TSTP Solution File: LAT166-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT166-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 06:25:53 EDT 2022
% Result : Unsatisfiable 10.86s 11.15s
% Output : Refutation 10.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT166-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Thu Jun 30 04:12:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 10.86/11.15 ============================== Prover9 ===============================
% 10.86/11.15 Prover9 (32) version 2009-11A, November 2009.
% 10.86/11.15 Process 29334 was started by sandbox on n011.cluster.edu,
% 10.86/11.15 Thu Jun 30 04:12:33 2022
% 10.86/11.15 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29166_n011.cluster.edu".
% 10.86/11.15 ============================== end of head ===========================
% 10.86/11.15
% 10.86/11.15 ============================== INPUT =================================
% 10.86/11.15
% 10.86/11.15 % Reading from file /tmp/Prover9_29166_n011.cluster.edu
% 10.86/11.15
% 10.86/11.15 set(prolog_style_variables).
% 10.86/11.15 set(auto2).
% 10.86/11.15 % set(auto2) -> set(auto).
% 10.86/11.15 % set(auto) -> set(auto_inference).
% 10.86/11.15 % set(auto) -> set(auto_setup).
% 10.86/11.15 % set(auto_setup) -> set(predicate_elim).
% 10.86/11.15 % set(auto_setup) -> assign(eq_defs, unfold).
% 10.86/11.15 % set(auto) -> set(auto_limits).
% 10.86/11.15 % set(auto_limits) -> assign(max_weight, "100.000").
% 10.86/11.15 % set(auto_limits) -> assign(sos_limit, 20000).
% 10.86/11.15 % set(auto) -> set(auto_denials).
% 10.86/11.15 % set(auto) -> set(auto_process).
% 10.86/11.15 % set(auto2) -> assign(new_constants, 1).
% 10.86/11.15 % set(auto2) -> assign(fold_denial_max, 3).
% 10.86/11.15 % set(auto2) -> assign(max_weight, "200.000").
% 10.86/11.15 % set(auto2) -> assign(max_hours, 1).
% 10.86/11.15 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 10.86/11.15 % set(auto2) -> assign(max_seconds, 0).
% 10.86/11.15 % set(auto2) -> assign(max_minutes, 5).
% 10.86/11.15 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 10.86/11.15 % set(auto2) -> set(sort_initial_sos).
% 10.86/11.15 % set(auto2) -> assign(sos_limit, -1).
% 10.86/11.15 % set(auto2) -> assign(lrs_ticks, 3000).
% 10.86/11.15 % set(auto2) -> assign(max_megs, 400).
% 10.86/11.15 % set(auto2) -> assign(stats, some).
% 10.86/11.15 % set(auto2) -> clear(echo_input).
% 10.86/11.15 % set(auto2) -> set(quiet).
% 10.86/11.15 % set(auto2) -> clear(print_initial_clauses).
% 10.86/11.15 % set(auto2) -> clear(print_given).
% 10.86/11.15 assign(lrs_ticks,-1).
% 10.86/11.15 assign(sos_limit,10000).
% 10.86/11.15 assign(order,kbo).
% 10.86/11.15 set(lex_order_vars).
% 10.86/11.15 clear(print_given).
% 10.86/11.15
% 10.86/11.15 % formulas(sos). % not echoed (10 formulas)
% 10.86/11.15
% 10.86/11.15 ============================== end of input ==========================
% 10.86/11.15
% 10.86/11.15 % From the command line: assign(max_seconds, 300).
% 10.86/11.15
% 10.86/11.15 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 10.86/11.15
% 10.86/11.15 % Formulas that are not ordinary clauses:
% 10.86/11.15
% 10.86/11.15 ============================== end of process non-clausal formulas ===
% 10.86/11.15
% 10.86/11.15 ============================== PROCESS INITIAL CLAUSES ===============
% 10.86/11.15
% 10.86/11.15 ============================== PREDICATE ELIMINATION =================
% 10.86/11.15
% 10.86/11.15 ============================== end predicate elimination =============
% 10.86/11.15
% 10.86/11.15 Auto_denials:
% 10.86/11.15 % copying label prove_H78 to answer in negative clause
% 10.86/11.15
% 10.86/11.15 Term ordering decisions:
% 10.86/11.15 Function symbol KB weights: a=1. b=1. c=1. d=1. meet=1. join=1.
