TSTP Solution File: LAT174-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT174-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 06:25:56 EDT 2022
% Result : Unsatisfiable 8.63s 8.95s
% Output : Refutation 8.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT174-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 29 14:55:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 8.63/8.95 ============================== Prover9 ===============================
% 8.63/8.95 Prover9 (32) version 2009-11A, November 2009.
% 8.63/8.95 Process 11698 was started by sandbox on n007.cluster.edu,
% 8.63/8.95 Wed Jun 29 14:55:38 2022
% 8.63/8.95 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11545_n007.cluster.edu".
% 8.63/8.95 ============================== end of head ===========================
% 8.63/8.95
% 8.63/8.95 ============================== INPUT =================================
% 8.63/8.95
% 8.63/8.95 % Reading from file /tmp/Prover9_11545_n007.cluster.edu
% 8.63/8.95
% 8.63/8.95 set(prolog_style_variables).
% 8.63/8.95 set(auto2).
% 8.63/8.95 % set(auto2) -> set(auto).
% 8.63/8.95 % set(auto) -> set(auto_inference).
% 8.63/8.95 % set(auto) -> set(auto_setup).
% 8.63/8.95 % set(auto_setup) -> set(predicate_elim).
% 8.63/8.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 8.63/8.95 % set(auto) -> set(auto_limits).
% 8.63/8.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 8.63/8.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 8.63/8.95 % set(auto) -> set(auto_denials).
% 8.63/8.95 % set(auto) -> set(auto_process).
% 8.63/8.95 % set(auto2) -> assign(new_constants, 1).
% 8.63/8.95 % set(auto2) -> assign(fold_denial_max, 3).
% 8.63/8.95 % set(auto2) -> assign(max_weight, "200.000").
% 8.63/8.95 % set(auto2) -> assign(max_hours, 1).
% 8.63/8.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 8.63/8.95 % set(auto2) -> assign(max_seconds, 0).
% 8.63/8.95 % set(auto2) -> assign(max_minutes, 5).
% 8.63/8.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 8.63/8.95 % set(auto2) -> set(sort_initial_sos).
% 8.63/8.95 % set(auto2) -> assign(sos_limit, -1).
% 8.63/8.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 8.63/8.95 % set(auto2) -> assign(max_megs, 400).
% 8.63/8.95 % set(auto2) -> assign(stats, some).
% 8.63/8.95 % set(auto2) -> clear(echo_input).
% 8.63/8.95 % set(auto2) -> set(quiet).
% 8.63/8.95 % set(auto2) -> clear(print_initial_clauses).
% 8.63/8.95 % set(auto2) -> clear(print_given).
% 8.63/8.95 assign(lrs_ticks,-1).
% 8.63/8.95 assign(sos_limit,10000).
% 8.63/8.95 assign(order,kbo).
% 8.63/8.95 set(lex_order_vars).
% 8.63/8.95 clear(print_given).
% 8.63/8.95
% 8.63/8.95 % formulas(sos). % not echoed (10 formulas)
% 8.63/8.95
% 8.63/8.95 ============================== end of input ==========================
% 8.63/8.95
% 8.63/8.95 % From the command line: assign(max_seconds, 300).
% 8.63/8.95
% 8.63/8.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 8.63/8.95
% 8.63/8.95 % Formulas that are not ordinary clauses:
% 8.63/8.95
% 8.63/8.95 ============================== end of process non-clausal formulas ===
% 8.63/8.95
% 8.63/8.95 ============================== PROCESS INITIAL CLAUSES ===============
% 8.63/8.95
% 8.63/8.95 ============================== PREDICATE ELIMINATION =================
% 8.63/8.95
% 8.63/8.95 ============================== end predicate elimination =============
% 8.63/8.95
% 8.63/8.95 Auto_denials:
% 8.63/8.95 % copying label prove_H6 to answer in negative clause
% 8.63/8.95
% 8.63/8.95 Term ordering decisions:
% 8.63/8.95 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 8.63/8.95
% 8.63/8.95 ============================== end of process initial clauses ========
% 8.63/8.95
% 8.63/8.95 ============================== CLAUSES FOR SEARCH ====================
% 8.63/8.95
% 8.63/8.95 ============================== end of clauses for search =============
% 8.63/8.95
% 8.63/8.95 ============================== SEARCH ================================
% 8.63/8.95
% 8.63/8.95 % Starting search at 0.01 seconds.
