TSTP Solution File: LAT248-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT248-1 : 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 06:26:23 EDT 2022
% Result : Timeout 290.27s 290.54s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT248-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 20:57:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.26/9.59 ============================== Prover9 ===============================
% 9.26/9.59 Prover9 (32) version 2009-11A, November 2009.
% 9.26/9.59 Process 9923 was started by sandbox2 on n007.cluster.edu,
% 9.26/9.59 Wed Jun 29 20:57:53 2022
% 9.26/9.59 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9769_n007.cluster.edu".
% 9.26/9.59 ============================== end of head ===========================
% 9.26/9.59
% 9.26/9.59 ============================== INPUT =================================
% 9.26/9.59
% 9.26/9.59 % Reading from file /tmp/Prover9_9769_n007.cluster.edu
% 9.26/9.59
% 9.26/9.59 set(prolog_style_variables).
% 9.26/9.59 set(auto2).
% 9.26/9.59 % set(auto2) -> set(auto).
% 9.26/9.59 % set(auto) -> set(auto_inference).
% 9.26/9.59 % set(auto) -> set(auto_setup).
% 9.26/9.59 % set(auto_setup) -> set(predicate_elim).
% 9.26/9.59 % set(auto_setup) -> assign(eq_defs, unfold).
% 9.26/9.59 % set(auto) -> set(auto_limits).
% 9.26/9.59 % set(auto_limits) -> assign(max_weight, "100.000").
% 9.26/9.59 % set(auto_limits) -> assign(sos_limit, 20000).
% 9.26/9.59 % set(auto) -> set(auto_denials).
% 9.26/9.59 % set(auto) -> set(auto_process).
% 9.26/9.59 % set(auto2) -> assign(new_constants, 1).
% 9.26/9.59 % set(auto2) -> assign(fold_denial_max, 3).
% 9.26/9.59 % set(auto2) -> assign(max_weight, "200.000").
% 9.26/9.59 % set(auto2) -> assign(max_hours, 1).
% 9.26/9.59 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 9.26/9.59 % set(auto2) -> assign(max_seconds, 0).
% 9.26/9.59 % set(auto2) -> assign(max_minutes, 5).
% 9.26/9.59 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 9.26/9.59 % set(auto2) -> set(sort_initial_sos).
% 9.26/9.59 % set(auto2) -> assign(sos_limit, -1).
% 9.26/9.59 % set(auto2) -> assign(lrs_ticks, 3000).
% 9.26/9.59 % set(auto2) -> assign(max_megs, 400).
% 9.26/9.59 % set(auto2) -> assign(stats, some).
% 9.26/9.59 % set(auto2) -> clear(echo_input).
% 9.26/9.59 % set(auto2) -> set(quiet).
% 9.26/9.59 % set(auto2) -> clear(print_initial_clauses).
% 9.26/9.59 % set(auto2) -> clear(print_given).
% 9.26/9.59 assign(lrs_ticks,-1).
% 9.26/9.59 assign(sos_limit,10000).
% 9.26/9.59 assign(order,kbo).
% 9.26/9.59 set(lex_order_vars).
% 9.26/9.59 clear(print_given).
% 9.26/9.59
% 9.26/9.59 % formulas(sos). % not echoed (14 formulas)
% 9.26/9.59
% 9.26/9.59 ============================== end of input ==========================
% 9.26/9.59
% 9.26/9.59 % From the command line: assign(max_seconds, 300).
% 9.26/9.59
% 9.26/9.59 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 9.26/9.59
% 9.26/9.59 % Formulas that are not ordinary clauses:
% 9.26/9.59
% 9.26/9.59 ============================== end of process non-clausal formulas ===
% 9.26/9.59
% 9.26/9.59 ============================== PROCESS INITIAL CLAUSES ===============
% 9.26/9.59
% 9.26/9.59 ============================== PREDICATE ELIMINATION =================
% 9.26/9.59
% 9.26/9.59 ============================== end predicate elimination =============
% 9.26/9.59
% 9.26/9.59 Auto_denials:
% 9.26/9.59 % copying label prove_distributivity to answer in negative clause
% 9.26/9.59
% 9.26/9.59 Term ordering decisions:
% 9.26/9.59
% 9.26/9.59 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 9.26/9.59 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 9.26/9.59
% 9.26/9.59 ============================== end of process initial clauses ========
% 9.26/9.59
% 9.26/9.59 ============================== CLAUSES FOR SEARCH ====================
% 9.26/9.59
% 9.26/9.59 ============================== end of clauses for search =============
% 9.26/9.59
% 9.26/9.59 ============================== SEARCH ================================
% 9.26/9.59
% 9.26/9.59 % Starting search at 0.01 seconds.