% 10.86/11.15
% 10.86/11.15 ============================== end of process initial clauses ========
% 10.86/11.15
% 10.86/11.15 ============================== CLAUSES FOR SEARCH ====================
% 10.86/11.15
% 10.86/11.15 ============================== end of clauses for search =============
% 10.86/11.15
% 10.86/11.15 ============================== SEARCH ================================
% 10.86/11.15
% 10.86/11.15 % Starting search at 0.01 seconds.
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=139.000, iters=3339
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=93.000, iters=3360
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=91.000, iters=3352
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=89.000, iters=3339
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=87.000, iters=3381
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=83.000, iters=3355
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=81.000, iters=3363
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=79.000, iters=3349
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=69.000, iters=3338
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=65.000, iters=3367
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=63.000, iters=3354
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=61.000, iters=3351
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=59.000, iters=3336
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=57.000, iters=3333
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=55.000, iters=3388
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=53.000, iters=3349
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=51.000, iters=3378
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=49.000, iters=3343
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=47.000, iters=3358
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=45.000, iters=3337
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=43.000, iters=3354
% 10.86/11.15
% 10.86/11.15 Low Water (keep): wt=41.000, iters=3371
% 10.86/11.15
% 10.86/11.15 ============================== PROOF =================================
% 10.86/11.15 % SZS status Unsatisfiable
% 10.86/11.15 % SZS output start Refutation
% 10.86/11.15
% 10.86/11.15 % Proof 1 at 10.06 (+ 0.09) seconds: prove_H78.
% 10.86/11.15 % Length of proof is 116.
% 10.86/11.15 % Level of proof is 36.
% 10.86/11.15 % Maximum clause weight is 43.000.
% 10.86/11.15 % Given clauses 298.
% 10.86/11.15
% 10.86/11.15 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 10.86/11.15 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 10.86/11.15 3 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 10.86/11.15 4 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 10.86/11.15 5 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 10.86/11.15 6 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 10.86/11.15 7 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 10.86/11.15 8 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(7),rewrite([5(2)]),flip(a)].
% 10.86/11.15 9 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 10.86/11.15 10 join(A,join(B,C)) = join(C,join(A,B)). [copy(9),rewrite([6(2)]),flip(a)].
% 10.86/11.15 11 meet(A,join(B,meet(C,join(B,D)))) = meet(A,join(B,meet(C,join(D,meet(A,meet(B,C)))))) # label(equation_H77) # label(axiom). [assumption].
% 10.86/11.15 12 meet(A,join(B,meet(C,join(D,meet(A,meet(B,C)))))) = meet(A,join(B,meet(C,join(B,D)))). [copy(11),flip(a)].
% 10.86/11.15 13 meet(a,join(b,meet(c,join(b,d)))) != meet(a,join(b,meet(c,join(d,meet(b,join(a,d)))))) # label(prove_H78) # label(negated_conjecture) # answer(prove_H78). [assumption].
% 10.86/11.15 14 meet(a,join(b,meet(c,join(d,meet(b,join(a,d)))))) != meet(a,join(b,meet(c,join(b,d)))) # answer(prove_H78). [copy(13),flip(a)].
% 10.86/11.15 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)])].
% 10.86/11.15 16 meet(A,meet(B,join(A,C))) = meet(A,B). [para(3(a,1),8(a,2,2)),rewrite([5(2),5(4)])].
% 10.86/11.15 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)])].
% 10.86/11.15 18 join(A,join(B,meet(A,C))) = join(A,B). [para(4(a,1),10(a,2,2)),rewrite([6(2),6(4)])].
% 10.86/11.15 19 meet(meet(A,B),join(A,meet(B,join(C,meet(A,B))))) = meet(meet(A,B),join(A,meet(B,join(A,C)))). [para(1(a,1),12(a,1,2,2,2,2))].
% 10.86/11.15 21 meet(join(A,meet(B,join(A,C))),join(A,meet(B,join(C,meet(meet(A,B),join(A,meet(B,join(A,C)))))))) = join(A,meet(B,join(A,C))). [para(1(a,1),12(a,2)),rewrite([5(8)])].
