TSTP Solution File: LAT030-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT030-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 06:25:12 EDT 2022
% Result : Unsatisfiable 1.33s 1.62s
% Output : Refutation 1.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT030-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 05:36:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.33/1.62 ============================== Prover9 ===============================
% 1.33/1.62 Prover9 (32) version 2009-11A, November 2009.
% 1.33/1.62 Process 26497 was started by sandbox on n017.cluster.edu,
% 1.33/1.62 Wed Jun 29 05:36:38 2022
% 1.33/1.62 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26343_n017.cluster.edu".
% 1.33/1.62 ============================== end of head ===========================
% 1.33/1.62
% 1.33/1.62 ============================== INPUT =================================
% 1.33/1.62
% 1.33/1.62 % Reading from file /tmp/Prover9_26343_n017.cluster.edu
% 1.33/1.62
% 1.33/1.62 set(prolog_style_variables).
% 1.33/1.62 set(auto2).
% 1.33/1.62 % set(auto2) -> set(auto).
% 1.33/1.62 % set(auto) -> set(auto_inference).
% 1.33/1.62 % set(auto) -> set(auto_setup).
% 1.33/1.62 % set(auto_setup) -> set(predicate_elim).
% 1.33/1.62 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.33/1.62 % set(auto) -> set(auto_limits).
% 1.33/1.62 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.33/1.62 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.33/1.62 % set(auto) -> set(auto_denials).
% 1.33/1.62 % set(auto) -> set(auto_process).
% 1.33/1.62 % set(auto2) -> assign(new_constants, 1).
% 1.33/1.62 % set(auto2) -> assign(fold_denial_max, 3).
% 1.33/1.62 % set(auto2) -> assign(max_weight, "200.000").
% 1.33/1.62 % set(auto2) -> assign(max_hours, 1).
% 1.33/1.62 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.33/1.62 % set(auto2) -> assign(max_seconds, 0).
% 1.33/1.62 % set(auto2) -> assign(max_minutes, 5).
% 1.33/1.62 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.33/1.62 % set(auto2) -> set(sort_initial_sos).
% 1.33/1.62 % set(auto2) -> assign(sos_limit, -1).
% 1.33/1.62 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.33/1.62 % set(auto2) -> assign(max_megs, 400).
% 1.33/1.62 % set(auto2) -> assign(stats, some).
% 1.33/1.62 % set(auto2) -> clear(echo_input).
% 1.33/1.62 % set(auto2) -> set(quiet).
% 1.33/1.62 % set(auto2) -> clear(print_initial_clauses).
% 1.33/1.62 % set(auto2) -> clear(print_given).
% 1.33/1.62 assign(lrs_ticks,-1).
% 1.33/1.62 assign(sos_limit,10000).
% 1.33/1.62 assign(order,kbo).
% 1.33/1.62 set(lex_order_vars).
% 1.33/1.62 clear(print_given).
% 1.33/1.62
% 1.33/1.62 % formulas(sos). % not echoed (2 formulas)
% 1.33/1.62
% 1.33/1.62 ============================== end of input ==========================
% 1.33/1.62
% 1.33/1.62 % From the command line: assign(max_seconds, 300).
% 1.33/1.62
% 1.33/1.62 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.33/1.62
% 1.33/1.62 % Formulas that are not ordinary clauses:
% 1.33/1.62
% 1.33/1.62 ============================== end of process non-clausal formulas ===
% 1.33/1.62
% 1.33/1.62 ============================== PROCESS INITIAL CLAUSES ===============
% 1.33/1.62
% 1.33/1.62 ============================== PREDICATE ELIMINATION =================
% 1.33/1.62
% 1.33/1.62 ============================== end predicate elimination =============
% 1.33/1.62
% 1.33/1.62 Auto_denials:
% 1.33/1.62 % copying label prove_wal_axioms to answer in negative clause
% 1.33/1.62
% 1.33/1.62 Term ordering decisions:
% 1.33/1.62 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 1.33/1.62
% 1.33/1.62 ============================== end of process initial clauses ========
% 1.33/1.62
% 1.33/1.62 ============================== CLAUSES FOR SEARCH ====================
% 1.33/1.62
% 1.33/1.62 ============================== end of clauses for search =============
% 1.33/1.62
% 1.33/1.62 ============================== SEARCH ================================
% 1.33/1.62
% 1.33/1.62 % Starting search at 0.01 seconds.
