TSTP Solution File: LAT212-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT212-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 06:26:09 EDT 2022
% Result : Unsatisfiable 33.57s 33.90s
% Output : Refutation 33.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT212-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 13:51:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.48/9.77 ============================== Prover9 ===============================
% 9.48/9.77 Prover9 (32) version 2009-11A, November 2009.
% 9.48/9.77 Process 5715 was started by sandbox on n023.cluster.edu,
% 9.48/9.77 Wed Jun 29 13:51:15 2022
% 9.48/9.77 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5562_n023.cluster.edu".
% 9.48/9.77 ============================== end of head ===========================
% 9.48/9.77
% 9.48/9.77 ============================== INPUT =================================
% 9.48/9.77
% 9.48/9.77 % Reading from file /tmp/Prover9_5562_n023.cluster.edu
% 9.48/9.77
% 9.48/9.77 set(prolog_style_variables).
% 9.48/9.77 set(auto2).
% 9.48/9.77 % set(auto2) -> set(auto).
% 9.48/9.77 % set(auto) -> set(auto_inference).
% 9.48/9.77 % set(auto) -> set(auto_setup).
% 9.48/9.77 % set(auto_setup) -> set(predicate_elim).
% 9.48/9.77 % set(auto_setup) -> assign(eq_defs, unfold).
% 9.48/9.77 % set(auto) -> set(auto_limits).
% 9.48/9.77 % set(auto_limits) -> assign(max_weight, "100.000").
% 9.48/9.77 % set(auto_limits) -> assign(sos_limit, 20000).
% 9.48/9.77 % set(auto) -> set(auto_denials).
% 9.48/9.77 % set(auto) -> set(auto_process).
% 9.48/9.77 % set(auto2) -> assign(new_constants, 1).
% 9.48/9.77 % set(auto2) -> assign(fold_denial_max, 3).
% 9.48/9.77 % set(auto2) -> assign(max_weight, "200.000").
% 9.48/9.77 % set(auto2) -> assign(max_hours, 1).
% 9.48/9.77 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 9.48/9.77 % set(auto2) -> assign(max_seconds, 0).
% 9.48/9.77 % set(auto2) -> assign(max_minutes, 5).
% 9.48/9.77 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 9.48/9.77 % set(auto2) -> set(sort_initial_sos).
% 9.48/9.77 % set(auto2) -> assign(sos_limit, -1).
% 9.48/9.77 % set(auto2) -> assign(lrs_ticks, 3000).
% 9.48/9.77 % set(auto2) -> assign(max_megs, 400).
% 9.48/9.77 % set(auto2) -> assign(stats, some).
% 9.48/9.77 % set(auto2) -> clear(echo_input).
% 9.48/9.77 % set(auto2) -> set(quiet).
% 9.48/9.77 % set(auto2) -> clear(print_initial_clauses).
% 9.48/9.77 % set(auto2) -> clear(print_given).
% 9.48/9.77 assign(lrs_ticks,-1).
% 9.48/9.77 assign(sos_limit,10000).
% 9.48/9.77 assign(order,kbo).
% 9.48/9.77 set(lex_order_vars).
% 9.48/9.77 clear(print_given).
% 9.48/9.77
% 9.48/9.77 % formulas(sos). % not echoed (13 formulas)
% 9.48/9.77
% 9.48/9.77 ============================== end of input ==========================
% 9.48/9.77
% 9.48/9.77 % From the command line: assign(max_seconds, 300).
% 9.48/9.77
% 9.48/9.77 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 9.48/9.77
% 9.48/9.77 % Formulas that are not ordinary clauses:
% 9.48/9.77
% 9.48/9.77 ============================== end of process non-clausal formulas ===
% 9.48/9.77
% 9.48/9.77 ============================== PROCESS INITIAL CLAUSES ===============
% 9.48/9.77
% 9.48/9.77 ============================== PREDICATE ELIMINATION =================
% 9.48/9.77
% 9.48/9.77 ============================== end predicate elimination =============
% 9.48/9.77
% 9.48/9.77 Auto_denials:
% 9.48/9.77 % copying label prove_distributivity to answer in negative clause
% 9.48/9.77
% 9.48/9.77 Term ordering decisions:
% 9.48/9.77
% 9.48/9.77 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 9.48/9.77 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. join=1. meet=1. complement=0.
% 9.48/9.77
% 9.48/9.77 ============================== end of process initial clauses ========
% 9.48/9.77
% 9.48/9.77 ============================== CLAUSES FOR SEARCH ====================
% 9.48/9.77
% 9.48/9.77 ============================== end of clauses for search =============
% 9.48/9.77
% 9.48/9.77 ============================== SEARCH ================================
% 9.48/9.77
% 9.48/9.77 % Starting search at 0.01 seconds.
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=139.000, iters=3358
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=130.000, iters=3334
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=102.000, iters=3341
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=92.000, iters=3364
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=78.000, iters=3335
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=75.000, iters=3333
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=74.000, iters=3392
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=72.000, iters=3385
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=65.000, iters=3333
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=64.000, iters=3365
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=63.000, iters=3384
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=62.000, iters=3340
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=60.000, iters=3353
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=59.000, iters=3351
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=58.000, iters=3378
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=56.000, iters=3372
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=55.000, iters=3358
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=54.000, iters=3371
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=53.000, iters=3380
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=52.000, iters=3392
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=51.000, iters=3350
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=50.000, iters=3361
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=49.000, iters=3369
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=48.000, iters=3441
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=47.000, iters=3364
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=46.000, iters=3346
% 9.48/9.77
% 9.48/9.77 Low Water (keep): wt=45.000, iters=3359
% 33.57/33.90
% 33.57/33.90 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 10.10 sec).
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=44.000, iters=3403
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=43.000, iters=3335
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=42.000, iters=3349
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=41.000, iters=3345
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=40.000, iters=3371
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=39.000, iters=3421
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=38.000, iters=3348
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=37.000, iters=3394
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=36.000, iters=3336
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=35.000, iters=3340
% 33.57/33.90
% 33.57/33.90 Low Water (displace): id=4612, wt=198.000
% 33.57/33.90
% 33.57/33.90 Low Water (displace): id=3807, wt=197.000
% 33.57/33.90
% 33.57/33.90 Low Water (displace): id=4619, wt=195.000
% 33.57/33.90
% 33.57/33.90 Low Water (displace): id=4468, wt=191.000
% 33.57/33.90
% 33.57/33.90 Low Water (displace): id=13006, wt=18.000
% 33.57/33.90
% 33.57/33.90 Low Water (displace): id=13020, wt=17.000
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=34.000, iters=3333
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=33.000, iters=3362
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=32.000, iters=3333
% 33.57/33.90
% 33.57/33.90 Low Water (displace): id=14557, wt=16.000
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=31.000, iters=3351
% 33.57/33.90
% 33.57/33.90 Low Water (keep): wt=30.000, iters=3338
% 33.57/33.90
% 33.57/33.90 ============================== PROOF =================================
% 33.57/33.90 % SZS status Unsatisfiable
% 33.57/33.90 % SZS output start Refutation
% 33.57/33.90
% 33.57/33.90 % Proof 1 at 32.52 (+ 0.37) seconds: prove_distributivity.
