TSTP Solution File: LAT204-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT204-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 06:26:06 EDT 2022
% Result : Unsatisfiable 223.65s 224.00s
% Output : Refutation 223.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT204-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 29 03:56:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 19.50/19.79 ============================== Prover9 ===============================
% 19.50/19.79 Prover9 (32) version 2009-11A, November 2009.
% 19.50/19.79 Process 14622 was started by sandbox2 on n007.cluster.edu,
% 19.50/19.79 Wed Jun 29 03:56:23 2022
% 19.50/19.79 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14469_n007.cluster.edu".
% 19.50/19.79 ============================== end of head ===========================
% 19.50/19.79
% 19.50/19.79 ============================== INPUT =================================
% 19.50/19.79
% 19.50/19.79 % Reading from file /tmp/Prover9_14469_n007.cluster.edu
% 19.50/19.79
% 19.50/19.79 set(prolog_style_variables).
% 19.50/19.79 set(auto2).
% 19.50/19.79 % set(auto2) -> set(auto).
% 19.50/19.79 % set(auto) -> set(auto_inference).
% 19.50/19.79 % set(auto) -> set(auto_setup).
% 19.50/19.79 % set(auto_setup) -> set(predicate_elim).
% 19.50/19.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 19.50/19.79 % set(auto) -> set(auto_limits).
% 19.50/19.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 19.50/19.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 19.50/19.79 % set(auto) -> set(auto_denials).
% 19.50/19.79 % set(auto) -> set(auto_process).
% 19.50/19.79 % set(auto2) -> assign(new_constants, 1).
% 19.50/19.79 % set(auto2) -> assign(fold_denial_max, 3).
% 19.50/19.79 % set(auto2) -> assign(max_weight, "200.000").
% 19.50/19.79 % set(auto2) -> assign(max_hours, 1).
% 19.50/19.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 19.50/19.79 % set(auto2) -> assign(max_seconds, 0).
% 19.50/19.79 % set(auto2) -> assign(max_minutes, 5).
% 19.50/19.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 19.50/19.79 % set(auto2) -> set(sort_initial_sos).
% 19.50/19.79 % set(auto2) -> assign(sos_limit, -1).
% 19.50/19.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 19.50/19.79 % set(auto2) -> assign(max_megs, 400).
% 19.50/19.79 % set(auto2) -> assign(stats, some).
% 19.50/19.79 % set(auto2) -> clear(echo_input).
% 19.50/19.79 % set(auto2) -> set(quiet).
% 19.50/19.79 % set(auto2) -> clear(print_initial_clauses).
% 19.50/19.79 % set(auto2) -> clear(print_given).
% 19.50/19.79 assign(lrs_ticks,-1).
% 19.50/19.79 assign(sos_limit,10000).
% 19.50/19.79 assign(order,kbo).
% 19.50/19.79 set(lex_order_vars).
% 19.50/19.79 clear(print_given).
% 19.50/19.79
% 19.50/19.79 % formulas(sos). % not echoed (13 formulas)
% 19.50/19.79
% 19.50/19.79 ============================== end of input ==========================
% 19.50/19.79
% 19.50/19.79 % From the command line: assign(max_seconds, 300).
% 19.50/19.79
% 19.50/19.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 19.50/19.79
% 19.50/19.79 % Formulas that are not ordinary clauses:
% 19.50/19.79
% 19.50/19.79 ============================== end of process non-clausal formulas ===
% 19.50/19.79
% 19.50/19.79 ============================== PROCESS INITIAL CLAUSES ===============
% 19.50/19.79
% 19.50/19.79 ============================== PREDICATE ELIMINATION =================
% 19.50/19.79
% 19.50/19.79 ============================== end predicate elimination =============
% 19.50/19.79
% 19.50/19.79 Auto_denials:
% 19.50/19.79 % copying label prove_distributivity to answer in negative clause
% 19.50/19.79
% 19.50/19.79 Term ordering decisions:
% 19.50/19.79
% 19.50/19.79 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 19.50/19.79 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. join=1. meet=1. complement=0.
% 19.50/19.79
% 19.50/19.79 ============================== end of process initial clauses ========
% 19.50/19.79
% 19.50/19.79 ============================== CLAUSES FOR SEARCH ====================
% 19.50/19.79
% 19.50/19.79 ============================== end of clauses for search =============
% 19.50/19.79
% 19.50/19.79 ============================== SEARCH ================================
% 19.50/19.79
% 19.50/19.79 % Starting search at 0.01 seconds.
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=175.000, iters=3337
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=157.000, iters=3350
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=151.000, iters=3338
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=137.000, iters=3470
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=127.000, iters=3443
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=117.000, iters=3391
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=111.000, iters=3346
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=110.000, iters=3376
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=108.000, iters=3344
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=107.000, iters=3358
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=103.000, iters=3333
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=99.000, iters=3381
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=97.000, iters=3355
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=96.000, iters=3337
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=95.000, iters=3363
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=92.000, iters=3355
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=91.000, iters=3395
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=90.000, iters=3363
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=88.000, iters=3340
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=85.000, iters=3351
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=82.000, iters=3405
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=80.000, iters=3371
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=78.000, iters=3336
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=74.000, iters=3376
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=72.000, iters=3354
% 19.50/19.79
% 19.50/19.79 Low Water (keep): wt=68.000, iters=3335
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=66.000, iters=3355
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=65.000, iters=3386
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=64.000, iters=3393
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=62.000, iters=3383
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=61.000, iters=3353
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=60.000, iters=3373
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=59.000, iters=3343
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=57.000, iters=3353
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=56.000, iters=3415
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=54.000, iters=3362
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=53.000, iters=3351
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=52.000, iters=3423
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=50.000, iters=3445
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=49.000, iters=3383
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=48.000, iters=3341
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=47.000, iters=3440
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=46.000, iters=3376
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=45.000, iters=3395
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=44.000, iters=3361
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=43.000, iters=3344
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=42.000, iters=3373
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=40.000, iters=3348
% 223.65/224.00
% 223.65/224.00 Low Water (displace): id=6588, wt=199.000
% 223.65/224.00
% 223.65/224.00 Low Water (displace): id=6314, wt=197.000
% 223.65/224.00
% 223.65/224.00 Low Water (displace): id=5041, wt=196.000
% 223.65/224.00
% 223.65/224.00 Low Water (displace): id=7580, wt=195.000
% 223.65/224.00
% 223.65/224.00 Low Water (displace): id=14910, wt=26.000
% 223.65/224.00
% 223.65/224.00 Low Water (displace): id=14911, wt=19.000
% 223.65/224.00
% 223.65/224.00 Low Water (displace): id=14916, wt=16.000
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=38.000, iters=3352
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=37.000, iters=3334
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=36.000, iters=3340
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=35.000, iters=3345
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=34.000, iters=3333
% 223.65/224.00
% 223.65/224.00 Low Water (displace): id=16192, wt=15.000
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=33.000, iters=3366
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=32.000, iters=3348
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=31.000, iters=3334
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=30.000, iters=3348
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=29.000, iters=3355
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=28.000, iters=3366
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=27.000, iters=3364
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=26.000, iters=3356
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=25.000, iters=3358
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=24.000, iters=3333
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=23.000, iters=3341
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=22.000, iters=3337
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=21.000, iters=3335
% 223.65/224.00
% 223.65/224.00 Low Water (displace): id=38434, wt=14.000
% 223.65/224.00
% 223.65/224.00 Low Water (keep): wt=20.000, iters=3338
% 223.65/224.00
% 223.65/224.00 ============================== PROOF =================================
% 223.65/224.00 % SZS status Unsatisfiable
% 223.65/224.00 % SZS output start Refutation
% 223.65/224.00
% 223.65/224.00 % Proof 1 at 220.58 (+ 2.35) seconds: prove_distributivity.
