TSTP Solution File: GRP170-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP170-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:17:52 EDT 2022
% Result : Unsatisfiable 8.57s 8.86s
% Output : Refutation 8.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : GRP170-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 22:01:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.35/3.64 ============================== Prover9 ===============================
% 3.35/3.64 Prover9 (32) version 2009-11A, November 2009.
% 3.35/3.64 Process 24083 was started by sandbox2 on n008.cluster.edu,
% 3.35/3.64 Mon Jun 13 22:01:38 2022
% 3.35/3.64 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23930_n008.cluster.edu".
% 3.35/3.64 ============================== end of head ===========================
% 3.35/3.64
% 3.35/3.64 ============================== INPUT =================================
% 3.35/3.64
% 3.35/3.64 % Reading from file /tmp/Prover9_23930_n008.cluster.edu
% 3.35/3.64
% 3.35/3.64 set(prolog_style_variables).
% 3.35/3.64 set(auto2).
% 3.35/3.64 % set(auto2) -> set(auto).
% 3.35/3.64 % set(auto) -> set(auto_inference).
% 3.35/3.64 % set(auto) -> set(auto_setup).
% 3.35/3.64 % set(auto_setup) -> set(predicate_elim).
% 3.35/3.64 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.35/3.64 % set(auto) -> set(auto_limits).
% 3.35/3.64 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.35/3.64 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.35/3.64 % set(auto) -> set(auto_denials).
% 3.35/3.64 % set(auto) -> set(auto_process).
% 3.35/3.64 % set(auto2) -> assign(new_constants, 1).
% 3.35/3.64 % set(auto2) -> assign(fold_denial_max, 3).
% 3.35/3.64 % set(auto2) -> assign(max_weight, "200.000").
% 3.35/3.64 % set(auto2) -> assign(max_hours, 1).
% 3.35/3.64 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.35/3.64 % set(auto2) -> assign(max_seconds, 0).
% 3.35/3.64 % set(auto2) -> assign(max_minutes, 5).
% 3.35/3.64 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.35/3.64 % set(auto2) -> set(sort_initial_sos).
% 3.35/3.64 % set(auto2) -> assign(sos_limit, -1).
% 3.35/3.64 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.35/3.64 % set(auto2) -> assign(max_megs, 400).
% 3.35/3.64 % set(auto2) -> assign(stats, some).
% 3.35/3.64 % set(auto2) -> clear(echo_input).
% 3.35/3.64 % set(auto2) -> set(quiet).
% 3.35/3.64 % set(auto2) -> clear(print_initial_clauses).
% 3.35/3.64 % set(auto2) -> clear(print_given).
% 3.35/3.64 assign(lrs_ticks,-1).
% 3.35/3.64 assign(sos_limit,10000).
% 3.35/3.64 assign(order,kbo).
% 3.35/3.64 set(lex_order_vars).
% 3.35/3.64 clear(print_given).
% 3.35/3.64
% 3.35/3.64 % formulas(sos). % not echoed (18 formulas)
% 3.35/3.64
% 3.35/3.64 ============================== end of input ==========================
% 3.35/3.64
% 3.35/3.64 % From the command line: assign(max_seconds, 300).
% 3.35/3.64
% 3.35/3.64 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.35/3.64
% 3.35/3.64 % Formulas that are not ordinary clauses:
% 3.35/3.64
% 3.35/3.64 ============================== end of process non-clausal formulas ===
% 3.35/3.64
% 3.35/3.64 ============================== PROCESS INITIAL CLAUSES ===============
% 3.35/3.64
% 3.35/3.64 ============================== PREDICATE ELIMINATION =================
% 3.35/3.64
% 3.35/3.64 ============================== end predicate elimination =============
% 3.35/3.64
% 3.35/3.64 Auto_denials:
% 3.35/3.64 % copying label prove_p03d to answer in negative clause
% 3.35/3.64
% 3.35/3.64 Term ordering decisions:
% 3.35/3.64
% 3.35/3.64 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 3.35/3.64 Function symbol KB weights: b=1. c=1. identity=1. a=1. d=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 3.35/3.64
% 3.35/3.64 ============================== end of process initial clauses ========
% 3.35/3.64
% 3.35/3.64 ============================== CLAUSES FOR SEARCH ====================
% 3.35/3.64
% 3.35/3.64 ============================== end of clauses for search =============
% 3.35/3.64
% 3.35/3.64 ============================== SEARCH ================================
% 3.35/3.64
% 3.35/3.64 % Starting search at 0.01 seconds.
