TSTP Solution File: LAT194-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT194-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 06:26:03 EDT 2022
% Result : Unsatisfiable 56.96s 57.22s
% Output : Refutation 56.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LAT194-1 : TPTP v8.1.0. Released v3.1.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 30 01:03:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 11.12/11.46 ============================== Prover9 ===============================
% 11.12/11.46 Prover9 (32) version 2009-11A, November 2009.
% 11.12/11.46 Process 17786 was started by sandbox2 on n008.cluster.edu,
% 11.12/11.46 Thu Jun 30 01:03:23 2022
% 11.12/11.46 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_17632_n008.cluster.edu".
% 11.12/11.46 ============================== end of head ===========================
% 11.12/11.46
% 11.12/11.46 ============================== INPUT =================================
% 11.12/11.46
% 11.12/11.46 % Reading from file /tmp/Prover9_17632_n008.cluster.edu
% 11.12/11.46
% 11.12/11.46 set(prolog_style_variables).
% 11.12/11.46 set(auto2).
% 11.12/11.46 % set(auto2) -> set(auto).
% 11.12/11.46 % set(auto) -> set(auto_inference).
% 11.12/11.46 % set(auto) -> set(auto_setup).
% 11.12/11.46 % set(auto_setup) -> set(predicate_elim).
% 11.12/11.46 % set(auto_setup) -> assign(eq_defs, unfold).
% 11.12/11.46 % set(auto) -> set(auto_limits).
% 11.12/11.46 % set(auto_limits) -> assign(max_weight, "100.000").
% 11.12/11.46 % set(auto_limits) -> assign(sos_limit, 20000).
% 11.12/11.46 % set(auto) -> set(auto_denials).
% 11.12/11.46 % set(auto) -> set(auto_process).
% 11.12/11.46 % set(auto2) -> assign(new_constants, 1).
% 11.12/11.46 % set(auto2) -> assign(fold_denial_max, 3).
% 11.12/11.46 % set(auto2) -> assign(max_weight, "200.000").
% 11.12/11.46 % set(auto2) -> assign(max_hours, 1).
% 11.12/11.46 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 11.12/11.46 % set(auto2) -> assign(max_seconds, 0).
% 11.12/11.46 % set(auto2) -> assign(max_minutes, 5).
% 11.12/11.46 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 11.12/11.46 % set(auto2) -> set(sort_initial_sos).
% 11.12/11.46 % set(auto2) -> assign(sos_limit, -1).
% 11.12/11.46 % set(auto2) -> assign(lrs_ticks, 3000).
% 11.12/11.46 % set(auto2) -> assign(max_megs, 400).
% 11.12/11.46 % set(auto2) -> assign(stats, some).
% 11.12/11.46 % set(auto2) -> clear(echo_input).
% 11.12/11.46 % set(auto2) -> set(quiet).
% 11.12/11.46 % set(auto2) -> clear(print_initial_clauses).
% 11.12/11.46 % set(auto2) -> clear(print_given).
% 11.12/11.46 assign(lrs_ticks,-1).
% 11.12/11.46 assign(sos_limit,10000).
% 11.12/11.46 assign(order,kbo).
% 11.12/11.46 set(lex_order_vars).
% 11.12/11.46 clear(print_given).
% 11.12/11.46
% 11.12/11.46 % formulas(sos). % not echoed (13 formulas)
% 11.12/11.46
% 11.12/11.46 ============================== end of input ==========================
% 11.12/11.46
% 11.12/11.46 % From the command line: assign(max_seconds, 300).
% 11.12/11.46
% 11.12/11.46 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 11.12/11.46
% 11.12/11.46 % Formulas that are not ordinary clauses:
% 11.12/11.46
% 11.12/11.46 ============================== end of process non-clausal formulas ===
% 11.12/11.46
% 11.12/11.46 ============================== PROCESS INITIAL CLAUSES ===============
% 11.12/11.46
% 11.12/11.46 ============================== PREDICATE ELIMINATION =================
% 11.12/11.46
% 11.12/11.46 ============================== end predicate elimination =============
% 11.12/11.46
% 11.12/11.46 Auto_denials:
% 11.12/11.46 % copying label prove_distributivity to answer in negative clause
% 11.12/11.46
% 11.12/11.46 Term ordering decisions:
% 11.12/11.46
% 11.12/11.46 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 11.12/11.46 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 11.12/11.46
% 11.12/11.46 ============================== end of process initial clauses ========
% 11.12/11.46
% 11.12/11.46 ============================== CLAUSES FOR SEARCH ====================
% 11.12/11.46
% 11.12/11.46 ============================== end of clauses for search =============
% 11.12/11.46
% 11.12/11.46 ============================== SEARCH ================================
% 11.12/11.46
% 11.12/11.46 % Starting search at 0.01 seconds.
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=185.000, iters=3333
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=131.000, iters=3420
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=127.000, iters=3401
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=123.000, iters=3373
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=113.000, iters=3393
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=103.000, iters=3370
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=95.000, iters=3386
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=93.000, iters=3353
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=89.000, iters=3409
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=87.000, iters=3370
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=83.000, iters=3360
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=81.000, iters=3359
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=79.000, iters=3350
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=77.000, iters=3375
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=73.000, iters=3438
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=71.000, iters=3420
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=69.000, iters=3370
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=67.000, iters=3360
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=65.000, iters=3361
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=63.000, iters=3360
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=61.000, iters=3387
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=59.000, iters=3346
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=57.000, iters=3376
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=55.000, iters=3366
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=54.000, iters=3350
% 11.12/11.46
% 11.12/11.46 Low Water (keep): wt=53.000, iters=3425
% 11.12/11.46
% 56.96/57.22 Low Water (keep): wt=51.000, iters=3367
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=50.000, iters=3360
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=49.000, iters=3418
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=48.000, iters=3394
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=47.000, iters=3395
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=46.000, iters=3392
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=45.000, iters=3366
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=44.000, iters=3355
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=43.000, iters=3333
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=42.000, iters=3334
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=41.000, iters=3349
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=40.000, iters=3350
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=6317, wt=199.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=8117, wt=197.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=9149, wt=195.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=5569, wt=193.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=5359, wt=191.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=5581, wt=187.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=6213, wt=185.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=5802, wt=183.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=5582, wt=179.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=7881, wt=175.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=6210, wt=173.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=6698, wt=171.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=4940, wt=169.000
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=16380, wt=18.000
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=39.000, iters=3405
% 56.96/57.22
% 56.96/57.22 Low Water (displace): id=16840, wt=16.000
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=38.000, iters=3387
% 56.96/57.22
% 56.96/57.22 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 17.92 sec).
