TSTP Solution File: LAT029-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT029-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 06:25:11 EDT 2022
% Result : Unsatisfiable 0.70s 1.05s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT029-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n007.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 : Wed Jun 29 21:42:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.70/1.05 ============================== Prover9 ===============================
% 0.70/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.05 Process 20986 was started by sandbox2 on n007.cluster.edu,
% 0.70/1.05 Wed Jun 29 21:42:08 2022
% 0.70/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20833_n007.cluster.edu".
% 0.70/1.05 ============================== end of head ===========================
% 0.70/1.05
% 0.70/1.05 ============================== INPUT =================================
% 0.70/1.05
% 0.70/1.05 % Reading from file /tmp/Prover9_20833_n007.cluster.edu
% 0.70/1.05
% 0.70/1.05 set(prolog_style_variables).
% 0.70/1.05 set(auto2).
% 0.70/1.05 % set(auto2) -> set(auto).
% 0.70/1.05 % set(auto) -> set(auto_inference).
% 0.70/1.05 % set(auto) -> set(auto_setup).
% 0.70/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.05 % set(auto) -> set(auto_limits).
% 0.70/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.05 % set(auto) -> set(auto_denials).
% 0.70/1.05 % set(auto) -> set(auto_process).
% 0.70/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.70/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.70/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.70/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.70/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.70/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.70/1.05 % set(auto2) -> assign(stats, some).
% 0.70/1.05 % set(auto2) -> clear(echo_input).
% 0.70/1.05 % set(auto2) -> set(quiet).
% 0.70/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.70/1.05 % set(auto2) -> clear(print_given).
% 0.70/1.05 assign(lrs_ticks,-1).
% 0.70/1.05 assign(sos_limit,10000).
% 0.70/1.05 assign(order,kbo).
% 0.70/1.05 set(lex_order_vars).
% 0.70/1.05 clear(print_given).
% 0.70/1.05
% 0.70/1.05 % formulas(sos). % not echoed (6 formulas)
% 0.70/1.05
% 0.70/1.05 ============================== end of input ==========================
% 0.70/1.05
% 0.70/1.05 % From the command line: assign(max_seconds, 300).
% 0.70/1.05
% 0.70/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/1.05
% 0.70/1.05 % Formulas that are not ordinary clauses:
% 0.70/1.05
% 0.70/1.05 ============================== end of process non-clausal formulas ===
% 0.70/1.05
% 0.70/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.05
% 0.70/1.05 ============================== PREDICATE ELIMINATION =================
% 0.70/1.05
% 0.70/1.05 ============================== end predicate elimination =============
% 0.70/1.05
% 0.70/1.05 Auto_denials:
% 0.70/1.05 % copying label prove_normal_axioms to answer in negative clause
% 0.70/1.05
% 0.70/1.05 Term ordering decisions:
% 0.70/1.05 Function symbol KB weights: a=1. b=1. join=1. meet=1.
% 0.70/1.05
% 0.70/1.05 ============================== end of process initial clauses ========
% 0.70/1.05
% 0.70/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.70/1.05
% 0.70/1.05 ============================== end of clauses for search =============
% 0.70/1.05
% 0.70/1.05 ============================== SEARCH ================================
% 0.70/1.05
% 0.70/1.05 % Starting search at 0.01 seconds.
% 0.70/1.05
% 0.70/1.05 ============================== PROOF =================================
% 0.70/1.05 % SZS status Unsatisfiable
% 0.70/1.05 % SZS output start Refutation
% 0.70/1.05
% 0.70/1.05 % Proof 1 at 0.09 (+ 0.01) seconds: prove_normal_axioms.
% 0.70/1.05 % Length of proof is 60.
% 0.70/1.05 % Level of proof is 20.
% 0.70/1.05 % Maximum clause weight is 41.000.
% 0.70/1.05 % Given clauses 63.
% 0.70/1.05
% 0.70/1.05 1 join(meet(A,B),meet(A,join(A,B))) = A # label(wal_absorbtion_1) # label(axiom). [assumption].
% 0.70/1.05 2 join(meet(A,A),meet(B,join(A,A))) = A # label(wal_absorbtion_2) # label(axiom). [assumption].
% 0.70/1.05 3 join(meet(A,B),meet(B,join(A,B))) = B # label(wal_absorbtion_3) # label(axiom). [assumption].
% 0.70/1.05 4 meet(meet(join(A,B),join(C,A)),A) = A # label(wal_absorbtion_4) # label(axiom). [assumption].
% 0.70/1.05 5 join(join(meet(A,B),meet(C,A)),A) = A # label(wal_absorbtion_5) # label(axiom). [assumption].
% 0.70/1.05 6 meet(a,a) != a | meet(b,a) != meet(a,b) | join(a,a) != a | join(b,a) != join(a,b) # label(prove_normal_axioms) # label(negated_conjecture) # answer(prove_normal_axioms). [assumption].
% 0.70/1.05 7 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))].
