TSTP Solution File: LAT001-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 06:25:00 EDT 2022
% Result : Unsatisfiable 46.00s 46.31s
% Output : Refutation 46.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LAT001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 29 19:40:57 EDT 2022
% 0.14/0.35 % CPUTime :
% 10.70/10.97 ============================== Prover9 ===============================
% 10.70/10.97 Prover9 (32) version 2009-11A, November 2009.
% 10.70/10.97 Process 10440 was started by sandbox on n021.cluster.edu,
% 10.70/10.97 Wed Jun 29 19:40:58 2022
% 10.70/10.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10287_n021.cluster.edu".
% 10.70/10.97 ============================== end of head ===========================
% 10.70/10.97
% 10.70/10.97 ============================== INPUT =================================
% 10.70/10.97
% 10.70/10.97 % Reading from file /tmp/Prover9_10287_n021.cluster.edu
% 10.70/10.97
% 10.70/10.97 set(prolog_style_variables).
% 10.70/10.97 set(auto2).
% 10.70/10.97 % set(auto2) -> set(auto).
% 10.70/10.97 % set(auto) -> set(auto_inference).
% 10.70/10.97 % set(auto) -> set(auto_setup).
% 10.70/10.97 % set(auto_setup) -> set(predicate_elim).
% 10.70/10.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 10.70/10.97 % set(auto) -> set(auto_limits).
% 10.70/10.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 10.70/10.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 10.70/10.97 % set(auto) -> set(auto_denials).
% 10.70/10.97 % set(auto) -> set(auto_process).
% 10.70/10.97 % set(auto2) -> assign(new_constants, 1).
% 10.70/10.97 % set(auto2) -> assign(fold_denial_max, 3).
% 10.70/10.97 % set(auto2) -> assign(max_weight, "200.000").
% 10.70/10.97 % set(auto2) -> assign(max_hours, 1).
% 10.70/10.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 10.70/10.97 % set(auto2) -> assign(max_seconds, 0).
% 10.70/10.97 % set(auto2) -> assign(max_minutes, 5).
% 10.70/10.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 10.70/10.97 % set(auto2) -> set(sort_initial_sos).
% 10.70/10.97 % set(auto2) -> assign(sos_limit, -1).
% 10.70/10.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 10.70/10.97 % set(auto2) -> assign(max_megs, 400).
% 10.70/10.97 % set(auto2) -> assign(stats, some).
% 10.70/10.97 % set(auto2) -> clear(echo_input).
% 10.70/10.97 % set(auto2) -> set(quiet).
% 10.70/10.97 % set(auto2) -> clear(print_initial_clauses).
% 10.70/10.97 % set(auto2) -> clear(print_given).
% 10.70/10.97 assign(lrs_ticks,-1).
% 10.70/10.97 assign(sos_limit,10000).
% 10.70/10.97 assign(order,kbo).
% 10.70/10.97 set(lex_order_vars).
% 10.70/10.97 clear(print_given).
% 10.70/10.97
% 10.70/10.97 % formulas(sos). % not echoed (19 formulas)
% 10.70/10.97
% 10.70/10.97 ============================== end of input ==========================
% 10.70/10.97
% 10.70/10.97 % From the command line: assign(max_seconds, 300).
% 10.70/10.97
% 10.70/10.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 10.70/10.97
% 10.70/10.97 % Formulas that are not ordinary clauses:
% 10.70/10.97
% 10.70/10.97 ============================== end of process non-clausal formulas ===
% 10.70/10.97
% 10.70/10.97 ============================== PROCESS INITIAL CLAUSES ===============
% 10.70/10.97
% 10.70/10.97 ============================== PREDICATE ELIMINATION =================
% 10.70/10.97
% 10.70/10.97 ============================== end predicate elimination =============
% 10.70/10.97
% 10.70/10.97 Auto_denials:
% 10.70/10.97 % copying label prove_complememt to answer in negative clause
% 10.70/10.97
% 10.70/10.97 Term ordering decisions:
% 10.70/10.97 Function symbol KB weights: n0=1. n1=1. a=1. b=1. r1=1. r2=1. meet=1. join=1.
% 10.70/10.97
% 10.70/10.97 ============================== end of process initial clauses ========
% 10.70/10.97
% 10.70/10.97 ============================== CLAUSES FOR SEARCH ====================
% 10.70/10.97
% 10.70/10.97 ============================== end of clauses for search =============
% 10.70/10.97
% 10.70/10.97 ============================== SEARCH ================================
% 10.70/10.97
% 10.70/10.97 % Starting search at 0.01 seconds.
