TSTP Solution File: LAT152-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT152-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 06:25:49 EDT 2022
% Result : Unsatisfiable 2.35s 2.60s
% Output : Refutation 2.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT152-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n009.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 : Thu Jun 30 08:17:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.35/2.60 ============================== Prover9 ===============================
% 2.35/2.60 Prover9 (32) version 2009-11A, November 2009.
% 2.35/2.60 Process 13822 was started by sandbox on n009.cluster.edu,
% 2.35/2.60 Thu Jun 30 08:17:38 2022
% 2.35/2.60 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13669_n009.cluster.edu".
% 2.35/2.60 ============================== end of head ===========================
% 2.35/2.60
% 2.35/2.60 ============================== INPUT =================================
% 2.35/2.60
% 2.35/2.60 % Reading from file /tmp/Prover9_13669_n009.cluster.edu
% 2.35/2.60
% 2.35/2.60 set(prolog_style_variables).
% 2.35/2.60 set(auto2).
% 2.35/2.60 % set(auto2) -> set(auto).
% 2.35/2.60 % set(auto) -> set(auto_inference).
% 2.35/2.60 % set(auto) -> set(auto_setup).
% 2.35/2.60 % set(auto_setup) -> set(predicate_elim).
% 2.35/2.60 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.35/2.60 % set(auto) -> set(auto_limits).
% 2.35/2.60 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.35/2.60 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.35/2.60 % set(auto) -> set(auto_denials).
% 2.35/2.60 % set(auto) -> set(auto_process).
% 2.35/2.60 % set(auto2) -> assign(new_constants, 1).
% 2.35/2.60 % set(auto2) -> assign(fold_denial_max, 3).
% 2.35/2.60 % set(auto2) -> assign(max_weight, "200.000").
% 2.35/2.60 % set(auto2) -> assign(max_hours, 1).
% 2.35/2.60 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.35/2.60 % set(auto2) -> assign(max_seconds, 0).
% 2.35/2.60 % set(auto2) -> assign(max_minutes, 5).
% 2.35/2.60 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.35/2.60 % set(auto2) -> set(sort_initial_sos).
% 2.35/2.60 % set(auto2) -> assign(sos_limit, -1).
% 2.35/2.60 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.35/2.60 % set(auto2) -> assign(max_megs, 400).
% 2.35/2.60 % set(auto2) -> assign(stats, some).
% 2.35/2.60 % set(auto2) -> clear(echo_input).
% 2.35/2.60 % set(auto2) -> set(quiet).
% 2.35/2.60 % set(auto2) -> clear(print_initial_clauses).
% 2.35/2.60 % set(auto2) -> clear(print_given).
% 2.35/2.60 assign(lrs_ticks,-1).
% 2.35/2.60 assign(sos_limit,10000).
% 2.35/2.60 assign(order,kbo).
% 2.35/2.60 set(lex_order_vars).
% 2.35/2.60 clear(print_given).
% 2.35/2.60
% 2.35/2.60 % formulas(sos). % not echoed (10 formulas)
% 2.35/2.60
% 2.35/2.60 ============================== end of input ==========================
% 2.35/2.60
% 2.35/2.60 % From the command line: assign(max_seconds, 300).
% 2.35/2.60
% 2.35/2.60 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.35/2.60
% 2.35/2.60 % Formulas that are not ordinary clauses:
% 2.35/2.60
% 2.35/2.60 ============================== end of process non-clausal formulas ===
% 2.35/2.60
% 2.35/2.60 ============================== PROCESS INITIAL CLAUSES ===============
% 2.35/2.60
% 2.35/2.60 ============================== PREDICATE ELIMINATION =================
% 2.35/2.60
% 2.35/2.60 ============================== end predicate elimination =============
% 2.35/2.60
% 2.35/2.60 Auto_denials:
% 2.35/2.60 % copying label prove_H6 to answer in negative clause
% 2.35/2.60
% 2.35/2.60 Term ordering decisions:
% 2.35/2.60 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 2.35/2.60
% 2.35/2.60 ============================== end of process initial clauses ========
% 2.35/2.60
% 2.35/2.60 ============================== CLAUSES FOR SEARCH ====================
% 2.35/2.60
% 2.35/2.60 ============================== end of clauses for search =============
% 2.35/2.60
% 2.35/2.60 ============================== SEARCH ================================
% 2.35/2.60
% 2.35/2.60 % Starting search at 0.01 seconds.
