TSTP Solution File: LAT183-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT183-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 06:25:59 EDT 2022
% Result : Unsatisfiable 111.89s 112.27s
% Output : Refutation 111.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT183-1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Wed Jun 29 02:53:57 EDT 2022
% 0.10/0.30 % CPUTime :
% 23.23/23.55 ============================== Prover9 ===============================
% 23.23/23.55 Prover9 (32) version 2009-11A, November 2009.
% 23.23/23.55 Process 13373 was started by sandbox on n032.cluster.edu,
% 23.23/23.55 Wed Jun 29 02:53:58 2022
% 23.23/23.55 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13220_n032.cluster.edu".
% 23.23/23.55 ============================== end of head ===========================
% 23.23/23.55
% 23.23/23.55 ============================== INPUT =================================
% 23.23/23.55
% 23.23/23.55 % Reading from file /tmp/Prover9_13220_n032.cluster.edu
% 23.23/23.55
% 23.23/23.55 set(prolog_style_variables).
% 23.23/23.55 set(auto2).
% 23.23/23.55 % set(auto2) -> set(auto).
% 23.23/23.55 % set(auto) -> set(auto_inference).
% 23.23/23.55 % set(auto) -> set(auto_setup).
% 23.23/23.55 % set(auto_setup) -> set(predicate_elim).
% 23.23/23.55 % set(auto_setup) -> assign(eq_defs, unfold).
% 23.23/23.55 % set(auto) -> set(auto_limits).
% 23.23/23.55 % set(auto_limits) -> assign(max_weight, "100.000").
% 23.23/23.55 % set(auto_limits) -> assign(sos_limit, 20000).
% 23.23/23.55 % set(auto) -> set(auto_denials).
% 23.23/23.55 % set(auto) -> set(auto_process).
% 23.23/23.55 % set(auto2) -> assign(new_constants, 1).
% 23.23/23.55 % set(auto2) -> assign(fold_denial_max, 3).
% 23.23/23.55 % set(auto2) -> assign(max_weight, "200.000").
% 23.23/23.55 % set(auto2) -> assign(max_hours, 1).
% 23.23/23.55 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 23.23/23.55 % set(auto2) -> assign(max_seconds, 0).
% 23.23/23.55 % set(auto2) -> assign(max_minutes, 5).
% 23.23/23.55 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 23.23/23.55 % set(auto2) -> set(sort_initial_sos).
% 23.23/23.55 % set(auto2) -> assign(sos_limit, -1).
% 23.23/23.55 % set(auto2) -> assign(lrs_ticks, 3000).
% 23.23/23.55 % set(auto2) -> assign(max_megs, 400).
% 23.23/23.55 % set(auto2) -> assign(stats, some).
% 23.23/23.55 % set(auto2) -> clear(echo_input).
% 23.23/23.55 % set(auto2) -> set(quiet).
% 23.23/23.55 % set(auto2) -> clear(print_initial_clauses).
% 23.23/23.55 % set(auto2) -> clear(print_given).
% 23.23/23.55 assign(lrs_ticks,-1).
% 23.23/23.55 assign(sos_limit,10000).
% 23.23/23.55 assign(order,kbo).
% 23.23/23.55 set(lex_order_vars).
% 23.23/23.55 clear(print_given).
% 23.23/23.55
% 23.23/23.55 % formulas(sos). % not echoed (13 formulas)
% 23.23/23.55
% 23.23/23.55 ============================== end of input ==========================
% 23.23/23.55
% 23.23/23.55 % From the command line: assign(max_seconds, 300).
% 23.23/23.55
% 23.23/23.55 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 23.23/23.55
% 23.23/23.55 % Formulas that are not ordinary clauses:
% 23.23/23.55
% 23.23/23.55 ============================== end of process non-clausal formulas ===
% 23.23/23.55
% 23.23/23.55 ============================== PROCESS INITIAL CLAUSES ===============
% 23.23/23.55
% 23.23/23.55 ============================== PREDICATE ELIMINATION =================
% 23.23/23.55
% 23.23/23.55 ============================== end predicate elimination =============
% 23.23/23.55
% 23.23/23.55 Auto_denials:
% 23.23/23.55 % copying label prove_distributivity to answer in negative clause
% 23.23/23.55
% 23.23/23.55 Term ordering decisions:
% 23.23/23.55
% 23.23/23.55 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 23.23/23.55 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 23.23/23.55
% 23.23/23.55 ============================== end of process initial clauses ========
% 23.23/23.55
% 23.23/23.55 ============================== CLAUSES FOR SEARCH ====================
% 23.23/23.55
% 23.23/23.55 ============================== end of clauses for search =============
% 23.23/23.55
% 23.23/23.55 ============================== SEARCH ================================
% 23.23/23.55
% 23.23/23.55 % Starting search at 0.01 seconds.
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=198.000, iters=3344
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=194.000, iters=3349
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=184.000, iters=3458
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=169.000, iters=3383
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=167.000, iters=3375
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=163.000, iters=3356
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=161.000, iters=3391
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=151.000, iters=3358
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=148.000, iters=3457
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=138.000, iters=3340
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=137.000, iters=3468
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=131.000, iters=3409
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=129.000, iters=3366
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=122.000, iters=3343
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=121.000, iters=3372
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=119.000, iters=3356
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=117.000, iters=3385
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=115.000, iters=3372
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=111.000, iters=3356
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=108.000, iters=3358
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=107.000, iters=3348
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=106.000, iters=3361
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=103.000, iters=3340
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=102.000, iters=3339
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=100.000, iters=3375
% 23.23/23.55
% 23.23/23.55 Low Water (keep): wt=98.000, iters=3346
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=95.000, iters=3373
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=93.000, iters=3361
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=91.000, iters=3348
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=89.000, iters=3352
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=88.000, iters=3343
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=87.000, iters=3333
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=86.000, iters=3334
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=84.000, iters=3363
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=82.000, iters=3405
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=80.000, iters=3364
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=79.000, iters=3376
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=76.000, iters=3341
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=75.000, iters=3373
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=74.000, iters=3370
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=72.000, iters=3368
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=69.000, iters=3350
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=68.000, iters=3352
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=67.000, iters=3415
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=66.000, iters=3358
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=64.000, iters=3410
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=63.000, iters=3398
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=61.000, iters=3338
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=59.000, iters=3340
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=58.000, iters=3351
% 111.89/112.27
% 111.89/112.27 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 33.16 sec).
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=57.000, iters=3371
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=56.000, iters=3359
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=55.000, iters=3403
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=54.000, iters=3347
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=53.000, iters=3384
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=52.000, iters=3343
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=51.000, iters=3362
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=50.000, iters=3383
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=7694, wt=200.000
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=9171, wt=199.000
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=14939, wt=49.000
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=14940, wt=40.000
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=14946, wt=36.000
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=14951, wt=34.000
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=14968, wt=33.000
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=15030, wt=20.000
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=15031, wt=18.000
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=49.000, iters=3361
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=48.000, iters=3335
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=47.000, iters=3336
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=46.000, iters=3333
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=45.000, iters=3348
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=43.000, iters=3341
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=42.000, iters=3348
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=41.000, iters=3335
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=40.000, iters=3349
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=39.000, iters=3390
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=38.000, iters=3336
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=37.000, iters=3376
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=19743, wt=17.000
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=36.000, iters=3406
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=35.000, iters=3368
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=34.000, iters=3363
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=33.000, iters=3460
% 111.89/112.27
% 111.89/112.27 Low Water (displace): id=21491, wt=16.000
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=32.000, iters=3411
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=31.000, iters=3383
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=30.000, iters=3357
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=29.000, iters=3336
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=28.000, iters=3343
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=27.000, iters=3333
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=26.000, iters=3335
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=25.000, iters=3337
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=24.000, iters=3350
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=23.000, iters=3357
% 111.89/112.27
% 111.89/112.27 Low Water (keep): wt=22.000, iters=3338
% 111.89/112.27
% 111.89/112.27 ============================== PROOF =================================
% 111.89/112.27 % SZS status Unsatisfiable
% 111.89/112.27 % SZS output start Refutation
% 111.89/112.27
% 111.89/112.27 % Proof 1 at 110.85 (+ 0.59) seconds: prove_distributivity.
% 111.89/112.27 % Length of proof is 275.
% 111.89/112.27 % Level of proof is 67.
% 111.89/112.27 % Maximum clause weight is 109.000.
% 111.89/112.27 % Given clauses 1015.
% 111.89/112.27
% 111.89/112.27 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 111.89/112.27 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 111.89/112.27 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 111.89/112.27 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 111.89/112.27 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 111.89/112.27 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 111.89/112.27 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 111.89/112.27 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 111.89/112.27 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 111.89/112.27 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 111.89/112.27 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 111.89/112.27 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 111.89/112.27 13 meet(A,join(B,meet(A,C))) = meet(A,join(B,meet(A,join(meet(A,B),meet(C,join(A,B)))))) # label(equation_H7) # label(axiom). [assumption].