% 10.86/11.15 22 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(2(a,1),12(a,1,2,2,2)),rewrite([8(3,R),5(2),8(2,R),1(1),12(10),2(5),5(5),4(6)])].
% 10.86/11.15 24 meet(A,join(B,meet(C,join(B,C)))) = meet(A,join(B,C)). [para(3(a,1),12(a,1,2,2)),flip(a)].
% 10.86/11.15 25 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(4(a,1),12(a,1,2,2,2)),rewrite([5(1),6(4)]),flip(a)].
% 10.86/11.15 26 meet(A,join(B,meet(C,join(D,meet(B,meet(C,A)))))) = meet(A,join(B,meet(C,join(B,D)))). [para(12(a,1),5(a,2)),rewrite([8(2),5(1),8(2,R),5(1),5(6)])].
% 10.86/11.15 27 meet(A,join(B,meet(C,join(D,meet(A,meet(C,B)))))) = meet(A,join(B,meet(C,join(D,B)))). [para(6(a,1),12(a,1,2)),rewrite([5(1),6(5),6(7)])].
% 10.86/11.15 32 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)])].
% 10.86/11.15 35 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)])].
% 10.86/11.15 36 meet(A,join(B,meet(A,B))) = meet(A,B). [para(1(a,1),22(a,1,2,2,2))].
% 10.86/11.15 37 meet(A,join(join(A,B),meet(A,C))) = A. [para(3(a,1),22(a,2)),rewrite([5(3),16(4)])].
% 10.86/11.15 39 meet(A,join(meet(B,C),meet(A,meet(B,meet(C,D))))) = meet(A,meet(B,C)). [para(8(a,1),22(a,2)),rewrite([5(3),8(3),5(2),8(3,R),5(2),8(8),5(7),8(8,R),5(7)])].
% 10.86/11.15 43 meet(A,join(meet(B,join(A,C)),meet(A,meet(B,D)))) = meet(A,B). [para(16(a,1),22(a,2)),rewrite([5(5),8(5,R),5(4),32(6)])].
% 10.86/11.15 59 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)])].
% 10.86/11.15 67 meet(A,meet(B,join(join(A,C),meet(A,D)))) = meet(A,B). [para(37(a,1),8(a,2,2)),rewrite([5(4),5(6)])].
% 10.86/11.15 70 meet(A,join(join(join(A,B),meet(A,C)),meet(A,D))) = A. [para(37(a,1),22(a,2)),rewrite([5(7),67(8)])].
% 10.86/11.15 71 meet(meet(A,B),join(join(C,meet(A,B)),meet(meet(A,B),join(A,meet(B,join(A,D)))))) = meet(A,B). [para(19(a,1),37(a,1,2,2)),rewrite([6(3)])].
% 10.86/11.15 72 join(A,meet(B,join(A,B))) = join(A,B). [para(24(a,1),1(a,1)),rewrite([5(5),24(5),1(3)]),flip(a)].
% 10.86/11.15 106 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(35(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)])].
% 10.86/11.15 120 meet(A,join(B,meet(join(C,meet(A,C)),join(D,meet(A,meet(B,C)))))) = meet(A,join(B,meet(join(C,meet(A,C)),join(B,D)))). [para(59(a,1),12(a,1,2,2,2,2)),rewrite([5(3)])].
% 10.86/11.15 210 meet(A,join(join(A,B),meet(C,join(A,B)))) = A. [para(17(a,1),25(a,1,2,2,2)),rewrite([37(9)])].
% 10.86/11.15 220 meet(A,join(join(A,meet(B,join(A,C))),meet(B,join(C,meet(meet(A,B),join(A,meet(B,join(A,C)))))))) = A. [para(21(a,1),25(a,1,2,2)),rewrite([6(11),3(23),6(20),3(21)])].
% 10.86/11.15 237 join(join(A,B),meet(A,C)) = join(A,B). [para(70(a,1),210(a,1,2,2)),rewrite([6(9),18(9),18(7),17(5),5(5),3(5)]),flip(a)].
% 10.86/11.15 240 join(join(A,B),meet(B,C)) = join(A,B). [para(6(a,1),237(a,1,1)),rewrite([6(4)])].
