TSTP Solution File: LAT252-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT252-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 15.94s 16.26s
% Output : Refutation 15.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT252-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n004.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 07:19:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.07/9.39 ============================== Prover9 ===============================
% 9.07/9.39 Prover9 (32) version 2009-11A, November 2009.
% 9.07/9.39 Process 3834 was started by sandbox on n004.cluster.edu,
% 9.07/9.39 Wed Jun 29 07:19:08 2022
% 9.07/9.39 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3681_n004.cluster.edu".
% 9.07/9.39 ============================== end of head ===========================
% 9.07/9.39
% 9.07/9.39 ============================== INPUT =================================
% 9.07/9.39
% 9.07/9.39 % Reading from file /tmp/Prover9_3681_n004.cluster.edu
% 9.07/9.39
% 9.07/9.39 set(prolog_style_variables).
% 9.07/9.39 set(auto2).
% 9.07/9.39 % set(auto2) -> set(auto).
% 9.07/9.39 % set(auto) -> set(auto_inference).
% 9.07/9.39 % set(auto) -> set(auto_setup).
% 9.07/9.39 % set(auto_setup) -> set(predicate_elim).
% 9.07/9.39 % set(auto_setup) -> assign(eq_defs, unfold).
% 9.07/9.39 % set(auto) -> set(auto_limits).
% 9.07/9.39 % set(auto_limits) -> assign(max_weight, "100.000").
% 9.07/9.39 % set(auto_limits) -> assign(sos_limit, 20000).
% 9.07/9.39 % set(auto) -> set(auto_denials).
% 9.07/9.39 % set(auto) -> set(auto_process).
% 9.07/9.39 % set(auto2) -> assign(new_constants, 1).
% 9.07/9.39 % set(auto2) -> assign(fold_denial_max, 3).
% 9.07/9.39 % set(auto2) -> assign(max_weight, "200.000").
% 9.07/9.39 % set(auto2) -> assign(max_hours, 1).
% 9.07/9.39 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 9.07/9.39 % set(auto2) -> assign(max_seconds, 0).
% 9.07/9.39 % set(auto2) -> assign(max_minutes, 5).
% 9.07/9.39 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 9.07/9.39 % set(auto2) -> set(sort_initial_sos).
% 9.07/9.39 % set(auto2) -> assign(sos_limit, -1).
% 9.07/9.39 % set(auto2) -> assign(lrs_ticks, 3000).
% 9.07/9.39 % set(auto2) -> assign(max_megs, 400).
% 9.07/9.39 % set(auto2) -> assign(stats, some).
% 9.07/9.39 % set(auto2) -> clear(echo_input).
% 9.07/9.39 % set(auto2) -> set(quiet).
% 9.07/9.39 % set(auto2) -> clear(print_initial_clauses).
% 9.07/9.39 % set(auto2) -> clear(print_given).
% 9.07/9.39 assign(lrs_ticks,-1).
% 9.07/9.39 assign(sos_limit,10000).
% 9.07/9.39 assign(order,kbo).
% 9.07/9.39 set(lex_order_vars).
% 9.07/9.39 clear(print_given).
% 9.07/9.39
% 9.07/9.39 % formulas(sos). % not echoed (14 formulas)
% 9.07/9.39
% 9.07/9.39 ============================== end of input ==========================
% 9.07/9.39
% 9.07/9.39 % From the command line: assign(max_seconds, 300).
