TSTP Solution File: LAT005-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT005-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 06:25:03 EDT 2022
% Result : Unsatisfiable 29.17s 29.44s
% Output : Refutation 29.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT005-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n006.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 14:11:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 7.64/7.94 ============================== Prover9 ===============================
% 7.64/7.94 Prover9 (32) version 2009-11A, November 2009.
% 7.64/7.94 Process 27766 was started by sandbox on n006.cluster.edu,
% 7.64/7.94 Wed Jun 29 14:11:39 2022
% 7.64/7.94 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27612_n006.cluster.edu".
% 7.64/7.94 ============================== end of head ===========================
% 7.64/7.94
% 7.64/7.94 ============================== INPUT =================================
% 7.64/7.94
% 7.64/7.94 % Reading from file /tmp/Prover9_27612_n006.cluster.edu
% 7.64/7.94
% 7.64/7.94 set(prolog_style_variables).
% 7.64/7.94 set(auto2).
% 7.64/7.94 % set(auto2) -> set(auto).
% 7.64/7.94 % set(auto) -> set(auto_inference).
% 7.64/7.94 % set(auto) -> set(auto_setup).
% 7.64/7.94 % set(auto_setup) -> set(predicate_elim).
% 7.64/7.94 % set(auto_setup) -> assign(eq_defs, unfold).
% 7.64/7.94 % set(auto) -> set(auto_limits).
% 7.64/7.94 % set(auto_limits) -> assign(max_weight, "100.000").
% 7.64/7.94 % set(auto_limits) -> assign(sos_limit, 20000).
% 7.64/7.94 % set(auto) -> set(auto_denials).
% 7.64/7.94 % set(auto) -> set(auto_process).
% 7.64/7.94 % set(auto2) -> assign(new_constants, 1).
% 7.64/7.94 % set(auto2) -> assign(fold_denial_max, 3).
% 7.64/7.94 % set(auto2) -> assign(max_weight, "200.000").
% 7.64/7.94 % set(auto2) -> assign(max_hours, 1).
% 7.64/7.94 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 7.64/7.94 % set(auto2) -> assign(max_seconds, 0).
% 7.64/7.94 % set(auto2) -> assign(max_minutes, 5).
% 7.64/7.94 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 7.64/7.94 % set(auto2) -> set(sort_initial_sos).
% 7.64/7.94 % set(auto2) -> assign(sos_limit, -1).
% 7.64/7.94 % set(auto2) -> assign(lrs_ticks, 3000).
% 7.64/7.94 % set(auto2) -> assign(max_megs, 400).
% 7.64/7.94 % set(auto2) -> assign(stats, some).
% 7.64/7.94 % set(auto2) -> clear(echo_input).
% 7.64/7.94 % set(auto2) -> set(quiet).
% 7.64/7.94 % set(auto2) -> clear(print_initial_clauses).
% 7.64/7.94 % set(auto2) -> clear(print_given).
% 7.64/7.94 assign(lrs_ticks,-1).
% 7.64/7.94 assign(sos_limit,10000).
% 7.64/7.94 assign(order,kbo).
% 7.64/7.94 set(lex_order_vars).
% 7.64/7.94 clear(print_given).
% 7.64/7.94
% 7.64/7.94 % formulas(sos). % not echoed (20 formulas)
% 7.64/7.94
% 7.64/7.94 ============================== end of input ==========================
% 7.64/7.94
% 7.64/7.94 % From the command line: assign(max_seconds, 300).
% 7.64/7.94
% 7.64/7.94 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 7.64/7.94
% 7.64/7.94 % Formulas that are not ordinary clauses:
% 7.64/7.94
% 7.64/7.94 ============================== end of process non-clausal formulas ===
% 7.64/7.94
% 7.64/7.94 ============================== PROCESS INITIAL CLAUSES ===============
% 7.64/7.94
% 7.64/7.94 ============================== PREDICATE ELIMINATION =================
% 7.64/7.94
% 7.64/7.94 ============================== end predicate elimination =============
% 7.64/7.94
% 7.64/7.94 Auto_denials:
% 7.64/7.94 % copying label prove_SAMs_lemma to answer in negative clause
% 7.64/7.94
% 7.64/7.94 Term ordering decisions:
% 7.64/7.94 Function symbol KB weights: a=1. b=1. n0=1. n1=1. r1=1. r2=1. a2=1. b2=1. meet=1. join=1.
% 7.64/7.94
% 7.64/7.94 ============================== end of process initial clauses ========
% 7.64/7.94
% 7.64/7.94 ============================== CLAUSES FOR SEARCH ====================
% 7.64/7.94
% 7.64/7.94 ============================== end of clauses for search =============
% 7.64/7.94
% 7.64/7.94 ============================== SEARCH ================================
% 7.64/7.94
% 7.64/7.94 % Starting search at 0.01 seconds.
% 7.64/7.94
% 7.64/7.94 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 1.21 sec).
