TSTP Solution File: LAT093-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT093-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 06:25:32 EDT 2022
% Result : Unsatisfiable 3.51s 3.79s
% Output : Refutation 3.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT093-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n014.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 : Thu Jun 30 00:44:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.51/3.79 ============================== Prover9 ===============================
% 3.51/3.79 Prover9 (32) version 2009-11A, November 2009.
% 3.51/3.79 Process 10181 was started by sandbox on n014.cluster.edu,
% 3.51/3.79 Thu Jun 30 00:44:42 2022
% 3.51/3.79 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10028_n014.cluster.edu".
% 3.51/3.79 ============================== end of head ===========================
% 3.51/3.79
% 3.51/3.79 ============================== INPUT =================================
% 3.51/3.79
% 3.51/3.79 % Reading from file /tmp/Prover9_10028_n014.cluster.edu
% 3.51/3.79
% 3.51/3.79 set(prolog_style_variables).
% 3.51/3.79 set(auto2).
% 3.51/3.79 % set(auto2) -> set(auto).
% 3.51/3.79 % set(auto) -> set(auto_inference).
% 3.51/3.79 % set(auto) -> set(auto_setup).
% 3.51/3.79 % set(auto_setup) -> set(predicate_elim).
% 3.51/3.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.51/3.79 % set(auto) -> set(auto_limits).
% 3.51/3.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.51/3.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.51/3.79 % set(auto) -> set(auto_denials).
% 3.51/3.79 % set(auto) -> set(auto_process).
% 3.51/3.79 % set(auto2) -> assign(new_constants, 1).
% 3.51/3.79 % set(auto2) -> assign(fold_denial_max, 3).
% 3.51/3.79 % set(auto2) -> assign(max_weight, "200.000").
% 3.51/3.79 % set(auto2) -> assign(max_hours, 1).
% 3.51/3.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.51/3.79 % set(auto2) -> assign(max_seconds, 0).
% 3.51/3.79 % set(auto2) -> assign(max_minutes, 5).
% 3.51/3.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.51/3.79 % set(auto2) -> set(sort_initial_sos).
% 3.51/3.79 % set(auto2) -> assign(sos_limit, -1).
% 3.51/3.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.51/3.79 % set(auto2) -> assign(max_megs, 400).
% 3.51/3.79 % set(auto2) -> assign(stats, some).
% 3.51/3.79 % set(auto2) -> clear(echo_input).
% 3.51/3.79 % set(auto2) -> set(quiet).
% 3.51/3.79 % set(auto2) -> clear(print_initial_clauses).
% 3.51/3.79 % set(auto2) -> clear(print_given).
% 3.51/3.79 assign(lrs_ticks,-1).
% 3.51/3.79 assign(sos_limit,10000).
% 3.51/3.79 assign(order,kbo).
% 3.51/3.79 set(lex_order_vars).
% 3.51/3.79 clear(print_given).
% 3.51/3.79
% 3.51/3.79 % formulas(sos). % not echoed (2 formulas)
% 3.51/3.79
% 3.51/3.79 ============================== end of input ==========================
% 3.51/3.79
% 3.51/3.79 % From the command line: assign(max_seconds, 300).
% 3.51/3.79
% 3.51/3.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.51/3.79
% 3.51/3.79 % Formulas that are not ordinary clauses:
% 3.51/3.79
% 3.51/3.79 ============================== end of process non-clausal formulas ===
% 3.51/3.79
% 3.51/3.79 ============================== PROCESS INITIAL CLAUSES ===============
% 3.51/3.79
% 3.51/3.79 ============================== PREDICATE ELIMINATION =================
% 3.51/3.79
% 3.51/3.79 ============================== end predicate elimination =============
% 3.51/3.79
% 3.51/3.79 Auto_denials:
% 3.51/3.79 % copying label prove_wal_axioms_2 to answer in negative clause
% 3.51/3.79
% 3.51/3.79 Term ordering decisions:
% 3.51/3.79 Function symbol KB weights: a=1. b=1. join=1. meet=1.
% 3.51/3.79
% 3.51/3.79 ============================== end of process initial clauses ========
% 3.51/3.79
% 3.51/3.79 ============================== CLAUSES FOR SEARCH ====================
% 3.51/3.79
% 3.51/3.79 ============================== end of clauses for search =============
% 3.51/3.79
% 3.51/3.79 ============================== SEARCH ================================
% 3.51/3.79
% 3.51/3.79 % Starting search at 0.01 seconds.
% 3.51/3.79
% 3.51/3.79 ============================== PROOF =================================
% 3.51/3.79 % SZS status Unsatisfiable
% 3.51/3.79 % SZS output start Refutation
% 3.51/3.79
% 3.51/3.79 % Proof 1 at 2.82 (+ 0.02) seconds: prove_wal_axioms_2.
% 3.51/3.79 % Length of proof is 141.
% 3.51/3.79 % Level of proof is 28.
% 3.51/3.79 % Maximum clause weight is 155.000.
% 3.51/3.79 % Given clauses 367.