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=122.000, iters=3346
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=103.000, iters=3335
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=70.000, iters=3376
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=69.000, iters=3369
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=63.000, iters=3356
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=61.000, iters=3383
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=59.000, iters=3381
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=57.000, iters=3356
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=56.000, iters=3380
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=55.000, iters=3434
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=53.000, iters=3366
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=52.000, iters=3354
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=50.000, iters=3397
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=49.000, iters=3390
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=48.000, iters=3341
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=46.000, iters=3430
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=45.000, iters=3376
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=44.000, iters=3338
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=43.000, iters=3353
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=42.000, iters=3390
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=41.000, iters=3342
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=40.000, iters=3408
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=39.000, iters=3334
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=38.000, iters=3365
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=37.000, iters=3341
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=36.000, iters=3378
% 9.26/9.59
% 9.26/9.59 Low Water (keep): wt=35.000, iters=3376
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=34.000, iters=3413
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8173, wt=160.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8174, wt=154.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8154, wt=148.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8085, wt=142.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7320, wt=136.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7300, wt=132.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7232, wt=126.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8153, wt=125.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=6663, wt=124.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8088, wt=120.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8084, wt=119.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=6664, wt=118.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=6644, wt=116.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7299, wt=115.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7104, wt=112.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=6576, wt=110.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8169, wt=109.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7235, wt=106.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8147, wt=105.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8093, wt=103.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=4936, wt=102.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8128, wt=101.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7597, wt=100.000
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=33.000, iters=3342
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8485, wt=99.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=5420, wt=98.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8472, wt=97.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8532, wt=96.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8538, wt=95.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8132, wt=94.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8146, wt=93.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8168, wt=92.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8464, wt=91.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8492, wt=90.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8466, wt=89.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=6312, wt=88.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8511, wt=87.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8113, wt=86.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7292, wt=85.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8471, wt=84.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8510, wt=83.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8103, wt=82.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8442, wt=81.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8412, wt=80.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8531, wt=79.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8455, wt=78.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8509, wt=77.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8144, wt=76.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8491, wt=75.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8390, wt=74.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8425, wt=73.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8441, wt=72.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8469, wt=71.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7290, wt=70.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=8318, wt=69.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=7270, wt=68.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=14014, wt=24.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=14063, wt=19.000
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=32.000, iters=3340
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=14745, wt=17.000
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=31.000, iters=3333
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=15232, wt=16.000
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=15557, wt=15.000
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=30.000, iters=3343
% 290.27/290.54
% 290.27/290.54 Low Water (displace): id=15947, wt=14.000
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=29.000, iters=3355
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=28.000, iters=3334
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=27.000, iters=3337
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=26.000, iters=3345
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=25.000, iters=3333
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=24.000, iters=5631
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=22.000, iters=4518
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=20.000, iters=3479
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=19.000, iters=3333
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=18.000, iters=5446
% 290.27/290.54
% 290.27/290.54 Low Water (keep): wt=17.000, iters=3668
% 290.27/290.54
% 290.27/290.54 ============================== PROOF =================================
% 290.27/290.54 % SZS status Unsatisfiable
% 290.27/290.54 % SZS output start Refutation
% 290.27/290.54
% 290.27/290.54 % Proof 1 at 285.23 (+ 4.34) seconds: prove_distributivity.
% 290.27/290.54 % Length of proof is 166.
% 290.27/290.54 % Level of proof is 36.
% 290.27/290.54 % Maximum clause weight is 35.000.
% 290.27/290.54 % Given clauses 4114.
% 290.27/290.54
% 290.27/290.54 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 290.27/290.54 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 290.27/290.54 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 290.27/290.54 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 290.27/290.54 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 290.27/290.54 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 290.27/290.54 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 290.27/290.54 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 290.27/290.54 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 290.27/290.54 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 290.27/290.54 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 290.27/290.54 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 290.27/290.54 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 290.27/290.54 14 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].
% 290.27/290.54 15 meet(A,join(B,meet(join(B,C),join(D,meet(B,C))))) = meet(A,meet(join(B,C),join(B,D))). [copy(14),flip(a)].
% 290.27/290.54 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 290.27/290.54 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 290.27/290.54 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 290.27/290.54 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 290.27/290.54 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 290.27/290.54 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 290.27/290.54 22 meet(A,meet(A,B)) = meet(A,B). [para(11(a,1),1(a,1)),rewrite([8(1),8(2),11(2,R),1(1),8(3)])].
% 290.27/290.54 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 290.27/290.54 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 290.27/290.54 25 join(A,join(A,B)) = join(A,B). [para(13(a,1),2(a,1)),rewrite([9(1),9(2),13(2,R),2(1),9(3)])].
