TSTP Solution File: LAT089-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : LAT089-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n008.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 06:25:30 EDT 2022

% Result   : Unsatisfiable 1.12s 1.44s
% Output   : Refutation 1.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LAT089-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.34  % Computer : n008.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 : Thu Jun 30 01:52:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.12/1.44  ============================== Prover9 ===============================
% 1.12/1.44  Prover9 (32) version 2009-11A, November 2009.
% 1.12/1.44  Process 4775 was started by sandbox on n008.cluster.edu,
% 1.12/1.44  Thu Jun 30 01:52:53 2022
% 1.12/1.44  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4611_n008.cluster.edu".
% 1.12/1.44  ============================== end of head ===========================
% 1.12/1.44  
% 1.12/1.44  ============================== INPUT =================================
% 1.12/1.44  
% 1.12/1.44  % Reading from file /tmp/Prover9_4611_n008.cluster.edu
% 1.12/1.44  
% 1.12/1.44  set(prolog_style_variables).
% 1.12/1.44  set(auto2).
% 1.12/1.44      % set(auto2) -> set(auto).
% 1.12/1.44      % set(auto) -> set(auto_inference).
% 1.12/1.44      % set(auto) -> set(auto_setup).
% 1.12/1.44      % set(auto_setup) -> set(predicate_elim).
% 1.12/1.44      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.12/1.44      % set(auto) -> set(auto_limits).
% 1.12/1.44      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.12/1.44      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.12/1.44      % set(auto) -> set(auto_denials).
% 1.12/1.44      % set(auto) -> set(auto_process).
% 1.12/1.44      % set(auto2) -> assign(new_constants, 1).
% 1.12/1.44      % set(auto2) -> assign(fold_denial_max, 3).
% 1.12/1.44      % set(auto2) -> assign(max_weight, "200.000").
% 1.12/1.44      % set(auto2) -> assign(max_hours, 1).
% 1.12/1.44      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.12/1.44      % set(auto2) -> assign(max_seconds, 0).
% 1.12/1.44      % set(auto2) -> assign(max_minutes, 5).
% 1.12/1.44      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.12/1.44      % set(auto2) -> set(sort_initial_sos).
% 1.12/1.44      % set(auto2) -> assign(sos_limit, -1).
% 1.12/1.44      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.12/1.44      % set(auto2) -> assign(max_megs, 400).
% 1.12/1.44      % set(auto2) -> assign(stats, some).
% 1.12/1.44      % set(auto2) -> clear(echo_input).
% 1.12/1.44      % set(auto2) -> set(quiet).
% 1.12/1.44      % set(auto2) -> clear(print_initial_clauses).
% 1.12/1.44      % set(auto2) -> clear(print_given).
% 1.12/1.44  assign(lrs_ticks,-1).
% 1.12/1.44  assign(sos_limit,10000).
% 1.12/1.44  assign(order,kbo).
% 1.12/1.44  set(lex_order_vars).
% 1.12/1.44  clear(print_given).
% 1.12/1.44  
% 1.12/1.44  % formulas(sos).  % not echoed (6 formulas)
% 1.12/1.44  
% 1.12/1.44  ============================== end of input ==========================
% 1.12/1.44  
% 1.12/1.44  % From the command line: assign(max_seconds, 300).
% 1.12/1.44  
% 1.12/1.44  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.12/1.44  
% 1.12/1.44  % Formulas that are not ordinary clauses:
% 1.12/1.44  
% 1.12/1.44  ============================== end of process non-clausal formulas ===
% 1.12/1.44  
% 1.12/1.44  ============================== PROCESS INITIAL CLAUSES ===============
% 1.12/1.44  
% 1.12/1.44  ============================== PREDICATE ELIMINATION =================
% 1.12/1.44  
% 1.12/1.44  ============================== end predicate elimination =============
% 1.12/1.44  
% 1.12/1.44  Auto_denials:
% 1.12/1.44    % copying label prove_normal_axioms_2 to answer in negative clause
% 1.12/1.44  
% 1.12/1.44  Term ordering decisions:
% 1.12/1.44  Function symbol KB weights:  a=1. b=1. join=1. meet=1.
