TSTP Solution File: LAT257-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT257-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 06:26:25 EDT 2022
% Result : Unsatisfiable 17.80s 18.10s
% Output : Refutation 17.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT257-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 29 18:44:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 15.17/15.50 ============================== Prover9 ===============================
% 15.17/15.50 Prover9 (32) version 2009-11A, November 2009.
% 15.17/15.50 Process 29303 was started by sandbox on n023.cluster.edu,
% 15.17/15.50 Wed Jun 29 18:45:00 2022
% 15.17/15.50 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29150_n023.cluster.edu".
% 15.17/15.50 ============================== end of head ===========================
% 15.17/15.50
% 15.17/15.50 ============================== INPUT =================================
% 15.17/15.50
% 15.17/15.50 % Reading from file /tmp/Prover9_29150_n023.cluster.edu
% 15.17/15.50
% 15.17/15.50 set(prolog_style_variables).
% 15.17/15.50 set(auto2).
% 15.17/15.50 % set(auto2) -> set(auto).
% 15.17/15.50 % set(auto) -> set(auto_inference).
% 15.17/15.50 % set(auto) -> set(auto_setup).
% 15.17/15.50 % set(auto_setup) -> set(predicate_elim).
% 15.17/15.50 % set(auto_setup) -> assign(eq_defs, unfold).
% 15.17/15.50 % set(auto) -> set(auto_limits).
% 15.17/15.50 % set(auto_limits) -> assign(max_weight, "100.000").
% 15.17/15.50 % set(auto_limits) -> assign(sos_limit, 20000).
% 15.17/15.50 % set(auto) -> set(auto_denials).
% 15.17/15.50 % set(auto) -> set(auto_process).
% 15.17/15.50 % set(auto2) -> assign(new_constants, 1).
% 15.17/15.50 % set(auto2) -> assign(fold_denial_max, 3).
% 15.17/15.50 % set(auto2) -> assign(max_weight, "200.000").
% 15.17/15.50 % set(auto2) -> assign(max_hours, 1).
% 15.17/15.50 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 15.17/15.50 % set(auto2) -> assign(max_seconds, 0).
% 15.17/15.50 % set(auto2) -> assign(max_minutes, 5).
% 15.17/15.50 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 15.17/15.50 % set(auto2) -> set(sort_initial_sos).
% 15.17/15.50 % set(auto2) -> assign(sos_limit, -1).
% 15.17/15.50 % set(auto2) -> assign(lrs_ticks, 3000).
% 15.17/15.50 % set(auto2) -> assign(max_megs, 400).
% 15.17/15.50 % set(auto2) -> assign(stats, some).
% 15.17/15.50 % set(auto2) -> clear(echo_input).
% 15.17/15.50 % set(auto2) -> set(quiet).
% 15.17/15.50 % set(auto2) -> clear(print_initial_clauses).
% 15.17/15.50 % set(auto2) -> clear(print_given).
% 15.17/15.50 assign(lrs_ticks,-1).
% 15.17/15.50 assign(sos_limit,10000).
% 15.17/15.50 assign(order,kbo).
% 15.17/15.50 set(lex_order_vars).
% 15.17/15.50 clear(print_given).
% 15.17/15.50
% 15.17/15.50 % formulas(sos). % not echoed (14 formulas)
% 15.17/15.50
% 15.17/15.50 ============================== end of input ==========================
% 15.17/15.50
% 15.17/15.50 % From the command line: assign(max_seconds, 300).
% 15.17/15.50
% 15.17/15.50 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 15.17/15.50
% 15.17/15.50 % Formulas that are not ordinary clauses:
% 15.17/15.50
% 15.17/15.50 ============================== end of process non-clausal formulas ===
% 15.17/15.50
% 15.17/15.50 ============================== PROCESS INITIAL CLAUSES ===============
% 15.17/15.50
% 15.17/15.50 ============================== PREDICATE ELIMINATION =================
% 15.17/15.50
% 15.17/15.50 ============================== end predicate elimination =============
% 15.17/15.50
% 15.17/15.50 Auto_denials:
% 15.17/15.50 % copying label prove_distributivity to answer in negative clause
% 15.17/15.50
% 15.17/15.50 Term ordering decisions:
% 15.17/15.50
% 15.17/15.50 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 15.17/15.50 Function symbol KB weights: a=1. one=1. zero=1. b=1. meet=1. join=1. complement=0.
