TSTP Solution File: LAT222-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT222-10 : TPTP v8.1.0. Released v7.3.0.
% 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 06:26:13 EDT 2022
% Result : Unsatisfiable 206.03s 206.29s
% Output : Refutation 206.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT222-10 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.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 : Wed Jun 29 02:38:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 10.41/10.72 ============================== Prover9 ===============================
% 10.41/10.72 Prover9 (32) version 2009-11A, November 2009.
% 10.41/10.72 Process 27748 was started by sandbox2 on n029.cluster.edu,
% 10.41/10.72 Wed Jun 29 02:38:08 2022
% 10.41/10.72 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27594_n029.cluster.edu".
% 10.41/10.72 ============================== end of head ===========================
% 10.41/10.72
% 10.41/10.72 ============================== INPUT =================================
% 10.41/10.72
% 10.41/10.72 % Reading from file /tmp/Prover9_27594_n029.cluster.edu
% 10.41/10.72
% 10.41/10.72 set(prolog_style_variables).
% 10.41/10.72 set(auto2).
% 10.41/10.72 % set(auto2) -> set(auto).
% 10.41/10.72 % set(auto) -> set(auto_inference).
% 10.41/10.72 % set(auto) -> set(auto_setup).
% 10.41/10.72 % set(auto_setup) -> set(predicate_elim).
% 10.41/10.72 % set(auto_setup) -> assign(eq_defs, unfold).
% 10.41/10.72 % set(auto) -> set(auto_limits).
% 10.41/10.72 % set(auto_limits) -> assign(max_weight, "100.000").
% 10.41/10.72 % set(auto_limits) -> assign(sos_limit, 20000).
% 10.41/10.72 % set(auto) -> set(auto_denials).
% 10.41/10.72 % set(auto) -> set(auto_process).
% 10.41/10.72 % set(auto2) -> assign(new_constants, 1).
% 10.41/10.72 % set(auto2) -> assign(fold_denial_max, 3).
% 10.41/10.72 % set(auto2) -> assign(max_weight, "200.000").
% 10.41/10.72 % set(auto2) -> assign(max_hours, 1).
% 10.41/10.72 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 10.41/10.72 % set(auto2) -> assign(max_seconds, 0).
% 10.41/10.72 % set(auto2) -> assign(max_minutes, 5).
% 10.41/10.72 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 10.41/10.72 % set(auto2) -> set(sort_initial_sos).
% 10.41/10.72 % set(auto2) -> assign(sos_limit, -1).
% 10.41/10.72 % set(auto2) -> assign(lrs_ticks, 3000).
% 10.41/10.72 % set(auto2) -> assign(max_megs, 400).
% 10.41/10.72 % set(auto2) -> assign(stats, some).
% 10.41/10.72 % set(auto2) -> clear(echo_input).
% 10.41/10.72 % set(auto2) -> set(quiet).
% 10.41/10.72 % set(auto2) -> clear(print_initial_clauses).
% 10.41/10.72 % set(auto2) -> clear(print_given).
% 10.41/10.72 assign(lrs_ticks,-1).
% 10.41/10.72 assign(sos_limit,10000).
% 10.41/10.72 assign(order,kbo).
% 10.41/10.72 set(lex_order_vars).
% 10.41/10.72 clear(print_given).
% 10.41/10.72
% 10.41/10.72 % formulas(sos). % not echoed (15 formulas)
% 10.41/10.72
% 10.41/10.72 ============================== end of input ==========================
% 10.41/10.72
% 10.41/10.72 % From the command line: assign(max_seconds, 300).
% 10.41/10.72
% 10.41/10.72 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 10.41/10.72
% 10.41/10.72 % Formulas that are not ordinary clauses:
% 10.41/10.72
% 10.41/10.72 ============================== end of process non-clausal formulas ===
% 10.41/10.72
% 10.41/10.72 ============================== PROCESS INITIAL CLAUSES ===============
% 10.41/10.72
% 10.41/10.72 ============================== PREDICATE ELIMINATION =================
% 10.41/10.72
% 10.41/10.72 ============================== end predicate elimination =============
% 10.41/10.72
% 10.41/10.72 Auto_denials:
% 10.41/10.72 % copying label prove_distributivity to answer in negative clause
% 10.41/10.72
% 10.41/10.72 Term ordering decisions:
% 10.41/10.72
% 10.41/10.72 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 10.41/10.72 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. ifeq=1. complement=0.
