TSTP Solution File: GRP178-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:17:56 EDT 2022
% Result : Unsatisfiable 32.02s 32.31s
% Output : Refutation 32.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP178-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 08:20:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.00/4.35 ============================== Prover9 ===============================
% 4.00/4.35 Prover9 (32) version 2009-11A, November 2009.
% 4.00/4.35 Process 27546 was started by sandbox2 on n025.cluster.edu,
% 4.00/4.35 Mon Jun 13 08:20:09 2022
% 4.00/4.35 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27393_n025.cluster.edu".
% 4.00/4.35 ============================== end of head ===========================
% 4.00/4.35
% 4.00/4.35 ============================== INPUT =================================
% 4.00/4.35
% 4.00/4.35 % Reading from file /tmp/Prover9_27393_n025.cluster.edu
% 4.00/4.35
% 4.00/4.35 set(prolog_style_variables).
% 4.00/4.35 set(auto2).
% 4.00/4.35 % set(auto2) -> set(auto).
% 4.00/4.35 % set(auto) -> set(auto_inference).
% 4.00/4.35 % set(auto) -> set(auto_setup).
% 4.00/4.35 % set(auto_setup) -> set(predicate_elim).
% 4.00/4.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.00/4.35 % set(auto) -> set(auto_limits).
% 4.00/4.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.00/4.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.00/4.35 % set(auto) -> set(auto_denials).
% 4.00/4.35 % set(auto) -> set(auto_process).
% 4.00/4.35 % set(auto2) -> assign(new_constants, 1).
% 4.00/4.35 % set(auto2) -> assign(fold_denial_max, 3).
% 4.00/4.35 % set(auto2) -> assign(max_weight, "200.000").
% 4.00/4.35 % set(auto2) -> assign(max_hours, 1).
% 4.00/4.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.00/4.35 % set(auto2) -> assign(max_seconds, 0).
% 4.00/4.35 % set(auto2) -> assign(max_minutes, 5).
% 4.00/4.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.00/4.35 % set(auto2) -> set(sort_initial_sos).
% 4.00/4.35 % set(auto2) -> assign(sos_limit, -1).
% 4.00/4.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.00/4.35 % set(auto2) -> assign(max_megs, 400).
% 4.00/4.35 % set(auto2) -> assign(stats, some).
% 4.00/4.35 % set(auto2) -> clear(echo_input).
% 4.00/4.35 % set(auto2) -> set(quiet).
% 4.00/4.35 % set(auto2) -> clear(print_initial_clauses).
% 4.00/4.35 % set(auto2) -> clear(print_given).
% 4.00/4.35 assign(lrs_ticks,-1).
% 4.00/4.35 assign(sos_limit,10000).
% 4.00/4.35 assign(order,kbo).
% 4.00/4.35 set(lex_order_vars).
% 4.00/4.35 clear(print_given).
% 4.00/4.35
% 4.00/4.35 % formulas(sos). % not echoed (20 formulas)
% 4.00/4.35
% 4.00/4.35 ============================== end of input ==========================
% 4.00/4.35
% 4.00/4.35 % From the command line: assign(max_seconds, 300).
% 4.00/4.35
% 4.00/4.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.00/4.35
% 4.00/4.35 % Formulas that are not ordinary clauses:
% 4.00/4.35
% 4.00/4.35 ============================== end of process non-clausal formulas ===
% 4.00/4.35
% 4.00/4.35 ============================== PROCESS INITIAL CLAUSES ===============
% 4.00/4.35
% 4.00/4.35 ============================== PREDICATE ELIMINATION =================
% 4.00/4.35
% 4.00/4.35 ============================== end predicate elimination =============
% 4.00/4.35
% 4.00/4.35 Auto_denials:
% 4.00/4.35 % copying label prove_p09b to answer in negative clause
% 4.00/4.35
% 4.00/4.35 Term ordering decisions:
% 4.00/4.35
% 4.00/4.35 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 4.00/4.35 Function symbol KB weights: identity=1. a=1. b=1. c=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 4.00/4.35
% 4.00/4.35 ============================== end of process initial clauses ========
% 4.00/4.35
% 4.00/4.35 ============================== CLAUSES FOR SEARCH ====================
% 4.00/4.35
% 4.00/4.35 ============================== end of clauses for search =============
% 4.00/4.35
% 4.00/4.35 ============================== SEARCH ================================
% 4.00/4.35
% 4.00/4.35 % Starting search at 0.01 seconds.