% 9.07/9.39
% 9.07/9.39 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 9.07/9.39
% 9.07/9.39 % Formulas that are not ordinary clauses:
% 9.07/9.39
% 9.07/9.39 ============================== end of process non-clausal formulas ===
% 9.07/9.39
% 9.07/9.39 ============================== PROCESS INITIAL CLAUSES ===============
% 9.07/9.39
% 9.07/9.39 ============================== PREDICATE ELIMINATION =================
% 9.07/9.39
% 9.07/9.39 ============================== end predicate elimination =============
% 9.07/9.39
% 9.07/9.39 Auto_denials:
% 9.07/9.39 % copying label prove_distributivity to answer in negative clause
% 9.07/9.39
% 9.07/9.39 Term ordering decisions:
% 9.07/9.39
% 9.07/9.39 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 9.07/9.39 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 9.07/9.39
% 9.07/9.39 ============================== end of process initial clauses ========
% 9.07/9.39
% 9.07/9.39 ============================== CLAUSES FOR SEARCH ====================
% 9.07/9.39
% 9.07/9.39 ============================== end of clauses for search =============
% 9.07/9.39
% 9.07/9.39 ============================== SEARCH ================================
% 9.07/9.39
% 9.07/9.39 % Starting search at 0.01 seconds.
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=137.000, iters=3370
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=135.000, iters=3366
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=133.000, iters=3351
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=132.000, iters=3345
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=117.000, iters=3424
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=111.000, iters=3361
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=109.000, iters=3549
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=98.000, iters=3409
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=95.000, iters=3376
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=93.000, iters=3346
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=91.000, iters=3470
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=89.000, iters=3415
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=87.000, iters=3376
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=86.000, iters=3345
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=85.000, iters=3380
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=83.000, iters=3346
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=81.000, iters=3408
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=80.000, iters=3368
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=79.000, iters=3361
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=78.000, iters=3367
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=75.000, iters=3385
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=73.000, iters=3352
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=72.000, iters=3367
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=71.000, iters=3356
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=69.000, iters=3434
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=67.000, iters=3341
% 9.07/9.39
% 9.07/9.39 Low Water (keep): wt=66.000, iters=3367
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=65.000, iters=3460
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=63.000, iters=3338
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=62.000, iters=3388
% 15.94/16.26
% 15.94/16.26 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 8.66 sec).
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=61.000, iters=3448
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=60.000, iters=3340
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=58.000, iters=3359
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=57.000, iters=3345
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=55.000, iters=3333
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=54.000, iters=3338
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=53.000, iters=3337
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=52.000, iters=3408
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=51.000, iters=3383
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=50.000, iters=3345
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=49.000, iters=3416
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=48.000, iters=3348
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=47.000, iters=3351
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=46.000, iters=3338
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=34.000, iters=3747
% 15.94/16.26
% 15.94/16.26 Low Water (keep): wt=32.000, iters=3438
% 15.94/16.26
% 15.94/16.26 ============================== PROOF =================================
% 15.94/16.26 % SZS status Unsatisfiable
% 15.94/16.26 % SZS output start Refutation
% 15.94/16.26
% 15.94/16.26 % Proof 1 at 15.17 (+ 0.13) seconds: prove_distributivity.
% 15.94/16.26 % Length of proof is 130.
% 15.94/16.26 % Level of proof is 38.
% 15.94/16.26 % Maximum clause weight is 45.000.
% 15.94/16.26 % Given clauses 671.
% 15.94/16.26
% 15.94/16.26 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 15.94/16.26 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 15.94/16.26 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 15.94/16.26 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 15.94/16.26 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 15.94/16.26 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 15.94/16.26 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 15.94/16.26 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 15.94/16.26 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 15.94/16.26 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 15.94/16.26 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 15.94/16.26 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 15.94/16.26 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 15.94/16.26 14 meet(A,join(B,meet(C,join(B,D)))) = meet(A,join(B,meet(C,join(D,meet(B,join(A,C)))))) # label(equation_H70) # label(axiom). [assumption].
% 15.94/16.26 15 meet(A,join(B,meet(C,join(D,meet(B,join(A,C)))))) = meet(A,join(B,meet(C,join(B,D)))). [copy(14),flip(a)].
% 15.94/16.26 16 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 15.94/16.26 17 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(16),rewrite([9(5)])].
% 15.94/16.26 18 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 15.94/16.26 19 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 15.94/16.26 20 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 15.94/16.26 21 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 15.94/16.26 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)])].