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=37.000, iters=3384
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=36.000, iters=3343
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=35.000, iters=3351
% 56.96/57.22
% 56.96/57.22 Low Water (keep): wt=34.000, iters=3356
% 56.96/57.22
% 56.96/57.22 ============================== PROOF =================================
% 56.96/57.22 % SZS status Unsatisfiable
% 56.96/57.22 % SZS output start Refutation
% 56.96/57.22
% 56.96/57.22 % Proof 1 at 55.85 (+ 0.34) seconds: prove_distributivity.
% 56.96/57.22 % Length of proof is 226.
% 56.96/57.22 % Level of proof is 73.
% 56.96/57.22 % Maximum clause weight is 47.000.
% 56.96/57.22 % Given clauses 870.
% 56.96/57.22
% 56.96/57.22 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 56.96/57.22 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 56.96/57.22 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 56.96/57.22 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 56.96/57.22 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 56.96/57.22 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 56.96/57.22 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 56.96/57.22 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 56.96/57.22 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 56.96/57.22 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 56.96/57.22 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 56.96/57.22 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 56.96/57.22 13 meet(A,join(B,meet(A,meet(C,D)))) = meet(A,join(B,meet(C,join(meet(A,D),meet(B,D))))) # label(equation_H32) # label(axiom). [assumption].
% 56.96/57.22 14 meet(A,join(B,meet(C,join(meet(A,D),meet(B,D))))) = meet(A,join(B,meet(A,meet(C,D)))). [copy(13),flip(a)].
% 56.96/57.22 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 56.96/57.22 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 56.96/57.22 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 56.96/57.22 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 56.96/57.22 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 56.96/57.22 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)])].
% 56.96/57.22 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 56.96/57.22 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 56.96/57.22 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)])].
% 56.96/57.22 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 56.96/57.22 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 56.96/57.22 27 meet(A,join(B,meet(A,meet(C,join(meet(A,C),meet(B,C)))))) = meet(A,join(B,meet(A,C))). [para(1(a,1),14(a,1,2,2)),rewrite([25(4),7(7)]),flip(a)].
% 56.96/57.22 28 meet(meet(A,B),join(C,meet(A,join(meet(A,B),meet(B,C))))) = meet(meet(A,B),join(C,meet(A,B))). [para(1(a,1),14(a,2,2,2)),rewrite([7(3),10(3,R),1(2),7(3)])].
% 56.96/57.22 29 meet(A,join(meet(A,meet(B,C)),meet(B,join(meet(A,C),meet(A,meet(B,C)))))) = meet(A,meet(B,C)). [para(2(a,1),14(a,2,2)),rewrite([7(6),10(6,R),7(5),10(5,R),1(4),20(12)])].
% 56.96/57.22 30 meet(A,join(B,meet(C,join(zero,meet(B,complement(A)))))) = meet(A,join(B,meet(C,zero))). [para(4(a,1),14(a,1,2,2,2,1)),rewrite([21(10)])].
% 56.96/57.22 31 meet(A,join(B,meet(C,join(zero,meet(A,complement(B)))))) = meet(A,join(B,meet(A,meet(C,complement(B))))). [para(4(a,1),14(a,1,2,2,2,2)),rewrite([8(4)])].
% 56.96/57.22 32 meet(A,join(B,meet(C,join(A,meet(B,join(A,D)))))) = meet(A,join(B,meet(A,C))). [para(5(a,1),14(a,1,2,2,2,1)),rewrite([22(9)])].
% 56.96/57.22 33 meet(A,join(B,meet(C,join(B,meet(A,join(B,D)))))) = meet(A,join(B,meet(A,meet(C,join(B,D))))). [para(5(a,1),14(a,1,2,2,2,2)),rewrite([8(3)])].
% 56.96/57.22 34 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(6(a,1),14(a,1,2)),flip(a)].
% 56.96/57.22 36 meet(A,join(B,meet(C,join(meet(A,D),meet(D,B))))) = meet(A,join(B,meet(A,meet(C,D)))). [para(8(a,1),14(a,1,2)),rewrite([7(2),8(5)])].
% 56.96/57.22 42 meet(A,B) != zero | one != A | meet(A,B) = complement(A). [para(6(a,1),17(b,1)),rewrite([20(2)]),flip(b),flip(c)].
% 56.96/57.22 43 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(18(a,1),14(a,1,2,2,2,1)),rewrite([18(2),18(6)])].
% 56.96/57.22 44 meet(A,zero) != zero | one != A | complement(A) = zero. [para(19(a,1),17(b,1)),flip(b)].
% 56.96/57.22 45 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 56.96/57.22 48 one != A | complement(A) = zero. [back_rewrite(44),rewrite([45(2)]),xx(a)].
% 56.96/57.22 49 meet(A,join(B,meet(C,join(zero,meet(B,complement(A)))))) = meet(A,B). [back_rewrite(30),rewrite([45(9),19(9)])].
% 56.96/57.22 50 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([45(5)])].
% 56.96/57.22 51 complement(one) = zero. [hyper(17,a,45,a,b,19,a)].
% 56.96/57.22 52 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)])].
% 56.96/57.22 55 complement(join(A,one)) = zero. [hyper(48,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 56.96/57.22 57 join(A,one) = one. [para(55(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 56.96/57.22 58 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([57(5)])].
