TSTP Solution File: LAT182-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT182-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 06:25:58 EDT 2022
% Result : Unsatisfiable 82.53s 82.82s
% Output : Refutation 82.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT182-1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.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 : Thu Jun 30 11:41:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 10.24/10.55 ============================== Prover9 ===============================
% 10.24/10.55 Prover9 (32) version 2009-11A, November 2009.
% 10.24/10.55 Process 30986 was started by sandbox on n027.cluster.edu,
% 10.24/10.55 Thu Jun 30 11:41:22 2022
% 10.24/10.55 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30833_n027.cluster.edu".
% 10.24/10.55 ============================== end of head ===========================
% 10.24/10.55
% 10.24/10.55 ============================== INPUT =================================
% 10.24/10.55
% 10.24/10.55 % Reading from file /tmp/Prover9_30833_n027.cluster.edu
% 10.24/10.55
% 10.24/10.55 set(prolog_style_variables).
% 10.24/10.55 set(auto2).
% 10.24/10.55 % set(auto2) -> set(auto).
% 10.24/10.55 % set(auto) -> set(auto_inference).
% 10.24/10.55 % set(auto) -> set(auto_setup).
% 10.24/10.55 % set(auto_setup) -> set(predicate_elim).
% 10.24/10.55 % set(auto_setup) -> assign(eq_defs, unfold).
% 10.24/10.55 % set(auto) -> set(auto_limits).
% 10.24/10.55 % set(auto_limits) -> assign(max_weight, "100.000").
% 10.24/10.55 % set(auto_limits) -> assign(sos_limit, 20000).
% 10.24/10.55 % set(auto) -> set(auto_denials).
% 10.24/10.55 % set(auto) -> set(auto_process).
% 10.24/10.55 % set(auto2) -> assign(new_constants, 1).
% 10.24/10.55 % set(auto2) -> assign(fold_denial_max, 3).
% 10.24/10.55 % set(auto2) -> assign(max_weight, "200.000").
% 10.24/10.55 % set(auto2) -> assign(max_hours, 1).
% 10.24/10.55 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 10.24/10.55 % set(auto2) -> assign(max_seconds, 0).
% 10.24/10.55 % set(auto2) -> assign(max_minutes, 5).
% 10.24/10.55 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 10.24/10.55 % set(auto2) -> set(sort_initial_sos).
% 10.24/10.55 % set(auto2) -> assign(sos_limit, -1).
% 10.24/10.55 % set(auto2) -> assign(lrs_ticks, 3000).
% 10.24/10.55 % set(auto2) -> assign(max_megs, 400).
% 10.24/10.55 % set(auto2) -> assign(stats, some).
% 10.24/10.55 % set(auto2) -> clear(echo_input).
% 10.24/10.55 % set(auto2) -> set(quiet).
% 10.24/10.55 % set(auto2) -> clear(print_initial_clauses).
% 10.24/10.55 % set(auto2) -> clear(print_given).
% 10.24/10.55 assign(lrs_ticks,-1).
% 10.24/10.55 assign(sos_limit,10000).
% 10.24/10.55 assign(order,kbo).
% 10.24/10.55 set(lex_order_vars).
% 10.24/10.55 clear(print_given).
% 10.24/10.55
% 10.24/10.55 % formulas(sos). % not echoed (13 formulas)
% 10.24/10.55
% 10.24/10.55 ============================== end of input ==========================
% 10.24/10.55
% 10.24/10.55 % From the command line: assign(max_seconds, 300).
% 10.24/10.55
% 10.24/10.55 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 10.24/10.55
% 10.24/10.55 % Formulas that are not ordinary clauses:
% 10.24/10.55
% 10.24/10.55 ============================== end of process non-clausal formulas ===
% 10.24/10.55
% 10.24/10.55 ============================== PROCESS INITIAL CLAUSES ===============
% 10.24/10.55
% 10.24/10.55 ============================== PREDICATE ELIMINATION =================
% 10.24/10.55
% 10.24/10.55 ============================== end predicate elimination =============
% 10.24/10.55
% 10.24/10.55 Auto_denials:
% 10.24/10.55 % copying label prove_distributivity to answer in negative clause
% 10.24/10.55
% 10.24/10.55 Term ordering decisions:
% 10.24/10.55
% 10.24/10.55 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 10.24/10.55 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 10.24/10.55
% 10.24/10.55 ============================== end of process initial clauses ========
% 10.24/10.55
% 10.24/10.55 ============================== CLAUSES FOR SEARCH ====================
% 10.24/10.55
% 10.24/10.55 ============================== end of clauses for search =============
% 10.24/10.55
% 10.24/10.55 ============================== SEARCH ================================
% 10.24/10.55
% 10.24/10.55 % Starting search at 0.01 seconds.
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=168.000, iters=3360
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=165.000, iters=3352
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=158.000, iters=3388
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=147.000, iters=3365
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=137.000, iters=3391
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=129.000, iters=3363
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=103.000, iters=3367
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=102.000, iters=3333
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=94.000, iters=3493
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=80.000, iters=3341
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=76.000, iters=3373
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=74.000, iters=3372
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=69.000, iters=3352
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=66.000, iters=3361
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=62.000, iters=3413
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=61.000, iters=3383
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=58.000, iters=3352
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=57.000, iters=3431
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=55.000, iters=3413
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=54.000, iters=3356
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=53.000, iters=3383
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=52.000, iters=3441
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=51.000, iters=3368
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=50.000, iters=3356
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=49.000, iters=3353
% 10.24/10.55
% 10.24/10.55 Low Water (keep): wt=48.000, iters=3336
% 10.24/10.55
% 82.53/82.82 Low Water (keep): wt=47.000, iters=3401
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=46.000, iters=3354
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=45.000, iters=3338
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=44.000, iters=3449
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=43.000, iters=3367
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=42.000, iters=3350
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=41.000, iters=3340
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=40.000, iters=3339
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=39.000, iters=3333
% 82.53/82.82
% 82.53/82.82 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 13.60 sec).
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=38.000, iters=3348
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7243, wt=200.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=6760, wt=199.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7591, wt=198.000
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=37.000, iters=3357
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7562, wt=196.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=6608, wt=195.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=6503, wt=194.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7227, wt=191.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=6464, wt=190.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7587, wt=189.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=5710, wt=188.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=6653, wt=187.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7580, wt=186.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7406, wt=185.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7340, wt=184.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7549, wt=183.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7548, wt=181.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=6432, wt=180.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=6421, wt=179.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=6510, wt=178.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=7074, wt=177.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=13271, wt=30.000
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=36.000, iters=3515
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=35.000, iters=3391
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=34.000, iters=3333
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=33.000, iters=3385
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=32.000, iters=3351
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=22218, wt=24.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=22325, wt=20.000
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=22641, wt=19.000
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=31.000, iters=3343
% 82.53/82.82
% 82.53/82.82 Low Water (displace): id=22809, wt=18.000
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=30.000, iters=3343
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=29.000, iters=3345
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=28.000, iters=3333
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=27.000, iters=3336
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=26.000, iters=3336
% 82.53/82.82
% 82.53/82.82 Low Water (keep): wt=25.000, iters=3334
% 82.53/82.82
% 82.53/82.82 ============================== PROOF =================================
% 82.53/82.82 % SZS status Unsatisfiable
% 82.53/82.82 % SZS output start Refutation
% 82.53/82.82
% 82.53/82.82 % Proof 1 at 81.35 (+ 0.51) seconds: prove_distributivity.
