TSTP Solution File: LAT217-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT217-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 06:26:11 EDT 2022
% Result : Unsatisfiable 51.06s 51.33s
% Output : Refutation 51.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT217-1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.31 % Computer : n016.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Thu Jun 30 10:25:10 EDT 2022
% 0.11/0.31 % CPUTime :
% 11.21/11.53 ============================== Prover9 ===============================
% 11.21/11.53 Prover9 (32) version 2009-11A, November 2009.
% 11.21/11.53 Process 3802 was started by sandbox on n016.cluster.edu,
% 11.21/11.53 Thu Jun 30 10:25:11 2022
% 11.21/11.53 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3649_n016.cluster.edu".
% 11.21/11.53 ============================== end of head ===========================
% 11.21/11.53
% 11.21/11.53 ============================== INPUT =================================
% 11.21/11.53
% 11.21/11.53 % Reading from file /tmp/Prover9_3649_n016.cluster.edu
% 11.21/11.53
% 11.21/11.53 set(prolog_style_variables).
% 11.21/11.53 set(auto2).
% 11.21/11.53 % set(auto2) -> set(auto).
% 11.21/11.53 % set(auto) -> set(auto_inference).
% 11.21/11.53 % set(auto) -> set(auto_setup).
% 11.21/11.53 % set(auto_setup) -> set(predicate_elim).
% 11.21/11.53 % set(auto_setup) -> assign(eq_defs, unfold).
% 11.21/11.53 % set(auto) -> set(auto_limits).
% 11.21/11.53 % set(auto_limits) -> assign(max_weight, "100.000").
% 11.21/11.53 % set(auto_limits) -> assign(sos_limit, 20000).
% 11.21/11.53 % set(auto) -> set(auto_denials).
% 11.21/11.53 % set(auto) -> set(auto_process).
% 11.21/11.53 % set(auto2) -> assign(new_constants, 1).
% 11.21/11.53 % set(auto2) -> assign(fold_denial_max, 3).
% 11.21/11.53 % set(auto2) -> assign(max_weight, "200.000").
% 11.21/11.53 % set(auto2) -> assign(max_hours, 1).
% 11.21/11.53 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 11.21/11.53 % set(auto2) -> assign(max_seconds, 0).
% 11.21/11.53 % set(auto2) -> assign(max_minutes, 5).
% 11.21/11.53 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 11.21/11.53 % set(auto2) -> set(sort_initial_sos).
% 11.21/11.53 % set(auto2) -> assign(sos_limit, -1).
% 11.21/11.53 % set(auto2) -> assign(lrs_ticks, 3000).
% 11.21/11.53 % set(auto2) -> assign(max_megs, 400).
% 11.21/11.53 % set(auto2) -> assign(stats, some).
% 11.21/11.53 % set(auto2) -> clear(echo_input).
% 11.21/11.53 % set(auto2) -> set(quiet).
% 11.21/11.53 % set(auto2) -> clear(print_initial_clauses).
% 11.21/11.53 % set(auto2) -> clear(print_given).
% 11.21/11.53 assign(lrs_ticks,-1).
% 11.21/11.53 assign(sos_limit,10000).
% 11.21/11.53 assign(order,kbo).
% 11.21/11.53 set(lex_order_vars).
% 11.21/11.53 clear(print_given).
% 11.21/11.53
% 11.21/11.53 % formulas(sos). % not echoed (13 formulas)
% 11.21/11.53
% 11.21/11.53 ============================== end of input ==========================
% 11.21/11.53
% 11.21/11.53 % From the command line: assign(max_seconds, 300).
% 11.21/11.53
% 11.21/11.53 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 11.21/11.53
% 11.21/11.53 % Formulas that are not ordinary clauses:
% 11.21/11.53
% 11.21/11.53 ============================== end of process non-clausal formulas ===
% 11.21/11.53
% 11.21/11.53 ============================== PROCESS INITIAL CLAUSES ===============
% 11.21/11.53
% 11.21/11.53 ============================== PREDICATE ELIMINATION =================
% 11.21/11.53
% 11.21/11.53 ============================== end predicate elimination =============
% 11.21/11.53
% 11.21/11.53 Auto_denials:
% 11.21/11.53 % copying label prove_distributivity to answer in negative clause
% 11.21/11.53
% 11.21/11.53 Term ordering decisions:
% 11.21/11.53
% 11.21/11.53 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 11.21/11.53 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 11.21/11.53
% 11.21/11.53 ============================== end of process initial clauses ========
% 11.21/11.53
% 11.21/11.53 ============================== CLAUSES FOR SEARCH ====================
% 11.21/11.53
% 11.21/11.53 ============================== end of clauses for search =============
% 11.21/11.53
% 11.21/11.53 ============================== SEARCH ================================
% 11.21/11.53
% 11.21/11.53 % Starting search at 0.01 seconds.
