TSTP Solution File: LAT197-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT197-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 06:26:04 EDT 2022
% Result : Unsatisfiable 13.98s 14.26s
% Output : Refutation 13.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : LAT197-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n015.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 : Thu Jun 30 01:28:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.17/5.50 ============================== Prover9 ===============================
% 5.17/5.50 Prover9 (32) version 2009-11A, November 2009.
% 5.17/5.50 Process 16950 was started by sandbox2 on n015.cluster.edu,
% 5.17/5.50 Thu Jun 30 01:28:42 2022
% 5.17/5.50 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16797_n015.cluster.edu".
% 5.17/5.50 ============================== end of head ===========================
% 5.17/5.50
% 5.17/5.50 ============================== INPUT =================================
% 5.17/5.50
% 5.17/5.50 % Reading from file /tmp/Prover9_16797_n015.cluster.edu
% 5.17/5.50
% 5.17/5.50 set(prolog_style_variables).
% 5.17/5.50 set(auto2).
% 5.17/5.50 % set(auto2) -> set(auto).
% 5.17/5.50 % set(auto) -> set(auto_inference).
% 5.17/5.50 % set(auto) -> set(auto_setup).
% 5.17/5.50 % set(auto_setup) -> set(predicate_elim).
% 5.17/5.50 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.17/5.50 % set(auto) -> set(auto_limits).
% 5.17/5.50 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.17/5.50 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.17/5.50 % set(auto) -> set(auto_denials).
% 5.17/5.50 % set(auto) -> set(auto_process).
% 5.17/5.50 % set(auto2) -> assign(new_constants, 1).
% 5.17/5.50 % set(auto2) -> assign(fold_denial_max, 3).
% 5.17/5.50 % set(auto2) -> assign(max_weight, "200.000").
% 5.17/5.50 % set(auto2) -> assign(max_hours, 1).
% 5.17/5.50 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.17/5.50 % set(auto2) -> assign(max_seconds, 0).
% 5.17/5.50 % set(auto2) -> assign(max_minutes, 5).
% 5.17/5.50 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.17/5.50 % set(auto2) -> set(sort_initial_sos).
% 5.17/5.50 % set(auto2) -> assign(sos_limit, -1).
% 5.17/5.50 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.17/5.50 % set(auto2) -> assign(max_megs, 400).
% 5.17/5.50 % set(auto2) -> assign(stats, some).
% 5.17/5.50 % set(auto2) -> clear(echo_input).
% 5.17/5.50 % set(auto2) -> set(quiet).
% 5.17/5.50 % set(auto2) -> clear(print_initial_clauses).
% 5.17/5.50 % set(auto2) -> clear(print_given).
% 5.17/5.50 assign(lrs_ticks,-1).
% 5.17/5.50 assign(sos_limit,10000).
% 5.17/5.50 assign(order,kbo).
% 5.17/5.50 set(lex_order_vars).
% 5.17/5.50 clear(print_given).
% 5.17/5.50
% 5.17/5.50 % formulas(sos). % not echoed (13 formulas)
% 5.17/5.50
% 5.17/5.50 ============================== end of input ==========================
% 5.17/5.50
% 5.17/5.50 % From the command line: assign(max_seconds, 300).
% 5.17/5.50
% 5.17/5.50 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.17/5.50
% 5.17/5.50 % Formulas that are not ordinary clauses:
% 5.17/5.50
% 5.17/5.50 ============================== end of process non-clausal formulas ===
% 5.17/5.50
% 5.17/5.50 ============================== PROCESS INITIAL CLAUSES ===============
% 5.17/5.50
% 5.17/5.50 ============================== PREDICATE ELIMINATION =================
% 5.17/5.50
% 5.17/5.50 ============================== end predicate elimination =============
% 5.17/5.50
% 5.17/5.50 Auto_denials:
% 5.17/5.50 % copying label prove_distributivity to answer in negative clause
% 5.17/5.50
% 5.17/5.50 Term ordering decisions:
% 5.17/5.50
% 5.17/5.50 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 5.17/5.50 Function symbol KB weights: one=1. zero=1. a=1. b=1. c=1. join=1. meet=1. complement=0.