% 15.17/15.50
% 15.17/15.50 ============================== end of process initial clauses ========
% 15.17/15.50
% 15.17/15.50 ============================== CLAUSES FOR SEARCH ====================
% 15.17/15.50
% 15.17/15.50 ============================== end of clauses for search =============
% 15.17/15.50
% 15.17/15.50 ============================== SEARCH ================================
% 15.17/15.50
% 15.17/15.50 % Starting search at 0.01 seconds.
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=143.000, iters=3406
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=125.000, iters=3390
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=105.000, iters=3355
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=101.000, iters=3345
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=75.000, iters=3386
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=71.000, iters=3356
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=69.000, iters=3465
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=67.000, iters=3421
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=64.000, iters=3361
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=62.000, iters=3385
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=61.000, iters=3348
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=58.000, iters=3462
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=57.000, iters=3501
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=53.000, iters=3353
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=51.000, iters=3390
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=49.000, iters=3351
% 15.17/15.50
% 15.17/15.50 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 5.05 sec).
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=48.000, iters=3420
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=47.000, iters=3400
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=46.000, iters=3390
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=45.000, iters=3357
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=41.000, iters=5375
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=33.000, iters=3758
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=32.000, iters=3497
% 15.17/15.50
% 15.17/15.50 Low Water (keep): wt=30.000, iters=3438
% 15.17/15.50
% 17.80/18.10 Low Water (keep): wt=29.000, iters=3336
% 17.80/18.10
% 17.80/18.10 Low Water (keep): wt=28.000, iters=3333
% 17.80/18.10
% 17.80/18.10 ============================== PROOF =================================
% 17.80/18.10 % SZS status Unsatisfiable
% 17.80/18.10 % SZS output start Refutation
% 17.80/18.10
% 17.80/18.10 % Proof 1 at 16.94 (+ 0.17) seconds: prove_distributivity.
% 17.80/18.10 % Length of proof is 125.
% 17.80/18.10 % Level of proof is 29.
% 17.80/18.10 % Maximum clause weight is 65.000.
% 17.80/18.10 % Given clauses 924.
% 17.80/18.10
% 17.80/18.10 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 17.80/18.10 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 17.80/18.10 3 meet(b,a) = a # label(prove_distributivity_hypothesis) # label(hypothesis). [assumption].
% 17.80/18.10 4 join(A,complement(A)) = one # label(complement_join) # label(axiom). [assumption].
% 17.80/18.10 5 meet(A,complement(A)) = zero # label(complement_meet) # label(axiom). [assumption].
% 17.80/18.10 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 17.80/18.10 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 17.80/18.10 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 17.80/18.10 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 17.80/18.10 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 17.80/18.10 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 17.80/18.10 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 17.80/18.10 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 17.80/18.10 14 meet(A,join(meet(B,join(A,C)),meet(C,join(A,B)))) = join(meet(A,B),meet(A,C)) # label(equation_H82) # label(axiom). [assumption].
% 17.80/18.10 15 join(complement(b),complement(a)) != complement(a) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 17.80/18.10 16 join(complement(a),complement(b)) != complement(a) # answer(prove_distributivity). [copy(15),rewrite([9(5)])].
% 17.80/18.10 17 meet(A,B) != zero | join(A,B) != one | complement(A) = B # label(meet_join_complement) # label(axiom). [assumption].
% 17.80/18.10 18 meet(a,b) = a. [back_rewrite(3),rewrite([8(3)])].
% 17.80/18.10 19 meet(A,one) = A. [para(4(a,1),6(a,1,2))].