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=81.000, iters=3357
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=79.000, iters=3358
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=75.000, iters=3338
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=72.000, iters=3465
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=71.000, iters=3459
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=67.000, iters=3390
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=61.000, iters=3389
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=59.000, iters=3421
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=57.000, iters=3397
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=55.000, iters=3348
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=52.000, iters=3360
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=51.000, iters=3338
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=50.000, iters=3366
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=49.000, iters=3374
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=48.000, iters=3415
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=47.000, iters=3424
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=46.000, iters=3375
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=45.000, iters=3353
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=44.000, iters=3368
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=43.000, iters=3362
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=42.000, iters=3337
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=41.000, iters=3350
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=39.000, iters=3355
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=38.000, iters=3335
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=37.000, iters=3383
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=36.000, iters=3352
% 11.21/11.53
% 11.21/11.53 Low Water (keep): wt=35.000, iters=3368
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=34.000, iters=3351
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=33.000, iters=3350
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=32.000, iters=3360
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=31.000, iters=3356
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5925, wt=198.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5621, wt=195.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=6151, wt=193.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=7353, wt=187.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5659, wt=185.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5926, wt=180.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5540, wt=179.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=7354, wt=177.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5614, wt=173.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5758, wt=171.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5612, wt=167.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5620, wt=161.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=7819, wt=159.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5613, wt=157.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=7763, wt=156.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5632, wt=153.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5732, wt=151.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=7637, wt=149.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=5583, wt=147.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=6993, wt=146.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=16063, wt=22.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=16071, wt=20.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=16102, wt=18.000
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=30.000, iters=3341
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=29.000, iters=3345
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=28.000, iters=3343
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=27.000, iters=3352
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=26.000, iters=3349
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=25.000, iters=3341
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=24.000, iters=3336
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=23.000, iters=3338
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=22.000, iters=3333
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=24147, wt=16.000
% 51.06/51.33
% 51.06/51.33 Low Water (displace): id=25649, wt=14.000
% 51.06/51.33
% 51.06/51.33 Low Water (keep): wt=20.000, iters=4572
% 51.06/51.33
% 51.06/51.33 ============================== PROOF =================================
% 51.06/51.33 % SZS status Unsatisfiable
% 51.06/51.33 % SZS output start Refutation
% 51.06/51.33
% 51.06/51.33 % Proof 1 at 49.83 (+ 0.54) seconds: prove_distributivity.
% 51.06/51.33 % Length of proof is 190.
% 51.06/51.33 % Level of proof is 41.
% 51.06/51.33 % Maximum clause weight is 45.000.
% 51.06/51.33 % Given clauses 1093.
% 51.06/51.33
% 51.06/51.33 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 51.06/51.33 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 51.06/51.33 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 51.06/51.33 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 51.06/51.33 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 51.06/51.33 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 51.06/51.33 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 51.06/51.33 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 51.06/51.33 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 51.06/51.33 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 51.06/51.33 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 51.06/51.33 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 51.06/51.33 13 meet(A,join(meet(B,join(A,C)),meet(C,join(A,B)))) = join(meet(A,B),meet(A,C)) # label(equation_H82) # label(axiom). [assumption].
% 51.06/51.33 14 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 51.06/51.33 15 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(14),flip(a)].
% 51.06/51.33 16 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 51.06/51.33 17 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 51.06/51.33 18 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 51.06/51.33 19 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)])].
% 51.06/51.33 20 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 51.06/51.33 21 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 51.06/51.33 22 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)])].
% 51.06/51.33 23 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 51.06/51.33 24 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 51.06/51.33 25 meet(A,join(join(A,B),meet(B,join(A,B)))) = A. [para(1(a,1),13(a,1,2,1)),rewrite([22(3),5(7),6(7)])].
% 51.06/51.33 26 meet(A,join(B,meet(complement(A),join(A,B)))) = join(zero,meet(A,B)). [para(3(a,1),13(a,1,2,1,2)),rewrite([17(2),4(8),8(8)])].
% 51.06/51.33 27 meet(A,join(meet(B,join(A,C)),meet(join(A,C),join(A,B)))) = A. [para(5(a,1),13(a,2,1)),rewrite([22(5),8(6),6(9)])].
% 51.06/51.33 28 meet(A,join(meet(A,B),meet(meet(A,C),join(A,B)))) = join(meet(A,B),meet(A,C)). [para(6(a,1),13(a,1,2,1,2)),rewrite([7(1),19(9)])].
% 51.06/51.33 29 meet(A,join(meet(B,join(A,C)),meet(C,join(B,A)))) = join(meet(B,A),meet(A,C)). [para(13(a,1),7(a,2)),rewrite([8(3),7(6),7(7)])].
% 51.06/51.33 30 meet(A,meet(B,join(meet(C,join(A,D)),meet(D,join(A,C))))) = meet(B,join(meet(A,C),meet(A,D))). [para(13(a,1),10(a,2,2)),rewrite([7(6)])].
% 51.06/51.33 31 meet(meet(A,join(B,C)),join(join(meet(A,B),meet(B,C)),meet(meet(C,join(A,B)),join(B,meet(A,join(B,C)))))) = join(meet(A,B),meet(A,meet(C,join(B,C)))). [para(13(a,1),13(a,1,2,1)),rewrite([7(3),8(6),8(10),7(16),21(16),7(14),8(17),10(19),7(18),10(18,R),7(17),10(19,R),21(19)])].
% 51.06/51.33 35 meet(A,zero) != zero | one != A | complement(A) = zero. [para(18(a,1),16(b,1)),flip(b)].
% 51.06/51.33 36 meet(A,zero) = zero. [para(4(a,1),19(a,1,2)),rewrite([4(4)])].
