TSTP Solution File: GRP178-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP178-1 : 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 11:17:56 EDT 2022
% Result : Unsatisfiable 120.05s 120.36s
% Output : Refutation 120.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP178-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n013.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 07:23:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 4.17/4.44 ============================== Prover9 ===============================
% 4.17/4.44 Prover9 (32) version 2009-11A, November 2009.
% 4.17/4.44 Process 4371 was started by sandbox2 on n013.cluster.edu,
% 4.17/4.44 Mon Jun 13 07:23:14 2022
% 4.17/4.44 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4217_n013.cluster.edu".
% 4.17/4.44 ============================== end of head ===========================
% 4.17/4.44
% 4.17/4.44 ============================== INPUT =================================
% 4.17/4.44
% 4.17/4.44 % Reading from file /tmp/Prover9_4217_n013.cluster.edu
% 4.17/4.44
% 4.17/4.44 set(prolog_style_variables).
% 4.17/4.44 set(auto2).
% 4.17/4.44 % set(auto2) -> set(auto).
% 4.17/4.44 % set(auto) -> set(auto_inference).
% 4.17/4.44 % set(auto) -> set(auto_setup).
% 4.17/4.44 % set(auto_setup) -> set(predicate_elim).
% 4.17/4.44 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.17/4.44 % set(auto) -> set(auto_limits).
% 4.17/4.44 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.17/4.44 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.17/4.44 % set(auto) -> set(auto_denials).
% 4.17/4.44 % set(auto) -> set(auto_process).
% 4.17/4.44 % set(auto2) -> assign(new_constants, 1).
% 4.17/4.44 % set(auto2) -> assign(fold_denial_max, 3).
% 4.17/4.44 % set(auto2) -> assign(max_weight, "200.000").
% 4.17/4.44 % set(auto2) -> assign(max_hours, 1).
% 4.17/4.44 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.17/4.44 % set(auto2) -> assign(max_seconds, 0).
% 4.17/4.44 % set(auto2) -> assign(max_minutes, 5).
% 4.17/4.44 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.17/4.44 % set(auto2) -> set(sort_initial_sos).
% 4.17/4.44 % set(auto2) -> assign(sos_limit, -1).
% 4.17/4.44 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.17/4.44 % set(auto2) -> assign(max_megs, 400).
% 4.17/4.44 % set(auto2) -> assign(stats, some).
% 4.17/4.44 % set(auto2) -> clear(echo_input).
% 4.17/4.44 % set(auto2) -> set(quiet).
% 4.17/4.44 % set(auto2) -> clear(print_initial_clauses).
% 4.17/4.44 % set(auto2) -> clear(print_given).
% 4.17/4.44 assign(lrs_ticks,-1).
% 4.17/4.44 assign(sos_limit,10000).
% 4.17/4.44 assign(order,kbo).
% 4.17/4.44 set(lex_order_vars).
% 4.17/4.44 clear(print_given).
% 4.17/4.44
% 4.17/4.44 % formulas(sos). % not echoed (20 formulas)
% 4.17/4.44
% 4.17/4.44 ============================== end of input ==========================
% 4.17/4.44
% 4.17/4.44 % From the command line: assign(max_seconds, 300).
% 4.17/4.44
% 4.17/4.44 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.17/4.44
% 4.17/4.44 % Formulas that are not ordinary clauses:
% 4.17/4.44
% 4.17/4.44 ============================== end of process non-clausal formulas ===
% 4.17/4.44
% 4.17/4.44 ============================== PROCESS INITIAL CLAUSES ===============
% 4.17/4.44
% 4.17/4.44 ============================== PREDICATE ELIMINATION =================
% 4.17/4.44
% 4.17/4.44 ============================== end predicate elimination =============
% 4.17/4.44
% 4.17/4.44 Auto_denials:
% 4.17/4.44 % copying label prove_p09a to answer in negative clause
% 4.17/4.44
% 4.17/4.44 Term ordering decisions:
% 4.17/4.44
% 4.17/4.44 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 4.17/4.44 Function symbol KB weights: identity=1. a=1. b=1. c=1. multiply=1. least_upper_bound=1. greatest_lower_bound=1. inverse=0.