% 290.27/290.54 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 290.27/290.54 27 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 290.27/290.54 28 join(A,meet(join(A,B),join(C,meet(A,B)))) = meet(join(A,B),join(A,C)). [para(15(a,1),1(a,1)),rewrite([8(9),15(9),1(7)]),flip(a)].
% 290.27/290.54 34 meet(A,B) != zero | one != A | meet(A,B) = complement(A). [para(7(a,1),18(b,1)),rewrite([22(2)]),flip(b),flip(c)].
% 290.27/290.54 35 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 290.27/290.54 36 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 290.27/290.54 37 one != A | complement(A) = zero. [back_rewrite(35),rewrite([36(2)]),xx(a)].
% 290.27/290.54 38 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([36(5)])].
% 290.27/290.54 39 complement(one) = zero. [hyper(18,a,36,a,b,21,a)].
% 290.27/290.54 40 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(24(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),11(6),8(5),11(6,R),8(5)])].
% 290.27/290.54 42 complement(join(A,one)) = zero. [hyper(37,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 290.27/290.54 44 join(A,one) = one. [para(42(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 290.27/290.54 45 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([44(5)])].
% 290.27/290.54 46 complement(zero) = one. [hyper(18,a,20,a,b,44,a)].
% 290.27/290.54 49 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(38(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),36(6)])].
% 290.27/290.54 50 join(A,join(B,join(C,complement(A)))) = one. [para(45(a,1),13(a,2,2)),rewrite([9(3),13(3,R),9(2),44(6)])].
% 290.27/290.54 54 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(27(a,1),13(a,2,2)),rewrite([9(3),13(3,R),9(2),13(6),9(5),13(6,R),9(5)])].
% 290.27/290.54 55 meet(A,join(B,meet(A,C))) != zero | join(A,B) != one | join(B,meet(A,C)) = complement(A). [para(27(a,1),18(b,1)),flip(c)].
% 290.27/290.54 58 join(A,join(B,join(C,join(D,complement(A))))) = one. [para(50(a,1),13(a,2,2)),rewrite([9(4),13(4,R),9(3),13(3,R),9(2),44(7)])].
% 290.27/290.54 60 join(A,meet(meet(A,B),join(A,B))) = A. [para(2(a,1),28(a,1,2,2)),rewrite([8(3),7(7),8(6),6(6)])].
% 290.27/290.54 61 meet(one,join(A,B)) = join(A,B). [para(4(a,1),28(a,1,2,1)),rewrite([5(3),21(3),8(2),20(2),4(3)]),flip(a)].
% 290.27/290.54 62 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(6(a,1),28(a,1,2,2,2)),rewrite([25(2),9(2),25(6)])].
% 290.27/290.54 63 join(A,join(B,meet(join(A,C),join(D,meet(A,C))))) = join(B,meet(join(A,C),join(A,D))). [para(28(a,1),13(a,2,2)),rewrite([9(5)])].
% 290.27/290.54 65 join(a,meet(join(a,b),join(A,a))) = meet(join(a,b),join(A,a)). [para(19(a,1),28(a,1,2,2,2)),rewrite([9(13)])].
% 290.27/290.54 66 join(A,meet(join(A,meet(B,join(A,C))),join(D,meet(A,B)))) = meet(join(A,meet(B,join(A,C))),join(A,D)). [para(24(a,1),28(a,1,2,2,2))].
% 290.27/290.54 67 join(A,meet(B,join(A,meet(C,complement(A))))) = meet(join(A,meet(C,complement(A))),join(A,B)). [para(38(a,1),28(a,1,2,2,2)),rewrite([21(5),8(4)])].
% 290.27/290.54 69 join(A,meet(join(A,B),join(C,meet(A,join(B,meet(A,D)))))) = meet(join(A,B),join(A,C)). [para(27(a,1),28(a,1,2,1)),rewrite([27(10)])].
% 290.27/290.54 71 join(A,meet(B,join(A,meet(C,meet(D,complement(A)))))) = meet(join(A,meet(C,meet(D,complement(A)))),join(A,B)). [para(49(a,1),28(a,1,2,2,2)),rewrite([21(6),8(5)])].
% 290.27/290.54 72 join(A,meet(meet(join(A,B),join(A,C)),join(D,meet(A,meet(join(A,B),join(C,meet(A,B))))))) = meet(meet(join(A,B),join(A,C)),join(A,D)). [para(28(a,1),28(a,1,2,1)),rewrite([28(16)])].
% 290.27/290.54 74 meet(one,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(28(a,1),61(a,1,2)),rewrite([28(10)])].
% 290.27/290.54 79 join(A,meet(meet(A,B),join(A,meet(B,join(A,C))))) = A. [para(24(a,1),60(a,1,2,1))].
% 290.27/290.54 82 meet(A,B) != zero | one != B | meet(A,B) = complement(B). [para(8(a,1),34(a,1)),rewrite([8(6)])].
