TSTP Solution File: LAT192-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT192-1 : 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 06:26:02 EDT 2022
% Result : Unsatisfiable 183.32s 183.65s
% Output : Refutation 183.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT192-1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 30 15:04:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.03/9.35 ============================== Prover9 ===============================
% 9.03/9.35 Prover9 (32) version 2009-11A, November 2009.
% 9.03/9.35 Process 29028 was started by sandbox on n027.cluster.edu,
% 9.03/9.35 Thu Jun 30 15:04:52 2022
% 9.03/9.35 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28874_n027.cluster.edu".
% 9.03/9.35 ============================== end of head ===========================
% 9.03/9.35
% 9.03/9.35 ============================== INPUT =================================
% 9.03/9.35
% 9.03/9.35 % Reading from file /tmp/Prover9_28874_n027.cluster.edu
% 9.03/9.35
% 9.03/9.35 set(prolog_style_variables).
% 9.03/9.35 set(auto2).
% 9.03/9.35 % set(auto2) -> set(auto).
% 9.03/9.35 % set(auto) -> set(auto_inference).
% 9.03/9.35 % set(auto) -> set(auto_setup).
% 9.03/9.35 % set(auto_setup) -> set(predicate_elim).
% 9.03/9.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 9.03/9.35 % set(auto) -> set(auto_limits).
% 9.03/9.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 9.03/9.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 9.03/9.35 % set(auto) -> set(auto_denials).
% 9.03/9.35 % set(auto) -> set(auto_process).
% 9.03/9.35 % set(auto2) -> assign(new_constants, 1).
% 9.03/9.35 % set(auto2) -> assign(fold_denial_max, 3).
% 9.03/9.35 % set(auto2) -> assign(max_weight, "200.000").
% 9.03/9.35 % set(auto2) -> assign(max_hours, 1).
% 9.03/9.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 9.03/9.35 % set(auto2) -> assign(max_seconds, 0).
% 9.03/9.35 % set(auto2) -> assign(max_minutes, 5).
% 9.03/9.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 9.03/9.35 % set(auto2) -> set(sort_initial_sos).
% 9.03/9.35 % set(auto2) -> assign(sos_limit, -1).
% 9.03/9.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 9.03/9.35 % set(auto2) -> assign(max_megs, 400).
% 9.03/9.35 % set(auto2) -> assign(stats, some).
% 9.03/9.35 % set(auto2) -> clear(echo_input).
% 9.03/9.35 % set(auto2) -> set(quiet).
% 9.03/9.35 % set(auto2) -> clear(print_initial_clauses).
% 9.03/9.35 % set(auto2) -> clear(print_given).
% 9.03/9.35 assign(lrs_ticks,-1).
% 9.03/9.35 assign(sos_limit,10000).
% 9.03/9.35 assign(order,kbo).
% 9.03/9.35 set(lex_order_vars).
% 9.03/9.35 clear(print_given).
% 9.03/9.35
% 9.03/9.35 % formulas(sos). % not echoed (13 formulas)
% 9.03/9.35
% 9.03/9.35 ============================== end of input ==========================
% 9.03/9.35
% 9.03/9.35 % From the command line: assign(max_seconds, 300).
% 9.03/9.35
% 9.03/9.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 9.03/9.35
% 9.03/9.35 % Formulas that are not ordinary clauses:
% 9.03/9.35
% 9.03/9.35 ============================== end of process non-clausal formulas ===
% 9.03/9.35
% 9.03/9.35 ============================== PROCESS INITIAL CLAUSES ===============
% 9.03/9.35
% 9.03/9.35 ============================== PREDICATE ELIMINATION =================
% 9.03/9.35
% 9.03/9.35 ============================== end predicate elimination =============
% 9.03/9.35
% 9.03/9.35 Auto_denials:
% 9.03/9.35 % copying label prove_distributivity to answer in negative clause
% 9.03/9.35
% 9.03/9.35 Term ordering decisions:
% 9.03/9.35
% 9.03/9.35 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 9.03/9.35 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 9.03/9.35
% 9.03/9.35 ============================== end of process initial clauses ========
% 9.03/9.35
% 9.03/9.35 ============================== CLAUSES FOR SEARCH ====================
% 9.03/9.35
% 9.03/9.35 ============================== end of clauses for search =============
% 9.03/9.35
% 9.03/9.35 ============================== SEARCH ================================
% 9.03/9.35
% 9.03/9.35 % Starting search at 0.01 seconds.
% 9.03/9.35
% 9.03/9.35 Low Water (keep): wt=139.000, iters=3350
% 9.03/9.35
% 9.03/9.35 Low Water (keep): wt=135.000, iters=3338
% 9.03/9.35
% 9.03/9.35 Low Water (keep): wt=106.000, iters=3355
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% 9.03/9.35 Low Water (keep): wt=103.000, iters=3361
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% 9.03/9.35 Low Water (keep): wt=102.000, iters=3343
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% 9.03/9.35 Low Water (keep): wt=96.000, iters=3398
% 9.03/9.35
% 9.03/9.35 Low Water (keep): wt=95.000, iters=3335
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% 9.03/9.35 Low Water (keep): wt=91.000, iters=3441
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% 9.03/9.35 Low Water (keep): wt=87.000, iters=3368
% 9.03/9.35
% 9.03/9.35 Low Water (keep): wt=83.000, iters=3391
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% 9.03/9.35 Low Water (keep): wt=82.000, iters=3339
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% 9.03/9.35 Low Water (keep): wt=79.000, iters=3343
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% 9.03/9.35 Low Water (keep): wt=78.000, iters=3336
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% 9.03/9.35 Low Water (keep): wt=77.000, iters=3353
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% 9.03/9.35 Low Water (keep): wt=74.000, iters=3333
% 9.03/9.35
% 9.03/9.35 Low Water (keep): wt=72.000, iters=3340
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% 9.03/9.35 Low Water (keep): wt=71.000, iters=3412
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% 9.03/9.35 Low Water (keep): wt=70.000, iters=3352
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% 9.03/9.35 Low Water (keep): wt=69.000, iters=3343
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% 9.03/9.35 Low Water (keep): wt=68.000, iters=3359
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% 9.03/9.35 Low Water (keep): wt=67.000, iters=3343
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% 9.03/9.35 Low Water (keep): wt=65.000, iters=3348
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% 9.03/9.35 Low Water (keep): wt=64.000, iters=3400
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% 9.03/9.35 Low Water (keep): wt=63.000, iters=3497
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% 9.03/9.35 Low Water (keep): wt=59.000, iters=3409
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% 9.03/9.35 Low Water (keep): wt=57.000, iters=3381
% 9.03/9.35
% 9.03/9.35 Low Water (keep): wt=55.000, iters=3347
% 183.32/183.65
% 183.32/183.65 Low Water (keep): wt=53.000, iters=3374
% 183.32/183.65
% 183.32/183.65 Low Water (keep): wt=52.000, iters=3373
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% 183.32/183.65 Low Water (keep): wt=51.000, iters=3376
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% 183.32/183.65 Low Water (keep): wt=49.000, iters=3343
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% 183.32/183.65 Low Water (keep): wt=48.000, iters=3363
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% 183.32/183.65 Low Water (keep): wt=47.000, iters=3345
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% 183.32/183.65 Low Water (keep): wt=46.000, iters=3343
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% 183.32/183.65 Low Water (keep): wt=45.000, iters=3338