% 82.53/82.82 % Length of proof is 270.
% 82.53/82.82 % Level of proof is 67.
% 82.53/82.82 % Maximum clause weight is 49.000.
% 82.53/82.82 % Given clauses 1151.
% 82.53/82.82
% 82.53/82.82 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 82.53/82.82 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 82.53/82.82 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 82.53/82.82 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 82.53/82.82 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 82.53/82.82 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 82.53/82.82 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 82.53/82.82 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 82.53/82.82 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 82.53/82.82 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 82.53/82.82 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 82.53/82.82 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 82.53/82.82 13 meet(A,join(B,meet(A,C))) = meet(A,join(meet(A,join(B,meet(A,C))),meet(C,join(A,B)))) # label(equation_H6) # label(axiom). [assumption].
% 82.53/82.82 14 meet(A,join(meet(B,join(A,C)),meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(A,B))). [copy(13),rewrite([8(9)]),flip(a)].
% 82.53/82.82 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 82.53/82.82 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 82.53/82.82 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 82.53/82.82 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 82.53/82.82 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 82.53/82.82 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)])].
% 82.53/82.82 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 82.53/82.82 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 82.53/82.82 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)])].
% 82.53/82.82 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 82.53/82.82 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 82.53/82.82 26 meet(A,join(B,meet(A,join(complement(A),meet(A,B))))) = meet(A,join(complement(A),meet(A,B))). [para(3(a,1),14(a,1,2,1,2)),rewrite([18(2)])].
% 82.53/82.82 27 meet(A,join(meet(A,B),meet(complement(A),join(A,B)))) = meet(A,B). [para(4(a,1),14(a,1,2,2,2,2)),rewrite([19(5),8(5),4(8),19(8)])].
% 82.53/82.82 29 meet(A,join(meet(B,join(A,C)),meet(A,join(C,meet(B,A))))) = meet(A,join(C,meet(B,A))). [para(14(a,1),7(a,2)),rewrite([7(3),7(7),7(8)])].
% 82.53/82.82 30 meet(A,meet(B,join(meet(C,join(A,D)),meet(A,join(D,meet(A,C)))))) = meet(A,meet(B,join(D,meet(A,C)))). [para(14(a,1),10(a,2,2)),rewrite([7(7),10(12,R),7(11)])].
% 82.53/82.82 31 meet(meet(A,join(B,C)),join(meet(B,join(C,meet(A,B))),meet(meet(A,join(B,C)),join(meet(A,B),meet(B,join(C,meet(A,B))))))) = meet(meet(A,join(B,C)),join(meet(A,B),meet(B,join(C,meet(A,B))))). [para(14(a,1),14(a,1,2,1)),rewrite([7(3),7(8),7(13),22(13),7(11),8(12),7(18),7(23),22(23),7(21),8(22)])].
% 82.53/82.82 32 meet(A,join(meet(A,join(B,meet(A,join(C,meet(A,D))))),meet(join(meet(D,join(A,C)),meet(A,join(C,meet(A,D)))),join(A,B)))) = meet(A,join(B,meet(A,join(C,meet(A,D))))). [para(14(a,1),14(a,1,2,2,2,2)),rewrite([8(14),14(22)])].
% 82.53/82.82 35 meet(A,B) != zero | one != A | meet(A,B) = complement(A). [para(6(a,1),17(b,1)),rewrite([20(2)]),flip(b),flip(c)].
% 82.53/82.82 37 meet(A,zero) != zero | one != A | complement(A) = zero. [para(19(a,1),17(b,1)),flip(b)].
% 82.53/82.82 38 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 82.53/82.82 39 meet(A,join(meet(A,join(B,meet(A,C))),meet(meet(A,C),join(A,B)))) = meet(A,join(B,meet(A,C))). [para(20(a,1),14(a,1,2,2,2,2)),rewrite([8(7),20(10)])].
% 82.53/82.82 40 one != A | complement(A) = zero. [back_rewrite(37),rewrite([38(2)]),xx(a)].
% 82.53/82.82 41 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([38(5)])].
% 82.53/82.82 42 complement(one) = zero. [hyper(17,a,38,a,b,19,a)].
% 82.53/82.82 46 meet(A,meet(meet(B,join(A,C)),join(C,meet(B,A)))) = meet(B,A). [para(14(a,1),22(a,1,2)),rewrite([7(3),10(6,R),7(5),7(9),22(9),7(7)])].
% 82.53/82.82 47 complement(join(A,one)) = zero. [hyper(40,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 82.53/82.82 49 join(A,one) = one. [para(47(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 82.53/82.82 50 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([49(5)])].
% 82.53/82.82 51 complement(zero) = one. [hyper(17,a,18,a,b,49,a)].
% 82.53/82.82 54 meet(A,join(meet(B,join(A,C)),meet(A,join(join(A,C),meet(A,B))))) = meet(A,join(join(A,C),meet(A,B))). [para(23(a,1),14(a,1,2,1,2))].
% 82.53/82.82 56 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(41(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),38(6)])].
% 82.53/82.83 59 meet(A,join(B,meet(A,join(join(C,complement(A)),meet(A,B))))) = meet(A,join(join(C,complement(A)),meet(A,B))). [para(50(a,1),14(a,1,2,1,2)),rewrite([18(2)])].
% 82.53/82.83 61 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)])].
% 82.53/82.83 63 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)].
% 82.53/82.83 81 meet(A,meet(B,join(complement(B),meet(A,B)))) = meet(A,B). [para(26(a,1),22(a,1,2)),rewrite([7(2)])].
% 82.53/82.83 82 meet(A,join(meet(B,join(A,C)),meet(A,join(complement(A),meet(A,B))))) = meet(A,join(complement(A),meet(A,B))). [para(22(a,1),26(a,1,2,2,2,2)),rewrite([22(12)])].
% 82.53/82.83 83 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(41(a,1),26(a,1,2,2,2,2)),rewrite([19(5),4(4),8(4),41(9),19(8),4(7)])].
% 82.53/82.83 87 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),83(a,1,2,2))].
% 82.53/82.83 90 join(zero,complement(A)) = complement(A). [hyper(17,a,87,a,b,50,a),flip(a)].
% 82.53/82.83 91 meet(zero,complement(A)) = zero. [para(87(a,1),14(a,1,2,1)),rewrite([7(6),38(6),19(6),6(6),1(3),7(5),38(5),19(5)]),flip(a)].
% 82.53/82.83 92 meet(A,join(zero,meet(A,B))) = meet(A,B). [para(6(a,1),27(a,1,2,2,2)),rewrite([20(2),7(3),4(3),8(3),20(6)])].
% 82.53/82.83 108 meet(A,meet(B,join(zero,meet(A,C)))) = meet(A,meet(C,B)). [para(92(a,1),10(a,2,2)),rewrite([7(4),10(7),7(6),10(7,R),7(6)])].
% 82.53/82.83 118 meet(A,B) != zero | one != B | meet(A,B) = complement(B). [para(7(a,1),35(a,1)),rewrite([7(6)])].
% 82.53/82.83 119 meet(A,meet(B,C)) != zero | one != B | meet(A,meet(B,C)) = complement(B). [para(10(a,1),35(a,1)),rewrite([7(7),10(8,R),7(7)])].
% 82.53/82.83 135 meet(meet(A,B),join(complement(B),meet(A,B))) = meet(A,B). [para(81(a,1),10(a,1)),rewrite([7(6)]),flip(a)].
