TSTP Solution File: GRP181-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP181-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 16.11s 16.41s
% Output : Refutation 16.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP181-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 07:31:39 EDT 2022
% 0.14/0.34 % CPUTime :
% 3.18/3.47 ============================== Prover9 ===============================
% 3.18/3.47 Prover9 (32) version 2009-11A, November 2009.
% 3.18/3.47 Process 12388 was started by sandbox2 on n004.cluster.edu,
% 3.18/3.47 Tue Jun 14 07:31:39 2022
% 3.18/3.47 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12235_n004.cluster.edu".
% 3.18/3.47 ============================== end of head ===========================
% 3.18/3.47
% 3.18/3.47 ============================== INPUT =================================
% 3.18/3.47
% 3.18/3.47 % Reading from file /tmp/Prover9_12235_n004.cluster.edu
% 3.18/3.47
% 3.18/3.47 set(prolog_style_variables).
% 3.18/3.47 set(auto2).
% 3.18/3.47 % set(auto2) -> set(auto).
% 3.18/3.47 % set(auto) -> set(auto_inference).
% 3.18/3.47 % set(auto) -> set(auto_setup).
% 3.18/3.47 % set(auto_setup) -> set(predicate_elim).
% 3.18/3.47 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.18/3.47 % set(auto) -> set(auto_limits).
% 3.18/3.47 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.18/3.47 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.18/3.47 % set(auto) -> set(auto_denials).
% 3.18/3.47 % set(auto) -> set(auto_process).
% 3.18/3.47 % set(auto2) -> assign(new_constants, 1).
% 3.18/3.47 % set(auto2) -> assign(fold_denial_max, 3).
% 3.18/3.47 % set(auto2) -> assign(max_weight, "200.000").
% 3.18/3.47 % set(auto2) -> assign(max_hours, 1).
% 3.18/3.47 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.18/3.47 % set(auto2) -> assign(max_seconds, 0).
% 3.18/3.47 % set(auto2) -> assign(max_minutes, 5).
% 3.18/3.47 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.18/3.47 % set(auto2) -> set(sort_initial_sos).
% 3.18/3.47 % set(auto2) -> assign(sos_limit, -1).
% 3.18/3.47 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.18/3.47 % set(auto2) -> assign(max_megs, 400).
% 3.18/3.47 % set(auto2) -> assign(stats, some).
% 3.18/3.47 % set(auto2) -> clear(echo_input).
% 3.18/3.47 % set(auto2) -> set(quiet).
% 3.18/3.47 % set(auto2) -> clear(print_initial_clauses).
% 3.18/3.47 % set(auto2) -> clear(print_given).
% 3.18/3.47 assign(lrs_ticks,-1).
% 3.18/3.47 assign(sos_limit,10000).
% 3.18/3.47 assign(order,kbo).
% 3.18/3.47 set(lex_order_vars).
% 3.18/3.47 clear(print_given).
% 3.18/3.47
% 3.18/3.47 % formulas(sos). % not echoed (21 formulas)
% 3.18/3.47
% 3.18/3.47 ============================== end of input ==========================
% 3.18/3.47
% 3.18/3.47 % From the command line: assign(max_seconds, 300).
% 3.18/3.47
% 3.18/3.47 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.18/3.47
% 3.18/3.47 % Formulas that are not ordinary clauses:
% 3.18/3.47
% 3.18/3.47 ============================== end of process non-clausal formulas ===
% 3.18/3.47
% 3.18/3.47 ============================== PROCESS INITIAL CLAUSES ===============
% 3.18/3.47
% 3.18/3.47 ============================== PREDICATE ELIMINATION =================
% 3.18/3.47
% 3.18/3.47 ============================== end predicate elimination =============
% 3.18/3.47
% 3.18/3.47 Auto_denials:
% 3.18/3.47 % copying label prove_p12 to answer in negative clause
% 3.18/3.47
% 3.18/3.47 Term ordering decisions:
% 3.18/3.47
% 3.18/3.47 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 3.18/3.47 Function symbol KB weights: c=1. identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 3.18/3.47
% 3.18/3.47 ============================== end of process initial clauses ========
% 3.18/3.47
% 3.18/3.47 ============================== CLAUSES FOR SEARCH ====================
% 3.18/3.47
% 3.18/3.47 ============================== end of clauses for search =============
% 3.18/3.47
% 3.18/3.47 ============================== SEARCH ================================
% 3.18/3.47
% 3.18/3.47 % Starting search at 0.01 seconds.
