TSTP Solution File: LAT213-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT213-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 06:26:10 EDT 2022
% Result : Unsatisfiable 9.54s 9.83s
% Output : Refutation 9.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT213-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n010.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 13:08:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.95/5.21 ============================== Prover9 ===============================
% 4.95/5.21 Prover9 (32) version 2009-11A, November 2009.
% 4.95/5.21 Process 6566 was started by sandbox on n010.cluster.edu,
% 4.95/5.21 Thu Jun 30 13:08:49 2022
% 4.95/5.21 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6413_n010.cluster.edu".
% 4.95/5.21 ============================== end of head ===========================
% 4.95/5.21
% 4.95/5.21 ============================== INPUT =================================
% 4.95/5.21
% 4.95/5.21 % Reading from file /tmp/Prover9_6413_n010.cluster.edu
% 4.95/5.21
% 4.95/5.21 set(prolog_style_variables).
% 4.95/5.21 set(auto2).
% 4.95/5.21 % set(auto2) -> set(auto).
% 4.95/5.21 % set(auto) -> set(auto_inference).
% 4.95/5.21 % set(auto) -> set(auto_setup).
% 4.95/5.21 % set(auto_setup) -> set(predicate_elim).
% 4.95/5.21 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.95/5.21 % set(auto) -> set(auto_limits).
% 4.95/5.21 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.95/5.21 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.95/5.21 % set(auto) -> set(auto_denials).
% 4.95/5.21 % set(auto) -> set(auto_process).
% 4.95/5.21 % set(auto2) -> assign(new_constants, 1).
% 4.95/5.21 % set(auto2) -> assign(fold_denial_max, 3).
% 4.95/5.21 % set(auto2) -> assign(max_weight, "200.000").
% 4.95/5.21 % set(auto2) -> assign(max_hours, 1).
% 4.95/5.21 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.95/5.21 % set(auto2) -> assign(max_seconds, 0).
% 4.95/5.21 % set(auto2) -> assign(max_minutes, 5).
% 4.95/5.21 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.95/5.21 % set(auto2) -> set(sort_initial_sos).
% 4.95/5.21 % set(auto2) -> assign(sos_limit, -1).
% 4.95/5.21 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.95/5.21 % set(auto2) -> assign(max_megs, 400).
% 4.95/5.21 % set(auto2) -> assign(stats, some).
% 4.95/5.21 % set(auto2) -> clear(echo_input).
% 4.95/5.21 % set(auto2) -> set(quiet).
% 4.95/5.21 % set(auto2) -> clear(print_initial_clauses).
% 4.95/5.21 % set(auto2) -> clear(print_given).
% 4.95/5.21 assign(lrs_ticks,-1).
% 4.95/5.21 assign(sos_limit,10000).
% 4.95/5.21 assign(order,kbo).
% 4.95/5.21 set(lex_order_vars).
% 4.95/5.21 clear(print_given).
% 4.95/5.21
% 4.95/5.21 % formulas(sos). % not echoed (13 formulas)
% 4.95/5.21
% 4.95/5.21 ============================== end of input ==========================
% 4.95/5.21
% 4.95/5.21 % From the command line: assign(max_seconds, 300).
% 4.95/5.21
% 4.95/5.21 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.95/5.21
% 4.95/5.21 % Formulas that are not ordinary clauses:
% 4.95/5.21
% 4.95/5.21 ============================== end of process non-clausal formulas ===
% 4.95/5.21
% 4.95/5.21 ============================== PROCESS INITIAL CLAUSES ===============
% 4.95/5.21
% 4.95/5.21 ============================== PREDICATE ELIMINATION =================
% 4.95/5.21
% 4.95/5.21 ============================== end predicate elimination =============
% 4.95/5.21
% 4.95/5.21 Auto_denials:
% 4.95/5.21 % copying label prove_distributivity to answer in negative clause
% 4.95/5.21
% 4.95/5.21 Term ordering decisions:
% 4.95/5.21
% 4.95/5.21 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 4.95/5.21 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 4.95/5.21
% 4.95/5.21 ============================== end of process initial clauses ========
% 4.95/5.21
% 4.95/5.21 ============================== CLAUSES FOR SEARCH ====================
% 4.95/5.21
% 4.95/5.21 ============================== end of clauses for search =============
% 4.95/5.21
% 4.95/5.21 ============================== SEARCH ================================
% 4.95/5.21
% 4.95/5.21 % Starting search at 0.01 seconds.
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=147.000, iters=3503
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=119.000, iters=3451
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=115.000, iters=3436
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=107.000, iters=3403
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=105.000, iters=3397
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=95.000, iters=3340
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=93.000, iters=3500
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=87.000, iters=3450
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=85.000, iters=3425
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=84.000, iters=3411
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=83.000, iters=3409
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=79.000, iters=3358
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=77.000, iters=3475
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=73.000, iters=3404
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=71.000, iters=3358
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=67.000, iters=3360
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=66.000, iters=3400
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=65.000, iters=3375
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=63.000, iters=3404
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=62.000, iters=3351
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=61.000, iters=3350
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=59.000, iters=3351
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=57.000, iters=3337
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=56.000, iters=3437
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=55.000, iters=3402
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=54.000, iters=3418
% 4.95/5.21
% 4.95/5.21 Low Water (keep): wt=52.000, iters=3346
% 9.54/9.83
% 9.54/9.83 Low Water (keep): wt=51.000, iters=3370
% 9.54/9.83
% 9.54/9.83 ============================== PROOF =================================
% 9.54/9.83 % SZS status Unsatisfiable
% 9.54/9.83 % SZS output start Refutation
% 9.54/9.83
% 9.54/9.83 % Proof 1 at 8.78 (+ 0.09) seconds: prove_distributivity.
