TSTP Solution File: LAT205-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT205-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 06:26:06 EDT 2022
% Result : Unsatisfiable 171.08s 171.33s
% Output : Refutation 171.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT205-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 29 20:21:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 12.18/12.49 ============================== Prover9 ===============================
% 12.18/12.49 Prover9 (32) version 2009-11A, November 2009.
% 12.18/12.49 Process 6817 was started by sandbox2 on n026.cluster.edu,
% 12.18/12.49 Wed Jun 29 20:21:49 2022
% 12.18/12.49 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6664_n026.cluster.edu".
% 12.18/12.49 ============================== end of head ===========================
% 12.18/12.49
% 12.18/12.49 ============================== INPUT =================================
% 12.18/12.49
% 12.18/12.49 % Reading from file /tmp/Prover9_6664_n026.cluster.edu
% 12.18/12.49
% 12.18/12.49 set(prolog_style_variables).
% 12.18/12.49 set(auto2).
% 12.18/12.49 % set(auto2) -> set(auto).
% 12.18/12.49 % set(auto) -> set(auto_inference).
% 12.18/12.49 % set(auto) -> set(auto_setup).
% 12.18/12.49 % set(auto_setup) -> set(predicate_elim).
% 12.18/12.49 % set(auto_setup) -> assign(eq_defs, unfold).
% 12.18/12.49 % set(auto) -> set(auto_limits).
% 12.18/12.49 % set(auto_limits) -> assign(max_weight, "100.000").
% 12.18/12.49 % set(auto_limits) -> assign(sos_limit, 20000).
% 12.18/12.49 % set(auto) -> set(auto_denials).
% 12.18/12.49 % set(auto) -> set(auto_process).
% 12.18/12.49 % set(auto2) -> assign(new_constants, 1).
% 12.18/12.49 % set(auto2) -> assign(fold_denial_max, 3).
% 12.18/12.49 % set(auto2) -> assign(max_weight, "200.000").
% 12.18/12.49 % set(auto2) -> assign(max_hours, 1).
% 12.18/12.49 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 12.18/12.49 % set(auto2) -> assign(max_seconds, 0).
% 12.18/12.49 % set(auto2) -> assign(max_minutes, 5).
% 12.18/12.49 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 12.18/12.49 % set(auto2) -> set(sort_initial_sos).
% 12.18/12.49 % set(auto2) -> assign(sos_limit, -1).
% 12.18/12.49 % set(auto2) -> assign(lrs_ticks, 3000).
% 12.18/12.49 % set(auto2) -> assign(max_megs, 400).
% 12.18/12.49 % set(auto2) -> assign(stats, some).
% 12.18/12.49 % set(auto2) -> clear(echo_input).
% 12.18/12.49 % set(auto2) -> set(quiet).
% 12.18/12.49 % set(auto2) -> clear(print_initial_clauses).
% 12.18/12.49 % set(auto2) -> clear(print_given).
% 12.18/12.49 assign(lrs_ticks,-1).
% 12.18/12.49 assign(sos_limit,10000).
% 12.18/12.49 assign(order,kbo).
% 12.18/12.49 set(lex_order_vars).
% 12.18/12.49 clear(print_given).
% 12.18/12.49
% 12.18/12.49 % formulas(sos). % not echoed (13 formulas)
% 12.18/12.49
% 12.18/12.49 ============================== end of input ==========================
% 12.18/12.49
% 12.18/12.49 % From the command line: assign(max_seconds, 300).
% 12.18/12.49
% 12.18/12.49 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 12.18/12.49
% 12.18/12.49 % Formulas that are not ordinary clauses:
% 12.18/12.49
% 12.18/12.49 ============================== end of process non-clausal formulas ===
% 12.18/12.49
% 12.18/12.49 ============================== PROCESS INITIAL CLAUSES ===============
% 12.18/12.49
% 12.18/12.49 ============================== PREDICATE ELIMINATION =================
% 12.18/12.49
% 12.18/12.49 ============================== end predicate elimination =============
% 12.18/12.49
% 12.18/12.49 Auto_denials:
% 12.18/12.49 % copying label prove_distributivity to answer in negative clause
% 12.18/12.49
% 12.18/12.49 Term ordering decisions:
% 12.18/12.49
% 12.18/12.49 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 12.18/12.49 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. join=1. meet=1. complement=0.
% 12.18/12.49
% 12.18/12.49 ============================== end of process initial clauses ========
% 12.18/12.49
% 12.18/12.49 ============================== CLAUSES FOR SEARCH ====================
% 12.18/12.49
% 12.18/12.49 ============================== end of clauses for search =============
% 12.18/12.49
% 12.18/12.49 ============================== SEARCH ================================
% 12.18/12.49
% 12.18/12.49 % Starting search at 0.01 seconds.
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=140.000, iters=3359
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=136.000, iters=3400
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=123.000, iters=3358
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=110.000, iters=3385
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=108.000, iters=3399
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=101.000, iters=3398
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=89.000, iters=3415
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=85.000, iters=3342
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=84.000, iters=3342
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=79.000, iters=3336
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=76.000, iters=3375
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=75.000, iters=3365
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=71.000, iters=3352
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=69.000, iters=3440
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=66.000, iters=3346
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=63.000, iters=3358
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=62.000, iters=3447
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=59.000, iters=3347
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=56.000, iters=3346
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=55.000, iters=3333
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=54.000, iters=3363
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=53.000, iters=3334
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=52.000, iters=3362
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=51.000, iters=3418
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=50.000, iters=3420
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=49.000, iters=3388
% 12.18/12.49
% 12.18/12.49 Low Water (keep): wt=47.000, iters=3361
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=46.000, iters=3356
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=45.000, iters=3350
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=44.000, iters=3376
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=43.000, iters=3425
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=42.000, iters=3343
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=41.000, iters=3345
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=40.000, iters=3337
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=39.000, iters=3333
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=38.000, iters=3340
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=37.000, iters=3446
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=36.000, iters=3336
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=35.000, iters=3388
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=34.000, iters=3338
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=33.000, iters=3338
% 171.08/171.33
% 171.08/171.33 Low Water (displace): id=2988, wt=200.000
% 171.08/171.33
% 171.08/171.33 Low Water (displace): id=6296, wt=199.000
% 171.08/171.33
% 171.08/171.33 Low Water (displace): id=7070, wt=197.000
% 171.08/171.33
% 171.08/171.33 Low Water (displace): id=14496, wt=31.000
% 171.08/171.33
% 171.08/171.33 Low Water (displace): id=14497, wt=19.000
% 171.08/171.33
% 171.08/171.33 Low Water (displace): id=14499, wt=16.000
% 171.08/171.33
% 171.08/171.33 Low Water (displace): id=14802, wt=15.000
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=32.000, iters=3348
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=31.000, iters=3353
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=30.000, iters=3349
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=29.000, iters=3355
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=28.000, iters=3336
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=27.000, iters=3350
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=26.000, iters=3341
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=25.000, iters=3340
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=24.000, iters=3339
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=23.000, iters=3336
% 171.08/171.33
% 171.08/171.33 Low Water (keep): wt=22.000, iters=3333
% 171.08/171.33
% 171.08/171.33 Low Water (displace): id=31153, wt=14.000
% 171.08/171.33
% 171.08/171.33 ============================== PROOF =================================
% 171.08/171.33 % SZS status Unsatisfiable
% 171.08/171.33 % SZS output start Refutation
% 171.08/171.33
% 171.08/171.33 % Proof 1 at 169.09 (+ 1.16) seconds: prove_distributivity.