% 82.53/82.83 138 meet(A,meet(join(meet(B,join(A,C)),meet(A,join(C,meet(A,B)))),join(meet(A,join(C,meet(A,B))),complement(join(meet(B,join(A,C)),meet(A,join(C,meet(A,B)))))))) = meet(A,join(C,meet(A,B))). [para(14(a,1),81(a,1,2,2,2)),rewrite([8(17),14(26)])].
% 82.53/82.83 143 meet(A,meet(join(meet(A,B),meet(complement(A),join(A,B))),join(meet(A,B),complement(join(meet(A,B),meet(complement(A),join(A,B))))))) = meet(A,B). [para(27(a,1),81(a,1,2,2,2)),rewrite([8(13),27(21)])].
% 82.53/82.83 147 meet(complement(A),join(meet(B,complement(A)),meet(A,join(B,complement(A))))) = meet(B,complement(A)). [para(4(a,1),29(a,1,2,2,2,2)),rewrite([8(3),19(7),7(6),8(7),4(11),19(11),7(10)])].
% 82.53/82.83 148 meet(join(A,B),join(A,meet(join(A,B),join(A,C)))) = meet(join(A,B),join(A,C)). [para(5(a,1),29(a,1,2,2,2,2)),rewrite([8(3),12(3),8(2),12(3,R),8(2),5(4),8(3),5(9),8(8)])].
% 82.53/82.83 150 meet(A,join(B,meet(A,B))) = meet(A,B). [para(6(a,1),29(a,2,2)),rewrite([7(3),14(7)])].
% 82.53/82.83 153 meet(one,join(A,meet(one,join(A,B)))) = meet(one,join(A,B)). [para(18(a,1),29(a,1,2,2,2,2)),rewrite([8(3),49(3),18(3),8(3),18(9),8(8)])].
% 82.53/82.83 161 meet(complement(A),join(meet(B,complement(A)),meet(zero,join(B,complement(A))))) = meet(B,complement(A)). [para(91(a,1),29(a,1,2,2,2,2)),rewrite([8(4),19(8),7(7),8(8),91(13),19(12),7(11)])].
% 82.53/82.83 172 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(22(a,1),150(a,1,2,2)),rewrite([8(4),22(8)])].
% 82.53/82.83 191 meet(A,meet(B,meet(C,join(meet(D,join(A,E)),meet(A,join(E,meet(A,D))))))) = meet(A,meet(B,meet(C,join(E,meet(A,D))))). [para(30(a,1),10(a,2,2)),rewrite([7(8),10(8,R),7(7),10(14,R),7(13),10(13,R),7(12)])].
% 82.53/82.83 261 meet(meet(A,join(B,C)),join(meet(B,join(C,meet(B,A))),meet(meet(A,join(B,C)),join(meet(B,A),meet(B,join(C,meet(B,A))))))) = meet(meet(A,join(B,C)),join(meet(B,A),meet(B,join(C,meet(B,A))))). [para(31(a,1),7(a,2)),rewrite([7(1),7(6),7(7),7(15),7(18),7(19)])].
% 82.53/82.83 447 meet(A,join(meet(A,B),meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(A,B))). [para(7(a,1),39(a,1,2,2)),rewrite([10(6),7(5),5(5),7(4),8(5)])].
% 82.53/82.83 462 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(61(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)])].
% 82.53/82.83 464 meet(A,join(B,join(C,meet(A,D)))) != zero | join(A,join(B,C)) != one | join(B,join(C,meet(A,D))) = complement(A). [para(61(a,1),17(b,1)),flip(c)].
% 82.53/82.83 497 meet(A,join(B,meet(one,join(B,C)))) = meet(A,meet(one,join(B,C))). [para(153(a,1),10(a,1,2)),rewrite([18(10),7(9)]),flip(a)].
% 82.53/82.83 502 meet(one,join(A,meet(one,join(B,A)))) = meet(one,join(B,A)). [para(153(a,1),32(a,1,2,1)),rewrite([7(4),18(4),8(6),49(6),18(6),7(7),18(7),8(10),49(10),7(10),447(12),7(10),18(10),497(12),20(11)])].
% 82.53/82.83 597 meet(meet(A,join(B,C)),join(meet(A,B),meet(B,join(C,meet(A,B))))) = meet(A,B). [para(14(a,1),172(a,1,2,2)),rewrite([7(5),22(5),7(3),7(4),7(11),22(11),7(9)])].
% 82.53/82.83 627 meet(complement(A),join(zero,meet(A,B))) = zero. [para(135(a,1),172(a,1,2,2)),rewrite([7(3),10(4),7(3),4(3),38(3),7(3),7(7),10(8),7(7),4(7),38(7)])].
% 82.53/82.83 663 meet(complement(meet(A,B)),join(zero,meet(A,B))) = zero. [para(135(a,1),627(a,1,2,2))].
% 82.53/82.83 674 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(46(a,1),10(a,1)),rewrite([22(6),7(4),7(5)]),flip(a)].
% 82.53/82.83 678 meet(A,meet(join(meet(B,join(A,C)),meet(A,join(C,meet(B,A)))),meet(join(D,meet(A,join(C,meet(B,A)))),join(D,join(meet(B,join(A,C)),meet(A,join(C,meet(B,A)))))))) = meet(A,join(C,meet(B,A))). [para(14(a,1),46(a,1,2,2,2)),rewrite([7(3),7(9),8(13),7(15),7(19),10(19,R),7(18),10(20,R),7(19),7(23),29(27)])].
% 82.53/82.83 709 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(46(a,1),108(a,2)),rewrite([7(1),22(6),108(7),7(5)])].
% 82.53/82.83 721 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(663(a,1),108(a,1,2)),rewrite([38(2)]),flip(a)].
% 82.53/82.83 724 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(721(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),38(7)])].
% 82.53/82.83 726 meet(A,join(zero,meet(B,complement(meet(A,B))))) = zero. [para(721(a,1),26(a,1,2,2,2,2)),rewrite([19(6),4(5),8(5),721(11),19(9),4(8)])].
% 82.53/82.83 741 meet(A,join(zero,meet(B,meet(C,complement(meet(A,B)))))) = zero. [para(724(a,1),26(a,1,2,2,2,2)),rewrite([19(7),4(6),8(6),724(13),19(10),4(9)])].
% 82.53/82.83 761 meet(A,join(zero,meet(B,complement(meet(B,A))))) = zero. [para(726(a,1),7(a,1)),rewrite([7(3),7(7)]),flip(a)].
% 82.53/82.83 861 meet(zero,join(A,B)) = zero. [para(5(a,1),761(a,1,2,2,2,1)),rewrite([4(4),2(4),7(3)])].
% 82.53/82.83 880 meet(complement(A),join(zero,meet(B,complement(A)))) = meet(B,complement(A)). [back_rewrite(161),rewrite([861(7),8(5)])].
% 82.53/82.83 884 meet(A,join(join(A,B),meet(A,C))) = A. [para(8(a,1),54(a,1,2,2,2)),rewrite([12(5),8(4),6(4),8(3),5(4),8(3),5(4)]),flip(a)].
% 82.53/82.83 900 meet(A,join(one,meet(A,B))) = A. [para(3(a,1),884(a,1,2,1))].
% 82.53/82.83 903 meet(complement(A),join(B,complement(A))) = complement(A). [para(627(a,1),884(a,1,2,2)),rewrite([8(3),8(5),12(5,R),19(4)])].