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=66.000, iters=3380
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=64.000, iters=3373
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=62.000, iters=3341
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=60.000, iters=3337
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=58.000, iters=3366
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=56.000, iters=3336
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=54.000, iters=3333
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=52.000, iters=3382
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=50.000, iters=3335
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=49.000, iters=3354
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=48.000, iters=3419
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=47.000, iters=3355
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=46.000, iters=3390
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=44.000, iters=3346
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=43.000, iters=3500
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=42.000, iters=3482
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=40.000, iters=3371
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=39.000, iters=3421
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=38.000, iters=3391
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=37.000, iters=3343
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=36.000, iters=3338
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=35.000, iters=3346
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=34.000, iters=3358
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=33.000, iters=3342
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=32.000, iters=3342
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=31.000, iters=3347
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=30.000, iters=3348
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=29.000, iters=3428
% 10.70/10.97
% 10.70/10.97 Low Water (keep): wt=28.000, iters=3443
% 46.00/46.31
% 46.00/46.31 Low Water (keep): wt=27.000, iters=3364
% 46.00/46.31
% 46.00/46.31 Low Water (keep): wt=26.000, iters=3358
% 46.00/46.31
% 46.00/46.31 Low Water (keep): wt=25.000, iters=3397
% 46.00/46.31
% 46.00/46.31 Low Water (displace): id=7447, wt=64.000
% 46.00/46.31
% 46.00/46.31 Low Water (displace): id=18398, wt=21.000
% 46.00/46.31
% 46.00/46.31 Low Water (displace): id=18690, wt=19.000
% 46.00/46.31
% 46.00/46.31 Low Water (displace): id=18807, wt=17.000
% 46.00/46.31
% 46.00/46.31 Low Water (displace): id=18904, wt=15.000
% 46.00/46.31
% 46.00/46.31 Low Water (keep): wt=24.000, iters=5870
% 46.00/46.31
% 46.00/46.31 Low Water (keep): wt=21.000, iters=4586
% 46.00/46.31
% 46.00/46.31 ============================== PROOF =================================
% 46.00/46.31 % SZS status Unsatisfiable
% 46.00/46.31 % SZS output start Refutation
% 46.00/46.31
% 46.00/46.31 % Proof 1 at 44.57 (+ 0.72) seconds: prove_complememt.
% 46.00/46.31 % Length of proof is 188.
% 46.00/46.31 % Level of proof is 29.
% 46.00/46.31 % Maximum clause weight is 28.000.
% 46.00/46.31 % Given clauses 2565.
% 46.00/46.31
% 46.00/46.31 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 46.00/46.31 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 46.00/46.31 3 meet(A,n0) = n0 # label(x_meet_0) # label(axiom). [assumption].
% 46.00/46.31 4 join(A,n0) = A # label(x_join_0) # label(axiom). [assumption].
% 46.00/46.31 5 meet(A,n1) = A # label(x_meet_1) # label(axiom). [assumption].
% 46.00/46.31 6 join(A,n1) = n1 # label(x_join_1) # label(axiom). [assumption].
% 46.00/46.31 7 complement(r1,join(a,b)) # label(complement_of_a_join_b) # label(hypothesis). [assumption].
% 46.00/46.31 8 complement(r2,meet(a,b)) # label(complement_of_a_meet_b) # label(hypothesis). [assumption].
% 46.00/46.31 9 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 46.00/46.31 10 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 46.00/46.31 11 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 46.00/46.31 12 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 46.00/46.31 13 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 46.00/46.31 14 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(13),rewrite([11(2)]),flip(a)].
% 46.00/46.31 15 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 46.00/46.31 16 join(A,join(B,C)) = join(C,join(A,B)). [copy(15),rewrite([12(2)]),flip(a)].
% 46.00/46.31 17 -complement(a,join(r1,meet(r2,b))) # label(prove_complememt) # label(negated_conjecture) # answer(prove_complememt). [assumption].
% 46.00/46.31 18 -complement(a,join(r1,meet(b,r2))) # answer(prove_complememt). [copy(17),rewrite([11(5)])].
% 46.00/46.31 19 -complement(A,B) | meet(A,B) = n0 # label(complement_meet) # label(axiom). [assumption].
% 46.00/46.31 20 -complement(A,B) | join(A,B) = n1 # label(complement_join) # label(axiom). [assumption].
% 46.00/46.31 21 meet(A,B) != n0 | join(A,B) != n1 | complement(A,B) # label(meet_join_complement) # label(axiom). [assumption].
% 46.00/46.31 22 meet(A,B) != A | meet(B,join(A,C)) = join(A,meet(C,B)) # label(modular) # label(axiom). [assumption].
% 46.00/46.31 23 meet(A,B) != A | join(A,meet(B,C)) = meet(B,join(A,C)). [copy(22),rewrite([11(5)]),flip(b)].
% 46.00/46.31 24 meet(A,meet(A,B)) = meet(A,B). [para(14(a,1),1(a,1)),rewrite([11(1),11(2),14(2,R),1(1),11(3)])].
% 46.00/46.31 25 meet(A,meet(B,join(A,C))) = meet(A,B). [para(9(a,1),14(a,2,2)),rewrite([11(2),11(4)])].
% 46.00/46.31 26 join(A,join(A,B)) = join(A,B). [para(16(a,1),2(a,1)),rewrite([12(1),12(2),16(2,R),2(1),12(3)])].
% 46.00/46.31 27 join(A,join(B,meet(A,C))) = join(A,B). [para(10(a,1),16(a,2,2)),rewrite([12(2),12(4)])].
% 46.00/46.31 28 meet(a,meet(b,r2)) = n0. [hyper(19,a,8,a),rewrite([14(5),11(4),14(5,R),11(4)])].
% 46.00/46.31 29 meet(r1,join(a,b)) = n0. [hyper(19,a,7,a)].
% 46.00/46.31 30 join(r2,meet(a,b)) = n1. [hyper(20,a,8,a)].
% 46.00/46.31 31 join(a,join(b,r1)) = n1. [hyper(20,a,7,a),rewrite([16(5),12(4),16(5,R),12(4)])].
% 46.00/46.31 37 meet(A,B) != n0 | n1 != A | complement(A,meet(A,B)). [para(10(a,1),21(b,1)),rewrite([24(2)]),flip(b)].