% 111.89/112.27 14 meet(A,join(B,meet(A,join(meet(A,B),meet(C,join(A,B)))))) = meet(A,join(B,meet(A,C))). [copy(13),flip(a)].
% 111.89/112.27 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 111.89/112.27 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 111.89/112.27 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 111.89/112.27 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 111.89/112.27 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 111.89/112.27 20 meet(A,meet(A,B)) = meet(A,B). [para(10(a,1),1(a,1)),rewrite([7(1),7(2),10(2,R),1(1),7(3)])].
% 111.89/112.27 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 111.89/112.27 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 111.89/112.27 23 join(A,join(A,B)) = join(A,B). [para(12(a,1),2(a,1)),rewrite([8(1),8(2),12(2,R),2(1),8(3)])].
% 111.89/112.27 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 111.89/112.27 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 111.89/112.27 26 meet(A,join(join(A,B),meet(A,C))) = A. [para(5(a,1),14(a,1,2,2,2,1)),rewrite([23(3),5(5),8(2),23(2),5(2)]),flip(a)].
% 111.89/112.27 27 meet(A,join(meet(A,B),meet(A,join(meet(A,B),meet(A,C))))) = meet(A,join(meet(A,B),meet(A,C))). [para(6(a,1),14(a,1,2,2,2,2,2)),rewrite([20(3),7(3)])].
% 111.89/112.27 28 meet(A,join(B,meet(A,join(meet(B,A),meet(C,join(B,A)))))) = meet(A,join(B,meet(A,C))). [para(14(a,1),7(a,2)),rewrite([7(1),8(2),7(7)])].
% 111.89/112.27 29 meet(A,meet(B,join(C,meet(A,join(meet(A,C),meet(D,join(A,C))))))) = meet(A,meet(B,join(C,meet(A,D)))). [para(14(a,1),10(a,2,2)),rewrite([7(7),10(12,R),7(11)])].
% 111.89/112.27 30 meet(A,join(join(B,meet(A,join(meet(A,B),meet(C,join(A,B))))),meet(A,join(meet(A,join(B,meet(A,C))),meet(D,join(A,B)))))) = meet(A,join(join(B,meet(A,join(meet(A,B),meet(C,join(A,B))))),meet(A,D))). [para(14(a,1),14(a,1,2,2,2,1)),rewrite([25(16)])].
% 111.89/112.27 31 meet(A,join(meet(B,join(meet(A,B),meet(C,join(A,B)))),meet(A,join(meet(B,join(A,meet(B,C))),meet(A,meet(B,join(meet(A,B),meet(C,join(A,B))))))))) = meet(A,join(meet(A,B),meet(B,join(meet(A,B),meet(C,join(A,B)))))). [para(14(a,1),14(a,1,2,2,2,2)),rewrite([7(1),8(2),7(6),8(7),8(15),7(19),8(20),8(25)])].
% 111.89/112.27 32 meet(A,join(B,meet(A,join(meet(A,B),meet(join(A,B),join(meet(A,B),meet(C,join(A,B)))))))) = meet(A,join(B,meet(A,C))). [para(14(a,1),14(a,2)),rewrite([7(7)])].
% 111.89/112.27 34 meet(A,B) != zero | one != A | meet(A,B) = complement(A). [para(6(a,1),17(b,1)),rewrite([20(2)]),flip(b),flip(c)].
% 111.89/112.27 35 meet(A,join(one,meet(A,B))) = A. [para(18(a,1),14(a,1,2,2,2,1)),rewrite([5(6),8(2),5(3)]),flip(a)].
% 111.89/112.27 37 meet(A,zero) != zero | one != A | complement(A) = zero. [para(19(a,1),17(b,1)),flip(b)].
% 111.89/112.27 38 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 111.89/112.27 39 one != A | complement(A) = zero. [back_rewrite(37),rewrite([38(2)]),xx(a)].
% 111.89/112.27 41 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([38(5)])].
% 111.89/112.27 42 complement(one) = zero. [hyper(17,a,38,a,b,19,a)].
% 111.89/112.27 43 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(22(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),10(6),7(5),10(6,R),7(5)])].
% 111.89/112.27 44 meet(A,join(meet(B,join(A,C)),meet(A,join(meet(A,B),meet(D,join(A,meet(B,join(A,C)))))))) = meet(A,join(meet(B,join(A,C)),meet(A,D))). [para(22(a,1),14(a,1,2,2,2,1))].
% 111.89/112.27 45 complement(join(A,one)) = zero. [hyper(39,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 111.89/112.27 47 join(A,one) = one. [para(45(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 111.89/112.27 48 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([47(5)])].
% 111.89/112.27 49 complement(zero) = one. [hyper(17,a,18,a,b,47,a)].
% 111.89/112.27 55 meet(A,join(join(B,complement(A)),meet(A,join(C,meet(A,join(B,complement(A))))))) = meet(A,join(join(B,complement(A)),meet(A,C))). [para(48(a,1),14(a,1,2,2,2,2,2)),rewrite([18(7),8(6)])].
% 111.89/112.27 56 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(48(a,1),17(b,1)),flip(c),xx(b)].
% 111.89/112.27 59 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(25(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),12(6),8(5),12(6,R),8(5)])].
% 111.89/112.27 60 meet(A,join(join(B,meet(A,C)),meet(A,join(meet(A,join(B,meet(A,C))),meet(D,join(A,B)))))) = meet(A,join(join(B,meet(A,C)),meet(A,D))). [para(25(a,1),14(a,1,2,2,2,2,2))].
% 111.89/112.27 61 meet(A,join(B,meet(A,C))) != zero | join(A,B) != one | join(B,meet(A,C)) = complement(A). [para(25(a,1),17(b,1)),flip(c)].
% 111.89/112.27 68 meet(A,join(join(join(A,B),meet(A,C)),meet(A,D))) = A. [para(26(a,1),14(a,1,2,2,2,1)),rewrite([25(7),23(5),5(7),8(4),25(4),23(2),5(2)]),flip(a)].
% 111.89/112.27 69 meet(A,join(meet(A,B),meet(A,join(zero,meet(A,B))))) = meet(A,join(zero,meet(A,B))). [para(4(a,1),27(a,1,2,2,2,2)),rewrite([8(4),4(10),8(10)])].
% 111.89/112.27 87 meet(join(A,B),join(C,meet(join(A,B),join(meet(C,join(A,B)),meet(D,join(A,join(B,C))))))) = meet(join(A,B),join(C,meet(D,join(A,B)))). [para(12(a,1),28(a,1,2,2,2,2,2)),rewrite([8(5),12(6,R),8(5),7(14)])].
% 111.89/112.27 88 meet(join(A,meet(B,join(meet(A,B),meet(C,join(A,B))))),join(B,meet(join(A,meet(B,join(meet(A,B),meet(C,join(A,B))))),join(meet(B,join(A,meet(B,C))),meet(D,join(A,B)))))) = meet(join(A,meet(B,join(meet(A,B),meet(C,join(A,B))))),join(B,meet(D,join(A,meet(B,join(meet(A,B),meet(C,join(A,B)))))))). [para(14(a,1),28(a,1,2,2,2,1)),rewrite([7(1),8(2),7(7),8(8),7(16),8(17),25(22),8(16),7(22),8(23),7(28),8(29),7(34)])].
% 111.89/112.27 90 meet(one,join(A,meet(one,join(A,B)))) = meet(one,join(A,B)). [para(18(a,1),28(a,1,2,2,2,1)),rewrite([47(4),18(4),7(9),18(9)])].
% 111.89/112.27 91 meet(meet(A,join(B,C)),join(B,meet(meet(A,join(B,C)),join(meet(A,B),meet(D,join(B,meet(A,join(B,C)))))))) = meet(meet(A,join(B,C)),join(B,meet(A,meet(D,join(B,C))))). [para(22(a,1),28(a,1,2,2,2,1)),rewrite([7(5),7(18),10(18,R),7(17)])].
% 111.89/112.27 115 meet(A,B) != zero | one != B | meet(A,B) = complement(B). [para(7(a,1),34(a,1)),rewrite([7(6)])].
% 111.89/112.27 168 meet(A,join(join(complement(A),meet(A,B)),meet(A,join(C,meet(A,join(complement(A),meet(A,B))))))) = meet(A,join(join(complement(A),meet(A,B)),meet(A,C))). [para(3(a,1),30(a,1,2,1,2,2,2,2)),rewrite([4(3),18(4),8(3),19(3),3(9),18(9),8(8),4(14),3(15),18(15),8(14),19(14)])].