% 10.41/10.72
% 10.41/10.72 ============================== end of process initial clauses ========
% 10.41/10.72
% 10.41/10.72 ============================== CLAUSES FOR SEARCH ====================
% 10.41/10.72
% 10.41/10.72 ============================== end of clauses for search =============
% 10.41/10.72
% 10.41/10.72 ============================== SEARCH ================================
% 10.41/10.72
% 10.41/10.72 % Starting search at 0.01 seconds.
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=92.000, iters=3371
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=83.000, iters=3350
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=80.000, iters=3473
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=77.000, iters=3425
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=74.000, iters=3409
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=70.000, iters=3337
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=68.000, iters=3337
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=67.000, iters=3372
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=64.000, iters=3403
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=62.000, iters=3371
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=60.000, iters=3338
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=51.000, iters=3347
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=50.000, iters=3340
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=49.000, iters=3333
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=48.000, iters=3343
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=47.000, iters=3386
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=46.000, iters=3341
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=44.000, iters=3340
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=43.000, iters=3335
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=42.000, iters=3336
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=41.000, iters=3401
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=40.000, iters=3348
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=39.000, iters=3380
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=38.000, iters=3345
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=37.000, iters=3333
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=36.000, iters=3340
% 10.41/10.72
% 10.41/10.72 Low Water (keep): wt=35.000, iters=3442
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=34.000, iters=3396
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=33.000, iters=3405
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=32.000, iters=3335
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=6352, wt=199.000
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=5100, wt=196.000
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=9339, wt=194.000
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=5164, wt=190.000
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=16917, wt=29.000
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=16918, wt=19.000
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=16946, wt=18.000
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=17080, wt=17.000
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=17130, wt=16.000
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=18111, wt=15.000
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=31.000, iters=3335
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=30.000, iters=3351
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=21313, wt=14.000
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=29.000, iters=3342
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=28.000, iters=3337
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=27.000, iters=3357
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=26.000, iters=3367
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=25.000, iters=3333
% 206.03/206.29
% 206.03/206.29 Low Water (displace): id=31633, wt=13.000
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=24.000, iters=3333
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=23.000, iters=3344
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=22.000, iters=3346
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=21.000, iters=3342
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=20.000, iters=3338
% 206.03/206.29
% 206.03/206.29 Low Water (keep): wt=19.000, iters=3341
% 206.03/206.29
% 206.03/206.29 ============================== PROOF =================================
% 206.03/206.29 % SZS status Unsatisfiable
% 206.03/206.29 % SZS output start Refutation
% 206.03/206.29
% 206.03/206.29 % Proof 1 at 203.26 (+ 2.02) seconds: prove_distributivity.
% 206.03/206.29 % Length of proof is 148.
% 206.03/206.29 % Level of proof is 38.
% 206.03/206.29 % Maximum clause weight is 49.000.
% 206.03/206.29 % Given clauses 3252.
% 206.03/206.29
% 206.03/206.29 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 206.03/206.29 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 206.03/206.29 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 206.03/206.29 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 206.03/206.29 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 206.03/206.29 6 ifeq(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 206.03/206.29 7 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 206.03/206.29 8 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 206.03/206.29 9 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 206.03/206.29 10 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 206.03/206.29 11 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 206.03/206.29 12 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(11),rewrite([9(2)]),flip(a)].
% 206.03/206.29 13 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 206.03/206.29 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([10(2)]),flip(a)].
% 206.03/206.29 15 ifeq(join(A,B),one,ifeq(meet(A,B),zero,complement(A),B),B) = B # label(meet_join_complement) # label(axiom). [assumption].
% 206.03/206.29 16 meet(A,join(B,meet(A,C))) = meet(A,join(meet(A,join(B,meet(A,C))),meet(C,join(A,B)))) # label(equation_H6) # label(axiom). [assumption].
% 206.03/206.29 17 meet(A,join(meet(B,join(A,C)),meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(A,B))). [copy(16),rewrite([10(9)]),flip(a)].
% 206.03/206.29 18 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 206.03/206.29 19 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(18),rewrite([10(5)])].
% 206.03/206.29 20 meet(a,b) = a. [back_rewrite(3),rewrite([9(3)])].
% 206.03/206.29 21 meet(A,one) = A. [para(4(a,1),7(a,1,2))].