% 9.54/9.83 % Length of proof is 208.
% 9.54/9.83 % Level of proof is 40.
% 9.54/9.83 % Maximum clause weight is 65.000.
% 9.54/9.83 % Given clauses 471.
% 9.54/9.83
% 9.54/9.83 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 9.54/9.83 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 9.54/9.83 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 9.54/9.83 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 9.54/9.83 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 9.54/9.83 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 9.54/9.83 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 9.54/9.83 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 9.54/9.83 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 9.54/9.83 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 9.54/9.83 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 9.54/9.83 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 9.54/9.83 13 meet(A,join(B,meet(C,join(B,D)))) = meet(A,join(B,meet(C,join(D,meet(A,B))))) # label(equation_H76) # label(axiom). [assumption].
% 9.54/9.83 14 meet(A,join(B,meet(C,join(D,meet(A,B))))) = meet(A,join(B,meet(C,join(B,D)))). [copy(13),flip(a)].
% 9.54/9.83 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 9.54/9.83 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 9.54/9.83 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 9.54/9.83 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 9.54/9.83 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 9.54/9.83 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)])].
% 9.54/9.83 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 9.54/9.83 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 9.54/9.83 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)])].
% 9.54/9.83 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 9.54/9.83 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 9.54/9.83 26 meet(A,join(B,join(C,meet(A,B)))) = meet(A,join(B,C)). [para(1(a,1),14(a,1,2,2)),rewrite([7(8),14(10),1(7),23(6)])].
% 9.54/9.83 27 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(2(a,1),14(a,1,2,2,2)),rewrite([10(2),7(1),10(2,R),7(1),14(9),2(5),7(5),6(6)])].
% 9.54/9.83 28 meet(A,join(complement(A),meet(B,join(C,complement(A))))) = meet(A,join(complement(A),meet(B,C))). [para(4(a,1),14(a,1,2,2,2,2)),rewrite([19(3),8(7)]),flip(a)].
% 9.54/9.83 29 meet(A,join(join(A,B),meet(C,join(A,join(B,D))))) = meet(A,join(join(A,B),meet(C,join(A,D)))). [para(5(a,1),14(a,1,2,2,2,2)),rewrite([8(2),8(8),12(8),8(7),12(8,R),8(7)]),flip(a)].
% 9.54/9.83 30 meet(A,join(B,meet(C,join(B,C)))) = meet(A,join(B,C)). [para(5(a,1),14(a,1,2,2)),flip(a)].
% 9.54/9.83 31 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(6(a,1),14(a,1,2,2,2)),rewrite([7(1),8(4)]),flip(a)].
% 9.54/9.83 32 meet(A,join(B,meet(C,join(D,meet(B,A))))) = meet(A,join(B,meet(C,join(B,D)))). [para(14(a,1),7(a,2)),rewrite([7(1),7(5)])].
% 9.54/9.83 34 meet(A,join(join(B,meet(C,join(D,meet(A,B)))),meet(E,join(F,meet(A,join(B,meet(C,join(B,D)))))))) = meet(A,join(join(B,meet(C,join(D,meet(A,B)))),meet(E,join(B,join(F,meet(C,join(D,meet(A,B)))))))). [para(14(a,1),14(a,1,2,2,2,2)),rewrite([8(21),12(21,R),8(20)])].
% 9.54/9.83 35 meet(A,join(join(B,meet(C,D)),meet(C,join(D,meet(A,join(B,D)))))) = meet(A,join(join(B,meet(C,D)),meet(C,join(B,join(D,meet(C,D)))))). [para(14(a,1),14(a,1,2,2)),rewrite([8(3),8(13),12(13,R),8(12)])].
% 9.54/9.83 38 meet(A,join(one,meet(B,join(C,one)))) = meet(A,join(one,meet(B,join(A,C)))). [para(18(a,1),14(a,1,2,2,2,2)),rewrite([8(2),8(8)]),flip(a)].
% 9.54/9.83 39 meet(A,zero) != zero | one != A | complement(A) = zero. [para(19(a,1),17(b,1)),flip(b)].
% 9.54/9.83 40 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 9.54/9.83 41 one != A | complement(A) = zero. [back_rewrite(39),rewrite([40(2)]),xx(a)].
% 9.54/9.83 42 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([40(5)])].
% 9.54/9.83 43 complement(one) = zero. [hyper(17,a,40,a,b,19,a)].
% 9.54/9.83 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)])].
% 9.54/9.83 46 complement(join(A,one)) = zero. [hyper(41,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 9.54/9.83 48 join(A,one) = one. [para(46(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 9.54/9.83 49 meet(A,join(one,meet(B,join(A,C)))) = A. [back_rewrite(38),rewrite([48(3),18(3),8(2),48(2),18(2)]),flip(a)].
% 9.54/9.83 50 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([48(5)])].
% 9.54/9.83 51 complement(zero) = one. [hyper(17,a,18,a,b,48,a)].
% 9.54/9.83 55 meet(A,join(meet(B,complement(A)),meet(C,join(D,meet(B,complement(A)))))) = meet(A,join(meet(B,complement(A)),meet(C,D))). [para(42(a,1),14(a,1,2,2,2,2)),rewrite([19(4),8(10)]),flip(a)].
% 9.54/9.83 56 join(A,join(B,join(C,complement(A)))) = one. [para(50(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),48(6)])].
% 9.54/9.83 57 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(50(a,1),17(b,1)),flip(c),xx(b)].
% 9.54/9.83 59 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)].
% 9.54/9.83 70 meet(A,join(B,meet(A,B))) = meet(A,B). [para(2(a,1),26(a,2,2)),rewrite([23(3)])].
