TSTP Solution File: LAT400-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT400-3 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 : Sun Jul 17 06:28:40 EDT 2022
% Result : Unsatisfiable 133.74s 134.07s
% Output : Refutation 133.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT400-3 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n013.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 : Wed Jun 29 17:33:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 18.19/18.46 ============================== Prover9 ===============================
% 18.19/18.46 Prover9 (32) version 2009-11A, November 2009.
% 18.19/18.46 Process 29934 was started by sandbox on n013.cluster.edu,
% 18.19/18.46 Wed Jun 29 17:34:00 2022
% 18.19/18.46 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29781_n013.cluster.edu".
% 18.19/18.46 ============================== end of head ===========================
% 18.19/18.46
% 18.19/18.46 ============================== INPUT =================================
% 18.19/18.46
% 18.19/18.46 % Reading from file /tmp/Prover9_29781_n013.cluster.edu
% 18.19/18.46
% 18.19/18.46 set(prolog_style_variables).
% 18.19/18.46 set(auto2).
% 18.19/18.46 % set(auto2) -> set(auto).
% 18.19/18.46 % set(auto) -> set(auto_inference).
% 18.19/18.46 % set(auto) -> set(auto_setup).
% 18.19/18.46 % set(auto_setup) -> set(predicate_elim).
% 18.19/18.46 % set(auto_setup) -> assign(eq_defs, unfold).
% 18.19/18.46 % set(auto) -> set(auto_limits).
% 18.19/18.46 % set(auto_limits) -> assign(max_weight, "100.000").
% 18.19/18.46 % set(auto_limits) -> assign(sos_limit, 20000).
% 18.19/18.46 % set(auto) -> set(auto_denials).
% 18.19/18.46 % set(auto) -> set(auto_process).
% 18.19/18.46 % set(auto2) -> assign(new_constants, 1).
% 18.19/18.46 % set(auto2) -> assign(fold_denial_max, 3).
% 18.19/18.46 % set(auto2) -> assign(max_weight, "200.000").
% 18.19/18.46 % set(auto2) -> assign(max_hours, 1).
% 18.19/18.46 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 18.19/18.46 % set(auto2) -> assign(max_seconds, 0).
% 18.19/18.46 % set(auto2) -> assign(max_minutes, 5).
% 18.19/18.46 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 18.19/18.46 % set(auto2) -> set(sort_initial_sos).
% 18.19/18.46 % set(auto2) -> assign(sos_limit, -1).
% 18.19/18.46 % set(auto2) -> assign(lrs_ticks, 3000).
% 18.19/18.46 % set(auto2) -> assign(max_megs, 400).
% 18.19/18.46 % set(auto2) -> assign(stats, some).
% 18.19/18.46 % set(auto2) -> clear(echo_input).
% 18.19/18.46 % set(auto2) -> set(quiet).
% 18.19/18.46 % set(auto2) -> clear(print_initial_clauses).
% 18.19/18.46 % set(auto2) -> clear(print_given).
% 18.19/18.46 assign(lrs_ticks,-1).
% 18.19/18.46 assign(sos_limit,10000).
% 18.19/18.46 assign(order,kbo).
% 18.19/18.46 set(lex_order_vars).
% 18.19/18.46 clear(print_given).
% 18.19/18.46
% 18.19/18.46 % formulas(sos). % not echoed (13 formulas)
% 18.19/18.46
% 18.19/18.46 ============================== end of input ==========================
% 18.19/18.46
% 18.19/18.46 % From the command line: assign(max_seconds, 300).
% 18.19/18.46
% 18.19/18.46 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 18.19/18.46
% 18.19/18.46 % Formulas that are not ordinary clauses:
% 18.19/18.46
% 18.19/18.46 ============================== end of process non-clausal formulas ===
% 18.19/18.46
% 18.19/18.46 ============================== PROCESS INITIAL CLAUSES ===============
% 18.19/18.46
% 18.19/18.46 ============================== PREDICATE ELIMINATION =================
% 18.19/18.46
% 18.19/18.46 ============================== end predicate elimination =============
% 18.19/18.46
% 18.19/18.46 Auto_denials:
% 18.19/18.46 % copying label conjecture_1 to answer in negative clause
% 18.19/18.46
% 18.19/18.46 Term ordering decisions:
% 18.19/18.46 Function symbol KB weights: a=1. x2=1. y2=1. z2=1. meet=1. join=1. upme=1. lome=1.
% 18.19/18.46
% 18.19/18.46 ============================== end of process initial clauses ========
% 18.19/18.46
% 18.19/18.46 ============================== CLAUSES FOR SEARCH ====================
% 18.19/18.46
% 18.19/18.46 ============================== end of clauses for search =============
% 18.19/18.46
% 18.19/18.46 ============================== SEARCH ================================
% 18.19/18.46
% 18.19/18.46 % Starting search at 0.01 seconds.
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=139.000, iters=3365
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=131.000, iters=3396
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=111.000, iters=3370
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=99.000, iters=3365
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=91.000, iters=3348
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=85.000, iters=3445
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=83.000, iters=3440
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=73.000, iters=3358
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=69.000, iters=3373
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=67.000, iters=3352
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=65.000, iters=3368
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=61.000, iters=3333
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=59.000, iters=3338
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=55.000, iters=3389
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=53.000, iters=3335
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=51.000, iters=3430
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=49.000, iters=3353
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=47.000, iters=3356
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=45.000, iters=3334
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=43.000, iters=3348
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=41.000, iters=3333
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=39.000, iters=3337
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=37.000, iters=3344
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=35.000, iters=3336
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=33.000, iters=3340
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=31.000, iters=3345
% 18.19/18.46
% 18.19/18.46 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 14.44 sec).
% 18.19/18.46
% 18.19/18.46 Low Water (keep): wt=29.000, iters=3345
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=7687, wt=191.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=15068, wt=189.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=7091, wt=179.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=9522, wt=171.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=6729, wt=167.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=8303, wt=165.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=8644, wt=163.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=6682, wt=161.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=7312, wt=159.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=5579, wt=157.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=15024, wt=151.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=7092, wt=149.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=21675, wt=27.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=21683, wt=23.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=21693, wt=21.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=21704, wt=19.000
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=21746, wt=17.000
% 133.74/134.07
% 133.74/134.07 Low Water (keep): wt=27.000, iters=3333
% 133.74/134.07
% 133.74/134.07 Low Water (displace): id=24507, wt=15.000
% 133.74/134.07
% 133.74/134.07 Low Water (keep): wt=25.000, iters=3334
% 133.74/134.07
% 133.74/134.07 Low Water (keep): wt=23.000, iters=3337
% 133.74/134.07
% 133.74/134.07 Low Water (keep): wt=21.000, iters=3336
% 133.74/134.07
% 133.74/134.07 ============================== PROOF =================================
% 133.74/134.07 % SZS status Unsatisfiable
% 133.74/134.07 % SZS output start Refutation
% 133.74/134.07
% 133.74/134.07 % Proof 1 at 132.13 (+ 0.95) seconds: conjecture_1.
% 133.74/134.07 % Length of proof is 279.
% 133.74/134.07 % Level of proof is 38.
% 133.74/134.07 % Maximum clause weight is 81.000.
% 133.74/134.07 % Given clauses 1972.
% 133.74/134.07
% 133.74/134.07 1 meet(A,B) = meet(B,A) # label(commutativity) # label(axiom). [assumption].
% 133.74/134.07 2 join(A,B) = join(B,A) # label(commutativity_001) # label(axiom). [assumption].
% 133.74/134.07 3 join(A,meet(A,B)) = A # label(absorption) # label(axiom). [assumption].
% 133.74/134.07 4 meet(A,join(A,B)) = A # label(absorption_003) # label(axiom). [assumption].
% 133.74/134.07 5 upme(a,x2,y2) = upme(a,x2,z2) # label(conjecture) # label(negated_conjecture). [assumption].
% 133.74/134.07 6 upme(a,x2,z2) = upme(a,x2,y2). [copy(5),flip(a)].
% 133.74/134.07 7 upme(A,B,C) = meet(A,join(B,C)) # label(definition_of_upme) # label(axiom). [assumption].
% 133.74/134.07 8 meet(A,meet(B,C)) = meet(meet(A,B),C) # label(associativity) # label(axiom). [assumption].
% 133.74/134.07 9 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(8),rewrite([1(4)])].
% 133.74/134.07 10 join(A,join(B,C)) = join(join(A,B),C) # label(associativity_002) # label(axiom). [assumption].
% 133.74/134.07 11 join(A,join(B,C)) = join(C,join(A,B)). [copy(10),rewrite([2(4)])].
% 133.74/134.07 12 lome(A,B,C) = join(meet(A,B),meet(A,C)) # label(definition_of_lome) # label(axiom). [assumption].
% 133.74/134.07 13 lome(A,B,C) = upme(A,upme(B,A,C),upme(C,A,B)) # label(rl1) # label(axiom). [assumption].
% 133.74/134.07 14 meet(A,join(meet(B,join(A,C)),meet(C,join(A,B)))) = join(meet(A,B),meet(A,C)). [copy(13),rewrite([12(1),7(4),7(6),7(8)]),flip(a)].
% 133.74/134.07 15 upme(A,B,C) = join(upme(A,B,meet(a,C)),upme(A,C,meet(a,B))) # label(rh2) # label(axiom). [assumption].
% 133.74/134.07 16 join(meet(A,join(B,meet(C,a))),meet(A,join(C,meet(B,a)))) = meet(A,join(B,C)). [copy(15),rewrite([7(1),1(4),7(5),1(8),7(9)]),flip(a)].
% 133.74/134.07 17 join(upme(meet(a,A),B,C),meet(B,C)) = meet(join(meet(meet(a,A),B),C),join(meet(meet(a,A),C),B)) # label(rh1) # label(axiom). [assumption].