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=135.000, iters=3386
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=129.000, iters=3365
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=101.000, iters=3400
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=97.000, iters=3408
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=95.000, iters=3388
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=91.000, iters=3349
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=85.000, iters=3474
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=75.000, iters=3383
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=73.000, iters=3353
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=69.000, iters=3337
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=67.000, iters=3357
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=65.000, iters=3352
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=63.000, iters=3358
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=61.000, iters=3343
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=59.000, iters=3353
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=57.000, iters=3381
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=55.000, iters=3389
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=53.000, iters=3351
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=51.000, iters=3340
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=49.000, iters=3345
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=47.000, iters=3340
% 8.63/8.95
% 8.63/8.95 Low Water (keep): wt=45.000, iters=3370
% 8.63/8.95
% 8.63/8.95 ============================== PROOF =================================
% 8.63/8.95 % SZS status Unsatisfiable
% 8.63/8.95 % SZS output start Refutation
% 8.63/8.95
% 8.63/8.95 % Proof 1 at 7.88 (+ 0.06) seconds: prove_H6.
% 8.63/8.95 % Length of proof is 90.
% 8.63/8.95 % Level of proof is 23.
% 8.63/8.95 % Maximum clause weight is 55.000.
% 8.63/8.95 % Given clauses 258.
% 8.63/8.95
% 8.63/8.95 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 8.63/8.95 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 8.63/8.95 3 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 8.63/8.95 4 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 8.63/8.95 5 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 8.63/8.95 6 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 8.63/8.95 7 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 8.63/8.95 8 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(7),rewrite([5(2)]),flip(a)].
% 8.63/8.95 9 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 8.63/8.95 10 join(A,join(B,C)) = join(C,join(A,B)). [copy(9),rewrite([6(2)]),flip(a)].
% 8.63/8.95 11 join(A,meet(B,join(C,meet(B,D)))) = join(A,meet(B,join(C,meet(D,join(A,B))))) # label(equation_H76_dual) # label(axiom). [assumption].
% 8.63/8.95 12 join(A,meet(B,join(C,meet(D,join(A,B))))) = join(A,meet(B,join(C,meet(B,D)))). [copy(11),flip(a)].
% 8.63/8.95 13 meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) # label(prove_H6) # label(negated_conjecture) # answer(prove_H6). [assumption].
% 8.63/8.95 14 meet(a,join(meet(c,join(a,b)),meet(a,join(b,meet(a,c))))) != meet(a,join(b,meet(a,c))) # answer(prove_H6). [copy(13),rewrite([6(21)]),flip(a)].
% 8.63/8.95 15 meet(A,meet(A,B)) = meet(A,B). [para(8(a,1),1(a,1)),rewrite([5(1),5(2),8(2,R),1(1),5(3)])].
% 8.63/8.95 16 meet(A,meet(B,join(A,C))) = meet(A,B). [para(3(a,1),8(a,2,2)),rewrite([5(2),5(4)])].
% 8.63/8.95 17 join(A,join(A,B)) = join(A,B). [para(10(a,1),2(a,1)),rewrite([6(1),6(2),10(2,R),2(1),6(3)])].
% 8.63/8.95 18 join(A,join(B,meet(A,C))) = join(A,B). [para(4(a,1),10(a,2,2)),rewrite([6(2),6(4)])].
% 8.63/8.95 19 join(A,meet(B,join(A,join(B,C)))) = join(A,B). [para(1(a,1),12(a,1,2,2,2)),rewrite([10(2),6(1),10(2,R),6(1),12(9),1(5),6(5),3(6)])].
