TSTP Solution File: LAT236-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT236-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 06:26:19 EDT 2022
% Result : Unsatisfiable 6.24s 6.58s
% Output : Refutation 6.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : LAT236-1 : TPTP v8.1.0. Released v3.1.0.
% 0.09/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 22:43:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.24/6.58 ============================== Prover9 ===============================
% 6.24/6.58 Prover9 (32) version 2009-11A, November 2009.
% 6.24/6.58 Process 5021 was started by sandbox on n027.cluster.edu,
% 6.24/6.58 Tue Jun 28 22:43:50 2022
% 6.24/6.58 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4868_n027.cluster.edu".
% 6.24/6.58 ============================== end of head ===========================
% 6.24/6.58
% 6.24/6.58 ============================== INPUT =================================
% 6.24/6.58
% 6.24/6.58 % Reading from file /tmp/Prover9_4868_n027.cluster.edu
% 6.24/6.58
% 6.24/6.58 set(prolog_style_variables).
% 6.24/6.58 set(auto2).
% 6.24/6.58 % set(auto2) -> set(auto).
% 6.24/6.58 % set(auto) -> set(auto_inference).
% 6.24/6.58 % set(auto) -> set(auto_setup).
% 6.24/6.58 % set(auto_setup) -> set(predicate_elim).
% 6.24/6.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.24/6.58 % set(auto) -> set(auto_limits).
% 6.24/6.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.24/6.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.24/6.58 % set(auto) -> set(auto_denials).
% 6.24/6.58 % set(auto) -> set(auto_process).
% 6.24/6.58 % set(auto2) -> assign(new_constants, 1).
% 6.24/6.58 % set(auto2) -> assign(fold_denial_max, 3).
% 6.24/6.58 % set(auto2) -> assign(max_weight, "200.000").
% 6.24/6.58 % set(auto2) -> assign(max_hours, 1).
% 6.24/6.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.24/6.58 % set(auto2) -> assign(max_seconds, 0).
% 6.24/6.58 % set(auto2) -> assign(max_minutes, 5).
% 6.24/6.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.24/6.58 % set(auto2) -> set(sort_initial_sos).
% 6.24/6.58 % set(auto2) -> assign(sos_limit, -1).
% 6.24/6.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.24/6.58 % set(auto2) -> assign(max_megs, 400).
% 6.24/6.58 % set(auto2) -> assign(stats, some).
% 6.24/6.58 % set(auto2) -> clear(echo_input).
% 6.24/6.58 % set(auto2) -> set(quiet).
% 6.24/6.58 % set(auto2) -> clear(print_initial_clauses).
% 6.24/6.58 % set(auto2) -> clear(print_given).
% 6.24/6.58 assign(lrs_ticks,-1).
% 6.24/6.58 assign(sos_limit,10000).
% 6.24/6.58 assign(order,kbo).
% 6.24/6.58 set(lex_order_vars).
% 6.24/6.58 clear(print_given).
% 6.24/6.58
% 6.24/6.58 % formulas(sos). % not echoed (14 formulas)
% 6.24/6.58
% 6.24/6.58 ============================== end of input ==========================
% 6.24/6.58
% 6.24/6.58 % From the command line: assign(max_seconds, 300).
% 6.24/6.58
% 6.24/6.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.24/6.58
% 6.24/6.58 % Formulas that are not ordinary clauses:
% 6.24/6.58
% 6.24/6.58 ============================== end of process non-clausal formulas ===
% 6.24/6.58
% 6.24/6.58 ============================== PROCESS INITIAL CLAUSES ===============
% 6.24/6.58
% 6.24/6.58 ============================== PREDICATE ELIMINATION =================
% 6.24/6.58
% 6.24/6.58 ============================== end predicate elimination =============
% 6.24/6.58
% 6.24/6.58 Auto_denials:
% 6.24/6.58 % copying label prove_distributivity to answer in negative clause
% 6.24/6.58
% 6.24/6.58 Term ordering decisions:
% 6.24/6.58
% 6.24/6.58 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 6.24/6.58 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 6.24/6.58
% 6.24/6.58 ============================== end of process initial clauses ========
% 6.24/6.58
% 6.24/6.58 ============================== CLAUSES FOR SEARCH ====================
% 6.24/6.58
% 6.24/6.58 ============================== end of clauses for search =============
% 6.24/6.58
% 6.24/6.58 ============================== SEARCH ================================
% 6.24/6.58
% 6.24/6.58 % Starting search at 0.01 seconds.
