TSTP Solution File: LAT190-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT190-10 : TPTP v8.1.0. Released v7.5.0.
% 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 06:26:01 EDT 2022
% Result : Unsatisfiable 164.48s 164.76s
% Output : Refutation 164.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : LAT190-10 : TPTP v8.1.0. Released v7.5.0.
% 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.37 % Computer : n007.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Wed Jun 29 08:54:07 EDT 2022
% 0.15/0.37 % CPUTime :
% 8.45/8.71 ============================== Prover9 ===============================
% 8.45/8.71 Prover9 (32) version 2009-11A, November 2009.
% 8.45/8.71 Process 19768 was started by sandbox on n007.cluster.edu,
% 8.45/8.71 Wed Jun 29 08:54:08 2022
% 8.45/8.71 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19615_n007.cluster.edu".
% 8.45/8.71 ============================== end of head ===========================
% 8.45/8.71
% 8.45/8.71 ============================== INPUT =================================
% 8.45/8.71
% 8.45/8.71 % Reading from file /tmp/Prover9_19615_n007.cluster.edu
% 8.45/8.71
% 8.45/8.71 set(prolog_style_variables).
% 8.45/8.71 set(auto2).
% 8.45/8.71 % set(auto2) -> set(auto).
% 8.45/8.71 % set(auto) -> set(auto_inference).
% 8.45/8.71 % set(auto) -> set(auto_setup).
% 8.45/8.71 % set(auto_setup) -> set(predicate_elim).
% 8.45/8.71 % set(auto_setup) -> assign(eq_defs, unfold).
% 8.45/8.71 % set(auto) -> set(auto_limits).
% 8.45/8.71 % set(auto_limits) -> assign(max_weight, "100.000").
% 8.45/8.71 % set(auto_limits) -> assign(sos_limit, 20000).
% 8.45/8.71 % set(auto) -> set(auto_denials).
% 8.45/8.71 % set(auto) -> set(auto_process).
% 8.45/8.71 % set(auto2) -> assign(new_constants, 1).
% 8.45/8.71 % set(auto2) -> assign(fold_denial_max, 3).
% 8.45/8.71 % set(auto2) -> assign(max_weight, "200.000").
% 8.45/8.71 % set(auto2) -> assign(max_hours, 1).
% 8.45/8.71 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 8.45/8.71 % set(auto2) -> assign(max_seconds, 0).
% 8.45/8.71 % set(auto2) -> assign(max_minutes, 5).
% 8.45/8.71 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 8.45/8.71 % set(auto2) -> set(sort_initial_sos).
% 8.45/8.71 % set(auto2) -> assign(sos_limit, -1).
% 8.45/8.71 % set(auto2) -> assign(lrs_ticks, 3000).
% 8.45/8.71 % set(auto2) -> assign(max_megs, 400).
% 8.45/8.71 % set(auto2) -> assign(stats, some).
% 8.45/8.71 % set(auto2) -> clear(echo_input).
% 8.45/8.71 % set(auto2) -> set(quiet).
% 8.45/8.71 % set(auto2) -> clear(print_initial_clauses).
% 8.45/8.71 % set(auto2) -> clear(print_given).
% 8.45/8.71 assign(lrs_ticks,-1).
% 8.45/8.71 assign(sos_limit,10000).
% 8.45/8.71 assign(order,kbo).
% 8.45/8.71 set(lex_order_vars).
% 8.45/8.71 clear(print_given).
% 8.45/8.71
% 8.45/8.71 % formulas(sos). % not echoed (14 formulas)
% 8.45/8.71
% 8.45/8.71 ============================== end of input ==========================
% 8.45/8.71
% 8.45/8.71 % From the command line: assign(max_seconds, 300).
% 8.45/8.71
% 8.45/8.71 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 8.45/8.71
% 8.45/8.71 % Formulas that are not ordinary clauses:
% 8.45/8.71
% 8.45/8.71 ============================== end of process non-clausal formulas ===
% 8.45/8.71
% 8.45/8.71 ============================== PROCESS INITIAL CLAUSES ===============
% 8.45/8.71
% 8.45/8.71 ============================== PREDICATE ELIMINATION =================
% 8.45/8.71
% 8.45/8.71 ============================== end predicate elimination =============
% 8.45/8.71
% 8.45/8.71 Auto_denials:
% 8.45/8.71 % copying label prove_distributivity to answer in negative clause
% 8.45/8.71
% 8.45/8.71 Term ordering decisions:
% 8.45/8.71
% 8.45/8.71 % Assigning unary symbol complement kb_weight 0 and highest precedence (10).
% 8.45/8.71 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. ifeq=1. complement=0.
% 8.45/8.71
% 8.45/8.71 ============================== end of process initial clauses ========
% 8.45/8.71
% 8.45/8.71 ============================== CLAUSES FOR SEARCH ====================
% 8.45/8.71
% 8.45/8.71 ============================== end of clauses for search =============
% 8.45/8.71
% 8.45/8.71 ============================== SEARCH ================================
% 8.45/8.71
% 8.45/8.71 % Starting search at 0.01 seconds.
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=118.000, iters=3421
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=76.000, iters=3342
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=71.000, iters=3419
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=67.000, iters=3364
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=66.000, iters=3348
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=62.000, iters=3413
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=59.000, iters=3351
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=57.000, iters=3450
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=56.000, iters=3390
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=54.000, iters=3391
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=53.000, iters=3432
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=52.000, iters=3423
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=50.000, iters=3342
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=49.000, iters=3388
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=47.000, iters=3340
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=46.000, iters=3358
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=45.000, iters=3349
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=44.000, iters=3367
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=43.000, iters=3375
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=42.000, iters=3444
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=41.000, iters=3359
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=40.000, iters=3351
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=39.000, iters=3344
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=38.000, iters=3353
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=37.000, iters=3333
% 8.45/8.71
% 8.45/8.71 Low Water (keep): wt=36.000, iters=3360
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=35.000, iters=3373
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=34.000, iters=3351
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=3391, wt=164.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=6274, wt=160.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=3476, wt=156.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=3638, wt=152.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=3395, wt=148.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=4359, wt=140.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=4027, wt=132.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=7342, wt=128.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=3399, wt=124.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=2756, wt=123.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=3991, wt=122.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=3451, wt=120.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=7279, wt=118.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=6296, wt=116.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=2732, wt=114.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=2747, wt=113.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=7426, wt=112.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=6308, wt=110.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=6295, wt=109.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=3477, wt=108.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=13438, wt=29.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=13447, wt=23.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=13451, wt=21.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=13461, wt=20.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=13511, wt=18.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=13658, wt=17.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=14049, wt=16.000
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=33.000, iters=3430
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=32.000, iters=3343
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=31.000, iters=3377
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=30.000, iters=3355
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=29.000, iters=3448
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=28.000, iters=3336
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=27.000, iters=3369
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=26.000, iters=3365
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=25.000, iters=3338
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=24.000, iters=3361
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=23.000, iters=3339
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=22.000, iters=3333
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=21.000, iters=3338
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=34543, wt=15.000
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=35295, wt=14.000
% 164.48/164.76
% 164.48/164.76 Low Water (keep): wt=20.000, iters=3344
% 164.48/164.76
% 164.48/164.76 Low Water (displace): id=37513, wt=13.000
% 164.48/164.76
% 164.48/164.76 ============================== PROOF =================================
% 164.48/164.76 % SZS status Unsatisfiable
% 164.48/164.76 % SZS output start Refutation
% 164.48/164.76
% 164.48/164.76 % Proof 1 at 161.75 (+ 1.92) seconds: prove_distributivity.