% 171.08/171.33 % Length of proof is 261.
% 171.08/171.33 % Level of proof is 54.
% 171.08/171.33 % Maximum clause weight is 49.000.
% 171.08/171.33 % Given clauses 1475.
% 171.08/171.33
% 171.08/171.33 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 171.08/171.33 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 171.08/171.33 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 171.08/171.33 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 171.08/171.33 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 171.08/171.33 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 171.08/171.33 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 171.08/171.33 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 171.08/171.33 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 171.08/171.33 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 171.08/171.33 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 171.08/171.33 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 171.08/171.33 13 meet(A,meet(join(B,C),join(B,D))) = meet(A,join(B,meet(join(B,D),join(C,meet(A,B))))) # label(equation_H59) # label(axiom). [assumption].
% 171.08/171.33 14 meet(A,join(B,meet(join(B,C),join(D,meet(A,B))))) = meet(A,meet(join(B,D),join(B,C))). [copy(13),flip(a)].
% 171.08/171.33 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 171.08/171.33 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 171.08/171.33 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 171.08/171.33 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 171.08/171.33 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 171.08/171.33 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)])].
% 171.08/171.33 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 171.08/171.33 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 171.08/171.33 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)])].
% 171.08/171.33 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 171.08/171.33 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 171.08/171.33 26 meet(A,join(B,meet(A,B))) = meet(A,B). [para(1(a,1),14(a,1,2,2)),rewrite([23(3),2(4),5(6)])].
% 171.08/171.33 27 meet(meet(join(A,B),join(A,C)),join(A,meet(join(A,C),join(A,B)))) = meet(join(A,B),join(A,C)). [para(1(a,1),14(a,2)),rewrite([7(8),22(8),5(6),8(5)])].
% 171.08/171.33 28 meet(A,meet(join(B,meet(A,B)),join(B,C))) = meet(A,B). [para(2(a,1),14(a,1,2,2,2)),rewrite([10(3),7(2),22(3),7(1),26(3)]),flip(a)].
% 171.08/171.33 29 meet(A,join(B,meet(one,join(C,meet(A,B))))) = meet(A,meet(one,join(B,C))). [para(3(a,1),14(a,1,2,2,1)),rewrite([3(9),7(9)])].
% 171.08/171.33 30 meet(A,meet(join(B,complement(A)),join(C,complement(A)))) = meet(A,join(complement(A),meet(B,join(C,complement(A))))). [para(4(a,1),14(a,1,2,2,2,2)),rewrite([8(3),19(5),7(4),8(8),8(10)]),flip(a)].
% 171.08/171.33 32 meet(A,meet(join(A,B),join(B,C))) = meet(A,join(B,meet(A,join(B,C)))). [para(6(a,1),14(a,1,2,2,2)),rewrite([7(2),8(5)]),flip(a)].
% 171.08/171.33 33 meet(A,join(B,meet(join(B,C),join(D,meet(B,A))))) = meet(A,meet(join(B,D),join(B,C))). [para(14(a,1),7(a,2)),rewrite([7(2),7(6)])].
% 171.08/171.33 34 meet(A,join(B,meet(join(C,meet(A,B)),join(B,D)))) = meet(A,meet(join(B,C),join(B,D))). [para(7(a,1),14(a,1,2,2))].
% 171.08/171.33 35 meet(A,meet(B,join(C,meet(join(C,D),join(E,meet(A,C)))))) = meet(A,meet(B,meet(join(C,E),join(C,D)))). [para(14(a,1),10(a,2,2)),rewrite([7(6),10(12,R),7(11)])].
% 171.08/171.33 36 meet(A,join(meet(B,C),meet(join(D,meet(B,C)),join(E,meet(A,meet(B,C)))))) = meet(A,meet(join(E,meet(B,C)),join(D,meet(B,C)))). [para(10(a,1),14(a,1,2,2,2,2)),rewrite([8(3),10(5),7(4),10(5,R),7(4),8(11),8(13)])].
% 171.08/171.33 41 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(7(a,1),17(a,1)),rewrite([8(4)])].
% 171.08/171.33 42 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)])].
% 171.08/171.33 47 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 171.08/171.33 51 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([47(5)])].
% 171.08/171.33 52 complement(one) = zero. [hyper(17,a,47,a,b,19,a)].
% 171.08/171.33 53 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(47(a,1),14(a,1,2,2,2,2)),rewrite([8(3),19(3),19(3),8(6),19(6),8(6),19(6),7(5)])].
% 171.08/171.33 54 one != A | complement(A) = zero. [para(47(a,1),17(a,1)),rewrite([19(5)]),flip(b),xx(a)].
% 171.08/171.33 57 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)].
% 171.08/171.33 58 complement(join(A,one)) = zero. [hyper(54,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 171.08/171.33 60 join(A,one) = one. [para(58(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 171.08/171.33 62 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([60(5)])].
% 171.08/171.33 63 complement(zero) = one. [hyper(17,a,18,a,b,60,a)].
% 171.08/171.33 64 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(51(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),47(6)])].
% 171.08/171.33 65 meet(A,meet(join(B,meet(C,complement(A))),join(D,meet(C,complement(A))))) = meet(A,join(meet(C,complement(A)),meet(B,join(D,meet(C,complement(A)))))). [para(51(a,1),14(a,1,2,2,2,2)),rewrite([8(5),19(7),7(6),8(11),8(14)]),flip(a)].
% 171.08/171.33 70 meet(A,meet(join(B,meet(C,meet(D,complement(A)))),join(E,meet(C,meet(D,complement(A)))))) = meet(A,join(meet(C,meet(D,complement(A))),meet(B,join(E,meet(C,meet(D,complement(A))))))). [para(64(a,1),14(a,1,2,2,2,2)),rewrite([8(7),19(9),7(8),8(14),8(18)]),flip(a)].
% 171.08/171.33 77 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(22(a,1),26(a,1,2,2)),rewrite([8(4),22(8)])].
% 171.08/171.33 88 meet(join(A,B),meet(join(A,meet(join(A,C),join(A,D))),join(A,meet(join(A,B),meet(join(A,D),join(A,C)))))) = meet(join(A,meet(join(A,C),join(A,D))),join(A,B)). [para(14(a,1),27(a,1,2,2)),rewrite([7(3),5(3),8(2),7(13),10(13),7(12),7(16),5(16),8(15)])].
% 171.08/171.33 95 join(zero,meet(A,B)) = meet(A,B). [para(53(a,1),1(a,1)),rewrite([7(5),53(5),1(3)]),flip(a)].
% 171.08/171.33 96 meet(A,meet(complement(A),join(B,complement(A)))) = zero. [para(4(a,1),28(a,1,2,1,2)),rewrite([19(3),8(3),4(7)])].
% 171.08/171.33 97 meet(A,meet(B,meet(join(C,meet(A,C)),join(C,D)))) = meet(A,meet(C,B)). [para(28(a,1),10(a,2,2)),rewrite([7(5),10(8),7(7),10(8,R),7(7)])].