% 1.12/1.44  
% 1.12/1.44  ============================== end of process initial clauses ========
% 1.12/1.44  
% 1.12/1.44  ============================== CLAUSES FOR SEARCH ====================
% 1.12/1.44  
% 1.12/1.44  ============================== end of clauses for search =============
% 1.12/1.44  
% 1.12/1.44  ============================== SEARCH ================================
% 1.12/1.44  
% 1.12/1.44  % Starting search at 0.01 seconds.
% 1.12/1.44  
% 1.12/1.44  ============================== PROOF =================================
% 1.12/1.44  % SZS status Unsatisfiable
% 1.12/1.44  % SZS output start Refutation
% 1.12/1.44  
% 1.12/1.44  % Proof 1 at 0.34 (+ 0.01) seconds: prove_normal_axioms_2.
% 1.12/1.44  % Length of proof is 107.
% 1.12/1.44  % Level of proof is 19.
% 1.12/1.44  % Maximum clause weight is 99.000.
% 1.12/1.44  % Given clauses 157.
% 1.12/1.44  
% 1.12/1.44  1 join(meet(A,B),meet(A,join(A,B))) = A # label(wal_absorbtion_1) # label(axiom).  [assumption].
% 1.12/1.44  2 join(meet(A,A),meet(B,join(A,A))) = A # label(wal_absorbtion_2) # label(axiom).  [assumption].
% 1.12/1.44  3 join(meet(A,B),meet(B,join(A,B))) = B # label(wal_absorbtion_3) # label(axiom).  [assumption].
% 1.12/1.44  4 meet(meet(join(A,B),join(C,A)),A) = A # label(wal_absorbtion_4) # label(axiom).  [assumption].
% 1.12/1.44  5 join(join(meet(A,B),meet(C,A)),A) = A # label(wal_absorbtion_5) # label(axiom).  [assumption].
% 1.12/1.44  6 meet(b,a) != meet(a,b) # label(prove_normal_axioms_2) # label(negated_conjecture) # answer(prove_normal_axioms_2).  [assumption].
% 1.12/1.44  7 meet(b,a) = c_0.  [new_symbol(6)].
% 1.12/1.44  8 meet(a,b) != c_0 # answer(prove_normal_axioms_2).  [back_rewrite(6),rewrite([7(3)]),flip(a)].
% 1.12/1.44  9 join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)) = meet(A,B).  [para(1(a,1),1(a,1,2,2))].
% 1.12/1.44  10 join(meet(meet(A,A),meet(B,join(A,A))),meet(meet(A,A),A)) = meet(A,A).  [para(2(a,1),1(a,1,2,2))].
% 1.12/1.44  11 join(meet(meet(A,B),meet(B,join(A,B))),meet(meet(A,B),B)) = meet(A,B).  [para(3(a,1),1(a,1,2,2))].
% 1.12/1.44  12 join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,join(A,B)),A)) = meet(A,join(A,B)).  [para(1(a,1),3(a,1,2,2))].
% 1.12/1.44  13 join(meet(meet(A,A),meet(B,join(A,A))),meet(meet(B,join(A,A)),A)) = meet(B,join(A,A)).  [para(2(a,1),3(a,1,2,2))].
% 1.12/1.44  14 join(meet(meet(A,B),meet(B,join(A,B))),meet(meet(B,join(A,B)),B)) = meet(B,join(A,B)).  [para(3(a,1),3(a,1,2,2))].
% 1.12/1.44  15 join(A,meet(meet(join(A,B),join(C,A)),join(meet(join(A,B),join(C,A)),A))) = meet(join(A,B),join(C,A)).  [para(4(a,1),1(a,1,1))].
% 1.12/1.44  18 join(meet(A,A),join(A,A)) = A.  [para(4(a,1),2(a,1,2))].
% 1.12/1.44  21 meet(meet(A,join(B,meet(C,A))),meet(C,A)) = meet(C,A).  [para(3(a,1),4(a,1,1,1))].
% 1.12/1.44  26 meet(meet(join(A,B),A),A) = A.  [para(5(a,1),4(a,1,1,2))].
% 1.12/1.44  28 join(join(meet(A,B),A),A) = A.  [para(4(a,1),5(a,1,1,2))].
% 1.12/1.44  29 join(c_0,meet(b,join(b,a))) = b.  [para(7(a,1),1(a,1,1))].
% 1.12/1.44  30 join(c_0,meet(a,join(b,a))) = a.  [para(7(a,1),3(a,1,1))].
