TSTP Solution File: LAT010-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT010-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 06:25:05 EDT 2022
% Result : Unsatisfiable 1.30s 1.61s
% Output : Refutation 1.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT010-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 30 01:16:21 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.30/1.61 ============================== Prover9 ===============================
% 1.30/1.61 Prover9 (32) version 2009-11A, November 2009.
% 1.30/1.61 Process 22342 was started by sandbox on n003.cluster.edu,
% 1.30/1.61 Thu Jun 30 01:16:22 2022
% 1.30/1.61 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22187_n003.cluster.edu".
% 1.30/1.61 ============================== end of head ===========================
% 1.30/1.61
% 1.30/1.61 ============================== INPUT =================================
% 1.30/1.61
% 1.30/1.61 % Reading from file /tmp/Prover9_22187_n003.cluster.edu
% 1.30/1.61
% 1.30/1.61 set(prolog_style_variables).
% 1.30/1.61 set(auto2).
% 1.30/1.61 % set(auto2) -> set(auto).
% 1.30/1.61 % set(auto) -> set(auto_inference).
% 1.30/1.61 % set(auto) -> set(auto_setup).
% 1.30/1.61 % set(auto_setup) -> set(predicate_elim).
% 1.30/1.61 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.30/1.61 % set(auto) -> set(auto_limits).
% 1.30/1.61 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.30/1.61 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.30/1.61 % set(auto) -> set(auto_denials).
% 1.30/1.61 % set(auto) -> set(auto_process).
% 1.30/1.61 % set(auto2) -> assign(new_constants, 1).
% 1.30/1.61 % set(auto2) -> assign(fold_denial_max, 3).
% 1.30/1.61 % set(auto2) -> assign(max_weight, "200.000").
% 1.30/1.61 % set(auto2) -> assign(max_hours, 1).
% 1.30/1.61 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.30/1.61 % set(auto2) -> assign(max_seconds, 0).
% 1.30/1.61 % set(auto2) -> assign(max_minutes, 5).
% 1.30/1.61 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.30/1.61 % set(auto2) -> set(sort_initial_sos).
% 1.30/1.61 % set(auto2) -> assign(sos_limit, -1).
% 1.30/1.61 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.30/1.61 % set(auto2) -> assign(max_megs, 400).
% 1.30/1.61 % set(auto2) -> assign(stats, some).
% 1.30/1.61 % set(auto2) -> clear(echo_input).
% 1.30/1.61 % set(auto2) -> set(quiet).
% 1.30/1.61 % set(auto2) -> clear(print_initial_clauses).
% 1.30/1.61 % set(auto2) -> clear(print_given).
% 1.30/1.61 assign(lrs_ticks,-1).
% 1.30/1.61 assign(sos_limit,10000).
% 1.30/1.61 assign(order,kbo).
% 1.30/1.61 set(lex_order_vars).
% 1.30/1.61 clear(print_given).
% 1.30/1.61
% 1.30/1.61 % formulas(sos). % not echoed (12 formulas)
% 1.30/1.61
% 1.30/1.61 ============================== end of input ==========================
% 1.30/1.61
% 1.30/1.61 % From the command line: assign(max_seconds, 300).
% 1.30/1.61
% 1.30/1.61 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.30/1.61
% 1.30/1.61 % Formulas that are not ordinary clauses:
% 1.30/1.61
% 1.30/1.61 ============================== end of process non-clausal formulas ===
% 1.30/1.61
% 1.30/1.61 ============================== PROCESS INITIAL CLAUSES ===============
% 1.30/1.61
% 1.30/1.61 ============================== PREDICATE ELIMINATION =================
% 1.30/1.61
% 1.30/1.61 ============================== end predicate elimination =============
% 1.30/1.61
% 1.30/1.61 Auto_denials:
% 1.30/1.61 % copying label prove_this to answer in negative clause
% 1.30/1.61
% 1.30/1.61 Term ordering decisions:
% 1.30/1.61 Function symbol KB weights: a=1. b=1. c=1. d=1. meet=1. join=1.