% 46.00/46.31 38 join(A,meet(B,join(A,C))) = meet(join(A,C),join(A,B)). [hyper(23,a,9,a),rewrite([11(2)])].
% 46.00/46.31 39 meet(n1,join(A,B)) = join(A,B). [hyper(23,a,5,a),rewrite([11(2),5(2)]),flip(a)].
% 46.00/46.31 41 meet(A,B) != B | join(B,meet(A,C)) = meet(A,join(B,C)). [para(11(a,1),23(a,1))].
% 46.00/46.31 45 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(25(a,1),14(a,2,2)),rewrite([11(3),14(3,R),11(2),14(6),11(5),14(6,R),11(5)])].
% 46.00/46.31 46 meet(A,B) != A | join(A,meet(B,meet(C,join(A,D)))) = meet(meet(B,join(A,D)),join(A,C)). [para(25(a,1),23(a,1)),rewrite([11(5),14(5,R),11(4)])].
% 46.00/46.31 47 join(n0,a) = a. [para(28(a,1),10(a,1,2)),rewrite([12(3)])].
% 46.00/46.31 49 meet(n0,a) = n0. [para(28(a,1),24(a,1,2)),rewrite([11(3),28(8)])].
% 46.00/46.31 54 join(n0,r1) = r1. [para(29(a,1),10(a,1,2)),rewrite([12(3)])].
% 46.00/46.31 57 meet(a,r1) = n0. [para(29(a,1),25(a,1,2)),rewrite([11(3),49(3)]),flip(a)].
% 46.00/46.31 64 meet(A,join(B,meet(A,C))) != n0 | join(A,B) != n1 | complement(A,join(B,meet(A,C))). [para(27(a,1),21(b,1))].
% 46.00/46.31 65 meet(n1,r2) = r2. [para(30(a,1),9(a,1,2)),rewrite([11(3)])].
% 46.00/46.31 67 join(a,r2) = join(n1,a). [para(30(a,1),27(a,1,2)),rewrite([12(3)]),flip(a)].
% 46.00/46.31 68 join(r2,join(meet(a,b),meet(A,r2))) = n1. [para(30(a,1),27(a,2)),rewrite([11(6)])].
% 46.00/46.31 71 meet(n1,a) = a. [para(31(a,1),9(a,1,2)),rewrite([11(3)])].
% 46.00/46.31 73 join(n1,a) = n1. [para(31(a,1),26(a,1,2)),rewrite([12(3),31(8)])].
% 46.00/46.31 75 join(a,r2) = n1. [back_rewrite(67),rewrite([73(6)])].
% 46.00/46.31 86 meet(A,meet(B,C)) != n0 | n1 != C | complement(C,meet(A,meet(B,C))). [para(14(a,2),37(a,1)),rewrite([14(8),11(7),14(8,R),11(7)])].
% 46.00/46.31 91 join(A,join(B,meet(C,join(A,D)))) = join(B,meet(join(A,D),join(A,C))). [para(38(a,1),16(a,2,2)),rewrite([12(3)])].
% 46.00/46.31 93 meet(join(a,b),join(a,r1)) = a. [para(29(a,1),38(a,1,2)),rewrite([12(3),47(3)]),flip(a)].
% 46.00/46.31 94 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(38(a,1),27(a,1,2)),rewrite([12(2),38(4)])].
% 46.00/46.31 97 join(a,meet(r2,join(A,a))) = join(A,a). [para(75(a,1),38(a,2,2)),rewrite([12(4),12(8),11(10),39(10)])].
% 46.00/46.31 98 meet(n1,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(38(a,1),39(a,1,2)),rewrite([38(8)])].
% 46.00/46.31 114 meet(join(a,b),meet(join(a,r1),join(A,join(a,b)))) = a. [para(93(a,1),25(a,2)),rewrite([12(10)])].
% 46.00/46.31 116 join(meet(A,B),meet(A,C)) = meet(A,join(C,meet(A,B))). [hyper(41,a,24,a),rewrite([12(5)])].
% 46.00/46.31 117 join(n0,meet(A,B)) = meet(A,B). [hyper(41,a,3,a),rewrite([12(5),4(5)])].
% 46.00/46.31 121 meet(A,meet(B,C)) != meet(A,B) | join(meet(A,B),meet(C,D)) = meet(C,join(D,meet(A,B))). [para(14(a,2),41(a,1)),rewrite([12(9)])].
% 46.00/46.31 122 meet(A,join(B,C)) != meet(B,A) | join(meet(A,join(B,C)),meet(B,D)) = meet(B,join(D,meet(A,join(B,C)))). [para(25(a,1),41(a,1)),rewrite([12(11)]),flip(a)].
% 46.00/46.31 131 join(n0,r2) = r2. [para(65(a,1),117(a,1,2)),rewrite([65(6)])].
% 46.00/46.31 188 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(45(a,1),14(a,2,2)),rewrite([11(4),14(4,R),11(3),14(3,R),11(2),14(8,R),11(7),14(7),11(6),14(7,R),11(6)])].
% 46.00/46.31 206 join(r2,join(meet(A,r2),meet(a,b))) = n1. [para(12(a,1),68(a,1,2))].
% 46.00/46.31 227 meet(a,join(A,a)) = a. [para(97(a,1),9(a,1,2))].