% 5.17/5.50
% 5.17/5.50 ============================== end of process initial clauses ========
% 5.17/5.50
% 5.17/5.50 ============================== CLAUSES FOR SEARCH ====================
% 5.17/5.50
% 5.17/5.50 ============================== end of clauses for search =============
% 5.17/5.50
% 5.17/5.50 ============================== SEARCH ================================
% 5.17/5.50
% 5.17/5.50 % Starting search at 0.01 seconds.
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=141.000, iters=3468
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=140.000, iters=3466
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=138.000, iters=3462
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=122.000, iters=3442
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=118.000, iters=3434
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=94.000, iters=3344
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=82.000, iters=3361
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=79.000, iters=3340
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=74.000, iters=3338
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=71.000, iters=3336
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=70.000, iters=3370
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=69.000, iters=3361
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=68.000, iters=3380
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=67.000, iters=3371
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=66.000, iters=3335
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=64.000, iters=3370
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=63.000, iters=3400
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=60.000, iters=3388
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=59.000, iters=3361
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=58.000, iters=3351
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=57.000, iters=3342
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=56.000, iters=3339
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=53.000, iters=3367
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=52.000, iters=3356
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=50.000, iters=3353
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=49.000, iters=3361
% 5.17/5.50
% 5.17/5.50 Low Water (keep): wt=48.000, iters=3362
% 13.98/14.26
% 13.98/14.26 Low Water (keep): wt=47.000, iters=3368
% 13.98/14.26
% 13.98/14.26 Low Water (keep): wt=46.000, iters=3353
% 13.98/14.26
% 13.98/14.26 Low Water (keep): wt=45.000, iters=3451
% 13.98/14.26
% 13.98/14.26 Low Water (keep): wt=44.000, iters=3365
% 13.98/14.26
% 13.98/14.26 Low Water (keep): wt=43.000, iters=3345
% 13.98/14.26
% 13.98/14.26 Low Water (keep): wt=42.000, iters=3334
% 13.98/14.26
% 13.98/14.26 Low Water (keep): wt=41.000, iters=3398
% 13.98/14.26
% 13.98/14.26 Low Water (keep): wt=40.000, iters=3357
% 13.98/14.26
% 13.98/14.26 ============================== PROOF =================================
% 13.98/14.26 % SZS status Unsatisfiable
% 13.98/14.26 % SZS output start Refutation
% 13.98/14.26
% 13.98/14.26 % Proof 1 at 13.15 (+ 0.14) seconds: prove_distributivity.
% 13.98/14.26 % Length of proof is 155.
% 13.98/14.26 % Level of proof is 48.
% 13.98/14.26 % Maximum clause weight is 43.000.
% 13.98/14.26 % Given clauses 543.
% 13.98/14.26
% 13.98/14.26 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 13.98/14.26 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 13.98/14.26 3 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 13.98/14.26 4 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 13.98/14.26 5 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 13.98/14.26 6 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 13.98/14.26 7 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 13.98/14.26 8 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 13.98/14.26 9 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 13.98/14.26 10 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(9),rewrite([7(2)]),flip(a)].
% 13.98/14.26 11 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 13.98/14.26 12 join(A,join(B,C)) = join(C,join(A,B)). [copy(11),rewrite([8(2)]),flip(a)].
% 13.98/14.26 13 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))) # label(equation_H40) # label(axiom). [assumption].
% 13.98/14.26 14 meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))) = meet(A,join(B,meet(C,join(A,D)))). [copy(13),flip(a)].
% 13.98/14.26 15 meet(a,join(b,c)) != join(meet(a,b),meet(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 13.98/14.26 16 join(meet(a,b),meet(a,c)) != meet(a,join(b,c)) # answer(prove_distributivity). [copy(15),flip(a)].
% 13.98/14.26 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 13.98/14.26 18 meet(A,one) = A. [para(3(a,1),5(a,1,2))].
% 13.98/14.26 19 join(A,zero) = A. [para(4(a,1),6(a,1,2))].
% 13.98/14.26 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)])].
% 13.98/14.26 21 meet(A,meet(B,complement(A))) = meet(B,zero). [para(4(a,1),10(a,2,2)),rewrite([7(2)])].
% 13.98/14.26 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(5(a,1),10(a,2,2)),rewrite([7(2),7(4)])].
% 13.98/14.26 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)])].
% 13.98/14.26 24 join(A,join(B,complement(A))) = join(B,one). [para(3(a,1),12(a,2,2)),rewrite([8(2)])].