% 51.06/51.33 37 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [para(13(a,1),19(a,1,2)),rewrite([13(10)])].
% 51.06/51.33 38 one != A | complement(A) = zero. [back_rewrite(35),rewrite([36(2)]),xx(a)].
% 51.06/51.33 40 meet(A,meet(B,complement(A))) = zero. [back_rewrite(20),rewrite([36(5)])].
% 51.06/51.33 41 complement(one) = zero. [hyper(16,a,36,a,b,18,a)].
% 51.06/51.33 42 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(21(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),10(6),7(5),10(6,R),7(5)])].
% 51.06/51.33 43 meet(meet(A,join(B,C)),join(meet(A,B),meet(B,C))) = meet(A,B). [para(13(a,1),21(a,1,2)),rewrite([7(3),7(9),21(9),7(7)])].
% 51.06/51.33 44 complement(join(A,one)) = zero. [hyper(38,a,6,a(flip)),rewrite([7(3),17(3),8(2)])].
% 51.06/51.33 46 join(A,one) = one. [para(44(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),18(3),8(2)])].
% 51.06/51.33 47 join(A,join(B,complement(A))) = one. [back_rewrite(23),rewrite([46(5)])].
% 51.06/51.33 49 meet(A,join(B,meet(one,join(A,B)))) = A. [para(46(a,1),13(a,1,2,1,2)),rewrite([17(2),17(8),8(7),6(7)])].
% 51.06/51.33 53 join(A,join(B,join(C,complement(A)))) = one. [para(47(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),46(6)])].
% 51.06/51.33 54 meet(A,join(B,meet(join(C,complement(A)),join(A,B)))) = join(meet(A,B),meet(A,join(C,complement(A)))). [para(47(a,1),13(a,1,2,1,2)),rewrite([17(2)])].
% 51.06/51.33 55 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(47(a,1),16(b,1)),flip(c),xx(b)].
% 51.06/51.33 57 meet(A,join(meet(B,join(A,C)),meet(join(C,meet(A,D)),join(A,B)))) = join(meet(A,B),meet(A,join(C,meet(A,D)))). [para(24(a,1),13(a,1,2,1,2))].
% 51.06/51.33 58 meet(A,join(B,meet(A,C))) != zero | join(A,B) != one | join(B,meet(A,C)) = complement(A). [para(24(a,1),16(b,1)),flip(c)].
% 51.06/51.33 63 meet(A,join(B,meet(one,join(B,A)))) = A. [para(49(a,1),7(a,2)),rewrite([8(2),7(5)])].
% 51.06/51.33 65 meet(A,join(join(A,B),meet(one,join(A,B)))) = A. [para(22(a,1),49(a,1,2,2,2))].
% 51.06/51.33 67 meet(join(A,B),join(C,meet(one,join(A,join(B,C))))) = join(A,B). [para(12(a,1),63(a,1,2,2,2)),rewrite([8(3),12(4,R),8(3)])].
% 51.06/51.33 68 meet(join(A,B),join(A,meet(one,join(A,B)))) = join(A,B). [para(22(a,1),63(a,1,2,2,2))].
% 51.06/51.33 70 meet(join(A,meet(B,C)),join(B,meet(one,join(A,B)))) = join(A,meet(B,C)). [para(24(a,1),63(a,1,2,2,2)),rewrite([8(4)])].
% 51.06/51.33 72 meet(A,join(one,complement(A))) = A. [para(3(a,1),25(a,1,2,1)),rewrite([3(4),17(4)])].
% 51.06/51.33 76 join(A,meet(one,complement(A))) = one. [para(72(a,1),13(a,1,2,1)),rewrite([8(4),46(4),17(4),3(3),1(3),7(3),17(3)]),flip(a)].
% 51.06/51.33 77 meet(one,complement(A)) = complement(A). [hyper(16,a,40,a,b,76,a),flip(a)].
% 51.06/51.33 78 join(one,complement(A)) = one. [para(77(a,1),6(a,1,2))].
% 51.06/51.33 80 meet(A,join(zero,meet(A,B))) = join(zero,meet(A,B)). [para(6(a,1),26(a,1,2,2,2)),rewrite([7(3),4(3),8(3),19(7)])].
% 51.06/51.33 86 join(zero,meet(A,B)) = meet(A,B). [para(26(a,1),21(a,1,2)),rewrite([7(2),80(4)])].
% 51.06/51.33 88 join(zero,complement(A)) = complement(A). [para(77(a,1),26(a,2,2)),rewrite([41(4),78(6),7(5),36(5),18(4),77(3)]),flip(a)].
% 51.06/51.33 93 meet(A,join(B,meet(complement(A),join(A,B)))) = meet(A,B). [back_rewrite(26),rewrite([86(8)])].
% 51.06/51.33 99 meet(A,meet(B,join(meet(C,join(A,D)),meet(join(A,D),join(A,C))))) = meet(A,B). [para(27(a,1),10(a,2,2)),rewrite([7(7),7(9)])].
% 51.06/51.33 101 meet(meet(A,join(B,C)),join(join(meet(A,B),meet(B,C)),meet(join(B,meet(A,join(B,C))),join(meet(A,join(B,C)),meet(C,join(A,B)))))) = meet(A,join(B,C)). [para(13(a,1),27(a,1,2,1)),rewrite([7(3),8(8),8(13),7(14)])].