% 3.18/3.47
% 3.18/3.47 Low Water (keep): wt=35.000, iters=3348
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=32.000, iters=3348
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=31.000, iters=3376
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=30.000, iters=3356
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=29.000, iters=3338
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=28.000, iters=3352
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=27.000, iters=3375
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=26.000, iters=3357
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=25.000, iters=3341
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=24.000, iters=3333
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=23.000, iters=3408
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=22.000, iters=3365
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=21.000, iters=3338
% 3.18/3.48
% 3.18/3.48 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 1.81 sec).
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=20.000, iters=3351
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=19.000, iters=3390
% 3.18/3.48
% 3.18/3.48 Low Water (displace): id=5264, wt=43.000
% 3.18/3.48
% 3.18/3.48 Low Water (displace): id=5822, wt=41.000
% 3.18/3.48
% 3.18/3.48 Low Water (displace): id=5707, wt=40.000
% 3.18/3.48
% 3.18/3.48 Low Water (displace): id=5699, wt=39.000
% 3.18/3.48
% 3.18/3.48 Low Water (displace): id=5698, wt=38.000
% 3.18/3.48
% 3.18/3.48 Low Water (displace): id=6147, wt=37.000
% 3.18/3.48
% 3.18/3.48 Low Water (displace): id=12377, wt=17.000
% 3.18/3.48
% 3.18/3.48 Low Water (keep): wt=18.000, iters=3383
% 3.18/3.48
% 3.18/3.48 Low Water (displace): id=13146, wt=16.000
% 16.11/16.41
% 16.11/16.41 Low Water (displace): id=13176, wt=15.000
% 16.11/16.41
% 16.11/16.41 Low Water (keep): wt=17.000, iters=3341
% 16.11/16.41
% 16.11/16.41 Low Water (displace): id=13760, wt=14.000
% 16.11/16.41
% 16.11/16.41 Low Water (displace): id=13840, wt=13.000
% 16.11/16.41
% 16.11/16.41 Low Water (keep): wt=16.000, iters=3333
% 16.11/16.41
% 16.11/16.41 Low Water (displace): id=18061, wt=12.000
% 16.11/16.41
% 16.11/16.41 Low Water (displace): id=19540, wt=11.000
% 16.11/16.41
% 16.11/16.41 Low Water (keep): wt=15.000, iters=3333
% 16.11/16.41
% 16.11/16.41 ============================== PROOF =================================
% 16.11/16.41 % SZS status Unsatisfiable
% 16.11/16.41 % SZS output start Refutation
% 16.11/16.41
% 16.11/16.41 % Proof 1 at 15.01 (+ 0.42) seconds: prove_p12.
% 16.11/16.41 % Length of proof is 103.
% 16.11/16.41 % Level of proof is 18.
% 16.11/16.41 % Maximum clause weight is 19.000.
% 16.11/16.41 % Given clauses 1710.
% 16.11/16.41
% 16.11/16.41 1 inverse(identity) = identity # label(p12_1) # label(hypothesis). [assumption].
% 16.11/16.41 2 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 16.11/16.41 3 least_upper_bound(A,A) = A # label(idempotence_of_lub) # label(axiom). [assumption].
% 16.11/16.41 5 inverse(inverse(A)) = A # label(p12_2) # label(hypothesis). [assumption].
% 16.11/16.41 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 16.11/16.41 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 16.11/16.41 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 16.11/16.41 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 16.11/16.41 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 16.11/16.41 11 greatest_lower_bound(a,c) = greatest_lower_bound(b,c) # label(p12_4) # label(hypothesis). [assumption].
