TSTP Solution File: LAT154-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT154-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 06:25:50 EDT 2022
% Result : Unsatisfiable 6.41s 6.69s
% Output : Refutation 6.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT154-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 29 03:05:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 6.41/6.69 ============================== Prover9 ===============================
% 6.41/6.69 Prover9 (32) version 2009-11A, November 2009.
% 6.41/6.69 Process 23856 was started by sandbox on n009.cluster.edu,
% 6.41/6.69 Wed Jun 29 03:05:38 2022
% 6.41/6.69 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23703_n009.cluster.edu".
% 6.41/6.69 ============================== end of head ===========================
% 6.41/6.69
% 6.41/6.69 ============================== INPUT =================================
% 6.41/6.69
% 6.41/6.69 % Reading from file /tmp/Prover9_23703_n009.cluster.edu
% 6.41/6.69
% 6.41/6.69 set(prolog_style_variables).
% 6.41/6.69 set(auto2).
% 6.41/6.69 % set(auto2) -> set(auto).
% 6.41/6.69 % set(auto) -> set(auto_inference).
% 6.41/6.69 % set(auto) -> set(auto_setup).
% 6.41/6.69 % set(auto_setup) -> set(predicate_elim).
% 6.41/6.69 % set(auto_setup) -> assign(eq_defs, unfold).
% 6.41/6.69 % set(auto) -> set(auto_limits).
% 6.41/6.69 % set(auto_limits) -> assign(max_weight, "100.000").
% 6.41/6.69 % set(auto_limits) -> assign(sos_limit, 20000).
% 6.41/6.69 % set(auto) -> set(auto_denials).
% 6.41/6.69 % set(auto) -> set(auto_process).
% 6.41/6.69 % set(auto2) -> assign(new_constants, 1).
% 6.41/6.69 % set(auto2) -> assign(fold_denial_max, 3).
% 6.41/6.69 % set(auto2) -> assign(max_weight, "200.000").
% 6.41/6.69 % set(auto2) -> assign(max_hours, 1).
% 6.41/6.69 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.41/6.69 % set(auto2) -> assign(max_seconds, 0).
% 6.41/6.69 % set(auto2) -> assign(max_minutes, 5).
% 6.41/6.69 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.41/6.69 % set(auto2) -> set(sort_initial_sos).
% 6.41/6.69 % set(auto2) -> assign(sos_limit, -1).
% 6.41/6.69 % set(auto2) -> assign(lrs_ticks, 3000).
% 6.41/6.69 % set(auto2) -> assign(max_megs, 400).
% 6.41/6.69 % set(auto2) -> assign(stats, some).
% 6.41/6.69 % set(auto2) -> clear(echo_input).
% 6.41/6.69 % set(auto2) -> set(quiet).
% 6.41/6.69 % set(auto2) -> clear(print_initial_clauses).
% 6.41/6.69 % set(auto2) -> clear(print_given).
% 6.41/6.69 assign(lrs_ticks,-1).
% 6.41/6.69 assign(sos_limit,10000).
% 6.41/6.69 assign(order,kbo).
% 6.41/6.69 set(lex_order_vars).
% 6.41/6.69 clear(print_given).
% 6.41/6.69
% 6.41/6.69 % formulas(sos). % not echoed (10 formulas)
% 6.41/6.69
% 6.41/6.69 ============================== end of input ==========================
% 6.41/6.69
% 6.41/6.69 % From the command line: assign(max_seconds, 300).
% 6.41/6.69
% 6.41/6.69 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.41/6.69
% 6.41/6.69 % Formulas that are not ordinary clauses:
% 6.41/6.69
% 6.41/6.69 ============================== end of process non-clausal formulas ===
% 6.41/6.69
% 6.41/6.69 ============================== PROCESS INITIAL CLAUSES ===============
% 6.41/6.69
% 6.41/6.69 ============================== PREDICATE ELIMINATION =================
% 6.41/6.69
% 6.41/6.69 ============================== end predicate elimination =============
% 6.41/6.69
% 6.41/6.69 Auto_denials:
% 6.41/6.69 % copying label prove_H6 to answer in negative clause
% 6.41/6.69
% 6.41/6.69 Term ordering decisions:
% 6.41/6.69 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 6.41/6.69
% 6.41/6.69 ============================== end of process initial clauses ========
% 6.41/6.69
% 6.41/6.69 ============================== CLAUSES FOR SEARCH ====================
% 6.41/6.69
% 6.41/6.69 ============================== end of clauses for search =============
% 6.41/6.69
% 6.41/6.69 ============================== SEARCH ================================
% 6.41/6.69
% 6.41/6.69 % Starting search at 0.01 seconds.
