TSTP Solution File: LAT015-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT015-1 : TPTP v8.1.0. Released v2.2.0.
% 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 06:25:07 EDT 2022
% Result : Unsatisfiable 25.22s 25.53s
% Output : Refutation 25.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LAT015-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % 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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 11:26:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 25.22/25.53 ============================== Prover9 ===============================
% 25.22/25.53 Prover9 (32) version 2009-11A, November 2009.
% 25.22/25.53 Process 4622 was started by sandbox2 on n011.cluster.edu,
% 25.22/25.53 Wed Jun 29 11:26:17 2022
% 25.22/25.53 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4469_n011.cluster.edu".
% 25.22/25.53 ============================== end of head ===========================
% 25.22/25.53
% 25.22/25.53 ============================== INPUT =================================
% 25.22/25.53
% 25.22/25.53 % Reading from file /tmp/Prover9_4469_n011.cluster.edu
% 25.22/25.53
% 25.22/25.53 set(prolog_style_variables).
% 25.22/25.53 set(auto2).
% 25.22/25.53 % set(auto2) -> set(auto).
% 25.22/25.53 % set(auto) -> set(auto_inference).
% 25.22/25.53 % set(auto) -> set(auto_setup).
% 25.22/25.53 % set(auto_setup) -> set(predicate_elim).
% 25.22/25.53 % set(auto_setup) -> assign(eq_defs, unfold).
% 25.22/25.53 % set(auto) -> set(auto_limits).
% 25.22/25.53 % set(auto_limits) -> assign(max_weight, "100.000").
% 25.22/25.53 % set(auto_limits) -> assign(sos_limit, 20000).
% 25.22/25.53 % set(auto) -> set(auto_denials).
% 25.22/25.53 % set(auto) -> set(auto_process).
% 25.22/25.53 % set(auto2) -> assign(new_constants, 1).
% 25.22/25.53 % set(auto2) -> assign(fold_denial_max, 3).
% 25.22/25.53 % set(auto2) -> assign(max_weight, "200.000").
% 25.22/25.53 % set(auto2) -> assign(max_hours, 1).
% 25.22/25.53 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 25.22/25.53 % set(auto2) -> assign(max_seconds, 0).
% 25.22/25.53 % set(auto2) -> assign(max_minutes, 5).
% 25.22/25.53 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 25.22/25.53 % set(auto2) -> set(sort_initial_sos).
% 25.22/25.53 % set(auto2) -> assign(sos_limit, -1).
% 25.22/25.53 % set(auto2) -> assign(lrs_ticks, 3000).
% 25.22/25.53 % set(auto2) -> assign(max_megs, 400).
% 25.22/25.53 % set(auto2) -> assign(stats, some).
% 25.22/25.53 % set(auto2) -> clear(echo_input).
% 25.22/25.53 % set(auto2) -> set(quiet).
% 25.22/25.53 % set(auto2) -> clear(print_initial_clauses).
% 25.22/25.53 % set(auto2) -> clear(print_given).
% 25.22/25.53 assign(lrs_ticks,-1).
% 25.22/25.53 assign(sos_limit,10000).
% 25.22/25.53 assign(order,kbo).
% 25.22/25.53 set(lex_order_vars).
% 25.22/25.53 clear(print_given).
% 25.22/25.53
% 25.22/25.53 % formulas(sos). % not echoed (2 formulas)
% 25.22/25.53
% 25.22/25.53 ============================== end of input ==========================
% 25.22/25.53
% 25.22/25.53 % From the command line: assign(max_seconds, 300).