% 133.74/134.07 18 meet(join(A,meet(B,meet(C,a))),join(C,meet(A,meet(B,a)))) = join(meet(A,C),meet(meet(B,a),join(A,C))). [copy(17),rewrite([1(2),7(3),2(6),1(8),1(9),9(9,R),1(8),2(10),1(12),1(13),9(13,R),1(12),2(14),1(15)]),flip(a),rewrite([9(7,R),1(6)])].
% 133.74/134.07 19 upme(x2,y2,z2) != lome(x2,y2,z2) # label(conjecture_1) # label(negated_conjecture) # answer(conjecture_1). [assumption].
% 133.74/134.07 20 join(meet(x2,y2),meet(x2,z2)) != meet(x2,join(y2,z2)) # answer(conjecture_1). [copy(19),rewrite([7(4),12(9)]),flip(a)].
% 133.74/134.07 21 meet(a,join(x2,z2)) = meet(a,join(x2,y2)). [back_rewrite(6),rewrite([7(4),7(9)])].
% 133.74/134.07 22 join(A,A) = A. [para(4(a,1),3(a,1,2))].
% 133.74/134.07 23 meet(A,A) = A. [para(3(a,1),4(a,1,2))].
% 133.74/134.07 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(4(a,1),9(a,2,2)),rewrite([1(2),1(4)])].
% 133.74/134.07 25 join(A,join(B,meet(A,C))) = join(A,B). [para(3(a,1),11(a,2,2)),rewrite([2(2),2(4)])].
% 133.74/134.07 26 meet(A,join(meet(B,join(A,C)),meet(C,join(B,A)))) = join(meet(B,A),meet(A,C)). [para(14(a,1),1(a,2)),rewrite([2(3),1(6),1(7)])].
% 133.74/134.07 28 meet(A,meet(B,join(meet(C,join(A,D)),meet(D,join(A,C))))) = meet(B,join(meet(A,C),meet(A,D))). [para(14(a,1),9(a,2,2)),rewrite([1(6)])].
% 133.74/134.07 29 meet(meet(A,join(B,C)),join(join(meet(A,B),meet(B,C)),meet(meet(C,join(A,B)),join(B,meet(A,join(B,C)))))) = join(meet(A,B),meet(A,meet(C,join(B,C)))). [para(14(a,1),14(a,1,2,1)),rewrite([1(3),2(6),2(10),1(16),24(16),1(14),2(17),9(19),1(18),9(18,R),1(17),9(19,R),24(19)])].
% 133.74/134.07 32 join(meet(A,join(B,meet(a,join(C,D)))),meet(A,join(join(C,D),meet(B,a)))) = meet(A,join(B,join(C,D))). [para(11(a,1),16(a,2,2)),rewrite([1(3),11(13),2(12),11(13,R),2(12)])].
% 133.74/134.07 35 join(meet(A,join(meet(B,join(A,C)),meet(C,meet(a,join(A,B))))),meet(A,join(meet(C,join(A,B)),meet(B,meet(a,join(A,C)))))) = join(meet(A,B),meet(A,C)). [para(14(a,1),16(a,2)),rewrite([1(6),9(6,R),1(5),1(14),9(14,R),1(13)])].
% 133.74/134.07 36 join(meet(A,join(meet(B,join(C,meet(D,a))),meet(B,meet(a,join(D,meet(C,a)))))),meet(A,join(meet(B,join(D,meet(C,a))),meet(B,meet(a,join(C,meet(D,a))))))) = meet(A,meet(B,join(C,D))). [para(16(a,1),16(a,2,2)),rewrite([1(10),9(10,R),1(9),1(22),9(22,R),1(21)])].
% 133.74/134.07 38 join(meet(A,B),meet(meet(C,a),join(A,B))) = join(meet(A,B),meet(C,meet(a,join(A,B)))). [para(1(a,1),18(a,2,2)),rewrite([18(9),9(11),1(10),9(11,R),1(10)])].
% 133.74/134.07 39 meet(join(A,meet(B,meet(C,a))),join(C,meet(B,meet(A,a)))) = join(meet(A,C),meet(B,meet(a,join(A,C)))). [para(2(a,1),18(a,1,1)),rewrite([2(4),9(7,R),1(6),1(9),1(10),2(13),38(15)])].
% 133.74/134.07 40 join(A,join(meet(B,meet(C,a)),meet(B,meet(a,join(A,C))))) = join(A,meet(B,meet(C,a))). [para(18(a,1),3(a,1,2)),rewrite([38(10),11(11),2(10),11(10,R),25(10),11(9),2(8),11(9,R),2(8)])].
% 133.74/134.07 41 meet(A,join(B,meet(A,meet(A,a)))) = join(meet(A,B),meet(A,a)). [para(3(a,1),18(a,1,1)),rewrite([38(11),24(10)])].
% 133.74/134.07 43 meet(join(A,meet(B,meet(a,join(A,C)))),join(join(A,C),meet(A,meet(B,a)))) = join(A,meet(meet(B,a),join(A,join(A,C)))). [para(4(a,1),18(a,2,1)),rewrite([1(3)])].
% 133.74/134.07 44 meet(join(A,meet(B,a)),join(meet(B,a),meet(B,meet(A,a)))) = join(meet(B,a),meet(B,meet(A,a))). [para(4(a,1),18(a,2,2)),rewrite([23(11),1(10),1(13),9(13,R),1(12),2(16)])].
% 133.74/134.07 45 meet(join(A,meet(B,meet(C,meet(D,a)))),join(meet(C,D),meet(A,meet(B,a)))) = join(meet(A,meet(C,D)),meet(B,meet(a,join(A,meet(C,D))))). [para(9(a,1),18(a,2,1)),rewrite([1(3),9(3),1(2),9(3,R),1(2),9(13),1(12),9(13,R),1(12),38(19)])].
% 133.74/134.07 46 meet(join(A,meet(B,meet(a,join(C,D)))),join(join(C,D),meet(A,meet(B,a)))) = join(meet(A,join(C,D)),meet(B,meet(a,join(A,join(C,D))))). [para(11(a,1),18(a,2,2,2)),rewrite([1(3),11(17),2(16),11(17,R),2(16),38(19)])].
% 133.74/134.07 48 meet(join(A,meet(B,meet(C,a))),join(meet(D,join(A,join(C,meet(B,meet(C,a))))),meet(join(C,meet(A,meet(B,a))),join(A,join(D,meet(B,meet(C,a))))))) = join(join(meet(A,C),meet(B,meet(a,join(A,C)))),meet(D,join(A,meet(B,meet(C,a))))). [para(18(a,1),14(a,2,1)),rewrite([2(13),11(13,R),2(12),11(23),2(22),11(22,R),2(21),11(23,R),25(23),2(21),38(28),1(33)])].
% 133.74/134.07 49 join(join(meet(A,B),meet(C,meet(a,join(A,B)))),meet(D,join(A,meet(C,meet(B,a))))) = join(meet(A,B),join(meet(C,meet(a,join(A,B))),meet(D,join(A,meet(C,meet(B,a)))))). [para(18(a,1),14(a,2,2)),rewrite([11(13),2(12),11(12,R),2(11),11(13,R),25(13),2(19),11(19,R),2(18),48(22),1(17),38(23),11(24),2(23),11(24,R),2(23)])].
% 133.74/134.07 56 meet(join(A,meet(B,meet(C,a))),join(C,meet(A,meet(B,a)))) = join(meet(A,C),meet(B,meet(a,join(A,C)))). [back_rewrite(18),rewrite([38(15)])].
% 133.74/134.07 57 join(A,meet(meet(B,a),join(A,join(A,C)))) = join(A,meet(B,meet(a,join(A,join(A,C))))). [back_rewrite(43),rewrite([46(11),4(2)]),flip(a)].
% 133.74/134.07 58 meet(join(A,meet(B,meet(C,a))),join(meet(D,join(A,join(C,meet(B,meet(C,a))))),meet(join(C,meet(A,meet(B,a))),join(A,join(D,meet(B,meet(C,a))))))) = join(meet(A,C),join(meet(B,meet(a,join(A,C))),meet(D,join(A,meet(B,meet(C,a)))))). [back_rewrite(48),rewrite([49(34)])].
% 133.74/134.07 61 join(A,join(A,B)) = join(A,B). [para(22(a,1),11(a,1)),rewrite([2(3),11(4,R),2(3),11(3,R),22(2)]),flip(a)].
% 133.74/134.07 62 join(meet(A,B),meet(A,meet(B,a))) = meet(A,B). [para(22(a,1),16(a,1,1,2)),rewrite([1(7),9(7,R),23(6),3(6),2(5),2(8),3(8)])].
% 133.74/134.07 63 join(A,meet(meet(B,a),join(A,C))) = join(A,meet(B,meet(a,join(A,C)))). [back_rewrite(57),rewrite([61(4),61(8)])].
% 133.74/134.07 64 meet(A,meet(A,B)) = meet(A,B). [para(23(a,1),9(a,1)),rewrite([1(3),9(4,R),1(3),9(3,R),23(2)]),flip(a)].
% 133.74/134.07 66 join(meet(A,join(B,a)),meet(A,join(a,meet(B,a)))) = meet(A,join(B,a)). [para(23(a,1),16(a,1,1,2,2))].
% 133.74/134.07 67 meet(join(A,B),join(A,meet(B,a))) = join(A,meet(B,a)). [para(23(a,1),16(a,1,1)),rewrite([3(11),1(8)]),flip(a)].
% 133.74/134.07 71 join(meet(A,B),meet(A,a)) = meet(A,join(B,meet(A,a))). [back_rewrite(41),rewrite([64(3)]),flip(a)].
% 133.74/134.07 77 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [para(14(a,1),64(a,1,2)),rewrite([14(10)])].
% 133.74/134.07 81 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(25(a,1),11(a,2,2)),rewrite([2(3),11(3,R),2(2),11(6),2(5),11(6,R),2(5)])].
