TSTP Solution File: LAT210-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT210-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 06:26:09 EDT 2022
% Result : Unsatisfiable 11.29s 11.59s
% Output : Refutation 11.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT210-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Tue Jun 28 18:53:46 EDT 2022
% 0.14/0.33 % CPUTime :
% 11.17/11.47 ============================== Prover9 ===============================
% 11.17/11.47 Prover9 (32) version 2009-11A, November 2009.
% 11.17/11.47 Process 396 was started by sandbox on n020.cluster.edu,
% 11.17/11.47 Tue Jun 28 18:53:47 2022
% 11.17/11.47 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32595_n020.cluster.edu".
% 11.17/11.47 ============================== end of head ===========================
% 11.17/11.47
% 11.17/11.47 ============================== INPUT =================================
% 11.17/11.47
% 11.17/11.47 % Reading from file /tmp/Prover9_32595_n020.cluster.edu
% 11.17/11.47
% 11.17/11.47 set(prolog_style_variables).
% 11.17/11.47 set(auto2).
% 11.17/11.47 % set(auto2) -> set(auto).
% 11.17/11.47 % set(auto) -> set(auto_inference).
% 11.17/11.47 % set(auto) -> set(auto_setup).
% 11.17/11.47 % set(auto_setup) -> set(predicate_elim).
% 11.17/11.47 % set(auto_setup) -> assign(eq_defs, unfold).
% 11.17/11.47 % set(auto) -> set(auto_limits).
% 11.17/11.47 % set(auto_limits) -> assign(max_weight, "100.000").
% 11.17/11.47 % set(auto_limits) -> assign(sos_limit, 20000).
% 11.17/11.47 % set(auto) -> set(auto_denials).
% 11.17/11.47 % set(auto) -> set(auto_process).
% 11.17/11.47 % set(auto2) -> assign(new_constants, 1).
% 11.17/11.47 % set(auto2) -> assign(fold_denial_max, 3).
% 11.17/11.47 % set(auto2) -> assign(max_weight, "200.000").
% 11.17/11.47 % set(auto2) -> assign(max_hours, 1).
% 11.17/11.47 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 11.17/11.47 % set(auto2) -> assign(max_seconds, 0).
% 11.17/11.47 % set(auto2) -> assign(max_minutes, 5).
% 11.17/11.47 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 11.17/11.47 % set(auto2) -> set(sort_initial_sos).
% 11.17/11.47 % set(auto2) -> assign(sos_limit, -1).
% 11.17/11.47 % set(auto2) -> assign(lrs_ticks, 3000).
% 11.17/11.47 % set(auto2) -> assign(max_megs, 400).
% 11.17/11.47 % set(auto2) -> assign(stats, some).
% 11.17/11.47 % set(auto2) -> clear(echo_input).
% 11.17/11.47 % set(auto2) -> set(quiet).
% 11.17/11.47 % set(auto2) -> clear(print_initial_clauses).
% 11.17/11.47 % set(auto2) -> clear(print_given).
% 11.17/11.47 assign(lrs_ticks,-1).
% 11.17/11.47 assign(sos_limit,10000).
% 11.17/11.47 assign(order,kbo).
% 11.17/11.47 set(lex_order_vars).
% 11.17/11.47 clear(print_given).
% 11.17/11.47
% 11.17/11.47 % formulas(sos). % not echoed (13 formulas)
% 11.17/11.47
% 11.17/11.47 ============================== end of input ==========================
% 11.17/11.47
% 11.17/11.47 % From the command line: assign(max_seconds, 300).
% 11.17/11.47
% 11.17/11.47 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 11.17/11.47
% 11.17/11.47 % Formulas that are not ordinary clauses:
% 11.17/11.47
% 11.17/11.47 ============================== end of process non-clausal formulas ===
% 11.17/11.47
% 11.17/11.47 ============================== PROCESS INITIAL CLAUSES ===============
% 11.17/11.47
% 11.17/11.47 ============================== PREDICATE ELIMINATION =================
% 11.17/11.47
% 11.17/11.47 ============================== end predicate elimination =============
% 11.17/11.47
% 11.17/11.47 Auto_denials:
% 11.17/11.47 % copying label prove_distributivity to answer in negative clause
% 11.17/11.47
% 11.17/11.47 Term ordering decisions:
% 11.17/11.47
% 11.17/11.47 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 11.17/11.47 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 11.17/11.47
% 11.17/11.47 ============================== end of process initial clauses ========
% 11.17/11.47
% 11.17/11.47 ============================== CLAUSES FOR SEARCH ====================
% 11.17/11.47
% 11.17/11.47 ============================== end of clauses for search =============
% 11.17/11.47
% 11.17/11.47 ============================== SEARCH ================================
% 11.17/11.47
% 11.17/11.47 % Starting search at 0.01 seconds.
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=135.000, iters=3395
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=125.000, iters=3370
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=115.000, iters=3340
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=113.000, iters=3333
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=107.000, iters=3455
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=97.000, iters=3394
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=95.000, iters=3378
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=93.000, iters=3358
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=91.000, iters=3341
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=85.000, iters=3355
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=81.000, iters=3333
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=77.000, iters=3372
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=75.000, iters=3371
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=74.000, iters=3361
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=72.000, iters=3405
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=70.000, iters=3350
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=68.000, iters=3402
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=67.000, iters=3395
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=63.000, iters=3391
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=62.000, iters=3380
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=59.000, iters=3358
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=57.000, iters=3338
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=55.000, iters=3398
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=54.000, iters=3373
% 11.17/11.47
% 11.17/11.47 Low Water (keep): wt=52.000, iters=3352
% 11.17/11.47
% 11.17/11.47 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 10.38 sec).