% 46.00/46.31 229 join(a,join(meet(r2,join(A,a)),meet(B,a))) = join(A,a). [para(97(a,1),27(a,2)),rewrite([11(7)])].
% 46.00/46.31 230 join(a,meet(A,join(B,a))) = meet(join(B,a),join(A,a)). [para(97(a,1),38(a,1,2,2)),rewrite([97(11),12(9)])].
% 46.00/46.31 231 join(a,meet(A,meet(join(B,a),join(C,a)))) = meet(meet(join(C,a),join(B,a)),join(A,a)). [hyper(46,a,227,a),rewrite([12(5),14(7,R),12(12),12(15)])].
% 46.00/46.31 313 join(join(A,B),meet(C,join(A,join(B,D)))) = meet(join(A,join(B,D)),join(A,join(B,C))). [hyper(23,a,94,a),rewrite([11(4),12(9),16(9),12(8),16(9,R),12(8)])].
% 46.00/46.31 320 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(117(a,1),94(a,1,1)),rewrite([12(4),16(5,R),12(4),117(4),117(7)])].
% 46.00/46.31 321 meet(r2,join(A,r2)) = r2. [para(131(a,1),94(a,1,1)),rewrite([12(4),16(5,R),12(4),131(4),131(7)])].
% 46.00/46.31 336 meet(A,join(B,C)) != n0 | join(A,B) != n1 | complement(A,meet(join(B,C),join(A,B))). [para(38(a,1),64(a,1,2)),rewrite([12(2),25(4),38(10),12(9)])].
% 46.00/46.31 342 join(r2,meet(A,join(B,r2))) = meet(join(B,r2),join(A,r2)). [hyper(23,a,321,a),rewrite([11(4),12(9)])].
% 46.00/46.31 411 meet(A,B) != n0 | join(B,C) != n1 | complement(join(B,C),meet(A,B)). [para(9(a,1),86(a,1,2)),rewrite([9(9)]),flip(b)].
% 46.00/46.31 438 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(91(a,1),9(a,1,2))].
% 46.00/46.31 440 join(A,meet(join(B,C),join(B,A))) = join(B,A). [para(10(a,1),91(a,1,2)),flip(a)].
% 46.00/46.31 450 join(A,meet(B,join(C,meet(join(A,D),join(A,E))))) = meet(join(A,join(C,meet(E,join(A,D)))),join(A,B)). [para(91(a,1),38(a,1,2,2))].
% 46.00/46.31 506 join(n1,meet(join(A,B),join(A,C))) = n1. [para(98(a,1),10(a,1,2))].
% 46.00/46.31 508 meet(n1,meet(join(A,join(B,C)),join(B,D))) = meet(join(A,join(B,C)),join(B,D)). [para(16(a,1),98(a,1,2,1)),rewrite([12(7),16(8,R),12(7)])].
% 46.00/46.31 526 join(n1,meet(A,meet(B,C))) = n1. [para(117(a,1),506(a,1,2,1)),rewrite([12(4),4(4),11(3),14(3),11(2),14(3,R),11(2)])].
% 46.00/46.31 527 join(A,B) != n0 | complement(join(A,B),n1). [para(506(a,1),64(a,1,2)),rewrite([11(3),39(3),12(6),16(6),12(5),6(5),6(5),506(12)]),xx(b)].
% 46.00/46.31 531 join(n1,meet(A,B)) = n1. [para(1(a,1),526(a,1,2,2))].
% 46.00/46.31 560 meet(A,B) != n0 | complement(meet(A,B),n1). [para(117(a,1),527(a,1)),rewrite([117(6)])].
% 46.00/46.31 577 join(meet(A,B),meet(C,join(D,meet(A,B)))) = meet(join(D,meet(A,B)),join(C,meet(A,B))). [hyper(23,a,320,a),rewrite([11(4),12(9)])].
% 46.00/46.31 591 meet(a,join(A,join(a,b))) = a. [para(114(a,1),14(a,1)),rewrite([93(12),11(7)]),flip(a)].
% 46.00/46.31 610 meet(A,join(join(A,B),meet(A,C))) = A. [para(9(a,1),116(a,1,2)),rewrite([12(2),10(2)]),flip(a)].
% 46.00/46.31 611 join(meet(A,B),meet(B,C)) = meet(B,join(C,meet(A,B))). [para(11(a,1),116(a,1,1)),rewrite([11(4)])].
% 46.00/46.31 612 meet(A,join(B,meet(A,C))) = meet(A,join(C,meet(A,B))). [para(116(a,1),12(a,1)),rewrite([116(6)])].
% 46.00/46.31 619 meet(r1,join(join(a,b),meet(A,r1))) = meet(A,r1). [para(29(a,1),116(a,1,2)),rewrite([11(2),12(4),117(4),11(8)]),flip(a)].
% 46.00/46.31 621 meet(A,join(meet(A,B),join(meet(B,C),meet(A,D)))) = meet(A,join(D,meet(A,B))). [para(116(a,1),27(a,2)),rewrite([11(4),14(4),11(3),14(4,R),11(3),116(5),116(6),12(5)])].
% 46.00/46.31 633 join(r2,meet(a,join(b,meet(a,r2)))) = n1. [para(116(a,1),206(a,1,2))].
% 46.00/46.31 637 meet(join(A,meet(B,C)),join(A,meet(B,join(D,meet(B,C))))) = join(A,meet(B,C)). [para(116(a,1),94(a,1,2,2))].
