TSTP Solution File: LAT165-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT165-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 67.63s 67.90s
% Output : Refutation 67.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT165-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n027.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 : Thu Jun 30 16:29:36 EDT 2022
% 0.18/0.33 % CPUTime :
% 13.01/13.28 ============================== Prover9 ===============================
% 13.01/13.28 Prover9 (32) version 2009-11A, November 2009.
% 13.01/13.28 Process 1007 was started by sandbox on n027.cluster.edu,
% 13.01/13.28 Thu Jun 30 16:29:37 2022
% 13.01/13.28 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_838_n027.cluster.edu".
% 13.01/13.28 ============================== end of head ===========================
% 13.01/13.28
% 13.01/13.28 ============================== INPUT =================================
% 13.01/13.28
% 13.01/13.28 % Reading from file /tmp/Prover9_838_n027.cluster.edu
% 13.01/13.28
% 13.01/13.28 set(prolog_style_variables).
% 13.01/13.28 set(auto2).
% 13.01/13.28 % set(auto2) -> set(auto).
% 13.01/13.28 % set(auto) -> set(auto_inference).
% 13.01/13.28 % set(auto) -> set(auto_setup).
% 13.01/13.28 % set(auto_setup) -> set(predicate_elim).
% 13.01/13.28 % set(auto_setup) -> assign(eq_defs, unfold).
% 13.01/13.28 % set(auto) -> set(auto_limits).
% 13.01/13.28 % set(auto_limits) -> assign(max_weight, "100.000").
% 13.01/13.28 % set(auto_limits) -> assign(sos_limit, 20000).
% 13.01/13.28 % set(auto) -> set(auto_denials).
% 13.01/13.28 % set(auto) -> set(auto_process).
% 13.01/13.28 % set(auto2) -> assign(new_constants, 1).
% 13.01/13.28 % set(auto2) -> assign(fold_denial_max, 3).
% 13.01/13.28 % set(auto2) -> assign(max_weight, "200.000").
% 13.01/13.28 % set(auto2) -> assign(max_hours, 1).
% 13.01/13.28 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 13.01/13.28 % set(auto2) -> assign(max_seconds, 0).
% 13.01/13.28 % set(auto2) -> assign(max_minutes, 5).
% 13.01/13.28 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 13.01/13.28 % set(auto2) -> set(sort_initial_sos).
% 13.01/13.28 % set(auto2) -> assign(sos_limit, -1).
% 13.01/13.28 % set(auto2) -> assign(lrs_ticks, 3000).
% 13.01/13.28 % set(auto2) -> assign(max_megs, 400).
% 13.01/13.28 % set(auto2) -> assign(stats, some).
% 13.01/13.28 % set(auto2) -> clear(echo_input).
% 13.01/13.28 % set(auto2) -> set(quiet).
% 13.01/13.28 % set(auto2) -> clear(print_initial_clauses).
% 13.01/13.28 % set(auto2) -> clear(print_given).
% 13.01/13.28 assign(lrs_ticks,-1).
% 13.01/13.28 assign(sos_limit,10000).
% 13.01/13.28 assign(order,kbo).
% 13.01/13.28 set(lex_order_vars).
% 13.01/13.28 clear(print_given).
% 13.01/13.28
% 13.01/13.28 % formulas(sos). % not echoed (10 formulas)
% 13.01/13.28
% 13.01/13.28 ============================== end of input ==========================
% 13.01/13.28
% 13.01/13.28 % From the command line: assign(max_seconds, 300).
% 13.01/13.28
% 13.01/13.28 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 13.01/13.28
% 13.01/13.28 % Formulas that are not ordinary clauses:
% 13.01/13.28
% 13.01/13.28 ============================== end of process non-clausal formulas ===
% 13.01/13.28
% 13.01/13.28 ============================== PROCESS INITIAL CLAUSES ===============
% 13.01/13.28
% 13.01/13.28 ============================== PREDICATE ELIMINATION =================
% 13.01/13.28
% 13.01/13.28 ============================== end predicate elimination =============
% 13.01/13.28
% 13.01/13.28 Auto_denials:
% 13.01/13.28 % copying label prove_H77 to answer in negative clause
% 13.01/13.28
% 13.01/13.28 Term ordering decisions:
% 13.01/13.28 Function symbol KB weights: a=1. b=1. c=1. d=1. meet=1. join=1.