% 11.29/11.59
% 11.29/11.59 ============================== PROOF =================================
% 11.29/11.59 % SZS status Unsatisfiable
% 11.29/11.59 % SZS output start Refutation
% 11.29/11.59
% 11.29/11.59 % Proof 1 at 10.49 (+ 0.10) seconds: prove_distributivity.
% 11.29/11.59 % Length of proof is 206.
% 11.29/11.59 % Level of proof is 56.
% 11.29/11.59 % Maximum clause weight is 67.000.
% 11.29/11.59 % Given clauses 510.
% 11.29/11.59
% 11.29/11.59 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 11.29/11.59 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 11.29/11.59 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 11.29/11.59 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 11.29/11.59 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 11.29/11.59 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 11.29/11.59 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 11.29/11.59 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 11.29/11.59 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 11.29/11.59 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 11.29/11.59 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 11.29/11.59 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 11.29/11.59 13 meet(A,join(B,C)) = meet(A,join(B,meet(A,join(C,meet(A,B))))) # label(equation_H68) # label(axiom). [assumption].
% 11.29/11.59 14 meet(A,join(B,meet(A,join(C,meet(A,B))))) = meet(A,join(B,C)). [copy(13),flip(a)].
% 11.29/11.59 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 11.29/11.59 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 11.29/11.59 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 11.29/11.59 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 11.29/11.59 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 11.29/11.59 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)])].
% 11.29/11.59 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 11.29/11.59 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 11.29/11.59 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)])].
% 11.29/11.59 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 11.29/11.59 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 11.29/11.59 26 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(4(a,1),14(a,1,2,2,2,2)),rewrite([19(3),8(6)])].
% 11.29/11.59 27 meet(A,join(B,meet(A,join(C,meet(B,A))))) = meet(A,join(B,C)). [para(14(a,1),7(a,2)),rewrite([7(1),7(5)])].
% 11.29/11.59 28 meet(A,meet(B,join(C,meet(A,join(D,meet(A,C)))))) = meet(A,meet(B,join(C,D))). [para(14(a,1),10(a,2,2)),rewrite([7(5),10(9,R),7(8)])].
% 11.29/11.59 29 meet(A,join(join(B,meet(A,join(C,meet(A,B)))),meet(A,join(D,meet(A,join(B,C)))))) = meet(A,join(B,join(D,meet(A,join(C,meet(A,B)))))). [para(14(a,1),14(a,1,2,2,2,2)),rewrite([8(15),12(15,R),8(14)])].
% 11.29/11.59 35 meet(A,zero) != zero | one != A | complement(A) = zero. [para(19(a,1),17(b,1)),flip(b)].
% 11.29/11.59 37 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 11.29/11.59 39 one != A | complement(A) = zero. [back_rewrite(35),rewrite([37(2)]),xx(a)].
% 11.29/11.59 40 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([37(5)])].
% 11.29/11.59 41 complement(one) = zero. [hyper(17,a,37,a,b,19,a)].
% 11.29/11.59 42 meet(A,join(zero,meet(A,B))) = meet(A,B). [para(37(a,1),14(a,1,2,2,2,2)),rewrite([19(3),8(6),19(6)])].
% 11.29/11.59 44 meet(A,join(meet(B,join(A,C)),meet(A,join(D,meet(A,B))))) = meet(A,join(D,meet(B,join(A,C)))). [para(22(a,1),14(a,1,2,2,2,2)),rewrite([8(10)])].
% 11.29/11.59 45 complement(join(A,one)) = zero. [hyper(39,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 11.29/11.59 46 join(A,one) = one. [para(45(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 11.29/11.59 47 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([46(5)])].
% 11.29/11.59 51 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(40(a,1),10(a,2,2)),rewrite([7(3),10(3,R),7(2),37(6)])].
% 11.29/11.59 52 meet(A,join(meet(B,complement(A)),meet(A,C))) = meet(A,join(C,meet(B,complement(A)))). [para(40(a,1),14(a,1,2,2,2,2)),rewrite([19(4),8(8)])].
% 11.29/11.59 54 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(47(a,1),17(b,1)),flip(c),xx(b)].
% 11.29/11.59 56 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)].
% 11.29/11.59 58 meet(A,join(meet(B,meet(C,complement(A))),meet(A,D))) = meet(A,join(D,meet(B,meet(C,complement(A))))). [para(51(a,1),14(a,1,2,2,2,2)),rewrite([19(5),8(10)])].
% 11.29/11.59 61 meet(A,meet(B,join(zero,meet(A,C)))) = meet(A,meet(C,B)). [para(42(a,1),10(a,2,2)),rewrite([7(4),10(7),7(6),10(7,R),7(6)])].
% 11.29/11.59 62 meet(A,join(join(zero,meet(A,B)),meet(A,join(C,meet(A,B))))) = meet(A,join(C,join(zero,meet(A,B)))). [para(42(a,1),14(a,1,2,2,2,2)),rewrite([8(12)])].
% 11.29/11.59 63 meet(A,join(B,meet(A,B))) = meet(A,B). [para(42(a,1),14(a,1,2,2)),rewrite([19(5)])].
% 11.29/11.59 67 meet(A,join(B,join(complement(A),meet(A,join(C,meet(A,B)))))) = meet(A,join(join(B,C),complement(A))). [para(14(a,1),26(a,1,2,2)),rewrite([26(5),8(10),12(10,R),8(9)]),flip(a)].
% 11.29/11.59 69 meet(A,join(zero,complement(A))) = zero. [para(37(a,1),26(a,1,2,2)),rewrite([19(3),4(2)]),flip(a)].
% 11.29/11.59 71 meet(A,join(complement(A),meet(B,join(A,C)))) = meet(A,join(B,complement(A))). [para(22(a,1),26(a,1,2,2)),rewrite([26(4),8(7)]),flip(a)].