% 2.35/2.60
% 2.35/2.60 ============================== PROOF =================================
% 2.35/2.60 % SZS status Unsatisfiable
% 2.35/2.60 % SZS output start Refutation
% 2.35/2.60
% 2.35/2.60 % Proof 1 at 1.60 (+ 0.03) seconds: prove_H6.
% 2.35/2.60 % Length of proof is 68.
% 2.35/2.60 % Level of proof is 24.
% 2.35/2.60 % Maximum clause weight is 27.000.
% 2.35/2.60 % Given clauses 156.
% 2.35/2.60
% 2.35/2.60 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 2.35/2.60 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 2.35/2.60 3 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 2.35/2.60 4 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 2.35/2.60 5 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 2.35/2.60 6 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 2.35/2.60 7 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 2.35/2.60 8 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(7),rewrite([5(2)]),flip(a)].
% 2.35/2.60 9 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 2.35/2.60 10 join(A,join(B,C)) = join(C,join(A,B)). [copy(9),rewrite([6(2)]),flip(a)].
% 2.35/2.60 11 meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))) # label(equation_H40) # label(axiom). [assumption].
% 2.35/2.60 12 meet(A,join(B,meet(C,join(D,meet(C,join(A,B)))))) = meet(A,join(B,meet(C,join(A,D)))). [copy(11),flip(a)].
% 2.35/2.60 13 meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) # label(prove_H6) # label(negated_conjecture) # answer(prove_H6). [assumption].
% 2.35/2.60 14 meet(a,join(meet(c,join(a,b)),meet(a,join(b,meet(a,c))))) != meet(a,join(b,meet(a,c))) # answer(prove_H6). [copy(13),rewrite([6(21)]),flip(a)].
% 2.35/2.60 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)])].
% 2.35/2.60 16 meet(A,meet(B,join(A,C))) = meet(A,B). [para(3(a,1),8(a,2,2)),rewrite([5(2),5(4)])].
% 2.35/2.60 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)])].
% 2.35/2.60 18 join(A,join(B,meet(A,C))) = join(A,B). [para(4(a,1),10(a,2,2)),rewrite([6(2),6(4)])].
% 2.35/2.60 19 meet(A,join(B,meet(join(A,B),join(A,join(B,C))))) = meet(A,join(B,meet(join(A,B),join(A,C)))). [para(1(a,1),12(a,1,2,2,2,2)),rewrite([10(3),6(2),10(3,R),6(2)])].
% 2.35/2.60 20 meet(A,join(B,meet(C,join(A,B)))) = meet(A,join(B,meet(A,C))). [para(2(a,1),12(a,1,2,2,2)),rewrite([15(3),12(10),2(5),5(5)])].
% 2.35/2.60 21 meet(A,join(B,meet(C,join(A,C)))) = meet(A,join(B,C)). [para(3(a,1),12(a,1,2,2)),flip(a)].
% 2.35/2.60 22 meet(A,join(meet(A,B),meet(C,join(D,meet(A,C))))) = meet(A,join(meet(A,B),meet(C,join(A,D)))). [para(4(a,1),12(a,1,2,2,2,2,2)),rewrite([5(2)])].
% 2.35/2.60 23 meet(A,join(B,meet(C,join(D,meet(C,join(B,A)))))) = meet(A,join(B,meet(C,join(D,A)))). [para(12(a,1),5(a,2)),rewrite([6(1),5(6),6(7)])].
% 2.35/2.60 26 meet(A,join(join(A,B),meet(C,join(D,meet(C,join(A,B)))))) = meet(A,join(join(A,B),meet(C,join(A,D)))). [para(17(a,1),12(a,1,2,2,2,2,2))].
% 2.35/2.60 28 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)])].
% 2.35/2.60 30 meet(join(A,B),join(A,meet(B,join(A,B)))) = join(A,B). [para(1(a,1),21(a,2)),rewrite([6(3),10(3,R),2(2)])].
% 2.35/2.60 35 meet(A,join(B,meet(join(A,B),join(A,C)))) = A. [para(5(a,1),19(a,2,2,2)),rewrite([19(6),20(10),3(7),6(6),3(7)])].
% 2.35/2.60 39 meet(A,join(B,meet(join(B,A),join(A,C)))) = A. [para(35(a,1),5(a,2)),rewrite([6(1),5(5)])].
% 2.35/2.60 42 meet(A,join(join(B,meet(A,C)),meet(join(A,B),join(A,D)))) = A. [para(18(a,1),35(a,1,2,2,1))].
% 2.35/2.60 46 meet(join(A,meet(B,C)),join(B,meet(join(A,B),join(A,join(D,meet(B,C)))))) = join(A,meet(B,C)). [para(18(a,1),39(a,1,2,2,1)),rewrite([6(3),6(6),10(6,R),6(5)])].
