TSTP Solution File: LAT011-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT011-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 06:25:06 EDT 2022
% Result : Unsatisfiable 2.44s 2.72s
% Output : Refutation 2.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT011-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n021.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 : Tue Jun 28 23:02:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.44/2.72 ============================== Prover9 ===============================
% 2.44/2.72 Prover9 (32) version 2009-11A, November 2009.
% 2.44/2.72 Process 27422 was started by sandbox on n021.cluster.edu,
% 2.44/2.72 Tue Jun 28 23:02:42 2022
% 2.44/2.72 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27269_n021.cluster.edu".
% 2.44/2.72 ============================== end of head ===========================
% 2.44/2.72
% 2.44/2.72 ============================== INPUT =================================
% 2.44/2.72
% 2.44/2.72 % Reading from file /tmp/Prover9_27269_n021.cluster.edu
% 2.44/2.72
% 2.44/2.72 set(prolog_style_variables).
% 2.44/2.72 set(auto2).
% 2.44/2.72 % set(auto2) -> set(auto).
% 2.44/2.72 % set(auto) -> set(auto_inference).
% 2.44/2.72 % set(auto) -> set(auto_setup).
% 2.44/2.72 % set(auto_setup) -> set(predicate_elim).
% 2.44/2.72 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.44/2.72 % set(auto) -> set(auto_limits).
% 2.44/2.72 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.44/2.72 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.44/2.72 % set(auto) -> set(auto_denials).
% 2.44/2.72 % set(auto) -> set(auto_process).
% 2.44/2.72 % set(auto2) -> assign(new_constants, 1).
% 2.44/2.72 % set(auto2) -> assign(fold_denial_max, 3).
% 2.44/2.72 % set(auto2) -> assign(max_weight, "200.000").
% 2.44/2.72 % set(auto2) -> assign(max_hours, 1).
% 2.44/2.72 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.44/2.72 % set(auto2) -> assign(max_seconds, 0).
% 2.44/2.72 % set(auto2) -> assign(max_minutes, 5).
% 2.44/2.72 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.44/2.72 % set(auto2) -> set(sort_initial_sos).
% 2.44/2.72 % set(auto2) -> assign(sos_limit, -1).
% 2.44/2.72 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.44/2.72 % set(auto2) -> assign(max_megs, 400).
% 2.44/2.72 % set(auto2) -> assign(stats, some).
% 2.44/2.72 % set(auto2) -> clear(echo_input).
% 2.44/2.72 % set(auto2) -> set(quiet).
% 2.44/2.72 % set(auto2) -> clear(print_initial_clauses).
% 2.44/2.72 % set(auto2) -> clear(print_given).
% 2.44/2.72 assign(lrs_ticks,-1).
% 2.44/2.72 assign(sos_limit,10000).
% 2.44/2.72 assign(order,kbo).
% 2.44/2.72 set(lex_order_vars).
% 2.44/2.72 clear(print_given).
% 2.44/2.72
% 2.44/2.72 % formulas(sos). % not echoed (14 formulas)
% 2.44/2.72
% 2.44/2.72 ============================== end of input ==========================
% 2.44/2.72
% 2.44/2.72 % From the command line: assign(max_seconds, 300).
% 2.44/2.72
% 2.44/2.72 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.44/2.72
% 2.44/2.72 % Formulas that are not ordinary clauses:
% 2.44/2.72
% 2.44/2.72 ============================== end of process non-clausal formulas ===
% 2.44/2.72
% 2.44/2.72 ============================== PROCESS INITIAL CLAUSES ===============
% 2.44/2.72
% 2.44/2.72 ============================== PREDICATE ELIMINATION =================
% 2.44/2.72
% 2.44/2.72 ============================== end predicate elimination =============
% 2.44/2.72
% 2.44/2.72 Auto_denials:
% 2.44/2.72 % copying label prove_meets_are_same to answer in negative clause
% 2.44/2.72
% 2.44/2.72 Term ordering decisions:
% 2.44/2.72 Function symbol KB weights: a=1. b=1. join=1. meet=1. meet2=1.