% 33.57/33.90 % Length of proof is 238.
% 33.57/33.90 % Level of proof is 49.
% 33.57/33.90 % Maximum clause weight is 71.000.
% 33.57/33.90 % Given clauses 980.
% 33.57/33.90
% 33.57/33.90 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 33.57/33.90 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 33.57/33.90 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 33.57/33.90 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 33.57/33.90 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 33.57/33.90 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 33.57/33.90 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 33.57/33.90 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 33.57/33.90 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 33.57/33.90 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 33.57/33.90 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 33.57/33.90 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 33.57/33.90 13 meet(A,join(B,meet(C,join(B,D)))) = meet(A,join(B,meet(C,join(D,meet(B,join(A,C)))))) # label(equation_H70) # label(axiom). [assumption].
% 33.57/33.90 14 meet(A,join(B,meet(C,join(D,meet(B,join(A,C)))))) = meet(A,join(B,meet(C,join(B,D)))). [copy(13),flip(a)].
% 33.57/33.90 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 33.57/33.90 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 33.57/33.90 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 33.57/33.90 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 33.57/33.90 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 33.57/33.90 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)])].
% 33.57/33.90 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 33.57/33.90 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 33.57/33.90 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)])].
% 33.57/33.90 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 33.57/33.90 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 33.57/33.90 26 meet(A,join(B,meet(A,join(C,meet(A,B))))) = meet(A,join(B,meet(A,join(B,C)))). [para(2(a,1),14(a,1,2,2,2,2,2)),rewrite([7(1)])].
% 33.57/33.90 27 meet(A,join(B,meet(C,join(B,C)))) = meet(A,join(B,C)). [para(5(a,1),14(a,1,2,2)),flip(a)].
% 33.57/33.90 28 meet(A,join(B,meet(meet(A,C),join(D,meet(A,B))))) = meet(A,join(B,meet(meet(A,C),join(B,D)))). [para(6(a,1),14(a,1,2,2,2,2,2)),rewrite([7(2)])].
% 33.57/33.90 29 meet(A,join(B,meet(C,join(D,meet(B,join(C,A)))))) = meet(A,join(B,meet(C,join(B,D)))). [para(14(a,1),7(a,2)),rewrite([8(1),7(6)])].
% 33.57/33.90 31 meet(A,join(B,meet(meet(C,join(D,meet(A,join(B,C)))),join(E,meet(B,join(A,meet(C,join(A,D)))))))) = meet(A,join(B,meet(meet(C,join(D,meet(A,join(B,C)))),join(B,E)))). [para(14(a,1),14(a,1,2,2,2,2))].
% 33.57/33.90 34 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(7(a,1),17(a,1)),rewrite([8(4)])].
% 33.57/33.90 39 meet(A,join(B,meet(zero,join(C,meet(A,B))))) = meet(A,join(B,meet(zero,join(B,C)))). [para(19(a,1),14(a,1,2,2,2,2,2)),rewrite([7(2)])].
% 33.57/33.90 40 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 33.57/33.90 42 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([40(5)])].
% 33.57/33.90 43 complement(one) = zero. [hyper(17,a,40,a,b,19,a)].
% 33.57/33.90 44 one != A | complement(A) = zero. [para(40(a,1),17(a,1)),rewrite([19(5)]),flip(b),xx(a)].
% 33.57/33.90 46 meet(A,B) != zero | join(A,meet(B,join(A,C))) != one | meet(B,join(A,C)) = complement(A). [para(22(a,1),17(a,1)),flip(c)].
% 33.57/33.90 47 complement(join(A,one)) = zero. [hyper(44,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 33.57/33.90 49 join(A,one) = one. [para(47(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 33.57/33.90 51 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([49(5)])].
% 33.57/33.90 52 complement(zero) = one. [hyper(17,a,18,a,b,49,a)].
% 33.57/33.90 53 meet(A,join(B,meet(join(A,C),join(D,meet(B,join(A,C)))))) = meet(A,join(B,meet(join(A,C),join(B,D)))). [para(23(a,1),14(a,1,2,2,2,2,2))].
% 33.57/33.90 58 meet(A,join(B,meet(join(C,meet(A,D)),join(E,meet(B,join(A,C)))))) = meet(A,join(B,meet(join(C,meet(A,D)),join(B,E)))). [para(25(a,1),14(a,1,2,2,2,2,2))].
% 33.57/33.90 65 meet(A,join(complement(A),meet(A,join(B,complement(A))))) = meet(A,join(complement(A),meet(A,B))). [para(4(a,1),26(a,1,2,2,2,2)),rewrite([19(3),8(7)]),flip(a)].
% 33.57/33.90 68 meet(A,join(B,meet(meet(B,join(C,meet(A,B))),join(D,meet(B,join(A,meet(B,join(A,C)))))))) = meet(A,join(B,meet(meet(B,join(C,meet(A,B))),join(B,D)))). [para(26(a,1),14(a,1,2,2,2,2)),rewrite([7(1),7(12)])].
% 33.57/33.90 72 meet(A,join(B,meet(A,join(B,C)))) != zero | join(A,B) != one | join(B,meet(A,join(C,meet(A,B)))) = complement(A). [para(26(a,1),17(a,1)),rewrite([25(11)]),flip(c)].
% 33.57/33.90 79 complement(complement(A)) = A. [hyper(34,a,4,a,b,3,a)].
% 33.57/33.90 93 join(A,meet(B,join(A,B))) = join(A,B). [para(27(a,1),1(a,1)),rewrite([7(5),27(5),1(3)]),flip(a)].
% 33.57/33.90 100 join(A,meet(one,join(B,complement(A)))) = one. [para(51(a,1),93(a,1,2,2)),rewrite([7(4),51(8)])].
% 33.57/33.90 101 join(A,meet(join(A,B),join(B,meet(A,C)))) = join(A,B). [para(25(a,1),93(a,1,2,2)),rewrite([7(4),25(8)])].