% 17.80/18.10 20 join(A,zero) = A. [para(5(a,1),7(a,1,2))].
% 17.80/18.10 21 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)])].
% 17.80/18.10 22 meet(A,meet(B,complement(A))) = meet(B,zero). [para(5(a,1),11(a,2,2)),rewrite([8(2)])].
% 17.80/18.10 23 meet(A,meet(B,join(A,C))) = meet(A,B). [para(6(a,1),11(a,2,2)),rewrite([8(2),8(4)])].
% 17.80/18.10 24 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)])].
% 17.80/18.10 25 join(A,join(B,complement(A))) = join(B,one). [para(4(a,1),13(a,2,2)),rewrite([9(2)])].
% 17.80/18.10 26 join(A,join(B,meet(A,C))) = join(A,B). [para(7(a,1),13(a,2,2)),rewrite([9(2),9(4)])].
% 17.80/18.10 27 meet(A,join(join(A,B),meet(B,join(A,B)))) = A. [para(1(a,1),14(a,1,2,1)),rewrite([24(3),6(7),7(7)])].
% 17.80/18.10 28 meet(A,join(B,meet(complement(A),join(A,B)))) = join(zero,meet(A,B)). [para(4(a,1),14(a,1,2,1,2)),rewrite([19(2),5(8),9(8)])].
% 17.80/18.10 29 meet(A,join(meet(B,join(A,C)),meet(join(A,C),join(A,B)))) = A. [para(6(a,1),14(a,2,1)),rewrite([24(5),9(6),7(9)])].
% 17.80/18.10 30 meet(A,join(meet(A,B),meet(meet(A,C),join(A,B)))) = join(meet(A,B),meet(A,C)). [para(7(a,1),14(a,1,2,1,2)),rewrite([8(1),21(9)])].
% 17.80/18.10 31 meet(A,join(meet(B,join(A,C)),meet(C,join(B,A)))) = join(meet(B,A),meet(A,C)). [para(14(a,1),8(a,2)),rewrite([9(3),8(6),8(7)])].
% 17.80/18.10 32 meet(A,meet(B,join(meet(C,join(A,D)),meet(D,join(A,C))))) = meet(B,join(meet(A,C),meet(A,D))). [para(14(a,1),11(a,2,2)),rewrite([8(6)])].
% 17.80/18.10 33 meet(meet(A,join(B,C)),join(join(meet(A,B),meet(B,C)),meet(meet(C,join(A,B)),join(B,meet(A,join(B,C)))))) = join(meet(A,B),meet(A,meet(C,join(B,C)))). [para(14(a,1),14(a,1,2,1)),rewrite([8(3),9(6),9(10),8(16),23(16),8(14),9(17),11(19),8(18),11(18,R),8(17),11(19,R),23(19)])].
% 17.80/18.10 37 meet(A,zero) != zero | one != A | complement(A) = zero. [para(20(a,1),17(b,1)),flip(b)].
% 17.80/18.10 38 meet(A,zero) = zero. [para(5(a,1),21(a,1,2)),rewrite([5(4)])].
% 17.80/18.10 40 one != A | complement(A) = zero. [back_rewrite(37),rewrite([38(2)]),xx(a)].
% 17.80/18.10 42 meet(A,meet(B,complement(A))) = zero. [back_rewrite(22),rewrite([38(5)])].
% 17.80/18.10 45 meet(meet(A,join(B,C)),join(meet(A,B),meet(B,C))) = meet(A,B). [para(14(a,1),23(a,1,2)),rewrite([8(3),8(9),23(9),8(7)])].
% 17.80/18.10 47 complement(join(A,one)) = zero. [hyper(40,a,7,a(flip)),rewrite([8(3),19(3),9(2)])].
% 17.80/18.10 49 join(A,one) = one. [para(47(a,1),4(a,1,2)),rewrite([9(4),13(4),9(3),20(3),9(2)])].