% 9.54/9.83 71 meet(A,join(B,join(C,meet(A,C)))) = meet(A,join(B,C)). [para(8(a,1),26(a,1,2)),rewrite([8(3),12(3,R),8(2),8(5)])].
% 9.54/9.83 76 meet(A,join(B,join(meet(A,C),meet(C,join(A,D))))) = meet(A,join(B,meet(C,join(A,D)))). [para(22(a,1),26(a,1,2,2,2)),rewrite([12(5),8(4),12(5,R),8(4),8(9)])].
% 9.54/9.83 80 meet(A,join(join(B,meet(C,D)),meet(C,join(D,meet(A,join(B,D)))))) = meet(A,join(B,join(meet(C,D),meet(C,join(B,D))))). [back_rewrite(35),rewrite([71(14),8(13),12(13),8(12),12(13,R),8(12)])].
% 9.54/9.83 86 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(22(a,1),70(a,1,2,2)),rewrite([8(4),22(8)])].
% 9.54/9.83 87 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(42(a,1),70(a,1,2,2)),rewrite([8(4),42(8)])].
% 9.54/9.83 90 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),87(a,1,2,2))].
% 9.54/9.83 93 join(zero,complement(A)) = complement(A). [hyper(17,a,90,a,b,50,a),flip(a)].
% 9.54/9.83 94 meet(A,join(join(A,B),meet(A,C))) = A. [para(5(a,1),27(a,2)),rewrite([7(3),22(4)])].
% 9.54/9.83 95 meet(A,meet(B,join(C,meet(A,meet(C,D))))) = meet(A,meet(C,B)). [para(27(a,1),10(a,2,2)),rewrite([7(4),10(7),7(6),10(7,R),7(6)])].
% 9.54/9.83 96 meet(A,join(meet(B,C),meet(A,meet(B,meet(C,D))))) = meet(A,meet(B,C)). [para(10(a,1),27(a,2)),rewrite([7(3),10(3),7(2),10(3,R),7(2),10(8),7(7),10(8,R),7(7)])].
% 9.54/9.83 100 meet(A,join(meet(B,join(A,C)),meet(A,meet(B,D)))) = meet(A,B). [para(22(a,1),27(a,2)),rewrite([7(5),10(5,R),7(4),44(6)])].
% 9.54/9.83 108 meet(zero,complement(A)) = zero. [para(93(a,1),5(a,1,2))].
% 9.54/9.83 115 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(3(a,1),28(a,1,2,2,2)),rewrite([18(3),8(2),7(5)]),flip(a)].
% 9.54/9.83 135 meet(one,join(A,B)) = join(A,B). [para(94(a,1),49(a,1,2,2)),rewrite([8(3),48(3),7(3)])].
% 9.54/9.83 136 meet(A,join(B,join(join(A,C),meet(A,D)))) = A. [para(94(a,1),26(a,1,2,2,2)),rewrite([8(4),12(5),8(4),25(4),23(2),12(2),8(1),12(2,R),8(1),5(3),8(4)]),flip(a)].
% 9.54/9.83 138 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(135(a,1),27(a,2)),rewrite([7(5),10(6,R),7(5),135(5),135(6)])].
% 9.54/9.83 139 meet(one,complement(A)) = complement(A). [para(93(a,1),135(a,1,2)),rewrite([93(6)])].
% 9.54/9.83 140 meet(A,join(complement(A),join(join(B,C),complement(A)))) = meet(A,join(B,join(C,complement(A)))). [para(135(a,1),28(a,2,2,2)),rewrite([135(6),12(9),8(8),12(9,R),8(8)])].
% 9.54/9.83 144 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(8(a,1),29(a,2,2)),rewrite([29(6),12(9),8(8),12(9,R),8(8),5(10)])].
% 9.54/9.83 152 join(one,complement(A)) = one. [para(139(a,1),6(a,1,2))].
% 9.54/9.83 153 join(complement(A),meet(B,complement(A))) = complement(A). [para(139(a,1),27(a,2)),rewrite([7(5),10(6,R),18(5),135(6)])].
% 9.54/9.83 156 meet(complement(A),join(one,meet(B,complement(A)))) = complement(A). [para(153(a,1),49(a,1,2,2,2))].
% 9.54/9.83 158 join(A,meet(B,join(A,B))) = join(A,B). [para(30(a,1),1(a,1)),rewrite([7(5),30(5),1(3)]),flip(a)].
% 9.54/9.83 161 join(A,join(B,meet(C,join(A,C)))) = join(A,join(C,B)). [para(158(a,1),12(a,2,2)),rewrite([8(3),12(6),8(5),12(6,R),8(5)])].
% 9.54/9.83 162 meet(A,B) != zero | join(A,B) != one | meet(B,join(A,B)) = complement(A). [para(158(a,1),17(b,1)),rewrite([22(3)]),flip(c)].
% 9.54/9.83 172 meet(A,meet(B,join(C,meet(D,join(A,C))))) = meet(A,meet(B,join(C,meet(A,D)))). [para(31(a,1),10(a,2,2)),rewrite([7(4),10(9,R),7(8)])].
% 9.54/9.83 178 meet(A,join(join(B,meet(A,C)),meet(D,join(A,B)))) = meet(A,join(join(B,meet(A,C)),meet(A,D))). [para(25(a,1),31(a,1,2,2,2))].
% 9.54/9.83 179 meet(A,join(join(B,join(C,complement(A))),meet(A,D))) = meet(A,join(B,join(C,join(D,complement(A))))). [para(56(a,1),31(a,1,2,2,2)),rewrite([18(5),8(4),12(4,R),8(3),12(3,R),8(2)]),flip(a)].