% 223.65/224.00 % Length of proof is 246.
% 223.65/224.00 % Level of proof is 60.
% 223.65/224.00 % Maximum clause weight is 51.000.
% 223.65/224.00 % Given clauses 1887.
% 223.65/224.00
% 223.65/224.00 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 223.65/224.00 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 223.65/224.00 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 223.65/224.00 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 223.65/224.00 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 223.65/224.00 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 223.65/224.00 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 223.65/224.00 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 223.65/224.00 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 223.65/224.00 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 223.65/224.00 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 223.65/224.00 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 223.65/224.00 13 meet(A,join(B,C)) = meet(A,join(B,meet(join(A,B),join(C,meet(A,B))))) # label(equation_H58) # label(axiom). [assumption].
% 223.65/224.00 14 meet(A,join(B,meet(join(A,B),join(C,meet(A,B))))) = meet(A,join(B,C)). [copy(13),flip(a)].
% 223.65/224.00 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 223.65/224.00 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 223.65/224.00 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 223.65/224.00 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 223.65/224.00 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 223.65/224.00 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)])].
% 223.65/224.00 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 223.65/224.00 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 223.65/224.00 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)])].
% 223.65/224.00 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 223.65/224.00 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 223.65/224.00 26 meet(A,join(meet(A,B),meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(A,B))). [para(6(a,1),14(a,1,2,2,1)),rewrite([20(3),8(8)])].
% 223.65/224.00 27 meet(A,join(B,meet(join(B,A),join(C,meet(B,A))))) = meet(A,join(B,C)). [para(14(a,1),7(a,2)),rewrite([8(1),7(2),7(6)])].
% 223.65/224.00 28 meet(A,meet(B,join(C,meet(join(A,C),join(D,meet(A,C)))))) = meet(A,meet(B,join(C,D))). [para(14(a,1),10(a,2,2)),rewrite([7(6),10(10,R),7(9)])].
% 223.65/224.00 29 meet(A,join(join(B,meet(join(A,B),join(C,meet(A,B)))),meet(join(A,join(B,meet(join(A,B),join(C,meet(A,B))))),join(D,meet(A,join(B,C)))))) = meet(A,join(B,join(D,meet(join(A,B),join(C,meet(A,B)))))). [para(14(a,1),14(a,1,2,2,2,2)),rewrite([8(23),12(23,R),8(22)])].
% 223.65/224.00 33 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(7(a,1),17(a,1)),rewrite([8(4)])].
% 223.65/224.00 34 meet(A,meet(B,C)) != zero | join(B,meet(A,C)) != one | complement(B) = meet(A,C). [para(10(a,1),17(a,1)),rewrite([7(5),7(10)])].
% 223.65/224.00 35 meet(A,meet(B,C)) != zero | join(C,meet(A,B)) != one | complement(C) = meet(A,B). [para(10(a,2),17(a,1))].
% 223.65/224.00 39 meet(A,join(zero,meet(A,join(B,meet(A,zero))))) = meet(A,B). [para(19(a,1),14(a,1,2,2,1)),rewrite([8(9),19(9)])].
% 223.65/224.00 40 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 223.65/224.00 42 meet(A,join(zero,meet(A,B))) = meet(A,B). [back_rewrite(39),rewrite([40(3),19(3)])].
% 223.65/224.00 43 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([40(5)])].
% 223.65/224.00 44 complement(one) = zero. [hyper(17,a,40,a,b,19,a)].
% 223.65/224.00 45 one != A | complement(A) = zero. [para(40(a,1),17(a,1)),rewrite([19(5)]),flip(b),xx(a)].
% 223.65/224.00 47 meet(A,join(meet(B,join(A,C)),meet(join(A,meet(B,join(A,C))),join(D,meet(A,B))))) = meet(A,join(D,meet(B,join(A,C)))). [para(22(a,1),14(a,1,2,2,2,2)),rewrite([8(13)])].
% 223.65/224.00 49 complement(join(A,one)) = zero. [hyper(45,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 223.65/224.00 51 join(A,one) = one. [para(49(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 223.65/224.00 53 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([51(5)])].
% 223.65/224.00 54 complement(zero) = one. [hyper(17,a,18,a,b,51,a)].
% 223.65/224.00 55 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(43(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),40(6)])].
% 223.65/224.00 56 meet(A,join(meet(B,complement(A)),meet(C,join(A,meet(B,complement(A)))))) = meet(A,join(C,meet(B,complement(A)))). [para(43(a,1),14(a,1,2,2,2,2)),rewrite([19(7),7(6),8(11)])].
% 223.65/224.00 60 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)])].
% 223.65/224.00 61 meet(A,join(join(B,meet(A,C)),meet(join(A,B),join(D,meet(A,join(B,meet(A,C))))))) = meet(A,join(B,join(D,meet(A,C)))). [para(25(a,1),14(a,1,2,2,1)),rewrite([8(13),12(13,R),8(12)])].
% 223.65/224.00 62 meet(A,meet(B,meet(C,meet(D,complement(A))))) = zero. [para(55(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),10(3,R),7(2),40(7)])].
% 223.65/224.00 71 meet(A,join(meet(B,meet(C,meet(D,complement(A)))),meet(E,join(A,meet(B,meet(C,meet(D,complement(A)))))))) = meet(A,join(E,meet(B,meet(C,meet(D,complement(A)))))). [para(62(a,1),14(a,1,2,2,2,2)),rewrite([19(11),7(10),8(17)])].