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=39.000, iters=3408
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=37.000, iters=3361
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=35.000, iters=3366
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=33.000, iters=3478
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=32.000, iters=3412
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=31.000, iters=3366
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=30.000, iters=3339
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=29.000, iters=3367
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=28.000, iters=3369
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=27.000, iters=3364
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=26.000, iters=3351
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=25.000, iters=3399
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=24.000, iters=3347
% 3.35/3.64
% 3.35/3.64 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 1.54 sec).
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=23.000, iters=3361
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=22.000, iters=3354
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=21.000, iters=3380
% 3.35/3.64
% 3.35/3.64 Low Water (keep): wt=20.000, iters=3427
% 3.35/3.64
% 3.35/3.64 Low Water (displace): id=4997, wt=53.000
% 3.35/3.64
% 3.35/3.64 Low Water (displace): id=5008, wt=50.000
% 3.35/3.64
% 3.35/3.64 Low Water (displace): id=5009, wt=49.000
% 3.35/3.64
% 3.35/3.64 Low Water (displace): id=4774, wt=46.000
% 3.35/3.64
% 3.35/3.64 Low Water (displace): id=4447, wt=45.000
% 3.35/3.64
% 3.35/3.64 Low Water (displace): id=5078, wt=43.000
% 3.35/3.64
% 3.35/3.64 Low Water (displace): id=5082, wt=42.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=6906, wt=41.000
% 8.57/8.86
% 8.57/8.86 Low Water (keep): wt=19.000, iters=3333
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=5027, wt=40.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=4700, wt=39.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=5014, wt=38.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=6908, wt=37.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=13251, wt=18.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=13252, wt=17.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=13398, wt=16.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=13463, wt=15.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=13914, wt=14.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=14221, wt=13.000
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=14226, wt=12.000
% 8.57/8.86
% 8.57/8.86 Low Water (keep): wt=18.000, iters=3348
% 8.57/8.86
% 8.57/8.86 Low Water (keep): wt=17.000, iters=3341
% 8.57/8.86
% 8.57/8.86 Low Water (displace): id=17909, wt=11.000
% 8.57/8.86
% 8.57/8.86 Low Water (keep): wt=16.000, iters=3335
% 8.57/8.86
% 8.57/8.86 ============================== PROOF =================================
% 8.57/8.86 % SZS status Unsatisfiable
% 8.57/8.86 % SZS output start Refutation
% 8.57/8.86
% 8.57/8.86 % Proof 1 at 7.72 (+ 0.19) seconds: prove_p03d.
% 8.57/8.86 % Length of proof is 90.
% 8.57/8.86 % Level of proof is 19.
% 8.57/8.86 % Maximum clause weight is 15.000.
% 8.57/8.86 % Given clauses 1263.
% 8.57/8.86
% 8.57/8.86 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 8.57/8.86 3 greatest_lower_bound(A,A) = A # label(idempotence_of_gld) # label(axiom). [assumption].
% 8.57/8.86 4 least_upper_bound(a,b) = b # label(p03d_1) # label(hypothesis). [assumption].
% 8.57/8.86 5 greatest_lower_bound(c,d) = c # label(p03d_2) # label(hypothesis). [assumption].
% 8.57/8.86 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 8.57/8.86 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 8.57/8.86 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 8.57/8.86 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 8.57/8.86 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 8.57/8.86 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 8.57/8.86 14 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C) # label(associativity_of_lub) # label(axiom). [assumption].
% 8.57/8.86 15 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(14),rewrite([8(4)])].
