TSTP Solution File: LAT023-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT023-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 06:25:10 EDT 2022
% Result : Unsatisfiable 0.97s 1.29s
% Output : Refutation 0.97s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT023-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n018.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 03:54:01 EDT 2022
% 0.20/0.34 % CPUTime :
% 0.97/1.29 ============================== Prover9 ===============================
% 0.97/1.29 Prover9 (32) version 2009-11A, November 2009.
% 0.97/1.29 Process 6062 was started by sandbox on n018.cluster.edu,
% 0.97/1.29 Thu Jun 30 03:54:01 2022
% 0.97/1.29 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5909_n018.cluster.edu".
% 0.97/1.29 ============================== end of head ===========================
% 0.97/1.29
% 0.97/1.29 ============================== INPUT =================================
% 0.97/1.29
% 0.97/1.29 % Reading from file /tmp/Prover9_5909_n018.cluster.edu
% 0.97/1.29
% 0.97/1.29 set(prolog_style_variables).
% 0.97/1.29 set(auto2).
% 0.97/1.29 % set(auto2) -> set(auto).
% 0.97/1.29 % set(auto) -> set(auto_inference).
% 0.97/1.29 % set(auto) -> set(auto_setup).
% 0.97/1.29 % set(auto_setup) -> set(predicate_elim).
% 0.97/1.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.97/1.29 % set(auto) -> set(auto_limits).
% 0.97/1.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.97/1.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.97/1.29 % set(auto) -> set(auto_denials).
% 0.97/1.29 % set(auto) -> set(auto_process).
% 0.97/1.29 % set(auto2) -> assign(new_constants, 1).
% 0.97/1.29 % set(auto2) -> assign(fold_denial_max, 3).
% 0.97/1.29 % set(auto2) -> assign(max_weight, "200.000").
% 0.97/1.29 % set(auto2) -> assign(max_hours, 1).
% 0.97/1.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.97/1.29 % set(auto2) -> assign(max_seconds, 0).
% 0.97/1.29 % set(auto2) -> assign(max_minutes, 5).
% 0.97/1.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.97/1.29 % set(auto2) -> set(sort_initial_sos).
% 0.97/1.29 % set(auto2) -> assign(sos_limit, -1).
% 0.97/1.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.97/1.29 % set(auto2) -> assign(max_megs, 400).
% 0.97/1.29 % set(auto2) -> assign(stats, some).
% 0.97/1.29 % set(auto2) -> clear(echo_input).
% 0.97/1.29 % set(auto2) -> set(quiet).
% 0.97/1.29 % set(auto2) -> clear(print_initial_clauses).
% 0.97/1.29 % set(auto2) -> clear(print_given).
% 0.97/1.29 assign(lrs_ticks,-1).
% 0.97/1.29 assign(sos_limit,10000).
% 0.97/1.29 assign(order,kbo).
% 0.97/1.29 set(lex_order_vars).
% 0.97/1.29 clear(print_given).
% 0.97/1.29
% 0.97/1.29 % formulas(sos). % not echoed (10 formulas)
% 0.97/1.29
% 0.97/1.29 ============================== end of input ==========================
% 0.97/1.29
% 0.97/1.29 % From the command line: assign(max_seconds, 300).
% 0.97/1.29
% 0.97/1.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.97/1.29
% 0.97/1.29 % Formulas that are not ordinary clauses:
% 0.97/1.29
% 0.97/1.29 ============================== end of process non-clausal formulas ===
% 0.97/1.29
% 0.97/1.29 ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.29
% 0.97/1.29 ============================== PREDICATE ELIMINATION =================
% 0.97/1.29
% 0.97/1.29 ============================== end predicate elimination =============
% 0.97/1.29
% 0.97/1.29 Auto_denials:
% 0.97/1.29 % copying label prove_modularity to answer in negative clause
% 0.97/1.29
% 0.97/1.29 Term ordering decisions:
% 0.97/1.29 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 0.97/1.29
% 0.97/1.29 ============================== end of process initial clauses ========
% 0.97/1.29
% 0.97/1.29 ============================== CLAUSES FOR SEARCH ====================
% 0.97/1.29
% 0.97/1.29 ============================== end of clauses for search =============
% 0.97/1.29
% 0.97/1.29 ============================== SEARCH ================================
% 0.97/1.29
% 0.97/1.29 % Starting search at 0.01 seconds.
% 0.97/1.29
% 0.97/1.29 ============================== PROOF =================================
% 0.97/1.29 % SZS status Unsatisfiable
% 0.97/1.29 % SZS output start Refutation
% 0.97/1.29
% 0.97/1.29 % Proof 1 at 0.30 (+ 0.01) seconds: prove_modularity.
% 0.97/1.29 % Length of proof is 28.
% 0.97/1.29 % Level of proof is 7.
% 0.97/1.29 % Maximum clause weight is 19.000.
