TSTP Solution File: REL027-2 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : REL027-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n011.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 : Mon Jul 18 19:54:00 EDT 2022

% Result   : Unsatisfiable 1.39s 1.67s
% Output   : Refutation 1.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : REL027-2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.33  % Computer : n011.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Fri Jul  8 07:36:09 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 1.39/1.67  ============================== Prover9 ===============================
% 1.39/1.67  Prover9 (32) version 2009-11A, November 2009.
% 1.39/1.67  Process 4415 was started by sandbox on n011.cluster.edu,
% 1.39/1.67  Fri Jul  8 07:36:10 2022
% 1.39/1.67  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4261_n011.cluster.edu".
% 1.39/1.67  ============================== end of head ===========================
% 1.39/1.67  
% 1.39/1.67  ============================== INPUT =================================
% 1.39/1.67  
% 1.39/1.67  % Reading from file /tmp/Prover9_4261_n011.cluster.edu
% 1.39/1.67  
% 1.39/1.67  set(prolog_style_variables).
% 1.39/1.67  set(auto2).
% 1.39/1.67      % set(auto2) -> set(auto).
% 1.39/1.67      % set(auto) -> set(auto_inference).
% 1.39/1.67      % set(auto) -> set(auto_setup).
% 1.39/1.67      % set(auto_setup) -> set(predicate_elim).
% 1.39/1.67      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.39/1.67      % set(auto) -> set(auto_limits).
% 1.39/1.67      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.39/1.67      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.39/1.67      % set(auto) -> set(auto_denials).
% 1.39/1.67      % set(auto) -> set(auto_process).
% 1.39/1.67      % set(auto2) -> assign(new_constants, 1).
% 1.39/1.67      % set(auto2) -> assign(fold_denial_max, 3).
% 1.39/1.67      % set(auto2) -> assign(max_weight, "200.000").
% 1.39/1.67      % set(auto2) -> assign(max_hours, 1).
% 1.39/1.67      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.39/1.67      % set(auto2) -> assign(max_seconds, 0).
% 1.39/1.67      % set(auto2) -> assign(max_minutes, 5).
% 1.39/1.67      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.39/1.67      % set(auto2) -> set(sort_initial_sos).
% 1.39/1.67      % set(auto2) -> assign(sos_limit, -1).
% 1.39/1.67      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.39/1.67      % set(auto2) -> assign(max_megs, 400).
% 1.39/1.67      % set(auto2) -> assign(stats, some).
% 1.39/1.67      % set(auto2) -> clear(echo_input).
% 1.39/1.67      % set(auto2) -> set(quiet).
% 1.39/1.67      % set(auto2) -> clear(print_initial_clauses).
% 1.39/1.67      % set(auto2) -> clear(print_given).
% 1.39/1.67  assign(lrs_ticks,-1).
% 1.39/1.67  assign(sos_limit,10000).
% 1.39/1.67  assign(order,kbo).
% 1.39/1.67  set(lex_order_vars).
% 1.39/1.67  clear(print_given).
% 1.39/1.67  
% 1.39/1.67  % formulas(sos).  % not echoed (15 formulas)
% 1.39/1.67  
% 1.39/1.67  ============================== end of input ==========================
% 1.39/1.67  
% 1.39/1.67  % From the command line: assign(max_seconds, 300).
% 1.39/1.67  
% 1.39/1.67  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.39/1.67  
% 1.39/1.67  % Formulas that are not ordinary clauses:
% 1.39/1.67  
% 1.39/1.67  ============================== end of process non-clausal formulas ===
% 1.39/1.67  
% 1.39/1.67  ============================== PROCESS INITIAL CLAUSES ===============
% 1.39/1.67  
% 1.39/1.67  ============================== PREDICATE ELIMINATION =================
% 1.39/1.67  
% 1.39/1.67  ============================== end predicate elimination =============
% 1.39/1.67  
% 1.39/1.67  Auto_denials:
% 1.39/1.67    % copying label goals_15 to answer in negative clause
% 1.39/1.67  
% 1.39/1.67  Term ordering decisions:
% 1.39/1.67  Function symbol KB weights:  one=1. sk1=1. top=1. zero=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 1.39/1.67  
% 1.39/1.67  ============================== end of process initial clauses ========
% 1.39/1.67  
% 1.39/1.67  ============================== CLAUSES FOR SEARCH ====================
% 1.39/1.67  
% 1.39/1.67  ============================== end of clauses for search =============
% 1.39/1.67  
% 1.39/1.67  ============================== SEARCH ================================
% 1.39/1.67  
% 1.39/1.67  % Starting search at 0.01 seconds.
