TSTP Solution File: LAT143-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT143-1 : TPTP v8.1.0. Released v3.1.0.
% 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 06:25:46 EDT 2022
% Result : Unsatisfiable 0.87s 1.15s
% Output : Refutation 0.87s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LAT143-1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 30 13:01:43 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.87/1.15 ============================== Prover9 ===============================
% 0.87/1.15 Prover9 (32) version 2009-11A, November 2009.
% 0.87/1.15 Process 4617 was started by sandbox2 on n021.cluster.edu,
% 0.87/1.15 Thu Jun 30 13:01:43 2022
% 0.87/1.15 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4445_n021.cluster.edu".
% 0.87/1.15 ============================== end of head ===========================
% 0.87/1.15
% 0.87/1.15 ============================== INPUT =================================
% 0.87/1.15
% 0.87/1.15 % Reading from file /tmp/Prover9_4445_n021.cluster.edu
% 0.87/1.15
% 0.87/1.15 set(prolog_style_variables).
% 0.87/1.15 set(auto2).
% 0.87/1.15 % set(auto2) -> set(auto).
% 0.87/1.15 % set(auto) -> set(auto_inference).
% 0.87/1.15 % set(auto) -> set(auto_setup).
% 0.87/1.15 % set(auto_setup) -> set(predicate_elim).
% 0.87/1.15 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.87/1.15 % set(auto) -> set(auto_limits).
% 0.87/1.15 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.87/1.15 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.87/1.15 % set(auto) -> set(auto_denials).
% 0.87/1.15 % set(auto) -> set(auto_process).
% 0.87/1.15 % set(auto2) -> assign(new_constants, 1).
% 0.87/1.15 % set(auto2) -> assign(fold_denial_max, 3).
% 0.87/1.15 % set(auto2) -> assign(max_weight, "200.000").
% 0.87/1.15 % set(auto2) -> assign(max_hours, 1).
% 0.87/1.15 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.87/1.15 % set(auto2) -> assign(max_seconds, 0).
% 0.87/1.15 % set(auto2) -> assign(max_minutes, 5).
% 0.87/1.15 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.87/1.15 % set(auto2) -> set(sort_initial_sos).
% 0.87/1.15 % set(auto2) -> assign(sos_limit, -1).
% 0.87/1.15 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.87/1.15 % set(auto2) -> assign(max_megs, 400).
% 0.87/1.15 % set(auto2) -> assign(stats, some).
% 0.87/1.15 % set(auto2) -> clear(echo_input).
% 0.87/1.15 % set(auto2) -> set(quiet).
% 0.87/1.15 % set(auto2) -> clear(print_initial_clauses).
% 0.87/1.15 % set(auto2) -> clear(print_given).
% 0.87/1.15 assign(lrs_ticks,-1).
% 0.87/1.15 assign(sos_limit,10000).
% 0.87/1.15 assign(order,kbo).
% 0.87/1.15 set(lex_order_vars).
% 0.87/1.15 clear(print_given).
% 0.87/1.15
% 0.87/1.15 % formulas(sos). % not echoed (10 formulas)
% 0.87/1.15
% 0.87/1.15 ============================== end of input ==========================
% 0.87/1.15
% 0.87/1.15 % From the command line: assign(max_seconds, 300).
% 0.87/1.15
% 0.87/1.15 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.87/1.15
% 0.87/1.15 % Formulas that are not ordinary clauses:
% 0.87/1.15
% 0.87/1.15 ============================== end of process non-clausal formulas ===
% 0.87/1.15
% 0.87/1.15 ============================== PROCESS INITIAL CLAUSES ===============
% 0.87/1.15
% 0.87/1.15 ============================== PREDICATE ELIMINATION =================
% 0.87/1.15
% 0.87/1.15 ============================== end predicate elimination =============
% 0.87/1.15
% 0.87/1.15 Auto_denials:
% 0.87/1.15 % copying label prove_H15 to answer in negative clause
% 0.87/1.15
% 0.87/1.15 Term ordering decisions:
% 0.87/1.15 Function symbol KB weights: a=1. b=1. c=1. meet=1. join=1.
