TSTP Solution File: LAT230-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT230-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 06:26:16 EDT 2022
% Result : Unsatisfiable 142.68s 143.01s
% Output : Refutation 142.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : LAT230-10 : TPTP v8.1.0. Released v7.3.0.
% 0.08/0.09 % Command : tptp2X_and_run_prover9 %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Wed Jun 29 15:21:58 EDT 2022
% 0.08/0.28 % CPUTime :
% 6.72/7.01 ============================== Prover9 ===============================
% 6.72/7.01 Prover9 (32) version 2009-11A, November 2009.
% 6.72/7.01 Process 23122 was started by sandbox2 on n032.cluster.edu,
% 6.72/7.01 Wed Jun 29 15:21:59 2022
% 6.72/7.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22969_n032.cluster.edu".
% 6.72/7.01 ============================== end of head ===========================
% 6.72/7.01
% 6.72/7.01 ============================== INPUT =================================
% 6.72/7.01
% 6.72/7.01 % Reading from file /tmp/Prover9_22969_n032.cluster.edu
% 6.72/7.01
% 6.72/7.01 set(prolog_style_variables).
% 6.72/7.01 set(auto2).
% 6.72/7.01 % set(auto2) -> set(auto).
% 6.72/7.01 % set(auto) -> set(auto_inference).
% 6.72/7.01 % set(auto) -> set(auto_setup).
% 6.72/7.01 % set(auto_setup) -> set(predicate_elim).
% 6.72/7.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.72/7.01 % set(auto) -> set(auto_limits).
% 6.72/7.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.72/7.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.72/7.01 % set(auto) -> set(auto_denials).
% 6.72/7.01 % set(auto) -> set(auto_process).
% 6.72/7.01 % set(auto2) -> assign(new_constants, 1).
% 6.72/7.01 % set(auto2) -> assign(fold_denial_max, 3).
% 6.72/7.01 % set(auto2) -> assign(max_weight, "200.000").
% 6.72/7.01 % set(auto2) -> assign(max_hours, 1).
% 6.72/7.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.72/7.01 % set(auto2) -> assign(max_seconds, 0).
% 6.72/7.01 % set(auto2) -> assign(max_minutes, 5).
% 6.72/7.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.72/7.01 % set(auto2) -> set(sort_initial_sos).
% 6.72/7.01 % set(auto2) -> assign(sos_limit, -1).
% 6.72/7.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.72/7.01 % set(auto2) -> assign(max_megs, 400).
% 6.72/7.01 % set(auto2) -> assign(stats, some).
% 6.72/7.01 % set(auto2) -> clear(echo_input).
% 6.72/7.01 % set(auto2) -> set(quiet).
% 6.72/7.01 % set(auto2) -> clear(print_initial_clauses).
% 6.72/7.01 % set(auto2) -> clear(print_given).
% 6.72/7.01 assign(lrs_ticks,-1).
% 6.72/7.01 assign(sos_limit,10000).
% 6.72/7.01 assign(order,kbo).
% 6.72/7.01 set(lex_order_vars).
% 6.72/7.01 clear(print_given).
% 6.72/7.01
% 6.72/7.01 % formulas(sos). % not echoed (15 formulas)
% 6.72/7.01
% 6.72/7.01 ============================== end of input ==========================
% 6.72/7.01
% 6.72/7.01 % From the command line: assign(max_seconds, 300).
% 6.72/7.01
% 6.72/7.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.72/7.01
% 6.72/7.01 % Formulas that are not ordinary clauses:
% 6.72/7.01
% 6.72/7.01 ============================== end of process non-clausal formulas ===
% 6.72/7.01
% 6.72/7.01 ============================== PROCESS INITIAL CLAUSES ===============
% 6.72/7.01
% 6.72/7.01 ============================== PREDICATE ELIMINATION =================
% 6.72/7.01
% 6.72/7.01 ============================== end predicate elimination =============
% 6.72/7.01
% 6.72/7.01 Auto_denials:
% 6.72/7.01 % copying label prove_distributivity to answer in negative clause
% 6.72/7.01
% 6.72/7.01 Term ordering decisions:
% 6.72/7.01
% 6.72/7.01 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 6.72/7.01 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. ifeq=1. complement=0.
