TSTP Solution File: LAT009-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 0.80s 1.12s
% Output : Refutation 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT009-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n011.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 : Wed Jun 29 22:16:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.80/1.12 ============================== Prover9 ===============================
% 0.80/1.12 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.12 Process 15249 was started by sandbox2 on n011.cluster.edu,
% 0.80/1.12 Wed Jun 29 22:16:48 2022
% 0.80/1.12 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15096_n011.cluster.edu".
% 0.80/1.12 ============================== end of head ===========================
% 0.80/1.12
% 0.80/1.12 ============================== INPUT =================================
% 0.80/1.12
% 0.80/1.12 % Reading from file /tmp/Prover9_15096_n011.cluster.edu
% 0.80/1.12
% 0.80/1.12 set(prolog_style_variables).
% 0.80/1.12 set(auto2).
% 0.80/1.12 % set(auto2) -> set(auto).
% 0.80/1.12 % set(auto) -> set(auto_inference).
% 0.80/1.12 % set(auto) -> set(auto_setup).
% 0.80/1.12 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.12 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.12 % set(auto) -> set(auto_limits).
% 0.80/1.12 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.12 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.12 % set(auto) -> set(auto_denials).
% 0.80/1.12 % set(auto) -> set(auto_process).
% 0.80/1.12 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.12 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.12 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.12 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.12 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.12 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.12 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.12 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.12 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.12 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.12 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.12 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.12 % set(auto2) -> assign(stats, some).
% 0.80/1.12 % set(auto2) -> clear(echo_input).
% 0.80/1.12 % set(auto2) -> set(quiet).
% 0.80/1.12 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.12 % set(auto2) -> clear(print_given).
% 0.80/1.12 assign(lrs_ticks,-1).
% 0.80/1.12 assign(sos_limit,10000).
% 0.80/1.12 assign(order,kbo).
% 0.80/1.12 set(lex_order_vars).
% 0.80/1.12 clear(print_given).
% 0.80/1.12
% 0.80/1.12 % formulas(sos). % not echoed (10 formulas)
% 0.80/1.12
% 0.80/1.12 ============================== end of input ==========================
% 0.80/1.12
% 0.80/1.12 % From the command line: assign(max_seconds, 300).
% 0.80/1.12
% 0.80/1.12 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.12
% 0.80/1.12 % Formulas that are not ordinary clauses:
% 0.80/1.12
% 0.80/1.12 ============================== end of process non-clausal formulas ===
% 0.80/1.12
% 0.80/1.12 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.12
% 0.80/1.12 ============================== PREDICATE ELIMINATION =================
% 0.80/1.12
% 0.80/1.12 ============================== end predicate elimination =============
% 0.80/1.12
% 0.80/1.12 Auto_denials:
% 0.80/1.12 % copying label prove_distributivity to answer in negative clause
% 0.80/1.12
% 0.80/1.12 Term ordering decisions:
% 0.80/1.12 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 0.80/1.12
% 0.80/1.12 ============================== end of process initial clauses ========
% 0.80/1.12
% 0.80/1.12 ============================== CLAUSES FOR SEARCH ====================
% 0.80/1.12
% 0.80/1.12 ============================== end of clauses for search =============
% 0.80/1.12
% 0.80/1.12 ============================== SEARCH ================================
% 0.80/1.12
% 0.80/1.12 % Starting search at 0.01 seconds.
% 0.80/1.12
% 0.80/1.12 ============================== PROOF =================================
% 0.80/1.12 % SZS status Unsatisfiable
% 0.80/1.12 % SZS output start Refutation
% 0.80/1.12
% 0.80/1.12 % Proof 1 at 0.24 (+ 0.01) seconds: prove_distributivity.
% 0.80/1.12 % Length of proof is 72.
% 0.80/1.12 % Level of proof is 22.
% 0.80/1.12 % Maximum clause weight is 51.000.
% 0.80/1.12 % Given clauses 49.
% 0.80/1.12
% 0.80/1.12 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 0.80/1.12 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 0.80/1.12 3 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 0.80/1.12 4 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 0.80/1.12 5 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 0.80/1.12 6 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 0.80/1.12 7 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 0.80/1.12 8 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(7),rewrite([5(2)]),flip(a)].