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% 183.32/183.65 Low Water (keep): wt=44.000, iters=3371
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% 183.32/183.65 Low Water (keep): wt=43.000, iters=3344
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% 183.32/183.65 Low Water (keep): wt=42.000, iters=3347
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% 183.32/183.65 Low Water (keep): wt=41.000, iters=3341
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% 183.32/183.65 Low Water (keep): wt=40.000, iters=3338
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% 183.32/183.65 Low Water (keep): wt=39.000, iters=3363
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% 183.32/183.65 Low Water (keep): wt=38.000, iters=3362
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% 183.32/183.65 Low Water (keep): wt=37.000, iters=3351
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% 183.32/183.65 Low Water (keep): wt=36.000, iters=3380
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% 183.32/183.65 Low Water (keep): wt=35.000, iters=3355
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% 183.32/183.65 Low Water (keep): wt=34.000, iters=3393
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% 183.32/183.65 Low Water (keep): wt=33.000, iters=3351
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% 183.32/183.65 Low Water (keep): wt=32.000, iters=3345
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% 183.32/183.65 Low Water (keep): wt=31.000, iters=3348
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% 183.32/183.65 Low Water (keep): wt=30.000, iters=3351
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% 183.32/183.65 Low Water (keep): wt=29.000, iters=3360
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% 183.32/183.65 Low Water (keep): wt=28.000, iters=3350
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% 183.32/183.65 Low Water (keep): wt=27.000, iters=3389
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% 183.32/183.65 Low Water (keep): wt=26.000, iters=3334
% 183.32/183.65
% 183.32/183.65 Low Water (keep): wt=25.000, iters=3363
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% 183.32/183.65 Low Water (keep): wt=24.000, iters=3337
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% 183.32/183.65 Low Water (keep): wt=23.000, iters=3336
% 183.32/183.65
% 183.32/183.65 Low Water (displace): id=23560, wt=22.000
% 183.32/183.65
% 183.32/183.65 Low Water (displace): id=23571, wt=21.000
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% 183.32/183.65 Low Water (displace): id=23575, wt=20.000
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% 183.32/183.65 Low Water (displace): id=23595, wt=18.000
% 183.32/183.65
% 183.32/183.65 Low Water (displace): id=24908, wt=16.000
% 183.32/183.65
% 183.32/183.65 Low Water (keep): wt=22.000, iters=3357
% 183.32/183.65
% 183.32/183.65 Low Water (keep): wt=20.000, iters=4124
% 183.32/183.65
% 183.32/183.65 ============================== PROOF =================================
% 183.32/183.65 % SZS status Unsatisfiable
% 183.32/183.65 % SZS output start Refutation
% 183.32/183.65
% 183.32/183.65 % Proof 1 at 180.52 (+ 2.14) seconds: prove_distributivity.
% 183.32/183.65 % Length of proof is 242.
% 183.32/183.65 % Level of proof is 58.
% 183.32/183.65 % Maximum clause weight is 65.000.
% 183.32/183.65 % Given clauses 1810.
% 183.32/183.65
% 183.32/183.65 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 183.32/183.65 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 183.32/183.65 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 183.32/183.65 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 183.32/183.65 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 183.32/183.65 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 183.32/183.65 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 183.32/183.65 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 183.32/183.65 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 183.32/183.65 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 183.32/183.65 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 183.32/183.65 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 183.32/183.65 13 join(meet(A,B),meet(A,C)) = meet(A,join(meet(B,join(C,meet(A,B))),meet(C,join(A,B)))) # label(equation_H22) # label(axiom). [assumption].
% 183.32/183.65 14 meet(A,join(meet(B,join(A,C)),meet(C,join(B,meet(A,C))))) = join(meet(A,C),meet(A,B)). [copy(13),rewrite([8(9)]),flip(a)].
% 183.32/183.65 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 183.32/183.65 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 183.32/183.65 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 183.32/183.65 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 183.32/183.65 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 183.32/183.65 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)])].
% 183.32/183.65 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 183.32/183.65 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 183.32/183.65 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)])].
% 183.32/183.65 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 183.32/183.65 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 183.32/183.65 27 join(zero,meet(A,B)) = meet(A,B). [para(3(a,1),14(a,1,2,1,2)),rewrite([18(2),4(3),19(3),7(2),6(3),4(3)]),flip(a)].
% 183.32/183.65 28 meet(A,join(meet(B,join(A,C)),meet(join(A,C),join(A,B)))) = A. [para(5(a,1),14(a,1,2,2,2,2)),rewrite([23(2),8(4),5(9),6(9)])].
% 183.32/183.65 29 meet(A,join(meet(A,B),meet(meet(A,C),join(B,meet(A,C))))) = join(meet(A,C),meet(A,B)). [para(6(a,1),14(a,1,2,1,2)),rewrite([7(1),20(4),20(9)])].
% 183.32/183.65 30 meet(A,meet(B,join(meet(C,join(A,D)),meet(D,join(C,meet(A,D)))))) = meet(B,join(meet(A,D),meet(A,C))). [para(14(a,1),10(a,2,2)),rewrite([7(7)])].
% 183.32/183.65 31 meet(meet(A,join(B,C)),join(join(meet(B,C),meet(A,B)),meet(meet(C,join(A,meet(B,C))),join(B,meet(C,meet(meet(A,join(B,C)),join(A,meet(B,C)))))))) = join(meet(A,B),meet(C,meet(meet(A,join(B,C)),join(A,meet(B,C))))). [para(14(a,1),14(a,1,2,1)),rewrite([7(4),10(14,R),7(13),10(24,R),7(23),7(27),22(27),7(25),8(26)])].
% 183.32/183.65 32 meet(A,join(meet(B,join(A,join(meet(C,join(A,D)),meet(D,join(C,meet(A,D)))))),meet(join(meet(C,join(A,D)),meet(D,join(C,meet(A,D)))),join(B,join(meet(A,D),meet(A,C)))))) = join(join(meet(A,D),meet(A,C)),meet(A,B)). [para(14(a,1),14(a,1,2,2,2,2)),rewrite([14(28)])].
% 183.32/183.65 34 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)].
% 183.32/183.65 35 meet(A,join(meet(B,join(A,one)),meet(one,join(A,B)))) = A. [para(18(a,1),14(a,1,2,2,2,2)),rewrite([8(5),18(10),6(10)])].
% 183.32/183.65 37 meet(A,zero) != zero | one != A | complement(A) = zero. [para(19(a,1),17(b,1)),flip(b)].
% 183.32/183.65 38 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 183.32/183.65 40 one != A | complement(A) = zero. [back_rewrite(37),rewrite([38(2)]),xx(a)].
% 183.32/183.65 41 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([38(5)])].
% 183.32/183.65 42 complement(one) = zero. [hyper(17,a,38,a,b,19,a)].
% 183.32/183.65 44 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)])].
% 183.32/183.65 45 meet(A,join(meet(B,join(A,meet(C,join(A,D)))),meet(meet(C,join(A,D)),join(B,meet(A,C))))) = join(meet(A,C),meet(A,B)). [para(22(a,1),14(a,1,2,2,2,2)),rewrite([22(14)])].
