TSTP Solution File: LAT196-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT196-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 191.03s 191.37s
% Output : Refutation 191.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT196-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 11:14:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.77/10.13 ============================== Prover9 ===============================
% 9.77/10.13 Prover9 (32) version 2009-11A, November 2009.
% 9.77/10.13 Process 22070 was started by sandbox on n015.cluster.edu,
% 9.77/10.13 Wed Jun 29 11:14:11 2022
% 9.77/10.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21917_n015.cluster.edu".
% 9.77/10.13 ============================== end of head ===========================
% 9.77/10.13
% 9.77/10.13 ============================== INPUT =================================
% 9.77/10.13
% 9.77/10.13 % Reading from file /tmp/Prover9_21917_n015.cluster.edu
% 9.77/10.13
% 9.77/10.13 set(prolog_style_variables).
% 9.77/10.13 set(auto2).
% 9.77/10.13 % set(auto2) -> set(auto).
% 9.77/10.13 % set(auto) -> set(auto_inference).
% 9.77/10.13 % set(auto) -> set(auto_setup).
% 9.77/10.13 % set(auto_setup) -> set(predicate_elim).
% 9.77/10.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 9.77/10.13 % set(auto) -> set(auto_limits).
% 9.77/10.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 9.77/10.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 9.77/10.13 % set(auto) -> set(auto_denials).
% 9.77/10.13 % set(auto) -> set(auto_process).
% 9.77/10.13 % set(auto2) -> assign(new_constants, 1).
% 9.77/10.13 % set(auto2) -> assign(fold_denial_max, 3).
% 9.77/10.13 % set(auto2) -> assign(max_weight, "200.000").
% 9.77/10.13 % set(auto2) -> assign(max_hours, 1).
% 9.77/10.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 9.77/10.13 % set(auto2) -> assign(max_seconds, 0).
% 9.77/10.13 % set(auto2) -> assign(max_minutes, 5).
% 9.77/10.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 9.77/10.13 % set(auto2) -> set(sort_initial_sos).
% 9.77/10.13 % set(auto2) -> assign(sos_limit, -1).
% 9.77/10.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 9.77/10.13 % set(auto2) -> assign(max_megs, 400).
% 9.77/10.13 % set(auto2) -> assign(stats, some).
% 9.77/10.13 % set(auto2) -> clear(echo_input).
% 9.77/10.13 % set(auto2) -> set(quiet).
% 9.77/10.13 % set(auto2) -> clear(print_initial_clauses).
% 9.77/10.13 % set(auto2) -> clear(print_given).
% 9.77/10.13 assign(lrs_ticks,-1).
% 9.77/10.13 assign(sos_limit,10000).
% 9.77/10.13 assign(order,kbo).
% 9.77/10.13 set(lex_order_vars).
% 9.77/10.13 clear(print_given).
% 9.77/10.13
% 9.77/10.13 % formulas(sos). % not echoed (13 formulas)
% 9.77/10.13
% 9.77/10.13 ============================== end of input ==========================
% 9.77/10.13
% 9.77/10.13 % From the command line: assign(max_seconds, 300).
% 9.77/10.13
% 9.77/10.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 9.77/10.13
% 9.77/10.13 % Formulas that are not ordinary clauses:
% 9.77/10.13
% 9.77/10.13 ============================== end of process non-clausal formulas ===
% 9.77/10.13
% 9.77/10.13 ============================== PROCESS INITIAL CLAUSES ===============
% 9.77/10.13
% 9.77/10.13 ============================== PREDICATE ELIMINATION =================
% 9.77/10.13
% 9.77/10.13 ============================== end predicate elimination =============
% 9.77/10.13
% 9.77/10.13 Auto_denials:
% 9.77/10.13 % copying label prove_distributivity to answer in negative clause
% 9.77/10.13
% 9.77/10.13 Term ordering decisions:
% 9.77/10.13
% 9.77/10.13 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 9.77/10.13 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 9.77/10.13
% 9.77/10.13 ============================== end of process initial clauses ========
% 9.77/10.13
% 9.77/10.13 ============================== CLAUSES FOR SEARCH ====================
% 9.77/10.13
% 9.77/10.13 ============================== end of clauses for search =============
% 9.77/10.13
% 9.77/10.13 ============================== SEARCH ================================
% 9.77/10.13
% 9.77/10.13 % Starting search at 0.01 seconds.
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=193.000, iters=3376
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=189.000, iters=3373
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=149.000, iters=3335
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=99.000, iters=3346
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=98.000, iters=3333
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=93.000, iters=3447
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=87.000, iters=3354
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=86.000, iters=3341
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=83.000, iters=3401
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=81.000, iters=3379
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=79.000, iters=3343
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=75.000, iters=3333
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=72.000, iters=3333
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=70.000, iters=3381
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=69.000, iters=3343
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=68.000, iters=3401
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=67.000, iters=3375
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=66.000, iters=3431
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=65.000, iters=3393
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=64.000, iters=3381
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=63.000, iters=3391
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=62.000, iters=3348
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=61.000, iters=3396
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=60.000, iters=3376
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=58.000, iters=3350
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=57.000, iters=3343
% 9.77/10.13
% 9.77/10.13 Low Water (keep): wt=56.000, iters=3336
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=55.000, iters=3333
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=54.000, iters=3341
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=53.000, iters=3339
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=52.000, iters=3369
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=50.000, iters=3341
% 191.03/191.37
% 191.03/191.37 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 16.55 sec).