% 2.35/2.60 49 join(A,join(B,join(join(A,B),meet(C,join(A,B))))) = join(A,B). [para(2(a,1),28(a,2)),rewrite([5(3),10(6,R),6(5),10(5,R),6(4)])].
% 2.35/2.60 50 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(28(a,1),10(a,2,2)),rewrite([6(4),10(4,R),6(3),10(3,R),6(2),10(8,R),6(7),10(7),6(6),10(7,R),6(6)])].
% 2.35/2.60 57 meet(A,meet(B,join(C,meet(D,join(A,C))))) = meet(A,meet(B,join(C,meet(A,D)))). [para(20(a,1),8(a,2,2)),rewrite([5(4),8(9,R),5(8)])].
% 2.35/2.60 60 meet(A,join(join(A,B),meet(C,join(A,B)))) = meet(A,join(join(A,B),meet(A,C))). [para(17(a,1),20(a,1,2,2,2))].
% 2.35/2.60 64 meet(A,join(meet(B,join(A,C)),meet(C,join(A,meet(B,C))))) = meet(A,join(meet(A,C),meet(B,join(A,C)))). [para(20(a,1),20(a,1,2,2)),rewrite([6(1),5(3),6(8),6(11)])].
% 2.35/2.60 96 meet(A,join(meet(B,join(C,meet(A,B))),meet(A,D))) = meet(A,join(meet(A,D),meet(B,join(A,C)))). [para(6(a,1),22(a,1,2))].
% 2.35/2.60 133 meet(join(A,B),join(A,join(B,C))) = join(A,B). [para(30(a,1),42(a,1,2,1,2)),rewrite([10(3),6(2),10(3,R),6(2),6(5),10(5),6(4),10(5,R),6(4),6(7),10(7),6(6),10(7,R),6(6),4(9)])].
% 2.35/2.60 139 meet(A,join(join(B,C),meet(join(A,B),join(A,D)))) = A. [para(133(a,1),12(a,1,2,2,2,2)),rewrite([10(4),6(3),10(4,R),6(3),133(5),10(3),6(2),10(3,R),6(2),17(2),3(3)]),flip(a)].
% 2.35/2.60 173 meet(A,join(join(B,C),meet(join(B,A),join(A,D)))) = A. [para(139(a,1),5(a,2)),rewrite([6(2),5(6)])].
% 2.35/2.60 219 meet(meet(A,B),join(join(A,C),meet(A,join(D,meet(A,B))))) = meet(A,B). [para(4(a,1),173(a,1,2,2,1)),rewrite([6(4)])].
% 2.35/2.60 377 meet(A,join(join(A,B),meet(C,join(A,D)))) = A. [para(6(a,1),26(a,2,2)),rewrite([26(7),10(9),6(8),10(9,R),6(8),3(10)])].
% 2.35/2.60 400 meet(A,join(join(A,B),meet(A,C))) = A. [back_rewrite(60),rewrite([377(5)]),flip(a)].
% 2.35/2.60 405 meet(meet(A,B),join(A,C)) = meet(A,B). [para(400(a,1),23(a,1,2,2,2,2)),rewrite([6(3),3(4),6(3),17(3),219(10)])].
% 2.35/2.60 418 meet(A,join(B,meet(meet(B,C),join(D,meet(B,C))))) = meet(A,join(B,meet(meet(B,C),join(A,D)))). [para(405(a,1),23(a,1,2,2,2,2)),rewrite([6(8)])].
% 2.35/2.60 422 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(405(a,1),400(a,1,2,2)),rewrite([6(3),6(5),10(5,R),2(4)])].
% 2.35/2.60 424 meet(A,join(B,meet(meet(B,C),join(A,D)))) = meet(A,B). [back_rewrite(418),rewrite([422(4),4(2)]),flip(a)].
% 2.35/2.60 526 meet(A,join(join(A,B),meet(C,D))) = A. [para(422(a,1),377(a,1,2,2))].
% 2.35/2.60 704 meet(A,join(B,meet(A,meet(B,C)))) = meet(A,B). [para(2(a,1),424(a,1,2,2,2)),rewrite([5(2)])].
% 2.35/2.60 856 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [para(4(a,1),46(a,1,2,2,2,2)),rewrite([1(5),10(4,R),2(3),5(4)])].
% 2.35/2.60 983 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(49(a,1),10(a,1)),rewrite([6(7),17(7)]),flip(a)].