% 8.63/8.95 20 join(A,meet(B,meet(C,join(A,B)))) = join(A,meet(B,C)). [para(2(a,1),12(a,1,2,2)),rewrite([6(8),12(10),2(7),15(6)])].
% 8.63/8.95 21 join(A,meet(B,join(C,meet(A,B)))) = join(A,meet(B,join(A,C))). [para(3(a,1),12(a,1,2,2,2)),rewrite([6(1),5(4)]),flip(a)].
% 8.63/8.95 22 join(A,meet(meet(A,B),join(C,meet(A,meet(B,D))))) = join(A,meet(meet(A,B),join(C,meet(A,D)))). [para(4(a,1),12(a,1,2,2,2,2)),rewrite([5(2),5(8),8(8),5(7),8(8,R),5(7)]),flip(a)].
% 8.63/8.95 23 join(A,meet(B,join(C,meet(B,C)))) = join(A,meet(B,C)). [para(4(a,1),12(a,1,2,2)),flip(a)].
% 8.63/8.95 24 join(A,meet(B,join(C,meet(D,join(B,A))))) = join(A,meet(B,join(C,meet(B,D)))). [para(12(a,1),6(a,2)),rewrite([6(1),6(5)])].
% 8.63/8.95 29 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(18(a,1),10(a,2,2)),rewrite([6(3),10(3,R),6(2),10(6),6(5),10(6,R),6(5)])].
% 8.63/8.95 30 join(A,meet(join(B,meet(A,C)),join(D,meet(E,join(B,meet(A,C)))))) = join(A,meet(join(B,meet(A,C)),join(D,meet(E,join(A,B))))). [para(18(a,1),12(a,1,2,2,2,2)),rewrite([5(12)]),flip(a)].
% 8.63/8.95 31 join(A,meet(B,join(A,B))) = join(A,B). [para(2(a,1),19(a,1,2,2,2))].
% 8.63/8.95 32 join(A,meet(meet(A,B),join(A,C))) = A. [para(4(a,1),19(a,2)),rewrite([6(3),18(4)])].
% 8.63/8.95 37 join(A,meet(join(A,B),join(A,join(B,C)))) = join(A,B). [para(17(a,1),19(a,2)),rewrite([6(3),10(3),6(2),10(3,R),6(2),17(4)])].
% 8.63/8.95 38 join(A,meet(join(B,meet(A,C)),join(A,join(B,D)))) = join(A,B). [para(18(a,1),19(a,2)),rewrite([6(5),10(5,R),6(4),29(6)])].
% 8.63/8.95 44 join(A,meet(B,meet(join(A,B),join(C,meet(D,join(A,B)))))) = join(A,meet(B,join(C,meet(B,D)))). [para(12(a,1),20(a,2)),rewrite([5(5)])].
% 8.63/8.95 53 join(A,meet(B,meet(join(C,meet(D,join(A,B))),join(A,meet(B,join(C,meet(B,D))))))) = join(A,meet(B,join(C,meet(B,D)))). [para(12(a,1),31(a,1,2,2)),rewrite([5(9),8(9),5(8),8(9,R),5(8),12(15)])].
% 8.63/8.95 54 join(A,meet(join(A,B),join(B,meet(A,C)))) = join(A,B). [para(18(a,1),31(a,1,2,2)),rewrite([5(4),18(8)])].
% 8.63/8.95 60 join(A,meet(B,meet(meet(A,C),join(A,D)))) = A. [para(32(a,1),20(a,1,2,2,2)),rewrite([5(4),8(5),5(4),16(4),15(2),8(2),5(1),8(2,R),5(1),4(3),5(4)]),flip(a)].
% 8.63/8.95 65 meet(A,join(B,meet(A,B))) = meet(A,B). [para(23(a,1),2(a,1)),rewrite([6(5),23(5),2(3)]),flip(a)].
