TSTP Solution File: REL004-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : REL004-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n027.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 19:53:23 EDT 2022

% Result   : Unsatisfiable 0.94s 1.29s
% Output   : Refutation 0.94s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : REL004-1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.08  % Command  : tptp2X_and_run_prover9 %d %s
% 0.07/0.27  % Computer : n027.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 600
% 0.07/0.27  % DateTime : Fri Jul  8 12:04:45 EDT 2022
% 0.07/0.27  % CPUTime  : 
% 0.94/1.29  ============================== Prover9 ===============================
% 0.94/1.29  Prover9 (32) version 2009-11A, November 2009.
% 0.94/1.29  Process 14616 was started by sandbox on n027.cluster.edu,
% 0.94/1.29  Fri Jul  8 12:04:46 2022
% 0.94/1.29  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_14463_n027.cluster.edu".
% 0.94/1.29  ============================== end of head ===========================
% 0.94/1.29  
% 0.94/1.29  ============================== INPUT =================================
% 0.94/1.29  
% 0.94/1.29  % Reading from file /tmp/Prover9_14463_n027.cluster.edu
% 0.94/1.29  
% 0.94/1.29  set(prolog_style_variables).
% 0.94/1.29  set(auto2).
% 0.94/1.29      % set(auto2) -> set(auto).
% 0.94/1.29      % set(auto) -> set(auto_inference).
% 0.94/1.29      % set(auto) -> set(auto_setup).
% 0.94/1.29      % set(auto_setup) -> set(predicate_elim).
% 0.94/1.29      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.94/1.29      % set(auto) -> set(auto_limits).
% 0.94/1.29      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.94/1.29      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.94/1.29      % set(auto) -> set(auto_denials).
% 0.94/1.29      % set(auto) -> set(auto_process).
% 0.94/1.29      % set(auto2) -> assign(new_constants, 1).
% 0.94/1.29      % set(auto2) -> assign(fold_denial_max, 3).
% 0.94/1.29      % set(auto2) -> assign(max_weight, "200.000").
% 0.94/1.29      % set(auto2) -> assign(max_hours, 1).
% 0.94/1.29      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.94/1.29      % set(auto2) -> assign(max_seconds, 0).
% 0.94/1.29      % set(auto2) -> assign(max_minutes, 5).
% 0.94/1.29      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.94/1.29      % set(auto2) -> set(sort_initial_sos).
% 0.94/1.29      % set(auto2) -> assign(sos_limit, -1).
% 0.94/1.29      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.94/1.29      % set(auto2) -> assign(max_megs, 400).
% 0.94/1.29      % set(auto2) -> assign(stats, some).
% 0.94/1.29      % set(auto2) -> clear(echo_input).
% 0.94/1.29      % set(auto2) -> set(quiet).
% 0.94/1.29      % set(auto2) -> clear(print_initial_clauses).
% 0.94/1.29      % set(auto2) -> clear(print_given).
% 0.94/1.29  assign(lrs_ticks,-1).
% 0.94/1.29  assign(sos_limit,10000).
% 0.94/1.29  assign(order,kbo).
% 0.94/1.29  set(lex_order_vars).
% 0.94/1.29  clear(print_given).
% 0.94/1.29  
% 0.94/1.29  % formulas(sos).  % not echoed (14 formulas)
% 0.94/1.29  
% 0.94/1.29  ============================== end of input ==========================
% 0.94/1.29  
% 0.94/1.29  % From the command line: assign(max_seconds, 300).
% 0.94/1.29  
% 0.94/1.29  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.94/1.29  
% 0.94/1.29  % Formulas that are not ordinary clauses:
% 0.94/1.29  
% 0.94/1.29  ============================== end of process non-clausal formulas ===
% 0.94/1.29  
% 0.94/1.29  ============================== PROCESS INITIAL CLAUSES ===============
% 0.94/1.29  
% 0.94/1.29  ============================== PREDICATE ELIMINATION =================
% 0.94/1.29  
% 0.94/1.29  ============================== end predicate elimination =============
% 0.94/1.29  
% 0.94/1.29  Auto_denials:
% 0.94/1.29    % copying label goals_14 to answer in negative clause
% 0.94/1.29  
% 0.94/1.29  Term ordering decisions:
% 0.94/1.29  Function symbol KB weights:  one=1. top=1. zero=1. sk1=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 0.94/1.29  
% 0.94/1.29  ============================== end of process initial clauses ========
% 0.94/1.29  
% 0.94/1.29  ============================== CLAUSES FOR SEARCH ====================
% 0.94/1.29  
% 0.94/1.29  ============================== end of clauses for search =============
% 0.94/1.29  
% 0.94/1.29  ============================== SEARCH ================================
% 0.94/1.29  
% 0.94/1.29  % Starting search at 0.01 seconds.
% 0.94/1.29  
% 0.94/1.29  ============================== PROOF =================================
% 0.94/1.29  % SZS status Unsatisfiable
% 0.94/1.29  % SZS output start Refutation
% 0.94/1.29  
% 0.94/1.29  % Proof 1 at 0.40 (+ 0.02) seconds: goals_14.