% 13.01/13.28
% 13.01/13.28 ============================== end of process initial clauses ========
% 13.01/13.28
% 13.01/13.28 ============================== CLAUSES FOR SEARCH ====================
% 13.01/13.28
% 13.01/13.28 ============================== end of clauses for search =============
% 13.01/13.28
% 13.01/13.28 ============================== SEARCH ================================
% 13.01/13.28
% 13.01/13.28 % Starting search at 0.01 seconds.
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=135.000, iters=3366
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=129.000, iters=3348
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=105.000, iters=3460
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=97.000, iters=3425
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=95.000, iters=3405
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=91.000, iters=3366
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=89.000, iters=3346
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=85.000, iters=3450
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=73.000, iters=3333
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=71.000, iters=3373
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=67.000, iters=3366
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=63.000, iters=3336
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=61.000, iters=3361
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=59.000, iters=3358
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=57.000, iters=3348
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=55.000, iters=3354
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=53.000, iters=3333
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=51.000, iters=3370
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=49.000, iters=3353
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=47.000, iters=3370
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=45.000, iters=3357
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=43.000, iters=3337
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=41.000, iters=3375
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=39.000, iters=3366
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=37.000, iters=3378
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=35.000, iters=3394
% 13.01/13.28
% 13.01/13.28 Low Water (keep): wt=33.000, iters=3349
% 13.01/13.28
% 13.01/13.28 Low Water (displace): id=8442, wt=199.000
% 13.01/13.28
% 13.01/13.28 Low Water (displace): id=8313, wt=197.000
% 67.63/67.90
% 67.63/67.90 Low Water (displace): id=8558, wt=195.000
% 67.63/67.90
% 67.63/67.90 Low Water (displace): id=8527, wt=193.000
% 67.63/67.90
% 67.63/67.90 Low Water (displace): id=8543, wt=191.000
% 67.63/67.90
% 67.63/67.90 Low Water (displace): id=8478, wt=173.000
% 67.63/67.90
% 67.63/67.90 Low Water (displace): id=8475, wt=171.000
% 67.63/67.90
% 67.63/67.90 Low Water (displace): id=14642, wt=25.000
% 67.63/67.90
% 67.63/67.90 Low Water (displace): id=14676, wt=23.000
% 67.63/67.90
% 67.63/67.90 Low Water (keep): wt=31.000, iters=3343
% 67.63/67.90
% 67.63/67.90 Low Water (displace): id=16039, wt=21.000
% 67.63/67.90
% 67.63/67.90 Low Water (keep): wt=29.000, iters=3335
% 67.63/67.90
% 67.63/67.90 Low Water (displace): id=26575, wt=19.000
% 67.63/67.90
% 67.63/67.90 ============================== PROOF =================================
% 67.63/67.90 % SZS status Unsatisfiable
% 67.63/67.90 % SZS output start Refutation
% 67.63/67.90
% 67.63/67.90 % Proof 1 at 66.43 (+ 0.51) seconds: prove_H77.
% 67.63/67.90 % Length of proof is 110.
% 67.63/67.90 % Level of proof is 26.
% 67.63/67.90 % Maximum clause weight is 55.000.
% 67.63/67.90 % Given clauses 704.
% 67.63/67.90
% 67.63/67.90 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 67.63/67.90 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 67.63/67.90 3 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 67.63/67.90 4 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 67.63/67.90 5 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 67.63/67.90 6 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 67.63/67.90 7 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 67.63/67.90 8 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(7),rewrite([5(2)]),flip(a)].
% 67.63/67.90 9 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 67.63/67.90 10 join(A,join(B,C)) = join(C,join(A,B)). [copy(9),rewrite([6(2)]),flip(a)].
% 67.63/67.90 11 meet(A,join(B,meet(C,join(B,D)))) = meet(A,join(B,meet(C,join(D,meet(A,B))))) # label(equation_H76) # label(axiom). [assumption].
% 67.63/67.90 12 meet(A,join(B,meet(C,join(D,meet(A,B))))) = meet(A,join(B,meet(C,join(B,D)))). [copy(11),flip(a)].