% 183.32/183.65 46 meet(meet(A,join(B,C)),join(meet(B,C),meet(A,B))) = meet(A,B). [para(14(a,1),22(a,1,2)),rewrite([7(4),7(9),22(9),7(7)])].
% 183.32/183.65 47 complement(join(A,one)) = zero. [hyper(40,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 183.32/183.65 49 join(A,one) = one. [para(47(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 183.32/183.65 50 meet(A,join(B,meet(one,join(A,B)))) = A. [back_rewrite(35),rewrite([49(2),18(2)])].
% 183.32/183.65 51 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([49(5)])].
% 183.32/183.65 52 complement(zero) = one. [hyper(17,a,18,a,b,49,a)].
% 183.32/183.65 57 join(A,join(B,join(C,complement(A)))) = one. [para(51(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),49(6)])].
% 183.32/183.65 58 meet(A,join(B,meet(join(C,complement(A)),join(B,meet(A,join(C,complement(A))))))) = join(meet(A,join(C,complement(A))),meet(A,B)). [para(51(a,1),14(a,1,2,1,2)),rewrite([18(2)])].
% 183.32/183.65 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)].
% 183.32/183.65 67 meet(A,join(B,meet(join(C,join(D,complement(A))),join(B,meet(A,join(C,join(D,complement(A)))))))) = join(meet(A,join(C,join(D,complement(A)))),meet(A,B)). [para(57(a,1),14(a,1,2,1,2)),rewrite([18(2)])].
% 183.32/183.65 69 meet(A,join(B,meet(one,join(B,A)))) = A. [para(50(a,1),7(a,2)),rewrite([8(2),7(5)])].
% 183.32/183.65 72 meet(A,join(join(A,B),meet(one,join(A,B)))) = A. [para(23(a,1),50(a,1,2,2,2))].
% 183.32/183.65 81 meet(join(A,B),join(C,meet(one,join(A,join(B,C))))) = join(A,B). [para(12(a,1),69(a,1,2,2,2)),rewrite([8(3),12(4,R),8(3)])].
% 183.32/183.65 83 meet(one,join(A,complement(B))) = join(A,complement(B)). [para(51(a,1),69(a,1,2,2,2)),rewrite([1(5),49(4),7(4)])].
% 183.32/183.65 84 meet(join(A,meet(B,C)),join(B,meet(one,join(A,B)))) = join(A,meet(B,C)). [para(25(a,1),69(a,1,2,2,2)),rewrite([8(4)])].
% 183.32/183.65 86 meet(one,complement(A)) = complement(A). [para(2(a,1),83(a,1,2)),rewrite([2(6)])].
% 183.32/183.65 91 meet(complement(A),join(B,complement(A))) = complement(A). [para(83(a,1),69(a,1,2,2)),rewrite([23(4)])].
% 183.32/183.65 95 meet(A,meet(B,join(meet(C,join(A,D)),meet(join(A,D),join(A,C))))) = meet(A,B). [para(28(a,1),10(a,2,2)),rewrite([7(7),7(9)])].
% 183.32/183.65 120 join(complement(A),meet(B,complement(A))) = complement(A). [para(91(a,1),29(a,1,2,1)),rewrite([7(4),7(8),5(12),7(3),91(7),8(5)]),flip(a)].
% 183.32/183.65 140 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(30(a,1),6(a,1,2))].
% 183.32/183.65 142 meet(A,join(meet(B,join(A,meet(C,join(meet(D,join(A,E)),meet(E,join(D,meet(A,E))))))),meet(meet(C,join(meet(D,join(A,E)),meet(E,join(D,meet(A,E))))),join(B,meet(C,join(meet(A,E),meet(A,D))))))) = join(meet(C,join(meet(A,E),meet(A,D))),meet(A,B)). [para(30(a,1),14(a,1,2,2,2,2)),rewrite([30(32)])].
% 183.32/183.65 165 complement(join(one,meet(A,join(B,C)))) = zero. [hyper(40,a,140,a(flip)),rewrite([7(3),18(3),7(3),18(3)])].
% 183.32/183.65 179 complement(join(one,meet(A,B))) = zero. [para(2(a,1),165(a,1,1,2,2))].
% 183.32/183.65 182 join(one,meet(A,B)) = one. [para(179(a,1),3(a,1,2)),rewrite([8(5),12(5,R),8(4),27(4)])].
% 183.32/183.65 184 join(one,join(meet(A,B),meet(A,C))) = one. [para(14(a,1),182(a,1,2))].
% 183.32/183.65 185 join(meet(A,B),meet(B,meet(meet(A,B),join(A,B)))) = meet(meet(A,B),join(B,meet(A,B))). [para(1(a,1),31(a,1,2,1,1)),rewrite([2(1),1(4),2(6),1(7),6(10),7(6),20(6),8(6),12(6),8(5),6(5),8(3),2(6),1(7)]),flip(a)].
% 183.32/183.65 186 meet(meet(A,B),join(B,meet(A,B))) = meet(meet(A,B),join(A,B)). [para(2(a,1),31(a,1,2,2,1,2)),rewrite([7(6),20(6),2(6),10(6,R),1(5),2(11),7(10),20(10),6(12),7(5),20(5),7(5),20(5),2(10),7(9),20(9),185(9)]),flip(a)].
% 183.32/183.65 188 meet(meet(A,join(B,C)),join(join(B,meet(A,B)),meet(meet(join(B,C),join(A,B)),join(B,meet(A,join(B,C)))))) = join(meet(A,B),meet(A,join(B,C))). [para(5(a,1),31(a,1,2,1,1)),rewrite([23(2),5(7),23(10),5(12),7(12),10(12,R),22(12),10(11,R),1(10),23(17),5(19),7(19),10(19,R),22(19),10(18,R),1(17)])].
% 183.32/183.65 216 meet(A,meet(zero,meet(meet(B,A),join(B,A)))) = meet(zero,meet(meet(B,A),join(B,A))). [para(27(a,1),31(a,1,2,2,1,2)),rewrite([7(6),38(6),8(6),27(6),10(6,R),1(5),27(11),7(10),10(10,R),7(9),6(14),7(5),10(5,R),7(4),7(7),38(7),27(12),7(11),10(11,R),7(10),27(13)]),flip(a)].
% 183.32/183.65 217 meet(zero,meet(meet(A,B),join(A,B))) = zero. [para(27(a,1),31(a,1,2,2,2,2,2,2)),rewrite([7(6),38(6),8(6),27(6),27(7),10(6,R),1(5),7(10),10(10,R),7(9),216(11),6(13),7(5),10(5,R),7(4),7(7),38(7),27(12),7(11),10(11,R),7(10),216(12),6(12)])].
% 183.32/183.65 262 join(one,join(meet(A,meet(B,C)),meet(B,D))) = one. [para(10(a,1),184(a,1,2,1))].
% 183.32/183.65 273 meet(zero,join(A,B)) = zero. [para(217(a,1),10(a,1)),rewrite([10(5),7(4),38(4),38(4),7(4)]),flip(a)].