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=39.000, iters=3344
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=33.000, iters=3341
% 4.00/4.35
% 4.00/4.35 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 57 (0.00 of 1.00 sec).
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=32.000, iters=3421
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=31.000, iters=3382
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=30.000, iters=3404
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=29.000, iters=3366
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=28.000, iters=3394
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=27.000, iters=3405
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=26.000, iters=3420
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=25.000, iters=3340
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=24.000, iters=3363
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=23.000, iters=3338
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=22.000, iters=3353
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=21.000, iters=3343
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=20.000, iters=3352
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=19.000, iters=3350
% 4.00/4.35
% 4.00/4.35 Low Water (displace): id=5232, wt=46.000
% 4.00/4.35
% 4.00/4.35 Low Water (displace): id=4885, wt=45.000
% 4.00/4.35
% 4.00/4.35 Low Water (displace): id=5142, wt=43.000
% 4.00/4.35
% 4.00/4.35 Low Water (displace): id=6702, wt=41.000
% 4.00/4.35
% 4.00/4.35 Low Water (displace): id=6920, wt=39.000
% 4.00/4.35
% 4.00/4.35 Low Water (displace): id=13590, wt=18.000
% 4.00/4.35
% 4.00/4.35 Low Water (displace): id=13602, wt=17.000
% 4.00/4.35
% 4.00/4.35 Low Water (keep): wt=18.000, iters=3336
% 32.02/32.31
% 32.02/32.31 Low Water (displace): id=13770, wt=15.000
% 32.02/32.31
% 32.02/32.31 Low Water (displace): id=13773, wt=13.000
% 32.02/32.31
% 32.02/32.31 Low Water (keep): wt=17.000, iters=3344
% 32.02/32.31
% 32.02/32.31 Low Water (displace): id=14714, wt=11.000
% 32.02/32.31
% 32.02/32.31 Low Water (keep): wt=16.000, iters=3414
% 32.02/32.31
% 32.02/32.31 Low Water (keep): wt=15.000, iters=3350
% 32.02/32.31
% 32.02/32.31 Low Water (keep): wt=14.000, iters=3333
% 32.02/32.31
% 32.02/32.31 Low Water (keep): wt=13.000, iters=3333
% 32.02/32.31
% 32.02/32.31 ============================== PROOF =================================
% 32.02/32.31 % SZS status Unsatisfiable
% 32.02/32.31 % SZS output start Refutation
% 32.02/32.31
% 32.02/32.31 % Proof 1 at 30.49 (+ 0.85) seconds: prove_p09b.
% 32.02/32.31 % Length of proof is 95.
% 32.02/32.31 % Level of proof is 18.
% 32.02/32.31 % Maximum clause weight is 17.000.
% 32.02/32.31 % Given clauses 3605.
% 32.02/32.31
% 32.02/32.31 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 32.02/32.31 2 least_upper_bound(A,A) = A # label(idempotence_of_lub) # label(axiom). [assumption].
% 32.02/32.31 4 greatest_lower_bound(identity,a) = identity # label(p09b_1) # label(hypothesis). [assumption].
% 32.02/32.31 5 greatest_lower_bound(identity,b) = identity # label(p09b_2) # label(hypothesis). [assumption].
% 32.02/32.31 6 greatest_lower_bound(identity,c) = identity # label(p09b_3) # label(hypothesis). [assumption].