% 133.74/134.07 82 meet(A,join(meet(B,join(A,C)),meet(join(C,meet(A,D)),join(A,B)))) = join(meet(A,B),meet(A,join(C,meet(A,D)))). [para(25(a,1),14(a,1,2,1,2))].
% 133.74/134.07 84 join(meet(A,join(B,meet(C,a))),join(meet(A,join(C,meet(B,a))),meet(A,meet(D,join(B,meet(C,a)))))) = meet(A,join(B,C)). [para(16(a,1),25(a,2)),rewrite([1(13),9(13,R),1(12)])].
% 133.74/134.07 93 meet(join(A,B),join(B,meet(A,a))) = join(B,meet(A,a)). [para(2(a,1),67(a,1,1))].
% 133.74/134.07 95 meet(join(A,join(B,C)),join(C,meet(a,join(A,B)))) = join(C,meet(a,join(A,B))). [para(11(a,2),67(a,1,1)),rewrite([1(5),1(10)])].
% 133.74/134.07 107 join(meet(A,B),meet(B,a)) = meet(B,join(A,meet(B,a))). [para(1(a,1),71(a,1,1))].
% 133.74/134.07 108 join(meet(A,a),meet(A,B)) = meet(A,join(B,meet(A,a))). [para(71(a,1),2(a,1)),flip(a)].
% 133.74/134.07 109 meet(A,meet(meet(A,B),join(B,meet(A,a)))) = meet(A,B). [para(71(a,1),4(a,1,2)),rewrite([9(6,R),1(5)])].
% 133.74/134.07 110 meet(A,join(join(A,B),meet(A,a))) = A. [para(4(a,1),71(a,1,1)),rewrite([3(3)]),flip(a)].
% 133.74/134.07 111 join(meet(A,a),meet(B,meet(A,C))) = meet(A,join(meet(B,C),meet(A,a))). [para(9(a,1),71(a,1,1)),rewrite([2(5),1(6)])].
% 133.74/134.07 117 join(a,meet(A,a)) = meet(a,join(A,a)). [para(23(a,1),71(a,1,2)),rewrite([1(2),2(4),23(8)])].
% 133.74/134.07 121 join(meet(A,B),meet(A,join(meet(B,C),meet(A,a)))) = meet(A,join(B,meet(A,a))). [para(71(a,1),25(a,2)),rewrite([1(5),9(5),1(4),9(5,R),1(4),108(6)])].
% 133.74/134.07 125 meet(A,meet(join(B,meet(A,a)),join(meet(B,a),meet(A,a)))) = meet(A,join(meet(B,a),meet(A,a))). [back_rewrite(44),rewrite([9(8,R),1(7),111(9),9(10,R),1(9),9(15,R),1(14),111(16)])].
% 133.74/134.07 126 join(meet(A,join(B,a)),meet(A,meet(a,join(B,a)))) = meet(A,join(B,a)). [back_rewrite(66),rewrite([117(7)])].
% 133.74/134.07 128 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(4(a,1),26(a,2,1)),rewrite([2(3),11(3),2(2),11(3,R),2(2),4(4),61(3),1(7)])].
% 133.74/134.07 129 meet(meet(A,B),join(meet(C,join(D,meet(A,B))),meet(D,join(C,meet(A,B))))) = join(meet(A,meet(B,C)),meet(A,meet(B,D))). [para(9(a,1),26(a,2,1)),rewrite([2(3),1(10),9(11,R),1(10),1(13),9(13),1(12),9(13,R),1(12)])].
% 133.74/134.07 130 meet(join(A,B),join(meet(C,join(A,join(B,D))),meet(D,join(A,join(B,C))))) = join(meet(C,join(A,B)),meet(D,join(A,B))). [para(11(a,1),26(a,1,2,2,2)),rewrite([2(3),11(3),2(2),11(3,R),2(2),2(5),11(6,R),2(5),1(13)])].
% 133.74/134.07 131 meet(meet(A,join(B,C)),join(join(meet(B,C),meet(A,B)),meet(meet(C,join(A,B)),join(B,meet(A,join(B,C)))))) = join(meet(A,B),meet(A,meet(C,join(B,C)))). [para(14(a,1),26(a,1,2,2)),rewrite([2(3),2(7),1(10),2(12),2(14),1(18),9(18),1(17),9(17,R),1(16),9(18,R),24(18),1(19),24(19),1(17),2(18)])].
% 133.74/134.07 132 meet(join(meet(A,join(B,C)),meet(C,join(A,B))),join(meet(B,join(D,join(meet(A,join(B,C)),meet(C,join(A,B))))),meet(D,join(B,join(meet(A,join(B,C)),meet(C,join(A,B))))))) = join(join(meet(A,B),meet(B,C)),meet(D,join(meet(A,join(B,C)),meet(C,join(A,B))))). [para(14(a,1),26(a,2,1)),rewrite([2(3),2(8),2(11),2(15),1(22),2(27),1(30)])].
% 133.74/134.07 135 meet(join(A,meet(B,C)),join(meet(D,join(A,B)),meet(B,join(A,join(D,meet(B,C)))))) = join(meet(B,join(A,meet(B,C))),meet(D,join(A,meet(B,C)))). [para(25(a,1),26(a,1,2,2,2)),rewrite([2(5),11(5,R),2(4),2(7),2(9),1(16)])].
% 133.74/134.07 139 join(meet(A,meet(B,a)),meet(meet(A,a),join(A,B))) = meet(meet(A,a),join(B,meet(A,a))). [para(67(a,1),26(a,1,2,2)),rewrite([2(5),11(6),2(5),3(5),2(3),11(8),2(7),3(7),2(5),9(9,R),1(8),2(12)]),flip(a)].
% 133.74/134.07 147 meet(a,join(A,a)) = a. [para(23(a,1),110(a,1,2,2)),rewrite([2(3),2(5),11(5,R),22(4)])].
% 133.74/134.07 151 meet(A,join(join(B,a),meet(A,a))) = meet(A,join(B,a)). [back_rewrite(126),rewrite([147(7),2(6),108(6)])].
% 133.74/134.07 152 join(a,meet(A,a)) = a. [back_rewrite(117),rewrite([147(8)])].
% 133.74/134.07 160 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(28(a,1),3(a,1,2))].
% 133.74/134.07 164 meet(A,meet(B,meet(C,join(meet(D,join(A,E)),meet(E,join(A,D)))))) = meet(B,meet(C,join(meet(A,D),meet(A,E)))). [para(28(a,1),9(a,2,2)),rewrite([1(7),9(7,R),1(6),9(13,R),1(12)])].
% 133.74/134.07 166 meet(A,meet(B,join(meet(A,C),meet(A,D)))) = meet(B,join(meet(A,C),meet(A,D))). [para(28(a,1),64(a,1,2)),rewrite([28(12)])].
% 133.74/134.07 183 join(A,meet(B,meet(a,join(meet(A,C),meet(A,D))))) = A. [para(160(a,1),67(a,1,1)),rewrite([1(6),9(6,R),1(5),4(8),1(6),9(6,R),1(5)]),flip(a)].
% 133.74/134.07 203 join(meet(A,B),join(meet(A,join(B,C)),meet(A,meet(C,join(B,C))))) = meet(A,join(B,C)). [para(29(a,1),3(a,1,2)),rewrite([11(8,R),2(7)])].
% 133.74/134.07 274 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(81(a,1),11(a,2,2)),rewrite([2(4),11(4,R),2(3),11(3,R),2(2),11(8,R),2(7),11(7),2(6),11(7,R),2(6)])].
% 133.74/134.07 286 meet(join(A,join(B,C)),join(join(A,B),meet(C,a))) = join(join(A,B),meet(C,a)). [para(11(a,2),93(a,1,1))].
% 133.74/134.07 291 join(join(A,B),meet(A,a)) = join(A,B). [para(61(a,1),93(a,1,1)),rewrite([4(6)]),flip(a)].
% 133.74/134.07 302 join(join(A,B),meet(B,a)) = join(A,B). [para(2(a,1),291(a,1,1)),rewrite([2(5)])].
% 133.74/134.07 313 join(join(A,B),meet(a,join(A,B))) = join(A,B). [para(291(a,1),291(a,1,1)),rewrite([1(4),291(9)])].
% 133.74/134.07 322 join(join(A,B),meet(a,join(B,meet(A,C)))) = join(A,B). [para(25(a,1),302(a,1,1)),rewrite([1(5),25(9)])].
% 133.74/134.07 331 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(4(a,1),32(a,1,2)),rewrite([2(8),3(8),11(4),2(3),11(4,R),2(3)]),flip(a)].
% 133.74/134.07 334 meet(A,join(join(A,B),meet(B,join(A,a)))) = A. [para(14(a,1),32(a,1,1)),rewrite([71(4),1(10),9(10,R),1(9),147(9),302(8),4(6),2(5),3(5),2(5)]),flip(a)].
% 133.74/134.07 358 join(join(x2,z2),meet(a,join(x2,y2))) = join(x2,z2). [para(21(a,1),313(a,1,2))].
% 133.74/134.07 369 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(62(a,1),331(a,1,1)),rewrite([2(6),11(7,R),2(6),62(6),62(9)])].
% 133.74/134.07 376 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(331(a,1),29(a,1,2,1,1)),rewrite([2(4),11(4,R),2(3),11(3),2(2),11(3,R),2(2),331(5),1(5),11(10,R),11(9),2(8),11(9,R),2(8),61(8),61(9),2(15),11(15,R),2(14),11(14),2(13),11(14,R),2(13),331(16),2(13),11(13,R),11(12),2(11),11(12,R),2(11),61(11),61(12),1(12),9(12,R),23(11),2(10),11(10,R),22(9),4(7),331(5),2(6),11(6,R),2(5),11(5),2(4),11(5,R),2(4),9(8,R),1(7),331(7)]),flip(a)].