% 17.80/18.10 50 join(A,join(B,complement(A))) = one. [back_rewrite(25),rewrite([49(5)])].
% 17.80/18.10 52 meet(A,join(B,meet(one,join(A,B)))) = A. [para(49(a,1),14(a,1,2,1,2)),rewrite([19(2),19(8),9(7),7(7)])].
% 17.80/18.10 58 meet(A,join(B,complement(A))) != zero | join(B,complement(A)) = complement(A). [para(50(a,1),17(b,1)),flip(c),xx(b)].
% 17.80/18.10 70 meet(A,join(one,complement(A))) = A. [para(4(a,1),27(a,1,2,1)),rewrite([4(4),19(4)])].
% 17.80/18.10 74 join(A,meet(one,complement(A))) = one. [para(70(a,1),14(a,1,2,1)),rewrite([9(4),49(4),19(4),4(3),1(3),8(3),19(3)]),flip(a)].
% 17.80/18.10 75 meet(one,complement(A)) = complement(A). [hyper(17,a,42,a,b,74,a),flip(a)].
% 17.80/18.10 79 meet(A,join(zero,meet(A,B))) = join(zero,meet(A,B)). [para(7(a,1),28(a,1,2,2,2)),rewrite([8(3),5(3),9(3),21(7)])].
% 17.80/18.10 85 join(zero,meet(A,B)) = meet(A,B). [para(28(a,1),23(a,1,2)),rewrite([8(2),79(4)])].
% 17.80/18.10 93 meet(A,join(B,meet(complement(A),join(A,B)))) = meet(A,B). [back_rewrite(28),rewrite([85(8)])].
% 17.80/18.10 95 meet(A,join(B,meet(one,join(B,A)))) = A. [para(52(a,1),8(a,2)),rewrite([9(2),8(5)])].
% 17.80/18.10 113 meet(join(A,B),join(C,meet(one,join(A,join(B,C))))) = join(A,B). [para(13(a,1),95(a,1,2,2,2)),rewrite([9(3),13(4,R),9(3)])].
% 17.80/18.10 146 meet(meet(A,B),join(meet(C,join(D,meet(A,B))),meet(D,join(C,meet(A,B))))) = join(meet(A,meet(B,C)),meet(A,meet(B,D))). [para(11(a,1),31(a,2,1)),rewrite([9(3),8(10),11(11,R),8(10),8(13),11(13),8(12),11(13,R),8(12)])].
% 17.80/18.10 149 meet(join(meet(A,join(B,C)),meet(C,join(A,B))),join(meet(B,join(D,join(meet(A,join(B,C)),meet(C,join(A,B))))),meet(D,join(B,join(meet(A,join(B,C)),meet(C,join(A,B))))))) = join(join(meet(A,B),meet(B,C)),meet(D,join(meet(A,join(B,C)),meet(C,join(A,B))))). [para(14(a,1),31(a,2,1)),rewrite([9(3),9(8),9(11),9(15),8(22),9(27),8(30)])].
% 17.80/18.10 151 meet(one,join(A,B)) = join(A,B). [para(19(a,1),31(a,2,1)),rewrite([9(3),49(3),19(3),49(3),19(3),8(5),19(5)])].
% 17.80/18.10 160 meet(join(A,B),join(meet(C,join(A,B)),meet(B,join(A,join(B,C))))) = join(B,meet(C,join(A,B))). [para(52(a,1),31(a,2,1)),rewrite([9(2),151(3),24(2),9(3),151(4),24(3),9(3),13(3),9(2),13(3,R),9(2),9(6),151(7),24(6),13(6,R),2(5),9(7),9(10),151(11),24(10),8(10)])].
% 17.80/18.10 161 meet(meet(join(A,B),join(A,C)),join(A,meet(meet(C,join(A,B)),join(A,meet(join(A,B),join(A,C)))))) = join(A,meet(C,meet(join(A,B),join(A,C)))). [para(29(a,1),31(a,1,2,2)),rewrite([9(9),9(11),11(18),8(17),11(17,R),1(16),11(16,R),8(20),23(20),6(18),9(17)])].