% 6.41/6.69
% 6.41/6.69 Low Water (keep): wt=113.000, iters=3351
% 6.41/6.69
% 6.41/6.69 Low Water (keep): wt=109.000, iters=3338
% 6.41/6.69
% 6.41/6.69 Low Water (keep): wt=103.000, iters=3377
% 6.41/6.69
% 6.41/6.69 Low Water (keep): wt=95.000, iters=3378
% 6.41/6.69
% 6.41/6.69 Low Water (keep): wt=91.000, iters=3353
% 6.41/6.69
% 6.41/6.69 ============================== PROOF =================================
% 6.41/6.69 % SZS status Unsatisfiable
% 6.41/6.69 % SZS output start Refutation
% 6.41/6.69
% 6.41/6.69 % Proof 1 at 5.66 (+ 0.05) seconds: prove_H6.
% 6.41/6.69 % Length of proof is 98.
% 6.41/6.69 % Level of proof is 22.
% 6.41/6.69 % Maximum clause weight is 43.000.
% 6.41/6.69 % Given clauses 232.
% 6.41/6.69
% 6.41/6.69 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 6.41/6.69 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 6.41/6.69 3 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 6.41/6.69 4 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 6.41/6.69 5 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 6.41/6.69 6 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 6.41/6.69 7 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 6.41/6.69 8 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(7),rewrite([5(2)]),flip(a)].
% 6.41/6.69 9 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 6.41/6.69 10 join(A,join(B,C)) = join(C,join(A,B)). [copy(9),rewrite([6(2)]),flip(a)].
% 6.41/6.69 11 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(B,join(D,meet(A,C)))))) # label(equation_H42) # label(axiom). [assumption].
% 6.41/6.69 12 meet(A,join(B,meet(C,join(B,join(D,meet(A,C)))))) = meet(A,join(B,meet(C,join(A,D)))). [copy(11),flip(a)].
% 6.41/6.69 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].
% 6.41/6.69 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)].
% 6.41/6.69 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)])].
% 6.41/6.69 16 meet(A,meet(B,join(A,C))) = meet(A,B). [para(3(a,1),8(a,2,2)),rewrite([5(2),5(4)])].
% 6.41/6.69 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)])].
% 6.41/6.69 18 join(A,join(B,meet(A,C))) = join(A,B). [para(4(a,1),10(a,2,2)),rewrite([6(2),6(4)])].
% 6.41/6.69 20 meet(A,join(B,meet(C,join(B,meet(A,C))))) = meet(A,join(B,meet(A,C))). [para(2(a,1),12(a,1,2,2,2,2)),rewrite([4(7),5(6)])].
% 6.41/6.69 21 meet(A,join(join(B,meet(A,C)),meet(C,join(B,meet(A,C))))) = meet(A,join(join(B,meet(A,C)),meet(C,join(A,B)))). [para(2(a,1),12(a,1,2,2,2))].
% 6.41/6.69 22 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(2(a,1),12(a,2,2,2,2)),rewrite([4(2),6(1),5(5)])].
% 6.41/6.69 24 meet(A,join(B,meet(join(A,C),join(A,join(B,D))))) = meet(A,join(B,meet(join(A,C),join(A,D)))). [para(3(a,1),12(a,1,2,2,2,2,2)),rewrite([6(2),10(3,R),6(2)])].
% 6.41/6.69 25 meet(A,join(B,meet(C,join(B,join(D,meet(C,A)))))) = meet(A,join(B,meet(C,join(D,A)))). [para(12(a,1),5(a,2)),rewrite([5(1),5(6),6(7)])].
% 6.41/6.69 26 meet(A,meet(B,join(C,meet(D,join(C,join(E,meet(A,D))))))) = meet(A,meet(B,join(C,meet(D,join(A,E))))). [para(12(a,1),8(a,2,2)),rewrite([5(6),8(12,R),5(11)])].
