TSTP Solution File: LAT019-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 06:25:08 EDT 2022
% Result : Unsatisfiable 0.73s 1.02s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 30 10:28:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.73/1.02 ============================== Prover9 ===============================
% 0.73/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.02 Process 6108 was started by sandbox on n014.cluster.edu,
% 0.73/1.02 Thu Jun 30 10:28:12 2022
% 0.73/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5955_n014.cluster.edu".
% 0.73/1.02 ============================== end of head ===========================
% 0.73/1.02
% 0.73/1.02 ============================== INPUT =================================
% 0.73/1.02
% 0.73/1.02 % Reading from file /tmp/Prover9_5955_n014.cluster.edu
% 0.73/1.02
% 0.73/1.02 set(prolog_style_variables).
% 0.73/1.02 set(auto2).
% 0.73/1.02 % set(auto2) -> set(auto).
% 0.73/1.02 % set(auto) -> set(auto_inference).
% 0.73/1.02 % set(auto) -> set(auto_setup).
% 0.73/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.02 % set(auto) -> set(auto_limits).
% 0.73/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.02 % set(auto) -> set(auto_denials).
% 0.73/1.02 % set(auto) -> set(auto_process).
% 0.73/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.02 % set(auto2) -> assign(stats, some).
% 0.73/1.02 % set(auto2) -> clear(echo_input).
% 0.73/1.02 % set(auto2) -> set(quiet).
% 0.73/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.02 % set(auto2) -> clear(print_given).
% 0.73/1.02 assign(lrs_ticks,-1).
% 0.73/1.02 assign(sos_limit,10000).
% 0.73/1.02 assign(order,kbo).
% 0.73/1.02 set(lex_order_vars).
% 0.73/1.02 clear(print_given).
% 0.73/1.02
% 0.73/1.02 % formulas(sos). % not echoed (10 formulas)
% 0.73/1.02
% 0.73/1.02 ============================== end of input ==========================
% 0.73/1.02
% 0.73/1.02 % From the command line: assign(max_seconds, 300).
% 0.73/1.02
% 0.73/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.02
% 0.73/1.02 % Formulas that are not ordinary clauses:
% 0.73/1.02
% 0.73/1.02 ============================== end of process non-clausal formulas ===
% 0.73/1.02
% 0.73/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.02
% 0.73/1.02 ============================== PREDICATE ELIMINATION =================
% 0.73/1.02
% 0.73/1.02 ============================== end predicate elimination =============
% 0.73/1.02
% 0.73/1.02 Auto_denials:
% 0.73/1.02 % copying label prove_distributivity_law_dual to answer in negative clause
% 0.73/1.02
% 0.73/1.02 Term ordering decisions:
% 0.73/1.02 Function symbol KB weights: a=1. b=1. c=1. meet=1. join=1.
% 0.73/1.02
% 0.73/1.02 ============================== end of process initial clauses ========
% 0.73/1.02
% 0.73/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.02
% 0.73/1.02 ============================== end of clauses for search =============
% 0.73/1.02
% 0.73/1.02 ============================== SEARCH ================================
% 0.73/1.02
% 0.73/1.02 % Starting search at 0.01 seconds.
% 0.73/1.02
% 0.73/1.02 ============================== PROOF =================================
% 0.73/1.02 % SZS status Unsatisfiable
% 0.73/1.02 % SZS output start Refutation
% 0.73/1.02
% 0.73/1.02 % Proof 1 at 0.04 (+ 0.00) seconds: prove_distributivity_law_dual.
% 0.73/1.02 % Length of proof is 26.
% 0.73/1.02 % Level of proof is 7.
% 0.73/1.02 % Maximum clause weight is 19.000.
% 0.73/1.02 % Given clauses 22.
% 0.73/1.02
% 0.73/1.02 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 0.73/1.02 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 0.73/1.02 3 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 0.73/1.02 4 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 0.73/1.02 5 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 0.73/1.02 6 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(5),rewrite([3(2)]),flip(a)].
% 0.73/1.02 7 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 0.73/1.02 8 join(A,join(B,C)) = join(C,join(A,B)). [copy(7),rewrite([4(2)]),flip(a)].
% 0.73/1.02 9 meet(A,join(B,C)) = join(meet(A,B),meet(A,C)) # label(distributivity_law) # label(hypothesis). [assumption].
