TSTP Solution File: LAT065-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT065-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 06:25:23 EDT 2022
% Result : Unsatisfiable 132.56s 132.85s
% Output : Refutation 132.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT065-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Wed Jun 29 16:14:03 EDT 2022
% 0.12/0.32 % CPUTime :
% 11.93/12.27 ============================== Prover9 ===============================
% 11.93/12.27 Prover9 (32) version 2009-11A, November 2009.
% 11.93/12.27 Process 1466 was started by sandbox on n012.cluster.edu,
% 11.93/12.27 Wed Jun 29 16:14:03 2022
% 11.93/12.27 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1310_n012.cluster.edu".
% 11.93/12.27 ============================== end of head ===========================
% 11.93/12.27
% 11.93/12.27 ============================== INPUT =================================
% 11.93/12.27
% 11.93/12.27 % Reading from file /tmp/Prover9_1310_n012.cluster.edu
% 11.93/12.27
% 11.93/12.27 set(prolog_style_variables).
% 11.93/12.27 set(auto2).
% 11.93/12.27 % set(auto2) -> set(auto).
% 11.93/12.27 % set(auto) -> set(auto_inference).
% 11.93/12.27 % set(auto) -> set(auto_setup).
% 11.93/12.27 % set(auto_setup) -> set(predicate_elim).
% 11.93/12.27 % set(auto_setup) -> assign(eq_defs, unfold).
% 11.93/12.27 % set(auto) -> set(auto_limits).
% 11.93/12.27 % set(auto_limits) -> assign(max_weight, "100.000").
% 11.93/12.27 % set(auto_limits) -> assign(sos_limit, 20000).
% 11.93/12.27 % set(auto) -> set(auto_denials).
% 11.93/12.27 % set(auto) -> set(auto_process).
% 11.93/12.27 % set(auto2) -> assign(new_constants, 1).
% 11.93/12.27 % set(auto2) -> assign(fold_denial_max, 3).
% 11.93/12.27 % set(auto2) -> assign(max_weight, "200.000").
% 11.93/12.27 % set(auto2) -> assign(max_hours, 1).
% 11.93/12.27 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 11.93/12.27 % set(auto2) -> assign(max_seconds, 0).
% 11.93/12.27 % set(auto2) -> assign(max_minutes, 5).
% 11.93/12.27 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 11.93/12.27 % set(auto2) -> set(sort_initial_sos).
% 11.93/12.27 % set(auto2) -> assign(sos_limit, -1).
% 11.93/12.27 % set(auto2) -> assign(lrs_ticks, 3000).
% 11.93/12.27 % set(auto2) -> assign(max_megs, 400).
% 11.93/12.27 % set(auto2) -> assign(stats, some).
% 11.93/12.27 % set(auto2) -> clear(echo_input).
% 11.93/12.27 % set(auto2) -> set(quiet).
% 11.93/12.27 % set(auto2) -> clear(print_initial_clauses).
% 11.93/12.27 % set(auto2) -> clear(print_given).
% 11.93/12.27 assign(lrs_ticks,-1).
% 11.93/12.27 assign(sos_limit,10000).
% 11.93/12.27 assign(order,kbo).
% 11.93/12.27 set(lex_order_vars).
% 11.93/12.27 clear(print_given).
% 11.93/12.27
% 11.93/12.27 % formulas(sos). % not echoed (13 formulas)
% 11.93/12.27
% 11.93/12.27 ============================== end of input ==========================
% 11.93/12.27
% 11.93/12.27 % From the command line: assign(max_seconds, 300).
% 11.93/12.27
% 11.93/12.27 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 11.93/12.27
% 11.93/12.27 % Formulas that are not ordinary clauses:
% 11.93/12.27
% 11.93/12.27 ============================== end of process non-clausal formulas ===
% 11.93/12.27
% 11.93/12.27 ============================== PROCESS INITIAL CLAUSES ===============
% 11.93/12.27
% 11.93/12.27 ============================== PREDICATE ELIMINATION =================
% 11.93/12.27
% 11.93/12.27 ============================== end predicate elimination =============
% 11.93/12.27
% 11.93/12.27 Auto_denials:
% 11.93/12.27 % copying label prove_distributivity to answer in negative clause
% 11.93/12.27
% 11.93/12.27 Term ordering decisions:
% 11.93/12.27
% 11.93/12.27 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 11.93/12.27 Function symbol KB weights: n0=1. n1=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 11.93/12.27
% 11.93/12.27 ============================== end of process initial clauses ========
% 11.93/12.27
% 11.93/12.27 ============================== CLAUSES FOR SEARCH ====================
% 11.93/12.27
% 11.93/12.27 ============================== end of clauses for search =============
% 11.93/12.27
% 11.93/12.27 ============================== SEARCH ================================
% 11.93/12.27
% 11.93/12.27 % Starting search at 0.01 seconds.
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=127.000, iters=3417
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=111.000, iters=3345
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=109.000, iters=3382
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=103.000, iters=3355
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=87.000, iters=3333
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=81.000, iters=3381
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=79.000, iters=3407
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=75.000, iters=3346
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=74.000, iters=3395
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=72.000, iters=3408
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=71.000, iters=3396
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=69.000, iters=3373
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=68.000, iters=3351
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=65.000, iters=3336
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=64.000, iters=3347
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=63.000, iters=3376
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=62.000, iters=3445
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=59.000, iters=3355
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=58.000, iters=3358
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=57.000, iters=3360
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=53.000, iters=3348
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=50.000, iters=3346
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=49.000, iters=3350
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=48.000, iters=3342
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=47.000, iters=3420
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=46.000, iters=3405
% 11.93/12.27
% 11.93/12.27 Low Water (keep): wt=45.000, iters=3356
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=44.000, iters=3361
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=43.000, iters=3356
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=42.000, iters=3336
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=41.000, iters=3371
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=40.000, iters=3341
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=39.000, iters=3340
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=38.000, iters=3343
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=37.000, iters=3360
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=36.000, iters=3339
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=35.000, iters=3420
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=34.000, iters=3348
% 132.56/132.85
% 132.56/132.85 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 32.63 sec).
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=32.000, iters=3340
% 132.56/132.85
% 132.56/132.85 Low Water (displace): id=6641, wt=199.000
% 132.56/132.85
% 132.56/132.85 Low Water (displace): id=7331, wt=195.000
% 132.56/132.85
% 132.56/132.85 Low Water (displace): id=7193, wt=191.000
% 132.56/132.85
% 132.56/132.85 Low Water (displace): id=14567, wt=27.000
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=31.000, iters=3346
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=30.000, iters=3349
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=29.000, iters=3336
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=28.000, iters=3338
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=27.000, iters=3384
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=26.000, iters=3365
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=25.000, iters=3356
% 132.56/132.85
% 132.56/132.85 Low Water (displace): id=18888, wt=20.000
% 132.56/132.85
% 132.56/132.85 Low Water (displace): id=18889, wt=19.000
% 132.56/132.85
% 132.56/132.85 Low Water (displace): id=18894, wt=18.000
% 132.56/132.85
% 132.56/132.85 Low Water (displace): id=18949, wt=17.000
% 132.56/132.85
% 132.56/132.85 Low Water (displace): id=19383, wt=16.000
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=24.000, iters=3348
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=23.000, iters=3341
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=22.000, iters=3336
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=21.000, iters=3335
% 132.56/132.85
% 132.56/132.85 Low Water (keep): wt=20.000, iters=5247
% 132.56/132.85
% 132.56/132.85 ============================== PROOF =================================
% 132.56/132.85 % SZS status Unsatisfiable
% 132.56/132.85 % SZS output start Refutation
% 132.56/132.85
% 132.56/132.85 % Proof 1 at 130.60 (+ 1.39) seconds: prove_distributivity.