% 0.87/1.15
% 0.87/1.15 ============================== end of process initial clauses ========
% 0.87/1.15
% 0.87/1.15 ============================== CLAUSES FOR SEARCH ====================
% 0.87/1.15
% 0.87/1.15 ============================== end of clauses for search =============
% 0.87/1.15
% 0.87/1.15 ============================== SEARCH ================================
% 0.87/1.15
% 0.87/1.15 % Starting search at 0.01 seconds.
% 0.87/1.15
% 0.87/1.15 ============================== PROOF =================================
% 0.87/1.15 % SZS status Unsatisfiable
% 0.87/1.15 % SZS output start Refutation
% 0.87/1.15
% 0.87/1.15 % Proof 1 at 0.16 (+ 0.00) seconds: prove_H15.
% 0.87/1.15 % Length of proof is 34.
% 0.87/1.15 % Level of proof is 12.
% 0.87/1.15 % Maximum clause weight is 31.000.
% 0.87/1.15 % Given clauses 34.
% 0.87/1.15
% 0.87/1.15 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 0.87/1.15 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 0.87/1.15 3 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 0.87/1.15 4 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 0.87/1.15 5 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 0.87/1.15 6 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 0.87/1.15 7 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 0.87/1.15 8 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(7),rewrite([5(2)]),flip(a)].
% 0.87/1.15 9 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 0.87/1.15 10 join(A,join(B,C)) = join(C,join(A,B)). [copy(9),rewrite([6(2)]),flip(a)].
% 0.87/1.15 11 join(meet(A,B),meet(B,C)) = join(meet(A,B),meet(B,join(meet(A,B),meet(C,join(A,B))))) # label(equation_H24) # label(axiom). [assumption].
% 0.87/1.15 12 join(meet(A,B),meet(B,join(meet(A,B),meet(C,join(A,B))))) = join(meet(A,B),meet(B,C)). [copy(11),flip(a)].
% 0.87/1.15 13 meet(a,join(meet(a,b),meet(a,c))) != meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) # label(prove_H15) # label(negated_conjecture) # answer(prove_H15). [assumption].
% 0.87/1.15 14 meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) != meet(a,join(meet(a,b),meet(a,c))) # answer(prove_H15). [copy(13),flip(a)].
% 0.87/1.15 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)])].
% 0.87/1.15 16 meet(A,meet(B,join(A,C))) = meet(A,B). [para(3(a,1),8(a,2,2)),rewrite([5(2),5(4)])].
% 0.87/1.15 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)])].
% 0.87/1.15 18 join(A,join(B,meet(A,C))) = join(A,B). [para(4(a,1),10(a,2,2)),rewrite([6(2),6(4)])].
% 0.87/1.15 19 join(A,meet(join(A,B),join(A,meet(C,join(A,B))))) = join(A,meet(C,join(A,B))). [para(3(a,1),12(a,1,1)),rewrite([3(3),17(3),3(8),5(8)])].
% 0.87/1.15 21 join(meet(A,B),meet(A,join(meet(A,B),meet(C,join(A,B))))) = join(meet(A,B),meet(A,C)). [para(5(a,1),12(a,1,1)),rewrite([5(2),6(3),5(8)])].
% 0.87/1.15 26 meet(A,meet(B,meet(C,join(A,D)))) = meet(A,meet(B,C)). [para(16(a,1),8(a,2,2)),rewrite([5(3),8(3,R),5(2),8(6),5(5),8(6,R),5(5)])].
% 0.87/1.15 36 join(A,join(join(A,B),meet(C,join(A,B)))) = join(A,B). [para(19(a,1),18(a,1,2)),rewrite([10(5,R),6(4),6(7),17(7)])].