% 1.30/1.61
% 1.30/1.61 ============================== end of process initial clauses ========
% 1.30/1.61
% 1.30/1.61 ============================== CLAUSES FOR SEARCH ====================
% 1.30/1.61
% 1.30/1.61 ============================== end of clauses for search =============
% 1.30/1.61
% 1.30/1.61 ============================== SEARCH ================================
% 1.30/1.61
% 1.30/1.61 % Starting search at 0.01 seconds.
% 1.30/1.61
% 1.30/1.61 ============================== PROOF =================================
% 1.30/1.61 % SZS status Unsatisfiable
% 1.30/1.61 % SZS output start Refutation
% 1.30/1.61
% 1.30/1.61 % Proof 1 at 0.64 (+ 0.01) seconds: prove_this.
% 1.30/1.61 % Length of proof is 79.
% 1.30/1.61 % Level of proof is 15.
% 1.30/1.61 % Maximum clause weight is 67.000.
% 1.30/1.61 % Given clauses 58.
% 1.30/1.61
% 1.30/1.61 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 1.30/1.61 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 1.30/1.61 3 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 1.30/1.61 4 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 1.30/1.61 5 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 1.30/1.61 6 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 1.30/1.61 7 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 1.30/1.61 8 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(7),rewrite([5(2)]),flip(a)].
% 1.30/1.61 9 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 1.30/1.61 10 join(A,join(B,C)) = join(C,join(A,B)). [copy(9),rewrite([6(2)]),flip(a)].
% 1.30/1.61 11 meet(join(A,meet(B,C)),join(C,meet(A,B))) = join(meet(C,join(A,meet(B,C))),meet(A,join(B,C))) # label(nr_3) # label(hypothesis). [assumption].
% 1.30/1.61 12 join(meet(A,join(B,C)),meet(C,join(A,meet(B,C)))) = meet(join(A,meet(B,C)),join(C,meet(A,B))). [copy(11),rewrite([6(11)]),flip(a)].
% 1.30/1.61 13 meet(A,join(B,meet(C,join(A,D)))) = join(meet(A,join(B,meet(A,C))),meet(A,join(meet(A,B),meet(C,D)))) # label(n5_1) # label(hypothesis). [assumption].
% 1.30/1.61 14 join(meet(A,join(B,meet(A,C))),meet(A,join(meet(A,B),meet(C,D)))) = meet(A,join(B,meet(C,join(A,D)))). [copy(13),flip(a)].
% 1.30/1.61 15 join(A,meet(B,join(C,meet(A,D)))) = meet(join(A,meet(B,join(A,C))),join(A,meet(join(A,B),join(C,D)))) # label(n5_2) # label(hypothesis). [assumption].
% 1.30/1.61 16 meet(join(A,meet(B,join(A,C))),join(A,meet(join(A,B),join(C,D)))) = join(A,meet(B,join(C,meet(A,D)))). [copy(15),flip(a)].
% 1.30/1.61 17 meet(a,meet(join(b,c),join(b,d))) != meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))) # label(prove_this) # label(negated_conjecture) # answer(prove_this). [assumption].
% 1.30/1.61 18 meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,c),join(meet(a,d),meet(a,join(b,meet(c,d)))))) != meet(a,meet(join(b,c),join(b,d))) # answer(prove_this). [copy(17),rewrite([10(33),6(32),10(33,R),6(32)]),flip(a)].
% 1.30/1.61 19 meet(A,meet(A,B)) = meet(A,B). [para(8(a,1),1(a,1)),rewrite([5(1),5(2),8(2,R),1(1),5(3)])].
% 1.30/1.61 20 meet(A,meet(B,join(A,C))) = meet(A,B). [para(3(a,1),8(a,2,2)),rewrite([5(2),5(4)])].
% 1.30/1.61 21 join(A,join(A,B)) = join(A,B). [para(10(a,1),2(a,1)),rewrite([6(1),6(2),10(2,R),2(1),6(3)])].
% 1.30/1.61 22 join(A,join(B,meet(A,C))) = join(A,B). [para(4(a,1),10(a,2,2)),rewrite([6(2),6(4)])].
% 1.30/1.61 23 join(join(A,B),meet(B,join(A,B))) = join(A,B). [para(1(a,1),12(a,1,1)),rewrite([6(4),10(4),6(3),4(3),6(2),6(7),10(7),6(6),4(6),6(5),5(7),3(7),6(6),1(7)])].
