TSTP Solution File: LAT082-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT082-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 06:25:28 EDT 2022
% Result : Unsatisfiable 26.00s 26.28s
% Output : Refutation 26.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT082-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n013.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 15:49:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 26.00/26.28 ============================== Prover9 ===============================
% 26.00/26.28 Prover9 (32) version 2009-11A, November 2009.
% 26.00/26.28 Process 27734 was started by sandbox2 on n013.cluster.edu,
% 26.00/26.28 Wed Jun 29 15:50:00 2022
% 26.00/26.28 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27579_n013.cluster.edu".
% 26.00/26.28 ============================== end of head ===========================
% 26.00/26.28
% 26.00/26.28 ============================== INPUT =================================
% 26.00/26.28
% 26.00/26.28 % Reading from file /tmp/Prover9_27579_n013.cluster.edu
% 26.00/26.28
% 26.00/26.28 set(prolog_style_variables).
% 26.00/26.28 set(auto2).
% 26.00/26.28 % set(auto2) -> set(auto).
% 26.00/26.28 % set(auto) -> set(auto_inference).
% 26.00/26.28 % set(auto) -> set(auto_setup).
% 26.00/26.28 % set(auto_setup) -> set(predicate_elim).
% 26.00/26.28 % set(auto_setup) -> assign(eq_defs, unfold).
% 26.00/26.28 % set(auto) -> set(auto_limits).
% 26.00/26.28 % set(auto_limits) -> assign(max_weight, "100.000").
% 26.00/26.28 % set(auto_limits) -> assign(sos_limit, 20000).
% 26.00/26.28 % set(auto) -> set(auto_denials).
% 26.00/26.28 % set(auto) -> set(auto_process).
% 26.00/26.28 % set(auto2) -> assign(new_constants, 1).
% 26.00/26.28 % set(auto2) -> assign(fold_denial_max, 3).
% 26.00/26.28 % set(auto2) -> assign(max_weight, "200.000").
% 26.00/26.28 % set(auto2) -> assign(max_hours, 1).
% 26.00/26.28 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 26.00/26.28 % set(auto2) -> assign(max_seconds, 0).
% 26.00/26.28 % set(auto2) -> assign(max_minutes, 5).
% 26.00/26.28 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 26.00/26.28 % set(auto2) -> set(sort_initial_sos).
% 26.00/26.28 % set(auto2) -> assign(sos_limit, -1).
% 26.00/26.28 % set(auto2) -> assign(lrs_ticks, 3000).
% 26.00/26.28 % set(auto2) -> assign(max_megs, 400).
% 26.00/26.28 % set(auto2) -> assign(stats, some).
% 26.00/26.28 % set(auto2) -> clear(echo_input).
% 26.00/26.28 % set(auto2) -> set(quiet).
% 26.00/26.28 % set(auto2) -> clear(print_initial_clauses).
% 26.00/26.28 % set(auto2) -> clear(print_given).
% 26.00/26.28 assign(lrs_ticks,-1).
% 26.00/26.28 assign(sos_limit,10000).
% 26.00/26.28 assign(order,kbo).
% 26.00/26.28 set(lex_order_vars).
% 26.00/26.28 clear(print_given).
% 26.00/26.28
% 26.00/26.28 % formulas(sos). % not echoed (2 formulas)
% 26.00/26.28
% 26.00/26.28 ============================== end of input ==========================
% 26.00/26.28
% 26.00/26.28 % From the command line: assign(max_seconds, 300).
% 26.00/26.28
% 26.00/26.28 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 26.00/26.28
% 26.00/26.28 % Formulas that are not ordinary clauses:
% 26.00/26.28
% 26.00/26.28 ============================== end of process non-clausal formulas ===
% 26.00/26.28
% 26.00/26.28 ============================== PROCESS INITIAL CLAUSES ===============
% 26.00/26.28
% 26.00/26.28 ============================== PREDICATE ELIMINATION =================
% 26.00/26.28
% 26.00/26.28 ============================== end predicate elimination =============
% 26.00/26.28
% 26.00/26.28 Auto_denials:
% 26.00/26.28 % copying label prove_normal_axioms_3 to answer in negative clause
% 26.00/26.28
% 26.00/26.28 Term ordering decisions:
% 26.00/26.28 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 26.00/26.28
% 26.00/26.28 ============================== end of process initial clauses ========
% 26.00/26.28
% 26.00/26.28 ============================== CLAUSES FOR SEARCH ====================
% 26.00/26.28
% 26.00/26.28 ============================== end of clauses for search =============
% 26.00/26.28
% 26.00/26.28 ============================== SEARCH ================================
% 26.00/26.28
% 26.00/26.28 % Starting search at 0.01 seconds.