% 46.00/46.31 638 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(94(a,1),116(a,1,1)),rewrite([11(3),94(9),16(7),12(6),16(7,R),12(6),94(8)])].
% 46.00/46.31 642 join(r2,meet(A,r2)) = r2. [para(321(a,1),116(a,1,1)),rewrite([11(3),321(9),321(8)])].
% 46.00/46.31 662 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(320(a,1),116(a,1,1)),rewrite([11(3),14(3),11(2),14(3,R),11(2),116(4),320(9),320(8)])].
% 46.00/46.31 746 meet(a,join(b,meet(a,r2))) = a. [para(633(a,1),116(a,2,2)),rewrite([12(11),116(11),12(10),16(10,R),2(9),11(10),71(10)])].
% 46.00/46.31 832 join(meet(A,B),meet(C,join(A,D))) = meet(join(A,D),join(C,meet(A,B))). [hyper(121,a,25,a),rewrite([11(3)])].
% 46.00/46.31 834 join(meet(A,B),meet(C,join(B,D))) = meet(join(B,D),join(C,meet(A,B))). [para(9(a,1),121(a,1,2)),rewrite([11(6)]),xx(a)].
% 46.00/46.31 950 complement(meet(n0,join(A,meet(B,C))),n1). [hyper(560,a,438,a),rewrite([12(3),4(3),12(3),4(3)])].
% 46.00/46.31 978 complement(meet(n0,join(A,B)),n1). [para(1(a,1),950(a,1,2,2))].
% 46.00/46.31 981 meet(n0,join(A,B)) = n0. [hyper(19,a,978,a),rewrite([11(5),14(5,R),11(4),39(4)])].
% 46.00/46.31 982 meet(n0,meet(join(A,B),join(A,C))) = n0. [para(38(a,1),981(a,1,2))].
% 46.00/46.31 1010 meet(n0,meet(join(A,B),join(B,C))) = n0. [para(12(a,1),982(a,1,2,1))].
% 46.00/46.31 1028 meet(n0,meet(r2,join(A,meet(B,r2)))) = n0. [para(642(a,1),1010(a,1,2,1)),rewrite([12(5)])].
% 46.00/46.31 1029 join(A,meet(join(A,B),join(B,C))) = join(A,B). [para(11(a,1),440(a,1,2)),rewrite([12(1),12(5)])].
% 46.00/46.31 1032 meet(join(A,B),join(A,join(C,join(D,B)))) = join(A,B). [para(16(a,2),440(a,1,2,1)),rewrite([12(3),38(5),12(6)])].
% 46.00/46.31 1038 join(A,meet(join(B,A),join(B,C))) = join(B,A). [para(440(a,1),91(a,1,2)),rewrite([26(2),26(4)]),flip(a)].
% 46.00/46.31 1097 meet(r1,join(a,join(b,meet(A,r1)))) = meet(A,r1). [para(12(a,1),619(a,1,2)),rewrite([16(7),12(6),16(7,R),12(6)])].
% 46.00/46.31 1104 meet(A,meet(meet(B,r1),join(a,b))) = n0. [para(619(a,1),45(a,1,2,2)),rewrite([14(7,R),14(13),11(12),14(13,R),11(12),29(12),3(9)])].
% 46.00/46.31 1128 meet(meet(A,r1),join(a,b)) = n0. [para(1104(a,1),1(a,1)),flip(a)].
% 46.00/46.31 1133 meet(meet(A,r1),meet(join(a,b),join(B,meet(A,r1)))) = n0. [para(1128(a,1),25(a,2)),rewrite([12(8)])].
% 46.00/46.31 1210 join(join(A,B),meet(A,C)) = join(A,B). [para(610(a,1),638(a,1,2)),rewrite([12(4),27(4),26(2)]),flip(a)].
% 46.00/46.31 1212 join(b,meet(a,r2)) = join(a,b). [para(746(a,1),638(a,1,2)),rewrite([12(7),27(7)]),flip(a)].
% 46.00/46.31 1215 join(meet(A,join(B,C)),meet(D,join(B,C))) = meet(join(B,C),join(D,meet(A,join(B,C)))). [para(638(a,1),122(a,1,2)),rewrite([11(4),638(9),11(9),638(15)]),xx(a)].
% 46.00/46.31 1266 meet(join(a,b),join(join(A,b),meet(a,r2))) = join(a,b). [para(1212(a,1),440(a,1,2,2)),rewrite([12(5),832(10),1212(15)])].
% 46.00/46.31 1435 meet(meet(A,B),join(A,C)) = meet(A,B). [para(1210(a,1),320(a,1,2))].
% 46.00/46.31 1441 meet(n0,meet(r2,join(A,B))) = n0. [para(1210(a,1),1028(a,1,2,2))].
% 46.00/46.31 1518 meet(n0,meet(r2,meet(join(A,B),join(A,C)))) = n0. [para(38(a,1),1441(a,1,2,2))].
% 46.00/46.31 1622 meet(meet(A,B),join(B,C)) = meet(A,B). [para(11(a,1),1435(a,1,1)),rewrite([11(4)])].
% 46.00/46.31 1623 meet(meet(A,meet(B,C)),join(B,D)) = meet(A,meet(B,C)). [para(14(a,1),1435(a,1,1)),rewrite([11(5),14(6,R),11(5)])].