% 32.02/32.31 7 greatest_lower_bound(a,b) = identity # label(p09b_4) # label(hypothesis). [assumption].
% 32.02/32.31 8 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 32.02/32.31 9 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 32.02/32.31 10 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 32.02/32.31 11 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 32.02/32.31 13 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 32.02/32.31 14 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].
% 32.02/32.31 15 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(14),rewrite([9(4)])].
% 32.02/32.31 16 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].
% 32.02/32.31 17 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(16),rewrite([10(4)])].
% 32.02/32.31 18 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 32.02/32.31 19 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(18),flip(a)].
% 32.02/32.31 20 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 32.02/32.31 21 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(20),flip(a)].
% 32.02/32.31 22 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 32.02/32.31 23 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(22),flip(a)].
% 32.02/32.31 24 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 32.02/32.31 25 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(24),flip(a)].
% 32.02/32.31 26 greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) # label(prove_p09b) # label(negated_conjecture) # answer(prove_p09b). [assumption].
% 32.02/32.31 28 multiply(inverse(A),multiply(A,B)) = B. [para(8(a,1),13(a,1,1)),rewrite([1(2)]),flip(a)].
% 32.02/32.31 31 least_upper_bound(A,least_upper_bound(A,B)) = least_upper_bound(A,B). [para(17(a,1),2(a,1)),rewrite([10(1),10(2),17(2,R),2(1),10(3)])].
% 32.02/32.31 33 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(8(a,1),19(a,1,1))].
% 32.02/32.31 36 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(8(a,1),23(a,1,1)),rewrite([10(5)])].
% 32.02/32.31 40 greatest_lower_bound(A,multiply(a,A)) = A. [para(4(a,1),25(a,2,1)),rewrite([1(2),1(5)])].
% 32.02/32.31 41 greatest_lower_bound(A,multiply(b,A)) = A. [para(5(a,1),25(a,2,1)),rewrite([1(2),1(5)])].
% 32.02/32.31 42 greatest_lower_bound(A,multiply(c,A)) = A. [para(6(a,1),25(a,2,1)),rewrite([1(2),1(5)])].
% 32.02/32.31 43 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(8(a,1),25(a,1,1)),rewrite([9(5)])].
% 32.02/32.31 44 greatest_lower_bound(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(greatest_lower_bound(D,multiply(A,B)),C). [para(13(a,1),25(a,1,1)),rewrite([9(6)])].
% 32.02/32.31 45 greatest_lower_bound(multiply(A,B),multiply(C,multiply(D,B))) = multiply(greatest_lower_bound(A,multiply(C,D)),B). [para(13(a,1),25(a,1,2))].
% 32.02/32.31 47 greatest_lower_bound(A,greatest_lower_bound(B,multiply(a,A))) = greatest_lower_bound(A,B). [para(40(a,1),15(a,2,2)),rewrite([9(3),9(5)])].
% 32.02/32.31 48 greatest_lower_bound(A,greatest_lower_bound(B,multiply(b,A))) = greatest_lower_bound(A,B). [para(41(a,1),15(a,2,2)),rewrite([9(3),9(5)])].
% 32.02/32.31 49 greatest_lower_bound(A,greatest_lower_bound(B,multiply(c,A))) = greatest_lower_bound(A,B). [para(42(a,1),15(a,2,2)),rewrite([9(3),9(5)])].
% 32.02/32.31 51 multiply(inverse(inverse(A)),identity) = A. [para(8(a,1),28(a,1,2))].
% 32.02/32.31 54 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(28(a,1),21(a,1,1)),rewrite([9(6)]),flip(a)].
% 32.02/32.31 57 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(28(a,1),28(a,1,2))].
% 32.02/32.31 58 multiply(A,identity) = A. [back_rewrite(51),rewrite([57(4)])].