% 56.96/57.22 59 complement(zero) = one. [hyper(17,a,18,a,b,57,a)].
% 56.96/57.22 62 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(50(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),45(6)])].
% 56.96/57.22 66 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(58(a,1),17(b,1)),flip(c),xx(b)].
% 56.96/57.22 68 meet(A,join(B,meet(A,C))) != zero | join(A,B) != one | join(B,meet(A,C)) = complement(A). [para(25(a,1),17(b,1)),flip(c)].
% 56.96/57.22 99 meet(A,join(B,meet(A,B))) = meet(A,B). [para(1(a,1),34(a,1,2,2,2))].
% 56.96/57.22 100 meet(A,join(join(A,B),meet(A,C))) = A. [para(5(a,1),34(a,2)),rewrite([7(3),22(4)])].
% 56.96/57.22 101 meet(A,meet(B,join(C,meet(A,meet(C,D))))) = meet(A,meet(C,B)). [para(34(a,1),10(a,2,2)),rewrite([7(4),10(7),7(6),10(7,R),7(6)])].
% 56.96/57.22 102 meet(A,join(meet(B,C),meet(A,meet(B,meet(C,D))))) = meet(A,meet(B,C)). [para(10(a,1),34(a,2)),rewrite([7(3),10(3),7(2),10(3,R),7(2),10(8),7(7),10(8,R),7(7)])].
% 56.96/57.22 106 meet(A,join(one,meet(A,B))) = A. [para(18(a,1),34(a,2)),rewrite([7(3),18(3)])].
% 56.96/57.22 108 meet(A,join(meet(B,join(A,C)),meet(A,meet(B,D)))) = meet(A,B). [para(22(a,1),34(a,2)),rewrite([7(5),10(5,R),7(4),52(6)])].
% 56.96/57.22 109 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(50(a,1),34(a,2)),rewrite([7(5),10(5,R),7(4),62(6),8(4)])].
% 56.96/57.22 119 meet(A,join(one,meet(B,join(C,meet(A,C))))) = A. [para(106(a,1),14(a,2)),rewrite([7(4),18(4),8(3)])].
% 56.96/57.22 122 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),109(a,1,2,2))].
% 56.96/57.22 128 join(zero,complement(A)) = complement(A). [hyper(17,a,122,a,b,58,a),flip(a)].
% 56.96/57.22 159 meet(zero,complement(A)) = zero. [para(128(a,1),5(a,1,2))].
% 56.96/57.22 168 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(22(a,1),99(a,1,2,2)),rewrite([8(4),22(8)])].
% 56.96/57.22 177 meet(A,meet(B,join(join(A,C),meet(A,D)))) = meet(A,B). [para(100(a,1),10(a,2,2)),rewrite([7(4),7(6)])].
% 56.96/57.22 181 meet(A,join(join(join(A,B),meet(A,C)),meet(A,D))) = A. [para(100(a,1),34(a,2)),rewrite([7(7),177(8)])].
% 56.96/57.22 182 meet(meet(A,B),join(join(C,meet(A,B)),meet(meet(A,B),join(D,meet(A,B))))) = meet(A,B). [para(28(a,1),100(a,1,2,2)),rewrite([8(3)])].
% 56.96/57.22 185 meet(A,meet(B,join(meet(A,meet(C,D)),meet(C,join(meet(A,D),meet(A,meet(C,D))))))) = meet(A,meet(C,meet(D,B))). [para(29(a,1),10(a,2,2)),rewrite([7(9),10(13,R),7(12),10(12),7(11),10(12,R),7(11)])].
% 56.96/57.22 232 meet(A,join(B,join(one,meet(A,B)))) = A. [para(1(a,1),119(a,1,2,2)),rewrite([12(4,R),8(3)])].
% 56.96/57.22 260 meet(A,join(one,join(zero,meet(B,complement(A))))) = A. [para(109(a,1),232(a,1,2,2,2)),rewrite([19(7),8(6)])].
% 56.96/57.22 267 meet(A,join(one,complement(A))) = A. [para(1(a,1),260(a,1,2,2,2)),rewrite([128(4)])].
% 56.96/57.22 274 meet(A,meet(B,join(one,complement(A)))) = meet(A,B). [para(267(a,1),10(a,2,2)),rewrite([7(4),7(6)])].
% 56.96/57.22 278 meet(A,join(join(one,complement(A)),meet(A,B))) = A. [para(267(a,1),34(a,2)),rewrite([7(7),274(8)])].
% 56.96/57.22 280 meet(A,join(join(A,B),meet(C,join(A,B)))) = A. [para(1(a,1),32(a,1,2,2,2,2)),rewrite([23(3),100(9)])].
% 56.96/57.22 292 meet(A,join(meet(A,meet(B,join(C,meet(B,D)))),meet(B,join(meet(A,meet(B,join(C,meet(B,D)))),meet(A,join(C,meet(D,join(B,meet(C,join(B,E)))))))))) = meet(A,meet(B,join(C,meet(B,D)))). [para(32(a,1),29(a,1,2,1,2)),rewrite([32(16),8(15),32(24)])].
% 56.96/57.22 293 meet(zero,join(A,meet(B,join(zero,meet(A,B))))) = zero. [para(31(a,1),32(a,1,2,2)),rewrite([59(4),18(4),7(3),7(10),45(10),19(10),7(9),45(9)])].
% 56.96/57.22 310 meet(A,join(complement(A),join(one,meet(A,B)))) = A. [para(8(a,1),278(a,1,2)),rewrite([12(5),8(4)])].
% 56.96/57.22 319 meet(A,meet(B,join(complement(A),join(one,meet(A,C))))) = meet(A,B). [para(310(a,1),10(a,2,2)),rewrite([7(6),7(8)])].
% 56.96/57.22 327 meet(complement(A),join(A,meet(B,complement(A)))) = meet(complement(A),join(A,B)). [para(310(a,1),32(a,1,2,2,2,2)),rewrite([8(3),3(3),18(3),7(6)]),flip(a)].