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=187.000, iters=3376
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=171.000, iters=3344
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=157.000, iters=3338
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=155.000, iters=3343
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=151.000, iters=3350
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=141.000, iters=3342
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=137.000, iters=3338
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=133.000, iters=3468
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=125.000, iters=3403
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=123.000, iters=3374
% 26.00/26.28
% 26.00/26.28 Low Water (keep): wt=121.000, iters=3402
% 26.00/26.28
% 26.00/26.28 ============================== PROOF =================================
% 26.00/26.28 % SZS status Unsatisfiable
% 26.00/26.28 % SZS output start Refutation
% 26.00/26.28
% 26.00/26.28 % Proof 1 at 25.08 (+ 0.19) seconds: prove_normal_axioms_3.
% 26.00/26.28 % Length of proof is 104.
% 26.00/26.28 % Level of proof is 32.
% 26.00/26.28 % Maximum clause weight is 167.000.
% 26.00/26.28 % Given clauses 681.
% 26.00/26.28
% 26.00/26.28 1 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(D,B),meet(B,E)),B)),meet(join(meet(B,meet(meet(join(D,join(B,E)),join(F,B)),B)),meet(V6,join(B,meet(meet(join(D,join(B,E)),join(F,B)),B)))),join(A,join(join(meet(D,B),meet(B,E)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B # label(single_axiom) # label(axiom). [assumption].
% 26.00/26.28 2 meet(meet(a,b),c) != meet(a,meet(b,c)) # label(prove_normal_axioms_3) # label(negated_conjecture) # answer(prove_normal_axioms_3). [assumption].
% 26.00/26.28 3 join(meet(join(meet(A,join(meet(B,C),meet(C,join(B,C)))),meet(join(meet(B,C),meet(C,join(B,C))),join(A,join(meet(B,C),meet(C,join(B,C)))))),D),meet(join(meet(A,join(join(meet(E,join(meet(B,C),meet(C,join(B,C)))),meet(join(meet(B,C),meet(C,join(B,C))),F)),join(meet(B,C),meet(C,join(B,C))))),meet(C,join(A,join(join(meet(E,join(meet(B,C),meet(C,join(B,C)))),meet(join(meet(B,C),meet(C,join(B,C))),F)),join(meet(B,C),meet(C,join(B,C))))))),join(join(meet(A,join(meet(B,C),meet(C,join(B,C)))),meet(join(meet(B,C),meet(C,join(B,C))),join(A,join(meet(B,C),meet(C,join(B,C)))))),D))) = join(meet(B,C),meet(C,join(B,C))). [para(1(a,1),1(a,1,2,1,2,1))].
% 26.00/26.28 4 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(D,B),meet(B,E)),B)),meet(join(meet(F,join(join(meet(V6,B),meet(B,V7)),B)),meet(join(meet(B,meet(meet(join(V6,join(B,V7)),join(V8,B)),B)),meet(V9,join(B,meet(meet(join(V6,join(B,V7)),join(V8,B)),B)))),join(F,join(join(meet(V6,B),meet(B,V7)),B)))),join(A,join(join(meet(D,B),meet(B,E)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [para(1(a,1),3(a,1,1,1,1,2)),rewrite([1(91),1(91),1(95),1(96),1(98),1(126),1(127),1(129),1(133),1(134),1(134),1(140)])].
% 26.00/26.28 5 join(meet(join(meet(join(meet(A,B),meet(B,join(A,B))),B),meet(B,join(join(meet(A,B),meet(B,join(A,B))),B))),C),meet(B,join(join(meet(join(meet(A,B),meet(B,join(A,B))),B),meet(B,join(join(meet(A,B),meet(B,join(A,B))),B))),C))) = B. [para(1(a,1),4(a,1,2,1))].
% 26.00/26.28 6 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(D,B),meet(B,E)),B)),meet(join(meet(F,join(join(meet(V6,B),meet(B,V7)),B)),meet(join(meet(V8,join(join(meet(V9,B),meet(B,V10)),B)),meet(join(meet(B,meet(meet(join(V9,join(B,V10)),join(V11,B)),B)),meet(V12,join(B,meet(meet(join(V9,join(B,V10)),join(V11,B)),B)))),join(V8,join(join(meet(V9,B),meet(B,V10)),B)))),join(F,join(join(meet(V6,B),meet(B,V7)),B)))),join(A,join(join(meet(D,B),meet(B,E)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [para(4(a,1),3(a,1,1,1,1,2)),rewrite([4(127),4(127),4(131),4(132),4(134),4(174),4(175),4(177),4(181),4(182),4(182),4(188)])].