% 290.27/290.54 84 meet(A,meet(B,C)) != zero | one != C | meet(A,meet(B,C)) = complement(C). [para(11(a,2),34(a,1)),rewrite([11(8),8(7),11(8,R),8(7)])].
% 290.27/290.54 85 join(A,join(B,join(C,join(D,join(E,complement(A)))))) = one. [para(58(a,1),13(a,2,2)),rewrite([9(5),13(5,R),9(4),13(4,R),9(3),13(3,R),9(2),44(8)])].
% 290.27/290.54 94 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(40(a,1),11(a,2,2)),rewrite([8(4),11(4,R),8(3),11(3,R),8(2),11(8,R),8(7),11(7),8(6),11(7,R),8(6)])].
% 290.27/290.54 103 zero != A | join(A,B) != one | complement(join(A,B)) = A. [para(6(a,1),82(a,1)),rewrite([6(7)]),flip(a),flip(b),flip(c)].
% 290.27/290.54 120 join(A,join(B,join(C,join(D,join(E,join(F,complement(A))))))) = one. [para(85(a,1),13(a,2,2)),rewrite([9(6),13(6,R),9(5),13(5,R),9(4),13(4,R),9(3),13(3,R),9(2),44(9)])].
% 290.27/290.54 124 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(54(a,1),13(a,2,2)),rewrite([9(4),13(4,R),9(3),13(3,R),9(2),13(8,R),9(7),13(7),9(6),13(7,R),9(6)])].
% 290.27/290.54 181 join(A,join(B,meet(join(A,C),join(A,D)))) = join(B,meet(join(A,C),join(A,D))). [para(62(a,1),13(a,2,2)),rewrite([9(4)])].
% 290.27/290.54 198 join(meet(join(A,B),join(A,C)),meet(join(A,B),join(C,meet(A,B)))) = meet(join(A,B),join(A,C)). [para(2(a,1),63(a,1,2)),rewrite([28(5),9(11)]),flip(a)].
% 290.27/290.54 199 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(63(a,1),6(a,1,2))].
% 290.27/290.54 227 meet(zero,join(A,meet(B,C))) = zero. [hyper(103,a,199,a(flip),b,120,a),rewrite([9(3),21(3),9(3),21(3),9(7),21(7),9(7),21(7),120(15),39(2),9(4),21(4),9(4),21(4)]),flip(a)].
% 290.27/290.54 235 meet(zero,join(A,B)) = zero. [para(1(a,1),227(a,1,2,2))].
% 290.27/290.54 237 meet(zero,meet(join(A,B),join(A,C))) = zero. [para(28(a,1),227(a,1,2))].
% 290.27/290.54 239 join(zero,meet(A,join(B,C))) = meet(A,join(B,C)). [para(235(a,1),28(a,1,2,2,2)),rewrite([13(4),9(3),21(3),9(2),21(4),8(3),13(7),9(6),21(6),9(5),9(7),21(7),8(6)])].
% 290.27/290.54 243 meet(zero,meet(join(A,join(B,C)),join(C,D))) = zero. [para(13(a,2),237(a,1,2,1))].
% 290.27/290.54 279 join(zero,meet(A,B)) = meet(A,B). [para(2(a,1),239(a,1,2,2)),rewrite([2(4)])].
% 290.27/290.54 352 meet(zero,meet(join(A,B),join(C,meet(B,D)))) = zero. [para(7(a,1),243(a,1,2,1,2)),rewrite([9(4)])].
% 290.27/290.54 375 join(A,meet(join(B,A),join(B,complement(A)))) = join(B,A). [para(67(a,1),63(a,1,2)),rewrite([45(6),8(5),61(5),27(4),8(5)]),flip(a)].
% 290.27/290.54 383 meet(zero,meet(join(A,meet(B,C)),join(B,D))) = zero. [para(8(a,1),352(a,1,2)),rewrite([9(4)])].
% 290.27/290.54 409 meet(zero,meet(join(A,meet(B,C)),join(C,D))) = zero. [para(8(a,1),383(a,1,2,1,2))].
% 290.27/290.54 463 meet(zero,meet(join(A,a),join(B,b))) = zero. [para(19(a,1),409(a,1,2,1,2)),rewrite([9(5)])].
% 290.27/290.54 482 meet(zero,meet(b,join(A,a))) = zero. [para(2(a,1),463(a,1,2,2)),rewrite([8(5)])].
% 290.27/290.54 489 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(28(a,1),69(a,1,2,2,2,2)),rewrite([9(3),25(3),22(7),7(8),9(3),25(3),9(4),13(4),9(3),13(4,R),9(3)]),flip(a)].
% 290.27/290.54 490 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(60(a,1),69(a,1,2,2,2,2)),rewrite([9(3),7(3),8(3),22(3),9(7),7(7),9(7)])].
