TSTP Solution File: LAT022-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT022-1 : 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 06:25:09 EDT 2022
% Result : Unsatisfiable 1.21s 1.50s
% Output : Refutation 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT022-1 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 28 23:48:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.21/1.50 ============================== Prover9 ===============================
% 1.21/1.50 Prover9 (32) version 2009-11A, November 2009.
% 1.21/1.50 Process 28122 was started by sandbox2 on n007.cluster.edu,
% 1.21/1.50 Tue Jun 28 23:48:37 2022
% 1.21/1.50 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27968_n007.cluster.edu".
% 1.21/1.50 ============================== end of head ===========================
% 1.21/1.50
% 1.21/1.50 ============================== INPUT =================================
% 1.21/1.50
% 1.21/1.50 % Reading from file /tmp/Prover9_27968_n007.cluster.edu
% 1.21/1.50
% 1.21/1.50 set(prolog_style_variables).
% 1.21/1.50 set(auto2).
% 1.21/1.50 % set(auto2) -> set(auto).
% 1.21/1.50 % set(auto) -> set(auto_inference).
% 1.21/1.50 % set(auto) -> set(auto_setup).
% 1.21/1.50 % set(auto_setup) -> set(predicate_elim).
% 1.21/1.50 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.21/1.50 % set(auto) -> set(auto_limits).
% 1.21/1.50 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.21/1.50 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.21/1.50 % set(auto) -> set(auto_denials).
% 1.21/1.50 % set(auto) -> set(auto_process).
% 1.21/1.50 % set(auto2) -> assign(new_constants, 1).
% 1.21/1.50 % set(auto2) -> assign(fold_denial_max, 3).
% 1.21/1.50 % set(auto2) -> assign(max_weight, "200.000").
% 1.21/1.50 % set(auto2) -> assign(max_hours, 1).
% 1.21/1.50 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.21/1.50 % set(auto2) -> assign(max_seconds, 0).
% 1.21/1.50 % set(auto2) -> assign(max_minutes, 5).
% 1.21/1.50 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.21/1.50 % set(auto2) -> set(sort_initial_sos).
% 1.21/1.50 % set(auto2) -> assign(sos_limit, -1).
% 1.21/1.50 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.21/1.50 % set(auto2) -> assign(max_megs, 400).
% 1.21/1.50 % set(auto2) -> assign(stats, some).
% 1.21/1.50 % set(auto2) -> clear(echo_input).
% 1.21/1.50 % set(auto2) -> set(quiet).
% 1.21/1.50 % set(auto2) -> clear(print_initial_clauses).
% 1.21/1.50 % set(auto2) -> clear(print_given).
% 1.21/1.50 assign(lrs_ticks,-1).
% 1.21/1.50 assign(sos_limit,10000).
% 1.21/1.50 assign(order,kbo).
% 1.21/1.50 set(lex_order_vars).
% 1.21/1.50 clear(print_given).
% 1.21/1.50
% 1.21/1.50 % formulas(sos). % not echoed (10 formulas)
% 1.21/1.50
% 1.21/1.50 ============================== end of input ==========================
% 1.21/1.50
% 1.21/1.50 % From the command line: assign(max_seconds, 300).
% 1.21/1.50
% 1.21/1.50 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.21/1.50
% 1.21/1.50 % Formulas that are not ordinary clauses:
% 1.21/1.50
% 1.21/1.50 ============================== end of process non-clausal formulas ===
% 1.21/1.50
% 1.21/1.50 ============================== PROCESS INITIAL CLAUSES ===============
% 1.21/1.50
% 1.21/1.50 ============================== PREDICATE ELIMINATION =================
% 1.21/1.50
% 1.21/1.50 ============================== end predicate elimination =============
% 1.21/1.50
% 1.21/1.50 Auto_denials:
% 1.21/1.50 % copying label prove_modularity to answer in negative clause
% 1.21/1.50
% 1.21/1.50 Term ordering decisions:
% 1.21/1.50 Function symbol KB weights: a=1. b=1. c=1. join=1. meet=1.
% 1.21/1.50
% 1.21/1.50 ============================== end of process initial clauses ========
% 1.21/1.50
% 1.21/1.50 ============================== CLAUSES FOR SEARCH ====================
% 1.21/1.50
% 1.21/1.50 ============================== end of clauses for search =============
% 1.21/1.50
% 1.21/1.50 ============================== SEARCH ================================
% 1.21/1.50
% 1.21/1.50 % Starting search at 0.01 seconds.
% 1.21/1.50
% 1.21/1.50 ============================== PROOF =================================
% 1.21/1.50 % SZS status Unsatisfiable
% 1.21/1.50 % SZS output start Refutation
% 1.21/1.50
% 1.21/1.50 % Proof 1 at 0.53 (+ 0.01) seconds: prove_modularity.
% 1.21/1.50 % Length of proof is 52.
% 1.21/1.50 % Level of proof is 12.
% 1.21/1.50 % Maximum clause weight is 23.000.
