TSTP Solution File: LAT208-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT208-1 : 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 06:26:08 EDT 2022
% Result : Unsatisfiable 70.22s 70.57s
% Output : Refutation 70.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT208-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.35 % Computer : n007.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 600
% 0.12/0.35 % DateTime : Tue Jun 28 22:32:37 EDT 2022
% 0.12/0.35 % CPUTime :
% 17.62/17.91 ============================== Prover9 ===============================
% 17.62/17.91 Prover9 (32) version 2009-11A, November 2009.
% 17.62/17.91 Process 24099 was started by sandbox on n007.cluster.edu,
% 17.62/17.91 Tue Jun 28 22:32:37 2022
% 17.62/17.91 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23727_n007.cluster.edu".
% 17.62/17.91 ============================== end of head ===========================
% 17.62/17.91
% 17.62/17.91 ============================== INPUT =================================
% 17.62/17.91
% 17.62/17.91 % Reading from file /tmp/Prover9_23727_n007.cluster.edu
% 17.62/17.91
% 17.62/17.91 set(prolog_style_variables).
% 17.62/17.91 set(auto2).
% 17.62/17.91 % set(auto2) -> set(auto).
% 17.62/17.91 % set(auto) -> set(auto_inference).
% 17.62/17.91 % set(auto) -> set(auto_setup).
% 17.62/17.91 % set(auto_setup) -> set(predicate_elim).
% 17.62/17.91 % set(auto_setup) -> assign(eq_defs, unfold).
% 17.62/17.91 % set(auto) -> set(auto_limits).
% 17.62/17.91 % set(auto_limits) -> assign(max_weight, "100.000").
% 17.62/17.91 % set(auto_limits) -> assign(sos_limit, 20000).
% 17.62/17.91 % set(auto) -> set(auto_denials).
% 17.62/17.91 % set(auto) -> set(auto_process).
% 17.62/17.91 % set(auto2) -> assign(new_constants, 1).
% 17.62/17.91 % set(auto2) -> assign(fold_denial_max, 3).
% 17.62/17.91 % set(auto2) -> assign(max_weight, "200.000").
% 17.62/17.91 % set(auto2) -> assign(max_hours, 1).
% 17.62/17.91 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 17.62/17.91 % set(auto2) -> assign(max_seconds, 0).
% 17.62/17.91 % set(auto2) -> assign(max_minutes, 5).
% 17.62/17.91 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 17.62/17.91 % set(auto2) -> set(sort_initial_sos).
% 17.62/17.91 % set(auto2) -> assign(sos_limit, -1).
% 17.62/17.91 % set(auto2) -> assign(lrs_ticks, 3000).
% 17.62/17.91 % set(auto2) -> assign(max_megs, 400).
% 17.62/17.91 % set(auto2) -> assign(stats, some).
% 17.62/17.91 % set(auto2) -> clear(echo_input).
% 17.62/17.91 % set(auto2) -> set(quiet).
% 17.62/17.91 % set(auto2) -> clear(print_initial_clauses).
% 17.62/17.91 % set(auto2) -> clear(print_given).
% 17.62/17.91 assign(lrs_ticks,-1).
% 17.62/17.91 assign(sos_limit,10000).
% 17.62/17.91 assign(order,kbo).
% 17.62/17.91 set(lex_order_vars).
% 17.62/17.91 clear(print_given).
% 17.62/17.91
% 17.62/17.91 % formulas(sos). % not echoed (13 formulas)
% 17.62/17.91
% 17.62/17.91 ============================== end of input ==========================
% 17.62/17.91
% 17.62/17.91 % From the command line: assign(max_seconds, 300).
% 17.62/17.91
% 17.62/17.91 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 17.62/17.91
% 17.62/17.91 % Formulas that are not ordinary clauses:
% 17.62/17.91
% 17.62/17.91 ============================== end of process non-clausal formulas ===
% 17.62/17.91
% 17.62/17.91 ============================== PROCESS INITIAL CLAUSES ===============
% 17.62/17.91
% 17.62/17.91 ============================== PREDICATE ELIMINATION =================
% 17.62/17.91
% 17.62/17.91 ============================== end predicate elimination =============
% 17.62/17.91
% 17.62/17.91 Auto_denials:
% 17.62/17.91 % copying label prove_distributivity to answer in negative clause
% 17.62/17.91
% 17.62/17.91 Term ordering decisions:
% 17.62/17.91
% 17.62/17.91 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 17.62/17.91 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. join=1. meet=1. complement=0.
% 17.62/17.91
% 17.62/17.91 ============================== end of process initial clauses ========
% 17.62/17.91
% 17.62/17.91 ============================== CLAUSES FOR SEARCH ====================
% 17.62/17.91
% 17.62/17.91 ============================== end of clauses for search =============
% 17.62/17.91
% 17.62/17.91 ============================== SEARCH ================================
% 17.62/17.91
% 17.62/17.91 % Starting search at 0.01 seconds.