% 290.27/290.54 500 meet(join(a,b),join(A,join(a,b))) = join(a,b). [para(65(a,1),69(a,1,2,2,2,2)),rewrite([9(8),25(8),22(16),7(15),9(8),25(8),9(10)]),flip(a)].
% 290.27/290.54 525 meet(zero,b) = zero. [para(6(a,1),482(a,1,2))].
% 290.27/290.54 622 meet(join(A,B),join(B,meet(join(A,C),join(A,D)))) = join(A,B). [para(63(a,1),489(a,1,2))].
% 290.27/290.54 624 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(279(a,1),489(a,1,1)),rewrite([9(4),13(5,R),9(4),279(4),279(7)])].
% 290.27/290.54 627 join(A,meet(join(A,meet(B,join(A,C))),join(D,join(meet(A,B),meet(B,join(A,C)))))) = join(A,meet(B,join(A,C))). [para(489(a,1),66(a,2)),rewrite([9(6),9(8),13(8,R),9(7)])].
% 290.27/290.54 640 join(a,join(zero,b)) = join(a,b). [para(500(a,1),279(a,1,2)),rewrite([13(5,R),9(4),500(13)])].
% 290.27/290.54 742 join(a,join(join(zero,b),meet(A,a))) = join(a,b). [para(640(a,1),27(a,2)),rewrite([8(6)])].
% 290.27/290.54 767 join(one,meet(join(A,B),join(A,C))) = one. [para(74(a,1),7(a,1,2))].
% 290.27/290.54 773 meet(one,meet(join(A,B),join(C,meet(join(A,D),join(A,E))))) = meet(join(A,B),join(C,meet(join(A,D),join(A,E)))). [para(63(a,1),74(a,1,2,2)),rewrite([63(15)])].
% 290.27/290.54 783 join(a,join(one,b)) = one. [para(500(a,1),767(a,1,2)),rewrite([13(5,R),9(4)])].
% 290.27/290.54 786 join(a,meet(meet(A,a),join(A,a))) = a. [para(783(a,1),79(a,1,2,2,2,2)),rewrite([8(3),20(6),9(5)])].
% 290.27/290.54 839 join(a,meet(A,a)) = a. [para(786(a,1),79(a,1,2,2,2,2)),rewrite([8(3),624(8)])].
% 290.27/290.54 840 join(meet(A,a),meet(a,join(meet(A,a),meet(join(A,a),join(B,meet(A,a)))))) = meet(a,join(meet(A,a),meet(join(A,a),join(B,meet(A,a))))). [para(786(a,1),66(a,1,2,2)),rewrite([9(9),8(13),9(21),9(27),839(27),8(25)])].
% 290.27/290.54 900 meet(join(A,B),meet(join(A,C),join(B,meet(A,C)))) = meet(join(A,C),join(B,meet(A,C))). [para(28(a,1),624(a,1,2)),rewrite([8(8),11(8),8(7),22(7),11(6),8(5)])].
% 290.27/290.54 901 meet(meet(A,B),join(A,B)) = meet(A,B). [para(60(a,1),624(a,1,2)),rewrite([8(4),24(4),22(2)]),flip(a)].
% 290.27/290.54 917 join(meet(A,B),meet(join(A,B),join(C,meet(A,B)))) = meet(join(A,B),join(C,meet(A,B))). [para(901(a,1),28(a,1,2,2,2)),rewrite([13(4),9(3),7(3),9(2),13(9),9(8),7(8),9(7),9(9)])].
% 290.27/290.54 929 join(meet(A,a),meet(a,meet(join(A,a),join(B,meet(A,a))))) = meet(a,meet(join(A,a),join(B,meet(A,a)))). [back_rewrite(840),rewrite([917(12),917(21)])].
% 290.27/290.54 1010 meet(A,meet(B,C)) != zero | join(D,meet(B,C)) != one | complement(join(D,meet(B,C))) = meet(A,meet(B,C)). [para(624(a,1),84(a,1,2)),rewrite([624(12)]),flip(b),flip(c)].
% 290.27/290.54 1122 join(A,meet(one,complement(A))) = one. [para(2(a,1),375(a,1,2,2)),rewrite([9(2),4(2),9(6),4(6)])].
% 290.27/290.54 1125 join(join(A,B),meet(join(A,join(B,C)),join(C,complement(join(A,B))))) = join(A,join(B,C)). [para(13(a,1),375(a,1,2,1)),rewrite([9(2),13(3,R),9(2),13(10),9(9),13(10,R),9(9)])].
% 290.27/290.54 1147 join(join(join(zero,b),meet(A,a)),meet(join(a,b),join(a,complement(join(join(zero,b),meet(A,a)))))) = join(a,b). [para(742(a,1),375(a,1,2,1)),rewrite([742(28)])].