% 25.22/25.53
% 25.22/25.53 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 25.22/25.53
% 25.22/25.53 % Formulas that are not ordinary clauses:
% 25.22/25.53
% 25.22/25.53 ============================== end of process non-clausal formulas ===
% 25.22/25.53
% 25.22/25.53 ============================== PROCESS INITIAL CLAUSES ===============
% 25.22/25.53
% 25.22/25.53 ============================== PREDICATE ELIMINATION =================
% 25.22/25.53
% 25.22/25.53 ============================== end predicate elimination =============
% 25.22/25.53
% 25.22/25.53 Auto_denials:
% 25.22/25.53 % copying label prove_normal_axioms to answer in negative clause
% 25.22/25.53
% 25.22/25.53 Term ordering decisions:
% 25.22/25.53 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 25.22/25.53
% 25.22/25.53 ============================== end of process initial clauses ========
% 25.22/25.53
% 25.22/25.53 ============================== CLAUSES FOR SEARCH ====================
% 25.22/25.53
% 25.22/25.53 ============================== end of clauses for search =============
% 25.22/25.53
% 25.22/25.53 ============================== SEARCH ================================
% 25.22/25.53
% 25.22/25.53 % Starting search at 0.01 seconds.
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=187.000, iters=3376
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=171.000, iters=3344
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=157.000, iters=3338
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=155.000, iters=3343
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=151.000, iters=3350
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=141.000, iters=3342
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=137.000, iters=3338
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=133.000, iters=3468
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=125.000, iters=3403
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=123.000, iters=3374
% 25.22/25.53
% 25.22/25.53 Low Water (keep): wt=121.000, iters=3402
% 25.22/25.53
% 25.22/25.53 ============================== PROOF =================================
% 25.22/25.53 % SZS status Unsatisfiable
% 25.22/25.53 % SZS output start Refutation
% 25.22/25.53
% 25.22/25.53 % Proof 1 at 24.35 (+ 0.21) seconds: prove_normal_axioms.
% 25.22/25.53 % Length of proof is 148.
% 25.22/25.53 % Level of proof is 33.
% 25.22/25.53 % Maximum clause weight is 167.000.
% 25.22/25.53 % Given clauses 686.
% 25.22/25.53
% 25.22/25.53 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].
% 25.22/25.53 2 meet(a,a) != a | meet(a,b) != meet(b,a) | meet(meet(a,b),c) != meet(a,meet(b,c)) | join(a,a) != a | join(a,b) != join(b,a) | join(join(a,b),c) != join(a,join(b,c)) | meet(a,join(a,b)) != a | join(a,meet(a,b)) != a # label(prove_normal_axioms) # label(negated_conjecture) # answer(prove_normal_axioms). [assumption].
% 25.22/25.53 3 meet(a,a) != a | meet(b,a) != meet(a,b) | meet(meet(a,b),c) != meet(a,meet(b,c)) | join(a,a) != a | join(b,a) != join(a,b) | join(join(a,b),c) != join(a,join(b,c)) | meet(a,join(a,b)) != a | join(a,meet(a,b)) != a # answer(prove_normal_axioms). [copy(2),flip(b),flip(e)].
% 25.22/25.53 4 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))].
% 25.22/25.53 5 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),4(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)])].
% 25.22/25.53 6 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),5(a,1,2,1))].
% 25.22/25.53 7 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(5(a,1),4(a,1,1,1,1,2)),rewrite([5(127),5(127),5(131),5(132),5(134),5(174),5(175),5(177),5(181),5(182),5(182),5(188)])].
% 25.22/25.53 9 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(6(a,1),1(a,1,2,1,1,2,1)),rewrite([6(99)])].
% 25.22/25.53 10 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(6(a,1),4(a,1,1,1,1,2)),rewrite([6(29),6(29),6(33),6(34),6(36),6(38),6(39),6(41),6(45),6(46),6(46),6(52)])].
% 25.22/25.53 11 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(6(a,1),4(a,1,2,1,1,2,1)),rewrite([6(139)])].
% 25.22/25.53 18 join(meet(A,B),meet(A,join(A,B))) = A. [para(6(a,1),6(a,1,1,1)),rewrite([6(29)])].
% 25.22/25.53 29 join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)) = meet(A,B). [para(18(a,1),18(a,1,2,2))].
% 25.22/25.53 33 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(7(a,1),4(a,1,1,1,1,2)),rewrite([7(163),7(163),7(167),7(168),7(170),7(222),7(223),7(225),7(229),7(230),7(230),7(236)])].
% 25.22/25.53 50 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(7(a,1),10(a,1,1,1)),rewrite([7(371),7(163),18(4)]),flip(a)].