% 9.54/9.83 180 meet(A,join(B,join(C,join(meet(D,join(A,B)),meet(A,join(B,meet(A,D))))))) = meet(A,join(B,join(C,meet(D,join(A,B))))). [para(31(a,1),26(a,1,2,2,2)),rewrite([12(8,R),12(7),8(6),12(7,R),8(6),12(8,R),8(7),8(13),12(13,R),8(12)])].
% 9.54/9.83 183 meet(A,join(join(B,meet(C,join(A,B))),meet(A,meet(D,join(B,meet(A,C)))))) = meet(A,join(B,meet(A,C))). [para(31(a,1),27(a,2)),rewrite([7(7),172(8)])].
% 9.54/9.83 188 meet(A,join(meet(B,join(A,C)),meet(C,join(A,meet(B,C))))) = meet(A,join(meet(A,C),meet(B,join(A,C)))). [para(31(a,1),31(a,1,2,2)),rewrite([8(1),7(3),8(8),8(11)])].
% 9.54/9.83 196 meet(complement(A),join(B,complement(A))) = complement(A). [para(156(a,1),94(a,1,2,2)),rewrite([8(3),8(5),12(5,R),2(4)])].
% 9.54/9.83 207 meet(complement(A),join(A,meet(B,join(A,C)))) = meet(complement(A),join(A,meet(B,C))). [para(4(a,1),32(a,1,2,2,2,2)),rewrite([19(3)]),flip(a)].
% 9.54/9.83 218 meet(complement(A),join(B,meet(A,B))) = meet(B,complement(A)). [para(87(a,1),32(a,1,2,2)),rewrite([19(3),7(2),19(5)]),flip(a)].
% 9.54/9.83 219 meet(meet(A,B),join(C,meet(A,C))) = meet(A,meet(B,C)). [para(27(a,1),32(a,1,2,2)),rewrite([7(2),8(6),6(8),7(6),10(6),7(5),10(6,R),7(5)])].
% 9.54/9.83 290 meet(zero,join(A,B)) = zero. [para(108(a,1),136(a,1,2,2,2)),rewrite([8(3),19(3),19(3)])].
% 9.54/9.83 383 join(join(A,B),meet(A,C)) = join(A,B). [para(94(a,1),138(a,1,2)),rewrite([8(4),25(4),23(2)]),flip(a)].
% 9.54/9.83 395 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),383(a,1,1)),rewrite([8(4)])].
% 9.54/9.83 428 meet(A,join(join(A,B),complement(C))) = A. [para(196(a,1),144(a,1,2,2))].
% 9.54/9.83 435 meet(A,meet(B,join(join(A,C),complement(D)))) = meet(A,B). [para(428(a,1),10(a,2,2)),rewrite([7(4),7(6)])].
% 9.54/9.83 437 meet(A,join(B,join(join(A,C),complement(D)))) = A. [para(428(a,1),26(a,1,2,2,2)),rewrite([8(4),12(5),8(4),12(5,R),8(4),5(6),8(4)]),flip(a)].
% 9.54/9.83 803 meet(zero,meet(complement(A),join(B,complement(C)))) = zero. [para(108(a,1),435(a,2)),rewrite([8(4),19(4)])].
% 9.54/9.83 842 meet(zero,meet(complement(A),complement(B))) = zero. [para(2(a,1),803(a,1,2,2))].
% 9.54/9.83 847 join(zero,meet(complement(A),complement(B))) = meet(one,meet(complement(A),complement(B))). [para(842(a,1),218(a,1,2,2)),rewrite([51(2),8(6),135(7),51(10),7(10)])].
% 9.54/9.83 1242 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(5(a,1),76(a,1,2,2,1)),rewrite([12(5,R),8(4),5(6)]),flip(a)].
% 9.54/9.83 1319 meet(A,join(join(B,meet(C,join(meet(join(C,D),join(C,E)),meet(A,B)))),meet(F,join(B,join(V6,meet(C,join(meet(join(C,D),join(C,E)),meet(A,B)))))))) = meet(A,join(join(B,meet(C,join(meet(join(C,D),join(C,E)),meet(A,B)))),meet(F,join(V6,meet(A,join(B,C)))))). [para(1242(a,1),34(a,1,2,2,2,2,2,2)),flip(a)].
% 9.54/9.83 1387 meet(A,join(join(B,C),meet(D,join(B,join(C,join(E,meet(A,B))))))) = meet(A,join(join(B,C),meet(D,join(B,join(C,E))))). [para(86(a,1),34(a,2,2,2,2,2,2)),rewrite([7(2),383(7),7(4),383(7),14(7),8(3),12(3),8(2),12(3,R),8(2),7(8),383(13),7(9),12(11,R),12(10),8(9),12(10,R),8(9),12(11,R),8(10),12(10,R),8(9)]),flip(a)].
% 9.54/9.83 1392 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(86(a,1),144(a,1,2,2)),rewrite([8(3),8(5),12(5,R),2(4)])].
% 9.54/9.83 1438 meet(A,join(join(B,meet(C,meet(D,E))),meet(E,join(meet(C,D),meet(A,join(B,meet(C,D))))))) = meet(A,join(B,join(meet(C,meet(D,E)),meet(E,join(B,meet(C,D)))))). [para(10(a,2),80(a,1,2,1,2)),rewrite([10(13),7(12),10(13,R),7(12)])].
% 9.54/9.83 1564 meet(meet(A,B),join(A,C)) = meet(A,B). [para(383(a,1),1392(a,1,2))].
% 9.54/9.83 1565 meet(A,join(join(A,B),meet(C,D))) = A. [para(1392(a,1),144(a,1,2,2))].