% 10.86/11.15 249 meet(A,join(join(B,C),meet(A,B))) = meet(A,join(B,C)). [para(237(a,1),25(a,1,2)),flip(a)].
% 10.86/11.15 250 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(237(a,1),237(a,1,1)),rewrite([5(3),237(7)])].
% 10.86/11.15 252 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [back_rewrite(71),rewrite([240(9)])].
% 10.86/11.15 256 join(join(A,join(B,C)),meet(D,join(A,C))) = join(A,join(B,C)). [para(10(a,1),240(a,1,1)),rewrite([6(3),5(4),6(6),10(7,R),6(6)])].
% 10.86/11.15 260 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)])].
% 10.86/11.15 265 meet(A,join(join(B,C),meet(A,C))) = meet(A,join(B,C)). [para(240(a,1),25(a,1,2)),flip(a)].
% 10.86/11.15 288 join(A,join(join(A,meet(B,join(A,C))),meet(B,join(C,meet(meet(A,B),join(A,meet(B,join(A,C)))))))) = join(A,meet(B,join(C,meet(meet(A,B),join(A,meet(B,join(A,C))))))). [para(21(a,1),250(a,1,2)),rewrite([6(12),10(12,R),6(11)])].
% 10.86/11.15 292 join(join(A,B),meet(C,meet(D,join(A,B)))) = join(A,B). [para(250(a,1),240(a,1,1)),rewrite([5(4),8(4,R),5(3),250(9)])].
% 10.86/11.15 296 meet(meet(A,B),join(A,C)) = meet(A,B). [para(237(a,1),252(a,1,2))].
% 10.86/11.15 298 join(A,join(join(A,meet(B,join(A,C))),meet(B,join(C,meet(A,B))))) = join(A,meet(B,join(C,meet(A,B)))). [back_rewrite(288),rewrite([296(8),296(13)])].
% 10.86/11.15 303 meet(A,join(join(A,meet(B,join(A,C))),meet(B,join(C,meet(A,B))))) = A. [back_rewrite(220),rewrite([296(8)])].
% 10.86/11.15 325 meet(meet(A,B),join(B,C)) = meet(A,B). [para(5(a,1),296(a,1,1)),rewrite([5(4)])].
% 10.86/11.15 335 meet(meet(A,meet(B,C)),join(D,meet(A,B))) = meet(A,meet(B,C)). [para(8(a,2),325(a,1,1)),rewrite([6(4),8(7),5(6),8(7,R),5(6)])].
% 10.86/11.15 340 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(16(a,1),325(a,1,1)),rewrite([6(4),16(8)])].
% 10.86/11.15 461 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(4(a,1),260(a,1,1)),rewrite([4(7)])].
% 10.86/11.15 462 join(join(A,B),meet(C,join(A,meet(B,D)))) = join(A,B). [para(260(a,1),6(a,2)),rewrite([6(4),6(5),6(6)])].
% 10.86/11.15 487 join(meet(A,B),meet(C,join(meet(A,B),meet(A,meet(B,D))))) = meet(A,B). [para(252(a,1),461(a,1,2,2,1)),rewrite([5(4),8(4),5(3),8(4,R),5(3)])].
% 10.86/11.15 496 meet(A,join(B,join(C,meet(A,C)))) = meet(A,join(B,C)). [para(265(a,1),36(a,1,2,2)),rewrite([6(6),10(6),6(5),250(5),10(3),6(2),10(3,R),6(2),265(8)])].
% 10.86/11.15 520 join(join(A,meet(B,C)),meet(B,meet(C,D))) = join(A,meet(B,C)). [para(252(a,1),292(a,1,2,2)),rewrite([8(4),5(3),8(4,R),5(3)])].
% 10.86/11.15 640 meet(meet(A,B),join(C,meet(A,join(B,D)))) = meet(A,B). [para(340(a,1),5(a,2)),rewrite([5(4),5(5),5(6)])].
% 10.86/11.15 934 meet(meet(A,B),join(C,join(D,meet(A,join(B,E))))) = meet(A,B). [para(640(a,1),325(a,1,1)),rewrite([6(5),10(5,R),6(4),640(11)])].