% 46.00/46.31 1697 meet(meet(A,B),join(C,join(D,meet(A,B)))) = meet(A,B). [para(320(a,1),1622(a,1,1)),rewrite([12(4),16(4,R),12(3),320(9)])].
% 46.00/46.31 2410 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(662(a,1),1029(a,1,2)),rewrite([11(3),38(4),11(4)])].
% 46.00/46.31 2444 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [para(1038(a,1),91(a,2))].
% 46.00/46.31 2498 meet(b,r1) = n0. [para(10(a,1),1097(a,1,2,2)),rewrite([29(5)]),flip(a)].
% 46.00/46.31 2993 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(638(a,1),188(a,1,2,2,2,2)),rewrite([14(6,R),11(5),14(5,R),11(4),14(4,R),1(3),14(8,R)]),flip(a)].
% 46.00/46.31 5714 meet(n0,meet(r2,meet(join(A,a),join(B,a)))) = n0. [para(229(a,1),1518(a,1,2,2,1)),rewrite([12(6)])].
% 46.00/46.31 5764 meet(n1,meet(join(A,a),meet(join(B,a),join(C,a)))) = meet(meet(join(A,a),join(B,a)),join(C,a)). [para(230(a,1),98(a,1,2,1)),rewrite([12(8),2993(10),230(15),12(17)])].
% 46.00/46.31 5765 meet(meet(join(A,a),join(B,a)),join(C,a)) = meet(join(A,a),meet(join(B,a),join(C,a))). [para(230(a,1),98(a,1,2,2)),rewrite([12(3),5764(10),12(10),230(15)])].
% 46.00/46.31 5805 join(a,meet(A,meet(join(B,a),join(C,a)))) = meet(join(C,a),meet(join(B,a),join(A,a))). [back_rewrite(231),rewrite([5765(16)])].
% 46.00/46.31 5995 meet(join(A,r2),join(r2,meet(B,A))) = join(r2,meet(B,A)). [para(1622(a,1),342(a,1,2)),rewrite([12(8)]),flip(a)].
% 46.00/46.31 6140 join(A,meet(B,A)) = A. [para(1(a,1),611(a,1,2)),rewrite([12(2),9(5)])].
% 46.00/46.31 6144 meet(meet(A,B),join(C,meet(A,meet(B,D)))) = meet(A,join(meet(B,C),meet(A,meet(B,D)))). [para(14(a,2),611(a,1,1)),rewrite([11(4),14(4),11(3),14(4,R),11(3),116(5),14(8),11(7),14(8,R),11(7)]),flip(a)].
% 46.00/46.31 6351 meet(A,join(B,meet(C,A))) = meet(A,join(C,meet(A,B))). [para(612(a,1),11(a,2)),rewrite([11(3),11(4)]),flip(a)].
% 46.00/46.31 6356 join(A,meet(B,join(C,meet(A,B)))) = join(A,meet(B,C)). [para(612(a,1),38(a,1,2)),rewrite([11(1),11(8),2410(8)])].
% 46.00/46.31 7627 meet(meet(A,r1),meet(join(a,b),join(A,B))) = n0. [para(1210(a,1),1133(a,1,2,2))].
% 46.00/46.31 7660 meet(r1,meet(join(A,B),join(a,b))) = n0. [para(1210(a,1),7627(a,1,2,2)),rewrite([11(3),14(9),11(8),14(8,R),14(9,R),11(8),24(8)])].
% 46.00/46.31 7754 meet(r1,meet(join(a,b),join(A,B))) = n0. [para(11(a,1),7660(a,1,2))].
% 46.00/46.31 8960 join(join(A,b),meet(a,r2)) = join(A,join(a,b)). [para(1266(a,1),2444(a,1,2,2)),rewrite([16(9),12(8),10(8),12(5),16(6),12(5),16(5,R),12(4),16(6,R),12(5),16(5,R),2(4)]),flip(a)].
% 46.00/46.31 8990 meet(a,join(r2,meet(a,join(A,b)))) = a. [para(8960(a,1),612(a,1,2)),rewrite([591(6)]),flip(a)].
% 46.00/46.31 9125 join(r2,meet(a,join(A,b))) = n1. [para(8990(a,1),38(a,1,2)),rewrite([12(3),75(3),12(10),75(10),11(9),39(9)]),flip(a)].
% 46.00/46.31 9133 join(r2,meet(join(A,a),join(A,b))) = n1. [para(9125(a,1),91(a,1,2)),rewrite([6(2),11(7)]),flip(a)].
% 46.00/46.31 9139 join(A,join(r2,meet(b,join(A,a)))) = n1. [para(9133(a,1),91(a,2))].
% 46.00/46.31 11657 meet(A,join(meet(B,join(C,join(D,meet(A,B)))),meet(A,meet(B,E)))) = meet(A,B). [para(1697(a,1),116(a,1,2)),rewrite([11(2),14(2),11(1),14(2,R),11(1),12(4),116(4),662(4),11(7),14(7),11(6),14(7,R),11(6),6144(9)]),flip(a)].
% 46.00/46.31 11680 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(1697(a,1),313(a,1,2)),rewrite([1(10)])].
% 46.00/46.31 12248 complement(join(r2,meet(b,meet(join(A,a),join(B,a)))),n0). [hyper(411,a,5714,a,b,9139,a),rewrite([12(18),5805(18),12(16),75(16),11(15),39(15),16(17),12(16),10(16),12(9),5714(18)])].