% 4.17/4.44
% 4.17/4.44 ============================== end of process initial clauses ========
% 4.17/4.44
% 4.17/4.44 ============================== CLAUSES FOR SEARCH ====================
% 4.17/4.44
% 4.17/4.44 ============================== end of clauses for search =============
% 4.17/4.44
% 4.17/4.44 ============================== SEARCH ================================
% 4.17/4.44
% 4.17/4.44 % Starting search at 0.01 seconds.
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=39.000, iters=3426
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=37.000, iters=3382
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=33.000, iters=3478
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=32.000, iters=3424
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=31.000, iters=3388
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=30.000, iters=3370
% 4.17/4.44
% 4.17/4.44 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 72 (0.00 of 1.02 sec).
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=28.000, iters=3433
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=27.000, iters=3376
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=26.000, iters=3375
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=25.000, iters=3343
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=24.000, iters=3448
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=23.000, iters=3342
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=22.000, iters=3355
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=21.000, iters=3357
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=20.000, iters=3339
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=19.000, iters=3340
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=18.000, iters=3335
% 4.17/4.44
% 4.17/4.44 Low Water (displace): id=4264, wt=46.000
% 4.17/4.44
% 4.17/4.44 Low Water (displace): id=4126, wt=45.000
% 4.17/4.44
% 4.17/4.44 Low Water (displace): id=4190, wt=43.000
% 4.17/4.44
% 4.17/4.44 Low Water (displace): id=6814, wt=41.000
% 4.17/4.44
% 4.17/4.44 Low Water (displace): id=4191, wt=39.000
% 4.17/4.44
% 4.17/4.44 Low Water (displace): id=13510, wt=17.000
% 4.17/4.44
% 4.17/4.44 Low Water (keep): wt=17.000, iters=3336
% 120.05/120.36
% 120.05/120.36 Low Water (displace): id=13690, wt=15.000
% 120.05/120.36
% 120.05/120.36 Low Water (displace): id=13703, wt=14.000
% 120.05/120.36
% 120.05/120.36 Low Water (displace): id=13742, wt=13.000
% 120.05/120.36
% 120.05/120.36 Low Water (displace): id=14496, wt=12.000
% 120.05/120.36
% 120.05/120.36 Low Water (displace): id=14570, wt=11.000
% 120.05/120.36
% 120.05/120.36 Low Water (keep): wt=16.000, iters=3339
% 120.05/120.36
% 120.05/120.36 Low Water (keep): wt=15.000, iters=3353
% 120.05/120.36
% 120.05/120.36 Low Water (displace): id=20253, wt=10.000
% 120.05/120.36
% 120.05/120.36 Low Water (keep): wt=14.000, iters=3333
% 120.05/120.36
% 120.05/120.36 Low Water (keep): wt=13.000, iters=3336
% 120.05/120.36
% 120.05/120.36 ============================== PROOF =================================
% 120.05/120.36 % SZS status Unsatisfiable
% 120.05/120.36 % SZS output start Refutation
% 120.05/120.36
% 120.05/120.36 % Proof 1 at 115.92 (+ 3.48) seconds: prove_p09a.
% 120.05/120.36 % Length of proof is 110.
% 120.05/120.36 % Level of proof is 17.
% 120.05/120.36 % Maximum clause weight is 22.000.
% 120.05/120.36 % Given clauses 7932.
% 120.05/120.36
% 120.05/120.36 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 120.05/120.36 4 least_upper_bound(identity,a) = a # label(p09a_1) # label(hypothesis). [assumption].
% 120.05/120.36 5 least_upper_bound(identity,b) = b # label(p09a_2) # label(hypothesis). [assumption].
% 120.05/120.36 6 least_upper_bound(identity,c) = c # label(p09a_3) # label(hypothesis). [assumption].
% 120.05/120.36 7 greatest_lower_bound(a,b) = identity # label(p09a_4) # label(hypothesis). [assumption].
% 120.05/120.36 8 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 120.05/120.36 9 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 120.05/120.36 10 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 120.05/120.36 11 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 120.05/120.36 12 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 120.05/120.36 13 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 120.05/120.36 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].
% 120.05/120.36 15 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(14),rewrite([9(4)])].
% 120.05/120.36 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].
% 120.05/120.36 17 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(16),rewrite([10(4)])].
% 120.05/120.36 18 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 120.05/120.36 19 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(18),flip(a)].
% 120.05/120.36 20 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 120.05/120.36 21 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(20),flip(a)].