% 223.65/224.00 79 complement(complement(A)) = A. [hyper(33,a,4,a,b,3,a)].
% 223.65/224.00 84 meet(A,B) != zero | one != A | complement(meet(A,B)) = A. [para(20(a,1),33(a,1)),rewrite([6(5)]),flip(b)].
% 223.65/224.00 92 meet(meet(A,B),join(A,C)) = meet(A,B). [para(6(a,1),27(a,1,2,2,1)),rewrite([20(3),6(5),7(2),20(2)]),flip(a)].
% 223.65/224.00 93 meet(meet(A,B),join(C,meet(join(C,meet(A,B)),join(D,meet(A,meet(B,C)))))) = meet(meet(A,B),join(C,D)). [para(10(a,1),27(a,1,2,2,2,2)),rewrite([7(4),10(5,R),7(4)])].
% 223.65/224.00 97 meet(zero,join(A,B)) = zero. [para(19(a,1),27(a,1,2,2,1)),rewrite([40(3),19(3),6(3),7(2),40(2)]),flip(a)].
% 223.65/224.00 101 meet(join(A,meet(B,C)),join(B,meet(join(A,B),join(D,meet(B,join(A,meet(B,C))))))) = meet(join(A,meet(B,C)),join(B,D)). [para(25(a,1),27(a,1,2,2,1)),rewrite([8(3)])].
% 223.65/224.00 104 meet(join(zero,meet(A,B)),join(A,C)) = meet(A,B). [para(42(a,1),27(a,1,2,2,2,2)),rewrite([25(7),19(5),6(7),7(4),42(4)]),flip(a)].
% 223.65/224.00 110 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),92(a,1,1)),rewrite([7(4)])].
% 223.65/224.00 111 meet(meet(A,meet(B,C)),join(B,D)) = meet(A,meet(B,C)). [para(10(a,1),92(a,1,1)),rewrite([7(5),10(6,R),7(5)])].
% 223.65/224.00 113 meet(A,B) != zero | join(A,C) != one | complement(meet(A,B)) = join(A,C). [para(92(a,1),17(a,1)),rewrite([12(6),8(5),6(5),8(4)])].
% 223.65/224.00 117 meet(A,B) != zero | join(A,C) != one | complement(join(A,C)) = meet(A,B). [para(92(a,1),33(a,1)),rewrite([12(6),8(5),6(5),8(4)])].
% 223.65/224.00 126 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(22(a,1),110(a,1,1)),rewrite([8(4),22(8)])].
% 223.65/224.00 156 join(zero,meet(A,B)) = meet(A,B). [para(104(a,1),42(a,1,2,2)),rewrite([1(7),104(8)])].
% 223.65/224.00 157 meet(A,join(B,meet(A,B))) = meet(A,B). [para(156(a,1),14(a,1,2,2,2)),rewrite([10(3),7(2),5(2),7(1),19(5)])].
% 223.65/224.00 162 meet(A,B) != zero | join(A,B) != one | join(B,meet(A,B)) = complement(A). [para(157(a,1),17(a,1)),rewrite([25(6)]),flip(c)].
% 223.65/224.00 164 meet(A,B) != zero | join(A,B) != one | complement(join(B,meet(A,B))) = A. [para(157(a,1),33(a,1)),rewrite([25(6)])].
% 223.65/224.00 167 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(1(a,1),29(a,1,2,2,2,2)),rewrite([8(3),23(3),7(4),5(4),8(3),1(4),23(3),8(5),23(5),7(6),5(6),8(5),1(6),23(5),2(5),12(5),8(4),12(5,R),8(4),6(7),1(3),8(4),23(4),7(5),5(5),8(4),1(5),12(4),8(3),12(4,R),8(3),23(5)]),flip(a)].
% 223.65/224.00 212 meet(one,join(A,B)) = join(A,B). [para(3(a,1),167(a,1,2,2)),rewrite([51(3),7(3)])].
% 223.65/224.00 234 meet(A,meet(B,join(C,D))) != zero | join(B,meet(A,join(C,meet(join(B,C),join(D,meet(B,C)))))) != one | meet(A,join(C,meet(join(B,C),join(D,meet(B,C))))) = complement(B). [para(14(a,1),34(a,1,2)),flip(c)].
% 223.65/224.00 242 meet(A,meet(B,C)) != zero | join(B,meet(A,join(C,meet(B,C)))) != one | meet(A,join(C,meet(B,C))) = complement(B). [para(157(a,1),34(a,1,2)),flip(c)].
% 223.65/224.00 341 meet(A,B) != zero | one != B | complement(meet(A,B)) = B. [para(7(a,1),84(a,1)),rewrite([7(6)])].
% 223.65/224.00 398 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(60(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)])].
% 223.65/224.00 451 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(5(a,1),126(a,1,1)),rewrite([5(7)])].
% 223.65/224.00 452 meet(meet(A,B),join(C,meet(A,join(B,D)))) = meet(A,B). [para(126(a,1),7(a,2)),rewrite([7(4),7(5),7(6)])].
% 223.65/224.00 570 meet(A,join(one,meet(B,complement(A)))) = A. [para(212(a,1),56(a,1,2,2)),rewrite([12(6,R),2(5),5(4)]),flip(a)].
% 223.65/224.00 590 meet(complement(A),join(one,meet(A,B))) = complement(A). [para(79(a,1),570(a,1,2,2,2)),rewrite([7(3)])].
% 223.65/224.00 622 meet(A,join(B,join(join(A,B),meet(A,C)))) = A. [para(5(a,1),61(a,1,2,2)),rewrite([8(4),12(4,R),12(3),8(2),6(2),8(1),12(2,R),2(1),5(2)]),flip(a)].
% 223.65/224.00 663 meet(complement(A),join(B,complement(A))) = complement(A). [para(590(a,1),26(a,1,2,1)),rewrite([590(8),6(7),1(3),590(7)]),flip(a)].
% 223.65/224.01 668 join(zero,complement(A)) = complement(A). [para(590(a,1),156(a,1,2)),rewrite([590(8)])].
% 223.65/224.01 681 meet(meet(A,complement(B)),join(C,complement(B))) = meet(A,complement(B)). [para(590(a,1),111(a,1,1,2)),rewrite([8(4),590(10)])].
% 223.65/224.01 690 meet(zero,complement(A)) = zero. [para(668(a,1),5(a,1,2))].
% 223.65/224.01 691 meet(one,complement(A)) = complement(A). [para(668(a,1),212(a,1,2)),rewrite([668(6)])].
% 223.65/224.01 761 meet(A,join(one,meet(B,meet(C,meet(D,complement(A)))))) = A. [para(212(a,1),71(a,1,2,2)),rewrite([12(10,R),2(9),5(6)]),flip(a)].