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=62.000, iters=3366
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=59.000, iters=3346
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=58.000, iters=3343
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=54.000, iters=3334
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=53.000, iters=3358
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=51.000, iters=3349
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=50.000, iters=3363
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=48.000, iters=3333
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=47.000, iters=3370
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=46.000, iters=3335
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=45.000, iters=3350
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=43.000, iters=3378
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=42.000, iters=3383
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=41.000, iters=3351
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=39.000, iters=3337
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=38.000, iters=3371
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=37.000, iters=3411
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=36.000, iters=3335
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=35.000, iters=3334
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=34.000, iters=3336
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=33.000, iters=3354
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=32.000, iters=3349
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=31.000, iters=3339
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=30.000, iters=3335
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=29.000, iters=3360
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=28.000, iters=3355
% 17.62/17.91
% 17.62/17.91 Low Water (keep): wt=27.000, iters=3369
% 70.22/70.57
% 70.22/70.57 Low Water (keep): wt=26.000, iters=3336
% 70.22/70.57
% 70.22/70.57 Low Water (keep): wt=25.000, iters=3338
% 70.22/70.57
% 70.22/70.57 Low Water (keep): wt=24.000, iters=3336
% 70.22/70.57
% 70.22/70.57 Low Water (keep): wt=23.000, iters=3339
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=6222, wt=99.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=6226, wt=89.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=6596, wt=87.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=6220, wt=83.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=4340, wt=81.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=6594, wt=79.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=6286, wt=78.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=6211, wt=77.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=6195, wt=75.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=17699, wt=22.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=17739, wt=21.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=17756, wt=20.000
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=17820, wt=18.000
% 70.22/70.57
% 70.22/70.57 Low Water (keep): wt=22.000, iters=3341
% 70.22/70.57
% 70.22/70.57 Low Water (displace): id=18583, wt=16.000
% 70.22/70.57
% 70.22/70.57 Low Water (keep): wt=21.000, iters=3333
% 70.22/70.57
% 70.22/70.57 ============================== PROOF =================================
% 70.22/70.57 % SZS status Unsatisfiable
% 70.22/70.57 % SZS output start Refutation
% 70.22/70.57
% 70.22/70.57 % Proof 1 at 68.58 (+ 0.97) seconds: prove_distributivity.
% 70.22/70.57 % Length of proof is 235.
% 70.22/70.57 % Level of proof is 73.
% 70.22/70.57 % Maximum clause weight is 35.000.
% 70.22/70.57 % Given clauses 1360.
% 70.22/70.57
% 70.22/70.57 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 70.22/70.57 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 70.22/70.57 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 70.22/70.57 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 70.22/70.57 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 70.22/70.57 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 70.22/70.57 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 70.22/70.57 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 70.22/70.57 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 70.22/70.57 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 70.22/70.57 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 70.22/70.57 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 70.22/70.57 13 meet(A,meet(join(B,C),join(B,D))) = meet(A,join(B,meet(join(B,C),join(D,meet(B,C))))) # label(equation_H63) # label(axiom). [assumption].
% 70.22/70.57 14 meet(A,join(B,meet(join(B,C),join(D,meet(B,C))))) = meet(A,meet(join(B,C),join(B,D))). [copy(13),flip(a)].
% 70.22/70.57 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 70.22/70.57 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 70.22/70.57 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 70.22/70.57 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 70.22/70.57 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 70.22/70.57 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)])].
% 70.22/70.57 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 70.22/70.57 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 70.22/70.57 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)])].
% 70.22/70.57 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 70.22/70.57 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 70.22/70.57 26 join(A,meet(join(A,B),join(C,meet(A,B)))) = meet(join(A,B),join(A,C)). [para(14(a,1),1(a,1)),rewrite([7(9),14(9),1(7)]),flip(a)].
% 70.22/70.57 32 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(7(a,1),17(a,1)),rewrite([8(4)])].
% 70.22/70.57 33 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)])].
% 70.22/70.57 34 meet(A,meet(B,C)) != zero | join(C,meet(A,B)) != one | complement(C) = meet(A,B). [para(10(a,2),17(a,1))].
% 70.22/70.57 36 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 70.22/70.57 38 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([36(5)])].
% 70.22/70.57 39 complement(one) = zero. [hyper(17,a,36,a,b,19,a)].
% 70.22/70.57 40 one != A | complement(A) = zero. [para(36(a,1),17(a,1)),rewrite([19(5)]),flip(b),xx(a)].
% 70.22/70.57 41 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)])].
% 70.22/70.57 42 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)].
% 70.22/70.57 43 complement(join(A,one)) = zero. [hyper(40,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 70.22/70.57 45 join(A,one) = one. [para(43(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 70.22/70.57 47 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([45(5)])].
% 70.22/70.57 48 complement(zero) = one. [hyper(17,a,18,a,b,45,a)].
% 70.22/70.57 49 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(38(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),36(6)])].
% 70.22/70.57 51 join(A,join(B,join(C,complement(A)))) = one. [para(47(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),45(6)])].
% 70.22/70.57 52 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)])].
% 70.22/70.57 55 join(A,join(B,join(C,join(D,complement(A))))) = one. [para(51(a,1),12(a,2,2)),rewrite([8(4),12(4,R),8(3),12(3,R),8(2),45(7)])].
% 70.22/70.57 58 join(A,join(B,join(C,join(D,join(E,complement(A)))))) = one. [para(55(a,1),12(a,2,2)),rewrite([8(5),12(5,R),8(4),12(4,R),8(3),12(3,R),8(2),45(8)])].
% 70.22/70.57 59 meet(one,join(A,B)) = join(A,B). [para(3(a,1),26(a,1,2,1)),rewrite([4(3),19(3),7(2),18(2),3(3)]),flip(a)].
% 70.22/70.57 60 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(5(a,1),26(a,1,2,2,2)),rewrite([23(2),8(2),23(6)])].
% 70.22/70.57 61 join(A,join(B,meet(join(A,C),join(D,meet(A,C))))) = join(B,meet(join(A,C),join(A,D))). [para(26(a,1),12(a,2,2)),rewrite([8(5)])].
% 70.22/70.57 63 meet(join(A,meet(B,complement(A))),join(A,C)) = join(A,meet(C,join(A,meet(B,complement(A))))). [para(38(a,1),26(a,1,2,2,2)),rewrite([19(5),7(4)]),flip(a)].
% 70.22/70.57 64 join(A,meet(join(A,B),join(C,meet(A,join(B,meet(A,D)))))) = meet(join(A,B),join(A,C)). [para(25(a,1),26(a,1,2,1)),rewrite([25(10)])].
% 70.22/70.57 65 meet(join(A,meet(B,meet(C,complement(A)))),join(A,D)) = join(A,meet(D,join(A,meet(B,meet(C,complement(A)))))). [para(49(a,1),26(a,1,2,2,2)),rewrite([19(6),7(5)]),flip(a)].
% 70.22/70.57 68 join(join(A,B),meet(meet(join(A,B),join(A,C)),join(C,join(join(A,B),meet(A,B))))) = meet(join(A,B),join(C,join(join(A,B),meet(A,B)))). [para(26(a,1),26(a,1,2,2)),rewrite([12(5,R),8(4),7(9),12(14,R),8(13),8(16),23(16),7(16)])].