% 13.98/14.26 25 join(A,join(B,meet(A,C))) = join(A,B). [para(6(a,1),12(a,2,2)),rewrite([8(2),8(4)])].
% 13.98/14.26 26 meet(A,join(B,meet(join(A,B),join(A,join(B,C))))) = meet(A,join(B,meet(join(A,B),join(A,C)))). [para(1(a,1),14(a,1,2,2,2,2)),rewrite([12(3),8(2),12(3,R),8(2)])].
% 13.98/14.26 27 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(2(a,1),14(a,1,2,2,2)),rewrite([20(3),14(10),2(5),7(5)])].
% 13.98/14.26 28 meet(A,join(complement(A),meet(B,join(A,C)))) = meet(A,join(B,complement(A))). [para(3(a,1),14(a,1,2,2,2,2,2)),rewrite([18(3),8(2),5(3),8(2)]),flip(a)].
% 13.98/14.26 29 meet(A,join(B,meet(C,join(A,C)))) = meet(A,join(B,C)). [para(5(a,1),14(a,1,2,2)),flip(a)].
% 13.98/14.26 32 meet(A,meet(B,join(C,meet(D,join(E,meet(D,join(A,C))))))) = meet(A,meet(B,join(C,meet(D,join(A,E))))). [para(14(a,1),10(a,2,2)),rewrite([7(6),10(12,R),7(11)])].
% 13.98/14.26 33 meet(A,join(meet(B,join(C,meet(B,join(A,D)))),meet(D,join(E,meet(D,join(A,meet(B,join(C,D)))))))) = meet(A,join(meet(B,join(C,meet(B,join(A,D)))),meet(D,join(A,E)))). [para(14(a,1),14(a,1,2,2,2,2)),rewrite([8(1),8(5),8(13)])].
% 13.98/14.26 36 meet(A,B) != zero | join(A,B) != one | complement(B) = A. [para(7(a,1),17(a,1)),rewrite([8(4)])].
% 13.98/14.26 42 meet(A,zero) = zero. [para(4(a,1),20(a,1,2)),rewrite([4(4)])].
% 13.98/14.26 44 meet(A,meet(B,complement(A))) = zero. [back_rewrite(21),rewrite([42(5)])].
% 13.98/14.26 45 complement(one) = zero. [hyper(17,a,42,a,b,19,a)].
% 13.98/14.26 46 one != A | complement(A) = zero. [para(42(a,1),17(a,1)),rewrite([19(5)]),flip(b),xx(a)].
% 13.98/14.26 49 complement(join(A,one)) = zero. [hyper(46,a,6,a(flip)),rewrite([7(3),18(3),8(2)])].
% 13.98/14.26 51 join(A,one) = one. [para(49(a,1),3(a,1,2)),rewrite([8(4),12(4),8(3),19(3),8(2)])].
% 13.98/14.26 53 join(A,join(B,complement(A))) = one. [back_rewrite(24),rewrite([51(5)])].
% 13.98/14.26 54 complement(zero) = one. [hyper(17,a,18,a,b,51,a)].
% 13.98/14.26 55 meet(A,join(one,meet(B,join(A,C)))) = A. [para(51(a,1),14(a,1,2,2,2,2,2)),rewrite([18(3),8(2),5(3),8(2),51(2),18(2)]),flip(a)].
% 13.98/14.26 56 meet(A,join(join(A,B),meet(C,join(D,meet(C,join(A,B)))))) = meet(A,join(join(A,B),meet(C,join(A,D)))). [para(23(a,1),14(a,1,2,2,2,2,2))].
% 13.98/14.26 59 join(A,join(B,join(C,complement(A)))) = one. [para(53(a,1),12(a,2,2)),rewrite([8(3),12(3,R),8(2),51(6)])].
% 13.98/14.26 60 meet(A,join(join(B,complement(A)),meet(C,join(A,D)))) = meet(A,join(B,join(C,complement(A)))). [para(53(a,1),14(a,1,2,2,2,2,2)),rewrite([18(4),8(3),5(4),8(3),12(3,R),8(2)]),flip(a)].
% 13.98/14.27 68 meet(A,join(one,meet(A,B))) = A. [para(2(a,1),55(a,1,2,2,2)),rewrite([7(2)])].
% 13.98/14.27 77 meet(A,join(B,meet(join(A,B),join(A,C)))) = A. [para(7(a,1),26(a,2,2,2)),rewrite([26(6),27(10),5(7),8(6),5(7)])].