% 6.72/7.01
% 6.72/7.01 ============================== end of process initial clauses ========
% 6.72/7.01
% 6.72/7.01 ============================== CLAUSES FOR SEARCH ====================
% 6.72/7.01
% 6.72/7.01 ============================== end of clauses for search =============
% 6.72/7.01
% 6.72/7.01 ============================== SEARCH ================================
% 6.72/7.01
% 6.72/7.01 % Starting search at 0.01 seconds.
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=95.000, iters=3381
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=84.000, iters=3356
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=80.000, iters=3398
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=76.000, iters=3372
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=64.000, iters=3356
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=63.000, iters=3367
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=62.000, iters=3348
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=61.000, iters=3363
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=58.000, iters=3346
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=56.000, iters=3365
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=53.000, iters=3358
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=52.000, iters=3339
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=49.000, iters=3355
% 6.72/7.01
% 6.72/7.01 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 4.40 sec).
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=48.000, iters=3336
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=47.000, iters=3335
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=46.000, iters=3448
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=45.000, iters=3375
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=44.000, iters=3388
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=43.000, iters=3349
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=42.000, iters=3345
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=41.000, iters=3350
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=40.000, iters=3390
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=39.000, iters=3445
% 6.72/7.01
% 6.72/7.01 Low Water (keep): wt=38.000, iters=3338
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=37.000, iters=3336
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=36.000, iters=3344
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=35.000, iters=3370
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=34.000, iters=3334
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=33.000, iters=3404
% 142.68/143.01
% 142.68/143.01 Low Water (displace): id=5590, wt=130.000
% 142.68/143.01
% 142.68/143.01 Low Water (displace): id=5610, wt=124.000
% 142.68/143.01
% 142.68/143.01 Low Water (displace): id=14661, wt=24.000
% 142.68/143.01
% 142.68/143.01 Low Water (displace): id=14700, wt=18.000
% 142.68/143.01
% 142.68/143.01 Low Water (displace): id=15369, wt=17.000
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=32.000, iters=3371
% 142.68/143.01
% 142.68/143.01 Low Water (displace): id=16612, wt=16.000
% 142.68/143.01
% 142.68/143.01 Low Water (displace): id=16660, wt=15.000
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=31.000, iters=3333
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=30.000, iters=3351
% 142.68/143.01
% 142.68/143.01 Low Water (displace): id=20212, wt=14.000
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=29.000, iters=3407
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=28.000, iters=3338
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=27.000, iters=3351
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=26.000, iters=3333
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=25.000, iters=3403
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=24.000, iters=3333
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=23.000, iters=3379
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=22.000, iters=3375
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=21.000, iters=3334
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=20.000, iters=3333
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=19.000, iters=3335
% 142.68/143.01
% 142.68/143.01 Low Water (keep): wt=18.000, iters=3333
% 142.68/143.01
% 142.68/143.01 ============================== PROOF =================================
% 142.68/143.01 % SZS status Unsatisfiable
% 142.68/143.01 % SZS output start Refutation
% 142.68/143.01
% 142.68/143.01 % Proof 1 at 140.37 (+ 1.89) seconds: prove_distributivity.
% 142.68/143.01 % Length of proof is 121.
% 142.68/143.01 % Level of proof is 33.
% 142.68/143.01 % Maximum clause weight is 43.000.
% 142.68/143.01 % Given clauses 3040.
% 142.68/143.01
% 142.68/143.01 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 142.68/143.01 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 142.68/143.01 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 142.68/143.01 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 142.68/143.01 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 142.68/143.01 6 ifeq(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 142.68/143.01 7 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 142.68/143.01 8 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 142.68/143.01 9 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 142.68/143.01 10 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 142.68/143.01 11 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 142.68/143.01 12 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(11),rewrite([9(2)]),flip(a)].
% 142.68/143.01 13 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 142.68/143.01 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([10(2)]),flip(a)].
% 142.68/143.01 15 ifeq(join(A,B),one,ifeq(meet(A,B),zero,complement(A),B),B) = B # label(meet_join_complement) # label(axiom). [assumption].