% 67.63/67.90 13 meet(a,join(b,meet(c,join(b,d)))) != meet(a,join(b,meet(c,join(d,meet(a,meet(b,c)))))) # label(prove_H77) # label(negated_conjecture) # answer(prove_H77). [assumption].
% 67.63/67.90 14 meet(a,join(b,meet(c,join(d,meet(a,meet(b,c)))))) != meet(a,join(b,meet(c,join(b,d)))) # answer(prove_H77). [copy(13),flip(a)].
% 67.63/67.90 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)])].
% 67.63/67.90 16 meet(A,meet(B,join(A,C))) = meet(A,B). [para(3(a,1),8(a,2,2)),rewrite([5(2),5(4)])].
% 67.63/67.90 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)])].
% 67.63/67.90 18 join(A,join(B,meet(A,C))) = join(A,B). [para(4(a,1),10(a,2,2)),rewrite([6(2),6(4)])].
% 67.63/67.90 19 meet(A,join(B,join(C,meet(A,B)))) = meet(A,join(B,C)). [para(1(a,1),12(a,1,2,2)),rewrite([5(8),12(10),1(7),17(6)])].
% 67.63/67.90 20 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(2(a,1),12(a,1,2,2,2)),rewrite([8(2),5(1),8(2,R),5(1),12(9),2(5),5(5),4(6)])].
% 67.63/67.90 21 meet(A,join(join(A,B),meet(C,join(A,join(B,D))))) = meet(A,join(join(A,B),meet(C,join(A,D)))). [para(3(a,1),12(a,1,2,2,2,2)),rewrite([6(2),6(8),10(8),6(7),10(8,R),6(7)]),flip(a)].
% 67.63/67.90 22 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)].
% 67.63/67.90 23 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)].
% 67.63/67.90 24 meet(A,join(B,meet(C,join(D,meet(B,A))))) = meet(A,join(B,meet(C,join(B,D)))). [para(12(a,1),5(a,2)),rewrite([5(1),5(5)])].
% 67.63/67.90 28 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)])].
% 67.63/67.90 29 meet(A,join(meet(B,join(A,C)),meet(D,join(E,meet(B,join(A,C)))))) = meet(A,join(meet(B,join(A,C)),meet(D,join(E,meet(A,B))))). [para(16(a,1),12(a,1,2,2,2,2)),rewrite([6(12)]),flip(a)].
% 67.63/67.90 30 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)])].
% 67.63/67.90 31 meet(A,join(B,meet(A,B))) = meet(A,B). [para(1(a,1),20(a,1,2,2,2))].
% 67.63/67.90 32 meet(A,join(join(A,B),meet(A,C))) = A. [para(3(a,1),20(a,2)),rewrite([5(3),16(4)])].
% 67.63/67.90 37 meet(A,join(meet(A,B),meet(A,meet(B,C)))) = meet(A,B). [para(15(a,1),20(a,2)),rewrite([5(3),8(3),5(2),8(3,R),5(2),15(4)])].
% 67.63/67.90 38 meet(A,join(meet(B,join(A,C)),meet(A,meet(B,D)))) = meet(A,B). [para(16(a,1),20(a,2)),rewrite([5(5),8(5,R),5(4),28(6)])].
% 67.63/67.90 44 meet(A,join(B,join(meet(A,B),meet(C,join(D,meet(A,B)))))) = meet(A,join(B,meet(C,join(B,D)))). [para(12(a,1),19(a,2)),rewrite([6(5)])].
% 67.63/67.90 53 meet(A,join(B,join(meet(C,join(D,meet(A,B))),meet(A,join(B,meet(C,join(B,D))))))) = meet(A,join(B,meet(C,join(B,D)))). [para(12(a,1),31(a,1,2,2)),rewrite([6(9),10(9),6(8),10(9,R),6(8),12(15)])].
% 67.63/67.90 54 meet(A,join(meet(A,B),meet(B,join(A,C)))) = meet(A,B). [para(16(a,1),31(a,1,2,2)),rewrite([6(4),16(8)])].