% 0.80/1.12 9 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 0.80/1.12 10 join(A,join(B,C)) = join(C,join(A,B)). [copy(9),rewrite([6(2)]),flip(a)].
% 0.80/1.12 11 join(meet(join(meet(A,B),C),B),meet(C,A)) = meet(join(meet(join(A,B),C),B),join(C,A)) # label(distributivity_dual) # label(axiom). [assumption].
% 0.80/1.12 12 meet(join(A,B),join(C,meet(B,join(A,C)))) = join(meet(A,B),meet(C,join(B,meet(A,C)))). [copy(11),rewrite([6(2),5(3),5(4),6(5),5(7),6(8),6(9),5(10)]),flip(a)].
% 0.80/1.12 13 join(a,meet(b,c)) != meet(join(a,b),join(a,c)) # label(prove_distributivity) # label(negated_conjecture) # answer(prove_distributivity). [assumption].
% 0.80/1.12 14 meet(join(a,b),join(a,c)) != join(a,meet(b,c)) # answer(prove_distributivity). [copy(13),flip(a)].
% 0.80/1.12 15 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)])].
% 0.80/1.12 17 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)])].
% 0.80/1.12 18 join(A,join(B,meet(A,C))) = join(A,B). [para(4(a,1),10(a,2,2)),rewrite([6(2),6(4)])].
% 0.80/1.12 21 join(join(A,B),meet(A,B)) = join(A,B). [para(12(a,1),3(a,1)),rewrite([3(4),6(3),1(4),6(3)])].
% 0.80/1.12 22 meet(join(A,B),join(C,meet(join(A,B),join(A,C)))) = join(A,meet(C,join(join(A,B),meet(A,C)))). [para(3(a,1),12(a,2,1)),rewrite([17(2)])].
% 0.80/1.12 23 meet(join(A,B),join(join(A,C),meet(B,join(A,C)))) = join(meet(A,B),meet(join(A,C),join(A,B))). [para(3(a,1),12(a,2,2,2,2)),rewrite([17(4),6(9)])].
% 0.80/1.12 24 meet(A,join(B,A)) = join(A,meet(B,A)). [para(3(a,1),12(a,2,2)),rewrite([4(4),5(2),6(4)])].
% 0.80/1.12 26 join(meet(A,B),meet(C,join(meet(A,B),meet(A,C)))) = meet(A,join(C,meet(meet(A,B),join(A,C)))). [para(4(a,1),12(a,1,1)),rewrite([15(7)]),flip(a)].
% 0.80/1.12 29 meet(join(A,B),join(C,meet(A,join(B,C)))) = join(meet(A,B),meet(C,join(A,meet(B,C)))). [para(6(a,1),12(a,1,1)),rewrite([5(6)])].
% 0.80/1.12 30 meet(join(A,join(B,C)),join(D,meet(join(A,C),join(B,D)))) = join(meet(B,join(A,C)),meet(D,join(join(A,C),meet(B,D)))). [para(10(a,1),12(a,1,1)),rewrite([6(3),6(8),6(10)])].
% 0.80/1.12 39 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(18(a,1),10(a,2,2)),rewrite([6(3),10(3,R),6(2),10(6),6(5),10(6,R),6(5)])].
% 0.80/1.12 54 join(join(A,B),meet(A,join(B,meet(A,C)))) = join(A,B). [para(18(a,1),21(a,1,1)),rewrite([18(8)])].
% 0.80/1.12 55 meet(join(A,B),join(A,join(B,C))) = join(join(A,B),meet(C,join(A,B))). [para(10(a,1),24(a,1,2)),rewrite([6(2),10(3,R),6(2)])].
% 0.80/1.12 56 meet(join(A,B),join(B,meet(A,B))) = join(B,meet(A,B)). [para(24(a,1),12(a,1,2,2)),rewrite([17(4),3(8),6(6)])].
% 0.80/1.12 58 join(join(A,meet(B,C)),meet(B,join(A,meet(B,C)))) = meet(join(A,B),join(A,meet(B,C))). [para(18(a,1),24(a,1,2)),rewrite([6(3),5(4)]),flip(a)].