% 183.32/183.65 328 meet(one,join(complement(A),meet(join(B,meet(C,join(B,C))),join(B,join(C,complement(A)))))) = join(join(B,C),complement(A)). [para(86(a,1),32(a,2,2)),rewrite([8(5),49(5),18(5),7(5),18(5),12(7,R),8(6),182(6),49(4),18(4),8(4),49(4),18(4),7(4),18(4),7(8),18(8),7(8),18(8),8(7),12(8),8(7),12(8,R),8(7),7(13),18(13),7(13),18(13),8(12)])].
% 183.32/183.65 341 meet(join(A,B),join(meet(C,join(A,join(join(A,B),meet(meet(one,join(A,B)),join(A,meet(one,join(A,B))))))),meet(join(A,meet(meet(one,join(A,B)),join(A,meet(one,join(A,B))))),join(A,join(C,meet(one,join(A,B))))))) = join(join(A,meet(one,join(A,B))),meet(C,join(A,B))). [para(72(a,1),32(a,1,2,1,2,2,1)),rewrite([10(10,R),1(9),12(12,R),8(11),72(19),10(21,R),1(20),10(27,R),1(26),7(27),5(27),8(26),12(27,R),8(26),10(35,R),1(34),7(35),5(35),8(34),7(36)])].
% 183.32/183.65 350 join(meet(A,B),join(meet(B,C),join(meet(A,join(B,C)),meet(C,join(A,meet(B,C)))))) = join(meet(A,join(B,C)),meet(C,join(A,meet(B,C)))). [para(32(a,1),140(a,1,2)),rewrite([7(8),14(16),7(11),2(13),8(10),12(10,R),12(9),8(8),12(10,R),8(9),12(9,R),8(8)])].
% 183.32/183.65 360 meet(one,join(A,meet(B,join(A,B)))) = join(A,B). [para(184(a,1),32(a,1,2,1,2)),rewrite([18(3),8(3),49(3),18(3),7(3),18(3),2(2),1(2),2(2),7(3),18(3),7(3),18(3),2(2),7(7),18(7),7(7),18(7),2(6),7(7),18(7),8(6)])].
% 183.32/183.65 373 join(one,join(meet(A,B),complement(C))) = one. [para(86(a,1),262(a,1,2,2)),rewrite([7(3),18(3)])].
% 183.32/183.65 382 join(one,join(complement(A),meet(B,C))) = one. [para(8(a,1),373(a,1,2))].
% 183.32/183.65 390 meet(one,join(complement(A),meet(B,C))) = join(complement(A),meet(B,C)). [para(382(a,1),69(a,1,2,2,2)),rewrite([1(7),2(6),7(5)])].
% 183.32/183.65 393 join(complement(A),meet(join(B,meet(C,join(B,C))),join(B,join(C,complement(A))))) = join(join(B,C),complement(A)). [back_rewrite(328),rewrite([390(11)])].
% 183.32/183.65 418 meet(one,join(A,B)) = join(A,B). [para(8(a,1),360(a,1,2)),rewrite([8(2),5(3),8(4)])].
% 183.32/183.65 419 join(A,meet(B,join(A,B))) = join(A,B). [para(8(a,1),360(a,2)),rewrite([418(5),8(4)])].
% 183.32/183.65 425 meet(join(A,B),join(meet(C,join(A,B)),meet(join(A,B),join(A,join(B,C))))) = join(join(A,B),meet(C,join(A,B))). [back_rewrite(341),rewrite([418(5),418(6),23(5),1(5),2(4),23(3),418(6),418(7),23(6),1(6),23(5),418(7),12(6),8(5),12(6,R),8(5),23(7),418(12),23(11)])].
% 183.32/183.65 434 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [back_rewrite(84),rewrite([418(5),12(4,R),2(3),7(4)])].
% 183.32/183.65 435 meet(join(A,B),join(A,join(B,C))) = join(A,B). [back_rewrite(81),rewrite([418(5),12(4,R),8(3),12(3,R),2(2)])].
% 183.32/183.65 436 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [back_rewrite(393),rewrite([419(4),435(6),12(3),8(2),12(3,R),8(2)]),flip(a)].
% 183.32/183.65 439 join(join(A,B),meet(C,join(A,B))) = join(A,B). [back_rewrite(425),rewrite([435(7),8(5),5(6)]),flip(a)].
% 183.32/183.65 485 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(44(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)])].
% 183.32/183.65 499 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(27(a,1),435(a,1,1)),rewrite([8(4),12(5,R),8(4),27(4),27(7)])].
% 183.32/183.65 529 meet(meet(A,B),join(A,B)) = meet(A,B). [back_rewrite(186),rewrite([499(4)]),flip(a)].
% 183.32/183.65 564 join(A,join(B,complement(join(A,B)))) = one. [para(436(a,1),3(a,1))].
% 183.32/183.65 565 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(6(a,1),436(a,1,1)),flip(a)].
% 183.32/183.65 566 meet(join(A,B),join(meet(C,join(A,join(B,complement(D)))),meet(complement(D),join(C,meet(join(A,B),complement(D)))))) = join(meet(join(A,B),complement(D)),meet(C,join(A,B))). [para(436(a,1),14(a,1,2,1,2)),rewrite([7(18)])].
% 183.32/183.65 568 join(zero,join(meet(A,B),complement(C))) = join(meet(A,B),complement(C)). [para(27(a,1),436(a,1,1)),flip(a)].
% 183.32/183.65 625 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(45(a,1),140(a,1,2)),rewrite([7(3),22(6),7(4),2(5),8(4)])].
% 183.32/183.65 653 meet(meet(A,join(B,C)),join(join(B,meet(A,B)),meet(meet(join(B,C),join(A,B)),join(B,meet(A,join(B,C)))))) = meet(A,join(B,C)). [back_rewrite(188),rewrite([625(17)])].
% 183.32/183.65 684 meet(meet(A,join(B,C)),join(meet(B,C),meet(A,C))) = meet(A,C). [para(8(a,1),46(a,1,1,2)),rewrite([7(3)])].
% 183.32/183.65 692 meet(meet(A,join(B,C)),meet(join(meet(B,C),meet(A,B)),join(D,meet(A,join(B,C))))) = meet(A,B). [para(46(a,1),22(a,2)),rewrite([8(8)])].
% 183.32/183.65 701 meet(meet(A,join(B,join(meet(C,join(A,D)),meet(join(A,D),join(A,C))))),join(A,meet(B,join(meet(C,join(A,D)),meet(join(A,D),join(A,C)))))) = A. [para(28(a,1),46(a,1,2,2)),rewrite([8(7),7(15),8(16),28(24)])].
% 183.32/183.65 897 join(A,complement(meet(A,B))) = one. [para(3(a,1),565(a,1,2)),rewrite([49(2)]),flip(a)].
% 183.32/183.65 900 meet(A,join(meet(join(A,B),join(A,complement(C))),meet(join(meet(A,D),complement(C)),join(A,B)))) = A. [para(565(a,1),28(a,1,2,2,2)),rewrite([8(10)])].
% 183.32/183.65 912 meet(A,join(B,meet(complement(meet(A,C)),join(B,meet(A,complement(meet(A,C))))))) = join(meet(A,complement(meet(A,C))),meet(A,B)). [para(897(a,1),14(a,1,2,1,2)),rewrite([18(2)])].