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=49.000, iters=3340
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=48.000, iters=3390
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=47.000, iters=3371
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=46.000, iters=3340
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=45.000, iters=3425
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=44.000, iters=3338
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=43.000, iters=3374
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=42.000, iters=3343
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=6911, wt=195.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=4523, wt=191.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=4803, wt=186.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=4524, wt=185.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=7553, wt=182.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=3084, wt=181.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=7571, wt=178.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=6729, wt=175.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=3226, wt=174.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=5679, wt=171.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=7558, wt=170.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=3083, wt=169.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=7573, wt=168.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=7476, wt=166.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=7330, wt=165.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=4794, wt=164.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=6738, wt=163.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=4493, wt=162.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=6721, wt=161.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=7048, wt=160.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=6766, wt=159.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=13510, wt=35.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=13612, wt=33.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=13639, wt=32.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=13640, wt=30.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=13641, wt=26.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=13651, wt=22.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=13664, wt=20.000
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=41.000, iters=3376
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=13847, wt=16.000
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=40.000, iters=3353
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=39.000, iters=3360
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=38.000, iters=3340
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% 191.03/191.37 Low Water (keep): wt=37.000, iters=3350
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% 191.03/191.37 Low Water (keep): wt=36.000, iters=3350
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% 191.03/191.37 Low Water (keep): wt=35.000, iters=3341
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% 191.03/191.37 Low Water (keep): wt=34.000, iters=3359
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=33.000, iters=3340
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=32.000, iters=3351
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=31.000, iters=3386
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=30.000, iters=3338
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=29.000, iters=3369
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=28.000, iters=3334
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=27.000, iters=3353
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=26.000, iters=3339
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=25.000, iters=3336
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=24.000, iters=3333
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=23.000, iters=3336
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=22.000, iters=3333
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=33088, wt=15.000
% 191.03/191.37
% 191.03/191.37 Low Water (displace): id=33092, wt=13.000
% 191.03/191.37
% 191.03/191.37 Low Water (keep): wt=21.000, iters=3363
% 191.03/191.37
% 191.03/191.37 ============================== PROOF =================================
% 191.03/191.37 % SZS status Unsatisfiable
% 191.03/191.37 % SZS output start Refutation
% 191.03/191.37
% 191.03/191.37 % Proof 1 at 188.60 (+ 1.76) seconds: prove_distributivity.
% 191.03/191.37 % Length of proof is 227.
% 191.03/191.37 % Level of proof is 56.
% 191.03/191.37 % Maximum clause weight is 33.000.
% 191.03/191.37 % Given clauses 1501.
% 191.03/191.37
% 191.03/191.37 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 191.03/191.37 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 191.03/191.37 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 191.03/191.37 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 191.03/191.37 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 191.03/191.37 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 191.03/191.37 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 191.03/191.37 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 191.03/191.37 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 191.03/191.37 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 191.03/191.37 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 191.03/191.37 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 191.03/191.37 13 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(D,meet(A,C))))) # label(equation_H39) # label(axiom). [assumption].
% 191.03/191.37 14 meet(A,join(B,meet(C,join(D,meet(A,C))))) = meet(A,join(B,meet(C,join(A,D)))). [copy(13),flip(a)].
% 191.03/191.37 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 191.03/191.37 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 191.03/191.37 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 191.03/191.37 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 191.03/191.37 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 191.03/191.37 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)])].
% 191.03/191.37 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 191.03/191.37 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 191.03/191.37 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)])].
% 191.03/191.37 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 191.03/191.37 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 191.03/191.37 26 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(2(a,1),14(a,1,2)),rewrite([8(10),14(11),2(9),22(7)])].
% 191.03/191.37 27 meet(A,join(B,meet(complement(A),join(A,C)))) = meet(A,join(B,meet(C,complement(A)))). [para(4(a,1),14(a,1,2,2,2,2)),rewrite([19(3),7(2)]),flip(a)].
% 191.03/191.37 28 meet(A,join(B,meet(C,join(A,C)))) = meet(A,join(B,C)). [para(5(a,1),14(a,1,2,2)),flip(a)].
% 191.03/191.37 29 meet(A,join(B,meet(C,join(D,meet(C,A))))) = meet(A,join(B,meet(C,join(D,A)))). [para(14(a,1),7(a,2)),rewrite([7(1),7(5),8(6)])].
% 191.03/191.37 34 meet(A,zero) != zero | one != A | complement(A) = zero. [para(19(a,1),17(b,1)),flip(b)].
% 191.03/191.37 35 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 191.03/191.37 36 meet(A,join(B,meet(meet(A,C),join(D,meet(A,C))))) = meet(A,join(B,meet(meet(A,C),join(A,D)))). [para(20(a,1),14(a,1,2,2,2,2))].
% 191.03/191.37 37 one != A | complement(A) = zero. [back_rewrite(34),rewrite([35(2)]),xx(a)].
% 191.03/191.37 38 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([35(5)])].
% 191.03/191.37 39 complement(one) = zero. [hyper(17,a,35,a,b,19,a)].
% 191.03/191.37 41 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(22(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),10(6),7(5),10(6,R),7(5)])].
% 191.03/191.37 43 complement(join(A,one)) = zero. [hyper(37,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 191.03/191.37 45 join(A,one) = one. [para(43(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 191.03/191.37 46 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([45(5)])].
% 191.03/191.37 47 complement(zero) = one. [hyper(17,a,18,a,b,45,a)].
% 191.03/191.37 50 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(38(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),35(6)])].
% 191.03/191.37 53 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(46(a,1),17(b,1)),flip(c),xx(b)].
% 191.03/191.37 54 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(25(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),12(6),8(5),12(6,R),8(5)])].
% 191.03/191.37 55 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)].
% 191.03/191.37 57 meet(A,join(B,meet(meet(C,meet(D,complement(A))),join(A,E)))) = meet(A,join(B,meet(C,meet(D,meet(E,complement(A)))))). [para(50(a,1),14(a,1,2,2,2,2)),rewrite([19(5),7(4),10(4,R),7(3),10(3,R),7(2)]),flip(a)].
% 191.03/191.37 64 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(26(a,1),10(a,1)),rewrite([7(5)]),flip(a)].
% 191.03/191.37 65 meet(A,meet(B,meet(C,join(D,meet(A,B))))) = meet(A,meet(B,C)). [para(26(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),10(7),7(6),10(7,R),7(6)])].