% 15.94/16.26 23 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 15.94/16.26 24 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 15.94/16.26 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)])].
% 15.94/16.26 26 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 15.94/16.26 27 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 15.94/16.26 28 meet(A,join(B,meet(A,join(C,meet(A,B))))) = meet(A,join(B,meet(A,join(B,C)))). [para(2(a,1),15(a,1,2,2,2,2,2)),rewrite([8(1)])].
% 15.94/16.26 29 meet(A,join(B,meet(C,join(B,C)))) = meet(A,join(B,C)). [para(6(a,1),15(a,1,2,2)),flip(a)].
% 15.94/16.26 30 meet(A,join(B,meet(meet(A,C),join(D,meet(A,B))))) = meet(A,join(B,meet(meet(A,C),join(B,D)))). [para(7(a,1),15(a,1,2,2,2,2,2)),rewrite([8(2)])].
% 15.94/16.26 32 meet(A,meet(B,join(C,meet(D,join(E,meet(C,join(A,D))))))) = meet(A,meet(B,join(C,meet(D,join(C,E))))). [para(15(a,1),11(a,2,2)),rewrite([8(6),11(12,R),8(11)])].
% 15.94/16.26 33 meet(A,join(B,meet(meet(C,join(D,meet(A,join(B,C)))),join(E,meet(B,join(A,meet(C,join(A,D)))))))) = meet(A,join(B,meet(meet(C,join(D,meet(A,join(B,C)))),join(B,E)))). [para(15(a,1),15(a,1,2,2,2,2))].
% 15.94/16.26 36 meet(A,join(B,meet(zero,join(C,meet(A,B))))) = meet(A,join(B,meet(zero,join(B,C)))). [para(21(a,1),15(a,1,2,2,2,2,2)),rewrite([8(2)])].
% 15.94/16.26 37 meet(A,zero) != zero | one != A | complement(A) = zero. [para(21(a,1),18(b,1)),flip(b)].
% 15.94/16.26 38 meet(A,zero) = zero. [para(5(a,1),22(a,1,2)),rewrite([5(4)])].
% 15.94/16.26 39 one != A | complement(A) = zero. [back_rewrite(37),rewrite([38(2)]),xx(a)].
% 15.94/16.26 40 meet(A,meet(B,complement(A))) = zero. [back_rewrite(23),rewrite([38(5)])].
% 15.94/16.26 41 complement(one) = zero. [hyper(18,a,38,a,b,21,a)].
% 15.94/16.26 43 meet(a,meet(b,join(A,a))) = a. [para(19(a,1),24(a,2)),rewrite([9(4)])].
% 15.94/16.26 44 complement(join(A,one)) = zero. [hyper(39,a,7,a(flip)),rewrite([8(3),20(3),9(2)])].
% 15.94/16.26 46 join(A,one) = one. [para(44(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),21(3),9(2)])].
% 15.94/16.26 47 join(A,join(B,complement(A))) = one. [back_rewrite(26),rewrite([46(5)])].
% 15.94/16.26 48 complement(zero) = one. [hyper(18,a,20,a,b,46,a)].
% 15.94/16.26 52 meet(A,meet(B,meet(C,complement(A)))) = zero. [para(40(a,1),11(a,2,2)),rewrite([8(3),11(3,R),8(2),38(6)])].
% 15.94/16.26 64 meet(A,join(complement(A),meet(A,join(B,complement(A))))) = meet(A,join(complement(A),meet(A,B))). [para(5(a,1),28(a,1,2,2,2,2)),rewrite([21(3),9(7)]),flip(a)].
% 15.94/16.26 66 meet(A,meet(B,join(C,meet(A,join(D,meet(A,C)))))) = meet(A,meet(B,join(C,meet(A,join(C,D))))). [para(28(a,1),11(a,2,2)),rewrite([8(5),11(11,R),8(10)])].