% 183.32/183.65 919 join(A,join(B,complement(meet(C,join(A,B))))) = one. [para(897(a,1),436(a,1)),rewrite([7(3)]),flip(a)].
% 183.32/183.65 921 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [para(46(a,1),897(a,1,2,1)),rewrite([8(5)])].
% 183.32/183.65 984 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [para(27(a,1),919(a,1,2,2,1,2)),rewrite([10(4),7(3),10(4,R),7(3),568(7)])].
% 183.32/183.65 1033 join(complement(meet(A,B)),meet(B,join(A,C))) = one. [para(7(a,1),921(a,1,1,1))].
% 183.32/183.65 1062 join(meet(A,join(B,complement(A))),meet(A,complement(meet(A,B)))) = meet(A,join(B,join(complement(A),complement(meet(A,B))))). [para(921(a,1),58(a,1,2,2,2)),rewrite([7(6),418(6),8(5),436(5)]),flip(a)].
% 183.32/183.65 1123 join(A,complement(meet(B,A))) = one. [para(3(a,1),1033(a,1,2,2)),rewrite([18(4),8(3)])].
% 183.32/183.65 1129 join(meet(A,B),join(complement(meet(A,B)),meet(B,C))) = one. [para(14(a,1),1033(a,1,2)),rewrite([7(3),22(3),7(1),7(4),12(6)])].
% 183.32/183.65 1131 join(complement(meet(A,B)),meet(meet(A,B),join(A,C))) = one. [para(20(a,1),1033(a,1,1,1))].
% 183.32/183.65 1135 join(complement(complement(A)),meet(join(B,complement(A)),join(C,complement(A)))) = one. [para(91(a,1),1033(a,1,1,1)),rewrite([8(6)])].
% 183.32/183.65 1385 join(meet(A,complement(meet(A,B))),meet(A,join(B,join(C,complement(A))))) = meet(A,join(B,join(C,join(complement(A),complement(meet(A,B)))))). [para(921(a,1),67(a,1,2,2,2)),rewrite([7(7),418(7),12(6,R),436(5),8(15)]),flip(a)].
% 183.32/183.65 1631 meet(meet(A,B),join(A,meet(B,join(meet(C,join(A,D)),meet(join(A,D),join(A,C)))))) = meet(A,B). [para(95(a,1),529(a,1,1)),rewrite([95(18)])].
% 183.32/183.65 2096 join(A,join(complement(A),meet(B,join(A,C)))) = one. [para(5(a,1),1129(a,1,1)),rewrite([5(2),7(3)])].
% 183.32/183.65 2137 join(A,join(complement(A),meet(B,C))) = one. [para(499(a,1),2096(a,1,2,2))].
% 183.32/183.65 2253 meet(meet(A,B),join(A,C)) = complement(complement(meet(A,B))). [para(1131(a,1),17(b,1)),rewrite([10(6,R),41(6)]),flip(c),xx(a),xx(b)].
% 183.32/183.65 2271 complement(complement(meet(A,B))) = meet(A,B). [back_rewrite(1631),rewrite([2253(10)])].
% 183.32/183.65 2276 meet(A,join(B,join(meet(C,join(A,D)),meet(join(A,D),join(A,C))))) = A. [back_rewrite(701),rewrite([2253(17),2271(10)])].
% 183.32/183.65 2310 meet(meet(A,B),join(A,C)) = meet(A,B). [back_rewrite(2253),rewrite([2271(6)])].
% 183.32/183.65 2420 complement(complement(A)) = A. [para(1(a,1),2271(a,1,1,1)),rewrite([1(3)])].
% 183.32/183.65 2421 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [para(2271(a,1),41(a,1,2,2)),rewrite([10(4),7(3),10(4,R),7(3),10(5,R)])].
% 183.32/183.65 2422 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(2271(a,1),436(a,1,2)),rewrite([2420(6)])].
% 183.32/183.65 2424 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(2271(a,1),565(a,1,2,2)),rewrite([2420(7)])].
% 183.32/183.65 2456 join(A,meet(join(B,complement(A)),join(C,complement(A)))) = one. [back_rewrite(1135),rewrite([2420(2)])].
% 183.32/183.65 2931 meet(meet(A,join(B,C)),join(B,join(meet(A,B),meet(meet(join(B,C),join(A,B)),join(B,meet(A,join(B,C))))))) = meet(A,join(B,C)). [back_rewrite(653),rewrite([2422(12)])].
% 183.32/183.65 2968 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [back_rewrite(439),rewrite([2422(4)])].
% 183.32/183.65 3035 meet(A,B) != zero | one != A | complement(meet(A,B)) = A. [para(2310(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)].
% 183.32/183.65 3078 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(1(a,1),2421(a,1,2,1))].
% 183.32/183.65 3080 meet(A,meet(meet(B,C),complement(meet(A,C)))) = zero. [para(7(a,1),2421(a,1,2,1))].
% 183.32/183.65 3216 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(5(a,1),3080(a,1,2,1))].
% 183.32/183.65 3255 meet(A,meet(meet(B,C),complement(meet(A,join(B,D))))) = zero. [para(2310(a,1),3080(a,1,2,1))].
% 183.32/183.65 3360 meet(A,complement(join(A,B))) = zero. [hyper(34,a,3216,a,b,2420,a(flip)),rewrite([42(2),52(2),42(3),52(3),418(4),10(5,R),7(4),86(4),42(5),52(5),42(5)])].
% 183.32/183.65 3362 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(3216(a,1),10(a,1)),rewrite([7(6)]),flip(a)].
% 183.32/183.65 3557 meet(meet(A,B),complement(meet(B,join(A,C)))) = zero. [para(7(a,1),3362(a,1,1))].
% 183.32/183.65 3566 meet(complement(A),complement(join(B,complement(A)))) = zero. [para(86(a,1),3362(a,1,1)),rewrite([8(4),418(5)])].
% 183.32/183.65 3568 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(418(a,1),3362(a,1,1)),rewrite([8(4),12(4),8(3),12(4,R),8(3),418(5)])].
% 183.32/183.65 3600 meet(A,complement(B)) != zero | join(A,complement(B)) != one | A = B. [para(3566(a,1),63(a,1,2,2)),rewrite([19(3),7(2),8(6),3566(13),19(10),2420(10)])].
% 183.32/183.65 3865 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(5(a,1),3557(a,1,1))].
% 183.32/183.65 3917 join(A,join(B,meet(C,meet(D,join(A,B))))) = join(A,B). [para(3568(a,1),140(a,1,2,2,1)),rewrite([7(4),27(5),2422(5)])].
% 183.32/183.65 3978 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(28(a,1),142(a,1,2,2,2,2)),rewrite([23(4),2(6),1(5),23(6),1(8),2(7),1(6),2(5),5(4),8(3),23(3),23(5),2(7),1(6),23(7),1(9),2(8),1(7),2(6),5(5),8(4),5(5),8(4),1(8),23(9),1(9),2(8),5(7),7(7)])].
% 183.32/183.65 4342 join(A,join(B,join(C,meet(D,join(A,B))))) = join(A,join(B,C)). [para(2968(a,1),12(a,2,2)),rewrite([8(4),12(4,R),8(3),12(7),8(6),12(7,R),8(6)])].
