TSTP Solution File: GRP186-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP186-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 11:18:02 EDT 2022
% Result : Unsatisfiable 8.32s 8.61s
% Output : Refutation 8.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP186-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 19:05:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.06/4.38 ============================== Prover9 ===============================
% 4.06/4.38 Prover9 (32) version 2009-11A, November 2009.
% 4.06/4.38 Process 7642 was started by sandbox2 on n026.cluster.edu,
% 4.06/4.38 Mon Jun 13 19:05:06 2022
% 4.06/4.38 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7489_n026.cluster.edu".
% 4.06/4.38 ============================== end of head ===========================
% 4.06/4.38
% 4.06/4.38 ============================== INPUT =================================
% 4.06/4.38
% 4.06/4.38 % Reading from file /tmp/Prover9_7489_n026.cluster.edu
% 4.06/4.38
% 4.06/4.38 set(prolog_style_variables).
% 4.06/4.38 set(auto2).
% 4.06/4.38 % set(auto2) -> set(auto).
% 4.06/4.38 % set(auto) -> set(auto_inference).
% 4.06/4.38 % set(auto) -> set(auto_setup).
% 4.06/4.38 % set(auto_setup) -> set(predicate_elim).
% 4.06/4.38 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.06/4.38 % set(auto) -> set(auto_limits).
% 4.06/4.38 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.06/4.38 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.06/4.38 % set(auto) -> set(auto_denials).
% 4.06/4.38 % set(auto) -> set(auto_process).
% 4.06/4.38 % set(auto2) -> assign(new_constants, 1).
% 4.06/4.38 % set(auto2) -> assign(fold_denial_max, 3).
% 4.06/4.38 % set(auto2) -> assign(max_weight, "200.000").
% 4.06/4.38 % set(auto2) -> assign(max_hours, 1).
% 4.06/4.38 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.06/4.38 % set(auto2) -> assign(max_seconds, 0).
% 4.06/4.38 % set(auto2) -> assign(max_minutes, 5).
% 4.06/4.38 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.06/4.38 % set(auto2) -> set(sort_initial_sos).
% 4.06/4.38 % set(auto2) -> assign(sos_limit, -1).
% 4.06/4.38 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.06/4.38 % set(auto2) -> assign(max_megs, 400).
% 4.06/4.38 % set(auto2) -> assign(stats, some).
% 4.06/4.38 % set(auto2) -> clear(echo_input).
% 4.06/4.38 % set(auto2) -> set(quiet).
% 4.06/4.38 % set(auto2) -> clear(print_initial_clauses).
% 4.06/4.38 % set(auto2) -> clear(print_given).
% 4.06/4.38 assign(lrs_ticks,-1).
% 4.06/4.38 assign(sos_limit,10000).
% 4.06/4.38 assign(order,kbo).
% 4.06/4.38 set(lex_order_vars).
% 4.06/4.38 clear(print_given).
% 4.06/4.38
% 4.06/4.38 % formulas(sos). % not echoed (19 formulas)
% 4.06/4.38
% 4.06/4.38 ============================== end of input ==========================
% 4.06/4.38
% 4.06/4.38 % From the command line: assign(max_seconds, 300).
% 4.06/4.38
% 4.06/4.38 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.06/4.38
% 4.06/4.38 % Formulas that are not ordinary clauses:
% 4.06/4.38
% 4.06/4.38 ============================== end of process non-clausal formulas ===
% 4.06/4.38
% 4.06/4.38 ============================== PROCESS INITIAL CLAUSES ===============
% 4.06/4.38
% 4.06/4.38 ============================== PREDICATE ELIMINATION =================
% 4.06/4.38
% 4.06/4.38 ============================== end predicate elimination =============
% 4.06/4.38
% 4.06/4.38 Auto_denials:
% 4.06/4.38 % copying label prove_p23 to answer in negative clause
% 4.06/4.38
% 4.06/4.38 Term ordering decisions:
% 4.06/4.38
% 4.06/4.38 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 4.06/4.38 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 4.06/4.38
% 4.06/4.38 ============================== end of process initial clauses ========
% 4.06/4.38
% 4.06/4.38 ============================== CLAUSES FOR SEARCH ====================
% 4.06/4.38
% 4.06/4.38 ============================== end of clauses for search =============
% 4.06/4.38
% 4.06/4.38 ============================== SEARCH ================================
% 4.06/4.38
% 4.06/4.38 % Starting search at 0.01 seconds.