% 1.21/1.50 % Given clauses 64.
% 1.21/1.50
% 1.21/1.50 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 1.21/1.50 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 1.21/1.50 3 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 1.21/1.50 4 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 1.21/1.50 5 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 1.21/1.50 6 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(5),rewrite([3(2)]),flip(a)].
% 1.21/1.50 7 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 1.21/1.50 8 join(A,join(B,C)) = join(C,join(A,B)). [copy(7),rewrite([4(2)]),flip(a)].
% 1.21/1.50 9 join(meet(A,join(B,C)),meet(A,B)) = meet(A,join(B,C)) # label(quasi_lattice1) # label(axiom). [assumption].
% 1.21/1.50 10 join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)). [copy(9),rewrite([4(4)])].
% 1.21/1.50 11 meet(join(A,meet(B,C)),join(A,B)) = join(A,meet(B,C)) # label(quasi_lattice2) # label(axiom). [assumption].
% 1.21/1.50 12 meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)). [copy(11),rewrite([3(4)])].
% 1.21/1.50 13 join(meet(A,B),meet(C,join(A,B))) = meet(join(A,B),join(C,meet(A,B))) # label(self_dual_modularity) # label(hypothesis). [assumption].
% 1.21/1.50 14 meet(join(A,B),join(C,meet(A,B))) = join(meet(A,B),meet(C,join(A,B))). [copy(13),flip(a)].
% 1.21/1.50 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].
% 1.21/1.50 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)])].
% 1.21/1.50 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)])].
% 1.21/1.50 19 join(join(A,B),meet(A,join(A,B))) = join(A,B). [para(1(a,1),10(a,1,2)),rewrite([3(2),4(4),1(7)])].
% 1.21/1.50 20 join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)). [para(3(a,1),10(a,1,1))].
% 1.21/1.50 26 meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)). [para(4(a,1),12(a,1,1))].
% 1.21/1.50 30 join(A,join(meet(B,C),meet(A,join(A,B)))) = join(A,meet(B,C)). [para(12(a,1),10(a,1,2)),rewrite([3(2),8(5,R),12(9)])].
% 1.21/1.50 32 meet(A,meet(join(B,C),join(A,meet(A,B)))) = meet(A,join(B,C)). [para(10(a,1),12(a,1,2)),rewrite([4(2),6(5,R),10(9)])].
% 1.21/1.50 34 meet(A,join(A,B)) = join(A,meet(A,B)). [para(1(a,1),14(a,1,2,2)),rewrite([2(1),4(1),1(3),2(3),3(3)])].
% 1.21/1.50 44 join(A,join(meet(A,B),meet(B,C))) = join(A,meet(B,C)). [back_rewrite(30),rewrite([34(3),8(4,R),17(5)])].
% 1.21/1.50 45 join(A,join(join(A,B),meet(A,B))) = join(A,B). [back_rewrite(19),rewrite([34(3),8(4,R),4(3)])].
% 1.21/1.50 47 meet(join(A,meet(A,B)),join(C,meet(A,B))) = join(meet(A,B),meet(C,join(A,meet(A,B)))). [para(16(a,1),14(a,1,2,2)),rewrite([16(7)])].
% 1.21/1.50 51 meet(A,join(B,meet(B,C))) = meet(B,meet(A,join(B,C))). [para(34(a,1),6(a,2,2)),rewrite([3(2)]),flip(a)].
% 1.21/1.50 60 join(join(A,B),meet(A,B)) = join(A,B). [para(45(a,1),8(a,1)),rewrite([17(4),4(4)]),flip(a)].
% 1.21/1.50 72 meet(A,join(B,A)) = join(A,meet(B,A)). [para(20(a,1),14(a,2)),rewrite([26(4)]),flip(a)].
% 1.21/1.50 78 join(join(A,join(B,C)),meet(C,join(A,B))) = join(A,join(B,C)). [para(8(a,2),60(a,1,1)),rewrite([8(7),4(6),8(7,R),4(6)])].
% 1.21/1.50 82 join(A,join(join(B,C),meet(A,B))) = join(A,join(B,C)). [para(14(a,1),60(a,1,2)),rewrite([8(4,R),4(3),60(3),8(2),4(1),8(2,R),4(1),8(7,R),4(6),78(6),8(4,R),8(8,R),4(7),60(7),8(6),4(5),8(6,R),4(5)])].
% 1.21/1.50 89 join(A,join(meet(B,A),meet(B,C))) = join(A,meet(B,C)). [para(26(a,1),10(a,1,2)),rewrite([3(2),72(2),8(5,R),8(4,R),17(5),26(8)])].
% 1.21/1.50 97 join(A,join(B,meet(A,B))) = join(A,B). [para(1(a,1),44(a,1,2,2)),rewrite([4(2),1(4)])].
% 1.21/1.50 98 join(A,join(meet(B,C),meet(A,B))) = join(A,meet(B,C)). [para(4(a,1),44(a,1,2))].