% 8.57/8.86 16 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 8.57/8.86 17 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(16),flip(a)].
% 8.57/8.86 18 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 8.57/8.86 19 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(18),flip(a)].
% 8.57/8.86 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 8.57/8.86 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 8.57/8.86 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 8.57/8.86 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 8.57/8.86 24 least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d) # label(prove_p03d) # label(negated_conjecture) # answer(prove_p03d). [assumption].
% 8.57/8.86 25 least_upper_bound(multiply(b,d),multiply(a,c)) != multiply(b,d) # answer(prove_p03d). [copy(24),rewrite([8(7)])].
% 8.57/8.86 26 least_upper_bound(b,a) = b. [back_rewrite(4),rewrite([8(3)])].
% 8.57/8.86 27 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 8.57/8.86 32 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),17(a,1,1))].
% 8.57/8.86 33 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(6(a,1),19(a,1,1))].
% 8.57/8.86 34 least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A). [para(1(a,1),21(a,1,1)),rewrite([8(4)])].
% 8.57/8.86 35 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),21(a,1,1)),rewrite([8(5)])].
% 8.57/8.86 39 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(6(a,1),23(a,1,1)),rewrite([7(5)])].
% 8.57/8.86 43 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),27(a,1,2))].
% 8.57/8.86 45 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(27(a,1),17(a,1,1)),rewrite([8(6)]),flip(a)].
% 8.57/8.86 46 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(27(a,1),19(a,1,1)),rewrite([7(6)]),flip(a)].
% 8.57/8.86 49 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(27(a,1),27(a,1,2))].
% 8.57/8.86 50 multiply(A,identity) = A. [back_rewrite(43),rewrite([49(4)])].
% 8.57/8.86 51 inverse(identity) = identity. [para(50(a,1),6(a,1))].
% 8.57/8.86 58 multiply(A,inverse(A)) = identity. [para(49(a,1),6(a,1))].
% 8.57/8.86 63 multiply(A,multiply(inverse(A),B)) = B. [para(49(a,1),27(a,1))].
% 8.57/8.86 64 inverse(inverse(A)) = A. [para(49(a,1),50(a,1)),rewrite([50(2)]),flip(a)].
% 8.57/8.86 65 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(58(a,1),11(a,1)),flip(a)].
% 8.57/8.86 67 greatest_lower_bound(identity,multiply(A,B)) = multiply(A,greatest_lower_bound(B,inverse(A))). [para(58(a,1),19(a,1,1)),rewrite([7(5)])].
% 8.57/8.86 72 multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))) = greatest_lower_bound(C,multiply(A,B)). [para(63(a,1),19(a,1,1)),rewrite([7(5)]),flip(a)].
% 8.57/8.86 85 least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity. [para(9(a,1),32(a,2,2)),rewrite([6(7)])].
% 8.57/8.86 86 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(32(a,1),10(a,1,2))].
% 8.57/8.86 101 least_upper_bound(identity,multiply(inverse(b),a)) = identity. [para(26(a,1),32(a,2,2)),rewrite([6(10)])].
% 8.57/8.86 116 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(65(a,1),27(a,1,2)),rewrite([50(3)]),flip(a)].
% 8.57/8.86 125 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(116(a,1),27(a,1,2)),flip(a)].
% 8.57/8.86 132 least_upper_bound(identity,multiply(A,greatest_lower_bound(B,inverse(A)))) = identity. [para(64(a,1),85(a,1,2,1)),rewrite([7(3)])].
% 8.57/8.86 134 greatest_lower_bound(identity,multiply(inverse(c),d)) = identity. [para(5(a,1),33(a,2,2)),rewrite([6(10)])].
% 8.57/8.86 158 greatest_lower_bound(A,multiply(inverse(c),multiply(d,A))) = A. [para(134(a,1),23(a,2,1)),rewrite([1(2),11(5),1(8)])].
% 8.57/8.86 170 least_upper_bound(A,multiply(B,multiply(C,A))) = multiply(least_upper_bound(identity,multiply(B,C)),A). [para(11(a,1),34(a,1,2)),rewrite([8(6)])].