% 223.65/224.01 803 meet(A,join(B,join(join(B,A),meet(A,C)))) = A. [para(622(a,1),7(a,2)),rewrite([8(1),7(5)])].
% 223.65/224.01 808 meet(A,join(join(A,B),meet(A,C))) = A. [para(23(a,1),622(a,1,2,2,1)),rewrite([23(5)])].
% 223.65/224.01 1271 join(one,meet(A,B)) = one. [hyper(341,a,761,a,b,6,a(flip)),rewrite([54(5),18(5),10(5),7(4),18(4),7(3),97(5),54(2),54(5),18(5),10(5),7(4),18(4),7(3)]),flip(a)].
% 223.65/224.01 1396 meet(A,meet(B,meet(join(A,C),join(C,B)))) = meet(A,B). [para(452(a,1),28(a,1,2)),rewrite([7(2),22(3),7(3),7(5),10(5,R)]),flip(a)].
% 223.65/224.01 1631 meet(A,join(join(A,B),meet(C,join(A,B)))) = A. [para(803(a,1),1396(a,1,2,2)),rewrite([12(2,R),2(1),7(3),7(6),5(6),5(2),12(2,R),2(1),7(3)]),flip(a)].
% 223.65/224.01 1716 meet(A,join(join(A,complement(B)),meet(C,complement(B)))) = A. [para(681(a,1),1631(a,1,2,2))].
% 223.65/224.01 1729 meet(A,join(join(A,B),meet(B,C))) = A. [para(79(a,1),1716(a,1,2,1,2)),rewrite([79(3),7(2)])].
% 223.65/224.01 1744 meet(A,join(join(A,join(B,C)),meet(D,join(B,C)))) = A. [para(12(a,1),1729(a,1,2,1)),rewrite([12(2,R),8(1),8(3),7(4)])].
% 223.65/224.01 1764 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(7(a,1),93(a,2)),rewrite([93(9),10(6),7(5),10(6,R),7(5)])].
% 223.65/224.01 1765 meet(A,meet(B,join(C,meet(join(C,meet(A,B)),join(D,meet(A,meet(B,C))))))) = meet(A,meet(B,join(C,D))). [para(8(a,1),93(a,1,2,2,1)),rewrite([8(3),1764(9),1764(12)])].
% 223.65/224.01 1779 meet(A,meet(B,join(complement(A),meet(C,join(complement(A),meet(A,B)))))) = meet(A,meet(B,join(C,complement(A)))). [para(43(a,1),93(a,1,2,2,2,2)),rewrite([19(7),7(6),1764(8),8(11),1764(12)])].
% 223.65/224.01 1827 meet(A,meet(B,join(C,meet(B,join(A,D))))) = meet(A,B). [para(126(a,1),93(a,2)),rewrite([1764(11),1765(11)])].
% 223.65/224.01 1881 meet(A,meet(B,join(C,meet(A,join(B,D))))) = meet(A,B). [para(452(a,1),93(a,2)),rewrite([1764(11),1765(11)])].
% 223.65/224.01 2394 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(51(a,1),101(a,2,2)),rewrite([1271(8),7(5),212(5),12(4,R),2(3),7(4),7(8),212(8)])].
% 223.65/224.01 2586 meet(A,join(join(A,meet(B,C)),meet(B,meet(C,D)))) = A. [para(156(a,1),1744(a,1,2,1,2)),rewrite([156(5),10(4),7(3),10(4,R),7(3)])].
% 223.65/224.01 2628 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(5(a,1),1764(a,1,1)),flip(a)].
% 223.65/224.01 2666 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(668(a,1),1764(a,1,2)),rewrite([668(6)])].
% 223.65/224.01 2671 meet(one,meet(complement(A),join(B,C))) = meet(complement(A),join(B,C)). [para(691(a,1),1764(a,1,1)),flip(a)].
% 223.65/224.01 2912 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(2666(a,1),4(a,1))].
% 223.65/224.01 2913 meet(A,meet(join(A,B),complement(C))) = meet(A,complement(C)). [para(5(a,1),2666(a,1,1)),flip(a)].
% 223.65/224.01 2914 join(meet(A,B),meet(A,meet(B,complement(C)))) = meet(A,B). [para(2666(a,1),6(a,1,2))].
% 223.65/224.01 2919 meet(A,meet(B,meet(join(A,C),complement(D)))) = meet(A,meet(B,complement(D))). [para(22(a,1),2666(a,1,1)),rewrite([2666(3),2666(7)]),flip(a)].
% 223.65/224.01 2926 meet(join(A,B),meet(join(A,join(B,C)),complement(D))) = meet(join(A,B),complement(D)). [para(167(a,1),2666(a,1,1)),flip(a)].
% 223.65/224.01 2996 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(2912(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),40(7)])].
% 223.65/224.01 3023 meet(A,meet(B,meet(C,complement(meet(A,C))))) = zero. [para(2996(a,1),7(a,1)),rewrite([7(2),7(6),10(6,R),7(5),10(5,R),7(4)]),flip(a)].
% 223.65/224.01 3218 meet(A,complement(join(A,B))) = zero. [para(4(a,1),2913(a,1,2)),rewrite([40(2)]),flip(a)].
% 223.65/224.01 3243 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(2913(a,1),3023(a,1,2))].
% 223.65/224.01 3259 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(3218(a,1),2666(a,1)),rewrite([8(3)]),flip(a)].
% 223.65/224.01 3389 meet(A,meet(B,complement(meet(A,join(C,meet(B,join(A,D))))))) = zero. [para(47(a,1),3243(a,1,2,2,1)),rewrite([2666(8),2919(9)])].
% 223.65/224.01 3426 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(167(a,1),3259(a,1,2,2,1,2)),rewrite([12(5),8(4),12(5,R),8(4),2926(8)])].
% 223.65/224.01 3673 meet(join(A,B),meet(complement(C),complement(join(A,join(B,D))))) = zero. [para(3426(a,1),2666(a,1,1)),rewrite([690(3),7(7)]),flip(a)].
% 223.65/224.01 4189 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(79(a,1),2914(a,1,2,2,2))].
% 223.65/224.01 4214 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(167(a,1),4189(a,1,1)),rewrite([7(5),10(6,R),7(5),167(5),167(8)])].
% 223.65/224.01 4374 join(join(A,B),meet(A,C)) = join(A,B). [para(808(a,1),4214(a,1,2)),rewrite([8(4),25(4),23(2)]),flip(a)].
% 223.65/224.01 4375 join(A,join(join(A,B),meet(B,C))) = join(A,B). [para(803(a,1),4214(a,1,2)),rewrite([8(5),60(5),23(2),12(2,R),2(1)]),flip(a)].