% 1.30/1.61 24 join(meet(A,B),meet(B,join(A,B))) = meet(join(A,B),join(B,meet(A,B))). [para(1(a,1),12(a,1,2,2,2)),rewrite([2(1),1(5)])].
% 1.30/1.61 25 meet(meet(A,B),join(B,meet(A,B))) = meet(A,B). [para(2(a,1),12(a,1,2,2)),rewrite([8(5,R),1(4),6(5),4(5),2(4),5(4),19(4)]),flip(a)].
% 1.30/1.61 27 meet(meet(A,join(B,C)),meet(join(A,meet(B,C)),join(C,meet(A,B)))) = meet(A,join(B,C)). [para(12(a,1),3(a,1,2))].
% 1.30/1.61 29 join(A,meet(B,join(A,meet(B,join(A,C))))) = meet(join(A,B),join(A,meet(B,join(A,C)))). [para(3(a,1),12(a,2,2,2)),rewrite([6(2),10(2),6(1),10(2,R),6(1),3(3),5(2),5(7),6(9),5(10)])].
% 1.30/1.61 32 join(meet(A,join(B,meet(C,D))),meet(B,join(A,meet(C,meet(D,B))))) = meet(join(A,meet(C,meet(D,B))),join(B,meet(A,meet(C,D)))). [para(8(a,1),12(a,2,2,2)),rewrite([6(2),5(5),8(5),5(4),8(5,R),5(4),5(10),8(10),5(9),8(10,R),5(9),8(13),5(12),8(13,R),5(12)])].
% 1.30/1.61 33 join(meet(A,join(B,join(C,D))),meet(join(B,D),join(A,meet(C,join(B,D))))) = meet(join(A,meet(C,join(B,D))),join(join(B,D),meet(A,C))). [para(10(a,1),12(a,1,1,2)),rewrite([6(4),6(5),6(10),6(13)])].
% 1.30/1.61 38 join(meet(A,join(B,meet(A,C))),meet(A,join(C,meet(A,B)))) = meet(A,join(B,meet(C,join(A,C)))). [para(1(a,1),14(a,1,2,2,2)),rewrite([6(5)])].
% 1.30/1.61 42 meet(A,meet(join(B,meet(A,C)),join(B,meet(C,join(A,D))))) = meet(A,join(B,meet(A,C))). [para(14(a,1),3(a,1,2)),rewrite([8(8,R),8(7),5(6),8(7,R),5(6),19(8)])].
% 1.30/1.61 43 meet(A,join(B,meet(join(A,C),join(A,D)))) = A. [para(3(a,1),14(a,1,1,2,2)),rewrite([6(1),3(2),5(3),4(6)]),flip(a)].
% 1.30/1.61 44 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(3(a,1),14(a,1,2,2,1)),rewrite([3(7),6(5),4(5)]),flip(a)].
% 1.30/1.61 68 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(4(a,1),16(a,1,1,2,2)),rewrite([5(1),4(2),6(3),3(6)]),flip(a)].
% 1.30/1.61 69 join(A,meet(meet(A,B),join(C,meet(A,D)))) = A. [para(4(a,1),16(a,1,2,2,1)),rewrite([4(7),5(5),3(5)]),flip(a)].
% 1.30/1.61 78 meet(join(meet(A,join(B,C)),meet(meet(C,join(A,meet(B,C))),join(D,meet(A,join(B,C))))),join(meet(A,join(B,C)),meet(meet(join(A,meet(B,C)),join(C,meet(A,B))),join(D,E)))) = join(meet(A,join(B,C)),meet(meet(C,join(A,meet(B,C))),join(D,meet(A,meet(E,join(B,C)))))). [para(12(a,1),16(a,1,2,2,1)),rewrite([6(8),5(29),8(29,R),5(28)])].
% 1.30/1.61 96 join(meet(A,join(B,C)),meet(join(A,meet(B,C)),join(C,meet(A,B)))) = meet(join(A,meet(B,C)),join(C,meet(A,B))). [para(12(a,1),21(a,1,2)),rewrite([12(14)])].
% 1.30/1.61 106 join(meet(A,join(meet(B,join(A,C)),meet(A,D))),meet(A,join(meet(A,B),meet(D,E)))) = meet(A,join(meet(B,join(A,C)),meet(D,join(A,E)))). [para(20(a,1),14(a,1,2,2,1))].