% 26.00/26.28 8 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(B,B)),meet(join(meet(B,meet(meet(join(join(meet(join(meet(D,B),meet(B,join(D,B))),B),meet(B,join(join(meet(D,B),meet(B,join(D,B))),B))),join(B,join(join(meet(join(meet(D,B),meet(B,join(D,B))),B),meet(B,join(join(meet(D,B),meet(B,join(D,B))),B))),B))),join(E,B)),B)),meet(F,join(B,meet(meet(join(join(meet(join(meet(D,B),meet(B,join(D,B))),B),meet(B,join(join(meet(D,B),meet(B,join(D,B))),B))),join(B,join(join(meet(join(meet(D,B),meet(B,join(D,B))),B),meet(B,join(join(meet(D,B),meet(B,join(D,B))),B))),B))),join(E,B)),B)))),join(A,join(B,B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [para(5(a,1),1(a,1,2,1,1,2,1)),rewrite([5(99)])].
% 26.00/26.28 9 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(D,B),meet(B,E)),B)),meet(B,join(A,join(join(meet(D,B),meet(B,E)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [para(5(a,1),3(a,1,1,1,1,2)),rewrite([5(29),5(29),5(33),5(34),5(36),5(38),5(39),5(41),5(45),5(46),5(46),5(52)])].
% 26.00/26.28 10 join(meet(join(meet(A,join(meet(B,C),meet(C,join(B,C)))),meet(join(meet(B,C),meet(C,join(B,C))),join(A,join(meet(B,C),meet(C,join(B,C)))))),D),meet(join(meet(A,join(join(meet(B,C),meet(C,join(B,C))),join(meet(B,C),meet(C,join(B,C))))),meet(C,join(A,join(join(meet(B,C),meet(C,join(B,C))),join(meet(B,C),meet(C,join(B,C))))))),join(join(meet(A,join(meet(B,C),meet(C,join(B,C)))),meet(join(meet(B,C),meet(C,join(B,C))),join(A,join(meet(B,C),meet(C,join(B,C)))))),D))) = join(meet(B,C),meet(C,join(B,C))). [para(5(a,1),3(a,1,2,1,1,2,1)),rewrite([5(139)])].
% 26.00/26.28 17 join(meet(A,B),meet(A,join(A,B))) = A. [para(5(a,1),5(a,1,1,1)),rewrite([5(29)])].
% 26.00/26.28 28 join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)) = meet(A,B). [para(17(a,1),17(a,1,2,2))].
% 26.00/26.28 32 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(D,B),meet(B,E)),B)),meet(join(meet(F,join(join(meet(V6,B),meet(B,V7)),B)),meet(join(meet(V8,join(join(meet(V9,B),meet(B,V10)),B)),meet(join(meet(V11,join(join(meet(V12,B),meet(B,V13)),B)),meet(join(meet(B,meet(meet(join(V12,join(B,V13)),join(V14,B)),B)),meet(V15,join(B,meet(meet(join(V12,join(B,V13)),join(V14,B)),B)))),join(V11,join(join(meet(V12,B),meet(B,V13)),B)))),join(V8,join(join(meet(V9,B),meet(B,V10)),B)))),join(F,join(join(meet(V6,B),meet(B,V7)),B)))),join(A,join(join(meet(D,B),meet(B,E)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [para(6(a,1),3(a,1,1,1,1,2)),rewrite([6(163),6(163),6(167),6(168),6(170),6(222),6(223),6(225),6(229),6(230),6(230),6(236)])].
% 26.00/26.28 49 join(meet(A,join(join(meet(B,C),meet(C,D)),C)),meet(join(meet(E,join(join(meet(F,C),meet(C,V6)),C)),meet(join(meet(V7,join(join(meet(V8,C),meet(C,V9)),C)),meet(join(meet(C,meet(meet(join(V8,join(C,V9)),join(V10,C)),C)),meet(V11,join(C,meet(meet(join(V8,join(C,V9)),join(V10,C)),C)))),join(V7,join(join(meet(V8,C),meet(C,V9)),C)))),join(E,join(join(meet(F,C),meet(C,V6)),C)))),join(A,join(join(meet(B,C),meet(C,D)),C)))) = C. [para(6(a,1),9(a,1,1,1)),rewrite([6(371),6(163),17(4)]),flip(a)].