% 11.29/11.59 77 join(zero,complement(A)) = complement(A). [hyper(17,a,69,a,b,47,a),flip(a)].
% 11.29/11.59 78 meet(zero,complement(A)) = zero. [para(77(a,1),5(a,1,2))].
% 11.29/11.59 80 meet(complement(A),join(A,meet(B,complement(A)))) = meet(complement(A),join(A,B)). [para(4(a,1),27(a,1,2,2,2,2)),rewrite([19(4),7(3)])].
% 11.29/11.59 82 meet(meet(A,B),join(C,meet(meet(A,B),join(D,meet(A,meet(B,C)))))) = meet(meet(A,B),join(C,D)). [para(10(a,1),27(a,1,2,2,2,2)),rewrite([7(3),10(4,R),7(3)])].
% 11.29/11.59 83 meet(join(A,meet(B,join(C,meet(A,B)))),join(B,meet(join(A,meet(B,join(C,meet(A,B)))),join(D,meet(B,join(A,C)))))) = meet(join(A,meet(B,join(C,meet(A,B)))),join(B,D)). [para(14(a,1),27(a,1,2,2,2,2)),rewrite([7(1),7(5),7(15)])].
% 11.29/11.59 85 meet(meet(A,B),join(A,meet(meet(A,B),join(C,meet(A,B))))) = meet(meet(A,B),join(A,C)). [para(20(a,1),27(a,1,2,2,2,2))].
% 11.29/11.59 93 meet(complement(A),join(zero,meet(B,complement(A)))) = meet(B,complement(A)). [para(78(a,1),27(a,1,2,2,2,2)),rewrite([19(5),7(4),8(9),19(9),7(8)])].
% 11.29/11.59 100 meet(A,join(B,join(meet(A,join(B,C)),meet(A,join(C,meet(A,B)))))) = meet(A,join(B,C)). [para(14(a,1),63(a,1,2,2)),rewrite([8(7),12(7,R),8(6),14(13)])].
% 11.29/11.59 101 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(22(a,1),63(a,1,2,2)),rewrite([8(4),22(8)])].
% 11.29/11.59 102 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(40(a,1),63(a,1,2,2)),rewrite([8(4),40(8)])].
% 11.29/11.59 146 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(1(a,1),29(a,1,2,2,2,2)),rewrite([7(4),5(4),8(3),1(4),23(3),12(5),8(4),12(5,R),8(4),6(7),1(3),7(5),5(5),8(4),1(5),12(4),8(3),12(4,R),8(3),23(5)]),flip(a)].
% 11.29/11.59 152 meet(A,join(B,join(meet(A,join(C,meet(A,B))),meet(A,join(D,meet(A,join(B,C))))))) = meet(A,join(D,join(B,meet(A,join(C,meet(A,B)))))). [para(8(a,1),29(a,1,2)),rewrite([12(9),8(8),12(9,R),8(8),12(15,R),8(14)])].
% 11.29/11.59 157 meet(A,join(B,join(meet(A,join(B,C)),meet(A,join(meet(A,C),meet(A,B)))))) = meet(A,join(B,join(C,meet(A,join(meet(A,C),meet(A,B)))))). [para(14(a,1),29(a,1,2,2)),rewrite([8(6),8(8),12(8,R),8(7)])].
% 11.29/11.59 166 meet(A,join(join(meet(B,meet(C,complement(A))),meet(A,D)),meet(A,join(E,meet(A,join(D,meet(B,meet(C,complement(A))))))))) = meet(A,join(E,join(meet(A,D),meet(B,meet(C,complement(A)))))). [para(51(a,1),29(a,1,2,1,2,2,2)),rewrite([19(5),8(9),51(21),19(19),12(20,R)])].
% 11.29/11.59 300 meet(one,join(A,B)) = join(A,B). [para(3(a,1),146(a,1,2,2)),rewrite([46(3),7(3)])].
% 11.29/11.59 304 meet(complement(A),join(B,complement(A))) = complement(A). [para(77(a,1),146(a,1,1)),rewrite([8(4),12(5,R),19(4),77(7)])].
% 11.29/11.59 310 meet(one,complement(A)) = complement(A). [para(77(a,1),300(a,1,2)),rewrite([77(6)])].
% 11.29/11.59 389 meet(A,join(zero,meet(B,join(A,C)))) = meet(A,B). [para(42(a,1),44(a,1,2,2)),rewrite([8(4),101(5)]),flip(a)].
% 11.29/11.59 462 meet(complement(A),join(zero,meet(A,join(B,complement(A))))) = zero. [para(26(a,1),389(a,1,2,2)),rewrite([7(9),4(9)])].
% 11.29/11.59 473 meet(complement(A),join(complement(complement(A)),join(zero,meet(A,join(B,complement(A)))))) = zero. [para(462(a,1),26(a,1,2,2)),rewrite([19(5),4(4),8(10)]),flip(a)].
% 11.29/11.59 480 join(complement(A),meet(B,complement(A))) = complement(A). [para(93(a,1),6(a,1,2))].
% 11.29/11.59 503 meet(A,join(meet(B,complement(A)),meet(C,complement(A)))) = zero. [para(40(a,1),52(a,1,2,2)),rewrite([8(4),102(5)]),flip(a)].
% 11.29/11.59 697 meet(A,join(meet(A,B),meet(C,meet(D,complement(A))))) = meet(A,join(B,meet(C,meet(D,complement(A))))). [para(8(a,1),58(a,1,2))].
% 11.29/11.59 886 meet(A,join(B,join(zero,meet(A,C)))) = meet(A,join(B,meet(A,C))). [para(12(a,1),62(a,2,2)),rewrite([62(8),19(8),8(7)])].
% 11.29/11.59 889 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(62(a,1),22(a,1,2)),rewrite([886(8),10(7,R),61(7),7(8),42(8)])].