% 10.86/11.15 1011 meet(A,join(meet(B,C),meet(B,meet(C,D)))) = meet(A,meet(B,C)). [para(39(a,1),25(a,2)),rewrite([335(6)])].
% 10.86/11.15 1014 meet(meet(A,B),join(C,meet(A,C))) = meet(A,meet(B,C)). [para(39(a,1),26(a,1,2,2)),rewrite([5(2),8(3,R),1(2),5(6),3(8),2(6),5(6),8(6),5(5),8(6,R),5(5)])].
% 10.86/11.15 1039 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [back_rewrite(487),rewrite([1011(6),8(3),5(2),8(3,R),5(2)])].
% 10.86/11.15 1084 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(250(a,1),1014(a,1,2))].
% 10.86/11.15 1148 meet(A,meet(B,join(C,join(D,meet(A,join(B,E)))))) = meet(A,B). [back_rewrite(934),rewrite([1084(6)])].
% 10.86/11.15 1335 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [back_rewrite(252),rewrite([1084(4)])].
% 10.86/11.15 1348 meet(A,join(meet(A,B),meet(B,join(C,meet(A,B))))) = meet(A,B). [para(1335(a,1),36(a,1,2,2)),rewrite([6(5),1335(10)])].
% 10.86/11.15 1467 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(3(a,1),1084(a,1,1)),flip(a)].
% 10.86/11.15 1695 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(1(a,1),1467(a,2)),rewrite([6(3),10(3),6(2),10(3,R),6(2),5(5),15(6)])].
% 10.86/11.15 1697 meet(A,join(B,meet(C,join(D,meet(B,meet(C,join(A,E))))))) = meet(A,join(B,meet(C,join(B,D)))). [para(12(a,1),1467(a,1,2)),rewrite([1467(6),8(7),5(6),8(7,R),5(6)]),flip(a)].
% 10.86/11.15 1745 meet(A,join(meet(A,meet(B,C)),meet(B,join(A,D)))) = meet(A,B). [para(6(a,1),43(a,1,2))].
% 10.86/11.15 1927 join(A,join(join(B,C),meet(D,join(A,B)))) = join(A,join(B,C)). [para(256(a,1),6(a,2)),rewrite([6(3),10(5,R),6(6)])].
% 10.86/11.15 2363 meet(A,join(B,meet(C,join(D,meet(B,C))))) = meet(A,join(B,meet(C,join(B,D)))). [para(520(a,1),26(a,1,2,2,2)),rewrite([18(8)])].
% 10.86/11.15 2377 meet(join(A,meet(B,C)),join(A,join(D,meet(B,C)))) = join(A,meet(B,C)). [para(520(a,1),1695(a,1,1)),rewrite([6(7),10(8,R),10(7),6(6),10(7,R),6(6),1039(6),10(5,R),6(4),520(11)])].
% 10.86/11.15 2979 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(1084(a,1),106(a,1,2,2,2,2)),rewrite([10(8,R),6(7),10(7,R),6(6),10(6,R),6(5),1039(5),10(8,R)]),flip(a)].
% 10.86/11.15 3020 join(A,join(B,join(C,meet(D,join(A,B))))) = join(A,join(B,C)). [back_rewrite(1927),rewrite([2979(5)])].
% 10.86/11.15 3045 join(A,join(meet(B,join(A,C)),meet(B,join(C,meet(A,B))))) = join(A,meet(B,join(C,meet(A,B)))). [back_rewrite(298),rewrite([2979(8),17(8)])].
% 10.86/11.15 3233 meet(A,join(meet(A,B),meet(join(B,meet(A,B)),join(C,meet(A,B))))) = meet(A,B). [para(36(a,1),1348(a,1,2,1)),rewrite([36(6),36(11)])].
% 10.86/11.15 3560 join(A,meet(B,meet(A,C))) = join(A,meet(B,A)). [para(1745(a,1),462(a,1,2)),rewrite([6(3),6(5),10(5,R),6(4),1039(4),6(5)]),flip(a)].
% 10.86/11.15 4036 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [para(2(a,1),3020(a,2,2)),rewrite([17(4)])].