% 1.21/1.50 160 meet(A,meet(B,join(A,meet(A,C)))) = meet(A,meet(B,join(A,C))). [para(51(a,2),16(a,1,2))].
% 1.21/1.50 162 join(meet(A,B),meet(A,meet(B,join(A,C)))) = meet(B,join(A,meet(A,C))). [para(51(a,1),20(a,1,2))].
% 1.21/1.50 165 meet(A,join(B,meet(A,B))) = meet(A,B). [para(51(a,1),72(a,1)),rewrite([3(3),6(3),3(2),34(2),160(4),72(2),16(6),2(6)])].
% 1.21/1.50 178 meet(A,meet(join(B,C),join(A,B))) = meet(A,join(B,C)). [back_rewrite(32),rewrite([160(5)])].
% 1.21/1.50 211 join(A,join(join(B,C),meet(A,C))) = join(A,join(B,C)). [para(4(a,1),82(a,1,2,1)),rewrite([4(5)])].
% 1.21/1.50 237 join(join(A,meet(A,B)),meet(B,C)) = join(A,meet(B,C)). [para(165(a,1),89(a,1,2,1)),rewrite([3(1),3(3),8(6,R),8(5,R),44(5),8(4,R),98(4),3(3)]),flip(a)].
% 1.21/1.50 283 meet(A,meet(join(B,C),join(B,A))) = meet(A,join(B,C)). [para(178(a,1),3(a,2)),rewrite([4(2),3(4)])].
% 1.21/1.50 287 meet(join(A,B),join(C,meet(A,C))) = meet(C,join(A,B)). [para(178(a,1),6(a,2)),rewrite([4(2),3(3),72(3)])].
% 1.21/1.50 350 join(A,join(join(B,C),meet(C,A))) = join(B,join(C,A)). [para(211(a,1),4(a,2)),rewrite([3(2),4(4),8(6),4(5),8(6,R),4(5)])].
% 1.21/1.50 506 join(join(A,meet(B,A)),meet(B,C)) = join(A,meet(B,C)). [para(237(a,1),26(a,1,2)),rewrite([3(1),97(3),26(4),3(3)]),flip(a)].
% 1.21/1.50 593 join(meet(A,B),meet(A,meet(B,C))) = meet(meet(A,B),join(A,C)). [para(12(a,1),283(a,1,2)),rewrite([72(4),6(3),3(2),6(3,R),3(2),4(6)])].
% 1.21/1.50 611 meet(meet(A,B),join(A,C)) = meet(B,join(A,meet(A,C))). [back_rewrite(162),rewrite([593(5),17(3)])].
% 1.21/1.50 614 join(meet(A,B),meet(A,meet(B,C))) = meet(B,join(A,meet(A,C))). [back_rewrite(593),rewrite([611(7)])].
% 1.21/1.50 676 meet(join(A,meet(A,B)),join(B,C)) = meet(A,join(B,C)). [para(287(a,1),3(a,1)),rewrite([3(3)]),flip(a)].
% 1.21/1.50 777 join(A,meet(B,join(C,meet(C,A)))) = join(A,meet(C,B)). [para(44(a,1),350(a,2)),rewrite([3(2),3(4),6(6),3(5),16(5),6(5,R),3(4),506(6),8(5,R),4(4),614(4)])].
% 1.21/1.50 1224 join(meet(A,B),meet(C,join(A,meet(A,B)))) = meet(A,join(C,meet(A,B))). [para(16(a,1),676(a,1,1,2)),rewrite([4(4),47(5),4(7)])].
% 1.21/1.50 1524 meet(A,join(B,meet(A,C))) = join(meet(A,C),meet(A,B)). [para(16(a,1),777(a,1,2,2,2)),rewrite([1224(5)])].
% 1.21/1.50 1572 $F # answer(prove_modularity). [back_rewrite(15),rewrite([1524(7),4(7)]),xx(a)].
% 1.21/1.50
% 1.21/1.50 % SZS output end Refutation
% 1.21/1.50 ============================== end of proof ==========================
% 1.21/1.50
% 1.21/1.50 ============================== STATISTICS ============================
% 1.21/1.50
% 1.21/1.50 Given=64. Generated=7944. Kept=1566. proofs=1.
% 1.21/1.50 Usable=51. Sos=876. Demods=957. Limbo=48, Disabled=601. Hints=0.
% 1.21/1.50 Megabytes=2.19.
% 1.21/1.50 User_CPU=0.53, System_CPU=0.01, Wall_clock=1.
% 1.21/1.50
% 1.21/1.50 ============================== end of statistics =====================
% 1.21/1.50
% 1.21/1.50 ============================== end of search =========================
% 1.21/1.50
% 1.21/1.50 THEOREM PROVED
% 1.21/1.50 % SZS status Unsatisfiable
% 1.21/1.50
% 1.21/1.50 Exiting with 1 proof.
% 1.21/1.50
% 1.21/1.50 Process 28122 exit (max_proofs) Tue Jun 28 23:48:38 2022
% 1.24/1.50 Prover9 interrupted
%------------------------------------------------------------------------------