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=37.000, iters=3387
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=33.000, iters=3354
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=31.000, iters=3378
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=30.000, iters=3446
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=29.000, iters=3404
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=27.000, iters=3340
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=26.000, iters=3380
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=25.000, iters=3403
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=24.000, iters=3335
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=23.000, iters=3379
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=22.000, iters=3360
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=21.000, iters=3360
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=20.000, iters=3351
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=19.000, iters=3349
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=5318, wt=43.000
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=6435, wt=41.000
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=5728, wt=40.000
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=6461, wt=39.000
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=18.000, iters=3346
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=6455, wt=38.000
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=6081, wt=37.000
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=12613, wt=17.000
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=13302, wt=16.000
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=13310, wt=15.000
% 4.06/4.38
% 4.06/4.38 Low Water (keep): wt=17.000, iters=3357
% 4.06/4.38
% 4.06/4.38 Low Water (displace): id=13821, wt=14.000
% 8.32/8.61
% 8.32/8.61 Low Water (displace): id=14969, wt=13.000
% 8.32/8.61
% 8.32/8.61 ============================== PROOF =================================
% 8.32/8.61 % SZS status Unsatisfiable
% 8.32/8.61 % SZS output start Refutation
% 8.32/8.61
% 8.32/8.61 % Proof 1 at 7.39 (+ 0.23) seconds: prove_p23.
% 8.32/8.61 % Length of proof is 101.
% 8.32/8.61 % Level of proof is 15.
% 8.32/8.61 % Maximum clause weight is 19.000.
% 8.32/8.61 % Given clauses 1043.
% 8.32/8.61
% 8.32/8.61 1 inverse(identity) = identity # label(p23_1) # label(hypothesis). [assumption].
% 8.32/8.61 2 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 8.32/8.61 5 inverse(inverse(A)) = A # label(p23_2) # label(hypothesis). [assumption].
% 8.32/8.61 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 8.32/8.61 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 8.32/8.61 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 8.32/8.61 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 8.32/8.61 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 8.32/8.61 11 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)) # label(p23_3) # label(hypothesis). [assumption].
% 8.32/8.61 12 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 8.32/8.61 13 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].
% 8.32/8.61 14 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(13),rewrite([7(4)])].
% 8.32/8.61 15 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].
% 8.32/8.61 16 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(15),rewrite([8(4)])].
% 8.32/8.61 17 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 8.32/8.61 18 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(17),flip(a)].
% 8.32/8.61 19 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 8.32/8.61 20 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(19),flip(a)].
% 8.32/8.61 21 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 8.32/8.61 22 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(21),flip(a)].
% 8.32/8.61 23 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 8.32/8.61 24 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(23),flip(a)].
% 8.32/8.61 25 least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) # label(prove_p23) # label(negated_conjecture) # answer(prove_p23). [assumption].
% 8.32/8.61 26 least_upper_bound(identity,multiply(a,b)) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) # answer(prove_p23). [copy(25),rewrite([8(5)])].
% 8.32/8.61 27 multiply(A,inverse(A)) = identity. [para(5(a,1),6(a,1,1))].
% 8.32/8.61 28 multiply(inverse(A),identity) = inverse(A). [para(1(a,1),11(a,2,2)),rewrite([2(2)]),flip(a)].
% 8.32/8.61 30 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),12(a,1,1)),rewrite([2(2)]),flip(a)].
% 8.32/8.61 34 least_upper_bound(A,least_upper_bound(B,greatest_lower_bound(A,C))) = least_upper_bound(A,B). [para(9(a,1),16(a,2,2)),rewrite([8(2),8(4)])].
% 8.32/8.61 35 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),18(a,1,1))].
% 8.32/8.61 36 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(6(a,1),20(a,1,1))].
% 8.32/8.61 37 least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A). [para(2(a,1),22(a,1,1)),rewrite([8(4)])].
% 8.32/8.61 38 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),22(a,1,1)),rewrite([8(5)])].