% 1.30/1.61 110 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(22(a,1),10(a,2,2)),rewrite([6(3),10(3,R),6(2),10(6),6(5),10(6,R),6(5)])].
% 1.30/1.61 158 meet(A,join(B,meet(C,join(A,C)))) = meet(A,join(B,C)). [para(43(a,1),14(a,2,2,2)),rewrite([20(8),3(6),6(5),38(7)])].
% 1.30/1.61 162 meet(join(A,B),join(A,meet(B,join(A,C)))) = join(A,meet(B,join(A,C))). [para(43(a,1),16(a,1,2,2)),rewrite([21(5),5(5),6(7),10(7),6(6),10(7,R),6(6),6(9),10(9),6(8),10(9,R),6(8),20(11),3(8),6(6)])].
% 1.30/1.61 166 join(meet(A,join(B,meet(A,C))),meet(A,join(C,meet(A,B)))) = meet(A,join(B,C)). [back_rewrite(38),rewrite([158(11)])].
% 1.30/1.61 167 join(A,meet(B,join(A,meet(B,join(A,C))))) = join(A,meet(B,join(A,C))). [back_rewrite(29),rewrite([162(10)])].
% 1.30/1.61 168 meet(A,join(join(A,B),meet(A,C))) = A. [para(2(a,1),44(a,1,2,2,2)),rewrite([5(2)])].
% 1.30/1.61 183 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(44(a,1),44(a,1,2,2)),rewrite([6(3),10(3),6(2),10(3,R),6(2),6(4),21(4)])].
% 1.30/1.61 190 meet(A,join(B,meet(C,join(A,join(join(C,D),meet(C,E)))))) = meet(A,join(B,C)). [para(168(a,1),14(a,1,2,2,2)),rewrite([6(5),166(7)]),flip(a)].
% 1.30/1.61 194 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(25(a,1),168(a,1,2,2)),rewrite([6(3),6(5),10(5,R),2(4)])].
% 1.30/1.61 204 join(A,meet(meet(A,B),join(A,B))) = A. [para(24(a,1),12(a,2,2)),rewrite([6(1),5(2),6(3),10(3),6(2),4(2),6(1),3(2),5(1),6(2),5(3),5(4),167(7),6(5),5(6),5(7),6(9),5(10),4(11),5(10),3(10),5(9),3(9)])].
% 1.30/1.61 233 meet(join(meet(A,B),meet(A,C)),join(meet(A,B),meet(join(A,B),join(C,meet(A,B))))) = join(meet(A,B),meet(A,C)). [para(204(a,1),16(a,2,2,2)),rewrite([6(3),4(3),5(2),6(6),21(8),5(8),5(12)])].
% 1.30/1.61 253 join(A,meet(meet(A,B),join(A,C))) = A. [para(1(a,1),69(a,1,2,2,2)),rewrite([6(2)])].
% 1.30/1.61 277 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(23(a,1),253(a,1,2,2)),rewrite([5(3),5(5),8(5,R),1(4)])].
% 1.30/1.61 300 meet(join(A,meet(B,C)),meet(meet(B,join(A,meet(C,join(B,D)))),join(B,meet(C,meet(A,join(B,D)))))) = meet(B,join(A,meet(C,join(B,D)))). [para(20(a,1),27(a,1,2,2,2)),rewrite([6(3),5(7),8(7,R),5(6),5(11),8(12,R),5(11),6(15)])].
% 1.30/1.61 320 meet(meet(A,B),join(A,C)) = meet(A,B). [para(253(a,1),27(a,1,2,2)),rewrite([6(3),21(3),5(6),3(6),6(5),4(5),1(4),5(4),20(4),19(2),6(4),21(4)]),flip(a)].
% 1.30/1.61 327 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(A,C))). [back_rewrite(300),rewrite([8(9,R),5(8),320(11),8(7,R),5(6),42(7)]),flip(a)].
% 1.30/1.61 347 meet(A,join(B,meet(A,C))) = meet(A,join(B,C)). [back_rewrite(190),rewrite([327(7)])].