% 25.22/25.53 54 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(10(a,1),10(a,1,1,1)),rewrite([10(105),10(49),18(4)]),flip(a)].
% 25.22/25.53 61 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(33),rewrite([50(60),54(17)])].
% 25.22/25.53 66 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(9),rewrite([61(19),61(19),61(26),61(26)])].
% 25.22/25.53 68 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(54(a,1),18(a,1,2,2))].
% 25.22/25.53 69 join(meet(A,join(B,B)),meet(B,join(A,join(B,B)))) = B. [para(18(a,1),54(a,1,1,2,1)),rewrite([18(6)])].
% 25.22/25.53 76 join(meet(A,B),meet(B,join(A,B))) = B. [para(18(a,1),11(a,1,1,1)),rewrite([61(35),18(29),61(12)]),flip(a)].
% 25.22/25.53 80 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(66),rewrite([76(4),76(27)])].
% 25.22/25.53 92 join(meet(meet(A,B),meet(B,join(A,B))),meet(meet(A,B),B)) = meet(A,B). [para(76(a,1),18(a,1,2,2))].
% 25.22/25.53 99 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(69(a,1),76(a,1,2,2))].
% 25.22/25.53 207 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(76(a,1),50(a,1,2,1,2,1,2,1))].
% 25.22/25.53 218 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(18(a,1),80(a,1,2,1))].
% 25.22/25.53 225 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(76(a,1),80(a,1,2,1,2,1))].
% 25.22/25.53 230 join(meet(A,B),meet(meet(meet(join(A,join(A,join(A,A))),join(C,A)),A),join(A,B))) = A. [para(18(a,1),225(a,1,2,1))].
% 25.22/25.53 255 meet(meet(join(A,join(A,join(A,A))),join(B,A)),A) = A. [para(230(a,1),54(a,1)),flip(a)].
% 25.22/25.53 263 join(meet(A,B),meet(join(meet(A,A),meet(C,join(A,A))),join(A,B))) = A. [back_rewrite(218),rewrite([255(7),255(8)])].
% 25.22/25.53 272 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(54(a,1),255(a,1,1,2))].
% 25.22/25.53 286 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(255(a,1),99(a,1,1,1))].
% 25.22/25.53 297 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(255(a,1),68(a,1,1,1)),rewrite([255(66),255(72)])].
% 25.22/25.53 316 join(meet(A,A),meet(B,join(A,A))) = A. [para(263(a,1),54(a,1)),flip(a)].
% 25.22/25.53 322 join(meet(meet(A,A),meet(B,join(A,A))),meet(meet(A,A),A)) = meet(A,A). [para(316(a,1),18(a,1,2,2))].
% 25.22/25.53 323 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(316(a,1),29(a,1,1,2,2))].
% 25.22/25.53 325 join(join(meet(A,B),meet(B,C)),B) = B. [para(316(a,1),54(a,1))].
% 25.22/25.53 326 join(A,A) = A. [para(316(a,1),69(a,1))].
% 25.22/25.53 371 join(meet(A,meet(A,join(meet(A,join(B,A)),A))),meet(A,A)) = A. [back_rewrite(297),rewrite([325(4),325(4),325(4),325(4),325(4),326(1),326(1),326(1),325(4),325(6),325(9),325(11)])].
% 25.22/25.53 372 meet(meet(meet(A,join(B,A)),A),meet(A,join(B,A))) = meet(A,join(B,A)). [back_rewrite(272),rewrite([325(4),325(6),325(8),325(10),326(9),326(7),326(5),325(7),325(10)])].
% 25.22/25.53 377 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(207),rewrite([325(4),325(5),325(6),325(12),325(15),325(18)])].
% 25.22/25.53 394 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(323),rewrite([326(2),326(8),326(14)])].
% 25.22/25.53 395 join(meet(meet(A,A),meet(B,A)),meet(meet(A,A),A)) = meet(A,A). [back_rewrite(322),rewrite([326(2)])].
% 25.22/25.53 398 join(meet(A,A),meet(B,A)) = A. [back_rewrite(316),rewrite([326(2)])].