% 132.56/132.85 % Length of proof is 250.
% 132.56/132.85 % Level of proof is 63.
% 132.56/132.85 % Maximum clause weight is 65.000.
% 132.56/132.85 % Given clauses 1616.
% 132.56/132.85
% 132.56/132.85 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 132.56/132.85 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 132.56/132.85 3 join(A,complement(A)) = n1 # label(top) # label(axiom). [assumption].
% 132.56/132.85 4 meet(A,complement(A)) = n0 # label(bottom) # label(axiom). [assumption].
% 132.56/132.85 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 132.56/132.85 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 132.56/132.85 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 132.56/132.85 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 132.56/132.85 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 132.56/132.85 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 132.56/132.85 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 132.56/132.85 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 132.56/132.85 13 meet(A,join(meet(B,join(C,meet(A,B))),meet(C,join(A,B)))) = join(meet(A,B),meet(A,C)) # label(c94_37) # label(axiom). [assumption].
% 132.56/132.85 14 meet(A,join(meet(B,join(A,C)),meet(C,join(B,meet(A,C))))) = join(meet(A,C),meet(A,B)). [copy(13),rewrite([8(6)])].
% 132.56/132.85 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 132.56/132.85 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 132.56/132.85 17 join(A,B) != n1 | meet(A,B) != n0 | complement(A) = B # label(complements_are_unique) # label(axiom). [assumption].
% 132.56/132.85 18 meet(A,n1) = A. [para(3(a,1),5(a,1,2))].
% 132.56/132.85 19 join(A,n0) = A. [para(4(a,1),6(a,1,2))].
% 132.56/132.85 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)])].
% 132.56/132.85 21 meet(A,meet(B,complement(A))) = meet(B,n0). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 132.56/132.85 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 132.56/132.85 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)])].
% 132.56/132.85 24 join(A,join(B,complement(A))) = join(B,n1). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 132.56/132.85 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 132.56/132.85 27 join(n0,meet(A,B)) = meet(A,B). [para(3(a,1),14(a,1,2,1,2)),rewrite([18(2),4(3),19(3),7(2),6(3),4(3)]),flip(a)].
% 132.56/132.85 28 meet(A,join(meet(B,join(A,C)),meet(join(A,C),join(A,B)))) = A. [para(5(a,1),14(a,1,2,2,2,2)),rewrite([23(2),8(4),5(9),6(9)])].
% 132.56/132.85 29 meet(A,join(meet(A,B),meet(meet(A,C),join(B,meet(A,C))))) = join(meet(A,C),meet(A,B)). [para(6(a,1),14(a,1,2,1,2)),rewrite([7(1),20(4),20(9)])].
% 132.56/132.85 30 meet(A,meet(B,join(meet(C,join(A,D)),meet(D,join(C,meet(A,D)))))) = meet(B,join(meet(A,D),meet(A,C))). [para(14(a,1),10(a,2,2)),rewrite([7(7)])].
% 132.56/132.85 31 meet(meet(A,join(B,C)),join(join(meet(B,C),meet(A,B)),meet(meet(C,join(A,meet(B,C))),join(B,meet(C,meet(meet(A,join(B,C)),join(A,meet(B,C)))))))) = join(meet(A,B),meet(C,meet(meet(A,join(B,C)),join(A,meet(B,C))))). [para(14(a,1),14(a,1,2,1)),rewrite([7(4),10(14,R),7(13),10(24,R),7(23),7(27),22(27),7(25),8(26)])].
% 132.56/132.85 32 meet(A,join(meet(B,join(A,join(meet(C,join(A,D)),meet(D,join(C,meet(A,D)))))),meet(join(meet(C,join(A,D)),meet(D,join(C,meet(A,D)))),join(B,join(meet(A,D),meet(A,C)))))) = join(join(meet(A,D),meet(A,C)),meet(A,B)). [para(14(a,1),14(a,1,2,2,2,2)),rewrite([14(28)])].
% 132.56/132.85 35 join(A,B) != n1 | meet(A,B) != n0 | complement(B) = A. [para(8(a,1),17(a,1)),rewrite([7(4)])].
% 132.56/132.85 36 join(A,join(B,C)) != n1 | meet(B,join(A,C)) != n0 | complement(B) = join(A,C). [para(12(a,1),17(a,1)),rewrite([8(5),8(10)])].
% 132.56/132.85 38 meet(A,join(meet(B,join(A,n1)),meet(n1,join(A,B)))) = A. [para(18(a,1),14(a,1,2,2,2,2)),rewrite([8(5),18(10),6(10)])].
% 132.56/132.85 40 n1 != A | meet(A,n0) != n0 | complement(A) = n0. [para(19(a,1),17(a,1)),flip(a)].
% 132.56/132.85 41 meet(A,n0) = n0. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 132.56/132.85 42 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [para(14(a,1),20(a,1,2)),rewrite([14(11)])].
% 132.56/132.85 43 n1 != A | complement(A) = n0. [back_rewrite(40),rewrite([41(4)]),xx(b)].
% 132.56/132.85 44 meet(A,meet(B,complement(A))) = n0. [back_rewrite(21),rewrite([41(5)])].
% 132.56/132.85 45 complement(n1) = n0. [hyper(17,a,19,a,b,41,a)].
% 132.56/132.85 47 join(n0,n1) = n1. [para(45(a,1),3(a,1,2)),rewrite([8(3)])].
% 132.56/132.85 48 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)])].
% 132.56/132.85 49 meet(A,join(meet(B,join(A,meet(C,join(A,D)))),meet(meet(C,join(A,D)),join(B,meet(A,C))))) = join(meet(A,C),meet(A,B)). [para(22(a,1),14(a,1,2,2,2,2)),rewrite([22(14)])].
% 132.56/132.85 50 meet(meet(A,join(B,C)),join(meet(B,C),meet(A,B))) = meet(A,B). [para(14(a,1),22(a,1,2)),rewrite([7(4),7(9),22(9),7(7)])].
% 132.56/132.85 51 complement(n0) = n1. [hyper(17,a,47,a,b,18,a)].
% 132.56/132.85 52 complement(join(A,n1)) = n0. [hyper(43,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 132.56/132.85 54 join(A,n1) = n1. [para(52(a,1),3(a,1,2)),rewrite([8(4),12(4,R),8(3),47(3)])].
% 132.56/132.85 55 meet(A,join(B,meet(n1,join(A,B)))) = A. [back_rewrite(38),rewrite([54(2),18(2)])].