% 206.03/206.29 22 join(A,zero) = A. [para(5(a,1),8(a,1,2))].
% 206.03/206.29 23 meet(A,meet(A,B)) = meet(A,B). [para(12(a,1),1(a,1)),rewrite([9(1),9(2),12(2,R),1(1),9(3)])].
% 206.03/206.29 24 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),12(a,2,2)),rewrite([9(2)])].
% 206.03/206.29 25 meet(A,meet(B,join(A,C))) = meet(A,B). [para(7(a,1),12(a,2,2)),rewrite([9(2),9(4)])].
% 206.03/206.29 26 join(A,join(A,B)) = join(A,B). [para(14(a,1),2(a,1)),rewrite([10(1),10(2),14(2,R),2(1),10(3)])].
% 206.03/206.29 27 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),14(a,2,2)),rewrite([10(2)])].
% 206.03/206.29 28 join(A,join(B,meet(A,C))) = join(A,B). [para(8(a,1),14(a,2,2)),rewrite([10(2),10(4)])].
% 206.03/206.29 32 ifeq(join(A,B),one,ifeq(meet(A,B),zero,complement(B),A),A) = A. [para(10(a,1),15(a,1,1)),rewrite([9(3)])].
% 206.03/206.29 35 meet(A,join(B,meet(A,join(complement(A),meet(A,B))))) = meet(A,join(complement(A),meet(A,B))). [para(4(a,1),17(a,1,2,1,2)),rewrite([21(2)])].
% 206.03/206.29 36 meet(A,join(meet(A,B),meet(complement(A),join(A,B)))) = meet(A,B). [para(5(a,1),17(a,1,2,2,2,2)),rewrite([22(5),10(5),5(8),22(8)])].
% 206.03/206.29 38 meet(A,join(meet(B,join(A,C)),meet(A,join(C,meet(B,A))))) = meet(A,join(C,meet(B,A))). [para(17(a,1),9(a,2)),rewrite([9(3),9(7),9(8)])].
% 206.03/206.29 41 meet(meet(A,join(B,C)),join(meet(B,join(C,meet(A,B))),meet(meet(A,join(B,C)),join(meet(A,B),meet(B,join(C,meet(A,B))))))) = meet(meet(A,join(B,C)),join(meet(A,B),meet(B,join(C,meet(A,B))))). [para(17(a,1),17(a,1,2,1)),rewrite([9(3),9(8),9(13),25(13),9(11),10(12),9(18),9(23),25(23),9(21),10(22)])].
% 206.03/206.29 46 ifeq(join(A,one),one,ifeq(A,zero,complement(A),one),one) = one. [para(21(a,1),15(a,1,3,1))].
% 206.03/206.29 49 meet(A,zero) = zero. [para(5(a,1),23(a,1,2)),rewrite([5(4)])].
% 206.03/206.29 52 meet(A,meet(B,complement(A))) = zero. [back_rewrite(24),rewrite([49(5)])].
% 206.03/206.29 53 meet(A,join(meet(A,B),meet(zero,join(A,B)))) = meet(A,B). [para(49(a,1),17(a,1,2,2,2,2)),rewrite([22(5),10(5),49(8),22(8)])].
% 206.03/206.29 58 meet(A,meet(meet(B,join(A,C)),join(C,meet(B,A)))) = meet(B,A). [para(17(a,1),25(a,1,2)),rewrite([9(3),12(6,R),9(5),9(9),25(9),9(7)])].
% 206.03/206.29 59 meet(a,meet(b,join(A,a))) = a. [para(20(a,1),25(a,2)),rewrite([10(4)])].
% 206.03/206.29 64 join(A,one) = one. [para(4(a,1),26(a,1,2)),rewrite([4(4)])].
% 206.03/206.29 65 meet(A,join(meet(B,join(A,C)),meet(A,join(join(A,C),meet(A,B))))) = meet(A,join(join(A,C),meet(A,B))). [para(26(a,1),17(a,1,2,1,2))].
% 206.03/206.29 67 ifeq(A,zero,complement(A),one) = one. [back_rewrite(46),rewrite([64(2),6(8)])].
% 206.03/206.29 68 join(A,join(B,complement(A))) = one. [back_rewrite(27),rewrite([64(5)])].
% 206.03/206.29 70 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(28(a,1),14(a,2,2)),rewrite([10(3),14(3,R),10(2),14(6),10(5),14(6,R),10(5)])].
