TSTP Solution File: LAT211-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT211-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 5.43s 5.73s
% Output : Refutation 5.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT211-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 29 16:46:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 5.43/5.73 ============================== Prover9 ===============================
% 5.43/5.73 Prover9 (32) version 2009-11A, November 2009.
% 5.43/5.73 Process 25702 was started by sandbox on n019.cluster.edu,
% 5.43/5.73 Wed Jun 29 16:46:54 2022
% 5.43/5.73 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25545_n019.cluster.edu".
% 5.43/5.73 ============================== end of head ===========================
% 5.43/5.73
% 5.43/5.73 ============================== INPUT =================================
% 5.43/5.73
% 5.43/5.73 % Reading from file /tmp/Prover9_25545_n019.cluster.edu
% 5.43/5.73
% 5.43/5.73 set(prolog_style_variables).
% 5.43/5.73 set(auto2).
% 5.43/5.73 % set(auto2) -> set(auto).
% 5.43/5.73 % set(auto) -> set(auto_inference).
% 5.43/5.73 % set(auto) -> set(auto_setup).
% 5.43/5.73 % set(auto_setup) -> set(predicate_elim).
% 5.43/5.73 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.43/5.73 % set(auto) -> set(auto_limits).
% 5.43/5.73 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.43/5.73 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.43/5.73 % set(auto) -> set(auto_denials).
% 5.43/5.73 % set(auto) -> set(auto_process).
% 5.43/5.73 % set(auto2) -> assign(new_constants, 1).
% 5.43/5.73 % set(auto2) -> assign(fold_denial_max, 3).
% 5.43/5.73 % set(auto2) -> assign(max_weight, "200.000").
% 5.43/5.73 % set(auto2) -> assign(max_hours, 1).
% 5.43/5.73 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.43/5.73 % set(auto2) -> assign(max_seconds, 0).
% 5.43/5.73 % set(auto2) -> assign(max_minutes, 5).
% 5.43/5.73 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.43/5.73 % set(auto2) -> set(sort_initial_sos).
% 5.43/5.73 % set(auto2) -> assign(sos_limit, -1).
% 5.43/5.73 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.43/5.73 % set(auto2) -> assign(max_megs, 400).
% 5.43/5.73 % set(auto2) -> assign(stats, some).
% 5.43/5.73 % set(auto2) -> clear(echo_input).
% 5.43/5.73 % set(auto2) -> set(quiet).
% 5.43/5.73 % set(auto2) -> clear(print_initial_clauses).
% 5.43/5.73 % set(auto2) -> clear(print_given).
% 5.43/5.73 assign(lrs_ticks,-1).
% 5.43/5.73 assign(sos_limit,10000).
% 5.43/5.73 assign(order,kbo).
% 5.43/5.73 set(lex_order_vars).
% 5.43/5.73 clear(print_given).
% 5.43/5.73
% 5.43/5.73 % formulas(sos). % not echoed (13 formulas)
% 5.43/5.73
% 5.43/5.73 ============================== end of input ==========================
% 5.43/5.73
% 5.43/5.73 % From the command line: assign(max_seconds, 300).
% 5.43/5.73
% 5.43/5.73 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.43/5.73
% 5.43/5.73 % Formulas that are not ordinary clauses:
% 5.43/5.73
% 5.43/5.73 ============================== end of process non-clausal formulas ===
% 5.43/5.73
% 5.43/5.73 ============================== PROCESS INITIAL CLAUSES ===============
% 5.43/5.73
% 5.43/5.73 ============================== PREDICATE ELIMINATION =================
% 5.43/5.73
% 5.43/5.73 ============================== end predicate elimination =============
% 5.43/5.73
% 5.43/5.73 Auto_denials:
% 5.43/5.73 % copying label prove_distributivity to answer in negative clause
% 5.43/5.73
% 5.43/5.73 Term ordering decisions:
% 5.43/5.73
% 5.43/5.73 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 5.43/5.73 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. meet=1. join=1. complement=0.
% 5.43/5.73
% 5.43/5.73 ============================== end of process initial clauses ========
% 5.43/5.73
% 5.43/5.73 ============================== CLAUSES FOR SEARCH ====================
% 5.43/5.73
% 5.43/5.73 ============================== end of clauses for search =============
% 5.43/5.73
% 5.43/5.73 ============================== SEARCH ================================
% 5.43/5.73
% 5.43/5.73 % Starting search at 0.01 seconds.
% 5.43/5.73
% 5.43/5.73 ============================== PROOF =================================
% 5.43/5.73 % SZS status Unsatisfiable
% 5.43/5.73 % SZS output start Refutation
% 5.43/5.73
% 5.43/5.73 % Proof 1 at 4.69 (+ 0.06) seconds: prove_distributivity.
% 5.43/5.73 % Length of proof is 210.
% 5.43/5.73 % Level of proof is 46.
% 5.43/5.73 % Maximum clause weight is 59.000.
% 5.43/5.73 % Given clauses 393.
% 5.43/5.73
% 5.43/5.73 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 5.43/5.73 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 5.43/5.73 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 5.43/5.73 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 5.43/5.73 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 5.43/5.73 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 5.43/5.73 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 5.43/5.73 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 5.43/5.73 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 5.43/5.73 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 5.43/5.73 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 5.43/5.73 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 5.43/5.73 13 meet(A,join(B,C)) = join(meet(A,join(C,meet(A,B))),meet(A,join(B,meet(A,C)))) # label(equation_H69) # label(axiom). [assumption].
% 5.43/5.73 14 join(meet(A,join(B,meet(A,C))),meet(A,join(C,meet(A,B)))) = meet(A,join(B,C)). [copy(13),rewrite([8(9)]),flip(a)].