% 3.51/3.79
% 3.51/3.79 1 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(B,D),meet(E,B)),B)),meet(join(meet(B,meet(meet(join(B,D),join(E,B)),B)),meet(F,join(B,meet(meet(join(B,D),join(E,B)),B)))),join(A,join(join(meet(B,D),meet(E,B)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B # label(single_axiom) # label(axiom). [assumption].
% 3.51/3.79 2 meet(b,a) != meet(a,b) # label(prove_wal_axioms_2) # label(negated_conjecture) # answer(prove_wal_axioms_2). [assumption].
% 3.51/3.79 3 meet(b,a) = c_0. [new_symbol(2)].
% 3.51/3.79 4 meet(a,b) != c_0 # answer(prove_wal_axioms_2). [back_rewrite(2),rewrite([3(3)]),flip(a)].
% 3.51/3.79 5 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(join(meet(B,C),meet(C,join(B,C))),E),meet(F,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(join(meet(B,C),meet(C,join(B,C))),E),meet(F,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(1(a,1),1(a,1,2,1,2,1))].
% 3.51/3.79 6 join(meet(join(c_0,meet(a,join(b,a))),A),meet(join(meet(b,join(join(meet(a,B),meet(C,a)),a)),meet(join(meet(a,meet(meet(join(a,B),join(C,a)),a)),meet(D,join(a,meet(meet(join(a,B),join(C,a)),a)))),join(b,join(join(meet(a,B),meet(C,a)),a)))),join(join(c_0,meet(a,join(b,a))),A))) = a. [para(3(a,1),1(a,1,1,1,1)),rewrite([3(51)])].
% 3.51/3.79 7 join(meet(join(meet(A,b),meet(b,join(A,b))),B),meet(join(meet(A,join(join(c_0,meet(C,b)),b)),meet(join(meet(b,meet(meet(join(b,a),join(C,b)),b)),meet(D,join(b,meet(meet(join(b,a),join(C,b)),b)))),join(A,join(join(c_0,meet(C,b)),b)))),join(join(meet(A,b),meet(b,join(A,b))),B))) = b. [para(3(a,1),1(a,1,2,1,1,2,1,1)),rewrite([3(40)])].
% 3.51/3.79 8 join(meet(join(meet(A,a),meet(a,join(A,a))),B),meet(join(meet(A,join(join(meet(a,C),c_0),a)),meet(join(meet(a,meet(meet(join(a,C),join(b,a)),a)),meet(D,join(a,meet(meet(join(a,C),join(b,a)),a)))),join(A,join(join(meet(a,C),c_0),a)))),join(join(meet(A,a),meet(a,join(A,a))),B))) = a. [para(3(a,1),1(a,1,2,1,1,2,1,2)),rewrite([3(42)])].
% 3.51/3.79 9 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(B,D),meet(E,B)),B)),meet(join(meet(F,join(join(meet(B,V6),meet(V7,B)),B)),meet(join(meet(B,meet(meet(join(B,V6),join(V7,B)),B)),meet(V8,join(B,meet(meet(join(B,V6),join(V7,B)),B)))),join(F,join(join(meet(B,V6),meet(V7,B)),B)))),join(A,join(join(meet(B,D),meet(E,B)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [para(1(a,1),5(a,1,1,1,1,2)),rewrite([1(85),1(85),1(89),1(90),1(92),1(118),1(119),1(121),1(125),1(126),1(126),1(132)])].
% 3.51/3.79 10 join(meet(join(meet(A,join(c_0,meet(a,join(b,a)))),meet(join(c_0,meet(a,join(b,a))),join(A,join(c_0,meet(a,join(b,a)))))),B),meet(join(meet(A,join(join(meet(join(c_0,meet(a,join(b,a))),C),meet(D,join(c_0,meet(a,join(b,a))))),join(c_0,meet(a,join(b,a))))),meet(a,join(A,join(join(meet(join(c_0,meet(a,join(b,a))),C),meet(D,join(c_0,meet(a,join(b,a))))),join(c_0,meet(a,join(b,a))))))),join(join(meet(A,join(c_0,meet(a,join(b,a)))),meet(join(c_0,meet(a,join(b,a))),join(A,join(c_0,meet(a,join(b,a)))))),B))) = join(c_0,meet(a,join(b,a))). [para(3(a,1),5(a,1,1,1,1,2,1)),rewrite([3(11),3(18),3(29),3(37),3(46),3(56),3(64),3(73),3(84),3(92),3(99),3(112)])].
% 3.51/3.79 15 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),9(a,1,2,1))].
% 3.51/3.79 19 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(B,D),meet(E,B)),B)),meet(join(meet(F,join(join(meet(B,V6),meet(V7,B)),B)),meet(join(meet(V8,join(join(meet(B,V9),meet(V10,B)),B)),meet(join(meet(B,meet(meet(join(B,V9),join(V10,B)),B)),meet(V11,join(B,meet(meet(join(B,V9),join(V10,B)),B)))),join(V8,join(join(meet(B,V9),meet(V10,B)),B)))),join(F,join(join(meet(B,V6),meet(V7,B)),B)))),join(A,join(join(meet(B,D),meet(E,B)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [para(9(a,1),5(a,1,1,1,1,2)),rewrite([9(121),9(121),9(125),9(126),9(128),9(166),9(167),9(169),9(173),9(174),9(174),9(180)])].