% 0.80/1.12 81 join(A,meet(B,join(join(A,C),meet(A,B)))) = join(A,meet(B,join(A,C))). [para(6(a,1),22(a,2,2,2)),rewrite([22(6),10(8),6(7),4(7),6(6)])].
% 0.80/1.12 88 meet(join(A,B),join(A,meet(C,join(A,B)))) = join(A,meet(C,join(A,B))). [para(22(a,1),15(a,1,2)),rewrite([81(6),22(11),81(10)])].
% 0.80/1.12 92 meet(join(A,B),join(join(C,meet(A,D)),meet(join(A,B),join(A,C)))) = join(A,meet(join(C,meet(A,D)),join(A,B))). [para(18(a,1),22(a,1,2,2,2)),rewrite([81(17)])].
% 0.80/1.12 102 meet(join(A,B),join(C,meet(join(A,B),join(A,C)))) = join(A,meet(C,join(A,B))). [back_rewrite(22),rewrite([81(11)])].
% 0.80/1.12 114 join(join(A,B),meet(B,join(A,meet(B,C)))) = join(A,B). [para(6(a,1),54(a,1,1)),rewrite([6(6)])].
% 0.80/1.12 121 join(join(A,B),meet(A,join(join(A,B),meet(A,C)))) = join(A,B). [para(17(a,1),54(a,1,1)),rewrite([17(8)])].
% 0.80/1.12 131 meet(join(A,join(join(B,C),meet(C,join(B,A)))),join(meet(B,C),join(join(A,meet(C,join(B,A))),meet(A,join(C,meet(B,A)))))) = join(meet(B,C),join(join(A,meet(C,join(B,A))),meet(A,join(C,meet(B,A))))). [para(12(a,1),56(a,1,2,2)),rewrite([10(5,R),6(4),10(14,R),6(13),12(23),10(24,R),6(23)])].
% 0.80/1.12 142 join(A,join(join(A,B),meet(C,join(A,B)))) = join(A,B). [para(17(a,1),114(a,1,1)),rewrite([5(4),88(6),10(5,R),6(4),17(7)])].
% 0.80/1.12 159 meet(join(A,join(B,C)),join(meet(B,C),join(join(A,meet(C,join(A,B))),meet(A,join(C,meet(A,B)))))) = join(meet(A,join(B,C)),meet(join(A,join(B,C)),join(A,meet(C,join(A,B))))). [para(12(a,1),23(a,1,2,2)),rewrite([6(3),5(7),10(11,R),6(10),6(15),5(20)])].
% 0.80/1.12 174 meet(join(join(A,B),join(join(A,C),meet(B,join(A,C)))),join(meet(A,B),join(join(A,C),meet(B,join(A,C))))) = join(meet(A,B),join(join(A,C),meet(B,join(A,C)))). [para(23(a,1),56(a,1,2,2)),rewrite([10(16),6(15),10(16,R),6(15),10(15),6(14),4(14),6(11),23(23),10(23),6(22),10(23,R),6(22),10(22),6(21),4(21),6(18)])].
% 0.80/1.12 192 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(142(a,1),10(a,1)),rewrite([17(5),6(5)]),flip(a)].
% 0.80/1.12 198 meet(join(A,B),join(A,join(C,B))) = join(A,B). [back_rewrite(174),rewrite([192(5),10(3),6(2),17(2),10(2),6(1),10(2,R),6(1),192(7),10(5),6(4),4(4),6(3),5(4),192(9),10(7),6(6),4(6),6(5)])].
% 0.80/1.12 214 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [back_rewrite(58),rewrite([192(6)]),flip(a)].
% 0.80/1.12 215 meet(join(A,B),join(A,join(B,C))) = join(A,B). [back_rewrite(55),rewrite([192(8)])].
% 0.80/1.12 236 join(A,meet(join(B,C),join(A,B))) = join(A,B). [para(198(a,1),12(a,1,2,2)),rewrite([17(2),6(2),10(4),6(3),10(4,R),6(3),17(3),215(4),3(3),6(2),6(4),81(8)]),flip(a)].