% 206.03/206.29 72 meet(A,join(meet(B,join(A,C)),meet(A,join(join(C,meet(A,D)),meet(A,B))))) = meet(A,join(join(C,meet(A,D)),meet(A,B))). [para(28(a,1),17(a,1,2,1,2))].
% 206.03/206.29 73 complement(zero) = one. [para(67(a,1),6(a,1)),flip(a)].
% 206.03/206.29 77 meet(A,join(B,meet(A,join(join(C,complement(A)),meet(A,B))))) = meet(A,join(join(C,complement(A)),meet(A,B))). [para(68(a,1),17(a,1,2,1,2)),rewrite([21(2)])].
% 206.03/206.29 78 meet(a,join(A,a)) = a. [para(59(a,1),12(a,1)),rewrite([20(6),9(5)]),flip(a)].
% 206.03/206.29 109 complement(complement(A)) = A. [para(4(a,1),32(a,1,1)),rewrite([5(4),6(7),6(5)])].
% 206.03/206.29 151 meet(A,join(zero,meet(A,B))) = meet(A,B). [para(8(a,1),53(a,1,2,2,2)),rewrite([23(2),9(3),49(3),10(3),23(6)])].
% 206.03/206.29 160 meet(A,meet(B,join(zero,meet(A,C)))) = meet(A,meet(C,B)). [para(151(a,1),12(a,2,2)),rewrite([9(4),12(7),9(6),12(7,R),9(6)])].
% 206.03/206.29 189 join(A,join(B,join(join(A,B),meet(C,join(A,B))))) = join(A,B). [para(2(a,1),70(a,2)),rewrite([9(3),14(6,R),10(5),14(5,R),10(4)])].
% 206.03/206.29 218 meet(A,meet(B,join(complement(B),meet(A,B)))) = meet(A,B). [para(35(a,1),25(a,1,2)),rewrite([9(2)])].
% 206.03/206.29 220 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(52(a,1),35(a,1,2,2,2,2)),rewrite([22(5),5(4),10(4),52(9),22(8),5(7)])].
% 206.03/206.29 225 meet(complement(A),join(B,meet(complement(A),join(A,meet(B,complement(A)))))) = meet(complement(A),join(A,meet(B,complement(A)))). [para(109(a,1),35(a,1,2,2,2,1)),rewrite([9(4),109(11),9(11)])].
% 206.03/206.29 234 meet(A,join(zero,complement(A))) = zero. [para(1(a,1),220(a,1,2,2))].
% 206.03/206.29 239 meet(complement(A),join(zero,meet(A,B))) = zero. [para(109(a,1),220(a,1,2,2,2)),rewrite([9(3)])].
% 206.03/206.29 241 join(zero,complement(A)) = complement(A). [para(234(a,1),15(a,1,3,1)),rewrite([68(4),6(9),6(7)]),flip(a)].
% 206.03/206.29 242 meet(zero,complement(A)) = zero. [para(234(a,1),17(a,1,2,1)),rewrite([9(6),49(6),22(6),8(6),1(3),9(5),49(5),22(5)]),flip(a)].
% 206.03/206.29 272 meet(complement(A),meet(join(zero,meet(A,B)),join(C,complement(A)))) = zero. [para(239(a,1),25(a,2)),rewrite([10(6)])].
% 206.03/206.29 295 meet(A,meet(B,join(complement(A),meet(A,B)))) = meet(A,B). [para(218(a,1),9(a,2)),rewrite([9(2),9(5),12(5,R),9(4),9(6)])].
% 206.03/206.29 296 meet(meet(A,B),join(complement(B),meet(A,B))) = meet(A,B). [para(218(a,1),12(a,1)),rewrite([9(6)]),flip(a)].
% 206.03/206.29 334 meet(A,join(B,meet(A,B))) = meet(A,B). [para(8(a,1),38(a,2,2)),rewrite([9(3),17(7)])].
% 206.03/206.29 371 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(25(a,1),334(a,1,2,2)),rewrite([10(4),25(8)])].
% 206.03/206.29 542 meet(complement(meet(A,B)),join(zero,meet(A,B))) = zero. [para(296(a,1),239(a,1,2,2))].
% 206.03/206.29 546 join(zero,meet(A,B)) = meet(A,B). [para(542(a,1),15(a,1,3,1)),rewrite([14(6),10(5),241(5),4(4),109(7),6(9),6(7)]),flip(a)].