% 8.57/8.86 206 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(35(a,1),10(a,1,2))].
% 8.57/8.86 223 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(35(a,2),27(a,1,2))].
% 8.57/8.86 228 multiply(least_upper_bound(inverse(b),inverse(a)),a) = identity. [para(35(a,1),101(a,1))].
% 8.57/8.86 237 inverse(least_upper_bound(inverse(b),inverse(a))) = a. [para(228(a,1),27(a,1,2)),rewrite([50(8)])].
% 8.57/8.86 240 least_upper_bound(inverse(b),inverse(a)) = inverse(a). [para(237(a,1),64(a,1,1)),flip(a)].
% 8.57/8.86 243 greatest_lower_bound(inverse(b),inverse(a)) = inverse(b). [para(240(a,1),10(a,1,2))].
% 8.57/8.86 302 least_upper_bound(A,multiply(A,multiply(B,greatest_lower_bound(C,inverse(B))))) = A. [para(132(a,1),17(a,2,2)),rewrite([50(2),50(7)])].
% 8.57/8.86 348 greatest_lower_bound(inverse(c),inverse(d)) = inverse(d). [para(58(a,1),158(a,1,2,2)),rewrite([50(6),7(5)])].
% 8.57/8.86 350 least_upper_bound(inverse(c),inverse(d)) = inverse(c). [para(348(a,1),9(a,1,2))].
% 8.57/8.86 355 least_upper_bound(identity,multiply(inverse(c),d)) = multiply(inverse(c),d). [para(350(a,1),35(a,2,1))].
% 8.57/8.86 357 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(39(a,1),9(a,1,2))].
% 8.57/8.86 384 greatest_lower_bound(identity,multiply(inverse(b),a)) = multiply(inverse(b),a). [para(243(a,1),39(a,2,1))].
% 8.57/8.86 597 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(64(a,1),206(a,1,2,1,2))].
% 8.57/8.86 788 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(64(a,1),357(a,1,2,1,2))].
% 8.57/8.86 955 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(A))) = identity. [para(8(a,1),597(a,1,2,1))].
% 8.57/8.86 975 greatest_lower_bound(inverse(A),inverse(least_upper_bound(B,A))) = inverse(least_upper_bound(B,A)). [para(597(a,1),46(a,1,2)),rewrite([50(4),50(7)]),flip(a)].
% 8.57/8.86 1059 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),A)) = identity. [para(86(a,1),788(a,1,2,1)),rewrite([125(6),64(6),1(6)])].
% 8.57/8.86 1064 least_upper_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(greatest_lower_bound(B,A)). [para(788(a,1),45(a,1,2)),rewrite([50(4),50(7)]),flip(a)].
% 8.57/8.86 1207 greatest_lower_bound(identity,multiply(least_upper_bound(A,least_upper_bound(B,C)),inverse(B))) = identity. [para(15(a,1),955(a,1,2,1))].
% 8.57/8.86 1373 least_upper_bound(identity,multiply(inverse(least_upper_bound(A,B)),B)) = identity. [para(8(a,1),1059(a,1,2,1,1))].
% 8.57/8.86 1777 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(B,A))) = identity. [para(1373(a,1),597(a,1,2,1)),rewrite([125(6),64(6),1(6)])].
% 8.57/8.86 4369 least_upper_bound(A,multiply(A,greatest_lower_bound(identity,multiply(B,C)))) = A. [para(67(a,2),302(a,1,2,2))].
% 8.57/8.86 4391 greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(A,B)))) = identity. [para(4369(a,1),1777(a,1,2,2)),rewrite([125(6),11(8),6(7),50(7)])].
% 8.57/8.86 4661 greatest_lower_bound(identity,multiply(inverse(a),b)) = identity. [para(384(a,1),4391(a,1,2,1)),rewrite([125(6),64(6)])].
% 8.57/8.86 7706 greatest_lower_bound(identity,least_upper_bound(A,multiply(inverse(c),d))) = identity. [para(355(a,1),1207(a,1,2,1,2)),rewrite([51(8),50(8)])].