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=62.000, iters=3446
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=56.000, iters=3371
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=50.000, iters=3356
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=48.000, iters=3424
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=46.000, iters=3342
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=44.000, iters=3341
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=42.000, iters=3333
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=41.000, iters=3371
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=40.000, iters=3394
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=39.000, iters=3340
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=38.000, iters=3358
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=36.000, iters=3333
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=35.000, iters=3333
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=34.000, iters=3397
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=33.000, iters=3441
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=32.000, iters=3336
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=31.000, iters=3363
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=30.000, iters=3441
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=29.000, iters=3336
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=28.000, iters=3403
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=27.000, iters=3333
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=5724, wt=64.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=6701, wt=62.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=5619, wt=60.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=6918, wt=58.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=6702, wt=56.000
% 29.17/29.44
% 29.17/29.44 Low Water (displace): id=7581, wt=54.000
% 29.17/29.44
% 29.17/29.44 Low Water (displace): id=17221, wt=23.000
% 29.17/29.44
% 29.17/29.44 Low Water (displace): id=17427, wt=21.000
% 29.17/29.44
% 29.17/29.44 Low Water (displace): id=17443, wt=19.000
% 29.17/29.44
% 29.17/29.44 Low Water (displace): id=17444, wt=15.000
% 29.17/29.44
% 29.17/29.44 Low Water (keep): wt=26.000, iters=3335
% 29.17/29.44
% 29.17/29.44 Low Water (keep): wt=25.000, iters=3350
% 29.17/29.44
% 29.17/29.44 Low Water (keep): wt=24.000, iters=3338
% 29.17/29.44
% 29.17/29.44 Low Water (keep): wt=23.000, iters=3339
% 29.17/29.44
% 29.17/29.44 Low Water (keep): wt=22.000, iters=3341
% 29.17/29.44
% 29.17/29.44 Low Water (displace): id=23947, wt=13.000
% 29.17/29.44
% 29.17/29.44 Low Water (keep): wt=21.000, iters=3338
% 29.17/29.44
% 29.17/29.44 Low Water (keep): wt=20.000, iters=3345
% 29.17/29.44
% 29.17/29.44 Low Water (keep): wt=19.000, iters=3345
% 29.17/29.44
% 29.17/29.44 ============================== PROOF =================================
% 29.17/29.44 % SZS status Unsatisfiable
% 29.17/29.44 % SZS output start Refutation
% 29.17/29.44
% 29.17/29.44 % Proof 1 at 28.04 (+ 0.44) seconds: prove_SAMs_lemma.
% 29.17/29.44 % Length of proof is 190.
% 29.17/29.44 % Level of proof is 32.
% 29.17/29.44 % Maximum clause weight is 28.000.
% 29.17/29.44 % Given clauses 2814.
% 29.17/29.44
% 29.17/29.44 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 29.17/29.44 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 29.17/29.44 3 meet(A,n0) = n0 # label(x_meet_0) # label(axiom). [assumption].
% 29.17/29.44 4 join(A,n0) = A # label(x_join_0) # label(axiom). [assumption].
% 29.17/29.44 5 meet(A,n1) = A # label(x_meet_1) # label(axiom). [assumption].
% 29.17/29.44 7 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 29.17/29.44 8 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 29.17/29.44 9 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 29.17/29.44 10 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 29.17/29.44 11 join(r2,meet(a,b)) = n1 # label(r2_complement_meet_a_b_1) # label(negated_conjecture). [assumption].
% 29.17/29.44 12 meet(r2,meet(a,b)) = n0 # label(r2_complement_meet_a_b_2) # label(negated_conjecture). [assumption].
% 29.17/29.44 13 join(r1,join(a,b)) = n1 # label(r1_complement_join_a_b_1) # label(negated_conjecture). [assumption].
% 29.17/29.44 14 meet(r1,join(a,b)) = n0 # label(r1_complement_join_a_b_2) # label(negated_conjecture). [assumption].
% 29.17/29.44 15 join(r1,meet(a,r2)) = b2 # label(define_b2) # label(negated_conjecture). [assumption].
% 29.17/29.44 16 join(r1,meet(b,r2)) = a2 # label(define_a2) # label(negated_conjecture). [assumption].
% 29.17/29.44 17 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 29.17/29.44 18 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(17),rewrite([9(2)]),flip(a)].
% 29.17/29.44 19 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 29.17/29.44 20 join(A,join(B,C)) = join(C,join(A,B)). [copy(19),rewrite([10(2)]),flip(a)].
% 29.17/29.44 21 meet(a2,b2) != r1 # label(prove_SAMs_lemma) # label(negated_conjecture) # answer(prove_SAMs_lemma). [assumption].
% 29.17/29.44 22 meet(A,B) != A | meet(B,join(A,C)) = join(A,meet(C,B)) # label(modular) # label(axiom). [assumption].
% 29.17/29.44 23 meet(A,B) != A | join(A,meet(B,C)) = meet(B,join(A,C)). [copy(22),rewrite([9(5)]),flip(b)].
% 29.17/29.44 24 meet(a,meet(b,r2)) = n0. [back_rewrite(12),rewrite([18(5),9(4),18(5,R),9(4)])].
% 29.17/29.44 25 join(a,join(b,r1)) = n1. [back_rewrite(13),rewrite([20(5),10(4),20(5,R),10(4)])].
% 29.17/29.44 26 meet(n1,r2) = r2. [para(11(a,1),7(a,1,2)),rewrite([9(3)])].
% 29.17/29.44 27 join(n0,r1) = r1. [para(14(a,1),8(a,1,2)),rewrite([10(3)])].
% 29.17/29.44 28 meet(r1,b2) = r1. [para(15(a,1),7(a,1,2))].
% 29.17/29.44 29 meet(r1,a2) = r1. [para(16(a,1),7(a,1,2))].