% 206.03/206.29 548 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [para(542(a,1),160(a,1,2,2,2)),rewrite([2(5),49(4),9(4),242(4),546(6),9(5),12(5),9(4),12(5,R),9(4),12(6,R)]),flip(a)].
% 206.03/206.29 549 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(542(a,1),160(a,1,2)),rewrite([49(2)]),flip(a)].
% 206.03/206.29 558 meet(complement(A),meet(meet(A,B),join(C,complement(A)))) = zero. [back_rewrite(272),rewrite([546(4)])].
% 206.03/206.29 562 meet(meet(A,join(B,C)),join(meet(B,join(C,meet(B,A))),meet(meet(A,join(B,C)),join(meet(B,A),meet(B,join(C,meet(B,A))))))) = meet(meet(A,join(B,C)),join(meet(B,A),meet(B,join(C,meet(B,A))))). [para(41(a,1),9(a,2)),rewrite([9(1),9(6),9(7),9(15),9(18),9(19)])].
% 206.03/206.29 629 meet(a,meet(complement(a),join(A,a))) = zero. [para(78(a,1),549(a,1,2,2,1)),rewrite([9(6)])].
% 206.03/206.29 723 meet(A,meet(meet(B,C),complement(meet(A,C)))) = zero. [para(9(a,1),548(a,1,2,1))].
% 206.03/206.29 913 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(7(a,1),723(a,1,2,1))].
% 206.03/206.29 973 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(58(a,1),12(a,1)),rewrite([25(6),9(4),9(5)]),flip(a)].
% 206.03/206.29 979 meet(a,meet(b,meet(join(A,a),join(A,b)))) = a. [para(20(a,1),58(a,1,2,2,2)),rewrite([10(4),9(8),12(8,R),9(7),12(9,R),9(8),20(12)])].
% 206.03/206.29 1157 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(913(a,1),12(a,1)),rewrite([9(6)]),flip(a)].
% 206.03/206.29 1190 meet(A,join(meet(B,join(A,C)),meet(A,join(join(A,C),meet(B,A))))) = meet(A,join(join(A,C),meet(B,A))). [para(65(a,1),9(a,2)),rewrite([9(4),9(8),9(10)])].
% 206.03/206.29 1191 meet(A,join(join(A,B),meet(A,C))) = A. [para(10(a,1),65(a,1,2,2,2)),rewrite([14(5),10(4),8(4),10(3),7(4),10(3),7(4)]),flip(a)].
% 206.03/206.29 1206 meet(A,join(one,meet(A,B))) = A. [para(4(a,1),1191(a,1,2,1))].
% 206.03/206.29 1225 meet(A,meet(B,complement(meet(A,join(one,meet(B,C)))))) = zero. [para(1206(a,1),723(a,1,2,1))].
% 206.03/206.29 1380 meet(a,join(meet(A,join(B,a)),meet(a,join(B,meet(A,a))))) = meet(a,join(B,meet(A,a))). [para(629(a,1),72(a,1,2,2,2,1,2)),rewrite([10(3),22(7),9(7),629(19),22(14),9(14)])].
% 206.03/206.29 1454 meet(meet(A,B),complement(meet(B,join(A,C)))) = zero. [para(9(a,1),1157(a,1,1))].
% 206.03/206.29 1580 meet(A,join(B,meet(A,join(C,join(complement(A),meet(A,B)))))) = meet(A,join(join(C,complement(A)),meet(A,B))). [para(10(a,1),77(a,1,2,2,2)),rewrite([14(4),10(3),14(4,R),10(3)])].
% 206.03/206.29 1581 meet(A,join(join(B,complement(A)),meet(A,C))) = meet(A,join(B,join(complement(A),meet(A,C)))). [para(10(a,1),77(a,2,2)),rewrite([77(7),14(9),10(8),14(9,R),10(8)])].
% 206.03/206.29 1678 meet(A,join(B,meet(A,join(C,join(complement(A),meet(A,B)))))) = meet(A,join(C,join(complement(A),meet(A,B)))). [back_rewrite(1580),rewrite([1581(12)])].
% 206.03/206.29 1819 meet(A,complement(meet(join(one,meet(A,B)),join(A,C)))) = zero. [para(1206(a,1),1454(a,1,1))].
% 206.03/206.29 2094 meet(complement(A),join(B,complement(A))) = complement(A). [para(558(a,1),1191(a,1,2,2)),rewrite([10(3),10(5),14(5,R),22(4)])].