% 1.33/1.62
% 1.33/1.62 ============================== PROOF =================================
% 1.33/1.62 % SZS status Unsatisfiable
% 1.33/1.62 % SZS output start Refutation
% 1.33/1.62
% 1.33/1.62 % Proof 1 at 0.63 (+ 0.01) seconds: prove_wal_axioms.
% 1.33/1.62 % Length of proof is 100.
% 1.33/1.62 % Level of proof is 34.
% 1.33/1.62 % Maximum clause weight is 175.000.
% 1.33/1.62 % Given clauses 85.
% 1.33/1.62
% 1.33/1.62 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].
% 1.33/1.62 2 meet(a,a) != a | meet(b,a) != meet(a,b) | join(a,a) != a | join(b,a) != join(a,b) | meet(meet(join(a,b),join(c,b)),b) != b | join(join(meet(a,b),meet(c,b)),b) != b # label(prove_wal_axioms) # label(negated_conjecture) # answer(prove_wal_axioms). [assumption].
% 1.33/1.62 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(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))].
% 1.33/1.63 4 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),3(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)])].
% 1.33/1.63 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))].
% 1.33/1.63 6 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(4(a,1),3(a,1,1,1,1,2)),rewrite([4(121),4(121),4(125),4(126),4(128),4(166),4(167),4(169),4(173),4(174),4(174),4(180)])].
% 1.33/1.63 8 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(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)])].
% 1.33/1.63 11 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(5(a,1),4(a,1,2,1,2,1))].
% 1.33/1.63 13 join(meet(A,B),meet(A,join(A,B))) = A. [para(5(a,1),5(a,1,1,1)),rewrite([5(29)])].
% 1.33/1.63 15 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(13(a,1),3(a,1,2,1))].
% 1.33/1.63 23 join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)) = meet(A,B). [para(13(a,1),13(a,1,2,2))].
% 1.33/1.63 25 join(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(A,B),meet(A,join(A,B))). [para(23(a,1),13(a,1,2,2))].
% 1.33/1.63 27 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(V11,join(join(meet(B,V12),meet(V13,B)),B)),meet(join(meet(B,meet(meet(join(B,V12),join(V13,B)),B)),meet(V14,join(B,meet(meet(join(B,V12),join(V13,B)),B)))),join(V11,join(join(meet(B,V12),meet(V13,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(6(a,1),3(a,1,1,1,1,2)),rewrite([6(157),6(157),6(161),6(162),6(164),6(214),6(215),6(217),6(221),6(222),6(222),6(228)])].
% 1.33/1.63 37 join(meet(join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,join(A,B)),A)),C),meet(join(meet(meet(A,B),join(join(meet(meet(A,join(A,B)),D),meet(E,meet(A,join(A,B)))),meet(A,join(A,B)))),meet(meet(A,join(A,B)),join(meet(A,B),join(join(meet(meet(A,join(A,B)),D),meet(E,meet(A,join(A,B)))),meet(A,join(A,B)))))),join(join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,join(A,B)),A)),C))) = meet(A,join(A,B)). [para(13(a,1),8(a,1,1,1,2,2)),rewrite([13(47)])].
% 1.33/1.63 40 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(V7,join(join(meet(B,V8),meet(V9,B)),B)),meet(join(meet(B,meet(meet(join(B,V8),join(V9,B)),B)),meet(V10,join(B,meet(meet(join(B,V8),join(V9,B)),B)))),join(V7,join(join(meet(B,V8),meet(V9,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(6(a,1),8(a,1,1,1)),rewrite([6(357),6(157),13(4)]),flip(a)].
% 1.33/1.63 42 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(8(a,1),8(a,1,1,1)),rewrite([8(105),8(49),13(4)]),flip(a)].
% 1.33/1.63 49 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(27),rewrite([40(58),42(17)])].