% 15.94/16.26 69 meet(A,join(join(B,meet(A,C)),meet(A,join(C,meet(A,join(B,C)))))) = meet(A,join(join(B,meet(A,C)),meet(A,join(B,join(C,meet(A,C)))))). [para(15(a,1),28(a,1,2,2)),rewrite([2(1),8(1),9(3),2(9),8(9),2(11),8(11),9(13),13(13,R),9(12)])].
% 15.94/16.26 70 meet(A,join(B,meet(A,join(meet(A,B),meet(C,join(D,meet(B,join(A,C)))))))) = meet(A,join(B,meet(A,join(B,meet(C,join(B,D)))))). [para(15(a,1),28(a,2,2,2)),rewrite([9(6)])].
% 15.94/16.26 76 meet(A,join(meet(B,meet(C,complement(A))),meet(A,join(D,meet(B,meet(C,complement(A))))))) = meet(A,join(meet(B,meet(C,complement(A))),meet(A,D))). [para(52(a,1),28(a,1,2,2,2,2)),rewrite([21(5),9(13)]),flip(a)].
% 15.94/16.26 88 join(A,meet(B,join(A,B))) = join(A,B). [para(29(a,1),1(a,1)),rewrite([8(5),29(5),1(3)]),flip(a)].
% 15.94/16.26 96 join(A,meet(one,join(B,complement(A)))) = one. [para(47(a,1),88(a,1,2,2)),rewrite([8(4),47(8)])].
% 15.94/16.26 100 join(A,meet(one,complement(A))) = one. [para(2(a,1),96(a,1,2,2))].
% 15.94/16.26 103 meet(one,complement(A)) = complement(A). [hyper(18,a,40,a,b,100,a),flip(a)].
% 15.94/16.26 104 join(one,complement(A)) = one. [para(103(a,1),7(a,1,2))].
% 15.94/16.26 110 meet(A,join(B,meet(meet(A,C),join(B,D)))) = meet(A,join(B,meet(A,meet(C,join(B,D))))). [para(8(a,1),30(a,2,2,2)),rewrite([30(6),11(8),8(7),11(8,R),8(7)])].
% 15.94/16.26 111 meet(A,meet(B,join(C,meet(meet(A,D),join(E,meet(A,C)))))) = meet(A,meet(B,join(C,meet(A,meet(D,join(C,E)))))). [para(30(a,1),11(a,2,2)),rewrite([8(6),110(12),11(13,R),8(12)])].
% 15.94/16.26 112 meet(A,join(B,meet(meet(meet(B,C),join(D,meet(A,B))),join(E,meet(B,join(A,meet(B,meet(C,join(A,D))))))))) = meet(A,join(B,meet(meet(meet(B,C),join(D,meet(A,B))),join(B,E)))). [para(30(a,1),15(a,1,2,2,2,2)),rewrite([8(2),110(9),8(15)])].
% 15.94/16.26 120 meet(a,join(meet(b,join(A,a)),meet(meet(B,a),join(C,meet(b,join(A,a)))))) = meet(a,join(meet(b,join(A,a)),meet(meet(B,a),join(C,a)))). [para(43(a,1),30(a,1,2,2,2,2)),rewrite([8(7),8(19),9(24)]),flip(a)].
% 15.94/16.26 159 meet(A,meet(B,meet(C,join(D,meet(E,join(F,meet(D,join(A,E)))))))) = meet(A,meet(B,meet(C,join(D,meet(E,join(D,F)))))). [para(32(a,1),11(a,2,2)),rewrite([8(7),11(7,R),8(6),11(14,R),8(13),11(13,R),8(12)])].
% 15.94/16.26 184 meet(A,join(B,meet(meet(C,join(D,meet(A,join(B,C)))),join(B,E)))) = meet(A,join(B,meet(C,meet(join(D,meet(A,join(B,C))),join(B,E))))). [para(8(a,1),33(a,2,2,2)),rewrite([33(12),11(14,R)])].