% 1.12/1.44  31 join(join(c_0,meet(A,b)),b) = b.  [para(7(a,1),5(a,1,1,1))].
% 1.12/1.44  34 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(2(a,1),9(a,1,1,2,2))].
% 1.12/1.44  41 join(meet(meet(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)),meet(meet(meet(A,B),meet(A,join(A,B))),meet(A,B))),meet(meet(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)),meet(meet(A,B),meet(A,join(A,B))))) = meet(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)).  [para(9(a,1),9(a,1,1,2,2))].
% 1.12/1.44  42 join(meet(meet(A,A),join(A,A)),meet(meet(A,A),A)) = meet(A,A).  [para(18(a,1),1(a,1,2,2))].
% 1.12/1.44  43 join(meet(meet(A,A),join(A,A)),meet(join(A,A),A)) = join(A,A).  [para(18(a,1),3(a,1,2,2))].
% 1.12/1.44  49 meet(meet(A,meet(B,A)),meet(B,A)) = meet(B,A).  [para(3(a,1),26(a,1,1,1))].
% 1.12/1.44  53 join(meet(join(meet(A,B),A),A),meet(join(meet(A,B),A),A)) = join(meet(A,B),A).  [para(28(a,1),1(a,1,2,2))].
% 1.12/1.44  56 join(join(A,meet(join(A,B),join(C,A))),meet(join(A,B),join(C,A))) = meet(join(A,B),join(C,A)).  [para(4(a,1),28(a,1,1,1))].
% 1.12/1.44  57 join(join(c_0,b),b) = b.  [para(7(a,1),28(a,1,1,1))].
% 1.12/1.44  61 join(meet(join(c_0,b),b),meet(join(c_0,b),b)) = join(c_0,b).  [para(57(a,1),1(a,1,2,2))].
% 1.12/1.44  69 meet(meet(b,join(A,c_0)),c_0) = c_0.  [para(29(a,1),4(a,1,1,1))].
% 1.12/1.44  71 meet(meet(b,c_0),c_0) = c_0.  [para(29(a,1),26(a,1,1,1))].
% 1.12/1.44  73 join(c_0,meet(c_0,join(meet(b,c_0),c_0))) = c_0.  [para(71(a,1),3(a,1,1))].
% 1.12/1.44  79 meet(meet(a,join(A,c_0)),c_0) = c_0.  [para(30(a,1),4(a,1,1,1))].
% 1.12/1.44  92 join(meet(A,meet(A,join(meet(join(A,B),join(C,A)),A))),meet(A,A)) = A.  [para(4(a,1),11(a,1,1,1)),rewrite([4(10),4(12)])].
% 1.12/1.44  111 meet(meet(b,join(A,join(c_0,meet(B,b)))),join(c_0,meet(B,b))) = join(c_0,meet(B,b)).  [para(31(a,1),4(a,1,1,1))].
% 1.12/1.44  155 meet(meet(c_0,join(A,c_0)),c_0) = c_0.  [para(73(a,1),4(a,1,1,1))].
% 1.12/1.44  156 join(meet(meet(c_0,meet(c_0,join(meet(b,c_0),c_0))),meet(c_0,c_0)),meet(meet(c_0,meet(c_0,join(meet(b,c_0),c_0))),c_0)) = meet(c_0,meet(c_0,join(meet(b,c_0),c_0))).  [para(73(a,1),9(a,1,1,2,2))].
% 1.12/1.44  157 meet(meet(c_0,c_0),c_0) = c_0.  [para(73(a,1),26(a,1,1,1))].
% 1.12/1.44  159 join(meet(meet(c_0,meet(c_0,join(meet(b,c_0),c_0))),meet(c_0,c_0)),c_0) = meet(c_0,c_0).  [para(73(a,1),12(a,1,1,2,2)),rewrite([73(23),157(18),73(25)])].
% 1.12/1.44  167 join(meet(meet(c_0,c_0),meet(A,join(c_0,c_0))),c_0) = meet(c_0,c_0).  [para(157(a,1),10(a,1,2))].
% 1.12/1.44  178 meet(c_0,join(c_0,c_0)) = meet(c_0,c_0).  [para(155(a,1),12(a,1,2)),rewrite([167(11)]),flip(a)].
% 1.12/1.44  181 join(meet(meet(A,A),meet(join(A,B),join(A,A))),A) = meet(join(A,B),join(A,A)).  [para(4(a,1),13(a,1,2))].