% 120.05/120.36 22 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 120.05/120.36 23 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(22),flip(a)].
% 120.05/120.36 24 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 120.05/120.36 25 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(24),flip(a)].
% 120.05/120.36 26 greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) # label(prove_p09a) # label(negated_conjecture) # answer(prove_p09a). [assumption].
% 120.05/120.36 27 greatest_lower_bound(identity,a) = identity. [para(4(a,1),12(a,1,2))].
% 120.05/120.36 28 greatest_lower_bound(identity,b) = identity. [para(5(a,1),12(a,1,2))].
% 120.05/120.36 29 greatest_lower_bound(identity,c) = identity. [para(6(a,1),12(a,1,2))].
% 120.05/120.36 30 multiply(inverse(A),multiply(A,B)) = B. [para(8(a,1),13(a,1,1)),rewrite([1(2)]),flip(a)].
% 120.05/120.36 34 least_upper_bound(A,least_upper_bound(B,greatest_lower_bound(A,C))) = least_upper_bound(A,B). [para(11(a,1),17(a,2,2)),rewrite([10(2),10(4)])].
% 120.05/120.36 35 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(8(a,1),19(a,1,1))].
% 120.05/120.36 36 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(8(a,1),21(a,1,1))].
% 120.05/120.36 37 least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A). [para(1(a,1),23(a,1,1)),rewrite([10(4)])].
% 120.05/120.36 38 least_upper_bound(A,multiply(a,A)) = multiply(a,A). [para(4(a,1),23(a,2,1)),rewrite([1(2)])].
% 120.05/120.36 40 least_upper_bound(A,multiply(c,A)) = multiply(c,A). [para(6(a,1),23(a,2,1)),rewrite([1(2)])].
% 120.05/120.36 41 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)])].
% 120.05/120.36 45 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)])].
% 120.05/120.36 46 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)])].
% 120.05/120.36 48 greatest_lower_bound(A,multiply(a,A)) = A. [para(27(a,1),25(a,2,1)),rewrite([1(2),1(5)])].
% 120.05/120.36 49 greatest_lower_bound(A,multiply(b,A)) = A. [para(28(a,1),25(a,2,1)),rewrite([1(2),1(5)])].
% 120.05/120.36 50 greatest_lower_bound(A,multiply(c,A)) = A. [para(29(a,1),25(a,2,1)),rewrite([1(2),1(5)])].
% 120.05/120.36 51 greatest_lower_bound(A,greatest_lower_bound(B,multiply(a,A))) = greatest_lower_bound(A,B). [para(48(a,1),15(a,2,2)),rewrite([9(3),9(5)])].
% 120.05/120.36 52 greatest_lower_bound(A,greatest_lower_bound(B,multiply(b,A))) = greatest_lower_bound(A,B). [para(49(a,1),15(a,2,2)),rewrite([9(3),9(5)])].
% 120.05/120.36 54 multiply(inverse(inverse(A)),identity) = A. [para(8(a,1),30(a,1,2))].
% 120.05/120.36 57 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(30(a,1),21(a,1,1)),rewrite([9(6)]),flip(a)].
% 120.05/120.36 60 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(30(a,1),30(a,1,2))].
% 120.05/120.36 61 multiply(A,identity) = A. [back_rewrite(54),rewrite([60(4)])].
% 120.05/120.36 62 inverse(identity) = identity. [para(61(a,1),8(a,1))].
% 120.05/120.36 63 least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(B,identity)). [para(61(a,1),19(a,1,1)),rewrite([10(4)])].
% 120.05/120.36 64 greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(B,identity)). [para(61(a,1),21(a,1,1)),rewrite([9(4)])].
% 120.05/120.36 75 least_upper_bound(A,least_upper_bound(B,multiply(c,A))) = least_upper_bound(B,multiply(c,A)). [para(40(a,1),17(a,2,2)),rewrite([10(3)])].
% 120.05/120.36 81 least_upper_bound(multiply(A,B),least_upper_bound(multiply(C,B),greatest_lower_bound(D,multiply(A,B)))) = multiply(least_upper_bound(A,C),B). [para(23(a,1),34(a,2)),rewrite([9(4)])].
% 120.05/120.36 82 multiply(A,inverse(A)) = identity. [para(60(a,1),8(a,1))].
% 120.05/120.36 87 multiply(A,multiply(inverse(A),B)) = B. [para(60(a,1),30(a,1))].