% 16.11/16.41 12 greatest_lower_bound(c,b) = greatest_lower_bound(c,a). [copy(11),rewrite([7(3),7(6)]),flip(a)].
% 16.11/16.41 13 least_upper_bound(a,c) = least_upper_bound(b,c) # label(p12_5) # label(hypothesis). [assumption].
% 16.11/16.41 14 least_upper_bound(c,b) = least_upper_bound(c,a). [copy(13),rewrite([8(3),8(6)]),flip(a)].
% 16.11/16.41 15 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)) # label(p12_3) # label(hypothesis). [assumption].
% 16.11/16.41 16 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 16.11/16.41 17 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].
% 16.11/16.41 18 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(17),rewrite([7(4)])].
% 16.11/16.41 19 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].
% 16.11/16.41 20 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(19),rewrite([8(4)])].
% 16.11/16.41 21 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 16.11/16.41 22 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(21),flip(a)].
% 16.11/16.41 23 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 16.11/16.41 24 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(23),flip(a)].
% 16.11/16.41 25 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 16.11/16.41 26 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(25),flip(a)].
% 16.11/16.41 27 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 16.11/16.41 28 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(27),flip(a)].
% 16.11/16.41 29 a != b # label(prove_p12) # label(negated_conjecture) # answer(prove_p12). [assumption].
% 16.11/16.41 30 b != a # answer(prove_p12). [copy(29),flip(a)].
% 16.11/16.41 31 multiply(A,inverse(A)) = identity. [para(5(a,1),6(a,1,1))].
% 16.11/16.41 32 multiply(inverse(A),identity) = inverse(A). [para(1(a,1),15(a,2,2)),rewrite([2(2)]),flip(a)].
% 16.11/16.41 34 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),16(a,1,1)),rewrite([2(2)]),flip(a)].
% 16.11/16.41 39 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),22(a,1,1))].
% 16.11/16.41 40 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(6(a,1),24(a,1,1))].
% 16.11/16.41 41 least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A). [para(2(a,1),26(a,1,1)),rewrite([8(4)])].
% 16.11/16.41 42 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),26(a,1,1)),rewrite([8(5)])].
% 16.11/16.41 45 greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(B,identity),A). [para(2(a,1),28(a,1,1)),rewrite([7(4)])].
% 16.11/16.41 46 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(6(a,1),28(a,1,1)),rewrite([7(5)])].
% 16.11/16.41 50 multiply(A,multiply(inverse(A),B)) = B. [para(31(a,1),16(a,1,1)),rewrite([2(2)]),flip(a)].
% 16.11/16.41 51 least_upper_bound(identity,multiply(A,B)) = multiply(A,least_upper_bound(B,inverse(A))). [para(31(a,1),22(a,1,1)),rewrite([8(5)])].
% 16.11/16.41 52 greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(B,inverse(A))). [para(31(a,1),24(a,1,1)),rewrite([7(5)])].
% 16.11/16.41 55 multiply(A,identity) = A. [para(5(a,1),32(a,1,1)),rewrite([5(4)])].
% 16.11/16.41 60 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(34(a,1),22(a,1,1)),rewrite([8(6)]),flip(a)].
% 16.11/16.41 61 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(34(a,1),24(a,1,1)),rewrite([7(6)]),flip(a)].
% 16.11/16.41 64 multiply(A,least_upper_bound(B,multiply(inverse(A),C))) = least_upper_bound(C,multiply(A,B)). [para(50(a,1),22(a,1,1)),rewrite([8(5)]),flip(a)].
% 16.11/16.41 76 multiply(least_upper_bound(inverse(A),identity),A) = least_upper_bound(A,identity). [para(6(a,1),41(a,1,2)),flip(a)].
% 16.11/16.41 94 multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(B,multiply(A,B))) = B. [para(41(a,2),34(a,1,2))].
% 16.11/16.41 99 least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity. [para(9(a,1),39(a,2,2)),rewrite([6(7)])].
