TSTP Solution File: LAT253-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT253-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 06:26:24 EDT 2022
% Result : Unsatisfiable 4.11s 4.38s
% Output : Refutation 4.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT253-1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n029.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 : Tue Jun 28 18:10:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 4.11/4.38 ============================== Prover9 ===============================
% 4.11/4.38 Prover9 (32) version 2009-11A, November 2009.
% 4.11/4.38 Process 11432 was started by sandbox on n029.cluster.edu,
% 4.11/4.38 Tue Jun 28 18:10:07 2022
% 4.11/4.38 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11279_n029.cluster.edu".
% 4.11/4.38 ============================== end of head ===========================
% 4.11/4.38
% 4.11/4.38 ============================== INPUT =================================
% 4.11/4.38
% 4.11/4.38 % Reading from file /tmp/Prover9_11279_n029.cluster.edu
% 4.11/4.38
% 4.11/4.38 set(prolog_style_variables).
% 4.11/4.38 set(auto2).
% 4.11/4.38 % set(auto2) -> set(auto).
% 4.11/4.38 % set(auto) -> set(auto_inference).
% 4.11/4.38 % set(auto) -> set(auto_setup).
% 4.11/4.38 % set(auto_setup) -> set(predicate_elim).
% 4.11/4.38 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.11/4.38 % set(auto) -> set(auto_limits).
% 4.11/4.38 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.11/4.38 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.11/4.38 % set(auto) -> set(auto_denials).
% 4.11/4.38 % set(auto) -> set(auto_process).
% 4.11/4.38 % set(auto2) -> assign(new_constants, 1).
% 4.11/4.38 % set(auto2) -> assign(fold_denial_max, 3).
% 4.11/4.38 % set(auto2) -> assign(max_weight, "200.000").
% 4.11/4.38 % set(auto2) -> assign(max_hours, 1).
% 4.11/4.38 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.11/4.38 % set(auto2) -> assign(max_seconds, 0).
% 4.11/4.38 % set(auto2) -> assign(max_minutes, 5).
% 4.11/4.38 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.11/4.38 % set(auto2) -> set(sort_initial_sos).
% 4.11/4.38 % set(auto2) -> assign(sos_limit, -1).
% 4.11/4.38 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.11/4.38 % set(auto2) -> assign(max_megs, 400).
% 4.11/4.38 % set(auto2) -> assign(stats, some).
% 4.11/4.38 % set(auto2) -> clear(echo_input).
% 4.11/4.38 % set(auto2) -> set(quiet).
% 4.11/4.38 % set(auto2) -> clear(print_initial_clauses).
% 4.11/4.38 % set(auto2) -> clear(print_given).
% 4.11/4.38 assign(lrs_ticks,-1).
% 4.11/4.38 assign(sos_limit,10000).
% 4.11/4.38 assign(order,kbo).
% 4.11/4.38 set(lex_order_vars).
% 4.11/4.38 clear(print_given).
% 4.11/4.38
% 4.11/4.38 % formulas(sos). % not echoed (14 formulas)
% 4.11/4.38
% 4.11/4.38 ============================== end of input ==========================
% 4.11/4.38
% 4.11/4.38 % From the command line: assign(max_seconds, 300).
% 4.11/4.38
% 4.11/4.38 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.11/4.38
% 4.11/4.38 % Formulas that are not ordinary clauses:
% 4.11/4.38
% 4.11/4.38 ============================== end of process non-clausal formulas ===
% 4.11/4.38
% 4.11/4.38 ============================== PROCESS INITIAL CLAUSES ===============
% 4.11/4.38
% 4.11/4.38 ============================== PREDICATE ELIMINATION =================
% 4.11/4.38
% 4.11/4.38 ============================== end predicate elimination =============
% 4.11/4.38
% 4.11/4.38 Auto_denials:
% 4.11/4.38 % copying label prove_distributivity to answer in negative clause
% 4.11/4.38
% 4.11/4.38 Term ordering decisions:
% 4.11/4.38
% 4.11/4.38 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 4.11/4.38 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 4.11/4.38
% 4.11/4.38 ============================== end of process initial clauses ========
% 4.11/4.38
% 4.11/4.38 ============================== CLAUSES FOR SEARCH ====================
% 4.11/4.38
% 4.11/4.38 ============================== end of clauses for search =============
% 4.11/4.38
% 4.11/4.38 ============================== SEARCH ================================
% 4.11/4.38
% 4.11/4.38 % Starting search at 0.01 seconds.