% 111.89/112.27 195 meet(one,join(A,meet(B,join(one,meet(A,C))))) = meet(one,join(A,B)). [para(35(a,1),30(a,1,2,1,2,2,2)),rewrite([10(6),7(5),18(5),7(4),8(5),6(5),7(4),18(4),8(3),6(3),7(6),18(6),8(5),6(5),7(4),18(4),90(10),10(13),7(12),18(12),7(11),35(15),8(12),6(12),7(11),18(11),8(10),6(10),7(10),18(10)])].
% 111.89/112.27 239 meet(A,meet(B,meet(meet(A,B),join(C,meet(A,B))))) = meet(A,B). [para(1(a,1),43(a,2)),rewrite([8(3),10(6,R),7(5),10(5,R),7(4)])].
% 111.89/112.27 240 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(43(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),10(3,R),7(2),10(8,R),7(7),10(7),7(6),10(7,R),7(6)])].
% 111.89/112.27 298 join(A,join(B,join(join(A,B),meet(C,join(A,B))))) = join(A,B). [para(2(a,1),59(a,2)),rewrite([7(3),12(6,R),8(5),12(5,R),8(4)])].
% 111.89/112.27 299 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(59(a,1),12(a,2,2)),rewrite([8(4),12(4,R),8(3),12(3,R),8(2),12(8,R),8(7),12(7),8(6),12(7,R),8(6)])].
% 111.89/112.27 312 meet(A,join(zero,join(join(A,B),meet(A,C)))) = A. [para(4(a,1),68(a,1,2,2)),rewrite([8(5)])].
% 111.89/112.27 313 meet(A,join(meet(A,B),join(join(A,C),meet(A,D)))) = A. [para(8(a,1),68(a,1,2))].
% 111.89/112.27 326 meet(zero,join(meet(join(join(A,B),meet(A,C)),join(A,meet(zero,join(join(A,B),meet(A,C))))),meet(zero,join(A,meet(zero,meet(join(join(A,B),meet(A,C)),join(A,meet(zero,join(join(A,B),meet(A,C)))))))))) = meet(zero,join(meet(zero,join(join(A,B),meet(A,C))),meet(join(join(A,B),meet(A,C)),join(A,meet(zero,join(join(A,B),meet(A,C))))))). [para(312(a,1),31(a,1,2,1,2,2)),rewrite([8(10),7(20),26(20),8(17),19(17),7(16),26(16),312(27),8(22),312(48),8(43)])].
% 111.89/112.27 357 meet(zero,join(join(join(A,B),meet(A,C)),meet(zero,join(meet(zero,join(join(A,B),meet(A,C))),meet(join(zero,join(join(A,B),meet(A,C))),join(A,meet(zero,join(join(A,B),meet(A,C))))))))) = zero. [para(312(a,1),32(a,1,2,2,2,2,2,2)),rewrite([8(21),7(32),38(32),8(32),5(33)])].
% 111.89/112.27 361 meet(A,join(B,meet(one,join(B,C)))) = meet(A,meet(one,join(B,C))). [para(90(a,1),10(a,1,2)),rewrite([18(10),7(9)]),flip(a)].
% 111.89/112.27 389 meet(meet(A,B),join(meet(join(join(A,C),meet(A,D)),join(A,meet(meet(A,B),join(join(A,C),meet(A,D))))),meet(meet(A,B),join(A,meet(meet(A,B),meet(join(join(A,C),meet(A,D)),join(A,meet(meet(A,B),join(join(A,C),meet(A,D)))))))))) = meet(meet(A,B),join(meet(meet(A,B),join(join(A,C),meet(A,D))),meet(join(join(A,C),meet(A,D)),join(A,meet(meet(A,B),join(join(A,C),meet(A,D))))))). [para(313(a,1),31(a,1,2,1,2,2)),rewrite([8(10),7(20),26(20),8(17),6(17),7(16),26(16),313(27),8(22),313(48),8(43)])].
% 111.89/112.27 391 meet(meet(A,B),join(join(join(A,C),meet(A,D)),meet(meet(A,B),join(meet(meet(A,B),join(join(A,C),meet(A,D))),meet(join(meet(A,B),join(join(A,C),meet(A,D))),join(A,meet(meet(A,B),join(join(A,C),meet(A,D))))))))) = meet(meet(A,B),join(join(join(A,C),meet(A,D)),meet(A,B))). [para(313(a,1),32(a,1,2,2,2,2,2,2)),rewrite([8(21),7(32),20(32)])].
% 111.89/112.27 438 meet(A,join(meet(join(A,B),join(A,C)),meet(A,D))) = A. [para(5(a,1),44(a,1,2,2,2,1)),rewrite([5(10),8(4),5(5)]),flip(a)].
% 111.89/112.27 442 meet(A,join(meet(one,join(A,B)),meet(A,C))) = A. [para(18(a,1),44(a,1,2,2,2,1)),rewrite([361(8),5(9),8(4),5(5)]),flip(a)].
% 111.89/112.27 486 meet(A,join(zero,meet(one,join(A,B)))) = A. [para(4(a,1),442(a,1,2,2)),rewrite([8(5)])].
% 111.89/112.27 516 meet(A,join(zero,meet(join(A,B),join(A,C)))) = A. [para(4(a,1),438(a,1,2,2)),rewrite([8(5)])].
% 111.89/112.27 517 meet(A,join(meet(A,B),meet(join(A,C),join(A,D)))) = A. [para(8(a,1),438(a,1,2))].
% 111.89/112.27 542 meet(zero,join(meet(join(A,B),join(A,C)),meet(zero,join(A,meet(zero,meet(join(A,B),join(A,C))))))) = zero. [para(516(a,1),14(a,1,2,2,2,2)),rewrite([8(11),7(20),38(20),8(20),5(21)])].
% 111.89/112.27 570 meet(meet(A,B),join(meet(join(A,C),join(A,D)),meet(meet(A,B),join(A,meet(meet(A,B),meet(join(A,C),join(A,D))))))) = meet(meet(A,B),join(meet(join(A,C),join(A,D)),meet(A,B))). [para(517(a,1),14(a,1,2,2,2,2)),rewrite([8(11),7(20),20(20)])].
% 111.89/112.27 580 meet(A,join(join(B,complement(A)),meet(A,C))) = meet(A,join(B,join(complement(A),meet(A,C)))). [para(8(a,1),55(a,2,2)),rewrite([55(9),12(9),8(8),12(9,R),8(8)])].
% 111.89/112.27 588 meet(A,join(B,join(complement(A),meet(A,join(C,meet(A,join(B,complement(A)))))))) = meet(A,join(B,join(complement(A),meet(A,C)))). [para(14(a,1),55(a,2)),rewrite([48(8),18(7),8(6),8(10),12(10,R),2(9),580(9),580(14)])].
% 111.89/112.27 591 meet(meet(A,join(B,meet(A,join(C,complement(A))))),join(join(C,complement(A)),meet(meet(A,join(B,meet(A,join(C,complement(A))))),join(meet(A,join(C,join(complement(A),meet(A,B)))),meet(A,meet(join(C,complement(A)),join(B,meet(A,join(C,complement(A)))))))))) = meet(meet(A,join(B,meet(A,join(C,complement(A))))),join(join(C,complement(A)),meet(A,join(B,meet(A,join(C,complement(A))))))). [para(55(a,1),28(a,1,2,2,2,2)),rewrite([10(20,R),7(19),580(25),8(26),7(42),20(42)])].
% 111.89/112.27 603 meet(A,join(meet(join(join(B,complement(A)),meet(A,join(C,meet(A,join(B,complement(A)))))),join(A,D)),meet(A,join(meet(A,join(B,join(complement(A),meet(A,C)))),meet(E,join(A,meet(join(join(B,complement(A)),meet(A,join(C,meet(A,join(B,complement(A)))))),join(A,D)))))))) = meet(A,join(meet(join(join(B,complement(A)),meet(A,join(C,meet(A,join(B,complement(A)))))),join(A,D)),meet(A,E))). [para(55(a,1),44(a,1,2,2,2,1)),rewrite([580(15)])].
% 111.89/112.27 649 meet(A,join(join(B,meet(A,C)),meet(A,D))) = meet(A,join(B,join(meet(A,C),meet(A,D)))). [para(8(a,1),60(a,2,2)),rewrite([60(11),12(9,R)])].