% 82.53/82.83 912 meet(one,complement(meet(A,B))) = complement(meet(A,B)). [para(663(a,1),900(a,1,2,2)),rewrite([19(5),7(4)])].
% 82.53/82.83 920 meet(complement(A),meet(complement(complement(A)),join(B,complement(A)))) = zero. [para(903(a,1),721(a,1,2,2,1)),rewrite([7(6)])].
% 82.53/82.83 960 meet(one,complement(A)) = complement(A). [para(1(a,1),912(a,1,2,1)),rewrite([1(4)])].
% 82.53/82.83 966 meet(A,join(B,meet(A,join(C,join(complement(A),meet(A,B)))))) = meet(A,join(join(C,complement(A)),meet(A,B))). [para(8(a,1),59(a,1,2,2,2)),rewrite([12(4),8(3),12(4,R),8(3)])].
% 82.53/82.83 967 meet(A,join(join(B,complement(A)),meet(A,C))) = meet(A,join(B,join(complement(A),meet(A,C)))). [para(8(a,1),59(a,2,2)),rewrite([59(7),12(9),8(8),12(9,R),8(8)])].
% 82.53/82.83 1014 meet(A,join(meet(A,join(B,join(complement(A),meet(A,C)))),meet(join(C,meet(A,join(B,join(complement(A),meet(A,C))))),join(A,D)))) = meet(A,join(B,join(complement(A),meet(A,C)))). [para(59(a,1),172(a,1,2,1)),rewrite([967(5),967(10),967(20),966(22),967(20)])].
% 82.53/82.83 1224 meet(complement(A),join(meet(B,complement(A)),meet(meet(complement(complement(A)),join(C,complement(A))),join(B,complement(A))))) = meet(B,complement(A)). [para(920(a,1),14(a,1,2,2,2,2)),rewrite([8(8),19(12),7(11),8(12),920(21),19(16),7(15)])].
% 82.53/82.83 1253 meet(A,complement(B)) != zero | join(A,complement(B)) != one | complement(complement(B)) = A. [para(627(a,1),63(a,1,2,2)),rewrite([19(3),7(2),8(6),627(13),19(10)]),flip(c)].
% 82.53/82.83 1398 meet(A,join(zero,meet(B,meet(C,complement(meet(B,A)))))) = zero. [para(741(a,1),7(a,1)),rewrite([7(3),7(8)]),flip(a)].
% 82.53/82.83 1618 join(complement(A),meet(B,complement(A))) = complement(A). [para(880(a,1),6(a,1,2))].
% 82.53/82.83 1634 meet(complement(A),join(one,meet(B,complement(A)))) = complement(A). [para(880(a,1),900(a,1,2,2))].
% 82.53/82.83 1643 join(complement(A),join(meet(B,complement(A)),meet(C,complement(A)))) = complement(A). [para(1618(a,1),25(a,2)),rewrite([7(5)])].
% 82.53/82.83 1881 meet(meet(A,complement(B)),join(zero,meet(B,C))) = zero. [para(41(a,1),1398(a,1,2,2,2,2,1)),rewrite([51(5),18(5)])].
% 82.53/82.83 1882 meet(meet(A,meet(B,complement(C))),join(zero,meet(C,D))) = zero. [para(56(a,1),1398(a,1,2,2,2,2,1)),rewrite([51(6),18(6)])].
% 82.53/82.83 1906 meet(meet(A,complement(meet(A,B))),join(zero,meet(B,C))) = zero. [para(721(a,1),1398(a,1,2,2,2,2,1)),rewrite([7(1),51(6),18(6)])].
% 82.53/82.83 1932 join(zero,meet(A,complement(B))) = meet(A,complement(B)). [para(1881(a,1),6(a,1,2)),rewrite([8(4)])].
% 82.53/82.83 2392 meet(A,meet(B,meet(meet(C,complement(B)),complement(D)))) = zero. [para(1932(a,1),1882(a,1,2)),rewrite([10(6,R),10(5,R),10(6,R),7(5)])].
% 82.53/82.83 2466 meet(A,meet(meet(B,complement(A)),complement(C))) = zero. [para(2392(a,1),1(a,1)),flip(a)].
% 82.53/82.83 2485 meet(A,meet(complement(meet(B,A)),join(zero,meet(B,C)))) = zero. [para(1906(a,1),7(a,1)),rewrite([7(5),10(8,R)]),flip(a)].
% 82.53/82.83 2779 meet(A,meet(complement(meet(A,B)),join(zero,meet(B,C)))) = zero. [para(7(a,1),2485(a,1,2,1,1))].
% 82.53/82.83 2829 meet(one,meet(join(zero,meet(A,B)),meet(meet(C,complement(A)),complement(D)))) = zero. [para(2466(a,1),2485(a,1,2,1,1)),rewrite([51(6),10(10,R)])].
% 82.53/82.83 2843 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [para(20(a,1),2779(a,1,2,1,1)),rewrite([7(5),10(5),7(4),10(5,R),7(4),108(8)])].
% 82.53/82.83 2896 meet(A,meet(meet(B,C),complement(meet(A,C)))) = zero. [para(7(a,1),2843(a,1,2,1))].
% 82.53/82.83 2975 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(5(a,1),2896(a,1,2,1))].
% 82.53/82.83 2997 meet(A,meet(B,complement(meet(A,join(one,meet(B,C)))))) = zero. [para(900(a,1),2896(a,1,2,1))].
% 82.53/82.83 3011 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(2975(a,1),10(a,1)),rewrite([7(6)]),flip(a)].
% 82.53/82.83 3065 meet(A,complement(join(A,B))) = zero. [para(1(a,1),3011(a,1,2,1)),rewrite([7(2),5(2)])].
% 82.53/82.83 3066 join(zero,meet(A,B)) = meet(A,B). [para(3011(a,1),6(a,1,2)),rewrite([8(3)])].
% 82.53/82.83 3067 meet(meet(A,B),complement(meet(B,join(A,C)))) = zero. [para(7(a,1),3011(a,1,1))].
% 82.53/82.83 3132 meet(one,meet(meet(A,B),meet(meet(C,complement(A)),complement(D)))) = zero. [back_rewrite(2829),rewrite([3066(4)])].
% 82.53/82.83 3431 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(5(a,1),3067(a,1,1))].
% 82.53/82.83 4040 meet(meet(A,B),complement(meet(A,join(one,meet(B,C))))) = zero. [para(2997(a,1),10(a,1)),rewrite([7(8)]),flip(a)].
% 82.53/82.83 4684 meet(A,complement(join(one,meet(A,B)))) = zero. [para(1(a,1),4040(a,1,2,1)),rewrite([7(4),900(4)])].
% 82.53/82.83 4773 complement(join(one,meet(A,B))) = zero. [para(4684(a,1),1634(a,1,2,2)),rewrite([19(7),7(6),3065(6)]),flip(a)].
% 82.53/82.83 4774 join(one,meet(A,B)) = one. [para(4773(a,1),3(a,1,2)),rewrite([8(5),12(5,R),8(4),3066(4)])].
% 82.53/82.83 5459 meet(one,meet(join(A,meet(one,join(A,B))),join(C,meet(one,join(A,B))))) = meet(one,join(A,B)). [para(502(a,1),709(a,1,2,2,2)),rewrite([8(3),8(7),8(14),497(17),20(16)])].