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=143.000, iters=3543
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=97.000, iters=3363
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=95.000, iters=3345
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=93.000, iters=3409
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=91.000, iters=3393
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=83.000, iters=3340
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=81.000, iters=3382
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=79.000, iters=3351
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=43.000, iters=3961
% 4.11/4.38
% 4.11/4.38 Low Water (keep): wt=39.000, iters=3498
% 4.11/4.38
% 4.11/4.38 ============================== PROOF =================================
% 4.11/4.38 % SZS status Unsatisfiable
% 4.11/4.38 % SZS output start Refutation
% 4.11/4.38
% 4.11/4.38 % Proof 1 at 3.37 (+ 0.03) seconds: prove_distributivity.
% 4.11/4.38 % Length of proof is 100.
% 4.11/4.38 % Level of proof is 26.
% 4.11/4.38 % Maximum clause weight is 31.000.
% 4.11/4.38 % Given clauses 366.
% 4.11/4.38
% 4.11/4.38 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 4.11/4.38 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 4.11/4.38 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 4.11/4.38 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 4.11/4.38 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 4.11/4.38 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 4.11/4.38 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 4.11/4.38 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 4.11/4.38 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 4.11/4.38 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 4.11/4.38 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 4.11/4.38 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 4.11/4.38 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 4.11/4.38 14 meet(A,join(B,meet(C,join(B,D)))) = meet(A,join(B,meet(C,join(D,meet(A,B))))) # label(equation_H76) # label(axiom). [assumption].
% 4.11/4.38 15 meet(A,join(B,meet(C,join(D,meet(A,B))))) = meet(A,join(B,meet(C,join(B,D)))). [copy(14),flip(a)].
% 4.11/4.38 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 4.11/4.38 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 4.11/4.38 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 4.11/4.38 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 4.11/4.38 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 4.11/4.38 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 4.11/4.38 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)])].
% 4.11/4.38 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 4.11/4.38 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 4.11/4.38 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)])].
% 4.11/4.38 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 4.11/4.38 27 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 4.11/4.38 29 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(2(a,1),15(a,1,2,2,2)),rewrite([11(2),8(1),11(2,R),8(1),15(9),2(5),8(5),7(6)])].
% 4.11/4.38 30 meet(A,join(complement(A),meet(B,join(C,complement(A))))) = meet(A,join(complement(A),meet(B,C))). [para(5(a,1),15(a,1,2,2,2,2)),rewrite([21(3),9(7)]),flip(a)].
% 4.11/4.38 31 meet(A,join(join(A,B),meet(C,join(A,join(B,D))))) = meet(A,join(join(A,B),meet(C,join(A,D)))). [para(6(a,1),15(a,1,2,2,2,2)),rewrite([9(2),9(8),13(8),9(7),13(8,R),9(7)]),flip(a)].
% 4.11/4.38 33 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(7(a,1),15(a,1,2,2,2)),rewrite([8(1),9(4)]),flip(a)].
% 4.11/4.38 34 meet(A,join(B,meet(C,join(D,meet(B,A))))) = meet(A,join(B,meet(C,join(B,D)))). [para(15(a,1),8(a,2)),rewrite([8(1),8(5)])].
% 4.11/4.38 41 meet(A,join(one,meet(B,join(C,one)))) = meet(A,join(one,meet(B,join(A,C)))). [para(20(a,1),15(a,1,2,2,2,2)),rewrite([9(2),9(8)]),flip(a)].
% 4.11/4.38 42 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 4.11/4.38 43 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 4.11/4.38 44 one != A | complement(A) = zero. [back_rewrite(42),rewrite([43(2)]),xx(a)].
% 4.11/4.38 45 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([43(5)])].
% 4.11/4.38 46 complement(one) = zero. [hyper(18,a,43,a,b,21,a)].