% 8.32/8.61 41 greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(B,identity),A). [para(2(a,1),24(a,1,1)),rewrite([7(4)])].
% 8.32/8.61 42 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(6(a,1),24(a,1,1)),rewrite([7(5)])].
% 8.32/8.61 43 greatest_lower_bound(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(greatest_lower_bound(D,multiply(A,B)),C). [para(12(a,1),24(a,1,1)),rewrite([7(6)])].
% 8.32/8.61 44 greatest_lower_bound(multiply(A,B),multiply(C,multiply(D,B))) = multiply(greatest_lower_bound(A,multiply(C,D)),B). [para(12(a,1),24(a,1,2))].
% 8.32/8.61 46 multiply(A,multiply(inverse(A),B)) = B. [para(27(a,1),12(a,1,1)),rewrite([2(2)]),flip(a)].
% 8.32/8.61 47 least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))). [para(27(a,1),18(a,1,1)),rewrite([8(5)])].
% 8.32/8.61 48 greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(B,inverse(A))). [para(27(a,1),20(a,1,1)),rewrite([7(5)])].
% 8.32/8.61 51 multiply(A,identity) = A. [para(5(a,1),28(a,1,1)),rewrite([5(4)])].
% 8.32/8.61 54 least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(B,identity)). [para(51(a,1),18(a,1,1)),rewrite([8(4)])].
% 8.32/8.61 55 greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(B,identity)). [para(51(a,1),20(a,1,1)),rewrite([7(4)])].
% 8.32/8.61 56 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(30(a,1),18(a,1,1)),rewrite([8(6)]),flip(a)].
% 8.32/8.61 57 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(30(a,1),20(a,1,1)),rewrite([7(6)]),flip(a)].
% 8.32/8.61 70 multiply(least_upper_bound(inverse(A),identity),A) = least_upper_bound(A,identity). [para(6(a,1),37(a,1,2)),flip(a)].
% 8.32/8.61 71 greatest_lower_bound(A,multiply(least_upper_bound(B,identity),A)) = A. [para(37(a,1),10(a,1,2))].
% 8.32/8.61 87 multiply(least_upper_bound(A,identity),inverse(A)) = least_upper_bound(inverse(A),identity). [para(27(a,1),37(a,1,2)),flip(a)].
% 8.32/8.61 88 multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(B,multiply(A,B))) = B. [para(37(a,2),30(a,1,2))].
% 8.32/8.61 97 multiply(A,least_upper_bound(identity,multiply(inverse(B),C))) = multiply(A,multiply(inverse(B),least_upper_bound(B,C))). [para(35(a,2),12(a,2,2)),rewrite([12(4)]),flip(a)].
% 8.32/8.61 109 multiply(inverse(A),least_upper_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [para(51(a,1),35(a,1,2)),flip(a)].
% 8.32/8.61 112 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(34(a,1),35(a,2,2))].
% 8.32/8.61 117 greatest_lower_bound(identity,least_upper_bound(A,identity)) = identity. [para(51(a,1),71(a,1,2))].
% 8.32/8.61 119 greatest_lower_bound(A,multiply(A,least_upper_bound(B,identity))) = A. [para(117(a,1),20(a,2,2)),rewrite([51(2),51(6)])].
% 8.32/8.61 121 greatest_lower_bound(A,greatest_lower_bound(B,multiply(A,least_upper_bound(C,identity)))) = greatest_lower_bound(A,B). [para(119(a,1),14(a,2,2)),rewrite([7(4),7(6)])].
% 8.32/8.61 151 multiply(inverse(A),greatest_lower_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)). [para(51(a,1),36(a,1,2)),flip(a)].
% 8.32/8.61 171 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(38(a,1),10(a,1,2))].
% 8.32/8.61 190 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(38(a,2),30(a,1,2))].
% 8.32/8.61 245 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(5(a,1),171(a,1,2,1,2))].
% 8.32/8.61 304 multiply(greatest_lower_bound(inverse(A),identity),A) = greatest_lower_bound(A,identity). [para(6(a,1),41(a,1,2)),flip(a)].
% 8.32/8.61 320 multiply(greatest_lower_bound(A,identity),inverse(A)) = greatest_lower_bound(inverse(A),identity). [para(27(a,1),41(a,1,2)),flip(a)].