% 5.43/5.73 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 5.43/5.73 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 5.43/5.73 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 5.43/5.73 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 5.43/5.73 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 5.43/5.73 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)])].
% 5.43/5.73 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 5.43/5.73 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 5.43/5.73 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)])].
% 5.43/5.73 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 5.43/5.73 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 5.43/5.73 26 meet(A,join(B,meet(A,B))) = meet(A,B). [para(14(a,1),2(a,1)),rewrite([2(1)]),flip(a)].
% 5.43/5.73 27 join(meet(A,B),meet(A,join(complement(A),meet(A,B)))) = meet(A,join(B,complement(A))). [para(4(a,1),14(a,1,1,2,2)),rewrite([19(2)])].
% 5.43/5.73 28 meet(A,meet(meet(A,join(B,C)),join(B,meet(A,C)))) = meet(A,join(B,meet(A,C))). [para(14(a,1),5(a,1,2)),rewrite([7(6),10(6,R),7(5)])].
% 5.43/5.73 29 join(meet(A,join(B,meet(A,C))),meet(A,join(C,meet(B,A)))) = meet(A,join(B,C)). [para(7(a,1),14(a,1,1)),rewrite([7(3),7(4)])].
% 5.43/5.73 30 join(meet(A,join(B,C)),meet(A,join(join(C,meet(A,B)),meet(A,join(B,meet(A,C)))))) = meet(A,join(join(C,meet(A,B)),meet(A,join(B,meet(A,C))))). [para(14(a,1),14(a,1,1,2)),rewrite([20(3),20(8),8(16)])].
% 5.43/5.73 36 meet(A,zero) != zero | one != A | complement(A) = zero. [para(19(a,1),17(b,1)),flip(b)].
% 5.43/5.73 38 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 5.43/5.73 39 join(meet(A,join(B,meet(A,C))),meet(A,join(meet(A,C),meet(A,B)))) = meet(A,join(B,meet(A,C))). [para(20(a,1),14(a,1,1,2,2))].
% 5.43/5.73 40 one != A | complement(A) = zero. [back_rewrite(36),rewrite([38(2)]),xx(a)].
% 5.43/5.73 41 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([38(5)])].
% 5.43/5.73 42 complement(one) = zero. [hyper(17,a,38,a,b,19,a)].
% 5.43/5.73 45 join(meet(A,join(B,meet(A,C))),meet(A,join(meet(C,join(A,D)),meet(A,B)))) = meet(A,join(B,meet(C,join(A,D)))). [para(22(a,1),14(a,1,1,2,2))].
% 5.43/5.73 46 meet(A,meet(B,meet(join(C,D),join(C,meet(A,D))))) = meet(A,meet(B,join(C,meet(A,D)))). [para(14(a,1),22(a,1,2,2)),rewrite([10(6,R),7(5),10(7,R),10(6,R),10(5),7(4),10(5,R),7(4),20(7),7(10),10(10,R),7(9)])].
% 5.43/5.73 47 complement(join(A,one)) = zero. [hyper(40,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 5.43/5.73 48 join(A,one) = one. [para(47(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 5.43/5.73 49 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([48(5)])].
% 5.43/5.73 50 complement(zero) = one. [hyper(17,a,18,a,b,48,a)].
% 5.43/5.73 52 join(meet(A,join(B,C)),meet(A,join(B,meet(A,C)))) = meet(A,join(B,C)). [para(14(a,1),23(a,1,2)),rewrite([8(6),14(13)])].
% 5.43/5.73 56 join(A,join(B,join(C,complement(A)))) = one. [para(49(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),48(6)])].
% 5.43/5.73 57 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(49(a,1),17(b,1)),flip(c),xx(b)].
% 5.43/5.73 59 join(meet(A,join(B,meet(A,C))),join(meet(A,join(C,meet(A,B))),meet(A,meet(D,join(B,meet(A,C)))))) = meet(A,join(B,C)). [para(14(a,1),25(a,2)),rewrite([7(10),10(10,R),7(9)])].
% 5.43/5.73 60 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)].
% 5.43/5.73 64 meet(A,join(B,join(C,complement(A)))) != zero | join(B,join(C,complement(A))) = complement(A). [para(56(a,1),17(b,1)),flip(c),xx(b)].
% 5.43/5.73 71 join(meet(A,B),meet(B,join(complement(B),meet(A,B)))) = meet(B,join(A,complement(B))). [para(7(a,1),27(a,1,1)),rewrite([7(3)])].
% 5.43/5.73 77 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(20(a,1),27(a,1,1)),rewrite([20(4),27(6),8(6)]),flip(a)].
% 5.43/5.73 79 meet(A,join(zero,complement(A))) = zero. [para(38(a,1),27(a,1,1)),rewrite([38(4),19(4),4(3),2(3)]),flip(a)].
% 5.43/5.73 89 join(zero,complement(A)) = complement(A). [hyper(17,a,79,a,b,49,a),flip(a)].
% 5.43/5.73 92 meet(A,meet(meet(A,B),join(B,meet(A,meet(B,C))))) = meet(A,join(B,meet(A,meet(B,C)))). [para(6(a,1),28(a,1,2,1,2))].
% 5.43/5.73 100 meet(A,meet(meet(A,join(B,C)),join(B,meet(A,join(B,C))))) = meet(A,join(B,meet(A,join(B,C)))). [para(23(a,1),28(a,1,2,1,2))].
% 5.43/5.73 111 join(meet(A,complement(B)),meet(complement(B),join(B,meet(A,complement(B))))) = meet(complement(B),join(B,A)). [para(4(a,1),29(a,1,2,2,2)),rewrite([7(3),19(8),7(7),8(8)])].