% 1.33/1.63 52 join(meet(join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,join(A,B)),A)),C),meet(meet(A,join(A,B)),join(join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,join(A,B)),A)),C))) = meet(A,join(A,B)). [back_rewrite(37),rewrite([42(37)])].
% 1.33/1.63 55 join(meet(meet(A,join(join(meet(B,C),meet(D,B)),B)),meet(B,join(A,join(join(meet(B,C),meet(D,B)),B)))),meet(meet(A,join(join(meet(B,C),meet(D,B)),B)),B)) = meet(A,join(join(meet(B,C),meet(D,B)),B)). [para(42(a,1),13(a,1,2,2))].
% 1.33/1.63 69 join(meet(A,join(join(meet(B,C),meet(D,B)),B)),meet(join(meet(B,meet(meet(join(B,E),join(F,B)),B)),meet(V6,join(B,meet(meet(join(B,E),join(F,B)),B)))),join(A,join(join(meet(B,C),meet(D,B)),B)))) = B. [para(11(a,1),42(a,1)),flip(a)].
% 1.33/1.63 76 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(69(a,1),13(a,1)),flip(a)].
% 1.33/1.63 85 join(meet(A,B),meet(B,join(A,B))) = B. [para(15(a,1),42(a,1))].
% 1.33/1.63 87 join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,join(A,B)),A)) = meet(A,join(A,B)). [para(49(a,1),15(a,1,1,1,1,2,2,2)),rewrite([85(4),85(6),85(7),85(10),85(15),85(16),85(19),85(21),85(22),13(21),85(23),85(25),85(26),85(29),85(31),85(32),13(31),85(32),85(13),85(15),85(17),85(18),85(21),85(23),85(24),13(23),85(26),85(27),85(30),85(32),85(33),13(32),85(34),85(36),85(37),85(40),85(42),85(43),13(42),85(43),52(22),85(6),85(7),85(10),85(12),85(13),13(12)]),flip(a)].
% 1.33/1.63 90 join(meet(meet(A,B),meet(B,join(A,B))),meet(meet(A,B),B)) = meet(A,B). [para(85(a,1),13(a,1,2,2))].
% 1.33/1.63 94 join(meet(meet(A,B),meet(B,join(A,B))),meet(meet(B,join(A,B)),B)) = meet(B,join(A,B)). [para(85(a,1),85(a,1,2,2))].
% 1.33/1.63 106 join(meet(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(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)))) = 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)))). [para(25(a,1),87(a,1,1,2,2)),rewrite([25(48),25(69)])].
% 1.33/1.63 134 meet(meet(join(A,B),join(C,A)),A) = A. [para(76(a,1),85(a,1)),flip(a)].
% 1.33/1.63 154 join(meet(A,A),meet(B,join(A,A))) = A. [back_rewrite(76),rewrite([134(4),134(5)])].
% 1.33/1.63 158 meet(meet(A,join(B,meet(A,C))),meet(A,C)) = meet(A,C). [para(13(a,1),134(a,1,1,1))].
% 1.33/1.63 171 join(meet(meet(join(A,B),join(join(meet(A,C),meet(D,A)),A)),meet(A,join(join(A,B),join(join(meet(A,C),meet(D,A)),A)))),A) = meet(join(A,B),join(join(meet(A,C),meet(D,A)),A)). [para(134(a,1),55(a,1,2))].
% 1.33/1.63 174 meet(meet(A,join(B,meet(C,A))),meet(C,A)) = meet(C,A). [para(85(a,1),134(a,1,1,1))].
% 1.33/1.63 176 join(meet(A,meet(A,join(meet(join(A,B),join(C,A)),A))),meet(A,A)) = A. [para(134(a,1),90(a,1,1,1)),rewrite([134(10),134(12)])].
% 1.33/1.63 179 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(134(a,1),94(a,1,1,1))].
% 1.33/1.63 181 join(join(meet(A,B),meet(C,A)),A) = A. [para(154(a,1),42(a,1))].
% 1.33/1.63 183 join(meet(A,A),join(A,A)) = A. [para(134(a,1),154(a,1,2))].
