TSTP Solution File: GRP181-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP181-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 11:17:58 EDT 2022
% Result : Unsatisfiable 7.67s 8.00s
% Output : Refutation 7.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP181-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 17:49:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.13/3.47 ============================== Prover9 ===============================
% 3.13/3.47 Prover9 (32) version 2009-11A, November 2009.
% 3.13/3.47 Process 26365 was started by sandbox on n028.cluster.edu,
% 3.13/3.47 Mon Jun 13 17:49:08 2022
% 3.13/3.47 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26208_n028.cluster.edu".
% 3.13/3.47 ============================== end of head ===========================
% 3.13/3.47
% 3.13/3.47 ============================== INPUT =================================
% 3.13/3.47
% 3.13/3.47 % Reading from file /tmp/Prover9_26208_n028.cluster.edu
% 3.13/3.47
% 3.13/3.47 set(prolog_style_variables).
% 3.13/3.47 set(auto2).
% 3.13/3.47 % set(auto2) -> set(auto).
% 3.13/3.47 % set(auto) -> set(auto_inference).
% 3.13/3.47 % set(auto) -> set(auto_setup).
% 3.13/3.47 % set(auto_setup) -> set(predicate_elim).
% 3.13/3.47 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.13/3.47 % set(auto) -> set(auto_limits).
% 3.13/3.47 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.13/3.47 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.13/3.47 % set(auto) -> set(auto_denials).
% 3.13/3.47 % set(auto) -> set(auto_process).
% 3.13/3.47 % set(auto2) -> assign(new_constants, 1).
% 3.13/3.47 % set(auto2) -> assign(fold_denial_max, 3).
% 3.13/3.47 % set(auto2) -> assign(max_weight, "200.000").
% 3.13/3.47 % set(auto2) -> assign(max_hours, 1).
% 3.13/3.47 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.13/3.47 % set(auto2) -> assign(max_seconds, 0).
% 3.13/3.47 % set(auto2) -> assign(max_minutes, 5).
% 3.13/3.47 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.13/3.47 % set(auto2) -> set(sort_initial_sos).
% 3.13/3.47 % set(auto2) -> assign(sos_limit, -1).
% 3.13/3.47 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.13/3.47 % set(auto2) -> assign(max_megs, 400).
% 3.13/3.47 % set(auto2) -> assign(stats, some).
% 3.13/3.47 % set(auto2) -> clear(echo_input).
% 3.13/3.47 % set(auto2) -> set(quiet).
% 3.13/3.47 % set(auto2) -> clear(print_initial_clauses).
% 3.13/3.47 % set(auto2) -> clear(print_given).
% 3.13/3.47 assign(lrs_ticks,-1).
% 3.13/3.47 assign(sos_limit,10000).
% 3.13/3.47 assign(order,kbo).
% 3.13/3.47 set(lex_order_vars).
% 3.13/3.47 clear(print_given).
% 3.13/3.47
% 3.13/3.47 % formulas(sos). % not echoed (18 formulas)
% 3.13/3.47
% 3.13/3.47 ============================== end of input ==========================
% 3.13/3.47
% 3.13/3.47 % From the command line: assign(max_seconds, 300).
% 3.13/3.47
% 3.13/3.47 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.13/3.47
% 3.13/3.47 % Formulas that are not ordinary clauses:
% 3.13/3.47
% 3.13/3.47 ============================== end of process non-clausal formulas ===
% 3.13/3.47
% 3.13/3.47 ============================== PROCESS INITIAL CLAUSES ===============
% 3.13/3.47
% 3.13/3.47 ============================== PREDICATE ELIMINATION =================
% 3.13/3.47
% 3.13/3.47 ============================== end predicate elimination =============
% 3.13/3.47
% 3.13/3.47 Auto_denials:
% 3.13/3.47 % copying label prove_p12 to answer in negative clause
% 3.13/3.47
% 3.13/3.47 Term ordering decisions:
% 3.13/3.47
% 3.13/3.47 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 3.13/3.47 Function symbol KB weights: c=1. a=1. b=1. identity=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 3.13/3.47
% 3.13/3.47 ============================== end of process initial clauses ========
% 3.13/3.47
% 3.13/3.47 ============================== CLAUSES FOR SEARCH ====================
% 3.13/3.47
% 3.13/3.47 ============================== end of clauses for search =============
% 3.13/3.47
% 3.13/3.47 ============================== SEARCH ================================
% 3.13/3.47
% 3.13/3.47 % Starting search at 0.01 seconds.