% 132.56/132.85 56 join(A,join(B,complement(A))) = n1. [back_rewrite(24),rewrite([54(5)])].
% 132.56/132.85 62 meet(A,join(B,meet(join(C,complement(A)),join(B,meet(A,join(C,complement(A))))))) = join(meet(A,join(C,complement(A))),meet(A,B)). [para(56(a,1),14(a,1,2,1,2)),rewrite([18(2)])].
% 132.56/132.85 64 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)])].
% 132.56/132.85 66 join(A,B) != n1 | meet(A,join(B,meet(A,C))) != n0 | join(B,meet(A,C)) = complement(A). [para(25(a,1),17(a,1)),flip(c)].
% 132.56/132.85 80 meet(A,join(B,meet(n1,join(B,A)))) = A. [para(55(a,1),7(a,2)),rewrite([8(2),7(5)])].
% 132.56/132.85 83 meet(A,join(join(A,B),meet(n1,join(A,B)))) = A. [para(23(a,1),55(a,1,2,2,2))].
% 132.56/132.85 85 meet(join(A,B),join(C,meet(n1,join(A,join(B,C))))) = join(A,B). [para(12(a,1),80(a,1,2,2,2)),rewrite([8(3),12(4,R),8(3)])].
% 132.56/132.85 87 meet(n1,join(A,complement(B))) = join(A,complement(B)). [para(56(a,1),80(a,1,2,2,2)),rewrite([1(5),54(4),7(4)])].
% 132.56/132.85 88 meet(join(A,meet(B,C)),join(B,meet(n1,join(A,B)))) = join(A,meet(B,C)). [para(25(a,1),80(a,1,2,2,2)),rewrite([8(4)])].
% 132.56/132.85 90 meet(n1,complement(A)) = complement(A). [para(2(a,1),87(a,1,2)),rewrite([2(6)])].
% 132.56/132.85 95 meet(complement(A),join(B,complement(A))) = complement(A). [para(87(a,1),80(a,1,2,2)),rewrite([23(4)])].
% 132.56/132.85 125 join(complement(A),meet(B,complement(A))) = complement(A). [para(95(a,1),29(a,1,2,1)),rewrite([7(4),7(8),5(12),7(3),95(7),8(5)]),flip(a)].
% 132.56/132.85 139 meet(join(meet(A,B),meet(A,C)),join(meet(C,join(A,B)),meet(B,join(C,meet(A,B))))) = join(meet(A,B),meet(A,C)). [para(1(a,1),30(a,1,2)),rewrite([14(7),7(13)]),flip(a)].
% 132.56/132.85 140 meet(meet(A,join(B,C)),join(meet(B,C),meet(B,A))) = meet(B,A). [para(5(a,1),30(a,1,2)),rewrite([22(3)]),flip(a)].
% 132.56/132.85 141 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(30(a,1),6(a,1,2))].
% 132.56/132.85 142 meet(A,meet(B,meet(C,join(meet(D,join(A,E)),meet(E,join(D,meet(A,E))))))) = meet(B,meet(C,join(meet(A,E),meet(A,D)))). [para(30(a,1),10(a,2,2)),rewrite([7(8),10(8,R),7(7),10(14,R),7(13)])].
% 132.56/132.85 145 meet(A,meet(B,join(meet(A,C),meet(A,D)))) = meet(B,join(meet(A,C),meet(A,D))). [para(30(a,1),20(a,1,2)),rewrite([30(13)])].
% 132.56/132.85 169 complement(join(n1,meet(A,join(B,C)))) = n0. [hyper(43,a,141,a(flip)),rewrite([7(3),18(3),7(3),18(3)])].
% 132.56/132.85 183 complement(join(n1,meet(A,B))) = n0. [para(2(a,1),169(a,1,1,2,2))].
% 132.56/132.85 189 meet(n0,join(n1,meet(A,B))) = n0. [para(183(a,1),4(a,1,2)),rewrite([7(5)])].
% 132.56/132.85 190 join(A,join(n1,meet(B,C))) = n1. [para(183(a,1),56(a,1,2,2)),rewrite([19(5),8(4)])].
% 132.56/132.85 191 join(meet(A,B),meet(B,meet(meet(A,B),join(A,B)))) = meet(meet(A,B),join(B,meet(A,B))). [para(1(a,1),31(a,1,2,1,1)),rewrite([2(1),1(4),2(6),1(7),6(10),7(6),20(6),8(6),12(6),8(5),6(5),8(3),2(6),1(7)]),flip(a)].
% 132.56/132.85 192 meet(meet(A,B),join(B,meet(A,B))) = meet(meet(A,B),join(A,B)). [para(2(a,1),31(a,1,2,2,1,2)),rewrite([7(6),20(6),2(6),10(6,R),1(5),2(11),7(10),20(10),6(12),7(5),20(5),7(5),20(5),2(10),7(9),20(9),191(9)]),flip(a)].
% 132.56/132.85 248 meet(meet(A,join(B,complement(C))),join(complement(C),meet(meet(join(B,complement(C)),join(A,complement(C))),join(complement(C),meet(A,join(B,complement(C))))))) = join(meet(A,complement(C)),meet(A,join(B,complement(C)))). [para(95(a,1),31(a,1,2,1,1)),rewrite([12(4,R),2(3),125(7),95(10),12(16,R),2(15),95(19),7(18),10(18,R),22(18),10(16,R),1(15),12(25,R),2(24),95(28),7(27),10(27,R),22(27),10(25,R),1(24)])].
% 132.56/132.85 268 join(n1,meet(A,B)) = n1. [hyper(17,a,190,a,b,189,a),rewrite([51(2)]),flip(a)].
% 132.56/132.85 272 join(n1,join(meet(A,B),meet(A,C))) = n1. [para(14(a,1),268(a,1,2))].
% 132.56/132.85 291 meet(A,meet(join(B,join(meet(C,join(B,D)),meet(D,join(C,meet(B,D))))),join(join(meet(B,D),meet(B,C)),meet(A,B)))) = meet(A,B). [para(32(a,1),22(a,1,2)),rewrite([7(12),7(14),10(14,R),7(23),22(23),7(15)])].
% 132.56/132.85 317 meet(n1,join(complement(A),meet(join(B,meet(C,join(B,C))),join(B,join(C,complement(A)))))) = join(join(B,C),complement(A)). [para(90(a,1),32(a,2,2)),rewrite([8(5),54(5),18(5),7(5),18(5),12(7,R),8(6),268(6),54(4),18(4),8(4),54(4),18(4),7(4),18(4),7(8),18(8),7(8),18(8),8(7),12(8),8(7),12(8,R),8(7),7(13),18(13),7(13),18(13),8(12)])].
% 132.56/132.85 334 meet(join(A,B),join(meet(C,join(A,join(join(A,B),meet(meet(n1,join(A,B)),join(A,meet(n1,join(A,B))))))),meet(join(A,meet(meet(n1,join(A,B)),join(A,meet(n1,join(A,B))))),join(A,join(C,meet(n1,join(A,B))))))) = join(join(A,meet(n1,join(A,B))),meet(C,join(A,B))). [para(83(a,1),32(a,1,2,1,2,2,1)),rewrite([10(10,R),1(9),12(12,R),8(11),83(19),10(21,R),1(20),10(27,R),1(26),7(27),5(27),8(26),12(27,R),8(26),10(35,R),1(34),7(35),5(35),8(34),7(36)])].