% 223.65/224.01 4385 join(join(A,B),meet(B,C)) = join(A,B). [para(1729(a,1),4214(a,1,2)),rewrite([8(4),4375(4)]),flip(a)].
% 223.65/224.01 4505 join(join(A,join(B,C)),meet(B,D)) = join(A,join(B,C)). [para(12(a,1),4374(a,1,1)),rewrite([8(5),12(6,R),8(5)])].
% 223.65/224.01 4511 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(4374(a,1),47(a,1,2,2,2)),rewrite([451(9)]),flip(a)].
% 223.65/224.01 4582 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(25(a,1),4385(a,1,1)),rewrite([7(4),25(8)])].
% 223.65/224.01 4630 meet(A,join(join(A,B),complement(C))) = A. [para(663(a,1),4511(a,1,2,2))].
% 223.65/224.01 4670 join(A,join(join(A,B),complement(C))) = join(join(A,B),complement(C)). [para(4630(a,1),4214(a,1,2)),rewrite([8(4)])].
% 223.65/224.01 6711 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(8(a,1),2394(a,1,1))].
% 223.65/224.01 8442 meet(A,meet(B,join(join(meet(A,B),meet(C,D)),meet(C,meet(D,E))))) = meet(A,B). [para(2586(a,1),1764(a,1)),flip(a)].
% 223.65/224.01 8536 meet(A,join(join(join(A,B),meet(C,D)),meet(C,meet(D,E)))) = A. [para(2586(a,1),2628(a,1,2)),rewrite([5(2)]),flip(a)].
% 223.65/224.01 9318 join(join(A,meet(B,C)),meet(B,meet(C,D))) = join(A,meet(B,C)). [para(4189(a,1),4505(a,1,1,2)),rewrite([7(4),10(4),7(3),10(4,R),7(3),4189(9)])].
% 223.65/224.01 9331 meet(A,join(join(A,B),meet(C,D))) = A. [back_rewrite(8536),rewrite([9318(6)])].
% 223.65/224.01 9333 meet(A,meet(B,join(meet(A,B),meet(C,D)))) = meet(A,B). [back_rewrite(8442),rewrite([9318(6)])].
% 223.65/224.01 9389 join(A,join(join(A,B),meet(C,D))) = join(join(A,B),meet(C,D)). [para(9331(a,1),4214(a,1,2)),rewrite([8(4)])].
% 223.65/224.01 9618 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(6(a,1),4582(a,1,1)),rewrite([6(7)])].
% 223.65/224.01 9655 meet(A,meet(complement(join(B,C)),join(B,meet(C,D)))) = zero. [para(4582(a,1),3259(a,1,2,2,1)),rewrite([8(3),7(5)])].
% 223.65/224.01 9836 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [hyper(162,a,9655,a,b,1271,a),rewrite([9655(12),8(7),156(7),44(7)])].
% 223.65/224.01 9859 join(A,join(join(B,C),complement(join(A,B)))) = one. [hyper(113,a,9836,a,b,53,a),rewrite([9836(5),54(2),79(6),12(5),8(4),12(5,R),8(4),12(6,R)]),flip(a)].
% 223.65/224.01 9860 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),9836(a,1,1,1))].
% 223.65/224.01 9862 meet(complement(join(A,join(B,C))),join(C,meet(D,join(A,B)))) = zero. [para(12(a,2),9836(a,1,1,1)),rewrite([7(5)])].
% 223.65/224.01 9865 meet(complement(join(A,B)),join(A,meet(C,join(A,B)))) = zero. [para(23(a,1),9836(a,1,1,1)),rewrite([7(4)])].
% 223.65/224.01 9873 meet(A,join(meet(B,complement(A)),complement(join(A,B)))) = zero. [para(9836(a,1),56(a,1,2,2)),rewrite([8(4),156(4),43(3),8(6)]),flip(a)].
% 223.65/224.01 9914 join(A,join(B,complement(join(A,B)))) = one. [para(2(a,1),9859(a,1,2,1))].
% 223.65/224.01 9916 join(A,join(join(B,C),complement(join(A,C)))) = one. [para(8(a,1),9859(a,1,2,1))].
% 223.65/224.01 10103 meet(A,complement(join(B,join(C,A)))) = zero. [para(3426(a,1),9860(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1),19(5),7(4)])].
% 223.65/224.01 10135 meet(join(A,meet(B,C)),complement(join(A,join(B,D)))) = zero. [para(25(a,1),10103(a,1,2,1,2)),rewrite([8(3),12(4),8(3),12(4,R),8(3)])].
% 223.65/224.01 10169 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(6(a,1),9916(a,1,2,1))].
% 223.65/224.01 10182 join(A,join(meet(B,C),complement(join(A,meet(B,meet(C,D)))))) = one. [para(4189(a,1),9916(a,1,2,1))].
% 223.65/224.01 10323 join(A,complement(meet(A,B))) = one. [hyper(162,a,4630,a,b,10169,a),rewrite([8(2),19(2),8(3),19(3),156(3),8(6),19(6),8(7),19(7),156(7),97(8),8(5),12(5,R),8(4),668(4),54(5)])].
% 223.65/224.01 10326 join(join(A,B),complement(join(A,meet(B,C)))) = one. [para(10169(a,1),12(a,1)),rewrite([8(6)]),flip(a)].
% 223.65/224.01 10351 join(join(A,B),complement(meet(C,join(A,B)))) = one. [hyper(113,a,3673,a,b,10323,a),rewrite([3673(7),54(2),7(4)]),flip(a)].
% 223.65/224.01 10417 join(join(A,B),complement(join(A,meet(C,join(A,B))))) = one. [para(23(a,1),10326(a,1,1)),rewrite([7(3)])].
% 223.65/224.01 10420 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [para(156(a,1),10326(a,1,1)),rewrite([7(4),10(4),7(3),10(4,R),7(3),156(5)])].
% 223.65/224.01 10467 join(A,join(complement(B),meet(join(B,C),join(B,D)))) = one. [para(451(a,1),10351(a,1,2,1)),rewrite([8(6),12(6,R),8(5)])].
% 223.65/224.01 10476 join(join(A,B),complement(meet(C,meet(D,join(A,B))))) = one. [para(1764(a,1),10351(a,1,2,1))].
% 223.65/224.01 10496 join(complement(A),join(join(A,B),meet(C,D))) = one. [para(9331(a,1),10351(a,1,2,1)),rewrite([8(5)])].
% 223.65/224.01 10959 meet(complement(A),join(meet(A,B),complement(join(B,complement(A))))) = zero. [hyper(117,a,9873,a,b,10496,a),rewrite([10496(5),44(2),79(4),7(3),8(5)]),flip(a)].