% 32.02/32.31 70 multiply(A,inverse(A)) = identity. [para(57(a,1),8(a,1))].
% 32.02/32.31 76 inverse(inverse(A)) = A. [para(57(a,1),58(a,1)),rewrite([58(2)]),flip(a)].
% 32.02/32.31 77 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(70(a,1),13(a,1)),flip(a)].
% 32.02/32.31 79 greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(B,inverse(A))). [para(70(a,1),21(a,1,1)),rewrite([9(5)])].
% 32.02/32.31 80 least_upper_bound(identity,multiply(A,inverse(B))) = multiply(least_upper_bound(A,B),inverse(B)). [para(70(a,1),23(a,1,1)),rewrite([10(5)])].
% 32.02/32.31 81 greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(A,B),inverse(B)). [para(70(a,1),25(a,1,1)),rewrite([9(5)])].
% 32.02/32.31 83 greatest_lower_bound(identity,inverse(b)) = inverse(b). [para(70(a,1),41(a,1,2)),rewrite([9(4)])].
% 32.02/32.31 84 greatest_lower_bound(identity,inverse(c)) = inverse(c). [para(70(a,1),42(a,1,2)),rewrite([9(4)])].
% 32.02/32.31 227 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(36(a,2),28(a,1,2))].
% 32.02/32.31 402 multiply(greatest_lower_bound(A,multiply(B,C)),inverse(C)) = greatest_lower_bound(B,multiply(A,inverse(C))). [para(70(a,1),44(a,1,1,2)),rewrite([58(2)]),flip(a)].
% 32.02/32.31 466 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(77(a,1),28(a,1,2)),rewrite([58(3)]),flip(a)].
% 32.02/32.31 485 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(466(a,1),28(a,1,2)),flip(a)].
% 32.02/32.31 506 greatest_lower_bound(A,multiply(a,greatest_lower_bound(A,B))) = greatest_lower_bound(A,multiply(a,B)). [para(21(a,1),47(a,1,2)),rewrite([9(2)])].
% 32.02/32.31 510 greatest_lower_bound(identity,greatest_lower_bound(a,inverse(b))) = inverse(b). [para(83(a,1),47(a,2)),rewrite([58(6),9(5)])].
% 32.02/32.31 511 greatest_lower_bound(identity,greatest_lower_bound(a,inverse(c))) = inverse(c). [para(84(a,1),47(a,2)),rewrite([58(6),9(5)])].
% 32.02/32.31 535 greatest_lower_bound(A,multiply(b,greatest_lower_bound(A,B))) = greatest_lower_bound(A,multiply(b,B)). [para(21(a,1),48(a,1,2)),rewrite([9(2)])].
% 32.02/32.31 561 greatest_lower_bound(a,inverse(b)) = inverse(b). [para(510(a,1),15(a,2)),rewrite([9(5),83(5)])].
% 32.02/32.31 563 greatest_lower_bound(A,multiply(c,greatest_lower_bound(A,B))) = greatest_lower_bound(A,multiply(c,B)). [para(21(a,1),49(a,1,2)),rewrite([9(2)])].
% 32.02/32.31 579 least_upper_bound(a,inverse(b)) = a. [para(561(a,1),11(a,1,2))].
% 32.02/32.31 585 least_upper_bound(identity,multiply(a,b)) = multiply(a,b). [para(579(a,1),36(a,2,1))].
% 32.02/32.31 590 greatest_lower_bound(a,inverse(c)) = inverse(c). [para(511(a,1),15(a,2)),rewrite([9(5),84(5)])].
% 32.02/32.31 622 greatest_lower_bound(identity,multiply(a,c)) = identity. [para(590(a,1),43(a,2,1)),rewrite([8(9)])].
% 32.02/32.31 627 greatest_lower_bound(A,multiply(a,multiply(c,A))) = A. [para(622(a,1),25(a,2,1)),rewrite([1(2),13(4),1(7)])].