% 51.06/51.33 116 join(A,meet(one,join(A,B))) = join(A,B). [para(65(a,1),13(a,1,2,1)),rewrite([8(6),22(6),7(6),10(6,R),1(5),68(6),7(3),5(3),10(6,R),1(5)]),flip(a)].
% 51.06/51.33 117 meet(A,meet(B,join(meet(A,C),meet(meet(A,D),join(A,C))))) = meet(B,join(meet(A,C),meet(A,D))). [para(28(a,1),10(a,2,2)),rewrite([7(6)])].
% 51.06/51.33 118 meet(meet(A,B),join(meet(A,C),join(meet(A,B),meet(A,C)))) = meet(A,B). [para(28(a,1),13(a,1,2,1)),rewrite([8(9),6(9),7(8),21(8),19(6),8(6),7(9),19(9),6(14)])].
% 51.06/51.33 132 meet(one,join(A,B)) = join(A,B). [para(116(a,1),13(a,2)),rewrite([7(4),17(4),12(4),8(3),46(3),46(3),17(3),7(3),17(3),8(4),46(4),7(4),116(5),7(5),17(5)])].
% 51.06/51.33 136 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [back_rewrite(70),rewrite([132(5),12(4,R),2(3),7(4)])].
% 51.06/51.33 137 meet(join(A,B),join(A,join(B,C))) = join(A,B). [back_rewrite(67),rewrite([132(5),12(4,R),8(3),12(3,R),2(2)])].
% 51.06/51.33 142 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(86(a,1),137(a,1,1)),rewrite([8(4),12(5,R),8(4),86(4),86(7)])].
% 51.06/51.33 143 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(137(a,1),28(a,1,2,1)),rewrite([7(4),12(8,R),12(7),8(6),12(7,R),8(6),22(6),22(7),5(9),137(5),7(4)]),flip(a)].
% 51.06/51.33 146 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(5(a,1),29(a,2,1)),rewrite([8(3),12(3),8(2),12(3,R),8(2),5(4),22(3),7(7)])].
% 51.06/51.33 148 meet(meet(A,B),join(meet(C,join(D,meet(A,B))),meet(D,join(C,meet(A,B))))) = join(meet(A,meet(B,C)),meet(A,meet(B,D))). [para(10(a,1),29(a,2,1)),rewrite([8(3),7(10),10(11,R),7(10),7(13),10(13),7(12),10(13,R),7(12)])].
% 51.06/51.33 171 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(142(a,1),28(a,1,2,1)),rewrite([7(4),10(4),7(3),10(4,R),7(3),12(8,R),2(7),5(9),142(5),7(4),10(4),7(3),10(4,R),7(3)]),flip(a)].
% 51.06/51.33 177 join(meet(A,B),join(meet(C,A),join(meet(C,join(A,B)),meet(B,join(C,A))))) = join(meet(C,join(A,B)),meet(B,join(C,A))). [para(13(a,1),143(a,1,2)),rewrite([8(3),7(6),8(9),12(9),8(8),12(8),8(7),12(9,R),8(8),12(8),8(7),12(8,R),8(7),8(12)])].
% 51.06/51.33 182 join(meet(A,B),meet(meet(A,C),join(A,B))) = join(meet(A,C),meet(A,B)). [para(28(a,1),143(a,1,2)),rewrite([8(9),12(9),8(8),22(8),12(7),8(6),24(7)]),flip(a)].
% 51.06/51.33 187 meet(A,meet(B,join(meet(A,C),meet(A,D)))) = meet(B,join(meet(A,D),meet(A,C))). [back_rewrite(117),rewrite([182(5)])].
% 51.06/51.33 205 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(30(a,1),6(a,1,2))].
% 51.06/51.33 218 complement(join(one,meet(A,join(B,C)))) = zero. [hyper(38,a,205,a(flip)),rewrite([7(3),17(3),7(3),17(3)])].
% 51.06/51.33 232 complement(join(one,meet(A,B))) = zero. [para(2(a,1),218(a,1,1,2,2))].
% 51.06/51.33 236 join(one,meet(A,B)) = one. [para(232(a,1),3(a,1,2)),rewrite([8(5),12(5,R),8(4),86(4)])].
% 51.06/51.33 237 join(one,join(meet(A,B),meet(A,C))) = one. [para(13(a,1),236(a,1,2))].
% 51.06/51.33 244 meet(meet(A,join(B,C)),join(join(meet(B,A),meet(B,C)),meet(meet(C,join(B,A)),join(B,meet(A,join(B,C)))))) = join(meet(B,A),meet(C,meet(A,join(B,C)))). [para(7(a,1),31(a,1,1)),rewrite([7(2),7(3),8(6),7(14),10(17,R),7(16)])].
% 51.06/51.33 312 join(one,join(meet(A,meet(B,C)),meet(B,D))) = one. [para(10(a,1),237(a,1,2,1))].
% 51.06/51.33 313 join(one,join(meet(A,meet(B,C)),meet(C,D))) = one. [para(10(a,2),237(a,1,2,1))].