% 1.33/1.63 184 join(meet(meet(join(A,B),A),meet(A,join(join(A,B),A))),A) = meet(join(A,B),A). [back_rewrite(171),rewrite([181(5),181(7),181(12)])].
% 1.33/1.63 185 join(meet(meet(A,A),join(A,A)),meet(meet(A,A),A)) = meet(A,A). [para(183(a,1),13(a,1,2,2))].
% 1.33/1.63 188 join(meet(meet(A,A),join(A,A)),meet(join(A,A),A)) = join(A,A). [para(183(a,1),85(a,1,2,2))].
% 1.33/1.63 202 meet(meet(join(A,B),A),A) = A. [para(181(a,1),134(a,1,1,2))].
% 1.33/1.63 203 join(join(A,meet(B,meet(join(A,C),join(D,A)))),meet(join(A,C),join(D,A))) = meet(join(A,C),join(D,A)). [para(134(a,1),181(a,1,1,1))].
% 1.33/1.63 204 join(join(meet(A,B),A),A) = A. [para(134(a,1),181(a,1,1,2))].
% 1.33/1.63 206 meet(meet(A,meet(A,B)),meet(A,B)) = meet(A,B). [para(13(a,1),202(a,1,1,1))].
% 1.33/1.63 218 join(meet(join(meet(A,B),A),A),meet(join(meet(A,B),A),A)) = join(meet(A,B),A). [para(204(a,1),13(a,1,2,2))].
% 1.33/1.63 226 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(134(a,1),204(a,1,1,1))].
% 1.33/1.63 228 join(join(A,meet(join(A,B),A)),meet(join(A,B),A)) = meet(join(A,B),A). [para(202(a,1),204(a,1,1,1))].
% 1.33/1.63 238 meet(A,A) = A. [para(134(a,1),206(a,1,1,2)),rewrite([134(4),134(4),134(5)])].
% 1.33/1.63 240 join(join(meet(A,B),meet(A,meet(A,B))),meet(A,meet(A,B))) = meet(A,meet(A,B)). [para(206(a,1),204(a,1,1,1))].
% 1.33/1.63 259 join(meet(A,join(A,A)),meet(join(A,A),A)) = join(A,A). [back_rewrite(188),rewrite([238(1)])].
% 1.33/1.63 262 join(meet(A,join(A,A)),A) = A. [back_rewrite(185),rewrite([238(1),238(3),238(3),238(4)])].
% 1.33/1.63 264 join(meet(A,meet(A,join(meet(join(A,B),join(C,A)),A))),A) = A. [back_rewrite(176),rewrite([238(7)])].
% 1.33/1.63 267 join(A,meet(B,join(A,A))) = A. [back_rewrite(154),rewrite([238(1)])].
% 1.33/1.63 274 meet(b,a) != meet(a,b) | join(a,a) != a | join(b,a) != join(a,b) | meet(meet(join(a,b),join(c,b)),b) != b | join(join(meet(a,b),meet(c,b)),b) != b # answer(prove_wal_axioms). [back_rewrite(2),rewrite([238(3)]),xx(a)].
% 1.33/1.63 288 meet(join(A,A),A) = A. [para(238(a,1),134(a,1,1))].
% 1.33/1.63 291 join(A,A) = A. [back_rewrite(259),rewrite([288(4),262(3)]),flip(a)].
% 1.33/1.63 292 meet(b,a) != meet(a,b) | join(b,a) != join(a,b) | meet(meet(join(a,b),join(c,b)),b) != b | join(join(meet(a,b),meet(c,b)),b) != b # answer(prove_wal_axioms). [back_rewrite(274),rewrite([291(10)]),xx(b)].
% 1.33/1.63 299 join(A,meet(B,A)) = A. [back_rewrite(267),rewrite([291(1)])].
% 1.33/1.63 305 meet(join(meet(A,B),A),A) = join(meet(A,B),A). [back_rewrite(218),rewrite([291(7)])].
% 1.33/1.63 310 meet(A,meet(A,B)) = meet(A,B). [back_rewrite(240),rewrite([299(4),299(4)]),flip(a)].
% 1.33/1.63 311 meet(join(A,B),A) = A. [back_rewrite(228),rewrite([299(3),299(3)]),flip(a)].