% 206.03/206.29 2098 meet(complement(A),meet(one,join(B,complement(A)))) = complement(A). [para(2094(a,1),295(a,1,2,2,2)),rewrite([109(5),4(5),9(5),2094(10)])].
% 206.03/206.29 2247 meet(one,complement(A)) = complement(A). [para(2098(a,1),12(a,2)),rewrite([9(5),2094(5)])].
% 206.03/206.29 2315 meet(a,meet(join(A,a),join(A,b))) = a. [para(979(a,1),12(a,1)),rewrite([20(9),9(8)]),flip(a)].
% 206.03/206.29 2330 meet(a,join(A,b)) = a. [para(2315(a,1),12(a,1)),rewrite([78(7),9(5)]),flip(a)].
% 206.03/206.29 4014 meet(meet(A,B),complement(meet(A,join(one,meet(B,C))))) = zero. [para(1225(a,1),12(a,1)),rewrite([9(8)]),flip(a)].
% 206.03/206.29 5761 meet(A,complement(meet(A,join(one,meet(B,join(A,C)))))) = zero. [para(7(a,1),4014(a,1,1)),rewrite([9(3)])].
% 206.03/206.29 8102 meet(join(A,B),complement(meet(one,join(A,B)))) = zero. [para(1191(a,1),5761(a,1,2,1,2,2)),rewrite([10(4),64(4),9(4)])].
% 206.03/206.29 8121 meet(one,join(A,B)) = join(A,B). [para(8102(a,1),1206(a,1,2,2)),rewrite([22(4),9(3)])].
% 206.03/206.29 8124 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(8102(a,1),1819(a,1,2,1,1,2)),rewrite([22(4),10(4),14(4),10(3),14(4,R),10(3),8121(5)])].
% 206.03/206.29 9015 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(189(a,1),14(a,1)),rewrite([10(7),26(7)]),flip(a)].
% 206.03/206.29 9018 join(join(A,B),meet(A,C)) = join(A,B). [para(1191(a,1),189(a,1,2,2,2)),rewrite([10(6),28(6),26(4),14(4),10(3),8(3),10(2),2(3)]),flip(a)].
% 206.03/206.29 9019 join(A,join(a,b)) = join(A,b). [para(2330(a,1),189(a,1,2,2,2)),rewrite([10(5),14(5,R),10(4),14(6,R),10(5),14(5,R),2(4),26(5)])].
% 206.03/206.29 9034 join(a,b) = b. [para(9019(a,1),2(a,1)),rewrite([10(5),9019(5),2(3)]),flip(a)].
% 206.03/206.29 9057 join(a,join(b,meet(A,a))) = b. [para(9034(a,1),28(a,2)),rewrite([9(4)])].
% 206.03/206.29 9470 join(b,meet(A,a)) = b. [para(9057(a,1),14(a,1)),rewrite([9034(6),10(5)]),flip(a)].
% 206.03/206.29 10235 join(join(A,B),meet(B,C)) = join(A,B). [para(10(a,1),9018(a,1,1)),rewrite([10(4)])].
% 206.03/206.29 10272 join(b,meet(A,b)) = b. [para(9470(a,1),9018(a,1,1)),rewrite([9(3),9470(8)])].
% 206.03/206.29 11318 join(complement(A),meet(B,complement(A))) = complement(A). [para(241(a,1),10235(a,1,1)),rewrite([9(3),241(7)])].
% 206.03/206.29 12400 meet(A,complement(join(B,A))) = zero. [para(10235(a,1),225(a,1,2,2,2)),rewrite([9(6),5(6),22(4),9(3),10235(10),9(7),5(7)])].
% 206.03/206.29 12405 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [para(28(a,1),12400(a,1,2,1)),rewrite([10(3),9(5)])].
% 206.03/206.29 12442 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(10(a,1),12405(a,1,1,1))].
% 206.03/206.29 12686 meet(A,complement(join(B,join(C,A)))) = zero. [para(8124(a,1),12442(a,1,2,2)),rewrite([10(2),14(2),10(1),14(2,R),10(1),22(5),9(4)])].
% 206.03/206.29 12701 meet(join(A,meet(B,C)),complement(join(A,join(B,D)))) = zero. [para(28(a,1),12686(a,1,2,1,2)),rewrite([10(3),14(4),10(3),14(4,R),10(3)])].