% 8.32/8.61 348 multiply(greatest_lower_bound(identity,inverse(A)),A) = greatest_lower_bound(A,identity). [para(7(a,1),304(a,1,1))].
% 8.32/8.61 366 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(42(a,1),9(a,1,2))].
% 8.32/8.61 379 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(42(a,2),20(a,2)),rewrite([20(9)])].
% 8.32/8.61 389 greatest_lower_bound(identity,least_upper_bound(A,multiply(B,A))) = multiply(greatest_lower_bound(least_upper_bound(B,identity),inverse(A)),A). [para(37(a,2),42(a,1,2))].
% 8.32/8.61 413 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(5(a,1),366(a,1,2,1,2))].
% 8.32/8.61 459 multiply(greatest_lower_bound(A,multiply(B,C)),multiply(inverse(C),D)) = multiply(greatest_lower_bound(B,multiply(A,inverse(C))),D). [para(46(a,1),43(a,1,1,2)),rewrite([44(5)]),flip(a)].
% 8.32/8.61 566 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(47(a,2),24(a,2)),rewrite([24(9)])].
% 8.32/8.61 567 multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != multiply(a,least_upper_bound(b,inverse(a))) # answer(prove_p23). [para(47(a,1),26(a,1)),flip(a)].
% 8.32/8.61 568 multiply(A,least_upper_bound(identity,inverse(A))) = least_upper_bound(A,identity). [para(51(a,1),47(a,1,2)),rewrite([8(2)]),flip(a)].
% 8.32/8.61 602 multiply(A,least_upper_bound(inverse(A),identity)) = least_upper_bound(A,identity). [para(8(a,1),568(a,1,2))].
% 8.32/8.61 638 multiply(A,greatest_lower_bound(identity,inverse(A))) = greatest_lower_bound(A,identity). [para(51(a,1),48(a,1,2)),rewrite([7(2)]),flip(a)].
% 8.32/8.61 665 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(602(a,1),41(a,1,2)),rewrite([7(6)])].
% 8.32/8.61 669 multiply(A,greatest_lower_bound(inverse(A),identity)) = greatest_lower_bound(A,identity). [para(7(a,1),638(a,1,2))].
% 8.32/8.61 678 least_upper_bound(greatest_lower_bound(A,identity),greatest_lower_bound(identity,inverse(A))) = multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,inverse(A))). [para(638(a,1),37(a,1,2)),rewrite([8(6)])].
% 8.32/8.61 692 least_upper_bound(greatest_lower_bound(A,identity),greatest_lower_bound(inverse(A),identity)) = multiply(least_upper_bound(A,identity),greatest_lower_bound(inverse(A),identity)). [para(669(a,1),37(a,1,2)),rewrite([8(6)])].
% 8.32/8.61 771 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(304(a,1),54(a,1,2)),rewrite([8(6),692(6)])].
% 8.32/8.61 774 multiply(least_upper_bound(A,identity),greatest_lower_bound(identity,inverse(A))) = multiply(greatest_lower_bound(identity,inverse(A)),least_upper_bound(A,identity)). [para(348(a,1),54(a,1,2)),rewrite([8(6),678(6)])].
% 8.32/8.61 785 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)). [back_rewrite(692),rewrite([771(12)])].
% 8.32/8.61 786 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)). [back_rewrite(678),rewrite([774(12)])].
% 8.32/8.61 806 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(70(a,1),55(a,1,2)),rewrite([7(6),665(6)]),flip(a)].
% 8.32/8.61 839 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(87(a,1),55(a,1,2)),rewrite([665(6),771(12)]),flip(a)].
% 8.32/8.61 841 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(785),rewrite([839(12)])].
% 8.32/8.61 951 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(413(a,1),56(a,1,2)),rewrite([51(4),51(7)]),flip(a)].
% 8.32/8.61 999 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(245(a,1),57(a,1,2)),rewrite([51(4),51(7)]),flip(a)].
% 8.32/8.61 1035 multiply(inverse(greatest_lower_bound(A,identity)),A) = inverse(greatest_lower_bound(identity,inverse(A))). [para(151(a,1),11(a,1,1)),rewrite([5(9)]),flip(a)].