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=33.000, iters=3345
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=32.000, iters=3356
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=31.000, iters=3371
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=30.000, iters=3358
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=28.000, iters=3333
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=27.000, iters=3406
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=26.000, iters=3335
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=25.000, iters=3333
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=24.000, iters=3391
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=23.000, iters=3340
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=22.000, iters=3342
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=21.000, iters=3381
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=20.000, iters=3403
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=19.000, iters=3341
% 3.13/3.47
% 3.13/3.47 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 1.89 sec).
% 3.13/3.47
% 3.13/3.47 Low Water (displace): id=5326, wt=43.000
% 3.13/3.47
% 3.13/3.47 Low Water (displace): id=5854, wt=41.000
% 3.13/3.47
% 3.13/3.47 Low Water (keep): wt=18.000, iters=3365
% 3.13/3.47
% 3.13/3.47 Low Water (displace): id=6329, wt=40.000
% 3.13/3.47
% 3.13/3.47 Low Water (displace): id=5709, wt=39.000
% 3.13/3.47
% 3.13/3.47 Low Water (displace): id=5708, wt=38.000
% 3.13/3.47
% 3.13/3.47 Low Water (displace): id=6493, wt=37.000
% 3.13/3.47
% 3.13/3.47 Low Water (displace): id=6496, wt=36.000
% 3.13/3.47
% 3.13/3.47 Low Water (displace): id=6490, wt=35.000
% 3.13/3.47
% 3.13/3.47 Low Water (displace): id=12526, wt=17.000
% 7.67/8.00
% 7.67/8.00 Low Water (displace): id=12532, wt=16.000
% 7.67/8.00
% 7.67/8.00 Low Water (displace): id=13110, wt=15.000
% 7.67/8.00
% 7.67/8.00 Low Water (displace): id=13117, wt=14.000
% 7.67/8.00
% 7.67/8.00 Low Water (keep): wt=17.000, iters=3333
% 7.67/8.00
% 7.67/8.00 Low Water (displace): id=15330, wt=13.000
% 7.67/8.00
% 7.67/8.00 Low Water (keep): wt=16.000, iters=3334
% 7.67/8.00
% 7.67/8.00 ============================== PROOF =================================
% 7.67/8.00 % SZS status Unsatisfiable
% 7.67/8.00 % SZS output start Refutation
% 7.67/8.00
% 7.67/8.00 % Proof 1 at 6.81 (+ 0.19) seconds: prove_p12.
% 7.67/8.00 % Length of proof is 114.
% 7.67/8.00 % Level of proof is 18.
% 7.67/8.00 % Maximum clause weight is 21.000.
% 7.67/8.00 % Given clauses 1072.
% 7.67/8.00
% 7.67/8.00 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 7.67/8.00 4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 7.67/8.00 5 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 7.67/8.00 6 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 7.67/8.00 7 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 7.67/8.00 8 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 7.67/8.00 9 greatest_lower_bound(a,c) = greatest_lower_bound(b,c) # label(p12_1) # label(hypothesis). [assumption].
% 7.67/8.00 10 greatest_lower_bound(c,b) = greatest_lower_bound(c,a). [copy(9),rewrite([5(3),5(6)]),flip(a)].
% 7.67/8.00 11 least_upper_bound(a,c) = least_upper_bound(b,c) # label(p12_2) # label(hypothesis). [assumption].