% 120.05/120.36 88 inverse(inverse(A)) = A. [para(60(a,1),61(a,1)),rewrite([61(2)]),flip(a)].
% 120.05/120.36 89 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(82(a,1),13(a,1)),flip(a)].
% 120.05/120.36 90 least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))). [para(82(a,1),19(a,1,1)),rewrite([10(5)])].
% 120.05/120.36 91 greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(B,inverse(A))). [para(82(a,1),21(a,1,1)),rewrite([9(5)])].
% 120.05/120.36 92 least_upper_bound(identity,multiply(A,inverse(B))) = multiply(least_upper_bound(A,B),inverse(B)). [para(82(a,1),23(a,1,1)),rewrite([10(5)])].
% 120.05/120.36 93 greatest_lower_bound(identity,multiply(A,inverse(B))) = multiply(greatest_lower_bound(A,B),inverse(B)). [para(82(a,1),25(a,1,1)),rewrite([9(5)])].
% 120.05/120.36 96 greatest_lower_bound(identity,inverse(c)) = inverse(c). [para(82(a,1),50(a,1,2)),rewrite([9(4)])].
% 120.05/120.36 97 least_upper_bound(identity,inverse(a)) = identity. [para(82(a,1),38(a,1,2)),rewrite([10(4),82(8)])].
% 120.05/120.36 108 least_upper_bound(A,multiply(A,multiply(inverse(B),C))) = multiply(A,multiply(inverse(B),least_upper_bound(B,C))). [para(35(a,1),19(a,2,2)),rewrite([61(2)])].
% 120.05/120.36 157 multiply(inverse(A),greatest_lower_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)). [para(61(a,1),36(a,1,2)),flip(a)].
% 120.05/120.36 162 greatest_lower_bound(A,multiply(A,inverse(c))) = multiply(A,inverse(c)). [para(96(a,1),21(a,2,2)),rewrite([61(2)])].
% 120.05/120.36 166 multiply(A,least_upper_bound(B,multiply(inverse(A),C))) = least_upper_bound(C,multiply(A,B)). [para(87(a,1),19(a,1,1)),rewrite([10(5)]),flip(a)].
% 120.05/120.36 180 least_upper_bound(A,least_upper_bound(B,multiply(C,A))) = least_upper_bound(B,multiply(least_upper_bound(C,identity),A)). [para(37(a,1),17(a,2,2)),rewrite([10(2)])].
% 120.05/120.36 394 multiply(greatest_lower_bound(A,multiply(B,inverse(C))),C) = greatest_lower_bound(B,multiply(A,C)). [para(8(a,1),46(a,1,1,2)),rewrite([61(2)]),flip(a)].
% 120.05/120.36 404 multiply(greatest_lower_bound(A,multiply(B,C)),inverse(C)) = greatest_lower_bound(B,multiply(A,inverse(C))). [para(82(a,1),46(a,1,1,2)),rewrite([61(2)]),flip(a)].
% 120.05/120.36 418 greatest_lower_bound(multiply(A,least_upper_bound(identity,multiply(B,C))),multiply(D,C)) = multiply(greatest_lower_bound(D,multiply(A,least_upper_bound(B,inverse(C)))),C). [para(41(a,2),46(a,1,1,2))].
% 120.05/120.36 467 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(89(a,1),30(a,1,2)),rewrite([61(3)]),flip(a)].
% 120.05/120.36 485 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(467(a,1),30(a,1,2)),flip(a)].
% 120.05/120.36 542 greatest_lower_bound(identity,greatest_lower_bound(b,inverse(c))) = inverse(c). [para(96(a,1),52(a,2)),rewrite([61(6),9(5)])].
% 120.05/120.36 919 greatest_lower_bound(b,inverse(c)) = inverse(c). [para(542(a,1),15(a,2)),rewrite([9(5),96(5)])].
% 120.05/120.36 923 greatest_lower_bound(identity,multiply(b,c)) = identity. [para(919(a,1),45(a,2,1)),rewrite([8(9)])].
% 120.05/120.36 931 greatest_lower_bound(identity,greatest_lower_bound(a,multiply(b,c))) = identity. [para(923(a,1),51(a,2)),rewrite([61(7),9(6)])].