% 29.17/29.44 30 meet(A,meet(A,B)) = meet(A,B). [para(18(a,1),1(a,1)),rewrite([9(1),9(2),18(2,R),1(1),9(3)])].
% 29.17/29.44 31 meet(A,meet(B,join(A,C))) = meet(A,B). [para(7(a,1),18(a,2,2)),rewrite([9(2),9(4)])].
% 29.17/29.44 32 join(A,join(A,B)) = join(A,B). [para(20(a,1),2(a,1)),rewrite([10(1),10(2),20(2,R),2(1),10(3)])].
% 29.17/29.44 33 join(A,join(B,meet(A,C))) = join(A,B). [para(8(a,1),20(a,2,2)),rewrite([10(2),10(4)])].
% 29.17/29.44 34 join(A,meet(B,join(A,C))) = meet(join(A,C),join(A,B)). [hyper(23,a,7,a),rewrite([9(2)])].
% 29.17/29.44 35 meet(n1,join(A,B)) = join(A,B). [hyper(23,a,5,a),rewrite([9(2),5(2)]),flip(a)].
% 29.17/29.44 37 meet(A,B) != B | join(B,meet(A,C)) = meet(A,join(B,C)). [para(9(a,1),23(a,1))].
% 29.17/29.44 39 meet(A,meet(B,C)) != B | join(B,meet(A,meet(C,D))) = meet(meet(A,C),join(B,D)). [para(18(a,1),23(a,1)),rewrite([9(4),9(5),18(5),9(4),18(5,R),9(4),9(7)])].
% 29.17/29.44 45 join(r1,meet(A,b2)) = meet(b2,join(A,r1)). [hyper(23,a,28,a),rewrite([9(3),10(7)])].
% 29.17/29.44 49 join(r1,b2) = b2. [para(15(a,1),32(a,1,2)),rewrite([15(8)])].
% 29.17/29.44 50 join(r1,a2) = a2. [para(16(a,1),32(a,1,2)),rewrite([16(8)])].
% 29.17/29.44 51 meet(a,r1) = n0. [para(14(a,1),31(a,1,2)),rewrite([3(3)]),flip(a)].
% 29.17/29.44 53 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(31(a,1),18(a,2,2)),rewrite([9(3),18(3,R),9(2),18(6),9(5),18(6,R),9(5)])].
% 29.17/29.44 69 join(r2,join(meet(a,b),meet(A,r2))) = n1. [para(11(a,1),33(a,2)),rewrite([9(6)])].
% 29.17/29.44 70 join(a,b2) = join(a,r1). [para(15(a,1),33(a,1,2))].
% 29.17/29.44 72 join(b,a2) = join(b,r1). [para(16(a,1),33(a,1,2))].
% 29.17/29.44 74 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(33(a,1),20(a,2,2)),rewrite([10(3),20(3,R),10(2),20(6),10(5),20(6,R),10(5)])].
% 29.17/29.44 76 join(r1,join(b2,meet(A,r1))) = b2. [para(49(a,1),33(a,2)),rewrite([9(4)])].
% 29.17/29.44 77 join(r1,join(a2,meet(A,r1))) = a2. [para(50(a,1),33(a,2)),rewrite([9(4)])].
% 29.17/29.44 81 join(r2,meet(meet(a,b),join(A,r2))) = join(A,r2). [para(11(a,1),34(a,2,2)),rewrite([10(6),10(10),9(12),35(12)])].
% 29.17/29.44 85 join(A,join(B,meet(C,join(A,D)))) = join(B,meet(join(A,D),join(A,C))). [para(34(a,1),20(a,2,2)),rewrite([10(3)])].
% 29.17/29.44 89 meet(n1,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(34(a,1),35(a,1,2)),rewrite([34(8)])].
% 29.17/29.44 90 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(34(a,1),33(a,1,2)),rewrite([10(2),34(4)])].
% 29.17/29.44 96 join(b,meet(a2,join(A,b))) = meet(join(A,b),join(b,r1)). [para(72(a,1),34(a,2,2)),rewrite([10(4),10(8)])].
% 29.17/29.44 108 join(meet(A,B),meet(A,C)) = meet(A,join(C,meet(A,B))). [hyper(37,a,30,a),rewrite([10(5)])].
% 29.17/29.44 109 join(n0,meet(A,B)) = meet(A,B). [hyper(37,a,3,a),rewrite([10(5),4(5)])].
% 29.17/29.44 114 meet(A,meet(B,C)) != meet(A,B) | join(meet(A,B),meet(C,D)) = meet(C,join(D,meet(A,B))). [para(18(a,2),37(a,1)),rewrite([10(9)])].
% 29.17/29.44 119 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(31(a,1),37(a,1)),rewrite([10(11)]),flip(a)].
% 29.17/29.44 126 join(b2,meet(A,r1)) = b2. [para(76(a,1),20(a,1)),rewrite([49(6),10(5)]),flip(a)].
% 29.17/29.44 131 join(b2,join(meet(A,r1),meet(B,b2))) = b2. [para(126(a,1),33(a,2)),rewrite([9(5)])].
% 29.17/29.44 132 join(b2,meet(A,b2)) = meet(b2,join(A,b2)). [para(126(a,1),34(a,1,2,2)),rewrite([126(8),10(7)])].
% 29.17/29.44 134 join(a2,meet(A,r1)) = a2. [para(77(a,1),20(a,1)),rewrite([50(6),10(5)]),flip(a)].