% 111.89/112.27 675 meet(meet(A,join(meet(A,join(B,meet(A,C))),meet(D,join(A,B)))),join(join(B,meet(A,C)),meet(meet(A,join(meet(A,join(B,meet(A,C))),meet(D,join(A,B)))),join(meet(A,join(B,join(meet(A,C),meet(A,D)))),meet(A,meet(join(B,meet(A,C)),join(meet(A,join(B,meet(A,C))),meet(D,join(A,B))))))))) = meet(meet(A,join(meet(A,join(B,meet(A,C))),meet(D,join(A,B)))),join(join(B,meet(A,C)),meet(A,join(meet(A,join(B,meet(A,C))),meet(D,join(A,B)))))). [para(60(a,1),28(a,1,2,2,2,2)),rewrite([10(26,R),7(25),649(31),8(32),7(52),20(52)])].
% 111.89/112.27 711 meet(join(A,B),join(zero,meet(one,join(A,join(B,C))))) = join(A,B). [para(60(a,1),486(a,1,2,2)),rewrite([7(2),18(2),7(5),18(5),7(6),18(6),8(5),12(5),8(4),12(5,R),8(4),7(10),18(10)])].
% 111.89/112.27 756 meet(A,join(complement(A),join(meet(A,B),meet(A,join(C,meet(A,join(complement(A),meet(A,B)))))))) = meet(A,join(complement(A),join(meet(A,B),meet(A,C)))). [back_rewrite(168),rewrite([649(11),649(17)])].
% 111.89/112.27 804 meet(A,join(B,meet(C,join(one,meet(B,D))))) = meet(A,meet(one,join(B,C))). [para(195(a,1),10(a,1,2)),rewrite([18(11),7(10)]),flip(a)].
% 111.89/112.27 806 meet(join(A,meet(B,join(one,meet(A,C)))),join(one,meet(D,meet(one,join(A,B))))) = join(A,meet(B,join(one,meet(A,C)))). [para(195(a,1),28(a,1,2,2,2,1)),rewrite([12(21,R),8(20),35(26),7(17),804(17)]),flip(a)].
% 111.89/112.27 821 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(239(a,1),10(a,1)),rewrite([7(7),20(7)]),flip(a)].
% 111.89/112.27 823 meet(meet(A,join(meet(A,join(B,meet(A,C))),meet(D,join(A,B)))),join(join(B,meet(A,C)),meet(meet(A,join(meet(A,join(B,meet(A,C))),meet(D,join(A,B)))),join(meet(A,join(B,join(meet(A,C),meet(A,D)))),meet(A,meet(join(B,meet(A,C)),join(meet(A,join(B,meet(A,C))),meet(D,join(A,B))))))))) = meet(A,join(meet(A,join(B,meet(A,C))),meet(D,join(A,B)))). [back_rewrite(675),rewrite([821(53)])].
% 111.89/112.27 825 meet(meet(A,join(B,meet(A,join(C,complement(A))))),join(join(C,complement(A)),meet(meet(A,join(B,meet(A,join(C,complement(A))))),join(meet(A,join(C,join(complement(A),meet(A,B)))),meet(A,meet(join(C,complement(A)),join(B,meet(A,join(C,complement(A)))))))))) = meet(A,join(B,meet(A,join(C,complement(A))))). [back_rewrite(591),rewrite([821(43)])].
% 111.89/112.27 827 meet(meet(A,B),join(meet(join(A,C),join(A,D)),meet(meet(A,B),join(A,meet(meet(A,B),meet(join(A,C),join(A,D))))))) = meet(A,B). [back_rewrite(570),rewrite([821(21)])].
% 111.89/112.27 831 meet(meet(A,B),join(join(join(A,C),meet(A,D)),meet(meet(A,B),join(meet(meet(A,B),join(join(A,C),meet(A,D))),meet(join(meet(A,B),join(join(A,C),meet(A,D))),join(A,meet(meet(A,B),join(join(A,C),meet(A,D))))))))) = meet(A,B). [back_rewrite(391),rewrite([821(33)])].
% 111.89/112.27 846 meet(A,meet(join(B,meet(A,C)),join(meet(A,B),meet(C,join(A,B))))) = meet(A,join(meet(A,B),meet(C,join(A,B)))). [para(821(a,1),29(a,1,2)),rewrite([20(6),7(13),10(13,R),7(12),20(14)]),flip(a)].
% 111.89/112.27 936 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(298(a,1),12(a,1)),rewrite([8(7),23(7)]),flip(a)].
% 111.89/112.27 937 join(A,join(meet(B,join(A,meet(B,C))),meet(B,join(meet(A,B),meet(C,join(A,B)))))) = join(A,meet(B,join(meet(A,B),meet(C,join(A,B))))). [para(14(a,1),298(a,1,2,2,2)),rewrite([7(1),8(2),7(6),8(7),8(15),12(15,R),8(14),12(16,R),8(15),12(15,R),2(14),23(11),7(11),8(12)])].
% 111.89/112.27 938 join(join(A,B),meet(A,C)) = join(A,B). [para(26(a,1),298(a,1,2,2,2)),rewrite([8(6),25(6),23(4),12(4),8(3),6(3),8(2),2(3)]),flip(a)].
% 111.89/112.27 950 join(A,join(zero,meet(join(A,B),join(A,C)))) = join(zero,meet(join(A,B),join(A,C))). [para(516(a,1),298(a,1,2,2,2)),rewrite([8(10),12(11,R),8(10),12(10,R),2(9),12(8,R),8(7),23(7)])].
% 111.89/112.27 957 meet(meet(A,B),join(join(A,C),meet(meet(A,B),join(meet(meet(A,B),join(A,C)),meet(join(A,C),join(A,meet(meet(A,B),join(A,C)))))))) = meet(A,B). [back_rewrite(831),rewrite([938(4),938(7),938(10),12(9),8(8),6(8),8(7),938(11)])].
% 111.89/112.27 962 meet(meet(A,B),join(meet(meet(A,B),join(A,C)),meet(join(A,C),join(A,meet(meet(A,B),join(A,C)))))) = meet(A,B). [back_rewrite(389),rewrite([938(4),938(6),938(12),938(14),827(20),938(6),938(8),938(10)]),flip(a)].
% 111.89/112.27 964 meet(zero,join(join(A,B),meet(zero,join(meet(zero,join(A,B)),meet(join(A,B),join(A,meet(zero,join(A,B)))))))) = zero. [back_rewrite(357),rewrite([938(4),938(7),938(10),12(9),8(8),19(8),8(7),938(11)])].
% 111.89/112.27 965 meet(zero,join(meet(zero,join(A,B)),meet(join(A,B),join(A,meet(zero,join(A,B)))))) = zero. [back_rewrite(326),rewrite([938(4),938(6),938(12),938(14),542(20),938(6),938(8),938(10)]),flip(a)].
% 111.89/112.27 986 meet(meet(A,B),join(A,C)) = meet(A,B). [back_rewrite(957),rewrite([962(14),938(4)])].
% 111.89/112.27 987 meet(zero,join(A,B)) = zero. [back_rewrite(964),rewrite([965(14),8(4),12(4),8(3),19(3),8(2)])].
% 111.89/112.27 1030 meet(A,join(B,meet(A,join(zero,meet(A,B))))) = meet(A,B). [para(987(a,1),14(a,1,2,2,2,2)),rewrite([8(3),38(8),19(8)])].
% 111.89/112.27 1035 meet(A,join(meet(B,join(A,C)),meet(A,join(zero,meet(A,B))))) = meet(A,join(zero,meet(B,join(A,C)))). [para(987(a,1),44(a,1,2,2,2,2)),rewrite([8(5),38(12),8(12)])].
% 111.89/112.27 1036 join(one,meet(A,B)) = one. [para(3(a,1),938(a,1,1)),rewrite([3(5)])].
% 111.89/112.27 1037 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),938(a,1,1)),rewrite([8(4)])].
% 111.89/112.27 1038 join(join(A,join(B,C)),meet(B,D)) = join(A,join(B,C)). [para(12(a,1),938(a,1,1)),rewrite([8(5),12(6,R),8(5)])].
% 111.89/112.27 1060 meet(one,join(A,B)) = join(A,B). [back_rewrite(806),rewrite([1036(3),18(2),1036(7),7(3),1036(6),18(5)])].
% 111.89/112.27 1072 meet(join(A,B),join(A,join(B,C))) = join(A,B). [back_rewrite(711),rewrite([1060(6),12(5,R),8(4),12(4),8(3),19(3),8(2)])].
% 111.89/112.27 1075 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),986(a,1,1)),rewrite([7(4)])].
% 111.89/112.27 1085 meet(A,join(B,meet(A,join(meet(A,B),meet(join(A,B),join(meet(A,B),meet(A,C))))))) = meet(A,join(B,meet(A,C))). [para(986(a,1),32(a,1,2,2,2,2,2,2)),rewrite([20(12)])].
% 111.89/112.27 1102 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(25(a,1),1037(a,1,1)),rewrite([7(4),25(8)])].
% 111.89/112.27 1116 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(22(a,1),1075(a,1,1)),rewrite([8(4),22(8)])].