% 0.80/1.12 266 join(A,meet(join(B,C),join(B,A))) = join(B,A). [para(236(a,1),6(a,2)),rewrite([6(2),6(4),6(5)])].
% 0.80/1.12 267 join(A,meet(join(B,C),join(A,C))) = join(A,C). [para(6(a,1),236(a,1,2,1))].
% 0.80/1.12 287 meet(join(A,B),join(A,C)) = join(A,meet(C,join(A,B))). [back_rewrite(102),rewrite([266(5)])].
% 0.80/1.12 302 join(A,meet(meet(B,C),join(A,B))) = join(A,meet(B,C)). [back_rewrite(214),rewrite([287(4)])].
% 0.80/1.12 307 meet(join(A,join(B,C)),join(meet(B,C),join(join(A,meet(C,join(A,B))),meet(A,join(C,meet(A,B)))))) = join(A,join(meet(A,join(B,C)),meet(C,join(A,B)))). [back_rewrite(159),rewrite([287(20),5(19),8(19),5(18),8(19,R),5(18),287(18),236(18),10(18,R),6(17)])].
% 0.80/1.12 310 join(A,meet(join(B,meet(A,C)),join(A,D))) = join(A,meet(B,join(A,D))). [back_rewrite(92),rewrite([287(6),10(7,R),10(6,R),18(6),18(4),287(3)]),flip(a)].
% 0.80/1.12 311 join(a,meet(c,join(a,b))) != join(a,meet(b,c)) # answer(prove_distributivity). [back_rewrite(14),rewrite([287(7)])].
% 0.80/1.12 320 join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)). [para(4(a,1),267(a,1,2,1))].
% 0.80/1.12 336 join(A,meet(join(B,C),join(A,meet(D,join(B,C))))) = join(A,meet(D,join(B,C))). [para(192(a,1),267(a,1,2,1))].
% 0.80/1.12 344 join(join(A,B),meet(A,C)) = join(A,B). [back_rewrite(121),rewrite([320(6)])].
% 0.80/1.12 348 join(A,meet(join(A,join(B,C)),join(meet(B,C),meet(C,join(A,B))))) = join(A,join(meet(A,join(B,C)),meet(C,join(A,B)))). [back_rewrite(307),rewrite([344(10),10(7,R),6(6),287(8),5(7)])].
% 0.80/1.12 351 join(A,meet(join(meet(B,C),meet(C,join(A,B))),join(A,join(join(B,C),meet(C,join(A,B)))))) = join(A,join(meet(B,C),meet(C,join(A,B)))). [back_rewrite(131),rewrite([6(2),6(7),5(10),344(13),10(10,R),6(9),287(11),6(13),5(16),344(19),10(16,R),6(15)])].
% 0.80/1.12 357 meet(A,join(B,meet(A,C))) = join(meet(A,C),meet(B,A)). [para(26(a,1),6(a,2)),rewrite([5(2),6(6),320(6),6(5),302(7)]),flip(a)].
% 0.80/1.12 429 join(join(A,B),meet(B,C)) = join(A,B). [para(6(a,1),344(a,1,1)),rewrite([6(4)])].
% 0.80/1.12 432 join(meet(A,B),join(meet(C,join(A,D)),meet(A,meet(C,B)))) = meet(join(A,D),join(C,meet(meet(A,B),join(A,join(D,C))))). [para(344(a,1),12(a,1,1)),rewrite([6(4),10(4),6(3),10(4,R),6(3),8(10),5(9),3(9),5(8),5(11),357(13),5(12),8(12,R),5(11)]),flip(a)].
% 0.80/1.12 437 meet(meet(A,B),join(A,C)) = meet(A,B). [para(344(a,1),24(a,1,2)),rewrite([8(7),5(6),3(6),5(5),2(6)])].
% 0.80/1.12 439 join(A,meet(join(B,C),join(A,meet(B,D)))) = join(A,meet(B,D)). [para(344(a,1),267(a,1,2,1))].