% 13.98/14.27 81 meet(A,join(B,join(one,complement(A)))) = A. [para(53(a,1),26(a,1,2,2,1)),rewrite([8(6),12(6,R),8(5),59(7),1(5),8(4),12(4,R),51(3),51(2),18(2),53(5),60(7)]),flip(a)].
% 13.98/14.27 93 meet(A,join(complement(A),meet(A,B))) = meet(A,join(B,complement(A))). [para(3(a,1),27(a,1,2,2,2)),rewrite([18(3),8(2)]),flip(a)].
% 13.98/14.27 94 meet(A,join(B,meet(A,B))) = meet(A,B). [para(6(a,1),27(a,1,2)),flip(a)].
% 13.98/14.27 95 meet(A,join(B,meet(C,join(B,A)))) = meet(A,join(B,meet(C,A))). [para(27(a,1),7(a,2)),rewrite([8(1),7(4),7(5)])].
% 13.98/14.27 100 meet(A,join(join(A,B),meet(C,join(A,B)))) = meet(A,join(join(A,B),meet(A,C))). [para(23(a,1),27(a,1,2,2,2))].
% 13.98/14.27 104 meet(A,join(join(one,complement(B)),meet(A,B))) = A. [para(81(a,1),27(a,1,2,2)),rewrite([8(4),53(4),18(2)]),flip(a)].
% 13.98/14.27 110 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(44(a,1),94(a,1,2,2)),rewrite([8(4),44(8)])].
% 13.98/14.27 114 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),110(a,1,2,2))].
% 13.98/14.27 115 meet(A,meet(B,join(zero,meet(C,complement(A))))) = zero. [para(110(a,1),10(a,2,2)),rewrite([7(5),42(8)])].
% 13.98/14.27 121 meet(A,meet(complement(A),join(B,complement(A)))) = zero. [para(28(a,1),22(a,1,2)),rewrite([10(5,R),7(4),7(7),4(7)])].
% 13.98/14.27 126 join(zero,complement(A)) = complement(A). [hyper(17,a,114,a,b,53,a),flip(a)].
% 13.98/14.27 141 join(A,meet(complement(A),join(B,complement(A)))) != one | meet(complement(A),join(B,complement(A))) = complement(A). [para(121(a,1),17(a,1)),flip(c),xx(a)].
% 13.98/14.27 220 meet(A,join(complement(B),join(one,meet(A,B)))) = A. [para(8(a,1),104(a,1,2)),rewrite([12(5),8(4)])].
% 13.98/14.27 230 join(one,complement(A)) = one. [para(104(a,1),55(a,1,2,2)),rewrite([8(5),51(5),7(5),5(5)]),flip(a)].
% 13.98/14.27 241 meet(A,join(zero,meet(B,join(zero,meet(C,complement(A)))))) = zero. [para(115(a,1),94(a,1,2,2)),rewrite([8(7),115(14)])].
% 13.98/14.27 258 meet(A,join(complement(B),join(one,meet(B,A)))) = A. [para(220(a,1),7(a,2)),rewrite([7(3),7(6)])].
% 13.98/14.27 271 meet(one,join(A,B)) = join(A,B). [para(5(a,1),258(a,1,2,2,2)),rewrite([8(4),51(4),51(4),7(3)])].
% 13.98/14.27 277 join(one,meet(A,B)) = one. [para(68(a,1),258(a,1,2,2,2)),rewrite([8(6),51(6),51(6),7(5),5(5)]),flip(a)].
% 13.98/14.27 281 meet(one,complement(A)) = complement(A). [para(126(a,1),271(a,1,2)),rewrite([126(6)])].
% 13.98/14.27 335 join(A,meet(complement(B),join(C,complement(B)))) = join(A,complement(B)). [para(230(a,1),33(a,1,2,1,2,2,2)),rewrite([18(3),8(2),5(3),277(8),18(5),271(7),230(9),18(8),8(7),5(8),8(9),51(9),18(9),271(9)])].
% 13.98/14.27 343 meet(complement(A),join(B,complement(A))) = complement(A). [back_rewrite(141),rewrite([335(5),3(2)]),xx(a)].
% 13.98/14.27 374 meet(A,join(B,meet(join(B,A),join(A,C)))) = A. [para(77(a,1),7(a,2)),rewrite([8(1),7(5)])].