% 120.05/120.36 1299 least_upper_bound(greatest_lower_bound(A,multiply(B,C)),multiply(least_upper_bound(B,D),C)) = multiply(least_upper_bound(B,D),C). [para(81(a,1),17(a,1)),rewrite([23(7)]),flip(a)].
% 120.05/120.36 1407 multiply(least_upper_bound(A,inverse(B)),B) = multiply(A,least_upper_bound(B,inverse(A))). [para(90(a,1),41(a,1)),flip(a)].
% 120.05/120.36 1428 least_upper_bound(identity,greatest_lower_bound(A,multiply(A,B))) = multiply(A,least_upper_bound(greatest_lower_bound(B,identity),inverse(A))). [para(64(a,2),90(a,1,2))].
% 120.05/120.36 1549 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(92(a,1),12(a,1,2))].
% 120.05/120.36 1577 multiply(greatest_lower_bound(A,least_upper_bound(B,A)),inverse(A)) = identity. [para(92(a,2),45(a,1,2)),rewrite([12(6),88(4),9(3)]),flip(a)].
% 120.05/120.36 1633 greatest_lower_bound(identity,multiply(a,inverse(b))) = inverse(b). [para(7(a,1),93(a,2,1)),rewrite([1(10)])].
% 120.05/120.36 1634 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(93(a,1),11(a,1,2))].
% 120.05/120.36 1821 greatest_lower_bound(inverse(a),inverse(b)) = multiply(inverse(a),inverse(b)). [para(1633(a,1),57(a,1,2)),rewrite([61(11),9(10)]),flip(a)].
% 120.05/120.36 1824 greatest_lower_bound(identity,multiply(b,inverse(a))) = inverse(a). [para(1633(a,1),93(a,2,1)),rewrite([485(7),88(5),1(7),485(13),88(11),30(13)])].
% 120.05/120.36 2283 multiply(b,multiply(inverse(a),inverse(b))) = inverse(a). [para(1824(a,1),91(a,1)),rewrite([1821(8)]),flip(a)].
% 120.05/120.36 4367 least_upper_bound(A,multiply(A,greatest_lower_bound(identity,inverse(B)))) = A. [para(157(a,1),108(a,1,2,2)),rewrite([11(9),8(7),61(7)])].
% 120.05/120.36 4548 greatest_lower_bound(A,greatest_lower_bound(B,multiply(A,inverse(c)))) = greatest_lower_bound(B,multiply(A,inverse(c))). [para(162(a,1),15(a,2,2)),rewrite([9(4)])].
% 120.05/120.36 5318 least_upper_bound(identity,inverse(greatest_lower_bound(a,multiply(b,c)))) = identity. [para(931(a,1),1634(a,1,2,1)),rewrite([1(9)])].
% 120.05/120.36 6385 multiply(b,multiply(a,inverse(b))) = a. [para(2283(a,1),485(a,1,1)),rewrite([88(3),485(7),88(4),88(5),13(7)]),flip(a)].
% 120.05/120.36 6393 multiply(inverse(b),a) = multiply(a,inverse(b)). [para(6385(a,1),30(a,1,2))].
% 120.05/120.36 6432 multiply(inverse(a),b) = multiply(b,inverse(a)). [para(6393(a,1),485(a,1,1)),rewrite([485(5),88(3),88(9)]),flip(a)].
% 120.05/120.36 6457 multiply(a,greatest_lower_bound(A,multiply(b,inverse(a)))) = greatest_lower_bound(b,multiply(a,A)). [para(6432(a,1),57(a,1,2,2)),rewrite([88(3),88(11)])].
% 120.05/120.36 6547 least_upper_bound(identity,multiply(least_upper_bound(inverse(A),identity),B)) = least_upper_bound(B,multiply(inverse(A),least_upper_bound(B,A))). [para(35(a,1),180(a,1,2)),rewrite([10(2)]),flip(a)].
% 120.05/120.37 6618 least_upper_bound(c,greatest_lower_bound(identity,inverse(A))) = c. [para(4367(a,1),75(a,1,2)),rewrite([10(5),63(12),10(11),11(11),61(8)])].
% 120.05/120.37 6759 least_upper_bound(c,greatest_lower_bound(identity,multiply(inverse(A),inverse(B)))) = c. [para(485(a,1),6618(a,1,2,2))].
% 120.05/120.37 8753 least_upper_bound(A,multiply(A,inverse(greatest_lower_bound(a,multiply(b,c))))) = A. [para(5318(a,1),19(a,2,2)),rewrite([61(2),61(10)])].