% 29.17/29.44 139 meet(A,B) != B | join(B,meet(A,meet(B,C))) = meet(meet(A,B),join(B,C)). [para(1(a,1),39(a,1,2))].
% 29.17/29.44 162 join(a2,join(meet(A,r1),meet(B,a2))) = a2. [para(134(a,1),33(a,2)),rewrite([9(5)])].
% 29.17/29.44 163 join(a2,meet(A,a2)) = meet(a2,join(A,a2)). [para(134(a,1),34(a,1,2,2)),rewrite([134(8),10(7)])].
% 29.17/29.44 195 join(n0,r2) = r2. [para(26(a,1),109(a,1,2)),rewrite([26(6)])].
% 29.17/29.44 199 meet(join(A,r1),join(A,b2)) = join(A,r1). [para(45(a,1),33(a,1,2)),rewrite([34(5)])].
% 29.17/29.44 223 join(r2,join(meet(A,r2),meet(a,b))) = n1. [para(10(a,1),69(a,1,2))].
% 29.17/29.44 281 meet(b2,join(A,b2)) = b2. [para(131(a,1),20(a,1)),rewrite([126(7),10(5),132(5)]),flip(a)].
% 29.17/29.44 289 meet(b2,join(a,r1)) = b2. [para(70(a,1),281(a,1,2))].
% 29.17/29.44 301 meet(a2,join(A,a2)) = a2. [para(162(a,1),20(a,1)),rewrite([134(7),10(5),163(5)]),flip(a)].
% 29.17/29.44 312 meet(a2,join(b,r1)) = a2. [para(72(a,1),301(a,1,2))].
% 29.17/29.44 325 join(join(A,r1),meet(B,join(A,b2))) = meet(join(A,b2),join(A,join(B,r1))). [hyper(23,a,199,a),rewrite([9(5),10(11),20(11,R),10(10)])].
% 29.17/29.44 331 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(74(a,1),20(a,2,2)),rewrite([10(4),20(4,R),10(3),20(3,R),10(2),20(8,R),10(7),20(7),10(6),20(7,R),10(6)])].
% 29.17/29.44 371 join(r2,meet(a,meet(b,join(A,r2)))) = join(A,r2). [para(9(a,1),81(a,1,2)),rewrite([18(7),9(6),18(7,R),9(6)])].
% 29.17/29.44 392 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(85(a,1),7(a,1,2))].
% 29.17/29.44 394 join(A,meet(join(B,C),join(B,A))) = join(B,A). [para(8(a,1),85(a,1,2)),flip(a)].
% 29.17/29.44 399 join(A,join(B,meet(join(A,C),join(A,D)))) = join(A,join(B,meet(D,join(A,C)))). [para(85(a,1),32(a,1,2))].
% 29.17/29.44 403 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(85(a,1),34(a,1,2,2))].
% 29.17/29.44 430 meet(n1,meet(join(A,join(B,C)),join(B,D))) = meet(join(A,join(B,C)),join(B,D)). [para(20(a,1),89(a,1,2,1)),rewrite([10(7),20(8,R),10(7)])].
% 29.17/29.44 446 meet(join(A,join(B,meet(C,join(A,D)))),join(B,E)) = meet(join(B,meet(join(A,D),join(A,C))),join(B,E)). [para(85(a,2),89(a,1,2,1)),rewrite([430(8)])].
% 29.17/29.44 476 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(109(a,1),90(a,1,1)),rewrite([10(4),20(5,R),10(4),109(4),109(7)])].
% 29.17/29.44 547 meet(b,join(A,b)) = b. [para(96(a,1),7(a,1,2)),rewrite([31(8)])].
% 29.17/29.44 559 join(b,meet(A,join(B,b))) = meet(join(B,b),join(A,b)). [hyper(23,a,547,a),rewrite([9(4),10(9)])].
% 29.17/29.44 658 meet(A,join(join(A,B),meet(A,C))) = A. [para(7(a,1),108(a,1,2)),rewrite([10(2),8(2)]),flip(a)].
% 29.17/29.44 659 join(meet(A,B),meet(B,C)) = meet(B,join(C,meet(A,B))). [para(9(a,1),108(a,1,1)),rewrite([9(4)])].
% 29.17/29.44 660 meet(A,join(B,meet(A,C))) = meet(A,join(C,meet(A,B))). [para(108(a,1),10(a,1)),rewrite([108(6)])].
% 29.17/29.44 661 meet(r1,join(join(a,b),meet(A,r1))) = meet(A,r1). [para(14(a,1),108(a,1,2)),rewrite([9(2),10(4),109(4),9(8)]),flip(a)].
% 29.17/29.44 662 meet(a,b2) = meet(a,r2). [para(15(a,1),108(a,2,2)),rewrite([51(6),10(5),109(5)]),flip(a)].
% 29.17/29.44 663 meet(b,join(r2,meet(b,r1))) = meet(b,a2). [para(16(a,1),108(a,2,2)),rewrite([10(7),108(7)])].
% 29.17/29.44 664 join(meet(A,meet(B,C)),meet(B,D)) = meet(B,join(D,meet(A,meet(B,C)))). [para(18(a,1),108(a,1,1)),rewrite([9(5),18(6,R),9(5)])].