% 142.68/143.01 16 join(meet(A,B),meet(A,C)) = meet(A,join(meet(A,B),join(meet(A,C),meet(B,join(A,C))))) # label(equation_H18) # label(axiom). [assumption].
% 142.68/143.01 17 meet(A,join(meet(A,B),join(meet(A,C),meet(B,join(A,C))))) = join(meet(A,B),meet(A,C)). [copy(16),flip(a)].
% 142.68/143.01 18 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 142.68/143.01 19 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(18),rewrite([10(5)])].
% 142.68/143.01 20 meet(a,b) = a. [back_rewrite(3),rewrite([9(3)])].
% 142.68/143.01 21 meet(A,one) = A. [para(4(a,1),7(a,1,2))].
% 142.68/143.01 22 join(A,zero) = A. [para(5(a,1),8(a,1,2))].
% 142.68/143.01 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)])].
% 142.68/143.01 24 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),12(a,2,2)),rewrite([9(2)])].
% 142.68/143.01 25 meet(A,meet(B,join(A,C))) = meet(A,B). [para(7(a,1),12(a,2,2)),rewrite([9(2),9(4)])].
% 142.68/143.01 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)])].
% 142.68/143.01 27 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),14(a,2,2)),rewrite([10(2)])].
% 142.68/143.01 28 join(A,join(B,meet(A,C))) = join(A,B). [para(8(a,1),14(a,2,2)),rewrite([10(2),10(4)])].
% 142.68/143.01 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)])].
% 142.68/143.01 36 meet(A,join(B,meet(A,B))) = join(zero,meet(A,B)). [para(4(a,1),17(a,1,2,2,2,2)),rewrite([5(3),21(4),10(3),22(3),10(2),5(6),10(6)])].
% 142.68/143.01 39 meet(A,meet(B,join(meet(A,C),join(meet(A,D),meet(C,join(A,D)))))) = meet(B,join(meet(A,C),meet(A,D))). [para(17(a,1),12(a,2,2)),rewrite([9(7)])].
% 142.68/143.01 40 meet(A,join(meet(A,B),join(meet(A,C),meet(C,join(A,B))))) = join(meet(A,C),meet(A,B)). [para(14(a,1),17(a,1,2)),rewrite([14(6),10(5)])].
% 142.68/143.01 42 meet(A,join(join(meet(A,B),meet(A,C)),join(meet(A,D),meet(join(meet(A,B),join(meet(A,C),meet(B,join(A,C)))),join(A,D))))) = join(join(meet(A,B),meet(A,C)),meet(A,D)). [para(17(a,1),17(a,1,2,1)),rewrite([17(22)])].
% 142.68/143.01 47 ifeq(A,one,ifeq(meet(A,zero),zero,complement(A),zero),zero) = zero. [para(22(a,1),15(a,1,1))].
% 142.68/143.01 50 meet(A,zero) = zero. [para(5(a,1),23(a,1,2)),rewrite([5(4)])].
% 142.68/143.01 52 ifeq(A,one,complement(A),zero) = zero. [back_rewrite(47),rewrite([50(3),6(6)])].
% 142.68/143.01 53 meet(A,meet(B,complement(A))) = zero. [back_rewrite(24),rewrite([50(5)])].
% 142.68/143.01 60 complement(one) = zero. [para(52(a,1),6(a,1)),flip(a)].
% 142.68/143.01 66 join(A,one) = one. [para(4(a,1),26(a,1,2)),rewrite([4(4)])].
% 142.68/143.01 69 join(A,join(B,complement(A))) = one. [back_rewrite(27),rewrite([66(5)])].
% 142.68/143.01 76 join(A,join(B,join(C,complement(A)))) = one. [para(69(a,1),14(a,2,2)),rewrite([10(3),14(3,R),10(2),66(6)])].
% 142.68/143.01 78 meet(A,join(B,join(meet(A,join(C,complement(A))),meet(A,B)))) = join(meet(A,B),meet(A,join(C,complement(A)))). [para(69(a,1),17(a,1,2,2,2,2)),rewrite([21(6),10(5),14(6,R)])].