% 25.22/25.53 409 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(286),rewrite([326(1),326(1),326(1),326(1),326(1),326(1),326(1),326(1),326(1),326(3),326(6),326(6),326(6),326(6),326(6),326(6),326(6),326(6),326(8),326(12),326(12),326(12),326(12),326(12),326(12),326(12),326(12),326(14)])].
% 25.22/25.53 419 meet(meet(A,join(B,A)),A) = A. [back_rewrite(255),rewrite([326(1),326(1),326(1)])].
% 25.22/25.53 440 join(meet(meet(A,B),meet(B,join(A,B))),B) = meet(B,join(A,B)). [back_rewrite(99),rewrite([326(1),326(2),326(5),419(7),326(6)])].
% 25.22/25.53 441 meet(a,a) != a | meet(b,a) != meet(a,b) | meet(meet(a,b),c) != meet(a,meet(b,c)) | join(b,a) != join(a,b) | join(join(a,b),c) != join(a,join(b,c)) | meet(a,join(a,b)) != a | join(a,meet(a,b)) != a # answer(prove_normal_axioms). [back_rewrite(3),rewrite([326(26)]),xx(d)].
% 25.22/25.53 481 join(meet(A,meet(A,join(meet(A,join(B,A)),A))),A) = meet(A,join(meet(A,join(B,A)),A)). [back_rewrite(409),rewrite([419(10)])].
% 25.22/25.53 487 meet(A,meet(A,join(B,A))) = meet(A,join(B,A)). [back_rewrite(372),rewrite([419(3)])].
% 25.22/25.53 489 join(meet(A,join(meet(A,join(B,A)),A)),A) = meet(A,join(meet(A,join(B,A)),A)). [back_rewrite(481),rewrite([487(5)])].
% 25.22/25.53 504 join(meet(A,join(meet(A,join(B,A)),A)),meet(A,A)) = A. [back_rewrite(371),rewrite([487(5)])].
% 25.22/25.53 505 meet(A,A) = A. [para(326(a,1),18(a,1,2,2)),rewrite([326(3)])].
% 25.22/25.53 506 meet(A,join(meet(A,join(B,A)),A)) = A. [back_rewrite(504),rewrite([505(5),489(5)])].
% 25.22/25.53 516 meet(b,a) != meet(a,b) | meet(meet(a,b),c) != meet(a,meet(b,c)) | join(b,a) != join(a,b) | join(join(a,b),c) != join(a,join(b,c)) | meet(a,join(a,b)) != a | join(a,meet(a,b)) != a # answer(prove_normal_axioms). [back_rewrite(441),rewrite([505(3)]),xx(a)].
% 25.22/25.53 517 join(A,meet(B,A)) = A. [back_rewrite(398),rewrite([505(1)])].
% 25.22/25.53 518 join(meet(A,meet(B,A)),A) = A. [back_rewrite(395),rewrite([505(1),505(3),505(3),505(4)])].
% 25.22/25.53 519 meet(meet(A,meet(B,A)),A) = meet(A,meet(B,A)). [back_rewrite(394),rewrite([505(1),505(3),505(3),505(4),505(6),326(7),505(4)])].
% 25.22/25.53 550 meet(join(meet(A,B),meet(B,C)),B) = join(meet(A,B),meet(B,C)). [para(325(a,1),18(a,1,2,2)),rewrite([326(9)])].
% 25.22/25.53 551 join(join(A,meet(A,B)),A) = A. [para(505(a,1),325(a,1,1,1))].
% 25.22/25.53 553 join(meet(A,B),B) = B. [para(517(a,1),325(a,1,1))].
% 25.22/25.53 555 meet(meet(A,B),B) = meet(A,B). [para(553(a,1),18(a,1,2,2)),rewrite([326(5)])].
% 25.22/25.53 579 join(meet(meet(A,B),meet(B,join(A,B))),meet(A,B)) = meet(A,B). [back_rewrite(92),rewrite([555(6)])].
% 25.22/25.53 583 meet(join(A,meet(A,B)),A) = join(A,meet(A,B)). [para(551(a,1),18(a,1,2,2)),rewrite([326(7)])].
% 25.22/25.53 612 join(meet(A,meet(A,meet(B,A))),A) = A. [para(519(a,1),518(a,1,1,2))].