% 17.80/18.10 164 join(A,meet(B,join(A,B))) = join(A,B). [para(95(a,1),31(a,1,2,2)),rewrite([151(3),151(4),9(3),13(3,R),2(2),6(3),1(3),151(4),6(3),151(4),8(3)]),flip(a)].
% 17.80/18.10 173 meet(join(A,B),join(A,join(B,C))) = join(A,B). [back_rewrite(113),rewrite([151(5),13(4,R),9(3),13(3,R),2(2)])].
% 17.80/18.10 176 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(151(a,1),31(a,2,1)),rewrite([9(4),13(4),9(3),13(4,R),9(3),151(5),13(6),9(5),49(5),49(5),19(5),9(4),13(4,R),9(3),13(3,R),2(2),173(4),8(4)]),flip(a)].
% 17.80/18.10 192 meet(meet(A,join(B,C)),join(meet(B,A),meet(B,C))) = meet(B,A). [para(6(a,1),32(a,1,2)),rewrite([23(3)]),flip(a)].
% 17.80/18.10 193 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(32(a,1),7(a,1,2))].
% 17.80/18.10 194 meet(A,meet(B,meet(C,join(meet(D,join(A,E)),meet(E,join(A,D)))))) = meet(B,meet(C,join(meet(A,D),meet(A,E)))). [para(32(a,1),11(a,2,2)),rewrite([8(7),11(7,R),8(6),11(13,R),8(12)])].
% 17.80/18.10 196 meet(A,meet(B,join(meet(A,C),meet(A,D)))) = meet(B,join(meet(A,C),meet(A,D))). [para(32(a,1),21(a,1,2)),rewrite([32(12)])].
% 17.80/18.10 208 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(85(a,1),173(a,1,1)),rewrite([9(4),13(5,R),9(4),85(4),85(7)])].
% 17.80/18.10 215 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(85(a,1),176(a,1,1)),rewrite([85(4),11(3),8(2),11(3,R),8(2),85(7)])].
% 17.80/18.10 218 join(meet(A,B),meet(meet(A,C),join(A,B))) = join(meet(A,C),meet(A,B)). [para(30(a,1),176(a,1,2)),rewrite([9(9),13(9),9(8),24(8),13(7),9(6),26(7)]),flip(a)].
% 17.80/18.10 225 complement(join(one,meet(A,join(B,C)))) = zero. [hyper(40,a,193,a(flip)),rewrite([8(3),19(3),8(3),19(3)])].
% 17.80/18.10 324 complement(join(one,meet(A,B))) = zero. [para(2(a,1),225(a,1,1,2,2))].
% 17.80/18.10 328 join(one,meet(A,B)) = one. [para(324(a,1),4(a,1,2)),rewrite([9(5),13(5,R),9(4),85(4)])].
% 17.80/18.10 329 join(one,join(meet(A,B),meet(A,C))) = one. [para(14(a,1),328(a,1,2))].
% 17.80/18.10 331 join(one,join(meet(A,meet(B,C)),meet(B,D))) = one. [para(11(a,1),329(a,1,2,1))].
% 17.80/18.10 332 join(one,join(meet(A,meet(B,C)),meet(C,D))) = one. [para(11(a,2),329(a,1,2,1))].
% 17.80/18.10 361 meet(meet(A,join(B,C)),join(meet(B,C),meet(B,A))) = meet(B,A). [para(208(a,1),32(a,1,2)),rewrite([23(3)]),flip(a)].
% 17.80/18.10 404 join(one,join(meet(A,B),complement(C))) = one. [para(75(a,1),331(a,1,2,2)),rewrite([8(3),19(3)])].
% 17.80/18.10 420 join(one,join(join(A,B),complement(C))) = one. [para(151(a,1),404(a,1,2,1))].
% 17.80/18.10 434 join(one,join(meet(A,B),meet(C,join(B,D)))) = one. [para(6(a,1),332(a,1,2,1,2)),rewrite([8(4)])].