% 8.63/8.95 73 join(A,meet(B,join(meet(A,B),meet(B,C)))) = join(A,meet(B,join(A,meet(B,C)))). [para(12(a,1),21(a,2)),rewrite([6(4),12(6)])].
% 8.63/8.95 84 join(A,meet(join(B,meet(A,B)),join(C,meet(A,B)))) = join(A,meet(join(B,meet(A,B)),join(A,C))). [para(65(a,1),21(a,1,2,2,2))].
% 8.63/8.95 102 join(A,meet(meet(A,B),join(C,meet(A,D)))) = A. [para(5(a,1),22(a,2,2)),rewrite([22(6),8(9),5(8),8(9,R),5(8),4(10)])].
% 8.63/8.95 112 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(32(a,1),102(a,1,2,2)),rewrite([5(3),8(3),5(2),8(3,R),5(2),5(4),15(4)])].
% 8.63/8.95 125 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(37(a,1),102(a,1,2,2)),rewrite([5(3),5(5),8(5,R),1(4)])].
% 8.63/8.95 132 join(join(A,B),meet(C,meet(D,join(A,B)))) = join(A,B). [para(125(a,1),60(a,1,2,2,2)),rewrite([5(3),5(5),8(5,R),1(4)])].
% 8.63/8.95 133 join(A,meet(meet(A,B),join(C,D))) = A. [para(125(a,1),102(a,1,2,2))].
% 8.63/8.95 140 join(join(A,B),meet(C,join(A,C))) = join(A,join(B,C)). [para(19(a,1),24(a,1,2,2)),rewrite([6(2),5(6),3(8),6(6),10(6),6(5),10(6,R),6(5)])].
% 8.63/8.95 351 join(join(A,B),meet(A,C)) = join(A,B). [para(3(a,1),132(a,1,2,2)),rewrite([5(2)])].
% 8.63/8.95 363 join(join(A,B),meet(B,C)) = join(A,B). [para(6(a,1),351(a,1,1)),rewrite([6(4)])].
% 8.63/8.95 383 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(18(a,1),363(a,1,1)),rewrite([5(4),18(8)])].
% 8.63/8.95 403 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(140(a,1),3(a,1,2))].
% 8.63/8.95 486 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(112(a,1),403(a,1,1)),rewrite([6(5),10(6,R),6(5),112(5),112(8)])].
% 8.63/8.95 536 meet(A,meet(meet(A,B),join(C,D))) = meet(meet(A,B),join(C,D)). [para(133(a,1),486(a,1,2)),rewrite([5(4)])].
% 8.63/8.95 542 meet(meet(A,B),join(A,C)) = meet(A,B). [para(351(a,1),486(a,1,2))].
% 8.63/8.95 543 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(486(a,1),140(a,1,2))].
% 8.63/8.95 593 join(A,join(B,meet(C,join(B,meet(A,D))))) = join(A,B). [back_rewrite(383),rewrite([543(5)])].
% 8.63/8.95 627 meet(meet(A,B),join(B,C)) = meet(A,B). [para(5(a,1),542(a,1,1)),rewrite([5(4)])].
% 8.63/8.95 653 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(16(a,1),627(a,1,1)),rewrite([6(4),16(8)])].
% 8.63/8.95 659 meet(meet(A,B),join(C,join(D,meet(A,B)))) = meet(A,B). [para(486(a,1),627(a,1,1)),rewrite([6(4),10(4,R),6(3),486(9)])].
% 8.63/8.95 775 join(A,join(B,meet(C,join(A,meet(B,D))))) = join(A,B). [para(593(a,1),10(a,2)),rewrite([6(4),6(6)])].
% 8.63/8.95 867 meet(meet(A,B),join(C,meet(A,join(B,D)))) = meet(A,B). [para(653(a,1),5(a,2)),rewrite([5(4),5(5),5(6)])].