% 16.11/16.41 100 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(39(a,1),10(a,1,2))].
% 16.11/16.41 101 least_upper_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),least_upper_bound(c,a)). [para(14(a,1),39(a,2,2))].
% 16.11/16.41 116 multiply(inverse(A),least_upper_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [para(55(a,1),39(a,1,2)),flip(a)].
% 16.11/16.41 130 multiply(least_upper_bound(identity,inverse(A)),A) = least_upper_bound(A,identity). [para(8(a,1),76(a,1,1))].
% 16.11/16.41 165 least_upper_bound(identity,greatest_lower_bound(A,identity)) = identity. [para(1(a,1),99(a,1,2,1)),rewrite([7(4),2(5)])].
% 16.11/16.41 172 least_upper_bound(A,multiply(greatest_lower_bound(B,identity),A)) = A. [para(165(a,1),26(a,2,1)),rewrite([2(2),2(6)])].
% 16.11/16.41 177 least_upper_bound(A,least_upper_bound(B,multiply(greatest_lower_bound(C,identity),A))) = least_upper_bound(A,B). [para(172(a,1),20(a,2,2)),rewrite([8(4),8(6)])].
% 16.11/16.41 179 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(42(a,1),10(a,1,2))].
% 16.11/16.41 197 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(42(a,2),34(a,1,2))].
% 16.11/16.41 205 greatest_lower_bound(A,multiply(A,multiply(inverse(B),least_upper_bound(B,C)))) = A. [para(100(a,1),24(a,2,2)),rewrite([55(2),55(7)])].
% 16.11/16.41 215 multiply(inverse(least_upper_bound(identity,inverse(A))),least_upper_bound(A,identity)) = A. [para(130(a,1),34(a,1,2))].
% 16.11/16.41 252 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(5(a,1),179(a,1,2,1,2))].
% 16.11/16.41 308 multiply(greatest_lower_bound(inverse(A),identity),A) = greatest_lower_bound(A,identity). [para(6(a,1),45(a,1,2)),flip(a)].
% 16.11/16.41 324 multiply(greatest_lower_bound(A,identity),inverse(A)) = greatest_lower_bound(inverse(A),identity). [para(31(a,1),45(a,1,2)),flip(a)].
% 16.11/16.41 361 greatest_lower_bound(A,greatest_lower_bound(identity,multiply(B,A))) = multiply(greatest_lower_bound(B,greatest_lower_bound(inverse(A),identity)),A). [para(308(a,1),28(a,1,2)),rewrite([18(4),7(3),18(4,R),7(3)])].
% 16.11/16.41 370 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(46(a,1),9(a,1,2))].
% 16.11/16.41 371 inverse(greatest_lower_bound(identity,multiply(A,B))) = multiply(inverse(B),inverse(greatest_lower_bound(A,inverse(B)))). [para(46(a,2),15(a,1,1))].
% 16.11/16.41 426 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(5(a,1),370(a,1,2,1,2))].
% 16.11/16.41 535 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),A)) = identity. [para(100(a,1),426(a,1,2,1)),rewrite([15(6),5(6),2(6)])].
% 16.11/16.41 573 multiply(A,least_upper_bound(identity,inverse(A))) = least_upper_bound(A,identity). [para(55(a,1),51(a,1,2)),rewrite([8(2)]),flip(a)].
% 16.11/16.41 622 multiply(greatest_lower_bound(A,B),greatest_lower_bound(C,inverse(greatest_lower_bound(A,B)))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(A,B),C)). [para(52(a,2),28(a,2)),rewrite([28(9)])].
% 16.11/16.41 634 greatest_lower_bound(identity,multiply(greatest_lower_bound(A,identity),B)) = multiply(greatest_lower_bound(A,greatest_lower_bound(inverse(B),identity)),B). [para(45(a,2),52(a,1,2)),rewrite([18(4,R),7(3),361(4),622(12)]),flip(a)].