% 13.98/14.27 390 complement(complement(A)) = A. [hyper(36,a,4,a,b,3,a)].
% 13.98/14.27 412 join(A,B) != zero | complement(join(A,B)) = one. [para(271(a,1),36(a,1)),rewrite([12(6),8(5),51(5),51(5)]),xx(b)].
% 13.98/14.27 671 meet(complement(A),join(zero,meet(B,join(zero,meet(A,C))))) = zero. [para(390(a,1),241(a,1,2,2,2,2,2)),rewrite([7(4)])].
% 13.98/14.27 680 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(8(a,1),56(a,2,2)),rewrite([56(7),12(9),8(8),12(9,R),8(8),5(10)])].
% 13.98/14.27 700 meet(A,join(join(A,B),meet(A,C))) = A. [back_rewrite(100),rewrite([680(5)]),flip(a)].
% 13.98/14.27 718 meet(A,join(join(A,B),complement(C))) = A. [para(343(a,1),680(a,1,2,2))].
% 13.98/14.27 724 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(700(a,1),680(a,1,2,2)),rewrite([8(3),12(3),8(2),12(3,R),8(2),8(4),23(4)])].
% 13.98/14.27 785 meet(A,join(B,join(complement(A),meet(C,join(A,D))))) = meet(A,join(C,join(B,complement(A)))). [para(8(a,1),60(a,1,2)),rewrite([12(5),8(4),12(5,R),8(4),12(9,R),8(8)])].
% 13.98/14.27 848 meet(A,meet(complement(B),join(zero,meet(A,B)))) = zero. [para(671(a,1),32(a,1,2)),rewrite([42(2),19(5),7(4)]),flip(a)].
% 13.98/14.27 870 meet(meet(A,complement(B)),join(zero,meet(A,B))) = zero. [para(848(a,1),10(a,1)),rewrite([7(7)]),flip(a)].
% 13.98/14.27 897 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(724(a,1),848(a,1,2,2,2)),rewrite([12(7),8(6),19(6),8(5),7(6),20(7)])].
% 13.98/14.27 989 join(zero,meet(A,complement(B))) = meet(A,complement(B)). [para(870(a,1),6(a,1,2)),rewrite([8(4)])].
% 13.98/14.27 1014 join(zero,meet(A,B)) = meet(A,B). [para(390(a,1),989(a,1,2,2)),rewrite([390(5)])].
% 13.98/14.27 1121 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(1014(a,1),724(a,1,1)),rewrite([8(4),12(5,R),8(4),1014(4),1014(7)])].
% 13.98/14.27 1180 meet(meet(A,B),complement(join(C,meet(A,B)))) = zero. [para(1014(a,1),897(a,1,1)),rewrite([8(4),12(5,R),8(4),1014(4)])].
% 13.98/14.27 1227 meet(A,join(join(B,C),complement(A))) = meet(A,join(B,join(C,complement(A)))). [para(29(a,1),93(a,1,2,2)),rewrite([93(5),8(9),12(9,R),8(8),785(10),12(7,R),8(6)])].
% 13.98/14.27 1332 meet(meet(A,B),join(A,C)) = meet(A,B). [para(700(a,1),95(a,1,2,2)),rewrite([8(3),23(3),20(7),1121(8)])].
% 13.98/14.27 1345 meet(meet(A,B),join(B,C)) = meet(A,B). [para(7(a,1),1332(a,1,1)),rewrite([7(4)])].
% 13.98/14.27 1364 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(1332(a,1),95(a,1,2,2)),rewrite([6(2),7(3)]),flip(a)].
% 13.98/14.27 1391 meet(A,join(B,join(join(A,C),complement(D)))) = A. [para(718(a,1),1345(a,1,1)),rewrite([8(4),718(9)])].
% 13.98/14.27 1478 meet(A,join(join(A,B),meet(C,D))) = A. [para(1121(a,1),680(a,1,2,2))].
% 13.98/14.27 1764 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(271(a,1),1364(a,2)),rewrite([7(5),10(6,R),7(5),271(5),271(6)])].
% 13.98/14.27 1767 join(complement(A),meet(B,complement(A))) = complement(A). [para(281(a,1),1364(a,2)),rewrite([7(5),10(6,R),18(5),271(6)])].
% 13.98/14.27 1823 meet(complement(A),join(B,join(complement(A),complement(C)))) = complement(A). [para(1767(a,1),1391(a,1,2,2,1))].