% 5.43/5.73 113 join(meet(meet(A,B),join(C,meet(A,meet(B,D)))),meet(meet(A,B),join(D,meet(A,meet(B,C))))) = meet(meet(A,B),join(C,D)). [para(10(a,1),29(a,1,2,2,2)),rewrite([7(3),10(3),7(2),10(3,R),7(2),7(7),10(8,R),7(7)])].
% 5.43/5.73 114 meet(meet(A,B),join(A,C)) = meet(A,B). [para(20(a,1),29(a,1,2,2,2)),rewrite([7(3),10(3),7(2),10(3,R),7(2),6(4),7(2),20(2),6(6)]),flip(a)].
% 5.43/5.73 128 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),114(a,1,1)),rewrite([7(4)])].
% 5.43/5.73 132 meet(meet(A,B),meet(join(A,C),join(D,meet(A,B)))) = meet(A,B). [para(114(a,1),22(a,2)),rewrite([8(4)])].
% 5.43/5.73 135 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(114(a,1),114(a,1,1)),rewrite([8(3),114(7)])].
% 5.43/5.73 136 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [back_rewrite(92),rewrite([128(5),20(2)]),flip(a)].
% 5.43/5.73 138 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [back_rewrite(100),rewrite([135(6),20(3)]),flip(a)].
% 5.43/5.73 140 meet(meet(A,meet(B,C)),join(D,meet(A,C))) = meet(A,meet(B,C)). [para(10(a,1),128(a,1,1)),rewrite([7(3),8(4),7(6),10(7,R),7(6)])].
% 5.43/5.73 148 join(meet(A,join(B,C)),meet(A,join(join(C,meet(B,A)),meet(A,join(B,meet(C,A)))))) = meet(A,join(join(C,meet(B,A)),meet(A,join(B,meet(C,A))))). [para(7(a,1),30(a,1,1)),rewrite([7(2),7(3),7(5),7(11),7(13)])].
% 5.43/5.73 153 join(meet(A,join(join(B,meet(A,C)),meet(A,join(C,meet(A,B))))),meet(A,join(meet(A,join(C,B)),join(join(B,meet(A,C)),meet(A,join(C,meet(A,B))))))) = meet(A,join(meet(A,join(C,B)),join(join(B,meet(A,C)),meet(A,join(C,meet(A,B)))))). [para(14(a,1),30(a,1,2,2,2,2)),rewrite([8(6),20(13),20(16),8(16),20(24),14(31),20(27),8(27)])].
% 5.43/5.73 164 join(meet(A,join(B,meet(C,complement(A)))),meet(A,join(meet(A,B),join(meet(C,complement(A)),meet(A,B))))) = meet(A,join(meet(A,B),join(meet(C,complement(A)),meet(A,B)))). [para(41(a,1),30(a,1,2,2,2,2,2)),rewrite([19(10),8(10),41(19),19(18),8(18)])].
% 5.43/5.73 184 meet(A,join(meet(A,join(B,C)),join(join(C,meet(A,B)),meet(A,join(B,meet(A,C)))))) = meet(A,join(join(C,meet(A,B)),meet(A,join(B,meet(A,C))))). [para(30(a,1),30(a,1,2,2,2,2)),rewrite([20(19),8(19),20(27),8(27),12(27),8(26),30(26),26(25),8(18),153(18),20(19),8(19),30(29),20(27),8(27),12(27),8(26),30(26),26(25)])].
% 5.43/5.73 270 meet(A,join(join(A,B),meet(A,C))) = A. [para(5(a,1),136(a,2)),rewrite([7(3),22(4)])].
% 5.43/5.73 274 join(meet(A,B),meet(A,join(meet(B,C),meet(A,B)))) = meet(A,B). [para(136(a,1),14(a,1,1)),rewrite([6(8)])].
% 5.43/5.73 364 join(meet(A,join(B,meet(A,C))),meet(A,join(meet(A,C),meet(B,A)))) = meet(A,join(B,meet(A,C))). [para(7(a,1),39(a,1,1)),rewrite([7(3),7(5)])].
% 5.43/5.73 502 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(5(a,1),45(a,1,2,2,2)),rewrite([270(4),8(3),5(4),2(1)]),flip(a)].
% 5.43/5.73 509 meet(A,join(B,meet(one,join(A,C)))) = A. [para(18(a,1),45(a,1,1,2,2)),rewrite([8(1),5(2),6(7)]),flip(a)].
% 5.43/5.73 613 meet(one,join(A,B)) = join(A,B). [para(30(a,1),509(a,1,2)),rewrite([7(2),18(2),7(4),18(4),7(6),18(6),8(5),26(8),10(5,R),1(4),7(5),18(5)])].
% 5.43/5.73 620 meet(one,complement(A)) = complement(A). [para(89(a,1),613(a,1,2)),rewrite([89(6)])].
% 5.43/5.73 622 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(613(a,1),128(a,1,1)),rewrite([8(3),12(3),8(2),12(3,R),8(2),613(7)])].
% 5.43/5.73 623 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(613(a,1),136(a,2)),rewrite([7(5),10(6,R),7(5),613(5),613(6)])].
% 5.43/5.73 628 meet(complement(A),join(B,complement(A))) = complement(A). [para(620(a,1),128(a,1,1)),rewrite([8(3),620(7)])].
% 5.43/5.73 629 join(complement(A),meet(B,complement(A))) = complement(A). [para(620(a,1),136(a,2)),rewrite([7(5),10(6,R),18(5),613(6)])].
% 5.43/5.73 640 meet(A,meet(B,meet(join(C,D),join(C,meet(A,join(C,D)))))) = meet(A,meet(B,join(C,meet(A,join(C,D))))). [para(23(a,1),46(a,1,2,2,1))].
