TSTP Solution File: LAT043-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT043-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 06:25:16 EDT 2022
% Result : Unsatisfiable 1.09s 1.42s
% Output : Refutation 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT043-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n028.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 29 01:40:57 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.09/1.42 ============================== Prover9 ===============================
% 1.09/1.42 Prover9 (32) version 2009-11A, November 2009.
% 1.09/1.42 Process 6737 was started by sandbox on n028.cluster.edu,
% 1.09/1.42 Wed Jun 29 01:40:58 2022
% 1.09/1.42 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6583_n028.cluster.edu".
% 1.09/1.42 ============================== end of head ===========================
% 1.09/1.42
% 1.09/1.42 ============================== INPUT =================================
% 1.09/1.42
% 1.09/1.42 % Reading from file /tmp/Prover9_6583_n028.cluster.edu
% 1.09/1.42
% 1.09/1.42 set(prolog_style_variables).
% 1.09/1.42 set(auto2).
% 1.09/1.42 % set(auto2) -> set(auto).
% 1.09/1.42 % set(auto) -> set(auto_inference).
% 1.09/1.42 % set(auto) -> set(auto_setup).
% 1.09/1.42 % set(auto_setup) -> set(predicate_elim).
% 1.09/1.42 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.09/1.42 % set(auto) -> set(auto_limits).
% 1.09/1.42 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.09/1.42 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.09/1.42 % set(auto) -> set(auto_denials).
% 1.09/1.42 % set(auto) -> set(auto_process).
% 1.09/1.42 % set(auto2) -> assign(new_constants, 1).
% 1.09/1.42 % set(auto2) -> assign(fold_denial_max, 3).
% 1.09/1.42 % set(auto2) -> assign(max_weight, "200.000").
% 1.09/1.42 % set(auto2) -> assign(max_hours, 1).
% 1.09/1.42 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.09/1.42 % set(auto2) -> assign(max_seconds, 0).
% 1.09/1.42 % set(auto2) -> assign(max_minutes, 5).
% 1.09/1.42 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.09/1.42 % set(auto2) -> set(sort_initial_sos).
% 1.09/1.42 % set(auto2) -> assign(sos_limit, -1).
% 1.09/1.42 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.09/1.42 % set(auto2) -> assign(max_megs, 400).
% 1.09/1.42 % set(auto2) -> assign(stats, some).
% 1.09/1.42 % set(auto2) -> clear(echo_input).
% 1.09/1.42 % set(auto2) -> set(quiet).
% 1.09/1.42 % set(auto2) -> clear(print_initial_clauses).
% 1.09/1.42 % set(auto2) -> clear(print_given).
% 1.09/1.42 assign(lrs_ticks,-1).
% 1.09/1.42 assign(sos_limit,10000).
% 1.09/1.42 assign(order,kbo).
% 1.09/1.42 set(lex_order_vars).
% 1.09/1.42 clear(print_given).
% 1.09/1.42
% 1.09/1.42 % formulas(sos). % not echoed (13 formulas)
% 1.09/1.42
% 1.09/1.42 ============================== end of input ==========================
% 1.09/1.42
% 1.09/1.42 % From the command line: assign(max_seconds, 300).
% 1.09/1.42
% 1.09/1.42 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.09/1.42
% 1.09/1.42 % Formulas that are not ordinary clauses:
% 1.09/1.42
% 1.09/1.42 ============================== end of process non-clausal formulas ===
% 1.09/1.42
% 1.09/1.42 ============================== PROCESS INITIAL CLAUSES ===============
% 1.09/1.42
% 1.09/1.42 ============================== PREDICATE ELIMINATION =================
% 1.09/1.42
% 1.09/1.42 ============================== end predicate elimination =============
% 1.09/1.42
% 1.09/1.42 Auto_denials:
% 1.09/1.42 % copying label prove_compatability_law to answer in negative clause
% 1.09/1.42
% 1.09/1.42 Term ordering decisions:
% 1.09/1.42
% 1.09/1.42 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 1.09/1.42 Function symbol KB weights: n0=1. n1=1. c=1. d=1. meet=1. join=1. complement=0.