% 10.86/11.15 4110 join(A,meet(join(A,B),join(B,meet(C,join(A,B))))) = join(A,B). [para(4036(a,1),72(a,1,2,2)),rewrite([5(5),4036(10)])].
% 10.86/11.15 4111 join(A,join(meet(B,join(A,B)),meet(C,join(A,B)))) = join(A,B). [para(72(a,1),4036(a,1,2,2,2)),rewrite([72(9)])].
% 10.86/11.15 4967 join(join(A,meet(B,join(A,C))),meet(B,join(C,meet(A,B)))) = join(A,meet(B,join(C,meet(A,B)))). [para(303(a,1),250(a,1,2)),rewrite([6(8),2979(8),3045(7),17(5)]),flip(a)].
% 10.86/11.15 5028 join(A,meet(B,join(C,meet(A,B)))) = join(A,meet(B,join(A,C))). [para(303(a,1),4111(a,1,2,2)),rewrite([4967(13),2363(11),1084(10),6(11),10(12,R),6(11),292(11),17(4),4967(10)]),flip(a)].
% 10.86/11.15 5118 join(A,meet(B,meet(C,join(A,B)))) = join(A,meet(B,C)). [para(3560(a,1),5028(a,1,2,2)),rewrite([1084(4),16(4),1084(5)]),flip(a)].
% 10.86/11.15 5144 join(A,meet(B,meet(C,join(A,C)))) = join(A,meet(B,C)). [para(5(a,1),5118(a,1,2)),rewrite([5(3),8(3,R),5(2),5(5)])].
% 10.86/11.15 5304 join(A,meet(B,join(A,join(B,C)))) = join(A,B). [para(3(a,1),5144(a,2,2)),rewrite([1467(5)])].
% 10.86/11.15 5339 join(A,meet(join(B,meet(A,C)),join(A,join(B,D)))) = join(A,B). [para(18(a,1),5304(a,2)),rewrite([6(5),10(5,R),6(4),35(6)])].
% 10.86/11.15 5383 join(A,meet(B,meet(C,join(A,join(B,D))))) = join(A,meet(B,C)). [para(5304(a,1),5118(a,1,2,2,2)),rewrite([8(6),5(5),8(5,R),5(4),8(6,R),5(5),8(5,R),5(4),1695(4),5118(4),5(6),8(6,R),5(5)]),flip(a)].
% 10.86/11.15 5582 meet(join(A,meet(B,C)),join(A,join(B,D))) = meet(join(A,B),join(A,meet(B,C))). [para(5339(a,1),1335(a,1,2,2)),rewrite([10(4,R),6(3),6(5),5(6),1695(6),5(4),10(8,R),6(7)]),flip(a)].
% 10.86/11.15 5663 meet(A,join(join(A,join(B,C)),meet(D,join(B,meet(A,D))))) = A. [para(5383(a,1),27(a,1,2,2,2)),rewrite([10(2,R),6(1),10(9,R),6(8),10(11,R),6(10),10(12,R),6(11),17(11),250(13),3(10)])].
% 10.86/11.15 6242 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(5339(a,1),5663(a,1,2,2,2)),rewrite([10(6),6(5),18(5),6(3),10(4),6(3),10(4,R),6(3),10(6,R),6(5),6(7),5(8),1695(8),6(6),10(6,R),10(5),6(4),10(5,R),6(4),17(4),17(5),5582(5)])].
% 10.86/11.15 6253 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(6(a,1),6242(a,1,1))].
% 10.86/11.15 6346 meet(A,join(B,A)) = A. [para(461(a,1),6253(a,1,2)),rewrite([5(2),461(7)])].
% 10.86/11.15 6392 meet(A,join(meet(A,B),meet(B,C))) = meet(A,B). [para(6253(a,1),120(a,2,2,2)),rewrite([5(6),8(6,R),1(5),15(6),3233(9),17(6)]),flip(a)].
% 10.86/11.15 6628 join(A,meet(B,join(A,join(B,C)))) = join(A,B). [para(6346(a,1),5383(a,2,2)),rewrite([6(1),1467(5)])].
% 10.86/11.15 6878 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(6(a,1),6392(a,1,2))].