% 56.96/57.22 349 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(310(a,1),33(a,1,2,2,2,2)),rewrite([8(3),3(3),18(3),8(2),319(11)]),flip(a)].
% 56.96/57.22 442 meet(A,join(meet(B,join(meet(B,C),meet(A,meet(B,C)))),meet(C,join(meet(A,C),meet(B,C))))) = meet(A,join(meet(A,C),meet(B,join(meet(B,C),meet(A,meet(B,C)))))). [para(27(a,1),36(a,1,2,2)),rewrite([7(1),7(3),10(3,R),7(2),7(7),7(12),7(14),10(14,R),7(13),1(17),8(18)])].
% 56.96/57.22 545 meet(zero,join(A,meet(B,join(zero,meet(B,A))))) = zero. [para(8(a,1),293(a,1,2)),rewrite([7(3),8(6)])].
% 56.96/57.22 715 meet(zero,join(A,B)) = zero. [para(5(a,1),545(a,1,2,2,2,2)),rewrite([8(4),19(4),1(3),8(3),23(3)])].
% 56.96/57.22 971 meet(A,join(B,meet(C,join(B,A)))) = meet(A,join(B,meet(C,A))). [para(43(a,1),7(a,2)),rewrite([8(1),7(4),7(5)])].
% 56.96/57.22 1275 meet(A,join(zero,meet(A,B))) = meet(A,B). [para(20(a,1),49(a,2)),rewrite([7(5),10(5),7(4),4(4),45(4),2(4),45(3),8(3)])].
% 56.96/57.22 1933 join(join(A,B),meet(A,C)) = join(A,B). [para(181(a,1),280(a,1,2,2)),rewrite([8(9),25(9),25(7),23(5),7(5),5(5)]),flip(a)].
% 56.96/57.22 1941 join(one,meet(A,B)) = one. [para(3(a,1),1933(a,1,1)),rewrite([3(5)])].
% 56.96/57.22 1942 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),1933(a,1,1)),rewrite([8(4)])].
% 56.96/57.22 1956 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [back_rewrite(182),rewrite([1942(8)])].
% 56.96/57.22 2049 join(complement(A),meet(B,complement(A))) = complement(A). [para(128(a,1),1942(a,1,1)),rewrite([7(3),128(7)])].
% 56.96/57.22 2163 meet(meet(A,B),join(A,C)) = meet(A,B). [para(1933(a,1),1956(a,1,2))].
% 56.96/57.22 2165 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),2163(a,1,1)),rewrite([7(4)])].
% 56.96/57.22 2459 meet(complement(A),join(zero,meet(A,join(B,complement(A))))) = zero. [para(349(a,1),168(a,1,2,2)),rewrite([7(3),4(3),7(9),4(9)])].
% 56.96/57.22 2558 meet(complement(meet(A,B)),join(zero,meet(A,B))) = zero. [para(2163(a,1),2459(a,1,2,2))].
% 56.96/57.22 2567 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(2558(a,1),33(a,1,2,2)),rewrite([2(3),45(2),8(4),19(4),8(6),19(6),7(5),1275(8)]),flip(a)].
% 56.96/57.22 2587 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(2567(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),45(7)])].
% 56.96/57.22 2717 meet(A,meet(B,meet(C,complement(meet(A,C))))) = zero. [para(2587(a,1),7(a,1)),rewrite([7(2),7(6),10(6,R),7(5),10(5,R),7(4)]),flip(a)].
% 56.96/57.22 2718 meet(A,meet(B,meet(C,meet(D,complement(meet(A,B)))))) = zero. [para(2587(a,1),10(a,2,2)),rewrite([7(5),10(5,R),7(4),10(4,R),7(3),45(8)])].
% 56.96/57.22 2723 meet(A,join(zero,meet(B,meet(C,complement(meet(A,B)))))) = zero. [para(2587(a,1),34(a,2)),rewrite([7(9),10(9,R),7(8),10(8,R),7(7),2718(10),8(6)])].
% 56.96/57.22 2847 meet(A,meet(B,meet(C,meet(D,complement(meet(A,C)))))) = zero. [para(2717(a,1),10(a,2,2)),rewrite([7(5),10(5,R),7(4),10(4,R),7(3),45(8)])].
% 56.96/57.22 2852 meet(A,join(zero,meet(B,meet(C,complement(meet(A,C)))))) = zero. [para(2717(a,1),34(a,2)),rewrite([7(9),10(9,R),7(8),10(8,R),7(7),2847(10),8(6)])].
% 56.96/57.22 3260 meet(A,join(zero,meet(B,meet(C,complement(meet(B,A)))))) = zero. [para(2723(a,1),7(a,1)),rewrite([7(3),7(8)]),flip(a)].
% 56.96/57.22 3578 meet(complement(meet(A,B)),join(zero,meet(C,meet(one,join(zero,meet(A,B)))))) = zero. [para(2558(a,1),2852(a,1,2,2,2,2,1)),rewrite([59(8),7(8)])].
% 56.96/57.22 3660 meet(complement(A),join(zero,meet(A,B))) = zero. [para(4(a,1),3260(a,1,2,2,2,2,1)),rewrite([59(4),18(4)])].
% 56.96/57.22 3664 meet(meet(A,complement(B)),join(zero,meet(B,C))) = zero. [para(50(a,1),3260(a,1,2,2,2,2,1)),rewrite([59(5),18(5)])].
% 56.96/57.22 3665 meet(meet(A,meet(B,complement(C))),join(zero,meet(C,D))) = zero. [para(62(a,1),3260(a,1,2,2,2,2,1)),rewrite([59(6),18(6)])].
% 56.96/57.22 3749 meet(complement(A),join(complement(complement(A)),join(zero,meet(A,B)))) = zero. [para(3660(a,1),349(a,1,2,2)),rewrite([19(5),4(4),8(8)]),flip(a)].