% 9.54/9.83 1599 meet(A,B) != zero | one != A | complement(meet(A,B)) = A. [para(1564(a,1),59(a,1)),rewrite([8(5),6(5),7(7),10(7),7(6),10(7,R),7(6),6(8)]),flip(b),flip(c)].
% 9.54/9.83 1845 meet(A,B) != zero | one != B | complement(meet(A,B)) = B. [para(7(a,1),1599(a,1)),rewrite([7(6)])].
% 9.54/9.83 1867 meet(A,join(meet(B,join(C,meet(A,meet(C,D)))),meet(E,join(F,meet(B,join(C,meet(A,meet(C,D)))))))) = meet(A,join(meet(B,join(C,meet(A,meet(C,D)))),meet(E,join(F,meet(A,meet(B,C)))))). [para(95(a,1),14(a,1,2,2,2,2)),rewrite([7(5),8(19)]),flip(a)].
% 9.54/9.83 1973 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(4(a,1),96(a,1,2,2,2,2)),rewrite([40(3),40(3),8(3)])].
% 9.54/9.83 1983 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(96(a,1),135(a,1)),rewrite([10(3),7(2),18(2),7(1),10(6,R),7(5),10(5),7(4),18(4),7(3)]),flip(a)].
% 9.54/9.83 2025 join(zero,meet(A,B)) = meet(A,B). [para(1973(a,1),1(a,1)),rewrite([7(5),1973(5),1(3)]),flip(a)].
% 9.54/9.83 2050 meet(one,meet(complement(A),complement(B))) = meet(complement(A),complement(B)). [back_rewrite(847),rewrite([2025(5)]),flip(a)].
% 9.54/9.83 2309 meet(A,join(meet(A,meet(B,C)),meet(B,join(A,D)))) = meet(A,B). [para(8(a,1),100(a,1,2))].
% 9.54/9.83 2409 meet(A,join(meet(B,complement(A)),meet(B,join(complement(A),complement(B))))) = zero. [para(115(a,1),55(a,1,2,2)),rewrite([4(12),8(12),2025(12),42(11)])].
% 9.54/9.83 2620 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(219(a,1),28(a,2)),rewrite([2(8),153(7),4(4)]),flip(a)].
% 9.54/9.83 2623 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(153(a,1),219(a,1,2))].
% 9.54/9.83 2634 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(138(a,1),219(a,1,2))].
% 9.54/9.83 2657 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(219(a,1),1565(a,1)),rewrite([8(2)])].
% 9.54/9.83 2798 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(2620(a,1),10(a,2,2)),rewrite([7(4),10(4,R),7(3),40(7)])].
% 9.54/9.83 2825 meet(A,meet(B,meet(C,complement(meet(A,C))))) = zero. [para(2798(a,1),7(a,1)),rewrite([7(2),7(6),10(6,R),7(5),10(5,R),7(4)]),flip(a)].
% 9.54/9.83 2941 meet(A,meet(join(A,B),complement(C))) = meet(A,complement(C)). [para(5(a,1),2623(a,1,1)),flip(a)].
% 9.54/9.83 3164 meet(A,complement(join(A,B))) = zero. [para(4(a,1),2941(a,1,2)),rewrite([40(2)]),flip(a)].
% 9.54/9.83 3184 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(2941(a,1),2825(a,1,2))].
% 9.54/9.83 3192 meet(complement(A),complement(join(B,complement(A)))) = zero. [para(3164(a,1),2050(a,1,2)),rewrite([40(3),8(4)]),flip(a)].
% 9.54/9.83 3193 meet(A,join(complement(A),complement(join(A,B)))) = zero. [para(3164(a,1),115(a,1,2,2)),rewrite([19(3),4(2),8(5)]),flip(a)].
% 9.54/9.83 3194 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(3164(a,1),2623(a,1)),rewrite([8(3)]),flip(a)].
% 9.54/9.83 3271 meet(complement(A),join(complement(complement(A)),complement(join(B,complement(A))))) = zero. [para(3192(a,1),115(a,1,2,2)),rewrite([19(5),4(4),8(8)]),flip(a)].
% 9.54/9.83 3284 meet(A,meet(B,complement(meet(B,join(A,C))))) = zero. [para(3184(a,1),10(a,2)),rewrite([7(4)])].
% 9.54/9.83 3422 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(3284(a,1),2941(a,1)),flip(a)].
% 9.54/9.83 3450 meet(A,join(B,join(join(C,complement(B)),complement(A)))) = A. [para(50(a,1),140(a,1,2,2,1)),rewrite([152(4),48(3),18(2)]),flip(a)].
% 9.54/9.83 3673 join(A,join(join(B,complement(A)),complement(C))) = one. [para(3450(a,1),138(a,1,2)),rewrite([8(6),56(6)]),flip(a)].
% 9.54/9.83 3681 join(A,join(complement(A),complement(B))) = one. [hyper(1845,a,437,a,b,3673,a(flip)),rewrite([93(4),290(6),51(2),93(4)]),flip(a)].
% 9.54/9.83 3695 join(complement(A),complement(join(A,B))) = complement(A). [hyper(17,a,3193,a,b,3681,a),flip(a)].
% 9.54/9.83 3714 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(3695(a,1),196(a,1,2)),rewrite([7(4)])].
% 9.54/9.83 3762 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(3714(a,1),3194(a,1,2))].
% 9.54/9.83 3813 meet(A,join(complement(A),complement(join(B,meet(A,complement(B)))))) = zero. [para(3762(a,1),115(a,1,2,2)),rewrite([19(3),4(2),8(7)]),flip(a)].
% 9.54/9.83 4513 join(complement(complement(A)),complement(join(B,complement(A)))) = complement(complement(A)). [hyper(162,a,3271,a,b,3681,a),rewrite([3681(14),7(8),135(8)])].