% 1.12/1.44  184 meet(b,join(c_0,c_0)) = meet(c_0,c_0).  [para(69(a,1),13(a,1,2)),rewrite([167(11)]),flip(a)].
% 1.12/1.44  185 meet(a,join(c_0,c_0)) = meet(c_0,c_0).  [para(79(a,1),13(a,1,2)),rewrite([167(11)]),flip(a)].
% 1.12/1.44  189 join(meet(c_0,c_0),meet(c_0,c_0)) = c_0.  [para(178(a,1),1(a,1,2))].
% 1.12/1.44  212 join(c_0,c_0) = c_0.  [para(189(a,1),5(a,1,1))].
% 1.12/1.44  227 meet(c_0,c_0) = meet(a,c_0).  [back_rewrite(185),rewrite([212(4)]),flip(a)].
% 1.12/1.44  228 meet(b,c_0) = meet(a,c_0).  [back_rewrite(184),rewrite([212(4),227(6)])].
% 1.12/1.44  246 join(meet(meet(c_0,meet(c_0,join(meet(a,c_0),c_0))),meet(a,c_0)),c_0) = meet(a,c_0).  [back_rewrite(159),rewrite([228(5),227(12),227(18)])].
% 1.12/1.44  247 join(meet(meet(c_0,meet(c_0,join(meet(a,c_0),c_0))),meet(a,c_0)),meet(meet(c_0,meet(c_0,join(meet(a,c_0),c_0))),c_0)) = meet(c_0,meet(c_0,join(meet(a,c_0),c_0))).  [back_rewrite(156),rewrite([228(5),227(12),228(18),228(30)])].
% 1.12/1.44  253 join(meet(A,meet(A,join(meet(join(A,B),join(C,A)),A))),meet(meet(A,join(meet(join(A,B),join(C,A)),A)),A)) = meet(A,join(meet(join(A,B),join(C,A)),A)).  [para(4(a,1),14(a,1,1,1))].
% 1.12/1.44  277 join(meet(a,c_0),meet(A,c_0)) = c_0.  [para(212(a,1),2(a,1,2,2)),rewrite([227(3)])].
% 1.12/1.44  278 join(meet(a,c_0),c_0) = c_0.  [para(212(a,1),18(a,1,2)),rewrite([227(3)])].
% 1.12/1.44  282 meet(c_0,meet(a,c_0)) = c_0.  [back_rewrite(247),rewrite([278(7),227(4),49(9),278(10),227(7),277(11),278(8),227(5)]),flip(a)].
% 1.12/1.44  283 meet(a,c_0) = c_0.  [back_rewrite(246),rewrite([278(7),227(4),282(5),282(5),212(3)]),flip(a)].
% 1.12/1.44  299 join(join(c_0,meet(A,a)),a) = a.  [para(283(a,1),5(a,1,1,1))].
% 1.12/1.44  316 meet(A,A) = A.  [para(15(a,1),26(a,1,1,1)),rewrite([4(4)])].
% 1.12/1.44  355 join(meet(A,meet(join(A,B),join(A,A))),A) = meet(join(A,B),join(A,A)).  [back_rewrite(181),rewrite([316(1)])].
% 1.12/1.44  374 join(meet(A,meet(A,join(meet(join(A,B),join(C,A)),A))),A) = A.  [back_rewrite(92),rewrite([316(7)])].
% 1.12/1.44  382 join(meet(A,join(A,A)),meet(join(A,A),A)) = join(A,A).  [back_rewrite(43),rewrite([316(1)])].
% 1.12/1.44  383 join(meet(A,join(A,A)),A) = A.  [back_rewrite(42),rewrite([316(1),316(3),316(3),316(4)])].
% 1.12/1.44  385 join(meet(meet(A,meet(B,join(A,A))),A),meet(meet(A,meet(B,join(A,A))),A)) = meet(A,meet(B,join(A,A))).  [back_rewrite(34),rewrite([316(1),316(4),316(4),316(5),316(8),316(10)])].
% 1.12/1.44  389 join(meet(A,meet(B,join(A,A))),A) = A.  [back_rewrite(10),rewrite([316(1),316(4),316(4),316(5)])].
% 1.12/1.44  390 join(A,meet(B,join(A,A))) = A.  [back_rewrite(2),rewrite([316(1)])].