% 25.22/25.53 614 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(506(a,1),519(a,1,1,2)),rewrite([506(15)])].
% 25.22/25.53 615 meet(meet(A,meet(A,meet(B,A))),A) = meet(A,meet(A,meet(B,A))). [para(519(a,1),519(a,1,1,2)),rewrite([519(7)])].
% 25.22/25.53 619 join(meet(A,meet(A,meet(A,meet(B,A)))),A) = A. [para(519(a,1),612(a,1,1,2,2))].
% 25.22/25.53 624 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(377(a,1),18(a,1)),flip(a)].
% 25.22/25.53 675 join(join(join(A,meet(A,B)),meet(A,C)),A) = A. [para(583(a,1),325(a,1,1,1))].
% 25.22/25.53 693 join(meet(A,meet(A,meet(A,meet(A,meet(B,A))))),A) = A. [para(519(a,1),619(a,1,1,2,2,2))].
% 25.22/25.53 699 meet(join(join(A,meet(A,B)),meet(A,C)),A) = join(join(A,meet(A,B)),meet(A,C)). [para(675(a,1),18(a,1,2,2)),rewrite([326(11)])].
% 25.22/25.53 783 join(A,join(meet(B,A),meet(A,C))) = A. [para(550(a,1),517(a,1,2))].
% 25.22/25.53 807 join(A,join(join(meet(B,A),meet(A,C)),meet(A,D))) = A. [para(550(a,1),783(a,1,2,1))].
% 25.22/25.53 953 join(meet(A,meet(A,meet(A,meet(A,meet(A,meet(A,meet(B,A))))))),A) = A. [para(615(a,1),693(a,1,1,2,2,2,2))].
% 25.22/25.53 1798 join(meet(A,meet(A,meet(A,meet(A,meet(A,meet(A,meet(A,meet(A,meet(B,A))))))))),A) = A. [para(615(a,1),953(a,1,1,2,2,2,2,2,2))].
% 25.22/25.53 2803 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(419(a,1),699(a,1,1,2)),rewrite([419(19)])].
% 25.22/25.53 6973 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(614(a,1),1798(a,1,1,2,2,2,2,2,2,2,2))].
% 25.22/25.53 7203 join(meet(A,B),meet(meet(meet(join(C,join(B,D)),join(E,B)),B),join(A,B))) = B. [para(624(a,1),18(a,1)),flip(a)].
% 25.22/25.53 7531 meet(meet(join(A,join(B,C)),join(D,B)),B) = B. [para(7203(a,1),18(a,1)),flip(a)].
% 25.22/25.53 7813 meet(meet(join(A,B),join(C,B)),B) = B. [para(326(a,1),7531(a,1,1,1,2))].
% 25.22/25.53 7814 meet(meet(join(A,B),join(C,A)),A) = A. [para(326(a,1),7531(a,1,1,1))].
% 25.22/25.53 7815 meet(join(A,join(B,C)),B) = B. [para(326(a,1),7531(a,1,1,2)),rewrite([555(4)])].
% 25.22/25.53 7817 join(join(meet(A,meet(join(B,join(C,D)),join(E,C))),C),meet(join(B,join(C,D)),join(E,C))) = meet(join(B,join(C,D)),join(E,C)). [para(7531(a,1),325(a,1,1,2))].
% 25.22/25.53 7853 meet(meet(A,join(B,meet(C,A))),meet(C,A)) = meet(C,A). [para(783(a,1),7531(a,1,1,1))].
% 25.22/25.53 7875 join(meet(join(A,join(B,C)),join(D,B)),join(join(meet(E,meet(join(A,join(B,C)),join(D,B))),meet(meet(join(A,join(B,C)),join(D,B)),F)),B)) = meet(join(A,join(B,C)),join(D,B)). [para(7531(a,1),807(a,1,2,2))].
% 25.22/25.53 7876 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(807(a,1),7531(a,1,1,1))].
% 25.22/25.53 8644 meet(join(A,B),meet(B,C)) = meet(B,C). [para(18(a,1),7815(a,1,1,2))].