% 191.03/191.37 67 meet(A,meet(join(B,meet(C,join(D,meet(A,C)))),join(E,meet(A,join(B,meet(C,join(A,D))))))) = meet(A,join(B,meet(C,join(A,D)))). [para(14(a,1),26(a,1,2,2,2)),rewrite([14(16)])].
% 191.03/191.37 70 meet(A,join(B,meet(meet(A,C),join(A,D)))) = meet(A,join(B,meet(A,C))). [back_rewrite(36),rewrite([64(4)]),flip(a)].
% 191.03/191.37 80 meet(A,join(complement(A),meet(B,complement(A)))) = zero. [para(6(a,1),27(a,1,2)),rewrite([4(2)]),flip(a)].
% 191.03/191.37 83 meet(A,join(B,meet(zero,complement(A)))) = meet(A,B). [para(27(a,1),14(a,1)),rewrite([4(2),2(7),7(7),4(7),19(7)])].
% 191.03/191.37 87 meet(A,join(B,meet(complement(A),join(C,meet(A,D))))) = meet(A,join(B,meet(C,complement(A)))). [para(25(a,1),27(a,1,2,2,2)),rewrite([27(5),7(8)]),flip(a)].
% 191.03/191.37 99 meet(A,join(meet(zero,complement(A)),meet(B,join(A,C)))) = meet(A,B). [para(22(a,1),83(a,2)),rewrite([8(6)])].
% 191.03/191.37 100 meet(A,join(meet(zero,complement(A)),meet(B,meet(C,complement(A))))) = zero. [para(50(a,1),83(a,2)),rewrite([8(7)])].
% 191.03/191.37 105 meet(A,join(complement(A),join(meet(B,complement(A)),meet(zero,complement(A))))) = zero. [para(80(a,1),83(a,2)),rewrite([8(8),12(8,R)])].
% 191.03/191.37 112 meet(join(A,B),join(A,meet(B,join(A,B)))) = join(A,B). [para(1(a,1),28(a,2)),rewrite([8(3),12(3,R),2(2)])].
% 191.03/191.37 113 meet(A,meet(B,join(C,meet(D,join(A,D))))) = meet(A,meet(B,join(C,D))). [para(28(a,1),10(a,2,2)),rewrite([7(4),10(8,R),7(7)])].
% 191.03/191.37 148 meet(meet(A,complement(B)),join(C,meet(B,join(D,meet(A,complement(B)))))) = meet(meet(A,complement(B)),join(C,meet(B,D))). [para(38(a,1),29(a,1,2,2,2,2)),rewrite([19(4)]),flip(a)].
% 191.03/191.37 159 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(41(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),10(3,R),7(2),10(8,R),7(7),10(7),7(6),10(7,R),7(6)])].
% 191.03/191.37 165 join(A,join(B,join(join(A,B),meet(C,join(A,B))))) = join(A,B). [para(2(a,1),54(a,2)),rewrite([7(3),12(6,R),8(5),12(5,R),8(4)])].
% 191.03/191.37 166 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(54(a,1),12(a,2,2)),rewrite([8(4),12(4,R),8(3),12(3,R),8(2),12(8,R),8(7),12(7),8(6),12(7,R),8(6)])].
% 191.03/191.37 275 meet(A,join(meet(zero,complement(A)),meet(B,complement(A)))) = zero. [para(1(a,1),100(a,1,2,2,2))].
% 191.03/191.37 279 meet(zero,complement(A)) = zero. [para(100(a,1),22(a,1,2)),rewrite([7(5),20(5),7(7),38(7)])].
% 191.03/191.37 286 meet(A,join(zero,meet(B,complement(A)))) = zero. [back_rewrite(275),rewrite([279(3)])].
% 191.03/191.37 296 meet(A,join(complement(A),join(zero,meet(B,complement(A))))) = zero. [back_rewrite(105),rewrite([279(6),8(5)])].
% 191.03/191.37 299 meet(A,join(zero,meet(B,join(A,C)))) = meet(A,B). [back_rewrite(99),rewrite([279(3)])].
% 191.03/191.37 301 meet(complement(A),join(B,meet(zero,join(C,complement(A))))) = meet(B,complement(A)). [para(279(a,1),29(a,1,2,2,2,2)),rewrite([19(4),7(3),35(3),19(3),7(2)]),flip(a)].
% 191.03/191.37 346 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),286(a,1,2,2))].
% 191.03/191.37 352 join(zero,complement(A)) = complement(A). [hyper(53,a,346,a)].
% 191.03/191.37 386 meet(A,join(zero,join(complement(A),meet(B,complement(A))))) = zero. [para(12(a,2),296(a,1,2)),rewrite([8(5)])].
% 191.03/191.37 395 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(64(a,1),299(a,1,2,2))].
% 191.03/191.37 414 join(zero,meet(A,B)) = meet(A,B). [para(395(a,1),1(a,1)),rewrite([7(5),395(5),1(3)]),flip(a)].
% 191.03/191.37 451 meet(zero,join(A,meet(B,meet(C,meet(one,join(complement(meet(B,C)),meet(D,complement(meet(B,C))))))))) = zero. [para(386(a,1),57(a,1,2,2)),rewrite([19(3),7(2),35(2),47(4),18(4),47(6),18(6),47(10),7(10)]),flip(a)].
% 191.03/191.37 462 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(112(a,1),64(a,1,1)),rewrite([112(6),12(3),8(2),12(3,R),8(2),112(9)])].
% 191.03/191.37 530 meet(one,join(A,B)) = join(A,B). [para(3(a,1),462(a,1,2,2)),rewrite([45(3),7(3)])].
% 191.03/191.37 538 meet(complement(A),join(B,complement(A))) = complement(A). [para(352(a,1),462(a,1,1)),rewrite([8(4),12(5,R),19(4),352(7)])].
% 191.03/191.37 541 meet(zero,join(A,meet(B,meet(C,join(complement(meet(B,C)),meet(D,complement(meet(B,C)))))))) = zero. [back_rewrite(451),rewrite([530(9)])].