% 15.94/16.26 190 meet(A,join(B,meet(meet(C,join(zero,meet(A,join(B,C)))),join(D,meet(A,B))))) = meet(A,join(B,meet(C,meet(join(zero,meet(A,join(B,C))),join(B,D))))). [para(21(a,1),33(a,1,2,2,2,2,2,2,2)),rewrite([8(6),7(7),8(6),184(19)])].
% 15.94/16.26 250 meet(A,join(B,meet(zero,join(A,B)))) = meet(A,B). [para(7(a,1),36(a,1,2,2,2)),rewrite([8(2),38(2),21(2),9(3)]),flip(a)].
% 15.94/16.26 304 meet(A,join(zero,meet(A,B))) = meet(A,B). [para(7(a,1),250(a,1,2,2,2)),rewrite([8(3),38(3),9(3),22(6)])].
% 15.94/16.26 305 meet(A,join(B,meet(zero,join(B,A)))) = meet(B,A). [para(250(a,1),8(a,2)),rewrite([9(2),8(5),8(6)])].
% 15.94/16.26 327 meet(A,meet(B,join(zero,meet(A,C)))) = meet(A,meet(C,B)). [para(304(a,1),11(a,2,2)),rewrite([8(4),11(7),8(6),11(7,R),8(6)])].
% 15.94/16.26 330 meet(one,join(zero,complement(A))) = complement(A). [para(103(a,1),304(a,1,2,2)),rewrite([103(8)])].
% 15.94/16.26 335 meet(A,join(zero,complement(B))) = meet(A,complement(B)). [para(330(a,1),11(a,1,2)),rewrite([20(7),8(6)]),flip(a)].
% 15.94/16.26 369 join(zero,complement(A)) = complement(A). [para(335(a,1),1(a,1)),rewrite([8(5),335(5),1(3)]),flip(a)].
% 15.94/16.26 386 meet(join(A,B),join(A,meet(zero,join(A,B)))) = A. [para(6(a,1),305(a,2)),rewrite([25(4)])].
% 15.94/16.26 491 meet(join(A,B),join(B,meet(zero,join(A,B)))) = B. [para(9(a,1),386(a,1,1)),rewrite([9(3)])].
% 15.94/16.26 493 meet(join(A,join(B,C)),join(C,meet(zero,join(A,join(B,C))))) = C. [para(13(a,2),386(a,1,1)),rewrite([13(5),9(4),13(5,R),9(4)])].
% 15.94/16.26 508 meet(A,join(B,A)) = A. [para(491(a,1),22(a,1,2)),rewrite([8(2),491(8)])].
% 15.94/16.26 522 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(13(a,1),508(a,1,2)),rewrite([9(2),13(3,R),9(2)])].
% 15.94/16.26 523 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(27(a,1),508(a,1,2)),rewrite([9(3),8(4)])].
% 15.94/16.26 525 meet(zero,join(A,B)) = zero. [para(508(a,1),36(a,2)),rewrite([8(8),24(8),38(6),21(6),8(5),38(5),21(5),8(4),24(4),38(2)]),flip(a)].
% 15.94/16.26 532 meet(A,join(B,join(C,A))) = A. [back_rewrite(493),rewrite([525(6),21(4),8(3)])].
% 15.94/16.26 551 meet(meet(A,B),join(A,C)) = meet(A,B). [para(7(a,1),532(a,1,2,2)),rewrite([9(2)])].
% 15.94/16.26 574 meet(meet(A,B),join(B,C)) = meet(A,B). [para(8(a,1),551(a,1,1)),rewrite([8(4)])].
% 15.94/16.26 621 meet(a,join(A,meet(b,join(B,a)))) = a. [para(43(a,1),574(a,1,1)),rewrite([9(6),43(13)])].
% 15.94/16.26 714 meet(one,join(A,B)) = join(A,B). [para(4(a,1),522(a,1,2,2)),rewrite([46(3),8(3)])].