% 56.96/57.22 3831 join(zero,meet(A,complement(B))) = meet(A,complement(B)). [para(3664(a,1),6(a,1,2)),rewrite([8(4)])].
% 56.96/57.22 3896 meet(A,meet(complement(A),complement(B))) = zero. [para(3831(a,1),3660(a,1,2)),rewrite([10(4,R),7(3)])].
% 56.96/57.22 4849 meet(A,meet(B,meet(meet(C,complement(B)),complement(D)))) = zero. [para(3831(a,1),3665(a,1,2)),rewrite([10(6,R),10(5,R),10(6,R),7(5)])].
% 56.96/57.22 5178 meet(A,meet(meet(B,complement(A)),complement(C))) = zero. [hyper(17,a,4849,a,b,1941,a),rewrite([51(2)]),flip(a)].
% 56.96/57.22 5193 meet(A,join(complement(A),meet(meet(B,complement(A)),complement(C)))) = zero. [para(5178(a,1),349(a,1,2,2)),rewrite([19(3),4(2),8(7)]),flip(a)].
% 56.96/57.22 5593 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(1(a,1),3749(a,1,2,2,2)),rewrite([8(5),19(5),8(4)])].
% 56.96/57.22 5627 join(A,complement(complement(A))) = complement(complement(A)). [hyper(66,a,5593,a)].
% 56.96/57.22 5635 join(A,join(B,complement(complement(A)))) = join(B,complement(complement(A))). [para(5627(a,1),12(a,2,2)),rewrite([8(3)])].
% 56.96/57.22 6094 meet(meet(A,B),join(C,complement(complement(B)))) = meet(A,B). [para(5635(a,1),2165(a,1,2))].
% 56.96/57.22 6384 meet(A,join(B,complement(complement(join(A,C))))) = A. [para(5(a,1),6094(a,1,1)),rewrite([5(7)])].
% 56.96/57.22 6470 meet(A,complement(complement(join(A,B)))) = A. [para(2(a,1),6384(a,1,2))].
% 56.96/57.22 6513 meet(A,complement(join(A,B))) = zero. [para(6470(a,1),50(a,1,2)),rewrite([7(3)])].
% 56.96/57.22 6738 meet(A,join(complement(A),complement(join(A,B)))) = zero. [para(6513(a,1),349(a,1,2,2)),rewrite([19(3),4(2),8(5)]),flip(a)].
% 56.96/57.22 6745 meet(A,complement(complement(complement(A)))) = zero. [para(5627(a,1),6513(a,1,2,1))].
% 56.96/57.22 6991 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(4(a,1),102(a,1,2,2,2,2)),rewrite([45(3),45(3),8(3)])].
% 56.96/57.22 6993 meet(A,meet(B,join(meet(C,D),meet(A,meet(C,meet(D,E)))))) = meet(A,meet(C,meet(D,B))). [para(102(a,1),10(a,2,2)),rewrite([7(6),10(10,R),7(9),10(9),7(8),10(9,R),7(8)])].
% 56.96/57.22 7294 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [back_rewrite(3578),rewrite([6991(8),10(6),7(5),18(5),7(4),10(5),7(4),10(5,R),7(4),6991(7),10(5,R)])].
% 56.96/57.22 7677 meet(A,meet(meet(B,C),complement(meet(A,C)))) = zero. [para(7(a,1),7294(a,1,2,1))].
% 56.96/57.22 7715 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(5(a,1),7677(a,1,2,1))].
% 56.96/57.22 7747 meet(A,meet(meet(B,C),complement(meet(A,join(B,D))))) = zero. [para(2163(a,1),7677(a,1,2,1))].
% 56.96/57.22 7897 meet(A,complement(meet(one,join(A,B)))) = zero. [hyper(17,a,7715,a,b,1941,a),rewrite([51(2)]),flip(a)].
% 56.96/57.22 7898 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(7715(a,1),10(a,1)),rewrite([7(6)]),flip(a)].
% 56.96/57.22 7923 meet(complement(A),complement(meet(one,complement(A)))) = zero. [para(2049(a,1),7897(a,1,2,1,2))].
% 56.96/57.22 7938 meet(complement(A),meet(one,complement(meet(one,complement(A))))) = zero. [para(7923(a,1),2567(a,1,2,2,1)),rewrite([59(7),7(7)])].
% 56.96/57.22 8230 join(zero,meet(A,B)) = meet(A,B). [para(7898(a,1),6(a,1,2)),rewrite([8(3)])].
% 56.96/57.22 8231 meet(meet(A,B),complement(meet(B,join(A,C)))) = zero. [para(7(a,1),7898(a,1,1))].
% 56.96/57.22 8334 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(8230(a,1),1942(a,1,1)),rewrite([7(3),10(3),7(2),10(3,R),7(2),8230(7)])].
% 56.96/57.22 8343 meet(A,join(meet(one,join(A,B)),meet(A,C))) = A. [para(18(a,1),108(a,2)),rewrite([7(5),18(5)])].
% 56.96/57.22 8655 meet(complement(A),meet(one,join(B,complement(A)))) = complement(A). [para(7938(a,1),108(a,1,2,2)),rewrite([8(4),8(7),8230(7),18(9)])].
% 56.96/57.22 8866 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(5(a,1),8231(a,1,1))].
% 56.96/57.22 8934 meet(complement(A),join(B,complement(A))) = complement(A). [para(8655(a,1),10(a,1)),rewrite([18(6),7(5)]),flip(a)].
% 56.96/57.22 8935 meet(one,complement(A)) = complement(A). [para(8655(a,1),10(a,2)),rewrite([7(5),8934(5)])].
% 56.96/57.22 10501 meet(A,meet(meet(B,C),complement(join(B,D)))) = zero. [para(6513(a,1),185(a,2,2,2)),rewrite([7(3),7(6),8334(8),10(6),7(5),10(6,R),7(5),2(7),10(5,R),20(6),45(7),45(7)])].