% 67.63/67.90 60 meet(A,join(B,join(join(A,C),meet(A,D)))) = A. [para(32(a,1),19(a,1,2,2,2)),rewrite([6(4),10(5),6(4),18(4),17(2),10(2),6(1),10(2,R),6(1),3(3),6(4)]),flip(a)].
% 67.63/67.90 65 join(A,meet(B,join(A,B))) = join(A,B). [para(22(a,1),1(a,1)),rewrite([5(5),22(5),1(3)]),flip(a)].
% 67.63/67.90 70 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(6(a,1),21(a,2,2)),rewrite([21(6),10(9),6(8),10(9,R),6(8),3(10)])].
% 67.63/67.90 75 join(A,join(B,meet(C,join(A,C)))) = join(A,join(C,B)). [para(65(a,1),10(a,2,2)),rewrite([6(3),10(6),6(5),10(6,R),6(5)])].
% 67.63/67.90 81 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(32(a,1),70(a,1,2,2)),rewrite([6(3),10(3),6(2),10(3,R),6(2),6(4),17(4)])].
% 67.63/67.90 96 meet(A,join(meet(B,join(C,meet(A,D))),meet(D,join(A,meet(B,join(A,C)))))) = meet(A,join(meet(A,D),meet(B,join(C,meet(A,D))))). [para(12(a,1),23(a,1,2,2)),rewrite([5(1),5(10),6(14)])].
% 67.63/67.90 97 meet(A,join(B,meet(join(A,B),join(B,C)))) = meet(A,join(B,meet(A,join(B,C)))). [para(12(a,1),23(a,2)),rewrite([5(4),12(6)])].
% 67.63/67.90 104 meet(A,join(meet(B,join(A,B)),meet(C,join(A,B)))) = meet(A,join(meet(B,join(A,B)),meet(A,C))). [para(65(a,1),23(a,1,2,2,2))].
% 67.63/67.90 118 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(37(a,1),70(a,1,2,2)),rewrite([6(3),6(5),10(5,R),2(4)])].
% 67.63/67.90 125 meet(meet(A,B),join(C,join(D,meet(A,B)))) = meet(A,B). [para(118(a,1),60(a,1,2,2,2)),rewrite([6(3),6(5),10(5,R),2(4)])].
% 67.63/67.90 126 meet(A,join(join(A,B),meet(C,D))) = A. [para(118(a,1),70(a,1,2,2))].
% 67.63/67.90 129 meet(A,join(B,meet(C,join(B,join(C,D))))) = meet(A,join(B,C)). [para(126(a,1),12(a,1,2,2)),flip(a)].
% 67.63/67.90 138 meet(meet(A,B),join(C,meet(A,C))) = meet(A,meet(B,C)). [para(20(a,1),24(a,1,2,2)),rewrite([5(2),6(6),4(8),5(6),8(6),5(5),8(6,R),5(5)])].
% 67.63/67.90 243 meet(meet(A,B),join(A,C)) = meet(A,B). [para(4(a,1),125(a,1,2,2)),rewrite([6(2)])].
% 67.63/67.90 355 meet(meet(A,B),join(B,C)) = meet(A,B). [para(5(a,1),243(a,1,1)),rewrite([5(4)])].
% 67.63/67.90 375 meet(meet(A,B),join(C,meet(B,join(A,D)))) = meet(A,B). [para(16(a,1),355(a,1,1)),rewrite([6(4),16(8)])].
% 67.63/67.90 456 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(138(a,1),4(a,1,2))].
% 67.63/67.90 474 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(138(a,1),126(a,1)),rewrite([6(2)])].
% 67.63/67.90 503 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(81(a,1),456(a,1,1)),rewrite([5(5),8(6,R),5(5),81(5),81(8)])].
% 67.63/67.90 553 join(A,join(join(A,B),meet(C,D))) = join(join(A,B),meet(C,D)). [para(126(a,1),503(a,1,2)),rewrite([6(4)])].
% 67.63/67.90 560 join(join(A,B),meet(A,C)) = join(A,B). [para(243(a,1),503(a,1,2))].
% 67.63/67.90 563 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(503(a,1),138(a,1,2))].
% 67.63/67.90 615 meet(A,meet(B,join(C,meet(B,join(A,D))))) = meet(A,B). [back_rewrite(375),rewrite([563(5)])].