% 11.29/11.59 926 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(889(a,1),10(a,1)),rewrite([7(5)]),flip(a)].
% 11.29/11.59 960 meet(meet(A,B),join(A,C)) = meet(A,B). [back_rewrite(85),rewrite([926(5),6(3),7(2),20(2)]),flip(a)].
% 11.29/11.59 969 meet(complement(meet(A,B)),join(zero,meet(A,B))) = zero. [para(960(a,1),462(a,1,2,2))].
% 11.29/11.59 975 meet(A,B) != zero | one != A | complement(meet(A,B)) = A. [para(960(a,1),56(a,1)),rewrite([8(5),6(5),7(7),10(7),7(6),10(7,R),7(6),6(8)]),flip(b),flip(c)].
% 11.29/11.59 1010 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(969(a,1),28(a,1,2)),rewrite([37(2),37(3),19(3),8(5),19(5),7(4)]),flip(a)].
% 11.29/11.59 1257 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(926(a,1),389(a,1,2,2))].
% 11.29/11.59 1323 join(zero,meet(A,B)) = meet(A,B). [para(1257(a,1),1(a,1)),rewrite([7(5),1257(5),1(3)]),flip(a)].
% 11.29/11.59 1356 meet(complement(A),join(complement(complement(A)),meet(A,join(B,complement(A))))) = zero. [back_rewrite(473),rewrite([1323(8)])].
% 11.29/11.59 1380 meet(A,join(complement(A),join(meet(A,B),meet(C,meet(D,complement(A)))))) = meet(A,join(B,join(complement(A),meet(C,meet(D,complement(A)))))). [para(51(a,1),67(a,1,2,2,2,2,2)),rewrite([19(6),12(7,R),8(12),8(14),12(14,R),8(13)])].
% 11.29/11.59 1467 join(A,B) != zero | complement(join(A,B)) = one. [para(300(a,1),975(a,1)),rewrite([300(9)]),xx(b)].
% 11.29/11.59 1468 meet(A,B) != zero | complement(meet(A,B)) = one. [para(1323(a,1),1467(a,1)),rewrite([1323(6)])].
% 11.29/11.59 1470 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(26(a,1),71(a,1,2,2)),rewrite([1356(8)]),flip(a)].
% 11.29/11.59 1492 join(A,complement(complement(A))) = complement(complement(A)). [hyper(54,a,1470,a)].
% 11.29/11.59 1493 meet(A,complement(complement(A))) = A. [para(1492(a,1),5(a,1,2))].
% 11.29/11.59 1515 meet(complement(A),join(A,meet(B,complement(complement(A))))) = zero. [para(1493(a,1),503(a,1,2,1))].
% 11.29/11.59 1651 complement(complement(A)) = A. [para(1515(a,1),56(a,1)),rewrite([8(5),3(5),4(10),19(8)]),flip(c),xx(a),xx(b)].
% 11.29/11.59 1684 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(7(a,1),82(a,2)),rewrite([82(8),10(6),7(5),10(6,R),7(5)])].
% 11.29/11.59 1685 meet(A,meet(B,join(C,meet(A,meet(B,join(D,meet(A,meet(B,C)))))))) = meet(A,meet(B,join(C,D))). [para(8(a,1),82(a,1,2,2,2)),rewrite([8(5),1684(6),1684(8),1684(11)])].
% 11.29/11.59 1735 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(480(a,1),82(a,2,2)),rewrite([1684(10),1684(12),1685(12),480(4)]),flip(a)].
% 11.29/11.59 1898 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [para(1651(a,1),503(a,1,2,1,2)),rewrite([7(2),1651(4),7(3)])].
% 11.29/11.59 1899 meet(complement(A),join(A,B)) != zero | join(A,B) = A. [para(1651(a,1),54(a,1,2,2)),rewrite([8(2),1651(7),8(6),1651(8)])].
% 11.29/11.59 2328 meet(A,meet(join(A,B),complement(C))) = meet(A,complement(C)). [para(5(a,1),1735(a,1,1)),flip(a)].
% 11.29/11.59 2343 meet(join(A,B),meet(join(A,join(B,C)),complement(D))) = meet(join(A,B),complement(D)). [para(146(a,1),1735(a,1,1)),flip(a)].
% 11.29/11.59 2345 meet(one,meet(complement(A),complement(B))) = meet(complement(A),complement(B)). [para(310(a,1),1735(a,1,1)),flip(a)].
% 11.29/11.59 2355 join(complement(A),meet(B,meet(C,complement(A)))) = complement(A). [para(1735(a,1),480(a,1,2))].
% 11.29/11.59 2414 meet(A,join(complement(A),join(meet(A,B),meet(C,meet(D,complement(A)))))) = meet(A,join(B,complement(A))). [back_rewrite(1380),rewrite([2355(13)])].
% 11.29/11.59 2610 meet(A,complement(join(A,B))) = zero. [para(4(a,1),2328(a,1,2)),rewrite([37(2)]),flip(a)].
% 11.29/11.59 2672 meet(A,join(complement(A),complement(join(A,B)))) = zero. [para(2610(a,1),26(a,1,2,2)),rewrite([19(3),4(2),8(5)]),flip(a)].
% 11.29/11.59 2683 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(2610(a,1),1735(a,1)),rewrite([8(3)]),flip(a)].
% 11.29/11.59 2708 meet(complement(A),join(A,complement(join(B,complement(A))))) = zero. [para(1651(a,1),2672(a,1,2,1)),rewrite([8(3)])].
% 11.29/11.59 2831 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(146(a,1),2683(a,1,2,2,1,2)),rewrite([12(5),8(4),12(5,R),8(4),2343(8)])].
% 11.29/11.59 3048 join(A,complement(join(B,complement(A)))) = A. [hyper(1899,a,2708,a)].
