TSTP Solution File: GRP179-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP179-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 8.47s 8.74s
% Output : Refutation 8.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP179-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Tue Jun 14 05:25:56 EDT 2022
% 0.14/0.34 % CPUTime :
% 3.25/3.51 ============================== Prover9 ===============================
% 3.25/3.51 Prover9 (32) version 2009-11A, November 2009.
% 3.25/3.51 Process 11833 was started by sandbox2 on n006.cluster.edu,
% 3.25/3.51 Tue Jun 14 05:25:57 2022
% 3.25/3.51 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_11680_n006.cluster.edu".
% 3.25/3.51 ============================== end of head ===========================
% 3.25/3.51
% 3.25/3.51 ============================== INPUT =================================
% 3.25/3.51
% 3.25/3.51 % Reading from file /tmp/Prover9_11680_n006.cluster.edu
% 3.25/3.51
% 3.25/3.51 set(prolog_style_variables).
% 3.25/3.51 set(auto2).
% 3.25/3.51 % set(auto2) -> set(auto).
% 3.25/3.51 % set(auto) -> set(auto_inference).
% 3.25/3.51 % set(auto) -> set(auto_setup).
% 3.25/3.51 % set(auto_setup) -> set(predicate_elim).
% 3.25/3.51 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.25/3.51 % set(auto) -> set(auto_limits).
% 3.25/3.51 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.25/3.51 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.25/3.51 % set(auto) -> set(auto_denials).
% 3.25/3.51 % set(auto) -> set(auto_process).
% 3.25/3.51 % set(auto2) -> assign(new_constants, 1).
% 3.25/3.51 % set(auto2) -> assign(fold_denial_max, 3).
% 3.25/3.51 % set(auto2) -> assign(max_weight, "200.000").
% 3.25/3.51 % set(auto2) -> assign(max_hours, 1).
% 3.25/3.51 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.25/3.51 % set(auto2) -> assign(max_seconds, 0).
% 3.25/3.51 % set(auto2) -> assign(max_minutes, 5).
% 3.25/3.51 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.25/3.51 % set(auto2) -> set(sort_initial_sos).
% 3.25/3.51 % set(auto2) -> assign(sos_limit, -1).
% 3.25/3.51 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.25/3.51 % set(auto2) -> assign(max_megs, 400).
% 3.25/3.51 % set(auto2) -> assign(stats, some).
% 3.25/3.51 % set(auto2) -> clear(echo_input).
% 3.25/3.51 % set(auto2) -> set(quiet).
% 3.25/3.51 % set(auto2) -> clear(print_initial_clauses).
% 3.25/3.51 % set(auto2) -> clear(print_given).
% 3.25/3.51 assign(lrs_ticks,-1).
% 3.25/3.51 assign(sos_limit,10000).
% 3.25/3.51 assign(order,kbo).
% 3.25/3.51 set(lex_order_vars).
% 3.25/3.51 clear(print_given).
% 3.25/3.51
% 3.25/3.51 % formulas(sos). % not echoed (16 formulas)
% 3.25/3.51
% 3.25/3.51 ============================== end of input ==========================
% 3.25/3.51
% 3.25/3.51 % From the command line: assign(max_seconds, 300).
% 3.25/3.51
% 3.25/3.51 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.25/3.51
% 3.25/3.51 % Formulas that are not ordinary clauses:
% 3.25/3.51
% 3.25/3.51 ============================== end of process non-clausal formulas ===
% 3.25/3.51
% 3.25/3.51 ============================== PROCESS INITIAL CLAUSES ===============
% 3.25/3.51
% 3.25/3.51 ============================== PREDICATE ELIMINATION =================
% 3.25/3.51
% 3.25/3.51 ============================== end predicate elimination =============
% 3.25/3.51
% 3.25/3.51 Auto_denials:
% 3.25/3.51 % copying label prove_p18 to answer in negative clause
% 3.25/3.51
% 3.25/3.51 Term ordering decisions:
% 3.25/3.51
% 3.25/3.51 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 3.25/3.51 Function symbol KB weights: identity=1. a=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 3.25/3.51
% 3.25/3.51 ============================== end of process initial clauses ========
% 3.25/3.51
% 3.25/3.51 ============================== CLAUSES FOR SEARCH ====================
% 3.25/3.51
% 3.25/3.51 ============================== end of clauses for search =============
% 3.25/3.51
% 3.25/3.51 ============================== SEARCH ================================
% 3.25/3.51
% 3.25/3.51 % Starting search at 0.01 seconds.