% 67.63/67.90 662 join(join(A,B),meet(B,C)) = join(A,B). [para(6(a,1),560(a,1,1)),rewrite([6(4)])].
% 67.63/67.90 675 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(18(a,1),662(a,1,1)),rewrite([5(4),18(8)])].
% 67.63/67.90 681 join(join(A,B),meet(C,meet(D,join(A,B)))) = join(A,B). [para(503(a,1),662(a,1,1)),rewrite([5(4),8(4,R),5(3),503(9)])].
% 67.63/67.90 721 meet(A,meet(join(A,B),join(C,D))) = meet(A,join(C,D)). [para(3(a,1),563(a,1,1)),flip(a)].
% 67.63/67.90 778 meet(A,meet(B,join(C,meet(A,join(B,D))))) = meet(A,B). [para(615(a,1),8(a,2)),rewrite([5(4),5(6)])].
% 67.63/67.90 869 join(join(A,B),meet(C,join(A,meet(B,D)))) = join(A,B). [para(675(a,1),6(a,2)),rewrite([6(4),6(5),6(6)])].
% 67.63/67.90 986 join(join(meet(A,B),meet(B,join(A,C))),meet(A,meet(B,D))) = join(meet(A,B),meet(B,join(A,C))). [para(54(a,1),681(a,1,2,2)),rewrite([8(6),5(5),8(6,R),5(5)])].
% 67.63/67.90 1013 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(721(a,1),615(a,1)),rewrite([3(7)])].
% 67.63/67.90 1054 meet(A,join(meet(A,meet(B,C)),meet(B,join(A,D)))) = meet(A,B). [para(6(a,1),38(a,1,2))].
% 67.63/67.90 1115 join(join(A,B),meet(C,join(A,meet(D,join(A,B))))) = join(A,B). [para(17(a,1),869(a,1,1)),rewrite([5(3),17(8)])].
% 67.63/67.90 1217 join(A,meet(B,join(A,join(B,C)))) = join(A,B). [para(129(a,1),1(a,1)),rewrite([5(6),129(6),1(3)]),flip(a)].
% 67.63/67.90 1237 join(A,meet(join(B,meet(A,C)),join(A,join(B,D)))) = join(A,B). [para(18(a,1),1217(a,2)),rewrite([6(5),10(5,R),6(4),30(6)])].
% 67.63/67.90 1677 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(6(a,1),553(a,1,2)),rewrite([10(3),6(2),10(3,R),6(2),17(4)]),flip(a)].
% 67.63/67.90 1689 join(A,join(B,meet(C,join(A,B)))) = join(A,B). [para(503(a,1),553(a,1,2)),rewrite([17(2),1677(5)]),flip(a)].
% 67.63/67.90 1692 join(A,join(B,meet(C,join(B,meet(A,D))))) = join(A,B). [para(675(a,1),553(a,1,2)),rewrite([17(2),1677(6)]),flip(a)].
% 67.63/67.90 1701 join(A,join(B,meet(C,join(A,meet(B,D))))) = join(A,B). [para(869(a,1),553(a,1,2)),rewrite([17(2),1677(6)]),flip(a)].
% 67.63/67.90 1931 join(A,join(B,meet(C,join(A,meet(D,join(A,B)))))) = join(A,B). [back_rewrite(1115),rewrite([1677(6)])].
% 67.63/67.90 1959 join(meet(A,B),join(meet(B,join(A,C)),meet(A,meet(B,D)))) = join(meet(A,B),meet(B,join(A,C))). [back_rewrite(986),rewrite([1677(7)])].
% 67.63/67.90 2324 join(meet(A,join(B,C)),meet(A,meet(B,D))) = join(meet(A,B),meet(A,join(B,C))). [para(38(a,1),1689(a,1,2,2)),rewrite([8(4,R),5(3),5(5),6(6),456(6),6(4),8(8,R),5(7)]),flip(a)].
% 67.63/67.90 2600 meet(A,join(meet(B,join(C,D)),join(meet(C,join(meet(B,meet(C,E)),meet(A,meet(B,join(C,D))))),meet(A,join(meet(B,join(C,D)),meet(C,join(meet(B,C),meet(B,join(C,D))))))))) = meet(A,join(meet(B,C),meet(B,join(C,D)))). [para(38(a,1),53(a,2,2,2)),rewrite([8(4,R),5(3),8(15,R),5(14),2324(16),5(24),6(25)])].