% 132.56/132.85 339 join(meet(A,B),join(meet(B,C),join(meet(A,join(B,C)),meet(C,join(A,meet(B,C)))))) = join(meet(A,join(B,C)),meet(C,join(A,meet(B,C)))). [para(32(a,1),141(a,1,2)),rewrite([7(8),14(16),7(11),2(13),8(10),12(10,R),12(9),8(8),12(10,R),8(9),12(9,R),8(8)])].
% 132.56/132.85 350 join(n1,join(meet(A,meet(B,C)),meet(B,D))) = n1. [para(10(a,1),272(a,1,2,1))].
% 132.56/132.85 360 meet(n1,join(A,meet(B,join(A,B)))) = join(A,B). [para(272(a,1),32(a,1,2,1,2)),rewrite([18(3),8(3),54(3),18(3),7(3),18(3),2(2),1(2),2(2),7(3),18(3),7(3),18(3),2(2),7(7),18(7),7(7),18(7),2(6),7(7),18(7),8(6)])].
% 132.56/132.85 382 join(n1,join(meet(A,B),complement(C))) = n1. [para(90(a,1),350(a,1,2,2)),rewrite([7(3),18(3)])].
% 132.56/132.85 394 join(n1,join(complement(A),meet(B,C))) = n1. [para(8(a,1),382(a,1,2))].
% 132.56/132.85 402 meet(n1,join(complement(A),meet(B,C))) = join(complement(A),meet(B,C)). [para(394(a,1),80(a,1,2,2,2)),rewrite([1(7),2(6),7(5)])].
% 132.56/132.85 405 join(complement(A),meet(join(B,meet(C,join(B,C))),join(B,join(C,complement(A))))) = join(join(B,C),complement(A)). [back_rewrite(317),rewrite([402(11)])].
% 132.56/132.86 406 complement(complement(A)) = A. [hyper(35,a,3,a,b,4,a)].
% 132.56/132.86 410 join(A,B) != n1 | n0 != A | complement(join(A,B)) = A. [para(23(a,1),35(a,1)),rewrite([5(5)]),flip(b)].
% 132.56/132.86 430 meet(n1,join(A,B)) = join(A,B). [para(406(a,1),87(a,1,2,2)),rewrite([406(5)])].
% 132.56/132.86 435 join(A,meet(B,join(A,B))) = join(A,B). [back_rewrite(360),rewrite([430(5)])].
% 132.56/132.86 436 meet(join(A,B),join(meet(C,join(A,B)),meet(join(A,B),join(A,join(B,C))))) = join(join(A,B),meet(C,join(A,B))). [back_rewrite(334),rewrite([430(5),430(6),23(5),1(5),2(4),23(3),430(6),430(7),23(6),1(6),23(5),430(7),12(6),8(5),12(6,R),8(5),23(7),430(12),23(11)])].
% 132.56/132.86 445 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [back_rewrite(88),rewrite([430(5),12(4,R),2(3),7(4)])].
% 132.56/132.86 446 meet(join(A,B),join(A,join(B,C))) = join(A,B). [back_rewrite(85),rewrite([430(5),12(4,R),8(3),12(3,R),2(2)])].
% 132.56/132.86 447 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [back_rewrite(405),rewrite([435(4),446(6),12(3),8(2),12(3,R),8(2)]),flip(a)].
% 132.56/132.86 450 join(join(A,B),meet(C,join(A,B))) = join(A,B). [back_rewrite(436),rewrite([446(7),8(5),5(6)]),flip(a)].
% 132.56/132.86 525 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(27(a,1),446(a,1,1)),rewrite([8(4),12(5,R),8(4),27(4),27(7)])].
% 132.56/132.86 555 meet(meet(A,B),join(A,B)) = meet(A,B). [back_rewrite(192),rewrite([525(4)]),flip(a)].
% 132.56/132.86 581 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(555(a,1),42(a,1,2,1)),rewrite([7(4),10(4),7(3),10(4,R),7(3),5(6),555(4),7(4),10(4),7(3),10(4,R),7(3)]),flip(a)].
% 132.56/132.86 590 join(A,join(B,complement(join(A,B)))) = n1. [para(447(a,1),3(a,1))].
% 132.56/132.86 591 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(6(a,1),447(a,1,1)),flip(a)].
% 132.56/132.86 596 join(n0,join(meet(A,B),complement(C))) = join(meet(A,B),complement(C)). [para(27(a,1),447(a,1,1)),flip(a)].
% 132.56/132.86 607 join(A,join(B,complement(C))) != n1 | meet(join(A,B),complement(C)) != n0 | join(A,B) = C. [para(447(a,1),35(a,1)),rewrite([406(12)]),flip(c)].
% 132.56/132.86 616 join(A,join(B,join(C,complement(join(A,B))))) = n1. [para(590(a,1),12(a,2,2)),rewrite([8(4),12(4,R),8(3),54(7)])].
% 132.56/132.86 625 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(48(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)])].
% 132.56/132.86 645 join(A,join(B,join(C,complement(join(A,C))))) = n1. [para(616(a,1),8(a,1)),rewrite([8(2),8(6),12(6,R),8(5),12(5,R),8(4)]),flip(a)].
% 132.56/132.86 688 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(49(a,1),141(a,1,2)),rewrite([7(3),22(6),7(4),2(5),8(4)])].
% 132.56/132.86 947 join(A,complement(meet(A,B))) = n1. [para(3(a,1),591(a,1,2)),rewrite([54(2)]),flip(a)].
% 132.56/132.86 961 join(A,join(B,complement(join(A,meet(B,C))))) = n1. [para(591(a,1),645(a,1,2))].
% 132.56/132.86 975 join(A,join(B,complement(meet(C,join(A,B))))) = n1. [para(947(a,1),447(a,1)),rewrite([7(3)]),flip(a)].
% 132.56/132.86 977 join(complement(meet(A,B)),meet(A,join(B,C))) = n1. [para(50(a,1),947(a,1,2,1)),rewrite([8(5)])].
% 132.56/132.86 1003 join(A,join(B,join(C,complement(join(A,meet(D,join(B,C))))))) = n1. [para(447(a,1),961(a,1,2)),rewrite([7(2)])].
% 132.56/132.86 1046 join(A,join(complement(A),complement(B))) = n1. [para(3(a,1),975(a,1,2,2,1,2)),rewrite([18(3)])].
% 132.56/132.86 1053 join(meet(A,B),complement(meet(A,meet(B,C)))) = n1. [para(27(a,1),975(a,1,2,2,1,2)),rewrite([10(4),7(3),10(4,R),7(3),596(7)])].
% 132.56/132.86 1098 join(complement(meet(A,B)),meet(B,join(A,C))) = n1. [para(7(a,1),977(a,1,1,1))].