% 4.11/4.38 50 complement(join(A,one)) = zero. [hyper(44,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 4.11/4.38 52 join(A,one) = one. [para(50(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 4.11/4.38 53 meet(A,join(one,meet(B,join(A,C)))) = A. [back_rewrite(41),rewrite([52(3),20(3),9(2),52(2),20(2)]),flip(a)].
% 4.11/4.38 54 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([52(5)])].
% 4.11/4.38 57 zero != A | join(A,B) != one | join(A,B) = complement(A). [para(25(a,1),18(b,1)),rewrite([6(2)]),flip(a),flip(c)].
% 4.11/4.38 58 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(45(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),43(6)])].
% 4.11/4.38 60 join(A,join(B,join(C,complement(A)))) = one. [para(54(a,1),13(a,2,2)),rewrite([9(3),13(3,R),9(2),52(6)])].
% 4.11/4.38 71 join(A,join(B,join(C,join(D,complement(A))))) = one. [para(60(a,1),13(a,2,2)),rewrite([9(4),13(4,R),9(3),13(3,R),9(2),52(7)])].
% 4.11/4.38 85 meet(A,join(one,meet(A,B))) = A. [para(2(a,1),53(a,1,2,2,2)),rewrite([8(2)])].
% 4.11/4.38 89 meet(A,meet(B,join(one,meet(A,C)))) = meet(A,B). [para(85(a,1),11(a,2,2)),rewrite([8(4),8(6)])].
% 4.11/4.38 97 meet(A,join(join(A,B),meet(A,C))) = A. [para(6(a,1),29(a,2)),rewrite([8(3),24(4)])].
% 4.11/4.38 99 meet(A,join(meet(B,C),meet(A,meet(B,meet(C,D))))) = meet(A,meet(B,C)). [para(11(a,1),29(a,2)),rewrite([8(3),11(3),8(2),11(3,R),8(2),11(8),8(7),11(8,R),8(7)])].
% 4.11/4.38 102 meet(a,join(b,meet(A,a))) = a. [para(19(a,1),29(a,2)),rewrite([8(5),11(6,R),8(5),19(5)])].
% 4.11/4.38 105 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(45(a,1),29(a,2)),rewrite([8(5),11(5,R),8(4),58(6),9(4)])].
% 4.11/4.38 113 meet(A,join(join(one,meet(A,B)),meet(A,C))) = A. [para(85(a,1),29(a,2)),rewrite([8(7),89(8)])].
% 4.11/4.38 119 meet(one,b) = b. [para(102(a,1),53(a,1,2,2)),rewrite([9(4),52(4),8(3)])].
% 4.11/4.38 122 meet(one,join(b,meet(A,b))) = b. [para(119(a,1),29(a,2)),rewrite([8(5),11(6,R),8(5),119(5)])].
% 4.11/4.38 123 meet(A,join(b,meet(B,b))) = meet(A,b). [para(122(a,1),11(a,1,2)),rewrite([20(8),8(7)]),flip(a)].
% 4.11/4.38 125 meet(one,join(a,b)) = b. [para(19(a,1),122(a,1,2,2)),rewrite([9(4)])].
% 4.11/4.38 127 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(4(a,1),30(a,1,2,2,2)),rewrite([20(3),9(2),8(5)]),flip(a)].
% 4.11/4.38 130 meet(A,meet(B,join(complement(A),meet(C,join(D,complement(A)))))) = meet(A,meet(B,join(complement(A),meet(C,D)))). [para(30(a,1),11(a,2,2)),rewrite([8(6),11(12,R),8(11)])].
% 4.11/4.38 136 meet(A,join(join(complement(A),meet(B,join(C,complement(A)))),meet(A,meet(D,join(complement(A),meet(B,C)))))) = meet(A,join(complement(A),meet(B,C))). [para(30(a,1),29(a,2)),rewrite([8(11),130(12)])].
% 4.11/4.38 137 meet(A,join(a,b)) = meet(A,b). [para(125(a,1),11(a,1,2)),rewrite([20(7),8(6)]),flip(a)].
% 4.11/4.38 142 join(a,b) = b. [para(137(a,1),1(a,1)),rewrite([8(5),137(5),1(3)]),flip(a)].
% 4.11/4.38 146 join(a,join(b,meet(A,a))) = b. [para(142(a,1),27(a,2)),rewrite([8(4)])].