% 56.96/57.22 10799 meet(meet(A,B),complement(join(A,C))) = zero. [hyper(17,a,10501,a,b,1941,a),rewrite([51(2)]),flip(a)].
% 56.96/57.22 10809 meet(meet(A,B),complement(join(B,C))) = zero. [para(7(a,1),10799(a,1,1))].
% 56.96/57.22 10813 meet(meet(A,B),complement(join(C,meet(A,B)))) = zero. [para(1956(a,1),10799(a,1,1)),rewrite([8(3)])].
% 56.96/57.22 10824 meet(meet(A,B),complement(join(C,meet(B,join(A,D))))) = zero. [para(22(a,1),10809(a,1,1)),rewrite([8(4)])].
% 56.96/57.22 11220 meet(A,meet(B,meet(C,complement(join(D,meet(B,C)))))) = zero. [para(10813(a,1),101(a,2,2)),rewrite([7(6),10(6),7(5),10(6,R),7(5),6993(10),45(8)])].
% 56.96/57.22 12305 meet(A,join(meet(A,B),meet(one,join(A,C)))) = A. [para(8(a,1),8343(a,1,2))].
% 56.96/57.22 14041 meet(meet(A,B),complement(meet(one,join(A,C)))) = zero. [hyper(17,a,7747,a,b,1941,a),rewrite([51(2)]),flip(a)].
% 56.96/57.22 14166 meet(meet(A,join(B,C)),complement(meet(one,join(B,C)))) = zero. [para(1933(a,1),14041(a,1,2,1,2)),rewrite([7(2)])].
% 56.96/57.22 14370 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(1956(a,1),292(a,1,2,2,2,2)),rewrite([7(9),7(12),10(12,R),10(11,R),22(11),7(13),7(16),10(16,R),10(15,R),22(15),971(20),22(13),7(9),8(10),8334(10),7(6),10(6,R),10(5),7(4),22(5),7(1),20(2),7(6),7(9),10(9,R),10(8,R),22(8)]),flip(a)].
% 56.96/57.22 15909 meet(A,complement(join(B,meet(one,join(A,C))))) = zero. [para(18(a,1),10824(a,1,1))].
% 56.96/57.22 16006 meet(join(A,B),complement(join(C,meet(one,join(A,B))))) = zero. [para(1933(a,1),15909(a,1,2,1,2,2))].
% 56.96/57.22 17124 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [hyper(17,a,11220,a,b,1941,a),rewrite([51(2)]),flip(a)].
% 56.96/57.22 19123 meet(A,meet(one,join(B,C))) = meet(A,join(B,C)). [para(14166(a,1),12305(a,1,2,1)),rewrite([8(7),8230(9),10(8,R),7(7),1956(7),10(4,R),7(3)])].
% 56.96/57.22 19162 meet(one,join(A,B)) = join(A,B). [para(19123(a,1),1(a,1)),rewrite([7(5),19123(5),1(3)]),flip(a)].
% 56.96/57.22 19203 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [back_rewrite(16006),rewrite([19162(4),12(3),8(2),12(3,R),8(2)])].
% 56.96/57.22 19237 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(19162(a,1),1956(a,1,1)),rewrite([19162(4),12(3),8(2),12(3,R),8(2),19162(7)])].
% 56.96/57.22 19401 meet(join(A,B),complement(join(A,complement(complement(B))))) = zero. [para(5627(a,1),19203(a,1,2,1,2))].
% 56.96/57.22 19420 complement(join(A,complement(complement(join(B,complement(A)))))) = zero. [hyper(42,a,19401,a,b,58,a(flip)),rewrite([58(3),8935(8),58(9),51(8)])].
% 56.96/57.22 19421 complement(join(A,complement(complement(complement(A))))) = zero. [hyper(42,a,19401,a,b,3,a(flip)),rewrite([3(2),8935(7),3(7),51(7)])].
% 56.96/57.22 19434 join(A,complement(complement(complement(A)))) = one. [para(19421(a,1),3(a,1,2)),rewrite([8(6),12(6,R),19(5)])].
% 56.96/57.22 19435 complement(complement(complement(A))) = complement(A). [hyper(17,a,6745,a,b,19434,a),flip(a)].
% 56.96/57.22 19485 join(A,complement(complement(join(B,complement(A))))) = one. [para(19420(a,1),3(a,1,2)),rewrite([8(7),12(7,R),8(6),128(6)])].
% 56.96/57.22 19740 meet(join(A,B),join(B,complement(complement(A)))) = join(A,B). [para(5635(a,1),19237(a,1,2))].
% 56.96/57.22 19977 meet(join(A,B),complement(join(B,join(C,complement(complement(A)))))) = zero. [para(19740(a,1),10809(a,1,1)),rewrite([8(5),12(5,R),8(4)])].
% 56.96/57.22 21182 meet(join(A,B),complement(join(join(B,C),complement(complement(A))))) = zero. [para(23(a,1),19977(a,1,1)),rewrite([12(6),8(5),12(5),8(4),12(5,R),8(4),12(6,R),5635(6)])].
% 56.96/57.22 21959 meet(join(A,B),complement(join(join(A,C),complement(complement(B))))) = zero. [para(21182(a,1),7(a,1)),rewrite([8(7),7(8)]),flip(a)].
% 56.96/57.22 22065 complement(join(join(A,B),complement(complement(join(C,complement(A)))))) = zero. [hyper(42,a,21959,a,b,19485,a(flip)),rewrite([19485(5),19435(7),8935(9),19485(12),51(9)])].
% 56.96/57.22 22094 complement(join(join(A,B),complement(complement(join(C,complement(B)))))) = zero. [para(8(a,1),22065(a,1,1,1))].
% 56.96/57.22 22104 complement(join(A,complement(complement(join(B,complement(meet(A,C))))))) = zero. [para(6(a,1),22094(a,1,1,1))].
% 56.96/57.22 22124 complement(join(A,complement(meet(A,B)))) = zero. [para(2(a,1),22104(a,1,1,2,1,1)),rewrite([19435(4)])].
