TSTP Solution File: GRP185-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP185-2 : 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 11:18:01 EDT 2022
% Result : Unsatisfiable 255.98s 256.24s
% Output : Refutation 255.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP185-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 07:26:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 4.08/4.37 ============================== Prover9 ===============================
% 4.08/4.37 Prover9 (32) version 2009-11A, November 2009.
% 4.08/4.37 Process 5268 was started by sandbox2 on n028.cluster.edu,
% 4.08/4.37 Mon Jun 13 07:26:38 2022
% 4.08/4.37 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5115_n028.cluster.edu".
% 4.08/4.37 ============================== end of head ===========================
% 4.08/4.37
% 4.08/4.37 ============================== INPUT =================================
% 4.08/4.37
% 4.08/4.37 % Reading from file /tmp/Prover9_5115_n028.cluster.edu
% 4.08/4.37
% 4.08/4.37 set(prolog_style_variables).
% 4.08/4.37 set(auto2).
% 4.08/4.37 % set(auto2) -> set(auto).
% 4.08/4.37 % set(auto) -> set(auto_inference).
% 4.08/4.37 % set(auto) -> set(auto_setup).
% 4.08/4.37 % set(auto_setup) -> set(predicate_elim).
% 4.08/4.37 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.08/4.37 % set(auto) -> set(auto_limits).
% 4.08/4.37 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.08/4.37 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.08/4.37 % set(auto) -> set(auto_denials).
% 4.08/4.37 % set(auto) -> set(auto_process).
% 4.08/4.37 % set(auto2) -> assign(new_constants, 1).
% 4.08/4.37 % set(auto2) -> assign(fold_denial_max, 3).
% 4.08/4.37 % set(auto2) -> assign(max_weight, "200.000").
% 4.08/4.37 % set(auto2) -> assign(max_hours, 1).
% 4.08/4.37 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.08/4.37 % set(auto2) -> assign(max_seconds, 0).
% 4.08/4.37 % set(auto2) -> assign(max_minutes, 5).
% 4.08/4.37 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.08/4.37 % set(auto2) -> set(sort_initial_sos).
% 4.08/4.37 % set(auto2) -> assign(sos_limit, -1).
% 4.08/4.37 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.08/4.37 % set(auto2) -> assign(max_megs, 400).
% 4.08/4.37 % set(auto2) -> assign(stats, some).
% 4.08/4.37 % set(auto2) -> clear(echo_input).
% 4.08/4.37 % set(auto2) -> set(quiet).
% 4.08/4.37 % set(auto2) -> clear(print_initial_clauses).
% 4.08/4.37 % set(auto2) -> clear(print_given).
% 4.08/4.37 assign(lrs_ticks,-1).
% 4.08/4.37 assign(sos_limit,10000).
% 4.08/4.37 assign(order,kbo).
% 4.08/4.37 set(lex_order_vars).
% 4.08/4.37 clear(print_given).
% 4.08/4.37
% 4.08/4.37 % formulas(sos). % not echoed (19 formulas)
% 4.08/4.37
% 4.08/4.37 ============================== end of input ==========================
% 4.08/4.37
% 4.08/4.37 % From the command line: assign(max_seconds, 300).
% 4.08/4.37
% 4.08/4.37 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.08/4.37
% 4.08/4.37 % Formulas that are not ordinary clauses:
% 4.08/4.37
% 4.08/4.37 ============================== end of process non-clausal formulas ===
% 4.08/4.37
% 4.08/4.37 ============================== PROCESS INITIAL CLAUSES ===============
% 4.08/4.37
% 4.08/4.37 ============================== PREDICATE ELIMINATION =================
% 4.08/4.37
% 4.08/4.37 ============================== end predicate elimination =============
% 4.08/4.37
% 4.08/4.37 Auto_denials:
% 4.08/4.37 % copying label prove_p22a to answer in negative clause
% 4.08/4.37
% 4.08/4.37 Term ordering decisions:
% 4.08/4.37
% 4.08/4.37 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 4.08/4.37 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 4.08/4.37
% 4.08/4.37 ============================== end of process initial clauses ========
% 4.08/4.37
% 4.08/4.37 ============================== CLAUSES FOR SEARCH ====================
% 4.08/4.37
% 4.08/4.37 ============================== end of clauses for search =============
% 4.08/4.37
% 4.08/4.37 ============================== SEARCH ================================
% 4.08/4.37
% 4.08/4.37 % Starting search at 0.01 seconds.