% 25.22/25.53 8652 meet(join(A,B),B) = B. [para(326(a,1),7815(a,1,1,2))].
% 25.22/25.53 8653 meet(join(A,B),A) = A. [para(326(a,1),7815(a,1,1))].
% 25.22/25.53 8659 join(join(A,join(B,C)),B) = join(A,join(B,C)). [para(7815(a,1),583(a,1,1,2)),rewrite([8653(6),7815(7)]),flip(a)].
% 25.22/25.53 8670 join(meet(A,meet(A,join(B,join(A,C)))),A) = meet(A,join(B,join(A,C))). [para(7815(a,1),440(a,1,1,1)),rewrite([8659(3),8659(8)])].
% 25.22/25.53 8672 join(A,meet(A,B)) = A. [para(7815(a,1),550(a,1,1,1)),rewrite([8653(3),7815(3)]),flip(a)].
% 25.22/25.53 8675 meet(A,meet(B,A)) = meet(B,A). [para(783(a,1),7815(a,1,1))].
% 25.22/25.53 8686 meet(A,join(B,join(A,C))) = A. [para(7815(a,1),579(a,1,1,1)),rewrite([8659(3),7815(7),8670(5),7815(6)])].
% 25.22/25.53 8763 join(meet(A,join(B,A)),A) = meet(A,join(B,A)). [back_rewrite(2803),rewrite([8672(6),8653(6),8672(8)]),flip(a)].
% 25.22/25.53 8788 meet(A,join(B,A)) = A. [back_rewrite(6973),rewrite([8763(3),8763(5),8763(7),8763(9),8763(11),8763(13),8763(15),8763(17),8763(19),419(19),419(17),419(15),419(13),419(11),419(9),419(7),419(5),419(3),8763(3),8672(3),8763(3)]),flip(a)].
% 25.22/25.53 8829 meet(b,a) != meet(a,b) | meet(meet(a,b),c) != meet(a,meet(b,c)) | join(b,a) != join(a,b) | join(join(a,b),c) != join(a,join(b,c)) | meet(a,join(a,b)) != a # answer(prove_normal_axioms). [back_rewrite(516),rewrite([8672(48)]),xx(f)].
% 25.22/25.53 8858 join(A,meet(join(B,A),join(join(B,A),A))) = join(B,A). [para(8652(a,1),18(a,1,1))].
% 25.22/25.53 8863 join(join(meet(A,join(B,C)),C),join(B,C)) = join(B,C). [para(8652(a,1),325(a,1,1,2))].
% 25.22/25.53 8896 join(A,meet(join(A,B),join(join(A,B),A))) = join(A,B). [para(8653(a,1),18(a,1,1))].
% 25.22/25.53 8897 meet(A,meet(A,B)) = meet(A,B). [para(18(a,1),8653(a,1,1))].
% 25.22/25.53 8898 join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(A,join(A,B))) = A. [para(8653(a,1),29(a,1,1,1)),rewrite([8653(7),8653(10)])].
% 25.22/25.53 8902 join(join(meet(A,join(B,C)),B),join(B,C)) = join(B,C). [para(8653(a,1),325(a,1,1,2))].
% 25.22/25.53 8925 join(meet(A,B),A) = A. [para(8672(a,1),18(a,1,2,2)),rewrite([8897(2),505(2)])].
% 25.22/25.53 8926 meet(meet(A,B),A) = meet(A,B). [para(8672(a,1),29(a,1,1,2,2)),rewrite([8897(2),505(2),8897(4),326(5),8897(4)])].
% 25.22/25.53 8928 join(join(A,B),B) = join(A,B). [para(8652(a,1),8672(a,1,2))].
% 25.22/25.53 8929 join(join(A,B),A) = join(A,B). [para(8653(a,1),8672(a,1,2))].
% 25.22/25.53 8930 join(A,join(B,A)) = join(B,A). [back_rewrite(8858),rewrite([8928(3),505(3)])].
% 25.22/25.53 8931 meet(A,join(A,B)) = A. [back_rewrite(8898),rewrite([8929(3),505(3),326(5)])].
% 25.22/25.53 8932 join(A,join(A,B)) = join(A,B). [back_rewrite(8896),rewrite([8929(3),505(3)])].