% 183.32/183.65 4356 join(A,meet(join(B,complement(C)),join(A,meet(C,join(B,complement(C)))))) = join(A,meet(C,join(B,complement(C)))). [para(58(a,1),2968(a,1,2,2)),rewrite([7(11),8(13),2422(13),4342(14),25(6)]),flip(a)].
% 183.32/183.65 4410 join(meet(A,join(B,complement(A))),meet(A,C)) = meet(A,join(C,meet(A,join(B,complement(A))))). [back_rewrite(58),rewrite([4356(8)]),flip(a)].
% 183.32/183.65 4500 meet(A,join(B,join(complement(A),complement(meet(A,B))))) = A. [back_rewrite(1062),rewrite([4410(7),921(6),18(2)]),flip(a)].
% 183.32/183.65 4825 meet(A,join(B,join(C,join(complement(A),complement(meet(A,B)))))) = A. [para(4500(a,1),46(a,1,2,2)),rewrite([8(6),12(6,R),8(5),7(13),8(14),2310(15),4500(13)])].
% 183.32/183.65 4855 join(meet(A,complement(meet(A,B))),meet(A,join(B,join(C,complement(A))))) = A. [back_rewrite(1385),rewrite([4825(15)])].
% 183.32/183.65 5613 meet(A,B) != zero | one != B | complement(meet(A,B)) = B. [para(7(a,1),3035(a,1)),rewrite([7(6)])].
% 183.32/183.65 6271 meet(meet(A,B),complement(join(A,C))) = zero. [hyper(17,a,3255,a,b,182,a),rewrite([42(2),418(5)]),flip(a)].
% 183.32/183.65 6309 meet(join(meet(A,B),meet(A,C)),complement(join(A,D))) = zero. [para(14(a,1),6271(a,1,1))].
% 183.32/183.65 9309 meet(join(meet(A,meet(B,C)),meet(C,D)),complement(join(C,E))) = zero. [para(10(a,2),6309(a,1,1,1))].
% 183.32/183.65 9760 join(meet(A,B),meet(B,join(A,B))) = join(B,meet(A,B)). [para(1(a,1),350(a,1,2,1)),rewrite([2(2),1(3),25(6),12(4,R),2(3),2(3),1(4)]),flip(a)].
% 183.32/183.65 9762 meet(meet(A,B),join(meet(A,join(B,C)),meet(C,join(A,meet(B,C))))) = meet(A,B). [para(350(a,1),5(a,1,2))].
% 183.32/183.65 9816 join(A,meet(complement(meet(B,C)),join(A,meet(B,complement(meet(B,C)))))) = join(A,meet(B,complement(meet(B,C)))). [para(897(a,1),350(a,1,2,2,1,2)),rewrite([18(6),12(13,R),8(12),2968(13),12(6,R),25(6),897(7),18(6)]),flip(a)].
% 183.32/183.65 10047 join(meet(A,complement(meet(A,B))),meet(A,C)) = meet(A,join(C,meet(A,complement(meet(A,B))))). [back_rewrite(912),rewrite([9816(8)]),flip(a)].
% 183.32/183.65 10384 meet(A,join(B,join(C,join(complement(A),meet(A,complement(meet(A,B))))))) = A. [back_rewrite(4855),rewrite([10047(8),2422(7),2422(6)])].
% 183.32/183.65 11449 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(8(a,1),434(a,1,1))].
% 183.32/183.65 11508 meet(join(A,meet(B,C)),complement(join(A,join(B,D)))) = zero. [para(434(a,1),6271(a,1,1)),rewrite([8(4),12(4),8(3),12(4,R),8(3)])].
% 183.32/183.65 12695 meet(complement(join(A,join(B,C))),join(A,meet(B,D))) = zero. [para(11508(a,1),7(a,1)),flip(a)].
% 183.32/183.65 12696 meet(join(A,meet(B,C)),complement(join(A,join(C,D)))) = zero. [para(7(a,1),11508(a,1,1,2))].
% 183.32/183.65 12917 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(436(a,1),485(a,1,2,2,2,2)),rewrite([10(8,R),7(7),10(7,R),7(6),10(6,R),7(5),435(5),10(8,R)]),flip(a)].
% 183.32/183.65 14153 meet(complement(join(A,join(B,C))),join(C,meet(A,D))) = zero. [para(8(a,1),12695(a,1,1,1)),rewrite([8(2),12(2),8(1),12(2,R),8(1)])].
% 183.32/183.65 14201 meet(join(A,meet(B,C)),complement(join(C,join(A,D)))) = zero. [para(8(a,1),12696(a,1,1)),rewrite([8(2),12(4,R),8(3)])].
% 183.32/183.65 15381 meet(complement(join(A,B)),join(meet(B,C),meet(A,D))) = zero. [para(6(a,1),14153(a,1,1,1,2))].
% 183.32/183.65 15387 meet(complement(join(A,join(B,C))),join(B,join(C,meet(A,D)))) = zero. [para(23(a,1),14153(a,1,1,1,2)),rewrite([2422(6)])].
% 183.32/183.65 15593 meet(complement(join(A,complement(B))),join(complement(B),meet(C,A))) = zero. [para(120(a,1),14201(a,1,2,1,2)),rewrite([7(7)])].
% 183.32/183.65 16170 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(15381(a,1),566(a,1,2,2)),rewrite([8(4),12(4),8(3),12(4,R),8(3),8(10),27(10),12917(9),10(9,R),7(8),10(8,R),7(7),435(7),8(6),12(6),8(5),12(6,R),8(5),3568(8),27(8)]),flip(a)].
% 183.32/183.65 16487 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [back_rewrite(9762),rewrite([16170(8),14(7),7(2)])].
% 183.32/183.65 16692 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [back_rewrite(2931),rewrite([16170(10),11449(9),3978(8),12(7,R),8(6),625(6),23(6),16170(6),3978(5)])].
% 183.32/183.65 16762 meet(A,meet(join(B,C),join(meet(B,C),meet(A,C)))) = meet(A,C). [back_rewrite(684),rewrite([16170(6)])].
% 183.32/183.65 16794 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(7(a,1),16487(a,1,2,1))].
% 183.32/183.65 17036 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(16794(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 183.32/183.65 17037 meet(A,meet(B,join(meet(C,D),meet(A,D)))) = meet(A,meet(D,B)). [para(16794(a,1),10(a,2,2)),rewrite([7(4),10(7),7(6),10(7,R),7(6)])].
% 183.32/183.65 17091 meet(A,meet(B,join(C,B))) = meet(A,B). [back_rewrite(16762),rewrite([17037(6)])].
% 183.32/183.65 17134 join(A,meet(B,A)) = A. [para(18(a,1),17036(a,1,2,2)),rewrite([8(3),418(4),18(4)])].
% 183.32/183.65 17139 join(meet(A,B),meet(B,join(A,B))) = B. [back_rewrite(9760),rewrite([17134(6)])].
% 183.32/183.65 17204 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(22(a,1),17139(a,1,1)),rewrite([16170(7),3978(6),16692(5)])].