% 164.48/164.76 % Length of proof is 237.
% 164.48/164.76 % Level of proof is 60.
% 164.48/164.76 % Maximum clause weight is 43.000.
% 164.48/164.76 % Given clauses 2068.
% 164.48/164.76
% 164.48/164.76 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 164.48/164.76 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 164.48/164.76 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 164.48/164.76 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 164.48/164.76 5 ifeq(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 164.48/164.76 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 164.48/164.76 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 164.48/164.76 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 164.48/164.76 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 164.48/164.76 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 164.48/164.76 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 164.48/164.76 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 164.48/164.76 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 164.48/164.76 14 ifeq(join(A,B),one,ifeq(meet(A,B),zero,complement(A),B),B) = B # label(meet_join_complement) # label(axiom). [assumption].
% 164.48/164.76 15 join(meet(A,B),meet(A,C)) = meet(A,join(meet(A,B),join(meet(A,C),meet(B,join(A,C))))) # label(equation_H18) # label(axiom). [assumption].
% 164.48/164.76 16 meet(A,join(meet(A,B),join(meet(A,C),meet(B,join(A,C))))) = join(meet(A,B),meet(A,C)). [copy(15),flip(a)].
% 164.48/164.76 17 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 164.48/164.76 18 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(17),flip(a)].
% 164.48/164.76 19 meet(A,one) = A. [para(3(a,1),6(a,1,2))].
% 164.48/164.76 20 join(A,zero) = A. [para(4(a,1),7(a,1,2))].
% 164.48/164.76 21 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)])].
% 164.48/164.76 23 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 164.48/164.76 24 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)])].
% 164.48/164.76 25 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),13(a,2,2)),rewrite([9(2)])].
% 164.48/164.76 26 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 164.48/164.76 30 ifeq(join(A,B),one,ifeq(meet(A,B),zero,complement(B),A),A) = A. [para(9(a,1),14(a,1,1)),rewrite([8(3)])].
% 164.48/164.76 32 ifeq(join(A,join(B,C)),one,ifeq(meet(C,join(A,B)),zero,complement(C),join(A,B)),join(A,B)) = join(A,B). [para(13(a,2),14(a,1,1))].
% 164.48/164.76 34 meet(A,join(B,meet(A,B))) = join(zero,meet(A,B)). [para(3(a,1),16(a,1,2,2,2,2)),rewrite([4(3),19(4),9(3),20(3),9(2),4(6),9(6)])].
% 164.48/164.76 37 meet(A,meet(B,join(meet(A,C),join(meet(A,D),meet(C,join(A,D)))))) = meet(B,join(meet(A,C),meet(A,D))). [para(16(a,1),11(a,2,2)),rewrite([8(7)])].
% 164.48/164.76 38 meet(A,join(meet(A,B),join(meet(A,C),meet(C,join(A,B))))) = join(meet(A,C),meet(A,B)). [para(13(a,1),16(a,1,2)),rewrite([13(6),9(5)])].
% 164.48/164.76 40 meet(A,join(join(meet(A,B),meet(A,C)),join(meet(A,D),meet(join(meet(A,B),join(meet(A,C),meet(B,join(A,C)))),join(A,D))))) = join(join(meet(A,B),meet(A,C)),meet(A,D)). [para(16(a,1),16(a,1,2,1)),rewrite([16(22)])].
% 164.48/164.76 42 ifeq(join(A,one),one,ifeq(A,zero,complement(A),one),one) = one. [para(19(a,1),14(a,1,3,1))].
% 164.48/164.76 43 ifeq(A,one,ifeq(meet(A,zero),zero,complement(A),zero),zero) = zero. [para(20(a,1),14(a,1,1))].
% 164.48/164.76 44 meet(A,zero) = zero. [para(4(a,1),21(a,1,2)),rewrite([4(4)])].
% 164.48/164.76 46 ifeq(A,one,complement(A),zero) = zero. [back_rewrite(43),rewrite([44(3),5(6)])].
% 164.48/164.76 49 complement(one) = zero. [para(46(a,1),5(a,1)),flip(a)].
% 164.48/164.76 50 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(23(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),11(6),8(5),11(6,R),8(5)])].
% 164.48/164.76 59 join(A,one) = one. [para(3(a,1),24(a,1,2)),rewrite([3(4)])].
% 164.48/164.76 61 ifeq(A,zero,complement(A),one) = one. [back_rewrite(42),rewrite([59(2),5(8)])].
% 164.48/164.76 62 join(A,join(B,complement(A))) = one. [back_rewrite(25),rewrite([59(5)])].
% 164.48/164.76 63 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(26(a,1),13(a,2,2)),rewrite([9(3),13(3,R),9(2),13(6),9(5),13(6,R),9(5)])].
% 164.48/164.76 65 meet(A,join(meet(A,B),join(meet(A,join(C,meet(A,D))),meet(B,join(A,C))))) = join(meet(A,B),meet(A,join(C,meet(A,D)))). [para(26(a,1),16(a,1,2,2,2,2))].
% 164.48/164.76 66 complement(zero) = one. [para(61(a,1),5(a,1)),flip(a)].
% 164.48/164.76 70 meet(A,join(B,join(meet(A,join(C,complement(A))),meet(A,B)))) = join(meet(A,B),meet(A,join(C,complement(A)))). [para(62(a,1),16(a,1,2,2,2,2)),rewrite([19(6),9(5),13(6,R)])].
% 164.48/164.76 88 join(zero,meet(A,B)) = meet(A,B). [para(34(a,1),8(a,2)),rewrite([8(1),7(2),8(3)]),flip(a)].