% 1.33/1.63 312 join(meet(A,join(meet(join(A,B),join(C,A)),A)),A) = A. [back_rewrite(264),rewrite([310(6)])].
% 1.33/1.63 314 join(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)). [back_rewrite(179),rewrite([310(6)])].
% 1.33/1.63 315 join(meet(A,join(join(A,B),A)),A) = A. [back_rewrite(184),rewrite([311(2),310(4),311(6)])].
% 1.33/1.63 316 meet(meet(A,join(B,A)),A) = A. [para(291(a,1),134(a,1,1,1))].
% 1.33/1.63 317 meet(A,join(meet(join(A,B),join(C,A)),A)) = A. [back_rewrite(314),rewrite([316(11),312(6)]),flip(a)].
% 1.33/1.63 327 join(A,meet(join(A,B),join(join(A,B),A))) = join(A,B). [para(311(a,1),13(a,1,1))].
% 1.33/1.63 328 join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(A,join(A,B))) = A. [para(311(a,1),23(a,1,1,1)),rewrite([311(7),311(10)])].
% 1.33/1.63 331 meet(A,meet(B,A)) = meet(B,A). [para(85(a,1),311(a,1,1))].
% 1.33/1.63 338 meet(A,join(meet(A,B),A)) = join(meet(A,B),A). [para(204(a,1),311(a,1,1))].
% 1.33/1.63 363 join(meet(A,B),meet(A,join(A,meet(A,B)))) = A. [para(310(a,1),13(a,1,1))].
% 1.33/1.63 364 join(meet(meet(A,B),meet(A,join(A,meet(A,B)))),meet(meet(A,B),A)) = meet(A,B). [para(310(a,1),23(a,1,1,1)),rewrite([310(7),310(10)])].
% 1.33/1.63 398 join(join(meet(A,B),meet(C,B)),B) = B. [para(331(a,1),181(a,1,1,1))].
% 1.33/1.63 399 meet(b,a) != meet(a,b) | join(b,a) != join(a,b) | meet(meet(join(a,b),join(c,b)),b) != b # answer(prove_wal_axioms). [back_rewrite(292),rewrite([398(34)]),xx(d)].
% 1.33/1.63 403 join(meet(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(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))))) = 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)))). [para(316(a,1),106(a,1,1,1,1,1,1)),rewrite([316(10),310(10),316(13),316(20),316(22),316(29),310(29),316(32),316(41),316(48),310(48),316(51),316(59),316(66),310(66),316(71),316(78),310(78),316(81)])].
% 1.33/1.63 405 meet(A,join(join(A,B),A)) = A. [para(315(a,1),13(a,1,2,2)),rewrite([316(4),316(4),291(1)]),flip(a)].
% 1.33/1.63 418 meet(join(join(A,B),A),A) = A. [para(405(a,1),331(a,1,2)),rewrite([405(6)])].
% 1.33/1.63 419 meet(join(A,meet(A,B)),meet(A,B)) = meet(A,B). [para(13(a,1),418(a,1,1,1))].
% 1.33/1.63 452 join(A,meet(A,join(B,A))) = meet(A,join(B,A)). [para(316(a,1),305(a,1,1,1)),rewrite([419(6),316(5)]),flip(a)].
% 1.33/1.63 465 join(join(meet(A,B),meet(A,join(C,meet(A,B)))),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(158(a,1),204(a,1,1,1))].
% 1.33/1.63 484 join(meet(A,join(B,A)),A) = A. [para(291(a,1),317(a,1,2,1,1)),rewrite([338(4)])].
% 1.33/1.63 493 meet(A,join(B,A)) = A. [back_rewrite(403),rewrite([484(5),316(3),238(1),310(3),484(7),316(5),238(3),238(3),316(3),484(5),316(3),238(1),310(3),484(7),316(5),238(3),316(3),238(1),484(5),316(3),238(1),310(3),484(7),316(5),238(3),316(3),484(5),316(3),238(1),310(3),310(3),452(3),484(7),316(5),238(3),310(5),484(9),316(7),238(5),316(5)])].