% 111.89/112.27 1161 join(join(A,B),meet(C,meet(D,join(A,B)))) = join(A,B). [para(936(a,1),1037(a,1,1)),rewrite([7(4),10(4,R),7(3),936(9)])].
% 111.89/112.27 1381 meet(A,join(zero,meet(A,B))) = meet(A,B). [para(20(a,1),1030(a,1,2,2,2,2)),rewrite([69(7),20(6)])].
% 111.89/112.27 1383 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(22(a,1),1030(a,1,2,2,2,2)),rewrite([1381(6),8(4),22(8)])].
% 111.89/112.27 1384 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(41(a,1),1030(a,1,2,2,2,2)),rewrite([2(5),38(4),8(4),41(8)])].
% 111.89/112.27 1411 meet(A,join(zero,meet(B,join(A,C)))) = meet(A,B). [back_rewrite(1035),rewrite([1381(6),8(4),1383(5)]),flip(a)].
% 111.89/112.27 1457 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),1384(a,1,2,2))].
% 111.89/112.27 1463 join(zero,complement(A)) = complement(A). [hyper(56,a,1457,a)].
% 111.89/112.27 1464 meet(one,complement(A)) = complement(A). [para(1463(a,1),1060(a,1,2)),rewrite([1463(6)])].
% 111.89/112.27 1465 join(complement(A),meet(B,complement(A))) = complement(A). [para(1463(a,1),1037(a,1,1)),rewrite([7(3),1463(7)])].
% 111.89/112.27 1506 join(complement(A),meet(B,meet(C,complement(A)))) = complement(A). [para(1465(a,1),1037(a,1,1)),rewrite([7(4),10(4,R),7(3),1465(9)])].
% 111.89/112.27 1825 join(complement(A),meet(B,meet(C,meet(D,complement(A))))) = complement(A). [para(1506(a,1),1037(a,1,1)),rewrite([7(5),10(5,R),7(4),10(4,R),7(3),1506(11)])].
% 111.89/112.27 1859 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(821(a,1),1411(a,1,2,2))].
% 111.89/112.27 1923 meet(meet(A,join(B,C)),join(B,meet(A,B))) = meet(A,B). [para(987(a,1),91(a,1,2,2,2,2)),rewrite([8(7),1859(8),7(6),10(6,R),10(5),7(4),22(5),7(3),20(4),987(10),38(9),19(9),7(8),22(8),7(6)])].
% 111.89/112.27 1952 join(zero,meet(A,B)) = meet(A,B). [para(1859(a,1),1(a,1)),rewrite([7(5),1859(5),1(3)]),flip(a)].
% 111.89/112.27 1953 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(1859(a,1),936(a,1,2)),rewrite([1952(3),10(3),7(2),10(3,R),7(2),1952(7)])].
% 111.89/112.27 1965 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [back_rewrite(950),rewrite([1952(5),1952(9)])].
% 111.89/112.27 2147 join(join(A,meet(B,C)),meet(B,meet(C,D))) = join(A,meet(B,C)). [para(1953(a,1),1038(a,1,1,2)),rewrite([7(4),10(4),7(3),10(4,R),7(3),1953(9)])].
% 111.89/112.27 2314 join(join(A,B),meet(C,join(A,meet(B,D)))) = join(A,B). [para(1102(a,1),8(a,2)),rewrite([8(4),8(5),8(6)])].
% 111.89/112.27 2772 join(join(meet(A,B),meet(B,join(A,C))),meet(A,meet(B,D))) = join(meet(A,B),meet(B,join(A,C))). [para(1383(a,1),1161(a,1,2,2)),rewrite([10(6),7(5),10(6,R),7(5)])].
% 111.89/112.27 2979 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(1923(a,1),6(a,1,2)),rewrite([8(4)])].
% 111.89/112.27 2980 meet(meet(A,join(B,C)),join(C,meet(A,C))) = meet(A,C). [para(8(a,1),1923(a,1,1,2))].
% 111.89/112.27 3521 join(join(A,B),meet(C,join(A,meet(D,join(A,B))))) = join(A,B). [para(23(a,1),2314(a,1,1)),rewrite([7(3),23(8)])].
% 111.89/112.27 3684 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(7(a,1),2979(a,1,1))].
% 111.89/112.27 3688 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(20(a,1),2979(a,1,1)),rewrite([8(3),8(7)])].
% 111.89/112.27 3752 join(meet(A,join(B,C)),meet(B,meet(A,D))) = meet(A,join(B,C)). [back_rewrite(2772),rewrite([3684(4),3684(9)])].
% 111.89/112.27 3863 join(meet(A,B),meet(A,join(C,B))) = meet(A,join(C,B)). [para(2980(a,1),6(a,1,2)),rewrite([8(4)])].
% 111.89/112.27 3865 meet(A,meet(B,join(C,A))) = meet(A,B). [para(7(a,1),2980(a,1,1)),rewrite([7(2),7(3),6(4),7(3),7(4)])].
% 111.89/112.27 3884 meet(A,join(B,A)) = A. [para(1060(a,1),2980(a,1,1)),rewrite([7(3),18(3),2(2),7(2),7(4),18(4)])].
% 111.89/112.27 3885 meet(meet(A,B),join(C,meet(A,join(D,B)))) = meet(A,B). [para(2980(a,1),986(a,2)),rewrite([2980(5),8(4)])].
% 111.89/112.27 3949 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(25(a,1),3884(a,1,2)),rewrite([8(3),7(4)])].
% 111.89/112.27 4081 join(A,meet(B,A)) = A. [para(3(a,1),3684(a,1,2,2)),rewrite([18(3),8(2),3(4),18(4)])].
% 111.89/112.27 4242 meet(join(A,B),join(meet(B,C),meet(join(A,B),join(meet(C,join(A,B)),meet(meet(B,C),join(A,B)))))) = meet(C,join(A,B)). [para(3863(a,1),87(a,2,2)),rewrite([7(2),7(4),7(7),6(8),8(9),10(16,R),1(15)])].
% 111.89/112.27 4309 meet(A,join(B,join(A,C))) = A. [para(1(a,1),3885(a,1,2,2)),rewrite([7(2),3884(2),12(2),8(1),12(2,R),8(1),7(5),3884(5)])].
% 111.89/112.27 4402 meet(A,join(join(B,C),meet(A,B))) = meet(A,join(B,C)). [para(4309(a,1),14(a,1,2,2,2,2)),rewrite([8(4),3521(6)]),flip(a)].
% 111.89/112.27 4411 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(8(a,1),3949(a,1,1))].
% 111.89/112.27 4414 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(23(a,1),3949(a,1,1)),rewrite([7(3),7(7)])].
% 111.89/112.27 4466 meet(A,join(join(B,C),meet(A,C))) = meet(A,join(B,C)). [para(8(a,1),4402(a,1,2,1)),rewrite([8(5)])].
% 111.89/112.27 4564 meet(join(A,B),join(meet(B,C),meet(D,join(A,B)))) = join(meet(B,C),meet(D,join(A,B))). [para(1037(a,1),4411(a,1,1)),rewrite([7(4),7(9)])].
% 111.89/112.27 4752 join(meet(A,B),meet(B,join(C,A))) = meet(B,join(C,A)). [para(4466(a,1),88(a,1,2,2,2,2)),rewrite([7(2),7(4),10(5),7(4),3884(4),7(3),7(5),1037(6),5(7),1037(3),7(2),7(4),7(6),10(7),7(6),3884(6),7(5),7(7),1037(8),5(9),1037(5),7(4),7(6),7(7),10(7),7(6),10(7,R),7(6),1037(8),8(9),4242(12),7(4),7(6),10(7),7(6),3884(6),7(5),7(7),1037(8),5(9),1037(5),7(4),7(6),7(8),10(9),7(8),3884(8),7(7),7(9),1037(10),5(11),1037(7),4564(8)]),flip(a)].
% 111.89/112.27 4822 join(A,meet(B,meet(C,A))) = A. [para(1036(a,1),4752(a,1,2,2)),rewrite([7(2),10(2),7(1),10(2,R),7(1),18(4),8(3),1036(6),18(5)])].
% 111.89/112.27 4823 meet(meet(A,B),join(C,A)) = meet(A,B). [para(986(a,1),4752(a,1,2)),rewrite([8(4),4081(4),8(3)]),flip(a)].
% 111.89/112.27 4825 meet(join(A,B),join(A,join(C,B))) = join(A,B). [para(1072(a,1),4752(a,1,2)),rewrite([8(2),8(4),8(5),4081(5),8(2),12(4),8(3),12(4,R),8(3)]),flip(a)].
% 111.89/112.27 4850 join(A,meet(B,meet(A,C))) = A. [para(4822(a,1),4411(a,1,2)),rewrite([7(2),3884(2),7(1)]),flip(a)].