% 5.43/5.73 704 join(meet(A,join(B,C)),meet(A,join(B,meet(C,A)))) = meet(A,join(B,C)). [para(7(a,1),52(a,1,1)),rewrite([7(2),7(3)])].
% 5.43/5.73 705 join(meet(A,join(B,C)),meet(A,join(C,meet(A,B)))) = meet(A,join(B,C)). [para(8(a,1),52(a,1,1,2)),rewrite([8(7)])].
% 5.43/5.73 775 meet(A,join(join(A,B),meet(C,D))) = A. [para(135(a,1),502(a,1,2,2))].
% 5.43/5.73 783 meet(A,join(join(A,B),complement(C))) = A. [para(628(a,1),502(a,1,2,2))].
% 5.43/5.73 788 meet(A,join(B,join(join(A,C),complement(D)))) = A. [para(783(a,1),14(a,1,1,2,2)),rewrite([8(1),5(2),6(7)]),flip(a)].
% 5.43/5.73 820 meet(complement(A),join(B,join(complement(A),complement(C)))) = complement(A). [para(629(a,1),788(a,1,2,2,1))].
% 5.43/5.73 838 join(meet(A,join(B,C)),meet(A,meet(D,join(B,C)))) = meet(A,join(B,C)). [para(14(a,1),623(a,1,1)),rewrite([14(9),10(5,R),7(4),14(13)])].
% 5.43/5.73 841 join(join(A,B),meet(A,C)) = join(A,B). [para(114(a,1),623(a,1,2))].
% 5.43/5.73 857 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),841(a,1,1)),rewrite([8(4)])].
% 5.43/5.73 889 join(complement(A),meet(B,meet(C,complement(A)))) = complement(A). [para(629(a,1),857(a,1,1)),rewrite([7(4),10(4,R),7(3),629(9)])].
% 5.43/5.73 936 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(2(a,1),59(a,1,1,2)),rewrite([20(2),20(3),26(4),2(5),10(4),7(3),10(4,R),7(3),20(5),23(6),8(6),26(7)])].
% 5.43/5.73 937 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(5(a,1),59(a,1,2,2,2)),rewrite([8(8),12(9,R),8(8),14(8)])].
% 5.43/5.73 1051 complement(A) != zero | complement(complement(A)) = one. [para(820(a,1),64(a,1)),rewrite([3(7),48(5)]),flip(b)].
% 5.43/5.73 1077 join(zero,meet(A,B)) = meet(A,B). [para(4(a,1),936(a,1,2,2)),rewrite([38(3),8(3)])].
% 5.43/5.73 1079 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(936(a,1),14(a,1,1,2)),rewrite([20(2),20(4),274(6)]),flip(a)].
% 5.43/5.73 1114 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(1079(a,1),59(a,1,2,2,2)),rewrite([7(1),7(5),20(6),7(8),20(9),8(9),12(10),8(9),12(10,R),8(9),705(9),7(6),8(7)])].
% 5.43/5.73 1275 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(4(a,1),71(a,1,1)),rewrite([4(6),19(6),4(5),2(3)]),flip(a)].
% 5.43/5.73 1330 join(A,complement(complement(A))) = complement(complement(A)). [hyper(57,a,1275,a)].
% 5.43/5.73 1341 meet(A,complement(complement(A))) = A. [para(1330(a,1),5(a,1,2))].
% 5.43/5.73 1342 join(A,join(B,complement(complement(A)))) = join(B,complement(complement(A))). [para(1330(a,1),12(a,2,2)),rewrite([8(3)])].
% 5.43/5.73 1353 meet(A,complement(complement(join(A,B)))) = A. [para(1330(a,1),783(a,1,2))].
% 5.43/5.73 1357 meet(join(A,B),join(A,complement(complement(B)))) = join(A,B). [para(1330(a,1),622(a,1,2,2))].
% 5.43/5.73 1417 meet(A,complement(join(A,B))) = zero. [para(1353(a,1),41(a,1,2)),rewrite([7(3)])].
% 5.43/5.73 1444 meet(A,complement(complement(complement(A)))) = zero. [para(1330(a,1),1417(a,1,2,1))].
% 5.43/5.73 1845 meet(A,complement(join(B,complement(complement(A))))) = zero. [para(1342(a,1),1417(a,1,2,1))].
% 5.43/5.73 2004 join(A,complement(complement(complement(A)))) = one. [para(3(a,1),1357(a,1,1)),rewrite([613(6),3(6)])].
% 5.43/5.73 2031 complement(complement(complement(A))) = complement(A). [hyper(17,a,1444,a,b,2004,a),flip(a)].
% 5.43/5.73 2046 meet(complement(A),complement(join(B,complement(A)))) = zero. [para(2031(a,1),1845(a,1,2,1,2))].
% 5.43/5.73 2141 meet(complement(A),join(complement(complement(A)),complement(join(B,complement(A))))) = zero. [para(2046(a,1),77(a,1,2,2)),rewrite([19(5),4(4),8(8)]),flip(a)].
% 5.43/5.73 2227 meet(complement(A),join(A,meet(B,complement(A)))) = meet(complement(A),join(A,B)). [para(111(a,1),14(a,1,1,2)),rewrite([20(5),10(11,R),1(10),8(10),12(10,R),2(9),704(9),12(10,R),2(9)]),flip(a)].
% 5.43/5.73 2258 meet(meet(A,B),complement(join(A,C))) = zero. [para(841(a,1),111(a,2,2)),rewrite([2227(13),841(9),7(8),4(8),8(6),1077(6),7(8),4(8)])].
% 5.43/5.73 2291 meet(meet(A,B),complement(join(B,C))) = zero. [para(7(a,1),2258(a,1,1))].