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=37.000, iters=3387
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=33.000, iters=3354
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=31.000, iters=3378
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=30.000, iters=3446
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=29.000, iters=3404
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=27.000, iters=3340
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=26.000, iters=3380
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=25.000, iters=3403
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=24.000, iters=3335
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=23.000, iters=3379
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=22.000, iters=3360
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=21.000, iters=3360
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=20.000, iters=3351
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=19.000, iters=3349
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=5319, wt=43.000
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=6436, wt=41.000
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=5729, wt=40.000
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=6462, wt=39.000
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=18.000, iters=3346
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=6456, wt=38.000
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=6082, wt=37.000
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=12614, wt=17.000
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=13303, wt=16.000
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=13311, wt=15.000
% 4.08/4.37
% 4.08/4.37 Low Water (keep): wt=17.000, iters=3357
% 4.08/4.37
% 4.08/4.37 Low Water (displace): id=13822, wt=14.000
% 255.98/256.24
% 255.98/256.24 Low Water (displace): id=14970, wt=13.000
% 255.98/256.24
% 255.98/256.24 Low Water (keep): wt=16.000, iters=3338
% 255.98/256.24
% 255.98/256.24 ============================== PROOF =================================
% 255.98/256.24 % SZS status Unsatisfiable
% 255.98/256.24 % SZS output start Refutation
% 255.98/256.24
% 255.98/256.24 % Proof 1 at 250.19 (+ 5.11) seconds: prove_p22a.
% 255.98/256.24 % Length of proof is 110.
% 255.98/256.24 % Level of proof is 15.
% 255.98/256.24 % Maximum clause weight is 21.000.
% 255.98/256.24 % Given clauses 5679.
% 255.98/256.24
% 255.98/256.24 1 inverse(identity) = identity # label(p22a_1) # label(hypothesis). [assumption].
% 255.98/256.24 2 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 255.98/256.24 3 least_upper_bound(A,A) = A # label(idempotence_of_lub) # label(axiom). [assumption].
% 255.98/256.24 5 inverse(inverse(A)) = A # label(p22a_2) # label(hypothesis). [assumption].
% 255.98/256.24 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 255.98/256.24 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 255.98/256.24 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 255.98/256.24 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 255.98/256.24 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 255.98/256.24 11 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)) # label(p22a_3) # label(hypothesis). [assumption].
% 255.98/256.24 12 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 255.98/256.24 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].
% 255.98/256.24 14 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(13),rewrite([7(4)])].
% 255.98/256.24 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].
% 255.98/256.24 16 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(15),rewrite([8(4)])].
% 255.98/256.24 17 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 255.98/256.24 18 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(17),flip(a)].
% 255.98/256.24 19 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 255.98/256.24 20 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(19),flip(a)].
% 255.98/256.24 21 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 255.98/256.24 22 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(21),flip(a)].
% 255.98/256.24 23 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 255.98/256.24 24 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(23),flip(a)].
% 255.98/256.24 25 least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) # label(prove_p22a) # label(negated_conjecture) # answer(prove_p22a). [assumption].
% 255.98/256.24 26 least_upper_bound(least_upper_bound(identity,multiply(a,b)),multiply(least_upper_bound(identity,a),least_upper_bound(identity,b))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)) # answer(prove_p22a). [copy(25),rewrite([8(5),8(8),8(11),8(16),8(19)])].
% 255.98/256.24 27 multiply(A,inverse(A)) = identity. [para(5(a,1),6(a,1,1))].
% 255.98/256.24 28 multiply(inverse(A),identity) = inverse(A). [para(1(a,1),11(a,2,2)),rewrite([2(2)]),flip(a)].
% 255.98/256.24 30 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),12(a,1,1)),rewrite([2(2)]),flip(a)].
% 255.98/256.24 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)])].
% 255.98/256.24 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))].
% 255.98/256.24 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))].
% 255.98/256.24 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)])].
% 255.98/256.24 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)])].
% 255.98/256.24 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)])].
% 255.98/256.24 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)])].
% 255.98/256.24 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)])].
% 255.98/256.24 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))].
% 255.98/256.24 46 multiply(A,multiply(inverse(A),B)) = B. [para(27(a,1),12(a,1,1)),rewrite([2(2)]),flip(a)].
% 255.98/256.24 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)])].
% 255.98/256.24 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)])].
% 255.98/256.24 51 multiply(A,identity) = A. [para(5(a,1),28(a,1,1)),rewrite([5(4)])].
% 255.98/256.24 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)])].
% 255.98/256.24 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)])].
% 255.98/256.24 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)].
% 255.98/256.24 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)].
% 255.98/256.24 60 multiply(A,least_upper_bound(B,multiply(inverse(A),C))) = least_upper_bound(C,multiply(A,B)). [para(46(a,1),18(a,1,1)),rewrite([8(5)]),flip(a)].