% 70.22/70.57 69 meet(one,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(26(a,1),59(a,1,2)),rewrite([26(10)])].
% 70.22/70.57 71 complement(complement(A)) = A. [hyper(32,a,4,a,b,3,a)].
% 70.22/70.57 72 zero != A | join(A,B) != one | complement(join(A,B)) = A. [para(5(a,1),32(a,1)),rewrite([23(4)]),flip(a)].
% 70.22/70.57 75 meet(A,B) != zero | one != A | complement(meet(A,B)) = A. [para(20(a,1),32(a,1)),rewrite([6(5)]),flip(b)].
% 70.22/70.57 96 join(A,join(B,join(C,join(D,join(E,join(F,complement(A))))))) = one. [para(58(a,1),12(a,2,2)),rewrite([8(6),12(6,R),8(5),12(5,R),8(4),12(4,R),8(3),12(3,R),8(2),45(9)])].
% 70.22/70.57 122 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(41(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)])].
% 70.22/70.57 132 meet(A,B) != zero | one != B | complement(meet(A,B)) = B. [para(7(a,1),75(a,1)),rewrite([7(6)])].
% 70.22/70.57 153 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(52(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)])].
% 70.22/70.57 170 join(one,meet(join(A,B),join(A,C))) = one. [para(69(a,1),6(a,1,2))].
% 70.22/70.57 179 join(one,meet(join(A,B),join(B,C))) = one. [para(8(a,1),170(a,1,2,1))].
% 70.22/70.57 185 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(61(a,1),5(a,1,2))].
% 70.22/70.57 209 join(one,meet(A,B)) = one. [para(19(a,1),179(a,1,2,1)),rewrite([8(3),19(3)])].
% 70.22/70.57 210 meet(zero,join(A,meet(B,C))) = zero. [hyper(72,a,185,a(flip),b,96,a),rewrite([8(3),19(3),8(3),19(3),8(7),19(7),8(7),19(7),96(15),39(2),8(4),19(4),8(4),19(4)]),flip(a)].
% 70.22/70.57 220 meet(zero,join(A,B)) = zero. [para(1(a,1),210(a,1,2,2))].
% 70.22/70.57 248 join(zero,meet(A,join(B,C))) = meet(A,join(B,C)). [para(220(a,1),26(a,1,2,2,2)),rewrite([12(4),8(3),19(3),8(2),19(4),7(3),12(7),8(6),19(6),8(5),8(7),19(7),7(6)])].
% 70.22/70.57 265 join(zero,meet(A,B)) = meet(A,B). [para(2(a,1),248(a,1,2,2)),rewrite([2(4)])].
% 70.22/70.57 271 join(A,meet(meet(A,B),join(A,meet(C,complement(A))))) = A. [para(6(a,1),63(a,1,2)),rewrite([7(4),5(4)]),flip(a)].
% 70.22/70.57 272 meet(join(A,B),join(A,meet(C,complement(A)))) = join(A,meet(B,join(A,meet(C,complement(A))))). [para(63(a,1),7(a,1)),flip(a)].
% 70.22/70.57 274 meet(join(A,meet(B,complement(A))),meet(join(A,C),join(A,join(D,meet(B,complement(A)))))) = join(A,meet(C,join(A,meet(B,complement(A))))). [para(63(a,1),22(a,2)),rewrite([8(8),12(8,R),8(7)])].
% 70.22/70.57 298 join(A,meet(join(B,meet(C,complement(A))),join(A,meet(C,complement(A))))) = join(A,meet(C,complement(A))). [para(63(a,1),185(a,1)),rewrite([8(4),12(4,R),8(3),8(8),12(8,R),8(7),7(13),274(13),23(9)])].
% 70.22/70.57 323 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(26(a,1),64(a,1,2,2,2,2)),rewrite([8(3),23(3),20(7),6(8),8(3),23(3),8(4),12(4),8(3),12(4,R),8(3)]),flip(a)].
% 70.22/70.57 406 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(265(a,1),323(a,1,1)),rewrite([8(4),12(5,R),8(4),265(4),265(7)])].
% 70.22/70.57 576 join(complement(A),meet(meet(B,complement(A)),join(complement(A),meet(A,C)))) = complement(A). [para(71(a,1),271(a,1,2,2,2,2)),rewrite([7(3),7(5)])].
% 70.22/70.57 587 meet(meet(A,B),join(A,meet(C,complement(A)))) = meet(A,B). [para(271(a,1),406(a,1,2)),rewrite([7(6),22(6),20(2)]),flip(a)].
% 70.22/70.57 595 meet(meet(A,complement(B)),join(complement(B),meet(B,C))) = meet(A,complement(B)). [para(71(a,1),587(a,1,2,2,2)),rewrite([7(2),7(4),7(8)])].
% 70.22/70.57 604 join(complement(A),meet(B,complement(A))) = complement(A). [back_rewrite(576),rewrite([595(7)])].
% 70.22/70.57 606 meet(complement(A),join(B,complement(A))) = complement(A). [para(604(a,1),26(a,1,2,1)),rewrite([10(6,R),1(5),6(7),604(5),8(4)]),flip(a)].
% 70.22/70.57 608 meet(one,complement(A)) = complement(A). [para(604(a,1),59(a,1,2)),rewrite([604(7)])].
% 70.22/70.57 660 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(220(a,1),68(a,1,2,2,2,2)),rewrite([12(3),8(2),19(2),8(1),12(4),8(3),19(3),8(2),8(4),19(4),7(3),12(6),8(5),19(5),8(4),8(6),12(6),8(5),19(5),8(4),12(5),8(4),12(5,R),8(4),7(6),10(6),7(5),10(6,R),7(5),323(5),12(7),8(6),19(6),8(5),12(8),8(7),19(7),8(6),220(9),8(8),12(8),8(7),19(7),8(6),12(7),8(6),12(7,R),8(6),323(8)])].