% 142.68/143.01 93 meet(A,join(B,join(meet(A,join(C,join(D,complement(A)))),meet(A,B)))) = join(meet(A,B),meet(A,join(C,join(D,complement(A))))). [para(76(a,1),17(a,1,2,2,2,2)),rewrite([21(7),10(6),14(7,R)])].
% 142.68/143.01 107 join(zero,meet(A,B)) = meet(A,B). [para(36(a,1),9(a,2)),rewrite([9(1),8(2),9(3)]),flip(a)].
% 142.68/143.01 123 complement(complement(A)) = A. [para(4(a,1),32(a,1,1)),rewrite([5(4),6(7),6(5)])].
% 142.68/143.01 260 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(39(a,1),8(a,1,2))].
% 142.68/143.01 324 meet(A,join(meet(A,B),meet(complement(A),join(A,B)))) = meet(A,B). [para(5(a,1),40(a,1,2,2,1)),rewrite([107(6),5(8),107(9)])].
% 142.68/143.01 332 meet(meet(A,B),join(meet(A,C),meet(A,B))) = meet(A,B). [para(40(a,1),25(a,1,2)),rewrite([9(7),23(7)])].
% 142.68/143.01 385 meet(meet(A,B),join(meet(B,C),meet(A,B))) = meet(A,B). [para(9(a,1),332(a,1,1)),rewrite([9(3),9(6)])].
% 142.68/143.01 389 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(332(a,1),17(a,1,2,1)),rewrite([9(4),12(4),9(3),12(4,R),9(3),10(9),7(13),332(6),9(4),12(4),9(3),12(4,R),9(3)]),flip(a)].
% 142.68/143.01 390 meet(meet(A,B),join(meet(A,C),meet(A,meet(B,C)))) = meet(A,meet(B,C)). [para(332(a,1),17(a,1,2,2,2)),rewrite([12(4),9(3),23(3),12(3),9(2),12(3,R),9(2),12(6),9(5),23(5),12(5),9(4),12(5,R),9(4),10(7),14(8,R),2(7),12(9),9(8),23(8),12(8),9(7),12(8,R),9(7),12(11),9(10),23(10),12(10),9(9),12(10,R),9(9),2(11)])].
% 142.68/143.01 463 meet(meet(A,B),join(B,meet(A,B))) = meet(A,B). [para(1(a,1),385(a,1,2,1))].
% 142.68/143.01 469 meet(zero,complement(A)) = zero. [para(5(a,1),463(a,1,1)),rewrite([5(4),22(4),5(5)])].
% 142.68/143.01 766 meet(A,join(zero,complement(A))) = zero. [para(4(a,1),324(a,1,2,2,2)),rewrite([5(2),21(4),5(6)])].
% 142.68/143.01 807 join(zero,complement(A)) = complement(A). [para(766(a,1),15(a,1,3,1)),rewrite([69(4),6(9),6(7)]),flip(a)].
% 142.68/143.01 809 meet(zero,meet(meet(A,B),complement(C))) = zero. [para(807(a,1),42(a,1,2,2,2,2)),rewrite([9(3),50(3),9(4),50(4),2(4),469(5),9(5),50(5),9(6),50(6),10(7),22(7),107(7),107(6),107(7),107(6),9(7),50(7),9(8),50(8),2(8),469(9),2(8)])].
% 142.68/143.01 846 meet(zero,meet(join(meet(A,B),meet(A,C)),complement(D))) = zero. [para(17(a,1),809(a,1,2,1))].
% 142.68/143.01 853 meet(zero,join(meet(A,B),meet(A,C))) = zero. [para(846(a,1),12(a,2)),rewrite([50(6),9(5)])].
% 142.68/143.01 863 meet(zero,join(meet(A,B),meet(B,C))) = zero. [para(9(a,1),853(a,1,2,1))].
% 142.68/143.01 949 meet(zero,join(A,B)) = zero. [para(21(a,1),863(a,1,2,1)),rewrite([9(3),21(3)])].
% 142.68/143.01 1193 meet(one,join(A,B)) = join(A,B). [para(60(a,1),78(a,1,2,2,1,2,2)),rewrite([22(4),9(3),21(3),9(3),21(3),10(2),26(3),9(5),21(5),60(6),22(6),9(5),21(5)])].