% 132.56/132.86 1106 join(complement(meet(A,B)),meet(A,join(C,meet(A,B)))) = n1. [para(20(a,1),977(a,1,1,1)),rewrite([8(4)])].
% 132.56/132.86 1159 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(64(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)])].
% 132.56/132.86 1206 join(A,complement(meet(B,A))) = n1. [para(3(a,1),1098(a,1,2,2)),rewrite([18(4),8(3)])].
% 132.56/132.86 1207 join(complement(A),meet(join(A,B),join(A,C))) = n1. [para(5(a,1),1098(a,1,1,1))].
% 132.56/132.86 1212 join(meet(A,B),join(complement(meet(A,B)),meet(B,C))) = n1. [para(14(a,1),1098(a,1,2)),rewrite([7(3),22(3),7(1),7(4),12(6)])].
% 132.56/132.86 1214 join(complement(meet(A,B)),meet(meet(A,B),join(A,C))) = n1. [para(20(a,1),1098(a,1,1,1))].
% 132.56/132.86 1239 join(A,complement(meet(B,meet(C,A)))) = n1. [para(1053(a,1),1098(a,1,2,2)),rewrite([7(2),10(2),7(1),10(2,R),7(1),18(5),8(4)])].
% 132.56/132.86 1314 join(meet(A,join(B,C)),complement(meet(A,meet(B,D)))) = n1. [para(22(a,1),1239(a,1,2,1,2)),rewrite([7(3),10(4),7(3),10(4,R),7(3)])].
% 132.56/132.86 1338 join(meet(complement(A),join(A,B)),meet(join(A,B),join(A,complement(join(A,B))))) = join(A,B). [para(1207(a,1),62(a,1,2,2,2)),rewrite([7(7),430(7),12(6,R),8(5),1046(6),7(3),430(3),7(9),8(10)]),flip(a)].
% 132.56/132.86 1511 join(A,B) != n1 | n0 != B | complement(join(A,B)) = B. [para(8(a,1),410(a,1)),rewrite([8(6)])].
% 132.56/132.86 2051 join(A,join(complement(A),meet(B,join(A,C)))) = n1. [para(5(a,1),1212(a,1,1)),rewrite([5(2),7(3)])].
% 132.56/132.86 2095 join(A,join(complement(A),meet(B,C))) = n1. [para(525(a,1),2051(a,1,2,2))].
% 132.56/132.86 2329 meet(meet(A,B),join(A,C)) = meet(A,B). [para(1214(a,1),17(a,1)),rewrite([10(9,R),44(9),406(9)]),flip(c),xx(a),xx(b)].
% 132.56/132.86 2405 meet(meet(A,meet(B,C)),join(B,D)) = meet(A,meet(B,C)). [para(10(a,1),2329(a,1,1)),rewrite([7(5),10(6,R),7(5)])].
% 132.56/132.86 2425 join(join(A,B),meet(A,C)) = join(A,B). [para(2329(a,1),450(a,1,2))].
% 132.56/132.86 2482 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),2425(a,1,1)),rewrite([8(4)])].
% 132.56/132.86 2529 join(A,meet(B,meet(C,join(meet(A,D),meet(A,E))))) = A. [para(141(a,1),2482(a,1,1)),rewrite([7(5),10(5,R),7(4),141(11)])].
% 132.56/132.86 2614 join(meet(A,join(B,C)),complement(meet(A,meet(C,D)))) = n1. [para(8(a,1),1314(a,1,1,2))].
% 132.56/132.86 3434 join(meet(A,join(B,C)),complement(meet(C,meet(A,D)))) = n1. [para(7(a,1),2614(a,1,1)),rewrite([7(2),10(4,R),7(3)])].
% 132.56/132.86 3516 meet(meet(A,B),meet(meet(C,complement(A)),join(A,B))) = n0. [para(44(a,1),140(a,1,2,2)),rewrite([8(7),27(7),7(6),44(9)])].
% 132.56/132.86 5481 join(complement(meet(A,complement(B))),meet(complement(B),join(C,A))) = n1. [para(95(a,1),3434(a,1,2,1,2)),rewrite([8(7)])].
% 132.56/132.86 5573 meet(complement(A),meet(meet(A,B),join(C,complement(A)))) = n0. [para(95(a,1),3516(a,1,1)),rewrite([406(3),7(2),12(6,R),2(5)])].
% 132.56/132.86 5684 meet(meet(A,B),complement(meet(A,join(B,C)))) = n0. [para(50(a,1),5573(a,1,2,1)),rewrite([10(10,R),7(9),95(9)])].
% 132.56/132.86 5686 meet(A,meet(meet(B,C),complement(meet(A,B)))) = n0. [para(947(a,1),5573(a,1,2,2)),rewrite([7(4),10(4),7(3),10(4,R),7(3),7(6),10(6,R),7(5),10(5),7(4),18(4),7(3),10(5,R)])].
% 132.56/132.86 5689 join(A,complement(B)) != n1 | meet(A,complement(B)) != n0 | A = B. [para(5573(a,1),66(b,1,2,2)),rewrite([8(2),19(7),7(6),5573(14),19(10),406(10)])].
% 132.56/132.86 5703 meet(A,complement(join(A,B))) = n0. [para(1(a,1),5684(a,1,2,1)),rewrite([7(2),5(2)])].
% 132.56/132.86 5704 meet(meet(A,B),complement(meet(B,join(A,C)))) = n0. [para(7(a,1),5684(a,1,1))].
% 132.56/132.86 5711 meet(meet(A,B),complement(meet(A,join(C,meet(A,B))))) = n0. [para(20(a,1),5684(a,1,1)),rewrite([8(3)])].
% 132.56/132.86 5714 meet(complement(A),complement(join(B,complement(A)))) = n0. [para(90(a,1),5684(a,1,1)),rewrite([8(4),430(5)])].
% 132.56/132.86 5721 meet(join(A,B),complement(join(A,join(B,C)))) = n0. [para(430(a,1),5684(a,1,1)),rewrite([8(4),12(4),8(3),12(4,R),8(3),430(5)])].
% 132.56/132.86 5892 meet(complement(A),complement(join(B,join(C,complement(A))))) = n0. [para(447(a,1),5714(a,1,2,1))].
% 132.56/132.86 6039 meet(A,meet(B,complement(meet(A,B)))) = n0. [para(1(a,1),5686(a,1,2,1))].
% 132.56/132.86 6130 meet(A,complement(meet(join(A,B),join(A,C)))) = n0. [para(5(a,1),5704(a,1,1))].
% 132.56/132.86 6328 meet(meet(A,B),complement(join(C,meet(A,B)))) = n0. [para(27(a,1),5721(a,1,1)),rewrite([8(4),12(5,R),8(4),27(4)])].
% 132.56/132.86 6355 meet(complement(A),complement(join(B,join(C,join(D,complement(A)))))) = n0. [para(447(a,1),5892(a,1,2,1,2))].
% 132.56/132.86 6788 meet(meet(A,B),complement(join(A,C))) = n0. [para(2425(a,1),6328(a,1,2,1))].
% 132.56/132.86 8178 meet(A,meet(complement(A),join(B,C))) = n0. [para(5481(a,1),5711(a,1,2,1,2)),rewrite([18(6),406(5),7(4)])].