% 223.65/224.01 11483 meet(complement(join(A,B)),join(B,meet(C,join(A,B)))) = zero. [para(8(a,1),9865(a,1,1,1)),rewrite([8(3)])].
% 223.65/224.01 11737 meet(complement(join(A,join(B,C))),join(A,meet(B,D))) = zero. [para(10135(a,1),7(a,1)),flip(a)].
% 223.65/224.01 11738 meet(join(A,meet(B,C)),complement(join(A,join(C,D)))) = zero. [para(7(a,1),10135(a,1,1,2))].
% 223.65/224.01 12380 join(join(A,B),complement(join(A,meet(C,meet(D,join(A,B)))))) = one. [para(1764(a,1),10417(a,1,2,1,2))].
% 223.65/224.01 12497 join(complement(A),meet(join(A,B),join(A,C))) = one. [hyper(17,a,9860,a,b,10467,a),rewrite([8(3),12(3),8(2),3(2),51(2),44(2),54(2)]),flip(a)].
% 223.65/224.01 12582 join(A,join(complement(meet(B,C)),meet(B,join(C,D)))) = one. [para(1827(a,1),10476(a,1,2,1)),rewrite([7(4),8(6),12(6,R),8(5)])].
% 223.65/224.01 13338 meet(complement(A),join(meet(A,B),complement(join(complement(A),meet(A,B))))) = zero. [para(20(a,1),10959(a,1,2,1)),rewrite([8(5)])].
% 223.65/224.01 13458 meet(complement(join(A,join(B,C))),join(C,meet(A,D))) = zero. [para(8(a,1),11737(a,1,1,1)),rewrite([8(2),12(2),8(1),12(2,R),8(1)])].
% 223.65/224.01 13496 meet(complement(join(A,B)),join(A,meet(C,B))) = zero. [para(2(a,1),11738(a,1,2,1,2)),rewrite([7(5)])].
% 223.65/224.01 13996 complement(join(A,join(B,complement(meet(C,A))))) = zero. [hyper(164,a,13496,a,b,12582,a),rewrite([12(9),8(8),12(9,R),8(8),9862(16),8(7),12582(7),44(2),12(5),8(4),12(5,R),8(4)]),flip(a)].
% 223.65/224.01 13999 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [hyper(17,a,13496,a,b,12582,a),rewrite([12(4),8(3),12(4,R),8(3),13996(5),54(2)]),flip(a)].
% 223.65/224.01 14000 join(A,complement(meet(B,A))) = one. [hyper(17,a,11483,a,b,12582,a),rewrite([7(1),10323(3),44(2),54(2),7(2),7(4),10323(6),18(5),8(4)]),flip(a)].
% 223.65/224.01 14071 join(complement(meet(A,B)),meet(A,join(C,meet(B,join(A,D))))) = one. [para(1881(a,1),14000(a,1,2,1)),rewrite([7(5),8(7)])].
% 223.65/224.01 14081 join(complement(meet(A,B)),meet(B,join(A,C))) = one. [para(7(a,1),13999(a,1,1,1))].
% 223.65/224.01 14229 join(A,complement(meet(B,meet(C,A)))) = one. [para(10420(a,1),14081(a,1,2,2)),rewrite([7(2),10(2),7(1),10(2,R),7(1),18(5),8(4)])].
% 223.65/224.01 14231 join(meet(A,join(B,C)),complement(meet(A,meet(B,D)))) = one. [para(22(a,1),14229(a,1,2,1,2)),rewrite([7(3),10(4),7(3),10(4,R),7(3)])].
% 223.65/224.01 15275 meet(complement(join(A,B)),join(meet(B,C),meet(A,D))) = zero. [para(6(a,1),13458(a,1,1,1,2))].
% 223.65/224.01 15824 join(complement(meet(A,meet(B,C))),meet(A,join(B,D))) = one. [para(14231(a,1),8(a,1)),flip(a)].
% 223.65/224.01 16442 meet(complement(join(A,complement(B))),join(meet(A,C),complement(B))) = zero. [para(663(a,1),15275(a,1,2,2)),rewrite([8(2)])].
% 223.65/224.01 16887 join(complement(meet(A,meet(B,C))),meet(C,join(A,D))) = one. [para(7(a,1),15824(a,1,1,1)),rewrite([7(2),10(2),7(1),10(2,R),7(1)])].
% 223.65/224.01 17707 join(zero,join(meet(A,B),complement(C))) = join(meet(A,B),complement(C)). [para(16442(a,1),4214(a,1,2)),rewrite([8(5)])].
% 223.65/224.01 17864 join(complement(meet(A,B)),meet(join(A,C),join(A,D))) = one. [para(22(a,1),16887(a,1,1,1))].
% 223.65/224.01 18579 join(meet(join(A,B),join(A,C)),complement(meet(A,D))) = one. [para(17864(a,1),8(a,1)),flip(a)].
% 223.65/224.01 18817 join(meet(join(A,B),join(B,C)),complement(meet(B,D))) = one. [para(8(a,1),18579(a,1,1,1))].
% 223.65/224.01 18859 join(complement(A),meet(join(B,A),join(A,C))) = one. [para(1(a,1),18817(a,1,2,1)),rewrite([8(5)])].
% 223.65/224.01 18900 meet(A,join(B,A)) = A. [para(18859(a,1),242(b,1)),rewrite([7(3),4(3),7(3),97(3),7(9),4(9),19(9),7(8),79(10)]),xx(a),xx(b)].
% 223.65/224.01 18977 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(8(a,1),4670(a,1,2)),rewrite([12(3),8(2),12(3,R),8(2),23(4)]),flip(a)].
% 223.65/224.01 19381 join(A,join(B,complement(join(A,meet(C,meet(D,join(A,B))))))) = one. [back_rewrite(12380),rewrite([18977(7)])].
% 223.65/224.01 19474 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(6(a,1),18977(a,1,1)),flip(a)].
% 223.65/224.01 19954 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [para(6(a,1),6711(a,1,1))].
% 223.65/224.01 20266 join(complement(meet(A,B)),meet(A,join(meet(A,B),meet(C,D)))) = one. [para(9333(a,1),14000(a,1,2,1)),rewrite([7(1),7(5),8(7)])].
% 223.65/224.01 23247 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(1764(a,1),398(a,1,2,2,2,2)),rewrite([12(8,R),8(7),12(7,R),8(6),12(6,R),8(5),4189(5),12(8,R)]),flip(a)].
% 223.65/224.01 23459 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [back_rewrite(9389),rewrite([23247(4),23(4)]),flip(a)].