% 142.68/143.01 1254 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(1193(a,1),332(a,1,1)),rewrite([9(3),21(3),1193(4),14(3),10(2),14(3,R),10(2),1193(7)])].
% 142.68/143.01 1255 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(1193(a,1),389(a,1,1)),rewrite([9(4),12(5,R),9(4),1193(4),1193(7)])].
% 142.68/143.01 1257 meet(one,complement(A)) = complement(A). [para(807(a,1),1193(a,1,2)),rewrite([807(6)])].
% 142.68/143.01 1268 join(one,complement(A)) = one. [para(1257(a,1),8(a,1,2))].
% 142.68/143.01 1269 join(one,meet(A,join(B,complement(C)))) = one. [para(1257(a,1),260(a,1,2,2,1)),rewrite([9(4),21(4),10(3)])].
% 142.68/143.01 1272 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(1257(a,1),42(a,1,2,2,1)),rewrite([9(3),21(3),9(3),21(3),9(5),21(5),9(5),21(5),10(5),66(5),21(5),10(4),26(5),1268(7),9(6),1193(6),14(5),10(4),14(5,R),10(4),14(6,R),14(5),10(4),14(5,R),10(4),26(4),26(5),1193(5),9(5),21(5),9(5),21(5),1257(7)]),flip(a)].
% 142.68/143.01 1278 join(one,meet(A,B)) = one. [para(60(a,1),1269(a,1,2,2,2)),rewrite([22(3)])].
% 142.68/143.01 1295 join(one,join(meet(A,B),meet(A,C))) = one. [para(17(a,1),1278(a,1,2))].
% 142.68/143.01 1296 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(1278(a,1),42(a,1,2,2,2,2)),rewrite([9(3),21(3),9(3),21(3),12(5),9(4),21(4),9(3),9(5),21(5),9(5),21(5),10(5),66(5),21(5),10(4),26(5),9(6),1193(6),14(5),10(4),14(5,R),10(4),14(6,R),14(5),10(4),14(5,R),10(4),26(4),26(5),1193(5),9(5),21(5),9(5),21(5),12(7),9(6),21(6),9(5)]),flip(a)].
% 142.68/143.01 1300 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [back_rewrite(1255),rewrite([1296(4)])].
% 142.68/143.01 1597 join(one,join(meet(A,meet(B,C)),meet(C,D))) = one. [para(12(a,2),1295(a,1,2,1))].
% 142.68/143.01 1623 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(107(a,1),1254(a,1,1)),rewrite([10(4),14(5,R),10(4),107(4),107(7)])].
% 142.68/143.01 1632 join(A,join(B,complement(join(A,B)))) = one. [para(1272(a,1),4(a,1))].
% 142.68/143.01 1633 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(8(a,1),1272(a,1,1)),flip(a)].
% 142.68/143.01 1669 join(A,join(B,join(C,complement(join(A,B))))) = one. [para(1632(a,1),14(a,2,2)),rewrite([10(4),14(4,R),10(3),66(7)])].
% 142.68/143.01 1741 join(A,join(B,join(C,complement(join(A,C))))) = one. [para(1669(a,1),10(a,1)),rewrite([10(2),10(6),14(6,R),10(5),14(5,R),10(4)]),flip(a)].
% 142.68/143.01 1801 join(A,join(B,join(meet(C,join(A,B)),complement(D)))) = join(A,join(B,complement(D))). [para(1300(a,1),1272(a,1,1)),rewrite([1272(3),1272(8)]),flip(a)].
% 142.68/143.01 1821 join(one,join(meet(A,a),meet(B,b))) = one. [para(20(a,1),1597(a,1,2,1,2)),rewrite([9(5)])].
% 142.68/143.01 1849 join(meet(A,B),meet(B,join(C,join(D,complement(B))))) = meet(B,join(A,meet(B,join(C,join(D,complement(B)))))). [para(93(a,1),9(a,2)),rewrite([9(5),28(7),9(6),9(7)]),flip(a)].
% 142.68/143.01 1890 join(one,join(b,meet(A,a))) = one. [para(1(a,1),1821(a,1,2,2)),rewrite([10(5)])].
% 142.68/143.01 1896 join(one,b) = one. [para(8(a,1),1890(a,1,2))].