% 1.09/1.42
% 1.09/1.42 ============================== end of process initial clauses ========
% 1.09/1.42
% 1.09/1.42 ============================== CLAUSES FOR SEARCH ====================
% 1.09/1.42
% 1.09/1.42 ============================== end of clauses for search =============
% 1.09/1.42
% 1.09/1.42 ============================== SEARCH ================================
% 1.09/1.42
% 1.09/1.42 % Starting search at 0.01 seconds.
% 1.09/1.42
% 1.09/1.42 ============================== PROOF =================================
% 1.09/1.42 % SZS status Unsatisfiable
% 1.09/1.42 % SZS output start Refutation
% 1.09/1.42
% 1.09/1.42 % Proof 1 at 0.49 (+ 0.02) seconds: prove_compatability_law.
% 1.09/1.42 % Length of proof is 79.
% 1.09/1.42 % Level of proof is 19.
% 1.09/1.42 % Maximum clause weight is 17.000.
% 1.09/1.42 % Given clauses 151.
% 1.09/1.42
% 1.09/1.42 1 meet(A,A) = A # label(idempotence_of_meet) # label(axiom). [assumption].
% 1.09/1.42 2 join(A,A) = A # label(idempotence_of_join) # label(axiom). [assumption].
% 1.09/1.42 3 complement(complement(A)) = A # label(invertability3) # label(axiom). [assumption].
% 1.09/1.42 4 join(complement(A),A) = n1 # label(invertability1) # label(axiom). [assumption].
% 1.09/1.42 5 meet(complement(A),A) = n0 # label(invertability2) # label(axiom). [assumption].
% 1.09/1.42 6 meet(A,join(A,B)) = A # label(absorption1) # label(axiom). [assumption].
% 1.09/1.42 7 join(A,meet(A,B)) = A # label(absorption2) # label(axiom). [assumption].
% 1.09/1.42 8 meet(A,B) = meet(B,A) # label(commutativity_of_meet) # label(axiom). [assumption].
% 1.09/1.42 9 join(A,B) = join(B,A) # label(commutativity_of_join) # label(axiom). [assumption].
% 1.09/1.42 10 meet(meet(A,B),C) = meet(A,meet(B,C)) # label(associativity_of_meet) # label(axiom). [assumption].
% 1.09/1.42 11 meet(A,meet(B,C)) = meet(C,meet(A,B)). [copy(10),rewrite([8(2)]),flip(a)].
% 1.09/1.42 12 join(join(A,B),C) = join(A,join(B,C)) # label(associativity_of_join) # label(axiom). [assumption].
% 1.09/1.42 13 join(A,join(B,C)) = join(C,join(A,B)). [copy(12),rewrite([9(2)]),flip(a)].
% 1.09/1.42 14 meet(A,join(B,C)) = join(meet(A,B),meet(A,C)) # label(distributivity) # label(axiom). [assumption].
% 1.09/1.42 15 join(meet(A,B),meet(A,C)) = meet(A,join(B,C)). [copy(14),flip(a)].
% 1.09/1.42 16 complement(join(c,d)) != meet(complement(c),complement(d)) # label(prove_compatability_law) # label(negated_conjecture) # answer(prove_compatability_law). [assumption].
% 1.09/1.42 17 meet(A,complement(A)) = n0. [back_rewrite(5),rewrite([8(2)])].
% 1.09/1.42 18 join(A,complement(A)) = n1. [back_rewrite(4),rewrite([9(2)])].
% 1.09/1.42 19 meet(A,meet(A,B)) = meet(A,B). [para(11(a,1),1(a,1)),rewrite([8(1),8(2),11(2,R),1(1),8(3)])].
