TSTP Solution File: GRP170-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP170-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 11:17:52 EDT 2022
% Result : Unsatisfiable 5.38s 5.70s
% Output : Refutation 5.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP170-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 09:57:18 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.51/3.77 ============================== Prover9 ===============================
% 3.51/3.77 Prover9 (32) version 2009-11A, November 2009.
% 3.51/3.77 Process 13681 was started by sandbox on n011.cluster.edu,
% 3.51/3.77 Mon Jun 13 09:57:19 2022
% 3.51/3.77 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13528_n011.cluster.edu".
% 3.51/3.77 ============================== end of head ===========================
% 3.51/3.77
% 3.51/3.77 ============================== INPUT =================================
% 3.51/3.77
% 3.51/3.77 % Reading from file /tmp/Prover9_13528_n011.cluster.edu
% 3.51/3.77
% 3.51/3.77 set(prolog_style_variables).
% 3.51/3.77 set(auto2).
% 3.51/3.77 % set(auto2) -> set(auto).
% 3.51/3.77 % set(auto) -> set(auto_inference).
% 3.51/3.77 % set(auto) -> set(auto_setup).
% 3.51/3.77 % set(auto_setup) -> set(predicate_elim).
% 3.51/3.77 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.51/3.77 % set(auto) -> set(auto_limits).
% 3.51/3.77 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.51/3.77 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.51/3.77 % set(auto) -> set(auto_denials).
% 3.51/3.77 % set(auto) -> set(auto_process).
% 3.51/3.77 % set(auto2) -> assign(new_constants, 1).
% 3.51/3.77 % set(auto2) -> assign(fold_denial_max, 3).
% 3.51/3.77 % set(auto2) -> assign(max_weight, "200.000").
% 3.51/3.77 % set(auto2) -> assign(max_hours, 1).
% 3.51/3.77 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.51/3.77 % set(auto2) -> assign(max_seconds, 0).
% 3.51/3.77 % set(auto2) -> assign(max_minutes, 5).
% 3.51/3.77 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.51/3.77 % set(auto2) -> set(sort_initial_sos).
% 3.51/3.77 % set(auto2) -> assign(sos_limit, -1).
% 3.51/3.77 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.51/3.77 % set(auto2) -> assign(max_megs, 400).
% 3.51/3.77 % set(auto2) -> assign(stats, some).
% 3.51/3.77 % set(auto2) -> clear(echo_input).
% 3.51/3.77 % set(auto2) -> set(quiet).
% 3.51/3.77 % set(auto2) -> clear(print_initial_clauses).
% 3.51/3.77 % set(auto2) -> clear(print_given).
% 3.51/3.77 assign(lrs_ticks,-1).
% 3.51/3.77 assign(sos_limit,10000).
% 3.51/3.77 assign(order,kbo).
% 3.51/3.77 set(lex_order_vars).
% 3.51/3.77 clear(print_given).
% 3.51/3.77
% 3.51/3.77 % formulas(sos). % not echoed (18 formulas)
% 3.51/3.77
% 3.51/3.77 ============================== end of input ==========================
% 3.51/3.77
% 3.51/3.77 % From the command line: assign(max_seconds, 300).
% 3.51/3.77
% 3.51/3.77 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.51/3.77
% 3.51/3.77 % Formulas that are not ordinary clauses:
% 3.51/3.77
% 3.51/3.77 ============================== end of process non-clausal formulas ===
% 3.51/3.77
% 3.51/3.77 ============================== PROCESS INITIAL CLAUSES ===============
% 3.51/3.77
% 3.51/3.77 ============================== PREDICATE ELIMINATION =================
% 3.51/3.77
% 3.51/3.77 ============================== end predicate elimination =============
% 3.51/3.77
% 3.51/3.77 Auto_denials:
% 3.51/3.77 % copying label prove_p03c to answer in negative clause
% 3.51/3.77
% 3.51/3.77 Term ordering decisions:
% 3.51/3.77
% 3.51/3.77 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 3.51/3.77 Function symbol KB weights: b=1. d=1. identity=1. a=1. c=1. multiply=1. least_upper_bound=1. greatest_lower_bound=1. inverse=0.
% 3.51/3.77
% 3.51/3.77 ============================== end of process initial clauses ========
% 3.51/3.77
% 3.51/3.77 ============================== CLAUSES FOR SEARCH ====================
% 3.51/3.77
% 3.51/3.77 ============================== end of clauses for search =============
% 3.51/3.77
% 3.51/3.77 ============================== SEARCH ================================
% 3.51/3.77
% 3.51/3.77 % Starting search at 0.01 seconds.