% 290.27/290.54 1151 meet(one,complement(A)) = complement(A). [hyper(18,a,38,a,b,1122,a),flip(a)].
% 290.27/290.54 1152 join(one,complement(A)) = one. [para(1151(a,1),7(a,1,2))].
% 290.27/290.54 1155 join(zero,complement(A)) = complement(A). [para(1151(a,1),279(a,1,2)),rewrite([1151(6)])].
% 290.27/290.54 1160 meet(complement(A),join(B,complement(A))) = complement(A). [para(1151(a,1),624(a,1,1)),rewrite([1151(4),1151(7)])].
% 290.27/290.54 1174 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(1155(a,1),71(a,2,2)),rewrite([46(5),20(5),279(5),11(4),8(3),11(4,R),8(3),279(5),46(6),20(6),279(6)]),flip(a)].
% 290.27/290.54 1224 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(1174(a,1),5(a,1))].
% 290.27/290.54 1225 meet(A,meet(join(A,B),complement(C))) = meet(A,complement(C)). [para(6(a,1),1174(a,1,1)),flip(a)].
% 290.27/290.54 1227 meet(a,meet(b,complement(A))) = meet(a,complement(A)). [para(19(a,1),1174(a,1,1)),flip(a)].
% 290.27/290.54 1300 meet(one,meet(complement(A),complement(B))) = meet(complement(A),complement(B)). [para(1151(a,1),1174(a,1,1)),flip(a)].
% 290.27/290.54 1331 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(1224(a,1),11(a,2,2)),rewrite([8(4),11(4,R),8(3),36(7)])].
% 290.27/290.54 1345 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(1224(a,1),71(a,1,2,2,2)),rewrite([9(4),279(4),11(3),8(2),11(3,R),8(2),1224(9),9(7),279(7),9(7),624(8)])].
% 290.27/290.54 1765 meet(A,meet(B,meet(C,complement(meet(A,C))))) = zero. [para(1331(a,1),8(a,1)),rewrite([8(2),8(6),11(6,R),8(5),11(5,R),8(4)]),flip(a)].
% 290.27/290.54 1851 meet(A,meet(a,complement(meet(A,b)))) = zero. [para(1227(a,1),1765(a,1,2))].
% 290.27/290.54 1861 join(meet(A,b),meet(A,meet(B,b))) = meet(A,b). [para(1851(a,1),71(a,1,2,2,2)),rewrite([9(6),279(6),11(5,R),8(4),1851(14),9(10),279(10),9(11),624(12)])].
% 290.27/290.54 1901 meet(A,complement(join(A,B))) = zero. [para(5(a,1),1225(a,1,2)),rewrite([36(2)]),flip(a)].
% 290.27/290.54 1931 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(1901(a,1),67(a,1,2,2,2)),rewrite([9(4),13(4),9(3),21(3),9(2),1901(8),9(7),13(7),9(6),21(6),9(5),9(7),13(7),9(6),13(7,R),9(6),489(8)])].
% 290.27/290.54 1938 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(1901(a,1),1174(a,1)),rewrite([9(3)]),flip(a)].
% 290.27/290.54 2087 meet(complement(A),complement(join(B,complement(A)))) = zero. [para(1151(a,1),1938(a,1,2,2,1,2)),rewrite([1300(7)])].
% 290.27/290.54 2107 join(complement(A),meet(B,join(complement(A),complement(join(C,complement(A)))))) = meet(join(complement(A),complement(join(C,complement(A)))),join(B,complement(A))). [para(2087(a,1),28(a,1,2,2,2)),rewrite([21(8),8(7),9(15)])].
% 290.27/290.54 2108 meet(A,complement(B)) != zero | join(A,complement(B)) != one | complement(complement(B)) = A. [para(2087(a,1),55(a,1,2,2)),rewrite([21(3),8(2),9(6),2087(13),21(10)]),flip(c)].
% 290.27/290.54 2200 join(join(A,B),meet(join(C,D),join(C,E))) = join(A,join(B,meet(join(C,D),join(C,E)))). [para(72(a,1),124(a,1,2,2,2)),rewrite([54(11),13(5),9(4),13(5,R),9(4),9(9),13(10,R),9(9),13(11,R),181(11)]),flip(a)].
% 290.27/290.54 2215 join(join(zero,b),join(meet(A,a),meet(join(a,b),join(a,complement(join(join(zero,b),meet(A,a))))))) = join(a,b). [back_rewrite(1147),rewrite([2200(20)])].
% 290.27/290.54 2586 join(A,meet(meet(A,B),join(A,meet(B,C)))) = A. [para(1345(a,1),28(a,1,2,2)),rewrite([8(4),7(9),8(8),6(8)])].