% 56.96/57.22 22127 join(A,complement(meet(A,B))) = one. [para(22124(a,1),3(a,1,2)),rewrite([8(5),12(5,R),8(4),128(4)])].
% 56.96/57.22 22134 complement(join(join(A,B),complement(meet(A,C)))) = zero. [hyper(42,a,21959,a,b,22127,a(flip)),rewrite([22127(3),19435(6),8935(7),22127(8),51(7)])].
% 56.96/57.22 22260 join(A,join(join(B,C),complement(meet(B,D)))) = one. [para(22134(a,1),58(a,1,2,2)),rewrite([19(6),8(5)])].
% 56.96/57.22 22381 join(join(A,B),complement(meet(A,C))) = one. [hyper(17,a,715,a,b,22260,a),rewrite([59(2)]),flip(a)].
% 56.96/57.22 22389 join(join(A,B),complement(meet(B,C))) = one. [para(8(a,1),22381(a,1,1))].
% 56.96/57.22 22400 join(A,join(join(B,C),complement(join(A,B)))) = one. [para(19237(a,1),22381(a,1,2,1)),rewrite([8(2),12(2),8(1),12(2,R),8(1),8(5),12(5,R)])].
% 56.96/57.22 22415 join(complement(A),complement(meet(B,meet(C,complement(A))))) = one. [para(2049(a,1),22389(a,1,1)),rewrite([7(4),10(4,R),7(3)])].
% 56.96/57.22 22765 join(A,join(join(B,C),complement(join(A,C)))) = one. [para(8(a,1),22400(a,1,2,1))].
% 56.96/57.22 22773 join(A,join(complement(A),complement(B))) = one. [para(128(a,1),22400(a,1,2,1)),rewrite([19(3),8(3)])].
% 56.96/57.22 22800 join(complement(A),complement(join(A,B))) = complement(A). [hyper(17,a,6738,a,b,22773,a),flip(a)].
% 56.96/57.22 22867 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(22800(a,1),8934(a,1,2)),rewrite([7(4)])].
% 56.96/57.22 23109 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(6(a,1),22765(a,1,2,1))].
% 56.96/57.22 23342 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(22867(a,1),17124(a,1,2))].
% 56.96/57.22 23356 meet(join(A,B),complement(join(A,meet(B,complement(A))))) = zero. [para(23342(a,1),327(a,1,2,2)),rewrite([8(9),12(9,R),8(8),8230(8),7(8),4(8),8(9),25(9),8(6),7(7)]),flip(a)].
% 56.96/57.22 23696 join(join(A,B),complement(join(A,meet(B,C)))) = one. [para(23109(a,1),12(a,1)),rewrite([8(6)]),flip(a)].
% 56.96/57.22 23854 join(join(A,B),complement(join(B,meet(A,C)))) = one. [para(8(a,1),23696(a,1,1))].
% 56.96/57.22 23925 join(A,complement(join(meet(A,B),meet(A,C)))) = one. [para(6(a,1),23854(a,1,1))].
% 56.96/57.22 24236 complement(join(A,meet(complement(A),complement(meet(A,B))))) = zero. [hyper(42,a,23356,a,b,22127,a(flip)),rewrite([22127(3),7(5),8935(8),22127(9),51(8)])].
% 56.96/57.22 24239 complement(join(A,meet(B,complement(A)))) = complement(join(A,B)). [hyper(17,a,23356,a,b,23696,a),flip(a)].
% 56.96/57.22 24245 meet(complement(join(A,B)),join(A,meet(B,complement(A)))) = zero. [para(23356(a,1),5193(a,1,2,2,1)),rewrite([24239(7),159(8),8(7),128(7),7(6)])].
% 56.96/57.22 24252 join(A,meet(complement(A),complement(meet(A,B)))) = one. [para(24236(a,1),3(a,1,2)),rewrite([8(7),12(7,R),8(6),8230(6)])].
% 56.96/57.22 24261 meet(complement(A),complement(meet(A,B))) = complement(A). [hyper(17,a,3896,a,b,24252,a),flip(a)].
% 56.96/57.22 24298 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(24261(a,1),2049(a,1,2)),rewrite([8(4)])].
% 56.96/57.22 24325 join(complement(meet(A,B)),complement(meet(C,complement(A)))) = one. [para(24261(a,1),22415(a,1,2,1,2))].
% 56.96/57.22 24556 join(complement(meet(A,B)),complement(meet(C,complement(B)))) = one. [para(7(a,1),24325(a,1,1,1))].
% 56.96/57.22 24648 join(complement(meet(A,complement(B))),complement(meet(C,B))) = one. [para(24556(a,1),19740(a,2)),rewrite([24556(6),19435(8),19162(8)])].
% 56.96/57.22 24775 meet(complement(join(A,B)),join(B,meet(A,complement(B)))) = zero. [para(8(a,1),24245(a,1,1,1))].
% 56.96/57.22 24926 meet(A,complement(join(B,A))) = zero. [para(24775(a,1),7715(a,1,2,2,1)),rewrite([59(4),18(4),7(3)])].
% 56.96/57.22 24941 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [para(25(a,1),24926(a,1,2,1)),rewrite([8(3),7(5)])].
% 56.96/57.22 24953 meet(complement(A),join(A,meet(B,complement(complement(A))))) = zero. [para(5627(a,1),24941(a,1,1,1)),rewrite([19435(3),7(4)])].
% 56.96/57.22 25000 complement(complement(A)) = A. [para(24953(a,1),68(a,1)),rewrite([8(5),3(5),4(10),19(8)]),flip(c),xx(a),xx(b)].
% 56.96/57.22 26053 join(A,meet(B,complement(A))) = join(A,B). [para(24239(a,1),25000(a,1,1)),rewrite([25000(3)]),flip(a)].
% 56.96/57.22 26214 join(A,B) != one | meet(B,complement(A)) = complement(A). [para(26053(a,1),17(b,1)),rewrite([50(3)]),flip(c),xx(a)].