% 1.12/1.44  392 meet(join(A,B),join(A,A)) = A.  [back_rewrite(355),rewrite([389(5)]),flip(a)].
% 1.12/1.44  403 meet(join(A,A),A) = A.  [para(316(a,1),4(a,1,1))].
% 1.12/1.44  407 join(A,A) = A.  [back_rewrite(382),rewrite([403(4),383(3)]),flip(a)].
% 1.12/1.44  410 meet(join(A,B),A) = A.  [back_rewrite(392),rewrite([407(2)])].
% 1.12/1.44  411 join(A,meet(B,A)) = A.  [back_rewrite(390),rewrite([407(1)])].
% 1.12/1.44  414 meet(meet(A,meet(B,A)),A) = meet(A,meet(B,A)).  [back_rewrite(385),rewrite([407(1),407(4),407(7),407(4)])].
% 1.12/1.44  429 meet(join(c_0,b),b) = join(c_0,b).  [back_rewrite(61),rewrite([407(11)])].
% 1.12/1.44  430 meet(join(meet(A,B),A),A) = join(meet(A,B),A).  [back_rewrite(53),rewrite([407(7)])].
% 1.12/1.44  438 meet(meet(A,join(B,A)),A) = A.  [para(407(a,1),4(a,1,1,1))].
% 1.12/1.44  444 meet(A,join(meet(join(A,B),join(C,A)),A)) = A.  [back_rewrite(253),rewrite([438(12),374(7)]),flip(a)].
% 1.12/1.44  498 join(A,meet(join(A,B),join(join(A,B),A))) = join(A,B).  [para(410(a,1),1(a,1,1))].
% 1.12/1.44  499 meet(A,meet(A,B)) = meet(A,B).  [para(1(a,1),410(a,1,1))].
% 1.12/1.44  501 meet(A,meet(B,A)) = meet(B,A).  [para(3(a,1),410(a,1,1))].
% 1.12/1.44  504 join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(A,join(A,B))) = A.  [para(410(a,1),9(a,1,1,1)),rewrite([410(7),410(10)])].
% 1.12/1.44  506 meet(A,join(meet(A,B),A)) = join(meet(A,B),A).  [para(28(a,1),410(a,1,1))].
% 1.12/1.44  507 meet(b,join(c_0,b)) = join(c_0,b).  [para(57(a,1),410(a,1,1))].
% 1.12/1.44  516 meet(meet(A,B),B) = meet(A,B).  [back_rewrite(414),rewrite([501(2),501(4)])].
% 1.12/1.44  536 meet(meet(join(A,B),B),meet(B,join(A,B))) = meet(B,join(A,B)).  [para(3(a,1),21(a,1,1,2))].
% 1.12/1.44  609 join(meet(meet(A,B),meet(A,join(A,meet(A,B)))),meet(meet(A,B),A)) = meet(A,B).  [para(499(a,1),9(a,1,1,1)),rewrite([499(7),499(10)])].
% 1.12/1.44  619 join(c_0,b) = b.  [para(507(a,1),438(a,1,1)),rewrite([429(5)])].
% 1.12/1.44  632 meet(c_0,b) = c_0.  [para(619(a,1),1(a,1,2,2)),rewrite([407(7)])].
% 1.12/1.44  634 join(b,c_0) = b.  [para(632(a,1),411(a,1,2))].
% 1.12/1.44  637 meet(meet(a,b),c_0) = c_0.  [para(634(a,1),79(a,1,1,2))].
% 1.12/1.44  642 join(meet(c_0,meet(meet(a,b),join(meet(a,b),c_0))),meet(c_0,meet(a,b))) = c_0.  [para(637(a,1),9(a,1,1,1)),rewrite([637(16),637(22)])].
% 1.12/1.44  822 join(meet(meet(meet(A,meet(meet(A,join(B,A)),join(meet(A,join(B,A)),A))),meet(A,join(B,A))),meet(meet(A,meet(meet(A,join(B,A)),join(meet(A,join(B,A)),A))),A)),meet(meet(meet(A,meet(meet(A,join(B,A)),join(meet(A,join(B,A)),A))),meet(A,join(B,A))),meet(A,meet(meet(A,join(B,A)),join(meet(A,join(B,A)),A))))) = meet(meet(A,meet(meet(A,join(B,A)),join(meet(A,join(B,A)),A))),meet(A,join(B,A))).  [para(438(a,1),41(a,1,1,1,1,1)),rewrite([438(10),499(10),438(13),438(20),438(22),438(29),499(29),438(32),438(41),438(48),499(48)])].