% 33.57/33.90 104 join(A,meet(one,complement(A))) = one. [para(2(a,1),100(a,1,2,2))].
% 33.57/33.90 106 join(complement(A),meet(one,join(A,B))) = one. [para(79(a,1),100(a,1,2,2,2)),rewrite([8(3)])].
% 33.57/33.90 108 meet(one,complement(A)) = complement(A). [hyper(17,a,42,a,b,104,a),flip(a)].
% 33.57/33.90 111 meet(A,join(complement(A),meet(meet(A,B),join(C,complement(A))))) = meet(A,join(complement(A),meet(A,meet(B,C)))). [para(4(a,1),28(a,1,2,2,2,2)),rewrite([19(4),7(3),10(3),7(2),10(3,R),7(2),8(9)]),flip(a)].
% 33.57/33.90 115 meet(A,join(B,meet(A,meet(C,join(D,meet(A,B)))))) = meet(A,join(B,meet(meet(A,C),join(B,D)))). [para(7(a,1),28(a,1,2,2)),rewrite([10(4),7(3),10(4,R),7(3)])].
% 33.57/33.90 116 meet(A,join(B,meet(meet(A,C),join(B,D)))) = meet(A,join(B,meet(A,meet(C,join(B,D))))). [para(7(a,1),28(a,2,2,2)),rewrite([28(6),10(8),7(7),10(8,R),7(7)])].
% 33.57/33.90 117 meet(A,meet(B,join(C,meet(meet(A,D),join(E,meet(A,C)))))) = meet(A,meet(B,join(C,meet(A,meet(D,join(C,E)))))). [para(28(a,1),10(a,2,2)),rewrite([7(6),116(12),10(13,R),7(12)])].
% 33.57/33.90 123 meet(A,join(one,meet(meet(A,B),join(A,C)))) = meet(A,join(one,meet(A,B))). [para(18(a,1),28(a,1,2,2,2,2)),rewrite([8(3),8(10),49(10),7(10),10(10),7(9),18(9),7(8)])].
% 33.57/33.90 135 meet(A,join(B,meet(A,meet(C,join(D,meet(A,B)))))) = meet(A,join(B,meet(A,meet(C,join(B,D))))). [back_rewrite(115),rewrite([116(11)])].
% 33.57/33.90 136 meet(A,join(B,meet(meet(A,C),join(D,meet(A,B))))) = meet(A,join(B,meet(A,meet(C,join(B,D))))). [back_rewrite(28),rewrite([116(11)])].
% 33.57/33.90 137 join(complement(A),join(meet(one,join(A,B)),meet(C,complement(A)))) = one. [para(106(a,1),25(a,2)),rewrite([7(6)])].
% 33.57/33.90 144 meet(join(A,B),join(C,meet(A,join(D,meet(C,join(A,B)))))) = meet(join(A,B),join(C,meet(A,join(C,D)))). [para(23(a,1),29(a,1,2,2,2,2,2))].
% 33.57/33.90 217 meet(meet(A,join(B,meet(C,join(B,D)))),join(meet(C,join(D,meet(B,join(A,C)))),meet(B,join(A,meet(C,meet(join(A,B),join(D,meet(B,join(A,C))))))))) = meet(meet(A,join(B,meet(C,join(B,D)))),join(meet(C,join(D,meet(B,join(A,C)))),meet(B,join(A,meet(C,join(D,meet(B,join(A,C)))))))). [para(31(a,1),29(a,1,2,2)),rewrite([7(14),10(14,R),7(13),8(31)])].
% 33.57/33.90 329 meet(A,join(B,meet(zero,join(A,B)))) = meet(A,B). [para(6(a,1),39(a,1,2,2,2)),rewrite([7(2),40(2),19(2),8(3)]),flip(a)].
% 33.57/33.90 333 meet(A,join(one,meet(zero,join(A,B)))) = A. [para(18(a,1),39(a,1,2,2,2,2)),rewrite([8(3),8(10),49(10),7(10),40(10),19(9),18(8)])].
% 33.57/33.90 408 meet(A,complement(B)) != zero | join(A,complement(B)) != one | A = B. [para(106(a,1),46(b,1,2,2)),rewrite([7(2),18(7),8(6),106(13),18(10),79(10)])].
% 33.57/33.90 409 meet(A,join(join(A,B),meet(zero,join(A,B)))) = A. [para(5(a,1),329(a,2)),rewrite([23(4)])].
% 33.57/33.90 410 meet(A,join(zero,meet(A,B))) = meet(A,B). [para(6(a,1),329(a,1,2,2,2)),rewrite([7(3),40(3),8(3),20(6)])].
% 33.57/33.90 446 meet(one,join(zero,complement(A))) = complement(A). [para(108(a,1),410(a,1,2,2)),rewrite([108(8)])].
% 33.57/33.90 456 meet(A,join(zero,complement(B))) = meet(A,complement(B)). [para(446(a,1),10(a,1,2)),rewrite([18(7),7(6)]),flip(a)].
% 33.57/33.90 459 meet(zero,complement(A)) = zero. [para(446(a,1),22(a,1,2)),rewrite([7(6),40(6)])].
% 33.57/33.90 471 meet(zero,join(complement(A),meet(zero,join(B,complement(A))))) = zero. [para(459(a,1),26(a,1,2,2,2,2)),rewrite([19(5),7(4),40(4),19(4),459(3),8(6)]),flip(a)].
% 33.57/33.90 473 meet(A,join(B,meet(join(A,C),join(A,join(B,C))))) = A. [para(5(a,1),53(a,1,2,2)),rewrite([12(2,R),8(1),5(3),12(3,R),8(2)]),flip(a)].
% 33.57/33.90 503 join(zero,complement(A)) = complement(A). [para(456(a,1),1(a,1)),rewrite([7(5),456(5),1(3)]),flip(a)].
% 33.57/33.90 519 meet(A,join(zero,meet(B,join(A,B)))) = meet(A,B). [para(409(a,1),29(a,1,2,2)),rewrite([8(2),19(2),8(4),12(5),8(4),19(4),8(3)]),flip(a)].
% 33.57/33.90 555 meet(A,join(one,meet(join(B,meet(A,C)),join(meet(one,join(A,B)),meet(zero,join(B,join(D,meet(A,C)))))))) = meet(A,join(B,join(one,meet(A,C)))). [para(333(a,1),58(a,2,2,2)),rewrite([8(7),12(7,R),8(6),8(12),12(19,R),8(18)])].