% 26.00/26.28 53 join(meet(A,join(join(meet(B,C),meet(C,D)),C)),meet(C,join(A,join(join(meet(B,C),meet(C,D)),C)))) = C. [para(9(a,1),9(a,1,1,1)),rewrite([9(105),9(49),17(4)]),flip(a)].
% 26.00/26.28 60 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(B,join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [back_rewrite(32),rewrite([49(60),53(17)])].
% 26.00/26.28 65 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(B,B)),meet(join(meet(B,meet(meet(join(B,join(B,join(B,B))),join(D,B)),B)),meet(E,join(B,meet(meet(join(B,join(B,join(B,B))),join(D,B)),B)))),join(A,join(B,B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [back_rewrite(8),rewrite([60(19),60(19),60(26),60(26)])].
% 26.00/26.28 67 join(meet(meet(A,join(join(meet(B,C),meet(C,D)),C)),meet(C,join(A,join(join(meet(B,C),meet(C,D)),C)))),meet(meet(A,join(join(meet(B,C),meet(C,D)),C)),C)) = meet(A,join(join(meet(B,C),meet(C,D)),C)). [para(53(a,1),17(a,1,2,2))].
% 26.00/26.28 68 join(meet(A,join(B,B)),meet(B,join(A,join(B,B)))) = B. [para(17(a,1),53(a,1,1,2,1)),rewrite([17(6)])].
% 26.00/26.28 75 join(meet(A,B),meet(B,join(A,B))) = B. [para(17(a,1),10(a,1,1,1)),rewrite([60(35),17(29),60(12)]),flip(a)].
% 26.00/26.28 79 join(meet(A,B),meet(join(meet(C,join(A,A)),meet(join(meet(A,meet(meet(join(A,join(A,join(A,A))),join(D,A)),A)),meet(E,join(A,meet(meet(join(A,join(A,join(A,A))),join(D,A)),A)))),join(C,join(A,A)))),join(A,B))) = A. [back_rewrite(65),rewrite([75(4),75(27)])].
% 26.00/26.28 98 join(meet(meet(A,join(B,B)),meet(B,join(A,join(B,B)))),meet(meet(B,join(A,join(B,B))),B)) = meet(B,join(A,join(B,B))). [para(68(a,1),75(a,1,2,2))].
% 26.00/26.28 206 join(meet(A,join(join(meet(B,C),meet(C,D)),C)),meet(join(meet(E,join(join(meet(F,C),meet(C,V6)),C)),meet(join(meet(V7,join(join(meet(V8,C),meet(C,V9)),C)),meet(meet(meet(join(V8,join(C,V9)),join(V10,C)),C),join(V7,join(join(meet(V8,C),meet(C,V9)),C)))),join(E,join(join(meet(F,C),meet(C,V6)),C)))),join(A,join(join(meet(B,C),meet(C,D)),C)))) = C. [para(75(a,1),49(a,1,2,1,2,1,2,1))].
% 26.00/26.28 217 join(meet(A,B),meet(join(meet(A,meet(meet(join(A,join(A,join(A,A))),join(C,A)),A)),meet(D,join(A,meet(meet(join(A,join(A,join(A,A))),join(C,A)),A)))),join(A,B))) = A. [para(17(a,1),79(a,1,2,1))].
% 26.00/26.28 224 join(meet(A,B),meet(join(meet(C,join(A,A)),meet(meet(meet(join(A,join(A,join(A,A))),join(D,A)),A),join(C,join(A,A)))),join(A,B))) = A. [para(75(a,1),79(a,1,2,1,2,1))].
% 26.00/26.28 229 join(meet(A,B),meet(meet(meet(join(A,join(A,join(A,A))),join(C,A)),A),join(A,B))) = A. [para(17(a,1),224(a,1,2,1))].
% 26.00/26.28 254 meet(meet(join(A,join(A,join(A,A))),join(B,A)),A) = A. [para(229(a,1),53(a,1)),flip(a)].
% 26.00/26.28 262 join(meet(A,B),meet(join(meet(A,A),meet(C,join(A,A))),join(A,B))) = A. [back_rewrite(217),rewrite([254(7),254(8)])].