% 133.74/134.07 392 join(meet(A,meet(B,a)),meet(meet(A,a),join(A,B))) = meet(A,a). [back_rewrite(139),rewrite([369(14)])].
% 133.74/134.07 426 meet(join(x2,z2),join(A,join(x2,z2))) = join(x2,z2). [para(358(a,1),331(a,1,1)),rewrite([2(12),11(13,R),2(12),358(12),358(17)])].
% 133.74/134.07 442 join(meet(x2,join(meet(A,join(x2,z2)),meet(a,meet(z2,join(A,x2))))),meet(x2,join(meet(z2,join(A,x2)),meet(A,meet(a,join(x2,y2)))))) = join(meet(x2,z2),meet(A,x2)). [para(21(a,1),35(a,1,1,2,2,2)),rewrite([2(4),2(22),9(24,R),1(23),2(27),1(32)])].
% 133.74/134.07 491 meet(meet(A,a),join(A,B)) = meet(A,a). [para(369(a,1),16(a,1,1)),rewrite([3(9),2(5)]),flip(a)].
% 133.74/134.07 492 meet(meet(A,B),meet(join(C,meet(A,B)),join(D,meet(A,B)))) = meet(A,B). [para(369(a,1),24(a,2)),rewrite([2(5)])].
% 133.74/134.07 495 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(369(a,1),26(a,1,2,2)),rewrite([22(4),9(3),1(2),9(3,R),1(2),2(5),4(6),9(3),1(2),9(3,R),1(2),23(6),2(5)]),flip(a)].
% 133.74/134.07 507 meet(A,join(meet(B,a),meet(A,a))) = meet(A,a). [back_rewrite(392),rewrite([491(7),2(6),108(6)])].
% 133.74/134.07 521 meet(A,meet(join(B,meet(A,a)),join(meet(B,a),meet(A,a)))) = meet(A,a). [back_rewrite(125),rewrite([507(16)])].
% 133.74/134.07 536 join(meet(A,join(B,C)),meet(A,meet(D,join(B,C)))) = meet(A,join(B,C)). [para(16(a,1),376(a,1,1)),rewrite([16(11),9(5,R),1(4),16(15)])].
% 133.74/134.07 538 join(join(A,B),meet(C,meet(a,join(A,B)))) = join(A,B). [para(376(a,1),67(a,1,1)),rewrite([1(6),9(6,R),1(5),4(8),1(6),9(6,R),1(5)]),flip(a)].
% 133.74/134.07 547 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [back_rewrite(203),rewrite([536(7)])].
% 133.74/134.07 569 join(meet(A,meet(B,a)),meet(A,meet(B,join(C,a)))) = meet(A,meet(B,join(C,a))). [para(4(a,1),36(a,1,1,2,2,2)),rewrite([23(3),2(6),108(6),151(6),152(8),23(10),147(10),22(9),2(8)])].
% 133.74/134.07 617 join(meet(A,B),meet(B,join(meet(A,C),meet(A,D)))) = meet(A,B). [para(28(a,1),495(a,1,2))].
% 133.74/134.07 630 meet(A,meet(B,join(meet(C,a),meet(A,a)))) = meet(A,meet(B,a)). [para(507(a,1),9(a,2,2)),rewrite([1(6),9(10,R),1(9)])].
% 133.74/134.07 636 meet(A,meet(a,join(B,meet(A,a)))) = meet(A,a). [back_rewrite(521),rewrite([630(10),1(5)])].
% 133.74/134.07 705 join(meet(A,meet(B,C)),meet(A,meet(B,a))) = meet(meet(A,B),join(C,meet(A,meet(B,a)))). [para(9(a,2),107(a,1,1)),rewrite([1(5),9(5),1(4),9(5,R),1(4),1(10),9(10),1(9),9(10,R),1(9)])].
% 133.74/134.07 706 join(A,join(meet(B,a),meet(C,B))) = join(A,meet(B,join(C,meet(B,a)))). [para(107(a,1),11(a,2,2)),rewrite([2(4),11(5,R)])].
% 133.74/134.07 707 meet(meet(A,B),join(meet(B,meet(C,join(A,meet(B,a)))),meet(meet(B,a),join(C,meet(A,B))))) = meet(meet(A,B),join(C,meet(A,meet(B,a)))). [para(107(a,1),14(a,1,2,1,2)),rewrite([9(6,R),1(5),2(10),1(15),9(15),1(14),9(15,R),1(14),9(19),1(18),9(18,R),23(17),9(18),1(17),9(18,R),1(17),705(19)])].
% 133.74/134.07 708 join(meet(A,meet(B,a)),meet(A,meet(B,C))) = meet(meet(A,B),join(C,meet(A,meet(B,a)))). [para(107(a,1),14(a,1,2,2,2)),rewrite([2(5),9(11,R),1(10),2(12),707(13),9(10),1(9),9(9,R),23(8),9(9),1(8),9(9,R),1(8),1(11),9(11),1(10),9(11,R),1(10)]),flip(a)].
% 133.74/134.07 740 meet(meet(A,B),join(join(C,a),meet(A,meet(B,a)))) = meet(A,meet(B,join(C,a))). [back_rewrite(569),rewrite([708(8)])].
% 133.74/134.07 752 meet(meet(A,B),join(B,meet(A,a))) = meet(A,B). [para(109(a,1),9(a,1)),rewrite([64(6),1(6)]),flip(a)].
% 133.74/134.07 768 meet(join(A,meet(B,a)),join(a,meet(A,meet(B,a)))) = join(meet(A,a),meet(B,a)). [para(23(a,1),39(a,1,1,2,2)),rewrite([9(7,R),1(6),147(15)])].
% 133.74/134.07 780 meet(a,join(join(A,a),meet(B,a))) = a. [para(147(a,1),39(a,2,1)),rewrite([1(5),147(5),152(4),23(6),11(13,R),22(12),147(12),152(11)])].
% 133.74/134.07 837 meet(a,join(A,join(B,a))) = a. [para(780(a,1),16(a,1,1)),rewrite([1(6),147(6),147(5),22(3),2(5)]),flip(a)].
% 133.74/134.07 864 join(a,meet(meet(A,a),join(B,join(C,a)))) = a. [para(837(a,1),38(a,1,1)),rewrite([11(8,R),2(7),11(7,R),22(6),837(13),11(15,R),2(14),11(14,R),22(13),837(14),152(12)])].
% 133.74/134.07 865 meet(a,join(join(A,join(B,a)),meet(C,a))) = a. [para(837(a,1),39(a,2,1)),rewrite([1(6),837(6),152(4),23(7),11(15,R),2(14),11(14,R),22(13),837(14),152(12)])].
% 133.74/134.07 866 meet(join(A,meet(B,a)),join(join(C,a),meet(A,meet(B,a)))) = join(meet(A,join(C,a)),meet(B,a)). [para(837(a,1),39(a,2,2,2)),rewrite([1(4),147(4),9(8,R),1(7)])].
% 133.74/134.07 867 meet(meet(A,B),join(A,meet(B,a))) = meet(A,B). [para(752(a,1),1(a,2)),rewrite([1(4),1(5),1(6)])].
% 133.74/134.07 872 meet(meet(A,B),join(A,B)) = meet(A,B). [para(752(a,1),16(a,1,1)),rewrite([867(6),22(3),2(3)]),flip(a)].
% 133.74/134.07 926 join(a,meet(A,meet(B,a))) = a. [para(4(a,1),40(a,1,2,2,2)),rewrite([2(7),108(7),507(7),152(4)]),flip(a)].
% 133.74/134.07 935 join(A,join(meet(B,a),meet(a,join(A,B)))) = join(A,meet(B,a)). [para(64(a,1),40(a,1,2,2)),rewrite([9(4,R),23(3),9(11,R),23(10)])].
% 133.74/134.07 953 join(join(A,a),meet(A,meet(B,a))) = join(join(A,a),meet(B,a)). [para(334(a,1),40(a,1,2,2,2)),rewrite([2(2),22(5),1(6),9(6,R),23(5),9(5,R),1(4),2(8),111(8),507(8),2(7),22(10),1(11),9(11,R),23(10),9(10,R),1(9)]),flip(a)].
% 133.74/134.07 963 join(join(A,a),meet(B,meet(C,a))) = join(join(A,a),meet(B,a)). [para(780(a,1),40(a,1,2,2,2)),rewrite([1(6),9(6,R),23(5),2(8),108(8),507(8),1(11),9(11,R),23(10)]),flip(a)].
% 133.74/134.07 966 join(meet(A,a),meet(B,a)) = meet(a,join(A,meet(B,a))). [back_rewrite(768),rewrite([926(8),1(5)]),flip(a)].
% 133.74/134.07 970 join(join(A,a),meet(B,a)) = join(A,a). [back_rewrite(953),rewrite([963(6),2(5),11(5),2(4),3(4),2(2)]),flip(a)].
% 133.74/134.07 971 join(meet(A,join(B,a)),meet(C,a)) = meet(join(A,meet(C,a)),join(B,a)). [back_rewrite(866),rewrite([963(9),970(8)]),flip(a)].
% 133.74/134.07 973 meet(meet(A,B),join(C,a)) = meet(A,meet(B,join(C,a))). [back_rewrite(740),rewrite([963(7),970(6)])].
% 133.74/134.07 1128 meet(meet(meet(A,a),join(B,join(C,a))),join(meet(D,a),meet(a,join(D,meet(meet(A,a),join(B,join(C,a))))))) = join(meet(a,meet(meet(A,a),join(B,join(C,a)))),meet(D,meet(meet(A,a),join(B,join(C,a))))). [para(864(a,1),26(a,1,2,2,2)),rewrite([2(14),2(18),1(34)])].