% 33.57/33.90 603 meet(complement(A),meet(zero,join(B,complement(A)))) = zero. [para(471(a,1),329(a,1,2,2)),rewrite([8(7),6(7),40(3)]),flip(a)].
% 33.57/33.90 610 meet(zero,join(A,complement(B))) = zero. [para(603(a,1),10(a,1)),rewrite([40(6),7(5)]),flip(a)].
% 33.57/33.90 618 meet(zero,join(A,B)) = zero. [para(79(a,1),610(a,1,2,2))].
% 33.57/33.90 623 meet(A,join(B,join(one,meet(A,C)))) = A. [back_rewrite(555),rewrite([618(11),8(8),58(11),19(6),7(5),6(6),18(2)]),flip(a)].
% 33.57/33.90 636 meet(A,join(one,meet(A,B))) = A. [para(2(a,1),623(a,1,2))].
% 33.57/33.90 644 meet(A,join(B,meet(join(A,C),join(B,join(one,meet(D,join(A,C))))))) = A. [para(623(a,1),53(a,2,2,2)),rewrite([7(4),53(11),12(11,R),8(10),5(12)])].
% 33.57/33.90 646 meet(A,join(one,meet(meet(A,B),join(A,C)))) = A. [back_rewrite(123),rewrite([636(10)])].
% 33.57/33.90 674 meet(A,join(complement(A),meet(A,join(B,join(complement(A),meet(A,join(C,meet(A,B)))))))) = meet(A,join(complement(A),meet(A,join(B,meet(A,join(B,C)))))). [para(26(a,1),65(a,2,2,2)),rewrite([8(7),12(7,R),8(6)])].
% 33.57/33.90 776 meet(complement(A),join(one,meet(B,complement(A)))) = complement(A). [para(106(a,1),646(a,1,2,2,2)),rewrite([7(4),7(6),10(6,R),18(5)])].
% 33.57/33.90 788 meet(complement(A),meet(join(one,meet(B,complement(A))),join(C,complement(A)))) = complement(A). [para(776(a,1),22(a,2)),rewrite([8(7)])].
% 33.57/33.90 829 meet(A,join(B,meet(meet(B,join(C,meet(A,B))),join(B,D)))) = meet(A,B). [para(7(a,1),68(a,2,2,2)),rewrite([68(11),10(12,R),22(12),6(11)])].
% 33.57/33.90 835 meet(A,join(B,meet(meet(B,join(zero,meet(A,B))),join(C,meet(A,B))))) = meet(A,B). [para(19(a,1),68(a,1,2,2,2,2,2,2,2)),rewrite([7(5),6(6),7(5),829(17)])].
% 33.57/33.90 931 join(A,meet(one,join(join(B,complement(A)),meet(A,C)))) = one. [para(51(a,1),101(a,1,2,1)),rewrite([51(10)])].
% 33.57/33.90 1021 join(complement(A),meet(one,join(join(A,B),meet(C,complement(A))))) = one. [para(79(a,1),931(a,1,2,2,1,2)),rewrite([8(3),7(5)])].
% 33.57/33.90 1161 join(one,meet(A,complement(B))) = one. [para(137(a,1),12(a,1)),rewrite([106(8),8(5)]),flip(a)].
% 33.57/33.90 1169 meet(complement(A),meet(one,join(B,complement(A)))) = complement(A). [back_rewrite(788),rewrite([1161(5)])].
% 33.57/33.90 1170 join(one,meet(A,B)) = one. [para(79(a,1),1161(a,1,2,2))].
% 33.57/33.90 1178 meet(A,join(B,meet(one,join(A,C)))) = A. [back_rewrite(644),rewrite([1170(5),49(3),7(3)])].
% 33.57/33.90 1185 meet(one,join(zero,meet(A,B))) = meet(A,B). [para(1170(a,1),519(a,1,2,2,2)),rewrite([7(5),10(5),7(4),18(4),7(3),10(8),7(7),18(7),7(6)])].
% 33.57/33.90 1292 meet(one,join(A,complement(B))) = join(A,complement(B)). [para(931(a,1),1178(a,1,2)),rewrite([7(4)])].
% 33.57/33.90 1297 meet(complement(A),join(B,complement(A))) = complement(A). [back_rewrite(1169),rewrite([1292(5)])].
% 33.57/33.90 1302 meet(complement(A),meet(join(B,complement(A)),join(C,complement(A)))) = complement(A). [para(1297(a,1),22(a,2)),rewrite([8(5)])].
% 33.57/33.90 1312 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(1185(a,1),10(a,1,2)),rewrite([18(7),7(6)]),flip(a)].
% 33.57/33.90 1330 meet(A,join(B,meet(A,B))) = meet(A,B). [back_rewrite(835),rewrite([1312(4),10(2,R),1(1),136(6),5(2)])].
% 33.57/33.90 1354 meet(one,join(A,B)) = join(A,B). [para(79(a,1),1292(a,1,2,2)),rewrite([79(5)])].
% 33.57/33.90 1355 join(A,join(complement(A),complement(B))) = one. [para(1292(a,1),106(a,1,2)),rewrite([12(4,R),8(3)])].
% 33.57/33.90 1381 join(complement(A),join(join(A,B),meet(C,complement(A)))) = one. [back_rewrite(1021),rewrite([1354(7)])].
% 33.57/33.90 1424 meet(A,meet(B,join(C,meet(A,C)))) = meet(A,meet(C,B)). [para(1330(a,1),10(a,2,2)),rewrite([7(3),10(6),7(5),10(6,R),7(5)])].
% 33.57/33.90 1426 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(22(a,1),1330(a,1,2,2)),rewrite([8(4),22(8)])].
% 33.57/33.90 1574 join(zero,meet(A,B)) = meet(A,B). [para(1312(a,1),1(a,1)),rewrite([7(5),1312(5),1(3)]),flip(a)].
% 33.57/33.90 1796 meet(A,join(B,meet(join(A,B),join(A,meet(B,C))))) = A. [para(6(a,1),473(a,1,2,2,2,2)),rewrite([7(4)])].
% 33.57/33.90 1924 meet(A,join(complement(A),meet(A,join(complement(A),meet(B,join(C,meet(A,C))))))) = meet(A,join(complement(A),meet(A,meet(B,C)))). [para(1424(a,1),65(a,2,2,2)),rewrite([8(6),7(11)])].
% 33.57/33.90 2031 meet(A,join(B,A)) = A. [para(1796(a,1),7(a,2)),rewrite([8(1),101(5),7(2)])].