% 164.48/164.76 89 meet(A,meet(B,join(C,meet(A,C)))) = meet(A,meet(C,B)). [para(34(a,1),11(a,2,2)),rewrite([8(3),88(7),11(6),8(5),11(6,R),8(5)])].
% 164.48/164.76 111 meet(A,meet(B,meet(meet(A,B),join(C,meet(A,B))))) = meet(A,B). [para(1(a,1),50(a,2)),rewrite([9(3),11(6,R),8(5),11(5,R),8(4)])].
% 164.48/164.76 112 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(50(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)])].
% 164.48/164.76 117 join(A,join(B,join(join(A,B),meet(C,join(A,B))))) = join(A,B). [para(2(a,1),63(a,2)),rewrite([8(3),13(6,R),9(5),13(5,R),9(4)])].
% 164.48/164.76 120 meet(A,join(meet(A,B),join(meet(A,join(C,join(D,meet(A,E)))),meet(B,join(A,join(C,D)))))) = join(meet(A,B),meet(A,join(C,join(D,meet(A,E))))). [para(63(a,1),16(a,1,2,2,2,2))].
% 164.48/164.76 121 complement(complement(A)) = A. [para(3(a,1),30(a,1,1)),rewrite([4(4),5(7),5(5)])].
% 164.48/164.76 125 ifeq(join(A,join(B,C)),one,ifeq(meet(C,join(A,B)),zero,complement(join(A,B)),C),C) = C. [para(13(a,2),30(a,1,1))].
% 164.48/164.76 148 meet(A,join(meet(A,meet(B,C)),join(meet(A,D),meet(meet(C,join(B,meet(A,B))),join(A,D))))) = join(meet(A,meet(B,C)),meet(A,D)). [para(89(a,1),16(a,1,2,1)),rewrite([89(15)])].
% 164.48/164.76 235 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(37(a,1),7(a,1,2))].
% 164.48/164.76 296 meet(A,join(meet(A,B),meet(complement(A),join(A,B)))) = meet(A,B). [para(4(a,1),38(a,1,2,2,1)),rewrite([88(6),4(8),88(9)])].
% 164.48/164.76 303 meet(meet(A,B),join(meet(A,C),meet(A,B))) = meet(A,B). [para(38(a,1),23(a,1,2)),rewrite([8(7),21(7)])].
% 164.48/164.76 308 meet(A,join(B,join(meet(A,B),meet(A,join(C,complement(A)))))) = join(meet(A,B),meet(A,join(C,complement(A)))). [para(62(a,1),38(a,1,2,2,2,2)),rewrite([19(6),9(5),13(6,R)])].
% 164.48/164.76 345 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(303(a,1),16(a,1,2,1)),rewrite([8(4),11(4),8(3),11(4,R),8(3),9(9),6(13),303(6),8(4),11(4),8(3),11(4,R),8(3)]),flip(a)].
% 164.48/164.76 422 meet(A,join(zero,complement(A))) = zero. [para(3(a,1),296(a,1,2,2,2)),rewrite([4(2),19(4),4(6)])].
% 164.48/164.76 545 join(zero,complement(A)) = complement(A). [para(422(a,1),14(a,1,3,1)),rewrite([62(4),5(9),5(7)]),flip(a)].
% 164.48/164.76 961 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(111(a,1),11(a,1)),rewrite([8(7),21(7)]),flip(a)].
% 164.48/164.76 969 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(117(a,1),13(a,1)),rewrite([9(7),24(7)]),flip(a)].
% 164.48/164.76 971 join(zero,join(complement(A),meet(B,complement(A)))) = complement(A). [para(545(a,1),117(a,1,2,2,1)),rewrite([545(6),24(7),545(9)])].
% 164.48/164.76 980 join(complement(A),meet(B,complement(A))) = complement(A). [para(971(a,1),13(a,1)),rewrite([545(6),9(5)]),flip(a)].
% 164.48/164.76 985 meet(A,join(meet(A,B),join(meet(B,join(A,C)),meet(A,join(C,meet(A,D)))))) = join(meet(A,B),meet(A,join(C,meet(A,D)))). [para(9(a,1),65(a,1,2,2))].
% 164.48/164.76 1101 join(meet(A,B),meet(B,join(C,complement(B)))) = meet(B,join(A,meet(B,join(C,complement(B))))). [para(70(a,1),8(a,2)),rewrite([8(4),26(6),8(5),8(6)]),flip(a)].
% 164.48/164.76 1104 meet(one,join(A,B)) = join(A,B). [para(49(a,1),70(a,1,2,2,1,2,2)),rewrite([20(4),8(3),19(3),8(3),19(3),9(2),24(3),8(5),19(5),49(6),20(6),8(5),19(5)])].
% 164.48/164.76 1164 meet(one,complement(A)) = complement(A). [para(545(a,1),1104(a,1,2)),rewrite([545(6)])].
% 164.48/164.76 1171 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(1104(a,1),961(a,1,1)),rewrite([1104(4),13(3),9(2),13(3,R),9(2),1104(7)])].
% 164.48/164.76 1172 join(one,complement(A)) = one. [para(1164(a,1),7(a,1,2))].
% 164.48/164.76 1173 join(one,meet(A,join(B,complement(C)))) = one. [para(1164(a,1),235(a,1,2,2,1)),rewrite([8(4),19(4),9(3)])].
% 164.48/164.76 1174 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(1164(a,1),40(a,1,2,2,1)),rewrite([8(3),19(3),8(3),19(3),8(5),19(5),8(5),19(5),9(5),59(5),19(5),9(4),24(5),1172(7),8(6),1104(6),13(5),9(4),13(5,R),9(4),13(6,R),13(5),9(4),13(5,R),9(4),24(4),24(5),1104(5),8(5),19(5),8(5),19(5),1164(7)]),flip(a)].
% 164.48/164.76 1177 meet(complement(A),join(B,complement(A))) = complement(A). [para(1164(a,1),961(a,1,1)),rewrite([1164(4),1164(7)])].
% 164.48/164.76 1179 join(one,meet(A,B)) = one. [para(49(a,1),1173(a,1,2,2,2)),rewrite([20(3)])].
% 164.48/164.76 1194 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(1179(a,1),40(a,1,2,2,2,2)),rewrite([8(3),19(3),8(3),19(3),11(5),8(4),19(4),8(3),8(5),19(5),8(5),19(5),9(5),59(5),19(5),9(4),24(5),8(6),1104(6),13(5),9(4),13(5,R),9(4),13(6,R),13(5),9(4),13(5,R),9(4),24(4),24(5),1104(5),8(5),19(5),8(5),19(5),11(7),8(6),19(6),8(5)]),flip(a)].