% 255.98/256.24 70 multiply(least_upper_bound(inverse(A),identity),A) = least_upper_bound(A,identity). [para(6(a,1),37(a,1,2)),flip(a)].
% 255.98/256.24 71 greatest_lower_bound(A,multiply(least_upper_bound(B,identity),A)) = A. [para(37(a,1),10(a,1,2))].
% 255.98/256.24 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)].
% 255.98/256.24 88 multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(B,multiply(A,B))) = B. [para(37(a,2),30(a,1,2))].
% 255.98/256.24 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)].
% 255.98/256.24 103 least_upper_bound(A,multiply(inverse(B),multiply(C,A))) = multiply(inverse(B),multiply(least_upper_bound(B,C),A)). [para(35(a,1),22(a,2,1)),rewrite([2(2),12(3),12(8)])].
% 255.98/256.24 109 multiply(inverse(A),least_upper_bound(A,identity)) = least_upper_bound(identity,inverse(A)). [para(51(a,1),35(a,1,2)),flip(a)].
% 255.98/256.24 112 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))].
% 255.98/256.24 117 greatest_lower_bound(identity,least_upper_bound(A,identity)) = identity. [para(51(a,1),71(a,1,2))].
% 255.98/256.24 119 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)])].
% 255.98/256.24 121 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)])].
% 255.98/256.24 151 multiply(inverse(A),greatest_lower_bound(A,identity)) = greatest_lower_bound(identity,inverse(A)). [para(51(a,1),36(a,1,2)),flip(a)].
% 255.98/256.24 171 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(38(a,1),10(a,1,2))].
% 255.98/256.24 190 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(38(a,2),30(a,1,2))].
% 255.98/256.24 245 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(5(a,1),171(a,1,2,1,2))].
% 255.98/256.24 304 multiply(greatest_lower_bound(inverse(A),identity),A) = greatest_lower_bound(A,identity). [para(6(a,1),41(a,1,2)),flip(a)].
% 255.98/256.24 320 multiply(greatest_lower_bound(A,identity),inverse(A)) = greatest_lower_bound(inverse(A),identity). [para(27(a,1),41(a,1,2)),flip(a)].
% 255.98/256.24 348 multiply(greatest_lower_bound(identity,inverse(A)),A) = greatest_lower_bound(A,identity). [para(7(a,1),304(a,1,1))].
% 255.98/256.24 366 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(42(a,1),9(a,1,2))].
% 255.98/256.24 379 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)])].
% 255.98/256.24 389 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))].
% 255.98/256.24 413 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(5(a,1),366(a,1,2,1,2))].
% 255.98/256.24 459 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)].
% 255.98/256.24 566 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)])].
% 255.98/256.24 568 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)].
% 255.98/256.24 602 multiply(A,least_upper_bound(inverse(A),identity)) = least_upper_bound(A,identity). [para(8(a,1),568(a,1,2))].
% 255.98/256.24 638 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)].
% 255.98/256.24 665 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)])].
% 255.98/256.24 669 multiply(A,greatest_lower_bound(inverse(A),identity)) = greatest_lower_bound(A,identity). [para(7(a,1),638(a,1,2))].
% 255.98/256.24 678 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)])].
% 255.98/256.24 692 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)])].
% 255.98/256.24 771 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)])].
% 255.98/256.24 774 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)])].
% 255.98/256.24 785 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)])].
% 255.98/256.24 786 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)])].
% 255.98/256.24 806 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)].
% 255.98/256.24 839 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)].
% 255.98/256.24 841 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)])].
% 255.98/256.24 951 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)].
% 255.98/256.24 968 least_upper_bound(least_upper_bound(A,multiply(B,C)),multiply(B,D)) = multiply(B,least_upper_bound(D,least_upper_bound(C,multiply(inverse(B),A)))). [para(56(a,1),56(a,1,2,2)),rewrite([5(2),5(9)]),flip(a)].
% 255.98/256.24 999 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)].
% 255.98/256.24 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)].
% 255.98/256.24 1282 multiply(A,least_upper_bound(B,least_upper_bound(C,multiply(inverse(A),D)))) = least_upper_bound(D,multiply(A,least_upper_bound(B,C))). [para(60(a,1),18(a,1,2)),rewrite([16(4,R),18(3),8(1)]),flip(a)].
% 255.98/256.24 1304 least_upper_bound(least_upper_bound(A,B),multiply(inverse(C),D)) = least_upper_bound(A,least_upper_bound(B,multiply(inverse(C),D))). [para(60(a,1),56(a,2,2)),rewrite([5(3),968(5),16(5,R),8(4),1282(6),56(5),16(8,R),8(7)])].