% 9.54/9.83 4527 join(complement(complement(A)),meet(B,complement(join(C,complement(A))))) = complement(complement(A)). [para(4513(a,1),395(a,1,1)),rewrite([7(6),4513(13)])].
% 9.54/9.83 5263 meet(A,join(B,join(meet(A,C),meet(D,join(A,B))))) = meet(A,join(join(B,meet(A,C)),meet(A,D))). [para(8(a,1),178(a,1,2)),rewrite([12(5,R)])].
% 9.54/9.83 5264 meet(A,join(join(B,meet(A,C)),meet(A,D))) = meet(A,join(B,join(meet(A,C),meet(A,D)))). [para(8(a,1),178(a,2,2)),rewrite([178(6),12(9,R)])].
% 9.54/9.83 5413 meet(A,join(B,join(meet(A,C),meet(D,join(A,B))))) = meet(A,join(B,join(meet(A,C),meet(A,D)))). [back_rewrite(5263),rewrite([5264(11)])].
% 9.54/9.83 5557 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(139(a,1),179(a,1,2,2)),rewrite([43(3),19(3),135(5),43(7),19(7),135(8)])].
% 9.54/9.83 6401 meet(A,join(B,join(meet(A,C),meet(A,join(B,C))))) = meet(A,join(B,meet(A,join(B,C)))). [para(31(a,1),183(a,1,2,2,2)),rewrite([8(1),7(5),2657(8),8(6),12(6,R),8(5),5413(7),8(7)])].
% 9.54/9.83 7087 join(A,join(B,complement(join(A,B)))) = one. [para(5557(a,1),3(a,1))].
% 9.54/9.83 7212 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(20(a,1),188(a,1,2,2,2,2)),rewrite([2634(7),2657(7),8(5),31(6),2309(11)])].
% 9.54/9.83 7534 join(A,join(meet(B,join(A,C)),meet(complement(A),join(A,meet(B,C))))) = join(A,meet(B,join(A,C))). [para(207(a,1),138(a,1,2)),rewrite([8(8),12(8),8(7),12(8,R),8(7)])].
% 9.54/9.83 8424 meet(A,join(meet(B,C),meet(B,A))) = meet(B,A). [para(7212(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 9.54/9.83 8425 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(7(a,1),7212(a,1,2,1))].
% 9.54/9.83 8784 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(5(a,1),8425(a,1,2,1))].
% 9.54/9.83 8785 meet(A,join(meet(B,C),meet(C,A))) = meet(C,A). [para(8425(a,1),7(a,2)),rewrite([7(2),7(4),7(5)])].
% 9.54/9.83 8797 meet(A,join(meet(B,C),meet(A,join(C,meet(B,meet(C,D)))))) = meet(A,join(C,meet(B,meet(C,D)))). [para(27(a,1),8425(a,1,2,1))].
% 9.54/9.83 8827 meet(A,join(meet(B,C),join(meet(A,meet(C,D)),meet(D,join(meet(B,C),meet(A,C)))))) = meet(A,join(meet(A,meet(C,D)),join(meet(B,C),meet(A,meet(C,D))))). [para(8425(a,1),80(a,1,2,2,2,2)),rewrite([10(3),7(2),10(3,R),7(2),2(7),10(6),7(5),10(6,R),7(5),8(7),10(11),7(10),10(11,R),7(10)]),flip(a)].
% 9.54/9.83 8852 meet(A,join(meet(B,C),meet(A,meet(C,join(D,meet(B,C)))))) = meet(A,meet(C,join(D,meet(B,C)))). [para(2657(a,1),8425(a,1,2,1))].
% 9.54/9.83 8935 meet(A,join(B,join(meet(A,C),meet(A,join(B,C))))) = meet(A,join(B,C)). [back_rewrite(6401),rewrite([8784(10)])].
% 9.54/9.83 9243 join(A,meet(B,A)) = A. [para(18(a,1),8785(a,1,2,2)),rewrite([8(3),135(4),18(4)])].
% 9.54/9.83 9320 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(22(a,1),9243(a,1,2)),rewrite([7(3),8(4)])].
% 9.54/9.83 9325 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(2657(a,1),9243(a,1,2)),rewrite([7(1),7(4),8(5),7(6)])].
% 9.54/9.83 9330 meet(A,join(B,join(meet(A,C),meet(A,join(meet(A,C),meet(A,D)))))) = meet(A,join(B,join(meet(A,D),meet(A,C)))). [para(9243(a,1),180(a,1,2,2,2,1,2)),rewrite([7(1),7(2),7(3),9325(7),12(7,R),8(6),7(9),7(10),6(11),7(10),12(12,R)])].
% 9.54/9.83 9369 meet(A,meet(B,join(complement(A),complement(B)))) = zero. [back_rewrite(2409),rewrite([9320(7)])].
% 9.54/9.83 9930 join(complement(A),complement(join(B,meet(A,complement(B))))) = complement(A). [hyper(162,a,3813,a,b,3681,a),rewrite([3681(13),7(8),135(8)])].
% 9.54/9.83 10086 join(A,join(complement(B),meet(B,complement(A)))) = one. [para(9930(a,1),50(a,1,2)),rewrite([8(5),12(5,R),8(4)])].
% 9.54/9.83 10109 join(complement(complement(A)),complement(complement(join(B,meet(A,complement(B)))))) = complement(complement(join(B,meet(A,complement(B))))). [para(9930(a,1),4513(a,1,2,1)),rewrite([8(8)])].
% 9.54/9.83 10138 join(complement(A),meet(A,complement(complement(A)))) = one. [para(10086(a,1),23(a,1)),flip(a)].