% 206.03/206.29 17379 meet(complement(join(A,join(B,C))),join(A,meet(B,D))) = zero. [para(12701(a,1),9(a,1)),flip(a)].
% 206.03/206.29 17380 meet(join(A,meet(B,C)),complement(join(A,join(C,D)))) = zero. [para(9(a,1),12701(a,1,1,2))].
% 206.03/206.29 17381 meet(join(A,meet(B,C)),complement(join(B,join(A,D)))) = zero. [para(10(a,1),12701(a,1,1)),rewrite([10(2),14(4,R),10(3)])].
% 206.03/206.29 17405 meet(meet(A,join(B,C)),join(meet(A,B),meet(B,join(C,meet(A,B))))) = meet(A,B). [para(17(a,1),371(a,1,2,2)),rewrite([9(5),25(5),9(3),9(4),9(11),25(11),9(9)])].
% 206.03/206.29 19539 meet(complement(join(A,join(B,C))),join(A,meet(C,D))) = zero. [para(10(a,1),17379(a,1,1,1,2))].
% 206.03/206.29 19540 meet(complement(join(A,join(B,C))),join(C,meet(A,D))) = zero. [para(10(a,1),17379(a,1,1,1)),rewrite([10(2),14(2),10(1),14(2,R),10(1)])].
% 206.03/206.29 19642 meet(join(A,meet(B,C)),complement(join(C,join(A,D)))) = zero. [para(10(a,1),17380(a,1,1)),rewrite([10(2),14(4,R),10(3)])].
% 206.03/206.29 19776 meet(complement(join(A,b)),join(a,meet(A,B))) = zero. [para(9034(a,1),17381(a,1,2,1,2)),rewrite([9(7)])].
% 206.03/206.29 19783 meet(join(a,complement(A)),complement(join(complement(A),b))) = zero. [para(2094(a,1),19776(a,1,2,2)),rewrite([9(8)])].
% 206.03/206.29 19799 complement(join(b,complement(a))) = zero. [para(4(a,1),19783(a,1,1)),rewrite([10(5),2247(7)])].
% 206.03/206.29 19818 join(b,complement(a)) = one. [para(19799(a,1),109(a,1,1)),rewrite([73(2)]),flip(a)].
% 206.03/206.29 19853 meet(b,join(complement(b),meet(b,complement(a)))) = meet(b,complement(a)). [para(19818(a,1),36(a,1,2,2,2)),rewrite([9(9),2247(9),10(8)])].
% 206.03/206.29 20666 meet(complement(join(A,join(B,C))),join(C,meet(B,D))) = zero. [para(10(a,1),19539(a,1,1,1)),rewrite([10(2),14(2),10(1),14(2,R),10(1)])].
% 206.03/206.29 20762 meet(complement(join(A,b)),join(meet(B,b),meet(A,C))) = zero. [para(10272(a,1),19540(a,1,1,1,2))].
% 206.03/206.29 20924 meet(complement(join(A,complement(B))),join(complement(B),meet(C,A))) = zero. [para(11318(a,1),19642(a,1,2,1,2)),rewrite([9(7)])].
% 206.03/206.29 23315 meet(complement(join(A,B)),join(meet(A,C),meet(B,D))) = zero. [para(28(a,1),20666(a,1,1,1))].
% 206.03/206.29 25015 meet(complement(join(A,complement(B))),join(meet(A,C),complement(B))) = zero. [para(2094(a,1),23315(a,1,2,2))].
% 206.03/206.29 26616 complement(join(A,complement(meet(A,B)))) = zero. [para(4(a,1),25015(a,1,2)),rewrite([9(6),2247(6)])].
% 206.03/206.29 26957 join(A,complement(meet(A,B))) = one. [para(26616(a,1),4(a,1,2)),rewrite([10(5),14(5,R),10(4),241(4)])].
% 206.03/206.29 27002 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [para(562(a,1),26957(a,1,2,1)),rewrite([9(5),9(6),17405(10),10(5)])].
% 206.03/206.29 27282 complement(join(join(A,B),complement(meet(A,C)))) = zero. [para(27002(a,1),20924(a,1,2)),rewrite([9(2),9(7),2247(7)])].
% 206.03/206.29 27392 join(join(A,B),complement(meet(A,C))) = one. [para(27282(a,1),109(a,1,1)),rewrite([73(2)]),flip(a)].