% 82.53/82.83 5859 meet(meet(A,B),meet(meet(C,complement(A)),complement(D))) = zero. [hyper(17,a,3132,a,b,4774,a),rewrite([42(2)]),flip(a)].
% 82.53/82.83 5865 meet(meet(A,meet(B,C)),meet(meet(D,complement(C)),complement(E))) = zero. [para(10(a,2),5859(a,1,1))].
% 82.53/82.83 5927 meet(one,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(148(a,1),143(a,1,2,1,1)),rewrite([25(12),8(8),23(8),7(8),4(8),8(6),3066(6),148(10),148(13),25(18),8(14),23(14),7(14),4(14),8(12),3066(12),3(12),7(6),10(7,R),7(6),20(6),148(11)])].
% 82.53/82.83 7624 meet(meet(A,B),meet(meet(C,complement(join(B,D))),complement(E))) = zero. [para(5(a,1),5865(a,1,1,2))].
% 82.53/82.83 8011 meet(meet(A,B),meet(complement(C),complement(join(B,D)))) = zero. [para(1(a,1),7624(a,1,2,1)),rewrite([7(5)])].
% 82.53/82.83 8073 meet(meet(A,B),complement(join(B,C))) = zero. [hyper(119,a,8011,a,b,51,a(flip)),rewrite([51(3),960(5),51(6),42(6)])].
% 82.53/82.83 8189 meet(A,meet(meet(B,C),complement(D))) = meet(A,meet(B,meet(C,complement(D)))). [para(920(a,1),191(a,1,2,2,2,2,2,2)),rewrite([8(8),19(12),7(11),8(12),10(15,R),7(14),10(14,R),7(13),1224(13),920(12),19(7),10(8,R)]),flip(a)].
% 82.53/82.83 8631 meet(meet(A,B),complement(join(A,C))) = zero. [para(7(a,1),8073(a,1,1))].
% 82.53/82.83 8635 meet(meet(A,B),complement(join(C,meet(A,B)))) = zero. [para(20(a,1),8073(a,1,1)),rewrite([8(3)])].
% 82.53/82.83 13223 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(261(a,1),6(a,1,2)),rewrite([7(5),7(6),597(10),8(4)])].
% 82.53/82.83 13289 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(7(a,1),13223(a,1,1))].
% 82.53/82.83 13301 meet(A,join(B,join(join(A,C),meet(A,D)))) = A. [para(884(a,1),13223(a,1,1)),rewrite([8(4),6(6),8(4)]),flip(a)].
% 82.53/82.83 13306 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(674(a,1),13223(a,1,2)),rewrite([7(2),10(2),7(1),10(2,R),7(1),8(4),674(8)])].
% 82.53/82.83 13318 meet(A,meet(one,join(B,C))) = meet(A,join(B,C)). [para(13223(a,1),138(a,1,2,1,2,2)),rewrite([6(3),7(2),20(5),2(5),13223(6),20(5),6(7),7(6),13223(10),20(9),2(9),3(8),7(4),10(4,R),7(3),20(5),13223(8),20(7)])].
% 82.53/82.83 13513 meet(meet(A,B),join(C,join(meet(A,join(B,D)),meet(A,meet(B,E))))) = meet(A,B). [para(13223(a,1),13301(a,1,2,2,1)),rewrite([7(5),10(5),7(4),10(5,R),7(4)])].
% 82.53/82.83 13552 meet(one,join(A,B)) = join(A,B). [para(13318(a,1),1(a,1)),rewrite([7(5),13318(5),1(3)]),flip(a)].
% 82.53/82.83 13591 meet(join(A,B),join(A,join(B,C))) = join(A,B). [back_rewrite(5459),rewrite([13552(4),23(3),13552(5),12(4),8(3),12(4,R),8(3),5927(6),13552(7)])].
% 82.53/82.83 13595 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(13552(a,1),3011(a,1,1)),rewrite([8(4),12(4),8(3),12(4,R),8(3),13552(5)])].
% 82.53/82.83 13602 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(13552(a,1),13306(a,1,1)),rewrite([7(4),10(5,R),7(4),13552(4),13552(7)])].
% 82.53/82.83 13611 meet(join(A,B),join(meet(C,join(A,B)),meet(complement(join(A,join(B,D))),join(A,join(B,C))))) = meet(C,join(A,B)). [para(13595(a,1),14(a,1,2,2,2,2)),rewrite([8(6),12(6),8(5),12(6,R),8(5),19(10),7(9),8(10),13595(17),19(14),7(13)])].
% 82.53/82.83 13621 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(13595(a,1),191(a,1,2,2,2,2,2,2)),rewrite([8(6),12(6),8(5),12(6,R),8(5),19(10),7(9),8(10),10(13,R),7(12),10(12,R),7(11),13611(11),13595(10),19(7),10(8,R)]),flip(a)].
% 82.53/82.83 13893 join(join(A,B),meet(A,C)) = join(A,B). [para(884(a,1),13602(a,1,2)),rewrite([8(4),25(4),23(2)]),flip(a)].
% 82.53/82.83 13946 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),13893(a,1,1)),rewrite([8(4)])].
% 82.53/82.83 13952 meet(A,join(join(B,C),meet(A,B))) = meet(A,join(B,C)). [para(13893(a,1),29(a,2,2)),rewrite([7(5),14(9)])].
% 82.53/82.83 13953 meet(meet(A,B),join(A,C)) = meet(A,B). [para(13893(a,1),674(a,1,2))].
% 82.53/82.83 13965 join(meet(A,join(B,C)),meet(A,meet(B,D))) = meet(A,join(B,C)). [para(13223(a,1),13893(a,1,1)),rewrite([7(4),10(4),7(3),10(4,R),7(3),13223(9)])].
% 82.53/82.83 13996 meet(meet(A,B),join(C,meet(A,join(B,D)))) = meet(A,B). [back_rewrite(13513),rewrite([13965(6)])].
% 82.53/82.83 14006 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(25(a,1),13946(a,1,1)),rewrite([7(4),25(8)])].
% 82.53/82.83 14011 join(complement(A),meet(B,join(meet(C,complement(A)),meet(D,complement(A))))) = complement(A). [para(1643(a,1),13946(a,1,1)),rewrite([7(7),1643(15)])].
% 82.53/82.83 14020 meet(A,B) != zero | one != A | complement(meet(A,B)) = A. [para(13953(a,1),63(a,1)),rewrite([8(5),6(5),7(7),10(7),7(6),10(7,R),7(6),6(8)]),flip(b),flip(c)].
% 82.53/82.83 14507 meet(A,B) != zero | one != B | complement(meet(A,B)) = B. [para(7(a,1),14020(a,1)),rewrite([7(6)])].
% 82.53/82.83 15004 join(A,meet(B,A)) = A. [para(3(a,1),13289(a,1,2,2)),rewrite([18(3),8(2),3(4),18(4)])].
% 82.53/82.83 15721 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(6(a,1),14006(a,1,1)),rewrite([6(7)])].
% 82.53/82.83 15752 meet(A,meet(complement(join(B,C)),join(B,meet(C,D)))) = zero. [para(14006(a,1),8635(a,1,2,1)),rewrite([8(4),7(6),10(6,R),7(5)])].
% 82.53/82.83 15804 meet(A,join(meet(B,complement(A)),meet(C,complement(A)))) = zero. [para(15721(a,1),82(a,1,2,2,2)),rewrite([7(2),7(4),4(9),8(9),3066(9),22(8),7(9),7(11),14011(14),4(8)])].