% 3.51/3.79 21 join(meet(join(meet(join(c_0,meet(a,join(b,a))),a),meet(a,join(join(c_0,meet(a,join(b,a))),a))),A),meet(a,join(join(meet(join(c_0,meet(a,join(b,a))),a),meet(a,join(join(c_0,meet(a,join(b,a))),a))),A))) = a. [para(6(a,1),9(a,1,2,1))].
% 3.51/3.79 23 join(meet(join(meet(A,a),meet(a,join(A,a))),B),meet(join(meet(A,join(join(meet(a,C),meet(D,a)),a)),meet(a,join(A,join(join(meet(a,C),meet(D,a)),a)))),join(join(meet(A,a),meet(a,join(A,a))),B))) = a. [para(21(a,1),5(a,1,1,1,1,2)),rewrite([21(51),21(52),21(57),21(59),21(62),21(66),21(68),21(71),21(76),21(78),21(79),21(86)])].
% 3.51/3.79 28 join(meet(join(meet(A,a),meet(a,join(A,a))),B),meet(join(meet(A,join(join(meet(a,C),c_0),a)),meet(a,join(A,join(join(meet(a,C),c_0),a)))),join(join(meet(A,a),meet(a,join(A,a))),B))) = a. [para(3(a,1),23(a,1,2,1,1,2,1,2)),rewrite([3(21)])].
% 3.51/3.79 30 join(meet(a,A),meet(a,join(a,A))) = a. [para(21(a,1),23(a,1,1,1)),rewrite([21(63),21(52)])].
% 3.51/3.79 43 join(meet(join(meet(a,join(c_0,meet(a,join(b,a)))),meet(join(c_0,meet(a,join(b,a))),join(a,join(c_0,meet(a,join(b,a)))))),A),meet(a,join(join(meet(a,join(c_0,meet(a,join(b,a)))),meet(join(c_0,meet(a,join(b,a))),join(a,join(c_0,meet(a,join(b,a)))))),A))) = join(c_0,meet(a,join(b,a))). [para(30(a,1),10(a,1,2,1))].
% 3.51/3.79 46 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(B,D),meet(E,B)),B)),meet(B,join(A,join(join(meet(B,D),meet(E,B)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [para(15(a,1),5(a,1,1,1,1,2)),rewrite([15(29),15(29),15(33),15(34),15(36),15(38),15(39),15(41),15(45),15(46),15(46),15(52)])].
% 3.51/3.79 51 join(meet(join(meet(A,B),meet(B,join(A,B))),C),meet(join(meet(A,join(join(meet(B,D),meet(E,B)),B)),meet(join(meet(B,meet(meet(join(B,F),join(V6,B)),B)),meet(V7,join(B,meet(meet(join(B,F),join(V6,B)),B)))),join(A,join(join(meet(B,D),meet(E,B)),B)))),join(join(meet(A,B),meet(B,join(A,B))),C))) = B. [para(15(a,1),9(a,1,2,1,2,1))].
% 3.51/3.79 58 join(meet(A,B),meet(A,join(A,B))) = A. [para(15(a,1),15(a,1,1,1)),rewrite([15(29)])].
% 3.51/3.79 62 join(c_0,meet(b,join(b,a))) = b. [para(3(a,1),58(a,1,1))].
% 3.51/3.79 64 join(meet(join(meet(A,join(meet(B,A),meet(A,join(B,A)))),meet(join(meet(B,A),meet(A,join(B,A))),join(A,join(meet(B,A),meet(A,join(B,A)))))),C),meet(A,join(join(meet(A,join(meet(B,A),meet(A,join(B,A)))),meet(join(meet(B,A),meet(A,join(B,A))),join(A,join(meet(B,A),meet(A,join(B,A)))))),C))) = join(meet(B,A),meet(A,join(B,A))). [para(58(a,1),5(a,1,2,1))].
% 3.51/3.79 68 join(meet(join(meet(A,b),meet(b,join(A,b))),B),meet(join(meet(A,join(join(c_0,meet(C,b)),b)),meet(b,join(A,join(join(c_0,meet(C,b)),b)))),join(join(meet(A,b),meet(b,join(A,b))),B))) = b. [para(58(a,1),7(a,1,2,1,2,1))].
% 3.51/3.79 89 join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)) = meet(A,B). [para(58(a,1),58(a,1,2,2))].
% 3.51/3.79 106 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(89(a,1),89(a,1,1,2,2))].
% 3.51/3.79 129 join(meet(A,join(join(c_0,meet(B,b)),b)),meet(join(meet(b,meet(meet(join(b,a),join(B,b)),b)),meet(C,join(b,meet(meet(join(b,a),join(B,b)),b)))),join(A,join(join(c_0,meet(B,b)),b)))) = b. [para(7(a,1),46(a,1,1,1)),rewrite([7(294),7(135),58(7)]),flip(a)].