% 26.00/26.28 271 meet(meet(join(meet(A,join(B,join(join(meet(C,A),meet(A,D)),A))),join(meet(A,join(B,join(join(meet(C,A),meet(A,D)),A))),join(meet(A,join(B,join(join(meet(C,A),meet(A,D)),A))),meet(A,join(B,join(join(meet(C,A),meet(A,D)),A)))))),A),meet(A,join(B,join(join(meet(C,A),meet(A,D)),A)))) = meet(A,join(B,join(join(meet(C,A),meet(A,D)),A))). [para(53(a,1),254(a,1,1,2))].
% 26.00/26.28 285 join(meet(join(A,A),meet(A,join(meet(join(join(A,A),join(join(A,A),join(join(A,A),join(A,A)))),join(B,join(A,A))),join(A,A)))),meet(meet(A,join(meet(join(join(A,A),join(join(A,A),join(join(A,A),join(A,A)))),join(B,join(A,A))),join(A,A))),A)) = meet(A,join(meet(join(join(A,A),join(join(A,A),join(join(A,A),join(A,A)))),join(B,join(A,A))),join(A,A))). [para(254(a,1),98(a,1,1,1))].
% 26.00/26.28 296 join(meet(join(join(meet(A,B),meet(B,C)),B),meet(B,join(meet(join(join(join(meet(A,B),meet(B,C)),B),join(join(join(meet(A,B),meet(B,C)),B),join(join(join(meet(A,B),meet(B,C)),B),join(join(meet(A,B),meet(B,C)),B)))),join(D,join(join(meet(A,B),meet(B,C)),B))),join(join(meet(A,B),meet(B,C)),B)))),meet(join(join(meet(A,B),meet(B,C)),B),B)) = join(join(meet(A,B),meet(B,C)),B). [para(254(a,1),67(a,1,1,1)),rewrite([254(66),254(72)])].
% 26.00/26.28 315 join(meet(A,A),meet(B,join(A,A))) = A. [para(262(a,1),53(a,1)),flip(a)].
% 26.00/26.28 321 join(meet(meet(A,A),meet(B,join(A,A))),meet(meet(A,A),A)) = meet(A,A). [para(315(a,1),17(a,1,2,2))].
% 26.00/26.28 322 join(meet(meet(meet(A,A),meet(B,join(A,A))),meet(meet(A,A),A)),meet(meet(meet(A,A),meet(B,join(A,A))),meet(A,A))) = meet(meet(A,A),meet(B,join(A,A))). [para(315(a,1),28(a,1,1,2,2))].
% 26.00/26.28 324 join(join(meet(A,B),meet(B,C)),B) = B. [para(315(a,1),53(a,1))].
% 26.00/26.28 325 join(A,A) = A. [para(315(a,1),68(a,1))].
% 26.00/26.28 370 join(meet(A,meet(A,join(meet(A,join(B,A)),A))),meet(A,A)) = A. [back_rewrite(296),rewrite([324(4),324(4),324(4),324(4),324(4),325(1),325(1),325(1),324(4),324(6),324(9),324(11)])].
% 26.00/26.28 371 meet(meet(meet(A,join(B,A)),A),meet(A,join(B,A))) = meet(A,join(B,A)). [back_rewrite(271),rewrite([324(4),324(6),324(8),324(10),325(9),325(7),325(5),324(7),324(10)])].
% 26.00/26.28 376 join(meet(A,B),meet(join(meet(C,B),meet(join(meet(D,B),meet(meet(meet(join(E,join(B,F)),join(V6,B)),B),join(D,B))),join(C,B))),join(A,B))) = B. [back_rewrite(206),rewrite([324(4),324(5),324(6),324(12),324(15),324(18)])].
% 26.00/26.28 393 join(meet(meet(meet(A,A),meet(B,A)),meet(meet(A,A),A)),meet(meet(meet(A,A),meet(B,A)),meet(A,A))) = meet(meet(A,A),meet(B,A)). [back_rewrite(322),rewrite([325(2),325(8),325(14)])].
% 26.00/26.28 394 join(meet(meet(A,A),meet(B,A)),meet(meet(A,A),A)) = meet(A,A). [back_rewrite(321),rewrite([325(2)])].
% 26.00/26.28 397 join(meet(A,A),meet(B,A)) = A. [back_rewrite(315),rewrite([325(2)])].