% 9.54/9.83 10164 meet(A,complement(complement(A))) = complement(complement(A)). [hyper(162,a,42,a,b,10138,a),rewrite([10138(8),7(5),10(5,R),18(4)])].
% 9.54/9.83 10173 join(A,complement(complement(A))) = A. [para(10164(a,1),6(a,1,2))].
% 9.54/9.83 10320 complement(complement(A)) = A. [para(10173(a,1),57(a,1,2)),rewrite([7(2),4(2),10173(6)]),flip(b),xx(a)].
% 9.54/9.83 10338 join(A,meet(B,complement(A))) = join(B,A). [back_rewrite(10109),rewrite([10320(2),10320(5),25(4),10320(6)]),flip(a)].
% 9.54/9.83 10592 join(A,meet(B,complement(join(C,complement(A))))) = A. [back_rewrite(4527),rewrite([10320(2),10320(7)])].
% 9.54/9.83 10663 meet(A,meet(complement(B),join(B,complement(A)))) = zero. [para(10320(a,1),9369(a,1,2,2,1)),rewrite([10(5,R),7(4)])].
% 9.54/9.83 10707 join(A,join(B,meet(C,complement(A)))) = join(A,join(C,B)). [para(10338(a,1),12(a,2,2)),rewrite([8(3),8(5),12(6),8(5),12(6,R),8(5)])].
% 9.54/9.83 10709 join(A,meet(B,meet(complement(A),join(A,B)))) = join(A,B). [para(10338(a,1),158(a,1,2,2)),rewrite([8(3),2634(4),10338(8),8(6)])].
% 9.54/9.83 10718 join(A,join(B,meet(C,meet(complement(A),join(A,C))))) = join(A,join(B,C)). [para(10338(a,1),161(a,1,2,2,2)),rewrite([8(3),2634(4),8(9),10707(10),8(7)])].
% 9.54/9.83 10722 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(3422(a,1),10338(a,1,2)),rewrite([8(5),2025(5)]),flip(a)].
% 9.54/9.83 10753 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(10320(a,1),10338(a,1,2,2)),rewrite([7(2)])].
% 9.54/9.83 11042 meet(complement(A),meet(complement(B),join(A,B))) = zero. [para(10320(a,1),10663(a,1,2,2,2)),rewrite([8(3)])].
% 9.54/9.83 11145 join(complement(A),meet(B,A)) = join(B,complement(A)). [para(10753(a,1),8(a,1)),rewrite([7(3),8(5)]),flip(a)].
% 9.54/9.83 11233 join(A,meet(complement(A),join(A,meet(B,C)))) = join(A,meet(B,join(A,C))). [para(207(a,1),10753(a,1,2)),rewrite([10320(2),10320(10),8(9),23(9)])].
% 9.54/9.83 11262 join(complement(A),complement(join(B,A))) = complement(A). [para(10753(a,1),10592(a,1)),rewrite([10320(2),8(4)])].
% 9.54/9.83 11619 join(A,meet(complement(B),join(A,B))) = A. [para(11042(a,1),10753(a,1,2)),rewrite([10320(2),19(2),10320(5),8(4)]),flip(a)].
% 9.54/9.83 11624 join(A,meet(complement(B),join(B,A))) = A. [para(11619(a,1),8(a,2)),rewrite([8(2),8(4)])].
% 9.54/9.83 11640 meet(A,meet(complement(B),join(B,A))) = meet(complement(B),join(B,A)). [para(11619(a,1),2657(a,1,2,2)),rewrite([8(2),7(3),10(4,R),7(3),8(6)])].
% 9.54/9.83 11685 join(A,join(B,meet(complement(A),join(A,C)))) = join(A,join(B,C)). [back_rewrite(10718),rewrite([11640(4)])].
% 9.54/9.83 11686 join(A,meet(complement(A),join(A,B))) = join(A,B). [back_rewrite(10709),rewrite([11640(4)])].
% 9.54/9.83 11765 join(A,join(meet(B,C),meet(B,join(A,C)))) = join(A,meet(B,join(A,C))). [back_rewrite(7534),rewrite([11685(8),8(4)])].
% 9.54/9.83 11766 join(A,meet(B,join(A,C))) = join(A,meet(B,C)). [back_rewrite(11233),rewrite([11686(5)]),flip(a)].
% 9.54/9.83 11796 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(8935),rewrite([11765(5),11766(3)])].
% 9.54/9.83 11935 meet(join(A,B),join(A,C)) = join(A,meet(B,C)). [back_rewrite(10722),rewrite([11766(4),7(2),11766(3),7(1)]),flip(a)].
% 9.54/9.83 12124 meet(A,join(B,join(meet(A,C),meet(A,D)))) = meet(A,join(B,join(D,C))). [back_rewrite(9330),rewrite([11796(5),8(3),11796(4),8(2),9320(4),11796(4)]),flip(a)].
% 9.54/9.83 13053 meet(A,join(B,meet(C,join(D,meet(A,B))))) = meet(A,join(B,meet(C,D))). [back_rewrite(14),rewrite([11766(8)])].
% 9.54/9.83 13191 meet(A,join(meet(B,C),meet(C,join(D,meet(B,C))))) = meet(A,meet(C,join(D,meet(B,C)))). [back_rewrite(8852),rewrite([11796(7)])].
% 9.54/9.83 13204 meet(A,join(B,meet(C,meet(B,D)))) = meet(A,B). [back_rewrite(8797),rewrite([11796(7),12(5,R),8(4),1983(4),9243(2)]),flip(a)].
% 9.54/9.83 13567 meet(A,join(B,join(C,meet(A,D)))) = meet(A,join(B,join(D,C))). [back_rewrite(5264),rewrite([11796(5),8(3),12(3,R),8(2),12124(9),8(5)])].