% 111.89/112.27 4889 meet(join(A,B),join(A,meet(C,B))) = join(A,meet(C,B)). [para(4081(a,1),4825(a,1,2,2)),rewrite([7(4)])].
% 111.89/112.27 5080 meet(join(A,B),join(B,meet(C,A))) = join(B,meet(C,A)). [para(4889(a,1),4752(a,1,2)),rewrite([8(2),1075(3),12(4,R),2(3),8(3)]),flip(a)].
% 111.89/112.27 5111 join(join(A,B),meet(C,A)) = join(A,B). [para(938(a,1),5080(a,1,2)),rewrite([7(4),3884(4),7(3)]),flip(a)].
% 111.89/112.27 5122 join(join(A,join(B,C)),meet(D,B)) = join(A,join(B,C)). [para(1038(a,1),5080(a,1,2)),rewrite([7(6),3884(6),7(5)]),flip(a)].
% 111.89/112.27 5249 join(A,join(join(B,C),meet(D,A))) = join(A,join(B,C)). [para(5122(a,1),8(a,2)),rewrite([12(3,R),8(2),12(4,R),12(6,R),8(5)])].
% 111.89/112.27 5483 join(complement(A),join(join(B,C),complement(A))) = join(B,join(C,complement(A))). [para(1464(a,1),5249(a,1,2,2)),rewrite([12(8),8(7),12(8,R),8(7)])].
% 111.89/112.27 5998 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(6(a,1),5483(a,1,2,1)),rewrite([12(4,R),2(3)]),flip(a)].
% 111.89/112.27 5999 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(5483(a,1),12(a,2)),rewrite([2(4)])].
% 111.89/112.27 6207 join(A,complement(meet(A,B))) = one. [para(3(a,1),5998(a,1,2)),rewrite([47(2)]),flip(a)].
% 111.89/112.27 6835 join(A,join(B,complement(meet(C,join(A,B))))) = one. [para(5999(a,1),6207(a,1)),rewrite([7(2)])].
% 111.89/112.27 6871 join(A,join(complement(meet(B,C)),meet(B,join(C,D)))) = one. [para(1116(a,1),6835(a,1,2,2,1)),rewrite([7(3),8(5)])].
% 111.89/112.27 6908 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(938(a,1),240(a,1,2,2,2,2)),rewrite([10(6,R),7(5),10(5,R),7(4),10(4,R),1(3),10(8,R)]),flip(a)].
% 111.89/112.27 6917 meet(A,meet(meet(B,C),complement(D))) = meet(A,meet(B,meet(C,complement(D)))). [para(1825(a,1),240(a,1,2,2,2,2)),rewrite([10(6,R),7(5),10(5,R),7(4),10(4,R),1(3),10(8,R)]),flip(a)].
% 111.89/112.27 7844 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(986(a,1),299(a,1,2,2,2,2)),rewrite([12(6,R),8(5),12(5,R),8(4),12(4,R),2(3),12(8,R)]),flip(a)].
% 111.89/112.27 8533 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [hyper(17,a,987,a,b,6871,a),rewrite([49(2)]),flip(a)].
% 111.89/112.27 8574 join(complement(meet(A,B)),meet(B,join(A,C))) = one. [para(7(a,1),8533(a,1,1,1))].
% 111.89/112.27 8661 join(A,complement(meet(B,A))) = one. [para(3(a,1),8574(a,1,2,2)),rewrite([18(4),8(3)])].
% 111.89/112.27 8662 join(complement(meet(A,meet(B,C))),meet(meet(A,C),join(B,D))) = one. [para(10(a,1),8574(a,1,1,1)),rewrite([7(4)])].
% 111.89/112.27 8728 join(complement(meet(A,B)),meet(A,join(C,B))) = one. [para(3865(a,1),8661(a,1,2,1)),rewrite([7(3),8(5)])].
% 111.89/112.27 8937 join(complement(meet(A,B)),meet(B,join(C,A))) = one. [para(8728(a,1),5080(a,1,2)),rewrite([7(2),5999(4),6207(3),47(2),1(3),7(2)]),flip(a)].
% 111.89/112.27 8983 join(complement(meet(A,meet(B,C))),meet(C,join(A,D))) = one. [para(938(a,1),8937(a,1,2,2)),rewrite([7(2),10(2),7(1),10(2,R),7(1)])].
% 111.89/112.27 10360 join(complement(meet(A,B)),meet(join(B,C),join(A,D))) = one. [para(5(a,1),8983(a,1,1,1,2))].
% 111.89/112.27 11428 join(complement(meet(A,complement(B))),meet(join(A,C),complement(B))) = one. [para(1825(a,1),10360(a,1,2,2)),rewrite([7(2)])].
% 111.89/112.27 11663 meet(A,join(B,join(complement(A),meet(A,complement(meet(A,B)))))) = A. [para(8533(a,1),588(a,1,2,2,2,2)),rewrite([18(3),8(2),3(2),47(2),18(2)]),flip(a)].
% 111.89/112.27 11691 complement(meet(A,complement(join(A,B)))) = one. [para(4(a,1),11428(a,1,2)),rewrite([8(6),1463(6)])].
% 111.89/112.27 11704 meet(A,complement(join(A,B))) = zero. [hyper(115,a,4,a,b,11691,a(flip)),rewrite([11691(7),7(5),10(5,R),7(4),1464(4),11691(7),42(5)])].
% 111.89/112.27 11713 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(2979(a,1),11704(a,1,2,1))].
% 111.89/112.27 11714 meet(meet(A,B),complement(meet(B,join(A,C)))) = zero. [para(3684(a,1),11704(a,1,2,1))].
% 111.89/112.27 11790 meet(meet(A,B),complement(meet(A,join(C,meet(A,B))))) = zero. [para(20(a,1),11713(a,1,1)),rewrite([8(3)])].
% 111.89/112.27 11798 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(1060(a,1),11713(a,1,1)),rewrite([8(4),12(4),8(3),12(4,R),8(3),1060(5)])].
% 111.89/112.27 11799 meet(complement(A),complement(join(B,complement(A)))) = zero. [para(1464(a,1),11713(a,1,1)),rewrite([8(4),1060(5)])].
% 111.89/112.27 11811 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(1116(a,1),11713(a,1,2,1)),rewrite([7(2),10(2),7(1),10(2,R),7(1),7(5),10(5,R),6917(5)])].
% 111.89/112.27 11863 meet(A,complement(B)) != zero | join(A,complement(B)) != one | complement(complement(B)) = A. [para(11799(a,1),61(a,1,2,2)),rewrite([19(3),7(2),8(6),11799(13),19(10)]),flip(c)].
% 111.89/112.27 11874 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(5(a,1),11714(a,1,1))].
% 111.89/112.27 11938 meet(meet(A,B),complement(join(C,meet(A,B)))) = zero. [para(1952(a,1),11798(a,1,1)),rewrite([8(4),12(5,R),8(4),1952(4)])].
% 111.89/112.27 11959 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(1(a,1),11811(a,1,2,2))].
% 111.89/112.27 12051 meet(meet(A,B),join(meet(join(join(C,complement(meet(A,B))),meet(meet(A,B),join(join(B,D),meet(meet(A,B),join(C,complement(meet(A,B))))))),join(E,meet(A,B))),meet(A,meet(B,F)))) = meet(A,B). [para(1075(a,1),603(a,1,2,2,2,1,2,2,2)),rewrite([8(16),8(23),3(23),47(21),7(21),10(21),7(20),18(20),7(19),8(35),5(40),8(19),5(20),8(17),7(20),10(20),7(19),10(20,R),7(19)]),flip(a)].
% 111.89/112.27 12086 meet(meet(A,B),complement(join(A,C))) = zero. [para(938(a,1),11938(a,1,2,1))].
% 111.89/112.27 12091 meet(meet(A,B),complement(join(B,C))) = zero. [para(5111(a,1),11938(a,1,2,1))].
% 111.89/112.27 12108 meet(join(A,meet(B,C)),complement(join(A,join(C,D)))) = zero. [para(4889(a,1),12086(a,1,1)),rewrite([8(4),12(4),8(3),12(4,R),8(3)])].
% 111.89/112.27 12364 meet(A,complement(join(B,A))) = zero. [para(4889(a,1),11790(a,1,2,1)),rewrite([7(2),3884(2),7(2),3884(2)])].
% 111.89/112.27 12376 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [para(25(a,1),12364(a,1,2,1)),rewrite([8(3),7(5)])].
% 111.89/112.27 12380 meet(complement(join(A,complement(B))),join(meet(A,C),complement(B))) = zero. [para(5998(a,1),12364(a,1,2,1)),rewrite([7(7)])].