% 26.00/26.28 408 join(meet(A,meet(A,join(meet(A,join(B,A)),A))),meet(meet(A,join(meet(A,join(B,A)),A)),A)) = meet(A,join(meet(A,join(B,A)),A)). [back_rewrite(285),rewrite([325(1),325(1),325(1),325(1),325(1),325(1),325(1),325(1),325(1),325(3),325(6),325(6),325(6),325(6),325(6),325(6),325(6),325(6),325(8),325(12),325(12),325(12),325(12),325(12),325(12),325(12),325(12),325(14)])].
% 26.00/26.28 418 meet(meet(A,join(B,A)),A) = A. [back_rewrite(254),rewrite([325(1),325(1),325(1)])].
% 26.00/26.28 479 join(meet(A,meet(A,join(meet(A,join(B,A)),A))),A) = meet(A,join(meet(A,join(B,A)),A)). [back_rewrite(408),rewrite([418(10)])].
% 26.00/26.28 485 meet(A,meet(A,join(B,A))) = meet(A,join(B,A)). [back_rewrite(371),rewrite([418(3)])].
% 26.00/26.28 487 join(meet(A,join(meet(A,join(B,A)),A)),A) = meet(A,join(meet(A,join(B,A)),A)). [back_rewrite(479),rewrite([485(5)])].
% 26.00/26.28 502 join(meet(A,join(meet(A,join(B,A)),A)),meet(A,A)) = A. [back_rewrite(370),rewrite([485(5)])].
% 26.00/26.28 503 meet(A,A) = A. [para(325(a,1),17(a,1,2,2)),rewrite([325(3)])].
% 26.00/26.28 504 meet(A,join(meet(A,join(B,A)),A)) = A. [back_rewrite(502),rewrite([503(5),487(5)])].
% 26.00/26.28 514 join(A,meet(B,A)) = A. [back_rewrite(397),rewrite([503(1)])].
% 26.00/26.28 515 join(meet(A,meet(B,A)),A) = A. [back_rewrite(394),rewrite([503(1),503(3),503(3),503(4)])].
% 26.00/26.28 516 meet(meet(A,meet(B,A)),A) = meet(A,meet(B,A)). [back_rewrite(393),rewrite([503(1),503(3),503(3),503(4),503(6),325(7),503(4)])].
% 26.00/26.28 547 meet(join(meet(A,B),meet(B,C)),B) = join(meet(A,B),meet(B,C)). [para(324(a,1),17(a,1,2,2)),rewrite([325(9)])].
% 26.00/26.28 548 join(join(A,meet(A,B)),A) = A. [para(503(a,1),324(a,1,1,1))].
% 26.00/26.28 550 join(meet(A,B),B) = B. [para(514(a,1),324(a,1,1))].
% 26.00/26.28 552 meet(meet(A,B),B) = meet(A,B). [para(550(a,1),17(a,1,2,2)),rewrite([325(5)])].
% 26.00/26.28 580 meet(join(A,meet(A,B)),A) = join(A,meet(A,B)). [para(548(a,1),17(a,1,2,2)),rewrite([325(7)])].
% 26.00/26.28 609 join(meet(A,meet(A,meet(B,A))),A) = A. [para(516(a,1),515(a,1,1,2))].
% 26.00/26.28 611 meet(meet(join(meet(A,join(B,A)),A),A),join(meet(A,join(B,A)),A)) = meet(join(meet(A,join(B,A)),A),A). [para(504(a,1),516(a,1,1,2)),rewrite([504(15)])].
% 26.00/26.28 612 meet(meet(A,meet(A,meet(B,A))),A) = meet(A,meet(A,meet(B,A))). [para(516(a,1),516(a,1,1,2)),rewrite([516(7)])].
% 26.00/26.28 616 join(meet(A,meet(A,meet(A,meet(B,A)))),A) = A. [para(516(a,1),609(a,1,1,2,2))].
% 26.00/26.28 621 join(meet(A,B),meet(join(meet(C,B),meet(meet(meet(join(D,join(B,E)),join(F,B)),B),join(C,B))),join(A,B))) = B. [para(376(a,1),17(a,1)),flip(a)].
% 26.00/26.28 672 join(join(join(A,meet(A,B)),meet(A,C)),A) = A. [para(580(a,1),324(a,1,1,1))].
% 26.00/26.28 690 join(meet(A,meet(A,meet(A,meet(A,meet(B,A))))),A) = A. [para(516(a,1),616(a,1,1,2,2,2))].
% 26.00/26.28 696 meet(join(join(A,meet(A,B)),meet(A,C)),A) = join(join(A,meet(A,B)),meet(A,C)). [para(672(a,1),17(a,1,2,2)),rewrite([325(11)])].