% 32.02/32.31 665 greatest_lower_bound(c,inverse(a)) = inverse(a). [para(622(a,1),54(a,1,2)),rewrite([58(4),58(7)]),flip(a)].
% 32.02/32.31 677 greatest_lower_bound(identity,multiply(c,a)) = identity. [para(665(a,1),43(a,2,1)),rewrite([8(9)])].
% 32.02/32.31 751 greatest_lower_bound(A,multiply(A,multiply(c,a))) = A. [para(677(a,1),21(a,2,2)),rewrite([58(2),58(7)])].
% 32.02/32.31 1280 greatest_lower_bound(A,greatest_lower_bound(B,multiply(a,multiply(c,A)))) = greatest_lower_bound(A,B). [para(627(a,1),15(a,2,2)),rewrite([9(5),9(7)])].
% 32.02/32.31 1310 least_upper_bound(identity,multiply(A,inverse(least_upper_bound(A,B)))) = identity. [para(31(a,1),80(a,2,1)),rewrite([70(9)])].
% 32.02/32.31 1366 greatest_lower_bound(identity,multiply(a,inverse(b))) = inverse(b). [para(7(a,1),81(a,2,1)),rewrite([1(10)])].
% 32.02/32.31 1446 greatest_lower_bound(A,greatest_lower_bound(B,multiply(A,multiply(c,a)))) = greatest_lower_bound(A,B). [para(751(a,1),15(a,2,2)),rewrite([9(5),9(7)])].
% 32.02/32.31 1759 greatest_lower_bound(inverse(a),inverse(b)) = multiply(inverse(a),inverse(b)). [para(1366(a,1),54(a,1,2)),rewrite([58(11),9(10)]),flip(a)].
% 32.02/32.31 1760 greatest_lower_bound(identity,multiply(b,inverse(a))) = inverse(a). [para(1366(a,1),81(a,2,1)),rewrite([485(7),76(5),1(7),485(13),76(11),28(13)])].
% 32.02/32.31 1799 multiply(inverse(b),inverse(a)) = multiply(inverse(a),inverse(b)). [para(1760(a,1),54(a,1,2)),rewrite([58(11),1759(10)])].
% 32.02/32.31 1800 multiply(b,multiply(inverse(a),inverse(b))) = inverse(a). [para(1760(a,1),79(a,1)),rewrite([1759(8)]),flip(a)].
% 32.02/32.31 2326 multiply(inverse(greatest_lower_bound(A,multiply(B,C))),B) = inverse(greatest_lower_bound(C,multiply(inverse(B),A))). [para(54(a,1),485(a,1,1)),rewrite([76(9)]),flip(a)].
% 32.02/32.31 3058 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),A)) = identity. [para(33(a,1),1310(a,1,2,2,1)),rewrite([485(6),76(6),1(6)])].
% 32.02/32.31 4274 multiply(b,multiply(a,inverse(b))) = a. [para(1800(a,1),485(a,1,1)),rewrite([76(3),485(7),76(4),76(5),13(7)]),flip(a)].
% 32.02/32.31 4281 multiply(inverse(b),a) = multiply(a,inverse(b)). [para(4274(a,1),28(a,1,2))].
% 32.02/32.31 5462 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),B)) = identity. [para(10(a,1),3058(a,1,2,1,1))].
% 32.02/32.31 9161 inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(B,A)))) = A. [para(5462(a,1),227(a,1,2)),rewrite([10(4),58(7)])].
% 32.02/32.31 9242 multiply(b,a) = multiply(a,b). [para(585(a,1),9161(a,1,1,2,1)),rewrite([485(4),1799(5),485(9),1799(10),2(11),485(6),76(3),76(4)])].
% 32.02/32.31 9286 multiply(b,multiply(a,A)) = multiply(a,multiply(b,A)). [para(9242(a,1),13(a,1,1)),rewrite([13(4)]),flip(a)].