% 6.41/6.69 28 meet(A,join(B,meet(C,join(B,join(meet(A,C),meet(D,join(A,join(E,meet(C,D))))))))) = meet(A,join(B,meet(C,join(A,meet(D,join(C,E)))))). [para(12(a,1),12(a,2,2,2)),rewrite([6(6)])].
% 6.41/6.69 30 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(16(a,1),8(a,2,2)),rewrite([5(3),8(3,R),5(2),8(6),5(5),8(6,R),5(5)])].
% 6.41/6.69 32 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)])].
% 6.41/6.69 33 meet(A,meet(B,meet(meet(A,B),join(C,meet(A,B))))) = meet(A,B). [para(1(a,1),30(a,2)),rewrite([6(3),8(6,R),5(5),8(5,R),5(4)])].
% 6.41/6.69 34 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(30(a,1),8(a,2,2)),rewrite([5(4),8(4,R),5(3),8(3,R),5(2),8(8,R),5(7),8(7),5(6),8(7,R),5(6)])].
% 6.41/6.69 36 meet(A,join(B,meet(A,B))) = meet(A,B). [para(3(a,1),20(a,1,2,2)),rewrite([2(1)]),flip(a)].
% 6.41/6.69 42 meet(A,join(B,meet(join(A,B),join(A,C)))) = A. [para(12(a,1),20(a,2)),rewrite([1(1),6(1),10(2,R),6(1),1(3),6(3),10(4,R),6(3),3(5),6(3),5(4),24(6),3(7),6(6),3(7)])].
% 6.41/6.69 47 meet(A,meet(B,join(C,meet(A,C)))) = meet(A,meet(C,B)). [para(36(a,1),8(a,2,2)),rewrite([5(3),8(6),5(5),8(6,R),5(5)])].
% 6.41/6.69 50 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(16(a,1),36(a,1,2,2)),rewrite([6(4),16(8)])].
% 6.41/6.69 54 meet(A,join(B,meet(join(B,A),join(A,C)))) = A. [para(42(a,1),5(a,2)),rewrite([6(1),5(5)])].
% 6.41/6.69 61 meet(join(A,meet(B,C)),join(B,meet(join(A,B),join(A,join(D,meet(B,C)))))) = join(A,meet(B,C)). [para(18(a,1),54(a,1,2,2,1)),rewrite([6(3),6(6),10(6,R),6(5)])].
% 6.41/6.69 62 join(A,join(B,join(join(A,B),meet(C,join(A,B))))) = join(A,B). [para(2(a,1),32(a,2)),rewrite([5(3),10(6,R),6(5),10(5,R),6(4)])].
% 6.41/6.69 63 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(32(a,1),10(a,2,2)),rewrite([6(4),10(4,R),6(3),10(3,R),6(2),10(8,R),6(7),10(7),6(6),10(7,R),6(6)])].
% 6.41/6.69 97 meet(A,join(meet(A,B),meet(B,join(C,meet(A,B))))) = meet(A,B). [para(50(a,1),12(a,2)),rewrite([10(5,R),2(4)])].
% 6.41/6.69 110 meet(A,join(B,meet(C,join(B,A)))) = meet(A,join(B,meet(C,A))). [para(22(a,1),5(a,2)),rewrite([6(1),5(4),5(5)])].
% 6.41/6.69 123 meet(A,join(join(meet(A,B),meet(C,join(A,B))),meet(B,join(meet(A,B),meet(C,join(A,B)))))) = meet(A,join(meet(A,B),join(meet(C,join(A,B)),meet(B,join(A,meet(C,B)))))). [para(22(a,1),21(a,2,2,2)),rewrite([6(1),6(4),6(5),6(8),6(12),6(15),5(16),6(19),10(19),6(18),10(19,R),6(18)])].
% 6.41/6.69 144 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(33(a,1),8(a,1)),rewrite([5(7),15(7)]),flip(a)].
% 6.41/6.69 191 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(62(a,1),10(a,1)),rewrite([6(7),17(7)]),flip(a)].
% 6.41/6.69 194 join(A,join(B,meet(join(A,B),join(B,C)))) = join(A,meet(join(A,B),join(B,C))). [para(42(a,1),62(a,1,2,2,2)),rewrite([6(1),6(4),6(8),10(8,R),6(7),10(9,R),6(8),10(8,R),2(7),17(6),6(6)])].