% 111.89/112.27 12481 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),12376(a,1,1,1))].
% 111.89/112.27 12508 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [para(6(a,1),12481(a,1,1,1))].
% 111.89/112.27 13078 meet(complement(join(A,B)),join(A,meet(C,B))) = zero. [para(2(a,1),12108(a,1,2,1,2)),rewrite([7(5)])].
% 111.89/112.27 13129 join(A,complement(join(A,B))) != one | complement(complement(join(A,B))) = A. [para(13078(a,1),61(a,1)),rewrite([8(6),7(11),12364(11),19(10)]),flip(c),xx(a)].
% 111.89/112.27 13156 meet(complement(join(A,B)),join(B,meet(C,A))) = zero. [para(13078(a,1),4752(a,1,2)),rewrite([8(2),12091(4),2(3),8(2)]),flip(a)].
% 111.89/112.27 13199 meet(complement(join(A,join(B,C))),join(C,meet(A,D))) = zero. [para(986(a,1),13156(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1)])].
% 111.89/112.27 13214 meet(complement(join(A,join(B,C))),join(C,meet(B,D))) = zero. [para(4823(a,1),13156(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1)])].
% 111.89/112.27 14492 meet(complement(join(A,B)),join(meet(B,C),meet(A,D))) = zero. [para(6(a,1),13199(a,1,1,1,2))].
% 111.89/112.27 14633 meet(complement(join(A,B)),join(meet(A,C),meet(B,D))) = zero. [para(25(a,1),13214(a,1,1,1))].
% 111.89/112.27 16097 meet(meet(A,B),join(meet(C,D),meet(A,meet(B,E)))) = meet(A,meet(B,join(meet(C,D),meet(A,meet(B,E))))). [para(14492(a,1),823(a,1,1,2,2)),rewrite([7(5),10(5),7(4),10(5,R),7(4),8(9),1952(9),20(8),7(9),10(9),7(8),10(9,R),7(8),7(15),10(15),7(14),10(15,R),7(14),8(18),14633(23),8(19),1952(19),20(18),7(20),10(20),7(19),10(20,R),7(19),8(22),12086(24),8(22),1952(22),7(26),10(26),7(25),10(26,R),7(25),7(31),10(31),7(30),10(31,R),7(30),8(34),14633(39),8(35),1952(35),6908(34),10(34,R),7(33),10(33,R),1(32),10(30,R),7(29),10(29,R),7(28),6908(29),10(29,R),7(28),20(28),20(29),8(29),3884(30),4081(17),7(11),6908(11),10(11,R),7(10),10(10,R),1(9),7(11),10(11),7(10),10(11,R),7(10),8(14),14633(19),8(15),1952(15),20(14)]),flip(a)].
% 111.89/112.27 16115 meet(A,meet(B,join(meet(join(join(C,complement(meet(A,B))),meet(meet(A,B),join(join(B,D),meet(meet(A,B),join(C,complement(meet(A,B))))))),join(E,meet(A,B))),meet(A,meet(B,F))))) = meet(A,B). [back_rewrite(12051),rewrite([16097(21)])].
% 111.89/112.27 16164 join(join(A,complement(B)),meet(B,join(C,meet(B,join(A,complement(B)))))) = join(A,join(complement(B),meet(B,join(C,meet(B,join(A,complement(B))))))). [para(825(a,1),1102(a,1,2)),rewrite([8(8),8(14),7844(14),12(14,R),8(13),12(13,R),2(12),8(16)]),flip(a)].
% 111.89/112.27 16200 meet(A,meet(B,join(meet(join(C,join(complement(meet(A,B)),meet(meet(A,B),join(join(B,D),meet(meet(A,B),join(C,complement(meet(A,B)))))))),join(E,meet(A,B))),meet(A,meet(B,F))))) = meet(A,B). [back_rewrite(16115),rewrite([16164(13)])].
% 111.89/112.27 16431 meet(A,meet(B,join(meet(A,B),meet(B,C)))) = meet(A,join(meet(A,B),meet(B,C))). [para(4822(a,1),846(a,1,2,1)),rewrite([7(2),4823(4),7(7),4823(9)])].
% 111.89/112.27 16577 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(12380(a,1),846(a,1,2,2,2)),rewrite([12086(7),19(4),8(7),1952(7),6917(6),10(6,R),7(5),10(5,R),1(4),10(5,R),10(4),7(3),10(4,R),7(3),20(3),20(4),12380(14),8(9),1952(9),20(8)]),flip(a)].
% 111.89/112.27 18300 join(A,join(meet(B,join(A,meet(B,C))),meet(B,join(meet(A,B),meet(B,C))))) = join(A,meet(B,join(meet(A,B),meet(B,C)))). [para(20(a,1),937(a,1,2,1,2,2)),rewrite([4823(7),4823(13)])].
% 111.89/112.27 18319 join(A,join(B,meet(join(B,C),join(A,B)))) = join(A,B). [para(4309(a,1),937(a,1,2,2,2,2)),rewrite([7(3),5(3),8(7),4414(8),12(7),8(6),12(7,R),8(6),3684(6),4309(11),8(9),4414(10),25(9)])].
% 111.89/112.27 18551 join(A,join(complement(B),meet(B,complement(meet(A,B))))) = one. [para(11663(a,1),4081(a,1,2)),rewrite([7(2),8(7),59(7),48(3),7(3)]),flip(a)].
% 111.89/112.27 18601 join(A,join(complement(B),meet(B,complement(meet(B,A))))) = one. [para(18551(a,1),8(a,1)),rewrite([7(3),8(7)]),flip(a)].
% 111.89/112.27 18682 join(complement(A),join(meet(A,B),meet(A,complement(meet(A,B))))) = one. [para(20(a,1),18601(a,1,2,2,2,1)),rewrite([12(7,R),8(6)])].
% 111.89/112.27 18947 complement(complement(A)) = A. [para(2(a,1),13129(a,1,2,1)),rewrite([3(2),2(4)]),xx(a)].
% 111.89/112.27 19010 meet(A,complement(B)) != zero | join(A,complement(B)) != one | B = A. [back_rewrite(11863),rewrite([18947(10)])].
% 111.89/112.27 19061 meet(A,join(B,meet(A,join(meet(B,A),meet(join(B,A),join(meet(B,A),meet(A,C))))))) = meet(A,join(B,meet(A,C))). [para(1085(a,1),7(a,2)),rewrite([7(1),8(2),7(3),7(10)])].
% 111.89/112.27 19102 meet(A,meet(B,meet(join(A,meet(B,C)),join(meet(A,B),meet(B,join(meet(A,B),meet(join(A,B),join(meet(A,B),meet(B,C))))))))) = meet(A,B). [para(1085(a,1),846(a,1,2,2,2)),rewrite([7(1),8(2),7(3),8(10),7(11),8(12),7(13),8(23),3752(23),7(14),6908(15),7(16),8(17),7(18),7(25),8(26),7(27),19061(34),8(28),3752(28),22(19)])].
% 111.89/112.27 19845 join(A,meet(join(B,C),join(B,A))) = join(B,A). [para(18319(a,1),8(a,2)),rewrite([8(2),1965(4),8(4),8(5)])].
% 111.89/112.27 19897 join(A,meet(join(B,C),join(A,C))) = join(A,C). [para(8(a,1),19845(a,1,2,1)),rewrite([8(2),8(5)])].
% 111.89/112.27 20021 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(6(a,1),19897(a,1,2,1))].
% 111.89/112.27 20033 join(A,meet(join(B,C),join(A,meet(C,D)))) = join(A,meet(C,D)). [para(1037(a,1),19897(a,1,2,1))].
% 111.89/112.27 20187 meet(A,meet(B,meet(join(A,meet(B,C)),join(meet(A,B),meet(B,C))))) = meet(A,B). [back_rewrite(19102),rewrite([20033(10),20021(8)])].
% 111.89/112.27 21679 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [hyper(17,a,12508,a,b,18682,a),rewrite([18947(2)]),flip(a)].
% 111.89/112.27 21684 join(meet(A,B),meet(B,complement(meet(A,B)))) = B. [para(7(a,1),21679(a,1,1)),rewrite([7(2)])].
% 111.89/112.27 21725 join(join(A,B),meet(C,meet(B,D))) = join(A,B). [para(21684(a,1),1038(a,2,2)),rewrite([21684(5),7(3),10(3),7(2),10(3,R),7(2)])].
% 111.89/112.27 21882 join(join(A,B),meet(C,meet(A,D))) = join(A,B). [para(21725(a,1),19845(a,1,2,2)),rewrite([8(3),8(4),12(4),8(3),12(4,R),8(3),8(5),7(6),1072(6),12(4),8(3),4850(3),8(1),8(2)]),flip(a)].