% 132.56/132.86 8182 meet(A,join(meet(B,complement(A)),meet(C,complement(A)))) = n0. [para(14(a,1),8178(a,1,2)),rewrite([7(2),7(4)])].
% 132.56/132.86 8330 meet(complement(A),join(meet(A,B),meet(C,A))) = n0. [hyper(1511,a,5481,a,b,8182,a(flip)),rewrite([406(2),7(3),10(3),7(2),44(3),51(2),406(4),7(3),406(5),268(7),45(2),406(4),7(3),406(5)]),flip(a)].
% 132.56/132.86 8353 meet(complement(join(A,B)),join(A,meet(C,join(A,B)))) = n0. [para(5(a,1),8330(a,1,2,2)),rewrite([7(4),8(5)])].
% 132.56/132.86 8788 join(meet(A,complement(B)),meet(A,join(C,complement(B)))) = meet(A,join(C,complement(B))). [para(248(a,1),6(a,1,2)),rewrite([12(10,R),2(9)])].
% 132.56/132.86 8943 meet(A,meet(meet(B,C),complement(D))) = meet(A,meet(B,meet(C,complement(D)))). [para(6355(a,1),142(a,1,2,2,2,2,2,2)),rewrite([19(16),7(15),8(16),8788(16),625(12),10(4,R),6355(11),7(7),27(8)])].
% 132.56/132.86 10477 meet(A,meet(B,join(meet(B,C),meet(A,B)))) = meet(A,B). [para(2(a,1),291(a,1,2,1,2,2,2)),rewrite([2329(3),10(3,R),1(2),2(3),6(2),20(3),2(3)])].
% 132.56/132.86 10749 meet(complement(join(A,B)),join(B,meet(C,join(A,B)))) = n0. [para(8(a,1),8353(a,1,1,1)),rewrite([8(3)])].
% 132.56/132.86 11568 meet(A,complement(join(B,A))) = n0. [hyper(1511,a,1106,a,b,10749,a(flip)),rewrite([7(4),4(4),51(2),7(7),4(7),19(5),7(4),268(5),45(2),7(7),4(7),19(5),7(4)]),flip(a)].
% 132.56/132.86 11587 meet(complement(join(A,B)),join(B,meet(A,C))) = n0. [para(2329(a,1),10749(a,1,2,2))].
% 132.56/132.86 11588 meet(complement(join(A,B)),join(meet(B,C),meet(D,join(A,B)))) = n0. [para(2482(a,1),10749(a,1,1,1)),rewrite([2482(6)])].
% 132.56/132.86 11602 meet(complement(join(A,complement(B))),join(meet(A,C),complement(B))) = n0. [para(591(a,1),11568(a,1,2,1)),rewrite([7(7)])].
% 132.56/132.86 11608 meet(complement(join(A,join(B,C))),join(join(A,C),meet(B,D))) = n0. [para(12(a,1),11587(a,1,1,1)),rewrite([8(4)])].
% 132.56/132.86 11642 meet(A,complement(join(B,join(C,A)))) = n0. [para(5721(a,1),11587(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1),19(5),7(4)])].
% 132.56/132.86 11651 meet(join(A,meet(B,C)),complement(join(A,join(B,D)))) = n0. [para(25(a,1),11642(a,1,2,1,2)),rewrite([8(3),12(4),8(3),12(4,R),8(3)])].
% 132.56/132.86 12029 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(11602(a,1),139(a,1,2,1)),rewrite([6788(8),8(5),27(5),27(14),10(13,R),7(12),525(12),8943(5),10(5,R),7(4),10(4,R),1(3),6788(11),8(8),27(8)]),flip(a)].
% 132.56/132.86 12668 meet(join(A,meet(B,C)),complement(join(A,join(C,D)))) = n0. [para(7(a,1),11651(a,1,1,2))].
% 132.56/132.86 13412 meet(complement(join(A,B)),join(A,meet(C,B))) = n0. [para(2(a,1),12668(a,1,2,1,2)),rewrite([7(5)])].
% 132.56/132.86 13440 meet(complement(join(A,B)),join(B,meet(C,A))) = n0. [hyper(1511,a,5481,a,b,13412,a(flip)),rewrite([8(2),12029(4),5703(3),41(2),51(2),8(2),268(7),45(2),8(2)]),flip(a)].
% 132.56/132.86 13464 meet(join(A,B),complement(join(B,join(meet(C,join(A,D)),meet(join(A,D),join(C,A)))))) = n0. [para(28(a,1),13440(a,1,2,2)),rewrite([8(4),8(7),8(9),7(10)])].
% 132.56/132.86 13574 join(meet(A,B),meet(B,join(A,B))) = join(B,meet(A,B)). [para(1(a,1),339(a,1,2,1)),rewrite([2(2),1(3),25(6),12(4,R),2(3),2(3),1(4)]),flip(a)].
% 132.56/132.86 14514 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(8(a,1),445(a,1,1))].
% 132.56/132.86 15013 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(7(a,1),688(a,1,1))].
% 132.56/132.86 15035 meet(A,meet(join(B,C),join(B,A))) = meet(A,join(B,C)). [para(688(a,1),140(a,1,2)),rewrite([8(2),7(6),10(6),7(5),10(5,R),1(4),10(4,R)])].
% 132.56/132.86 15091 join(A,meet(B,A)) = meet(A,join(B,A)). [back_rewrite(13574),rewrite([15013(4)]),flip(a)].
% 132.56/132.86 15094 meet(join(A,B),complement(join(B,join(meet(C,join(A,D)),meet(join(A,D),join(A,C)))))) = n0. [back_rewrite(13464),rewrite([8(5)])].
% 132.56/132.86 15515 meet(meet(A,complement(B)),join(C,complement(B))) = meet(A,complement(B)). [para(95(a,1),2405(a,1,1,2)),rewrite([8(4),95(9)])].
% 132.56/132.86 15578 join(join(A,complement(B)),meet(C,complement(B))) = join(A,complement(B)). [para(15515(a,1),15091(a,1,2)),rewrite([12(12),8(11),12(12,R),8(11),15091(11),95(11),1(10)])].
% 132.56/132.86 16305 meet(A,join(meet(B,C),meet(B,A))) = meet(B,A). [para(10477(a,1),7(a,2)),rewrite([7(2),42(4),7(4),7(5)])].
% 132.56/132.86 16347 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(7(a,1),16305(a,1,2,1)),rewrite([7(2),7(5)])].
% 132.56/132.86 16351 meet(A,join(meet(B,meet(C,D)),meet(A,C))) = meet(A,C). [para(10(a,1),16305(a,1,2,1)),rewrite([7(3),7(6)])].
% 132.56/132.86 16402 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(16347(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 132.56/132.86 16418 meet(A,join(meet(B,C),meet(A,join(B,D)))) = meet(A,join(B,D)). [para(2329(a,1),16347(a,1,2,1))].
% 132.56/132.86 16579 meet(A,join(B,A)) = A. [para(18(a,1),16402(a,1,2,2)),rewrite([8(3),15091(3),10(4,R),7(3),430(3),18(4)])].