% 191.03/191.37 542 meet(one,complement(A)) = complement(A). [para(352(a,1),530(a,1,2)),rewrite([352(6)])].
% 191.03/191.37 651 join(complement(A),meet(B,complement(A))) = complement(A). [para(301(a,1),6(a,1,2))].
% 191.03/191.37 661 meet(complement(A),meet(zero,join(B,complement(A)))) = zero. [para(414(a,1),301(a,1,2)),rewrite([279(9)])].
% 191.03/191.37 663 meet(zero,join(A,meet(B,meet(C,complement(meet(B,C)))))) = zero. [back_rewrite(541),rewrite([651(7)])].
% 191.03/191.37 665 join(complement(A),join(meet(B,complement(A)),meet(C,complement(A)))) = complement(A). [para(651(a,1),25(a,2)),rewrite([7(5)])].
% 191.03/191.37 668 meet(zero,join(A,complement(B))) = zero. [para(661(a,1),10(a,1)),rewrite([35(6),7(5)]),flip(a)].
% 191.03/191.37 670 meet(A,complement(B)) != zero | join(A,complement(B)) != one | complement(complement(B)) = A. [para(661(a,1),55(a,1,2,2)),rewrite([19(3),7(2),8(6),668(13),35(11),19(10)]),flip(c)].
% 191.03/191.37 675 meet(A,meet(join(B,meet(C,join(D,meet(C,A)))),join(E,meet(A,join(B,meet(C,join(D,A))))))) = meet(A,join(B,meet(C,join(D,A)))). [para(67(a,1),7(a,2)),rewrite([7(1),8(5),7(11),8(12)])].
% 191.03/191.37 677 meet(A,meet(join(B,meet(A,join(C,meet(D,join(E,A))))),join(C,meet(D,join(E,meet(D,A)))))) = meet(A,join(C,meet(D,join(E,A)))). [para(67(a,1),10(a,2)),rewrite([7(1),8(5),7(10),10(11,R),8(12)])].
% 191.03/191.37 727 meet(zero,join(A,meet(join(B,C),meet(complement(join(B,C)),join(B,meet(C,join(B,C))))))) = zero. [para(112(a,1),663(a,1,2,2,2,2,1)),rewrite([7(8)])].
% 191.03/191.37 737 join(complement(A),join(meet(B,complement(A)),join(meet(C,complement(A)),meet(D,complement(A))))) = complement(A). [para(665(a,1),54(a,2)),rewrite([7(7)])].
% 191.03/191.37 788 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(165(a,1),12(a,1)),rewrite([8(7),23(7)]),flip(a)].
% 191.03/191.37 790 join(A,join(meet(complement(B),join(B,C)),meet(B,join(A,meet(C,complement(B)))))) = join(A,meet(complement(B),join(B,C))). [para(27(a,1),165(a,1,2,2,2)),rewrite([8(12),12(12),8(11),12(12,R),8(11),12(13,R),8(12),23(12),23(10)])].
% 191.03/191.37 795 join(A,meet(B,join(A,B))) = join(A,B). [para(112(a,1),165(a,1,2,2,2)),rewrite([8(7),12(7,R),8(6),788(6),23(4),8(4),788(4),23(2)]),flip(a)].
% 191.03/191.37 798 meet(zero,join(A,meet(zero,join(B,C)))) = zero. [back_rewrite(727),rewrite([795(7),7(6),4(6),7(4)])].
% 191.03/191.37 808 meet(zero,join(A,B)) = zero. [para(2(a,1),798(a,1,2)),rewrite([20(5)])].
% 191.03/191.37 836 meet(A,join(B,join(meet(A,C),meet(C,join(A,B))))) = meet(A,join(B,meet(A,C))). [para(788(a,1),14(a,1,2)),rewrite([8(8),12(8),8(7),12(8,R),8(7)]),flip(a)].
% 191.03/191.37 847 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(414(a,1),788(a,1,1)),rewrite([414(4),10(3),7(2),10(3,R),7(2),414(7)])].
% 191.03/191.37 856 join(meet(A,join(B,C)),meet(A,meet(D,join(B,C)))) = meet(A,join(B,C)). [para(28(a,1),847(a,1,1)),rewrite([7(6),113(7),28(10)])].
% 191.03/191.37 892 meet(A,join(join(A,B),meet(A,C))) = A. [para(788(a,1),70(a,1,2)),rewrite([5(2)]),flip(a)].
% 191.03/191.37 898 meet(A,join(one,meet(A,B))) = A. [para(3(a,1),892(a,1,2,1))].
% 191.03/191.37 905 join(join(A,B),meet(A,C)) = join(A,B). [para(892(a,1),788(a,1,2)),rewrite([8(4),25(4),23(2)]),flip(a)].
% 191.03/191.37 911 join(one,meet(A,B)) = one. [para(898(a,1),788(a,1,2)),rewrite([8(4),25(4),45(2)]),flip(a)].
% 191.03/191.37 916 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),905(a,1,1)),rewrite([8(4)])].
% 191.03/191.37 917 join(join(A,join(B,C)),meet(B,D)) = join(A,join(B,C)). [para(12(a,1),905(a,1,1)),rewrite([8(5),12(6,R),8(5)])].
% 191.03/191.37 921 meet(meet(A,B),join(A,C)) = meet(A,B). [para(905(a,1),64(a,1,2))].
% 191.03/191.37 940 join(join(A,join(B,C)),meet(D,join(A,B))) = join(A,join(B,C)). [para(12(a,2),916(a,1,1)),rewrite([7(4),12(7),8(6),12(7,R),8(6)])].
% 191.03/191.37 943 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(25(a,1),916(a,1,1)),rewrite([7(4),25(8)])].
% 191.03/191.37 952 join(complement(A),meet(B,meet(C,complement(A)))) = complement(A). [para(651(a,1),916(a,1,1)),rewrite([7(4),10(4,R),7(3),651(9)])].