% 82.53/82.83 15864 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [hyper(17,a,15752,a,b,4774,a),rewrite([42(2)]),flip(a)].
% 82.53/82.83 15885 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),15864(a,1,1,1))].
% 82.53/82.83 15890 meet(complement(join(A,B)),join(A,meet(C,join(A,B)))) = zero. [para(23(a,1),15864(a,1,1,1)),rewrite([7(4)])].
% 82.53/82.83 15918 meet(A,complement(join(B,join(C,A)))) = zero. [para(13595(a,1),15885(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1),19(5),7(4)])].
% 82.53/82.83 15930 meet(join(A,meet(B,C)),complement(join(A,join(B,D)))) = zero. [para(25(a,1),15918(a,1,2,1,2)),rewrite([8(3),12(4),8(3),12(4,R),8(3)])].
% 82.53/82.83 16011 meet(complement(join(A,B)),join(B,meet(C,join(A,B)))) = zero. [para(8(a,1),15890(a,1,1,1)),rewrite([8(3)])].
% 82.53/82.83 16017 join(A,complement(join(A,B))) != one | complement(complement(join(A,B))) = A. [para(15890(a,1),63(a,1)),rewrite([8(6),7(12),4(12),19(10)]),flip(c),xx(a)].
% 82.53/82.83 16034 meet(complement(join(A,join(B,C))),join(A,meet(B,D))) = zero. [para(15930(a,1),7(a,1)),flip(a)].
% 82.53/82.83 16070 meet(complement(join(A,join(B,C))),join(C,meet(A,D))) = zero. [para(8(a,1),16034(a,1,1,1)),rewrite([8(2),12(2),8(1),12(2,R),8(1)])].
% 82.53/82.83 16230 meet(complement(join(A,B)),join(meet(B,C),meet(A,D))) = zero. [para(6(a,1),16070(a,1,1,1,2))].
% 82.53/82.83 16355 meet(complement(join(A,complement(B))),join(meet(A,C),complement(B))) = zero. [para(903(a,1),16230(a,1,2,2)),rewrite([8(2)])].
% 82.53/82.83 16528 complement(join(A,complement(meet(A,B)))) = zero. [hyper(118,a,16355,a,b,3,a(flip)),rewrite([3(8),7(6),960(6),3(8),42(6)])].
% 82.53/82.83 16534 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(16355(a,1),138(a,1,2,1,1)),rewrite([8631(9),19(6),3066(6),8631(11),19(8),16355(14),8631(15),19(12),3066(12),3(12),7(6),8189(6),10(6,R),7(5),10(5,R),18(4),10(5,R),10(4),7(3),10(4,R),7(3),20(3),20(4),8631(10),19(7)]),flip(a)].
% 82.53/82.83 17689 join(A,complement(meet(A,B))) = one. [para(16528(a,1),3(a,1,2)),rewrite([8(5),12(5,R),8(4),90(4)])].
% 82.53/82.83 17695 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [hyper(14507,a,16355,a,b,17689,a(flip)),rewrite([7(2),10(2),7(1),10(2,R),7(1),17689(4),42(2),7(4),10(4),7(3),10(4,R),7(3),861(7),51(2),7(4),10(4),7(3),10(4,R),7(3)]),flip(a)].
% 82.53/82.83 17892 join(join(A,B),complement(meet(C,join(A,B)))) = one. [para(13552(a,1),17695(a,1,1)),rewrite([7(4),10(5,R),7(4),13552(4)])].
% 82.53/82.83 17981 join(A,join(join(B,C),complement(join(A,B)))) = one. [para(13591(a,1),17892(a,1,2,1)),rewrite([8(5),12(5,R)])].
% 82.53/82.83 17982 join(join(A,B),complement(meet(A,C))) = one. [para(13953(a,1),17892(a,1,2,1))].
% 82.53/82.83 17986 join(A,join(complement(meet(B,C)),meet(B,join(C,D)))) = one. [para(13996(a,1),17892(a,1,2,1)),rewrite([8(6),12(6,R),8(5)])].
% 82.53/82.83 17990 join(one,join(meet(A,B),meet(C,D))) = one. [para(16230(a,1),17892(a,1,2,1)),rewrite([51(5),8(5)])].
% 82.53/82.83 17992 join(one,join(meet(A,B),complement(C))) = one. [para(16355(a,1),17892(a,1,2,1)),rewrite([51(5),8(5)])].
% 82.53/82.83 18185 join(meet(A,join(B,C)),complement(meet(A,meet(B,D)))) = one. [para(13223(a,1),17982(a,1,1)),rewrite([7(4),10(4),7(3),10(4,R),7(3)])].
% 82.53/82.83 18193 join(one,join(join(A,B),complement(C))) = one. [para(13552(a,1),17992(a,1,2,1))].
% 82.53/82.83 18256 join(zero,join(join(A,B),complement(C))) = join(join(A,B),complement(C)). [para(18193(a,1),27(a,1,2,2,2)),rewrite([13552(6),42(6),7(7),38(7),8(6),13552(7),13552(10)])].
% 82.53/82.83 18261 join(one,join(join(A,B),meet(C,D))) = one. [para(13552(a,1),17990(a,1,2,1))].
% 82.53/82.83 18263 join(zero,join(join(A,B),meet(C,D))) = join(join(A,B),meet(C,D)). [para(18261(a,1),27(a,1,2,2,2)),rewrite([13552(6),42(6),7(7),38(7),8(6),13552(7),13552(10)])].
% 82.53/82.83 18325 join(A,join(B,complement(join(A,B)))) = one. [para(2(a,1),17981(a,1,2,1))].
% 82.53/82.83 18327 join(A,join(join(B,C),complement(join(A,C)))) = one. [para(8(a,1),17981(a,1,2,1))].
% 82.53/82.83 18642 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(6(a,1),18327(a,1,2,1))].
% 82.53/82.83 18733 join(join(A,B),complement(join(A,meet(B,C)))) = one. [para(18642(a,1),12(a,1)),rewrite([8(6)]),flip(a)].
% 82.53/82.83 18755 join(join(A,B),complement(join(B,meet(A,C)))) = one. [para(8(a,1),18733(a,1,1))].
% 82.53/82.83 18911 join(A,complement(join(meet(A,B),meet(A,C)))) = one. [para(6(a,1),18755(a,1,1))].
% 82.53/82.83 19012 meet(one,meet(join(A,B),complement(C))) = meet(join(A,B),complement(C)). [para(13552(a,1),16534(a,1,1)),flip(a)].
% 82.53/82.83 19025 meet(A,join(meet(B,meet(C,complement(A))),meet(D,complement(A)))) = zero. [para(16534(a,1),15804(a,1,2,1))].
% 82.53/82.83 19414 join(A,join(join(B,C),complement(D))) = join(A,join(B,join(C,complement(D)))). [para(903(a,1),462(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)].
% 82.53/82.83 19415 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(674(a,1),462(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)].
% 82.53/82.83 19477 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [back_rewrite(18256),rewrite([19414(5),12(5,R),8(4),12(4,R),19(3)]),flip(a)].
% 82.53/82.83 19480 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [back_rewrite(18263),rewrite([19415(5),12(5,R),8(4),12(4,R),8(3),3066(3)]),flip(a)].
% 82.53/82.83 19723 meet(A,join(B,join(C,meet(A,B)))) = meet(A,join(B,C)). [back_rewrite(13952),rewrite([19480(3)])].