% 3.51/3.79 131 join(meet(A,join(join(meet(a,B),c_0),a)),meet(join(meet(a,meet(meet(join(a,B),join(b,a)),a)),meet(C,join(a,meet(meet(join(a,B),join(b,a)),a)))),join(A,join(join(meet(a,B),c_0),a)))) = a. [para(8(a,1),46(a,1,1,1)),rewrite([8(294),8(135),58(7)]),flip(a)].
% 3.51/3.79 133 join(meet(A,join(join(meet(B,C),meet(D,B)),B)),meet(join(meet(E,join(join(meet(B,F),meet(V6,B)),B)),meet(join(meet(B,meet(meet(join(B,F),join(V6,B)),B)),meet(V7,join(B,meet(meet(join(B,F),join(V6,B)),B)))),join(E,join(join(meet(B,F),meet(V6,B)),B)))),join(A,join(join(meet(B,C),meet(D,B)),B)))) = B. [para(9(a,1),46(a,1,1,1)),rewrite([9(273),9(121),58(4)]),flip(a)].
% 3.51/3.79 138 join(meet(A,join(join(meet(a,B),c_0),a)),meet(a,join(A,join(join(meet(a,B),c_0),a)))) = a. [para(28(a,1),46(a,1,1,1)),rewrite([28(147),28(72),58(7)]),flip(a)].
% 3.51/3.79 150 join(meet(A,join(join(c_0,meet(B,b)),b)),meet(b,join(A,join(join(c_0,meet(B,b)),b)))) = b. [para(68(a,1),46(a,1,1,1)),rewrite([68(147),68(72),58(7)]),flip(a)].
% 3.51/3.79 153 join(meet(A,join(join(meet(B,C),meet(D,B)),B)),meet(B,join(A,join(join(meet(B,C),meet(D,B)),B)))) = B. [para(46(a,1),46(a,1,1,1)),rewrite([46(105),46(49),58(4)]),flip(a)].
% 3.51/3.79 168 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(19),rewrite([133(46),153(17)])].
% 3.51/3.79 207 join(meet(b,meet(meet(join(b,a),join(A,b)),b)),meet(B,join(b,meet(meet(join(b,a),join(A,b)),b)))) = b. [para(129(a,1),58(a,1)),flip(a)].
% 3.51/3.79 208 join(meet(meet(b,meet(meet(join(b,a),join(A,b)),b)),meet(B,join(b,meet(meet(join(b,a),join(A,b)),b)))),meet(meet(b,meet(meet(join(b,a),join(A,b)),b)),b)) = meet(b,meet(meet(join(b,a),join(A,b)),b)). [para(207(a,1),58(a,1,2,2))].
% 3.51/3.79 212 join(meet(b,A),meet(meet(meet(join(b,a),join(B,b)),b),join(b,A))) = meet(meet(join(b,a),join(B,b)),b). [para(207(a,1),168(a,1,1,1)),rewrite([207(40)])].
% 3.51/3.79 219 meet(meet(join(b,a),join(A,b)),b) = b. [para(212(a,1),207(a,1))].
% 3.51/3.79 223 join(meet(meet(b,b),meet(A,join(b,b))),meet(meet(b,b),b)) = meet(b,b). [back_rewrite(208),rewrite([219(9),219(12),219(17),219(23)])].
% 3.51/3.79 233 join(meet(A,join(join(c_0,b),b)),meet(b,join(A,join(join(c_0,b),b)))) = b. [para(219(a,1),150(a,1,1,2,1,2)),rewrite([219(16)])].
% 3.51/3.79 236 join(meet(join(b,meet(b,join(meet(join(b,a),join(A,b)),b))),B),meet(b,join(join(b,meet(b,join(meet(join(b,a),join(A,b)),b))),B))) = b. [para(219(a,1),168(a,1,1,1,1)),rewrite([219(22)])].
% 3.51/3.79 275 join(c_0,meet(a,join(b,a))) = a. [para(43(a,1),138(a,1))].
% 3.51/3.79 298 join(meet(join(meet(join(meet(A,meet(meet(join(A,B),join(C,A)),A)),meet(D,join(A,meet(meet(join(A,B),join(C,A)),A)))),A),meet(A,join(join(meet(A,meet(meet(join(A,B),join(C,A)),A)),meet(D,join(A,meet(meet(join(A,B),join(C,A)),A)))),A))),E),meet(join(meet(A,meet(meet(join(A,B),join(C,A)),A)),meet(D,join(A,meet(meet(join(A,B),join(C,A)),A)))),join(join(meet(join(meet(A,meet(meet(join(A,B),join(C,A)),A)),meet(D,join(A,meet(meet(join(A,B),join(C,A)),A)))),A),meet(A,join(join(meet(A,meet(meet(join(A,B),join(C,A)),A)),meet(D,join(A,meet(meet(join(A,B),join(C,A)),A)))),A))),E))) = A. [para(58(a,1),51(a,1,2,1))].
% 3.51/3.79 335 join(meet(A,B),meet(B,join(A,B))) = B. [para(64(a,1),153(a,1))].
% 3.51/3.79 340 join(b,meet(b,join(meet(join(b,a),join(A,b)),b))) = b. [para(219(a,1),64(a,1,1,1,1,2,1)),rewrite([219(22),219(35),335(42),219(23),219(36),219(49),335(56),236(29),219(9)]),flip(a)].