% 8.57/8.86 7783 greatest_lower_bound(A,multiply(A,least_upper_bound(B,multiply(inverse(c),d)))) = A. [para(7706(a,1),19(a,2,2)),rewrite([50(2),50(9)])].
% 8.57/8.86 9577 inverse(least_upper_bound(A,greatest_lower_bound(B,A))) = inverse(A). [para(788(a,1),223(a,1,2)),rewrite([64(3),8(2),50(5)])].
% 8.57/8.86 9647 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(9577(a,1),975(a,1,2)),rewrite([7(4),9577(7)])].
% 8.57/8.86 9790 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(9647(a,1),1064(a,1,2,1)),rewrite([64(3),64(3),8(2),9647(6),64(4)])].
% 8.57/8.86 9815 least_upper_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),b). [para(4661(a,1),9790(a,1,2)),rewrite([8(6)])].
% 8.57/8.86 20805 greatest_lower_bound(c,least_upper_bound(d,multiply(c,A))) = c. [para(45(a,1),7783(a,1,2)),rewrite([64(3),64(5),64(9)])].
% 8.57/8.86 20814 greatest_lower_bound(c,least_upper_bound(d,greatest_lower_bound(A,multiply(c,B)))) = c. [para(72(a,1),20805(a,1,2,2))].
% 8.57/8.86 20848 greatest_lower_bound(c,least_upper_bound(d,greatest_lower_bound(A,B))) = c. [para(63(a,1),20814(a,1,2,2,2))].
% 8.57/8.86 20864 greatest_lower_bound(c,least_upper_bound(d,multiply(A,greatest_lower_bound(B,C)))) = c. [para(19(a,1),20848(a,1,2,2))].
% 8.57/8.86 21028 greatest_lower_bound(c,least_upper_bound(d,multiply(A,B))) = c. [para(3(a,1),20864(a,1,2,2,2))].
% 8.57/8.86 21053 greatest_lower_bound(c,multiply(least_upper_bound(identity,multiply(A,B)),d)) = c. [para(170(a,1),21028(a,1,2))].
% 8.57/8.86 21223 greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))) = c. [para(9815(a,1),21053(a,1,2,1)),rewrite([11(7)])].
% 8.57/8.86 21300 greatest_lower_bound(multiply(b,d),multiply(a,c)) = multiply(a,c). [para(21223(a,1),46(a,1,2)),rewrite([64(3),64(9)]),flip(a)].
% 8.57/8.86 21474 least_upper_bound(multiply(b,d),multiply(a,c)) = multiply(b,d). [para(21300(a,1),9(a,1,2))].
% 8.57/8.86 21475 $F # answer(prove_p03d). [resolve(21474,a,25,a)].
% 8.57/8.86
% 8.57/8.86 % SZS output end Refutation
% 8.57/8.86 ============================== end of proof ==========================
% 8.57/8.86
% 8.57/8.86 ============================== STATISTICS ============================
% 8.57/8.86
% 8.57/8.86 Given=1263. Generated=342869. Kept=21467. proofs=1.
% 8.57/8.86 Usable=1082. Sos=9999. Demods=10166. Limbo=0, Disabled=10403. Hints=0.
% 8.57/8.86 Megabytes=18.87.
% 8.57/8.86 User_CPU=7.72, System_CPU=0.19, Wall_clock=8.
% 8.57/8.86
% 8.57/8.86 ============================== end of statistics =====================
% 8.57/8.86
% 8.57/8.86 ============================== end of search =========================
% 8.57/8.86
% 8.57/8.86 THEOREM PROVED
% 8.57/8.86 % SZS status Unsatisfiable
% 8.57/8.86
% 8.57/8.86 Exiting with 1 proof.
% 8.57/8.86
% 8.57/8.86 Process 24083 exit (max_proofs) Mon Jun 13 22:01:46 2022
% 8.57/8.86 Prover9 interrupted
%------------------------------------------------------------------------------