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=181.000, iters=3363
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=178.000, iters=3354
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=173.000, iters=3347
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=169.000, iters=3339
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=137.000, iters=3436
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=135.000, iters=3420
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=131.000, iters=3400
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=127.000, iters=3381
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=123.000, iters=3355
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=109.000, iters=3369
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=107.000, iters=3339
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=103.000, iters=3374
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=102.000, iters=3371
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=98.000, iters=3475
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=92.000, iters=3369
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=90.000, iters=3352
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=87.000, iters=3360
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=86.000, iters=3416
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=84.000, iters=3365
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=82.000, iters=3348
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=55.000, iters=4056
% 6.24/6.58
% 6.24/6.58 Low Water (keep): wt=49.000, iters=3433
% 6.24/6.58
% 6.24/6.58 ============================== PROOF =================================
% 6.24/6.58 % SZS status Unsatisfiable
% 6.24/6.58 % SZS output start Refutation
% 6.24/6.58
% 6.24/6.58 % Proof 1 at 5.53 (+ 0.07) seconds: prove_distributivity.
% 6.24/6.58 % Length of proof is 95.
% 6.24/6.58 % Level of proof is 20.
% 6.24/6.58 % Maximum clause weight is 33.000.
% 6.24/6.58 % Given clauses 451.
% 6.24/6.58
% 6.24/6.58 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 6.24/6.58 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 6.24/6.58 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 6.24/6.58 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 6.24/6.58 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 6.24/6.58 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 6.24/6.58 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 6.24/6.58 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 6.24/6.58 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 6.24/6.58 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 6.24/6.58 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 6.24/6.58 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 6.24/6.58 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 6.24/6.58 14 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(D,meet(A,C))))) # label(equation_H39) # label(axiom). [assumption].
% 6.24/6.58 15 meet(A,join(B,meet(C,join(D,meet(A,C))))) = meet(A,join(B,meet(C,join(A,D)))). [copy(14),flip(a)].
% 6.24/6.58 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 6.24/6.58 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 6.24/6.58 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 6.24/6.58 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 6.24/6.58 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 6.24/6.58 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 6.24/6.58 22 meet(A,meet(A,B)) = meet(A,B). [para(11(a,1),1(a,1)),rewrite([8(1),8(2),11(2,R),1(1),8(3)])].
% 6.24/6.58 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 6.24/6.58 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 6.24/6.58 25 join(A,join(A,B)) = join(A,B). [para(13(a,1),2(a,1)),rewrite([9(1),9(2),13(2,R),2(1),9(3)])].
% 6.24/6.58 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 6.24/6.58 27 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 6.24/6.58 28 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(2(a,1),15(a,1,2)),rewrite([9(10),15(11),2(9),24(7)])].
% 6.24/6.58 29 meet(A,join(B,meet(complement(A),join(A,C)))) = meet(A,join(B,meet(C,complement(A)))). [para(5(a,1),15(a,1,2,2,2,2)),rewrite([21(3),8(2)]),flip(a)].
% 6.24/6.58 30 meet(A,join(B,meet(C,join(A,C)))) = meet(A,join(B,C)). [para(6(a,1),15(a,1,2,2)),flip(a)].
% 6.24/6.58 31 meet(A,join(B,meet(C,join(D,meet(C,A))))) = meet(A,join(B,meet(C,join(D,A)))). [para(15(a,1),8(a,2)),rewrite([8(1),8(5),9(6)])].
% 6.24/6.58 36 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 6.24/6.58 37 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 6.24/6.58 39 one != A | complement(A) = zero. [back_rewrite(36),rewrite([37(2)]),xx(a)].
% 6.24/6.58 40 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([37(5)])].