% 82.53/82.83 19849 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(6(a,1),19477(a,1,1)),flip(a)].
% 82.53/82.83 20666 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [hyper(464,a,861,a,b,17986,a),rewrite([7(6),38(6),8(6),3066(6),51(7)])].
% 82.53/82.83 20669 join(A,complement(meet(B,A))) = one. [hyper(17,a,16011,a,b,17986,a),rewrite([7(1),17689(3),42(2),51(2),7(2),7(4),17689(6),18(5),8(4)]),flip(a)].
% 82.53/82.83 20711 join(complement(meet(A,B)),meet(A,join(C,meet(A,B)))) = one. [para(709(a,1),20669(a,1,2,1)),rewrite([7(1),7(4),8(6)])].
% 82.53/82.83 20983 join(A,meet(B,meet(A,join(C,D)))) = A. [para(18185(a,1),13289(a,1,2,2)),rewrite([7(3),10(3,R),7(2),18(5),8(4),18185(10),18(6)])].
% 82.53/82.83 21632 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(20711(a,1),29(a,1,2,2,2)),rewrite([8(7),12(7),8(6),50(7),18(4),7(6),13552(6),25(5),8(3),7(4),20711(12),7(8),13552(8)])].
% 82.53/82.83 23268 complement(complement(A)) = A. [para(2(a,1),16017(a,1,2,1)),rewrite([3(2),2(4)]),xx(a)].
% 82.53/82.83 23397 meet(A,complement(B)) != zero | join(A,complement(B)) != one | B = A. [back_rewrite(1253),rewrite([23268(10)])].
% 82.53/82.83 23412 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(15721(a,1),678(a,1,2,2,1)),rewrite([7(5),7(13),5(18),7(9),30(10),709(5),7(3)]),flip(a)].
% 82.53/82.83 23622 meet(A,join(meet(B,C),meet(B,A))) = meet(B,A). [para(23412(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 82.53/82.83 23732 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(20983(a,1),23622(a,1,2)),rewrite([7(5),20(5),13621(7),20(7)])].
% 82.53/82.83 26036 meet(one,meet(complement(A),join(B,C))) = meet(join(B,C),complement(A)). [para(7(a,1),19012(a,1,2))].
% 82.53/82.83 26166 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(6(a,1),19480(a,1,1)),flip(a)].
% 82.53/82.83 26925 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(8(a,1),21632(a,1,1))].
% 82.53/82.83 27288 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(23268(a,1),23397(b,1,2)),rewrite([23268(2)])].
% 82.53/82.83 27500 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(5(a,1),23732(a,1,1)),flip(a)].
% 82.53/82.83 27988 meet(complement(A),join(meet(B,meet(C,A)),meet(A,D))) = zero. [para(19025(a,1),26036(a,1,2)),rewrite([38(3),23268(3),23268(5),7(4),7(7)]),flip(a)].
% 82.53/82.83 28016 meet(A,join(B,join(complement(A),meet(A,complement(meet(A,B)))))) = A. [para(20666(a,1),1014(a,1,2,2,1)),rewrite([13552(10),12(9),8(8),6(8),8(1),5(2)]),flip(a)].
% 82.53/82.83 28379 meet(A,join(B,A)) = A. [para(4(a,1),26925(a,1,2,2)),rewrite([19(3),7(2),4(4),19(4)])].
% 82.53/82.83 28922 join(A,join(complement(B),meet(B,complement(meet(A,B))))) = one. [para(28016(a,1),15004(a,1,2)),rewrite([7(2),8(7),61(7),50(3),7(3)]),flip(a)].
% 82.53/82.83 28961 join(A,join(complement(B),meet(B,complement(meet(B,A))))) = one. [para(28922(a,1),8(a,1)),rewrite([7(3),8(7)]),flip(a)].
% 82.53/82.83 28996 join(complement(A),join(meet(A,B),meet(A,complement(meet(A,B))))) = one. [para(20(a,1),28961(a,1,2,2,2,1)),rewrite([12(7,R),8(6)])].
% 82.53/82.83 29464 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [hyper(17,a,27988,a,b,28996,a),rewrite([23268(2),7(1),20(2),7(2),20(3)]),flip(a)].
% 82.53/82.83 29469 join(meet(A,B),meet(B,complement(meet(A,B)))) = B. [para(7(a,1),29464(a,1,1)),rewrite([7(2)])].
% 82.53/82.83 29490 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(5(a,1),29469(a,1,1)),rewrite([5(3),7(3)])].
% 82.53/82.83 29526 join(A,meet(B,complement(meet(A,B)))) = join(A,B). [para(29469(a,1),26166(a,1,2)),flip(a)].
% 82.53/82.83 29546 join(complement(A),meet(A,join(B,complement(A)))) = join(B,complement(A)). [para(23268(a,1),29490(a,1,2,1)),rewrite([8(3),8(7)])].
% 82.53/82.83 29567 join(A,B) != one | meet(B,complement(meet(A,B))) = complement(A). [para(29526(a,1),17(b,1)),rewrite([721(4)]),flip(c),xx(a)].
% 82.53/82.83 29596 join(A,B) != one | complement(meet(B,complement(meet(A,B)))) = A. [para(29526(a,1),27288(b,1)),rewrite([721(4)]),xx(a)].
% 82.53/82.83 29600 join(A,meet(B,complement(meet(A,meet(C,B))))) = join(A,B). [para(29526(a,1),26166(a,1,2)),rewrite([8(2),25(3),7(3),10(3),7(2),10(3,R),7(2)]),flip(a)].
% 82.53/82.83 29775 join(complement(A),join(meet(A,join(B,complement(A))),meet(C,D))) = join(B,join(complement(A),meet(C,D))). [para(29546(a,1),19480(a,1,1)),rewrite([19480(4)]),flip(a)].
% 82.53/82.83 29869 meet(complement(meet(A,B)),complement(meet(A,complement(meet(A,B))))) = complement(A). [hyper(29567,a,17689,a)].
% 82.53/82.83 29872 join(A,B) != one | meet(A,complement(meet(A,B))) = complement(B). [para(8(a,1),29567(a,1)),rewrite([7(4)])].
% 82.53/82.83 29880 join(A,B) != one | complement(meet(A,complement(meet(A,B)))) = B. [para(8(a,1),29596(a,1)),rewrite([7(4)])].
% 82.53/82.83 29887 join(A,meet(B,complement(meet(B,meet(A,C))))) = join(B,A). [para(29600(a,1),8(a,2)),rewrite([7(1),10(2,R),7(1),8(5),8(6)])].
% 82.53/82.83 30009 meet(A,complement(meet(A,complement(meet(A,B))))) = meet(A,B). [hyper(29872,a,20669,a),rewrite([7(1),7(6),23268(8)])].
% 82.53/82.83 30012 meet(A,complement(meet(A,complement(join(meet(A,B),meet(A,C)))))) = join(meet(A,B),meet(A,C)). [hyper(29872,a,18911,a),rewrite([23268(12)])].
% 82.53/82.83 30014 meet(A,complement(meet(A,join(B,complement(join(A,meet(B,C))))))) = complement(join(B,complement(join(A,meet(B,C))))). [hyper(29872,a,18642,a)].
% 82.53/82.83 30060 meet(A,join(complement(A),meet(A,B))) = meet(A,B). [para(30009(a,1),27(a,1,2,1)),rewrite([17689(7),18(4),8(3),30009(9)])].