% 17.80/18.10 437 join(one,join(meet(A,a),meet(B,b))) = one. [para(18(a,1),332(a,1,2,1,2)),rewrite([8(5)])].
% 17.80/18.10 456 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(45(a,1),7(a,1,2)),rewrite([9(4)])].
% 17.80/18.10 466 meet(meet(a,join(A,b)),join(a,meet(A,b))) = a. [para(18(a,1),45(a,1,2,1)),rewrite([9(3),8(7),18(12)])].
% 17.80/18.10 505 join(meet(A,meet(B,C)),meet(A,meet(B,join(C,D)))) = meet(A,meet(B,join(C,D))). [para(45(a,1),215(a,1,2,2)),rewrite([9(6)])].
% 17.80/18.10 521 join(one,join(b,meet(A,a))) = one. [para(1(a,1),437(a,1,2,2)),rewrite([9(5)])].
% 17.80/18.10 525 join(one,b) = one. [para(7(a,1),521(a,1,2))].
% 17.80/18.10 528 join(meet(one,b),meet(A,b)) = meet(b,join(A,b)). [para(525(a,1),31(a,1,2,2,2)),rewrite([9(4),151(5),19(5),9(4),24(4),8(9)]),flip(a)].
% 17.80/18.10 529 join(A,meet(one,b)) = join(A,b). [para(525(a,1),33(a,1,2,2,1,2)),rewrite([9(3),151(4),8(7),528(8),19(8),9(10),151(11),13(10,R),2(9),6(9),9(7),164(7),1(5),9(8),6(9),8(7),19(7),9(6)]),flip(a)].
% 17.80/18.10 530 meet(one,b) = b. [para(529(a,1),2(a,1)),rewrite([9(5),529(5),2(3)]),flip(a)].
% 17.80/18.10 534 meet(b,join(A,b)) = b. [para(529(a,1),208(a,1,2)),rewrite([530(3),530(7)])].
% 17.80/18.10 537 join(b,meet(A,b)) = b. [back_rewrite(528),rewrite([530(3),534(8)])].
% 17.80/18.10 585 join(a,b) = b. [para(18(a,1),537(a,1,2)),rewrite([9(3)])].
% 17.80/18.10 848 join(one,join(meet(A,B),meet(C,D))) = one. [para(208(a,1),434(a,1,2,2))].
% 17.80/18.10 863 join(one,join(join(A,B),meet(C,D))) = one. [para(151(a,1),848(a,1,2,1))].
% 17.80/18.10 909 meet(a,join(A,b)) = a. [para(466(a,1),7(a,1,2)),rewrite([9(6),7(6)]),flip(a)].
% 17.80/18.10 924 join(meet(A,a),meet(A,b)) = meet(A,b). [para(909(a,1),33(a,1,2,2,1)),rewrite([9(3),585(3),8(7),18(7),9(6),9(11),585(11),537(11),18(9),9(8),24(8),208(7),9(8),585(8),18(7),9(7)]),flip(a)].
% 17.80/18.10 993 meet(meet(A,a),join(meet(A,meet(B,b)),meet(meet(A,b),join(B,meet(A,a))))) = join(meet(A,a),meet(A,meet(B,a))). [para(924(a,1),14(a,1,2,1,2)),rewrite([11(5,R),8(4),9(10),8(16),11(16,R),8(15),11(21),8(20),21(20),11(20),8(19),11(20,R),8(19),18(19),9(19)])].
% 17.80/18.10 996 join(meet(A,a),meet(A,meet(B,a))) = meet(A,a). [para(924(a,1),29(a,1,2,1,2)),rewrite([11(5,R),8(4),924(10),9(10),993(13)])].