% 0.70/1.05 13 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))].
% 0.70/1.05 14 meet(meet(A,join(B,meet(A,C))),meet(A,C)) = meet(A,C). [para(1(a,1),4(a,1,1,1))].
% 0.70/1.05 16 join(meet(A,A),join(A,A)) = A. [para(4(a,1),2(a,1,2))].
% 0.70/1.05 19 meet(meet(A,join(B,meet(C,A))),meet(C,A)) = meet(C,A). [para(3(a,1),4(a,1,1,1))].
% 0.70/1.05 24 meet(meet(join(A,B),A),A) = A. [para(5(a,1),4(a,1,1,2))].
% 0.70/1.05 25 join(join(A,meet(B,meet(join(A,C),join(D,A)))),meet(join(A,C),join(D,A))) = meet(join(A,C),join(D,A)). [para(4(a,1),5(a,1,1,1))].
% 0.70/1.05 26 join(join(meet(A,B),A),A) = A. [para(4(a,1),5(a,1,1,2))].
% 0.70/1.05 35 join(meet(meet(A,A),join(A,A)),meet(meet(A,A),A)) = meet(A,A). [para(16(a,1),1(a,1,2,2))].
% 0.70/1.05 36 join(meet(meet(A,A),join(A,A)),meet(join(A,A),A)) = join(A,A). [para(16(a,1),3(a,1,2,2))].
% 0.70/1.05 40 meet(meet(A,meet(A,B)),meet(A,B)) = meet(A,B). [para(1(a,1),24(a,1,1,1))].
% 0.70/1.05 46 join(meet(join(meet(A,B),A),A),meet(join(meet(A,B),A),A)) = join(meet(A,B),A). [para(26(a,1),1(a,1,2,2))].
% 0.70/1.05 52 join(join(A,meet(join(A,B),A)),meet(join(A,B),A)) = meet(join(A,B),A). [para(24(a,1),26(a,1,1,1))].
% 0.70/1.05 55 meet(A,A) = A. [para(4(a,1),40(a,1,1,2)),rewrite([4(4),4(4),4(5)])].
% 0.70/1.05 58 join(join(meet(A,B),meet(A,meet(A,B))),meet(A,meet(A,B))) = meet(A,meet(A,B)). [para(40(a,1),26(a,1,1,1))].
% 0.70/1.05 62 join(meet(A,join(A,A)),meet(join(A,A),A)) = join(A,A). [back_rewrite(36),rewrite([55(1)])].
% 0.70/1.05 63 join(meet(A,join(A,A)),A) = A. [back_rewrite(35),rewrite([55(1),55(3),55(3),55(4)])].
% 0.70/1.05 70 meet(b,a) != meet(a,b) | join(a,a) != a | join(b,a) != join(a,b) # answer(prove_normal_axioms). [back_rewrite(6),rewrite([55(3)]),xx(a)].
% 0.70/1.05 71 join(A,meet(B,join(A,A))) = A. [back_rewrite(2),rewrite([55(1)])].
% 0.70/1.05 86 meet(join(A,A),A) = A. [para(55(a,1),4(a,1,1))].
% 0.70/1.05 89 join(A,A) = A. [back_rewrite(62),rewrite([86(4),63(3)]),flip(a)].
% 0.70/1.05 92 join(A,meet(B,A)) = A. [back_rewrite(71),rewrite([89(1)])].
% 0.70/1.05 93 meet(b,a) != meet(a,b) | join(b,a) != join(a,b) # answer(prove_normal_axioms). [back_rewrite(70),rewrite([89(10)]),xx(b)].
% 0.70/1.05 97 meet(join(meet(A,B),A),A) = join(meet(A,B),A). [back_rewrite(46),rewrite([89(7)])].
% 0.70/1.05 100 meet(A,meet(A,B)) = meet(A,B). [back_rewrite(58),rewrite([92(4),92(4)]),flip(a)].
% 0.70/1.05 101 meet(join(A,B),A) = A. [back_rewrite(52),rewrite([92(3),92(3)]),flip(a)].
% 0.70/1.05 105 meet(meet(A,join(B,A)),A) = A. [para(89(a,1),4(a,1,1,1))].
% 0.70/1.05 109 join(A,meet(join(A,B),join(join(A,B),A))) = join(A,B). [para(101(a,1),1(a,1,1))].
% 0.70/1.05 114 join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(A,join(A,B))) = A. [para(101(a,1),7(a,1,1,1)),rewrite([101(7),101(10)])].
% 0.70/1.05 116 meet(A,join(meet(A,B),A)) = join(meet(A,B),A). [para(26(a,1),101(a,1,1))].
% 0.70/1.05 131 join(meet(A,B),meet(A,join(A,meet(A,B)))) = A. [para(100(a,1),1(a,1,1))].