% 1.12/1.44  931 meet(meet(join(A,B),join(C,A)),join(A,meet(join(A,B),join(C,A)))) = join(A,meet(join(A,B),join(C,A))).  [para(56(a,1),410(a,1,1))].
% 1.12/1.44  1009 meet(join(c_0,meet(a,b)),meet(a,b)) = join(c_0,meet(a,b)).  [para(637(a,1),430(a,1,1,1)),rewrite([637(14)])].
% 1.12/1.44  1129 join(meet(A,join(B,A)),A) = A.  [para(407(a,1),444(a,1,2,1,1)),rewrite([506(4)])].
% 1.12/1.44  1161 meet(A,join(B,A)) = A.  [back_rewrite(822),rewrite([1129(5),438(3),316(1),499(3),1129(7),438(5),316(3),316(3),438(3),1129(5),438(3),316(1),499(3),1129(7),438(5),316(3),438(3),407(1),1129(5),438(3),316(1),499(3)]),flip(a)].
% 1.12/1.44  1162 join(A,meet(join(A,B),join(C,A))) = meet(join(A,B),join(C,A)).  [back_rewrite(931),rewrite([1161(8)]),flip(a)].
% 1.12/1.44  1166 meet(join(A,B),B) = B.  [back_rewrite(536),rewrite([1161(4),516(3),1161(4)])].
% 1.12/1.44  1168 meet(join(A,B),join(join(A,B),A)) = join(A,B).  [back_rewrite(498),rewrite([1162(5)])].
% 1.12/1.44  1179 join(c_0,meet(a,b)) = meet(a,b).  [back_rewrite(1009),rewrite([1166(9)]),flip(a)].
% 1.12/1.44  1189 meet(A,join(A,B)) = A.  [back_rewrite(504),rewrite([1168(4),407(5)])].
% 1.12/1.44  1237 meet(c_0,meet(a,b)) = c_0.  [back_rewrite(642),rewrite([1189(10),407(11)])].
% 1.12/1.44  1239 meet(meet(A,B),A) = meet(A,B).  [back_rewrite(609),rewrite([1189(4),407(5)])].
% 1.12/1.44  1261 join(join(A,B),A) = join(A,B).  [para(1189(a,1),411(a,1,2))].
% 1.12/1.44  1309 join(join(c_0,meet(a,A)),a) = a.  [para(1239(a,1),299(a,1,1,2))].
% 1.12/1.44  1454 join(a,join(c_0,meet(a,A))) = a.  [para(1309(a,1),1261(a,1,1)),rewrite([1309(12)])].
% 1.12/1.44  1510 meet(a,b) = c_0.  [para(1454(a,1),111(a,1,1,2)),rewrite([7(3),1179(6),1237(5),1179(6)]),flip(a)].
% 1.12/1.44  1511 $F # answer(prove_normal_axioms_2).  [resolve(1510,a,8,a)].
% 1.12/1.44  
% 1.12/1.44  % SZS output end Refutation
% 1.12/1.44  ============================== end of proof ==========================
% 1.12/1.44  
% 1.12/1.44  ============================== STATISTICS ============================
% 1.12/1.44  
% 1.12/1.44  Given=157. Generated=10415. Kept=1510. proofs=1.
% 1.12/1.44  Usable=72. Sos=354. Demods=427. Limbo=2, Disabled=1087. Hints=0.
% 1.12/1.44  Megabytes=2.42.
% 1.12/1.44  User_CPU=0.34, System_CPU=0.01, Wall_clock=1.
% 1.12/1.44  
% 1.12/1.44  ============================== end of statistics =====================
% 1.12/1.44  
% 1.12/1.44  ============================== end of search =========================
% 1.12/1.44  
% 1.12/1.44  THEOREM PROVED
% 1.12/1.44  % SZS status Unsatisfiable
% 1.12/1.44  
% 1.12/1.44  Exiting with 1 proof.
% 1.12/1.44  
% 1.12/1.44  Process 4775 exit (max_proofs) Thu Jun 30 01:52:54 2022
% 1.12/1.44  Prover9 interrupted
%------------------------------------------------------------------------------