% 15.94/16.26 808 meet(join(A,meet(B,C)),join(B,meet(meet(B,join(C,meet(B,join(A,C)))),join(D,meet(B,join(join(A,meet(B,C)),meet(B,join(A,join(C,meet(B,C)))))))))) = meet(B,join(A,meet(B,C))). [para(69(a,1),15(a,1,2,2,2,2)),rewrite([551(26),7(25),8(21)])].
% 15.94/16.26 918 meet(a,join(b,meet(a,join(b,meet(A,join(B,b)))))) = a. [para(19(a,1),70(a,1,2,2,2,1)),rewrite([9(7),6(12),9(4),6(5),9(7)]),flip(a)].
% 15.94/16.26 1156 meet(A,join(zero,meet(B,complement(A)))) = zero. [para(2(a,1),76(a,2,2)),rewrite([40(3),40(6),9(5),304(8),40(8),38(7)])].
% 15.94/16.26 1632 join(A,meet(one,meet(join(B,C),join(A,D)))) = join(A,meet(join(B,C),join(A,D))). [para(714(a,1),110(a,1,2,2,1)),rewrite([714(6),714(12)]),flip(a)].
% 15.94/16.26 1665 meet(A,meet(B,join(zero,meet(C,complement(meet(A,B)))))) = zero. [para(1156(a,1),110(a,1,2,2)),rewrite([2(3),38(2),304(11)]),flip(a)].
% 15.94/16.26 1695 meet(A,meet(B,complement(meet(A,B)))) = zero. [para(1(a,1),1665(a,1,2,2,2)),rewrite([369(4)])].
% 15.94/16.26 1726 meet(A,meet(B,meet(C,complement(meet(A,B))))) = zero. [para(1695(a,1),11(a,2,2)),rewrite([8(4),11(4,R),8(3),38(7)])].
% 15.94/16.26 2087 meet(A,join(one,meet(join(B,C),join(A,D)))) = A. [para(714(a,1),112(a,1,2,2,1,1)),rewrite([20(4),9(3),1632(11),714(10),13(9,R),9(8),532(10),714(10),20(10),9(9),9(12),46(12),8(12),7(13),20(8)])].
% 15.94/16.26 2591 meet(A,join(one,meet(B,join(A,C)))) = A. [para(2(a,1),2087(a,1,2,2,1))].
% 15.94/16.26 2899 meet(a,join(meet(b,join(A,a)),meet(meet(B,a),join(C,a)))) = meet(a,join(meet(b,join(A,a)),meet(B,a))). [para(8(a,1),120(a,1,2,2)),rewrite([11(13),8(12),11(13,R),8(12),621(12)]),flip(a)].
% 15.94/16.26 2900 meet(a,join(meet(b,join(A,a)),meet(B,a))) = a. [para(9(a,1),120(a,2,2)),rewrite([120(15),2899(12),621(21)])].
% 15.94/16.26 2917 meet(a,join(b,meet(A,a))) = a. [para(6(a,1),2900(a,1,2,1))].
% 15.94/16.26 2951 meet(one,b) = b. [para(2917(a,1),2591(a,1,2,2)),rewrite([9(4),46(4),8(3)])].
% 15.94/16.26 2955 join(zero,b) = b. [para(2951(a,1),304(a,1,2,2)),rewrite([714(5),2951(6)])].
% 15.94/16.26 4231 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(25(a,1),523(a,1,1)),rewrite([8(3),8(7)])].
% 15.94/16.26 4254 meet(A,join(zero,meet(B,complement(meet(A,B))))) = zero. [para(523(a,1),1665(a,1,2)),rewrite([9(3),21(3)])].
% 15.94/16.26 4594 meet(A,join(zero,meet(B,meet(C,complement(meet(A,B)))))) = zero. [para(1726(a,1),4254(a,1,2,2,2,1)),rewrite([48(7),8(7),11(7,R),8(6),11(6,R),8(5),103(5)])].