% 0.70/1.05 133 join(meet(meet(A,B),meet(A,join(A,meet(A,B)))),meet(meet(A,B),A)) = meet(A,B). [para(100(a,1),7(a,1,1,1)),rewrite([100(7),100(10)])].
% 0.70/1.05 154 join(join(meet(A,B),A),meet(meet(A,join(C,join(meet(A,B),A))),join(meet(A,join(C,join(meet(A,B),A))),join(meet(A,B),A)))) = meet(A,join(C,join(meet(A,B),A))). [para(26(a,1),13(a,1,2,1,1)),rewrite([26(9),26(18)])].
% 0.70/1.05 227 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(4(a,1),116(a,1,2,1)),rewrite([4(12)])].
% 0.70/1.05 228 join(meet(A,B),A) = A. [para(116(a,1),105(a,1,1)),rewrite([97(3)])].
% 0.70/1.05 229 meet(meet(A,join(B,meet(A,C))),join(meet(A,C),meet(A,join(B,meet(A,C))))) = join(meet(A,C),meet(A,join(B,meet(A,C)))). [para(14(a,1),116(a,1,2,1)),rewrite([14(14)])].
% 0.70/1.05 231 meet(A,join(B,A)) = A. [back_rewrite(154),rewrite([228(2),228(2),228(4),228(6),228(5),105(3),89(1),228(2)]),flip(a)].
% 0.70/1.05 233 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [back_rewrite(229),rewrite([231(9)]),flip(a)].
% 0.70/1.05 234 join(A,meet(join(A,B),join(C,A))) = meet(join(A,B),join(C,A)). [back_rewrite(227),rewrite([231(8)]),flip(a)].
% 0.70/1.05 236 meet(A,join(A,meet(A,B))) = A. [back_rewrite(131),rewrite([233(5)])].
% 0.70/1.05 237 meet(join(A,B),join(join(A,B),A)) = join(A,B). [back_rewrite(109),rewrite([234(5)])].
% 0.70/1.05 238 meet(meet(A,B),A) = meet(A,B). [back_rewrite(133),rewrite([236(4),89(5)])].
% 0.70/1.05 239 meet(A,join(A,B)) = A. [back_rewrite(114),rewrite([237(4),89(5)])].
% 0.70/1.05 255 meet(meet(join(A,B),join(C,B)),B) = B. [para(231(a,1),19(a,1,1,2,2)),rewrite([231(5),231(6)])].
% 0.70/1.05 257 join(join(A,B),A) = join(A,B). [para(239(a,1),92(a,1,2))].
% 0.70/1.05 260 join(A,meet(A,B)) = A. [para(238(a,1),92(a,1,2))].
% 0.70/1.05 278 meet(meet(A,B),meet(B,A)) = meet(B,A). [para(260(a,1),19(a,1,1,2))].
% 0.70/1.05 312 meet(meet(join(A,B),join(B,C)),B) = B. [para(257(a,1),255(a,1,1,2))].
% 0.70/1.05 357 meet(A,B) = meet(B,A). [para(278(a,1),238(a,1,1)),rewrite([278(3),278(4)])].
% 0.70/1.05 374 meet(A,meet(join(B,A),join(A,C))) = A. [back_rewrite(312),rewrite([357(4)])].
% 0.70/1.05 397 join(b,a) != join(a,b) # answer(prove_normal_axioms). [back_rewrite(93),rewrite([357(3)]),xx(a)].
% 0.70/1.05 412 meet(join(A,B),join(B,A)) = join(A,B). [para(374(a,1),25(a,1,1,2)),rewrite([260(5)]),flip(a)].
% 0.70/1.05 416 join(A,B) = join(B,A). [para(412(a,1),357(a,2)),rewrite([412(3)])].
% 0.70/1.05 417 $F # answer(prove_normal_axioms). [resolve(416,a,397,a)].
% 0.70/1.05
% 0.70/1.05 % SZS output end Refutation
% 0.70/1.05 ============================== end of proof ==========================
% 0.70/1.05
% 0.70/1.05 ============================== STATISTICS ============================
% 0.70/1.05
% 0.70/1.05 Given=63. Generated=2545. Kept=416. proofs=1.
% 0.70/1.05 Usable=24. Sos=82. Demods=107. Limbo=2, Disabled=313. Hints=0.
% 0.70/1.05 Megabytes=0.49.
% 0.70/1.05 User_CPU=0.09, System_CPU=0.01, Wall_clock=0.
% 0.70/1.05
% 0.70/1.05 ============================== end of statistics =====================
% 0.70/1.05
% 0.70/1.05 ============================== end of search =========================
% 0.70/1.05
% 0.70/1.05 THEOREM PROVED
% 0.70/1.05 % SZS status Unsatisfiable
% 0.70/1.05
% 0.70/1.05 Exiting with 1 proof.
% 0.70/1.05
% 0.70/1.05 Process 20986 exit (max_proofs) Wed Jun 29 21:42:08 2022
% 0.70/1.05 Prover9 interrupted
%------------------------------------------------------------------------------