% 51.06/51.33 348 join(one,join(meet(A,B),complement(C))) = one. [para(77(a,1),312(a,1,2,2)),rewrite([7(3),17(3)])].
% 51.06/51.33 359 join(one,join(complement(A),meet(B,C))) = one. [para(8(a,1),348(a,1,2))].
% 51.06/51.33 361 join(one,join(complement(A),complement(B))) = one. [para(77(a,1),348(a,1,2,1))].
% 51.06/51.33 362 join(one,join(join(A,B),complement(C))) = one. [para(132(a,1),348(a,1,2,1))].
% 51.06/51.33 368 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(42(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)])].
% 51.06/51.33 373 join(one,join(meet(A,B),meet(C,join(B,D)))) = one. [para(5(a,1),313(a,1,2,1,2)),rewrite([7(4)])].
% 51.06/51.33 388 meet(A,meet(meet(B,complement(A)),join(B,complement(A)))) = zero. [para(4(a,1),43(a,1,2,1)),rewrite([8(2),7(6),86(7),7(6),10(6,R),7(5),4(8)])].
% 51.06/51.33 390 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(43(a,1),6(a,1,2)),rewrite([8(4)])].
% 51.06/51.33 419 join(meet(A,meet(B,C)),meet(A,meet(B,join(C,D)))) = meet(A,meet(B,join(C,D))). [para(43(a,1),171(a,1,2,2)),rewrite([8(6)])].
% 51.06/51.33 428 meet(meet(meet(A,B),join(meet(B,C),meet(A,join(B,C)))),join(meet(A,meet(B,C)),meet(meet(A,B),join(meet(B,C),meet(meet(A,B),join(meet(B,C),meet(A,join(B,C)))))))) = meet(A,B). [para(43(a,1),31(a,1,2,2,1)),rewrite([10(9),7(8),10(8,R),1(7),10(8),7(7),10(8,R),7(7),10(12,R),7(11),171(13),10(23),7(22),10(22,R),1(21),10(22),7(21),10(22,R),7(21),142(30),10(26,R),10(25),7(24),21(25),7(23),19(24),8(24),171(24)])].
% 51.06/51.33 470 join(one,join(meet(A,B),meet(C,D))) = one. [para(142(a,1),373(a,1,2,2))].
% 51.06/51.33 489 meet(A,join(B,meet(complement(A),join(B,A)))) = meet(B,A). [para(93(a,1),7(a,2)),rewrite([8(2),7(5),7(6)])].
% 51.06/51.33 498 join(zero,join(meet(A,B),complement(C))) = join(meet(A,B),complement(C)). [para(348(a,1),93(a,1,2,2,2)),rewrite([41(6),7(7),36(7),8(6),132(7),132(10)])].
% 51.06/51.33 499 join(zero,join(complement(A),complement(B))) = join(complement(A),complement(B)). [para(361(a,1),93(a,1,2,2,2)),rewrite([41(6),7(7),36(7),8(6),132(7),132(10)])].
% 51.06/51.33 500 join(zero,join(complement(A),meet(B,C))) = join(complement(A),meet(B,C)). [para(359(a,1),93(a,1,2,2,2)),rewrite([41(6),7(7),36(7),8(6),132(7),132(10)])].
% 51.06/51.33 501 join(zero,join(join(A,B),complement(C))) = join(join(A,B),complement(C)). [para(362(a,1),93(a,1,2,2,2)),rewrite([41(6),7(7),36(7),8(6),132(7),132(10)])].
% 51.06/51.33 506 join(zero,join(meet(A,B),meet(C,D))) = join(meet(A,B),meet(C,D)). [para(470(a,1),93(a,1,2,2,2)),rewrite([41(6),7(7),36(7),8(6),132(7),132(10)])].
% 51.06/51.33 535 join(A,join(complement(A),complement(B))) = one. [para(499(a,1),53(a,1,2)),rewrite([8(3)])].
% 51.06/51.33 538 meet(A,join(complement(A),complement(B))) != zero | join(complement(A),complement(B)) = complement(A). [para(535(a,1),16(b,1)),flip(c),xx(b)].
% 51.06/51.33 625 meet(A,join(B,join(meet(A,C),meet(complement(A),join(A,B))))) = meet(A,join(B,meet(A,C))). [para(3(a,1),57(a,1,2,2,2)),rewrite([7(7),132(7),12(6,R),4(9),86(12)])].
% 51.06/51.33 634 meet(A,join(B,join(meet(A,C),meet(join(D,complement(A)),join(A,B))))) = join(meet(A,join(D,complement(A))),meet(A,join(B,meet(A,C)))). [para(47(a,1),57(a,1,2,2,2)),rewrite([7(8),132(8),12(7,R)])].
% 51.06/51.33 710 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(3(a,1),489(a,1,2,2,2)),rewrite([17(5),4(7)])].
% 51.06/51.33 712 meet(join(A,complement(B)),join(B,complement(join(A,complement(B))))) = meet(B,join(A,complement(B))). [para(47(a,1),489(a,1,2,2,2)),rewrite([7(7),77(7)])].
% 51.06/51.33 728 join(A,complement(complement(A))) = complement(complement(A)). [hyper(55,a,710,a)].
% 51.06/51.33 729 meet(complement(A),meet(complement(complement(A)),join(B,complement(A)))) = zero. [para(710(a,1),21(a,2)),rewrite([728(4),8(5)])].