% 133.74/134.07 1130 meet(meet(a,join(A,meet(meet(B,a),join(C,join(D,a))))),join(join(meet(a,meet(meet(B,a),join(C,join(D,a)))),meet(A,meet(meet(B,a),join(C,join(D,a))))),meet(meet(A,a),join(meet(meet(B,a),join(C,join(D,a))),meet(a,join(A,meet(meet(B,a),join(C,join(D,a))))))))) = join(meet(a,meet(meet(B,a),join(C,join(D,a)))),meet(A,a)). [para(864(a,1),29(a,1,2,2,1,2)),rewrite([2(8),1(24),2(41),2(62),4(63),1(56)])].
% 133.74/134.07 1131 meet(a,meet(meet(A,a),join(B,join(C,a)))) = meet(meet(A,a),join(B,join(C,a))). [para(864(a,1),369(a,1,2)),rewrite([1(8)])].
% 133.74/134.07 1135 meet(meet(a,join(A,meet(meet(B,a),join(C,join(D,a))))),join(join(meet(meet(B,a),join(C,join(D,a))),meet(A,meet(meet(B,a),join(C,join(D,a))))),meet(meet(A,a),join(meet(meet(B,a),join(C,join(D,a))),meet(a,join(A,meet(meet(B,a),join(C,join(D,a))))))))) = join(meet(meet(B,a),join(C,join(D,a))),meet(A,a)). [back_rewrite(1130),rewrite([1131(17),1131(52)])].
% 133.74/134.07 1137 meet(meet(meet(A,a),join(B,join(C,a))),join(meet(D,a),meet(a,join(D,meet(meet(A,a),join(B,join(C,a))))))) = join(meet(meet(A,a),join(B,join(C,a))),meet(D,meet(meet(A,a),join(B,join(C,a))))). [back_rewrite(1128),rewrite([1131(27)])].
% 133.74/134.07 1139 meet(a,join(A,join(B,join(C,a)))) = a. [para(865(a,1),16(a,1,1)),rewrite([1(7),837(7),147(5),22(3),2(6)]),flip(a)].
% 133.74/134.07 1150 meet(meet(a,join(A,meet(B,a))),join(join(C,join(D,a)),meet(B,meet(A,a)))) = meet(a,join(A,meet(B,a))). [para(865(a,1),39(a,2,2,2)),rewrite([1(7),9(7,R),23(6),1(14),837(14),966(12),1(13),9(19),1(18),9(19,R),1(18),837(18),966(18)])].
% 133.74/134.07 1151 join(join(A,join(B,a)),meet(C,meet(D,a))) = join(join(A,join(B,a)),meet(C,a)). [para(865(a,1),40(a,1,2,2,2)),rewrite([1(7),9(7,R),23(6),2(9),108(9),966(8),636(9),1(13),9(13,R),23(12)]),flip(a)].
% 133.74/134.07 1157 meet(meet(a,join(A,meet(B,a))),join(join(C,join(D,a)),meet(A,a))) = meet(a,join(A,meet(B,a))). [back_rewrite(1150),rewrite([9(11,R),1(10),1151(12)])].
% 133.74/134.07 1181 meet(join(A,meet(a,join(B,C))),join(join(B,C),meet(A,a))) = join(meet(A,join(B,C)),meet(a,join(A,join(B,C)))). [para(23(a,1),46(a,1,2,2,2)),rewrite([64(5),64(17)])].
% 133.74/134.07 1210 join(meet(A,join(join(B,join(C,a)),meet(D,a))),meet(E,meet(a,join(A,join(join(B,join(C,a)),meet(D,a)))))) = meet(join(A,meet(E,a)),join(join(join(B,join(C,a)),meet(D,a)),meet(A,meet(E,a)))). [para(865(a,1),46(a,1,1,2,2)),flip(a)].
% 133.74/134.07 1553 join(join(x2,z2),meet(A,meet(a,join(x2,y2)))) = join(x2,z2). [para(426(a,1),183(a,1,2,2,2,1)),rewrite([1(11),376(12),21(8)])].
% 133.74/134.07 1724 join(join(A,B),meet(a,join(A,meet(B,C)))) = join(A,B). [para(322(a,1),2(a,2)),rewrite([2(5),2(6),2(7)])].
% 133.74/134.07 1789 join(join(A,join(B,a)),meet(C,a)) = join(A,join(B,a)). [para(837(a,1),538(a,1,2,2))].
% 133.74/134.07 1798 join(meet(A,join(B,join(C,a))),meet(D,a)) = meet(join(A,meet(D,a)),join(B,join(C,a))). [back_rewrite(1210),rewrite([1789(6),1789(11),1139(10),1789(16),1151(17),1789(16)])].
% 133.74/134.07 1799 meet(meet(a,join(A,meet(B,a))),join(C,join(D,a))) = meet(a,join(A,meet(B,a))). [back_rewrite(1157),rewrite([1789(11)])].
% 133.74/134.07 1815 meet(meet(a,join(A,meet(meet(B,a),join(C,join(D,a))))),join(join(meet(meet(B,a),join(C,join(D,a))),meet(A,meet(meet(B,a),join(C,join(D,a))))),meet(meet(A,a),join(meet(meet(B,a),join(C,join(D,a))),meet(a,join(A,meet(meet(B,a),join(C,join(D,a))))))))) = meet(a,join(B,meet(A,a))). [back_rewrite(1135),rewrite([1798(53),966(49),1799(53)])].
% 133.74/134.07 1863 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(1(a,1),547(a,1,1))].
% 133.74/134.07 1865 join(meet(A,meet(B,C)),meet(C,join(D,meet(A,B)))) = meet(C,join(D,meet(A,B))). [para(9(a,2),547(a,1,1)),rewrite([2(4),2(8)])].
% 133.74/134.07 1888 meet(join(A,meet(B,C)),join(A,meet(B,join(C,D)))) = join(A,meet(B,C)). [para(547(a,1),331(a,1,2,2))].
% 133.74/134.07 1892 meet(meet(A,B),join(C,join(D,meet(A,B)))) = meet(A,B). [para(369(a,1),547(a,1,1)),rewrite([2(5),11(5,R),2(4),3(7),2(5),11(5,R),2(4)]),flip(a)].
% 133.74/134.07 1901 meet(meet(A,B),join(A,join(B,C))) = meet(A,B). [para(872(a,1),547(a,1,1)),rewrite([2(4),11(4),2(3),11(4,R),2(3),3(6),2(4),11(4),2(3),11(4,R),2(3)]),flip(a)].
% 133.74/134.07 1922 join(meet(A,meet(B,C)),meet(A,meet(B,join(C,D)))) = meet(A,meet(B,join(C,D))). [para(547(a,1),547(a,1,2,2)),rewrite([547(10)])].
% 133.74/134.07 1928 join(meet(meet(A,a),join(B,join(C,a))),meet(D,meet(meet(A,a),join(B,join(C,a))))) = meet(meet(A,a),join(B,join(C,a))). [back_rewrite(1137),rewrite([1863(18),9(16,R),1(15),369(15),1131(8)]),flip(a)].
% 133.74/134.07 1964 meet(meet(a,join(A,meet(meet(B,a),join(C,join(D,a))))),join(meet(meet(B,a),join(C,join(D,a))),meet(A,meet(a,join(meet(meet(B,a),join(C,join(D,a))),meet(a,join(A,meet(meet(B,a),join(C,join(D,a)))))))))) = meet(a,join(B,meet(A,a))). [back_rewrite(1815),rewrite([1928(23),63(35)])].
% 133.74/134.07 2010 meet(meet(A,B),join(A,C)) = meet(A,B). [para(64(a,1),1901(a,1,1)),rewrite([2(3),25(4),64(5)])].
% 133.74/134.07 2065 meet(meet(A,B),join(B,C)) = meet(A,B). [para(1(a,1),2010(a,1,1)),rewrite([1(4)])].
% 133.74/134.07 2074 meet(meet(A,meet(B,C)),join(meet(A,B),meet(A,D))) = meet(A,meet(B,C)). [para(2010(a,1),28(a,2)),rewrite([1(2),9(2),1(1),9(2,R),1(1),28(9),1(8),9(8),1(7),9(8,R),1(7)])].
% 133.74/134.07 2083 join(join(A,B),meet(A,C)) = join(A,B). [para(2010(a,1),376(a,1,2))].
% 133.74/134.07 2122 meet(join(A,B),join(A,meet(C,meet(a,join(A,B))))) = join(A,meet(C,meet(a,join(A,B)))). [para(4(a,1),56(a,2,1)),rewrite([1(3),2083(10),1(7),61(10)])].
% 133.74/134.07 2133 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(24(a,1),2065(a,1,1)),rewrite([2(4),24(8)])].
% 133.74/134.07 2143 meet(meet(A,join(B,join(C,meet(D,B)))),join(join(meet(D,B),meet(A,meet(D,B))),meet(meet(join(B,C),join(A,meet(D,B))),join(meet(D,B),meet(A,join(B,join(C,meet(D,B)))))))) = join(meet(A,meet(D,B)),meet(A,join(B,C))). [para(2065(a,1),29(a,1,2,1,2)),rewrite([11(3),2(2),11(3,R),2(2),2(8),11(16),2(15),11(16,R),2(15),11(27),2(26),11(27,R),2(26),331(28)])].
% 133.74/134.07 2180 join(join(A,B),meet(B,C)) = join(A,B). [para(2(a,1),2083(a,1,1)),rewrite([2(4)])].
% 133.74/134.07 2190 meet(meet(join(A,B),join(C,meet(A,D))),join(meet(A,D),meet(C,join(A,B)))) = join(meet(A,D),meet(C,join(A,B))). [para(2083(a,1),29(a,1,2,2,1,2)),rewrite([2(3),9(7),1(6),4(6),1(5),1(7),9(7),1(6),9(7,R),1(6),495(8),2(11),2133(14),9(12),1(11),4(11),1(10),2(13),4(14),1(12)])].