% 29.17/29.44 681 meet(A,join(meet(B,meet(C,join(A,D))),meet(A,E))) = meet(A,join(meet(B,C),meet(A,E))). [para(53(a,1),108(a,1,2)),rewrite([108(4)]),flip(a)].
% 29.17/29.44 693 join(r2,meet(a,join(b,meet(a,r2)))) = n1. [para(108(a,1),223(a,1,2))].
% 29.17/29.44 705 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(90(a,1),108(a,1,1)),rewrite([9(3),90(9),20(7),10(6),20(7,R),10(6),90(8)])].
% 29.17/29.44 777 meet(b,meet(r2,a2)) = meet(b,r2). [para(663(a,1),31(a,1,2)),rewrite([18(5,R),9(4),9(8)])].
% 29.17/29.44 779 meet(join(b,r2),join(r2,meet(b,r1))) = join(r2,meet(b,a2)). [para(663(a,1),34(a,1,2)),rewrite([10(13),9(14)]),flip(a)].
% 29.17/29.44 926 meet(a,join(b,meet(a,r2))) = a. [para(693(a,1),108(a,2,2)),rewrite([10(11),108(11),10(10),20(10,R),2(9),5(10)])].
% 29.17/29.44 928 join(meet(A,B),meet(C,join(A,D))) = meet(join(A,D),join(C,meet(A,B))). [hyper(114,a,31,a),rewrite([9(3)])].
% 29.17/29.44 937 join(meet(A,r1),meet(B,b2)) = meet(b2,join(B,meet(A,r1))). [para(28(a,1),114(a,1,2)),rewrite([9(9)]),xx(a)].
% 29.17/29.44 1054 join(meet(A,b2),meet(B,b2)) = meet(b2,join(B,meet(A,b2))). [para(126(a,1),119(a,1,2)),rewrite([9(4),126(9),9(9),126(15)]),xx(a)].
% 29.17/29.44 1289 join(b,r2) = n1. [para(7(a,1),371(a,1,2,2)),rewrite([11(5)]),flip(a)].
% 29.17/29.44 1295 join(r2,meet(b,a2)) = join(r2,meet(b,r1)). [back_rewrite(779),rewrite([1289(3),35(7)]),flip(a)].
% 29.17/29.44 1317 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [hyper(139,a,30,a),rewrite([9(3),18(3),9(2),18(3,R),9(2),30(4),108(4),30(6),10(7),476(8)])].
% 29.17/29.44 1373 meet(r1,join(A,meet(a2,join(B,r1)))) = r1. [para(16(a,1),392(a,1,2,2,1)),rewrite([10(4)])].
% 29.17/29.44 1671 meet(r1,meet(a2,join(join(A,r1),meet(B,a2)))) = r1. [para(108(a,1),1373(a,1,2)),rewrite([9(6)])].
% 29.17/29.44 2097 join(A,meet(join(A,B),join(B,C))) = join(A,B). [para(9(a,1),394(a,1,2)),rewrite([10(1),10(5)])].
% 29.17/29.44 2113 join(A,meet(join(B,A),join(B,C))) = join(B,A). [para(394(a,1),85(a,1,2)),rewrite([32(2),32(4)]),flip(a)].
% 29.17/29.44 2254 meet(meet(b,a2),join(r2,meet(b,r1))) = meet(b,a2). [para(1295(a,1),476(a,1,2))].
% 29.17/29.44 2266 meet(r1,join(a,join(b,meet(A,r1)))) = meet(A,r1). [para(10(a,1),661(a,1,2)),rewrite([20(7),10(6),20(7,R),10(6)])].
% 29.17/29.44 2371 join(join(A,B),meet(A,C)) = join(A,B). [para(658(a,1),705(a,1,2)),rewrite([10(4),33(4),32(2)]),flip(a)].
% 29.17/29.44 2378 join(b,meet(a,r2)) = join(a,b). [para(926(a,1),705(a,1,2)),rewrite([10(7),33(7)]),flip(a)].
% 29.17/29.44 2476 join(join(A,B),meet(B,C)) = join(A,B). [para(10(a,1),2371(a,1,1)),rewrite([10(4)])].
% 29.17/29.44 2500 meet(meet(A,B),join(A,C)) = meet(A,B). [para(2371(a,1),476(a,1,2))].
% 29.17/29.44 2661 join(join(a,r1),meet(A,b2)) = join(a,r1). [para(70(a,1),2476(a,1,1)),rewrite([9(5),70(9)])].
% 29.17/29.44 2961 meet(meet(A,B),join(B,C)) = meet(A,B). [para(9(a,1),2500(a,1,1)),rewrite([9(4)])].
% 29.17/29.44 3027 meet(meet(A,b2),join(a,r1)) = meet(A,b2). [para(2661(a,1),476(a,1,2))].
% 29.17/29.44 3028 join(join(a,r1),meet(A,meet(B,b2))) = join(a,r1). [para(2661(a,1),2476(a,1,1)),rewrite([9(6),18(6,R),9(5),2661(13)])].
% 29.17/29.44 3235 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(31(a,1),2961(a,1,1)),rewrite([10(4),31(8)])].
% 29.17/29.44 3260 meet(meet(a,r2),join(A,b2)) = meet(a,r2). [para(662(a,1),2961(a,1,1)),rewrite([10(5),662(9)])].
% 29.17/29.44 3583 meet(join(a,r1),join(a,meet(A,b2))) = join(a,meet(A,b2)). [para(3027(a,1),34(a,1,2)),flip(a)].