% 5.43/5.73 2297 meet(meet(A,B),complement(join(C,meet(A,B)))) = zero. [para(114(a,1),2258(a,1,1)),rewrite([8(3)])].
% 5.43/5.73 2314 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [para(936(a,1),2258(a,1,2,1)),rewrite([7(2),10(2),7(1),10(2,R),7(1),7(5),10(5,R)])].
% 5.43/5.73 2337 meet(complement(A),complement(join(B,join(C,complement(A))))) = zero. [para(628(a,1),2291(a,1,1)),rewrite([8(4),12(4,R),8(3)])].
% 5.43/5.73 2377 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(7(a,1),113(a,2)),rewrite([113(11),10(6),7(5),10(6,R),7(5)])].
% 5.43/5.73 2378 join(meet(A,meet(B,join(C,meet(A,meet(B,D))))),meet(A,meet(B,join(D,meet(A,meet(B,C)))))) = meet(A,meet(B,join(C,D))). [para(113(a,1),8(a,1)),rewrite([2377(3),2377(8),2377(13),8(14)]),flip(a)].
% 5.43/5.73 2442 meet(meet(A,B),complement(C)) = meet(A,meet(B,complement(C))). [para(889(a,1),113(a,2,2)),rewrite([2377(9),2377(18),2378(19),889(5)]),flip(a)].
% 5.43/5.73 2448 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(936(a,1),113(a,1,1,2)),rewrite([1(3),10(4,R),1(3),20(4),2377(5),936(6),8(4),2377(5)]),flip(a)].
% 5.43/5.73 2769 meet(A,meet(B,meet(C,join(D,meet(A,C))))) = meet(A,meet(B,C)). [back_rewrite(140),rewrite([2377(5),2377(4)])].
% 5.43/5.73 2794 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [back_rewrite(2314),rewrite([2442(4)])].
% 5.43/5.73 2799 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [back_rewrite(2297),rewrite([2442(5)])].
% 5.43/5.73 2843 meet(A,meet(B,join(C,meet(A,join(C,D))))) = meet(A,meet(B,join(C,D))). [back_rewrite(640),rewrite([2769(7)]),flip(a)].
% 5.43/5.73 2939 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(1(a,1),2794(a,1,2,2))].
% 5.43/5.73 2940 meet(A,meet(B,meet(C,complement(meet(A,C))))) = zero. [para(2794(a,1),7(a,1)),rewrite([7(2),7(6),10(6,R),7(5),10(5,R),7(4)]),flip(a)].
% 5.43/5.73 3049 meet(A,join(complement(A),meet(B,complement(meet(A,B))))) = zero. [para(2939(a,1),77(a,1,2,2)),rewrite([19(3),4(2),8(6)]),flip(a)].
% 5.43/5.73 3489 meet(join(A,meet(B,C)),join(meet(C,join(A,meet(B,C))),meet(C,join(B,meet(A,C))))) = meet(C,join(A,meet(B,C))). [para(29(a,1),148(a,1,2,2,1)),rewrite([7(3),6(6),7(3),8(6),7(10),7(15),10(15,R),7(14),6(16),7(10),704(11),7(8),2377(8),838(9),7(6),8(12),7(15),7(20),10(20,R),7(19),6(21),7(15),8(16),23(16)]),flip(a)].
% 5.43/5.73 3490 meet(A,meet(join(B,C),join(B,meet(C,A)))) = meet(A,join(B,meet(C,A))). [para(29(a,1),148(a,2,2,1)),rewrite([7(3),6(6),7(3),7(6),8(12),7(15),7(20),10(20,R),7(19),6(21),7(15),8(16),23(16),3489(13),2(7),8(6),7(10),7(15),10(15,R),7(14),6(16),7(10),704(11),7(8),2377(8)]),flip(a)].
% 5.43/5.73 3874 meet(A,meet(join(A,B),complement(C))) = meet(A,complement(C)). [para(5(a,1),2442(a,1,1)),flip(a)].
% 5.43/5.73 3885 meet(one,meet(complement(A),complement(B))) = meet(complement(A),complement(B)). [para(620(a,1),2442(a,1,1)),flip(a)].
% 5.43/5.73 4704 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(3874(a,1),2940(a,1,2))].
% 5.43/5.73 4722 meet(A,meet(B,complement(meet(B,join(A,C))))) = zero. [para(4704(a,1),10(a,2)),rewrite([7(4)])].
% 5.43/5.73 4778 meet(A,complement(meet(join(A,B),join(A,C)))) = zero. [para(4722(a,1),3874(a,1)),flip(a)].
% 5.43/5.73 4804 meet(A,join(meet(B,complement(A)),meet(C,complement(A)))) = zero. [para(41(a,1),164(a,1,2,2,1)),rewrite([41(12),8(11),1077(11),1077(10),41(9),8(8),1077(8),41(9),41(12),8(11),1077(11),1077(10),41(9)])].
% 5.43/5.73 5112 meet(A,join(join(B,meet(A,C)),meet(A,join(C,meet(A,B))))) = meet(A,join(B,meet(A,join(C,B)))). [para(12(a,1),184(a,1,2)),rewrite([12(8),8(7),12(8,R),8(7),937(7),12(7),8(6),12(7,R),8(6),52(6)]),flip(a)].
% 5.43/5.73 5451 meet(complement(A),join(A,meet(B,complement(complement(A))))) = zero. [para(1341(a,1),4804(a,1,2,1))].
% 5.43/5.73 5476 complement(complement(A)) = A. [para(5451(a,1),60(a,1)),rewrite([8(5),3(5),4(10),19(8)]),flip(c),xx(a),xx(b)].