% 0.97/1.29 % Given clauses 53.
% 0.97/1.29
% 0.97/1.29 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 0.97/1.29 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 0.97/1.29 3 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 0.97/1.29 4 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 0.97/1.29 5 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 0.97/1.29 6 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(5),rewrite([3(2)]),flip(a)].
% 0.97/1.29 7 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 0.97/1.29 8 join(A,join(B,C)) = join(C,join(A,B)). [copy(7),rewrite([4(2)]),flip(a)].
% 0.97/1.29 9 join(meet(A,join(B,C)),meet(A,B)) = meet(A,join(B,C)) # label(quasi_lattice1) # label(axiom). [assumption].
% 0.97/1.29 10 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [copy(9),rewrite([4(4)])].
% 0.97/1.29 11 meet(join(A,meet(B,C)),join(A,B)) = join(A,meet(B,C)) # label(quasi_lattice2) # label(axiom). [assumption].
% 0.97/1.29 12 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [copy(11),rewrite([3(4)])].
% 0.97/1.29 13 join(meet(join(A,B),C),B) = join(meet(join(C,B),A),B) # label(modularity_axiom) # label(hypothesis). [assumption].
% 0.97/1.29 14 join(A,meet(B,join(A,C))) = join(A,meet(C,join(A,B))). [copy(13),rewrite([3(2),4(3),4(4),3(5),4(6)]),rewrite([4(1)])].
% 0.97/1.29 15 meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)) # label(prove_modularity) # label(negated_conjecture) # answer(prove_modularity). [assumption].
% 0.97/1.29 16 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)])].
% 0.97/1.29 17 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)])].
% 0.97/1.29 18 join(A,meet(A,join(A,B))) = meet(A,join(A,B)). [para(1(a,1),10(a,1,1))].
% 0.97/1.29 35 meet(A,join(A,B)) = join(A,meet(A,B)). [para(2(a,1),14(a,1,2,2)),rewrite([3(1),18(5)]),flip(a)].
% 0.97/1.29 36 join(A,meet(B,join(C,A))) = join(A,meet(C,join(A,B))). [para(14(a,1),4(a,2)),rewrite([4(3),4(4)]),flip(a)].
% 0.97/1.29 43 join(A,meet(meet(B,C),join(A,B))) = join(A,meet(B,C)). [para(12(a,1),14(a,1,2)),rewrite([17(3),17(5)]),flip(a)].
% 0.97/1.29 47 join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(16(a,1),10(a,1,1)),rewrite([4(3),4(7)])].
% 0.97/1.29 53 meet(A,join(B,meet(B,C))) = meet(B,meet(A,join(B,C))). [para(35(a,1),6(a,2,2)),rewrite([3(2)]),flip(a)].
% 0.97/1.29 150 join(A,meet(B,meet(C,join(A,B)))) = join(A,meet(B,C)). [para(3(a,1),43(a,1,2)),rewrite([6(3),3(2),6(3,R),3(2)])].
% 0.97/1.29 240 join(meet(A,B),meet(A,meet(C,join(A,B)))) = meet(A,join(C,meet(A,B))). [para(53(a,1),36(a,1,2)),rewrite([4(8),47(10)])].
% 0.97/1.29 412 join(A,meet(B,meet(C,join(B,A)))) = join(A,meet(B,C)). [para(150(a,1),4(a,2)),rewrite([4(1),4(4)])].
% 0.97/1.29 854 meet(A,join(B,meet(A,C))) = join(meet(A,C),meet(A,B)). [para(53(a,1),412(a,1,2,2)),rewrite([16(5),240(5)])].
% 0.97/1.29 879 $F # answer(prove_modularity). [back_rewrite(15),rewrite([854(7),4(7)]),xx(a)].
% 0.97/1.29
% 0.97/1.29 % SZS output end Refutation
% 0.97/1.29 ============================== end of proof ==========================
% 0.97/1.29
% 0.97/1.29 ============================== STATISTICS ============================
% 0.97/1.29
% 0.97/1.29 Given=53. Generated=5066. Kept=873. proofs=1.
% 0.97/1.29 Usable=44. Sos=645. Demods=682. Limbo=25, Disabled=169. Hints=0.
% 0.97/1.29 Megabytes=1.35.
% 0.97/1.29 User_CPU=0.31, System_CPU=0.01, Wall_clock=1.
% 0.97/1.29
% 0.97/1.29 ============================== end of statistics =====================
% 0.97/1.29
% 0.97/1.29 ============================== end of search =========================
% 0.97/1.29
% 0.97/1.29 THEOREM PROVED
% 0.97/1.29 % SZS status Unsatisfiable
% 0.97/1.29
% 0.97/1.29 Exiting with 1 proof.
% 0.97/1.29
% 0.97/1.29 Process 6062 exit (max_proofs) Thu Jun 30 03:54:02 2022
% 0.97/1.29 Prover9 interrupted
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