% 164.48/164.76 1269 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [back_rewrite(969),rewrite([1194(4)])].
% 164.48/164.76 1541 join(A,join(B,complement(join(A,B)))) = one. [para(1174(a,1),3(a,1))].
% 164.48/164.76 1542 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(7(a,1),1174(a,1,1)),flip(a)].
% 164.48/164.76 1547 join(zero,join(meet(A,B),complement(C))) = join(meet(A,B),complement(C)). [para(88(a,1),1174(a,1,1)),flip(a)].
% 164.48/164.76 1557 join(zero,join(complement(A),complement(B))) = join(complement(A),complement(B)). [para(545(a,1),1174(a,1,1)),flip(a)].
% 164.48/164.76 1577 join(A,join(B,join(C,complement(join(A,B))))) = one. [para(1541(a,1),13(a,2,2)),rewrite([9(4),13(4,R),9(3),59(7)])].
% 164.48/164.76 1589 meet(A,join(complement(A),meet(A,join(B,complement(join(A,B)))))) = meet(A,join(B,complement(join(A,B)))). [para(1541(a,1),296(a,1,2,2,2)),rewrite([19(7),9(6)])].
% 164.48/164.76 1616 join(A,join(B,join(C,complement(join(A,C))))) = one. [para(1577(a,1),9(a,1)),rewrite([9(2),9(6),13(6,R),9(5),13(5,R),9(4)]),flip(a)].
% 164.48/164.76 1716 join(A,complement(meet(A,B))) = one. [para(3(a,1),1542(a,1,2)),rewrite([59(2)]),flip(a)].
% 164.48/164.76 1754 meet(A,join(B,join(meet(A,complement(meet(A,C))),meet(A,B)))) = join(meet(A,B),meet(A,complement(meet(A,C)))). [para(1716(a,1),16(a,1,2,2,2,2)),rewrite([19(6),9(5),13(6,R)])].
% 164.48/164.76 1762 meet(A,join(complement(A),meet(A,complement(meet(A,B))))) = meet(A,complement(meet(A,B))). [para(1716(a,1),296(a,1,2,2,2)),rewrite([19(6),9(5)])].
% 164.48/164.76 1766 join(A,join(B,complement(meet(C,join(A,B))))) = one. [para(1716(a,1),1174(a,1)),rewrite([8(3)]),flip(a)].
% 164.48/164.76 1826 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [para(88(a,1),1766(a,1,2,2,1,2)),rewrite([11(4),8(3),11(4,R),8(3),1547(7)])].
% 164.48/164.76 1848 join(A,join(B,join(C,complement(meet(D,join(A,C)))))) = one. [para(1766(a,1),1616(a,1,2,2,2,1)),rewrite([49(6),9(6),13(6,R),9(5),545(5)])].
% 164.48/164.76 2535 join(A,join(B,complement(meet(C,join(A,meet(B,D)))))) = one. [para(1542(a,1),1848(a,1,2))].
% 164.48/164.76 2609 meet(A,meet(meet(B,C),complement(D))) = meet(A,meet(B,meet(C,complement(D)))). [para(980(a,1),112(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)].
% 164.48/164.76 2612 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(1174(a,1),112(a,1,2,2,2,2)),rewrite([11(8,R),8(7),11(7,R),8(6),11(6,R),8(5),1171(5),11(8,R)]),flip(a)].
% 164.48/164.76 3195 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(7(a,1),1194(a,1,1)),flip(a)].
% 164.48/164.76 3225 meet(meet(A,B),join(C,join(D,meet(A,B)))) = meet(A,B). [para(1194(a,1),961(a,1,2))].
% 164.48/164.76 4360 meet(meet(A,B),join(A,C)) = meet(A,B). [para(7(a,1),3225(a,1,2,2)),rewrite([9(2)])].
% 164.48/164.76 4371 meet(meet(A,complement(B)),join(C,complement(B))) = meet(A,complement(B)). [para(980(a,1),3225(a,1,2,2))].
% 164.48/164.76 4383 meet(meet(A,B),join(B,C)) = meet(A,B). [para(8(a,1),4360(a,1,1)),rewrite([8(4)])].
% 164.48/164.76 4443 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(23(a,1),4383(a,1,1)),rewrite([9(4),23(8)])].
% 164.48/164.76 4482 join(meet(A,complement(B)),meet(A,meet(C,complement(B)))) = meet(A,complement(B)). [para(4371(a,1),16(a,1,2,1)),rewrite([8(7),11(7,R),8(6),9(12),6(16),4371(7),8(7),11(7,R),8(6)]),flip(a)].
% 164.48/164.76 4483 meet(A,join(meet(B,complement(C)),meet(A,complement(C)))) = meet(A,complement(C)). [para(4371(a,1),16(a,1,2,2,2)),rewrite([13(9),9(8),4482(8),9(12),4482(12)])].
% 164.48/164.76 4712 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(6(a,1),4443(a,1,1)),rewrite([6(7)])].
% 164.48/164.76 4747 join(A,join(complement(meet(B,C)),meet(B,join(C,D)))) = one. [para(4443(a,1),1766(a,1,2,2,1)),rewrite([8(3),9(5)])].
% 164.48/164.76 4812 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [para(4747(a,1),2(a,1)),flip(a)].
% 164.48/164.76 4848 join(complement(meet(A,B)),meet(B,join(A,C))) = one. [para(8(a,1),4812(a,1,1,1))].
% 164.48/164.76 4883 join(complement(meet(A,B)),join(meet(A,join(B,C)),meet(D,E))) = one. [para(4812(a,1),1194(a,1,1)),rewrite([1179(3)]),flip(a)].
% 164.48/164.76 4891 join(A,complement(meet(B,A))) = one. [para(3(a,1),4848(a,1,2,2)),rewrite([19(4),9(3)])].
% 164.48/164.76 4893 join(complement(meet(A,meet(B,C))),meet(meet(A,C),join(B,D))) = one. [para(11(a,1),4848(a,1,1,1)),rewrite([8(4)])].
% 164.48/164.76 4923 join(A,complement(meet(B,meet(C,A)))) = one. [para(1826(a,1),4848(a,1,2,2)),rewrite([8(2),11(2),8(1),11(2,R),8(1),19(5),9(4)])].
% 164.48/164.76 4948 join(complement(meet(A,meet(B,C))),meet(A,meet(B,join(C,D)))) = one. [para(50(a,1),4891(a,1,2,1)),rewrite([11(5),8(4),11(5,R),8(4),9(7)])].