% 70.22/70.57 703 join(zero,complement(A)) = complement(A). [para(608(a,1),265(a,1,2)),rewrite([608(6)])].
% 70.22/70.57 707 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(703(a,1),65(a,1,2)),rewrite([48(3),18(3),265(3),48(8),18(8),265(8),10(7),7(6),10(7,R),7(6),265(8)])].
% 70.22/70.57 782 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(265(a,1),660(a,1,1)),rewrite([265(4),10(3),7(2),10(3,R),7(2),265(7)])].
% 70.22/70.57 801 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(707(a,1),4(a,1))].
% 70.22/70.57 802 meet(A,meet(join(A,B),complement(C))) = meet(A,complement(C)). [para(5(a,1),707(a,1,1)),flip(a)].
% 70.22/70.57 807 meet(one,meet(join(A,B),complement(C))) = meet(join(A,B),complement(C)). [para(59(a,1),707(a,1,1)),flip(a)].
% 70.22/70.57 828 meet(one,meet(complement(A),complement(B))) = meet(complement(A),complement(B)). [para(608(a,1),707(a,1,1)),flip(a)].
% 70.22/70.57 841 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(801(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),36(7)])].
% 70.22/70.57 849 meet(join(A,meet(B,complement(A))),meet(join(A,C),complement(join(A,meet(C,join(A,meet(B,complement(A)))))))) = zero. [para(63(a,1),801(a,1,2,2,1))].
% 70.22/70.57 865 meet(A,meet(B,meet(C,complement(meet(A,C))))) = zero. [para(841(a,1),7(a,1)),rewrite([7(2),7(6),10(6,R),7(5),10(5,R),7(4)]),flip(a)].
% 70.22/70.57 892 join(A,meet(meet(A,B),join(A,meet(B,C)))) = A. [para(782(a,1),26(a,1,2,2)),rewrite([7(4),6(9),7(8),5(8)])].
% 70.22/70.57 906 meet(A,complement(join(A,B))) = zero. [para(4(a,1),802(a,1,2)),rewrite([36(2)]),flip(a)].
% 70.22/70.57 921 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(802(a,1),865(a,1,2))].
% 70.22/70.57 934 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(906(a,1),707(a,1)),rewrite([8(3)]),flip(a)].
% 70.22/70.57 964 meet(A,meet(B,meet(C,complement(meet(A,join(D,meet(B,C))))))) = zero. [para(707(a,1),921(a,1,2)),rewrite([8(2)])].
% 70.22/70.57 988 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(59(a,1),934(a,1,2,2,1,2)),rewrite([12(4),8(3),12(4,R),8(3),807(7)])].
% 70.22/70.57 1002 meet(complement(A),complement(join(B,complement(A)))) = zero. [para(608(a,1),934(a,1,2,2,1,2)),rewrite([828(7)])].
% 70.22/70.57 1026 meet(join(A,complement(B)),join(A,join(C,complement(B)))) = join(A,complement(B)). [para(1002(a,1),63(a,1,1,2)),rewrite([8(4),12(4,R),19(3),8(5),12(5,R),8(4),1002(15),8(12),12(12,R),19(11),660(12)])].
% 70.22/70.57 1153 meet(meet(A,B),join(A,meet(B,C))) = meet(A,B). [para(892(a,1),406(a,1,2)),rewrite([7(5),22(5),20(2)]),flip(a)].
% 70.22/70.57 1235 meet(meet(A,B),join(B,meet(A,C))) = meet(A,B). [para(7(a,1),1153(a,1,1)),rewrite([7(5)])].
% 70.22/70.57 1261 meet(A,join(join(A,B),meet(A,C))) = A. [para(5(a,1),1235(a,1,1)),rewrite([5(6)])].
% 70.22/70.57 1316 join(join(A,B),meet(A,C)) = join(A,B). [para(1261(a,1),660(a,1,2)),rewrite([8(4),25(4),23(2)]),flip(a)].
% 70.22/70.57 1327 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),1316(a,1,1)),rewrite([8(4)])].
% 70.22/70.57 1328 join(join(A,join(B,C)),meet(B,D)) = join(A,join(B,C)). [para(12(a,1),1316(a,1,1)),rewrite([8(5),12(6,R),8(5)])].
% 70.22/70.57 1342 meet(meet(A,B),join(A,C)) = meet(A,B). [para(1316(a,1),406(a,1,2))].
% 70.22/70.57 1355 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(25(a,1),1327(a,1,1)),rewrite([7(4),25(8)])].
% 70.22/70.57 1380 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),1342(a,1,1)),rewrite([7(4)])].
% 70.22/70.57 1411 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(22(a,1),1380(a,1,1)),rewrite([8(4),22(8)])].
% 70.22/70.57 1425 meet(meet(A,B),join(C,join(D,meet(A,B)))) = meet(A,B). [para(406(a,1),1380(a,1,1)),rewrite([8(4),12(4,R),8(3),406(9)])].
% 70.22/70.57 2454 join(join(A,complement(B)),meet(C,complement(B))) = join(A,complement(B)). [para(604(a,1),1328(a,1,1,2)),rewrite([7(4),604(9)])].
% 70.22/70.57 2466 join(A,meet(join(A,complement(B)),join(C,complement(B)))) = join(A,complement(B)). [para(2454(a,1),26(a,1,2,2)),rewrite([1026(12)])].
% 70.22/70.57 2576 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(6(a,1),1355(a,1,1)),rewrite([6(7)])].
% 70.22/70.57 2577 join(join(A,B),meet(C,join(A,meet(B,D)))) = join(A,B). [para(1355(a,1),8(a,2)),rewrite([8(4),8(5),8(6)])].
% 70.22/70.57 2610 meet(A,meet(complement(join(B,C)),join(B,meet(C,D)))) = zero. [para(1355(a,1),934(a,1,2,2,1)),rewrite([8(3),7(5)])].