% 26.00/26.28 780 join(A,join(meet(B,A),meet(A,C))) = A. [para(547(a,1),514(a,1,2))].
% 26.00/26.28 804 join(A,join(join(meet(B,A),meet(A,C)),meet(A,D))) = A. [para(547(a,1),780(a,1,2,1))].
% 26.00/26.28 950 join(meet(A,meet(A,meet(A,meet(A,meet(A,meet(A,meet(B,A))))))),A) = A. [para(612(a,1),690(a,1,1,2,2,2,2))].
% 26.00/26.28 1795 join(meet(A,meet(A,meet(A,meet(A,meet(A,meet(A,meet(A,meet(A,meet(B,A))))))))),A) = A. [para(612(a,1),950(a,1,1,2,2,2,2,2,2))].
% 26.00/26.28 2800 meet(join(join(meet(A,join(B,A)),meet(meet(A,join(B,A)),C)),A),meet(A,join(B,A))) = join(join(meet(A,join(B,A)),meet(meet(A,join(B,A)),C)),A). [para(418(a,1),696(a,1,1,2)),rewrite([418(19)])].
% 26.00/26.28 6970 join(meet(join(meet(A,join(B,A)),A),meet(join(meet(A,join(B,A)),A),meet(join(meet(A,join(B,A)),A),meet(join(meet(A,join(B,A)),A),meet(join(meet(A,join(B,A)),A),meet(join(meet(A,join(B,A)),A),meet(join(meet(A,join(B,A)),A),meet(join(meet(A,join(B,A)),A),meet(join(meet(A,join(B,A)),A),A))))))))),join(meet(A,join(B,A)),A)) = join(meet(A,join(B,A)),A). [para(611(a,1),1795(a,1,1,2,2,2,2,2,2,2,2))].
% 26.00/26.28 7200 join(meet(A,B),meet(meet(meet(join(C,join(B,D)),join(E,B)),B),join(A,B))) = B. [para(621(a,1),17(a,1)),flip(a)].
% 26.00/26.28 7528 meet(meet(join(A,join(B,C)),join(D,B)),B) = B. [para(7200(a,1),17(a,1)),flip(a)].
% 26.00/26.28 7810 meet(meet(join(A,B),join(C,B)),B) = B. [para(325(a,1),7528(a,1,1,1,2))].
% 26.00/26.28 7812 meet(join(A,join(B,C)),B) = B. [para(325(a,1),7528(a,1,1,2)),rewrite([552(4)])].
% 26.00/26.28 7850 meet(meet(A,join(B,meet(C,A))),meet(C,A)) = meet(C,A). [para(780(a,1),7528(a,1,1,1))].
% 26.00/26.28 7873 meet(meet(A,join(B,join(meet(C,A),meet(A,D)))),join(meet(C,A),meet(A,D))) = join(meet(C,A),meet(A,D)). [para(804(a,1),7528(a,1,1,1))].
% 26.00/26.28 8641 meet(join(A,B),meet(B,C)) = meet(B,C). [para(17(a,1),7812(a,1,1,2))].
% 26.00/26.28 8650 meet(join(A,B),A) = A. [para(325(a,1),7812(a,1,1))].
% 26.00/26.28 8669 join(A,meet(A,B)) = A. [para(7812(a,1),547(a,1,1,1)),rewrite([8650(3),7812(3)]),flip(a)].
% 26.00/26.28 8672 meet(A,meet(B,A)) = meet(B,A). [para(780(a,1),7812(a,1,1))].
% 26.00/26.28 8760 join(meet(A,join(B,A)),A) = meet(A,join(B,A)). [back_rewrite(2800),rewrite([8669(6),8650(6),8669(8)]),flip(a)].
% 26.00/26.28 8785 meet(A,join(B,A)) = A. [back_rewrite(6970),rewrite([8760(3),8760(5),8760(7),8760(9),8760(11),8760(13),8760(15),8760(17),8760(19),418(19),418(17),418(15),418(13),418(11),418(9),418(7),418(5),418(3),8760(3),8669(3),8760(3)]),flip(a)].
% 26.00/26.28 8893 meet(A,meet(A,B)) = meet(A,B). [para(17(a,1),8650(a,1,1))].
% 26.00/26.28 8921 join(meet(A,B),A) = A. [para(8669(a,1),17(a,1,2,2)),rewrite([8893(2),503(2)])].