% 223.65/224.01 23916 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(6(a,1),23459(a,1,1)),flip(a)].
% 223.65/224.01 24657 meet(A,meet(B,complement(meet(A,join(C,meet(A,B)))))) = zero. [para(2(a,1),3389(a,1,2,2,1,2,2,2)),rewrite([7(1)])].
% 223.65/224.01 24690 meet(A,meet(join(meet(B,C),meet(B,D)),complement(meet(A,B)))) = zero. [para(9618(a,1),24657(a,1,2,2,1,2))].
% 223.65/224.01 27613 join(meet(A,B),complement(join(complement(A),meet(A,B)))) = A. [hyper(162,a,13338,a,b,9914,a),rewrite([13338(14),8(8),17707(8),79(8)])].
% 223.65/224.01 27622 join(meet(A,B),complement(join(complement(B),meet(A,B)))) = B. [para(7(a,1),27613(a,1,1)),rewrite([7(3)])].
% 223.65/224.01 27666 join(A,complement(join(complement(A),meet(A,B)))) = A. [para(27613(a,1),19474(a,1,2)),rewrite([2(1)]),flip(a)].
% 223.65/224.01 27717 meet(complement(A),join(meet(A,B),complement(join(complement(A),meet(A,C))))) = zero. [para(27666(a,1),16442(a,1,1,1))].
% 223.65/224.01 27773 meet(A,meet(B,join(complement(B),meet(complement(meet(A,B)),complement(join(complement(B),meet(A,B))))))) = zero. [para(27622(a,1),9873(a,1,2,2,1)),rewrite([7(8),8(10),1764(11)])].
% 223.65/224.01 27788 join(A,complement(join(complement(B),meet(A,B)))) = join(A,B). [para(27622(a,1),19474(a,1,2)),flip(a)].
% 223.65/224.01 31878 join(A,join(meet(B,join(C,D)),complement(join(A,meet(B,C))))) = one. [para(1827(a,1),19381(a,1,2,2,1,2)),rewrite([7(3)])].
% 223.65/224.01 33027 meet(A,join(meet(B,C),meet(B,join(A,D)))) = meet(A,B). [hyper(35,a,24690,a,b,14071,a),rewrite([79(3)]),flip(a)].
% 223.65/224.01 33045 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(2(a,1),33027(a,1,2,2,2)),rewrite([7(2)])].
% 223.65/224.01 33080 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(7(a,1),33045(a,1,2,1))].
% 223.65/224.01 33139 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(5(a,1),33080(a,1,2,1))].
% 223.65/224.01 34554 join(meet(A,B),complement(join(complement(A),meet(A,meet(B,C))))) = A. [hyper(17,a,27717,a,b,10182,a),rewrite([79(2)]),flip(a)].
% 223.65/224.01 34563 join(meet(A,B),complement(join(complement(B),meet(A,meet(B,C))))) = B. [para(7(a,1),34554(a,1,1)),rewrite([10(4,R),7(3)])].
% 223.65/224.01 34580 join(complement(A),complement(join(A,meet(complement(A),join(B,C))))) = complement(A). [para(2671(a,1),34563(a,1,2,1,2)),rewrite([691(3),79(3)])].
% 223.65/224.01 36297 join(meet(A,join(B,C)),complement(join(complement(A),meet(A,B)))) = A. [hyper(17,a,27717,a,b,31878,a),rewrite([79(2)]),flip(a)].
% 223.65/224.01 36323 join(complement(join(complement(A),meet(A,B))),meet(A,join(B,C))) = A. [para(36297(a,1),8(a,1)),flip(a)].
% 223.65/224.01 36770 meet(A,meet(B,join(complement(A),complement(join(B,complement(A)))))) = zero. [para(13496(a,1),1779(a,1,2,2,2)),rewrite([19(3),43(3),8(3),8(6)]),flip(a)].
% 223.65/224.01 36873 meet(A,meet(complement(B),join(B,complement(join(B,A))))) = zero. [hyper(117,a,36770,a,b,36323,a),rewrite([44(2),7(3),18(3),8(2),19(2),212(4),12(3),8(2),3(2),51(2),44(2),44(3),7(4),18(4),8(3),19(3),44(4),7(5),18(5),8(4),19(4),79(4),44(4),7(5),18(5),8(4),19(4),79(4),8(3),10(7,R),7(6)]),flip(a)].
% 223.65/224.01 36919 meet(A,join(complement(A),meet(A,B))) = meet(A,B). [hyper(234,a,36873,a,b,20266,a),rewrite([8(5),3(5),8(4),6(4),7(7),4(7),19(5),691(4),8(3),79(7)])].
% 223.65/224.01 36920 meet(join(A,B),join(B,complement(join(A,B)))) = B. [hyper(234,a,36873,a,b,18859,a),rewrite([8(3),3(3),12(4,R),2(3),7(6),4(6),8(6),668(6),691(5),79(7)])].
% 223.65/224.01 36921 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(234,a,36873,a,b,12497,a),rewrite([8(3),3(3),23(4),7(6),4(6),8(6),668(6),691(5),79(7)])].
% 223.65/224.01 36959 meet(A,meet(B,join(complement(A),meet(A,C)))) = meet(A,meet(C,B)). [para(36919(a,1),10(a,2,2)),rewrite([7(4),10(7),7(6),10(7,R),7(6)])].
% 223.65/224.01 36961 meet(complement(A),join(A,meet(B,complement(A)))) = meet(B,complement(A)). [para(79(a,1),36919(a,1,2,1)),rewrite([7(3),7(7)])].
% 223.65/224.01 37049 meet(A,join(B,complement(join(A,B)))) = meet(A,B). [para(36920(a,1),2628(a,1,2)),flip(a)].
% 223.65/224.01 37062 meet(A,join(complement(A),complement(join(complement(A),meet(B,A))))) = complement(join(complement(A),meet(B,A))). [para(27622(a,1),36920(a,1,2,2,1)),rewrite([27622(6),8(6)])].
% 223.65/224.01 37178 meet(A,join(B,complement(join(B,A)))) = meet(B,A). [para(37049(a,1),7(a,2)),rewrite([8(1),7(4),7(5)])].
% 223.65/224.01 37182 meet(A,B) != zero | join(B,complement(join(A,B))) = complement(A). [para(37049(a,1),17(a,1)),rewrite([9914(7)]),flip(c),xx(b)].
% 223.65/224.01 37195 meet(A,join(B,complement(join(A,join(C,B))))) = meet(A,B). [para(37049(a,1),2628(a,1,2)),rewrite([7(2),22(3),8(3),12(3),8(2),12(3,R),8(2)]),flip(a)].