% 2.44/2.72
% 2.44/2.72 ============================== end of process initial clauses ========
% 2.44/2.72
% 2.44/2.72 ============================== CLAUSES FOR SEARCH ====================
% 2.44/2.72
% 2.44/2.72 ============================== end of clauses for search =============
% 2.44/2.72
% 2.44/2.72 ============================== SEARCH ================================
% 2.44/2.72
% 2.44/2.72 % Starting search at 0.01 seconds.
% 2.44/2.72
% 2.44/2.72 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 108 (0.00 of 1.29 sec).
% 2.44/2.72
% 2.44/2.72 ============================== PROOF =================================
% 2.44/2.72 % SZS status Unsatisfiable
% 2.44/2.72 % SZS output start Refutation
% 2.44/2.72
% 2.44/2.72 % Proof 1 at 1.72 (+ 0.03) seconds: prove_meets_are_same.
% 2.44/2.72 % Length of proof is 74.
% 2.44/2.72 % Level of proof is 17.
% 2.44/2.72 % Maximum clause weight is 19.000.
% 2.44/2.72 % Given clauses 600.
% 2.44/2.72
% 2.44/2.72 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 2.44/2.72 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 2.44/2.72 3 meet2(A,A) = A # label(idempotence_of_meet2) # label(axiom). [assumption].
% 2.44/2.72 4 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 2.44/2.72 5 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 2.44/2.72 6 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 2.44/2.72 7 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 2.44/2.72 8 meet2(A,B) = meet2(B,A) # label(commutativity_of_meet2) # label(axiom). [assumption].
% 2.44/2.72 9 meet2(A,join(A,B)) = A # label(absorption1_2) # label(axiom). [assumption].
% 2.44/2.72 10 join(A,meet2(A,B)) = A # label(absorption2_2) # label(axiom). [assumption].
% 2.44/2.72 11 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 2.44/2.72 12 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(11),rewrite([6(2)]),flip(a)].
% 2.44/2.72 13 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 2.44/2.72 14 join(A,join(B,C)) = join(C,join(A,B)). [copy(13),rewrite([7(2)]),flip(a)].
% 2.44/2.72 15 meet2(meet2(A,B),C) = meet2(A,meet2(B,C)) # label(associativity_of_meet2) # label(axiom). [assumption].
% 2.44/2.72 16 meet2(A,meet2(B,C)) = meet2(C,meet2(A,B)). [copy(15),rewrite([8(2)]),flip(a)].
% 2.44/2.72 17 meet(a,b) != meet2(a,b) # label(prove_meets_are_same) # label(negated_conjecture) # answer(prove_meets_are_same). [assumption].
% 2.44/2.72 18 meet2(a,b) != meet(a,b) # answer(prove_meets_are_same). [copy(17),flip(a)].
% 2.44/2.72 19 meet2(a,b) = c_0. [new_symbol(18)].
% 2.44/2.72 20 meet(a,b) != c_0 # answer(prove_meets_are_same). [back_rewrite(18),rewrite([19(3)]),flip(a)].
% 2.44/2.72 21 meet(A,meet(A,B)) = meet(A,B). [para(12(a,1),1(a,1)),rewrite([6(1),6(2),12(2,R),1(1),6(3)])].
% 2.44/2.72 22 meet(A,meet(B,join(A,C))) = meet(A,B). [para(4(a,1),12(a,2,2)),rewrite([6(2),6(4)])].
% 2.44/2.72 23 join(A,join(A,B)) = join(A,B). [para(14(a,1),2(a,1)),rewrite([7(1),7(2),14(2,R),2(1),7(3)])].
% 2.44/2.72 24 join(A,join(B,meet(A,C))) = join(A,B). [para(5(a,1),14(a,2,2)),rewrite([7(2),7(4)])].