% 6.41/6.69 196 meet(A,join(join(A,B),meet(A,C))) = A. [para(62(a,1),22(a,1,2,2,2)),rewrite([191(4),10(2,R),2(1),191(4),3(2),191(4),10(2,R),2(1)]),flip(a)].
% 6.41/6.69 200 meet(A,join(meet(A,B),join(meet(C,join(A,B)),meet(B,join(A,meet(B,C)))))) = meet(A,join(meet(A,B),meet(C,join(A,B)))). [back_rewrite(123),rewrite([191(10),5(9)]),flip(a)].
% 6.41/6.69 230 meet(join(A,B),join(C,meet(join(A,B),join(A,join(B,C))))) = join(A,B). [para(191(a,1),42(a,1,2,2,2)),rewrite([6(3),10(3),6(2),10(3,R),6(2),5(5)])].
% 6.41/6.69 239 join(join(A,B),meet(A,C)) = join(A,B). [para(196(a,1),191(a,1,2)),rewrite([6(4),18(4),17(2)]),flip(a)].
% 6.41/6.69 240 join(join(A,B),meet(B,C)) = join(A,B). [para(6(a,1),239(a,1,1)),rewrite([6(4)])].
% 6.41/6.69 247 meet(meet(A,B),join(A,C)) = meet(A,B). [para(239(a,1),54(a,1,2,2,1)),rewrite([6(5),4(7)])].
% 6.41/6.69 255 join(join(A,B),join(meet(B,C),meet(D,join(A,B)))) = join(A,B). [para(240(a,1),18(a,2)),rewrite([5(4)])].
% 6.41/6.69 256 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(18(a,1),240(a,1,1)),rewrite([5(4),18(8)])].
% 6.41/6.69 289 meet(join(A,B),join(C,meet(D,join(A,join(B,C))))) = meet(join(A,B),join(C,meet(D,join(A,B)))). [para(191(a,1),25(a,1,2,2,2,2)),rewrite([10(3),6(2),10(3,R),6(2),2(10)])].
% 6.41/6.69 293 meet(join(A,B),join(A,join(B,C))) = join(A,B). [back_rewrite(230),rewrite([289(7),1(4),10(3),6(2),10(3,R),6(2)])].
% 6.41/6.69 294 meet(meet(A,B),join(B,C)) = meet(A,B). [para(5(a,1),247(a,1,1)),rewrite([5(4)])].
% 6.41/6.69 298 meet(A,join(B,meet(meet(B,C),join(A,D)))) = meet(A,B). [para(247(a,1),12(a,1,2,2)),rewrite([4(2)]),flip(a)].
% 6.41/6.69 299 meet(meet(A,B),meet(join(A,C),join(D,meet(A,B)))) = meet(A,B). [para(247(a,1),16(a,2)),rewrite([6(4)])].
% 6.41/6.69 300 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(247(a,1),20(a,1,2,2)),rewrite([4(2)]),flip(a)].
% 6.41/6.69 304 meet(meet(A,meet(B,C)),join(D,meet(A,C))) = meet(A,meet(B,C)). [para(8(a,1),294(a,1,1)),rewrite([5(3),6(4),5(6),8(7,R),5(6)])].
% 6.41/6.69 326 meet(A,join(B,meet(join(B,C),join(A,C)))) = meet(A,join(B,C)). [para(293(a,1),12(a,1,2,2)),rewrite([17(2)]),flip(a)].
% 6.41/6.69 355 meet(meet(A,B),join(join(B,C),meet(A,meet(B,D)))) = meet(A,B). [para(294(a,1),300(a,2)),rewrite([5(5),8(6,R),8(5),5(4),16(5),5(3),8(4),5(3),8(4,R),5(3)])].
% 6.41/6.69 520 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(4(a,1),256(a,1,1)),rewrite([4(7)])].
% 6.41/6.69 521 join(join(A,B),meet(C,join(A,meet(B,D)))) = join(A,B). [para(256(a,1),6(a,2)),rewrite([6(4),6(5),6(6)])].
% 6.41/6.69 1026 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(191(a,1),34(a,1,2,2,2,2)),rewrite([8(6,R),5(5),8(5,R),5(4),8(4,R),1(3),8(8,R)]),flip(a)].