% 133.74/134.07 2198 join(meet(A,a),meet(B,join(A,C))) = meet(join(A,C),join(B,meet(A,a))). [para(2083(a,1),39(a,1,1)),rewrite([1(4),24(5),1(7),2(10),11(10),2(9),11(10,R),2(9),24(12),2(10)]),flip(a)].
% 133.74/134.07 2254 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(25(a,1),2180(a,1,1)),rewrite([1(4),25(8)])].
% 133.74/134.07 2430 join(meet(A,join(B,meet(C,a))),meet(A,meet(a,join(C,meet(B,a))))) = meet(A,join(B,meet(C,a))). [para(966(a,1),16(a,1,1,2)),rewrite([1(10),9(10,R),23(9),2(11),2(14)])].
% 133.74/134.07 2431 join(meet(A,meet(a,join(B,meet(C,a)))),meet(A,meet(a,join(C,meet(B,a))))) = meet(A,meet(a,join(B,meet(C,a)))). [para(966(a,1),16(a,2,2)),rewrite([1(6),9(6,R),23(5),966(5),1(12),9(12,R),23(11),966(11)])].
% 133.74/134.07 2447 join(meet(A,a),meet(a,join(B,A))) = meet(a,join(B,A)). [para(2180(a,1),966(a,2,2)),rewrite([1(3),2(6)])].
% 133.74/134.07 2466 join(meet(A,meet(B,join(C,meet(D,a)))),meet(A,meet(B,join(D,meet(C,a))))) = meet(A,meet(B,join(C,D))). [back_rewrite(36),rewrite([2430(11),2430(16)])].
% 133.74/134.07 2470 join(A,meet(a,join(A,B))) = join(A,meet(B,a)). [back_rewrite(935),rewrite([2447(6)])].
% 133.74/134.07 2472 meet(A,meet(a,join(B,meet(C,a)))) = meet(A,meet(a,join(B,C))). [back_rewrite(2431),rewrite([2466(13)]),flip(a)].
% 133.74/134.07 2553 join(x2,meet(a,z2)) = join(x2,meet(a,y2)). [para(21(a,1),2470(a,1,2)),rewrite([2470(7),1(4),1(9)]),flip(a)].
% 133.74/134.07 2562 meet(meet(a,join(A,B)),join(A,meet(B,a))) = meet(a,join(A,B)). [para(2470(a,1),93(a,1,1)),rewrite([2(9),1863(9),1(7),2(13),1863(13)])].
% 133.74/134.07 2605 meet(meet(a,z2),join(x2,meet(a,y2))) = meet(a,z2). [para(2553(a,1),369(a,1,2))].
% 133.74/134.07 2617 meet(meet(a,z2),meet(join(x2,meet(a,y2)),join(A,meet(a,z2)))) = join(meet(a,z2),meet(A,meet(a,z2))). [para(2605(a,1),14(a,2,1)),rewrite([2(12),11(22),2(21),2553(21),11(22,R),22(21),2(20),1863(20),1(21)])].
% 133.74/134.07 2618 join(meet(a,z2),meet(A,meet(a,z2))) = meet(a,z2). [para(2605(a,1),24(a,2)),rewrite([2(12),2617(14)])].
% 133.74/134.07 2630 join(meet(a,z2),meet(a,meet(x2,z2))) = meet(a,z2). [para(2605(a,1),547(a,1,2)),rewrite([1(5),9(5,R),1(4),2(9),2605(18)])].
% 133.74/134.07 2989 join(a,meet(A,meet(a,z2))) = a. [para(2618(a,1),160(a,1,2,2))].
% 133.74/134.07 3000 join(a,join(meet(A,meet(a,z2)),meet(B,a))) = a. [para(2989(a,1),25(a,2)),rewrite([1(7)])].
% 133.74/134.07 3469 join(A,meet(a,join(B,A))) = join(A,meet(B,a)). [para(93(a,1),84(a,2)),rewrite([1(5),9(5,R),23(4),93(5),966(9),2472(10),9(8,R),23(7),1(11),9(11,R),23(10),9(12,R),1(11),93(11),11(12,R),2(11),376(11),11(7),2(6),11(7,R),2(6),1863(6)])].
% 133.74/134.07 3533 meet(a,meet(meet(a,join(A,meet(B,a))),join(B,meet(meet(A,a),join(C,join(D,a)))))) = meet(a,join(A,meet(B,a))). [back_rewrite(1964),rewrite([3469(32),1798(25),966(21),1799(25),64(22),2472(21),2(17),24(19),1798(18),966(14),1799(18),1(15),9(15,R),1(14)])].
% 133.74/134.07 3795 join(a,join(meet(a,z2),meet(A,a))) = a. [para(23(a,1),3000(a,1,2,1))].
% 133.74/134.07 3823 join(a,meet(A,join(meet(a,z2),meet(B,a)))) = a. [para(3795(a,1),2180(a,1,1)),rewrite([1(8),3795(17)])].
% 133.74/134.07 4081 join(z2,meet(a,join(x2,y2))) = join(z2,meet(a,x2)). [para(21(a,1),3469(a,1,2)),rewrite([1(11)])].
% 133.74/134.07 4091 join(meet(a,z2),meet(a,join(x2,meet(a,y2)))) = join(meet(a,x2),meet(a,z2)). [para(2553(a,1),3469(a,1,2,2)),rewrite([1(17),2(18)])].
% 133.74/134.07 4201 join(meet(A,meet(B,a)),meet(B,meet(a,join(A,B)))) = meet(B,meet(a,join(A,B))). [para(111(a,1),45(a,1,2)),rewrite([23(3),64(3),966(8),2472(9),9(8),1(7),9(8,R),1(7),2562(7),2472(13)]),flip(a)].
% 133.74/134.07 4259 meet(A,join(meet(a,z2),meet(B,a))) = meet(A,meet(a,join(B,meet(a,z2)))). [para(3823(a,1),369(a,1,2)),rewrite([1(9),9(9,R),1(8),2472(9),2(5)]),flip(a)].
% 133.74/134.07 4608 meet(A,meet(B,join(a,meet(A,B)))) = meet(A,B). [para(973(a,1),4(a,1)),rewrite([2(3)])].
% 133.74/134.07 4708 meet(meet(A,a),join(B,join(C,a))) = meet(A,a). [para(864(a,1),4608(a,1,2,2)),rewrite([1(7),837(7),1(4),9(4,R),23(3)]),flip(a)].
% 133.74/134.07 4733 meet(a,join(A,meet(B,a))) = meet(a,join(A,B)). [back_rewrite(3533),rewrite([4708(12),1(10),9(10),1(9),2472(10),2(6),1(8),2562(8),64(5)]),flip(a)].
% 133.74/134.07 4921 join(meet(A,a),meet(B,a)) = meet(a,join(A,B)). [back_rewrite(966),rewrite([4733(10)])].
% 133.74/134.07 5109 meet(a,join(x2,meet(a,y2))) = meet(a,join(x2,y2)). [para(21(a,1),4733(a,2)),rewrite([1(5),2553(6)])].
% 133.74/134.07 5126 meet(a,meet(join(A,B),join(C,a))) = meet(a,join(A,B)). [para(4733(a,1),2010(a,1,1)),rewrite([2(5),973(6),4733(11)])].
% 133.74/134.07 5217 join(meet(a,z2),meet(a,join(x2,y2))) = join(meet(a,x2),meet(a,z2)). [back_rewrite(4091),rewrite([5109(10)])].
% 133.74/134.07 5274 join(meet(a,x2),meet(a,z2)) = meet(a,join(x2,y2)). [para(21(a,1),4921(a,2)),rewrite([1(3),1(6)])].
% 133.74/134.07 5290 meet(a,join(z2,meet(a,x2))) = meet(a,join(x2,y2)). [para(4081(a,1),4921(a,2,2)),rewrite([1(3),1(10),64(10),5217(9),5274(7)]),flip(a)].
% 133.74/134.07 5306 join(meet(a,y2),meet(a,join(x2,y2))) = meet(a,join(x2,y2)). [para(5109(a,1),16(a,2)),rewrite([1(7),64(7),5109(7),1(12),2(13),77(14),11(13),2(12),547(12)])].
% 133.74/134.07 5331 join(meet(a,x2),meet(a,y2)) = meet(a,join(x2,y2)). [para(5109(a,1),3469(a,1,2)),rewrite([5306(9),1(11),2(12)]),flip(a)].
% 133.74/134.07 5342 join(A,join(meet(B,meet(a,join(A,C))),meet(join(A,C),join(B,meet(A,a))))) = join(A,meet(B,join(A,C))). [para(128(a,1),16(a,2)),rewrite([1(5),9(5,R),1(4),2122(7),2(11),2198(11),64(12),2(11),11(11),2(10),11(11,R),2(10)])].
% 133.74/134.07 5426 meet(a,meet(z2,join(x2,y2))) = meet(a,z2). [para(5290(a,1),14(a,1,2,1)),rewrite([2(12),2010(13),2(10),547(10),9(7,R),1(6),1(10),9(15),1(14),9(15,R),1(14),2630(16)])].
% 133.74/134.07 5465 meet(meet(a,z2),join(x2,y2)) = meet(a,z2). [para(5426(a,1),9(a,1)),rewrite([1(10)]),flip(a)].
% 133.74/134.07 5475 meet(a,meet(z2,join(A,a))) = meet(a,z2). [para(5426(a,1),2010(a,1,1)),rewrite([2(5),973(6),5426(13)])].
% 133.74/134.07 5478 join(meet(a,z2),meet(A,a)) = meet(a,join(A,meet(a,z2))). [para(5426(a,1),77(a,1,2,1)),rewrite([1(6),4259(8),64(8),5426(13),1(11)]),flip(a)].