% 70.22/70.57 2654 join(A,meet(B,meet(C,join(meet(A,D),meet(A,E))))) = A. [para(2576(a,1),1327(a,1,1)),rewrite([7(5),10(5,R),7(4),2576(11)])].
% 70.22/70.57 2663 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [hyper(17,a,2610,a,b,209,a),rewrite([39(2)]),flip(a)].
% 70.22/70.57 2690 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),2663(a,1,1,1))].
% 70.22/70.57 2695 meet(complement(join(A,B)),join(A,meet(C,join(A,B)))) = zero. [para(23(a,1),2663(a,1,1,1)),rewrite([7(4)])].
% 70.22/70.57 2714 meet(A,complement(join(B,A))) = zero. [para(4(a,1),2690(a,1,2,2)),rewrite([19(4),7(3)])].
% 70.22/70.57 2715 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [para(6(a,1),2690(a,1,1,1))].
% 70.22/70.57 2740 meet(A,complement(join(B,join(C,A)))) = zero. [para(988(a,1),2690(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1),19(5),7(4)])].
% 70.22/70.57 2785 meet(join(A,meet(B,C)),complement(join(A,join(B,D)))) = zero. [para(25(a,1),2740(a,1,2,1,2)),rewrite([8(3),12(4),8(3),12(4,R),8(3)])].
% 70.22/70.57 2968 meet(join(A,B),meet(complement(join(A,B)),join(A,C))) = zero. [para(60(a,1),2695(a,1,2)),rewrite([10(6)])].
% 70.22/70.57 2982 meet(complement(join(A,join(B,C))),join(A,meet(B,D))) = zero. [para(2785(a,1),7(a,1)),flip(a)].
% 70.22/70.57 2983 meet(join(A,meet(B,C)),complement(join(A,join(C,D)))) = zero. [para(7(a,1),2785(a,1,1,2))].
% 70.22/70.57 3167 meet(join(A,B),meet(complement(join(A,B)),join(B,C))) = zero. [para(8(a,1),2968(a,1,1)),rewrite([8(2)])].
% 70.22/70.57 3209 meet(complement(join(A,join(B,C))),join(C,meet(A,D))) = zero. [para(8(a,1),2982(a,1,1,1)),rewrite([8(2),12(2),8(1),12(2,R),8(1)])].
% 70.22/70.57 3230 meet(join(A,meet(B,C)),complement(join(C,join(A,D)))) = zero. [para(8(a,1),2983(a,1,1)),rewrite([8(2),12(4,R),8(3)])].
% 70.22/70.57 3362 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(660(a,1),122(a,1,2,2,2,2)),rewrite([10(6,R),7(5),10(5,R),7(4),10(4,R),1(3),10(8,R)]),flip(a)].
% 70.22/70.57 3577 meet(A,meet(complement(A),join(B,meet(A,C)))) = zero. [para(6(a,1),3167(a,1,1)),rewrite([6(2),8(3)])].
% 70.22/70.57 3621 meet(A,meet(complement(A),join(B,C))) = zero. [para(660(a,1),3577(a,1,2,2))].
% 70.22/70.57 3965 meet(complement(join(A,B)),join(meet(B,C),meet(A,D))) = zero. [para(6(a,1),3209(a,1,1,1,2))].
% 70.22/70.57 4068 meet(complement(join(A,complement(B))),join(complement(B),meet(C,A))) = zero. [para(604(a,1),3230(a,1,2,1,2)),rewrite([7(7)])].
% 70.22/70.57 4288 meet(complement(join(A,complement(B))),join(meet(A,C),complement(B))) = zero. [para(606(a,1),3965(a,1,2,2)),rewrite([8(2)])].
% 70.22/70.57 4531 join(A,complement(meet(A,B))) = one. [hyper(132,a,4288,a,b,3,a(flip)),rewrite([3(8),7(6),608(6),71(5),3(7)])].
% 70.22/70.57 4554 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [hyper(132,a,4288,a,b,4531,a(flip)),rewrite([7(2),10(2),7(1),10(2,R),7(1),4531(4),39(2),7(4),10(4),7(3),10(4,R),7(3),220(7),48(2),7(4),10(4),7(3),10(4,R),7(3)]),flip(a)].
% 70.22/70.57 4575 join(join(A,B),complement(meet(C,join(A,B)))) = one. [para(59(a,1),4554(a,1,1)),rewrite([7(4),10(5,R),7(4),59(4)])].
% 70.22/70.57 4586 join(complement(A),complement(meet(B,complement(A)))) = one. [para(608(a,1),4554(a,1,1)),rewrite([7(4),10(5,R),18(4)])].
% 70.22/70.57 4598 meet(A,complement(B)) != zero | join(A,complement(B)) != one | A = B. [para(4586(a,1),42(b,1,2,2)),rewrite([7(2),18(7),8(6),4586(13),18(10),71(10)])].
% 70.22/70.57 4625 join(A,join(complement(B),meet(join(B,C),join(B,D)))) = one. [para(185(a,1),4575(a,1,2,1)),rewrite([8(6),12(6,R),8(5)])].
% 70.22/70.57 4632 join(A,join(join(B,C),complement(join(A,B)))) = one. [para(323(a,1),4575(a,1,2,1)),rewrite([8(5),12(5,R)])].
% 70.22/70.57 4716 join(A,join(B,complement(join(A,B)))) = one. [para(2(a,1),4632(a,1,2,1))].
% 70.22/70.57 4718 join(A,join(join(B,C),complement(join(A,C)))) = one. [para(8(a,1),4632(a,1,2,1))].
% 70.22/70.57 4869 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(6(a,1),4718(a,1,2,1))].
% 70.22/70.57 4921 join(join(A,B),complement(join(A,meet(B,C)))) = one. [para(4869(a,1),12(a,1)),rewrite([8(6)]),flip(a)].
% 70.22/70.57 4934 join(join(A,B),complement(join(B,meet(A,C)))) = one. [para(8(a,1),4921(a,1,1))].
% 70.22/70.57 4975 join(A,complement(join(meet(A,B),meet(A,C)))) = one. [para(6(a,1),4934(a,1,1))].