% 32.02/32.31 19711 greatest_lower_bound(a,multiply(b,b)) = identity. [para(7(a,1),535(a,1,2,2)),rewrite([58(4),7(3)]),flip(a)].
% 32.02/32.31 19989 greatest_lower_bound(b,multiply(a,inverse(b))) = inverse(b). [para(19711(a,1),54(a,1,2)),rewrite([58(4),4281(7)]),flip(a)].
% 32.02/32.31 20027 greatest_lower_bound(b,multiply(a,multiply(a,inverse(b)))) = inverse(b). [para(19989(a,1),506(a,1,2,2)),rewrite([19989(6)]),flip(a)].
% 32.02/32.31 20538 greatest_lower_bound(a,multiply(c,b)) = greatest_lower_bound(a,c). [para(7(a,1),563(a,1,2,2)),rewrite([58(4)]),flip(a)].
% 32.02/32.31 20826 greatest_lower_bound(c,multiply(a,inverse(b))) = multiply(greatest_lower_bound(a,c),inverse(b)). [para(20538(a,1),402(a,1,1)),flip(a)].
% 32.02/32.31 28917 greatest_lower_bound(b,multiply(a,a)) = identity. [para(20027(a,1),535(a,1,2,2)),rewrite([70(5),9(3),5(3),9286(10),9286(9),70(8),58(6)]),flip(a)].
% 32.02/32.31 28926 greatest_lower_bound(b,multiply(a,greatest_lower_bound(a,c))) = identity. [para(28917(a,1),1280(a,2)),rewrite([21(10),20538(7)])].
% 32.02/32.31 28944 greatest_lower_bound(a,multiply(b,inverse(greatest_lower_bound(a,c)))) = inverse(greatest_lower_bound(a,c)). [para(28926(a,1),402(a,1,1)),rewrite([1(6)]),flip(a)].
% 32.02/32.31 29271 greatest_lower_bound(b,multiply(greatest_lower_bound(a,multiply(b,c)),a)) = identity. [para(28917(a,1),1446(a,2)),rewrite([45(10)])].
% 32.02/32.31 30027 inverse(greatest_lower_bound(a,multiply(b,c))) = inverse(greatest_lower_bound(a,c)). [para(29271(a,1),54(a,1,2)),rewrite([58(8),2326(15),4281(12),20826(13),485(14),76(10),28944(14)])].
% 32.02/32.31 30633 greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c). [para(30027(a,1),76(a,1,1)),rewrite([76(5)]),flip(a)].
% 32.02/32.31 30634 $F # answer(prove_p09b). [resolve(30633,a,26,a)].
% 32.02/32.31
% 32.02/32.31 % SZS output end Refutation
% 32.02/32.31 ============================== end of proof ==========================
% 32.02/32.31
% 32.02/32.31 ============================== STATISTICS ============================
% 32.02/32.31
% 32.02/32.31 Given=3605. Generated=1608092. Kept=30627. proofs=1.
% 32.02/32.31 Usable=3230. Sos=9897. Demods=12697. Limbo=0, Disabled=17519. Hints=0.
% 32.02/32.31 Megabytes=21.43.
% 32.02/32.31 User_CPU=30.49, System_CPU=0.85, Wall_clock=31.
% 32.02/32.31
% 32.02/32.31 ============================== end of statistics =====================
% 32.02/32.31
% 32.02/32.31 ============================== end of search =========================
% 32.02/32.31
% 32.02/32.31 THEOREM PROVED
% 32.02/32.31 % SZS status Unsatisfiable
% 32.02/32.31
% 32.02/32.31 Exiting with 1 proof.
% 32.02/32.31
% 32.02/32.31 Process 27546 exit (max_proofs) Mon Jun 13 08:20:40 2022
% 32.02/32.31 Prover9 interrupted
%------------------------------------------------------------------------------