% 7.67/8.00 12 least_upper_bound(c,b) = least_upper_bound(c,a). [copy(11),rewrite([6(3),6(6)]),flip(a)].
% 7.67/8.00 13 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 7.67/8.00 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].
% 7.67/8.00 15 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(14),rewrite([5(4)])].
% 7.67/8.00 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].
% 7.67/8.00 17 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(16),rewrite([6(4)])].
% 7.67/8.00 18 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 7.67/8.00 19 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(18),flip(a)].
% 7.67/8.00 20 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 7.67/8.00 21 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(20),flip(a)].
% 7.67/8.00 22 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 7.67/8.00 23 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(22),flip(a)].
% 7.67/8.00 24 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 7.67/8.00 25 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(24),flip(a)].
% 7.67/8.00 26 a != b # label(prove_p12) # label(negated_conjecture) # answer(prove_p12). [assumption].
% 7.67/8.00 27 b != a # answer(prove_p12). [copy(26),flip(a)].
% 7.67/8.00 28 multiply(inverse(A),multiply(A,B)) = B. [para(4(a,1),13(a,1,1)),rewrite([1(2)]),flip(a)].
% 7.67/8.00 32 least_upper_bound(A,least_upper_bound(B,greatest_lower_bound(A,C))) = least_upper_bound(A,B). [para(7(a,1),17(a,2,2)),rewrite([6(2),6(4)])].
% 7.67/8.00 33 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(4(a,1),19(a,1,1))].
% 7.67/8.00 34 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(4(a,1),21(a,1,1))].
% 7.67/8.00 35 least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A). [para(1(a,1),23(a,1,1)),rewrite([6(4)])].
% 7.67/8.00 36 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(4(a,1),23(a,1,1)),rewrite([6(5)])].
% 7.67/8.00 39 greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(B,identity),A). [para(1(a,1),25(a,1,1)),rewrite([5(4)])].
% 7.67/8.00 40 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(4(a,1),25(a,1,1)),rewrite([5(5)])].
% 7.67/8.00 41 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([5(6)])].
% 7.67/8.00 42 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))].
% 7.67/8.00 44 multiply(inverse(inverse(A)),identity) = A. [para(4(a,1),28(a,1,2))].
% 7.67/8.00 46 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(28(a,1),19(a,1,1)),rewrite([6(6)]),flip(a)].
% 7.67/8.00 47 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([5(6)]),flip(a)].
% 7.67/8.00 50 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(28(a,1),28(a,1,2))].
% 7.67/8.00 51 multiply(A,identity) = A. [back_rewrite(44),rewrite([50(4)])].
% 7.67/8.00 52 inverse(identity) = identity. [para(51(a,1),4(a,1))].
% 7.67/8.00 53 least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(B,identity)). [para(51(a,1),19(a,1,1)),rewrite([6(4)])].
% 7.67/8.00 54 greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(B,identity)). [para(51(a,1),21(a,1,1)),rewrite([5(4)])].
% 7.67/8.00 59 multiply(A,inverse(A)) = identity. [para(50(a,1),4(a,1))].
% 7.67/8.00 64 multiply(A,multiply(inverse(A),B)) = B. [para(50(a,1),28(a,1))].
% 7.67/8.00 65 inverse(inverse(A)) = A. [para(50(a,1),51(a,1)),rewrite([51(2)]),flip(a)].
% 7.67/8.00 66 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(59(a,1),13(a,1)),flip(a)].
% 7.67/8.00 67 least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))). [para(59(a,1),19(a,1,1)),rewrite([6(5)])].
% 7.67/8.00 85 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(66(a,1),28(a,1,2)),rewrite([51(3)]),flip(a)].
% 7.67/8.00 93 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(85(a,1),28(a,1,2)),flip(a)].
% 7.67/8.00 94 multiply(least_upper_bound(inverse(A),identity),A) = least_upper_bound(A,identity). [para(4(a,1),35(a,1,2)),flip(a)].