% 1.09/1.42 21 join(A,join(A,B)) = join(A,B). [para(13(a,1),2(a,1)),rewrite([9(1),9(2),13(2,R),2(1),9(3)])].
% 1.09/1.42 23 join(A,meet(B,join(A,B))) = join(A,B). [para(1(a,1),15(a,2)),rewrite([8(2),6(2),8(2)])].
% 1.09/1.42 24 join(meet(A,B),meet(B,C)) = meet(B,join(A,C)). [para(8(a,1),15(a,1,1))].
% 1.09/1.42 25 join(meet(A,meet(B,C)),meet(B,D)) = meet(B,join(D,meet(A,C))). [para(11(a,1),15(a,1,1)),rewrite([8(5),9(6)])].
% 1.09/1.42 27 join(A,n0) = A. [para(17(a,1),7(a,1,2))].
% 1.09/1.42 29 join(n0,meet(A,B)) = meet(A,join(B,complement(A))). [para(17(a,1),15(a,1,1)),rewrite([9(5)])].
% 1.09/1.42 30 meet(A,n1) = A. [para(18(a,1),6(a,1,2))].
% 1.09/1.42 31 join(A,join(B,complement(A))) = join(B,n1). [para(18(a,1),13(a,2,2)),rewrite([9(2)])].
% 1.09/1.42 33 meet(A,n0) = n0. [para(17(a,1),19(a,1,2)),rewrite([17(4)])].
% 1.09/1.42 35 join(n0,meet(A,B)) = meet(A,B). [para(27(a,1),15(a,2,2)),rewrite([33(3),9(3)])].
% 1.09/1.42 36 meet(A,join(B,complement(A))) = meet(A,B). [back_rewrite(29),rewrite([35(3)]),flip(a)].
% 1.09/1.42 43 join(A,n1) = n1. [para(18(a,1),21(a,1,2)),rewrite([18(4)])].
% 1.09/1.42 44 join(A,join(B,complement(A))) = n1. [back_rewrite(31),rewrite([43(5)])].
% 1.09/1.42 47 meet(complement(A),join(A,B)) = meet(B,complement(A)). [para(3(a,1),36(a,1,2,2)),rewrite([9(2),8(5)])].
% 1.09/1.42 49 meet(A,join(B,join(C,complement(A)))) = meet(A,join(B,C)). [para(36(a,1),15(a,1,1)),rewrite([15(3),9(5),13(5,R),9(4)]),flip(a)].
% 1.09/1.42 54 join(A,meet(n1,join(B,complement(A)))) = n1. [para(44(a,1),23(a,1,2,2)),rewrite([8(4),44(8)])].
% 1.09/1.42 57 join(A,meet(n1,complement(A))) = n1. [para(2(a,1),54(a,1,2,2))].
% 1.09/1.42 61 join(A,join(B,meet(n1,complement(A)))) = n1. [para(57(a,1),13(a,2,2)),rewrite([9(4),43(7)])].
% 1.09/1.42 62 meet(n1,complement(n0)) = n1. [para(57(a,1),35(a,1)),flip(a)].
% 1.09/1.42 63 meet(A,complement(n0)) = A. [para(62(a,1),11(a,1,2)),rewrite([30(2),30(4),8(3)]),flip(a)].
% 1.09/1.42 65 join(A,meet(B,A)) = meet(A,join(B,A)). [para(1(a,1),24(a,1,2)),rewrite([9(2)])].
% 1.09/1.42 66 join(A,meet(B,join(A,C))) = meet(join(A,C),join(A,B)). [para(6(a,1),24(a,1,1)),rewrite([8(2)])].
% 1.09/1.42 70 meet(n1,join(A,B)) = join(A,B). [para(30(a,1),24(a,1,1)),rewrite([8(2),30(2)]),flip(a)].
% 1.09/1.42 71 meet(A,join(B,A)) = A. [para(30(a,1),24(a,1,2)),rewrite([9(2),65(2),43(4),30(4)])].