% 171.08/171.33 102 meet(A,B) != zero | join(A,meet(join(B,meet(A,B)),join(B,C))) != one | meet(join(B,meet(A,B)),join(B,C)) = complement(A). [para(28(a,1),17(a,1)),flip(c)].
% 171.08/171.33 123 meet(A,join(join(A,B),meet(one,join(A,C)))) = A. [para(5(a,1),29(a,1,2,2,2,2)),rewrite([8(3),8(9),12(9),8(8),12(9,R),8(8),22(11),18(8)])].
% 171.08/171.33 126 meet(A,meet(one,join(B,C))) = meet(A,join(B,C)). [para(10(a,1),29(a,2)),rewrite([29(6),18(7),7(6)])].
% 171.08/171.33 131 meet(A,join(B,meet(join(B,C),join(B,D)))) = meet(A,meet(one,meet(join(B,D),join(B,C)))). [para(14(a,1),29(a,2,2)),rewrite([7(4),18(4),8(3),29(9),126(7)])].
% 171.08/171.33 143 meet(A,join(meet(join(B,meet(A,B)),join(B,C)),meet(one,join(D,meet(A,B))))) = meet(A,join(D,meet(join(B,meet(A,B)),join(B,C)))). [para(28(a,1),29(a,1,2,2,2,2)),rewrite([8(16),126(18)])].
% 171.08/171.33 146 meet(A,join(B,meet(one,join(C,meet(A,B))))) = meet(A,join(B,C)). [back_rewrite(29),rewrite([126(10)])].
% 171.08/171.33 160 meet(zero,join(A,meet(B,C))) = zero. [para(95(a,1),123(a,1,2,1)),rewrite([8(5),19(5),7(4),18(4),8(3)])].
% 171.08/171.33 168 meet(A,join(complement(A),meet(B,complement(A)))) = zero. [para(2(a,1),30(a,1,2,2)),rewrite([7(4),96(5),2(5)]),flip(a)].
% 171.08/171.33 178 meet(zero,join(A,B)) = zero. [para(1(a,1),160(a,1,2,2))].
% 171.08/171.33 180 meet(zero,meet(join(A,B),join(A,C))) = zero. [para(160(a,1),14(a,1)),flip(a)].
% 171.08/171.33 181 meet(A,meet(B,join(complement(A),meet(C,complement(A))))) = zero. [para(168(a,1),10(a,2,2)),rewrite([7(5),47(8)])].
% 171.08/171.33 184 meet(A,join(zero,join(complement(A),meet(B,complement(A))))) = zero. [para(168(a,1),26(a,1,2,2)),rewrite([8(6),168(12)])].
% 171.08/171.33 193 meet(zero,meet(join(A,join(B,C)),join(B,D))) = zero. [para(12(a,1),180(a,1,2,1))].
% 171.08/171.33 201 meet(one,join(A,B)) = join(A,B). [para(126(a,1),1(a,1)),rewrite([7(5),126(5),1(3)]),flip(a)].
% 171.08/171.33 202 meet(A,join(join(B,C),meet(join(B,join(C,D)),join(E,meet(A,join(B,C)))))) = meet(A,meet(join(B,join(C,E)),join(B,join(C,D)))). [para(126(a,1),14(a,1,2,2,2,2)),rewrite([201(3),201(4),8(3),12(3),8(2),12(3,R),8(2),201(12),8(11),12(11),8(10),12(11,R),8(10),201(14),8(13),12(13),8(12),12(13,R),8(12)])].
% 171.08/171.33 204 meet(A,join(B,join(C,meet(A,B)))) = meet(A,join(B,C)). [back_rewrite(146),rewrite([201(4)])].
% 171.08/171.33 207 meet(A,join(B,join(meet(A,C),meet(join(C,meet(A,C)),join(C,D))))) = meet(A,join(B,meet(join(C,meet(A,C)),join(C,D)))). [back_rewrite(143),rewrite([201(8),12(7),8(6),12(7,R),8(6)])].
% 171.08/171.33 219 meet(one,meet(join(A,B),join(A,join(B,C)))) = join(A,B). [para(201(a,1),28(a,1,2,1,2)),rewrite([2(4),8(4),12(4),8(3),12(4,R),8(3),201(9)])].
% 171.08/171.33 221 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(7(a,1),32(a,1,2)),rewrite([22(4)]),flip(a)].
% 171.08/171.33 222 meet(A,meet(B,meet(join(A,C),join(C,D)))) = meet(A,meet(B,join(C,D))). [para(32(a,1),10(a,2,2)),rewrite([7(4),221(9),10(8,R),7(7)])].
% 171.08/171.33 242 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),184(a,1,2,2,2)),rewrite([2(4)])].
% 171.08/171.33 247 join(zero,complement(A)) = complement(A). [hyper(17,a,242,a,b,62,a),flip(a)].
% 171.08/171.33 248 meet(complement(A),meet(join(A,B),join(A,C))) = meet(complement(A),join(A,meet(B,join(A,C)))). [para(4(a,1),33(a,1,2,2,2,2)),rewrite([19(4),7(3)]),flip(a)].
% 171.08/171.33 249 meet(meet(A,B),join(C,meet(join(C,D),join(E,meet(A,meet(B,C)))))) = meet(meet(A,B),meet(join(C,E),join(C,D))). [para(10(a,1),33(a,1,2,2,2,2)),rewrite([7(3),10(4,R),7(3)])].
% 171.08/171.33 250 meet(join(A,meet(join(A,B),join(C,meet(A,D)))),join(D,meet(join(D,E),join(F,meet(D,meet(join(A,C),join(A,B))))))) = meet(join(A,meet(join(A,B),join(C,meet(A,D)))),meet(join(D,F),join(D,E))). [para(14(a,1),33(a,1,2,2,2,2)),rewrite([7(2),7(16)])].
% 171.08/171.33 252 meet(meet(A,B),join(A,meet(join(A,C),join(D,meet(A,B))))) = meet(meet(A,B),meet(join(A,D),join(A,C))). [para(20(a,1),33(a,1,2,2,2,2))].
% 171.08/171.33 262 meet(A,complement(join(A,B))) = zero. [para(168(a,1),33(a,1,2,2)),rewrite([19(4),7(3),7(10),10(11,R),7(10),96(11)])].
% 171.08/171.33 266 meet(one,complement(A)) = complement(A). [para(247(a,1),201(a,1,2)),rewrite([247(6)])].
% 171.08/171.33 269 meet(one,meet(complement(A),join(B,complement(A)))) = complement(A). [para(266(a,1),28(a,1,2,1,2)),rewrite([2(4),8(4),266(9)])].
% 171.08/171.33 275 meet(A,join(B,meet(meet(A,B),join(B,C)))) = meet(A,B). [para(2(a,1),34(a,1,2,2,1)),rewrite([28(10)])].
% 171.08/171.33 282 meet(A,meet(join(B,C),join(B,D))) != zero | join(A,join(B,meet(join(C,meet(A,B)),join(B,D)))) != one | join(B,meet(join(C,meet(A,B)),join(B,D))) = complement(A). [para(34(a,1),17(a,1)),flip(c)].