% 15.94/16.26 5509 meet(A,meet(meet(B,C),join(D,meet(A,E)))) = meet(A,meet(B,meet(C,join(D,meet(A,E))))). [para(69(a,1),159(a,1,2,2,2,2,2,2)),rewrite([11(20,R),8(19),11(19,R),8(18),808(18),11(4,R),8(3),11(5,R),8(4),551(13),7(12),8(8),11(9,R),8(8),11(10,R)]),flip(a)].
% 15.94/16.26 6593 meet(A,join(zero,meet(B,meet(C,complement(meet(B,A)))))) = zero. [para(4594(a,1),8(a,1)),rewrite([8(3),8(8)]),flip(a)].
% 15.94/16.26 7215 meet(complement(A),join(zero,meet(A,B))) = zero. [para(5(a,1),6593(a,1,2,2,2,2,1)),rewrite([48(4),20(4)])].
% 15.94/16.26 7320 meet(A,join(B,meet(C,meet(join(zero,meet(A,B)),join(zero,meet(A,join(B,C))))))) = meet(A,B). [para(21(a,1),190(a,2,2,2,2,2)),rewrite([8(9),11(9,R),8(8),8(16),11(17,R),8(16),7(18)])].
% 15.94/16.26 7607 meet(A,meet(meet(B,C),complement(meet(A,B)))) = zero. [para(7215(a,1),111(a,1,2)),rewrite([38(2),9(6),21(6),327(9)]),flip(a)].
% 15.94/16.26 7610 meet(complement(join(A,B)),join(A,join(zero,meet(B,C)))) = zero. [para(523(a,1),7215(a,1,2,2)),rewrite([13(6,R),9(5)])].
% 15.94/16.26 8638 meet(A,meet(meet(B,C),complement(meet(A,C)))) = zero. [para(8(a,1),7607(a,1,2,1))].
% 15.94/16.26 9256 meet(A,meet(B,complement(meet(A,join(B,C))))) = zero. [para(6(a,1),8638(a,1,2,1))].
% 15.94/16.26 9507 meet(meet(A,B),complement(meet(A,join(B,C)))) = zero. [para(9256(a,1),11(a,1)),rewrite([8(6)]),flip(a)].
% 15.94/16.26 9925 join(zero,meet(A,B)) = meet(A,B). [para(9507(a,1),7(a,1,2)),rewrite([9(3)])].
% 15.94/16.26 9944 meet(join(A,B),complement(join(A,join(B,C)))) = zero. [para(714(a,1),9507(a,1,1)),rewrite([9(4),13(4),9(3),13(4,R),9(3),714(5)])].
% 15.94/16.26 10208 meet(complement(join(A,B)),join(A,meet(B,C))) = zero. [back_rewrite(7610),rewrite([9925(5)])].
% 15.94/16.26 10320 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [back_rewrite(7320),rewrite([9925(3),9925(5),11(4,R),11(3),8(2),24(3),8(1),22(2),11(2),8(1),11(2,R),8(1)])].
% 15.94/16.26 10954 meet(complement(join(A,B)),join(B,meet(A,C))) = zero. [para(9(a,1),10208(a,1,1,1))].
% 15.94/16.26 11622 meet(A,complement(join(B,join(C,A)))) = zero. [para(9944(a,1),10954(a,1,2,2)),rewrite([9(2),13(2),9(1),13(2,R),9(1),21(5),8(4)])].
% 15.94/16.26 11718 meet(meet(A,B),complement(join(A,C))) = zero. [para(7(a,1),11622(a,1,2,1,2)),rewrite([9(2)])].
% 15.94/16.26 11747 meet(meet(A,B),complement(join(B,C))) = zero. [para(8(a,1),11718(a,1,1))].
% 15.94/16.26 12557 meet(A,join(join(A,B),meet(A,C))) = A. [para(6(a,1),10320(a,2)),rewrite([8(3),24(4)])].
% 15.94/16.26 12587 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(714(a,1),10320(a,2)),rewrite([8(5),11(6,R),8(5),714(5),714(6)])].