% 223.65/224.01 37223 meet(A,B) != zero | join(A,complement(join(A,B))) = complement(B). [para(37178(a,1),17(a,1)),rewrite([12(7,R),8(6),9914(7)]),flip(c),xx(b)].
% 223.65/224.01 37368 meet(A,join(B,complement(join(B,join(A,C))))) = meet(B,A). [para(37195(a,1),7(a,2)),rewrite([8(1),12(2,R),8(1),7(5),7(6)])].
% 223.65/224.01 37468 meet(join(A,B),join(A,complement(join(A,join(B,C))))) = A. [para(5(a,1),37368(a,2)),rewrite([8(3),12(3),8(2),12(3,R),8(2),23(4)])].
% 223.65/224.01 37530 meet(join(A,meet(B,C)),join(A,complement(join(A,B)))) = A. [para(27613(a,1),37468(a,1,2,2,1,2))].
% 223.65/224.01 37586 join(complement(A),complement(join(complement(A),meet(A,B)))) = complement(meet(A,B)). [hyper(37182,a,37530,a),rewrite([8(3),19(3),668(3),156(4),8(5),19(5),668(5),8(4),156(9)])].
% 223.65/224.01 37621 complement(join(complement(A),meet(A,B))) = meet(A,complement(meet(A,B))). [para(36323(a,1),37530(a,1,1)),rewrite([8(9),27666(9),8(6),37586(6)]),flip(a)].
% 223.65/224.01 37686 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [back_rewrite(27613),rewrite([37621(5)])].
% 223.65/224.01 37691 join(meet(A,B),meet(B,complement(meet(A,B)))) = B. [para(7(a,1),37686(a,1,1)),rewrite([7(2)])].
% 223.65/224.01 37710 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(36920(a,1),37686(a,1,1)),rewrite([8(1),8(2),8(3),36921(6),7(3),8(5)])].
% 223.65/224.01 37721 join(A,meet(B,complement(meet(A,B)))) = join(A,B). [para(37691(a,1),23916(a,1,2)),flip(a)].
% 223.65/224.01 37764 join(complement(A),complement(join(A,B))) = complement(A). [para(37710(a,1),34580(a,1,2,1))].
% 223.65/224.01 37791 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(37764(a,1),18900(a,1,2)),rewrite([7(4)])].
% 223.65/224.01 38313 join(A,meet(B,meet(join(A,C),complement(meet(A,B))))) = join(A,meet(B,join(A,C))). [para(22(a,1),37721(a,1,2,2,1)),rewrite([7(5),10(5,R)])].
% 223.65/224.01 38481 meet(complement(A),complement(meet(B,A))) = complement(A). [para(27622(a,1),37791(a,1,2,1)),rewrite([7(4),27622(10)])].
% 223.65/224.01 38609 meet(complement(A),complement(join(B,A))) = complement(join(B,A)). [para(18900(a,1),38481(a,1,2,1)),rewrite([7(4)])].
% 223.65/224.01 38702 meet(A,complement(join(complement(B),meet(A,B)))) = zero. [back_rewrite(27773),rewrite([38609(8),37062(7)])].
% 223.65/224.01 39031 join(complement(A),meet(B,A)) = join(B,complement(join(B,A))). [hyper(37223,a,38702,a),rewrite([27788(5),79(8)]),flip(a)].
% 223.65/224.01 41195 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(39031(a,1),23(a,1,2)),rewrite([8(2),12(5,R),8(4),37764(4),7(4)]),flip(a)].
% 223.65/224.01 41196 join(A,complement(join(B,A))) = join(A,complement(B)). [para(39031(a,1),23(a,2)),rewrite([7(3),41195(4),12(4,R),2(3),8(3)]),flip(a)].
% 223.65/224.01 41197 join(A,complement(join(A,B))) = join(A,complement(B)). [para(39031(a,2),23(a,1,2)),rewrite([25(4)]),flip(a)].
% 223.65/224.01 41200 join(A,meet(B,complement(A))) = join(A,B). [para(79(a,1),39031(a,1,1)),rewrite([41197(7),79(5),8(4)])].
% 223.65/224.01 41218 join(A,meet(B,meet(C,complement(A)))) = join(A,meet(B,C)). [para(2666(a,1),39031(a,1,2)),rewrite([79(2),41197(10),79(7),8(6)])].
% 223.65/224.01 41584 complement(meet(A,B)) = join(complement(A),complement(B)). [para(39031(a,1),39031(a,2,2,1)),rewrite([10(5),7(4),43(5),8(4),668(4),41197(6),41196(7),8(5)])].
% 223.65/224.01 41607 meet(A,meet(B,join(C,complement(A)))) = meet(A,meet(B,C)). [back_rewrite(36959),rewrite([41195(3),7(5)])].
% 223.65/224.01 41775 meet(complement(A),join(A,B)) = meet(B,complement(A)). [back_rewrite(36961),rewrite([41200(4)])].
% 223.65/224.01 42144 join(A,meet(B,join(A,C))) = join(A,meet(B,C)). [back_rewrite(38313),rewrite([41584(3),41607(6),7(3),41775(3),41218(4)]),flip(a)].
% 223.65/224.01 45810 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(33139),rewrite([42144(3)])].
% 223.65/224.01 45957 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(19954),rewrite([45810(4),8(2),45810(3),8(1)]),flip(a)].
% 223.65/224.01 45958 $F # answer(prove_distributivity). [resolve(45957,a,16,a)].
% 223.65/224.01
% 223.65/224.01 % SZS output end Refutation
% 223.65/224.01 ============================== end of proof ==========================
% 223.65/224.01
% 223.65/224.01 ============================== STATISTICS ============================
% 223.65/224.01
% 223.65/224.01 Given=1887. Generated=4082248. Kept=45953. proofs=1.
% 223.65/224.01 Usable=307. Sos=4349. Demods=4102. Limbo=147, Disabled=41162. Hints=0.
% 223.65/224.01 Megabytes=49.08.
% 223.65/224.01 User_CPU=220.58, System_CPU=2.35, Wall_clock=223.
% 223.65/224.01
% 223.65/224.01 ============================== end of statistics =====================
% 223.65/224.01
% 223.65/224.01 ============================== end of search =========================
% 223.65/224.01
% 223.65/224.01 THEOREM PROVED
% 223.65/224.01 % SZS status Unsatisfiable
% 223.65/224.01
% 223.65/224.01 Exiting with 1 proof.
% 223.65/224.01
% 223.65/224.01 Process 14622 exit (max_proofs) Wed Jun 29 04:00:06 2022
% 223.65/224.01 Prover9 interrupted
%------------------------------------------------------------------------------