% 6.24/6.58 45 meet(a,meet(b,join(A,a))) = a. [para(19(a,1),24(a,2)),rewrite([9(4)])].
% 6.24/6.58 46 complement(join(A,one)) = zero. [hyper(39,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 6.24/6.58 48 join(A,one) = one. [para(46(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 6.24/6.58 49 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([48(5)])].
% 6.24/6.58 53 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(40(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),37(6)])].
% 6.24/6.58 54 meet(A,join(B,meet(meet(C,complement(A)),join(A,D)))) = meet(A,join(B,meet(C,meet(D,complement(A))))). [para(40(a,1),15(a,1,2,2,2,2)),rewrite([21(4),8(3),11(3,R),8(2)]),flip(a)].
% 6.24/6.58 56 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(49(a,1),18(b,1)),flip(c),xx(b)].
% 6.24/6.58 57 meet(a,join(A,a)) = a. [para(45(a,1),11(a,1)),rewrite([19(6),8(5)]),flip(a)].
% 6.24/6.58 60 meet(A,join(B,meet(A,C))) != zero | join(A,B) != one | join(B,meet(A,C)) = complement(A). [para(27(a,1),18(b,1)),flip(c)].
% 6.24/6.58 66 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(28(a,1),11(a,1)),rewrite([8(5)]),flip(a)].
% 6.24/6.58 68 meet(A,join(B,meet(meet(C,join(D,meet(A,C))),join(E,meet(A,C))))) = meet(A,join(B,meet(meet(C,join(D,meet(A,C))),join(A,E)))). [para(28(a,1),15(a,1,2,2,2,2))].
% 6.24/6.58 85 meet(A,join(complement(A),meet(B,complement(A)))) = zero. [para(7(a,1),29(a,1,2)),rewrite([5(2)]),flip(a)].
% 6.24/6.58 88 meet(A,join(B,meet(zero,complement(A)))) = meet(A,B). [para(29(a,1),15(a,1)),rewrite([5(2),2(7),8(7),5(7),21(7)])].
% 6.24/6.58 109 meet(join(A,B),join(A,meet(B,join(A,B)))) = join(A,B). [para(1(a,1),30(a,2)),rewrite([9(3),13(3,R),2(2)])].
% 6.24/6.58 113 meet(A,join(B,meet(join(A,C),join(C,meet(A,D))))) = meet(A,join(B,join(C,meet(A,D)))). [para(27(a,1),30(a,1,2,2,2)),rewrite([8(4)])].
% 6.24/6.58 122 meet(A,join(meet(zero,complement(A)),meet(B,join(A,C)))) = meet(A,B). [para(24(a,1),88(a,2)),rewrite([9(6)])].
% 6.24/6.58 124 meet(A,join(meet(zero,complement(A)),meet(B,meet(C,complement(A))))) = zero. [para(53(a,1),88(a,2)),rewrite([9(7)])].
% 6.24/6.58 141 meet(complement(A),join(B,meet(A,join(C,complement(A))))) = meet(complement(A),join(B,meet(A,C))). [para(5(a,1),31(a,1,2,2,2,2)),rewrite([21(3)]),flip(a)].
% 6.24/6.58 145 meet(b,join(A,meet(a,join(B,b)))) = meet(b,join(A,a)). [para(19(a,1),31(a,1,2,2,2,2)),rewrite([57(5)]),flip(a)].
% 6.24/6.58 147 meet(meet(A,complement(B)),join(C,meet(B,join(D,meet(A,complement(B)))))) = meet(meet(A,complement(B)),join(C,meet(B,D))). [para(40(a,1),31(a,1,2,2,2,2)),rewrite([21(4)]),flip(a)].
% 6.24/6.58 368 meet(A,join(meet(B,complement(A)),meet(B,meet(C,complement(A))))) = zero. [para(7(a,1),54(a,1,2)),rewrite([40(3)]),flip(a)].
% 6.24/6.58 523 meet(one,join(A,meet(one,join(B,complement(A))))) = one. [para(49(a,1),109(a,1,1)),rewrite([49(6),8(5),49(10)])].