% 3.51/3.79 376 join(meet(A,B),meet(join(meet(A,meet(meet(join(A,C),join(D,A)),A)),meet(E,join(A,meet(meet(join(A,C),join(D,A)),A)))),join(A,B))) = A. [back_rewrite(298),rewrite([335(28),335(41)])].
% 3.51/3.79 386 join(meet(meet(A,B),meet(B,join(A,B))),meet(meet(A,B),B)) = meet(A,B). [para(335(a,1),58(a,1,2,2))].
% 3.51/3.79 394 join(meet(meet(A,B),meet(B,join(A,B))),meet(meet(B,join(A,B)),B)) = meet(B,join(A,B)). [para(335(a,1),335(a,1,2,2))].
% 3.51/3.79 395 join(meet(b,meet(b,join(meet(join(b,a),join(A,b)),b))),meet(b,b)) = b. [para(340(a,1),58(a,1,2,2))].
% 3.51/3.79 434 join(meet(A,join(b,b)),meet(b,join(A,join(b,b)))) = b. [para(395(a,1),153(a,1,1,2,1)),rewrite([395(21)])].
% 3.51/3.79 697 join(meet(a,meet(meet(join(a,A),join(b,a)),a)),meet(B,join(a,meet(meet(join(a,A),join(b,a)),a)))) = a. [para(131(a,1),58(a,1)),flip(a)].
% 3.51/3.79 699 join(meet(meet(a,meet(meet(join(a,A),join(b,a)),a)),meet(B,join(a,meet(meet(join(a,A),join(b,a)),a)))),meet(meet(a,meet(meet(join(a,A),join(b,a)),a)),a)) = meet(a,meet(meet(join(a,A),join(b,a)),a)). [para(697(a,1),58(a,1,2,2))].
% 3.51/3.79 703 meet(meet(join(a,A),join(b,a)),a) = a. [para(697(a,1),335(a,1)),flip(a)].
% 3.51/3.79 721 join(meet(meet(a,a),meet(A,join(a,a))),meet(meet(a,a),a)) = meet(a,a). [back_rewrite(699),rewrite([703(9),703(12),703(17),703(23)])].
% 3.51/3.79 731 join(a,meet(a,join(meet(join(a,A),join(b,a)),a))) = a. [para(703(a,1),335(a,1,1))].
% 3.51/3.79 745 meet(meet(a,join(b,a)),a) = a. [para(731(a,1),703(a,1,1,1))].
% 3.51/3.79 763 join(meet(a,meet(a,join(meet(a,join(b,a)),a))),meet(a,a)) = a. [para(745(a,1),386(a,1,1,1)),rewrite([745(18),745(22)])].
% 3.51/3.79 781 join(meet(A,join(a,a)),meet(a,join(A,join(a,a)))) = a. [para(763(a,1),153(a,1,1,2,1)),rewrite([763(20)])].
% 3.51/3.79 1182 join(meet(A,meet(meet(join(A,B),join(C,A)),A)),meet(D,join(A,meet(meet(join(A,B),join(C,A)),A)))) = A. [para(376(a,1),153(a,1)),flip(a)].
% 3.51/3.79 1204 join(meet(A,B),meet(meet(meet(join(A,C),join(D,A)),A),join(A,B))) = A. [para(335(a,1),376(a,1,2,1))].
% 3.51/3.79 1250 meet(meet(join(A,B),join(C,A)),A) = A. [para(1204(a,1),153(a,1)),flip(a)].
% 3.51/3.79 1298 join(meet(A,A),meet(B,join(A,A))) = A. [back_rewrite(1182),rewrite([1250(4),1250(5)])].
% 3.51/3.79 1302 meet(meet(b,join(A,c_0)),c_0) = c_0. [para(62(a,1),1250(a,1,1,1))].
% 3.51/3.79 1324 join(meet(meet(b,b),join(b,b)),meet(meet(b,b),b)) = meet(b,b). [para(1250(a,1),223(a,1,1,2))].
% 3.51/3.79 1338 meet(meet(a,join(A,c_0)),c_0) = c_0. [para(275(a,1),1250(a,1,1,1))].
% 3.51/3.79 1347 meet(meet(A,join(B,meet(C,A))),meet(C,A)) = meet(C,A). [para(335(a,1),1250(a,1,1,1))].
% 3.51/3.79 1349 meet(meet(b,join(A,b)),b) = b. [para(340(a,1),1250(a,1,1,1))].
% 3.51/3.79 1369 meet(meet(a,join(A,a)),a) = a. [para(731(a,1),1250(a,1,1,1))].
% 3.51/3.79 1378 join(meet(meet(a,a),join(a,a)),meet(meet(a,a),a)) = meet(a,a). [para(1250(a,1),721(a,1,1,2))].
% 3.51/3.79 1531 join(meet(b,meet(b,join(meet(b,join(A,b)),b))),meet(b,b)) = b. [para(1349(a,1),386(a,1,1,1)),rewrite([1349(16),1349(20)])].