% 8.63/8.95 987 meet(meet(join(A,B),join(B,meet(A,C))),join(A,join(B,D))) = meet(join(A,B),join(B,meet(A,C))). [para(54(a,1),659(a,1,2,2)),rewrite([10(6),6(5),10(6,R),6(5)])].
% 8.63/8.95 1031 join(A,meet(join(A,join(B,C)),join(B,meet(A,D)))) = join(A,B). [para(5(a,1),38(a,1,2))].
% 8.63/8.95 1116 meet(meet(A,B),join(C,meet(A,join(D,meet(A,B))))) = meet(A,B). [para(15(a,1),867(a,1,1)),rewrite([6(3),15(8)])].
% 8.63/8.95 1773 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(5(a,1),536(a,1,2)),rewrite([8(3),5(2),8(3,R),5(2),15(4)]),flip(a)].
% 8.63/8.95 1785 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(486(a,1),536(a,1,2)),rewrite([15(2),1773(5)]),flip(a)].
% 8.63/8.95 1788 meet(A,meet(B,join(C,meet(B,join(A,D))))) = meet(A,B). [para(653(a,1),536(a,1,2)),rewrite([15(2),1773(6)]),flip(a)].
% 8.63/8.95 1797 meet(A,meet(B,join(C,meet(A,join(B,D))))) = meet(A,B). [para(867(a,1),536(a,1,2)),rewrite([15(2),1773(6)]),flip(a)].
% 8.63/8.95 2060 meet(A,meet(B,join(C,meet(A,join(D,meet(A,B)))))) = meet(A,B). [back_rewrite(1116),rewrite([1773(6)])].
% 8.63/8.95 2086 meet(join(A,B),meet(join(B,meet(A,C)),join(A,join(B,D)))) = meet(join(A,B),join(B,meet(A,C))). [back_rewrite(987),rewrite([1773(7)])].
% 8.63/8.95 2383 meet(join(A,meet(B,C)),join(A,join(B,D))) = meet(join(A,B),join(A,meet(B,C))). [para(38(a,1),1785(a,1,2,2)),rewrite([10(4,R),6(3),6(5),5(6),403(6),5(4),10(8,R),6(7)]),flip(a)].
% 8.63/8.95 2651 join(A,meet(join(B,meet(C,D)),meet(join(C,meet(join(B,join(C,E)),join(A,join(B,meet(C,D))))),join(A,meet(join(B,meet(C,D)),join(C,meet(join(B,C),join(B,meet(C,D))))))))) = join(A,meet(join(B,C),join(B,meet(C,D)))). [para(38(a,1),53(a,2,2,2)),rewrite([10(4,R),6(3),10(15,R),6(14),2383(16),6(24),5(25)])].
% 8.63/8.95 2981 meet(join(A,join(B,C)),join(B,meet(A,D))) = meet(join(A,B),join(B,meet(A,D))). [para(1031(a,1),1785(a,1,2,2)),rewrite([5(6),8(7,R),2086(7)]),flip(a)].
% 8.63/8.95 3532 meet(join(A,meet(B,C)),join(B,meet(join(A,B),join(A,meet(B,C))))) = join(A,meet(B,C)). [para(30(a,1),2060(a,1,2,2)),rewrite([6(9),5(10),30(13),6(8),1(9),10(8),6(7),10(8,R),6(7),2383(9),15(11),1(13)])].
% 8.63/8.96 3558 join(A,meet(join(B,C),join(B,meet(C,D)))) = join(A,join(B,meet(C,D))). [back_rewrite(2651),rewrite([3532(17),5(13),44(15),2383(7),3532(8)]),flip(a)].
% 8.63/8.96 3561 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [back_rewrite(3532),rewrite([3558(7),18(5),6(3),5(4)])].
% 8.63/8.96 3566 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(6(a,1),3561(a,1,1))].
% 8.63/8.96 3571 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(17(a,1),3561(a,1,1)),rewrite([5(3),5(7)])].