% 51.06/51.33 730 meet(A,complement(complement(A))) = A. [para(710(a,1),27(a,1,2,1)),rewrite([728(4),3(5),17(5),88(4)])].
% 51.06/51.33 887 meet(A,complement(B)) != zero | join(A,complement(B)) != one | complement(complement(B)) = A. [para(729(a,1),58(a,1,2,2)),rewrite([18(3),7(2),8(6),729(15),18(10)]),flip(c)].
% 51.06/51.33 1520 meet(meet(A,B),join(meet(B,C),meet(A,join(B,C)))) = meet(A,B). [para(43(a,1),101(a,1,2,2,2,2)),rewrite([10(9),7(8),10(8,R),1(7),10(8),7(7),10(8,R),7(7),10(12,R),7(11),171(13),8(24),6(24),7(18),428(20)]),flip(a)].
% 51.06/51.33 2379 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(7(a,1),390(a,1,1))].
% 51.06/51.33 2385 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(19(a,1),390(a,1,1)),rewrite([8(3),8(7)])].
% 51.06/51.33 3186 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(8(a,1),501(a,1,2)),rewrite([12(4),8(3),12(4,R),8(3),12(5,R),8(4),12(4,R),18(3)]),flip(a)].
% 51.06/51.33 3243 join(A,join(B,complement(join(A,B)))) = one. [para(3186(a,1),3(a,1))].
% 51.06/51.33 3244 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(6(a,1),3186(a,1,1)),flip(a)].
% 51.06/51.33 3328 meet(A,join(B,join(complement(A),complement(join(A,B))))) = meet(A,join(B,complement(join(A,B)))). [para(3243(a,1),93(a,1,2,2,2)),rewrite([17(6),8(5),12(5,R),8(4)])].
% 51.06/51.33 3655 join(A,complement(meet(A,B))) = one. [para(3(a,1),3244(a,1,2)),rewrite([46(2)]),flip(a)].
% 51.06/51.33 3710 join(A,complement(join(meet(A,B),meet(A,C)))) = one. [para(13(a,1),3655(a,1,2,1))].
% 51.06/51.33 3719 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [para(43(a,1),3655(a,1,2,1)),rewrite([8(5)])].
% 51.06/51.33 3736 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [para(3655(a,1),498(a,1,2)),rewrite([8(3),18(3),7(4),10(4),7(3),10(4,R),7(3)]),flip(a)].
% 51.06/51.33 3737 join(A,join(B,complement(meet(C,join(A,B))))) = one. [para(3655(a,1),3186(a,1)),rewrite([7(3)]),flip(a)].
% 51.06/51.33 4040 join(complement(meet(A,B)),meet(B,join(A,C))) = one. [para(7(a,1),3719(a,1,1,1))].
% 51.06/51.33 4407 join(A,complement(meet(B,A))) = one. [para(3(a,1),4040(a,1,2,2)),rewrite([17(4),8(3)])].
% 51.06/51.33 4439 join(complement(A),meet(complement(complement(A)),join(A,B))) = one. [para(730(a,1),4040(a,1,1,1))].
% 51.06/51.33 4472 join(meet(A,B),complement(meet(A,meet(C,B)))) = one. [para(118(a,1),4040(a,1,2)),rewrite([10(3),7(2),19(2),10(2),7(1),10(2,R),7(1),8(5)])].
% 51.06/51.33 4486 join(A,complement(meet(B,meet(C,A)))) = one. [para(3736(a,1),4040(a,1,2,2)),rewrite([7(2),10(2),7(1),10(2,R),7(1),17(5),8(4)])].
% 51.06/51.33 4595 join(meet(A,join(B,C)),complement(meet(A,meet(B,D)))) = one. [para(21(a,1),4486(a,1,2,1,2)),rewrite([7(3),10(4),7(3),10(4,R),7(3)])].
% 51.06/51.33 4656 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(1(a,1),148(a,1,2,1)),rewrite([8(7),12(7,R),2(6),5(6),8(4),22(4),142(4),8(8),419(8)]),flip(a)].
% 51.06/51.33 5059 meet(complement(A),meet(complement(complement(A)),join(A,B))) != zero | meet(complement(complement(A)),join(A,B)) = complement(complement(A)). [para(4439(a,1),16(b,1)),flip(c),xx(b)].
% 51.06/51.33 5066 meet(complement(A),meet(complement(complement(A)),join(A,B))) = zero. [para(4439(a,1),93(a,1,2,2,2)),rewrite([17(9),8(8),6(8),4(4)]),flip(a)].
% 51.06/51.33 5084 meet(complement(complement(A)),join(A,B)) = complement(complement(A)). [back_rewrite(5059),rewrite([5066(6)]),xx(a)].
% 51.06/51.33 5100 complement(complement(A)) = A. [para(2(a,1),5084(a,1,2)),rewrite([7(3),730(3)]),flip(a)].
% 51.06/51.33 5244 meet(A,complement(B)) != zero | join(A,complement(B)) != one | B = A. [back_rewrite(887),rewrite([5100(10)])].
% 51.06/51.33 5494 meet(complement(A),meet(meet(A,B),join(A,B))) = zero. [para(5100(a,1),388(a,1,2,1,2)),rewrite([7(2),5100(4),8(3)])].