% 3.51/3.79 1532 join(meet(meet(meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))),meet(b,meet(b,join(A,b)))),meet(meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))),b)),meet(meet(meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))),meet(b,meet(b,join(A,b)))),meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))))) = meet(meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))),meet(b,meet(b,join(A,b)))). [para(1349(a,1),106(a,1,1,1,1,1)),rewrite([1349(19),1349(26),1349(39),1349(42),1349(55),1349(62),1349(77),1349(90)])].
% 3.51/3.79 1538 join(meet(b,meet(b,join(meet(b,join(A,b)),b))),b) = meet(b,join(meet(b,join(A,b)),b)). [para(1349(a,1),394(a,1,1,1)),rewrite([1349(20)])].
% 3.51/3.79 1556 join(meet(a,meet(a,join(meet(a,join(A,a)),a))),meet(a,a)) = a. [para(1369(a,1),386(a,1,1,1)),rewrite([1369(16),1369(20)])].
% 3.51/3.79 1557 join(meet(meet(meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))),meet(a,meet(a,join(A,a)))),meet(meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))),a)),meet(meet(meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))),meet(a,meet(a,join(A,a)))),meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))))) = meet(meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))),meet(a,meet(a,join(A,a)))). [para(1369(a,1),106(a,1,1,1,1,1)),rewrite([1369(19),1369(26),1369(39),1369(42),1369(55),1369(62),1369(77),1369(90)])].
% 3.51/3.79 1563 join(meet(a,meet(a,join(meet(a,join(A,a)),a))),a) = meet(a,join(meet(a,join(A,a)),a)). [para(1369(a,1),394(a,1,1,1)),rewrite([1369(20)])].
% 3.51/3.79 1587 join(join(meet(A,B),meet(C,A)),A) = A. [para(1298(a,1),153(a,1))].
% 3.51/3.79 1588 join(join(c_0,b),b) = b. [para(1298(a,1),233(a,1))].
% 3.51/3.79 1591 join(b,b) = b. [para(1298(a,1),434(a,1))].
% 3.51/3.79 1597 join(a,a) = a. [para(1298(a,1),781(a,1))].
% 3.51/3.79 1600 join(meet(A,A),join(A,A)) = A. [para(1250(a,1),1298(a,1,2))].
% 3.51/3.79 1677 join(meet(meet(b,b),b),meet(meet(b,b),b)) = meet(b,b). [back_rewrite(1324),rewrite([1591(6)])].
% 3.51/3.79 1737 join(meet(meet(a,a),a),meet(meet(a,a),a)) = meet(a,a). [back_rewrite(1378),rewrite([1597(6)])].
% 3.51/3.79 1767 meet(meet(b,b),b) = b. [para(1591(a,1),1349(a,1,1,2))].
% 3.51/3.79 1785 meet(b,b) = b. [back_rewrite(1677),rewrite([1767(5),1767(6),1591(3)]),flip(a)].
% 3.51/3.79 1845 meet(b,join(meet(b,join(A,b)),b)) = b. [back_rewrite(1531),rewrite([1785(13),1538(12)])].
% 3.51/3.79 1856 meet(meet(a,a),a) = a. [para(1597(a,1),1369(a,1,1,2))].
% 3.51/3.79 1857 join(meet(a,a),meet(A,a)) = a. [para(1597(a,1),1298(a,1,2,2))].
% 3.51/3.79 1870 meet(a,a) = a. [back_rewrite(1737),rewrite([1856(5),1856(6),1597(3)]),flip(a)].
% 3.51/3.79 1936 join(a,meet(A,a)) = a. [back_rewrite(1857),rewrite([1870(3)])].
% 3.51/3.79 1949 meet(a,join(meet(a,join(A,a)),a)) = a. [back_rewrite(1556),rewrite([1870(13),1563(12)])].
% 3.51/3.79 2007 join(a,c_0) = a. [para(3(a,1),1936(a,1,2))].
% 3.51/3.79 2027 join(meet(a,c_0),meet(c_0,a)) = c_0. [para(2007(a,1),335(a,1,2,2))].
% 3.51/3.79 2035 meet(c_0,c_0) = c_0. [para(2007(a,1),1302(a,1,1,2)),rewrite([3(3)])].
% 3.51/3.79 2036 meet(a,c_0) = c_0. [para(2007(a,1),1338(a,1,1,2)),rewrite([1870(3)])].
% 3.51/3.79 2047 join(c_0,meet(c_0,a)) = c_0. [back_rewrite(2027),rewrite([2036(3)])].
% 3.51/3.79 2094 meet(meet(c_0,join(A,c_0)),c_0) = c_0. [para(2047(a,1),1250(a,1,1,1))].
% 3.51/3.79 2147 join(meet(meet(A,A),join(A,A)),meet(meet(A,A),A)) = meet(A,A). [para(1600(a,1),58(a,1,2,2))].
% 3.51/3.79 2150 join(meet(meet(A,A),join(A,A)),meet(join(A,A),A)) = join(A,A). [para(1600(a,1),335(a,1,2,2))].