% 142.68/143.01 1901 join(one,join(b,complement(A))) = one. [para(1896(a,1),1272(a,1,1)),rewrite([1268(3)]),flip(a)].
% 142.68/143.01 1908 join(zero,join(b,complement(A))) = join(b,complement(A)). [para(1901(a,1),324(a,1,2,2,2)),rewrite([1193(6),60(6),9(7),50(7),10(6),1193(7),1193(10)])].
% 142.68/143.01 1926 join(b,complement(join(zero,b))) = one. [para(1908(a,1),1632(a,1))].
% 142.68/143.01 1927 meet(one,b) = b. [para(1926(a,1),7(a,1,2)),rewrite([9(3)])].
% 142.68/143.01 1942 join(b,meet(A,b)) = b. [para(1927(a,1),389(a,1,1)),rewrite([9(4),12(5,R),9(4),1927(4),1927(7)])].
% 142.68/143.01 1970 join(a,b) = b. [para(20(a,1),1942(a,1,2)),rewrite([10(3)])].
% 142.68/143.01 1997 join(a,join(b,complement(A))) = join(b,complement(A)). [para(1970(a,1),1272(a,1,1)),flip(a)].
% 142.68/143.01 2239 join(a,join(complement(A),b)) = join(b,complement(A)). [para(10(a,1),1997(a,1,2))].
% 142.68/143.01 2242 join(b,complement(a)) = one. [para(1997(a,1),69(a,1))].
% 142.68/143.01 2320 meet(b,join(complement(b),meet(b,complement(a)))) = meet(b,complement(a)). [para(2242(a,1),324(a,1,2,2,2)),rewrite([9(9),1257(9),10(8)])].
% 142.68/143.01 2526 meet(join(a,complement(A)),join(b,complement(A))) = join(a,complement(A)). [para(2239(a,1),1254(a,1,2))].
% 142.68/143.01 2878 join(A,complement(meet(A,B))) = one. [para(4(a,1),1633(a,1,2)),rewrite([66(2)]),flip(a)].
% 142.68/143.01 2970 join(A,join(B,complement(meet(C,join(A,B))))) = one. [para(2878(a,1),1272(a,1)),rewrite([9(3)]),flip(a)].
% 142.68/143.01 5401 meet(join(complement(A),a),join(b,complement(A))) = join(a,complement(A)). [para(10(a,1),2526(a,1,1))].
% 142.68/143.01 7393 join(complement(A),join(a,complement(B))) = join(a,join(complement(A),complement(B))). [para(5401(a,1),1633(a,1,2,1)),rewrite([1272(8),14(9,R),14(8),10(7),26(7),26(7),1272(10)]),flip(a)].
% 142.68/143.01 10950 meet(meet(A,B),join(C,join(D,meet(A,B)))) = meet(A,B). [para(1296(a,1),1623(a,1,2))].
% 142.68/143.01 13795 meet(a,join(complement(A),join(a,complement(B)))) = a. [para(7393(a,2),7(a,1,2))].
% 142.68/143.01 13903 meet(a,join(A,join(a,complement(B)))) = a. [para(123(a,1),13795(a,1,2,1))].
% 142.68/143.01 14907 meet(meet(A,B),join(A,C)) = meet(A,B). [para(8(a,1),10950(a,1,2,2)),rewrite([10(2)])].
% 142.68/143.01 14964 meet(meet(A,B),join(B,C)) = meet(A,B). [para(9(a,1),14907(a,1,1)),rewrite([9(4)])].
% 142.68/143.01 15060 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(25(a,1),14964(a,1,1)),rewrite([10(4),25(8)])].
% 142.68/143.01 17561 meet(meet(A,B),join(meet(A,C),meet(A,D))) = meet(B,join(meet(A,C),meet(A,D))). [para(17(a,1),390(a,1,2,1)),rewrite([39(12),1296(9),1300(9),39(13)])].
% 142.68/143.01 17985 meet(meet(A,a),join(B,meet(A,b))) = meet(A,a). [para(1970(a,1),15060(a,1,2,2,2)),rewrite([9(2),9(8)])].