% 33.57/33.90 2064 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(25(a,1),2031(a,1,2)),rewrite([8(3),7(4)])].
% 33.57/33.90 2141 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(8(a,1),2064(a,1,1))].
% 33.57/33.90 2147 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(23(a,1),2064(a,1,1)),rewrite([7(3),7(7)])].
% 33.57/33.90 2219 join(join(A,B),meet(A,C)) = join(A,B). [para(23(a,1),2141(a,1,1)),rewrite([5(5)]),flip(a)].
% 33.57/33.90 2343 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),2219(a,1,1)),rewrite([8(4)])].
% 33.57/33.90 2364 meet(meet(A,B),join(A,C)) = meet(A,B). [para(2219(a,1),2031(a,1,2))].
% 33.57/33.90 2367 meet(join(A,B),join(meet(A,C),meet(D,join(A,B)))) = join(meet(A,C),meet(D,join(A,B))). [para(2219(a,1),2141(a,1,1)),rewrite([7(4),7(9)])].
% 33.57/33.90 2446 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(25(a,1),2343(a,1,1)),rewrite([7(4),25(8)])].
% 33.57/33.90 2462 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(1574(a,1),2343(a,1,1)),rewrite([7(3),10(3),7(2),10(3,R),7(2),1574(7)])].
% 33.57/33.90 2487 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),2364(a,1,1)),rewrite([7(4)])].
% 33.57/33.90 2524 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(22(a,1),2487(a,1,1)),rewrite([8(4),22(8)])].
% 33.57/33.90 2836 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(6(a,1),2446(a,1,1)),rewrite([6(7)])].
% 33.57/33.90 2930 meet(A,join(complement(A),meet(A,meet(B,join(C,complement(A)))))) = meet(A,join(complement(A),meet(A,meet(C,B)))). [para(7(a,1),111(a,1,2,2)),rewrite([10(5),7(4),10(5,R),7(4),7(9)])].
% 33.57/33.90 2936 meet(A,join(complement(A),meet(A,join(complement(A),complement(B))))) = meet(A,join(complement(A),meet(A,complement(B)))). [para(108(a,1),111(a,2,2,2,2)),rewrite([18(3),8(4)])].
% 33.57/33.90 3098 meet(A,meet(meet(A,B),complement(C))) = meet(A,meet(B,complement(C))). [para(503(a,1),116(a,1,2,2,2)),rewrite([1574(5),503(8),1574(9),20(8)])].
% 33.57/33.90 3317 meet(A,meet(B,join(C,meet(A,meet(D,join(E,meet(A,C))))))) = meet(A,meet(B,join(C,meet(A,meet(D,join(C,E)))))). [para(7(a,1),117(a,1,2,2,2)),rewrite([10(4),7(3),10(4,R),7(3)])].
% 33.57/33.90 3463 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(4(a,1),3098(a,1,2)),rewrite([40(2)]),flip(a)].
% 33.57/33.90 3464 meet(A,meet(join(A,B),complement(C))) = meet(A,complement(C)). [para(5(a,1),3098(a,1,2,1)),rewrite([20(3)]),flip(a)].
% 33.57/33.90 3514 meet(A,join(complement(A),meet(A,meet(B,join(complement(A),complement(C)))))) = meet(A,join(complement(A),meet(A,meet(B,complement(C))))). [para(3098(a,1),111(a,2,2,2)),rewrite([20(3),8(5),116(8)])].
% 33.57/33.90 3737 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(3463(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),40(7)])].
% 33.57/33.90 4124 meet(A,meet(B,meet(C,complement(meet(A,C))))) = zero. [para(3737(a,1),7(a,1)),rewrite([7(2),7(6),10(6,R),7(5),10(5,R),7(4)]),flip(a)].
% 33.57/33.90 4202 meet(A,meet(B,meet(C,complement(meet(A,meet(B,C)))))) = zero. [para(3098(a,1),4124(a,1,2))].
% 33.57/33.90 4208 meet(A,complement(join(A,B))) = zero. [para(4(a,1),3464(a,1,2)),rewrite([40(2)]),flip(a)].
% 33.57/33.90 4236 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(3464(a,1),4124(a,1,2))].
% 33.57/33.90 4303 meet(A,meet(B,complement(join(A,C)))) = zero. [para(4208(a,1),10(a,2,2)),rewrite([7(3),40(6)])].
% 33.57/33.90 4309 join(A,join(join(B,C),complement(join(A,B)))) = one. [para(4208(a,1),1381(a,1,2,2)),rewrite([8(4),12(4),8(3),12(4,R),8(3),8(6),12(6,R),8(5),12(5),8(4),19(4),8(3),12(5,R)])].
% 33.57/33.90 4315 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(4208(a,1),3098(a,1,2)),rewrite([40(2),8(3)]),flip(a)].
% 33.57/33.90 4321 meet(A,join(complement(A),meet(A,join(complement(A),meet(B,complement(join(A,C))))))) = zero. [para(4303(a,1),65(a,2,2,2)),rewrite([8(6),19(12),4(11)])].
% 33.57/33.90 4333 meet(A,meet(B,complement(meet(B,join(A,C))))) = zero. [para(4236(a,1),10(a,2)),rewrite([7(4)])].
% 33.57/33.90 4355 join(A,join(join(B,C),complement(join(B,A)))) = one. [para(4309(a,1),8(a,1)),rewrite([8(3),8(6)]),flip(a)].
% 33.57/33.90 4356 join(A,join(join(B,C),complement(join(A,C)))) = one. [para(8(a,1),4309(a,1,2,1))].
% 33.57/33.90 4660 meet(A,meet(complement(join(B,C)),join(B,meet(C,D)))) = zero. [para(2446(a,1),4315(a,1,2,2,1)),rewrite([8(3),7(5)])].
% 33.57/33.90 4821 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(4333(a,1),3464(a,1)),flip(a)].
% 33.57/33.90 4826 meet(meet(A,join(B,C)),join(B,meet(A,meet(join(B,C),join(C,meet(A,B)))))) = meet(A,join(B,C)). [para(1(a,1),135(a,2,2,2)),rewrite([7(7),22(7),7(5),10(8),7(7),20(7),10(7),7(6),10(7,R),7(6),2031(15)])].
% 33.57/33.90 4975 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(6(a,1),4356(a,1,2,1))].
% 33.57/33.90 5753 join(A,complement(meet(A,B))) = one. [hyper(72,a,618,a,b,4975,a),rewrite([1574(3),1574(8),618(9),19(6),7(5),40(5),8(5),12(5,R),8(4),503(4),52(5)])].