% 16.11/16.41 658 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),B)) = identity. [para(8(a,1),535(a,1,2,1,1))].
% 16.11/16.41 775 greatest_lower_bound(least_upper_bound(A,identity),multiply(B,least_upper_bound(identity,inverse(A)))) = multiply(greatest_lower_bound(A,B),least_upper_bound(identity,inverse(A))). [para(573(a,1),28(a,1,1))].
% 16.11/16.41 780 greatest_lower_bound(least_upper_bound(A,identity),least_upper_bound(identity,inverse(A))) = multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,inverse(A))). [para(573(a,1),45(a,1,2)),rewrite([7(6)])].
% 16.11/16.41 1001 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(426(a,1),60(a,1,2)),rewrite([55(4),55(7)]),flip(a)].
% 16.11/16.41 1049 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(252(a,1),61(a,1,2)),rewrite([55(4),55(7)]),flip(a)].
% 16.11/16.41 1399 multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(identity,inverse(A))) = inverse(A). [para(215(a,1),15(a,1,1)),rewrite([5(9)]),flip(a)].
% 16.11/16.41 1402 multiply(inverse(least_upper_bound(identity,inverse(A))),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,inverse(A)))) = greatest_lower_bound(A,identity). [para(215(a,1),40(a,1,2)),rewrite([7(2),7(12),780(12)]),flip(a)].
% 16.11/16.41 1932 multiply(inverse(least_upper_bound(inverse(A),identity)),least_upper_bound(identity,inverse(A))) = identity. [para(39(a,1),94(a,1,2)),rewrite([116(8)])].
% 16.11/16.41 2030 greatest_lower_bound(A,multiply(A,least_upper_bound(identity,inverse(B)))) = A. [para(116(a,1),205(a,1,2,2))].
% 16.11/16.41 2141 greatest_lower_bound(identity,inverse(least_upper_bound(identity,inverse(A)))) = inverse(least_upper_bound(identity,inverse(A))). [para(6(a,1),2030(a,1,2)),rewrite([7(6)])].
% 16.11/16.41 6378 multiply(inverse(least_upper_bound(A,identity)),multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,inverse(A)))) = greatest_lower_bound(identity,inverse(A)). [para(1399(a,1),40(a,1,2)),rewrite([780(12)]),flip(a)].
% 16.11/16.41 8912 least_upper_bound(A,multiply(greatest_lower_bound(B,identity),least_upper_bound(A,C))) = least_upper_bound(A,multiply(greatest_lower_bound(B,identity),C)). [para(22(a,1),177(a,1,2)),rewrite([8(3)])].
% 16.11/16.41 11035 multiply(inverse(least_upper_bound(inverse(A),inverse(B))),multiply(inverse(A),least_upper_bound(A,B))) = B. [para(39(a,1),197(a,1,2))].
% 16.11/16.41 11036 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(426(a,1),197(a,1,2)),rewrite([5(3),8(2),55(5)])].
% 16.11/16.41 11038 inverse(least_upper_bound(inverse(A),inverse(least_upper_bound(B,A)))) = A. [para(658(a,1),197(a,1,2)),rewrite([8(4),55(7)])].
% 16.11/16.41 11045 multiply(inverse(least_upper_bound(inverse(c),inverse(b))),multiply(inverse(c),least_upper_bound(c,a))) = b. [para(101(a,1),197(a,1,2))].
% 16.11/16.41 11052 inverse(least_upper_bound(inverse(least_upper_bound(inverse(A),identity)),inverse(least_upper_bound(identity,inverse(A))))) = least_upper_bound(identity,inverse(A)). [para(1932(a,1),197(a,1,2,2)),rewrite([3(13),55(12)])].
% 16.11/16.41 11064 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(11036(a,1),1049(a,1,2)),rewrite([7(4),11036(7)])].
% 16.11/16.41 11079 greatest_lower_bound(A,least_upper_bound(B,A)) = A. [para(11038(a,1),1049(a,1,2)),rewrite([5(3),7(2),11038(7)])].