% 171.08/171.33 304 meet(complement(A),join(B,complement(A))) = complement(A). [para(269(a,1),10(a,1)),rewrite([266(6),7(5)]),flip(a)].
% 171.08/171.33 307 meet(complement(A),meet(join(B,complement(A)),join(C,complement(A)))) = complement(A). [para(304(a,1),22(a,2)),rewrite([8(5)])].
% 171.08/171.33 316 meet(A,meet(B,join(C,meet(A,join(C,D))))) = meet(A,meet(B,join(C,D))). [para(6(a,1),35(a,1,2,2,2,2)),rewrite([7(2),8(6),222(10)])].
% 171.08/171.33 334 meet(A,meet(one,meet(join(B,C),join(B,D)))) = meet(A,meet(join(B,C),join(B,D))). [para(201(a,1),35(a,1,2)),rewrite([14(6)]),flip(a)].
% 171.08/171.33 346 meet(A,join(B,meet(join(B,C),join(B,D)))) = meet(A,meet(join(B,D),join(B,C))). [back_rewrite(131),rewrite([334(11)])].
% 171.08/171.33 352 meet(zero,meet(join(A,B),complement(C))) = zero. [para(247(a,1),193(a,1,2,2)),rewrite([8(3),19(3)])].
% 171.08/171.33 356 meet(zero,meet(complement(A),complement(B))) = zero. [para(247(a,1),352(a,1,2,1))].
% 171.08/171.33 360 meet(meet(A,B),meet(join(C,meet(A,B)),join(D,meet(A,B)))) = meet(A,B). [para(1(a,1),36(a,1,2,2,2,2)),rewrite([5(9)]),flip(a)].
% 171.08/171.33 361 meet(meet(join(A,meet(B,C)),join(D,meet(B,C))),join(meet(B,C),meet(join(D,meet(B,C)),join(A,meet(B,C))))) = meet(join(A,meet(B,C)),join(D,meet(B,C))). [para(1(a,1),36(a,2)),rewrite([7(15),360(15)])].
% 171.08/171.33 362 meet(A,meet(meet(B,C),join(D,meet(B,C)))) = meet(A,meet(B,C)). [para(2(a,1),36(a,1,2,2,1)),rewrite([6(7),2(7),7(6)]),flip(a)].
% 171.08/171.33 363 meet(A,join(meet(B,C),meet(B,join(D,meet(A,meet(B,C)))))) = meet(A,meet(B,join(D,meet(B,C)))). [para(6(a,1),36(a,1,2,2,1)),rewrite([6(11),7(10)])].
% 171.08/171.33 365 meet(A,join(meet(B,C),meet(join(D,meet(B,C)),join(E,meet(B,meet(C,A)))))) = meet(A,meet(join(E,meet(B,C)),join(D,meet(B,C)))). [para(36(a,1),7(a,2)),rewrite([10(5),7(4),10(5,R),7(4),7(9)])].
% 171.08/171.33 376 join(meet(A,B),meet(join(C,meet(A,B)),join(D,meet(A,B)))) = meet(one,meet(join(D,meet(A,B)),join(C,meet(A,B)))). [para(36(a,1),201(a,1)),rewrite([10(13),7(12),18(12),7(11)]),flip(a)].
% 171.08/171.33 377 meet(A,join(meet(B,complement(A)),meet(C,join(complement(A),meet(B,complement(A)))))) = zero. [para(181(a,1),36(a,2)),rewrite([51(9),19(8),7(7)])].
% 171.08/171.33 386 meet(one,meet(join(A,meet(B,C)),join(D,meet(B,C)))) = meet(join(A,meet(B,C)),join(D,meet(B,C))). [back_rewrite(361),rewrite([376(12),10(13,R),1(12)])].
% 171.08/171.33 514 complement(complement(A)) = A. [hyper(41,a,4,a,b,3,a)].
% 171.08/171.33 519 meet(A,B) != zero | one != A | complement(meet(A,B)) = A. [para(20(a,1),41(a,1)),rewrite([6(5)]),flip(b)].
% 171.08/171.33 813 meet(A,B) != zero | one != B | complement(meet(A,B)) = B. [para(7(a,1),519(a,1)),rewrite([7(6)])].
% 171.08/171.33 856 meet(A,join(meet(B,complement(A)),meet(C,meet(B,complement(A))))) = zero. [para(2(a,1),65(a,1,2,2)),rewrite([7(6),362(7),51(3),2(8)]),flip(a)].
% 171.08/171.33 858 meet(A,meet(B,join(C,meet(B,complement(A))))) = meet(A,join(meet(B,complement(A)),meet(C,B))). [para(6(a,1),65(a,1,2,2)),rewrite([7(4),6(10)])].
% 171.08/171.33 1088 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(219(a,1),10(a,1)),rewrite([201(6),7(5)]),flip(a)].
% 171.08/171.33 1095 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(95(a,1),1088(a,1,1)),rewrite([8(4),12(5,R),8(4),95(4),95(7)])].
% 171.08/171.33 1134 meet(A,join(meet(A,join(B,C)),meet(join(B,meet(A,join(B,C))),join(A,D)))) = meet(A,join(B,C)). [para(221(a,1),77(a,1,2,1)),rewrite([221(13)])].
% 171.08/171.33 1261 meet(A,join(B,meet(meet(B,A),join(B,C)))) = meet(B,A). [para(275(a,1),7(a,2)),rewrite([7(1),7(5),7(6)])].
% 171.08/171.33 1355 meet(A,meet(complement(A),complement(B))) = zero. [para(356(a,1),856(a,1,2,2)),rewrite([7(3),8(5),95(5)])].
% 171.08/171.33 1506 meet(meet(A,B),join(A,C)) = meet(A,B). [para(20(a,1),1261(a,1,2,2,1)),rewrite([221(6),20(5)])].
% 171.08/171.33 1507 meet(meet(A,join(B,C)),join(B,meet(meet(A,B),join(B,D)))) = meet(A,B). [para(22(a,1),1261(a,1,2,2,1)),rewrite([7(3),22(10),7(8)])].
% 171.08/171.33 1510 meet(meet(A,B),meet(join(A,C),join(A,D))) = meet(A,B). [back_rewrite(252),rewrite([1506(7)]),flip(a)].
% 171.08/171.33 1538 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),1506(a,1,1)),rewrite([7(4)])].
% 171.08/171.33 1560 meet(meet(A,join(B,C)),join(B,meet(A,B))) = meet(A,B). [back_rewrite(1507),rewrite([1538(5)])].
% 171.08/171.33 1950 meet(join(A,B),meet(join(A,C),join(A,B))) = meet(join(A,C),join(A,B)). [para(1(a,1),88(a,1,2,1,2)),rewrite([23(3),1(6),346(7),20(6),1(8),23(7)])].
% 171.08/171.33 1951 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(1(a,1),88(a,2)),rewrite([7(16),346(16),1(15),346(13),7(12),346(12),10(11),7(10),1950(10),20(9),7(8),346(8),10(7),7(6),1950(6),20(5)]),flip(a)].
% 171.08/171.33 1975 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(247(a,1),88(a,1,1)),rewrite([8(4),19(4),8(4),19(4),95(4),247(6),8(6),19(6),8(6),19(6),7(5),10(6),7(5),10(6,R),7(5),95(7),10(6,R),10(5),7(4),10(5,R),7(4),20(4),20(5),10(5,R),7(4),10(4,R),1(3),8(6),19(6),8(6),19(6),95(6),247(7)]),flip(a)].