% 132.56/132.86 17034 join(A,meet(B,A)) = A. [para(14514(a,1),16402(a,1)),rewrite([5(4),8(2),5(5)])].
% 132.56/132.86 17540 join(A,meet(meet(A,B),join(C,meet(A,D)))) = A. [para(15035(a,1),2529(a,1,2)),rewrite([8(3)])].
% 132.56/132.86 17542 join(meet(A,join(B,C)),meet(join(B,C),join(B,A))) = meet(join(B,C),join(B,A)). [para(15035(a,1),17034(a,1,2)),rewrite([8(6)])].
% 132.56/132.86 17557 meet(join(A,B),complement(join(B,meet(join(A,C),join(A,D))))) = n0. [back_rewrite(15094),rewrite([17542(7)])].
% 132.56/132.86 17650 join(A,meet(meet(A,B),join(C,complement(D)))) = A. [para(15578(a,1),17540(a,1,2,2))].
% 132.56/132.86 17701 join(A,meet(meet(A,B),join(C,D))) = A. [para(406(a,1),17650(a,1,2,2,2))].
% 132.56/132.86 18824 meet(A,join(meet(B,meet(C,D)),meet(C,A))) = meet(C,A). [para(16351(a,1),7(a,2)),rewrite([7(3),7(5),7(6)])].
% 132.56/132.86 19880 meet(A,join(meet(B,A),meet(B,C))) = meet(B,A). [para(18824(a,1),30(a,2)),rewrite([6(2),7(1),20(4),16579(5),145(5)])].
% 132.56/132.86 19900 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(19880(a,1),30(a,2)),rewrite([16418(7)])].
% 132.56/132.86 19985 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(17701(a,1),19900(a,1,2,2)),rewrite([7(3),10(4,R),10(3),7(2),10(3,R),7(2),20(4)]),flip(a)].
% 132.56/132.86 20651 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(5(a,1),19985(a,1,1)),flip(a)].
% 132.56/132.86 22435 join(A,join(B,complement(join(A,meet(C,join(A,B)))))) = n1. [para(1003(a,1),23(a,1)),flip(a)].
% 132.56/132.86 22455 join(A,join(B,complement(join(B,meet(C,join(A,B)))))) = n1. [para(22435(a,1),8(a,1)),rewrite([8(2),8(7),12(7,R),8(6)]),flip(a)].
% 132.56/132.86 24972 join(n0,join(join(A,B),meet(C,D))) = join(join(A,B),meet(C,D)). [para(11608(a,1),17034(a,1,2)),rewrite([8(5)])].
% 132.56/132.86 27252 join(A,meet(join(B,C),join(B,A))) = join(B,A). [hyper(607,a,22455,a,b,17557,a),flip(a)].
% 132.56/132.86 27359 join(A,meet(join(A,B),join(B,C))) = join(A,B). [para(7(a,1),27252(a,1,2)),rewrite([8(1),8(5)])].
% 132.56/132.86 27360 join(A,meet(join(B,C),join(A,C))) = join(A,C). [para(8(a,1),27252(a,1,2,1)),rewrite([8(2),8(5)])].
% 132.56/132.86 27361 join(A,meet(join(B,C),join(A,B))) = join(A,B). [para(8(a,1),27252(a,1,2,2)),rewrite([8(5)])].
% 132.56/132.86 27455 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(16305(a,1),27359(a,1,2))].
% 132.56/132.86 28310 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(12029(a,1),1159(a,1,2,2,2,2)),rewrite([12(8,R),8(7),12(7,R),8(6),12(6,R),8(5),581(5),12(8,R)]),flip(a)].
% 132.56/132.86 28362 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [back_rewrite(24972),rewrite([28310(5),12(5,R),8(4),12(4,R),8(3),27(3)]),flip(a)].
% 132.56/132.86 28546 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(6(a,1),28362(a,1,1)),flip(a)].
% 132.56/132.86 30136 join(A,join(complement(join(A,B)),meet(complement(A),join(A,B)))) = n1. [para(1338(a,1),590(a,1,2,2,1)),rewrite([8(11),27252(11),12(7),8(6),12(7,R),8(6)])].
% 132.56/132.86 30143 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [hyper(36,a,30136,a,b,11588,a),rewrite([8(2),6(2),406(2),8(5),6(5),7(4)]),flip(a)].
% 132.56/132.86 30144 join(A,meet(complement(A),join(A,B))) = join(A,B). [hyper(36,a,30136,a,b,8353,a),rewrite([406(3)]),flip(a)].
% 132.56/132.86 30152 join(meet(A,B),meet(B,complement(meet(A,B)))) = B. [para(7(a,1),30143(a,1,1)),rewrite([7(2)])].
% 132.56/132.86 30187 join(A,join(B,meet(complement(A),join(A,C)))) = join(A,join(C,B)). [para(30144(a,1),12(a,2,2)),rewrite([8(4),12(7),8(6),12(7,R),8(6)])].
% 132.56/132.86 30247 join(A,meet(B,complement(meet(A,B)))) = join(A,B). [para(30152(a,1),28546(a,1,2)),flip(a)].
% 132.56/132.86 30252 join(A,meet(B,complement(meet(B,A)))) = join(B,A). [para(30247(a,1),8(a,2)),rewrite([7(1),8(4),8(5)])].
% 132.56/132.86 30255 join(A,B) != n1 | meet(B,complement(meet(A,B))) = complement(A). [para(30247(a,1),17(a,1)),rewrite([6039(7)]),flip(c),xx(b)].
% 132.56/132.86 30289 join(A,meet(B,complement(meet(A,meet(C,B))))) = join(A,B). [para(30247(a,1),28546(a,1,2)),rewrite([8(2),25(3),7(3),10(3),7(2),10(3,R),7(2)]),flip(a)].
% 132.56/132.86 30294 join(A,B) != n1 | meet(A,complement(meet(A,B))) = complement(B). [para(30252(a,1),17(a,1)),rewrite([10(7,R),7(6),6039(7)]),flip(c),xx(b)].
% 132.56/132.86 30296 join(A,B) != n1 | complement(meet(A,complement(meet(A,B)))) = B. [para(30252(a,1),35(a,1)),rewrite([10(7,R),7(6),6039(7)]),xx(b)].
% 132.56/132.86 30460 meet(complement(meet(A,B)),complement(meet(A,complement(meet(A,B))))) = complement(A). [hyper(30255,a,947,a)].
% 132.56/132.86 30495 join(A,meet(B,complement(meet(B,meet(A,C))))) = join(B,A). [para(30289(a,1),8(a,2)),rewrite([7(1),10(2,R),7(1),8(5),8(6)])].
% 132.56/132.86 30527 meet(A,complement(meet(A,join(complement(A),meet(B,C))))) = complement(join(complement(A),meet(B,C))). [hyper(30294,a,2095,a)].
% 132.56/132.86 30528 meet(A,complement(meet(A,complement(meet(A,B))))) = meet(A,B). [hyper(30294,a,1206,a),rewrite([7(1),7(6),406(8)])].