% 4.11/4.38 151 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(9(a,1),31(a,2,2)),rewrite([31(6),13(9),9(8),13(9,R),9(8),6(10)])].
% 4.11/4.38 155 meet(one,join(A,B)) = join(A,B). [para(31(a,1),53(a,1,2,2)),rewrite([151(7),9(3),52(3),8(3)])].
% 4.11/4.38 166 join(b,meet(A,a)) = b. [para(146(a,1),13(a,1)),rewrite([142(6),9(5)]),flip(a)].
% 4.11/4.38 170 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(155(a,1),29(a,2)),rewrite([8(5),11(6,R),8(5),155(5),155(6)])].
% 4.11/4.38 181 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),105(a,1,2,2))].
% 4.11/4.38 184 join(zero,complement(A)) = complement(A). [hyper(18,a,181,a,b,54,a),flip(a)].
% 4.11/4.38 186 meet(one,complement(A)) = complement(A). [para(184(a,1),155(a,1,2)),rewrite([184(6)])].
% 4.11/4.38 188 meet(A,meet(B,join(C,meet(D,join(A,C))))) = meet(A,meet(B,join(C,meet(A,D)))). [para(33(a,1),11(a,2,2)),rewrite([8(4),11(9,R),8(8)])].
% 4.11/4.38 198 meet(A,join(join(B,meet(C,join(A,B))),meet(A,meet(D,join(B,meet(A,C)))))) = meet(A,join(B,meet(A,C))). [para(33(a,1),29(a,2)),rewrite([8(7),188(8)])].
% 4.11/4.38 204 join(one,complement(A)) = one. [para(186(a,1),7(a,1,2))].
% 4.11/4.38 205 join(complement(A),meet(B,complement(A))) = complement(A). [para(186(a,1),29(a,2)),rewrite([8(5),11(6,R),20(5),155(6)])].
% 4.11/4.38 206 meet(complement(A),join(A,meet(B,join(A,C)))) = meet(complement(A),join(A,meet(B,C))). [para(5(a,1),34(a,1,2,2,2,2)),rewrite([21(3)]),flip(a)].
% 4.11/4.38 230 meet(complement(A),join(one,meet(B,complement(A)))) = complement(A). [para(205(a,1),53(a,1,2,2,2))].
% 4.11/4.38 284 join(b,meet(A,b)) = b. [para(123(a,1),1(a,1)),rewrite([8(6),6(6)]),flip(a)].
% 4.11/4.38 559 meet(complement(A),join(B,complement(A))) = complement(A). [para(230(a,1),97(a,1,2,2)),rewrite([9(3),9(5),13(5,R),2(4)])].
% 4.11/4.38 696 join(one,meet(A,B)) = one. [para(113(a,1),53(a,1,2,2)),rewrite([9(5),52(5),8(5),6(5)]),flip(a)].
% 4.11/4.38 730 complement(meet(zero,join(A,meet(B,C)))) = one. [hyper(57,a,151,a(flip),b,71,a),rewrite([9(3),21(3),9(3),21(3),9(7),21(7),9(7),21(7),71(13),9(4),21(4),9(4),21(4)]),flip(a)].
% 4.11/4.38 738 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(97(a,1),151(a,1,2,2)),rewrite([9(3),13(3),9(2),13(3,R),9(2),9(4),25(4)])].
% 4.11/4.38 746 meet(A,join(join(A,B),complement(C))) = A. [para(559(a,1),151(a,1,2,2))].
% 4.11/4.38 753 complement(meet(zero,b)) = one. [para(166(a,1),730(a,1,1,2))].
% 4.11/4.38 775 meet(A,meet(zero,b)) = zero. [para(753(a,1),45(a,1,2,2)),rewrite([20(5),8(4)])].
% 4.11/4.38 778 meet(zero,b) = zero. [hyper(18,a,775,a,b,696,a),rewrite([46(2)]),flip(a)].
% 4.11/4.38 781 join(zero,b) = b. [para(778(a,1),284(a,1,2)),rewrite([9(3)])].
% 4.11/4.38 859 meet(a,join(b,complement(A))) = a. [para(142(a,1),746(a,1,2,1))].