% 164.48/164.76 4952 join(meet(A,join(B,C)),complement(meet(A,meet(B,D)))) = one. [para(23(a,1),4923(a,1,2,1,2)),rewrite([8(3),11(4),8(3),11(4,R),8(3)])].
% 164.48/164.76 5035 join(complement(meet(A,meet(B,C))),meet(A,join(B,D))) = one. [para(4952(a,1),9(a,1)),flip(a)].
% 164.48/164.76 5036 join(meet(A,join(B,C)),complement(meet(A,meet(C,D)))) = one. [para(9(a,1),4952(a,1,1,2))].
% 164.48/164.76 5253 join(complement(meet(A,meet(B,C))),meet(C,join(A,D))) = one. [para(8(a,1),5035(a,1,1,1)),rewrite([8(2),11(2),8(1),11(2,R),8(1)])].
% 164.48/164.76 5275 join(meet(A,join(B,C)),complement(meet(C,meet(A,D)))) = one. [para(8(a,1),5036(a,1,1)),rewrite([8(2),11(4,R),8(3)])].
% 164.48/164.76 5466 join(complement(meet(A,B)),meet(join(B,C),join(A,D))) = one. [para(6(a,1),5253(a,1,1,1,2))].
% 164.48/164.76 5646 join(complement(meet(A,complement(B))),meet(complement(B),join(C,A))) = one. [para(1177(a,1),5275(a,1,2,1,2)),rewrite([9(7)])].
% 164.48/164.76 5745 join(complement(meet(A,complement(B))),meet(join(A,C),complement(B))) = one. [para(980(a,1),5466(a,1,2,2)),rewrite([8(2)])].
% 164.48/164.76 5805 join(meet(A,complement(B)),complement(meet(meet(A,C),complement(B)))) = one. [para(7(a,1),5646(a,1,2,2)),rewrite([8(6),9(7)])].
% 164.48/164.76 5817 meet(one,meet(complement(A),join(B,C))) = meet(complement(A),join(B,C)). [para(5646(a,1),961(a,1,2)),rewrite([8(5)])].
% 164.48/164.76 5944 complement(meet(A,complement(join(A,B)))) = one. [para(4(a,1),5745(a,1,2)),rewrite([9(6),545(6)])].
% 164.48/164.76 5954 meet(one,meet(join(A,B),complement(C))) = meet(join(A,B),complement(C)). [para(5745(a,1),961(a,1,2)),rewrite([8(5)])].
% 164.48/164.76 5966 meet(A,complement(join(A,B))) = zero. [para(5944(a,1),4(a,1,2)),rewrite([8(5),11(5,R),8(4),1164(4)])].
% 164.48/164.76 5980 meet(join(A,B),complement(join(A,join(B,complement(C))))) = zero. [para(1174(a,1),5966(a,1,2,1))].
% 164.48/164.76 6156 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(121(a,1),5980(a,1,2,1,2,2))].
% 164.48/164.76 6183 meet(meet(A,B),complement(join(C,meet(A,B)))) = zero. [para(88(a,1),6156(a,1,1)),rewrite([9(4),13(5,R),9(4),88(4)])].
% 164.48/164.76 6238 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(345(a,1),6183(a,1,2,1)),rewrite([8(5),11(5,R),2609(5)])].
% 164.48/164.76 6332 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(1(a,1),6238(a,1,2,2))].
% 164.48/164.76 6391 ifeq(join(A,meet(B,complement(meet(A,B)))),one,complement(meet(B,complement(meet(A,B)))),A) = A. [para(6332(a,1),30(a,1,3,1)),rewrite([5(12)])].
% 164.48/164.76 6664 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(4712(a,1),148(a,1,2,2,2,1)),rewrite([8(4),6(4),8(3),6(3),8(3),9(5),13(5),9(4),13(5,R),9(4),6(6),9(4),24(5),8(8),6(8),8(7),6(7),8(7)])].
% 164.48/164.76 6815 complement(meet(meet(A,B),complement(join(A,C)))) = one. [para(5966(a,1),5805(a,1,1)),rewrite([545(7)])].
% 164.48/164.76 6855 meet(meet(A,B),complement(join(A,C))) = zero. [para(6815(a,1),121(a,1,1)),rewrite([49(2)]),flip(a)].
% 164.48/164.76 7035 meet(meet(A,B),complement(join(B,C))) = zero. [para(8(a,1),6855(a,1,1))].
% 164.48/164.76 7071 meet(meet(A,meet(B,C)),complement(join(D,meet(A,C)))) = zero. [para(11(a,1),7035(a,1,1)),rewrite([8(3),9(4)])].
% 164.48/164.76 7078 meet(meet(A,B),complement(join(C,meet(B,join(A,D))))) = zero. [para(23(a,1),7035(a,1,1)),rewrite([9(4)])].
% 164.48/164.76 8461 meet(A,meet(B,meet(C,complement(join(D,meet(A,B)))))) = zero. [para(7071(a,1),8(a,1)),rewrite([8(5),11(7,R),2609(7)]),flip(a)].
% 164.48/164.76 8667 meet(meet(A,B),complement(meet(B,join(A,C)))) = zero. [para(2(a,1),7078(a,1,2,1))].
% 164.48/164.76 8750 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(8667(a,1),8(a,1)),rewrite([8(5),8(6)]),flip(a)].
% 164.48/164.76 9006 meet(meet(A,B),complement(meet(A,join(C,meet(A,B))))) = zero. [para(21(a,1),8750(a,1,1)),rewrite([9(3)])].
% 164.48/164.76 9570 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(1(a,1),8461(a,1,2,2))].
% 164.48/164.76 9720 meet(A,meet(B,complement(join(C,join(D,meet(A,B)))))) = zero. [para(1194(a,1),9570(a,1,2,2,1))].
% 164.48/164.76 10127 meet(A,meet(complement(A),join(B,C))) = zero. [para(5646(a,1),9006(a,1,2,1,2)),rewrite([19(6),121(5),8(4)])].
% 164.48/164.76 12079 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(88(a,1),5954(a,1,2,1)),rewrite([2609(5),11(5,R),8(4),11(4,R),19(3),88(6)]),flip(a)].
% 164.48/164.76 17047 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(121(a,1),4483(a,1,2,1,2)),rewrite([121(3),121(6)])].
% 164.48/164.76 17098 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(17047(a,1),8(a,1)),rewrite([8(2),8(5)]),flip(a)].
% 164.48/164.76 17099 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(17047(a,1),8(a,2)),rewrite([8(2),8(4),8(5)])].
% 164.48/164.76 17100 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(9(a,1),17047(a,1,2)),rewrite([8(2)])].