% 5.43/5.73 5599 meet(complement(A),join(A,complement(join(B,complement(A))))) = zero. [back_rewrite(2141),rewrite([5476(3)])].
% 5.43/5.73 5609 complement(A) != zero | one = A. [back_rewrite(1051),rewrite([5476(5)]),flip(b)].
% 5.43/5.73 5619 meet(complement(A),join(A,B)) != zero | join(A,B) = A. [para(5476(a,1),57(a,1,2,2)),rewrite([8(2),5476(7),8(6),5476(8)])].
% 5.43/5.73 5626 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [para(5476(a,1),4804(a,1,2,1,2)),rewrite([7(2),5476(4),7(3)])].
% 5.43/5.74 5763 join(A,complement(join(B,complement(A)))) = A. [hyper(5619,a,5599,a)].
% 5.43/5.74 5779 meet(A,complement(join(B,complement(A)))) = complement(join(B,complement(A))). [para(5763(a,1),628(a,1,2)),rewrite([7(4)])].
% 5.43/5.74 5787 meet(complement(join(A,complement(B))),complement(join(B,C))) = zero. [para(5763(a,1),2337(a,1,2,1,2)),rewrite([8(4)])].
% 5.43/5.74 5789 join(complement(A),complement(join(A,B))) = complement(A). [para(5476(a,1),5763(a,1,2,1,2)),rewrite([8(2)])].
% 5.43/5.74 5799 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(5789(a,1),628(a,1,2)),rewrite([7(4)])].
% 5.43/5.74 5846 meet(complement(join(A,B)),complement(join(C,complement(B)))) = zero. [para(5476(a,1),5787(a,1,1,1,2)),rewrite([8(4)])].
% 5.43/5.74 5873 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(5799(a,1),2799(a,1,2))].
% 5.43/5.74 5874 meet(complement(meet(A,join(B,C))),complement(meet(A,join(C,meet(A,join(B,C)))))) = complement(meet(A,join(C,meet(A,join(B,C))))). [para(148(a,1),5799(a,1,2,1)),rewrite([7(4),7(6),5112(10),7(12),7(14),5112(18),1114(16)])].
% 5.43/5.74 5900 meet(A,complement(join(complement(B),meet(A,B)))) = zero. [para(5476(a,1),5873(a,1,2,1,2,2))].
% 5.43/5.74 5928 meet(A,complement(join(meet(A,join(B,C)),complement(join(B,meet(A,join(B,C))))))) = zero. [para(138(a,1),5900(a,1,2,1,2)),rewrite([8(7)])].
% 5.43/5.74 6004 meet(complement(A),complement(join(B,complement(meet(A,C))))) = zero. [para(6(a,1),5846(a,1,1,1))].
% 5.43/5.74 6126 complement(join(A,complement(meet(A,B)))) = zero. [para(6004(a,1),5799(a,1)),flip(a)].
% 5.43/5.74 6127 join(A,complement(meet(A,B))) = one. [hyper(5609,a,6126,a),flip(a)].
% 5.43/5.74 6133 join(meet(A,B),complement(meet(A,meet(B,complement(C))))) = one. [para(2442(a,1),6127(a,1,2,1))].
% 5.43/5.74 6426 meet(complement(A),complement(join(B,A))) = complement(join(B,A)). [para(5779(a,1),3885(a,1,2)),rewrite([5476(3),620(4),5476(5)]),flip(a)].
% 5.43/5.74 6430 meet(complement(A),complement(meet(A,B))) = complement(A). [para(6(a,1),6426(a,1,2,1)),rewrite([7(4),6(6)])].
% 5.43/5.74 6436 meet(A,complement(meet(B,complement(A)))) = A. [para(629(a,1),6426(a,1,2,1)),rewrite([5476(5),7(4),629(8),5476(6)])].
% 5.43/5.74 6453 meet(A,meet(B,complement(meet(C,complement(A))))) = meet(A,B). [para(6436(a,1),10(a,2,2)),rewrite([7(4),7(6)])].
% 5.43/5.74 6460 join(A,complement(meet(B,complement(A)))) = complement(meet(B,complement(A))). [para(6436(a,1),629(a,1,2)),rewrite([8(4)])].
% 5.43/5.74 6517 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [para(6430(a,1),629(a,1,2)),rewrite([8(4)])].
% 5.43/5.74 7340 join(meet(A,B),complement(meet(A,meet(B,C)))) = one. [para(5476(a,1),6133(a,1,2,1,2,2))].
% 5.43/5.74 7347 join(join(A,B),complement(meet(C,join(A,B)))) = one. [para(613(a,1),7340(a,1,1)),rewrite([7(4),10(5,R),7(4),613(4)])].
% 5.43/5.74 7449 join(complement(A),join(join(A,B),meet(C,D))) = one. [para(775(a,1),7347(a,1,2,1)),rewrite([8(5)])].
% 5.43/5.74 7481 join(A,join(complement(A),meet(B,C))) = one. [para(629(a,1),7449(a,1,2,1)),rewrite([5476(2)])].
% 5.43/5.74 7572 join(complement(A),meet(B,complement(meet(A,B)))) = complement(A). [hyper(17,a,3049,a,b,7481,a),flip(a)].
% 5.43/5.74 7983 meet(complement(meet(A,join(B,meet(A,C)))),complement(meet(A,join(meet(A,C),meet(A,B))))) = complement(meet(A,join(B,meet(A,C)))). [para(364(a,1),6426(a,1,2,1)),rewrite([7(2),7(10),7(15),705(18)])].
% 5.43/5.74 8121 meet(A,meet(complement(B),complement(meet(A,B)))) = meet(A,complement(meet(A,B))). [para(7572(a,1),132(a,1,2,2)),rewrite([7(1),10(7),2377(6),22(6),10(5,R),7(4),7(6)])].