% 7.67/8.00 95 greatest_lower_bound(A,multiply(least_upper_bound(B,identity),A)) = A. [para(35(a,1),8(a,1,2))].
% 7.67/8.00 110 multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(B,multiply(A,B))) = B. [para(35(a,2),28(a,1,2))].
% 7.67/8.00 114 multiply(least_upper_bound(A,identity),inverse(A)) = least_upper_bound(inverse(A),identity). [para(59(a,1),35(a,1,2)),flip(a)].
% 7.67/8.00 117 least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity. [para(7(a,1),33(a,2,2)),rewrite([4(7)])].
% 7.67/8.00 119 least_upper_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),least_upper_bound(c,a)). [para(12(a,1),33(a,2,2))].
% 7.67/8.00 121 multiply(A,least_upper_bound(identity,multiply(inverse(B),C))) = multiply(A,multiply(inverse(B),least_upper_bound(B,C))). [para(33(a,2),13(a,2,2)),rewrite([13(4)]),flip(a)].
% 7.67/8.00 131 greatest_lower_bound(least_upper_bound(identity,multiply(inverse(A),B)),multiply(C,least_upper_bound(A,B))) = multiply(greatest_lower_bound(C,inverse(A)),least_upper_bound(A,B)). [para(33(a,2),25(a,1,1)),rewrite([5(9)])].
% 7.67/8.00 133 multiply(inverse(A),least_upper_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [para(51(a,1),33(a,1,2)),flip(a)].
% 7.67/8.00 136 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(32(a,1),33(a,2,2))].
% 7.67/8.00 141 greatest_lower_bound(identity,least_upper_bound(A,identity)) = identity. [para(51(a,1),95(a,1,2))].
% 7.67/8.00 144 greatest_lower_bound(A,multiply(A,least_upper_bound(B,identity))) = A. [para(141(a,1),21(a,2,2)),rewrite([51(2),51(6)])].
% 7.67/8.00 146 greatest_lower_bound(A,greatest_lower_bound(B,multiply(A,least_upper_bound(C,identity)))) = greatest_lower_bound(A,B). [para(144(a,1),15(a,2,2)),rewrite([5(4),5(6)])].
% 7.67/8.00 176 multiply(inverse(A),greatest_lower_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)). [para(51(a,1),34(a,1,2)),flip(a)].
% 7.67/8.00 186 least_upper_bound(identity,greatest_lower_bound(A,identity)) = identity. [para(52(a,1),117(a,1,2,1)),rewrite([5(4),1(5)])].
% 7.67/8.00 189 least_upper_bound(A,multiply(A,greatest_lower_bound(B,identity))) = A. [para(186(a,1),19(a,2,2)),rewrite([51(2),51(6)])].
% 7.67/8.00 192 least_upper_bound(identity,inverse(greatest_lower_bound(A,identity))) = inverse(greatest_lower_bound(A,identity)). [para(4(a,1),189(a,1,2)),rewrite([6(5)])].
% 7.67/8.00 197 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(36(a,1),8(a,1,2))].
% 7.67/8.00 214 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(36(a,2),28(a,1,2))].
% 7.67/8.00 273 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(65(a,1),197(a,1,2,1,2))].
% 7.67/8.00 326 multiply(greatest_lower_bound(inverse(A),identity),A) = greatest_lower_bound(A,identity). [para(4(a,1),39(a,1,2)),flip(a)].
% 7.67/8.00 344 multiply(greatest_lower_bound(A,identity),inverse(A)) = greatest_lower_bound(inverse(A),identity). [para(59(a,1),39(a,1,2)),flip(a)].
% 7.67/8.00 370 multiply(greatest_lower_bound(identity,inverse(A)),A) = greatest_lower_bound(A,identity). [para(5(a,1),326(a,1,1))].
% 7.67/8.00 388 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(40(a,1),7(a,1,2))].
% 7.67/8.00 400 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(40(a,2),21(a,2)),rewrite([21(9)])].
