TSTP Solution File: REL023+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : REL023+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n026.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 19:53:53 EDT 2022

% Result   : Theorem 0.73s 1.05s
% Output   : Refutation 0.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : REL023+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  8 09:27:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.43/1.00  ============================== Prover9 ===============================
% 0.43/1.00  Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00  Process 20939 was started by sandbox on n026.cluster.edu,
% 0.43/1.00  Fri Jul  8 09:27:25 2022
% 0.43/1.00  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20786_n026.cluster.edu".
% 0.43/1.00  ============================== end of head ===========================
% 0.43/1.00  
% 0.43/1.00  ============================== INPUT =================================
% 0.43/1.00  
% 0.43/1.00  % Reading from file /tmp/Prover9_20786_n026.cluster.edu
% 0.43/1.00  
% 0.43/1.00  set(prolog_style_variables).
% 0.43/1.00  set(auto2).
% 0.43/1.00      % set(auto2) -> set(auto).
% 0.43/1.00      % set(auto) -> set(auto_inference).
% 0.43/1.00      % set(auto) -> set(auto_setup).
% 0.43/1.00      % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00      % set(auto) -> set(auto_limits).
% 0.43/1.00      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00      % set(auto) -> set(auto_denials).
% 0.43/1.00      % set(auto) -> set(auto_process).
% 0.43/1.00      % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00      % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00      % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00      % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00      % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00      % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00      % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00      % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00      % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00      % set(auto2) -> assign(stats, some).
% 0.43/1.00      % set(auto2) -> clear(echo_input).
% 0.43/1.00      % set(auto2) -> set(quiet).
% 0.43/1.00      % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00      % set(auto2) -> clear(print_given).
% 0.43/1.00  assign(lrs_ticks,-1).
% 0.43/1.00  assign(sos_limit,10000).
% 0.43/1.00  assign(order,kbo).
% 0.43/1.00  set(lex_order_vars).
% 0.43/1.00  clear(print_given).
% 0.43/1.00  
% 0.43/1.00  % formulas(sos).  % not echoed (14 formulas)
% 0.43/1.00  
% 0.43/1.00  ============================== end of input ==========================
% 0.43/1.00  
% 0.43/1.00  % From the command line: assign(max_seconds, 300).
% 0.43/1.00  
% 0.43/1.00  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00  
% 0.43/1.00  % Formulas that are not ordinary clauses:
% 0.43/1.00  1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.00  13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  14 -(all X0 all X1 all X2 join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.73/1.05  
% 0.73/1.05  ============================== end of process non-clausal formulas ===
% 0.73/1.05  
% 0.73/1.05  ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.05  
% 0.73/1.05  ============================== PREDICATE ELIMINATION =================
% 0.73/1.05  
% 0.73/1.05  ============================== end predicate elimination =============
% 0.73/1.05  
% 0.73/1.05  Auto_denials:
% 0.73/1.05    % copying label goals to answer in negative clause
% 0.73/1.05  
% 0.73/1.05  Term ordering decisions:
% 0.73/1.05  Function symbol KB weights:  one=1. top=1. zero=1. c1=1. c2=1. c3=1. join=1. composition=1. meet=1. complement=1. converse=1.
% 0.73/1.05  
% 0.73/1.05  ============================== end of process initial clauses ========
% 0.73/1.05  
% 0.73/1.05  ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.05  
% 0.73/1.05  ============================== end of clauses for search =============
% 0.73/1.05  
% 0.73/1.05  ============================== SEARCH ================================
% 0.73/1.05  
% 0.73/1.05  % Starting search at 0.01 seconds.
% 0.73/1.05  
% 0.73/1.05  ============================== PROOF =================================
% 0.73/1.05  % SZS status Theorem
% 0.73/1.05  % SZS output start Refutation
% 0.73/1.05  
% 0.73/1.05  % Proof 1 at 0.05 (+ 0.01) seconds: goals.
% 0.73/1.05  % Length of proof is 55.
% 0.73/1.05  % Level of proof is 17.
% 0.73/1.05  % Maximum clause weight is 25.000.
% 0.73/1.05  % Given clauses 75.
% 0.73/1.05  
% 0.73/1.05  1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  2 (all X0 all X1 all X2 join(X0,join(X1,X2)) = join(join(X0,X1),X2)) # label(maddux2_join_associativity) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  3 (all X0 all X1 X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  4 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  5 (all X0 all X1 all X2 composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2)) # label(composition_associativity) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  7 (all X0 all X1 all X2 composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2))) # label(composition_distributivity) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  11 (all X0 all X1 join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1)) # label(converse_cancellativity) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.05  14 -(all X0 all X1 all X2 join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.73/1.05  15 composition(A,one) = A # label(composition_identity) # label(axiom).  [clausify(6)].
% 0.73/1.05  16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom).  [clausify(8)].
% 0.73/1.05  17 join(A,complement(A)) = top # label(def_top) # label(axiom).  [clausify(12)].
% 0.73/1.05  18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom).  [clausify(13)].
% 0.73/1.05  19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom).  [clausify(1)].
% 0.73/1.05  20 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom).  [clausify(4)].
% 0.73/1.05  23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom).  [clausify(10)].
% 0.73/1.05  24 composition(converse(A),converse(B)) = converse(composition(B,A)).  [copy(23),flip(a)].
% 0.73/1.05  25 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom).  [clausify(2)].
% 0.73/1.05  26 join(A,join(B,C)) = join(C,join(A,B)).  [copy(25),rewrite([19(2)]),flip(a)].
% 0.73/1.05  27 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom).  [clausify(5)].