% 25.22/25.53 8933 meet(b,a) != meet(a,b) | meet(meet(a,b),c) != meet(a,meet(b,c)) | join(b,a) != join(a,b) | join(join(a,b),c) != join(a,join(b,c)) # answer(prove_normal_axioms). [back_rewrite(8829),rewrite([8931(41)]),xx(e)].
% 25.22/25.53 8945 join(A,join(meet(A,B),meet(A,C))) = A. [para(8925(a,1),807(a,1,2,1))].
% 25.22/25.53 9057 meet(A,join(join(A,B),C)) = A. [para(8929(a,1),8686(a,1,2))].
% 25.22/25.53 9158 meet(A,join(join(B,A),C)) = A. [para(8930(a,1),9057(a,1,2,1))].
% 25.22/25.53 9350 meet(A,meet(join(B,A),join(C,A))) = A. [para(7813(a,1),8926(a,1,1)),rewrite([7813(8)])].
% 25.22/25.53 9462 meet(A,meet(join(A,B),join(C,A))) = A. [para(7814(a,1),8926(a,1,1)),rewrite([7814(8)])].
% 25.22/25.53 9463 meet(meet(join(A,B),join(A,C)),A) = A. [para(8929(a,1),7814(a,1,1,2))].
% 25.22/25.53 9506 join(join(A,B),meet(B,C)) = join(A,B). [para(8644(a,1),8672(a,1,2))].
% 25.22/25.53 9675 join(A,join(meet(A,B),meet(C,A))) = A. [para(8675(a,1),8945(a,1,2,2))].
% 25.22/25.53 10038 meet(meet(A,B),meet(B,join(C,meet(A,B)))) = meet(A,B). [para(517(a,1),9350(a,1,2,1))].
% 25.22/25.53 10149 meet(A,meet(join(A,B),join(A,C))) = A. [para(8929(a,1),9462(a,1,2,2))].
% 25.22/25.53 10370 join(A,meet(meet(A,B),C)) = A. [para(8672(a,1),9506(a,1,1)),rewrite([8672(5)])].
% 25.22/25.53 10744 meet(meet(A,B),meet(B,A)) = meet(B,A). [para(8672(a,1),7853(a,1,1,2))].
% 25.22/25.53 10780 meet(meet(A,B),meet(meet(B,C),A)) = meet(meet(B,C),A). [para(10370(a,1),7853(a,1,1,2))].
% 25.22/25.53 12170 join(meet(join(A,join(B,C)),join(A,B)),join(join(meet(D,meet(join(A,join(B,C)),join(A,B))),A),B)) = meet(join(A,join(B,C)),join(A,B)). [para(9463(a,1),7875(a,1,2,1,2))].
% 25.22/25.53 12214 meet(join(A,join(B,C)),join(A,B)) = join(A,B). [para(10149(a,1),7817(a,1,1,1)),rewrite([517(6)]),flip(a)].
% 25.22/25.53 12221 join(join(A,B),join(join(meet(C,join(A,B)),A),B)) = join(A,B). [back_rewrite(12170),rewrite([12214(4),12214(5),12214(10)])].
% 25.22/25.53 12506 join(meet(A,B),meet(B,A)) = meet(B,A). [para(9675(a,1),7876(a,1,1,2)),rewrite([8788(5)]),flip(a)].
% 25.22/25.53 12874 meet(A,B) = meet(B,A). [para(10744(a,1),8672(a,1,2)),rewrite([12506(3)])].
% 25.22/25.53 14190 meet(meet(A,B),meet(A,meet(B,C))) = meet(A,meet(B,C)). [back_rewrite(10780),rewrite([12874(3),12874(6)])].
% 25.22/25.53 15129 meet(c,meet(a,b)) != meet(a,meet(b,c)) | join(b,a) != join(a,b) | join(join(a,b),c) != join(a,join(b,c)) # answer(prove_normal_axioms). [back_rewrite(8933),rewrite([12874(3),12874(12)]),xx(a)].
% 25.22/25.53 15631 join(join(A,B),join(join(C,A),B)) = join(join(C,A),B). [para(9158(a,1),8863(a,1,1,1))].