% 51.06/51.33 5936 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [para(37(a,1),5494(a,1,2,1)),rewrite([24(8),6(6),7(5),37(5)])].
% 51.06/51.33 5940 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(43(a,1),5494(a,1,2,1)),rewrite([12(10),8(9),390(9),1520(9),7(5)])].
% 51.06/51.33 5957 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [para(136(a,1),5494(a,1,2,1)),rewrite([12(8,R),12(7),8(6),24(7),8(5),22(6),7(6),136(6)])].
% 51.06/51.33 6337 meet(A,complement(join(A,B))) = zero. [para(5936(a,1),99(a,1,2)),rewrite([36(2)]),flip(a)].
% 51.06/51.33 6611 meet(meet(A,B),complement(meet(B,join(A,C)))) = zero. [para(7(a,1),5940(a,1,1))].
% 51.06/51.33 6665 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),5957(a,1,1,1))].
% 51.06/51.33 7221 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(5(a,1),6611(a,1,1))].
% 51.06/51.33 7385 meet(A,complement(join(B,A))) = zero. [para(4(a,1),6665(a,1,2,2)),rewrite([18(4),7(3)])].
% 51.06/51.33 7414 meet(complement(join(A,complement(B))),join(meet(A,C),complement(B))) = zero. [para(3244(a,1),7385(a,1,2,1)),rewrite([7(7)])].
% 51.06/51.33 7430 meet(A,join(B,A)) = A. [para(5(a,1),177(a,2,2)),rewrite([7(2),8(5),2(7),2379(5),2379(4),8(5),6(5)])].
% 51.06/51.33 7861 join(complement(meet(A,B)),meet(A,join(C,B))) = one. [para(7430(a,1),4472(a,1,2,1,2)),rewrite([8(5)])].
% 51.06/51.33 8227 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(187(a,1),4656(a,1)),rewrite([7(1),7(5)])].
% 51.06/51.33 8736 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(8(a,1),8227(a,1,2))].
% 51.06/51.33 8988 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(7(a,1),8736(a,1,2,1))].
% 51.06/51.33 9081 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(8988(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 51.06/51.33 9198 join(A,meet(B,A)) = A. [para(17(a,1),9081(a,1,2,2)),rewrite([8(3),132(4),17(4)])].
% 51.06/51.33 10164 join(A,complement(meet(B,meet(A,join(C,D))))) = one. [para(4595(a,1),4040(a,1,2,2)),rewrite([7(3),10(3,R),7(2),17(6),8(5)])].
% 51.06/51.33 10197 join(A,complement(meet(B,meet(meet(A,C),join(D,E))))) = one. [para(10164(a,1),3244(a,1,2)),rewrite([46(2)]),flip(a)].
% 51.06/51.33 11805 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(7414(a,1),29(a,1,2,2)),rewrite([8(10),86(10),21(9),10(3),7(2),10(3,R),7(2),7385(11),8(8),86(8)]),flip(a)].
% 51.06/51.33 12156 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(11805(a,1),6337(a,1)),rewrite([8(2)])].
% 51.06/51.33 13343 join(meet(A,B),meet(A,complement(meet(A,B)))) = meet(A,join(B,meet(A,complement(meet(A,B))))). [para(7861(a,1),244(a,1,2,2,2)),rewrite([8(3),4407(3),17(2),7(3),7(6),8(10),3655(10),17(9),17(9),8(8),24(8),7(8),8(11),4407(11),17(10),7(9),8(10)]),flip(a)].
% 51.06/51.33 13520 join(A,complement(meet(meet(A,B),join(C,D)))) = one. [para(1(a,1),10197(a,1,2,1))].
% 51.06/51.33 13657 join(meet(A,meet(meet(B,C),join(D,E))),meet(one,meet(meet(B,C),join(D,E)))) = meet(meet(B,C),join(D,E)). [para(13520(a,1),54(a,1,2,2,1)),rewrite([8(8),132(9),22(8),7430(8),7(7),13520(15),7(12)]),flip(a)].
% 51.06/51.33 16790 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(3186(a,1),368(a,1,2,2,2,2)),rewrite([10(8,R),7(7),10(7,R),7(6),10(6,R),7(5),137(5),10(8,R)]),flip(a)].
% 51.06/51.33 16914 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [back_rewrite(13657),rewrite([16790(4),16790(9),10(9,R),7(8),10(8,R),7(7),132(7),8(8),9198(8)]),flip(a)].
% 51.06/51.33 18798 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(5100(a,1),5244(b,1,2)),rewrite([5100(2)])].
% 51.06/51.33 19785 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(5(a,1),16914(a,1,1)),flip(a)].
% 51.06/51.33 23214 join(meet(A,B),meet(A,join(C,complement(A)))) = meet(A,join(B,meet(A,join(C,complement(A))))). [para(2379(a,1),634(a,1,2,2)),rewrite([54(6),2385(14)])].
% 51.06/51.33 23215 join(meet(A,join(B,complement(A))),meet(A,C)) = meet(A,join(C,meet(A,join(B,complement(A))))). [para(506(a,1),634(a,1,2)),rewrite([18(5),7(4),23214(5),19(6),86(11),19(10)]),flip(a)].