% 191.03/191.37 956 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),921(a,1,1)),rewrite([7(4)])].
% 191.03/191.37 962 meet(A,B) != zero | one != A | complement(meet(A,B)) = A. [para(921(a,1),55(a,1)),rewrite([8(5),6(5),7(7),10(7),7(6),10(7,R),7(6),6(8)]),flip(b),flip(c)].
% 191.03/191.37 972 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(22(a,1),956(a,1,1)),rewrite([8(4),22(8)])].
% 191.03/191.37 1014 meet(A,B) != zero | one != B | complement(meet(A,B)) = B. [para(7(a,1),962(a,1)),rewrite([7(6)])].
% 191.03/191.37 1420 join(A,join(meet(complement(B),join(C,meet(B,D))),meet(B,join(A,meet(C,complement(B)))))) = join(A,meet(complement(B),join(C,meet(B,D)))). [para(87(a,1),788(a,1,2)),rewrite([8(10),12(10,R)])].
% 191.03/191.37 2614 complement(complement(A)) = A. [hyper(670,a,4,a,b,3,a)].
% 191.03/191.37 2681 meet(complement(A),join(A,B)) != zero | join(A,B) = A. [para(2614(a,1),53(a,1,2,2)),rewrite([8(2),2614(7),8(6),2614(8)])].
% 191.03/191.37 2685 meet(complement(A),join(B,meet(A,join(C,meet(D,complement(A)))))) = meet(complement(A),join(B,meet(A,C))). [para(2614(a,1),87(a,1,2,2,1)),rewrite([7(3),2614(10),7(9)])].
% 191.03/191.37 3695 meet(meet(A,complement(B)),join(C,meet(B,D))) = meet(A,meet(complement(B),join(C,meet(B,D)))). [para(7(a,1),148(a,2)),rewrite([148(8),10(10),7(9),10(10,R),7(9)])].
% 191.03/191.37 3709 meet(meet(A,complement(B)),complement(C)) = meet(A,meet(complement(B),complement(C))). [para(651(a,1),148(a,2,2)),rewrite([3695(10),2685(9),651(5)]),flip(a)].
% 191.03/191.37 4242 meet(A,meet(complement(B),complement(meet(A,complement(B))))) = zero. [para(3709(a,1),4(a,1))].
% 191.03/191.37 4248 meet(one,meet(complement(A),complement(B))) = meet(complement(A),complement(B)). [para(542(a,1),3709(a,1,1)),flip(a)].
% 191.03/191.37 4283 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(2614(a,1),3709(a,1,1,2)),rewrite([2614(5)])].
% 191.03/191.37 4532 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(2614(a,1),4242(a,1,2,1)),rewrite([2614(2)])].
% 191.03/191.37 4536 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(4532(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),35(7)])].
% 191.03/191.37 4658 meet(A,meet(B,meet(C,complement(meet(A,C))))) = zero. [para(4536(a,1),7(a,1)),rewrite([7(2),7(6),10(6,R),7(5),10(5,R),7(4)]),flip(a)].
% 191.03/191.37 4890 meet(A,meet(join(A,B),complement(C))) = meet(A,complement(C)). [para(5(a,1),4283(a,1,1)),flip(a)].
% 191.03/191.37 4904 meet(join(A,B),meet(join(A,join(B,C)),complement(D))) = meet(join(A,B),complement(D)). [para(462(a,1),4283(a,1,1)),flip(a)].
% 191.03/191.37 4978 meet(A,complement(join(A,B))) = zero. [para(4(a,1),4890(a,1,2)),rewrite([35(2)]),flip(a)].
% 191.03/191.37 5001 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(4890(a,1),4658(a,1,2))].
% 191.03/191.37 5014 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(788(a,1),159(a,1,2,2,2,2)),rewrite([10(6,R),7(5),10(5,R),7(4),10(4,R),1(3),10(8,R)]),flip(a)].
% 191.03/191.37 5224 meet(complement(A),complement(join(B,complement(A)))) = zero. [para(4978(a,1),4248(a,1,2)),rewrite([35(3),8(4)]),flip(a)].
% 191.03/191.37 5225 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(4978(a,1),4283(a,1)),rewrite([8(3)]),flip(a)].
% 191.03/191.37 5237 meet(A,complement(B)) != zero | join(A,complement(B)) != one | A = B. [para(5224(a,1),55(a,1,2,2)),rewrite([19(3),7(2),8(6),5224(13),19(10),2614(10)])].
% 191.03/191.37 5241 meet(A,meet(B,complement(meet(B,join(A,C))))) = zero. [para(5001(a,1),10(a,2)),rewrite([7(4)])].
% 191.03/191.37 5490 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(462(a,1),5225(a,1,2,2,1,2)),rewrite([12(5),8(4),12(5,R),8(4),4904(8)])].
% 191.03/191.37 5492 meet(A,meet(complement(join(B,C)),join(B,meet(C,D)))) = zero. [para(943(a,1),5225(a,1,2,2,1)),rewrite([8(3),7(5)])].
% 191.03/191.37 5533 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(5241(a,1),4890(a,1)),flip(a)].
% 191.03/191.37 5779 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(64(a,1),166(a,1,2,2,2,2)),rewrite([12(6,R),8(5),12(5,R),8(4),12(4,R),2(3),12(8,R)]),flip(a)].
% 191.03/191.37 5789 join(A,join(join(B,C),complement(D))) = join(A,join(B,join(C,complement(D)))). [para(538(a,1),166(a,1,2,2,2,2)),rewrite([12(6,R),8(5),12(5,R),8(4),12(4,R),2(3),12(8,R)]),flip(a)].
% 191.03/191.37 6134 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [hyper(17,a,5492,a,b,911,a),rewrite([39(2)]),flip(a)].
% 191.03/191.37 6147 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),6134(a,1,1,1))].
% 191.03/191.37 6173 meet(complement(join(A,join(B,C))),join(join(A,C),meet(B,D))) = zero. [para(12(a,1),6147(a,1,1,1)),rewrite([8(4)])].