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=37.000, iters=3366
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=36.000, iters=3360
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=35.000, iters=3385
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=32.000, iters=3422
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=31.000, iters=3394
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=30.000, iters=3334
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=29.000, iters=3483
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=28.000, iters=3393
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=27.000, iters=3365
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=26.000, iters=3338
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=25.000, iters=3360
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=24.000, iters=3336
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=23.000, iters=3350
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=22.000, iters=3337
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=21.000, iters=3333
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=20.000, iters=3341
% 3.25/3.51
% 3.25/3.51 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 2.01 sec).
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=19.000, iters=3340
% 3.25/3.51
% 3.25/3.51 Low Water (keep): wt=18.000, iters=3341
% 3.25/3.51
% 3.25/3.51 Low Water (displace): id=5288, wt=43.000
% 3.25/3.51
% 3.25/3.51 Low Water (displace): id=5750, wt=41.000
% 3.25/3.51
% 3.25/3.51 Low Water (displace): id=6151, wt=40.000
% 3.25/3.51
% 3.25/3.51 Low Water (displace): id=5692, wt=39.000
% 3.25/3.51
% 3.25/3.51 Low Water (displace): id=5691, wt=38.000
% 3.25/3.51
% 3.25/3.51 Low Water (displace): id=6241, wt=37.000
% 8.47/8.74
% 8.47/8.74 Low Water (displace): id=12571, wt=17.000
% 8.47/8.74
% 8.47/8.74 Low Water (displace): id=12654, wt=16.000
% 8.47/8.74
% 8.47/8.74 Low Water (displace): id=13158, wt=15.000
% 8.47/8.74
% 8.47/8.74 Low Water (keep): wt=17.000, iters=3345
% 8.47/8.74
% 8.47/8.74 Low Water (displace): id=13351, wt=14.000
% 8.47/8.74
% 8.47/8.74 Low Water (displace): id=15117, wt=13.000
% 8.47/8.74
% 8.47/8.74 ============================== PROOF =================================
% 8.47/8.74 % SZS status Unsatisfiable
% 8.47/8.74 % SZS output start Refutation
% 8.47/8.74
% 8.47/8.74 % Proof 1 at 7.54 (+ 0.24) seconds: prove_p18.
% 8.47/8.74 % Length of proof is 98.
% 8.47/8.74 % Level of proof is 17.
% 8.47/8.74 % Maximum clause weight is 19.000.
% 8.47/8.74 % Given clauses 1060.
% 8.47/8.74
% 8.47/8.74 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 8.47/8.74 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 8.47/8.74 5 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 8.47/8.74 6 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 8.47/8.74 7 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 8.47/8.74 8 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 8.47/8.74 9 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 8.47/8.74 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].
% 8.47/8.74 11 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(10),rewrite([5(4)])].
% 8.47/8.74 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].
% 8.47/8.74 13 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(12),rewrite([6(4)])].
% 8.47/8.74 14 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 8.47/8.74 15 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(14),flip(a)].
% 8.47/8.74 16 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 8.47/8.74 17 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(16),flip(a)].
% 8.47/8.74 18 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 8.47/8.74 19 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(18),flip(a)].
% 8.47/8.74 20 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 8.47/8.74 21 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(20),flip(a)].
% 8.47/8.74 22 least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)) # label(prove_p18) # label(negated_conjecture) # answer(prove_p18). [assumption].
% 8.47/8.74 23 inverse(greatest_lower_bound(identity,a)) != least_upper_bound(identity,inverse(a)) # answer(prove_p18). [copy(22),rewrite([6(4),5(7)]),flip(a)].
% 8.47/8.74 24 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),9(a,1,1)),rewrite([1(2)]),flip(a)].
% 8.47/8.74 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)])].
% 8.47/8.74 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))].
% 8.47/8.74 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))].
% 8.47/8.74 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)])].
% 8.47/8.74 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)])].
% 8.47/8.74 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)])].
% 8.47/8.74 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)])].
% 8.47/8.74 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)])].
% 8.47/8.74 38 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))].
% 8.47/8.74 40 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),24(a,1,2))].
% 8.47/8.74 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)].
% 8.47/8.74 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)].
% 8.47/8.74 46 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(24(a,1),24(a,1,2))].
% 8.47/8.74 47 multiply(A,identity) = A. [back_rewrite(40),rewrite([46(4)])].
% 8.47/8.74 48 inverse(identity) = identity. [para(47(a,1),4(a,1))].
% 8.47/8.74 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)])].
% 8.47/8.74 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)])].
% 8.47/8.74 54 multiply(A,inverse(A)) = identity. [para(46(a,1),4(a,1))].