% 6.41/6.69 1109 join(join(A,B),meet(C,join(A,meet(D,join(A,B))))) = join(A,B). [para(17(a,1),521(a,1,1)),rewrite([5(3),17(8)])].
% 6.41/6.69 1411 meet(join(A,B),join(C,meet(join(A,C),join(A,B)))) = meet(join(A,B),join(A,C)). [para(293(a,1),110(a,1,2,2)),rewrite([6(2),10(3,R),2(2),6(5)]),flip(a)].
% 6.41/6.69 1723 join(join(A,B),join(meet(B,C),meet(A,D))) = join(A,B). [para(247(a,1),255(a,1,2,2))].
% 6.41/6.69 1864 join(join(A,B),meet(C,join(meet(B,D),meet(A,E)))) = join(A,B). [para(1723(a,1),240(a,1,1)),rewrite([5(5),1723(11)])].
% 6.41/6.69 1920 meet(A,meet(join(A,B),join(C,meet(A,join(join(A,B),meet(D,join(A,E))))))) = A. [para(28(a,1),299(a,1,2)),rewrite([5(2),3(2),10(4,R),10(3),6(2),4(2),6(1),10(2),6(1),10(2,R),6(1),10(5,R),6(4),3(6),5(11),3(11),10(13,R),10(12),6(11),4(11),6(10),10(11),6(10),10(11,R),6(10),10(14,R),6(13),3(15)])].
% 6.41/6.69 2120 meet(A,meet(B,meet(C,join(D,meet(A,B))))) = meet(A,meet(B,C)). [para(304(a,1),5(a,2)),rewrite([5(3),8(5,R),1026(5),5(6)])].
% 6.41/6.69 2933 meet(join(A,B),join(C,meet(A,C))) = meet(C,join(A,B)). [para(355(a,1),298(a,1,2,2)),rewrite([5(2),5(6)])].
% 6.41/6.69 2974 meet(join(A,B),join(C,meet(B,C))) = meet(C,join(A,B)). [para(6(a,1),2933(a,1,1)),rewrite([6(5)])].
% 6.41/6.69 2995 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(2933(a,1),26(a,2,2)),rewrite([10(6,R),10(5),6(4),4(4),6(3),10(4,R),2(3),191(5),16(4)]),flip(a)].
% 6.41/6.69 3126 meet(A,join(B,meet(A,join(join(A,C),meet(D,join(A,E)))))) = A. [back_rewrite(1920),rewrite([2995(9)])].
% 6.41/6.69 3139 meet(A,join(B,meet(A,meet(C,B)))) = meet(A,B). [para(4(a,1),2974(a,2,2)),rewrite([4(2),5(2),8(2),5(1),8(2,R),5(1),5(5)])].
% 6.41/6.69 3144 meet(meet(A,B),join(C,A)) = meet(A,meet(B,join(C,A))). [para(15(a,1),2974(a,1,2,2)),rewrite([2(4),8(3),5(2),8(3,R),5(2)]),flip(a)].
% 6.41/6.69 3153 meet(join(A,B),join(meet(B,meet(C,D)),meet(C,join(D,meet(B,D))))) = meet(meet(C,join(D,meet(B,D))),join(A,B)). [para(47(a,1),2974(a,1,2,2)),rewrite([5(5),6(7)])].
% 6.41/6.69 3508 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(97(a,1),3144(a,2,2)),rewrite([5(1),5(4),8(4,R),5(3),5(5),5(6),304(10),5(5),5(8),5(9),8(9,R),5(8),144(8),15(6)])].
% 6.41/6.69 4763 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(2(a,1),61(a,1,2,2,2,2)),rewrite([1411(8),5(4)])].
% 6.41/6.69 4844 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(6(a,1),4763(a,1,1))].
% 6.41/6.69 4913 meet(A,join(B,A)) = A. [para(520(a,1),4844(a,1,2)),rewrite([5(2),520(7)])].
% 6.41/6.69 4989 join(A,meet(B,A)) = A. [para(4913(a,1),2933(a,2)),rewrite([4844(4)])].
% 6.41/6.69 5011 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [back_rewrite(3153),rewrite([4989(5),6(5),4989(5),8(3),5(2),8(3,R),5(2),4989(5)]),flip(a)].