% 133.74/134.07 5512 join(x2,join(y2,meet(a,y2))) = join(x2,y2). [para(5465(a,1),376(a,1,2)),rewrite([2(7),11(7),2(6),2553(6),11(7,R),2(6)])].
% 133.74/134.07 5532 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(23(a,1),129(a,1,2,1)),rewrite([2(7),11(7,R),22(6),4(6),2(4),61(4),369(4),2(8),1922(8)]),flip(a)].
% 133.74/134.07 5631 meet(a,join(A,meet(a,z2))) = meet(a,join(A,z2)). [para(5475(a,1),39(a,2,1)),rewrite([1(7),5475(7),2989(6),23(8),971(8),5126(9),4733(6),2(3),4(15),5478(10)]),flip(a)].
% 133.74/134.07 6004 meet(a,meet(y2,join(x2,y2))) = meet(a,y2). [para(5331(a,1),5532(a,1,2,2)),rewrite([9(8,R),1(7),64(9)])].
% 133.74/134.07 6028 meet(a,meet(y2,join(A,a))) = meet(a,y2). [para(6004(a,1),2010(a,1,1)),rewrite([2(5),973(6),6004(13)])].
% 133.74/134.07 6031 join(meet(a,y2),meet(A,a)) = meet(a,join(A,meet(a,y2))). [para(6004(a,1),77(a,1,2,1)),rewrite([1(6),4733(8),2(5),6004(13),1(11)]),flip(a)].
% 133.74/134.07 6037 join(a,meet(A,meet(a,y2))) = a. [para(6004(a,1),111(a,1,2,2)),rewrite([23(3),23(16),2(15),4(16)])].
% 133.74/134.07 6108 join(join(A,B),meet(C,a)) = join(A,join(B,meet(C,a))). [para(32(a,1),131(a,1,2,1)),rewrite([2(13),11(13),2(12),11(12,R),2(11),376(11),11(8),2(7),11(8,R),2(7),11(9,R),2180(8),1(7),286(7),11(10),2(9),11(10,R),2(9),1(11),286(11),22(21),1181(17),11(13),2(12),11(13,R),2(12),2(32),11(32),2(31),11(31,R),2(30),376(30),11(27),2(26),11(27,R),2(26),11(28,R),2180(27),1(26),286(26),22(24),1(20),3(21),23(9),23(13),2(25),11(25),2(24),11(24,R),2(23),376(23),11(20),2(19),11(20,R),2(19),11(21,R),2180(20),1(19),95(19),1(17),1181(17),11(13),2(12),11(13,R),2(12),11(16),2(15),11(15),2(14),376(14),11(12),2(11),11(12,R),2(11),11(13),2(12),2470(12),1(10),11(12),2(11),11(12,R),2(11),11(11),2(10),2470(10),11(10,R),22(9)])].
% 133.74/134.07 6412 meet(a,join(A,meet(a,y2))) = meet(a,join(A,y2)). [para(6028(a,1),39(a,2,1)),rewrite([1(7),6028(7),6037(6),23(8),971(8),5126(9),4733(6),2(3),4(15),6031(10)]),flip(a)].
% 133.74/134.07 6466 meet(a,join(A,join(a,z2))) = a. [para(2083(a,1),5631(a,1,2)),rewrite([2(3),147(4),2(4),2(6),11(6),2(5),11(6,R),2(5)]),flip(a)].
% 133.74/134.07 6496 join(A,meet(B,A)) = meet(A,join(B,A)). [para(22(a,1),132(a,1,1,1,2)),rewrite([1863(4),22(3),1863(6),22(7),1863(10),3(9),1(7),2(8),547(8),9(7,R),1(6),369(6),64(3),23(4),2(4),22(5),1863(8),9(7,R),1(6),2083(8)]),flip(a)].
% 133.74/134.07 6822 join(x2,meet(y2,join(a,y2))) = join(x2,y2). [back_rewrite(5512),rewrite([6496(6)])].
% 133.74/134.07 6835 join(meet(A,meet(B,C)),meet(A,join(B,D))) = meet(A,join(B,D)). [back_rewrite(2143),rewrite([1(1),25(3),1(3),1(4),6496(6),369(6),1(5),1(8),1(9),25(11),2190(12),61(8),369(7),1(3)]),flip(a)].
% 133.74/134.07 6903 join(a,join(z2,meet(A,a))) = join(a,z2). [para(6466(a,1),3469(a,1,2)),rewrite([2(5),61(5),6108(9)]),flip(a)].
% 133.74/134.07 6926 meet(A,meet(a,join(B,A))) = meet(A,a). [para(6496(a,1),45(a,1,2)),rewrite([23(3),64(3),369(9),1(6),369(6),4733(10),4201(10)]),flip(a)].
% 133.74/134.07 6945 meet(join(A,a),join(A,meet(B,a))) = join(A,meet(B,a)). [para(4733(a,1),6496(a,1,2)),rewrite([2(7),11(7),2(6),2470(6),11(6,R),22(5),11(11,R),2(10),6496(10),147(10),1(9)]),flip(a)].
% 133.74/134.07 6952 join(meet(a,y2),meet(y2,join(x2,y2))) = meet(y2,join(x2,y2)). [para(6004(a,1),6496(a,1,2)),rewrite([2(9),369(22)])].
% 133.74/134.07 7029 meet(y2,meet(join(a,y2),join(x2,y2))) = meet(y2,join(a,y2)). [para(6822(a,1),369(a,1,2)),rewrite([1(9),9(9),1(8),9(9,R),1(8)])].
% 133.74/134.07 7031 join(meet(A,y2),meet(y2,join(x2,y2))) = meet(y2,meet(join(x2,y2),join(A,y2))). [para(6822(a,1),82(a,1,2,2,1)),rewrite([2(4),2(10),1863(12),1(10),6822(18)]),flip(a)].
% 133.74/134.07 7037 meet(y2,join(x2,y2)) = meet(y2,join(a,y2)). [back_rewrite(6952),rewrite([7031(9),1(8),7029(9)]),flip(a)].
% 133.74/134.07 7038 join(meet(A,y2),meet(y2,join(a,y2))) = meet(y2,meet(join(x2,y2),join(A,y2))). [back_rewrite(7031),rewrite([7037(7)])].
% 133.74/134.07 7130 meet(join(a,z2),join(z2,meet(A,a))) = join(z2,meet(A,a)). [para(6903(a,1),6496(a,2,2)),rewrite([4733(10),2(7),2(9),11(9),2(8),3469(8),11(7,R),22(6),1(12)]),flip(a)].
% 133.74/134.07 7272 meet(A,join(B,A)) = A. [para(58(a,1),135(a,2,1)),rewrite([64(3),3(3),22(1),64(4),3(4),64(4),25(5),2(2),1863(4),64(5),3(5),22(3),64(6),3(6),2(4),6496(4),9(5,R),1(4),64(8),3(8),64(8),3(8),22(6),64(9),3(9),64(9),25(10),2(7),11(10,R),2(9),1863(9),6835(10),9(7,R),1(6),369(6),64(3),23(3),22(4),1(4),64(5),64(7),3(7),706(7),3(7),64(5),3(5),22(3),64(6),3(6),64(6),25(7),2(4),1863(6),9(5,R),1(4),3(6)])].
% 133.74/134.07 7440 meet(y2,meet(join(x2,y2),join(A,y2))) = y2. [back_rewrite(7038),rewrite([7272(7),2(4),6496(4),7272(4)]),flip(a)].
% 133.74/134.07 8049 join(y2,meet(A,y2)) = y2. [para(7440(a,1),495(a,1,1)),rewrite([1(9),9(10,R),1(9),7440(9),7440(12)])].
% 133.74/134.07 8057 meet(y2,meet(join(A,y2),join(B,y2))) = y2. [para(7440(a,1),82(a,1,2,2,1,2)),rewrite([2(3),2(8),1863(10),1(9),7440(18),7272(13),2(11),8049(11)])].
% 133.74/134.07 8268 meet(A,meet(B,meet(C,join(meet(A,D),meet(A,E))))) = meet(B,meet(C,join(meet(A,D),meet(A,E)))). [para(3(a,1),164(a,1,2,2,2,1,2)),rewrite([1(1),2010(4),64(9)])].
% 133.74/134.07 8427 meet(y2,join(A,meet(join(B,y2),join(C,y2)))) = y2. [para(8057(a,1),547(a,1,1)),rewrite([2(8),3(10),2(8)]),flip(a)].
% 133.74/134.07 8890 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(166(a,1),5532(a,1)),rewrite([1(2),1(5)])].
% 133.74/134.07 9127 meet(a,join(A,join(a,y2))) = a. [para(2083(a,1),6412(a,1,2)),rewrite([2(3),7272(4),2(4),2(6),11(6),2(5),11(6,R),2(5)]),flip(a)].
% 133.74/134.07 9159 join(a,join(y2,meet(A,a))) = join(a,y2). [para(9127(a,1),3469(a,1,2)),rewrite([2(5),61(5),6108(9)]),flip(a)].
% 133.74/134.07 9205 meet(join(a,y2),join(y2,meet(A,a))) = join(y2,meet(A,a)). [para(9159(a,1),7272(a,1,2)),rewrite([1(8)])].
% 133.74/134.07 10689 meet(A,join(meet(B,meet(C,D)),meet(A,C))) = meet(A,C). [para(9(a,1),8890(a,1,2,1))].
% 133.74/134.07 12996 join(x2,join(z2,meet(a,y2))) = join(x2,z2). [para(6926(a,1),1553(a,1,2)),rewrite([1(6),2(7),11(7),2(6),11(7,R),2(6)])].
% 133.74/134.07 13026 meet(join(x2,z2),join(z2,meet(a,y2))) = join(z2,meet(a,y2)). [para(12996(a,1),7272(a,1,2)),rewrite([1(9)])].