% 206.03/206.29 27407 join(join(A,B),complement(meet(B,C))) = one. [para(10(a,1),27392(a,1,1))].
% 206.03/206.29 27433 join(join(A,B),complement(meet(C,join(B,meet(A,D))))) = one. [para(28(a,1),27407(a,1,1)),rewrite([9(4)])].
% 206.03/206.29 31730 join(A,join(complement(A),meet(B,join(A,C)))) = one. [para(1190(a,1),27433(a,1,2,1)),rewrite([9(5),9018(6),7(5),10(5),14(5,R),10(4)])].
% 206.03/206.29 31737 join(A,join(complement(A),meet(B,C))) = one. [para(973(a,1),31730(a,1,2,2))].
% 206.03/206.29 32724 meet(a,join(A,meet(a,join(A,B)))) = meet(a,join(A,B)). [para(9018(a,1),1380(a,1,2,2,2)),rewrite([10(4),14(4),10(3),14(4,R),10(3),7(5),9018(11)])].
% 206.03/206.29 37626 meet(A,join(B,join(complement(A),meet(A,complement(meet(A,B)))))) = A. [para(27002(a,1),1678(a,1,2)),rewrite([21(2)]),flip(a)].
% 206.03/206.29 42653 meet(complement(b),join(meet(A,b),meet(a,join(B,C)))) = zero. [para(32724(a,1),20762(a,1,2,2)),rewrite([9034(3)])].
% 206.03/206.29 42679 meet(complement(b),join(b,meet(a,join(A,B)))) = zero. [para(1(a,1),42653(a,1,2,1))].
% 206.03/206.29 42683 join(b,meet(a,join(A,B))) = b. [para(42679(a,1),15(a,1,3,1)),rewrite([14(8,R),10(7),31737(8),109(7),6(11),6(9)]),flip(a)].
% 206.03/206.29 42687 meet(a,meet(b,join(A,B))) = meet(a,join(A,B)). [para(42683(a,1),973(a,1,2)),rewrite([9(5),12(5,R),9(4)])].
% 206.03/206.29 42751 meet(a,join(complement(b),meet(b,complement(a)))) = zero. [para(19853(a,1),42687(a,1,2)),rewrite([52(6)]),flip(a)].
% 206.03/206.29 44085 join(A,join(complement(B),meet(B,complement(meet(A,B))))) = one. [para(37626(a,1),9015(a,1,2)),rewrite([9(2),10(7),70(7),68(3),9(3)]),flip(a)].
% 206.03/206.29 44092 join(a,join(complement(b),meet(b,complement(a)))) = one. [para(20(a,1),44085(a,1,2,2,2,1))].
% 206.03/206.29 44104 join(complement(b),meet(b,complement(a))) = complement(a). [para(44092(a,1),15(a,1,1)),rewrite([42751(11),6(14),6(12)]),flip(a)].
% 206.03/206.29 44134 join(complement(a),complement(b)) = complement(a). [para(44104(a,1),26(a,1,2)),rewrite([10(5),44104(12)])].
% 206.03/206.29 44135 $F # answer(prove_distributivity). [resolve(44134,a,19,a)].
% 206.03/206.29
% 206.03/206.29 % SZS output end Refutation
% 206.03/206.29 ============================== end of proof ==========================
% 206.03/206.29
% 206.03/206.29 ============================== STATISTICS ============================
% 206.03/206.29
% 206.03/206.29 Given=3252. Generated=3645470. Kept=44130. proofs=1.
% 206.03/206.29 Usable=2365. Sos=9978. Demods=12339. Limbo=1, Disabled=31800. Hints=0.
% 206.03/206.29 Megabytes=46.11.
% 206.03/206.29 User_CPU=203.26, System_CPU=2.02, Wall_clock=205.
% 206.03/206.29
% 206.03/206.29 ============================== end of statistics =====================
% 206.03/206.29
% 206.03/206.29 ============================== end of search =========================
% 206.03/206.29
% 206.03/206.29 THEOREM PROVED
% 206.03/206.29 % SZS status Unsatisfiable
% 206.03/206.29
% 206.03/206.29 Exiting with 1 proof.
% 206.03/206.29
% 206.03/206.29 Process 27748 exit (max_proofs) Wed Jun 29 02:41:33 2022
% 206.03/206.29 Prover9 interrupted
%------------------------------------------------------------------------------