% 46.00/46.31 12266 complement(join(r1,join(r2,meet(b,join(a,r1)))),n0). [hyper(411,a,2498,a,b,9139,a),rewrite([12(6),2498(12)])].
% 46.00/46.31 12350 join(n0,join(r1,join(r2,meet(b,join(a,r1))))) = n1. [hyper(20,a,12266,a),rewrite([12(11)])].
% 46.00/46.31 12548 complement(join(r2,meet(b,join(A,a))),n0). [para(1(a,1),12248(a,1,2,2))].
% 46.00/46.31 12549 join(n0,join(r2,meet(b,join(A,a)))) = n1. [hyper(20,a,12548,a),rewrite([12(8)])].
% 46.00/46.31 12551 complement(n0,join(r2,join(meet(b,join(A,a)),meet(B,C)))). [hyper(336,a,438,a,b,12549,a),rewrite([12(9),4(9),12(9),4(9),11680(9),12549(17),11(11),39(11)])].
% 46.00/46.31 12668 meet(n1,meet(b,join(a,r1))) = meet(b,join(a,r1)). [para(12350(a,1),1032(a,1,2)),rewrite([117(7),11(7),117(14)])].
% 46.00/46.31 12797 complement(n0,join(r2,join(meet(a,b),meet(A,B)))). [para(2(a,1),12551(a,2,2,1,2)),rewrite([11(5)])].
% 46.00/46.31 12881 complement(n0,join(r2,meet(b,join(a,r1)))). [para(12668(a,1),12797(a,2,2,2)),rewrite([611(11),12(10),16(10),12(9),10(9),12(6)])].
% 46.00/46.31 12882 join(n0,join(r2,meet(b,join(a,r1)))) = n1. [hyper(20,a,12881,a)].
% 46.00/46.31 12884 complement(n0,join(r2,join(meet(b,join(a,r1)),meet(A,B)))). [hyper(336,a,438,a,b,12882,a),rewrite([12(10),4(10),12(10),4(10),11680(10),12882(19),11(12),39(12)])].
% 46.00/46.31 13547 meet(meet(A,B),join(C,meet(D,E))) = meet(A,meet(B,join(C,meet(D,E)))). [para(117(a,1),450(a,2,2)),rewrite([12(4),4(4),12(4),4(4),117(6),12(7),4(7),11(6),16(8,R),12(7),117(7),14(8),11(7),14(8,R),11(7)])].
% 46.00/46.31 13850 meet(A,join(meet(B,C),meet(A,meet(B,D)))) = meet(A,meet(B,join(C,meet(A,meet(B,D))))). [back_rewrite(6144),rewrite([13547(5)]),flip(a)].
% 46.00/46.31 13984 meet(A,meet(B,join(C,join(D,meet(A,B))))) = meet(A,B). [back_rewrite(11657),rewrite([13850(8),11680(6),11680(5),116(4),662(4)])].
% 46.00/46.31 15030 meet(r1,join(a,meet(A,b))) = n0. [para(2410(a,1),7754(a,1,2)),rewrite([11(4)])].
% 46.00/46.31 16193 meet(n1,meet(r1,join(A,B))) = meet(r1,join(A,B)). [para(54(a,1),508(a,1,2,2)),rewrite([12(3),4(3),11(4),12(7),4(7),54(9),11(8)])].
% 46.00/46.31 16255 meet(n1,meet(r1,r2)) = meet(r1,r2). [para(131(a,1),16193(a,1,2,2)),rewrite([131(9)])].
% 46.00/46.31 16281 meet(meet(r1,r2),join(A,r1)) = meet(r1,r2). [para(16255(a,1),1623(a,1,1)),rewrite([12(5),16255(11)])].
% 46.00/46.31 16312 join(meet(r1,r2),meet(A,join(B,r1))) = meet(join(B,r1),join(A,meet(r1,r2))). [hyper(23,a,16281,a),rewrite([11(6),12(13)])].
% 46.00/46.31 16329 complement(n0,join(r2,meet(join(a,r1),join(b,meet(r1,r2))))). [para(16281(a,1),12884(a,2,2,2)),rewrite([12(11),16312(11)])].
% 46.00/46.31 16434 join(n0,join(r2,meet(join(a,r1),join(b,meet(r1,r2))))) = n1. [hyper(20,a,16329,a)].
% 46.00/46.31 16819 meet(join(A,meet(B,C)),join(meet(D,meet(A,E)),meet(B,C))) = join(meet(B,C),meet(D,meet(A,E))). [para(1623(a,1),577(a,1,2)),flip(a)].
% 46.00/46.31 18229 meet(a,join(n0,join(meet(A,meet(b,r2)),meet(B,a)))) = meet(B,a). [para(28(a,1),621(a,1,2,1)),rewrite([11(6),11(8),28(17),4(14),11(13)])].
% 46.00/46.31 18552 meet(A,meet(join(B,C),join(B,A))) = meet(A,join(B,C)). [para(440(a,1),637(a,1,2)),rewrite([11(2),11(4),2(5),11(4),38(5),14(6),11(5),14(5,R),1(4),14(4,R),11(6),11(8),2(9)])].
% 46.00/46.31 18972 join(n0,join(r2,meet(A,B))) = join(r2,meet(A,B)). [para(5995(a,1),117(a,1,2)),rewrite([5995(11)])].
% 46.00/46.31 19042 join(r2,meet(join(a,r1),join(b,meet(r1,r2)))) = n1. [back_rewrite(16434),rewrite([18972(13)])].