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=35.000, iters=3391
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=33.000, iters=3485
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=32.000, iters=3418
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=31.000, iters=3372
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=29.000, iters=3377
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=28.000, iters=3378
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=27.000, iters=3380
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=26.000, iters=3476
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=25.000, iters=3356
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=24.000, iters=3413
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=23.000, iters=3346
% 3.51/3.77
% 3.51/3.77 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 1.53 sec).
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=22.000, iters=3374
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=21.000, iters=3363
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=20.000, iters=3336
% 3.51/3.77
% 3.51/3.77 Low Water (displace): id=5046, wt=53.000
% 3.51/3.77
% 3.51/3.77 Low Water (displace): id=5060, wt=50.000
% 3.51/3.77
% 3.51/3.77 Low Water (displace): id=5061, wt=49.000
% 3.51/3.77
% 3.51/3.77 Low Water (displace): id=4834, wt=46.000
% 3.51/3.77
% 3.51/3.77 Low Water (displace): id=4500, wt=45.000
% 3.51/3.77
% 3.51/3.77 Low Water (displace): id=5137, wt=43.000
% 3.51/3.77
% 3.51/3.77 Low Water (keep): wt=19.000, iters=3350
% 3.51/3.77
% 3.51/3.77 Low Water (displace): id=5141, wt=42.000
% 3.51/3.77
% 3.51/3.77 Low Water (displace): id=6890, wt=41.000
% 3.51/3.77
% 3.51/3.77 Low Water (displace): id=5080, wt=40.000
% 5.38/5.70
% 5.38/5.70 Low Water (displace): id=4760, wt=39.000
% 5.38/5.70
% 5.38/5.70 Low Water (displace): id=5066, wt=38.000
% 5.38/5.70
% 5.38/5.70 Low Water (displace): id=6892, wt=37.000
% 5.38/5.70
% 5.38/5.70 Low Water (displace): id=6164, wt=36.000
% 5.38/5.70
% 5.38/5.70 Low Water (displace): id=13322, wt=15.000
% 5.38/5.70
% 5.38/5.70 Low Water (displace): id=13879, wt=14.000
% 5.38/5.70
% 5.38/5.70 Low Water (displace): id=14518, wt=13.000
% 5.38/5.70
% 5.38/5.70 Low Water (displace): id=15028, wt=12.000
% 5.38/5.70
% 5.38/5.70 Low Water (keep): wt=18.000, iters=3350
% 5.38/5.70
% 5.38/5.70 Low Water (keep): wt=17.000, iters=3344
% 5.38/5.70
% 5.38/5.70 ============================== PROOF =================================
% 5.38/5.70 % SZS status Unsatisfiable
% 5.38/5.70 % SZS output start Refutation
% 5.38/5.70
% 5.38/5.70 % Proof 1 at 4.60 (+ 0.12) seconds: prove_p03c.
% 5.38/5.70 % Length of proof is 85.
% 5.38/5.70 % Level of proof is 15.
% 5.38/5.70 % Maximum clause weight is 17.000.
% 5.38/5.70 % Given clauses 942.
% 5.38/5.70
% 5.38/5.70 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 5.38/5.70 4 least_upper_bound(a,b) = b # label(p03c_1) # label(hypothesis). [assumption].
% 5.38/5.70 5 least_upper_bound(c,d) = d # label(p03c_2) # label(hypothesis). [assumption].
% 5.38/5.70 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 5.38/5.70 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 5.38/5.70 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 5.38/5.70 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 5.38/5.70 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 5.38/5.70 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 5.38/5.70 14 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].
% 5.38/5.70 15 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(14),rewrite([8(4)])].
% 5.38/5.70 16 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 5.38/5.70 17 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(16),flip(a)].
% 5.38/5.70 18 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 5.38/5.70 19 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(18),flip(a)].
% 5.38/5.70 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 5.38/5.70 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 5.38/5.70 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 5.38/5.70 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 5.38/5.70 24 greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c) # label(prove_p03c) # label(negated_conjecture) # answer(prove_p03c). [assumption].
% 5.38/5.70 25 greatest_lower_bound(multiply(b,d),multiply(a,c)) != multiply(a,c) # answer(prove_p03c). [copy(24),rewrite([7(7)])].
% 5.38/5.70 26 least_upper_bound(d,c) = d. [back_rewrite(5),rewrite([8(3)])].
% 5.38/5.70 27 least_upper_bound(b,a) = b. [back_rewrite(4),rewrite([8(3)])].
% 5.38/5.70 28 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 5.38/5.70 33 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),17(a,1,1))].
% 5.38/5.70 35 least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A). [para(1(a,1),21(a,1,1)),rewrite([8(4)])].
% 5.38/5.70 36 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),21(a,1,1)),rewrite([8(5)])].
% 5.38/5.70 37 least_upper_bound(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(least_upper_bound(D,multiply(A,B)),C). [para(11(a,1),21(a,1,1)),rewrite([8(6)])].