% 6.24/6.58 529 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(109(a,1),66(a,1,1)),rewrite([109(6),13(3),9(2),13(3,R),9(2),109(9)])].
% 6.24/6.58 536 meet(one,join(A,meet(one,complement(A)))) = one. [para(2(a,1),523(a,1,2,2,2))].
% 6.24/6.58 542 meet(A,join(B,meet(one,complement(B)))) = A. [para(536(a,1),11(a,1,2)),rewrite([20(2),20(6),8(5)]),flip(a)].
% 6.24/6.58 648 meet(one,join(A,meet(one,complement(B)))) = meet(one,join(A,complement(B))). [para(542(a,1),68(a,1,2,2)),rewrite([15(9),9(4),48(4),20(4),9(13),48(13),8(13),28(13)]),flip(a)].
% 6.24/6.58 660 meet(one,join(A,B)) = join(A,B). [para(4(a,1),529(a,1,2,2)),rewrite([48(3),8(3)])].
% 6.24/6.58 669 join(A,meet(one,complement(B))) = join(A,complement(B)). [back_rewrite(648),rewrite([660(6),660(8)])].
% 6.24/6.58 672 join(one,complement(A)) = one. [para(669(a,1),7(a,1))].
% 6.24/6.58 848 meet(zero,complement(A)) = zero. [para(124(a,1),24(a,1,2)),rewrite([8(5),22(5),8(7),40(7)])].
% 6.24/6.58 886 meet(A,join(zero,meet(B,join(A,C)))) = meet(A,B). [back_rewrite(122),rewrite([848(3)])].
% 6.24/6.58 993 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(66(a,1),886(a,1,2,2))].
% 6.24/6.58 1018 join(zero,meet(A,B)) = meet(A,B). [para(993(a,1),1(a,1)),rewrite([8(5),993(5),1(3)]),flip(a)].
% 6.24/6.58 1222 meet(b,join(a,b)) = b. [para(145(a,1),6(a,1)),rewrite([9(4)])].
% 6.24/6.58 1244 meet(b,join(A,b)) = b. [para(1222(a,1),66(a,1,1)),rewrite([1222(6),1222(9)])].
% 6.24/6.58 1251 join(zero,b) = b. [para(1222(a,1),1018(a,1,2)),rewrite([1244(8)])].
% 6.24/6.58 1666 meet(A,join(B,join(join(A,C),meet(A,D)))) = A. [para(25(a,1),113(a,1,2,2,1)),rewrite([6(5),13(2,R),9(1),6(3)]),flip(a)].
% 6.24/6.58 1724 meet(meet(A,B),join(C,join(D,meet(A,B)))) = meet(A,B). [para(66(a,1),1666(a,1,2,2,2)),rewrite([9(3),9(5),13(5,R),2(4)])].
% 6.24/6.58 1899 meet(complement(A),join(B,meet(A,join(C,meet(D,complement(A)))))) = meet(complement(A),join(B,meet(A,C))). [para(29(a,1),141(a,2,2,2)),rewrite([9(7),27(7),9(3),141(6)]),flip(a)].
% 6.24/6.58 1900 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(85(a,1),141(a,2)),rewrite([9(7),4(7),20(5),9(4)])].
% 6.24/6.58 1967 join(A,complement(complement(A))) = complement(complement(A)). [hyper(56,a,1900,a)].
% 6.24/6.58 1970 join(A,join(B,complement(complement(A)))) = join(B,complement(complement(A))). [para(1967(a,1),13(a,2,2)),rewrite([9(3)])].
% 6.24/6.59 2613 meet(meet(A,complement(B)),join(C,meet(B,D))) = meet(A,meet(complement(B),join(C,meet(B,D)))). [para(8(a,1),147(a,2)),rewrite([147(8),11(10),8(9),11(10,R),8(9)])].
% 6.24/6.59 2616 meet(meet(A,complement(B)),join(B,C)) = meet(A,meet(complement(B),join(B,C))). [para(20(a,1),147(a,2,2,2)),rewrite([2613(9),1899(8),20(3),9(2),9(7)]),flip(a)].