% 15.94/16.26 13267 meet(A,meet(B,join(join(C,meet(A,B)),meet(A,meet(B,join(C,join(D,meet(A,B)))))))) = meet(A,B). [para(12557(a,1),111(a,1,2)),rewrite([22(2),9(4),9(6),9(7),13(7,R),9(6),5509(12),22(12)]),flip(a)].
% 15.94/16.26 13885 join(join(A,B),meet(A,C)) = join(A,B). [para(551(a,1),12587(a,1,2))].
% 15.94/16.26 14527 meet(A,meet(B,join(join(C,meet(A,D)),meet(A,meet(D,join(C,join(E,meet(A,D)))))))) = meet(A,meet(B,join(C,meet(A,D)))). [para(13885(a,1),111(a,1,2,2)),rewrite([9(2),9(6),9(8),9(9),13(9,R),9(8)]),flip(a)].
% 15.94/16.26 14562 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [back_rewrite(13267),rewrite([14527(10)])].
% 15.94/16.26 15199 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(14562(a,1),32(a,2)),rewrite([2(2),8(2),66(7),4231(5)])].
% 15.94/16.26 15623 meet(a,join(b,meet(A,join(B,b)))) = a. [back_rewrite(918),rewrite([15199(11)])].
% 15.94/16.26 15803 meet(a,join(b,meet(A,B))) = a. [para(551(a,1),15623(a,1,2,2))].
% 15.94/16.26 15838 meet(a,join(b,complement(A))) = a. [para(103(a,1),15803(a,1,2,2))].
% 15.94/16.26 15976 meet(a,complement(join(A,join(b,complement(B))))) = zero. [para(15838(a,1),11747(a,1,1)),rewrite([9(5)])].
% 15.94/16.26 16076 meet(a,complement(join(b,complement(A)))) = zero. [para(2(a,1),15976(a,1,2,1))].
% 15.94/16.26 16087 meet(a,join(complement(a),complement(join(b,complement(A))))) = zero. [para(16076(a,1),64(a,2,2,2)),rewrite([9(11),15199(14),9(14),369(14),5(13)])].
% 15.94/16.26 18063 meet(a,join(complement(a),complement(b))) = zero. [para(41(a,1),16087(a,1,2,2,1,2)),rewrite([9(6),2955(6)])].
% 15.94/16.26 18100 join(a,join(complement(a),complement(b))) != one # answer(prove_distributivity). [ur(18,a,18063,a,c,17,a(flip))].
% 15.94/16.26 18160 $F # answer(prove_distributivity). [para(13(a,1),18100(a,1)),rewrite([4(6),9(4),104(4)]),xx(a)].
% 15.94/16.26
% 15.94/16.26 % SZS output end Refutation
% 15.94/16.26 ============================== end of proof ==========================
% 15.94/16.26
% 15.94/16.26 ============================== STATISTICS ============================
% 15.94/16.26
% 15.94/16.26 Given=671. Generated=176218. Kept=18155. proofs=1.
% 15.94/16.26 Usable=413. Sos=8448. Demods=8106. Limbo=0, Disabled=9308. Hints=0.
% 15.94/16.26 Megabytes=36.91.
% 15.94/16.26 User_CPU=15.17, System_CPU=0.13, Wall_clock=16.
% 15.94/16.26
% 15.94/16.26 ============================== end of statistics =====================
% 15.94/16.26
% 15.94/16.26 ============================== end of search =========================
% 15.94/16.26
% 15.94/16.26 THEOREM PROVED
% 15.94/16.26 % SZS status Unsatisfiable
% 15.94/16.26
% 15.94/16.26 Exiting with 1 proof.
% 15.94/16.26
% 15.94/16.26 Process 3834 exit (max_proofs) Wed Jun 29 07:19:24 2022
% 15.94/16.26 Prover9 interrupted
%------------------------------------------------------------------------------