% 33.57/33.90 5755 join(join(A,B),complement(join(A,meet(B,C)))) = one. [para(4975(a,1),12(a,1)),rewrite([8(6)]),flip(a)].
% 33.57/33.90 5765 join(join(A,B),complement(join(B,meet(A,C)))) = one. [para(2141(a,1),5753(a,1,2,1))].
% 33.57/33.90 5915 meet(join(A,B),join(C,meet(A,C))) = meet(C,join(A,B)). [para(6(a,1),144(a,2,2,2,2)),rewrite([2836(7),7(2)]),flip(a)].
% 33.57/33.90 6121 join(join(A,B),complement(join(A,meet(C,join(A,B))))) = one. [para(23(a,1),5755(a,1,1)),rewrite([7(3)])].
% 33.57/33.90 6128 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [para(1574(a,1),5755(a,1,1)),rewrite([7(4),10(4),7(3),10(4,R),7(3),1574(5)])].
% 33.57/33.90 6251 join(A,complement(join(meet(A,B),meet(A,C)))) = one. [para(6(a,1),5765(a,1,1))].
% 33.57/33.90 6405 join(join(A,B),complement(meet(C,join(A,B)))) = one. [para(1354(a,1),6128(a,1,1)),rewrite([7(4),10(5,R),7(4),1354(4)])].
% 33.57/33.90 6527 join(A,join(complement(meet(B,C)),meet(B,join(C,D)))) = one. [para(2524(a,1),6405(a,1,2,1)),rewrite([7(4),8(6),12(6,R),8(5)])].
% 33.57/33.90 6529 join(A,join(join(B,C),complement(meet(D,join(A,B))))) = one. [para(6405(a,1),4355(a,1,2,2,1)),rewrite([8(5),12(5),8(4),12(5,R),8(4),43(7),8(7),12(7,R),8(6),12(6),8(5),19(5),8(4),12(6,R)])].
% 33.57/33.90 8493 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [hyper(17,a,4660,a,b,1170,a),rewrite([43(2)]),flip(a)].
% 33.57/33.90 8506 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),8493(a,1,1,1))].
% 33.57/33.90 10405 join(join(A,B),complement(join(B,meet(C,join(A,B))))) = one. [para(8(a,1),6121(a,1,1)),rewrite([8(2)])].
% 33.57/33.90 10500 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [hyper(17,a,8506,a,b,6527,a),rewrite([5753(3),43(2),52(2)]),flip(a)].
% 33.57/33.90 10551 join(complement(meet(A,B)),meet(A,join(C,meet(A,B)))) = one. [para(20(a,1),10500(a,1,1,1)),rewrite([8(4)])].
% 33.57/33.90 10784 join(A,join(B,complement(meet(C,join(A,B))))) = one. [para(2(a,1),6529(a,1,2,1))].
% 33.57/33.90 11052 meet(meet(A,B),join(meet(B,join(C,meet(A,B))),meet(A,join(meet(A,B),meet(B,join(C,meet(A,B))))))) = meet(A,B). [para(2524(a,1),217(a,1,1)),rewrite([8(3),1330(4),8(7),6(7),8(7),1330(8),10(9,R),7(8),2462(10),20(6),8(6),5(7),2364(6),8(4),1330(5),8(8),1330(9)]),flip(a)].
% 33.57/33.90 12740 join(complement(meet(A,B)),meet(B,join(C,meet(A,B)))) = one. [para(7(a,1),10551(a,1,1,1)),rewrite([7(3)])].
% 33.57/33.90 18171 join(A,meet(B,A)) = A. [para(3(a,1),5915(a,2,2)),rewrite([3(2),1354(4),18(4)])].
% 33.57/33.90 18172 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(10(a,1),5915(a,1,2,2)),rewrite([10(4),7(3),10(4,R),7(3),18171(5),10(3),7(2),10(3,R),7(2)]),flip(a)].
% 33.57/33.90 18272 meet(A,join(complement(A),meet(A,join(complement(A),meet(B,C))))) = meet(A,join(complement(A),meet(A,meet(B,C)))). [back_rewrite(1924),rewrite([18171(4)])].
% 33.57/33.90 18439 meet(A,meet(B,join(meet(B,join(C,meet(A,B))),meet(A,join(meet(A,B),meet(B,join(C,meet(A,B)))))))) = meet(A,B). [back_rewrite(11052),rewrite([18172(12)])].
% 33.57/33.90 18526 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [back_rewrite(4826),rewrite([18172(9),3317(9),1(4),2147(5)])].
% 33.57/33.90 18632 meet(A,join(complement(A),meet(B,complement(join(A,C))))) = zero. [back_rewrite(4321),rewrite([18526(9)])].
% 33.57/33.90 18646 meet(A,join(complement(A),meet(A,meet(B,C)))) = meet(A,join(complement(A),meet(B,C))). [back_rewrite(18272),rewrite([18526(7)]),flip(a)].
% 33.57/33.90 18721 meet(A,join(complement(A),meet(A,complement(B)))) = meet(A,join(complement(A),complement(B))). [back_rewrite(2936),rewrite([18526(7)]),flip(a)].
% 33.57/33.90 18743 meet(A,join(complement(A),meet(A,join(B,join(complement(A),meet(A,join(C,meet(A,B)))))))) = meet(A,join(complement(A),meet(A,join(B,C)))). [back_rewrite(674),rewrite([18526(15)])].
% 33.57/33.90 18760 meet(A,join(complement(A),meet(B,join(complement(A),complement(C))))) = meet(A,join(complement(A),meet(B,complement(C)))). [back_rewrite(3514),rewrite([18646(8),18646(13)])].
% 33.57/33.90 18763 meet(A,join(complement(A),meet(B,join(C,complement(A))))) = meet(A,join(complement(A),meet(B,C))). [back_rewrite(2930),rewrite([18646(7),7(8),18646(11)])].
% 33.57/33.90 19256 meet(A,join(complement(A),complement(join(A,B)))) = zero. [para(1(a,1),18632(a,1,2,2))].
% 33.57/33.90 19265 join(complement(A),complement(join(A,B))) = complement(A). [hyper(17,a,19256,a,b,1355,a),flip(a)].
% 33.57/33.90 19274 join(A,complement(join(B,complement(A)))) = A. [para(79(a,1),19265(a,1,1)),rewrite([8(2),79(6)])].
% 33.57/33.90 19275 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(19265(a,1),1302(a,1,2,1)),rewrite([10(8,R),7(7),2031(7)])].