% 0.94/1.29  % Length of proof is 64.
% 0.94/1.29  % Level of proof is 25.
% 0.94/1.29  % Maximum clause weight is 14.000.
% 0.94/1.29  % Given clauses 283.
% 0.94/1.29  
% 0.94/1.29  1 composition(A,one) = A # label(composition_identity_6) # label(axiom).  [assumption].
% 0.94/1.29  2 converse(converse(A)) = A # label(converse_idempotence_8) # label(axiom).  [assumption].
% 0.94/1.29  3 top = join(A,complement(A)) # label(def_top_12) # label(axiom).  [assumption].
% 0.94/1.29  4 join(A,complement(A)) = top.  [copy(3),flip(a)].
% 0.94/1.29  5 zero = meet(A,complement(A)) # label(def_zero_13) # label(axiom).  [assumption].
% 0.94/1.29  6 meet(A,complement(A)) = zero.  [copy(5),flip(a)].
% 0.94/1.29  7 join(A,B) = join(B,A) # label(maddux1_join_commutativity_1) # label(axiom).  [assumption].
% 0.94/1.29  8 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet_4) # label(axiom).  [assumption].
% 0.94/1.29  9 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity_9) # label(axiom).  [assumption].
% 0.94/1.29  10 join(converse(A),converse(B)) = converse(join(A,B)).  [copy(9),flip(a)].
% 0.94/1.29  11 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity_10) # label(axiom).  [assumption].
% 0.94/1.29  12 composition(converse(A),converse(B)) = converse(composition(B,A)).  [copy(11),flip(a)].
% 0.94/1.29  13 join(A,join(B,C)) = join(join(A,B),C) # label(maddux2_join_associativity_2) # label(axiom).  [assumption].
% 0.94/1.29  14 join(A,join(B,C)) = join(C,join(A,B)).  [copy(13),rewrite([7(4)])].
% 0.94/1.29  15 composition(A,composition(B,C)) = composition(composition(A,B),C) # label(composition_associativity_5) # label(axiom).  [assumption].
% 0.94/1.29  16 composition(composition(A,B),C) = composition(A,composition(B,C)).  [copy(15),flip(a)].
% 0.94/1.29  19 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity_11) # label(axiom).  [assumption].
% 0.94/1.29  20 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(19),rewrite([7(6)])].
% 0.94/1.29  21 A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) # label(maddux3_a_kind_of_de_Morgan_3) # label(axiom).  [assumption].
% 0.94/1.29  22 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(21),rewrite([7(6),7(8)]),flip(a),rewrite([7(6)])].
% 0.94/1.29  23 converse(complement(sk1)) != complement(converse(sk1)) # label(goals_14) # label(negated_conjecture) # answer(goals_14).  [assumption].
% 0.94/1.29  24 complement(top) = zero.  [back_rewrite(6),rewrite([8(2),4(4)])].
% 0.94/1.29  25 converse(complement(sk1)) = c_0.  [new_symbol(23)].
% 0.94/1.29  26 complement(converse(sk1)) != c_0 # answer(goals_14).  [back_rewrite(23),rewrite([25(3)]),flip(a)].
% 0.94/1.29  27 converse(join(A,converse(B))) = join(B,converse(A)).  [para(2(a,1),10(a,1,1)),rewrite([7(4)]),flip(a)].
% 0.94/1.29  29 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(2(a,1),12(a,1,2)),flip(a)].
% 0.94/1.29  30 join(A,join(B,complement(A))) = join(B,top).  [para(4(a,1),14(a,2,2)),rewrite([7(2)])].
% 0.94/1.29  31 composition(A,composition(one,B)) = composition(A,B).  [para(1(a,1),16(a,1,1)),flip(a)].
% 0.94/1.29  42 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(4(a,1),22(a,1,1,1)),rewrite([24(2)])].
% 0.94/1.29  50 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A.  [para(24(a,1),22(a,1,2,1,1))].
% 0.94/1.29  51 converse(c_0) = complement(sk1).  [para(25(a,1),2(a,1,1))].
% 0.94/1.29  52 converse(join(A,complement(sk1))) = join(c_0,converse(A)).  [para(25(a,1),10(a,1,1)),rewrite([7(6)]),flip(a)].
% 0.94/1.29  61 join(complement(sk1),converse(A)) = converse(join(A,c_0)).  [para(25(a,1),27(a,1,1,2)),flip(a)].
% 0.94/1.29  64 join(converse(A),complement(sk1)) = converse(join(A,c_0)).  [para(51(a,1),10(a,1,2))].
% 0.94/1.29  73 composition(converse(one),A) = A.  [para(1(a,1),29(a,1,1)),rewrite([2(2)]),flip(a)].
% 0.94/1.29  77 converse(one) = one.  [para(73(a,1),1(a,1)),flip(a)].
% 0.94/1.29  81 join(complement(A),complement(composition(one,A))) = complement(A).  [para(73(a,1),20(a,1,2))].
% 0.94/1.29  82 composition(one,A) = A.  [para(73(a,1),31(a,2)),rewrite([77(2),31(4)])].