% 1.30/1.61 356 join(meet(A,join(B,C)),meet(A,join(meet(A,B),meet(C,D)))) = meet(A,join(B,C)). [back_rewrite(106),rewrite([347(5),6(3),327(4),347(3),6(1),327(13),347(12),6(10),327(11),347(10),6(8)])].
% 1.30/1.61 374 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,C)). [back_rewrite(327),rewrite([347(7)])].
% 1.30/1.61 400 meet(meet(A,B),join(B,C)) = meet(A,B). [para(5(a,1),320(a,1,1)),rewrite([5(4)])].
% 1.30/1.61 403 join(meet(A,B),meet(C,join(meet(A,B),meet(A,C)))) = meet(join(C,meet(A,B)),join(meet(A,B),meet(A,C))). [para(320(a,1),12(a,1,1)),rewrite([5(11),19(11),5(12)])].
% 1.30/1.61 405 join(meet(A,B),meet(A,join(C,B))) = meet(A,join(C,B)). [para(320(a,1),12(a,1,2)),rewrite([347(3),6(4),8(6,R),5(5),4(7),347(8),6(6),347(7)])].
% 1.30/1.61 406 meet(join(A,meet(B,C)),join(meet(B,C),meet(A,join(B,D)))) = join(meet(B,C),meet(A,join(B,D))). [para(320(a,1),12(a,2,2,2)),rewrite([6(3),10(3),6(2),10(3,R),6(2),320(4),5(4),347(6),10(4),6(3),4(3),6(2),5(7),5(11)]),flip(a)].
% 1.30/1.61 422 meet(A,meet(meet(B,join(C,D)),join(D,meet(B,C)))) = meet(A,meet(B,join(C,D))). [para(12(a,1),400(a,1,2)),rewrite([8(9),5(8),8(8),5(7),8(8,R),5(7),320(7),8(6),5(5),8(6,R),5(5)])].
% 1.30/1.61 445 meet(A,join(meet(B,C),meet(B,D))) = meet(A,meet(B,join(C,D))). [para(68(a,1),194(a,1,2)),rewrite([5(5),8(5,R),5(4),347(4),6(2),347(3),6(1)]),flip(a)].
% 1.30/1.61 450 join(meet(A,B),meet(A,meet(C,join(B,C)))) = meet(meet(A,join(B,C)),join(C,meet(A,B))). [back_rewrite(403),rewrite([445(5),8(4,R),5(3),445(11),5(10)])].
% 1.30/1.61 507 join(join(A,B),meet(A,C)) = join(A,B). [para(320(a,1),277(a,1,2))].
% 1.30/1.61 578 meet(join(A,meet(B,meet(A,meet(C,D)))),join(meet(B,A),meet(A,meet(C,D)))) = join(meet(B,A),meet(A,join(meet(B,A),meet(C,D)))). [para(400(a,1),32(a,1,1)),rewrite([5(3),8(4,R),5(3),347(6),5(8),8(9,R),5(8),8(13),5(12),8(12),5(11),8(12,R),5(11),8(13,R),5(12),8(12),5(11),8(12,R),5(11),5(15)]),flip(a)].
% 1.30/1.61 626 join(A,meet(B,join(A,C))) = join(A,meet(B,C)). [para(347(a,1),277(a,1,2)),rewrite([6(5),10(5),6(4),10(5,R),6(4),405(4)])].
% 1.30/1.61 640 join(meet(A,B),meet(A,meet(C,D))) = meet(A,join(meet(A,B),meet(C,D))). [back_rewrite(578),rewrite([8(3,R),5(2),4(4),5(1),347(5),5(5),5(6),626(10)]),flip(a)].
% 1.30/1.61 698 meet(meet(A,join(B,C)),join(C,meet(A,B))) = meet(A,join(meet(A,B),meet(C,join(B,C)))). [back_rewrite(450),rewrite([640(5)]),flip(a)].
% 1.30/1.61 725 meet(A,meet(B,join(meet(B,C),meet(D,join(C,D))))) = meet(A,meet(B,join(C,D))). [back_rewrite(422),rewrite([698(5)])].
