/3.52 Low Water (displace): id=5749, wt=41.000
% 3.19/3.52
% 3.19/3.52 Low Water (displace): id=6150, wt=40.000
% 3.19/3.52
% 3.19/3.52 Low Water (displace): id=5691, wt=39.000
% 3.19/3.52
% 3.19/3.52 Low Water (displace): id=5690, wt=38.000
% 3.19/3.52
% 3.19/3.52 Low Water (displace): id=6240, wt=37.000
% 7.94/8.22
% 7.94/8.22 Low Water (displace): id=12570, wt=17.000
% 7.94/8.22
% 7.94/8.22 Low Water (displace): id=12653, wt=16.000
% 7.94/8.22
% 7.94/8.22 Low Water (displace): id=13157, wt=15.000
% 7.94/8.22
% 7.94/8.22 Low Water (keep): wt=17.000, iters=3345
% 7.94/8.22
% 7.94/8.22 Low Water (displace): id=13350, wt=14.000
% 7.94/8.22
% 7.94/8.22 Low Water (displace): id=15116, wt=13.000
% 7.94/8.22
% 7.94/8.22 ============================== PROOF =================================
% 7.94/8.22 % SZS status Unsatisfiable
% 7.94/8.22 % SZS output start Refutation
% 7.94/8.22
% 7.94/8.22 % Proof 1 at 7.01 (+ 0.21) seconds: prove_p10.
% 7.94/8.22 % Length of proof is 95.
% 7.94/8.22 % Level of proof is 16.
% 7.94/8.22 % Maximum clause weight is 19.000.
% 7.94/8.22 % Given clauses 1058.
% 7.94/8.22
% 7.94/8.22 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 7.94/8.22 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 7.94/8.22 5 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 7.94/8.22 6 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 7.94/8.22 7 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 7.94/8.22 8 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 7.94/8.22 9 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 7.94/8.22 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].
% 7.94/8.22 11 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(10),rewrite([5(4)])].
% 7.94/8.22 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].
% 7.94/8.22 13 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(12),rewrite([6(4)])].
% 7.94/8.22 14 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 7.94/8.22 15 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(14),flip(a)].
% 7.94/8.22 16 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 7.94/8.22 17 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(16),flip(a)].
% 7.94/8.22 18 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 7.94/8.22 19 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(18),flip(a)].
% 7.94/8.22 20 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 7.94/8.22 21 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(20),flip(a)].
% 7.94/8.22 22 inverse(least_upper_bound(a,b)) != greatest_lower_bound(inverse(a),inverse(b)) # label(prove_p10) # label(negated_conjecture) # answer(prove_p10). [assumption].
% 7.94/8.22 23 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),9(a,1,1)),rewrite([1(2)]),flip(a)].
% 7.94/8.22 27 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)])].
% 7.94/8.22 28 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(4(a,1),15(a,1,1))].
% 7.94/8.22 29 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(4(a,1),17(a,1,1))].
% 7.94/8.22 30 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)])].
% 7.94/8.22 31 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)])].
% 7.94/8.22 34 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)])].
% 7.94/8.22 35 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)])].
% 7.94/8.22 36 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)])].
% 7.94/8.22 37 greatest_lower_bound(multiply(A,B),multiply(C,multiply(D,B))) = multiply(greatest_lower_bound(A,multiply(C,D)),B). [para(9(a,1),21(a,1,2))].
% 7.94/8.22 39 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),23(a,1,2))].
% 7.94/8.22 41 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(23(a,1),15(a,1,1)),rewrite([6(6)]),flip(a)].
% 7.94/8.22 42 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(23(a,1),17(a,1,1)),rewrite([5(6)]),flip(a)].
% 7.94/8.22 45 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(23(a,1),23(a,1,2))].
% 7.94/8.22 46 multiply(A,identity) = A. [back_rewrite(39),rewrite([45(4)])].
% 7.94/8.22 48 least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(B,identity)). [para(46(a,1),15(a,1,1)),rewrite([6(4)])].
% 7.94/8.22 49 greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(B,identity)). [para(46(a,1),17(a,1,1)),rewrite([5(4)])].
% 7.94/8.22 53 multiply(A,inverse(A)) = identity. [para(45(a,1),4(a,1))].
% 7.94/8.22 58 multiply(A,multiply(inverse(A),B)) = B. [para(45(a,1),23(a,1))].
% 7.94/8.22 59 inverse(inverse(A)) = A. [para(45(a,1),46(a,1)),rewrite([46(2)]),flip(a)].
% 7.94/8.22 60 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(53(a,1),9(a,1)),flip(a)].
% 7.94/8.22 61 least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))). [para(53(a,1),15(a,1,1)),rewrite([6(5)])].