% 171.08/171.33 2093 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(1975(a,1),4(a,1))].
% 171.08/171.33 2095 join(meet(A,B),meet(A,meet(B,complement(C)))) = meet(A,B). [para(1975(a,1),6(a,1,2))].
% 171.08/171.33 2107 meet(one,meet(join(A,B),complement(C))) = meet(join(A,B),complement(C)). [para(201(a,1),1975(a,1,1)),flip(a)].
% 171.08/171.33 2112 meet(one,meet(complement(A),complement(B))) = meet(complement(A),complement(B)). [para(266(a,1),1975(a,1,1)),flip(a)].
% 171.08/171.33 2113 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(1975(a,1),262(a,1)),rewrite([8(2)])].
% 171.08/171.33 2216 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(201(a,1),2113(a,1,2,2,1,2)),rewrite([12(4),8(3),12(4,R),8(3),2107(7)])].
% 171.08/171.33 2599 join(one,meet(complement(A),complement(B))) = one. [para(2112(a,1),6(a,1,2))].
% 171.08/171.33 2607 join(one,meet(A,complement(B))) = one. [para(514(a,1),2599(a,1,2,1))].
% 171.08/171.33 2741 join(one,meet(A,B)) = one. [para(514(a,1),2607(a,1,2,2))].
% 171.08/171.33 2860 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(514(a,1),2095(a,1,2,2,2))].
% 171.08/171.33 2896 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(201(a,1),2860(a,1,1)),rewrite([7(4),10(5,R),7(4),201(4),201(7)])].
% 171.08/171.33 2897 meet(meet(A,B),meet(join(C,meet(A,C)),join(C,D))) = meet(meet(A,B),join(C,meet(A,C))). [para(2860(a,1),33(a,1,2,2,2)),rewrite([7(3),10(4),7(3),22(4),7(2),7(6)]),flip(a)].
% 171.08/171.33 2898 join(complement(A),meet(B,complement(A))) = complement(A). [para(266(a,1),2860(a,1,1)),rewrite([7(4),10(5,R),18(4),266(7)])].
% 171.08/171.33 2939 meet(A,join(meet(B,complement(A)),meet(C,complement(A)))) = zero. [back_rewrite(377),rewrite([2898(6)])].
% 171.08/171.33 3065 join(join(A,B),meet(A,C)) = join(A,B). [para(1506(a,1),2896(a,1,2))].
% 171.08/171.33 3137 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),3065(a,1,1)),rewrite([8(4)])].
% 171.08/171.33 3184 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(25(a,1),3137(a,1,1)),rewrite([7(4),25(8)])].
% 171.08/171.33 3214 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [para(514(a,1),2939(a,1,2,1,2)),rewrite([7(2),514(4),7(3)])].
% 171.08/171.33 3244 meet(A,meet(complement(A),join(B,meet(A,C)))) = zero. [para(3214(a,1),70(a,2)),rewrite([514(3),7(2),20(3),6(3),514(3),7(2),20(3),10(5,R),7(4)])].
% 171.08/171.33 3353 meet(A,meet(complement(A),join(B,C))) = zero. [para(2896(a,1),3244(a,1,2,2))].
% 171.08/171.33 4578 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(1560(a,1),6(a,1,2)),rewrite([8(4)])].
% 171.08/171.33 4579 meet(meet(A,join(B,C)),join(C,meet(A,C))) = meet(A,C). [para(8(a,1),1560(a,1,1,2))].
% 171.08/171.33 5372 join(A,join(join(meet(B,C),meet(join(C,meet(B,C)),join(C,D))),meet(B,join(A,meet(join(C,meet(B,C)),join(C,D)))))) = join(A,join(meet(B,C),meet(join(C,meet(B,C)),join(C,D)))). [para(207(a,1),2896(a,1,2)),rewrite([8(14),12(14,R)])].
% 171.08/171.33 5726 meet(A,meet(join(B,join(C,meet(D,join(C,meet(B,E))))),join(B,join(C,F)))) = meet(A,join(B,C)). [para(3184(a,1),14(a,2,2,1)),rewrite([8(3),12(3),8(2),12(3,R),8(2),202(12),8(12),12(12),8(11),12(12,R),8(11),1088(13)])].
% 171.08/171.33 5746 meet(A,meet(complement(join(B,C)),join(B,meet(C,D)))) = zero. [para(3184(a,1),2113(a,1,2,2,1)),rewrite([8(3),7(5)])].
% 171.08/171.33 5930 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [hyper(102,a,5746,a,b,2741,a),rewrite([5746(12),8(7),95(7),8(11),1095(12),52(7)])].
% 171.08/171.33 5941 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),5930(a,1,1,1))].
% 171.08/171.33 5947 meet(complement(join(A,B)),join(A,meet(C,join(A,B)))) = zero. [para(23(a,1),5930(a,1,1,1)),rewrite([7(4)])].
% 171.08/171.33 6137 meet(A,complement(join(B,A))) = zero. [para(4(a,1),5941(a,1,2,2)),rewrite([19(4),7(3)])].
% 171.08/171.33 6153 meet(A,complement(join(B,join(C,A)))) = zero. [para(2216(a,1),5941(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1),19(5),7(4)])].
% 171.08/171.33 6177 meet(join(A,meet(B,C)),complement(join(A,join(B,D)))) = zero. [para(25(a,1),6153(a,1,2,1,2)),rewrite([8(3),12(4),8(3),12(4,R),8(3)])].
% 171.08/171.33 6550 meet(complement(join(A,B)),join(B,meet(C,join(A,B)))) = zero. [para(8(a,1),5947(a,1,1,1)),rewrite([8(3)])].
% 171.08/171.33 6586 meet(complement(join(A,join(B,C))),join(A,meet(B,D))) = zero. [para(6177(a,1),7(a,1)),flip(a)].
% 171.08/171.33 6587 meet(join(A,meet(B,C)),complement(join(A,join(C,D)))) = zero. [para(7(a,1),6177(a,1,1,2))].
% 171.08/171.33 6884 meet(complement(join(A,join(B,C))),join(C,meet(A,D))) = zero. [para(8(a,1),6586(a,1,1,1)),rewrite([8(2),12(2),8(1),12(2,R),8(1)])].
% 171.08/171.33 6912 meet(join(A,meet(B,C)),complement(join(C,join(A,D)))) = zero. [para(8(a,1),6587(a,1,1)),rewrite([8(2),12(4,R),8(3)])].
% 171.08/171.33 7334 meet(complement(join(A,B)),join(meet(B,C),meet(A,D))) = zero. [para(6(a,1),6884(a,1,1,1,2))].
% 171.08/171.33 7480 meet(complement(join(A,complement(B))),join(complement(B),meet(C,A))) = zero. [para(2898(a,1),6912(a,1,2,1,2)),rewrite([7(7)])].
% 171.08/171.33 7831 meet(complement(join(A,complement(B))),join(meet(A,C),complement(B))) = zero. [para(304(a,1),7334(a,1,2,2)),rewrite([8(2)])].