% 1.09/1.42 80 join(A,meet(B,A)) = A. [para(71(a,1),24(a,2)),rewrite([1(2),9(2)])].
% 1.09/1.42 81 join(A,complement(n0)) = complement(n0). [para(63(a,1),80(a,1,2)),rewrite([9(3)])].
% 1.09/1.42 82 complement(n0) = n1. [para(81(a,1),18(a,1))].
% 1.09/1.42 102 complement(n1) = n0. [para(82(a,1),3(a,1,1))].
% 1.09/1.42 129 join(A,join(complement(A),meet(B,C))) = n1. [para(25(a,1),61(a,1,2)),rewrite([70(5)])].
% 1.09/1.42 140 meet(complement(A),join(B,A)) = meet(B,complement(A)). [para(47(a,1),8(a,1)),rewrite([9(3),8(5)]),flip(a)].
% 1.09/1.42 145 meet(n1,complement(A)) = complement(A). [para(43(a,1),47(a,1,2)),rewrite([30(3)]),flip(a)].
% 1.09/1.42 158 join(n1,complement(A)) = n1. [para(145(a,1),7(a,1,2))].
% 1.09/1.42 161 join(A,join(complement(A),complement(B))) = n1. [para(145(a,1),129(a,1,2,2))].
% 1.09/1.42 168 join(A,join(B,join(complement(A),complement(C)))) = n1. [para(161(a,1),13(a,2,2)),rewrite([9(4),43(7)])].
% 1.09/1.42 170 meet(A,complement(join(A,B))) = n0. [para(21(a,1),140(a,1,2)),rewrite([8(4),17(4)]),flip(a)].
% 1.09/1.42 175 meet(A,complement(join(complement(A),complement(B)))) = complement(join(complement(A),complement(B))). [para(161(a,1),140(a,1,2)),rewrite([8(6),145(6)]),flip(a)].
% 1.09/1.42 190 meet(A,join(B,complement(join(A,C)))) = meet(A,B). [para(170(a,1),15(a,1,1)),rewrite([35(3),9(4)]),flip(a)].
% 1.09/1.42 287 meet(complement(A),complement(join(B,complement(A)))) = n0. [para(190(a,1),47(a,1)),rewrite([8(2),17(2),9(3),8(6)]),flip(a)].
% 1.09/1.42 298 meet(A,join(n1,join(complement(A),complement(B)))) = A. [para(158(a,1),49(a,2,2)),rewrite([9(4),30(8)])].
% 1.09/1.42 309 join(n1,join(complement(A),complement(B))) = n1. [para(298(a,1),80(a,1,2)),rewrite([9(6),168(6)]),flip(a)].
% 1.09/1.42 390 join(A,meet(B,complement(A))) = join(A,B). [para(18(a,1),66(a,2,2)),rewrite([47(3),8(6),70(6)])].
% 1.09/1.42 416 join(complement(A),meet(A,B)) = join(B,complement(A)). [para(3(a,1),390(a,1,2,2)),rewrite([8(2),9(5)])].
% 1.09/1.42 428 meet(join(A,B),complement(meet(A,complement(B)))) = meet(B,complement(meet(A,complement(B)))). [para(390(a,1),140(a,1,2)),rewrite([9(4),8(5)])].
% 1.09/1.42 466 join(complement(A),meet(B,A)) = join(B,complement(A)). [para(416(a,1),9(a,1)),rewrite([8(3),9(5)]),flip(a)].
% 1.09/1.42 481 join(A,complement(join(B,complement(A)))) = A. [para(287(a,1),416(a,1,2)),rewrite([3(2),27(2),3(5),9(4)]),flip(a)].
% 1.09/1.42 539 join(meet(A,B),complement(join(A,complement(B)))) = B. [para(481(a,1),416(a,2)),rewrite([8(6),36(6),8(4),9(5)])].