% 8.63/8.96 3626 meet(join(A,join(B,C)),join(B,meet(A,D))) = join(B,meet(A,D)). [back_rewrite(2981),rewrite([3566(9)])].
% 8.63/8.96 3663 meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)). [para(4(a,1),3566(a,1,1))].
% 8.63/8.96 3716 join(A,meet(B,join(A,meet(B,C)))) = join(A,join(meet(B,A),meet(B,C))). [para(73(a,1),3566(a,1,2)),rewrite([3566(6),5(5),3663(8)])].
% 8.63/8.96 4014 meet(A,meet(B,join(C,meet(A,join(C,B))))) = meet(A,B). [para(84(a,1),1797(a,1,2,2)),rewrite([5(1),4(2),5(1),4(2),5(6),4(7)])].
% 8.63/8.96 4050 meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)). [para(17(a,1),4014(a,1,2,2,2,2)),rewrite([3571(5)])].
% 8.63/8.96 4090 meet(A,join(B,join(meet(A,B),meet(A,C)))) = meet(A,join(B,meet(C,join(A,B)))). [para(12(a,1),4050(a,1,2)),rewrite([3716(4),6(6)])].
% 8.63/8.96 5044 join(A,meet(join(B,C),join(A,B))) = join(A,B). [para(3626(a,1),44(a,1,2,2)),rewrite([3(4),6(2),5(7),3571(9),18(8)])].
% 8.63/8.96 5077 join(A,meet(join(B,C),join(A,C))) = join(A,C). [para(6(a,1),5044(a,1,2,1))].
% 8.63/8.96 6349 meet(A,join(meet(B,C),meet(B,join(A,D)))) = meet(A,B). [para(3663(a,1),1788(a,1,2))].
% 8.63/8.96 6391 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(2(a,1),6349(a,1,2,2,2)),rewrite([5(2)])].
% 8.63/8.96 6669 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(6(a,1),6391(a,1,2))].
% 8.63/8.96 6681 join(A,join(meet(B,A),meet(B,C))) = join(A,meet(B,C)). [para(6391(a,1),775(a,1,2,2)),rewrite([5(2),10(4,R),6(6)])].
% 8.63/8.96 6724 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [back_rewrite(4090),rewrite([6681(4)]),flip(a)].
% 8.63/8.96 6885 meet(A,join(B,meet(A,join(C,B)))) = meet(A,join(C,B)). [para(5077(a,1),6669(a,1,2)),rewrite([6(3)])].
% 8.63/8.96 12212 meet(A,join(meet(B,join(A,C)),meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(A,B))). [para(6724(a,1),6885(a,1,2,2)),rewrite([6724(11)])].
% 8.63/8.96 12213 $F # answer(prove_H6). [resolve(12212,a,14,a)].
% 8.63/8.96
% 8.63/8.96 % SZS output end Refutation
% 8.63/8.96 ============================== end of proof ==========================
% 8.63/8.96
% 8.63/8.96 ============================== STATISTICS ============================
% 8.63/8.96
% 8.63/8.96 Given=258. Generated=99067. Kept=12208. proofs=1.
% 8.63/8.96 Usable=185. Sos=8092. Demods=8249. Limbo=93, Disabled=3847. Hints=0.
% 8.63/8.96 Megabytes=22.98.
% 8.63/8.96 User_CPU=7.88, System_CPU=0.06, Wall_clock=8.
% 8.63/8.96
% 8.63/8.96 ============================== end of statistics =====================
% 8.63/8.96
% 8.63/8.96 ============================== end of search =========================
% 8.63/8.96
% 8.63/8.96 THEOREM PROVED
% 8.63/8.96 % SZS status Unsatisfiable
% 8.63/8.96
% 8.63/8.96 Exiting with 1 proof.
% 8.63/8.96
% 8.63/8.96 Process 11698 exit (max_proofs) Wed Jun 29 14:55:46 2022
% 8.63/8.96 Prover9 interrupted
%------------------------------------------------------------------------------