% 67.63/67.90 2905 join(meet(A,meet(B,C)),meet(B,join(A,D))) = join(meet(A,B),meet(B,join(A,D))). [para(1054(a,1),1689(a,1,2,2)),rewrite([6(6),10(7,R),1959(7)]),flip(a)].
% 67.63/67.90 3107 meet(join(A,meet(B,C)),join(A,join(B,D))) = meet(join(A,B),join(A,meet(B,C))). [para(1237(a,1),474(a,1,2,2)),rewrite([10(4,R),6(3),6(5),5(6),81(6),5(4),10(8,R),6(7)]),flip(a)].
% 67.63/67.90 3248 join(meet(A,join(B,C)),meet(B,join(meet(A,B),meet(A,join(B,C))))) = meet(A,join(B,C)). [para(29(a,1),1931(a,1,2,2)),rewrite([5(9),6(10),29(13),5(8),2(9),8(8),5(7),8(8,R),5(7),2324(9),17(11),2(13)])].
% 67.63/67.90 3269 meet(A,join(meet(B,C),meet(B,join(C,D)))) = meet(A,meet(B,join(C,D))). [back_rewrite(2600),rewrite([3248(17),6(13),44(15),2324(7),3248(8)]),flip(a)].
% 67.63/67.90 3273 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [back_rewrite(3248),rewrite([3269(7),16(5),5(3),6(4)])].
% 67.63/67.90 3278 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(5(a,1),3273(a,1,1))].
% 67.63/67.90 3283 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(15(a,1),3273(a,1,1)),rewrite([6(3),6(7)])].
% 67.63/67.90 3339 join(meet(A,meet(B,C)),meet(B,join(A,D))) = meet(B,join(A,D)). [back_rewrite(2905),rewrite([3278(9)])].
% 67.63/67.90 3370 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(3(a,1),3278(a,1,1))].
% 67.63/67.90 3392 join(A,meet(B,A)) = A. [para(1013(a,1),3278(a,1,2)),rewrite([6(2),1013(7)])].
% 67.63/67.90 3442 join(meet(A,join(B,C)),meet(join(A,D),join(B,C))) = meet(join(A,D),join(B,C)). [para(721(a,1),3392(a,1,2)),rewrite([6(6)])].
% 67.63/67.90 3932 meet(A,join(B,meet(A,join(B,C)))) = meet(A,meet(join(B,A),join(B,C))). [para(97(a,1),5(a,2)),rewrite([6(1),3370(4),5(4)]),flip(a)].
% 67.63/67.90 3981 meet(join(A,B),meet(join(B,C),join(A,B))) = meet(join(A,B),join(B,C)). [para(97(a,1),96(a,1,2,1)),rewrite([3932(5),6(2),721(5),6(7),10(7,R),2(6),3(7),6(6),17(6),3278(7),97(14),3932(13),6(10),721(13),6(12),3442(12),15(10)])].
% 67.63/67.90 4487 join(A,join(B,meet(C,join(A,meet(C,B))))) = join(A,B). [para(104(a,1),1701(a,1,2,2)),rewrite([6(1),3(2),6(1),3(2),6(6),3(7)])].
% 67.63/67.90 4535 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(15(a,1),4487(a,1,2,2,2,2)),rewrite([3283(5)])].
% 67.63/67.90 4577 join(A,meet(B,meet(join(A,B),join(A,C)))) = join(A,meet(B,join(C,meet(A,B)))). [para(12(a,1),4535(a,1,2)),rewrite([3932(4),5(6)])].
% 67.63/67.90 4630 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(3339(a,1),44(a,1,2,2)),rewrite([4(4),5(2),6(7),3283(9),16(8)])].
% 67.63/67.90 4803 meet(A,join(meet(B,meet(C,D)),meet(A,D))) = meet(A,D). [para(8(a,2),4630(a,1,2,1))].
% 67.63/67.90 5233 meet(A,join(meet(B,C),meet(A,join(B,D)))) = meet(A,join(B,D)). [para(16(a,1),4803(a,1,2,1))].