% 2.35/2.60 1024 join(join(A,B),meet(A,C)) = join(A,B). [para(405(a,1),983(a,1,2))].
% 2.35/2.60 1025 join(A,join(join(A,B),meet(C,D))) = join(join(A,B),meet(C,D)). [para(526(a,1),983(a,1,2)),rewrite([6(4)])].
% 2.35/2.60 1044 join(join(A,B),meet(B,C)) = join(A,B). [para(6(a,1),1024(a,1,1)),rewrite([6(4)])].
% 2.35/2.60 1065 join(join(A,B),meet(C,join(B,meet(A,D)))) = join(A,B). [para(18(a,1),1044(a,1,1)),rewrite([5(4),18(8)])].
% 2.35/2.60 1096 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(405(a,1),50(a,1,2,2,2,2)),rewrite([10(6,R),6(5),10(5,R),6(4),10(4,R),2(3),10(8,R)]),flip(a)].
% 2.35/2.60 1107 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [back_rewrite(1025),rewrite([1096(4),17(4)]),flip(a)].
% 2.35/2.60 1132 join(A,join(B,meet(C,join(B,meet(A,D))))) = join(A,B). [back_rewrite(1065),rewrite([1107(5)])].
% 2.35/2.60 1315 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(6(a,1),856(a,1,1))].
% 2.35/2.60 1416 join(A,join(meet(A,B),meet(C,D))) = join(A,meet(C,D)). [para(4(a,1),1107(a,1,1)),flip(a)].
% 2.35/2.60 1734 join(A,meet(B,join(meet(A,C),meet(A,D)))) = A. [para(1416(a,1),1132(a,1)),rewrite([4(7)])].
% 2.35/2.60 1756 meet(A,join(B,A)) = A. [para(1734(a,1),1315(a,1,2)),rewrite([5(2),1734(7)])].
% 2.35/2.60 1810 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [para(1756(a,1),57(a,1,2)),rewrite([16(3),5(6),8(6),5(5),8(6,R),5(5),1315(5)]),flip(a)].
% 2.35/2.60 1837 meet(A,meet(B,meet(C,join(D,meet(A,B))))) = meet(A,meet(B,C)). [para(1810(a,1),8(a,2,2)),rewrite([5(4),8(4,R),5(3),8(7),5(6),8(7,R),5(6)])].
% 2.35/2.60 1853 meet(A,join(meet(A,meet(B,C)),meet(B,join(A,D)))) = meet(A,B). [para(1810(a,1),704(a,2)),rewrite([5(7),8(7,R),5(6),1837(8),96(7)])].
% 2.35/2.60 2350 meet(A,join(meet(B,C),meet(A,B))) = meet(A,B). [para(15(a,1),64(a,1,2,2,2,2)),rewrite([1756(7),6(5),20(6),1853(11)])].
% 2.35/2.60 2459 meet(A,join(meet(B,C),meet(A,C))) = meet(A,C). [para(5(a,1),2350(a,1,2,1))].
% 2.35/2.60 4303 meet(A,join(meet(B,join(A,C)),meet(A,join(C,meet(A,B))))) = meet(A,join(C,meet(A,B))). [para(96(a,1),2459(a,1)),rewrite([6(6)])].
% 2.35/2.60 4304 $F # answer(prove_H6). [resolve(4303,a,14,a)].
% 2.35/2.60
% 2.35/2.60 % SZS output end Refutation
% 2.35/2.60 ============================== end of proof ==========================
% 2.35/2.60
% 2.35/2.60 ============================== STATISTICS ============================
% 2.35/2.60
% 2.35/2.60 Given=156. Generated=31827. Kept=4299. proofs=1.
% 2.35/2.60 Usable=94. Sos=2428. Demods=2574. Limbo=93, Disabled=1693. Hints=0.
% 2.35/2.60 Megabytes=7.55.
% 2.35/2.60 User_CPU=1.60, System_CPU=0.03, Wall_clock=1.
% 2.35/2.60
% 2.35/2.60 ============================== end of statistics =====================
% 2.35/2.60
% 2.35/2.60 ============================== end of search =========================
% 2.35/2.60
% 2.35/2.60 THEOREM PROVED
% 2.35/2.60 % SZS status Unsatisfiable
% 2.35/2.60
% 2.35/2.60 Exiting with 1 proof.
% 2.35/2.60
% 2.35/2.60 Process 13822 exit (max_proofs) Thu Jun 30 08:17:39 2022
% 2.35/2.60 Prover9 interrupted
%------------------------------------------------------------------------------