% 1.39/1.67  
% 1.39/1.67  ============================== PROOF =================================
% 1.39/1.67  % SZS status Unsatisfiable
% 1.39/1.67  % SZS output start Refutation
% 1.39/1.67  
% 1.39/1.67  % Proof 1 at 0.66 (+ 0.03) seconds: goals_15.
% 1.39/1.67  % Length of proof is 72.
% 1.39/1.67  % Level of proof is 19.
% 1.39/1.67  % Maximum clause weight is 52.000.
% 1.39/1.67  % Given clauses 365.
% 1.39/1.67  
% 1.39/1.67  1 composition(A,one) = A # label(composition_identity_6) # label(axiom).  [assumption].
% 1.39/1.67  2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom).  [assumption].
% 1.39/1.67  3 join(sk1,one) = one # label(goals_14) # label(negated_conjecture).  [assumption].
% 1.39/1.67  4 top = join(A,complement(A)) # label(def_top_12) # label(axiom).  [assumption].
% 1.39/1.67  5 join(A,complement(A)) = top.  [copy(4),flip(a)].
% 1.39/1.67  6 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom).  [assumption].
% 1.39/1.67  7 meet(A,complement(A)) = zero.  [copy(6),flip(a)].
% 1.39/1.67  8 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom).  [assumption].
% 1.39/1.67  9 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom).  [assumption].
% 1.39/1.67  10 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom).  [assumption].
% 1.39/1.67  11 join(converse(A),converse(B)) = converse(join(A,B)).  [copy(10),flip(a)].
% 1.39/1.67  12 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom).  [assumption].
% 1.39/1.67  13 composition(converse(A),converse(B)) = converse(composition(B,A)).  [copy(12),flip(a)].
% 1.39/1.67  14 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom).  [assumption].
% 1.39/1.67  15 join(A,join(B,C)) = join(C,join(A,B)).  [copy(14),rewrite([8(4)])].
% 1.39/1.67  16 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom).  [assumption].
% 1.39/1.67  17 composition(composition(A,B),C) = composition(A,composition(B,C)).  [copy(16),flip(a)].
% 1.39/1.67  18 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity_7) # label(axiom).  [assumption].
% 1.39/1.67  19 join(composition(A,B),composition(C,B)) = composition(join(A,C),B).  [copy(18),flip(a)].
% 1.39/1.67  20 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom).  [assumption].
% 1.39/1.67  21 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(20),rewrite([8(6)])].
% 1.39/1.67  22 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom).  [assumption].
% 1.39/1.67  23 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(22),rewrite([8(6),8(8)]),flip(a),rewrite([8(6)])].
% 1.39/1.67  24 join(meet(complement(sk1),one),meet(complement(composition(sk1,top)),one)) != meet(complement(composition(sk1,top)),one) | join(meet(complement(composition(sk1,top)),one),meet(complement(sk1),one)) != meet(complement(sk1),one) # label(goals_15) # label(negated_conjecture) # answer(goals_15).  [assumption].
% 1.39/1.67  25 join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(composition(sk1,top))))) | join(complement(join(complement(one),complement(complement(sk1)))),complement(join(complement(one),complement(complement(composition(sk1,top)))))) != complement(join(complement(one),complement(complement(sk1)))) # answer(goals_15).  [copy(24),rewrite([9(4),8(6),9(13),8(15),9(23),8(25),9(33),8(35),9(40),8(42),8(44),9(48),8(50)])].
% 1.39/1.67  26 join(one,sk1) = one.  [back_rewrite(3),rewrite([8(3)])].
% 1.39/1.67  27 complement(top) = zero.  [back_rewrite(7),rewrite([9(2),5(4)])].
% 1.39/1.67  28 converse(join(A,converse(B))) = join(B,converse(A)).  [para(2(a,1),11(a,1,1)),rewrite([8(4)]),flip(a)].