% 67.63/67.90 6053 join(A,meet(join(B,C),join(B,meet(A,D)))) = join(A,B). [para(3370(a,1),1692(a,1,2))].
% 67.63/67.90 6094 join(A,meet(join(B,C),join(A,B))) = join(A,B). [para(1(a,1),6053(a,1,2,2,2)),rewrite([6(2)])].
% 67.63/67.90 6163 join(A,join(B,meet(join(C,D),join(A,C)))) = join(A,join(B,C)). [para(6053(a,1),6053(a,1,2,2)),rewrite([6(3),1677(5),6(7),10(7),6(6),10(7,R),6(6)])].
% 67.63/67.90 6166 join(A,meet(join(B,C),join(A,C))) = join(A,C). [para(6(a,1),6094(a,1,2,1))].
% 67.63/67.90 6174 join(A,join(B,meet(join(A,C),join(C,D)))) = join(A,join(B,C)). [para(6094(a,1),75(a,1,2,2,2)),rewrite([5(5),3981(5),6(9),6163(10)])].
% 67.63/67.90 6177 meet(A,meet(join(B,A),join(B,C))) = meet(A,join(B,C)). [para(6094(a,1),778(a,1,2,2)),rewrite([6(2),8(4,R),5(6)])].
% 67.63/67.90 6227 join(A,meet(B,join(C,meet(A,B)))) = join(A,meet(B,join(A,C))). [back_rewrite(4577),rewrite([6177(4)]),flip(a)].
% 67.63/67.90 6498 meet(join(A,B),join(A,join(C,B))) = join(A,B). [para(17(a,1),6166(a,1,2,2)),rewrite([10(2,R),6(1),5(4),3370(5),17(6)])].
% 67.63/67.90 6594 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(4(a,1),6498(a,1,2,2)),rewrite([5(4)])].
% 67.63/67.90 6640 meet(join(A,meet(B,C)),join(A,join(B,D))) = join(A,meet(B,C)). [back_rewrite(3107),rewrite([6594(9)])].
% 67.63/67.90 11755 join(A,join(B,meet(join(A,meet(C,D)),join(C,E)))) = join(A,join(B,meet(C,D))). [para(5233(a,1),6174(a,1,2,2))].
% 67.63/67.90 12310 meet(A,join(B,join(meet(A,B),meet(C,D)))) = meet(A,join(B,meet(C,D))). [para(6640(a,1),44(a,2,2,2)),rewrite([1677(6),11755(9),17(8)])].
% 67.63/67.90 26765 meet(A,join(B,meet(C,join(D,meet(A,meet(B,C)))))) = meet(A,join(B,meet(C,join(B,D)))). [para(6227(a,1),12310(a,1,2,2)),rewrite([6(3),12310(7),12(5),5(6),8(6),5(5),8(6,R),5(5)]),flip(a)].
% 67.63/67.90 26766 $F # answer(prove_H77). [resolve(26765,a,14,a)].
% 67.63/67.90
% 67.63/67.90 % SZS output end Refutation
% 67.63/67.90 ============================== end of proof ==========================
% 67.63/67.90
% 67.63/67.90 ============================== STATISTICS ============================
% 67.63/67.90
% 67.63/67.90 Given=704. Generated=925915. Kept=26761. proofs=1.
% 67.63/67.90 Usable=593. Sos=9999. Demods=10554. Limbo=19, Disabled=16159. Hints=0.
% 67.63/67.90 Megabytes=33.08.
% 67.63/67.90 User_CPU=66.44, System_CPU=0.51, Wall_clock=67.
% 67.63/67.90
% 67.63/67.90 ============================== end of statistics =====================
% 67.63/67.90
% 67.63/67.90 ============================== end of search =========================
% 67.63/67.90
% 67.63/67.90 THEOREM PROVED
% 67.63/67.90 % SZS status Unsatisfiable
% 67.63/67.90
% 67.63/67.90 Exiting with 1 proof.
% 67.63/67.90
% 67.63/67.90 Process 1007 exit (max_proofs) Thu Jun 30 16:30:44 2022
% 67.63/67.90 Prover9 interrupted
%------------------------------------------------------------------------------