% 13.98/14.27 1863 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(1014(a,1),1764(a,1,1)),rewrite([1014(4),10(3),7(2),10(3,R),7(2),1014(7)])].
% 13.98/14.27 1866 join(join(A,B),meet(A,C)) = join(A,B). [para(1332(a,1),1764(a,1,2))].
% 13.98/14.27 1897 join(join(A,B),meet(B,C)) = join(A,B). [para(8(a,1),1866(a,1,1)),rewrite([8(4)])].
% 13.98/14.27 1908 meet(meet(A,B),complement(join(A,C))) = zero. [para(1866(a,1),1180(a,1,2,1))].
% 13.98/14.27 1989 meet(meet(A,B),complement(join(B,C))) = zero. [para(7(a,1),1908(a,1,1))].
% 13.98/14.27 2027 meet(A,complement(join(B,join(join(A,C),meet(D,E))))) = zero. [para(1478(a,1),1989(a,1,1)),rewrite([8(4)])].
% 13.98/14.27 2054 join(complement(A),meet(B,meet(C,complement(A)))) = complement(A). [para(1767(a,1),1897(a,1,1)),rewrite([7(4),10(4,R),7(3),1767(9)])].
% 13.98/14.27 2265 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [para(1863(a,1),1180(a,1,2,1)),rewrite([7(5),10(5,R)])].
% 13.98/14.27 2279 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(1(a,1),2265(a,1,2,1))].
% 13.98/14.27 2280 meet(A,meet(meet(B,C),complement(meet(B,A)))) = zero. [para(2265(a,1),7(a,1)),rewrite([7(3),7(6)]),flip(a)].
% 13.98/14.27 2336 meet(A,join(complement(A),meet(B,complement(meet(A,B))))) = zero. [para(2279(a,1),93(a,1,2,2)),rewrite([19(3),4(2),8(6)]),flip(a)].
% 13.98/14.27 2365 meet(A,meet(meet(B,C),complement(join(D,meet(A,B))))) = zero. [para(1180(a,1),2280(a,1,2,2,1)),rewrite([7(5),10(5),7(4),10(5,R),7(4),54(7),7(7),10(7,R),7(6),10(6),7(5),18(5),7(4),10(6,R)])].
% 13.98/14.27 2838 meet(complement(A),join(A,meet(B,complement(meet(B,complement(A)))))) = zero. [para(390(a,1),2336(a,1,2,1)),rewrite([7(3)])].
% 13.98/14.27 4241 meet(complement(A),complement(join(B,join(complement(A),meet(C,D))))) = zero. [para(2054(a,1),2027(a,1,2,1,2,1))].
% 13.98/14.27 4986 meet(A,meet(B,complement(join(C,meet(A,B))))) = zero. [para(1(a,1),2365(a,1,2,1))].
% 13.98/14.27 4988 meet(A,meet(meet(B,C),complement(join(D,meet(B,A))))) = zero. [para(2365(a,1),7(a,1)),rewrite([7(3),7(7)]),flip(a)].
% 13.98/14.27 7153 join(A,join(complement(A),meet(B,complement(meet(B,complement(A)))))) != one | join(A,meet(B,complement(meet(B,complement(A))))) = A. [para(2838(a,1),17(a,1)),rewrite([12(10,R),8(9),390(14)]),flip(c),xx(a)].
% 13.98/14.27 8788 meet(meet(A,B),meet(meet(C,D),complement(meet(A,C)))) = zero. [para(1863(a,1),4988(a,1,2,2,1)),rewrite([7(3)])].
% 13.98/14.27 10124 meet(meet(A,B),meet(meet(C,D),complement(meet(B,C)))) = zero. [para(7(a,1),8788(a,1,1))].
% 13.98/14.27 10488 meet(complement(A),meet(meet(B,A),join(C,D))) = zero. [para(271(a,1),10124(a,1,2,1)),rewrite([18(4),10(5)])].
% 13.98/14.27 10569 meet(complement(join(A,B)),meet(meet(A,C),join(D,E))) = zero. [para(1332(a,1),10488(a,1,2,1))].
% 13.98/14.27 12707 meet(complement(join(A,B)),meet(meet(B,C),join(D,E))) = zero. [para(8(a,1),10569(a,1,1,1))].