% 11.29/11.59 3056 meet(A,complement(join(B,complement(A)))) = complement(join(B,complement(A))). [para(3048(a,1),304(a,1,2)),rewrite([7(4)])].
% 11.29/11.59 3062 join(complement(A),complement(join(A,B))) = complement(A). [para(1651(a,1),3048(a,1,2,1,2)),rewrite([8(2)])].
% 11.29/11.59 3073 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(3062(a,1),304(a,1,2)),rewrite([7(4)])].
% 11.29/11.59 3254 complement(join(A,B)) != zero | join(A,B) = one. [para(3073(a,1),1468(a,1)),rewrite([3073(8),1651(7)])].
% 11.29/11.59 3255 meet(A,join(meet(B,complement(A)),complement(join(A,C)))) = zero. [para(3073(a,1),1898(a,1,2,2)),rewrite([1651(2),7(2)])].
% 11.29/11.59 3257 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(3073(a,1),2683(a,1,2))].
% 11.29/11.59 3376 meet(join(A,B),complement(join(A,meet(B,complement(A))))) = zero. [para(3257(a,1),80(a,1,2,2)),rewrite([8(9),12(9,R),8(8),1323(8),7(8),4(8),8(9),25(9),8(6),7(7)]),flip(a)].
% 11.29/11.59 3377 meet(A,complement(join(complement(B),meet(A,B)))) = zero. [para(1651(a,1),3257(a,1,2,1,2,2))].
% 11.29/11.59 3386 meet(A,complement(join(complement(B),meet(B,A)))) = zero. [para(3377(a,1),7(a,1)),rewrite([7(3),7(6)]),flip(a)].
% 11.29/11.59 4184 meet(complement(A),complement(join(B,A))) = complement(join(B,A)). [para(3056(a,1),2345(a,1,2)),rewrite([1651(3),310(4),1651(5)]),flip(a)].
% 11.29/11.59 4187 meet(complement(A),complement(meet(A,B))) = complement(A). [para(6(a,1),4184(a,1,2,1)),rewrite([7(4),6(6)])].
% 11.29/11.59 4192 meet(A,complement(meet(B,complement(A)))) = A. [para(480(a,1),4184(a,1,2,1)),rewrite([1651(5),7(4),480(8),1651(6)])].
% 11.29/11.59 4263 join(A,complement(meet(B,complement(A)))) = complement(meet(B,complement(A))). [para(4192(a,1),480(a,1,2)),rewrite([8(4)])].
% 11.29/11.59 4274 meet(A,complement(meet(B,complement(join(A,C))))) = A. [para(4192(a,1),2328(a,1,2)),rewrite([5(2)]),flip(a)].
% 11.29/11.59 4288 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(4187(a,1),480(a,1,2)),rewrite([8(4)])].
% 11.29/11.59 4294 meet(A,complement(meet(complement(A),join(A,B)))) = A. [para(80(a,1),4187(a,1,2,1)),rewrite([1651(2),1651(7)])].
% 11.29/11.59 5670 join(complement(A),meet(B,complement(join(A,C)))) = complement(A). [para(4274(a,1),4263(a,1,2,1)),rewrite([8(5),4274(10)])].
% 11.29/11.59 5691 join(A,meet(B,complement(join(C,complement(A))))) = A. [para(1651(a,1),5670(a,1,1)),rewrite([8(2),1651(7)])].
% 11.29/11.59 5725 join(join(A,B),meet(A,C)) = join(A,B). [para(3062(a,1),5691(a,1,2,2,1)),rewrite([1651(3),7(2)])].
% 11.29/11.59 5730 meet(A,complement(join(B,A))) = zero. [para(5691(a,1),3386(a,1,2,1)),rewrite([1651(2),1651(4),7(3)])].
% 11.29/11.59 5762 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [para(25(a,1),5730(a,1,2,1)),rewrite([8(3),7(5)])].
% 11.29/11.59 5770 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(5725(a,1),27(a,1,2,2,2)),rewrite([23(6)])].
% 11.29/11.59 5953 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),5762(a,1,1,1))].
% 11.29/11.59 6023 meet(A,complement(join(B,join(C,A)))) = zero. [para(2831(a,1),5953(a,1,2,2)),rewrite([8(2),12(2),8(1),12(2,R),8(1),19(5),7(4)])].
% 11.29/11.59 6039 meet(complement(join(A,complement(B))),complement(join(B,C))) = zero. [para(3048(a,1),6023(a,1,2,1,2)),rewrite([8(4)])].
% 11.29/11.59 6219 meet(complement(join(A,B)),complement(join(C,complement(B)))) = zero. [para(1651(a,1),6039(a,1,1,1,2)),rewrite([8(4)])].
% 11.29/11.59 6385 meet(complement(A),complement(join(B,complement(meet(A,C))))) = zero. [para(6(a,1),6219(a,1,1,1))].
% 11.29/11.59 6426 complement(join(A,complement(meet(A,B)))) = zero. [para(6385(a,1),3073(a,1)),flip(a)].
% 11.29/11.59 6599 join(A,complement(meet(A,B))) = one. [hyper(3254,a,6426,a)].
% 11.29/11.59 6603 join(meet(A,B),complement(meet(A,meet(B,complement(C))))) = one. [para(1735(a,1),6599(a,1,2,1))].
% 11.29/11.59 6654 meet(A,join(meet(B,meet(C,complement(A))),join(meet(A,D),meet(A,join(E,meet(A,join(D,meet(B,meet(C,complement(A)))))))))) = meet(A,join(E,join(meet(B,meet(C,complement(A))),meet(A,D)))). [para(51(a,1),152(a,1,2,2,1,2,2)),rewrite([19(5),8(8),51(21),19(19)])].