% 17.80/18.10 1002 meet(meet(meet(A,a),join(B,meet(A,b))),join(join(meet(A,a),meet(A,meet(B,b))),meet(meet(A,meet(B,b)),join(meet(A,b),meet(meet(A,a),join(B,meet(A,b))))))) = meet(A,a). [para(924(a,1),33(a,1,2,2,1,2)),rewrite([9(5),11(11),8(10),21(10),11(10),8(9),11(10,R),8(9),18(9),8(11),11(11,R),8(10),11(15,R),8(14),9(22),11(32),8(31),21(31),11(31),8(30),11(31,R),8(30),18(30),9(34),6(35),8(32),11(32,R),8(31),996(33)])].
% 17.80/18.10 1224 meet(A,join(B,meet(complement(A),join(B,A)))) = meet(B,A). [para(93(a,1),8(a,2)),rewrite([9(2),8(5),8(6)])].
% 17.80/18.10 1641 meet(complement(A),join(A,complement(complement(A)))) = zero. [para(4(a,1),1224(a,1,2,2,2)),rewrite([19(5),5(7)])].
% 17.80/18.10 1659 join(A,complement(complement(A))) = complement(complement(A)). [hyper(58,a,1641,a)].
% 17.80/18.10 1660 meet(complement(A),meet(complement(complement(A)),join(B,complement(A)))) = zero. [para(1641(a,1),23(a,2)),rewrite([1659(4),9(5)])].
% 17.80/18.10 4888 join(meet(A,B),meet(C,meet(A,B))) = meet(A,B). [para(146(a,1),149(a,2,2)),rewrite([2(3),208(6),9(4),2(9),208(12),9(10),24(11),6(10),2(10),208(13),9(11),24(12),6(11),2(7),8(6),6(6),1(6),9(5),8(6),11(7,R),8(6),11(9,R),1(8),21(9),9(9),2(10)]),flip(a)].
% 17.80/18.10 5876 meet(A,join(B,A)) = A. [para(2(a,1),160(a,1,2,2,2,2)),rewrite([2(6),11(4,R),1(3),7(5)])].
% 17.80/18.10 5893 join(join(A,B),complement(C)) = join(A,join(B,complement(C))). [para(420(a,1),160(a,1,2,2,2)),rewrite([13(3),9(2),49(2),49(2),13(5),9(4),49(4),49(4),19(4),8(5),151(5),13(4),9(3),13(4,R),9(3),151(5),13(8),9(7),49(7),49(7),19(7)]),flip(a)].
% 17.80/18.10 5909 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(863(a,1),160(a,1,2,2,2)),rewrite([13(3),9(2),49(2),49(2),13(5),9(4),49(4),49(4),8(4),11(4),8(3),19(3),8(2),8(5),151(5),13(4),9(3),13(4,R),9(3),151(5),13(8),9(7),49(7),49(7),8(7),11(7),8(6),19(6),8(5)]),flip(a)].
% 17.80/18.10 7206 meet(meet(meet(A,a),join(B,meet(A,b))),join(meet(A,a),meet(A,meet(B,b)))) = meet(A,a). [back_rewrite(1002),rewrite([5909(26),7(25)])].
% 17.80/18.10 7519 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(161(a,1),7(a,1,2)),rewrite([13(9,R),9(8),4888(8)])].
% 17.80/18.10 7755 join(A,join(B,complement(join(A,B)))) = one. [para(5893(a,1),4(a,1))].
% 17.80/18.10 7756 join(A,join(meet(A,B),complement(C))) = join(A,complement(C)). [para(7(a,1),5893(a,1,1)),flip(a)].
% 17.80/18.10 7776 join(a,join(b,complement(A))) = join(b,complement(A)). [para(585(a,1),5893(a,1,1)),flip(a)].
% 17.80/18.10 7869 join(A,join(B,join(C,complement(join(A,B))))) = one. [para(7755(a,1),13(a,2,2)),rewrite([9(4),13(4,R),9(3),49(7)])].
% 17.80/18.10 8165 join(b,complement(a)) = one. [para(7776(a,1),50(a,1))].