% 0.73/1.02 10 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [copy(9),flip(a)].
% 0.73/1.02 13 meet(join(A,meet(B,C)),join(A,B)) = join(A,meet(B,C)) # label(quasi_lattice2) # label(axiom). [assumption].
% 0.73/1.02 14 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [copy(13),rewrite([3(4)])].
% 0.73/1.02 15 join(a,meet(b,c)) != meet(join(a,b),join(a,c)) # label(prove_distributivity_law_dual) # label(negated_conjecture) # answer(prove_distributivity_law_dual). [assumption].
% 0.73/1.02 16 meet(join(a,b),join(a,c)) != join(a,meet(b,c)) # answer(prove_distributivity_law_dual). [copy(15),flip(a)].
% 0.73/1.02 17 meet(A,meet(A,B)) = meet(A,B). [para(6(a,1),1(a,1)),rewrite([3(1),3(2),6(2,R),1(1),3(3)])].
% 0.73/1.02 18 join(A,join(A,B)) = join(A,B). [para(8(a,1),2(a,1)),rewrite([4(1),4(2),8(2,R),2(1),4(3)])].
% 0.73/1.02 19 join(A,meet(A,B)) = meet(A,join(A,B)). [para(1(a,1),10(a,1,1))].
% 0.73/1.02 21 join(meet(A,B),meet(B,C)) = meet(B,join(A,C)). [para(3(a,1),10(a,1,1))].
% 0.73/1.02 22 join(meet(A,meet(B,C)),meet(B,D)) = meet(B,join(D,meet(A,C))). [para(6(a,1),10(a,1,1)),rewrite([3(5),4(6)])].
% 0.73/1.02 33 meet(A,join(B,meet(A,C))) = meet(A,join(C,B)). [para(17(a,1),10(a,1,1)),rewrite([10(3),4(4)]),flip(a)].
% 0.73/1.02 36 join(A,meet(B,A)) = meet(A,join(B,A)). [para(1(a,1),21(a,1,2)),rewrite([4(2)])].
% 0.73/1.02 45 meet(join(A,meet(B,C)),join(A,meet(B,join(B,C)))) = join(A,meet(B,C)). [para(14(a,1),36(a,1,2)),rewrite([2(5),8(8,R),8(7),4(6),8(7,R),4(6),19(6),18(8)]),flip(a)].
% 0.73/1.02 60 join(A,meet(B,join(A,C))) = join(A,meet(B,C)). [para(33(a,1),36(a,1,2)),rewrite([4(3),4(5),8(5),4(4),8(5,R),4(4),10(4),8(2,R),2(1),8(8,R),4(7),19(7),45(9)])].
% 0.73/1.02 62 meet(A,join(B,meet(C,A))) = meet(A,join(C,B)). [para(1(a,1),22(a,1,1,2)),rewrite([21(3)]),flip(a)].
% 0.73/1.02 101 meet(join(A,B),join(A,C)) = join(A,meet(B,C)). [para(60(a,1),62(a,1,2)),rewrite([3(2),14(4),4(4)]),flip(a)].
% 0.73/1.02 102 $F # answer(prove_distributivity_law_dual). [resolve(101,a,16,a)].
% 0.73/1.02
% 0.73/1.02 % SZS output end Refutation
% 0.73/1.02 ============================== end of proof ==========================
% 0.73/1.02
% 0.73/1.02 ============================== STATISTICS ============================
% 0.73/1.02
% 0.73/1.02 Given=22. Generated=721. Kept=95. proofs=1.
% 0.73/1.02 Usable=20. Sos=57. Demods=74. Limbo=2, Disabled=25. Hints=0.
% 0.73/1.02 Megabytes=0.13.
% 0.73/1.02 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.73/1.02
% 0.73/1.02 ============================== end of statistics =====================
% 0.73/1.02
% 0.73/1.02 ============================== end of search =========================
% 0.73/1.02
% 0.73/1.02 THEOREM PROVED
% 0.73/1.02 % SZS status Unsatisfiable
% 0.73/1.02
% 0.73/1.02 Exiting with 1 proof.
% 0.73/1.02
% 0.73/1.02 Process 6108 exit (max_proofs) Thu Jun 30 10:28:12 2022
% 0.73/1.02 Prover9 interrupted
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