% 183.32/183.65 17208 meet(A,join(B,A)) = A. [para(419(a,1),17139(a,1,2,2)),rewrite([22(3),7(5),17091(5),7(3),17139(4)]),flip(a)].
% 183.32/183.65 17575 join(complement(A),meet(join(A,B),join(C,A))) = one. [hyper(5613,a,15593,a,b,2456,a(flip)),rewrite([2420(2),8(3),12(3),8(2),51(3),42(2),2420(4),8(3),2420(5),273(7),52(2),2420(4),8(3),2420(5)]),flip(a)].
% 183.32/183.65 18870 meet(A,meet(join(B,C),join(B,A))) = meet(A,join(B,C)). [para(17575(a,1),692(a,1,2,2)),rewrite([8(2),7(4),7(6),17204(7),7(7),10(7,R),7(6),418(6),7(6),10(6),7(5),10(5,R),1(4),10(4,R),7(6)])].
% 183.32/183.65 18890 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(2420(a,1),3600(b,1,2)),rewrite([2420(2)]),flip(c)].
% 183.32/183.65 19706 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(5(a,1),16170(a,1,1)),flip(a)].
% 183.32/183.65 20410 join(A,meet(B,meet(C,A))) = A. [para(984(a,1),17204(a,1,2,2)),rewrite([7(2),10(2),7(1),10(2,R),7(1),18(4),8(3),984(8),18(5)])].
% 183.32/183.65 20459 join(A,meet(B,meet(A,C))) = A. [para(20410(a,1),11449(a,1,2)),rewrite([7(2),17208(2),7(1)]),flip(a)].
% 183.32/183.65 20525 join(A,join(B,meet(C,join(A,meet(B,D))))) = join(A,B). [para(434(a,1),20459(a,1,2,2)),rewrite([2422(5)])].
% 183.32/183.65 20731 join(meet(A,join(B,C)),meet(join(B,C),join(B,A))) = meet(join(B,C),join(B,A)). [para(18870(a,1),17134(a,1,2)),rewrite([8(6)])].
% 183.32/183.65 20795 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [back_rewrite(2276),rewrite([20731(6)])].
% 183.32/183.65 20828 join(A,join(meet(join(B,C),join(B,D)),meet(B,E))) = join(A,meet(join(B,C),join(B,D))). [para(20795(a,1),3917(a,1,2,2,2)),rewrite([7(4)])].
% 183.32/183.65 21392 join(complement(A),meet(join(B,C),join(B,complement(A)))) = join(B,complement(A)). [para(900(a,1),20525(a,1,2,2)),rewrite([8(8),565(8),8(7),17134(7),12(10),20828(10)]),flip(a)].
% 183.32/183.65 23952 meet(complement(A),join(meet(B,meet(C,A)),meet(A,D))) = zero. [para(2(a,1),9309(a,1,2,1)),rewrite([7(6)])].
% 183.32/183.65 27591 join(A,meet(join(B,C),join(A,B))) = join(A,B). [para(2420(a,1),21392(a,1,1)),rewrite([2420(3),8(2),2420(6),8(5)])].
% 183.32/183.65 27623 join(A,meet(join(A,B),join(B,C))) = join(A,B). [para(7(a,1),27591(a,1,2))].
% 183.32/183.65 27625 join(A,meet(join(B,C),join(A,C))) = join(A,C). [para(8(a,1),27591(a,1,2,1))].
% 183.32/183.65 27696 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(16487(a,1),27623(a,1,2)),rewrite([7(3)])].
% 183.32/183.65 32479 meet(A,join(B,join(complement(A),meet(A,complement(meet(A,B)))))) = A. [para(2(a,1),10384(a,1,2,2))].
% 183.32/183.65 32500 join(A,join(complement(B),meet(B,complement(meet(A,B))))) = one. [para(32479(a,1),919(a,1,2,2,1)),rewrite([7(2),8(7),23(7)])].
% 183.32/183.65 32526 join(A,join(complement(B),meet(B,complement(meet(B,A))))) = one. [hyper(5613,a,15387,a,b,32500,a(flip)),rewrite([51(3),42(2),7(3),273(8),52(2),7(3)]),flip(a)].
% 183.32/183.65 32543 join(complement(A),join(meet(A,B),meet(A,complement(meet(A,B))))) = one. [para(20(a,1),32526(a,1,2,2,2,1)),rewrite([12(7,R),8(6)])].
% 183.32/183.65 32607 join(meet(A,B),meet(A,complement(meet(A,B)))) = A. [hyper(17,a,23952,a,b,32543,a),rewrite([2420(2),7(1),20(2),7(2),20(3)]),flip(a)].
% 183.32/183.65 32612 join(meet(A,B),meet(B,complement(meet(A,B)))) = B. [para(7(a,1),32607(a,1,1)),rewrite([7(2)])].
% 183.32/183.65 32651 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(5(a,1),32612(a,1,1)),rewrite([5(3),7(3)])].
% 183.32/183.65 32662 join(A,meet(B,complement(meet(A,B)))) = join(A,B). [para(32612(a,1),2424(a,1,2)),flip(a)].
% 183.32/183.65 32686 join(A,join(B,meet(complement(A),join(A,C)))) = join(A,join(C,B)). [para(32651(a,1),12(a,2,2)),rewrite([8(4),12(7),8(6),12(7,R),8(6)])].
% 183.32/183.65 32722 join(A,B) != one | meet(B,complement(meet(A,B))) = complement(A). [para(32662(a,1),17(b,1)),rewrite([3078(4)]),flip(c),xx(a)].
% 183.32/183.65 32734 join(A,meet(B,complement(meet(A,meet(C,B))))) = join(A,B). [para(32662(a,1),2424(a,1,2)),rewrite([8(2),25(3),7(3),10(3),7(2),10(3,R),7(2)]),flip(a)].
% 183.32/183.65 32735 join(A,B) != one | complement(meet(B,complement(meet(A,B)))) = A. [para(32662(a,1),18890(b,1)),rewrite([3078(4)]),xx(a)].
% 183.32/183.65 32899 meet(complement(meet(A,B)),complement(meet(A,complement(meet(A,B))))) = complement(A). [hyper(32722,a,897,a)].
% 183.32/183.65 32902 join(A,B) != one | meet(A,complement(meet(A,B))) = complement(B). [para(8(a,1),32722(a,1)),rewrite([7(4)])].
% 183.32/183.65 32906 join(A,meet(B,complement(meet(B,meet(A,C))))) = join(B,A). [para(32734(a,1),8(a,2)),rewrite([7(1),10(2,R),7(1),8(5),8(6)])].
% 183.32/183.65 32942 join(A,B) != one | complement(meet(A,complement(meet(A,B)))) = B. [para(8(a,1),32735(a,1)),rewrite([7(4)])].
% 183.32/183.65 33006 meet(A,complement(meet(A,join(complement(A),meet(B,C))))) = complement(join(complement(A),meet(B,C))). [hyper(32902,a,2137,a)].
% 183.32/183.65 33007 meet(A,complement(meet(A,complement(meet(A,B))))) = meet(A,B). [hyper(32902,a,1123,a),rewrite([7(1),7(6),2420(8)])].