% 29.17/29.44 3617 meet(a,meet(r2,join(A,b2))) = meet(a,r2). [para(3260(a,1),9(a,1)),rewrite([18(9),9(8),18(9,R),9(8)]),flip(a)].
% 29.17/29.44 3901 meet(a,meet(r2,b2)) = meet(a,r2). [para(2(a,1),3617(a,1,2,2))].
% 29.17/29.44 4041 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(10(a,1),1317(a,1,2)),rewrite([659(3)])].
% 29.17/29.44 4415 meet(r1,join(join(A,r1),meet(B,a2))) = r1. [para(1671(a,1),18(a,1)),rewrite([29(9),9(8)]),flip(a)].
% 29.17/29.44 4632 join(r1,meet(a2,join(A,meet(b,r2)))) = a2. [para(16(a,1),2097(a,1,2,1)),rewrite([10(6),16(13)])].
% 29.17/29.44 4673 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(1317(a,1),2097(a,1,2)),rewrite([9(3),34(4),9(4)])].
% 29.17/29.44 4776 join(r1,meet(a2,join(A,b))) = a2. [para(2371(a,1),4632(a,1,2,2)),rewrite([10(4)])].
% 29.17/29.44 6801 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [para(2113(a,1),85(a,2))].
% 29.17/29.44 6954 meet(meet(b,a2),meet(join(r2,meet(b,r1)),join(A,meet(b,a2)))) = meet(b,a2). [para(2254(a,1),31(a,2)),rewrite([10(12)])].
% 29.17/29.44 6975 meet(b,r1) = n0. [para(8(a,1),2266(a,1,2,2)),rewrite([14(5)]),flip(a)].
% 29.17/29.44 7012 meet(b,a2) = meet(b,r2). [back_rewrite(6954),rewrite([6975(7),10(6),195(6),18(10,R),9(9),476(9),18(5,R),9(4),777(5)]),flip(a)].
% 29.17/29.44 7156 meet(r1,join(join(A,r1),meet(b,r2))) = r1. [para(7012(a,1),4415(a,1,2,2))].
% 29.17/29.44 7386 join(r1,join(join(A,r1),meet(b,r2))) = join(join(A,r1),meet(b,r2)). [para(7156(a,1),705(a,1,2)),rewrite([10(8)])].
% 29.17/29.44 9761 join(join(A,r1),meet(a,r2)) = join(A,b2). [para(3260(a,1),325(a,1,2)),rewrite([10(13),15(13),1(11)])].
% 29.17/29.44 9771 join(join(A,b2),meet(B,join(A,r1))) = join(A,b2). [para(9761(a,1),2371(a,1,1)),rewrite([9(5),9761(12)])].
% 29.17/29.44 10038 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(476(a,1),331(a,1,2,2,2,2)),rewrite([20(6,R),10(5),20(5,R),10(4),20(4,R),2(3),20(8,R)]),flip(a)].
% 29.17/29.44 10093 join(join(A,r1),meet(b,r2)) = join(A,a2). [back_rewrite(7386),rewrite([10038(8),16(6),20(4,R),10(3),50(3)]),flip(a)].
% 29.17/29.44 10178 join(join(A,a2),meet(B,join(A,r1))) = join(A,a2). [para(10093(a,1),2371(a,1,1)),rewrite([9(5),10093(12)])].
% 29.17/29.44 12249 meet(meet(A,B),join(C,meet(D,E))) = meet(A,meet(B,join(C,meet(D,E)))). [para(109(a,1),403(a,2,2)),rewrite([10(4),4(4),10(4),4(4),109(6),10(7),4(7),9(6),20(8,R),10(7),109(7),18(8),9(7),18(8,R),9(7)])].
% 29.17/29.44 12777 meet(A,meet(B,join(C,meet(B,join(A,D))))) = meet(A,B). [back_rewrite(3235),rewrite([12249(5)])].
% 29.17/29.44 14141 join(b,join(a2,b2)) = join(b,b2). [para(312(a,1),9771(a,1,2)),rewrite([10(5),20(5,R),10(4)])].
% 29.17/29.44 14143 join(A,join(b2,meet(r1,join(A,B)))) = join(A,b2). [para(9771(a,1),85(a,2)),rewrite([10038(7),32(7)])].
% 29.17/29.44 14320 join(join(b,b2),meet(A,join(a2,b2))) = join(b,b2). [para(14141(a,1),2476(a,1,1)),rewrite([9(7),14141(13)])].
% 29.17/29.44 15010 meet(A,join(B,join(A,meet(C,join(B,D))))) = A. [para(2(a,1),446(a,1,2)),rewrite([9(5),2(10),9(10),7(10)])].
% 29.17/29.44 15208 join(join(A,a2),meet(join(A,r1),join(A,B))) = join(A,a2). [para(10178(a,1),85(a,1,2)),rewrite([32(3)]),flip(a)].
% 29.17/29.44 17114 join(b2,meet(join(A,B),join(A,r1))) = join(A,b2). [para(14143(a,1),20(a,2)),rewrite([10(5),34(5)])].
% 29.17/29.44 17537 join(b,b2) = n1. [para(3260(a,1),14320(a,1,2)),rewrite([10(7),20(7),10(6),2378(6),20(5),10(4),70(4),20(5,R),10(4),25(5)]),flip(a)].