% 13.98/14.27 13285 meet(A,meet(B,complement(join(C,A)))) = zero. [para(3(a,1),12707(a,1,2,2)),rewrite([7(5),10(5),7(4),18(4),7(3),10(4),7(3),10(4,R),7(3)])].
% 13.98/14.27 13308 meet(A,meet(complement(join(B,C)),join(B,meet(C,D)))) = zero. [para(25(a,1),13285(a,1,2,2,1)),rewrite([8(3),10(6),7(5),10(6,R),7(5)])].
% 13.98/14.27 13565 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [hyper(17,a,13308,a,b,277,a),rewrite([45(2)]),flip(a)].
% 13.98/14.27 13576 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(8(a,1),13565(a,1,1,1))].
% 13.98/14.27 13623 meet(complement(A),join(meet(A,B),meet(A,C))) = zero. [para(6(a,1),13576(a,1,1,1))].
% 13.98/14.27 13669 meet(meet(A,B),join(complement(A),complement(meet(A,B)))) = zero. [para(13623(a,1),28(a,1,2,2)),rewrite([8(5),126(5),4(4)]),flip(a)].
% 13.98/14.27 13737 join(complement(A),complement(meet(A,B))) = complement(meet(A,B)). [hyper(17,a,13669,a,b,53,a),flip(a)].
% 13.98/14.27 13738 meet(meet(A,B),join(complement(B),complement(meet(A,B)))) = zero. [para(7(a,1),13669(a,1,1)),rewrite([7(3)])].
% 13.98/14.27 13760 meet(complement(A),complement(meet(A,B))) = complement(A). [para(13737(a,1),5(a,1,2))].
% 13.98/14.27 13769 complement(meet(A,B)) != zero | meet(A,B) = one. [para(13737(a,1),412(a,1)),rewrite([13737(8),390(7)])].
% 13.98/14.27 13782 meet(complement(A),join(B,complement(meet(A,C)))) = complement(A). [para(13737(a,1),1823(a,1,2,2))].
% 13.98/14.27 13823 meet(A,complement(meet(B,complement(A)))) = A. [para(390(a,1),13760(a,1,1)),rewrite([7(2),390(6)])].
% 13.98/14.27 13840 meet(A,meet(B,complement(meet(C,complement(A))))) = meet(A,B). [para(13823(a,1),10(a,2,2)),rewrite([7(4),7(6)])].
% 13.98/14.27 13862 complement(join(A,B)) != zero | join(A,B) = one. [para(271(a,1),13769(a,1,1)),rewrite([271(7)])].
% 13.98/14.27 14116 join(complement(A),complement(meet(B,A))) = complement(meet(B,A)). [hyper(17,a,13738,a,b,53,a),flip(a)].
% 13.98/14.27 14147 join(complement(A),complement(join(A,B))) = complement(A). [para(5(a,1),14116(a,1,2,1)),rewrite([8(4),5(6)])].
% 13.98/14.27 14200 join(A,complement(join(B,complement(meet(A,C))))) = A. [para(13782(a,1),14116(a,1,2,1)),rewrite([390(6),8(5),13782(10),390(7)])].
% 13.98/14.27 14264 meet(complement(A),complement(join(A,B))) = complement(join(A,B)). [para(14147(a,1),343(a,1,2)),rewrite([7(4)])].
% 13.98/14.27 14329 join(A,join(B,complement(meet(B,C)))) = one. [para(14200(a,1),53(a,1,2)),rewrite([8(4),12(4,R),8(3)])].
% 13.98/14.27 14366 join(A,complement(meet(A,B))) = one. [hyper(17,a,718,a,b,14329,a),rewrite([54(2),8(3),19(3),8(3),19(3)]),flip(a)].
% 13.98/14.27 14378 meet(A,join(complement(meet(A,B)),meet(A,C))) = meet(A,join(C,complement(meet(A,B)))). [para(14366(a,1),27(a,1,2,2,2)),rewrite([18(4),8(3)]),flip(a)].
% 13.98/14.27 14629 meet(A,complement(join(B,meet(A,complement(B))))) = zero. [para(14264(a,1),4986(a,1,2))].
% 13.98/14.27 14635 complement(join(A,join(complement(A),meet(B,C)))) = zero. [para(14264(a,1),4241(a,1))].
% 13.98/14.27 14670 join(A,join(complement(A),meet(B,C))) = one. [hyper(13862,a,14635,a)].