% 1.33/1.63 503 join(join(A,B),B) = join(A,B). [para(493(a,1),299(a,1,2))].
% 1.33/1.63 505 meet(join(A,B),B) = B. [para(493(a,1),331(a,1,2)),rewrite([493(4)])].
% 1.33/1.63 508 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [back_rewrite(465),rewrite([503(9)])].
% 1.33/1.63 510 join(A,meet(join(A,B),join(C,A))) = meet(join(A,B),join(C,A)). [back_rewrite(226),rewrite([503(8)])].
% 1.33/1.63 511 meet(A,join(A,meet(A,B))) = A. [back_rewrite(363),rewrite([508(5)])].
% 1.33/1.63 512 meet(join(A,B),join(join(A,B),A)) = join(A,B). [back_rewrite(327),rewrite([510(5)])].
% 1.33/1.63 513 meet(meet(A,B),A) = meet(A,B). [back_rewrite(364),rewrite([511(4),291(5)])].
% 1.33/1.63 514 meet(A,join(A,B)) = A. [back_rewrite(328),rewrite([512(4),291(5)])].
% 1.33/1.63 522 meet(meet(join(A,B),join(C,B)),B) = B. [para(505(a,1),158(a,1,1,2,2)),rewrite([505(5),505(6)])].
% 1.33/1.63 523 meet(b,a) != meet(a,b) | join(b,a) != join(a,b) # answer(prove_wal_axioms). [back_rewrite(399),rewrite([522(23)]),xx(c)].
% 1.33/1.63 527 join(join(A,B),A) = join(A,B). [para(514(a,1),299(a,1,2))].
% 1.33/1.63 540 join(A,meet(A,B)) = A. [para(513(a,1),299(a,1,2))].
% 1.33/1.63 548 meet(meet(A,B),meet(B,A)) = meet(B,A). [para(540(a,1),174(a,1,1,2))].
% 1.33/1.63 582 meet(meet(join(A,B),join(B,C)),B) = B. [para(527(a,1),522(a,1,1,2))].
% 1.33/1.63 612 meet(A,B) = meet(B,A). [para(548(a,1),513(a,1,1)),rewrite([548(3),548(4)])].
% 1.33/1.63 614 meet(A,meet(join(B,A),join(A,C))) = A. [back_rewrite(582),rewrite([612(4)])].
% 1.33/1.63 632 join(b,a) != join(a,b) # answer(prove_wal_axioms). [back_rewrite(523),rewrite([612(3)]),xx(a)].
% 1.33/1.63 663 meet(join(A,B),join(B,A)) = join(A,B). [para(614(a,1),203(a,1,1,2)),rewrite([540(5)]),flip(a)].
% 1.33/1.63 668 join(A,B) = join(B,A). [para(663(a,1),612(a,2)),rewrite([663(3)])].
% 1.33/1.63 669 $F # answer(prove_wal_axioms). [resolve(668,a,632,a)].
% 1.33/1.63
% 1.33/1.63 % SZS output end Refutation
% 1.33/1.63 ============================== end of proof ==========================
% 1.33/1.63
% 1.33/1.63 ============================== STATISTICS ============================
% 1.33/1.63
% 1.33/1.63 Given=85. Generated=5660. Kept=668. proofs=1.
% 1.33/1.63 Usable=25. Sos=77. Demods=103. Limbo=2, Disabled=565. Hints=0.
% 1.33/1.63 Megabytes=1.60.
% 1.33/1.63 User_CPU=0.63, System_CPU=0.01, Wall_clock=0.
% 1.33/1.63
% 1.33/1.63 ============================== end of statistics =====================
% 1.33/1.63
% 1.33/1.63 ============================== end of search =========================
% 1.33/1.63
% 1.33/1.63 THEOREM PROVED
% 1.33/1.63 % SZS status Unsatisfiable
% 1.33/1.63
% 1.33/1.63 Exiting with 1 proof.
% 1.33/1.63
% 1.33/1.63 Process 26497 exit (max_proofs) Wed Jun 29 05:36:38 2022
% 1.33/1.63 Prover9 interrupted
%------------------------------------------------------------------------------