% 5.38/5.70 40 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(6(a,1),23(a,1,1)),rewrite([7(5)])].
% 5.38/5.70 44 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),28(a,1,2))].
% 5.38/5.70 46 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(28(a,1),17(a,1,1)),rewrite([8(6)]),flip(a)].
% 5.38/5.70 47 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(28(a,1),19(a,1,1)),rewrite([7(6)]),flip(a)].
% 5.38/5.70 50 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(28(a,1),28(a,1,2))].
% 5.38/5.70 51 multiply(A,identity) = A. [back_rewrite(44),rewrite([50(4)])].
% 5.38/5.70 52 inverse(identity) = identity. [para(51(a,1),6(a,1))].
% 5.38/5.70 58 multiply(A,inverse(A)) = identity. [para(50(a,1),6(a,1))].
% 5.38/5.70 64 inverse(inverse(A)) = A. [para(50(a,1),51(a,1)),rewrite([51(2)]),flip(a)].
% 5.38/5.70 65 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(58(a,1),11(a,1)),flip(a)].
% 5.38/5.70 67 greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(B,inverse(A))). [para(58(a,1),19(a,1,1)),rewrite([7(5)])].
% 5.38/5.70 86 least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity. [para(9(a,1),33(a,2,2)),rewrite([6(7)])].
% 5.38/5.70 87 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(33(a,1),10(a,1,2))].
% 5.38/5.70 102 least_upper_bound(identity,multiply(inverse(d),c)) = identity. [para(26(a,1),33(a,2,2)),rewrite([6(10)])].
% 5.38/5.70 103 least_upper_bound(identity,multiply(inverse(b),a)) = identity. [para(27(a,1),33(a,2,2)),rewrite([6(10)])].
% 5.38/5.70 123 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(65(a,1),28(a,1,2)),rewrite([51(3)]),flip(a)].
% 5.38/5.70 132 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(123(a,1),28(a,1,2)),flip(a)].
% 5.38/5.70 156 least_upper_bound(identity,multiply(A,greatest_lower_bound(B,inverse(A)))) = identity. [para(64(a,1),86(a,1,2,1)),rewrite([7(3)])].
% 5.38/5.70 171 least_upper_bound(A,multiply(B,multiply(C,A))) = multiply(least_upper_bound(identity,multiply(B,C)),A). [para(11(a,1),35(a,1,2)),rewrite([8(6)])].
% 5.38/5.70 207 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(36(a,1),10(a,1,2))].
% 5.38/5.70 224 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(36(a,2),28(a,1,2))].
% 5.38/5.70 229 multiply(least_upper_bound(inverse(d),inverse(c)),c) = identity. [para(36(a,1),102(a,1))].
% 5.38/5.70 230 multiply(least_upper_bound(inverse(b),inverse(a)),a) = identity. [para(36(a,1),103(a,1))].
% 5.38/5.70 239 inverse(least_upper_bound(inverse(d),inverse(c))) = c. [para(229(a,1),28(a,1,2)),rewrite([51(8)])].
% 5.38/5.70 242 least_upper_bound(inverse(d),inverse(c)) = inverse(c). [para(239(a,1),64(a,1,1)),flip(a)].
% 5.38/5.70 247 least_upper_bound(identity,multiply(d,inverse(c))) = multiply(d,inverse(c)). [para(242(a,1),33(a,2,2)),rewrite([64(4),64(9)])].
% 5.38/5.70 285 inverse(least_upper_bound(inverse(b),inverse(a))) = a. [para(230(a,1),28(a,1,2)),rewrite([51(8)])].
% 5.38/5.70 290 least_upper_bound(inverse(b),inverse(a)) = inverse(a). [para(285(a,1),64(a,1,1)),flip(a)].
% 5.38/5.70 293 greatest_lower_bound(inverse(b),inverse(a)) = inverse(b). [para(290(a,1),10(a,1,2))].
% 5.38/5.70 359 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(40(a,1),9(a,1,2))].
% 5.38/5.70 376 multiply(inverse(greatest_lower_bound(A,inverse(B))),greatest_lower_bound(identity,multiply(A,B))) = B. [para(40(a,2),28(a,1,2))].
% 5.38/5.70 395 greatest_lower_bound(identity,multiply(inverse(b),a)) = multiply(inverse(b),a). [para(293(a,1),40(a,2,1))].
% 5.38/5.70 496 least_upper_bound(A,multiply(A,multiply(B,greatest_lower_bound(C,inverse(B))))) = A. [para(156(a,1),17(a,2,2)),rewrite([51(2),51(7)])].
% 5.38/5.70 605 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(64(a,1),207(a,1,2,1,2))].
% 5.38/5.70 800 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(64(a,1),359(a,1,2,1,2))].
% 5.38/5.70 1027 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(A))) = identity. [para(8(a,1),605(a,1,2,1))].