% 5.43/5.74 8139 join(A,meet(B,complement(meet(B,complement(A))))) = A. [para(5476(a,1),7572(a,1,1)),rewrite([7(2),5476(7)])].
% 5.43/5.74 8168 join(meet(A,B),meet(A,join(meet(A,B),complement(meet(A,complement(B)))))) = meet(A,complement(meet(A,complement(B)))). [para(8139(a,1),14(a,1,1,2)),rewrite([8(6),6460(12)])].
% 5.43/5.74 8182 meet(A,complement(meet(A,complement(B)))) = meet(A,B). [para(8139(a,1),132(a,1,2,2)),rewrite([7(6),10(7,R),10(6,R),22(6),6453(5),7(1)]),flip(a)].
% 5.43/5.74 8185 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(4778(a,1),8139(a,1,2,2,1)),rewrite([50(5),18(5),8(4)])].
% 5.43/5.74 8186 join(A,meet(B,complement(A))) = join(A,B). [para(5873(a,1),8139(a,1,2,2,1)),rewrite([50(5),18(5),8(4),25(4),8(1)]),flip(a)].
% 5.43/5.74 8187 join(A,join(complement(B),meet(B,A))) = join(complement(B),meet(B,A)). [para(5900(a,1),8139(a,1,2,2,1)),rewrite([7(2),50(5),18(5),8(4),7(6)])].
% 5.43/5.74 8188 complement(join(A,meet(B,A))) = meet(complement(A),complement(meet(B,A))). [para(8139(a,1),6426(a,1,2,1)),rewrite([8182(4),7(4),8182(8)]),flip(a)].
% 5.43/5.74 8189 meet(complement(A),complement(meet(B,A))) = complement(A). [para(8139(a,1),6426(a,2,1)),rewrite([8182(4),8182(6),8188(5),10(7,R),1(6)])].
% 5.43/5.74 8203 join(meet(A,B),meet(A,join(meet(A,B),complement(meet(A,complement(B)))))) = meet(A,B). [back_rewrite(8168),rewrite([8182(12)])].
% 5.43/5.74 8235 meet(A,complement(meet(A,B))) = meet(A,complement(B)). [back_rewrite(8121),rewrite([8189(4)]),flip(a)].
% 5.43/5.74 8246 join(meet(A,join(B,meet(A,C))),meet(A,meet(join(C,meet(A,B)),complement(meet(A,join(B,meet(A,C))))))) = meet(A,join(B,C)). [para(14(a,1),8186(a,2)),rewrite([2442(11)])].
% 5.43/5.74 8265 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(5476(a,1),8186(a,1,2,2)),rewrite([7(2),8(5)])].
% 5.43/5.74 8271 complement(meet(A,B)) = join(complement(A),complement(B)). [para(6517(a,1),8186(a,2)),rewrite([5476(5),7(4),8235(4),8265(4),8(3)]),flip(a)].
% 5.43/5.74 8290 join(meet(A,join(B,meet(A,C))),meet(A,meet(join(C,meet(A,B)),join(complement(A),complement(join(B,meet(A,C))))))) = meet(A,join(B,C)). [back_rewrite(8246),rewrite([8271(9)])].
% 5.43/5.74 8303 join(complement(A),meet(B,A)) = join(B,complement(A)). [back_rewrite(8187),rewrite([7(2),25(4),7(4)]),flip(a)].
% 5.43/5.74 8365 meet(A,join(B,complement(A))) = meet(A,B). [back_rewrite(8203),rewrite([8271(5),5476(5),8(4),12(5),8(4),12(5,R),8(4),8265(4),23(4),937(5)])].
% 5.43/5.74 8452 meet(join(complement(A),complement(join(B,meet(A,C)))),join(complement(A),complement(join(meet(A,C),meet(A,B))))) = join(complement(A),complement(join(B,meet(A,C)))). [back_rewrite(7983),rewrite([8271(4),8271(10),8271(16)])].
% 5.43/5.74 9035 meet(join(complement(A),complement(join(B,C))),join(complement(A),complement(join(C,meet(A,join(B,C)))))) = join(complement(A),complement(join(C,meet(A,join(B,C))))). [back_rewrite(5874),rewrite([8271(3),8271(9),8271(16)])].
% 5.43/5.74 9612 complement(join(complement(A),complement(B))) = meet(A,B). [para(8271(a,1),5476(a,1,1))].
% 5.43/5.74 9848 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(5476(a,1),8365(a,1,2,2)),rewrite([8(2),7(5)])].
% 5.43/5.74 9949 complement(join(A,B)) = meet(complement(A),complement(B)). [para(3885(a,1),9612(a,2)),rewrite([42(2),8271(5),5476(3),5476(3),12(3),8(2),19(2),8(1)])].
% 5.43/5.74 10104 meet(A,meet(join(B,C),join(complement(A),meet(complement(B),complement(C))))) = zero. [back_rewrite(5928),rewrite([9949(6),8271(6),9949(6),9949(11),8271(3),9949(3),8271(13),5476(7),9949(11),5476(7),8271(9),5476(7),5476(7),2843(10),7(7)])].
% 5.43/5.74 10419 meet(join(complement(A),meet(complement(B),complement(C))),join(complement(A),meet(complement(C),join(complement(A),meet(complement(B),complement(C)))))) = join(complement(A),meet(complement(C),join(complement(A),meet(complement(B),complement(C))))). [back_rewrite(9035),rewrite([9949(3),9949(10),8271(10),9949(10),9949(20),8271(20),9949(20)])].