% 164.48/164.76 17271 meet(A,join(meet(B,meet(C,D)),meet(A,C))) = meet(A,C). [para(11(a,1),17098(a,1,2,1))].
% 164.48/164.76 17272 meet(A,join(meet(B,meet(C,D)),meet(A,D))) = meet(A,D). [para(11(a,2),17098(a,1,2,1))].
% 164.48/164.76 17319 join(A,meet(B,A)) = A. [para(19(a,1),17099(a,1,2,2)),rewrite([9(3),1104(4),19(4)])].
% 164.48/164.76 17445 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(23(a,1),17319(a,1,2)),rewrite([8(3),9(4)])].
% 164.48/164.76 17679 meet(A,join(meet(B,meet(C,D)),meet(C,A))) = meet(C,A). [para(17271(a,1),8(a,2)),rewrite([8(3),8(5),8(6)])].
% 164.48/164.76 17751 meet(A,join(meet(B,meet(C,D)),meet(D,A))) = meet(D,A). [para(17272(a,1),8(a,2)),rewrite([8(3),8(5),8(6)])].
% 164.48/164.76 17826 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(8(a,1),17445(a,1,1))].
% 164.48/164.76 18051 join(A,meet(B,meet(A,C))) = A. [para(19(a,1),17679(a,1,2,2)),rewrite([9(4),1104(5),19(5)])].
% 164.48/164.76 18154 join(A,meet(B,meet(C,A))) = A. [para(19(a,1),17751(a,1,2,2)),rewrite([9(4),1104(5),19(5)])].
% 164.48/164.76 18288 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(6(a,1),17826(a,1,1))].
% 164.48/164.76 18632 join(meet(A,join(B,complement(A))),meet(A,complement(meet(A,B)))) = A. [para(4883(a,1),70(a,1,2)),rewrite([19(2),9(7)]),flip(a)].
% 164.48/164.76 18657 join(meet(A,complement(meet(A,B))),meet(A,join(complement(A),meet(A,B)))) = A. [para(21(a,1),18632(a,1,2,2,1)),rewrite([9(3),9(8)])].
% 164.48/164.76 18750 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(4893(a,1),961(a,1,2)),rewrite([8(5),2612(5),11(5,R),8(4),11(4,R),8(3),1104(3)]),flip(a)].
% 164.48/164.76 18762 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(4893(a,1),120(a,1,2,2,1,2,2)),rewrite([8(3),11(3),8(2),11(3,R),8(2),59(6),8(6),11(6),8(5),19(5),8(4),8(6),13(10,R),9(9),1826(9),59(6),19(6),9(5),13(6),9(5),18154(5),9(3),18750(4),8(6),11(6),8(5),11(6,R),8(5),8(8),18750(13),4948(14),59(9),8(9),11(9),8(8),19(8),8(7),9(8),345(8)])].
% 164.48/164.76 20894 join(meet(A,B),meet(A,join(C,complement(A)))) = meet(A,join(B,meet(A,join(C,complement(A))))). [para(13(a,1),308(a,1,2)),rewrite([17319(5),9(4)]),flip(a)].
% 164.48/164.76 25372 meet(A,join(B,A)) = A. [para(3(a,1),1101(a,1,2,2)),rewrite([19(3),9(2),17319(2),3(2),19(2)]),flip(a)].
% 164.48/164.76 25391 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(26(a,1),25372(a,1,2)),rewrite([9(3),8(4)])].
% 164.48/164.76 25419 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(9(a,1),25391(a,1,1))].
% 164.48/164.76 25680 join(A,join(B,meet(C,join(B,meet(A,D))))) = join(A,B). [para(25419(a,1),18051(a,1,2,2)),rewrite([1194(5)])].
% 164.48/164.76 30793 join(meet(A,B),meet(A,complement(meet(A,C)))) = meet(A,join(B,meet(A,complement(meet(A,C))))). [para(13(a,2),1754(a,1,2)),rewrite([9(5),17319(5),9(4)]),flip(a)].
% 164.48/164.76 31753 join(A,meet(join(B,C),join(B,meet(A,D)))) = join(A,B). [para(18288(a,1),25680(a,1,2))].
% 164.48/164.76 31880 join(A,meet(join(B,C),join(A,B))) = join(A,B). [para(1(a,1),31753(a,1,2,2,2)),rewrite([9(2)])].
% 164.48/164.76 31927 join(A,meet(join(A,B),join(B,C))) = join(A,B). [para(8(a,1),31880(a,1,2))].
% 164.48/164.76 31929 join(A,meet(join(B,C),join(A,C))) = join(A,C). [para(9(a,1),31880(a,1,2,1))].
% 164.48/164.76 32059 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(17098(a,1),31927(a,1,2)),rewrite([8(3)])].
% 164.48/164.76 32142 join(A,meet(join(B,C),join(C,A))) = join(C,A). [para(31929(a,1),9(a,2)),rewrite([9(2),9(4),9(5)])].
% 164.48/164.76 33922 join(complement(A),meet(A,join(B,meet(A,complement(meet(A,B)))))) = one. [para(18657(a,1),1541(a,1,2,2,1)),rewrite([9(9),32059(9),13(7),9(6),13(7,R),9(6),30793(6)])].
% 164.48/164.76 33932 meet(A,join(B,meet(A,complement(meet(A,B))))) = A. [para(33922(a,1),14(a,1,1)),rewrite([11(9,R),8(8),10127(9),121(6),5(10),5(8)]),flip(a)].
% 164.48/164.76 33956 join(A,meet(B,complement(meet(A,B)))) = join(A,B). [para(33932(a,1),1269(a,1,2,2)),rewrite([8(1),9(4),7(4),8(2)]),flip(a)].
% 164.48/164.76 34006 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(33932(a,1),18288(a,1,2)),rewrite([24(2),8(5),6(5),8(5),6664(7)]),flip(a)].
% 164.48/164.76 34007 join(A,meet(complement(A),join(B,A))) = join(B,A). [para(33932(a,1),32142(a,1,2)),rewrite([8(3),25372(3),8(3),9(5),17319(5),8(4),25372(4),8(4)]),flip(a)].
% 164.48/164.76 34012 ifeq(join(A,B),one,complement(meet(B,complement(meet(A,B)))),A) = A. [back_rewrite(6391),rewrite([33956(4)])].
% 164.48/164.76 34014 join(A,meet(B,complement(meet(B,A)))) = join(B,A). [para(33956(a,1),9(a,2)),rewrite([8(1),9(4),9(5)])].
% 164.48/164.76 34035 join(A,meet(complement(meet(A,B)),join(meet(A,B),meet(B,C)))) = join(A,meet(B,C)). [para(17100(a,1),33956(a,1,2,2,1)),rewrite([8(6),3195(11)])].