% 191.03/191.37 6186 meet(A,join(meet(B,meet(C,complement(A))),meet(D,complement(A)))) = zero. [para(952(a,1),6147(a,1,1,1)),rewrite([2614(2),7(5)])].
% 191.03/191.37 6210 meet(A,complement(join(B,join(C,A)))) = zero. [para(5490(a,1),6147(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1),19(5),7(4)])].
% 191.03/191.37 6311 meet(join(A,meet(B,C)),complement(join(A,join(B,D)))) = zero. [para(25(a,1),6210(a,1,2,1,2)),rewrite([8(3),12(4),8(3),12(4,R),8(3)])].
% 191.03/191.37 7081 meet(complement(join(A,join(B,C))),join(A,meet(B,D))) = zero. [para(6311(a,1),7(a,1)),flip(a)].
% 191.03/191.37 7082 meet(join(A,meet(B,C)),complement(join(A,join(C,D)))) = zero. [para(7(a,1),6311(a,1,1,2))].
% 191.03/191.37 7419 meet(complement(join(A,join(B,C))),join(C,meet(A,D))) = zero. [para(8(a,1),7081(a,1,1,1)),rewrite([8(2),12(2),8(1),12(2,R),8(1)])].
% 191.03/191.37 7580 meet(join(A,meet(B,C)),complement(join(C,join(A,D)))) = zero. [para(8(a,1),7082(a,1,1)),rewrite([8(2),12(4,R),8(3)])].
% 191.03/191.37 8324 meet(complement(join(A,B)),join(meet(B,C),meet(A,D))) = zero. [para(6(a,1),7419(a,1,1,1,2))].
% 191.03/191.37 8582 meet(complement(join(A,complement(B))),join(complement(B),meet(C,A))) = zero. [para(651(a,1),7580(a,1,2,1,2)),rewrite([7(7)])].
% 191.03/191.37 8753 meet(complement(join(A,complement(B))),join(meet(A,C),complement(B))) = zero. [para(538(a,1),8324(a,1,2,2)),rewrite([8(2)])].
% 191.03/191.37 8871 join(zero,join(complement(A),meet(B,C))) = join(complement(A),meet(B,C)). [para(8582(a,1),788(a,1,2)),rewrite([8(5)])].
% 191.03/191.37 9115 join(A,complement(meet(A,B))) = one. [hyper(1014,a,8753,a,b,3,a(flip)),rewrite([3(8),7(6),542(6),2614(5),3(7)])].
% 191.03/191.37 9124 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [hyper(1014,a,8753,a,b,9115,a(flip)),rewrite([7(2),10(2),7(1),10(2,R),7(1),9115(4),39(2),7(4),10(4),7(3),10(4,R),7(3),808(7),47(2),7(4),10(4),7(3),10(4,R),7(3)]),flip(a)].
% 191.03/191.37 9160 join(join(A,B),complement(meet(C,join(A,B)))) = one. [para(462(a,1),9124(a,1,1)),rewrite([7(5),10(6,R),7(5),462(5)])].
% 191.03/191.37 9309 join(join(A,B),complement(meet(A,C))) = one. [para(921(a,1),9160(a,1,2,1))].
% 191.03/191.37 9313 join(A,join(complement(meet(B,C)),meet(B,join(C,D)))) = one. [para(972(a,1),9160(a,1,2,1)),rewrite([7(4),8(6),12(6,R),8(5)])].
% 191.03/191.37 9337 join(join(A,B),complement(meet(B,C))) = one. [para(8(a,1),9309(a,1,1))].
% 191.03/191.37 9359 join(join(A,join(B,C)),complement(meet(D,join(A,C)))) = one. [para(12(a,1),9337(a,1,1)),rewrite([8(3),7(4)])].
% 191.03/191.37 9979 join(complement(meet(A,B)),meet(B,join(A,C))) = one. [hyper(17,a,8582,a,b,9313,a),rewrite([7(2),9309(4),39(2),47(2),7(2)]),flip(a)].
% 191.03/191.37 10212 join(complement(meet(A,meet(B,C))),meet(meet(A,C),join(B,D))) = one. [para(10(a,1),9979(a,1,1,1)),rewrite([7(4)])].
% 191.03/191.37 10280 join(A,complement(meet(B,meet(C,A)))) = one. [para(9124(a,1),9979(a,1,2,2)),rewrite([7(2),10(2),7(1),10(2,R),7(1),18(5),8(4)])].
% 191.03/191.37 10337 join(meet(A,join(B,C)),complement(meet(A,meet(B,D)))) = one. [para(22(a,1),10280(a,1,2,1,2)),rewrite([7(3),10(4),7(3),10(4,R),7(3)])].
% 191.03/191.37 10567 join(A,join(B,join(C,complement(meet(D,join(A,B)))))) = one. [para(9359(a,1),8(a,1)),rewrite([8(5),12(7,R),5789(7)]),flip(a)].
% 191.03/191.37 11439 join(complement(meet(A,meet(B,C))),meet(A,join(B,D))) = one. [para(10337(a,1),8(a,1)),flip(a)].
% 191.03/191.37 11488 join(A,join(B,complement(meet(C,join(A,B))))) = one. [para(2(a,1),10567(a,1,2,2))].
% 191.03/191.37 12267 join(complement(meet(A,meet(B,C))),meet(C,join(A,D))) = one. [para(7(a,1),11439(a,1,1,1)),rewrite([7(2),10(2),7(1),10(2,R),7(1)])].
% 191.03/191.37 13086 join(complement(meet(A,B)),meet(join(B,C),join(A,D))) = one. [para(5(a,1),12267(a,1,1,1,2))].
% 191.03/191.37 13762 meet(one,meet(join(A,B),join(C,D))) = meet(join(A,B),join(C,D)). [para(13086(a,1),64(a,1,2)),rewrite([7(5)])].