% 171.08/171.33 8254 join(A,complement(meet(A,B))) = one. [hyper(813,a,7831,a,b,3,a(flip)),rewrite([3(8),7(6),266(6),514(5),3(7)])].
% 171.08/171.33 8287 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [hyper(813,a,7831,a,b,8254,a(flip)),rewrite([7(2),10(2),7(1),10(2,R),7(1),8254(4),52(2),7(4),10(4),7(3),10(4,R),7(3),178(7),63(2),7(4),10(4),7(3),10(4,R),7(3)]),flip(a)].
% 171.08/171.33 8294 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [para(1560(a,1),8254(a,1,2,1)),rewrite([8(5)])].
% 171.08/171.33 8376 join(complement(A),complement(meet(B,complement(A)))) = one. [para(266(a,1),8287(a,1,1)),rewrite([7(4),10(5,R),18(4)])].
% 171.08/171.33 8410 meet(A,complement(B)) != zero | join(A,complement(B)) != one | A = B. [para(8376(a,1),57(b,1,2,2)),rewrite([7(2),18(7),8(6),8376(13),18(10),514(10)])].
% 171.08/171.33 8433 join(A,complement(meet(B,A))) = one. [hyper(813,a,6550,a,b,8294,a(flip)),rewrite([7(1),8254(3),52(2),7(2),7(4),8254(6),18(5),8(4),178(5),63(2),7(2),7(4),8254(6),18(5),8(4)]),flip(a)].
% 171.08/171.33 8446 join(A,join(join(B,C),complement(join(A,B)))) = one. [para(201(a,1),8294(a,1,1,1)),rewrite([8(5),12(5),8(4),12(5,R),8(4),201(6),12(5,R)])].
% 171.08/171.33 8622 join(A,meet(join(B,complement(A)),join(C,complement(A)))) = one. [para(307(a,1),8433(a,1,2,1)),rewrite([514(7),8(6)])].
% 171.08/171.33 8626 join(meet(join(A,B),join(A,C)),complement(meet(A,D))) = one. [para(1510(a,1),8433(a,1,2,1))].
% 171.08/171.33 8695 meet(meet(A,B),meet(join(C,D),join(C,E))) = meet(A,meet(B,meet(join(C,D),join(C,E)))). [para(7(a,1),249(a,2)),rewrite([249(8),10(10),7(9),10(10,R),7(9)])].
% 171.08/171.33 8904 meet(meet(A,B),join(join(C,D),meet(join(C,join(D,E)),join(meet(F,join(D,meet(C,V6))),meet(A,meet(B,join(C,D))))))) = meet(meet(A,B),join(C,D)). [para(3184(a,1),249(a,2,2,1)),rewrite([8(4),12(4),8(3),12(4,R),8(3),8(18),12(18),8(17),12(18,R),8(17),1088(19)])].
% 171.08/171.33 9047 meet(meet(A,B),join(C,meet(A,C))) = meet(A,meet(B,C)). [back_rewrite(2897),rewrite([8695(6),97(6),7(1)]),flip(a)].
% 171.08/171.33 9108 meet(A,meet(B,join(C,B))) = meet(A,B). [back_rewrite(4579),rewrite([9047(5),7(2)])].
% 171.08/171.33 9156 meet(meet(A,B),join(join(C,D),meet(join(C,join(D,E)),join(F,meet(A,meet(B,join(C,D))))))) = meet(A,meet(B,meet(join(C,join(D,F)),join(C,join(D,E))))). [para(178(a,1),250(a,1,1,2,2,2)),rewrite([8(3),19(3),19(3),95(3),8(4),12(4),8(3),12(4,R),8(3),8(7),19(7),8(7),19(7),7(6),10(7),7(6),10(7,R),7(6),8(14),19(14),178(15),19(14),95(14),8(14),12(14),8(13),12(14,R),8(13),8(16),12(16),8(15),12(16,R),8(15),8695(18)])].
% 171.08/171.33 9254 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [back_rewrite(8904),rewrite([9156(14),5726(9)]),flip(a)].
% 171.08/171.33 10499 join(A,join(B,complement(join(A,B)))) = one. [para(2(a,1),8446(a,1,2,1))].
% 171.08/171.33 10501 join(A,join(join(B,C),complement(join(A,C)))) = one. [para(8(a,1),8446(a,1,2,1))].
% 171.08/171.33 11014 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(6(a,1),10501(a,1,2,1))].
% 171.08/171.33 11190 join(join(A,B),complement(join(A,meet(B,C)))) = one. [para(11014(a,1),12(a,1)),rewrite([8(6)]),flip(a)].
% 171.08/171.33 11262 join(join(A,B),complement(join(B,meet(A,C)))) = one. [para(8(a,1),11190(a,1,1))].
% 171.08/171.33 11301 join(A,complement(join(meet(A,B),meet(A,C)))) = one. [para(6(a,1),11262(a,1,1))].
% 171.08/171.33 11355 join(complement(A),meet(join(A,B),join(C,A))) = one. [hyper(813,a,7480,a,b,8622,a(flip)),rewrite([514(2),8(3),12(3),8(2),62(3),52(2),514(4),8(3),514(5),178(7),63(2),514(4),8(3),514(5)]),flip(a)].
% 171.08/171.33 11368 meet(complement(A),join(A,B)) != zero | join(A,B) = A. [para(11355(a,1),57(b,1)),rewrite([8(11),3(11),7(11),201(11),514(11)]),xx(b)].
% 171.08/171.33 11920 join(meet(join(A,B),join(B,C)),complement(meet(B,D))) = one. [para(8(a,1),8626(a,1,1,1))].
% 171.08/171.33 13533 join(complement(A),meet(join(B,A),join(A,C))) = one. [para(1(a,1),11920(a,1,2,1)),rewrite([8(5)])].
% 171.08/171.33 14575 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(6(a,1),363(a,1,2,2,2)),rewrite([7(2),22(8)])].
% 171.08/171.33 14683 meet(A,join(meet(B,C),meet(B,A))) = meet(B,A). [para(14575(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 171.08/171.33 14684 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(7(a,1),14575(a,1,2,1))].
% 171.08/171.33 14685 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(8(a,1),14575(a,1,2))].
% 171.08/171.33 14799 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(14684(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 171.08/171.33 14976 meet(A,join(meet(B,C),meet(join(D,meet(B,C)),join(B,E)))) = meet(A,meet(join(B,E),join(D,meet(B,C)))). [para(3065(a,1),365(a,1,2,2,2)),rewrite([3065(10)])].
% 171.08/171.33 14988 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [back_rewrite(1134),rewrite([14976(9),316(6)])].
% 171.08/171.33 15051 join(A,meet(B,A)) = A. [para(18(a,1),14799(a,1,2,2)),rewrite([8(3),201(4),18(4)])].
% 171.08/171.33 15157 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [back_rewrite(5372),rewrite([15051(3),5(3),8(2),15051(2),15051(2),5(2),15051(7),5(7),8(6),15051(6)])].
% 171.08/171.33 16097 meet(join(A,B),join(C,join(A,B))) = join(A,B). [para(386(a,1),316(a,1)),rewrite([201(3),201(5),23(4),7(4),201(8),7(9),9108(10),201(7)])].