% 1.09/1.42 567 join(A,complement(meet(A,B))) = n1. [para(19(a,1),466(a,1,2)),rewrite([9(4),18(4)]),flip(a)].
% 1.09/1.42 576 join(meet(A,complement(B)),complement(join(A,B))) = join(complement(B),complement(join(A,B))). [para(140(a,1),466(a,1,2)),rewrite([9(5)])].
% 1.09/1.42 601 meet(complement(A),complement(meet(A,B))) = complement(A). [para(567(a,1),47(a,1,2)),rewrite([30(3),8(5)]),flip(a)].
% 1.09/1.42 607 meet(A,complement(meet(B,complement(A)))) = A. [para(3(a,1),601(a,1,1)),rewrite([8(2),3(6)])].
% 1.09/1.42 620 meet(join(A,B),complement(meet(A,complement(B)))) = B. [back_rewrite(428),rewrite([607(9)])].
% 1.09/1.42 645 join(complement(A),complement(join(B,A))) = complement(A). [para(3(a,1),539(a,1,2,1,2)),rewrite([576(5)])].
% 1.09/1.42 694 join(complement(meet(A,complement(B))),complement(join(A,B))) = complement(meet(A,complement(B))). [para(390(a,1),645(a,1,2,1)),rewrite([9(4)])].
% 1.09/1.42 793 join(A,complement(join(B,A))) = complement(meet(B,complement(A))). [para(620(a,1),416(a,1,2)),rewrite([9(3),694(9)])].
% 1.09/1.42 795 meet(A,complement(meet(A,B))) = complement(join(B,complement(A))). [para(481(a,1),620(a,1,1)),rewrite([3(4),36(3)])].
% 1.09/1.42 1316 join(n0,join(complement(A),complement(B))) = join(complement(A),complement(B)). [para(161(a,1),793(a,1,2,1)),rewrite([102(5),9(5),175(10),3(10)])].
% 1.09/1.42 1319 complement(join(complement(A),complement(B))) = meet(A,B). [para(793(a,1),190(a,1,2)),rewrite([795(4),9(3)])].
% 1.09/1.42 1320 complement(meet(A,B)) = join(complement(A),complement(B)). [para(309(a,1),793(a,1,2,1)),rewrite([102(5),9(5),1316(5),1319(8),11(6),8(5),30(5),8(4)]),flip(a)].
% 1.09/1.42 1323 complement(join(A,B)) = meet(complement(A),complement(B)). [para(793(a,1),620(a,1,1)),rewrite([1320(3),3(3),9(2),3(5),71(4),8(4),47(4)]),flip(a)].
% 1.09/1.42 1324 $F # answer(prove_compatability_law). [resolve(1323,a,16,a)].
% 1.09/1.42
% 1.09/1.42 % SZS output end Refutation
% 1.09/1.42 ============================== end of proof ==========================
% 1.09/1.42
% 1.09/1.42 ============================== STATISTICS ============================
% 1.09/1.42
% 1.09/1.42 Given=151. Generated=14923. Kept=1320. proofs=1.
% 1.09/1.42 Usable=132. Sos=912. Demods=1054. Limbo=13, Disabled=275. Hints=0.
% 1.09/1.42 Megabytes=1.56.
% 1.09/1.42 User_CPU=0.49, System_CPU=0.02, Wall_clock=0.
% 1.09/1.42
% 1.09/1.42 ============================== end of statistics =====================
% 1.09/1.42
% 1.09/1.42 ============================== end of search =========================
% 1.09/1.42
% 1.09/1.42 THEOREM PROVED
% 1.09/1.42 % SZS status Unsatisfiable
% 1.09/1.42
% 1.09/1.42 Exiting with 1 proof.
% 1.09/1.42
% 1.09/1.42 Process 6737 exit (max_proofs) Wed Jun 29 01:40:58 2022
% 1.09/1.42 Prover9 interrupted
%------------------------------------------------------------------------------