% 255.98/256.24 1308 least_upper_bound(least_upper_bound(A,B),multiply(C,D)) = least_upper_bound(A,least_upper_bound(B,multiply(C,D))). [para(60(a,1),60(a,2,2)),rewrite([1304(6),18(5),60(5),16(6,R),8(5)])].
% 255.98/256.24 1340 least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)) # answer(prove_p22a). [back_rewrite(26),rewrite([1308(13)])].
% 255.98/256.24 1624 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)])].
% 255.98/256.24 4602 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))].
% 255.98/256.24 5058 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)])].
% 255.98/256.24 5169 least_upper_bound(multiply(least_upper_bound(A,B),C),multiply(A,D)) = least_upper_bound(multiply(B,C),multiply(A,least_upper_bound(D,C))). [para(103(a,2),56(a,1,2,2)),rewrite([5(2),1282(6),5(8)]),flip(a)].
% 255.98/256.24 6184 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)])].
% 255.98/256.24 9585 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(5058(a,1),112(a,1,2,2,2)),rewrite([5(5),5(11),8(13),566(14)])].
% 255.98/256.24 11362 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)])].
% 255.98/256.24 11390 greatest_lower_bound(inverse(A),inverse(greatest_lower_bound(B,A))) = inverse(A). [para(11362(a,1),999(a,1,2)),rewrite([7(4),11362(7)])].
% 255.98/256.24 11444 least_upper_bound(A,greatest_lower_bound(B,A)) = A. [para(11390(a,1),951(a,1,2,1)),rewrite([5(3),5(3),8(2),11390(6),5(4)])].
% 255.98/256.24 16938 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),6184(8),109(5),10(5),379(11),806(8)]),flip(a)].
% 255.98/256.24 16952 multiply(greatest_lower_bound(A,identity),least_upper_bound(inverse(A),identity)) = identity. [para(16938(a,1),11444(a,1,2)),rewrite([8(8),9585(8),320(5),11444(5)]),flip(a)].
% 255.98/256.24 16956 inverse(least_upper_bound(A,identity)) = greatest_lower_bound(inverse(A),identity). [back_rewrite(1624),rewrite([16952(9),51(5)])].
% 255.98/256.24 17184 inverse(least_upper_bound(identity,multiply(A,B))) = greatest_lower_bound(identity,multiply(inverse(B),inverse(A))). [para(11(a,1),16956(a,2,1)),rewrite([8(3),7(9)])].
% 255.98/256.24 17269 multiply(greatest_lower_bound(inverse(A),inverse(B)),least_upper_bound(A,B)) = identity. [back_rewrite(4602),rewrite([17184(5),5(4),459(8),2(4),7(3)])].
% 255.98/256.24 17657 inverse(greatest_lower_bound(inverse(A),inverse(B))) = least_upper_bound(A,B). [para(17269(a,1),30(a,1,2)),rewrite([51(6)])].
% 255.98/256.24 17689 inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)). [para(17657(a,1),5(a,1,1))].
% 255.98/256.24 30639 least_upper_bound(identity,multiply(least_upper_bound(identity,a),least_upper_bound(identity,b))) != multiply(least_upper_bound(identity,a),least_upper_bound(identity,b)) # answer(prove_p22a). [para(5169(a,2),1340(a,1,2)),rewrite([8(6),16(6,R),3(5),51(11),8(10),54(10),8(7)])].
% 255.98/256.24 30644 $F # answer(prove_p22a). [para(38(a,1),30639(a,1)),rewrite([17689(7),1(5),8(8),16(8),8(7),9(7),8(3)]),xx(a)].
% 255.98/256.24
% 255.98/256.24 % SZS output end Refutation
% 255.98/256.24 ============================== end of proof ==========================
% 255.98/256.24
% 255.98/256.24 ============================== STATISTICS ============================
% 255.98/256.24
% 255.98/256.24 Given=5679. Generated=9298880. Kept=30636. proofs=1.
% 255.98/256.24 Usable=4984. Sos=9254. Demods=13465. Limbo=0, Disabled=16417. Hints=0.
% 255.98/256.24 Megabytes=23.70.
% 255.98/256.24 User_CPU=250.19, System_CPU=5.11, Wall_clock=255.
% 255.98/256.24
% 255.98/256.24 ============================== end of statistics =====================
% 255.98/256.24
% 255.98/256.24 ============================== end of search =========================
% 255.98/256.24
% 255.98/256.24 THEOREM PROVED
% 255.98/256.24 % SZS status Unsatisfiable
% 255.98/256.24
% 255.98/256.24 Exiting with 1 proof.
% 255.98/256.24
% 255.98/256.24 Process 5268 exit (max_proofs) Mon Jun 13 07:30:53 2022
% 255.98/256.24 Prover9 interrupted
%------------------------------------------------------------------------------