% 164.48/164.76 34038 join(meet(A,B),meet(B,meet(join(A,C),complement(meet(A,B))))) = meet(B,join(A,C)). [para(17826(a,1),33956(a,2)),rewrite([11(7,R),11(6),8(5),6(5),8(4),11(5,R),1(4),8(6),11(6,R)])].
% 164.48/164.76 34069 join(complement(A),meet(A,join(B,complement(A)))) = join(B,complement(A)). [para(121(a,1),34006(a,1,2,1)),rewrite([9(3),9(7)])].
% 164.48/164.76 34108 join(meet(A,B),meet(B,complement(meet(A,B)))) = B. [para(17319(a,1),34007(a,1,2,2)),rewrite([8(4),17319(7)])].
% 164.48/164.76 34120 ifeq(join(A,B),one,complement(meet(A,complement(meet(A,B)))),B) = B. [para(34014(a,1),30(a,1,1)),rewrite([11(6,R),8(5),6332(6),5(9)])].
% 164.48/164.76 34128 join(A,join(meet(B,C),meet(B,A))) = join(A,meet(B,C)). [para(17098(a,1),34014(a,1,2,2,1)),rewrite([8(2),8(4),1194(7),34108(6),9(2),8(4)]),flip(a)].
% 164.48/164.76 34510 complement(meet(A,complement(meet(A,join(B,complement(join(A,B))))))) = join(B,complement(join(A,B))). [para(1541(a,1),34120(a,1,1)),rewrite([5(13)])].
% 164.48/164.76 34511 complement(meet(A,complement(meet(A,complement(meet(A,B)))))) = complement(meet(A,B)). [para(1716(a,1),34120(a,1,1)),rewrite([5(11)])].
% 164.48/164.76 34515 join(complement(A),meet(A,join(B,complement(join(A,B))))) = join(B,complement(join(A,B))). [para(1589(a,1),34120(a,1,3,1,2,1)),rewrite([26(7),3(2),34510(9),5(12)]),flip(a)].
% 164.48/164.76 34516 join(complement(A),meet(A,complement(meet(A,B)))) = complement(meet(A,B)). [para(1762(a,1),34120(a,1,3,1,2,1)),rewrite([26(6),3(2),34511(8),5(10)]),flip(a)].
% 164.48/164.76 34518 meet(complement(A),complement(meet(A,B))) = complement(A). [para(34516(a,1),6(a,1,2))].
% 164.48/164.76 34520 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(34516(a,1),24(a,1,2)),rewrite([34516(9)])].
% 164.48/164.76 34754 meet(A,complement(meet(B,complement(A)))) = A. [para(121(a,1),34518(a,1,1)),rewrite([8(2),121(6)])].
% 164.48/164.76 34894 join(A,complement(meet(B,complement(A)))) = complement(meet(B,complement(A))). [para(34754(a,1),17319(a,1,2)),rewrite([9(4)])].
% 164.48/164.76 35374 join(A,complement(meet(B,join(A,meet(C,complement(B)))))) = one. [para(34520(a,1),2535(a,1,2)),rewrite([8(2)])].
% 164.48/164.76 36010 join(complement(A),complement(meet(B,A))) = complement(meet(B,A)). [para(34894(a,1),1557(a,1,2)),rewrite([121(3),545(4),121(5)]),flip(a)].
% 164.48/164.76 36247 join(complement(A),complement(join(A,B))) = complement(A). [para(6(a,1),36010(a,1,2,1)),rewrite([9(4),6(6)])].
% 164.48/164.76 36336 join(A,complement(join(B,complement(A)))) = A. [para(121(a,1),36247(a,1,1)),rewrite([9(2),121(6)])].
% 164.48/164.76 36388 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(36247(a,1),25372(a,1,2)),rewrite([8(4)])].
% 164.48/164.76 36596 join(complement(join(A,complement(B))),meet(B,join(A,complement(B)))) = B. [para(36336(a,1),34007(a,1,2,2)),rewrite([121(7),8(6),36336(11)])].
% 164.48/164.76 37231 meet(A,complement(join(B,join(C,meet(A,complement(B)))))) = zero. [para(36388(a,1),9720(a,1,2))].
% 164.48/164.76 38252 join(A,complement(meet(B,meet(complement(C),join(A,C))))) = one. [para(34754(a,1),35374(a,1,2,1,2,2)),rewrite([18750(4)])].
% 164.48/164.76 38971 meet(A,complement(join(B,join(C,meet(A,complement(C)))))) = zero. [para(9(a,1),37231(a,1,2,1)),rewrite([9(4),13(4,R),9(3)])].
% 164.48/164.76 39339 complement(meet(A,meet(complement(B),join(B,complement(A))))) = one. [para(38252(a,1),34520(a,1)),rewrite([9(4)]),flip(a)].
% 164.48/164.76 39348 meet(A,meet(complement(B),join(B,complement(A)))) = zero. [para(39339(a,1),4(a,1,2)),rewrite([8(7),11(7,R),8(6),5817(6)])].
% 164.48/164.76 39371 meet(complement(A),meet(complement(B),join(A,B))) = zero. [para(121(a,1),39348(a,1,2,2,2)),rewrite([9(3)])].
% 164.48/164.76 40014 complement(join(A,join(B,meet(complement(A),complement(B))))) = zero. [para(38971(a,1),36388(a,1)),flip(a)].
% 164.48/164.76 40019 join(A,join(B,meet(complement(A),complement(B)))) = one. [para(40014(a,1),3(a,1,2)),rewrite([9(7),13(7,R),9(6),13(6,R),9(5),88(5)])].
% 164.48/164.76 40047 join(A,join(complement(B),meet(B,complement(A)))) = one. [para(121(a,1),40019(a,1,2,2,1)),rewrite([13(5,R),9(4)])].
% 164.48/164.76 40048 complement(meet(complement(A),complement(B))) = join(A,B). [para(40019(a,1),32(a,1,1)),rewrite([18750(7),39371(7),5(10),5(8)])].
% 164.48/164.76 40054 complement(join(A,B)) = meet(complement(A),complement(B)). [para(40019(a,1),125(a,1,1)),rewrite([18750(7),39371(7),5(10),5(8)])].
% 164.48/164.76 40385 meet(A,join(complement(B),meet(A,join(B,complement(A))))) = A. [back_rewrite(36596),rewrite([40054(3),121(3),8(2),20894(6)])].
% 164.48/164.76 40477 join(complement(A),meet(A,join(B,meet(complement(A),complement(B))))) = join(B,meet(complement(A),complement(B))). [back_rewrite(34515),rewrite([40054(3),40054(9)])].