% 17.80/18.10 8201 meet(b,join(complement(a),complement(b))) = meet(b,complement(a)). [para(8165(a,1),93(a,1,2,2,2)),rewrite([8(7),75(7)])].
% 17.80/18.10 8462 join(A,join(B,join(C,complement(join(A,C))))) = one. [para(7869(a,1),9(a,1)),rewrite([9(2),9(6),13(6,R),9(5),13(5,R),9(4)]),flip(a)].
% 17.80/18.10 9010 meet(meet(meet(A,B),join(A,C)),join(meet(A,B),meet(A,C))) = meet(A,B). [para(21(a,1),192(a,1,2,1)),rewrite([21(9)])].
% 17.80/18.10 11681 join(A,join(B,complement(join(A,meet(B,C))))) = one. [para(7756(a,1),8462(a,1,2))].
% 17.80/18.10 11793 meet(meet(A,B),join(A,C)) = meet(A,B). [para(218(a,1),5876(a,1,2)),rewrite([9010(7)]),flip(a)].
% 17.80/18.10 11889 meet(meet(A,a),join(B,meet(A,b))) = meet(A,a). [back_rewrite(7206),rewrite([11793(13)])].
% 17.80/18.10 12917 join(A,join(complement(A),complement(B))) = one. [para(1660(a,1),11681(a,1,2,2,1,2)),rewrite([20(3),9(3)])].
% 17.80/18.10 12943 meet(a,join(complement(a),complement(b))) != zero # answer(prove_distributivity). [ur(17,b,12917,a,c,16,a(flip))].
% 17.80/18.10 16707 meet(A,meet(join(B,C),join(B,A))) = meet(A,join(B,C)). [para(456(a,1),361(a,1,2)),rewrite([9(2),8(6),11(6),8(5),11(5,R),1(4),11(4,R)])].
% 17.80/18.10 19106 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(505(a,1),146(a,2)),rewrite([5909(4),6(5),7519(6),16707(6)])].
% 17.80/18.10 19527 meet(A,meet(a,join(B,meet(A,b)))) = meet(A,a). [back_rewrite(11889),rewrite([19106(6)])].
% 17.80/18.10 21356 meet(a,join(meet(A,B),meet(A,b))) = meet(A,a). [para(19527(a,1),194(a,2)),rewrite([32(10),196(7)])].
% 17.80/18.10 21746 meet(a,join(meet(A,B),meet(B,b))) = meet(B,a). [para(8(a,1),21356(a,1,2,1))].
% 17.80/18.10 22148 meet(a,join(complement(a),complement(b))) = zero. [para(8201(a,1),21746(a,1,2,1)),rewrite([8(12),8201(12),2(10),42(6),8(8)]),flip(a)].
% 17.80/18.10 22149 $F # answer(prove_distributivity). [resolve(22148,a,12943,a)].
% 17.80/18.10
% 17.80/18.10 % SZS output end Refutation
% 17.80/18.10 ============================== end of proof ==========================
% 17.80/18.10
% 17.80/18.10 ============================== STATISTICS ============================
% 17.80/18.10
% 17.80/18.10 Given=924. Generated=324355. Kept=22145. proofs=1.
% 17.80/18.10 Usable=572. Sos=8955. Demods=8718. Limbo=21, Disabled=12610. Hints=0.
% 17.80/18.10 Megabytes=31.98.
% 17.80/18.10 User_CPU=16.94, System_CPU=0.17, Wall_clock=17.
% 17.80/18.10
% 17.80/18.10 ============================== end of statistics =====================
% 17.80/18.10
% 17.80/18.10 ============================== end of search =========================
% 17.80/18.10
% 17.80/18.10 THEOREM PROVED
% 17.80/18.10 % SZS status Unsatisfiable
% 17.80/18.10
% 17.80/18.10 Exiting with 1 proof.
% 17.80/18.10
% 17.80/18.10 Process 29303 exit (max_proofs) Wed Jun 29 18:45:17 2022
% 17.80/18.10 Prover9 interrupted
%------------------------------------------------------------------------------