% 4.11/4.38 2035 meet(A,join(zero,meet(B,C))) = meet(A,meet(B,C)). [para(5(a,1),99(a,1,2,2,2,2)),rewrite([43(3),43(3),9(3)])].
% 4.11/4.38 3532 join(join(zero,meet(A,B)),meet(A,meet(B,C))) = meet(A,B). [para(46(a,1),136(a,1,2,1,1)),rewrite([46(4),21(4),46(7),2035(9),11(7),8(6),11(7,R),8(6),11(8,R),8(7),11(7),8(6),20(6),8(5),155(8),46(9),2035(11),11(9),8(8),20(8),8(7)])].
% 4.11/4.38 3545 join(zero,meet(A,B)) = meet(A,B). [para(155(a,1),136(a,2)),rewrite([46(3),46(4),21(4),46(7),2035(9),11(7),8(6),11(7,R),8(6),11(8,R),8(7),11(7),8(6),20(6),8(5),3532(7),11(3),8(2),20(2),8(1),46(3)]),flip(a)].
% 4.11/4.38 3657 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(3545(a,1),738(a,1,1)),rewrite([9(4),13(5,R),9(4),3545(4),3545(7)])].
% 4.11/4.38 6678 meet(complement(b),join(b,meet(a,complement(A)))) = zero. [para(859(a,1),206(a,1,2,2)),rewrite([9(5),142(5),8(4),5(4)]),flip(a)].
% 4.11/4.38 6792 meet(a,join(b,meet(a,complement(A)))) = a. [para(6678(a,1),198(a,1,2,2,2)),rewrite([142(6),284(6),43(5),9(4),781(4),19(3)]),flip(a)].
% 4.11/4.38 6804 join(b,meet(a,complement(A))) = b. [para(6792(a,1),170(a,1,2)),rewrite([9(7),27(7),142(3)]),flip(a)].
% 4.11/4.38 8165 meet(a,meet(complement(A),b)) = meet(a,complement(A)). [para(6804(a,1),3657(a,1,2)),rewrite([8(5),11(5,R)])].
% 4.11/4.38 9440 meet(a,meet(b,complement(A))) = meet(a,complement(A)). [para(8(a,1),8165(a,1,2))].
% 4.11/4.38 9658 meet(a,complement(b)) = zero. [para(5(a,1),9440(a,1,2)),rewrite([43(3)]),flip(a)].
% 4.11/4.38 9695 meet(a,join(complement(a),complement(b))) = zero. [para(9658(a,1),127(a,1,2,2)),rewrite([9(5),184(5),5(4),9(7)]),flip(a)].
% 4.11/4.38 9705 join(a,join(complement(a),complement(b))) != one # answer(prove_distributivity). [ur(18,a,9695,a,c,17,a(flip))].
% 4.11/4.38 9762 $F # answer(prove_distributivity). [para(13(a,1),9705(a,1)),rewrite([4(6),9(4),204(4)]),xx(a)].
% 4.11/4.38
% 4.11/4.38 % SZS output end Refutation
% 4.11/4.38 ============================== end of proof ==========================
% 4.11/4.38
% 4.11/4.38 ============================== STATISTICS ============================
% 4.11/4.38
% 4.11/4.38 Given=366. Generated=54123. Kept=9757. proofs=1.
% 4.11/4.38 Usable=246. Sos=6272. Demods=6067. Limbo=0, Disabled=3253. Hints=0.
% 4.11/4.38 Megabytes=21.19.
% 4.11/4.38 User_CPU=3.37, System_CPU=0.03, Wall_clock=4.
% 4.11/4.38
% 4.11/4.38 ============================== end of statistics =====================
% 4.11/4.38
% 4.11/4.38 ============================== end of search =========================
% 4.11/4.38
% 4.11/4.38 THEOREM PROVED
% 4.11/4.38 % SZS status Unsatisfiable
% 4.11/4.38
% 4.11/4.38 Exiting with 1 proof.
% 4.11/4.38
% 4.11/4.38 Process 11432 exit (max_proofs) Tue Jun 28 18:10:11 2022
% 4.11/4.38 Prover9 interrupted
%------------------------------------------------------------------------------