% 290.27/290.54 2800 join(b,meet(A,b)) = b. [para(1(a,1),1861(a,1,1)),rewrite([11(5,R),1(4),1(7)])].
% 290.27/290.54 2825 join(a,b) = b. [para(19(a,1),2800(a,1,2)),rewrite([9(3)])].
% 290.27/290.54 2841 join(zero,b) = b. [para(525(a,1),2800(a,1,2)),rewrite([9(3)])].
% 290.27/290.54 2879 join(b,meet(A,a)) = b. [back_rewrite(2215),rewrite([2841(3),2825(6),2841(8),27(14),2825(7)])].
% 290.27/290.54 3560 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(1931(a,1),94(a,1,2,2,2,2)),rewrite([11(6,R),8(5),11(5,R),8(4),11(4,R),1(3),11(8,R)]),flip(a)].
% 290.27/290.54 4201 meet(meet(A,B),join(A,meet(B,C))) = meet(A,B). [para(2586(a,1),624(a,1,2)),rewrite([8(5),24(5),22(2)]),flip(a)].
% 290.27/290.54 4532 meet(meet(A,B),join(B,meet(A,C))) = meet(A,B). [para(8(a,1),4201(a,1,1)),rewrite([8(5)])].
% 290.27/290.54 4558 join(meet(join(A,B),join(A,C)),meet(join(A,C),join(B,meet(A,C)))) = meet(join(A,C),join(A,B)). [para(8(a,1),198(a,1,1))].
% 290.27/290.54 5058 meet(A,join(join(A,B),meet(A,C))) = A. [para(6(a,1),4532(a,1,1)),rewrite([6(6)])].
% 290.27/290.54 5141 join(join(A,B),meet(A,C)) = join(A,B). [para(5058(a,1),1931(a,1,2)),rewrite([9(4),27(4),25(2)]),flip(a)].
% 290.27/290.54 5317 meet(meet(A,B),join(A,C)) = meet(A,B). [para(5141(a,1),624(a,1,2))].
% 290.27/290.54 5679 meet(meet(A,B),join(B,C)) = meet(A,B). [para(8(a,1),5317(a,1,1)),rewrite([8(4)])].
% 290.27/290.54 6389 meet(complement(A),join(B,join(C,complement(A)))) = complement(A). [para(1160(a,1),5679(a,1,1)),rewrite([9(4),13(4,R),9(3),1160(9)])].
% 290.27/290.54 12464 join(meet(A,B),meet(B,join(C,meet(A,B)))) = meet(B,join(C,meet(A,B))). [para(8(a,1),490(a,1,1)),rewrite([8(2),8(6)])].
% 290.27/290.54 12479 meet(A,meet(B,complement(meet(A,join(C,meet(A,B)))))) = zero. [para(490(a,1),1901(a,1,2,1)),rewrite([1174(6)])].
% 290.27/290.54 13313 meet(A,meet(B,complement(meet(B,join(C,meet(A,B)))))) = zero. [para(12479(a,1),8(a,1)),rewrite([8(2),8(7),11(7,R),8(6)]),flip(a)].
% 290.27/290.54 14926 join(complement(A),meet(join(A,B),join(A,C))) = one. [para(4(a,1),622(a,1,1)),rewrite([61(7),4(7)])].
% 290.27/290.54 14967 join(complement(a),meet(b,join(A,a))) = one. [para(2825(a,1),14926(a,1,2,1)),rewrite([9(5)])].
% 290.27/290.54 15000 join(b,complement(a)) = one. [para(6(a,1),14967(a,1,2)),rewrite([9(4)])].
% 290.27/290.54 15100 join(b,meet(join(A,b),join(A,B))) = join(A,b). [para(15000(a,1),627(a,1,2,1,2,2)),rewrite([20(4),9(3),8(5),15000(9),20(7),9(6),7(6),9(4),15000(11),20(9),9(8)])].
% 290.27/290.54 16261 meet(meet(A,B),join(C,meet(D,E))) = meet(A,meet(B,join(C,meet(D,E)))). [para(279(a,1),773(a,1,2,1)),rewrite([9(4),21(4),9(4),21(4),3560(6),11(6,R),8(5),11(5,R),8(4),61(4),279(7),9(7),21(7),9(7),21(7)]),flip(a)].
% 290.27/290.54 16428 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [back_rewrite(624),rewrite([16261(4)])].
% 290.27/290.54 17592 meet(A,join(B,A)) = A. [para(4(a,1),900(a,1,2,1)),rewrite([5(4),21(4),8(3),20(3),8(2),4(4),5(5),21(5),8(4),20(4)])].
% 290.27/290.54 17966 meet(a,meet(join(A,a),join(B,meet(A,a)))) = meet(a,join(B,meet(A,a))). [para(11(a,1),929(a,1,2)),rewrite([17592(9),8(7),12464(8)]),flip(a)].