% 70.22/70.57 5102 join(complement(A),meet(join(A,B),join(A,C))) = one. [hyper(17,a,4068,a,b,4625,a),rewrite([8(3),12(3),8(2),3(2),45(2),39(2),48(2)]),flip(a)].
% 70.22/70.57 5113 join(A,meet(join(B,complement(A)),join(C,complement(A)))) = one. [para(71(a,1),5102(a,1,1)),rewrite([8(2),8(4)])].
% 70.22/70.57 5124 join(complement(A),meet(join(A,B),join(C,A))) = one. [hyper(132,a,4068,a,b,5113,a(flip)),rewrite([71(2),8(3),12(3),8(2),47(3),39(2),71(4),8(3),71(5),220(7),48(2),71(4),8(3),71(5)]),flip(a)].
% 70.22/70.57 5144 join(complement(meet(A,B)),meet(A,join(C,meet(A,B)))) = one. [para(6(a,1),5124(a,1,2,2)),rewrite([8(4),7(5)])].
% 70.22/70.57 5631 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(406(a,1),153(a,1,2,2,2,2)),rewrite([12(6,R),8(5),12(5,R),8(4),12(4,R),2(3),12(8,R)]),flip(a)].
% 70.22/70.57 6669 join(complement(meet(A,B)),meet(B,join(C,meet(A,B)))) = one. [para(7(a,1),5144(a,1,1,1)),rewrite([7(3)])].
% 70.22/70.57 7390 join(A,complement(meet(B,A))) = one. [hyper(132,a,2695,a,b,6669,a(flip)),rewrite([8(4),3(4),39(2),8(7),3(7),18(5),8(4),220(5),48(2),8(7),3(7),18(5),8(4)]),flip(a)].
% 70.22/70.57 7405 join(complement(meet(A,B)),meet(join(B,C),join(D,meet(A,B)))) = one. [para(1380(a,1),6669(a,1,1,1)),rewrite([1380(6)])].
% 70.22/70.57 7415 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [para(22(a,1),7390(a,1,2,1)),rewrite([7(3),8(5)])].
% 70.22/70.57 7473 join(complement(meet(A,B)),meet(A,join(C,meet(B,join(A,D))))) = one. [para(22(a,1),7415(a,1,1,1)),rewrite([8(5)])].
% 70.22/70.57 9011 meet(meet(A,B),join(C,meet(A,join(B,D)))) = meet(A,B). [para(1411(a,1),7(a,2)),rewrite([7(4),7(5),7(6)])].
% 70.22/70.57 9425 join(join(A,B),meet(meet(C,join(A,meet(B,D))),join(join(A,B),meet(E,complement(join(A,B)))))) = join(A,B). [para(2577(a,1),63(a,1,2)),rewrite([7(7),5(7)]),flip(a)].
% 70.22/70.57 11402 meet(A,meet(join(B,C),join(B,A))) = meet(A,join(B,C)). [para(26(a,1),9011(a,1,2)),rewrite([7(2),10(6),7(5),10(5,R),1(4),10(4,R),7(6)])].
% 70.22/70.57 11709 meet(A,meet(join(B,A),join(B,C))) = meet(A,join(B,C)). [para(11402(a,1),10(a,2)),rewrite([7(3),10(4,R)])].
% 70.22/70.57 11734 join(A,meet(meet(A,B),join(C,meet(A,D)))) = A. [para(11402(a,1),2654(a,1,2)),rewrite([8(3)])].
% 70.22/70.57 11747 join(A,meet(meet(A,B),join(C,D))) = A. [para(660(a,1),11734(a,1,2,2))].
% 70.22/70.57 11823 meet(meet(meet(A,B),join(C,D)),join(A,E)) = meet(meet(A,B),join(C,D)). [para(11747(a,1),1425(a,1,2,2)),rewrite([8(4)])].
% 70.22/70.57 11829 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(11747(a,1),11402(a,1,2,2)),rewrite([7(5),5(5),7(4),3362(4),20(4),11823(8)]),flip(a)].
% 70.22/70.57 11878 join(join(A,B),meet(C,meet(join(A,meet(B,D)),join(join(A,B),meet(E,complement(join(A,B))))))) = join(A,B). [back_rewrite(9425),rewrite([11829(10)])].
% 70.22/70.57 12096 meet(join(A,B),join(B,meet(C,complement(B)))) = join(B,meet(A,join(B,meet(C,complement(B))))). [para(8(a,1),272(a,1,1))].
% 70.22/70.57 12724 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(5(a,1),11829(a,1,1)),flip(a)].
% 70.22/70.57 13356 meet(A,meet(B,complement(meet(A,join(C,meet(A,B)))))) = zero. [para(964(a,1),20(a,1)),flip(a)].
% 70.22/70.57 13386 meet(A,meet(join(meet(B,C),meet(B,D)),complement(meet(A,B)))) = zero. [para(2576(a,1),13356(a,1,2,2,1,2))].
% 70.22/70.57 14316 meet(A,join(B,A)) = A. [para(48(a,1),298(a,1,2,1,2,2)),rewrite([18(3),48(5),18(5),8(4),19(4),7(3),265(4),48(5),18(5),8(4),19(4)])].
% 70.22/70.57 14334 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(25(a,1),14316(a,1,2)),rewrite([8(3),7(4)])].
% 70.22/70.57 14356 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(8(a,1),14334(a,1,1))].
% 70.22/70.57 14457 meet(A,join(B,join(C,A))) = A. [para(988(a,1),14356(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1),19(4),7(3),988(8),19(5)])].
% 70.22/70.57 14464 meet(A,join(B,join(A,meet(C,D)))) = A. [para(2785(a,1),14356(a,1,2,2)),rewrite([8(3),12(3,R),8(2),19(5),7(4),2785(10),19(6)])].
% 70.22/70.57 14510 meet(join(A,meet(B,C)),join(A,join(B,D))) = join(A,meet(B,C)). [para(25(a,1),14457(a,1,2,2)),rewrite([8(3),12(4),8(3),12(4,R),8(3)])].