% 33.57/33.90 19475 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(19275(a,1),4315(a,1,2))].
% 33.57/33.90 19524 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [hyper(408,a,19475,a,b,6251,a),flip(a)].
% 33.57/33.90 19529 meet(A,complement(join(complement(B),meet(A,B)))) = zero. [para(79(a,1),19475(a,1,2,1,2,2))].
% 33.57/33.90 19546 meet(A,complement(join(complement(B),meet(B,A)))) = zero. [para(19529(a,1),7(a,1)),rewrite([7(3),7(6)]),flip(a)].
% 33.57/33.90 19571 join(complement(A),meet(A,join(B,complement(A)))) = join(B,complement(A)). [hyper(408,a,19546,a,b,10405,a),flip(a)].
% 33.57/33.90 19676 join(meet(A,B),meet(B,complement(meet(A,B)))) = B. [para(7(a,1),19524(a,1,1)),rewrite([7(2)])].
% 33.57/33.90 19699 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(19524(a,1),19265(a,1,2,1)),rewrite([8(4)])].
% 33.57/33.90 19702 meet(complement(A),complement(meet(A,B))) = complement(A). [para(19524(a,1),19275(a,1,2,1)),rewrite([7(4),19524(9)])].
% 33.57/33.90 19708 meet(A,complement(meet(B,complement(A)))) = A. [para(79(a,1),19702(a,1,1)),rewrite([7(2),79(6)])].
% 33.57/33.90 19944 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(5(a,1),19676(a,1,1)),rewrite([5(3),7(3)])].
% 33.57/33.90 19948 join(meet(A,B),meet(B,meet(join(A,C),complement(meet(A,B))))) = meet(B,join(A,C)). [para(22(a,1),19676(a,1,1)),rewrite([22(6),7(6),10(6,R)])].
% 33.57/33.90 19966 join(A,complement(join(meet(B,A),meet(A,C)))) = one. [para(19676(a,1),6121(a,1,2,1,2,2)),rewrite([19676(5),7(2)])].
% 33.57/33.90 20038 join(A,complement(meet(B,join(A,complement(B))))) = one. [para(19699(a,1),10784(a,1,2))].
% 33.57/33.90 20089 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(408,a,4821,a,b,20038,a),flip(a)].
% 33.57/33.90 20433 meet(A,join(complement(A),meet(A,B))) = meet(A,B). [para(19524(a,1),20089(a,1,1)),rewrite([19524(6),8(3)])].
% 33.57/33.90 20958 meet(A,join(B,join(complement(A),meet(A,join(C,meet(A,B)))))) = meet(A,join(B,C)). [back_rewrite(18743),rewrite([20433(10),20433(12)])].
% 33.57/33.90 20960 meet(A,join(complement(A),complement(B))) = meet(A,complement(B)). [back_rewrite(18721),rewrite([20433(5)]),flip(a)].
% 33.57/33.90 20961 meet(A,join(complement(A),meet(B,C))) = meet(A,meet(B,C)). [back_rewrite(18646),rewrite([20433(5)]),flip(a)].
% 33.57/33.90 20977 meet(A,meet(B,join(C,complement(A)))) = meet(A,meet(B,C)). [back_rewrite(18763),rewrite([20961(6),20961(8)])].
% 33.57/33.90 20979 meet(A,meet(B,join(complement(A),complement(C)))) = meet(A,meet(B,complement(C))). [back_rewrite(18760),rewrite([20961(7),20961(10)])].
% 33.57/33.90 21377 meet(A,join(B,complement(A))) = meet(A,B). [para(79(a,1),20960(a,1,2,2)),rewrite([8(2),79(5)])].
% 33.57/33.90 21424 join(complement(A),meet(A,B)) = join(B,complement(A)). [back_rewrite(19571),rewrite([21377(4)])].
% 33.57/33.90 21444 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [back_rewrite(20958),rewrite([21424(5),8(4),12(4,R),8(3),21424(3),12(3,R),8(2),23(4)])].
% 33.57/33.90 21460 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(79(a,1),21377(a,1,2,2)),rewrite([8(2),7(5)])].
% 33.57/33.90 21465 meet(join(A,complement(B)),join(B,meet(A,join(C,meet(A,B))))) = meet(join(A,complement(B)),join(B,meet(A,join(B,C)))). [para(21377(a,1),144(a,1,2,2,2,2)),rewrite([7(3)])].
% 33.57/33.90 21476 meet(A,join(meet(B,A),meet(A,C))) = join(meet(B,A),meet(A,C)). [para(19966(a,1),21377(a,1,2)),rewrite([7(5),1354(5),7(7)]),flip(a)].
% 33.57/33.90 21501 join(A,meet(B,complement(A))) = join(A,B). [back_rewrite(19944),rewrite([21460(3)])].
% 33.57/33.90 21605 join(complement(A),meet(B,A)) = join(B,complement(A)). [para(21424(a,1),8(a,1)),rewrite([7(3),8(5)]),flip(a)].
% 33.57/33.90 21608 join(complement(A),meet(B,join(A,C))) = join(B,complement(A)). [para(22(a,1),21424(a,1,2)),rewrite([21424(3),8(6)]),flip(a)].
% 33.57/33.90 21676 join(meet(A,B),complement(join(A,complement(B)))) = B. [para(19274(a,1),21424(a,2)),rewrite([7(6),21377(6),7(4),8(5)])].
% 33.57/33.90 21779 meet(complement(A),join(B,meet(A,C))) = meet(B,complement(A)). [para(25(a,1),21460(a,1,2)),rewrite([21460(3),7(6)]),flip(a)].
% 33.57/33.90 21861 meet(join(A,B),complement(meet(A,complement(B)))) = B. [para(19708(a,1),21460(a,2)),rewrite([8(6),21501(6),8(4),7(5)])].
% 33.57/33.90 21877 join(meet(A,B),complement(join(meet(A,B),meet(B,join(A,C))))) = join(A,complement(join(meet(A,B),meet(B,join(A,C))))). [para(1426(a,1),21605(a,1,2)),rewrite([8(7)])].
% 33.57/33.90 21957 join(meet(A,B),complement(join(A,complement(meet(B,join(A,C)))))) = meet(B,join(A,C)). [para(22(a,1),21676(a,1,1))].
% 33.57/33.90 21960 join(meet(A,B),complement(join(A,complement(join(meet(A,B),meet(B,join(A,C))))))) = join(meet(A,B),meet(B,join(A,C))). [para(1426(a,1),21676(a,1,1))].