% 290.27/290.54 17997 join(b,meet(a,meet(b,join(A,meet(B,a))))) = b. [para(929(a,1),15100(a,1,2,2)),rewrite([9(5),2879(5),17966(10),11(8,R),8(7),9(13),2879(13)])].
% 290.27/290.54 18016 join(b,meet(a,join(A,meet(B,a)))) = b. [para(11(a,1),17997(a,1,2)),rewrite([19(7),8(6)])].
% 290.27/290.54 18036 join(b,meet(a,join(A,B))) = b. [para(5141(a,1),18016(a,1,2,2))].
% 290.27/290.54 18080 meet(a,meet(b,join(A,B))) = meet(a,join(A,B)). [para(18036(a,1),16428(a,1,2,2)),rewrite([8(4)])].
% 290.27/290.54 20432 meet(A,complement(join(B,A))) = zero. [hyper(1010,a,13313,a,b,7,a),rewrite([20(5),61(5),1151(5),1152(4),39(2),20(5),61(5),1151(5)]),flip(a)].
% 290.27/290.54 20436 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [para(27(a,1),20432(a,1,2,1)),rewrite([9(3),8(5)])].
% 290.27/290.54 20528 meet(join(A,meet(B,complement(A))),join(A,complement(join(A,B)))) = A. [para(20436(a,1),67(a,1,2)),rewrite([21(2)]),flip(a)].
% 290.27/290.54 21324 join(A,join(B,complement(join(A,B)))) = one. [para(2(a,1),1125(a,1,2,2)),rewrite([8(8),6389(8),4(4)]),flip(a)].
% 290.27/290.54 32778 complement(complement(A)) = A. [hyper(2108,a,5,a,b,4,a)].
% 290.27/290.54 37176 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(3560(a,1),1(a,1)),rewrite([8(7),11(7),8(6),11(6,R),11(5),8(4),11(5,R),8(4),22(4),22(5),11(5,R),8(4),11(4,R),1(3)]),flip(a)].
% 290.27/290.54 38359 join(A,meet(B,meet(complement(A),join(A,complement(join(A,B)))))) = A. [para(20528(a,1),4558(a,1,1)),rewrite([1901(8),9(7),279(7),8(6),37176(6),8(14),20528(14)])].
% 290.27/290.54 39412 meet(A,meet(complement(B),join(B,complement(join(A,B))))) = zero. [para(38359(a,1),1938(a,1,2,2,1)),rewrite([9(2),8(7),22(7)])].
% 290.27/290.54 39432 meet(A,meet(B,join(complement(B),complement(join(A,complement(B)))))) = zero. [para(32778(a,1),39412(a,1,2,1))].
% 290.27/290.54 39455 meet(a,join(complement(b),complement(join(a,complement(b))))) = zero. [para(39432(a,1),18080(a,1)),flip(a)].
% 290.27/290.54 39458 join(complement(b),complement(join(a,complement(b)))) = complement(a). [hyper(18,a,39455,a,b,21324,a),flip(a)].
% 290.27/290.54 39459 meet(complement(a),join(a,complement(b))) = complement(b). [para(39455(a,1),2107(a,1,2)),rewrite([9(4),1155(4),39458(10)]),flip(a)].
% 290.27/290.54 39460 join(complement(a),complement(b)) = complement(a). [para(39459(a,1),7(a,1,2))].
% 290.27/290.54 39461 $F # answer(prove_distributivity). [resolve(39460,a,17,a)].
% 290.27/290.54
% 290.27/290.54 % SZS output end Refutation
% 290.27/290.54 ============================== end of proof ==========================
% 290.27/290.54
% 290.27/290.54 ============================== STATISTICS ============================
% 290.27/290.54
% 290.27/290.54 Given=4114. Generated=7773969. Kept=39456. proofs=1.
% 290.27/290.54 Usable=2884. Sos=9440. Demods=11545. Limbo=0, Disabled=27145. Hints=0.
% 290.27/290.54 Megabytes=37.58.
% 290.27/290.54 User_CPU=285.23, System_CPU=4.34, Wall_clock=290.
% 290.27/290.54
% 290.27/290.54 ============================== end of statistics =====================
% 290.27/290.54
% 290.27/290.54 ============================== end of search =========================
% 290.27/290.54
% 290.27/290.54 THEOREM PROVED
% 290.27/290.54 % SZS status Unsatisfiable
% 290.27/290.54
% 290.27/290.54 Exiting with 1 proof.
% 290.27/290.54
% 290.27/290.54 Process 9923 exit (max_proofs) Wed Jun 29 21:02:43 2022
% 290.27/290.54 Prover9 interrupted
%------------------------------------------------------------------------------