% 191.03/191.37 14940 meet(A,join(meet(complement(A),complement(B)),meet(C,complement(A)))) = zero. [para(4248(a,1),6186(a,1,2,1)),rewrite([7(3)])].
% 191.03/191.37 14951 meet(A,join(meet(complement(A),complement(B)),meet(C,meet(D,complement(A))))) = zero. [para(4283(a,1),14940(a,1,2,2))].
% 191.03/191.37 15166 join(join(complement(A),meet(B,C)),meet(D,complement(A))) = join(complement(A),meet(B,C)). [para(8871(a,1),917(a,1,1)),rewrite([7(5),8871(11)])].
% 191.03/191.37 19201 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(6173(a,1),788(a,1,2)),rewrite([8(5),5779(5),12(5,R),8(4),12(4,R),8(3),414(3)]),flip(a)].
% 191.03/191.37 19323 join(complement(A),join(meet(B,C),meet(D,complement(A)))) = join(complement(A),meet(B,C)). [back_rewrite(15166),rewrite([19201(6)])].
% 191.03/191.37 19482 join(A,join(B,join(C,meet(D,join(A,B))))) = join(A,join(B,C)). [back_rewrite(940),rewrite([19201(5),19201(4)])].
% 191.03/191.37 19486 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [back_rewrite(788),rewrite([19201(4)])].
% 191.03/191.37 19803 join(join(A,B),join(meet(C,D),meet(E,F))) = join(A,join(B,join(meet(C,D),meet(E,F)))). [para(19201(a,1),19201(a,1,1)),rewrite([19201(5),19201(4)]),flip(a)].
% 191.03/191.37 23172 meet(join(A,B),join(C,join(A,B))) = join(A,B). [para(18(a,1),677(a,1,2,2,2,2,2)),rewrite([45(4),18(4),530(4),8(4),5(5),7(5),13762(6),45(7),18(7),530(7)])].
% 191.03/191.37 23182 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(25(a,1),23172(a,1,2)),rewrite([8(3),7(4)])].
% 191.03/191.37 23200 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(8(a,1),23182(a,1,1))].
% 191.03/191.37 23336 meet(A,join(B,A)) = A. [para(4(a,1),23200(a,1,2,2)),rewrite([19(3),7(2),4(4),19(4)])].
% 191.03/191.37 24016 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(10212(a,1),23336(a,1,2)),rewrite([7(5),5014(5),10(5,R),7(4),10(4,R),7(3),530(3)]),flip(a)].
% 191.03/191.37 25011 join(A,meet(complement(B),join(B,meet(C,complement(B))))) = join(A,meet(complement(B),join(B,C))). [para(836(a,1),790(a,2,2)),rewrite([7(3),8(5),3(5),18(5),8(4),6(4),7(5),8(7),3(7),18(7),8(6),6(6),790(9),7(7)]),flip(a)].
% 191.03/191.37 25536 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(5(a,1),856(a,1,2,2)),rewrite([8(4)])].
% 191.03/191.37 25537 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(26(a,1),856(a,1,2)),rewrite([8(5)])].
% 191.03/191.37 25572 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(7(a,1),25536(a,1,1))].
% 191.03/191.37 25644 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(836(a,1),25536(a,1,2)),rewrite([25536(5),25572(7)]),flip(a)].
% 191.03/191.37 25698 join(A,meet(B,A)) = A. [para(3(a,1),25572(a,1,2,2)),rewrite([18(3),8(2),3(4),18(4)])].
% 191.03/191.37 25748 meet(A,join(meet(B,C),meet(C,join(A,B)))) = meet(A,C). [para(25572(a,1),675(a,1,2,2,2,2)),rewrite([7(2),25572(5),8(4),22(6),24016(6),65(7),26(4),8(3)]),flip(a)].
% 191.03/191.37 25997 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(5(a,1),25748(a,1,2,1)),rewrite([25644(5)])].
% 191.03/191.37 26184 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(25748(a,1),25997(a,1,2,2)),rewrite([25748(9)])].
% 191.03/191.37 26186 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(26184(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 191.03/191.37 26187 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(8(a,1),26184(a,1,2)),rewrite([7(2)])].
% 191.03/191.37 32566 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(25698(a,1),1420(a,2)),rewrite([8(11),12(11,R),25(11),8(10),19803(11),19482(11),25537(5)])].
% 191.03/191.37 32576 join(A,meet(complement(A),join(A,B))) = join(A,meet(B,complement(A))). [para(32566(a,1),790(a,2)),rewrite([7(3),7(7),7(9),10(9,R),1(8),5(9),8(6),25011(6),23(5),7(6)])].
% 191.03/191.37 32578 meet(A,join(meet(B,A),meet(A,C))) = join(meet(B,A),meet(A,C)). [para(32566(a,1),26186(a,1,2)),rewrite([1(7)]),flip(a)].
% 191.03/191.37 32591 meet(complement(A),join(A,meet(B,complement(A)))) = meet(complement(A),join(A,B)). [para(32576(a,1),26(a,1,2,2)),rewrite([23182(6)])].
% 191.03/191.37 32603 join(A,meet(complement(A),complement(meet(A,B)))) = one. [para(9115(a,1),32576(a,1,2,2)),rewrite([18(3),3(2),7(5)]),flip(a)].
% 191.03/191.37 32791 meet(complement(A),complement(meet(A,B))) = complement(A). [hyper(55,a,14951,a,b,32603,a),rewrite([38(7),8(6),414(6)])].
% 191.03/191.37 32804 meet(A,complement(meet(B,complement(A)))) = A. [para(2614(a,1),32791(a,1,1)),rewrite([7(2),2614(6)])].
% 191.03/191.37 32847 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(32791(a,1),737(a,1,2,1)),rewrite([12(12,R),8(11),19323(11),25698(7)])].
% 191.03/191.37 33371 join(A,complement(meet(B,join(A,complement(B))))) = one. [para(32847(a,1),11488(a,1,2))].