% 171.08/171.33 16102 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(25(a,1),16097(a,1,2)),rewrite([8(3),7(4)])].
% 171.08/171.33 17862 meet(A,join(join(B,C),meet(A,B))) = meet(A,join(B,C)). [para(4578(a,1),204(a,1,2,2)),rewrite([15051(4)]),flip(a)].
% 171.08/171.33 19160 meet(A,join(meet(B,join(A,C)),meet(B,D))) = meet(A,B). [para(14685(a,1),14988(a,1,2)),rewrite([7(2),22(3),7(3)]),flip(a)].
% 171.08/171.33 19176 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(8(a,1),16102(a,1,1))].
% 171.08/171.33 19620 meet(A,join(meet(A,B),meet(C,B))) = meet(A,B). [para(14684(a,1),17862(a,2)),rewrite([8(6),12(6),8(5),15051(5)])].
% 171.08/171.33 20566 meet(A,join(join(A,B),meet(complement(C),complement(D)))) = A. [para(2112(a,1),19160(a,1,2,2)),rewrite([201(3),18(8)])].
% 171.08/171.33 20634 meet(A,join(join(A,B),meet(C,complement(D)))) = A. [para(514(a,1),20566(a,1,2,2,1))].
% 171.08/171.33 20665 meet(A,join(join(A,B),meet(C,D))) = A. [para(514(a,1),20634(a,1,2,2,2))].
% 171.08/171.33 20749 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(20665(a,1),15157(a,1,2,2)),rewrite([8(3),12(4,R),12(3),8(2),12(3,R),8(2),23(4)]),flip(a)].
% 171.08/171.33 21004 meet(A,join(B,A)) = A. [para(4(a,1),19176(a,1,2,2)),rewrite([19(3),7(2),4(4),19(4)])].
% 171.08/171.33 21005 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [para(6(a,1),19176(a,1,1))].
% 171.08/171.33 21051 meet(A,join(B,meet(A,join(C,B)))) = meet(A,join(C,B)). [para(21004(a,1),19620(a,1,2,2)),rewrite([8(3)])].
% 171.08/171.33 21529 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(6(a,1),20749(a,1,1)),flip(a)].
% 171.08/171.33 29146 meet(A,meet(complement(B),join(B,meet(complement(A),complement(B))))) = zero. [para(4(a,1),858(a,2,2,2)),rewrite([7(4),7(10),8(12),95(12),1355(11)])].
% 171.08/171.33 29190 meet(join(A,B),join(A,meet(complement(A),complement(join(A,B))))) = A. [hyper(42,a,29146,a,b,13533,a),rewrite([514(2),8(1),8(2),7(5)]),flip(a)].
% 171.08/171.33 29197 meet(complement(A),meet(complement(B),join(B,meet(A,complement(B))))) = zero. [para(514(a,1),29146(a,1,2,2,2,1))].
% 171.08/171.33 29210 meet(A,meet(complement(B),join(complement(A),meet(B,A)))) = zero. [para(514(a,1),29197(a,1,2,1)),rewrite([514(4),10(6,R),7(5)])].
% 171.08/171.33 29225 meet(complement(A),join(A,meet(B,join(A,complement(join(A,B)))))) = zero. [para(5(a,1),29210(a,1,2,2,2)),rewrite([8(5),10(7,R),7(6),248(7)])].
% 171.08/171.33 29323 meet(join(A,B),join(A,join(C,B))) = join(A,B). [para(29190(a,1),19176(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1),8(3),7(4),29190(11),8(5)])].
% 171.08/171.33 29455 join(A,meet(B,join(A,complement(join(A,B))))) = A. [hyper(11368,a,29225,a)].
% 171.08/171.33 29493 meet(join(A,B),join(A,complement(join(A,B)))) = A. [para(23(a,1),29455(a,1,2,2,2,1)),rewrite([1951(6)])].
% 171.08/171.33 29499 meet(A,join(B,complement(join(A,B)))) = meet(A,B). [para(29455(a,1),221(a,1,2)),rewrite([8(2)]),flip(a)].
% 171.08/171.33 29513 meet(A,B) != zero | join(B,complement(join(A,B))) = complement(A). [para(29455(a,1),282(b,1,2,2,1)),rewrite([8(1),8(4),23(4),8(4),8(7),12(7,R),8(6),29323(8),29499(4),8(4),8(7),8(10),12(10,R),8(9),5(11),8(7),23(7),10499(7),8(7),8(10),29499(13),15051(11),8(10),8(13),12(13,R),8(12),5(14),8(10),23(10)]),xx(b)].
% 171.08/171.33 29517 meet(A,join(complement(A),meet(A,B))) = meet(A,B). [para(29455(a,1),14683(a,1,2)),rewrite([8(3),6(3),8(3),7(5),21004(5),8(4),6(4),8(4)]),flip(a)].
% 171.08/171.33 29564 meet(join(A,B),join(B,complement(join(A,B)))) = B. [para(8(a,1),29493(a,1,1)),rewrite([8(2)])].
% 171.08/171.33 29598 meet(A,join(B,complement(join(B,A)))) = meet(B,A). [para(29499(a,1),7(a,2)),rewrite([8(1),7(4),7(5)])].
% 171.08/171.33 29626 meet(A,join(B,complement(join(A,join(C,B))))) = meet(A,B). [para(29499(a,1),14988(a,1,2)),rewrite([7(2),22(3),8(3),12(3),8(2),12(3,R),8(2)]),flip(a)].
% 171.08/171.33 29665 meet(A,meet(B,join(complement(A),meet(A,C)))) = meet(A,meet(C,B)). [para(29517(a,1),10(a,2,2)),rewrite([7(4),10(7),7(6),10(7,R),7(6)])].
% 171.08/171.33 29824 meet(A,B) != zero | join(A,complement(join(A,B))) = complement(B). [para(29598(a,1),17(a,1)),rewrite([12(7,R),8(6),10499(7)]),flip(c),xx(b)].
% 171.08/171.33 29826 meet(A,B) != zero | complement(join(A,complement(join(A,B)))) = B. [para(29598(a,1),41(a,1)),rewrite([12(7,R),8(6),10499(7)]),xx(b)].
% 171.08/171.33 29842 meet(A,meet(B,join(C,complement(join(C,meet(A,B)))))) = meet(C,meet(A,B)). [para(29598(a,1),9254(a,1)),flip(a)].
% 171.08/171.33 29959 join(complement(join(A,B)),complement(join(A,complement(join(A,B))))) = complement(A). [hyper(29513,a,262,a)].
% 171.08/171.33 30067 meet(A,join(B,complement(join(B,join(A,C))))) = meet(B,A). [para(29626(a,1),7(a,2)),rewrite([8(1),12(2,R),8(1),7(5),7(6)])].
% 171.08/171.33 30162 join(A,complement(join(A,complement(join(A,B))))) = join(A,B). [hyper(29824,a,6137,a),rewrite([8(1),8(6),514(8)])].
% 171.08/171.33 30163 join(A,complement(join(A,meet(complement(A),join(B,C))))) = complement(meet(complement(A),join(B,C))). [hyper(29824,a,3353,a)].
% 171.08/171.33 30169 join(A,complement(join(A,meet(B,complement(A))))) = complement(meet(B,complement(A))). [hyper(29824,a,51,a)].