% 82.53/82.83 30127 complement(meet(A,complement(meet(A,B)))) = join(complement(A),meet(A,B)). [para(30009(a,1),29469(a,1,1)),rewrite([30009(10),7(8),29869(8),8(3)]),flip(a)].
% 82.53/82.83 30175 join(A,B) != one | join(complement(A),meet(A,B)) = B. [back_rewrite(29880),rewrite([30127(7)])].
% 82.53/82.83 30182 meet(complement(A),join(A,meet(B,complement(A)))) = meet(B,complement(A)). [para(147(a,1),30060(a,1,2,2)),rewrite([23268(3),147(13)])].
% 82.53/82.83 30234 join(complement(A),meet(A,complement(meet(A,B)))) = complement(meet(A,B)). [hyper(30175,a,20669,a),rewrite([7(2),7(6)])].
% 82.53/82.83 30239 join(complement(A),meet(A,join(B,complement(join(A,meet(B,C)))))) = join(B,complement(join(A,meet(B,C)))). [hyper(30175,a,18642,a)].
% 82.53/82.83 30244 join(complement(A),meet(A,join(B,complement(join(A,B))))) = join(B,complement(join(A,B))). [hyper(30175,a,18325,a)].
% 82.53/82.83 30331 join(A,complement(meet(B,meet(C,join(A,complement(B)))))) = one. [para(50(a,1),29887(a,2)),rewrite([7(5),19480(9),30234(8)])].
% 82.53/82.83 30364 join(A,complement(meet(B,join(A,complement(B))))) = one. [para(1(a,1),30331(a,1,2,1,2))].
% 82.53/82.83 30375 join(complement(A),meet(A,complement(meet(B,join(A,complement(B)))))) = complement(meet(B,join(A,complement(B)))). [hyper(30175,a,30364,a)].
% 82.53/82.83 30379 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(27288,a,3431,a,b,30364,a),rewrite([23268(7)])].
% 82.53/82.83 30433 meet(join(A,B),join(B,complement(join(A,B)))) = B. [para(8(a,1),30379(a,1,1)),rewrite([8(2)])].
% 82.53/82.83 30529 meet(A,join(B,complement(join(A,B)))) = meet(A,B). [para(30433(a,1),27500(a,1,2)),flip(a)].
% 82.53/82.83 30535 join(complement(A),meet(A,B)) = join(B,complement(join(A,B))). [back_rewrite(30244),rewrite([30529(5)])].
% 82.53/82.83 30606 meet(A,join(B,join(C,join(meet(A,B),complement(join(A,join(B,C))))))) = meet(A,join(B,C)). [para(19723(a,1),30529(a,2)),rewrite([61(7),8(7),12(7),8(6),12(7,R),8(6),19477(6)])].
% 82.53/82.83 31056 join(A,complement(join(A,B))) = join(A,complement(B)). [para(30535(a,2),23(a,1,2)),rewrite([7(2),25(4),8(3)]),flip(a)].
% 82.53/82.83 31167 join(A,complement(join(B,meet(A,C)))) = join(A,complement(B)). [para(30535(a,2),19849(a,1,2)),rewrite([10(3,R),7(2),25(5)]),flip(a)].
% 82.53/82.83 31207 join(A,meet(B,complement(A))) = join(A,B). [para(23268(a,1),30535(a,1,1)),rewrite([7(2),8(5),31056(7),23268(5),8(4)])].
% 82.53/82.83 31236 meet(A,join(B,complement(A))) = meet(A,B). [para(30535(a,1),19723(a,1,2,2)),rewrite([23(4),30529(4)]),flip(a)].
% 82.53/82.83 31237 join(A,join(B,join(meet(C,A),complement(join(C,join(A,B)))))) = join(complement(C),meet(C,join(A,B))). [para(19723(a,1),30535(a,1,2)),rewrite([61(11),8(11),12(11),8(10),12(11,R),8(10),19477(10)]),flip(a)].
% 82.53/82.83 31311 join(complement(A),meet(A,complement(meet(B,A)))) = complement(meet(B,A)). [para(29469(a,1),30535(a,2,2,1)),rewrite([41(7),8(4),90(4),8(7)]),flip(a)].
% 82.53/82.83 31334 meet(join(complement(A),meet(A,B)),join(complement(join(A,B)),complement(join(B,complement(join(A,B)))))) = complement(join(A,B)). [para(30535(a,2),30433(a,1,1))].
% 82.53/82.83 31450 join(complement(A),meet(A,B)) = join(B,complement(A)). [back_rewrite(30239),rewrite([31167(5),31236(4),31167(7)])].
% 82.53/82.83 31451 meet(A,complement(meet(A,B))) = complement(join(B,complement(A))). [back_rewrite(30014),rewrite([31167(4),31236(3),31167(7)])].
% 82.53/82.83 31468 meet(complement(A),join(A,B)) = meet(B,complement(A)). [back_rewrite(30182),rewrite([31207(4)])].
% 82.53/82.83 31477 join(complement(A),complement(join(B,complement(A)))) = complement(meet(A,B)). [back_rewrite(30375),rewrite([31236(4),7(2),31451(4),31236(8),7(6)])].
% 82.53/82.83 31483 join(complement(A),join(meet(A,B),meet(C,D))) = join(B,join(complement(A),meet(C,D))). [back_rewrite(29775),rewrite([31236(4)])].
% 82.53/82.83 31701 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [back_rewrite(30606),rewrite([31237(7),31450(4),19477(3)])].
% 82.53/82.83 31737 complement(join(A,B)) = meet(complement(A),complement(B)). [back_rewrite(31334),rewrite([31450(3),31477(9),7(4),28379(4),7(4),31468(4)]),flip(a)].
% 82.53/82.83 31740 complement(meet(A,B)) = join(complement(A),complement(B)). [back_rewrite(31311),rewrite([7(2),31451(4),31737(4),23268(4),7(3),31450(4),8(3),7(4)]),flip(a)].
% 82.53/82.83 31894 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(30012),rewrite([31737(4),31740(2),31740(5),31740(9),31740(9),31737(5),23268(3),23268(3),31737(6),23268(4),23268(4),31483(5),31450(3),31701(4)]),flip(a)].
% 82.53/82.83 31895 $F # answer(prove_distributivity). [resolve(31894,a,16,a)].
% 82.53/82.83
% 82.53/82.83 % SZS output end Refutation
% 82.53/82.83 ============================== end of proof ==========================
% 82.53/82.83
% 82.53/82.83 ============================== STATISTICS ============================
% 82.53/82.83
% 82.53/82.83 Given=1151. Generated=980731. Kept=31890. proofs=1.
% 82.53/82.83 Usable=525. Sos=8399. Demods=8652. Limbo=443, Disabled=22535. Hints=0.
% 82.53/82.83 Megabytes=40.85.
% 82.53/82.83 User_CPU=81.35, System_CPU=0.51, Wall_clock=82.
% 82.53/82.83
% 82.53/82.83 ============================== end of statistics =====================
% 82.53/82.83
% 82.53/82.83 ============================== end of search =========================
% 82.53/82.83
% 82.53/82.83 THEOREM PROVED
% 82.53/82.83 % SZS status Unsatisfiable
% 82.53/82.83
% 82.53/82.83 Exiting with 1 proof.
% 82.53/82.83
% 82.53/82.83 Process 30986 exit (max_proofs) Thu Jun 30 11:42:44 2022
% 82.53/82.83 Prover9 interrupted
%------------------------------------------------------------------------------