% 133.74/134.07 13133 join(A,meet(B,A)) = A. [para(107(a,1),1724(a,1,2,2)),rewrite([2(2),9(8,R),1(7),4733(7),6926(6),2(5),11(5,R),107(4),3(5),2(2)]),flip(a)].
% 133.74/134.07 13481 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(1892(a,1),130(a,1,2,1)),rewrite([1892(7),22(4),9(3),1(2),9(3,R),1(2),22(10)]),flip(a)].
% 133.74/134.07 15000 meet(A,meet(B,join(C,meet(B,join(A,D))))) = meet(A,B). [back_rewrite(2133),rewrite([13481(5)])].
% 133.74/134.07 15010 meet(A,meet(B,join(meet(C,A),meet(C,D)))) = meet(C,meet(A,B)). [back_rewrite(2074),rewrite([13481(6),13481(5),8268(6)])].
% 133.74/134.07 16333 join(join(A,B),meet(C,join(A,meet(B,D)))) = join(A,B). [para(2254(a,1),2(a,2)),rewrite([2(4),2(5),2(6)])].
% 133.74/134.07 19495 join(join(A,meet(B,a)),meet(join(A,a),join(B,meet(A,a)))) = meet(join(A,a),join(A,B)). [para(6945(a,1),16(a,1,1))].
% 133.74/134.07 19712 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(492(a,1),274(a,1,2,2,2,2)),rewrite([11(6,R),2(5),11(5,R),2(4),11(4,R),22(3),11(8,R)]),flip(a)].
% 133.74/134.07 19890 join(z2,meet(join(a,z2),join(a,meet(A,z2)))) = join(a,z2). [para(7130(a,1),121(a,2)),rewrite([1(5),7272(5),1(6),1(11),4(11),2(8),1(16),4(16),2(13)])].
% 133.74/134.07 20673 join(y2,meet(join(a,y2),join(a,meet(A,y2)))) = join(a,y2). [para(9205(a,1),121(a,2)),rewrite([1(5),7272(5),1(6),1(11),4(11),2(8),1(16),4(16),2(13)])].
% 133.74/134.07 21805 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(4(a,1),13481(a,1,1)),flip(a)].
% 133.74/134.07 23493 join(A,join(meet(B,C),meet(B,A))) = join(A,meet(B,C)). [para(8890(a,1),16333(a,1,2)),rewrite([2(2),1(3),2(4),11(4,R),2(6)])].
% 133.74/134.07 23529 join(A,meet(B,meet(A,C))) = A. [para(617(a,1),16333(a,1,2,2)),rewrite([2(2),13133(2),9(2),1(1),9(2,R),1(1),2(5),13133(5)])].
% 133.74/134.07 25873 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(21805(a,1),15000(a,1)),rewrite([4(7)])].
% 133.74/134.07 25903 meet(z2,meet(join(a,z2),join(A,B))) = meet(z2,join(A,B)). [para(19890(a,1),21805(a,1,2,1))].
% 133.74/134.07 25907 meet(y2,meet(join(a,y2),join(A,B))) = meet(y2,join(A,B)). [para(20673(a,1),21805(a,1,2,1))].
% 133.74/134.07 25924 meet(A,join(B,join(C,meet(join(A,D),join(A,E))))) = A. [para(25873(a,1),547(a,1,1)),rewrite([2(5),11(5,R),2(4),3(7),2(5),11(5,R),2(4)]),flip(a)].
% 133.74/134.07 27250 join(meet(A,meet(B,C)),meet(C,join(A,D))) = meet(C,join(A,D)). [para(2083(a,1),1865(a,1,2,2)),rewrite([2083(8)])].
% 133.74/134.07 27331 join(A,meet(join(A,B),join(C,meet(A,a)))) = join(A,meet(C,join(A,B))). [back_rewrite(5342),rewrite([27250(10)])].
% 133.74/134.07 27951 meet(join(A,y2),join(A,meet(B,y2))) = join(A,meet(B,y2)). [para(8427(a,1),1888(a,1,2,2)),rewrite([1(2),1(6),1(8)])].
% 133.74/134.07 28252 meet(z2,join(meet(A,z2),meet(B,meet(A,C)))) = meet(A,z2). [para(10689(a,1),25903(a,2)),rewrite([1(8),2(9),25903(11),1(9)])].
% 133.74/134.07 28501 meet(y2,join(meet(A,y2),meet(B,meet(A,C)))) = meet(A,y2). [para(10689(a,1),25907(a,2)),rewrite([1(8),2(9),25907(11),1(9)])].
% 133.74/134.07 28797 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(23493(a,1),25924(a,1,2)),rewrite([1(3)])].
% 133.74/134.07 28823 join(join(A,B),meet(C,join(A,D))) = join(A,join(B,meet(C,join(A,D)))). [para(28797(a,1),13133(a,1,2)),rewrite([2(5),19712(5),61(5)]),flip(a)].
% 133.74/134.07 28836 meet(A,join(join(A,B),meet(C,meet(D,join(A,E))))) = A. [para(13481(a,1),28797(a,1,2,2))].
% 133.74/134.07 29973 join(A,join(y2,meet(B,join(A,meet(C,y2))))) = join(A,y2). [para(27951(a,1),23529(a,1,2,2)),rewrite([28823(7)])].
% 133.74/134.07 30654 meet(A,join(join(A,B),meet(C,D))) = A. [para(5532(a,1),28836(a,1,2,2))].
% 133.74/134.07 30686 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(30654(a,1),13133(a,1,2)),rewrite([2(4),19712(4),61(4)]),flip(a)].
% 133.74/134.07 30881 join(A,meet(B,join(A,a))) = meet(join(A,a),join(A,B)). [back_rewrite(19495),rewrite([30686(10),2198(9),30686(8),13133(7),1(6),27331(7)])].
% 133.74/134.07 31883 join(y2,join(z2,meet(a,y2))) = join(y2,z2). [para(13026(a,1),29973(a,1,2,2)),rewrite([11(9,R),2(8),61(8),2(10)])].
% 133.74/134.07 31886 join(meet(A,join(y2,meet(a,z2))),meet(A,join(z2,meet(a,y2)))) = meet(A,join(y2,z2)). [para(31883(a,1),16(a,2,2)),rewrite([1(8),6412(8),2(5),2470(7),1(4),1(14),2(15),11(15,R),22(14)])].
% 133.74/134.07 32336 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(3(a,1),30686(a,1,1)),flip(a)].
% 133.74/134.07 32506 join(A,meet(join(B,a),join(A,B))) = join(A,B). [para(30881(a,1),25(a,1,2)),rewrite([2(3)])].
% 133.74/134.07 33725 join(z2,join(meet(A,z2),meet(B,C))) = join(z2,meet(B,C)). [para(28252(a,1),32336(a,1,2,1))].
% 133.74/134.07 33730 join(y2,join(meet(A,y2),meet(B,C))) = join(y2,meet(B,C)). [para(28501(a,1),32336(a,1,2,1))].
% 133.74/134.07 34195 join(z2,meet(join(A,a),join(A,meet(B,z2)))) = join(A,z2). [para(32506(a,1),33725(a,1,2)),rewrite([2(4),11(5,R),2(4),13133(4),2(8)]),flip(a)].
% 133.74/134.07 34218 join(y2,meet(join(A,a),join(A,meet(B,y2)))) = join(A,y2). [para(32506(a,1),33730(a,1,2)),rewrite([2(4),11(5,R),2(4),13133(4),2(8)]),flip(a)].
% 133.74/134.07 34393 join(meet(a,z2),meet(A,join(B,z2))) = meet(join(B,z2),join(A,meet(a,z2))). [para(34195(a,1),2198(a,1,2,2)),rewrite([1(3),34195(15),1(12)])].
% 133.74/134.07 34441 join(meet(a,y2),meet(A,join(B,y2))) = meet(join(B,y2),join(A,meet(a,y2))). [para(34218(a,1),2198(a,1,2,2)),rewrite([1(3),34218(15),1(12)])].
% 133.74/134.07 35941 meet(A,meet(B,join(C,A))) = meet(A,B). [para(7272(a,1),15010(a,1,2,2,1)),rewrite([3(3),1(2),9(3),1(2),7272(2),1(1),1(3)]),flip(a)].
% 133.74/134.07 35953 join(meet(x2,y2),meet(x2,z2)) = meet(x2,join(y2,z2)). [para(35941(a,1),442(a,1,2,2,2)),rewrite([2(11),5426(13),2(10),34393(10),21805(11),2(12),1(16),2(17),34441(17),21805(18),31886(15),1(11),2(12)]),flip(a)].
% 133.74/134.07 35954 $F # answer(conjecture_1). [resolve(35953,a,20,a)].
% 133.74/134.07
% 133.74/134.07 % SZS output end Refutation
% 133.74/134.07 ============================== end of proof ==========================
% 133.74/134.07
% 133.74/134.07 ============================== STATISTICS ============================
% 133.74/134.07
% 133.74/134.07 Given=1972. Generated=1590479. Kept=35946. proofs=1.
% 133.74/134.07 Usable=1015. Sos=9933. Demods=10913. Limbo=0, Disabled=25010. Hints=0.
% 133.74/134.07 Megabytes=42.81.
% 133.74/134.07 User_CPU=132.13, System_CPU=0.95, Wall_clock=133.
% 133.74/134.07
% 133.74/134.07 ============================== end of statistics =====================
% 133.74/134.07
% 133.74/134.07 ============================== end of search =========================
% 133.74/134.07
% 133.74/134.07 THEOREM PROVED
% 133.74/134.07 % SZS status Unsatisfiable
% 133.74/134.07
% 133.74/134.07 Exiting with 1 proof.
% 133.74/134.07
% 133.74/134.07 Process 29934 exit (max_proofs) Wed Jun 29 17:36:13 2022
% 133.74/134.07 Prover9 interrupted
%------------------------------------------------------------------------------