% 111.89/112.27 22666 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(18947(a,1),19010(b,1,2)),rewrite([18947(2)])].
% 111.89/112.27 25666 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(8662(a,1),3884(a,1,2)),rewrite([7(5),6908(5),10(5,R),7(4),10(4,R),7(3),1060(3)]),flip(a)].
% 111.89/112.27 25803 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [back_rewrite(16200),rewrite([25666(9),21882(10),1075(5),8(4),3(4),47(2),1060(4),2147(5)])].
% 111.89/112.27 26003 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(5(a,1),25666(a,1,1)),flip(a)].
% 111.89/112.27 26004 meet(A,meet(B,meet(join(A,C),join(D,E)))) = meet(A,meet(B,join(D,E))). [para(22(a,1),25666(a,1,1)),rewrite([25666(3),25666(7)]),flip(a)].
% 111.89/112.27 26192 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [back_rewrite(20187),rewrite([26004(8),16431(5)])].
% 111.89/112.27 26241 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(8(a,1),26192(a,1,2))].
% 111.89/112.27 26308 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(7(a,1),26241(a,1,2,1))].
% 111.89/112.27 26433 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(26308(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 111.89/112.27 26473 meet(A,join(meet(B,A),meet(A,C))) = join(meet(B,A),meet(A,C)). [para(20021(a,1),26433(a,1,2)),rewrite([1(7)]),flip(a)].
% 111.89/112.27 26479 join(A,join(meet(A,B),meet(B,C))) = join(A,meet(B,C)). [back_rewrite(18300),rewrite([26473(7),12(7),8(6),3684(6),3688(5),20021(4),26473(6)]),flip(a)].
% 111.89/112.27 27164 join(A,meet(B,complement(meet(A,B)))) = join(A,B). [para(21684(a,1),26479(a,1,2)),flip(a)].
% 111.89/112.27 27173 join(A,B) != one | meet(B,complement(meet(A,B))) = complement(A). [para(27164(a,1),17(b,1)),rewrite([11959(4)]),flip(c),xx(a)].
% 111.89/112.27 27213 join(A,B) != one | complement(meet(B,complement(meet(A,B)))) = A. [para(27164(a,1),22666(b,1)),rewrite([11959(4)]),xx(a)].
% 111.89/112.27 27521 meet(complement(meet(A,B)),complement(meet(A,complement(meet(A,B))))) = complement(A). [hyper(27173,a,6207,a)].
% 111.89/112.27 27528 join(A,B) != one | meet(A,complement(meet(A,B))) = complement(B). [para(8(a,1),27173(a,1)),rewrite([7(4)])].
% 111.89/112.27 27542 join(A,B) != one | complement(meet(A,complement(meet(A,B)))) = B. [para(8(a,1),27213(a,1)),rewrite([7(4)])].
% 111.89/112.27 27620 meet(A,complement(meet(A,complement(meet(A,B))))) = meet(A,B). [hyper(27528,a,8661,a),rewrite([7(1),7(6),18947(8)])].
% 111.89/112.27 27695 complement(meet(A,complement(meet(A,B)))) = join(complement(A),meet(A,B)). [para(27620(a,1),21684(a,1,1)),rewrite([27620(10),7(8),27521(8),8(3)]),flip(a)].
% 111.89/112.27 27709 join(A,meet(B,join(complement(B),meet(B,C)))) = join(A,meet(B,C)). [para(27620(a,1),20021(a,1,2,2,2)),rewrite([20021(4),27695(6)]),flip(a)].
% 111.89/112.27 27718 meet(A,meet(join(complement(A),meet(A,B)),join(C,meet(A,B)))) = meet(A,join(complement(A),meet(A,B))). [para(27620(a,1),25803(a,1,2,2,2)),rewrite([27695(4),27695(11)])].
% 111.89/112.27 27719 meet(A,join(complement(A),meet(A,B))) = meet(A,B). [para(27620(a,1),25803(a,2)),rewrite([27695(4),27695(7),27709(8),27718(7)])].
% 111.89/112.27 27744 join(A,B) != one | join(complement(A),meet(A,B)) = B. [back_rewrite(27542),rewrite([27695(7)])].
% 111.89/112.27 27745 meet(complement(meet(A,B)),join(complement(A),meet(A,B))) = complement(A). [back_rewrite(27521),rewrite([27695(6)])].
% 111.89/112.27 27751 meet(A,join(complement(A),join(meet(A,B),meet(A,C)))) = meet(A,join(C,meet(A,B))). [back_rewrite(756),rewrite([27719(6),3688(6),27719(6)]),flip(a)].
% 111.89/112.27 27824 join(A,B) != one | join(complement(B),meet(A,B)) = A. [para(8(a,1),27744(a,1)),rewrite([7(5)])].
% 111.89/112.27 28021 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(27745(a,1),6(a,1,2)),rewrite([8(4)])].
% 111.89/112.27 28439 join(A,complement(meet(B,join(A,complement(B))))) = one. [para(28021(a,1),6835(a,1,2))].
% 111.89/112.27 28498 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(22666,a,11874,a,b,28439,a),rewrite([18947(7)])].
% 111.89/112.27 28507 join(A,complement(meet(complement(B),join(A,B)))) = one. [para(18947(a,1),28439(a,1,2,1,2,2))].
% 111.89/112.27 28514 join(meet(complement(A),join(A,B)),meet(B,complement(meet(complement(A),join(A,B))))) = B. [hyper(27824,a,28507,a),rewrite([8(2),18947(5),8(5)])].
% 111.89/112.27 28709 meet(join(A,B),join(B,complement(join(A,B)))) = B. [para(8(a,1),28498(a,1,1)),rewrite([8(2)])].
% 111.89/112.27 28737 complement(meet(complement(A),join(A,B))) = join(A,complement(join(A,B))). [para(28498(a,1),27695(a,1,1,2,1)),rewrite([7(3),28498(11),8(7)])].
% 111.89/112.27 28743 join(meet(complement(A),join(A,B)),meet(B,join(A,complement(join(A,B))))) = B. [back_rewrite(28514),rewrite([28737(7)])].
% 111.89/112.27 29108 meet(A,join(B,complement(join(A,B)))) = meet(A,B). [para(28709(a,1),26003(a,1,2)),flip(a)].
% 111.89/112.27 29514 meet(A,join(B,complement(join(B,A)))) = meet(B,A). [para(29108(a,1),7(a,2)),rewrite([8(1),7(4),7(5)])].
% 111.89/112.27 29559 join(meet(A,B),meet(complement(A),join(A,B))) = B. [back_rewrite(28743),rewrite([29514(7),8(5)])].
% 111.89/112.27 29795 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(29559(a,1),3884(a,1,2)),rewrite([7(4),3865(4)]),flip(a)].
% 111.89/112.27 29797 join(meet(A,B),meet(B,meet(C,complement(A)))) = meet(B,join(A,C)). [para(3865(a,1),29559(a,1,1)),rewrite([8(3),29795(6),7(5),10(5,R),7(4),29795(4),8(6)])].
% 111.89/112.27 29827 join(meet(A,B),meet(A,C)) = meet(A,join(C,meet(A,B))). [para(12508(a,1),29559(a,1,1)),rewrite([18947(3),27751(7),1952(5)]),flip(a)].
% 111.89/112.27 29875 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [para(20021(a,1),29559(a,1,2,2)),rewrite([22(4),29795(5),16577(4),29797(5)]),flip(a)].
% 111.89/112.27 30311 $F # answer(prove_distributivity). [back_rewrite(16),rewrite([29827(7),29875(7),8(4)]),xx(a)].
% 111.89/112.27
% 111.89/112.27 % SZS output end Refutation
% 111.89/112.27 ============================== end of proof ==========================
% 111.89/112.27
% 111.89/112.27 ============================== STATISTICS ============================
% 111.89/112.27
% 111.89/112.27 Given=1015. Generated=1060794. Kept=30306. proofs=1.
% 111.89/112.27 Usable=545. Sos=7845. Demods=7922. Limbo=484, Disabled=21445. Hints=0.
% 111.89/112.27 Megabytes=53.14.
% 111.89/112.27 User_CPU=110.85, System_CPU=0.59, Wall_clock=111.
% 111.89/112.27
% 111.89/112.27 ============================== end of statistics =====================
% 111.89/112.27
% 111.89/112.27 ============================== end of search =========================
% 111.89/112.27
% 111.89/112.27 THEOREM PROVED
% 111.89/112.27 % SZS status Unsatisfiable
% 111.89/112.27
% 111.89/112.27 Exiting with 1 proof.
% 111.89/112.27
% 111.89/112.27 Process 13373 exit (max_proofs) Wed Jun 29 02:55:49 2022
% 111.89/112.27 Prover9 interrupted
%------------------------------------------------------------------------------