% 11.29/11.59 8139 meet(A,join(B,join(meet(A,join(B,join(meet(C,meet(D,complement(A))),meet(A,E)))),meet(A,join(meet(A,join(E,meet(C,meet(D,complement(A))))),meet(A,B)))))) = meet(A,join(B,join(join(meet(C,meet(D,complement(A))),meet(A,E)),meet(A,join(meet(A,join(E,meet(C,meet(D,complement(A))))),meet(A,B)))))). [para(58(a,1),157(a,1,2,2,2,2,1)),rewrite([58(29)])].
% 11.29/11.59 8896 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [para(1651(a,1),6603(a,1,2,1,2,2))].
% 11.29/11.59 8992 join(join(A,B),complement(meet(C,join(A,B)))) = one. [para(146(a,1),8896(a,1,1)),rewrite([7(5),10(6,R),7(5),146(5)])].
% 11.29/11.59 8993 join(complement(A),complement(meet(B,complement(A)))) = one. [para(310(a,1),8896(a,1,1)),rewrite([7(4),10(5,R),18(4)])].
% 11.29/11.59 9013 join(complement(A),complement(meet(B,meet(C,complement(A))))) = one. [para(1735(a,1),8993(a,1,2,1))].
% 11.29/11.59 9032 join(A,join(join(B,C),complement(join(A,B)))) = one. [para(146(a,1),8992(a,1,2,1)),rewrite([8(5),12(5,R)])].
% 11.29/11.59 9409 join(complement(meet(A,complement(B))),complement(meet(B,C))) = one. [para(4192(a,1),9013(a,1,2,1,2)),rewrite([7(4)])].
% 11.29/11.59 9436 join(A,join(B,complement(join(A,B)))) = one. [para(2(a,1),9032(a,1,2,1))].
% 11.29/11.59 9438 join(A,join(join(B,C),complement(join(A,C)))) = one. [para(8(a,1),9032(a,1,2,1))].
% 11.29/11.59 9475 meet(A,join(meet(A,B),join(meet(A,join(B,complement(A))),meet(C,meet(D,complement(A)))))) = meet(A,join(B,complement(A))). [para(26(a,1),166(a,1,2,2)),rewrite([8(11),12(11,R),8(10),2355(10),8(9),12(9),2414(18)])].
% 11.29/11.59 9533 join(meet(A,complement(B)),complement(join(B,meet(A,complement(B))))) = complement(B). [hyper(17,a,3255,a,b,9436,a),flip(a)].
% 11.29/11.59 9715 join(A,complement(meet(B,A))) = one. [para(304(a,1),9409(a,1,2,1)),rewrite([1651(2),1651(4),8(3)])].
% 11.29/11.59 9729 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [para(22(a,1),9715(a,1,2,1)),rewrite([7(3),8(5)])].
% 11.29/11.59 9801 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(6(a,1),9438(a,1,2,1))].
% 11.29/11.59 10155 join(complement(meet(A,B)),meet(B,join(A,C))) = one. [para(7(a,1),9729(a,1,1,1))].
% 11.29/11.59 10243 join(join(A,B),complement(join(A,meet(B,C)))) = one. [para(9801(a,1),12(a,1)),rewrite([8(6)]),flip(a)].
% 11.29/11.59 10256 join(complement(A),meet(join(A,B),join(A,C))) = one. [para(5(a,1),10155(a,1,1,1))].
% 11.29/11.59 10468 complement(join(A,meet(B,complement(A)))) = complement(join(A,B)). [hyper(17,a,3376,a,b,10243,a),flip(a)].
% 11.29/11.59 10495 join(meet(A,complement(B)),complement(join(A,B))) = complement(B). [back_rewrite(9533),rewrite([10468(6),8(3)])].
% 11.29/11.59 10558 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(10256(a,1),83(a,1,2,2,2)),rewrite([5(3),8(2),5(8),8(7),7(11),300(11),25(10),8(6),23(6),7(6),5770(6),5(6),8(5),8(10),12(10),8(9),3(9),46(9),7(9),300(9)]),flip(a)].
% 11.29/11.59 10625 join(A,meet(B,complement(A))) = join(A,B). [para(10468(a,1),1651(a,1,1)),rewrite([1651(3)]),flip(a)].
% 11.29/11.59 10779 join(A,meet(complement(A),join(A,B))) = join(A,B). [para(23(a,1),10625(a,2)),rewrite([7(3)])].
% 11.29/11.59 10785 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(1651(a,1),10625(a,1,2,2)),rewrite([7(2),8(5)])].
% 11.29/11.59 11143 join(complement(A),join(join(B,meet(A,join(C,meet(A,B)))),meet(A,join(D,meet(A,join(B,C)))))) = join(B,join(D,join(C,complement(A)))). [para(29(a,1),10785(a,1,2)),rewrite([10785(8),8(7),12(7,R),8(6),12(6,R),8(5),10785(5),8(4),12(4,R),8(3),10785(3),12(3,R),8(2),12(4,R),8(3),23(5),8(15)]),flip(a)].
% 11.29/11.59 11151 join(complement(A),join(meet(B,meet(C,complement(A))),meet(A,D))) = join(D,complement(A)). [para(58(a,1),10785(a,1,2)),rewrite([10785(7),8(6),12(6,R),8(5),2355(5),8(9)]),flip(a)].
% 11.29/11.59 11153 join(complement(A),meet(B,complement(meet(A,B)))) = complement(A). [para(1010(a,1),10785(a,1,2)),rewrite([19(3),8(6)]),flip(a)].
% 11.29/11.59 11529 join(meet(A,B),complement(join(A,complement(B)))) = B. [para(1651(a,1),10495(a,1,1,2)),rewrite([1651(7)])].