% 132.56/132.86 30594 complement(meet(A,complement(meet(A,B)))) = join(complement(A),meet(A,B)). [para(30528(a,1),30152(a,1,1)),rewrite([30528(10),7(8),30460(8),8(3)]),flip(a)].
% 132.56/132.86 30597 meet(A,join(complement(A),meet(A,B))) = meet(A,B). [para(30528(a,1),30528(a,2)),rewrite([30594(4),30527(6),406(5)])].
% 132.56/132.86 30620 join(A,B) != n1 | join(complement(A),meet(A,B)) = B. [back_rewrite(30296),rewrite([30594(7)])].
% 132.56/132.86 30635 join(meet(A,B),meet(A,C)) = meet(A,join(C,meet(A,B))). [para(30597(a,1),14(a,1,2,2,2,2)),rewrite([25(4),3(2),18(2),27360(7),30597(7)]),flip(a)].
% 132.56/132.86 30636 meet(complement(A),join(A,meet(B,complement(A)))) = meet(B,complement(A)). [para(406(a,1),30597(a,1,2,1)),rewrite([7(3),7(7)])].
% 132.56/132.86 30721 meet(a,join(c,meet(a,b))) != meet(a,join(b,c)) # answer(prove_distributivity). [back_rewrite(16),rewrite([30635(7)])].
% 132.56/132.86 30728 join(complement(A),meet(A,complement(meet(A,B)))) = complement(meet(A,B)). [hyper(30620,a,1206,a),rewrite([7(2),7(6)])].
% 132.56/132.86 30730 join(complement(A),meet(A,join(B,complement(join(A,B))))) = join(B,complement(join(A,B))). [hyper(30620,a,590,a)].
% 132.56/132.86 30818 join(A,complement(meet(B,meet(C,join(A,complement(B)))))) = n1. [para(56(a,1),30495(a,2)),rewrite([7(5),28362(9),30728(8)])].
% 132.56/132.86 30841 join(A,complement(meet(B,join(A,complement(B))))) = n1. [para(1(a,1),30818(a,1,2,1,2))].
% 132.56/132.86 30858 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(5689,a,30841,a,b,6130,a),flip(a)].
% 132.56/132.86 30951 meet(join(A,B),join(B,complement(join(A,B)))) = B. [para(8(a,1),30858(a,1,1)),rewrite([8(2)])].
% 132.56/132.86 30992 meet(A,join(B,complement(join(A,B)))) = meet(A,B). [para(30951(a,1),20651(a,1,2)),flip(a)].
% 132.56/132.86 31003 join(complement(A),meet(A,B)) = join(B,complement(join(A,B))). [back_rewrite(30730),rewrite([30992(5)])].
% 132.56/132.86 31025 meet(A,join(B,join(meet(A,C),complement(join(A,B))))) = meet(A,join(B,meet(A,C))). [para(25(a,1),30992(a,1,2,2,1)),rewrite([8(5),12(5,R)])].
% 132.56/132.86 31056 meet(A,join(complement(join(A,B)),meet(join(A,B),join(B,C)))) = meet(A,join(B,C)). [para(27359(a,1),30992(a,1,2,2,1)),rewrite([8(6),20651(11)])].
% 132.56/132.86 31591 join(A,complement(join(A,B))) = join(A,complement(B)). [para(31003(a,2),23(a,1,2)),rewrite([7(2),25(4),8(3)]),flip(a)].
% 132.56/132.86 31592 join(complement(A),meet(B,A)) = join(B,complement(A)). [para(31003(a,2),23(a,2)),rewrite([8(1),31591(3),23(3),7(4)]),flip(a)].
% 132.56/132.86 31598 join(A,meet(B,complement(A))) = join(A,B). [para(406(a,1),31003(a,1,1)),rewrite([7(2),8(5),31591(7),406(5),8(4)])].
% 132.56/132.86 31609 join(A,complement(join(B,meet(A,C)))) = join(A,complement(B)). [para(31003(a,2),591(a,1,2)),rewrite([10(3,R),7(2),25(5)]),flip(a)].
% 132.56/132.86 31632 join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A). [para(5703(a,1),31003(a,1,2)),rewrite([19(3),31591(6)]),flip(a)].
% 132.56/132.86 31710 join(complement(A),meet(A,join(B,C))) = join(B,join(C,complement(join(A,B)))). [para(15035(a,1),31003(a,1,2)),rewrite([8(6),8(9),27361(11),8(10),31592(10),447(8)])].
% 132.56/132.86 31778 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(27455(a,1),31003(a,2,2,1)),rewrite([22(5),8(10),31592(10),31609(7)])].
% 132.56/132.86 31867 meet(complement(A),join(A,complement(B))) = complement(join(A,B)). [para(31003(a,2),30951(a,1,2,2,1)),rewrite([8(1),31591(3),8(3),7(6),31592(7),31632(8),7(4),8(5)])].
% 132.56/132.86 31933 meet(complement(A),join(A,B)) = meet(B,complement(A)). [back_rewrite(30636),rewrite([31598(4)])].
% 132.56/132.86 31944 join(A,join(B,complement(join(C,A)))) = join(A,join(B,complement(C))). [back_rewrite(31710),rewrite([31778(4),447(3)]),flip(a)].
% 132.56/132.86 31956 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [back_rewrite(31056),rewrite([31778(6),447(4),31944(4)])].
% 132.56/132.86 32006 complement(join(A,B)) = meet(complement(A),complement(B)). [back_rewrite(31867),rewrite([31933(4),7(3)]),flip(a)].
% 132.56/132.86 32025 join(A,join(B,meet(C,complement(A)))) = join(A,join(B,C)). [back_rewrite(30187),rewrite([31933(3),8(5)])].
% 132.56/132.86 32032 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(31025),rewrite([32006(3),32025(6),8(3),31778(3),31956(4)]),flip(a)].
% 132.56/132.86 33928 $F # answer(prove_distributivity). [back_rewrite(30721),rewrite([32032(7),8(4)]),xx(a)].
% 132.56/132.86
% 132.56/132.86 % SZS output end Refutation
% 132.56/132.86 ============================== end of proof ==========================
% 132.56/132.86
% 132.56/132.86 ============================== STATISTICS ============================
% 132.56/132.86
% 132.56/132.86 Given=1616. Generated=2657020. Kept=33923. proofs=1.
% 132.56/132.86 Usable=648. Sos=4478. Demods=6220. Limbo=1896, Disabled=26914. Hints=0.
% 132.56/132.86 Megabytes=41.22.
% 132.56/132.86 User_CPU=130.60, System_CPU=1.39, Wall_clock=132.
% 132.56/132.86
% 132.56/132.86 ============================== end of statistics =====================
% 132.56/132.86
% 132.56/132.86 ============================== end of search =========================
% 132.56/132.86
% 132.56/132.86 THEOREM PROVED
% 132.56/132.86 % SZS status Unsatisfiable
% 132.56/132.86
% 132.56/132.86 Exiting with 1 proof.
% 132.56/132.86
% 132.56/132.86 Process 1466 exit (max_proofs) Wed Jun 29 16:16:15 2022
% 132.56/132.86 Prover9 interrupted
%------------------------------------------------------------------------------