% 120.05/120.37 14789 multiply(A,inverse(greatest_lower_bound(B,multiply(C,A)))) = inverse(greatest_lower_bound(C,multiply(B,inverse(A)))). [para(404(a,1),485(a,1,1)),rewrite([88(6)]),flip(a)].
% 120.05/120.37 17235 least_upper_bound(c,greatest_lower_bound(identity,multiply(A,inverse(B)))) = c. [para(88(a,1),6759(a,1,2,2,1))].
% 120.05/120.37 17252 least_upper_bound(c,multiply(greatest_lower_bound(A,B),inverse(B))) = c. [para(45(a,1),17235(a,1,2)),rewrite([88(3)])].
% 120.05/120.37 17412 least_upper_bound(c,multiply(A,inverse(least_upper_bound(B,A)))) = c. [para(1549(a,1),17252(a,1,2,1)),rewrite([485(6),88(4),1(6)])].
% 120.05/120.37 18036 least_upper_bound(c,inverse(greatest_lower_bound(a,multiply(b,c)))) = c. [para(5318(a,1),17412(a,1,2,2,1)),rewrite([62(9),61(9)])].
% 120.05/120.37 28037 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(97(a,1),1299(a,1,2,1)),rewrite([1(2),1(3),10(2),97(6),1(4)])].
% 120.05/120.37 28289 greatest_lower_bound(identity,multiply(A,least_upper_bound(inverse(A),inverse(B)))) = identity. [para(1407(a,1),93(a,1,2)),rewrite([10(4),88(8),9(8),1577(10)])].
% 120.05/120.37 29210 greatest_lower_bound(A,least_upper_bound(B,A)) = A. [para(28289(a,1),418(a,2,1)),rewrite([166(5),61(2),10(1),1(3),9(2),1(4)])].
% 120.05/120.37 30683 least_upper_bound(c,inverse(greatest_lower_bound(b,multiply(a,inverse(c))))) = c. [para(8753(a,1),75(a,1,2)),rewrite([10(8),18036(8),14789(10)]),flip(a)].
% 120.05/120.37 33698 least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(b,multiply(a,A)))) = identity. [para(6457(a,1),1428(a,1,2,2)),rewrite([9(16),15(16,R),9(15),1824(15),10(15),28037(15),82(12)])].
% 120.05/120.37 33703 least_upper_bound(identity,greatest_lower_bound(b,multiply(a,inverse(c)))) = identity. [para(4548(a,1),33698(a,1,2))].
% 120.05/120.37 33943 least_upper_bound(c,greatest_lower_bound(a,multiply(b,c))) = c. [para(30683(a,1),6547(a,2,2,2)),rewrite([88(9),10(9),33703(9),1(4),6(3),88(10),394(10)]),flip(a)].
% 120.05/120.37 33948 greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c). [para(33943(a,1),29210(a,1,2)),rewrite([9(7),52(7),9(3)]),flip(a)].
% 120.05/120.37 33949 $F # answer(prove_p09a). [resolve(33948,a,26,a)].
% 120.05/120.37
% 120.05/120.37 % SZS output end Refutation
% 120.05/120.37 ============================== end of proof ==========================
% 120.05/120.37
% 120.05/120.37 ============================== STATISTICS ============================
% 120.05/120.37
% 120.05/120.37 Given=7932. Generated=6641264. Kept=33942. proofs=1.
% 120.05/120.37 Usable=7251. Sos=8652. Demods=15484. Limbo=4, Disabled=18054. Hints=0.
% 120.05/120.37 Megabytes=23.50.
% 120.05/120.37 User_CPU=115.93, System_CPU=3.48, Wall_clock=120.
% 120.05/120.37
% 120.05/120.37 ============================== end of statistics =====================
% 120.05/120.37
% 120.05/120.37 ============================== end of search =========================
% 120.05/120.37
% 120.05/120.37 THEOREM PROVED
% 120.05/120.37 % SZS status Unsatisfiable
% 120.05/120.37
% 120.05/120.37 Exiting with 1 proof.
% 120.05/120.37
% 120.05/120.37 Process 4371 exit (max_proofs) Mon Jun 13 07:25:14 2022
% 120.05/120.37 Prover9 interrupted
%------------------------------------------------------------------------------