% 51.06/51.33 24396 meet(A,join(B,complement(join(A,complement(B))))) = meet(A,B). [para(712(a,1),19785(a,1,2)),rewrite([21(4)]),flip(a)].
% 51.06/51.33 24428 meet(A,join(B,complement(join(A,join(C,complement(B)))))) = meet(A,B). [para(24396(a,1),19785(a,1,2)),rewrite([7(2),21(3),3186(4)]),flip(a)].
% 51.06/51.33 24523 join(complement(A),complement(join(A,B))) = complement(A). [para(24428(a,1),538(a,1)),rewrite([4(2),5100(6),8(5),22(6)]),xx(a)].
% 51.06/51.33 24539 meet(A,join(B,complement(join(A,B)))) = meet(A,join(B,complement(A))). [back_rewrite(3328),rewrite([24523(4)]),flip(a)].
% 51.06/51.33 24617 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(24523(a,1),7430(a,1,2)),rewrite([7(4)])].
% 51.06/51.33 24943 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(24617(a,1),12156(a,1,2))].
% 51.06/51.33 25011 meet(A,join(B,meet(A,complement(meet(A,B))))) = A. [hyper(18798,a,24943,a,b,3710,a),rewrite([13343(5),5100(7)])].
% 51.06/51.33 25025 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [back_rewrite(13343),rewrite([25011(10)])].
% 51.06/51.33 25198 meet(A,join(B,meet(A,complement(meet(B,A))))) = A. [para(25011(a,1),7(a,2)),rewrite([7(1),7(5)])].
% 51.06/51.33 25208 join(A,meet(B,complement(meet(A,B)))) = join(A,B). [para(25011(a,1),146(a,1,2,2)),rewrite([7(1),7(6),136(6),7(5),25198(9)])].
% 51.06/51.33 25282 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(25025(a,1),24523(a,1,2,1)),rewrite([8(4)])].
% 51.06/51.33 25622 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(5(a,1),25208(a,1,2,2,1)),rewrite([7(3),22(6)])].
% 51.06/51.33 25786 join(A,complement(meet(B,join(A,complement(B))))) = one. [para(25282(a,1),3737(a,1,2))].
% 51.06/51.33 25866 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(18798,a,7221,a,b,25786,a),rewrite([5100(7)])].
% 51.06/51.33 26066 join(complement(A),meet(A,join(B,complement(A)))) = join(B,complement(A)). [para(25622(a,1),500(a,1,2)),rewrite([8(3),12(4,R),18(3),5100(5),8(5)]),flip(a)].
% 51.06/51.33 26372 meet(join(A,B),join(B,complement(join(A,B)))) = B. [para(8(a,1),25866(a,1,1)),rewrite([8(2)])].
% 51.06/51.33 26681 meet(A,join(B,complement(A))) = meet(A,B). [para(26372(a,1),19785(a,1,2)),rewrite([24539(5)]),flip(a)].
% 51.06/51.33 26712 join(complement(A),meet(A,B)) = join(B,complement(A)). [back_rewrite(26066),rewrite([26681(4)])].
% 51.06/51.33 26740 join(meet(A,B),meet(A,C)) = meet(A,join(C,meet(A,B))). [back_rewrite(23215),rewrite([26681(3),26681(6)])].
% 51.06/51.33 26898 meet(a,join(c,meet(a,b))) != meet(a,join(b,c)) # answer(prove_distributivity). [back_rewrite(15),rewrite([26740(7)])].
% 51.06/51.33 26903 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [para(3186(a,1),26681(a,1,2))].
% 51.06/51.33 26904 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(5100(a,1),26681(a,1,2,2)),rewrite([8(2),7(5)])].
% 51.06/51.33 26988 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [para(625(a,1),26681(a,2)),rewrite([26904(4),24(5),8(4),12(4,R),8(3),26712(3),26903(4)]),flip(a)].
% 51.06/51.33 27083 $F # answer(prove_distributivity). [back_rewrite(26898),rewrite([26988(7),8(4)]),xx(a)].
% 51.06/51.33
% 51.06/51.33 % SZS output end Refutation
% 51.06/51.33 ============================== end of proof ==========================
% 51.06/51.33
% 51.06/51.33 ============================== STATISTICS ============================
% 51.06/51.33
% 51.06/51.33 Given=1093. Generated=1068067. Kept=27079. proofs=1.
% 51.06/51.33 Usable=637. Sos=7263. Demods=7516. Limbo=95, Disabled=19097. Hints=0.
% 51.06/51.33 Megabytes=33.34.
% 51.06/51.33 User_CPU=49.83, System_CPU=0.54, Wall_clock=50.
% 51.06/51.33
% 51.06/51.33 ============================== end of statistics =====================
% 51.06/51.33
% 51.06/51.33 ============================== end of search =========================
% 51.06/51.33
% 51.06/51.33 THEOREM PROVED
% 51.06/51.33 % SZS status Unsatisfiable
% 51.06/51.33
% 51.06/51.33 Exiting with 1 proof.
% 51.06/51.33
% 51.06/51.33 Process 3802 exit (max_proofs) Thu Jun 30 10:26:01 2022
% 51.06/51.33 Prover9 interrupted
%------------------------------------------------------------------------------