% 164.48/164.76 41605 complement(meet(A,B)) = join(complement(A),complement(B)). [para(1557(a,1),40048(a,2)),rewrite([66(2),40054(5),121(3),121(3),11(3),8(2),19(2),8(1)])].
% 164.48/164.76 41917 ifeq(join(A,B),one,join(complement(B),meet(A,B)),A) = A. [back_rewrite(34012),rewrite([41605(4),41605(7),40054(7),121(5),121(5)])].
% 164.48/164.76 42578 join(meet(A,B),meet(B,meet(join(A,C),join(complement(A),complement(B))))) = meet(B,join(A,C)). [back_rewrite(34038),rewrite([41605(4)])].
% 164.48/164.76 42580 join(A,meet(join(complement(A),complement(B)),join(meet(A,B),meet(B,C)))) = join(A,meet(B,C)). [back_rewrite(34035),rewrite([41605(2)])].
% 164.48/164.76 44687 meet(A,join(complement(A),meet(A,complement(B)))) = meet(A,complement(B)). [para(34069(a,1),40054(a,1,1)),rewrite([40054(3),121(3),8(2),121(4),41605(6),40054(6),121(6),8(5)]),flip(a)].
% 164.48/164.76 46094 join(complement(A),meet(B,join(A,complement(B)))) = join(B,complement(A)). [para(40385(a,1),1269(a,1,2,2)),rewrite([9(5),7(5),9(2)]),flip(a)].
% 164.48/164.76 46690 join(meet(A,join(B,complement(A))),meet(B,join(complement(A),meet(A,complement(B))))) = B. [para(40047(a,1),41917(a,1,1)),rewrite([40054(7),121(4),41605(5),121(5),9(4),5(12)])].
% 164.48/164.76 46777 meet(A,join(complement(A),meet(A,B))) = meet(A,B). [para(121(a,1),44687(a,1,2,2,2)),rewrite([121(6)])].
% 164.48/164.76 46829 meet(A,meet(B,join(complement(A),meet(A,C)))) = meet(A,meet(C,B)). [para(46777(a,1),11(a,2,2)),rewrite([8(4),11(7),8(6),11(7,R),8(6)])].
% 164.48/164.76 46832 meet(complement(A),join(A,meet(B,complement(A)))) = meet(B,complement(A)). [para(121(a,1),46777(a,1,2,1)),rewrite([8(3),8(7)])].
% 164.48/164.76 46843 meet(A,meet(join(complement(A),meet(A,B)),join(C,D))) = meet(A,meet(B,join(C,D))). [para(46777(a,1),18750(a,1,1)),rewrite([18750(3)]),flip(a)].
% 164.48/164.76 46853 join(meet(A,B),meet(A,C)) = meet(A,join(B,meet(A,C))). [para(46777(a,1),985(a,1,2,2,2)),rewrite([3(3),19(3),13(4,R),34128(4),46777(8)]),flip(a)].
% 164.48/164.76 46971 meet(a,join(b,meet(a,c))) != meet(a,join(b,c)) # answer(prove_distributivity). [back_rewrite(18),rewrite([46853(7)])].
% 164.48/164.76 47024 meet(A,join(complement(B),meet(B,complement(A)))) = meet(A,complement(B)). [para(46094(a,1),40054(a,1,1)),rewrite([40054(3),121(3),8(2),121(4),41605(6),40054(6),121(6),8(5)]),flip(a)].
% 164.48/164.76 47029 join(meet(A,complement(B)),meet(B,join(A,complement(B)))) = A. [back_rewrite(46690),rewrite([47024(8),9(6)])].
% 164.48/164.76 47034 join(A,meet(B,complement(A))) = join(A,B). [para(47029(a,1),26(a,1,2)),flip(a)].
% 164.48/164.76 47050 meet(A,join(B,complement(A))) = meet(A,B). [para(47029(a,1),18762(a,1,2,2)),rewrite([8(3),6(3)]),flip(a)].
% 164.48/164.76 47086 meet(complement(A),join(A,B)) = meet(B,complement(A)). [back_rewrite(46832),rewrite([47034(4)])].
% 164.48/164.76 47098 join(complement(A),meet(A,B)) = join(B,complement(A)). [back_rewrite(40477),rewrite([47034(5),47050(4),47034(7)])].
% 164.48/164.76 47165 join(meet(A,B),meet(B,C)) = meet(B,join(A,meet(B,C))). [back_rewrite(1101),rewrite([47050(4),47050(6)])].
% 164.48/164.76 47247 meet(A,meet(join(B,complement(A)),join(C,D))) = meet(A,meet(B,join(C,D))). [back_rewrite(46843),rewrite([47098(3)])].
% 164.48/164.76 47250 meet(A,meet(B,join(C,complement(A)))) = meet(A,meet(B,C)). [back_rewrite(46829),rewrite([47098(3),8(5)])].
% 164.48/164.76 47387 join(A,meet(B,meet(C,complement(A)))) = join(A,meet(B,C)). [back_rewrite(42580),rewrite([47165(6),11(7,R),8(6),47247(7),47086(4),12079(3),21(4)])].
% 164.48/164.76 47388 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(42578),rewrite([47250(7),8(4),47086(4),47165(5),47387(4)])].
% 164.48/164.76 47389 $F # answer(prove_distributivity). [resolve(47388,a,46971,a)].
% 164.48/164.76
% 164.48/164.76 % SZS output end Refutation
% 164.48/164.76 ============================== end of proof ==========================
% 164.48/164.76
% 164.48/164.76 ============================== STATISTICS ============================
% 164.48/164.76
% 164.48/164.76 Given=2068. Generated=3592177. Kept=47384. proofs=1.
% 164.48/164.76 Usable=468. Sos=5141. Demods=5826. Limbo=223, Disabled=41565. Hints=0.
% 164.48/164.76 Megabytes=42.50.
% 164.48/164.76 User_CPU=161.75, System_CPU=1.92, Wall_clock=164.
% 164.48/164.76
% 164.48/164.76 ============================== end of statistics =====================
% 164.48/164.76
% 164.48/164.76 ============================== end of search =========================
% 164.48/164.76
% 164.48/164.76 THEOREM PROVED
% 164.48/164.76 % SZS status Unsatisfiable
% 164.48/164.76
% 164.48/164.76 Exiting with 1 proof.
% 164.48/164.76
% 164.48/164.76 Process 19768 exit (max_proofs) Wed Jun 29 08:56:52 2022
% 164.48/164.76 Prover9 interrupted
%------------------------------------------------------------------------------