% 13.98/14.27 14678 join(A,meet(B,complement(meet(B,complement(A))))) = A. [back_rewrite(7153),rewrite([14670(7)]),xx(a)].
% 13.98/14.27 15951 meet(A,complement(meet(A,complement(B)))) = meet(A,B). [para(14678(a,1),374(a,1,2,2,1)),rewrite([8(9),6(11),7(5),13840(5),7(1)]),flip(a)].
% 13.98/14.27 15960 join(A,meet(B,complement(A))) = join(A,B). [para(14629(a,1),14678(a,1,2,2,1)),rewrite([54(5),18(5),8(4),25(4),8(1)]),flip(a)].
% 13.98/14.27 15989 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(390(a,1),15960(a,1,2,2)),rewrite([7(2),8(5)])].
% 13.98/14.27 16090 meet(A,meet(B,complement(meet(A,complement(C))))) = meet(A,meet(C,B)). [para(15951(a,1),10(a,2,2)),rewrite([7(4),10(7),7(6),10(7,R),7(6)])].
% 13.98/14.27 16094 meet(A,complement(meet(A,B))) = meet(A,complement(B)). [para(390(a,1),15951(a,1,2,1,2))].
% 13.98/14.27 16099 meet(A,join(meet(B,C),complement(meet(A,complement(B))))) = meet(A,B). [para(15951(a,1),1364(a,2)),rewrite([7(7),16090(8),14378(7)])].
% 13.98/14.27 16128 join(meet(A,B),meet(A,complement(B))) = A. [para(15951(a,1),15960(a,1,2)),rewrite([8(4),8(7),6(7)])].
% 13.98/14.27 16148 join(meet(A,B),meet(B,complement(A))) = B. [para(7(a,1),16128(a,1,1))].
% 13.98/14.27 16267 join(complement(A),meet(B,join(A,C))) = join(B,complement(A)). [para(28(a,1),16148(a,1,1)),rewrite([7(9),5(9),8(5),15989(5),8(4),12(4,R),2(3)]),flip(a)].
% 13.98/14.27 16360 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [para(13623(a,1),16148(a,1,1)),rewrite([390(6),7(5),1014(6)])].
% 13.98/14.27 16361 complement(meet(A,B)) = join(complement(A),complement(B)). [para(13760(a,1),16148(a,1,1)),rewrite([390(5),7(4),16094(4),15989(4),8(3)]),flip(a)].
% 13.98/14.27 16759 meet(A,join(B,complement(A))) = meet(A,B). [back_rewrite(16099),rewrite([16361(4),390(4),8(3),12(4,R),25(4)])].
% 13.98/14.27 18179 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [back_rewrite(1227),rewrite([16759(4)]),flip(a)].
% 13.98/14.27 18562 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [para(27(a,1),16759(a,2)),rewrite([8(5),12(5,R),8(4),16267(4),18179(4)]),flip(a)].
% 13.98/14.27 19471 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(16360),rewrite([18562(4),8(2),18562(3),8(1)]),flip(a)].
% 13.98/14.27 19472 $F # answer(prove_distributivity). [resolve(19471,a,16,a)].
% 13.98/14.27
% 13.98/14.27 % SZS output end Refutation
% 13.98/14.27 ============================== end of proof ==========================
% 13.98/14.27
% 13.98/14.27 ============================== STATISTICS ============================
% 13.98/14.27
% 13.98/14.27 Given=543. Generated=223537. Kept=19467. proofs=1.
% 13.98/14.27 Usable=199. Sos=4315. Demods=4354. Limbo=909, Disabled=14056. Hints=0.
% 13.98/14.27 Megabytes=26.86.
% 13.98/14.27 User_CPU=13.15, System_CPU=0.14, Wall_clock=13.
% 13.98/14.27
% 13.98/14.27 ============================== end of statistics =====================
% 13.98/14.27
% 13.98/14.27 ============================== end of search =========================
% 13.98/14.27
% 13.98/14.27 THEOREM PROVED
% 13.98/14.27 % SZS status Unsatisfiable
% 13.98/14.27
% 13.98/14.27 Exiting with 1 proof.
% 13.98/14.27
% 13.98/14.27 Process 16950 exit (max_proofs) Thu Jun 30 01:28:55 2022
% 13.98/14.27 Prover9 interrupted
%------------------------------------------------------------------------------