% 142.68/143.01 17994 join(A,join(complement(meet(B,C)),meet(B,join(C,D)))) = one. [para(15060(a,1),2970(a,1,2,2,1)),rewrite([9(3),10(5)])].
% 142.68/143.01 18271 meet(a,join(meet(A,B),meet(A,b))) = meet(A,a). [para(17985(a,1),39(a,2)),rewrite([39(12),17561(7)])].
% 142.68/143.01 18403 meet(a,join(meet(A,B),meet(B,b))) = meet(B,a). [para(9(a,1),18271(a,1,2,1))].
% 142.68/143.01 19081 meet(a,meet(b,join(A,B))) = meet(a,join(A,B)). [para(949(a,1),18403(a,1,2,1)),rewrite([9(5),107(6),9(8)])].
% 142.68/143.01 19118 meet(a,join(complement(b),meet(b,complement(a)))) = zero. [para(2320(a,1),18403(a,1,2,1)),rewrite([9(14),2320(14),2(10),53(6),9(10)]),flip(a)].
% 142.68/143.01 20305 join(complement(meet(A,B)),meet(A,join(B,C))) = one. [para(17994(a,1),2(a,1)),flip(a)].
% 142.68/143.01 20375 join(complement(meet(A,B)),meet(B,join(A,C))) = one. [para(9(a,1),20305(a,1,1,1))].
% 142.68/143.01 20453 join(A,complement(meet(B,A))) = one. [para(4(a,1),20375(a,1,2,2)),rewrite([21(4),10(3)])].
% 142.68/143.01 20668 join(meet(b,join(A,B)),complement(meet(a,join(A,B)))) = one. [para(19081(a,1),20453(a,1,2,1))].
% 142.68/143.01 22345 join(complement(a),meet(b,join(A,join(a,complement(B))))) = one. [para(13903(a,1),20668(a,1,2,1)),rewrite([10(9)])].
% 142.68/143.01 30483 join(A,join(B,complement(join(A,meet(C,join(A,B)))))) = one. [para(1801(a,1),1741(a,1))].
% 142.68/143.01 30520 join(meet(b,complement(a)),meet(b,join(A,join(a,complement(b))))) = b. [para(22345(a,1),1849(a,2,2)),rewrite([9(4),9(15),1927(15)])].
% 142.68/143.01 38109 join(a,join(complement(b),meet(b,complement(a)))) = one. [para(30520(a,1),30483(a,1,2,2,1)),rewrite([10(11),14(11,R),2(10),14(9),10(8),14(9,R),10(8)])].
% 142.68/143.01 38115 join(complement(b),meet(b,complement(a))) = complement(a). [para(38109(a,1),15(a,1,1)),rewrite([19118(11),6(14),6(12)]),flip(a)].
% 142.68/143.01 38138 join(complement(a),complement(b)) = complement(a). [para(38115(a,1),26(a,1,2)),rewrite([10(5),38115(12)])].
% 142.68/143.01 38139 $F # answer(prove_distributivity). [resolve(38138,a,19,a)].
% 142.68/143.01
% 142.68/143.01 % SZS output end Refutation
% 142.68/143.01 ============================== end of proof ==========================
% 142.68/143.01
% 142.68/143.01 ============================== STATISTICS ============================
% 142.68/143.01
% 142.68/143.01 Given=3040. Generated=3544205. Kept=38134. proofs=1.
% 142.68/143.01 Usable=2166. Sos=9098. Demods=11229. Limbo=1, Disabled=26883. Hints=0.
% 142.68/143.01 Megabytes=38.24.
% 142.68/143.01 User_CPU=140.37, System_CPU=1.89, Wall_clock=142.
% 142.68/143.01
% 142.68/143.01 ============================== end of statistics =====================
% 142.68/143.01
% 142.68/143.01 ============================== end of search =========================
% 142.68/143.01
% 142.68/143.01 THEOREM PROVED
% 142.68/143.01 % SZS status Unsatisfiable
% 142.68/143.01
% 142.68/143.01 Exiting with 1 proof.
% 142.68/143.01
% 142.68/143.01 Process 23122 exit (max_proofs) Wed Jun 29 15:24:21 2022
% 142.68/143.02 Prover9 interrupted
%------------------------------------------------------------------------------