% 7.94/8.22 78 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(60(a,1),23(a,1,2)),rewrite([46(3)]),flip(a)].
% 7.94/8.22 86 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(78(a,1),23(a,1,2)),flip(a)].
% 7.94/8.22 87 multiply(least_upper_bound(inverse(A),identity),A) = least_upper_bound(A,identity). [para(4(a,1),30(a,1,2)),flip(a)].
% 7.94/8.22 88 greatest_lower_bound(A,multiply(least_upper_bound(B,identity),A)) = A. [para(30(a,1),8(a,1,2))].
% 7.94/8.22 103 multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(B,multiply(A,B))) = B. [para(30(a,2),23(a,1,2))].
% 7.94/8.22 107 multiply(least_upper_bound(A,identity),inverse(A)) = least_upper_bound(inverse(A),identity). [para(53(a,1),30(a,1,2)),flip(a)].
% 7.94/8.22 113 multiply(A,least_upper_bound(identity,multiply(inverse(B),C))) = multiply(A,multiply(inverse(B),least_upper_bound(B,C))). [para(28(a,2),9(a,2,2)),rewrite([9(4)]),flip(a)].
% 7.94/8.22 125 multiply(inverse(A),least_upper_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [para(46(a,1),28(a,1,2)),flip(a)].
% 7.94/8.22 128 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(27(a,1),28(a,2,2))].
% 7.94/8.22 133 greatest_lower_bound(identity,least_upper_bound(A,identity)) = identity. [para(46(a,1),88(a,1,2))].
% 7.94/8.22 136 greatest_lower_bound(A,multiply(A,least_upper_bound(B,identity))) = A. [para(133(a,1),17(a,2,2)),rewrite([46(2),46(6)])].
% 7.94/8.22 138 greatest_lower_bound(A,greatest_lower_bound(B,multiply(A,least_upper_bound(C,identity)))) = greatest_lower_bound(A,B). [para(136(a,1),11(a,2,2)),rewrite([5(4),5(6)])].
% 7.94/8.22 167 multiply(inverse(A),greatest_lower_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)). [para(46(a,1),29(a,1,2)),flip(a)].
% 7.94/8.22 188 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(31(a,1),8(a,1,2))].
% 7.94/8.22 205 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(31(a,2),23(a,1,2))].
% 7.94/8.22 264 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(59(a,1),188(a,1,2,1,2))].
% 7.94/8.22 320 multiply(greatest_lower_bound(inverse(A),identity),A) = greatest_lower_bound(A,identity). [para(4(a,1),34(a,1,2)),flip(a)].
% 7.94/8.22 338 multiply(greatest_lower_bound(A,identity),inverse(A)) = greatest_lower_bound(inverse(A),identity). [para(53(a,1),34(a,1,2)),flip(a)].
% 7.94/8.22 364 multiply(greatest_lower_bound(identity,inverse(A)),A) = greatest_lower_bound(A,identity). [para(5(a,1),320(a,1,1))].
% 7.94/8.22 382 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(35(a,1),7(a,1,2))].
% 7.94/8.22 394 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(35(a,2),17(a,2)),rewrite([17(9)])].
% 7.94/8.22 405 greatest_lower_bound(identity,least_upper_bound(A,multiply(B,A))) = multiply(greatest_lower_bound(least_upper_bound(B,identity),inverse(A)),A). [para(30(a,2),35(a,1,2))].
% 7.94/8.22 431 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(59(a,1),382(a,1,2,1,2))].
% 7.94/8.22 476 multiply(greatest_lower_bound(A,multiply(B,C)),multiply(inverse(C),D)) = multiply(greatest_lower_bound(B,multiply(A,inverse(C))),D). [para(58(a,1),36(a,1,1,2)),rewrite([37(5)]),flip(a)].
% 7.94/8.22 597 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(431(a,1),41(a,1,2)),rewrite([46(4),46(7)]),flip(a)].
% 7.94/8.22 644 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(264(a,1),42(a,1,2)),rewrite([46(4),46(7)]),flip(a)].
% 7.94/8.22 759 multiply(A,least_upper_bound(inverse(A),identity)) = least_upper_bound(A,identity). [para(53(a,1),48(a,1,2)),flip(a)].
% 7.94/8.22 781 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(320(a,1),48(a,1,2)),rewrite([6(6)])].
% 7.94/8.22 784 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(364(a,1),48(a,1,2)),rewrite([6(6)])].
% 7.94/8.22 812 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(759(a,1),34(a,1,2)),rewrite([5(6)])].
% 7.94/8.22 925 multiply(A,greatest_lower_bound(inverse(A),identity)) = greatest_lower_bound(A,identity). [para(53(a,1),49(a,1,2)),flip(a)].