% 10.86/11.15 6994 meet(A,join(meet(B,C),meet(B,A))) = meet(B,A). [para(6878(a,1),5(a,2)),rewrite([5(2),5(4),5(5)])].
% 10.86/11.15 6995 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(5(a,1),6878(a,1,2,1))].
% 10.86/11.15 6999 meet(A,join(meet(B,meet(C,D)),meet(A,D))) = meet(A,D). [para(8(a,2),6878(a,1,2,1))].
% 10.86/11.15 7009 join(A,join(meet(B,C),meet(B,A))) = join(A,meet(B,C)). [para(6878(a,1),462(a,1,2)),rewrite([6(2),5(3),6(4),10(4,R),6(6)])].
% 10.86/11.15 7294 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(6994(a,1),4110(a,1,2))].
% 10.86/11.15 7327 meet(A,join(meet(A,B),meet(C,B))) = meet(A,B). [para(6995(a,1),249(a,2)),rewrite([6(6),10(6),6(5),496(7)])].
% 10.86/11.15 7795 meet(A,join(B,meet(A,join(C,B)))) = meet(A,join(C,B)). [para(6346(a,1),7327(a,1,2,2)),rewrite([6(3)])].
% 10.86/11.15 8331 meet(A,join(meet(B,meet(C,D)),meet(D,A))) = meet(D,A). [para(6999(a,1),5(a,2)),rewrite([5(3),5(5),5(6)])].
% 10.86/11.15 8661 meet(A,meet(B,join(join(B,C),meet(A,D)))) = meet(A,B). [para(7009(a,1),1148(a,1,2,2))].
% 10.86/11.15 10104 join(A,meet(B,meet(C,A))) = A. [para(6628(a,1),8331(a,1,2)),rewrite([10(4),6(3),10(4,R),6(3),6(7),5(8),2377(8),10(7),6(6),10(7,R),6(6),3(8)])].
% 10.86/11.15 10472 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(8661(a,1),10104(a,1,2)),rewrite([5(4),6(5),2979(5),10(5,R),18(5)]),flip(a)].
% 10.86/11.15 12353 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(4(a,1),10472(a,1,1)),flip(a)].
% 10.86/11.15 12679 join(A,meet(B,join(meet(A,C),meet(B,D)))) = join(A,meet(B,D)). [para(7294(a,1),12353(a,1,2)),rewrite([12353(4)]),flip(a)].
% 10.86/11.15 17254 join(A,meet(B,join(C,meet(A,meet(B,D))))) = join(A,meet(B,join(C,meet(A,D)))). [para(12(a,1),12679(a,1,2)),rewrite([6(3),7795(6),5(6),8(6,R),5(5),8(7,R),5(6),15(6)]),flip(a)].
% 10.86/11.15 17352 meet(A,join(B,meet(C,join(D,meet(B,join(A,E)))))) = meet(A,join(B,meet(C,join(B,D)))). [back_rewrite(1697),rewrite([17254(6)])].
% 10.86/11.15 17353 $F # answer(prove_H78). [resolve(17352,a,14,a)].
% 10.86/11.15
% 10.86/11.15 % SZS output end Refutation
% 10.86/11.15 ============================== end of proof ==========================
% 10.86/11.15
% 10.86/11.15 ============================== STATISTICS ============================
% 10.86/11.15
% 10.86/11.15 Given=298. Generated=124059. Kept=17348. proofs=1.
% 10.86/11.15 Usable=172. Sos=7787. Demods=7898. Limbo=98, Disabled=9300. Hints=0.
% 10.86/11.15 Megabytes=28.01.
% 10.86/11.15 User_CPU=10.06, System_CPU=0.10, Wall_clock=10.
% 10.86/11.15
% 10.86/11.15 ============================== end of statistics =====================
% 10.86/11.15
% 10.86/11.15 ============================== end of search =========================
% 10.86/11.15
% 10.86/11.15 THEOREM PROVED
% 10.86/11.15 % SZS status Unsatisfiable
% 10.86/11.15
% 10.86/11.15 Exiting with 1 proof.
% 10.86/11.15
% 10.86/11.15 Process 29334 exit (max_proofs) Thu Jun 30 04:12:43 2022
% 10.86/11.15 Prover9 interrupted
%------------------------------------------------------------------------------