% 25.22/25.53 15659 join(join(meet(A,join(B,C)),B),C) = join(B,C). [back_rewrite(12221),rewrite([15631(6)])].
% 25.22/25.53 16158 join(join(A,B),join(B,A)) = join(B,A). [para(8788(a,1),8902(a,1,1,1))].
% 25.22/25.53 16212 join(A,B) = join(B,A). [para(16158(a,1),8929(a,1,1)),rewrite([16158(3),16158(4)])].
% 25.22/25.53 16375 join(A,join(B,meet(C,join(B,A)))) = join(B,A). [back_rewrite(15659),rewrite([16212(3),16212(4)])].
% 25.22/25.53 16523 meet(c,meet(a,b)) != meet(a,meet(b,c)) | join(c,join(a,b)) != join(a,join(b,c)) # answer(prove_normal_axioms). [back_rewrite(15129),rewrite([16212(14),16212(23)]),xx(b)].
% 25.22/25.53 17215 join(A,join(B,A)) = join(B,A). [back_rewrite(8928),rewrite([16212(2)])].
% 25.22/25.53 17728 join(join(A,B),join(A,C)) = join(C,join(A,B)). [para(8686(a,1),16375(a,1,2,2)),rewrite([16212(2)])].
% 25.22/25.53 17932 join(A,join(B,C)) = join(C,join(B,A)). [para(8932(a,1),17728(a,1,2)),rewrite([17728(3),17728(5)])].
% 25.22/25.53 17941 join(A,join(B,C)) = join(B,join(A,C)). [para(17728(a,1),16212(a,1)),rewrite([16212(3),17932(5),17215(4),17932(4)])].
% 25.22/25.53 18065 meet(c,meet(a,b)) != meet(a,meet(b,c)) # answer(prove_normal_axioms). [back_rewrite(16523),rewrite([17932(16),17941(16)]),xx(b)].
% 25.22/25.53 18853 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(14190(a,1),8672(a,1,2))].
% 25.22/25.53 18859 meet(meet(A,B),meet(B,meet(A,C))) = meet(B,meet(A,C)). [para(12874(a,1),14190(a,1,1))].
% 25.22/25.53 18931 meet(meet(A,B),meet(C,A)) = meet(C,meet(A,B)). [para(18853(a,1),10038(a,1,2,2)),rewrite([18859(6)])].
% 25.22/25.53 19071 meet(meet(A,B),meet(B,C)) = meet(A,meet(B,C)). [para(18931(a,1),12874(a,1)),flip(a)].
% 25.22/25.53 19072 meet(A,meet(B,C)) = meet(C,meet(A,B)). [para(12874(a,1),18931(a,1,1)),rewrite([12874(2),19071(3),12874(3)])].
% 25.22/25.53 19073 $F # answer(prove_normal_axioms). [resolve(19072,a,18065,a(flip))].
% 25.22/25.53
% 25.22/25.53 % SZS output end Refutation
% 25.22/25.53 ============================== end of proof ==========================
% 25.22/25.53
% 25.22/25.53 ============================== STATISTICS ============================
% 25.22/25.53
% 25.22/25.53 Given=686. Generated=328669. Kept=19071. proofs=1.
% 25.22/25.53 Usable=92. Sos=2363. Demods=2460. Limbo=6, Disabled=16611. Hints=0.
% 25.22/25.53 Megabytes=41.89.
% 25.22/25.53 User_CPU=24.35, System_CPU=0.21, Wall_clock=25.
% 25.22/25.53
% 25.22/25.53 ============================== end of statistics =====================
% 25.22/25.53
% 25.22/25.53 ============================== end of search =========================
% 25.22/25.53
% 25.22/25.53 THEOREM PROVED
% 25.22/25.53 % SZS status Unsatisfiable
% 25.22/25.53
% 25.22/25.53 Exiting with 1 proof.
% 25.22/25.53
% 25.22/25.53 Process 4622 exit (max_proofs) Wed Jun 29 11:26:42 2022
% 25.22/25.53 Prover9 interrupted
%------------------------------------------------------------------------------