% 56.96/57.22 26215 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(23(a,1),26053(a,2)),rewrite([7(3)])].
% 56.96/57.22 26220 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(8866(a,1),26053(a,1,2)),rewrite([8(5),8230(5),8(7)]),flip(a)].
% 56.96/57.22 26230 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(25000(a,1),26053(a,1,2,2)),rewrite([7(2),8(5)])].
% 56.96/57.22 26372 join(A,complement(B)) != one | meet(B,A) = B. [para(26230(a,1),17(b,1)),rewrite([10(3),7(2),4(2),45(2),25000(9)]),flip(c),xx(a)].
% 56.96/57.22 26401 join(complement(A),meet(B,complement(meet(A,B)))) = complement(A). [para(2567(a,1),26230(a,1,2)),rewrite([19(3),8(6)]),flip(a)].
% 56.96/57.22 26679 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [hyper(26372,a,23925,a),rewrite([7(4)])].
% 56.96/57.22 27121 meet(A,meet(complement(B),complement(meet(C,B)))) = meet(A,complement(B)). [hyper(26214,a,24648,a),rewrite([25000(6),10(5),7(4),10(5,R),7(4),25000(9)])].
% 56.96/57.22 27145 join(A,complement(B)) != one | meet(A,B) = B. [para(26230(a,1),26214(a,1)),rewrite([7(5),25000(7),7(6),10(6,R),1(5),25000(7)])].
% 56.96/57.22 27270 meet(A,meet(B,join(C,A))) = meet(A,B). [hyper(27145,a,22389,a),rewrite([10(3),7(2),10(3,R),7(2)])].
% 56.96/57.22 27274 meet(A,meet(B,join(C,B))) = meet(A,B). [para(27270(a,1),10(a,2)),rewrite([7(2),7(4)])].
% 56.96/57.22 27338 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(27274(a,1),442(a,1,2,1,2,2)),rewrite([8(1),5(2),5(3),8(1),8(2),8(4),5(5),8(4),26220(6),14370(6),8(3),8(5),5(6),8(5),5(6),5(7),8(5)]),flip(a)].
% 56.96/57.22 27471 join(A,meet(B,join(meet(A,C),meet(C,complement(A))))) = join(A,meet(B,meet(C,complement(A)))). [para(14(a,1),26215(a,1,2)),rewrite([10(4),7(3),10(4,R),7(3),26215(7),7(6),8(8)]),flip(a)].
% 56.96/57.22 27474 meet(A,join(B,meet(A,meet(complement(B),join(B,C))))) = meet(A,join(B,C)). [para(26215(a,1),33(a,1,2)),rewrite([27338(4)]),flip(a)].
% 56.96/57.22 27517 meet(A,complement(meet(A,B))) = meet(A,complement(B)). [para(26401(a,1),1956(a,1,2)),rewrite([7(1),7(5),10(5,R),7(4),27121(5),7(3)]),flip(a)].
% 56.96/57.22 27822 join(meet(A,B),meet(A,complement(B))) = A. [para(27517(a,1),26053(a,1,2)),rewrite([8(6),6(6)])].
% 56.96/57.22 27824 complement(meet(A,B)) = join(complement(A),complement(B)). [para(27517(a,1),26230(a,1,2)),rewrite([26230(4),8(3),8(7),24298(7)]),flip(a)].
% 56.96/57.22 27839 meet(A,complement(join(complement(A),complement(B)))) = meet(A,join(B,complement(A))). [para(27517(a,1),27517(a,1,2,1)),rewrite([27824(3),25000(3),8(2),27824(5)]),flip(a)].
% 56.96/57.22 29311 join(meet(A,B),meet(B,complement(A))) = B. [para(7(a,1),27822(a,1,1))].
% 56.96/57.22 29352 join(A,meet(B,meet(C,complement(A)))) = join(A,meet(B,C)). [back_rewrite(27471),rewrite([29311(4)]),flip(a)].
% 56.96/57.22 29514 complement(join(complement(A),complement(B))) = meet(A,B). [para(27824(a,1),25000(a,1,1))].
% 56.96/57.22 29552 meet(A,join(B,complement(A))) = meet(A,B). [back_rewrite(27839),rewrite([29514(4),20(2)]),flip(a)].
% 56.96/57.22 30934 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(25000(a,1),29552(a,1,2,2)),rewrite([8(2),7(5)])].
% 56.96/57.22 31205 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(27474),rewrite([30934(3),29352(4)])].
% 56.96/57.22 33289 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(26679),rewrite([31205(4),8(2),31205(3),8(1)]),flip(a)].
% 56.96/57.22 33290 $F # answer(prove_distributivity). [resolve(33289,a,16,a)].
% 56.96/57.22
% 56.96/57.22 % SZS output end Refutation
% 56.96/57.22 ============================== end of proof ==========================
% 56.96/57.22
% 56.96/57.22 ============================== STATISTICS ============================
% 56.96/57.22
% 56.96/57.22 Given=870. Generated=608802. Kept=33285. proofs=1.
% 56.96/57.22 Usable=188. Sos=3344. Demods=5376. Limbo=2084, Disabled=27681. Hints=0.
% 56.96/57.22 Megabytes=47.28.
% 56.96/57.22 User_CPU=55.86, System_CPU=0.34, Wall_clock=57.
% 56.96/57.22
% 56.96/57.22 ============================== end of statistics =====================
% 56.96/57.22
% 56.96/57.22 ============================== end of search =========================
% 56.96/57.22
% 56.96/57.22 THEOREM PROVED
% 56.96/57.22 % SZS status Unsatisfiable
% 56.96/57.22
% 56.96/57.22 Exiting with 1 proof.
% 56.96/57.22
% 56.96/57.22 Process 17786 exit (max_proofs) Thu Jun 30 01:04:20 2022
% 56.96/57.22 Prover9 interrupted
%------------------------------------------------------------------------------