% 29.17/29.44 18106 join(join(A,B),meet(C,join(A,D))) = join(A,join(B,meet(C,join(A,D)))). [para(15010(a,1),394(a,1,2)),rewrite([10(6),32(6),10038(9),32(9)])].
% 29.17/29.44 18124 join(A,join(a2,meet(B,join(A,r1)))) = join(A,a2). [back_rewrite(15208),rewrite([18106(7),399(7)])].
% 29.17/29.44 18519 join(meet(a,r2),meet(A,meet(r2,b2))) = meet(r2,meet(b2,join(A,meet(a,r2)))). [para(3901(a,1),659(a,1,1)),rewrite([9(7),3901(16),12249(16)])].
% 29.17/29.44 18677 join(A,meet(B,meet(A,C))) = A. [para(1(a,1),664(a,1,2)),rewrite([10(3),7(7)])].
% 29.17/29.44 18687 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(35(a,1),664(a,1,2)),rewrite([9(2),5(2),20(3),10(2),20(3,R),10(2),9(7),5(7),35(8)]),flip(a)].
% 29.17/29.44 19458 join(a,join(r1,meet(A,meet(B,b2)))) = join(a,r1). [back_rewrite(3028),rewrite([18687(7)])].
% 29.17/29.44 20229 join(b2,meet(join(A,B),join(B,r1))) = join(B,b2). [para(10(a,1),17114(a,1,2,1))].
% 29.17/29.44 20526 join(a2,meet(join(A,r1),join(B,A))) = join(A,a2). [para(18124(a,1),20(a,2)),rewrite([10(5),34(5),10(4)])].
% 29.17/29.44 21105 join(b2,meet(a2,join(A,b))) = join(a2,b2). [para(4776(a,1),20229(a,1,2,1)),rewrite([10(8),4776(8),1(4),10(3),10(9)]),flip(a)].
% 29.17/29.44 21130 join(b2,meet(r1,join(A,B))) = b2. [para(14143(a,1),20229(a,1,2,1)),rewrite([10(10),33(10),49(6),9(5),281(5),2(3),10(8),32(8)]),flip(a)].
% 29.17/29.44 21177 meet(r1,meet(b2,join(A,B))) = meet(r1,join(A,B)). [para(21130(a,1),4041(a,1,2,2)),rewrite([9(4)])].
% 29.17/29.44 21190 meet(a2,join(A,join(b,meet(a2,b2)))) = a2. [para(21105(a,1),108(a,2,2)),rewrite([10(8),108(8),18687(7),7(13)])].
% 29.17/29.44 21216 meet(a2,join(b,meet(a2,b2))) = a2. [para(2(a,1),21190(a,1,2))].
% 29.17/29.44 21226 join(meet(b,r2),meet(a2,b2)) = a2. [para(21216(a,1),108(a,2)),rewrite([9(6),7012(6),10(7)])].
% 29.17/29.44 21227 join(b,meet(a2,b2)) = join(b,r1). [para(21216(a,1),6801(a,1,2,2)),rewrite([10(6),8(6),72(3)]),flip(a)].
% 29.17/29.44 21236 join(meet(a2,b2),meet(b,meet(r2,b2))) = meet(a2,b2). [para(21226(a,1),659(a,2,2)),rewrite([18(8),9(7),18(8,R),9(7),9(12)])].
% 29.17/29.44 21243 meet(a2,meet(b2,join(b,r1))) = meet(a2,b2). [para(21227(a,1),4041(a,1,2,2))].
% 29.17/29.44 21247 meet(b2,join(a2,meet(b,b2))) = meet(b2,join(b,r1)). [para(21227(a,1),659(a,2,2)),rewrite([9(6),10(7),1054(7)])].
% 29.17/29.44 21254 meet(a2,meet(b2,join(A,meet(b2,join(b,r1))))) = meet(a2,b2). [para(21243(a,1),2961(a,1,1)),rewrite([10(9),12249(10),21243(17)])].
% 29.17/29.44 21971 meet(join(a,b),join(r1,meet(A,a))) = meet(A,a). [para(14(a,1),928(a,1,2)),rewrite([9(2),10(4),109(4),9(8)]),flip(a)].
% 29.17/29.44 22280 meet(b,meet(r2,meet(a2,b2))) = meet(b,meet(r2,b2)). [para(21236(a,1),4041(a,1,2,2)),rewrite([18(8),9(7),18(7,R),9(6),18(8,R),9(7),18(7,R),1(6)])].
% 29.17/29.44 22283 join(a2,meet(b,meet(r2,b2))) = a2. [para(21236(a,1),20526(a,1,2,2)),rewrite([10(8),9(12),12249(12),8(13),10(8)]),flip(a)].
% 29.17/29.44 22577 meet(b2,meet(join(a2,meet(b,b2)),join(A,meet(b2,join(b,r1))))) = meet(b2,join(b,r1)). [para(21247(a,1),4041(a,1,2,2,2)),rewrite([21247(21)])].
% 29.17/29.44 22722 join(r1,meet(A,meet(B,b2))) = meet(b2,join(r1,meet(A,B))). [para(681(a,1),937(a,2)),rewrite([9(3),28(3),10(3),9(7),18(7,R),9(6),18(6,R),9(5),281(5),9(10),28(10),10(9)])].
% 29.17/29.44 22742 join(a,meet(b2,join(r1,meet(A,B)))) = join(a,r1). [back_rewrite(19458),rewrite([22722(6)])].