% 1.30/1.61 774 meet(join(A,B),join(meet(A,C),meet(D,join(A,B)))) = join(meet(A,C),meet(D,join(A,B))). [para(320(a,1),33(a,1,1)),rewrite([626(8),8(5,R),1(4),5(11),8(11),5(10),8(11,R),5(10),507(12),5(10)]),flip(a)].
% 1.30/1.61 1123 join(meet(A,join(meet(A,B),meet(C,join(B,C)))),meet(meet(A,B),join(D,meet(A,join(B,C))))) = meet(A,join(B,C)). [para(27(a,1),78(a,2,2,2,2)),rewrite([698(5),8(10),5(9),8(10,R),5(9),6(11),445(12),10(9),6(8),4(8),6(7),8(9,R),8(8),5(7),20(8),5(6),19(7),698(11),374(13),6(7),320(8),6(7),626(7),640(5),698(10),8(14),5(13),8(14,R),5(13),6(15),5(19),8(19,R),5(18),640(20),5(21),445(21),10(18),6(17),4(17),6(16),5(18),725(18),1(15),10(15,R),6(14),320(16),6(13),356(13),5(8),725(8),1(5),698(7),8(12),5(11),8(12,R),5(11),6(13),445(14),10(11),6(10),4(10),6(9),8(11,R),8(10),5(9),20(10),5(8),19(9)]),flip(a)].
% 1.30/1.61 1230 meet(join(A,B),join(C,meet(D,join(A,B)))) = meet(join(A,B),join(C,D)). [para(277(a,1),374(a,1,2,2,2))].
% 1.30/1.61 1320 join(meet(A,B),meet(C,join(A,D))) = meet(join(A,D),join(C,meet(A,B))). [back_rewrite(774),rewrite([1230(6),6(3)]),flip(a)].
% 1.30/1.61 1400 meet(join(A,meet(B,C)),meet(join(B,D),join(A,meet(B,C)))) = meet(join(B,D),join(A,meet(B,C))). [back_rewrite(406),rewrite([1320(6),1320(11)])].
% 1.30/1.61 1521 join(meet(A,B),meet(join(A,C),join(D,meet(A,B)))) = meet(join(A,C),join(D,meet(A,B))). [para(320(a,1),96(a,1,2,2,2)),rewrite([6(3),10(3),6(2),10(3,R),6(2),320(4),5(4),1320(5),5(8),1400(8),5(9),1320(10),320(13),5(13),1400(13)])].
% 1.30/1.61 1547 meet(A,join(meet(A,B),meet(C,join(B,C)))) = join(meet(A,B),meet(A,C)). [back_rewrite(233),rewrite([1521(9),8(8),5(7),445(7),8(6,R),20(6),5(5),698(5)])].
% 1.30/1.61 1549 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [back_rewrite(1123),rewrite([1547(5),507(9)])].
% 1.30/1.61 1632 $F # answer(prove_this). [back_rewrite(18),rewrite([1549(23),10(20,R),6(19),1549(22),110(19),10(15,R),6(14),5(17),8(17,R),5(16),8(16),5(15),8(15,R),5(14),183(14),8(10),5(9),8(10,R),5(9),19(11)]),xx(a)].
% 1.30/1.61
% 1.30/1.61 % SZS output end Refutation
% 1.30/1.61 ============================== end of proof ==========================
% 1.30/1.61
% 1.30/1.61 ============================== STATISTICS ============================
% 1.30/1.61
% 1.30/1.61 Given=58. Generated=6028. Kept=1625. proofs=1.
% 1.30/1.61 Usable=34. Sos=494. Demods=606. Limbo=83, Disabled=1026. Hints=0.
% 1.30/1.61 Megabytes=3.15.
% 1.30/1.61 User_CPU=0.64, System_CPU=0.01, Wall_clock=1.
% 1.30/1.61
% 1.30/1.61 ============================== end of statistics =====================
% 1.30/1.61
% 1.30/1.61 ============================== end of search =========================
% 1.30/1.61
% 1.30/1.61 THEOREM PROVED
% 1.30/1.61 % SZS status Unsatisfiable
% 1.30/1.61
% 1.30/1.61 Exiting with 1 proof.
% 1.30/1.61
% 1.30/1.61 Process 22342 exit (max_proofs) Thu Jun 30 01:16:23 2022
% 1.30/1.61 Prover9 interrupted
%------------------------------------------------------------------------------