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