% 1.39/1.67  29 converse(composition(A,converse(B))) = composition(B,converse(A)).  [para(2(a,1),13(a,1,1)),flip(a)].
% 1.39/1.67  30 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(2(a,1),13(a,1,2)),flip(a)].
% 1.39/1.67  31 join(A,join(B,complement(A))) = join(B,top).  [para(5(a,1),15(a,2,2)),rewrite([8(2)])].
% 1.39/1.67  32 composition(A,composition(one,B)) = composition(A,B).  [para(1(a,1),17(a,1,1)),flip(a)].
% 1.39/1.67  36 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C).  [para(17(a,1),19(a,1,1)),rewrite([8(6)])].
% 1.39/1.67  38 join(complement(one),composition(converse(A),complement(A))) = complement(one).  [para(1(a,1),21(a,1,2,2,1))].
% 1.39/1.67  43 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(5(a,1),23(a,1,1,1)),rewrite([27(2)])].
% 1.39/1.67  51 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A.  [para(27(a,1),23(a,1,2,1,1))].
% 1.39/1.67  52 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)).  [para(28(a,1),11(a,1,1)),rewrite([8(7),15(7,R),8(6)]),flip(a)].
% 1.39/1.67  53 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))).  [para(28(a,1),11(a,1,2)),rewrite([15(4,R),8(3),11(3),52(7)]),flip(a)].
% 1.39/1.67  57 join(join(A,B),converse(C)) = join(A,join(B,converse(C))).  [para(28(a,1),28(a,2,2)),rewrite([53(4),28(4),15(6,R),8(5)])].
% 1.39/1.67  60 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)).  [para(29(a,1),11(a,1,1)),rewrite([8(7)]),flip(a)].
% 1.39/1.67  64 composition(converse(one),A) = A.  [para(1(a,1),30(a,1,1)),rewrite([2(2)]),flip(a)].
% 1.39/1.67  70 converse(one) = one.  [para(64(a,1),1(a,1)),flip(a)].
% 1.39/1.67  72 composition(join(A,one),B) = join(B,composition(A,B)).  [para(64(a,1),19(a,1,1)),rewrite([70(4),8(4)]),flip(a)].
% 1.39/1.67  74 join(complement(A),complement(composition(one,A))) = complement(A).  [para(64(a,1),21(a,1,2))].
% 1.39/1.67  75 composition(one,A) = A.  [para(64(a,1),32(a,2)),rewrite([70(2),32(4)])].
% 1.39/1.67  76 join(complement(A),complement(A)) = complement(A).  [back_rewrite(74),rewrite([75(3)])].
% 1.39/1.67  77 join(zero,complement(complement(A))) = A.  [back_rewrite(43),rewrite([76(4)])].
% 1.39/1.67  78 converse(join(A,one)) = join(one,converse(A)).  [para(70(a,1),11(a,1,1)),rewrite([8(5)]),flip(a)].
% 1.39/1.67  82 join(top,complement(A)) = top.  [para(76(a,1),31(a,1,2)),rewrite([5(2),8(4)]),flip(a)].
% 1.39/1.67  83 join(zero,complement(join(zero,complement(A)))) = A.  [back_rewrite(51),rewrite([82(3),27(2)])].
% 1.39/1.67  128 composition(join(one,composition(A,B)),C) = join(C,composition(A,composition(B,C))).  [para(75(a,1),36(a,1,2)),rewrite([8(3)]),flip(a)].
% 1.39/1.67  132 join(zero,complement(A)) = complement(A).  [para(77(a,1),83(a,1,2,1))].
% 1.39/1.67  133 complement(complement(A)) = A.  [back_rewrite(83),rewrite([132(4),132(4)])].
% 1.39/1.67  138 join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(complement(one),composition(sk1,top))) | join(complement(join(sk1,complement(one))),complement(join(complement(one),composition(sk1,top)))) != complement(join(sk1,complement(one))) # answer(goals_15).  [back_rewrite(25),rewrite([133(5),8(4),133(12),133(20),133(26),8(25),133(33),133(39),8(38)])].
% 1.39/1.67  142 join(A,A) = A.  [para(133(a,1),76(a,1,1)),rewrite([133(2),133(3)])].
% 1.39/1.67  146 join(A,join(A,B)) = join(A,B).  [para(142(a,1),15(a,1)),rewrite([8(3),15(4,R),8(3),15(3,R),142(2)]),flip(a)].