% 3.51/3.79 2238 join(meet(c_0,meet(c_0,join(meet(c_0,join(A,c_0)),c_0))),c_0) = c_0. [para(2094(a,1),386(a,1,1,1)),rewrite([2094(16),2035(13),2094(18)])].
% 3.51/3.79 2239 join(meet(meet(meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))),meet(c_0,meet(c_0,join(A,c_0)))),meet(meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))),c_0)),meet(meet(meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))),meet(c_0,meet(c_0,join(A,c_0)))),meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))))) = meet(meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))),meet(c_0,meet(c_0,join(A,c_0)))). [para(2094(a,1),106(a,1,1,1,1,1)),rewrite([2094(19),2094(26),2094(39),2094(42),2094(55),2094(62),2094(77),2094(90)])].
% 3.51/3.79 2244 meet(c_0,join(meet(c_0,join(A,c_0)),c_0)) = c_0. [para(2094(a,1),394(a,1,1,1)),rewrite([2094(20),2238(12)]),flip(a)].
% 3.51/3.79 2336 meet(meet(join(A,B),A),A) = A. [para(1587(a,1),1250(a,1,1,2))].
% 3.51/3.79 2338 join(join(meet(A,B),A),A) = A. [para(1250(a,1),1587(a,1,1,2))].
% 3.51/3.79 2362 meet(meet(A,meet(A,B)),meet(A,B)) = meet(A,B). [para(58(a,1),2336(a,1,1,1))].
% 3.51/3.79 2375 meet(meet(b,join(c_0,b)),join(c_0,b)) = join(c_0,b). [para(1588(a,1),2336(a,1,1,1))].
% 3.51/3.79 2424 join(join(A,meet(join(A,B),A)),meet(join(A,B),A)) = meet(join(A,B),A). [para(2336(a,1),2338(a,1,1,1))].
% 3.51/3.79 2977 meet(A,A) = A. [para(1250(a,1),2362(a,1,1,2)),rewrite([1250(4),1250(4),1250(5)])].
% 3.51/3.79 2979 join(join(meet(A,B),meet(A,meet(A,B))),meet(A,meet(A,B))) = meet(A,meet(A,B)). [para(2362(a,1),2338(a,1,1,1))].
% 3.51/3.79 3211 join(meet(A,join(A,A)),meet(join(A,A),A)) = join(A,A). [back_rewrite(2150),rewrite([2977(1)])].
% 3.51/3.79 3213 join(meet(A,join(A,A)),A) = A. [back_rewrite(2147),rewrite([2977(1),2977(3),2977(3),2977(4)])].
% 3.51/3.79 3264 join(A,meet(B,join(A,A))) = A. [back_rewrite(1298),rewrite([2977(1)])].
% 3.51/3.79 3266 meet(join(A,A),A) = A. [para(2977(a,1),1250(a,1,1))].
% 3.51/3.79 3270 join(A,A) = A. [back_rewrite(3211),rewrite([3266(4),3213(3)]),flip(a)].
% 3.51/3.79 3271 join(A,meet(B,A)) = A. [back_rewrite(3264),rewrite([3270(1)])].
% 3.51/3.79 3358 meet(A,meet(A,B)) = meet(A,B). [back_rewrite(2979),rewrite([3271(4),3271(4)]),flip(a)].
% 3.51/3.79 3359 meet(join(A,B),A) = A. [back_rewrite(2424),rewrite([3271(3),3271(3)]),flip(a)].
% 3.51/3.79 3468 join(meet(meet(meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))),meet(c_0,join(A,c_0))),meet(meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))),c_0)),meet(meet(meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))),meet(c_0,join(A,c_0))),meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))))) = meet(meet(c_0,meet(meet(c_0,join(A,c_0)),join(meet(c_0,join(A,c_0)),c_0))),meet(c_0,join(A,c_0))). [back_rewrite(2239),rewrite([3358(19),3358(53),3358(86)])].
% 3.51/3.79 3494 join(meet(meet(meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))),meet(a,join(A,a))),meet(meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))),a)),meet(meet(meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))),meet(a,join(A,a))),meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))))) = meet(meet(a,meet(meet(a,join(A,a)),join(meet(a,join(A,a)),a))),meet(a,join(A,a))). [back_rewrite(1557),rewrite([3358(19),3358(53),3358(86)])].
% 3.51/3.79 3500 join(meet(meet(meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))),meet(b,join(A,b))),meet(meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))),b)),meet(meet(meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))),meet(b,join(A,b))),meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))))) = meet(meet(b,meet(meet(b,join(A,b)),join(meet(b,join(A,b)),b))),meet(b,join(A,b))). [back_rewrite(1532),rewrite([3358(19),3358(53),3358(86)])].
% 3.51/3.79 3528 meet(meet(A,join(B,A)),A) = A. [para(3270(a,1),1250(a,1,1,1))].
% 3.51/3.79 3556 join(meet(b,join(A,b)),b) = b. [para(1845(a,1),3271(a,1,2)),rewrite([2338(8)]),flip(a)].
% 3.51/3.79 3557 join(meet(a,join(A,a)),a) = a. [para(1949(a,1),3271(a,1,2)),rewrite([2338(8)]),flip(a)].