% 0.94/1.29  83 join(complement(A),complement(A)) = complement(A).  [back_rewrite(81),rewrite([82(3)])].
% 0.94/1.29  84 join(zero,complement(complement(A))) = A.  [back_rewrite(42),rewrite([83(4)])].
% 0.94/1.29  90 join(top,complement(A)) = top.  [para(83(a,1),30(a,1,2)),rewrite([4(2),7(4)]),flip(a)].
% 0.94/1.29  91 join(zero,complement(join(zero,complement(A)))) = A.  [back_rewrite(50),rewrite([90(3),24(2)])].
% 0.94/1.29  92 join(top,top) = join(A,top).  [para(90(a,1),30(a,1,2)),flip(a)].
% 0.94/1.29  97 join(A,top) = join(B,top).  [para(92(a,1),30(a,2)),rewrite([90(3)])].
% 0.94/1.29  98 join(A,top) = c_1.  [new_symbol(97)].
% 0.94/1.29  101 join(A,join(B,complement(A))) = c_1.  [back_rewrite(30),rewrite([98(5)])].
% 0.94/1.29  109 c_1 = top.  [para(84(a,1),101(a,1,2)),rewrite([7(2),4(2)]),flip(a)].
% 0.94/1.29  110 join(A,join(B,complement(A))) = top.  [back_rewrite(101),rewrite([109(4)])].
% 0.94/1.29  141 join(zero,complement(A)) = complement(A).  [para(84(a,1),91(a,1,2,1))].
% 0.94/1.29  142 complement(complement(A)) = A.  [back_rewrite(91),rewrite([141(4),141(4)])].
% 0.94/1.29  148 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B).  [para(142(a,1),22(a,1,1,1,2)),rewrite([142(5),7(4)])].
% 0.94/1.29  174 join(c_0,converse(sk1)) = converse(top).  [para(4(a,1),52(a,1,1)),flip(a)].
% 0.94/1.29  213 join(sk1,converse(join(A,c_0))) = top.  [para(64(a,1),110(a,1,2))].
% 0.94/1.29  215 join(A,converse(top)) = converse(top).  [para(213(a,1),10(a,2,1)),rewrite([2(6),14(5),7(4),14(5,R),7(4),174(4)])].
% 0.94/1.29  223 join(top,converse(A)) = top.  [para(215(a,1),10(a,2,1)),rewrite([2(4),7(3),2(6)])].
% 0.94/1.29  229 converse(top) = top.  [para(223(a,1),215(a,1)),flip(a)].
% 0.94/1.29  231 join(c_0,converse(sk1)) = top.  [back_rewrite(174),rewrite([229(6)])].
% 0.94/1.29  1979 complement(join(complement(c_0),converse(sk1))) = complement(converse(sk1)).  [para(231(a,1),148(a,1,1,1)),rewrite([24(2),7(6),141(8)])].
% 0.94/1.29  2048 join(complement(c_0),converse(sk1)) = converse(sk1).  [para(1979(a,1),22(a,1,1,1,2)),rewrite([1979(12),22(12)]),flip(a)].
% 0.94/1.29  2056 join(sk1,converse(complement(c_0))) = sk1.  [para(2048(a,1),10(a,2,1)),rewrite([2(6),7(5),2(8)])].
% 0.94/1.29  2061 complement(converse(complement(c_0))) = complement(sk1).  [para(2056(a,1),148(a,1,1,1)),rewrite([7(8),61(8),7(6),4(6),229(4),24(4),7(4),141(4)]),flip(a)].
% 0.94/1.29  2149 converse(complement(c_0)) = sk1.  [para(2061(a,1),22(a,1,1,1,2)),rewrite([2061(9),22(10)]),flip(a)].
% 0.94/1.29  2156 converse(sk1) = complement(c_0).  [para(2149(a,1),2(a,1,1))].
% 0.94/1.29  2208 $F # answer(goals_14).  [back_rewrite(26),rewrite([2156(2),142(3)]),xx(a)].
% 0.94/1.29  
% 0.94/1.29  % SZS output end Refutation
% 0.94/1.29  ============================== end of proof ==========================
% 0.94/1.29  
% 0.94/1.29  ============================== STATISTICS ============================
% 0.94/1.29  
% 0.94/1.29  Given=283. Generated=15451. Kept=2198. proofs=1.
% 0.94/1.29  Usable=227. Sos=1584. Demods=1793. Limbo=52, Disabled=349. Hints=0.
% 0.94/1.29  Megabytes=2.79.
% 0.94/1.29  User_CPU=0.41, System_CPU=0.02, Wall_clock=0.
% 0.94/1.29  
% 0.94/1.29  ============================== end of statistics =====================
% 0.94/1.29  
% 0.94/1.29  ============================== end of search =========================
% 0.94/1.29  
% 0.94/1.29  THEOREM PROVED
% 0.94/1.29  % SZS status Unsatisfiable
% 0.94/1.29  
% 0.94/1.29  Exiting with 1 proof.
% 0.94/1.29  
% 0.94/1.29  Process 14616 exit (max_proofs) Fri Jul  8 12:04:46 2022
% 0.94/1.29  Prover9 interrupted
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