% 16.11/16.41 11131 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(11064(a,1),1001(a,1,2,1)),rewrite([5(3),5(3),8(2),11064(6),5(4)])].
% 16.11/16.41 16370 multiply(A,inverse(greatest_lower_bound(identity,multiply(B,A)))) = inverse(greatest_lower_bound(B,inverse(A))). [para(371(a,2),34(a,1,2)),rewrite([5(2)])].
% 16.11/16.41 21745 greatest_lower_bound(identity,multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,inverse(A)))) = identity. [para(634(a,2),775(a,2)),rewrite([7(8),2141(8),6(10),7(4),11079(4)]),flip(a)].
% 16.11/16.41 21753 multiply(greatest_lower_bound(A,identity),least_upper_bound(identity,inverse(A))) = identity. [para(21745(a,1),11131(a,1,2)),rewrite([8(8),8912(8),324(5),11131(5)]),flip(a)].
% 16.11/16.41 21755 inverse(least_upper_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)). [back_rewrite(6378),rewrite([21753(9),55(5)])].
% 16.11/16.41 21756 inverse(least_upper_bound(identity,inverse(A))) = greatest_lower_bound(A,identity). [back_rewrite(1402),rewrite([21753(10),55(6)])].
% 16.11/16.41 21806 inverse(greatest_lower_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [back_rewrite(11052),rewrite([21755(4),5(3),7(2),21756(6),3(5)])].
% 16.11/16.41 22076 inverse(greatest_lower_bound(identity,multiply(A,B))) = least_upper_bound(identity,multiply(inverse(B),inverse(A))). [para(15(a,1),21806(a,2,2)),rewrite([7(3)])].
% 16.11/16.41 22099 inverse(greatest_lower_bound(A,inverse(B))) = least_upper_bound(B,inverse(A)). [back_rewrite(16370),rewrite([22076(4),64(6),55(3),8(2)]),flip(a)].
% 16.11/16.41 22370 inverse(least_upper_bound(A,inverse(B))) = greatest_lower_bound(B,inverse(A)). [para(22099(a,1),5(a,1,1))].
% 16.11/16.41 22469 multiply(greatest_lower_bound(c,a),multiply(inverse(c),least_upper_bound(c,a))) = b. [back_rewrite(11045),rewrite([22370(6),5(4),7(3),12(3)])].
% 16.11/16.41 22471 multiply(greatest_lower_bound(A,B),multiply(inverse(A),least_upper_bound(A,B))) = B. [back_rewrite(11035),rewrite([22370(4),5(2),7(1)])].
% 16.11/16.41 22835 b = a. [back_rewrite(22469),rewrite([22471(10)]),flip(a)].
% 16.11/16.41 22836 $F # answer(prove_p12). [resolve(22835,a,30,a)].
% 16.11/16.41
% 16.11/16.41 % SZS output end Refutation
% 16.11/16.41 ============================== end of proof ==========================
% 16.11/16.41
% 16.11/16.41 ============================== STATISTICS ============================
% 16.11/16.41
% 16.11/16.41 Given=1710. Generated=756770. Kept=22826. proofs=1.
% 16.11/16.41 Usable=1093. Sos=6224. Demods=7217. Limbo=364, Disabled=15165. Hints=0.
% 16.11/16.41 Megabytes=18.94.
% 16.11/16.41 User_CPU=15.01, System_CPU=0.42, Wall_clock=16.
% 16.11/16.41
% 16.11/16.41 ============================== end of statistics =====================
% 16.11/16.41
% 16.11/16.41 ============================== end of search =========================
% 16.11/16.41
% 16.11/16.41 THEOREM PROVED
% 16.11/16.41 % SZS status Unsatisfiable
% 16.11/16.41
% 16.11/16.41 Exiting with 1 proof.
% 16.11/16.41
% 16.11/16.41 Process 12388 exit (max_proofs) Tue Jun 14 07:31:55 2022
% 16.11/16.41 Prover9 interrupted
%------------------------------------------------------------------------------