% 6.24/6.59 2620 meet(A,meet(complement(B),join(B,complement(meet(A,complement(B)))))) = zero. [para(85(a,1),147(a,2)),rewrite([9(11),4(11),20(7),9(6),2616(7)])].
% 6.24/6.59 5442 meet(meet(A,B),join(A,C)) = meet(A,B). [para(7(a,1),1724(a,1,2,2)),rewrite([9(2)])].
% 6.24/6.59 5474 meet(meet(A,B),join(B,C)) = meet(A,B). [para(8(a,1),5442(a,1,1)),rewrite([8(4)])].
% 6.24/6.59 5646 meet(meet(A,B),join(C,complement(complement(B)))) = meet(A,B). [para(1970(a,1),5474(a,1,2))].
% 6.24/6.59 6180 meet(a,join(A,complement(complement(b)))) = a. [para(19(a,1),5646(a,1,1)),rewrite([19(9)])].
% 6.24/6.59 6210 meet(b,join(A,complement(complement(join(B,b))))) = b. [para(1244(a,1),5646(a,1,1)),rewrite([1244(11)])].
% 6.24/6.59 6325 meet(a,complement(complement(b))) = a. [para(2(a,1),6180(a,1,2))].
% 6.24/6.59 6359 meet(a,meet(complement(complement(b)),join(complement(a),complement(b)))) = zero. [para(6325(a,1),2620(a,1,2,2,2,1)),rewrite([9(9)])].
% 6.24/6.59 7128 meet(b,complement(complement(join(A,b)))) = b. [para(2(a,1),6210(a,1,2))].
% 6.24/6.59 7166 meet(complement(join(A,b)),join(b,meet(B,b))) = zero. [para(7128(a,1),368(a,1,2,1)),rewrite([11(11,R),8(10),7128(10)])].
% 6.24/6.59 9095 meet(complement(b),join(b,meet(A,b))) = zero. [para(2(a,1),7166(a,1,1,1))].
% 6.24/6.59 9245 complement(complement(b)) = b. [para(9095(a,1),60(a,1)),rewrite([9(7),4(7),8(11),5(11),9(9),1251(9)]),flip(c),xx(a),xx(b)].
% 6.24/6.59 9339 meet(a,meet(b,join(complement(a),complement(b)))) = zero. [back_rewrite(6359),rewrite([9245(4)])].
% 6.24/6.59 9909 meet(a,join(complement(a),complement(b))) = zero. [para(9339(a,1),11(a,1)),rewrite([19(9),8(8)]),flip(a)].
% 6.24/6.59 9923 join(a,join(complement(a),complement(b))) != one # answer(prove_distributivity). [ur(18,a,9909,a,c,17,a(flip))].
% 6.24/6.59 9956 $F # answer(prove_distributivity). [para(13(a,1),9923(a,1)),rewrite([4(6),9(4),672(4)]),xx(a)].
% 6.24/6.59
% 6.24/6.59 % SZS output end Refutation
% 6.24/6.59 ============================== end of proof ==========================
% 6.24/6.59
% 6.24/6.59 ============================== STATISTICS ============================
% 6.24/6.59
% 6.24/6.59 Given=451. Generated=80306. Kept=9951. proofs=1.
% 6.24/6.59 Usable=297. Sos=6973. Demods=6638. Limbo=0, Disabled=2695. Hints=0.
% 6.24/6.59 Megabytes=28.51.
% 6.24/6.59 User_CPU=5.54, System_CPU=0.07, Wall_clock=6.
% 6.24/6.59
% 6.24/6.59 ============================== end of statistics =====================
% 6.24/6.59
% 6.24/6.59 ============================== end of search =========================
% 6.24/6.59
% 6.24/6.59 THEOREM PROVED
% 6.24/6.59 % SZS status Unsatisfiable
% 6.24/6.59
% 6.24/6.59 Exiting with 1 proof.
% 6.24/6.59
% 6.24/6.59 Process 5021 exit (max_proofs) Tue Jun 28 22:43:56 2022
% 6.24/6.59 Prover9 interrupted
%------------------------------------------------------------------------------