% 7.67/8.00 411 greatest_lower_bound(identity,least_upper_bound(A,multiply(B,A))) = multiply(greatest_lower_bound(least_upper_bound(B,identity),inverse(A)),A). [para(35(a,2),40(a,1,2))].
% 7.67/8.00 446 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(65(a,1),388(a,1,2,1,2))].
% 7.67/8.00 469 multiply(greatest_lower_bound(A,multiply(B,C)),multiply(inverse(C),D)) = multiply(greatest_lower_bound(B,multiply(A,inverse(C))),D). [para(64(a,1),41(a,1,1,2)),rewrite([42(5)]),flip(a)].
% 7.67/8.00 609 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(446(a,1),46(a,1,2)),rewrite([51(4),51(7)]),flip(a)].
% 7.67/8.00 649 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(273(a,1),47(a,1,2)),rewrite([51(4),51(7)]),flip(a)].
% 7.67/8.00 869 multiply(A,least_upper_bound(inverse(A),identity)) = least_upper_bound(A,identity). [para(59(a,1),53(a,1,2)),flip(a)].
% 7.67/8.00 891 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(326(a,1),53(a,1,2)),rewrite([6(6)])].
% 7.67/8.00 894 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(370(a,1),53(a,1,2)),rewrite([6(6)])].
% 7.67/8.00 939 multiply(A,greatest_lower_bound(inverse(A),identity)) = greatest_lower_bound(A,identity). [para(59(a,1),54(a,1,2)),flip(a)].
% 7.67/8.00 945 greatest_lower_bound(least_upper_bound(A,identity),least_upper_bound(inverse(A),identity)) = multiply(least_upper_bound(inverse(A),identity),greatest_lower_bound(A,identity)). [para(94(a,1),54(a,1,2)),rewrite([5(6)])].
% 7.67/8.00 1010 multiply(A,least_upper_bound(identity,inverse(A))) = least_upper_bound(A,identity). [para(6(a,1),869(a,1,2))].
% 7.67/8.00 1024 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(869(a,1),39(a,1,2)),rewrite([5(6),945(6)])].
% 7.67/8.00 1031 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)). [back_rewrite(945),rewrite([1024(12)])].
% 7.67/8.00 1041 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(939(a,1),35(a,1,2)),rewrite([6(6),891(6)]),flip(a)].
% 7.67/8.00 1119 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(114(a,1),54(a,1,2)),rewrite([1031(6),1041(12)]),flip(a)].
% 7.67/8.00 1121 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(891),rewrite([1119(12)])].
% 7.67/8.00 1327 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(67(a,2),25(a,2)),rewrite([25(9)])].
% 7.67/8.00 1375 multiply(A,inverse(greatest_lower_bound(A,identity))) = inverse(greatest_lower_bound(inverse(A),identity)). [para(344(a,1),93(a,1,1)),rewrite([65(6)]),flip(a)].
% 7.67/8.00 1997 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(939(a,1),110(a,1,2,2)),rewrite([6(9),1121(9)])].
% 7.67/8.00 4533 multiply(inverse(least_upper_bound(identity,multiply(inverse(A),B))),multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(121(a,1),4(a,1))].
% 7.67/8.00 5553 greatest_lower_bound(inverse(greatest_lower_bound(A,identity)),inverse(greatest_lower_bound(inverse(A),identity))) = identity. [para(1010(a,1),131(a,2)),rewrite([52(3),52(4),1(6),192(5),52(6),192(8),1375(7),52(10),6(12),186(12)])].
% 7.67/8.00 6648 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(25(a,1),146(a,1,2)),rewrite([5(1)])].
% 7.67/8.00 11053 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(5553(a,1),136(a,1,2,2,2)),rewrite([65(5),65(11),6(13),1327(14)])].
% 7.67/8.00 11370 multiply(inverse(least_upper_bound(inverse(A),inverse(B))),multiply(inverse(A),least_upper_bound(A,B))) = B. [para(33(a,1),214(a,1,2))].