% 8.32/8.61 1623 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(669(a,1),88(a,1,2,2)),rewrite([8(9),841(9)])].
% 8.32/8.61 4601 multiply(inverse(least_upper_bound(identity,multiply(inverse(A),B))),multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(97(a,1),6(a,1))].
% 8.32/8.61 5057 greatest_lower_bound(inverse(greatest_lower_bound(A,identity)),inverse(greatest_lower_bound(identity,inverse(A)))) = identity. [para(1035(a,1),55(a,1,2)),rewrite([6(14)])].
% 8.32/8.61 6183 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(24(a,1),121(a,1,2)),rewrite([7(1)])].
% 8.32/8.61 9584 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(5057(a,1),112(a,1,2,2,2)),rewrite([5(5),5(11),8(13),566(14)])].
% 8.32/8.61 11361 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(413(a,1),190(a,1,2)),rewrite([5(3),8(2),51(5)])].
% 8.32/8.61 11389 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(11361(a,1),999(a,1,2)),rewrite([7(4),11361(7)])].
% 8.32/8.61 11443 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(11389(a,1),951(a,1,2,1)),rewrite([5(3),5(3),8(2),11389(6),5(4)])].
% 8.32/8.61 16937 greatest_lower_bound(identity,multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity))) = identity. [para(151(a,1),389(a,1,2,2)),rewrite([786(7),6183(8),109(5),10(5),379(11),806(8)]),flip(a)].
% 8.32/8.61 16951 multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)) = identity. [para(16937(a,1),11443(a,1,2)),rewrite([8(8),9584(8),320(5),11443(5)]),flip(a)].
% 8.32/8.61 16955 inverse(least_upper_bound(A,identity)) = greatest_lower_bound(inverse(A),identity). [back_rewrite(1623),rewrite([16951(9),51(5)])].
% 8.32/8.61 17183 inverse(least_upper_bound(identity,multiply(A,B))) = greatest_lower_bound(identity,multiply(inverse(B),inverse(A))). [para(11(a,1),16955(a,2,1)),rewrite([8(3),7(9)])].
% 8.32/8.61 17268 multiply(greatest_lower_bound(inverse(A),inverse(B)),least_upper_bound(A,B)) = identity. [back_rewrite(4601),rewrite([17183(5),5(4),459(8),2(4),7(3)])].
% 8.32/8.61 17656 inverse(greatest_lower_bound(inverse(A),inverse(B))) = least_upper_bound(A,B). [para(17268(a,1),30(a,1,2)),rewrite([51(6)])].
% 8.32/8.61 17689 inverse(greatest_lower_bound(A,inverse(B))) = least_upper_bound(B,inverse(A)). [para(5(a,1),17656(a,1,1,1)),rewrite([8(5)])].
% 8.32/8.61 18298 $F # answer(prove_p23). [back_rewrite(567),rewrite([17689(6)]),xx(a)].
% 8.32/8.61
% 8.32/8.61 % SZS output end Refutation
% 8.32/8.61 ============================== end of proof ==========================
% 8.32/8.61
% 8.32/8.61 ============================== STATISTICS ============================
% 8.32/8.61
% 8.32/8.61 Given=1043. Generated=380945. Kept=18290. proofs=1.
% 8.32/8.61 Usable=648. Sos=5591. Demods=6189. Limbo=609, Disabled=11461. Hints=0.
% 8.32/8.61 Megabytes=16.64.
% 8.32/8.61 User_CPU=7.39, System_CPU=0.23, Wall_clock=8.
% 8.32/8.61
% 8.32/8.61 ============================== end of statistics =====================
% 8.32/8.61
% 8.32/8.61 ============================== end of search =========================
% 8.32/8.61
% 8.32/8.61 THEOREM PROVED
% 8.32/8.61 % SZS status Unsatisfiable
% 8.32/8.61
% 8.32/8.61 Exiting with 1 proof.
% 8.32/8.61
% 8.32/8.61 Process 7642 exit (max_proofs) Mon Jun 13 19:05:14 2022
% 8.32/8.61 Prover9 interrupted
%------------------------------------------------------------------------------