% 33.57/33.90 21973 complement(join(A,complement(meet(B,meet(C,complement(meet(A,meet(B,C)))))))) = meet(B,meet(C,complement(meet(A,meet(B,C))))). [para(4202(a,1),21676(a,1,1)),rewrite([503(10)])].
% 33.57/33.90 22001 join(A,complement(join(A,B))) = complement(meet(B,complement(A))). [para(19708(a,1),21676(a,1,1)),rewrite([79(4),21501(3)])].
% 33.57/33.90 22009 join(A,complement(join(meet(A,B),meet(B,join(A,C))))) = complement(meet(B,meet(join(A,C),complement(meet(A,B))))). [back_rewrite(21877),rewrite([22001(7),7(5),10(5,R)]),flip(a)].
% 33.57/33.90 22050 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [back_rewrite(21960),rewrite([22009(7),79(8),19948(7)]),flip(a)].
% 33.57/33.90 22051 complement(meet(A,meet(join(B,C),complement(meet(B,A))))) = join(B,complement(meet(A,join(B,C)))). [back_rewrite(22009),rewrite([22050(4)]),flip(a)].
% 33.57/33.90 22131 meet(A,complement(meet(A,complement(B)))) = meet(A,B). [para(21861(a,1),3464(a,1,2)),flip(a)].
% 33.57/33.90 22148 complement(meet(complement(meet(A,B)),complement(meet(B,join(C,meet(A,B)))))) = meet(B,join(C,meet(A,B))). [para(12740(a,1),21861(a,1,1)),rewrite([108(10)])].
% 33.57/33.90 22160 meet(A,complement(meet(A,B))) = complement(join(B,complement(A))). [para(19274(a,1),21861(a,1,1)),rewrite([79(4),21377(3)])].
% 33.57/33.90 22166 complement(join(complement(A),complement(B))) = meet(A,B). [back_rewrite(22131),rewrite([22160(4),8(3)])].
% 33.57/33.90 22217 complement(meet(A,B)) = join(complement(A),complement(B)). [para(22166(a,1),79(a,1,1))].
% 33.57/33.90 22218 complement(join(A,complement(B))) = meet(B,complement(A)). [para(79(a,1),22166(a,1,1,1)),rewrite([7(5)])].
% 33.57/33.90 22290 join(meet(A,B),meet(B,complement(A))) = B. [para(22166(a,1),21676(a,1,2)),rewrite([7(2),8(4)])].
% 33.57/33.90 22310 join(meet(A,B),meet(B,join(C,meet(A,B)))) = meet(B,join(C,meet(A,B))). [back_rewrite(22148),rewrite([22217(2),22217(7),22217(10),22218(4),79(2),7(1),22218(7),79(5),7(4)])].
% 33.57/33.90 22341 join(A,join(complement(B),complement(join(A,C)))) = join(A,join(complement(B),complement(C))). [back_rewrite(22051),rewrite([7(2),22217(3),20979(6),7(3),21460(3),22217(4),22217(4),79(4),8(3),12(4,R),8(3),22217(7)]),flip(a)].
% 33.57/33.90 22365 complement(join(A,join(complement(B),complement(C)))) = meet(B,meet(C,complement(A))). [back_rewrite(21973),rewrite([22217(3),22217(3),21444(6),20977(5),22217(4),22217(4),79(4),8(3),12(4,R),8(3),23(5),22217(8),22217(8),21444(11),20977(10)])].
% 33.57/33.90 22372 join(meet(A,B),meet(B,meet(C,complement(A)))) = meet(B,join(A,C)). [back_rewrite(21957),rewrite([22217(4),22341(6),22365(6)])].
% 33.57/33.90 22390 meet(join(A,B),join(B,complement(A))) = B. [back_rewrite(21861),rewrite([22217(4),79(4),8(3)])].
% 33.57/33.90 24482 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [back_rewrite(18439),rewrite([22310(8),18171(8),20(4)])].
% 33.57/33.90 29263 meet(join(A,complement(B)),join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(21608(a,1),22390(a,1,1)),rewrite([79(6),8(5)])].
% 33.57/33.90 29289 meet(join(A,complement(B)),join(B,meet(A,join(C,meet(A,B))))) = meet(A,join(B,C)). [back_rewrite(21465),rewrite([29263(13)])].
% 33.57/33.90 30107 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(24482(a,1),18171(a,1,2)),rewrite([7(1),7(4),8(5),7(6)])].
% 33.57/33.90 30118 meet(A,join(B,meet(C,A))) = meet(A,join(C,B)). [para(24482(a,1),22290(a,1,1)),rewrite([7(6),10(6,R),7(5),21779(5),22372(5)]),flip(a)].
% 33.57/33.90 30205 meet(join(A,B),join(C,meet(A,D))) = join(meet(A,D),meet(C,join(A,B))). [back_rewrite(2367),rewrite([30118(6)])].
% 33.57/33.90 30325 meet(A,join(B,meet(A,C))) = meet(A,join(C,B)). [back_rewrite(29289),rewrite([30205(7),21377(6),7(4),8(5),30107(5)])].
% 33.57/33.90 30922 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(21476),rewrite([7(1),30325(4),30325(3),7(3)]),flip(a)].
% 33.57/33.90 30923 $F # answer(prove_distributivity). [resolve(30922,a,16,a)].
% 33.57/33.90
% 33.57/33.90 % SZS output end Refutation
% 33.57/33.90 ============================== end of proof ==========================
% 33.57/33.90
% 33.57/33.90 ============================== STATISTICS ============================
% 33.57/33.90
% 33.57/33.90 Given=980. Generated=699136. Kept=30918. proofs=1.
% 33.57/33.90 Usable=217. Sos=4900. Demods=3979. Limbo=597, Disabled=25216. Hints=0.
% 33.57/33.90 Megabytes=37.49.
% 33.57/33.90 User_CPU=32.53, System_CPU=0.37, Wall_clock=33.
% 33.57/33.90
% 33.57/33.90 ============================== end of statistics =====================
% 33.57/33.90
% 33.57/33.90 ============================== end of search =========================
% 33.57/33.90
% 33.57/33.90 THEOREM PROVED
% 33.57/33.90 % SZS status Unsatisfiable
% 33.57/33.90
% 33.57/33.90 Exiting with 1 proof.
% 33.57/33.90
% 33.57/33.90 Process 5715 exit (max_proofs) Wed Jun 29 13:51:48 2022
% 33.57/33.90 Prover9 interrupted
%------------------------------------------------------------------------------