% 26.00/26.28 8922 meet(meet(A,B),A) = meet(A,B). [para(8669(a,1),28(a,1,1,2,2)),rewrite([8893(2),503(2),8893(4),325(5),8893(4)])].
% 26.00/26.28 8940 join(A,join(meet(A,B),meet(A,C))) = A. [para(8921(a,1),804(a,1,2,1))].
% 26.00/26.28 9345 meet(A,meet(join(B,A),join(C,A))) = A. [para(7810(a,1),8922(a,1,1)),rewrite([7810(8)])].
% 26.00/26.28 9501 join(join(A,B),meet(B,C)) = join(A,B). [para(8641(a,1),8669(a,1,2))].
% 26.00/26.28 9670 join(A,join(meet(A,B),meet(C,A))) = A. [para(8672(a,1),8940(a,1,2,2))].
% 26.00/26.28 10033 meet(meet(A,B),meet(B,join(C,meet(A,B)))) = meet(A,B). [para(514(a,1),9345(a,1,2,1))].
% 26.00/26.28 10365 join(A,meet(meet(A,B),C)) = A. [para(8669(a,1),9501(a,1,1)),rewrite([8669(5)])].
% 26.00/26.28 10739 meet(meet(A,B),meet(B,A)) = meet(B,A). [para(8669(a,1),7850(a,1,1,2))].
% 26.00/26.28 10775 meet(meet(A,B),meet(meet(B,C),A)) = meet(meet(B,C),A). [para(10365(a,1),7850(a,1,1,2))].
% 26.00/26.28 12501 join(meet(A,B),meet(B,A)) = meet(B,A). [para(9670(a,1),7873(a,1,1,2)),rewrite([8785(5)]),flip(a)].
% 26.00/26.28 12869 meet(A,B) = meet(B,A). [para(10739(a,1),8669(a,1,2)),rewrite([12501(3)])].
% 26.00/26.28 14185 meet(meet(A,B),meet(A,meet(B,C))) = meet(A,meet(B,C)). [back_rewrite(10775),rewrite([12869(3),12869(6)])].
% 26.00/26.28 15217 meet(c,meet(a,b)) != meet(a,meet(b,c)) # answer(prove_normal_axioms_3). [back_rewrite(2),rewrite([12869(5)])].
% 26.00/26.28 18846 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(14185(a,1),8669(a,1,2))].
% 26.00/26.28 18852 meet(meet(A,B),meet(B,meet(A,C))) = meet(B,meet(A,C)). [para(12869(a,1),14185(a,1,1))].
% 26.00/26.28 18924 meet(meet(A,B),meet(C,A)) = meet(C,meet(A,B)). [para(18846(a,1),10033(a,1,2,2)),rewrite([18852(6)])].
% 26.00/26.28 19064 meet(meet(A,B),meet(B,C)) = meet(A,meet(B,C)). [para(18924(a,1),12869(a,1)),flip(a)].
% 26.00/26.28 19065 meet(A,meet(B,C)) = meet(C,meet(A,B)). [para(12869(a,1),18924(a,1,1)),rewrite([12869(2),19064(3),12869(3)])].
% 26.00/26.28 19066 $F # answer(prove_normal_axioms_3). [resolve(19065,a,15217,a(flip))].
% 26.00/26.28
% 26.00/26.28 % SZS output end Refutation
% 26.00/26.28 ============================== end of proof ==========================
% 26.00/26.28
% 26.00/26.28 ============================== STATISTICS ============================
% 26.00/26.28
% 26.00/26.28 Given=681. Generated=328655. Kept=19065. proofs=1.
% 26.00/26.28 Usable=92. Sos=2363. Demods=2460. Limbo=6, Disabled=16605. Hints=0.
% 26.00/26.28 Megabytes=41.70.
% 26.00/26.28 User_CPU=25.08, System_CPU=0.19, Wall_clock=25.
% 26.00/26.28
% 26.00/26.28 ============================== end of statistics =====================
% 26.00/26.28
% 26.00/26.28 ============================== end of search =========================
% 26.00/26.28
% 26.00/26.28 THEOREM PROVED
% 26.00/26.28 % SZS status Unsatisfiable
% 26.00/26.28
% 26.00/26.28 Exiting with 1 proof.
% 26.00/26.28
% 26.00/26.28 Process 27734 exit (max_proofs) Wed Jun 29 15:50:25 2022
% 26.00/26.28 Prover9 interrupted
%------------------------------------------------------------------------------