% 8.47/8.74 59 multiply(A,multiply(inverse(A),B)) = B. [para(46(a,1),24(a,1))].
% 8.47/8.74 60 inverse(inverse(A)) = A. [para(46(a,1),47(a,1)),rewrite([47(2)]),flip(a)].
% 8.47/8.74 61 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(54(a,1),9(a,1)),flip(a)].
% 8.47/8.74 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)])].
% 8.47/8.74 79 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(61(a,1),24(a,1,2)),rewrite([47(3)]),flip(a)].
% 8.47/8.74 87 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(79(a,1),24(a,1,2)),flip(a)].
% 8.47/8.74 88 multiply(least_upper_bound(inverse(A),identity),A) = least_upper_bound(A,identity). [para(4(a,1),31(a,1,2)),flip(a)].
% 8.47/8.74 89 greatest_lower_bound(A,multiply(least_upper_bound(B,identity),A)) = A. [para(31(a,1),8(a,1,2))].
% 8.47/8.74 104 multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(B,multiply(A,B))) = B. [para(31(a,2),24(a,1,2))].
% 8.47/8.74 108 multiply(least_upper_bound(A,identity),inverse(A)) = least_upper_bound(inverse(A),identity). [para(54(a,1),31(a,1,2)),flip(a)].
% 8.47/8.74 114 multiply(A,least_upper_bound(identity,multiply(inverse(B),C))) = multiply(A,multiply(inverse(B),least_upper_bound(B,C))). [para(29(a,2),9(a,2,2)),rewrite([9(4)]),flip(a)].
% 8.47/8.74 126 multiply(inverse(A),least_upper_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [para(47(a,1),29(a,1,2)),flip(a)].
% 8.47/8.74 129 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))].
% 8.47/8.74 134 greatest_lower_bound(identity,least_upper_bound(A,identity)) = identity. [para(47(a,1),89(a,1,2))].
% 8.47/8.74 137 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)])].
% 8.47/8.74 139 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)])].
% 8.47/8.74 168 multiply(inverse(A),greatest_lower_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)). [para(47(a,1),30(a,1,2)),flip(a)].
% 8.47/8.74 189 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(32(a,1),8(a,1,2))].
% 8.47/8.74 206 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(32(a,2),24(a,1,2))].
% 8.47/8.74 265 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(60(a,1),189(a,1,2,1,2))].
% 8.47/8.74 321 multiply(greatest_lower_bound(inverse(A),identity),A) = greatest_lower_bound(A,identity). [para(4(a,1),35(a,1,2)),flip(a)].
% 8.47/8.74 339 multiply(greatest_lower_bound(A,identity),inverse(A)) = greatest_lower_bound(inverse(A),identity). [para(54(a,1),35(a,1,2)),flip(a)].
% 8.47/8.74 365 multiply(greatest_lower_bound(identity,inverse(A)),A) = greatest_lower_bound(A,identity). [para(5(a,1),321(a,1,1))].
% 8.47/8.74 383 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(36(a,1),7(a,1,2))].
% 8.47/8.74 395 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)])].
% 8.47/8.74 406 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))].
% 8.47/8.74 432 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(60(a,1),383(a,1,2,1,2))].
% 8.47/8.74 477 multiply(greatest_lower_bound(A,multiply(B,C)),multiply(inverse(C),D)) = multiply(greatest_lower_bound(B,multiply(A,inverse(C))),D). [para(59(a,1),37(a,1,1,2)),rewrite([38(5)]),flip(a)].
% 8.47/8.74 598 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(432(a,1),42(a,1,2)),rewrite([47(4),47(7)]),flip(a)].
% 8.47/8.74 645 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(265(a,1),43(a,1,2)),rewrite([47(4),47(7)]),flip(a)].
% 8.47/8.74 760 multiply(A,least_upper_bound(inverse(A),identity)) = least_upper_bound(A,identity). [para(54(a,1),49(a,1,2)),flip(a)].
% 8.47/8.74 782 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(321(a,1),49(a,1,2)),rewrite([6(6)])].
% 8.47/8.74 785 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(365(a,1),49(a,1,2)),rewrite([6(6)])].
% 8.47/8.74 813 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(760(a,1),35(a,1,2)),rewrite([5(6)])].
% 8.47/8.74 926 multiply(A,greatest_lower_bound(inverse(A),identity)) = greatest_lower_bound(A,identity). [para(54(a,1),50(a,1,2)),flip(a)].
% 8.47/8.74 932 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),813(6)]),flip(a)].
% 8.47/8.74 977 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(926(a,1),31(a,1,2)),rewrite([6(6),782(6)]),flip(a)].