% 0.80/1.12 444 join(A,join(meet(A,join(B,C)),meet(C,join(A,B)))) = join(A,join(meet(B,C),meet(C,join(A,B)))). [back_rewrite(351),rewrite([429(8),5(7),348(8)])].
% 0.80/1.12 450 join(meet(A,B),join(meet(C,join(A,D)),meet(A,meet(B,C)))) = meet(join(A,D),join(C,meet(A,B))). [back_rewrite(432),rewrite([5(4),6(10),437(12)])].
% 0.80/1.12 477 meet(join(A,B),join(C,meet(A,D))) = join(meet(A,D),meet(C,join(A,B))). [para(437(a,1),12(a,2,1)),rewrite([10(3),6(2),4(2),6(1),6(4),439(6),5(8),8(8),5(7),8(8,R),5(7),344(9)])].
% 0.80/1.12 478 meet(join(A,meet(B,C)),join(B,D)) = join(meet(B,C),meet(A,join(B,D))). [para(437(a,1),12(a,2,2,2,2)),rewrite([6(2),10(6),6(5),4(5),6(4),192(6),5(6),8(6),5(5),8(6,R),5(5),477(10),10(11,R),450(11),477(8)])].
% 0.80/1.12 490 join(meet(A,join(B,C)),meet(C,join(A,B))) = join(meet(A,B),meet(C,join(A,meet(B,C)))). [back_rewrite(29),rewrite([477(5)])].
% 0.80/1.12 494 join(A,join(meet(A,B),meet(C,join(A,D)))) = join(A,meet(C,join(A,D))). [back_rewrite(310),rewrite([478(4)])].
% 0.80/1.12 499 join(A,join(meet(B,C),meet(C,join(A,B)))) = join(A,meet(C,join(A,meet(B,C)))). [back_rewrite(444),rewrite([490(5),494(6)]),flip(a)].
% 0.80/1.12 536 join(A,meet(join(B,C),join(A,D))) = join(A,meet(D,join(B,C))). [para(30(a,1),24(a,2,2)),rewrite([6(2),6(5),6(8),10(11,R),6(10),287(12),267(12),6(6),5(12),357(14),5(13),10(16,R),6(15),10(15),6(14),10(14,R),6(13),494(14),10(13,R),6(12),494(13),10(11,R),6(10),499(11),336(10)])].
% 0.80/1.12 585 join(A,join(B,meet(C,B))) = join(A,B). [back_rewrite(267),rewrite([536(4),24(2)])].
% 0.80/1.12 691 join(A,meet(B,join(A,C))) = join(A,meet(B,C)). [para(12(a,1),287(a,2,2)),rewrite([6(1),6(4),5(6),287(6),5(5),8(5),5(4),8(5,R),5(4),287(4),536(4),24(2),585(3),5(4),5(5),357(7),5(6),39(9),18(7)])].
% 0.80/1.12 732 $F # answer(prove_distributivity). [back_rewrite(311),rewrite([691(7),5(4)]),xx(a)].
% 0.80/1.12
% 0.80/1.12 % SZS output end Refutation
% 0.80/1.12 ============================== end of proof ==========================
% 0.80/1.12
% 0.80/1.12 ============================== STATISTICS ============================
% 0.80/1.12
% 0.80/1.12 Given=49. Generated=3630. Kept=727. proofs=1.
% 0.80/1.12 Usable=30. Sos=213. Demods=279. Limbo=41, Disabled=453. Hints=0.
% 0.80/1.12 Megabytes=0.94.
% 0.80/1.12 User_CPU=0.24, System_CPU=0.01, Wall_clock=0.
% 0.80/1.12
% 0.80/1.12 ============================== end of statistics =====================
% 0.80/1.12
% 0.80/1.12 ============================== end of search =========================
% 0.80/1.12
% 0.80/1.12 THEOREM PROVED
% 0.80/1.12 % SZS status Unsatisfiable
% 0.80/1.12
% 0.80/1.12 Exiting with 1 proof.
% 0.80/1.12
% 0.80/1.12 Process 15249 exit (max_proofs) Wed Jun 29 22:16:48 2022
% 0.80/1.12 Prover9 interrupted
%------------------------------------------------------------------------------