% 11.29/11.59 11540 join(A,complement(join(A,B))) = complement(meet(B,complement(A))). [para(4192(a,1),10495(a,1,1)),rewrite([10625(3)])].
% 11.29/11.59 11542 complement(meet(complement(A),join(A,B))) = complement(meet(B,complement(A))). [para(4294(a,1),10495(a,1,1)),rewrite([10779(4),11540(3)]),flip(a)].
% 11.29/11.59 11567 meet(A,complement(join(B,complement(join(A,meet(B,C)))))) = complement(join(B,complement(join(A,meet(B,C))))). [para(9801(a,1),10495(a,1,2,1)),rewrite([41(8),8(8),1323(8)])].
% 11.29/11.59 11660 join(meet(A,join(B,C)),complement(join(A,complement(join(B,meet(A,join(C,meet(A,B)))))))) = join(B,meet(A,join(C,meet(A,B)))). [para(14(a,1),11529(a,1,1))].
% 11.29/11.59 11662 join(meet(A,B),complement(join(A,complement(meet(B,join(A,C)))))) = meet(B,join(A,C)). [para(22(a,1),11529(a,1,1))].
% 11.29/11.59 11663 join(A,meet(B,A)) = A. [para(11529(a,1),23(a,1,2)),rewrite([8(2),11529(7)])].
% 11.29/11.59 11679 join(meet(A,B),complement(join(A,complement(meet(B,join(C,meet(A,B))))))) = meet(B,join(C,meet(A,B))). [para(889(a,1),11529(a,1,1))].
% 11.29/11.59 11684 join(meet(A,join(B,C)),complement(join(A,complement(join(B,join(meet(A,join(B,C)),meet(A,join(C,meet(A,B))))))))) = join(B,join(meet(A,join(B,C)),meet(A,join(C,meet(A,B))))). [para(100(a,1),11529(a,1,1))].
% 11.29/11.59 11693 meet(complement(A),complement(meet(B,A))) = complement(A). [para(11529(a,1),3073(a,1,2,1)),rewrite([7(4),11529(9)])].
% 11.29/11.59 11933 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(889(a,1),11663(a,1,2)),rewrite([7(1),7(4),8(5),7(6)])].
% 11.29/11.59 12138 meet(complement(meet(A,join(B,C))),complement(join(B,meet(A,join(C,meet(B,A)))))) = complement(join(B,meet(A,join(C,meet(B,A))))). [para(14(a,1),11693(a,1,2,1)),rewrite([7(1),7(9),7(10)])].
% 11.29/11.59 12625 meet(A,complement(meet(A,B))) = meet(A,complement(B)). [para(11153(a,1),889(a,1,2,2)),rewrite([7(1),7(4),11693(4),7(3)]),flip(a)].
% 11.29/11.59 12735 meet(complement(A),complement(meet(B,complement(A)))) = complement(join(A,B)). [para(3073(a,1),12625(a,2)),rewrite([11542(5)])].
% 11.29/11.59 12738 complement(join(A,B)) = meet(complement(A),complement(B)). [para(12625(a,1),2345(a,1,2)),rewrite([2345(5),7(6),12735(8)]),flip(a)].
% 11.29/11.59 12785 join(meet(A,B),meet(A,complement(B))) = A. [para(12625(a,1),10625(a,1,2)),rewrite([8(6),6(6)])].
% 11.29/11.59 12787 complement(meet(A,B)) = join(complement(A),complement(B)). [para(12625(a,1),10785(a,1,2)),rewrite([10785(4),8(3),8(7),4288(7)]),flip(a)].
% 11.29/11.59 12794 meet(A,join(B,complement(A))) = meet(A,B). [para(12625(a,1),12625(a,1,2,1)),rewrite([12787(3),1651(3),8(2),12787(5),12738(7),1651(5),1651(5),20(5)])].
% 11.29/11.59 12944 meet(complement(A),meet(join(complement(B),meet(complement(A),complement(C))),join(complement(B),meet(complement(C),join(complement(B),complement(A)))))) = meet(complement(A),join(complement(B),meet(complement(C),join(complement(B),complement(A))))). [back_rewrite(12138),rewrite([12787(3),12738(3),7(6),12738(10),12787(10),12738(10),12787(10),10(15,R),7(14),7(16),12738(20),12787(20),12738(20),12787(20)])].
% 11.29/11.59 12989 join(meet(A,join(B,C)),meet(complement(A),join(B,meet(A,join(C,meet(A,B)))))) = join(B,join(meet(A,join(B,C)),meet(A,join(C,meet(A,B))))). [back_rewrite(11684),rewrite([12738(10),12738(10),12787(6),12738(6),12787(12),12738(12),12787(12),12944(17),12738(13),12787(13),1651(5),12738(11),1651(5),12787(9),1651(5),12738(7),1651(5),1651(5)])].
% 11.29/11.59 12992 join(meet(A,B),meet(B,meet(complement(A),join(C,meet(A,B))))) = meet(B,join(C,meet(A,B))). [back_rewrite(11679),rewrite([12787(5),12738(5),12787(5),12738(10),12738(10),1651(4),12787(8),1651(4),12738(6),1651(4),1651(4),10(6,R),7(5)])].
% 11.29/11.59 13003 join(meet(A,B),meet(B,meet(complement(A),join(A,C)))) = meet(B,join(A,C)). [back_rewrite(11662),rewrite([12787(4),12738(4),12738(8),12738(8),1651(4),12787(6),1651(4),1651(4),10(5,R),7(4)])].
% 11.29/11.59 13004 join(A,join(meet(B,join(A,C)),meet(B,join(C,meet(B,A))))) = join(A,meet(B,join(C,meet(B,A)))). [back_rewrite(11660),rewrite([12738(7),12787(7),12738(7),12787(7),12738(13),12787(13),1651(5),12738(11),1651(5),12787(9),1651(5),12738(7),1651(5),1651(5),12989(9)])].