% 70.22/70.57 14743 join(A,meet(join(A,B),join(B,C))) = join(A,B). [para(71(a,1),2466(a,1,2,1,2)),rewrite([71(3),8(2),71(6)])].
% 70.22/70.57 14777 join(A,meet(join(B,C),join(A,B))) = join(A,B). [para(7(a,1),14743(a,1,2))].
% 70.22/70.57 14829 join(A,meet(join(B,C),join(B,A))) = join(B,A). [para(14777(a,1),8(a,2)),rewrite([8(2),8(4),8(5)])].
% 70.22/70.57 14830 join(A,meet(join(B,C),join(A,C))) = join(A,C). [para(8(a,1),14777(a,1,2,1))].
% 70.22/70.57 14890 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(14464(a,1),14829(a,1,2)),rewrite([8(5),23(5),5631(7),23(7)])].
% 70.22/70.57 15000 join(A,join(B,meet(C,join(A,meet(B,D))))) = join(A,B). [back_rewrite(11878),rewrite([14890(8),14510(9),14890(5)])].
% 70.22/70.57 15117 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(6(a,1),14830(a,1,2,1))].
% 70.22/70.57 15356 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(6(a,1),14890(a,1,1)),flip(a)].
% 70.22/70.57 19829 meet(A,join(meet(B,C),meet(B,join(A,D)))) = meet(A,B). [hyper(34,a,13386,a,b,7473,a),rewrite([71(3)]),flip(a)].
% 70.22/70.57 19842 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(2(a,1),19829(a,1,2,2,2)),rewrite([7(2)])].
% 70.22/70.57 19878 meet(A,join(meet(B,C),meet(B,A))) = meet(B,A). [para(19842(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 70.22/70.57 19879 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(7(a,1),19842(a,1,2,1))].
% 70.22/70.57 19880 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(8(a,1),19842(a,1,2))].
% 70.22/70.57 19900 join(A,join(meet(B,A),meet(B,C))) = join(A,meet(B,C)). [para(19842(a,1),15000(a,1,2,2)),rewrite([7(2),12(4,R),8(6)])].
% 70.22/70.57 19975 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(5(a,1),19879(a,1,2,1))].
% 70.22/70.57 19976 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(19879(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 70.22/70.57 20082 meet(A,join(B,meet(A,join(C,B)))) = meet(A,join(C,B)). [para(14830(a,1),19880(a,1,2)),rewrite([8(3)])].
% 70.22/70.57 20127 meet(A,join(meet(B,A),meet(A,C))) = join(meet(B,A),meet(A,C)). [para(15117(a,1),19976(a,1,2)),rewrite([1(7)]),flip(a)].
% 70.22/70.57 20322 join(A,join(meet(B,C),meet(B,A))) = join(A,meet(B,C)). [para(19900(a,1),12(a,2)),rewrite([8(3),12(4,R)])].
% 70.22/70.57 21578 meet(A,meet(complement(meet(A,B)),join(complement(A),meet(A,B)))) = zero. [para(2715(a,1),849(a,1,2,2,1,2)),rewrite([8(8),8(11),265(11),7(11),10(12),7(11),19878(11),10(7),7(6),10(7,R),7(6)])].
% 70.22/70.57 21588 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(33,a,21578,a,b,7405,a),rewrite([7(2),5(2),71(2),7(5),5(5),8(4)]),flip(a)].
% 70.22/70.57 21598 meet(join(A,B),join(B,complement(join(A,B)))) = B. [para(8(a,1),21588(a,1,1)),rewrite([8(2)])].
% 70.22/70.57 21614 meet(A,join(B,complement(join(A,B)))) = meet(A,B). [para(21588(a,1),11709(a,1,2)),rewrite([8(2)]),flip(a)].
% 70.22/70.57 21720 meet(A,join(B,complement(join(B,A)))) = meet(B,A). [para(21614(a,1),7(a,2)),rewrite([8(1),7(4),7(5)])].
% 70.22/70.57 21723 meet(A,B) != zero | join(B,complement(join(A,B))) = complement(A). [para(21614(a,1),17(a,1)),rewrite([4716(7)]),flip(c),xx(b)].
% 70.22/70.57 21724 meet(A,join(B,join(meet(A,C),complement(join(A,B))))) = meet(A,join(B,meet(A,C))). [para(25(a,1),21614(a,1,2,2,1)),rewrite([8(5),12(5,R)])].
% 70.22/70.57 21738 meet(A,join(complement(join(A,B)),meet(join(A,B),join(B,C)))) = meet(A,join(B,C)). [para(11709(a,1),21614(a,2)),rewrite([8(1),8(4),14743(7),8(6)])].
% 70.22/70.57 21742 meet(A,join(B,complement(join(A,join(C,B))))) = meet(A,B). [para(21614(a,1),12724(a,1,2)),rewrite([7(2),22(3),8(3),12(3),8(2),12(3,R),8(2)]),flip(a)].
% 70.22/70.57 21780 meet(A,B) != zero | join(A,complement(join(A,B))) = complement(B). [para(21720(a,1),17(a,1)),rewrite([12(7,R),8(6),4716(7)]),flip(c),xx(b)].
% 70.22/70.57 21782 meet(A,B) != zero | complement(join(A,complement(join(A,B)))) = B. [para(21720(a,1),32(a,1)),rewrite([12(7,R),8(6),4716(7)]),xx(b)].
% 70.22/70.57 21911 join(complement(join(A,B)),complement(join(A,complement(join(A,B))))) = complement(A). [hyper(21723,a,906,a)].
% 70.22/70.57 21923 meet(A,join(B,complement(join(B,join(A,C))))) = meet(B,A). [para(21742(a,1),7(a,2)),rewrite([8(1),12(2,R),8(1),7(5),7(6)])].
% 70.22/70.57 21952 join(A,complement(join(A,meet(complement(A),join(B,C))))) = complement(meet(complement(A),join(B,C))). [hyper(21780,a,3621,a)].