% 171.08/171.33 30234 complement(join(A,complement(join(A,B)))) = meet(complement(A),join(A,B)). [para(30162(a,1),29564(a,1,1)),rewrite([30162(10),8(8),29959(8),7(3)]),flip(a)].
% 171.08/171.33 30236 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(30162(a,1),30162(a,2)),rewrite([30234(4),30163(6),514(5)])].
% 171.08/171.33 30241 meet(A,B) != zero | meet(complement(A),join(A,B)) = B. [back_rewrite(29826),rewrite([30234(7)])].
% 171.08/171.33 30243 join(complement(A),meet(A,join(B,complement(A)))) = join(B,complement(A)). [para(514(a,1),30236(a,1,2,1)),rewrite([8(3),8(7)])].
% 171.08/171.33 30307 meet(complement(A),join(A,complement(join(A,B)))) = complement(join(A,B)). [hyper(30241,a,6137,a),rewrite([8(2),8(6)])].
% 171.08/171.33 30311 meet(complement(A),join(A,meet(B,complement(meet(A,B))))) = meet(B,complement(meet(A,B))). [hyper(30241,a,2093,a)].
% 171.08/171.33 30423 meet(A,complement(join(B,join(C,meet(A,complement(B)))))) = zero. [para(51(a,1),30067(a,2)),rewrite([8(5),9254(9),30307(8)])].
% 171.08/171.33 30464 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(2(a,1),30423(a,1,2,1,2))].
% 171.08/171.33 30484 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [hyper(8410,a,30464,a,b,11301,a),flip(a)].
% 171.08/171.33 30584 join(meet(A,B),meet(B,complement(meet(A,B)))) = B. [para(7(a,1),30484(a,1,1)),rewrite([7(2)])].
% 171.08/171.33 30634 join(A,meet(B,complement(meet(A,B)))) = join(A,B). [para(30584(a,1),21529(a,1,2)),flip(a)].
% 171.08/171.33 30660 meet(complement(A),join(A,B)) = meet(B,complement(meet(A,B))). [back_rewrite(30311),rewrite([30634(5)])].
% 171.08/171.33 30732 join(A,meet(B,meet(C,complement(meet(A,meet(B,C)))))) = join(A,meet(B,C)). [para(10(a,1),30634(a,1,2,2,1)),rewrite([10(3),7(2),10(3,R),7(2),1975(5)])].
% 171.08/171.33 30734 join(A,meet(B,meet(join(A,C),complement(meet(A,B))))) = join(A,meet(B,join(A,C))). [para(22(a,1),30634(a,1,2,2,1)),rewrite([7(5),10(5,R)])].
% 171.08/171.33 31387 meet(A,complement(meet(A,B))) = meet(A,complement(B)). [para(30660(a,2),20(a,1,2)),rewrite([8(2),22(4),7(3)]),flip(a)].
% 171.08/171.33 31388 meet(complement(A),join(B,A)) = meet(B,complement(A)). [para(30660(a,2),20(a,2)),rewrite([7(1),31387(3),20(3),8(4)]),flip(a)].
% 171.08/171.33 31399 meet(A,join(B,complement(A))) = meet(A,B). [para(514(a,1),30660(a,1,1)),rewrite([8(2),7(5),31387(7),514(5),7(4)])].
% 171.08/171.34 31459 meet(complement(meet(A,B)),complement(meet(A,complement(B)))) = complement(A). [para(8254(a,1),30660(a,1,2)),rewrite([18(3),31387(6)]),flip(a)].
% 171.08/171.34 31614 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(30660(a,1),21051(a,1,2,2)),rewrite([6(5),7(2)]),flip(a)].
% 171.08/171.34 31615 meet(A,complement(meet(B,A))) = meet(A,complement(B)). [para(30660(a,1),21051(a,2)),rewrite([31614(4),6(4),7(2)]),flip(a)].
% 171.08/171.34 31864 join(A,meet(B,complement(A))) = join(A,B). [para(30660(a,1),30236(a,1,2)),rewrite([31615(3)])].
% 171.08/171.34 31881 join(complement(A),meet(A,complement(B))) = complement(meet(A,B)). [para(30660(a,2),30584(a,1,2,2,1)),rewrite([7(1),31387(3),7(3),8(6),31388(7),31459(8),8(4),7(5)])].
% 171.08/171.34 31937 join(complement(A),meet(A,B)) = join(B,complement(A)). [back_rewrite(30243),rewrite([31399(4)])].
% 171.08/171.34 32087 join(A,complement(join(A,B))) = complement(meet(B,complement(A))). [back_rewrite(30169),rewrite([31864(3)])].
% 171.08/171.34 32111 complement(meet(A,B)) = join(complement(A),complement(B)). [back_rewrite(31881),rewrite([31937(4),8(3)]),flip(a)].
% 171.08/171.34 32128 meet(A,meet(B,join(C,complement(A)))) = meet(A,meet(B,C)). [back_rewrite(29665),rewrite([31937(3),7(5)])].
% 171.08/171.34 32137 join(A,meet(B,meet(C,complement(A)))) = join(A,meet(B,join(A,C))). [back_rewrite(30734),rewrite([32111(3),32128(6),7(3),31614(3)])].
% 171.08/171.34 32213 meet(A,meet(B,join(C,join(complement(A),complement(B))))) = meet(A,meet(B,C)). [back_rewrite(29842),rewrite([32087(4),1975(3),32111(4),32111(4),514(4),8(3),12(4,R),8(3),10(8),7(7),10(8,R),7(7)])].
% 171.08/171.34 32406 join(A,meet(B,join(A,C))) = join(A,meet(B,C)). [back_rewrite(30732),rewrite([32111(3),32111(3),32213(7),32137(4)])].
% 171.08/171.34 34689 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(221),rewrite([32406(3)])].
% 171.08/171.34 34849 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(21005),rewrite([34689(4),8(2),34689(3),8(1)]),flip(a)].
% 171.08/171.34 34850 $F # answer(prove_distributivity). [resolve(34849,a,16,a)].
% 171.08/171.34
% 171.08/171.34 % SZS output end Refutation
% 171.08/171.34 ============================== end of proof ==========================
% 171.08/171.34
% 171.08/171.34 ============================== STATISTICS ============================
% 171.08/171.34
% 171.08/171.34 Given=1475. Generated=2028436. Kept=34845. proofs=1.
% 171.08/171.34 Usable=514. Sos=5859. Demods=5689. Limbo=160, Disabled=28324. Hints=0.
% 171.08/171.34 Megabytes=41.49.
% 171.08/171.34 User_CPU=169.10, System_CPU=1.16, Wall_clock=170.
% 171.08/171.34
% 171.08/171.34 ============================== end of statistics =====================
% 171.08/171.34
% 171.08/171.34 ============================== end of search =========================
% 171.08/171.34
% 171.08/171.34 THEOREM PROVED
% 171.08/171.34 % SZS status Unsatisfiable
% 171.08/171.34
% 171.08/171.34 Exiting with 1 proof.
% 171.08/171.34
% 171.08/171.34 Process 6817 exit (max_proofs) Wed Jun 29 20:24:39 2022
% 171.08/171.34 Prover9 interrupted
%------------------------------------------------------------------------------