% 2.44/2.72 26 meet2(A,meet2(A,B)) = meet2(A,B). [para(16(a,1),3(a,1)),rewrite([8(1),8(2),16(2,R),3(1),8(3)])].
% 2.44/2.72 27 meet2(A,meet2(B,join(A,C))) = meet2(A,B). [para(9(a,1),16(a,2,2)),rewrite([8(2),8(4)])].
% 2.44/2.72 29 meet2(a,c_0) = c_0. [para(19(a,1),26(a,1,2)),rewrite([19(6)])].
% 2.44/2.72 30 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(22(a,1),12(a,2,2)),rewrite([6(3),12(3,R),6(2),12(6),6(5),12(6,R),6(5)])].
% 2.44/2.72 31 join(A,join(B,join(C,meet(A,D)))) = join(A,join(B,C)). [para(24(a,1),14(a,2,2)),rewrite([7(3),14(3,R),7(2),14(6),7(5),14(6,R),7(5)])].
% 2.44/2.72 40 meet2(A,meet2(B,meet2(C,join(A,D)))) = meet2(A,meet2(B,C)). [para(27(a,1),16(a,2,2)),rewrite([8(3),16(3,R),8(2),16(6),8(5),16(6,R),8(5)])].
% 2.44/2.72 41 meet2(a,meet2(b,join(A,a))) = c_0. [para(19(a,1),27(a,2)),rewrite([7(4)])].
% 2.44/2.72 48 meet2(c_0,join(A,a)) = c_0. [para(41(a,1),16(a,1)),rewrite([19(6),8(5)]),flip(a)].
% 2.44/2.72 50 meet2(c_0,meet2(join(A,a),join(B,c_0))) = c_0. [para(48(a,1),27(a,2)),rewrite([7(5)])].
% 2.44/2.72 51 meet(A,meet(B,meet(meet(A,B),join(C,meet(A,B))))) = meet(A,B). [para(1(a,1),30(a,2)),rewrite([7(3),12(6,R),6(5),12(5,R),6(4)])].
% 2.44/2.72 52 meet(A,meet(B,meet(C,meet(D,join(A,E))))) = meet(A,meet(B,meet(C,D))). [para(30(a,1),12(a,2,2)),rewrite([6(4),12(4,R),6(3),12(3,R),6(2),12(8,R),6(7),12(7),6(6),12(7,R),6(6)])].
% 2.44/2.72 61 join(A,join(B,join(join(A,B),meet(C,join(A,B))))) = join(A,B). [para(2(a,1),31(a,2)),rewrite([6(3),14(6,R),7(5),14(5,R),7(4)])].
% 2.44/2.72 62 join(A,join(B,join(C,join(D,meet(A,E))))) = join(A,join(B,join(C,D))). [para(31(a,1),14(a,2,2)),rewrite([7(4),14(4,R),7(3),14(3,R),7(2),14(8,R),7(7),14(7),7(6),14(7,R),7(6)])].
% 2.44/2.72 71 meet2(c_0,join(A,c_0)) = c_0. [para(50(a,1),16(a,1)),rewrite([48(7),8(5)]),flip(a)].
% 2.44/2.72 118 meet2(A,meet2(B,meet2(meet2(A,B),join(C,meet2(A,B))))) = meet2(A,B). [para(3(a,1),40(a,2)),rewrite([7(3),16(6,R),8(5),16(5,R),8(4)])].
% 2.44/2.72 119 meet2(A,meet2(B,meet2(C,meet2(D,join(A,E))))) = meet2(A,meet2(B,meet2(C,D))). [para(40(a,1),16(a,2,2)),rewrite([8(4),16(4,R),8(3),16(3,R),8(2),16(8,R),8(7),16(7),8(6),16(7,R),8(6)])].
% 2.44/2.72 137 meet(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(51(a,1),12(a,1)),rewrite([6(7),21(7)]),flip(a)].