% 46.00/46.31 19623 join(a,join(r1,meet(b,r2))) = n1. [para(19042(a,1),6356(a,1,2,2)),rewrite([11(10),39(10),16(9),12(8),16(8,R),12(7),31(8),12(5),531(5),11(11),11680(12),6356(11),11(6)]),flip(a)].
% 46.00/46.31 19654 meet(a,join(r1,meet(b,r2))) != n0 # answer(prove_complememt). [ur(21,b,19623,a,c,18,a)].
% 46.00/46.31 20349 meet(A,join(B,A)) = A. [para(2410(a,1),834(a,2)),rewrite([12(2),611(4),12(3),16(3),12(2),10(2),12(1),6140(4)])].
% 46.00/46.31 20398 meet(join(A,B),join(B,meet(C,join(A,B)))) = meet(join(A,B),join(B,C)). [para(20349(a,1),6351(a,1,2,2)),rewrite([12(2),11(6)]),flip(a)].
% 46.00/46.31 22770 join(n0,join(meet(A,B),meet(C,D))) = join(meet(A,B),meet(C,D)). [para(117(a,1),11680(a,1,1)),flip(a)].
% 46.00/46.31 23073 meet(a,join(meet(A,meet(b,r2)),meet(B,a))) = meet(B,a). [back_rewrite(18229),rewrite([22770(10)])].
% 46.00/46.31 23794 join(A,meet(B,join(C,A))) = meet(join(C,A),join(B,A)). [para(20349(a,1),1215(a,1,2)),rewrite([12(3),20398(8),12(5)])].
% 46.00/46.31 24442 meet(r1,meet(join(a,meet(A,b)),join(B,C))) = n0. [para(15030(a,1),13984(a,1,2,2,2,2)),rewrite([4(7),15030(14)])].
% 46.00/46.31 24725 meet(r1,meet(join(A,B),join(a,meet(C,b)))) = n0. [para(11(a,1),24442(a,1,2))].
% 46.00/46.31 24835 meet(r1,meet(join(A,B),join(b,meet(a,join(A,B))))) = n0. [para(612(a,1),24725(a,1,2)),rewrite([11(6)])].
% 46.00/46.31 25982 meet(A,meet(join(A,B),join(B,C))) = meet(A,join(B,C)). [para(11(a,1),18552(a,1,2)),rewrite([12(1)])].
% 46.00/46.31 29053 meet(r1,join(meet(A,a),meet(B,meet(b,r2)))) = n0. [para(23073(a,1),24835(a,1,2,2,2)),rewrite([11(13),16819(13)])].
% 46.00/46.31 29078 meet(r1,join(a,meet(A,meet(b,r2)))) = n0. [para(1(a,1),29053(a,1,2,1))].
% 46.00/46.31 29083 meet(join(a,r1),join(a,meet(A,meet(b,r2)))) = a. [para(29078(a,1),38(a,1,2)),rewrite([12(3),47(3),11(11)]),flip(a)].
% 46.00/46.31 29101 meet(A,meet(b,meet(r2,join(a,r1)))) = n0. [para(29083(a,1),18552(a,1,2)),rewrite([11(6),14(6,R),11(5),28(5),3(2),11(9),14(9),11(8),14(9,R),11(8),2993(9)]),flip(a)].
% 46.00/46.31 29104 meet(b,meet(r2,join(a,r1))) = n0. [para(29101(a,1),1(a,1)),flip(a)].
% 46.00/46.31 29108 meet(meet(b,r2),join(a,r1)) = n0. [para(29104(a,1),14(a,1)),rewrite([11(8)]),flip(a)].
% 46.00/46.31 29123 meet(join(a,r1),join(r1,meet(b,r2))) = r1. [para(29108(a,1),23794(a,1,2)),rewrite([12(3),54(3),12(9)]),flip(a)].
% 46.00/46.31 29695 meet(a,join(r1,meet(b,r2))) = n0. [para(29123(a,1),25982(a,1,2)),rewrite([57(3)]),flip(a)].
% 46.00/46.31 29696 $F # answer(prove_complememt). [resolve(29695,a,19654,a)].
% 46.00/46.31
% 46.00/46.31 % SZS output end Refutation
% 46.00/46.31 ============================== end of proof ==========================
% 46.00/46.31
% 46.00/46.31 ============================== STATISTICS ============================
% 46.00/46.31
% 46.00/46.31 Given=2565. Generated=1261390. Kept=29691. proofs=1.
% 46.00/46.31 Usable=1479. Sos=9936. Demods=8124. Limbo=23, Disabled=18271. Hints=0.
% 46.00/46.31 Megabytes=29.00.
% 46.00/46.31 User_CPU=44.57, System_CPU=0.72, Wall_clock=45.
% 46.00/46.31
% 46.00/46.31 ============================== end of statistics =====================
% 46.00/46.31
% 46.00/46.31 ============================== end of search =========================
% 46.00/46.31
% 46.00/46.31 THEOREM PROVED
% 46.00/46.31 % SZS status Unsatisfiable
% 46.00/46.31
% 46.00/46.31 Exiting with 1 proof.
% 46.00/46.31
% 46.00/46.31 Process 10440 exit (max_proofs) Wed Jun 29 19:41:43 2022
% 46.00/46.31 Prover9 interrupted
%------------------------------------------------------------------------------