% 1.39/1.67  160 join(complement(one),composition(converse(complement(A)),A)) = complement(one).  [para(133(a,1),38(a,1,2,2))].
% 1.39/1.67  187 composition(join(A,join(B,one)),C) = join(C,composition(join(A,B),C)).  [para(72(a,1),19(a,1,2)),rewrite([15(4,R),19(3),8(1)]),flip(a)].
% 1.39/1.67  214 join(complement(one),converse(complement(one))) = complement(one).  [para(1(a,1),160(a,1,2))].
% 1.39/1.67  218 converse(complement(one)) = complement(one).  [para(214(a,1),11(a,2,1)),rewrite([2(7),8(6),214(6)]),flip(a)].
% 1.39/1.67  223 converse(top) = top.  [para(218(a,1),78(a,2,2)),rewrite([8(4),5(4),5(6)])].
% 1.39/1.67  454 join(one,join(sk1,converse(A))) = join(one,converse(A)).  [para(26(a,1),57(a,1,1)),flip(a)].
% 1.39/1.67  1349 join(A,join(one,converse(sk1))) = join(A,one).  [para(454(a,1),11(a,2,1)),rewrite([70(2),28(5),15(5,R),8(4),28(9),70(7)])].
% 1.39/1.67  1377 join(one,converse(sk1)) = one.  [para(142(a,1),1349(a,2)),rewrite([146(6)])].
% 1.39/1.67  1378 join(A,composition(converse(sk1),A)) = A.  [para(1377(a,1),19(a,2,1)),rewrite([75(2),75(6)])].
% 1.39/1.67  1385 join(A,composition(A,sk1)) = A.  [para(1378(a,1),60(a,1,1)),rewrite([2(2),2(3),2(4),8(3)]),flip(a)].
% 1.39/1.67  1767 join(A,composition(sk1,A)) = A.  [para(1385(a,1),128(a,1,1)),rewrite([75(2),75(4)]),flip(a)].
% 1.39/1.67  1785 join(A,join(B,composition(sk1,A))) = join(A,B).  [para(1767(a,1),15(a,2,2)),rewrite([8(3),8(5)])].
% 1.39/1.67  3832 join(A,composition(complement(one),A)) = composition(top,A).  [para(38(a,1),187(a,2,2,1)),rewrite([8(7),15(8,R),8(7),38(7),5(4)]),flip(a)].
% 1.39/1.67  3976 join(A,composition(A,complement(one))) = composition(A,top).  [para(3832(a,1),60(a,1,1)),rewrite([29(4),223(2),218(5),2(7),8(6)]),flip(a)].
% 1.39/1.67  4369 join(complement(one),composition(sk1,top)) = join(sk1,complement(one)).  [para(3976(a,1),1785(a,1,2)),rewrite([8(10)])].
% 1.39/1.67  4371 $F # answer(goals_15).  [back_rewrite(138),rewrite([4369(11),142(11),4369(11),4369(22),142(22)]),xx(a),xx(b)].
% 1.39/1.67  
% 1.39/1.67  % SZS output end Refutation
% 1.39/1.67  ============================== end of proof ==========================
% 1.39/1.67  
% 1.39/1.67  ============================== STATISTICS ============================
% 1.39/1.67  
% 1.39/1.67  Given=365. Generated=28340. Kept=4360. proofs=1.
% 1.39/1.67  Usable=310. Sos=3554. Demods=3557. Limbo=2, Disabled=509. Hints=0.
% 1.39/1.67  Megabytes=5.62.
% 1.39/1.67  User_CPU=0.66, System_CPU=0.03, Wall_clock=1.
% 1.39/1.67  
% 1.39/1.67  ============================== end of statistics =====================
% 1.39/1.67  
% 1.39/1.67  ============================== end of search =========================
% 1.39/1.68  
% 1.39/1.68  THEOREM PROVED
% 1.39/1.68  % SZS status Unsatisfiable
% 1.39/1.68  
% 1.39/1.68  Exiting with 1 proof.
% 1.39/1.68  
% 1.39/1.68  Process 4415 exit (max_proofs) Fri Jul  8 07:36:11 2022
% 1.39/1.68  Prover9 interrupted
%------------------------------------------------------------------------------