% 2.44/2.72 168 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(61(a,1),14(a,1)),rewrite([7(7),23(7)]),flip(a)].
% 2.44/2.72 171 meet(A,meet(meet(B,C),join(D,E))) = meet(A,meet(B,meet(C,join(D,E)))). [para(168(a,1),52(a,1,2,2,2,2)),rewrite([12(6,R),6(5),12(5,R),6(4),12(4,R),1(3),12(8,R)]),flip(a)].
% 2.44/2.72 189 join(A,join(join(B,C),meet(D,E))) = join(A,join(B,join(C,meet(D,E)))). [para(137(a,1),62(a,1,2,2,2,2)),rewrite([14(6,R),7(5),14(5,R),7(4),14(4,R),2(3),14(8,R)]),flip(a)].
% 2.44/2.72 371 meet2(meet2(A,B),join(C,meet2(A,B))) = meet2(A,B). [para(118(a,1),16(a,1)),rewrite([8(7),26(7)]),flip(a)].
% 2.44/2.72 372 meet2(a,meet2(b,c_0)) = c_0. [para(19(a,1),118(a,1,2,2,1)),rewrite([19(6),71(6),19(8)])].
% 2.44/2.72 375 meet2(b,c_0) = c_0. [para(372(a,1),16(a,2)),rewrite([8(4),29(4)])].
% 2.44/2.72 376 join(b,c_0) = b. [para(375(a,1),10(a,1,2))].
% 2.44/2.72 380 meet2(A,meet2(meet2(B,C),join(D,E))) = meet2(A,meet2(B,meet2(C,join(D,E)))). [para(168(a,1),119(a,1,2,2,2,2)),rewrite([16(6,R),8(5),16(5,R),8(4),16(4,R),3(3),16(8,R)]),flip(a)].
% 2.44/2.72 400 join(b,meet(A,b)) = b. [para(376(a,1),168(a,1,1)),rewrite([376(4),376(7)])].
% 2.44/2.72 701 meet(meet(A,B),join(C,D)) = meet(A,meet(B,join(C,D))). [para(171(a,1),1(a,1)),rewrite([6(7),12(7),6(6),12(6,R),12(5),6(4),12(5,R),6(4),21(4),21(5),12(5,R),6(4),12(4,R),1(3)]),flip(a)].
% 2.44/2.72 713 meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B). [back_rewrite(137),rewrite([701(4)])].
% 2.44/2.72 797 join(meet(A,B),meet(A,meet(B,join(C,D)))) = meet(A,B). [para(701(a,1),5(a,1,2))].
% 2.44/2.72 825 join(join(A,B),meet(C,D)) = join(A,join(B,meet(C,D))). [para(189(a,1),2(a,1)),rewrite([7(7),14(7),7(6),14(6,R),14(5),7(4),14(5,R),7(4),23(4),23(5),14(5,R),7(4),14(4,R),2(3)]),flip(a)].
% 2.44/2.72 942 join(meet(A,B),meet(A,meet(B,C))) = meet(A,B). [para(2(a,1),797(a,1,2,2,2))].
% 2.44/2.72 979 meet2(join(A,B),join(A,join(B,meet(C,D)))) = join(A,B). [para(825(a,1),9(a,1,2))].
% 2.44/2.72 980 join(A,join(meet2(A,B),meet(C,D))) = join(A,meet(C,D)). [para(10(a,1),825(a,1,1)),flip(a)].
% 2.44/2.72 1019 join(b,join(c_0,meet(A,B))) = join(b,meet(A,B)). [para(376(a,1),825(a,1,1)),flip(a)].
% 2.44/2.72 1792 meet2(join(A,B),join(A,join(B,C))) = join(A,B). [para(1(a,1),979(a,1,2,2,2))].
% 2.44/2.72 1805 meet2(meet(A,B),join(C,meet(A,B))) = meet(A,B). [para(942(a,1),1792(a,1,1)),rewrite([7(5),14(6,R),7(5),942(5),942(8)])].