% 0.87/1.15 37 meet(A,meet(B,meet(meet(A,B),join(C,meet(A,B))))) = meet(A,B). [para(1(a,1),26(a,2)),rewrite([6(3),8(6,R),5(5),8(5,R),5(4)])].
% 0.87/1.15 44 join(join(A,B),meet(C,join(A,B))) = join(A,B). [para(36(a,1),10(a,1)),rewrite([17(5),6(5)]),flip(a)].
% 0.87/1.15 45 join(meet(A,join(B,C)),meet(A,meet(D,join(B,C)))) = meet(A,join(B,C)). [para(44(a,1),12(a,1,2,2,2,2)),rewrite([8(4,R),1(3),8(8,R),1(7),3(10),2(5),8(6,R),1(5),5(7),8(7,R),5(6)]),flip(a)].
% 0.87/1.15 55 join(meet(A,B),meet(join(meet(A,B),meet(A,C)),join(meet(A,B),meet(C,join(A,B))))) = join(meet(A,B),meet(A,C)). [para(21(a,1),19(a,1,2,2)),rewrite([5(9),21(17)])].
% 0.87/1.15 61 meet(A,meet(join(meet(A,B),meet(A,C)),join(meet(A,B),meet(C,join(A,B))))) = meet(A,join(meet(A,B),meet(C,join(A,B)))). [para(12(a,1),37(a,1,2,2,2)),rewrite([5(1),6(2),5(5),6(6),5(10),5(13),8(13,R),5(12),8(14,R),5(13),8(13,R),1(12),15(10),5(10),6(11)])].
% 0.87/1.15 103 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [para(3(a,1),45(a,1,2,2)),rewrite([6(4)])].
% 0.87/1.15 109 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(5(a,1),103(a,1,1))].
% 0.87/1.15 120 meet(a,join(meet(a,b),meet(c,join(a,b)))) != meet(a,join(meet(a,b),meet(a,c))) # answer(prove_H15). [back_rewrite(14),rewrite([109(13)])].
% 0.87/1.15 146 join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)). [para(3(a,1),109(a,1,1))].
% 0.87/1.15 168 meet(join(meet(A,B),meet(A,C)),join(meet(A,B),meet(C,join(A,B)))) = join(meet(A,B),meet(A,C)). [back_rewrite(55),rewrite([146(10)])].
% 0.87/1.15 177 meet(A,join(meet(A,B),meet(C,join(A,B)))) = meet(A,join(meet(A,B),meet(A,C))). [back_rewrite(61),rewrite([168(8)]),flip(a)].
% 0.87/1.15 178 $F # answer(prove_H15). [resolve(177,a,120,a)].
% 0.87/1.15
% 0.87/1.15 % SZS output end Refutation
% 0.87/1.15 ============================== end of proof ==========================
% 0.87/1.15
% 0.87/1.15 ============================== STATISTICS ============================
% 0.87/1.15
% 0.87/1.15 Given=34. Generated=1919. Kept=173. proofs=1.
% 0.87/1.15 Usable=29. Sos=109. Demods=146. Limbo=9, Disabled=35. Hints=0.
% 0.87/1.15 Megabytes=0.39.
% 0.87/1.15 User_CPU=0.16, System_CPU=0.00, Wall_clock=1.
% 0.87/1.15
% 0.87/1.15 ============================== end of statistics =====================
% 0.87/1.15
% 0.87/1.15 ============================== end of search =========================
% 0.87/1.15
% 0.87/1.15 THEOREM PROVED
% 0.87/1.15 % SZS status Unsatisfiable
% 0.87/1.15
% 0.87/1.15 Exiting with 1 proof.
% 0.87/1.15
% 0.87/1.15 Process 4617 exit (max_proofs) Thu Jun 30 13:01:44 2022
% 0.87/1.15 Prover9 interrupted
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