% 11.29/11.59 13014 meet(complement(A),join(B,meet(A,C))) = meet(B,complement(A)). [back_rewrite(11567),rewrite([12738(3),12787(3),12738(7),12787(7),1651(3),12738(5),1651(3),1651(3),22(5),12738(5),12787(5),12738(9),12787(9),1651(5),12738(7),1651(5),1651(5)]),flip(a)].
% 11.29/11.59 13027 join(meet(A,B),meet(B,complement(A))) = B. [back_rewrite(11529),rewrite([12738(4),1651(4),7(3)])].
% 11.29/11.59 14521 meet(A,join(B,meet(C,meet(D,complement(A))))) = meet(A,B). [back_rewrite(9475),rewrite([12794(4),23(7),697(6),12794(8)])].
% 11.29/11.59 14579 join(meet(A,complement(B)),meet(B,join(A,C))) = join(A,meet(B,join(C,meet(B,A)))). [back_rewrite(12989),rewrite([13014(8),8(5),13004(12)])].
% 11.29/11.59 14653 join(meet(A,B),meet(B,meet(C,complement(A)))) = meet(B,join(C,meet(A,B))). [back_rewrite(12992),rewrite([13014(5)])].
% 11.29/11.59 14823 meet(A,join(B,join(meet(A,join(meet(A,C),meet(A,B))),meet(A,join(B,join(meet(D,meet(E,complement(A))),meet(A,C))))))) = meet(A,join(B,join(join(meet(D,meet(E,complement(A))),meet(A,C)),meet(A,join(meet(A,C),meet(A,B)))))). [back_rewrite(8139),rewrite([14521(12),8(12),14521(24)])].
% 11.29/11.59 14835 meet(A,join(B,join(meet(C,meet(D,complement(A))),meet(A,E)))) = meet(A,join(B,meet(A,E))). [back_rewrite(6654),rewrite([14521(9),11933(8),58(8),14521(7)]),flip(a)].
% 11.29/11.59 15182 meet(A,join(B,join(join(meet(C,meet(D,complement(A))),meet(A,E)),meet(A,join(meet(A,E),meet(A,B)))))) = meet(A,join(B,meet(A,E))). [back_rewrite(14823),rewrite([14835(11),8(8),13004(9),14(6)]),flip(a)].
% 11.29/11.59 15331 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [para(14(a,1),12794(a,2)),rewrite([8(6),12(6,R),8(5),10785(5),8(4),12(4,R),8(3),10785(3),12(3,R),8(2),23(4)])].
% 11.29/11.59 15335 meet(A,join(B,join(C,meet(A,join(D,meet(A,B)))))) = meet(A,join(B,join(D,join(C,complement(A))))). [para(29(a,1),12794(a,2)),rewrite([8(11),11143(11),12(3,R),8(2)]),flip(a)].
% 11.29/11.59 15337 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(1651(a,1),12794(a,1,2,2)),rewrite([8(2),7(5)])].
% 11.29/11.59 15432 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(15182),rewrite([15335(12),8(8),11151(8),12(4),8(3),11663(3),8(2),15331(4)]),flip(a)].
% 11.29/11.59 15640 meet(A,join(B,meet(C,A))) = meet(A,join(C,B)). [back_rewrite(13003),rewrite([15337(4),14653(5)])].
% 11.29/11.59 16247 join(meet(A,complement(B)),meet(B,join(A,C))) = join(A,meet(B,join(A,C))). [back_rewrite(14579),rewrite([7(6),15640(8)])].
% 11.29/11.59 19378 join(A,meet(B,join(A,C))) = join(A,meet(B,C)). [para(13014(a,1),13027(a,1,1)),rewrite([1651(6),7(5),15432(5),16247(5)])].
% 11.29/11.59 19761 meet(join(A,B),join(A,C)) = join(A,meet(B,C)). [back_rewrite(10558),rewrite([19378(4),7(2),19378(3),7(1)]),flip(a)].
% 11.29/11.59 20341 join(meet(A,B),meet(A,meet(C,complement(B)))) = join(meet(A,B),meet(A,C)). [para(12785(a,1),19378(a,1,2,2)),rewrite([7(2),10(7,R),7(6)]),flip(a)].
% 11.29/11.59 20510 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [para(12785(a,1),19761(a,1,1)),rewrite([8(2),15432(3),8(1),7(6),10(6,R),7(5),20341(7)]),flip(a)].
% 11.29/11.59 20511 $F # answer(prove_distributivity). [resolve(20510,a,16,a)].
% 11.29/11.59
% 11.29/11.59 % SZS output end Refutation
% 11.29/11.59 ============================== end of proof ==========================
% 11.29/11.59
% 11.29/11.59 ============================== STATISTICS ============================
% 11.29/11.59
% 11.29/11.59 Given=510. Generated=146905. Kept=20506. proofs=1.
% 11.29/11.59 Usable=162. Sos=1875. Demods=1624. Limbo=7, Disabled=18474. Hints=0.
% 11.29/11.59 Megabytes=32.13.
% 11.29/11.59 User_CPU=10.49, System_CPU=0.10, Wall_clock=10.
% 11.29/11.59
% 11.29/11.59 ============================== end of statistics =====================
% 11.29/11.59
% 11.29/11.59 ============================== end of search =========================
% 11.29/11.59
% 11.29/11.59 THEOREM PROVED
% 11.29/11.59 % SZS status Unsatisfiable
% 11.29/11.59
% 11.29/11.59 Exiting with 1 proof.
% 11.29/11.59
% 11.29/11.59 Process 396 exit (max_proofs) Tue Jun 28 18:53:57 2022
% 11.29/11.59 Prover9 interrupted
%------------------------------------------------------------------------------