% 70.22/70.57 21953 join(A,complement(join(A,complement(join(A,B))))) = join(A,B). [hyper(21780,a,2714,a),rewrite([8(1),8(6),71(8)])].
% 70.22/70.57 22011 complement(join(A,complement(join(A,B)))) = meet(complement(A),join(A,B)). [para(21953(a,1),21598(a,1,1)),rewrite([21953(10),8(8),21911(8),7(3)]),flip(a)].
% 70.22/70.57 22014 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(21953(a,1),21953(a,2)),rewrite([22011(4),21952(6),71(5)])].
% 70.22/70.57 22106 meet(A,B) != zero | meet(complement(A),join(A,B)) = B. [back_rewrite(21782),rewrite([22011(7)])].
% 70.22/70.57 22164 meet(complement(A),join(A,complement(join(A,B)))) = complement(join(A,B)). [hyper(22106,a,2714,a),rewrite([8(2),8(6)])].
% 70.22/70.57 22168 meet(complement(A),join(A,meet(B,complement(meet(A,B))))) = meet(B,complement(meet(A,B))). [hyper(22106,a,801,a)].
% 70.22/70.57 22295 meet(A,complement(join(B,join(C,meet(A,complement(B)))))) = zero. [para(38(a,1),21923(a,2)),rewrite([8(5),11829(9),22164(8)])].
% 70.22/70.57 22318 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(2(a,1),22295(a,1,2,1,2))].
% 70.22/70.57 22337 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [hyper(4598,a,22318,a,b,4975,a),flip(a)].
% 70.22/70.57 22460 join(A,meet(B,complement(meet(A,B)))) = join(A,B). [para(22337(a,1),19900(a,1,2)),rewrite([7(2)]),flip(a)].
% 70.22/70.57 22468 meet(complement(A),join(A,B)) = meet(B,complement(meet(A,B))). [back_rewrite(22168),rewrite([22460(5)])].
% 70.22/70.57 22521 join(A,meet(B,meet(join(A,C),complement(meet(A,B))))) = join(A,meet(B,join(A,C))). [para(22(a,1),22460(a,1,2,2,1)),rewrite([7(5),10(5,R)])].
% 70.22/70.57 22568 join(A,meet(complement(meet(A,B)),join(meet(A,B),meet(B,C)))) = join(A,meet(B,C)). [para(19880(a,1),22460(a,1,2,2,1)),rewrite([7(6),15356(11)])].
% 70.22/70.57 23120 meet(A,complement(meet(A,B))) = meet(A,complement(B)). [para(22468(a,2),20(a,1,2)),rewrite([8(2),22(4),7(3)]),flip(a)].
% 70.22/70.57 23121 meet(complement(A),join(B,A)) = meet(B,complement(A)). [para(22468(a,2),20(a,2)),rewrite([7(1),23120(3),20(3),8(4)]),flip(a)].
% 70.22/70.57 23140 meet(A,complement(meet(B,join(A,C)))) = meet(A,complement(B)). [para(22468(a,2),802(a,1,2)),rewrite([12(3,R),8(2),22(5)]),flip(a)].
% 70.22/70.57 23400 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(19975(a,1),22468(a,2,2,1)),rewrite([25(5),7(10),23121(10),23140(7)])].
% 70.22/70.57 23405 meet(A,complement(meet(B,A))) = meet(A,complement(B)). [para(22468(a,1),20082(a,2)),rewrite([23400(4),6(4),7(2)]),flip(a)].
% 70.22/70.57 23412 meet(A,meet(B,complement(meet(C,A)))) = meet(A,meet(B,complement(C))). [para(20322(a,1),22468(a,1,2)),rewrite([23400(4),707(3),7(5),7(8),19842(10),7(9),23121(9),707(7)]),flip(a)].
% 70.22/70.57 23448 join(A,meet(B,complement(A))) = join(A,B). [para(22468(a,1),22014(a,1,2)),rewrite([23405(3)])].
% 70.22/70.57 23590 join(A,meet(B,meet(C,complement(A)))) = join(A,meet(B,C)). [back_rewrite(22568),rewrite([23400(6),707(4),23412(4)])].
% 70.22/70.57 23669 join(A,meet(B,join(A,C))) = join(A,meet(B,C)). [back_rewrite(22521),rewrite([23412(5),7(3),23400(3),23590(4)]),flip(a)].
% 70.22/70.57 23714 meet(join(A,B),join(B,C)) = join(B,meet(A,C)). [back_rewrite(12096),rewrite([23448(4),23448(6),23669(6)])].
% 70.22/70.57 23802 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(21738),rewrite([23714(5),12(5,R),21724(6)])].
% 70.22/70.57 26025 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(20127),rewrite([7(1),23802(4),8(2),23802(3),8(1),7(3)]),flip(a)].
% 70.22/70.57 26026 $F # answer(prove_distributivity). [resolve(26025,a,16,a)].
% 70.22/70.57
% 70.22/70.57 % SZS output end Refutation
% 70.22/70.57 ============================== end of proof ==========================
% 70.22/70.57
% 70.22/70.57 ============================== STATISTICS ============================
% 70.22/70.57
% 70.22/70.57 Given=1360. Generated=1770125. Kept=26021. proofs=1.
% 70.22/70.57 Usable=498. Sos=3835. Demods=5482. Limbo=2223, Disabled=19477. Hints=0.
% 70.22/70.57 Megabytes=24.82.
% 70.22/70.57 User_CPU=68.59, System_CPU=0.97, Wall_clock=70.
% 70.22/70.57
% 70.22/70.57 ============================== end of statistics =====================
% 70.22/70.57
% 70.22/70.57 ============================== end of search =========================
% 70.22/70.57
% 70.22/70.57 THEOREM PROVED
% 70.22/70.57 % SZS status Unsatisfiable
% 70.22/70.57
% 70.22/70.57 Exiting with 1 proof.
% 70.22/70.57
% 70.22/70.57 Process 24099 exit (max_proofs) Tue Jun 28 22:33:47 2022
% 70.22/70.57 Prover9 interrupted
%------------------------------------------------------------------------------