% 183.32/183.65 33078 complement(meet(A,complement(meet(A,B)))) = join(complement(A),meet(A,B)). [para(33007(a,1),32612(a,1,1)),rewrite([33007(10),7(8),32899(8),8(3)]),flip(a)].
% 183.32/183.65 33081 meet(A,join(complement(A),meet(A,B))) = meet(A,B). [para(33007(a,1),33007(a,2)),rewrite([33078(4),33006(6),2420(5)])].
% 183.32/183.65 33100 join(A,B) != one | join(complement(A),meet(A,B)) = B. [back_rewrite(32942),rewrite([33078(7)])].
% 183.32/183.65 33103 join(meet(A,B),meet(A,C)) = meet(A,join(C,meet(A,B))). [para(33081(a,1),14(a,1,2,2,2,2)),rewrite([25(4),3(2),18(2),27625(7),33081(7)]),flip(a)].
% 183.32/183.65 33104 meet(complement(A),join(A,meet(B,complement(A)))) = meet(B,complement(A)). [para(2420(a,1),33081(a,1,2,1)),rewrite([7(3),7(7)])].
% 183.32/183.65 33219 meet(a,join(c,meet(a,b))) != meet(a,join(b,c)) # answer(prove_distributivity). [back_rewrite(16),rewrite([33103(7)])].
% 183.32/183.65 33230 join(complement(A),meet(A,complement(meet(A,B)))) = complement(meet(A,B)). [hyper(33100,a,1123,a),rewrite([7(2),7(6)])].
% 183.32/183.65 33231 join(complement(A),meet(A,join(B,complement(join(A,B))))) = join(B,complement(join(A,B))). [hyper(33100,a,564,a)].
% 183.32/183.65 33256 join(A,complement(meet(B,meet(C,join(A,complement(B)))))) = one. [para(51(a,1),32906(a,2)),rewrite([7(5),2422(9),33230(8)])].
% 183.32/183.65 33305 join(A,complement(meet(B,join(A,complement(B))))) = one. [para(1(a,1),33256(a,1,2,1,2))].
% 183.32/183.65 33331 meet(join(A,B),join(A,complement(join(A,B)))) = A. [hyper(18890,a,3865,a,b,33305,a),rewrite([2420(7)])].
% 183.32/183.65 33529 meet(join(A,B),join(B,complement(join(A,B)))) = B. [para(8(a,1),33331(a,1,1)),rewrite([8(2)])].
% 183.32/183.65 33574 meet(A,join(B,complement(join(A,B)))) = meet(A,B). [para(33529(a,1),19706(a,1,2)),flip(a)].
% 183.32/183.65 33587 join(complement(A),meet(A,B)) = join(B,complement(join(A,B))). [back_rewrite(33231),rewrite([33574(5)])].
% 183.32/183.65 33609 meet(A,join(B,join(meet(A,C),complement(join(A,B))))) = meet(A,join(B,meet(A,C))). [para(25(a,1),33574(a,1,2,2,1)),rewrite([8(5),12(5,R)])].
% 183.32/183.65 33638 meet(A,join(complement(join(A,B)),meet(join(A,B),join(B,C)))) = meet(A,join(B,C)). [para(27623(a,1),33574(a,1,2,2,1)),rewrite([8(6),19706(11)])].
% 183.32/183.65 34288 join(A,complement(join(A,B))) = join(A,complement(B)). [para(33587(a,2),23(a,1,2)),rewrite([7(2),25(4),8(3)]),flip(a)].
% 183.32/183.65 34289 join(complement(A),meet(B,A)) = join(B,complement(A)). [para(33587(a,2),23(a,2)),rewrite([8(1),34288(3),23(3),7(4)]),flip(a)].
% 183.32/183.65 34300 join(A,complement(join(B,meet(A,C)))) = join(A,complement(B)). [para(33587(a,2),565(a,1,2)),rewrite([10(3,R),7(2),25(5)]),flip(a)].
% 183.32/183.65 34318 join(A,meet(B,complement(A))) = join(A,B). [para(2420(a,1),33587(a,1,1)),rewrite([7(2),8(5),34288(7),2420(5),8(4)])].
% 183.32/183.65 34323 join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A). [para(3360(a,1),33587(a,1,2)),rewrite([19(3),34288(6)]),flip(a)].
% 183.32/183.65 34443 join(complement(A),meet(A,join(B,C))) = join(B,join(C,complement(join(A,B)))). [para(18870(a,1),33587(a,1,2)),rewrite([8(6),8(9),27591(11),8(10),34289(10),436(8)])].
% 183.32/183.65 34590 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(27696(a,1),33587(a,2,2,1)),rewrite([22(5),8(10),34289(10),34300(7)])].
% 183.32/183.65 34833 meet(complement(A),join(A,complement(B))) = complement(join(A,B)). [para(33587(a,2),33529(a,1,2,2,1)),rewrite([8(1),34288(3),8(3),7(6),34289(7),34323(8),7(4),8(5)])].
% 183.32/183.65 34894 meet(complement(A),join(A,B)) = meet(B,complement(A)). [back_rewrite(33104),rewrite([34318(4)])].
% 183.32/183.65 34912 join(A,join(B,complement(join(C,A)))) = join(A,join(B,complement(C))). [back_rewrite(34443),rewrite([34590(4),436(3)]),flip(a)].
% 183.32/183.65 34931 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [back_rewrite(33638),rewrite([34590(6),436(4),34912(4)])].
% 183.32/183.65 34979 complement(join(A,B)) = meet(complement(A),complement(B)). [back_rewrite(34833),rewrite([34894(4),7(3)]),flip(a)].
% 183.32/183.65 35000 join(A,join(B,meet(C,complement(A)))) = join(A,join(B,C)). [back_rewrite(32686),rewrite([34894(3),8(5)])].
% 183.32/183.65 35006 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(33609),rewrite([34979(3),35000(6),8(3),34590(3),34931(4)]),flip(a)].
% 183.32/183.65 37089 $F # answer(prove_distributivity). [back_rewrite(33219),rewrite([35006(7),8(4)]),xx(a)].
% 183.32/183.65
% 183.32/183.65 % SZS output end Refutation
% 183.32/183.65 ============================== end of proof ==========================
% 183.32/183.65
% 183.32/183.65 ============================== STATISTICS ============================
% 183.32/183.65
% 183.32/183.65 Given=1810. Generated=4161015. Kept=37084. proofs=1.
% 183.32/183.65 Usable=795. Sos=4675. Demods=7027. Limbo=2083, Disabled=29544. Hints=0.
% 183.32/183.65 Megabytes=44.00.
% 183.32/183.65 User_CPU=180.52, System_CPU=2.14, Wall_clock=183.
% 183.32/183.65
% 183.32/183.65 ============================== end of statistics =====================
% 183.32/183.65
% 183.32/183.65 ============================== end of search =========================
% 183.32/183.65
% 183.32/183.65 THEOREM PROVED
% 183.32/183.65 % SZS status Unsatisfiable
% 183.32/183.65
% 183.32/183.65 Exiting with 1 proof.
% 183.32/183.65
% 183.32/183.65 Process 29028 exit (max_proofs) Thu Jun 30 15:07:55 2022
% 183.32/183.65 Prover9 interrupted
%------------------------------------------------------------------------------