% 0.73/1.05  28 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom).  [clausify(7)].
% 0.73/1.05  29 join(composition(A,B),composition(C,B)) = composition(join(A,C),B).  [copy(28),flip(a)].
% 0.73/1.05  30 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom).  [clausify(11)].
% 0.73/1.05  31 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(30),rewrite([19(7)]),flip(a)].
% 0.73/1.05  32 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom).  [clausify(3)].
% 0.73/1.05  33 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(32),rewrite([19(6),19(8)]),rewrite([19(6)])].
% 0.73/1.05  34 composition(c1,meet(c2,c3)) != join(composition(meet(c1,converse(c2)),meet(c2,c3)),composition(c1,meet(c2,c3))) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(14)].
% 0.73/1.05  35 composition(join(c1,complement(join(complement(c1),complement(converse(c2))))),complement(join(complement(c2),complement(c3)))) != composition(c1,complement(join(complement(c2),complement(c3)))) # answer(goals).  [copy(34),rewrite([20(4),20(12),20(18),20(26),19(31),29(31)]),flip(a)].
% 0.73/1.05  36 complement(top) = zero.  [back_rewrite(18),rewrite([20(2),17(4)])].
% 0.73/1.05  39 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(16(a,1),24(a,1,2)),flip(a)].
% 0.73/1.05  40 join(A,join(B,complement(A))) = join(B,top).  [para(17(a,1),26(a,2,2)),rewrite([19(2)])].
% 0.73/1.05  41 composition(A,composition(one,B)) = composition(A,B).  [para(15(a,1),27(a,1,1)),flip(a)].
% 0.73/1.05  52 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(17(a,1),33(a,1,1,1)),rewrite([36(2)])].
% 0.73/1.05  56 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)).  [para(33(a,1),33(a,1,2,1)),rewrite([19(10)])].
% 0.73/1.05  60 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A.  [para(36(a,1),33(a,1,2,1,1))].
% 0.73/1.05  73 composition(converse(one),A) = A.  [para(15(a,1),39(a,1,1)),rewrite([16(2)]),flip(a)].
% 0.73/1.05  79 converse(one) = one.  [para(73(a,1),15(a,1)),flip(a)].
% 0.73/1.05  83 join(complement(A),complement(composition(one,A))) = complement(A).  [para(73(a,1),31(a,1,2))].
% 0.73/1.05  84 composition(one,A) = A.  [para(73(a,1),41(a,2)),rewrite([79(2),41(4)])].
% 0.73/1.05  85 join(complement(A),complement(A)) = complement(A).  [back_rewrite(83),rewrite([84(3)])].
% 0.73/1.05  86 join(zero,complement(complement(A))) = A.  [back_rewrite(52),rewrite([85(4)])].
% 0.73/1.05  91 join(top,complement(A)) = top.  [para(85(a,1),40(a,1,2)),rewrite([17(2),19(4)]),flip(a)].
% 0.73/1.05  92 join(zero,complement(join(zero,complement(A)))) = A.  [back_rewrite(60),rewrite([91(3),36(2)])].
% 0.73/1.05  141 join(zero,complement(A)) = complement(A).  [para(86(a,1),92(a,1,2,1))].
% 0.73/1.05  142 complement(complement(A)) = A.  [back_rewrite(92),rewrite([141(4),141(4)])].
% 0.73/1.05  150 join(A,A) = A.  [para(142(a,1),85(a,1,1)),rewrite([142(2),142(3)])].
% 0.73/1.05  154 join(A,join(A,B)) = join(A,B).  [para(150(a,1),26(a,1)),rewrite([19(3),26(4,R),19(3),26(3,R),150(2)]),flip(a)].
% 0.73/1.05  155 join(A,complement(join(B,complement(A)))) = A.  [para(33(a,1),154(a,1,2)),rewrite([19(4),33(12)])].
% 0.73/1.05  160 join(complement(A),complement(join(A,B))) = complement(A).  [para(142(a,1),155(a,1,2,1,2)),rewrite([19(2)])].
% 0.73/1.05  301 join(A,complement(join(complement(A),complement(B)))) = A.  [para(56(a,1),160(a,1,2,1)),rewrite([142(2),19(3),142(7)])].
% 0.73/1.05  306 $F # answer(goals).  [back_rewrite(35),rewrite([301(9)]),xx(a)].
% 0.73/1.05  
% 0.73/1.05  % SZS output end Refutation
% 0.73/1.05  ============================== end of proof ==========================
% 0.73/1.05  
% 0.73/1.05  ============================== STATISTICS ============================
% 0.73/1.05  
% 0.73/1.05  Given=75. Generated=1569. Kept=284. proofs=1.
% 0.73/1.05  Usable=56. Sos=146. Demods=194. Limbo=5, Disabled=91. Hints=0.
% 0.73/1.05  Megabytes=0.36.
% 0.73/1.05  User_CPU=0.06, System_CPU=0.01, Wall_clock=0.
% 0.73/1.05  
% 0.73/1.05  ============================== end of statistics =====================
% 0.73/1.05  
% 0.73/1.05  ============================== end of search =========================
% 0.73/1.05  
% 0.73/1.05  THEOREM PROVED
% 0.73/1.05  % SZS status Theorem
% 0.73/1.05  
% 0.73/1.05  Exiting with 1 proof.
% 0.73/1.05  
% 0.73/1.05  Process 20939 exit (max_proofs) Fri Jul  8 09:27:25 2022
% 0.73/1.05  Prover9 interrupted
%------------------------------------------------------------------------------