% 6.41/6.69 6114 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(16(a,1),4989(a,1,2)),rewrite([5(3),6(4)])].
% 6.41/6.69 6124 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(3508(a,1),4989(a,1,2)),rewrite([5(1),5(4),6(5),5(6)])].
% 6.41/6.69 6214 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(299(a,1),63(a,1,2,2,2,2)),rewrite([10(6,R),6(5),10(5,R),6(4),10(4,R),2(3),10(8,R)]),flip(a)].
% 6.41/6.69 6557 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(5(a,1),6114(a,1,1))].
% 6.41/6.69 7546 meet(A,meet(join(B,C),join(C,A))) = meet(A,join(B,C)). [para(326(a,1),2120(a,1,2,2)),rewrite([6(2),8(5,R),8(6,R),5(5),15(5),6(6),5(7),4913(7),5(6)])].
% 6.41/6.69 7590 meet(A,meet(B,join(C,A))) = meet(A,B). [para(3139(a,1),7546(a,1,2)),rewrite([5(2),8(3),5(2),4913(2),5(1),5(3),4913(3),5(2),15(2),5(3),8(4),5(3),4913(3),5(2),5011(4)]),flip(a)].
% 6.41/6.69 9284 join(join(A,B),meet(C,join(A,D))) = join(A,join(B,meet(C,join(A,D)))). [para(3126(a,1),1109(a,1,2)),rewrite([6(5),6214(5),17(5)]),flip(a)].
% 6.41/6.69 9291 join(A,join(B,meet(C,join(A,meet(B,D))))) = join(A,B). [para(3126(a,1),1864(a,1,2,2,2)),rewrite([6(3),9284(5)])].
% 6.41/6.69 9671 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [para(1(a,1),9291(a,1,2,2,2,2))].
% 6.41/6.69 10430 join(A,meet(join(A,B),join(B,C))) = join(A,B). [para(5(a,1),194(a,1,2,2)),rewrite([9671(5)]),flip(a)].
% 6.41/6.69 10431 join(A,meet(join(B,C),join(A,B))) = join(A,B). [para(5(a,1),194(a,2,2)),rewrite([194(5),10430(4)]),flip(a)].
% 6.41/6.69 10572 join(A,meet(join(B,C),join(A,C))) = join(A,C). [para(6(a,1),10431(a,1,2,1))].
% 6.41/6.69 10675 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(15(a,1),200(a,1,2,2,2,2,2)),rewrite([5011(4),7590(4),6124(6),6557(5),16(4),5011(5),7590(5)]),flip(a)].
% 6.41/6.69 11128 meet(A,join(B,meet(A,join(C,B)))) = meet(A,join(C,B)). [para(10572(a,1),10675(a,1,2)),rewrite([6(3)])].
% 6.41/6.69 12307 meet(A,join(meet(B,join(A,C)),meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(A,B))). [para(22(a,1),11128(a,1,2,2)),rewrite([22(11)])].
% 6.41/6.69 12308 $F # answer(prove_H6). [resolve(12307,a,14,a)].
% 6.41/6.69
% 6.41/6.69 % SZS output end Refutation
% 6.41/6.69 ============================== end of proof ==========================
% 6.41/6.69
% 6.41/6.69 ============================== STATISTICS ============================
% 6.41/6.69
% 6.41/6.69 Given=232. Generated=84928. Kept=12303. proofs=1.
% 6.41/6.69 Usable=135. Sos=5576. Demods=5636. Limbo=2, Disabled=6599. Hints=0.
% 6.41/6.69 Megabytes=21.55.
% 6.41/6.69 User_CPU=5.66, System_CPU=0.05, Wall_clock=5.
% 6.41/6.69
% 6.41/6.69 ============================== end of statistics =====================
% 6.41/6.69
% 6.41/6.69 ============================== end of search =========================
% 6.41/6.69
% 6.41/6.69 THEOREM PROVED
% 6.41/6.69 % SZS status Unsatisfiable
% 6.41/6.69
% 6.41/6.69 Exiting with 1 proof.
% 6.41/6.69
% 6.41/6.69 Process 23856 exit (max_proofs) Wed Jun 29 03:05:43 2022
% 6.41/6.69 Prover9 interrupted
%------------------------------------------------------------------------------