% 7.67/8.00 11371 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(446(a,1),214(a,1,2)),rewrite([65(3),6(2),51(5)])].
% 7.67/8.00 11378 multiply(inverse(least_upper_bound(inverse(c),inverse(b))),multiply(inverse(c),least_upper_bound(c,a))) = b. [para(119(a,1),214(a,1,2))].
% 7.67/8.00 11408 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(11371(a,1),649(a,1,2)),rewrite([5(4),11371(7)])].
% 7.67/8.00 11442 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(11408(a,1),609(a,1,2,1)),rewrite([65(3),65(3),6(2),11408(6),65(4)])].
% 7.67/8.00 17326 greatest_lower_bound(identity,multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity))) = identity. [para(176(a,1),411(a,1,2,2)),rewrite([894(7),6648(8),133(5),8(5),400(11),1024(8)]),flip(a)].
% 7.67/8.00 17335 multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)) = identity. [para(17326(a,1),11442(a,1,2)),rewrite([6(8),11053(8),344(5),11442(5)]),flip(a)].
% 7.67/8.00 17338 inverse(least_upper_bound(A,identity)) = greatest_lower_bound(inverse(A),identity). [back_rewrite(1997),rewrite([17335(9),51(5)])].
% 7.67/8.00 17541 inverse(least_upper_bound(identity,multiply(A,B))) = greatest_lower_bound(identity,multiply(inverse(B),inverse(A))). [para(93(a,1),17338(a,2,1)),rewrite([6(3),5(9)])].
% 7.67/8.00 17627 multiply(greatest_lower_bound(inverse(A),inverse(B)),least_upper_bound(A,B)) = identity. [back_rewrite(4533),rewrite([17541(5),65(4),469(8),1(4),5(3)])].
% 7.67/8.00 17965 inverse(greatest_lower_bound(inverse(A),inverse(B))) = least_upper_bound(A,B). [para(17627(a,1),28(a,1,2)),rewrite([51(6)])].
% 7.67/8.00 18008 inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)). [para(17965(a,1),65(a,1,1))].
% 7.67/8.00 18407 multiply(greatest_lower_bound(c,a),multiply(inverse(c),least_upper_bound(c,a))) = b. [back_rewrite(11378),rewrite([18008(6),65(3),65(4),10(3)])].
% 7.67/8.00 18409 multiply(greatest_lower_bound(A,B),multiply(inverse(A),least_upper_bound(A,B))) = B. [back_rewrite(11370),rewrite([18008(4),65(2),65(2)])].
% 7.67/8.00 18860 b = a. [back_rewrite(18407),rewrite([18409(10)]),flip(a)].
% 7.67/8.00 18861 $F # answer(prove_p12). [resolve(18860,a,27,a)].
% 7.67/8.00
% 7.67/8.00 % SZS output end Refutation
% 7.67/8.00 ============================== end of proof ==========================
% 7.67/8.00
% 7.67/8.00 ============================== STATISTICS ============================
% 7.67/8.00
% 7.67/8.00 Given=1072. Generated=340306. Kept=18851. proofs=1.
% 7.67/8.00 Usable=677. Sos=6072. Demods=6597. Limbo=451, Disabled=11668. Hints=0.
% 7.67/8.00 Megabytes=17.05.
% 7.67/8.00 User_CPU=6.81, System_CPU=0.19, Wall_clock=7.
% 7.67/8.00
% 7.67/8.00 ============================== end of statistics =====================
% 7.67/8.00
% 7.67/8.00 ============================== end of search =========================
% 7.67/8.00
% 7.67/8.00 THEOREM PROVED
% 7.67/8.00 % SZS status Unsatisfiable
% 7.67/8.00
% 7.67/8.00 Exiting with 1 proof.
% 7.67/8.00
% 7.67/8.00 Process 26365 exit (max_proofs) Mon Jun 13 17:49:15 2022
% 7.67/8.00 Prover9 interrupted
%------------------------------------------------------------------------------