% 5.43/5.74 10738 meet(join(complement(A),complement(B)),join(complement(A),meet(complement(C),join(complement(A),complement(B))))) = join(complement(A),meet(complement(C),join(complement(A),complement(B)))). [back_rewrite(8452),rewrite([9949(4),8271(4),9949(12),8271(10),8271(13),8185(16),7(15),2377(15),3490(15),9949(15),8271(15)])].
% 5.43/5.74 10765 join(meet(A,join(B,meet(A,C))),meet(A,meet(join(C,meet(A,B)),join(complement(A),meet(complement(B),join(complement(A),complement(C))))))) = meet(A,join(B,C)). [back_rewrite(8290),rewrite([9949(9),8271(9)])].
% 5.43/5.74 11020 meet(join(A,B),join(C,meet(complement(A),complement(B)))) = meet(C,join(A,B)). [para(9949(a,1),8365(a,1,2,2)),rewrite([7(8)])].
% 5.43/5.74 11021 meet(A,meet(complement(A),join(B,C))) = zero. [back_rewrite(10104),rewrite([11020(7)])].
% 5.43/5.74 11173 join(meet(A,B),meet(B,complement(A))) = B. [para(8365(a,1),8303(a,1,2)),rewrite([9949(3),5476(3),7(2),7(3),8(4),9949(7),5476(7),7(6),6(7)])].
% 5.43/5.74 11175 join(meet(A,B),meet(A,complement(B))) = A. [para(7(a,1),11173(a,1,1))].
% 5.43/5.74 11179 join(meet(A,B),meet(B,meet(C,complement(A)))) = meet(B,join(A,C)). [para(22(a,1),11173(a,1,1)),rewrite([7(5),10(5,R),7(4),9848(4)])].
% 5.43/5.74 11194 meet(join(A,B),join(A,meet(C,B))) = join(A,meet(C,B)). [para(11173(a,1),622(a,1,2,2)),rewrite([7(4)])].
% 5.43/5.74 11208 join(meet(A,B),meet(B,meet(complement(A),join(C,meet(A,B))))) = meet(B,join(C,meet(A,B))). [para(2448(a,1),11173(a,1,1)),rewrite([7(6),10(6,R),7(5)])].
% 5.43/5.74 11215 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [para(5626(a,1),11173(a,1,1)),rewrite([5476(6),7(5),1077(6)])].
% 5.43/5.74 11519 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(11175(a,1),622(a,1,2,2)),rewrite([7(4)])].
% 5.43/5.74 11542 meet(A,meet(join(B,meet(A,C)),join(complement(A),meet(complement(C),join(complement(A),complement(B)))))) = meet(A,meet(join(C,B),join(complement(A),meet(complement(C),join(complement(A),complement(B)))))). [para(14(a,1),9848(a,1,2)),rewrite([8271(4),9949(4),8271(4),7(10),2377(10),8271(17),9949(17),8271(17),2377(21)]),flip(a)].
% 5.43/5.74 11544 meet(complement(A),join(B,meet(A,C))) = meet(B,complement(A)). [para(25(a,1),9848(a,1,2)),rewrite([9848(3),7(6)]),flip(a)].
% 5.43/5.74 11573 join(meet(A,join(B,meet(A,C))),meet(A,meet(join(B,C),join(complement(A),meet(complement(B),join(complement(A),complement(C))))))) = meet(A,join(B,C)). [back_rewrite(10765),rewrite([11542(14)])].
% 5.43/5.74 11579 meet(A,join(B,meet(C,A))) = meet(A,join(C,B)). [back_rewrite(11208),rewrite([11544(5),11179(5)]),flip(a)].
% 5.43/5.74 11660 join(complement(A),meet(complement(B),join(complement(A),complement(C)))) = meet(join(complement(A),complement(C)),join(complement(A),complement(B))). [back_rewrite(10738),rewrite([11579(11),8(6)]),flip(a)].
% 5.43/5.74 11698 meet(join(complement(A),complement(B)),join(complement(A),complement(C))) = join(complement(A),meet(complement(B),complement(C))). [back_rewrite(10419),rewrite([11579(13),8(10),11660(12),10(13),7(12),11519(12),11194(9),11579(13),8(10),11660(12)]),flip(a)].
% 5.43/5.74 11801 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(11573),rewrite([11660(11),11698(11),7(8),11020(10),11021(7),8(5),1077(5)])].
% 5.43/5.74 12025 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(11215),rewrite([11801(4),8(2),11801(3),8(1)]),flip(a)].
% 5.43/5.74 12026 $F # answer(prove_distributivity). [resolve(12025,a,16,a)].
% 5.43/5.74
% 5.43/5.74 % SZS output end Refutation
% 5.43/5.74 ============================== end of proof ==========================
% 5.43/5.74
% 5.43/5.74 ============================== STATISTICS ============================
% 5.43/5.74
% 5.43/5.74 Given=393. Generated=93497. Kept=12021. proofs=1.
% 5.43/5.74 Usable=123. Sos=2387. Demods=2121. Limbo=224, Disabled=9299. Hints=0.
% 5.43/5.74 Megabytes=17.85.
% 5.43/5.74 User_CPU=4.69, System_CPU=0.06, Wall_clock=5.
% 5.43/5.74
% 5.43/5.74 ============================== end of statistics =====================
% 5.43/5.74
% 5.43/5.74 ============================== end of search =========================
% 5.43/5.74
% 5.43/5.74 THEOREM PROVED
% 5.43/5.74 % SZS status Unsatisfiable
% 5.43/5.74
% 5.43/5.74 Exiting with 1 proof.
% 5.43/5.74
% 5.43/5.74 Process 25702 exit (max_proofs) Wed Jun 29 16:46:59 2022
% 5.43/5.74 Prover9 interrupted
%------------------------------------------------------------------------------