% 191.03/191.37 33490 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(5237,a,5533,a,b,33371,a),flip(a)].
% 191.03/191.37 33834 meet(join(A,B),join(B,complement(join(A,B)))) = B. [para(8(a,1),33490(a,1,1)),rewrite([8(2)])].
% 191.03/191.37 33885 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(33490(a,1),32791(a,1,2,1)),rewrite([7(4)])].
% 191.03/191.37 33886 join(complement(A),complement(join(A,B))) = complement(A). [para(33490(a,1),32847(a,1,2,1)),rewrite([8(4),33490(9)])].
% 191.03/191.37 33893 join(A,complement(join(B,complement(A)))) = A. [para(2614(a,1),33886(a,1,1)),rewrite([8(2),2614(6)])].
% 191.03/191.37 34472 meet(A,join(complement(A),meet(A,B))) = meet(A,B). [para(6(a,1),33834(a,1,1)),rewrite([6(3),8(3)])].
% 191.03/191.37 34641 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(33885(a,1),5225(a,1,2))].
% 191.03/191.37 35014 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(2614(a,1),34472(a,1,2,1)),rewrite([7(3),32591(5),7(5)])].
% 191.03/191.37 35051 meet(A,complement(B)) != zero | join(B,A) = B. [back_rewrite(2681),rewrite([35014(3)])].
% 191.03/191.37 35092 meet(complement(A),join(B,A)) = meet(B,complement(A)). [para(35014(a,1),7(a,1)),rewrite([8(3),7(5)]),flip(a)].
% 191.03/191.37 35096 meet(A,join(B,complement(A))) = meet(A,B). [para(2614(a,1),35014(a,1,1)),rewrite([8(2),2614(5),7(4)])].
% 191.03/191.37 35625 join(A,meet(B,complement(A))) = join(A,B). [hyper(35051,a,34641,a),rewrite([8(4),25(4),8(1)]),flip(a)].
% 191.03/191.37 35637 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(2614(a,1),35625(a,1,2,2)),rewrite([7(2),8(5)])].
% 191.03/191.37 35732 meet(join(A,B),complement(meet(A,complement(B)))) = B. [para(32804(a,1),35092(a,2)),rewrite([35625(6),8(4),7(5)])].
% 191.03/191.37 35744 join(complement(A),meet(B,join(A,C))) = join(B,complement(A)). [para(22(a,1),35637(a,1,2)),rewrite([35637(3),8(6)]),flip(a)].
% 191.03/191.37 36027 meet(join(A,B),complement(meet(A,complement(join(B,meet(A,C)))))) = join(B,meet(A,C)). [para(25(a,1),35732(a,1,1))].
% 191.03/191.37 36035 meet(A,complement(meet(A,complement(B)))) = meet(A,B). [para(35732(a,1),4890(a,1,2)),flip(a)].
% 191.03/191.37 36100 meet(A,complement(meet(A,B))) = complement(join(B,complement(A))). [para(33893(a,1),35732(a,1,1)),rewrite([2614(4),35096(3)])].
% 191.03/191.37 36105 complement(join(complement(A),complement(B))) = meet(A,B). [back_rewrite(36035),rewrite([36100(4),8(3)])].
% 191.03/191.37 36143 complement(meet(A,B)) = join(complement(A),complement(B)). [para(36105(a,1),2614(a,1,1))].
% 191.03/191.37 36148 complement(join(A,B)) = meet(complement(A),complement(B)). [para(4248(a,1),36105(a,2)),rewrite([39(2),36143(5),2614(3),2614(3),12(3),8(2),19(2),8(1)])].
% 191.03/191.37 36313 meet(join(A,B),join(B,join(C,complement(A)))) = join(B,meet(A,C)). [back_rewrite(36027),rewrite([36148(4),36143(4),36143(8),36143(8),2614(4),36148(6),2614(4),2614(4),12(5,R),8(4),35637(4)])].
% 191.03/191.37 36360 meet(join(A,B),join(B,complement(A))) = B. [back_rewrite(35732),rewrite([36143(4),2614(4),8(3)])].
% 191.03/191.37 40387 join(A,meet(B,join(C,A))) = join(A,meet(C,B)). [para(19486(a,1),36360(a,1,1)),rewrite([8(6),12(6,R),8(5),35744(5),36313(5)]),flip(a)].
% 191.03/191.37 40403 meet(A,join(B,meet(A,C))) = meet(A,join(C,B)). [para(36360(a,1),26187(a,1,2,2)),rewrite([8(3),40387(3),7(1)])].
% 191.03/191.37 40525 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(32578),rewrite([7(1),40403(4),40403(3),7(3)]),flip(a)].
% 191.03/191.37 40526 $F # answer(prove_distributivity). [resolve(40525,a,16,a)].
% 191.03/191.37
% 191.03/191.37 % SZS output end Refutation
% 191.03/191.37 ============================== end of proof ==========================
% 191.03/191.37
% 191.03/191.37 ============================== STATISTICS ============================
% 191.03/191.37
% 191.03/191.37 Given=1501. Generated=3032791. Kept=40521. proofs=1.
% 191.03/191.37 Usable=321. Sos=5223. Demods=5110. Limbo=122, Disabled=34867. Hints=0.
% 191.03/191.37 Megabytes=44.48.
% 191.03/191.37 User_CPU=188.60, System_CPU=1.76, Wall_clock=190.
% 191.03/191.37
% 191.03/191.37 ============================== end of statistics =====================
% 191.03/191.37
% 191.03/191.37 ============================== end of search =========================
% 191.03/191.37
% 191.03/191.37 THEOREM PROVED
% 191.03/191.37 % SZS status Unsatisfiable
% 191.03/191.37
% 191.03/191.37 Exiting with 1 proof.
% 191.03/191.37
% 191.03/191.37 Process 22070 exit (max_proofs) Wed Jun 29 11:17:21 2022
% 191.03/191.37 Prover9 interrupted
%------------------------------------------------------------------------------