% 2.44/2.72 1825 meet2(A,meet(A,B)) = meet(A,B). [para(5(a,1),1805(a,1,2)),rewrite([8(2)])].
% 2.44/2.72 1828 meet2(b,meet(A,b)) = meet(A,b). [para(400(a,1),1805(a,1,2)),rewrite([8(4)])].
% 2.44/2.72 2251 meet2(meet2(A,B),join(C,D)) = meet2(A,meet2(B,join(C,D))). [para(380(a,1),3(a,1)),rewrite([8(7),16(7),8(6),16(6,R),16(5),8(4),16(5,R),8(4),26(4),26(5),16(5,R),8(4),16(4,R),3(3)]),flip(a)].
% 2.44/2.72 2343 meet2(A,meet2(B,join(C,meet2(A,B)))) = meet2(A,B). [back_rewrite(371),rewrite([2251(4)])].
% 2.44/2.72 2489 join(A,meet(B,meet2(A,C))) = A. [para(5(a,1),980(a,1,2)),rewrite([10(2),6(2)]),flip(a)].
% 2.44/2.72 2499 meet(A,meet(B,meet2(B,C))) = meet(A,meet2(B,C)). [para(2489(a,1),713(a,1,2,2)),rewrite([6(2)])].
% 2.44/2.72 2503 join(b,meet(A,meet2(B,b))) = b. [para(2489(a,1),1019(a,2)),rewrite([8(4),1019(7)])].
% 2.44/2.72 2522 meet(A,meet(b,meet2(B,b))) = meet(A,meet2(B,b)). [para(2503(a,1),713(a,1,2,2)),rewrite([6(4)])].
% 2.44/2.72 2887 join(meet(A,B),meet(A,meet2(B,C))) = meet(A,B). [para(2499(a,1),942(a,1,2))].
% 2.44/2.72 3002 meet(b,meet2(A,b)) = meet2(A,b). [para(2522(a,1),1(a,1)),rewrite([6(7),2522(7),1(5)]),flip(a)].
% 2.44/2.72 3302 join(meet(A,b),meet2(A,b)) = meet(A,b). [para(3002(a,1),2887(a,1,2)),rewrite([6(2),6(7)])].
% 2.44/2.72 3387 meet2(A,b) = meet(A,b). [para(3302(a,1),2343(a,1,2,2)),rewrite([1828(4),1825(3)]),flip(a)].
% 2.44/2.72 3427 meet(a,b) = c_0. [back_rewrite(19),rewrite([3387(3)])].
% 2.44/2.72 3428 $F # answer(prove_meets_are_same). [resolve(3427,a,20,a)].
% 2.44/2.72
% 2.44/2.72 % SZS output end Refutation
% 2.44/2.72 ============================== end of proof ==========================
% 2.44/2.72
% 2.44/2.72 ============================== STATISTICS ============================
% 2.44/2.72
% 2.44/2.72 Given=600. Generated=53904. Kept=3423. proofs=1.
% 2.44/2.72 Usable=279. Sos=979. Demods=1296. Limbo=40, Disabled=2138. Hints=0.
% 2.44/2.72 Megabytes=3.41.
% 2.44/2.72 User_CPU=1.73, System_CPU=0.03, Wall_clock=2.
% 2.44/2.72
% 2.44/2.72 ============================== end of statistics =====================
% 2.44/2.72
% 2.44/2.72 ============================== end of search =========================
% 2.44/2.72
% 2.44/2.72 THEOREM PROVED
% 2.44/2.72 % SZS status Unsatisfiable
% 2.44/2.72
% 2.44/2.72 Exiting with 1 proof.
% 2.44/2.72
% 2.44/2.72 Process 27422 exit (max_proofs) Tue Jun 28 23:02:44 2022
% 2.44/2.72 Prover9 interrupted
%------------------------------------------------------------------------------