% 7.94/8.22 931 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(87(a,1),49(a,1,2)),rewrite([5(6),812(6)]),flip(a)].
% 7.94/8.22 976 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(925(a,1),30(a,1,2)),rewrite([6(6),781(6)]),flip(a)].
% 7.94/8.22 1026 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(107(a,1),49(a,1,2)),rewrite([812(6),976(12)]),flip(a)].
% 7.94/8.22 1028 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(781),rewrite([1026(12)])].
% 7.94/8.22 1128 multiply(inverse(greatest_lower_bound(A,identity)),A) = inverse(greatest_lower_bound(identity,inverse(A))). [para(167(a,1),86(a,1,1)),rewrite([59(9)]),flip(a)].
% 7.94/8.22 1257 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(61(a,2),21(a,2)),rewrite([21(9)])].
% 7.94/8.22 1608 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(925(a,1),103(a,1,2,2)),rewrite([6(9),1028(9)])].
% 7.94/8.22 4535 multiply(inverse(least_upper_bound(identity,multiply(inverse(A),B))),multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(113(a,1),4(a,1))].
% 7.94/8.22 5022 greatest_lower_bound(inverse(greatest_lower_bound(A,identity)),inverse(greatest_lower_bound(identity,inverse(A)))) = identity. [para(1128(a,1),49(a,1,2)),rewrite([4(14)])].
% 7.94/8.22 6397 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),138(a,1,2)),rewrite([5(1)])].
% 7.94/8.22 9537 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(5022(a,1),128(a,1,2,2,2)),rewrite([59(5),59(11),6(13),1257(14)])].
% 7.94/8.22 11215 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(431(a,1),205(a,1,2)),rewrite([59(3),6(2),46(5)])].
% 7.94/8.22 11243 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(11215(a,1),644(a,1,2)),rewrite([5(4),11215(7)])].
% 7.94/8.22 11290 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(11243(a,1),597(a,1,2,1)),rewrite([59(3),59(3),6(2),11243(6),59(4)])].
% 7.94/8.22 17003 greatest_lower_bound(identity,multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity))) = identity. [para(167(a,1),405(a,1,2,2)),rewrite([784(7),6397(8),125(5),8(5),394(11),931(8)]),flip(a)].
% 7.94/8.22 17017 multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)) = identity. [para(17003(a,1),11290(a,1,2)),rewrite([6(8),9537(8),338(5),11290(5)]),flip(a)].
% 7.94/8.22 17021 inverse(least_upper_bound(A,identity)) = greatest_lower_bound(inverse(A),identity). [back_rewrite(1608),rewrite([17017(9),46(5)])].
% 7.94/8.22 17257 inverse(least_upper_bound(identity,multiply(A,B))) = greatest_lower_bound(identity,multiply(inverse(B),inverse(A))). [para(86(a,1),17021(a,2,1)),rewrite([6(3),5(9)])].
% 7.94/8.22 17348 multiply(greatest_lower_bound(inverse(A),inverse(B)),least_upper_bound(A,B)) = identity. [back_rewrite(4535),rewrite([17257(5),59(4),476(8),1(4),5(3)])].
% 7.94/8.22 17728 inverse(greatest_lower_bound(inverse(A),inverse(B))) = least_upper_bound(A,B). [para(17348(a,1),23(a,1,2)),rewrite([46(6)])].
% 7.94/8.22 17763 inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)). [para(17728(a,1),59(a,1,1))].
% 7.94/8.22 17764 $F # answer(prove_p10). [resolve(17763,a,22,a)].
% 7.94/8.22
% 7.94/8.22 % SZS output end Refutation
% 7.94/8.22 ============================== end of proof ==========================
% 7.94/8.22
% 7.94/8.22 ============================== STATISTICS ============================
% 7.94/8.22
% 7.94/8.22 Given=1058. Generated=384764. Kept=17757. proofs=1.
% 7.94/8.22 Usable=771. Sos=7853. Demods=7940. Limbo=2, Disabled=9146. Hints=0.
% 7.94/8.22 Megabytes=16.41.
% 7.94/8.22 User_CPU=7.01, System_CPU=0.21, Wall_clock=7.
% 7.94/8.22
% 7.94/8.22 ============================== end of statistics =====================
% 7.94/8.22
% 7.94/8.22 ============================== end of search =========================
% 7.94/8.22
% 7.94/8.22 THEOREM PROVED
% 7.94/8.22 % SZS status Unsatisfiable
% 7.94/8.22
% 7.94/8.22 Exiting with 1 proof.
% 7.94/8.22
% 7.94/8.22 Process 22488 exit (max_proofs) Mon Jun 13 09:47:51 2022
% 7.94/8.22 Prover9 interrupted
%------------------------------------------------------------------------------