% 3.51/3.79 3561 join(meet(c_0,join(A,c_0)),c_0) = c_0. [para(2244(a,1),3271(a,1,2)),rewrite([2338(8)]),flip(a)].
% 3.51/3.79 3564 meet(b,join(A,b)) = b. [back_rewrite(3500),rewrite([3556(11),3528(7),2977(3),3358(6),3556(15),3528(11),2977(7),2977(7),3528(6),3556(12),3528(8),2977(4),3358(7),3556(16),3528(12),2977(8),3528(7),3270(3),3556(12),3528(8),2977(4),3358(7)]),flip(a)].
% 3.51/3.79 3567 meet(a,join(A,a)) = a. [back_rewrite(3494),rewrite([3557(11),3528(7),2977(3),3358(6),3557(15),3528(11),2977(7),2977(7),3528(6),3557(12),3528(8),2977(4),3358(7),3557(16),3528(12),2977(8),3528(7),3270(3),3557(12),3528(8),2977(4),3358(7)]),flip(a)].
% 3.51/3.79 3569 meet(c_0,join(A,c_0)) = c_0. [back_rewrite(3468),rewrite([3561(11),3528(7),2977(3),3358(6),3561(15),3528(11),2977(7),2977(7),3528(6),3561(12),3528(8),2977(4),3358(7),3561(16),3528(12),2977(8),3528(7),3270(3),3561(12),3528(8),2977(4),3358(7)]),flip(a)].
% 3.51/3.79 3574 join(c_0,b) = b. [back_rewrite(2375),rewrite([3564(5),3564(5)]),flip(a)].
% 3.51/3.79 3598 meet(c_0,b) = c_0. [para(3574(a,1),58(a,1,2,2)),rewrite([3270(7)])].
% 3.51/3.79 3628 join(b,c_0) = b. [para(3598(a,1),3271(a,1,2))].
% 3.51/3.79 3631 meet(meet(a,b),c_0) = c_0. [para(3628(a,1),1338(a,1,1,2))].
% 3.51/3.79 3635 meet(A,meet(B,A)) = meet(B,A). [para(335(a,1),3359(a,1,1))].
% 3.51/3.79 3706 join(join(A,a),a) = join(A,a). [para(3567(a,1),3271(a,1,2))].
% 3.51/3.79 3714 join(join(A,c_0),c_0) = join(A,c_0). [para(3569(a,1),3271(a,1,2))].
% 3.51/3.79 3723 join(meet(c_0,A),c_0) = c_0. [para(3631(a,1),1587(a,1,1,2)),rewrite([3714(6)])].
% 3.51/3.79 3730 meet(meet(c_0,A),c_0) = meet(c_0,A). [para(3723(a,1),58(a,1,2,2)),rewrite([3270(9)])].
% 3.51/3.79 3827 meet(join(A,a),a) = a. [para(3567(a,1),3635(a,1,2)),rewrite([3567(8)])].
% 3.51/3.79 3834 join(meet(a,A),a) = a. [para(3827(a,1),1587(a,1,1,2)),rewrite([3706(6)])].
% 3.51/3.79 3840 meet(meet(a,A),a) = meet(a,A). [para(3834(a,1),58(a,1,2,2)),rewrite([3270(9)])].
% 3.51/3.79 3954 join(a,meet(a,A)) = a. [para(3840(a,1),3271(a,1,2))].
% 3.51/3.79 4078 meet(meet(A,a),meet(a,A)) = meet(a,A). [para(3954(a,1),1347(a,1,1,2))].
% 3.51/3.79 4180 meet(c_0,meet(a,b)) = meet(a,b). [para(3(a,1),4078(a,1,1))].
% 3.51/3.79 4210 meet(a,b) = c_0. [para(4180(a,1),3730(a,1,1)),rewrite([3631(5),4180(6)]),flip(a)].
% 3.51/3.79 4211 $F # answer(prove_wal_axioms_2). [resolve(4210,a,4,a)].
% 3.51/3.79
% 3.51/3.79 % SZS output end Refutation
% 3.51/3.79 ============================== end of proof ==========================
% 3.51/3.79
% 3.51/3.79 ============================== STATISTICS ============================
% 3.51/3.79
% 3.51/3.79 Given=367. Generated=36561. Kept=4210. proofs=1.
% 3.51/3.79 Usable=96. Sos=481. Demods=588. Limbo=12, Disabled=3622. Hints=0.
% 3.51/3.79 Megabytes=12.08.
% 3.51/3.79 User_CPU=2.82, System_CPU=0.02, Wall_clock=3.
% 3.51/3.79
% 3.51/3.79 ============================== end of statistics =====================
% 3.51/3.79
% 3.51/3.79 ============================== end of search =========================
% 3.51/3.79
% 3.51/3.79 THEOREM PROVED
% 3.51/3.79 % SZS status Unsatisfiable
% 3.51/3.79
% 3.51/3.79 Exiting with 1 proof.
% 3.51/3.79
% 3.51/3.79 Process 10181 exit (max_proofs) Thu Jun 30 00:44:45 2022
% 3.51/3.79 Prover9 interrupted
%------------------------------------------------------------------------------