% 29.17/29.44 23828 meet(b2,join(r1,join(meet(A,B),meet(a,r2)))) = b2. [para(22742(a,1),660(a,1,2)),rewrite([289(5),9(8),662(8),10(9),20(9,R)]),flip(a)].
% 29.17/29.44 24618 meet(b2,join(r1,meet(r2,meet(b2,join(a,b))))) = b2. [para(22280(a,1),23828(a,1,2,2,1)),rewrite([10(11),18519(11),2378(9)])].
% 29.17/29.44 24996 join(r1,meet(r2,meet(b2,join(a,b)))) = b2. [para(24618(a,1),6801(a,1,2,2)),rewrite([10(10),18677(10),49(3)]),flip(a)].
% 29.17/29.44 25002 meet(r2,meet(b2,join(a,b))) = meet(b2,join(a,b)). [para(24996(a,1),659(a,2,2)),rewrite([9(14),21177(14),14(12),10(9),109(9),9(14),30(14)])].
% 29.17/29.44 25157 join(r2,meet(b2,join(a,b))) = r2. [para(25002(a,1),8(a,1,2))].
% 29.17/29.44 25158 meet(meet(r2,b2),join(a,b)) = meet(b2,join(a,b)). [para(25002(a,1),18(a,1)),rewrite([9(12)]),flip(a)].
% 29.17/29.44 25163 meet(b2,join(a,join(b,meet(r2,b2)))) = meet(r2,b2). [para(25157(a,1),108(a,2,2)),rewrite([9(8),10(9),659(9),10(8),20(8),10(7),20(8,R),10(7),9(12)])].
% 29.17/29.44 25268 meet(join(a,b),join(b,meet(r2,b2))) = join(a,b). [para(25158(a,1),559(a,1,2)),rewrite([559(7),10(6),17537(6),9(5),35(5),10(11)]),flip(a)].
% 29.17/29.44 25384 join(a,join(b,meet(r2,b2))) = join(b,meet(r2,b2)). [para(25268(a,1),6801(a,1,2,2)),rewrite([20(8),10(7),20(8,R),10(7),20(9,R),10(8),32(8)])].
% 29.17/29.44 25387 meet(b2,join(b,meet(r2,b2))) = meet(r2,b2). [back_rewrite(25163),rewrite([25384(8)])].
% 29.17/29.44 25395 meet(b,meet(r2,b2)) = meet(b,b2). [para(25387(a,1),31(a,1,2))].
% 29.17/29.44 25408 join(a2,meet(b,b2)) = a2. [back_rewrite(22283),rewrite([25395(6)])].
% 29.17/29.44 25412 meet(b2,join(b,r1)) = meet(a2,b2). [back_rewrite(22577),rewrite([25408(6),18(10,R),9(9),21254(10)]),flip(a)].
% 29.17/29.44 29441 meet(r1,meet(join(a,b),join(A,meet(B,a)))) = n0. [para(21971(a,1),12777(a,1,2,2,2)),rewrite([14(14)])].
% 29.17/29.44 29486 meet(r1,meet(join(a,b),join(a,meet(A,B)))) = n0. [para(681(a,1),29441(a,1,2)),rewrite([9(10),7(10),10(7)])].
% 29.17/29.44 29539 meet(r1,join(a,meet(b,b2))) = n0. [para(25395(a,1),29486(a,1,2,2,2)),rewrite([4673(10)])].
% 29.17/29.44 29559 join(a,meet(b,b2)) = a. [para(29539(a,1),34(a,1,2)),rewrite([4(3),9(10),3583(10)]),flip(a)].
% 29.17/29.44 29566 meet(b,b2) = n0. [para(29559(a,1),4041(a,1,2,2)),rewrite([9(4),662(4),18(5,R),9(4),24(5)]),flip(a)].
% 29.17/29.44 29665 meet(a2,b2) = r1. [para(29566(a,1),45(a,1,2)),rewrite([10(3),27(3),25412(6)]),flip(a)].
% 29.17/29.44 29666 $F # answer(prove_SAMs_lemma). [resolve(29665,a,21,a)].
% 29.17/29.44
% 29.17/29.44 % SZS output end Refutation
% 29.17/29.44 ============================== end of proof ==========================
% 29.17/29.44
% 29.17/29.44 ============================== STATISTICS ============================
% 29.17/29.44
% 29.17/29.44 Given=2814. Generated=876571. Kept=29662. proofs=1.
% 29.17/29.44 Usable=1826. Sos=9555. Demods=10230. Limbo=3, Disabled=18297. Hints=0.
% 29.17/29.44 Megabytes=28.88.
% 29.17/29.44 User_CPU=28.05, System_CPU=0.44, Wall_clock=28.
% 29.17/29.44
% 29.17/29.44 ============================== end of statistics =====================
% 29.17/29.44
% 29.17/29.44 ============================== end of search =========================
% 29.17/29.44
% 29.17/29.44 THEOREM PROVED
% 29.17/29.44 % SZS status Unsatisfiable
% 29.17/29.44
% 29.17/29.44 Exiting with 1 proof.
% 29.17/29.44
% 29.17/29.44 Process 27766 exit (max_proofs) Wed Jun 29 14:12:07 2022
% 29.17/29.44 Prover9 interrupted
%------------------------------------------------------------------------------