% 8.47/8.74 1027 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([813(6),977(12)]),flip(a)].
% 8.47/8.74 1029 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(782),rewrite([1027(12)])].
% 8.47/8.74 1129 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)].
% 8.47/8.74 1258 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)])].
% 8.47/8.74 1609 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(926(a,1),104(a,1,2,2)),rewrite([6(9),1029(9)])].
% 8.47/8.74 4536 multiply(inverse(least_upper_bound(identity,multiply(inverse(A),B))),multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(114(a,1),4(a,1))].
% 8.47/8.74 5023 greatest_lower_bound(inverse(greatest_lower_bound(A,identity)),inverse(greatest_lower_bound(identity,inverse(A)))) = identity. [para(1129(a,1),50(a,1,2)),rewrite([4(14)])].
% 8.47/8.74 6398 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)])].
% 8.47/8.74 9538 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(5023(a,1),129(a,1,2,2,2)),rewrite([60(5),60(11),6(13),1258(14)])].
% 8.47/8.74 11216 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(432(a,1),206(a,1,2)),rewrite([60(3),6(2),47(5)])].
% 8.47/8.74 11244 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(11216(a,1),645(a,1,2)),rewrite([5(4),11216(7)])].
% 8.47/8.74 11291 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(11244(a,1),598(a,1,2,1)),rewrite([60(3),60(3),6(2),11244(6),60(4)])].
% 8.47/8.74 17004 greatest_lower_bound(identity,multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity))) = identity. [para(168(a,1),406(a,1,2,2)),rewrite([785(7),6398(8),126(5),8(5),395(11),932(8)]),flip(a)].
% 8.47/8.74 17018 multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)) = identity. [para(17004(a,1),11291(a,1,2)),rewrite([6(8),9538(8),339(5),11291(5)]),flip(a)].
% 8.47/8.74 17022 inverse(least_upper_bound(A,identity)) = greatest_lower_bound(inverse(A),identity). [back_rewrite(1609),rewrite([17018(9),47(5)])].
% 8.47/8.74 17258 inverse(least_upper_bound(identity,multiply(A,B))) = greatest_lower_bound(identity,multiply(inverse(B),inverse(A))). [para(87(a,1),17022(a,2,1)),rewrite([6(3),5(9)])].
% 8.47/8.74 17349 multiply(greatest_lower_bound(inverse(A),inverse(B)),least_upper_bound(A,B)) = identity. [back_rewrite(4536),rewrite([17258(5),60(4),477(8),1(4),5(3)])].
% 8.47/8.74 17729 inverse(greatest_lower_bound(inverse(A),inverse(B))) = least_upper_bound(A,B). [para(17349(a,1),24(a,1,2)),rewrite([47(6)])].
% 8.47/8.74 17765 inverse(greatest_lower_bound(A,inverse(B))) = least_upper_bound(B,inverse(A)). [para(60(a,1),17729(a,1,1,1)),rewrite([6(5)])].
% 8.47/8.74 18546 inverse(greatest_lower_bound(A,B)) = least_upper_bound(inverse(A),inverse(B)). [para(60(a,1),17765(a,1,1,2)),rewrite([6(5)])].
% 8.47/8.74 19432 $F # answer(prove_p18). [back_rewrite(23),rewrite([18546(4),48(2)]),xx(a)].
% 8.47/8.74
% 8.47/8.74 % SZS output end Refutation
% 8.47/8.74 ============================== end of proof ==========================
% 8.47/8.74
% 8.47/8.74 ============================== STATISTICS ============================
% 8.47/8.74
% 8.47/8.74 Given=1060. Generated=391446. Kept=19424. proofs=1.
% 8.47/8.74 Usable=558. Sos=4672. Demods=5475. Limbo=886, Disabled=13324. Hints=0.
% 8.47/8.74 Megabytes=16.97.
% 8.47/8.74 User_CPU=7.54, System_CPU=0.24, Wall_clock=8.
% 8.47/8.74
% 8.47/8.74 ============================== end of statistics =====================
% 8.47/8.74
% 8.47/8.74 ============================== end of search =========================
% 8.47/8.74
% 8.47/8.74 THEOREM PROVED
% 8.47/8.74 % SZS status Unsatisfiable
% 8.47/8.74
% 8.47/8.74 Exiting with 1 proof.
% 8.47/8.74
% 8.47/8.74 Process 11833 exit (max_proofs) Tue Jun 14 05:26:05 2022
% 8.47/8.74 Prover9 interrupted
%------------------------------------------------------------------------------