% 5.38/5.70 1050 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(605(a,1),47(a,1,2)),rewrite([51(4),51(7)]),flip(a)].
% 5.38/5.70 1072 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),A)) = identity. [para(87(a,1),800(a,1,2,1)),rewrite([132(6),64(6),1(6)])].
% 5.38/5.70 1076 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(800(a,1),46(a,1,2)),rewrite([51(4),51(7)]),flip(a)].
% 5.38/5.70 1222 greatest_lower_bound(identity,multiply(least_upper_bound(A,least_upper_bound(B,C)),inverse(B))) = identity. [para(15(a,1),1027(a,1,2,1))].
% 5.38/5.70 1386 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),B)) = identity. [para(8(a,1),1072(a,1,2,1,1))].
% 5.38/5.70 1787 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(B,A))) = identity. [para(1386(a,1),605(a,1,2,1)),rewrite([132(6),64(6),1(6)])].
% 5.38/5.70 4438 least_upper_bound(A,multiply(A,greatest_lower_bound(identity,multiply(B,C)))) = A. [para(67(a,2),496(a,1,2,2))].
% 5.38/5.70 4460 greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(A,B)))) = identity. [para(4438(a,1),1787(a,1,2,2)),rewrite([132(6),11(8),6(7),51(7)])].
% 5.38/5.70 4736 greatest_lower_bound(identity,multiply(inverse(a),b)) = identity. [para(395(a,1),4460(a,1,2,1)),rewrite([132(6),64(6)])].
% 5.38/5.70 7404 greatest_lower_bound(identity,least_upper_bound(A,multiply(d,inverse(c)))) = identity. [para(247(a,1),1222(a,1,2,1,2)),rewrite([52(8),51(8)])].
% 5.38/5.70 7484 greatest_lower_bound(identity,multiply(least_upper_bound(d,multiply(A,B)),inverse(c))) = identity. [para(37(a,1),7404(a,1,2))].
% 5.38/5.70 9941 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(800(a,1),224(a,1,2)),rewrite([64(3),8(2),51(5)])].
% 5.38/5.70 10002 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(9941(a,1),1050(a,1,2)),rewrite([7(4),9941(7)])].
% 5.38/5.70 10105 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(10002(a,1),1076(a,1,2,1)),rewrite([64(3),64(3),8(2),10002(6),64(4)])].
% 5.38/5.70 10144 least_upper_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),b). [para(4736(a,1),10105(a,1,2)),rewrite([8(6)])].
% 5.38/5.70 16448 inverse(greatest_lower_bound(c,least_upper_bound(d,multiply(A,B)))) = inverse(c). [para(7484(a,1),376(a,1,2)),rewrite([64(6),7(5),51(8)])].
% 5.38/5.70 16533 greatest_lower_bound(c,least_upper_bound(d,multiply(A,B))) = c. [para(16448(a,1),64(a,1,1)),rewrite([64(3)]),flip(a)].
% 5.38/5.70 16599 greatest_lower_bound(c,multiply(least_upper_bound(identity,multiply(A,B)),d)) = c. [para(171(a,1),16533(a,1,2))].
% 5.38/5.70 17121 greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))) = c. [para(10144(a,1),16599(a,1,2,1)),rewrite([11(7)])].
% 5.38/5.70 17215 greatest_lower_bound(multiply(b,d),multiply(a,c)) = multiply(a,c). [para(17121(a,1),47(a,1,2)),rewrite([64(3),64(9)]),flip(a)].
% 5.38/5.70 17216 $F # answer(prove_p03c). [resolve(17215,a,25,a)].
% 5.38/5.70
% 5.38/5.70 % SZS output end Refutation
% 5.38/5.70 ============================== end of proof ==========================
% 5.38/5.70
% 5.38/5.70 ============================== STATISTICS ============================
% 5.38/5.70
% 5.38/5.70 Given=942. Generated=211863. Kept=17208. proofs=1.
% 5.38/5.70 Usable=832. Sos=9999. Demods=9440. Limbo=2, Disabled=6392. Hints=0.
% 5.38/5.70 Megabytes=16.84.
% 5.38/5.70 User_CPU=4.60, System_CPU=0.12, Wall_clock=5.
% 5.38/5.70
% 5.38/5.70 ============================== end of statistics =====================
% 5.38/5.70
% 5.38/5.70 ============================== end of search =========================
% 5.38/5.70
% 5.38/5.70 THEOREM PROVED
% 5.38/5.70 % SZS status Unsatisfiable
% 5.38/5.70
% 5.38/5.70 Exiting with 1 proof.
% 5.38/5.70
% 5.38/5.70 Process 13681 exit (max_proofs) Mon Jun 13 09:57:24 2022
% 5.38/5.70 Prover9 interrupted
%------------------------------------------------------------------------------