% 9.54/9.83 13814 meet(A,join(join(B,C),meet(D,join(B,join(C,E))))) = meet(A,join(join(B,C),meet(D,E))). [back_rewrite(1319),rewrite([11935(3),1565(5),11935(4),1565(6),8(2),11935(9),1565(11),13053(13)])].
% 9.54/9.83 13990 meet(A,join(meet(B,C),meet(D,join(E,meet(B,C))))) = meet(A,join(meet(B,C),meet(D,E))). [back_rewrite(1867),rewrite([13204(4),13204(5),13204(10),13053(13)])].
% 9.54/9.83 14041 meet(A,join(meet(B,C),join(meet(A,meet(C,D)),meet(D,join(meet(B,C),meet(A,C)))))) = meet(A,join(meet(C,D),meet(B,C))). [back_rewrite(8827),rewrite([13567(18),12(16,R),26(17)])].
% 9.54/9.83 14225 meet(A,join(join(B,C),meet(D,join(E,meet(A,B))))) = meet(A,join(join(B,C),meet(D,E))). [back_rewrite(1387),rewrite([13814(8),13814(12)])].
% 9.54/9.83 14301 meet(A,join(meet(B,C),meet(C,D))) = meet(A,meet(C,join(D,meet(B,C)))). [back_rewrite(13191),rewrite([13990(6)])].
% 9.54/9.83 14517 meet(A,join(B,join(meet(C,meet(D,E)),meet(E,join(B,meet(C,D)))))) = meet(A,join(B,meet(C,meet(D,E)))). [back_rewrite(1438),rewrite([13990(9),14225(9),10(5),7(4),10(5,R),7(4),8(6),12(6,R),2(5)]),flip(a)].
% 9.54/9.83 14908 meet(A,join(meet(B,C),meet(D,B))) = meet(A,meet(B,join(C,meet(D,B)))). [back_rewrite(14041),rewrite([14517(10),11796(5),14301(4)]),flip(a)].
% 9.54/9.83 15155 join(A,complement(join(A,B))) = join(A,complement(B)). [para(7087(a,1),11624(a,1,2,2)),rewrite([8(1),18(6),8(5),12(5,R),8(4),11262(4),8(3)]),flip(a)].
% 9.54/9.83 15165 meet(A,join(B,complement(A))) = meet(A,B). [para(10753(a,1),11624(a,1,2,2)),rewrite([10320(3),9320(5)])].
% 9.54/9.83 15264 meet(complement(A),join(A,complement(B))) = complement(join(A,B)). [para(3714(a,1),15165(a,2)),rewrite([10320(5),8(4),15155(4)])].
% 9.54/9.83 15270 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(10320(a,1),15165(a,1,2,2)),rewrite([8(2),7(5)])].
% 9.54/9.83 15563 complement(join(A,B)) = meet(complement(A),complement(B)). [back_rewrite(15264),rewrite([15270(4),7(3)]),flip(a)].
% 9.54/9.83 17551 join(meet(A,B),meet(B,complement(A))) = B. [para(15165(a,1),11145(a,1,2)),rewrite([15563(3),10320(3),7(2),7(3),8(4),15563(7),10320(7),7(6),6(7)])].
% 9.54/9.83 17552 join(meet(A,B),meet(A,complement(B))) = A. [para(7(a,1),17551(a,1,1))].
% 9.54/9.83 17572 join(meet(A,B),meet(complement(B),join(meet(A,C),meet(A,B)))) = join(meet(A,C),meet(A,B)). [para(8424(a,1),17551(a,1,1)),rewrite([7(6)])].
% 9.54/9.83 18154 meet(A,join(meet(B,C),meet(B,D))) = meet(A,meet(B,join(C,D))). [back_rewrite(14908),rewrite([7(2),7(5),11796(7)])].
% 9.54/9.83 18243 join(meet(A,B),meet(A,meet(C,complement(B)))) = join(meet(A,C),meet(A,B)). [back_rewrite(17572),rewrite([18154(6),8(3),10(5,R),7(4),15270(4)])].
% 9.54/9.83 21310 join(meet(A,B),meet(A,C)) = meet(A,join(C,B)). [para(17552(a,1),11935(a,1,1)),rewrite([8(2),11796(3),8(1),7(6),10(6,R),7(5),18243(7)]),flip(a)].
% 9.54/9.83 21434 $F # answer(prove_distributivity). [back_rewrite(16),rewrite([21310(7),8(4)]),xx(a)].
% 9.54/9.83
% 9.54/9.83 % SZS output end Refutation
% 9.54/9.83 ============================== end of proof ==========================
% 9.54/9.83
% 9.54/9.83 ============================== STATISTICS ============================
% 9.54/9.83
% 9.54/9.83 Given=471. Generated=133461. Kept=21429. proofs=1.
% 9.54/9.83 Usable=156. Sos=2665. Demods=2506. Limbo=124, Disabled=18497. Hints=0.
% 9.54/9.83 Megabytes=31.22.
% 9.54/9.83 User_CPU=8.78, System_CPU=0.09, Wall_clock=9.
% 9.54/9.83
% 9.54/9.83 ============================== end of statistics =====================
% 9.54/9.83
% 9.54/9.83 ============================== end of search =========================
% 9.54/9.83
% 9.54/9.83 THEOREM PROVED
% 9.54/9.83 % SZS status Unsatisfiable
% 9.54/9.83
% 9.54/9.83 Exiting with 1 proof.
% 9.54/9.83
% 9.54/9.83 Process 6566 exit (max_proofs) Thu Jun 30 13:08:58 2022
% 9.54/9.84 Prover9 interrupted
%------------------------------------------------------------------------------