TSTP Solution File: REL024+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : REL024+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n020.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 19:53:54 EDT 2022

% Result   : Theorem 0.84s 1.13s
% Output   : Refutation 0.84s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : REL024+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n020.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 12:29:58 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.43/1.01  ============================== Prover9 ===============================
% 0.43/1.01  Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01  Process 8993 was started by sandbox2 on n020.cluster.edu,
% 0.43/1.01  Fri Jul  8 12:29:59 2022
% 0.43/1.01  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8839_n020.cluster.edu".
% 0.43/1.01  ============================== end of head ===========================
% 0.43/1.01  
% 0.43/1.01  ============================== INPUT =================================
% 0.43/1.01  
% 0.43/1.01  % Reading from file /tmp/Prover9_8839_n020.cluster.edu
% 0.43/1.01  
% 0.43/1.01  set(prolog_style_variables).
% 0.43/1.01  set(auto2).
% 0.43/1.01      % set(auto2) -> set(auto).
% 0.43/1.01      % set(auto) -> set(auto_inference).
% 0.43/1.01      % set(auto) -> set(auto_setup).
% 0.43/1.01      % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01      % set(auto) -> set(auto_limits).
% 0.43/1.01      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01      % set(auto) -> set(auto_denials).
% 0.43/1.01      % set(auto) -> set(auto_process).
% 0.43/1.01      % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01      % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01      % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01      % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01      % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01      % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01      % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01      % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01      % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01      % set(auto2) -> assign(stats, some).
% 0.43/1.01      % set(auto2) -> clear(echo_input).
% 0.43/1.01      % set(auto2) -> set(quiet).
% 0.43/1.01      % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01      % set(auto2) -> clear(print_given).
% 0.43/1.01  assign(lrs_ticks,-1).
% 0.43/1.01  assign(sos_limit,10000).
% 0.43/1.01  assign(order,kbo).
% 0.43/1.01  set(lex_order_vars).
% 0.43/1.01  clear(print_given).
% 0.43/1.01  
% 0.43/1.01  % formulas(sos).  % not echoed (14 formulas)
% 0.43/1.01  
% 0.43/1.01  ============================== end of input ==========================
% 0.43/1.01  
% 0.43/1.01  % From the command line: assign(max_seconds, 300).
% 0.43/1.01  
% 0.43/1.01  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.01  
% 0.43/1.01  % Formulas that are not ordinary clauses:
% 0.43/1.01  1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.01  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].
% 0.43/1.01  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].
% 0.43/1.01  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].
% 0.43/1.01  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].
% 0.43/1.01  6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.01  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].
% 0.43/1.01  8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.01  9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.01  10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.01  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].
% 0.43/1.01  12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
% 0.43/1.01  13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
% 0.84/1.13  14 -(all X0 all X1 all X2 join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(meet(X0,converse(X1)),X2)) = composition(meet(X0,converse(X1)),X2)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.84/1.13  
% 0.84/1.13  ============================== end of process non-clausal formulas ===
% 0.84/1.13  
% 0.84/1.13  ============================== PROCESS INITIAL CLAUSES ===============
% 0.84/1.13  
% 0.84/1.13  ============================== PREDICATE ELIMINATION =================
% 0.84/1.13  
% 0.84/1.13  ============================== end predicate elimination =============
% 0.84/1.13  
% 0.84/1.13  Auto_denials:
% 0.84/1.13    % copying label goals to answer in negative clause
% 0.84/1.13  
% 0.84/1.13  Term ordering decisions:
% 0.84/1.13  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.
% 0.84/1.13  
% 0.84/1.13  ============================== end of process initial clauses ========
% 0.84/1.13  
% 0.84/1.13  ============================== CLAUSES FOR SEARCH ====================
% 0.84/1.13  
% 0.84/1.13  ============================== end of clauses for search =============
% 0.84/1.13  
% 0.84/1.13  ============================== SEARCH ================================
% 0.84/1.13  
% 0.84/1.13  % Starting search at 0.01 seconds.
% 0.84/1.13  
% 0.84/1.13  ============================== PROOF =================================
% 0.84/1.13  % SZS status Theorem
% 0.84/1.13  % SZS output start Refutation
% 0.84/1.13  
% 0.84/1.13  % Proof 1 at 0.13 (+ 0.01) seconds: goals.
% 0.84/1.13  % Length of proof is 58.
% 0.84/1.13  % Level of proof is 15.
% 0.84/1.13  % Maximum clause weight is 34.000.
% 0.84/1.13  % Given clauses 125.
% 0.84/1.13  
% 0.84/1.13  1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.84/1.13  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].
% 0.84/1.13  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].
% 0.84/1.13  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].
% 0.84/1.13  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].
% 0.84/1.13  6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.84/1.13  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].
% 0.84/1.13  8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.84/1.13  9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
% 0.84/1.13  10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
% 0.84/1.13  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].
% 0.84/1.13  12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
% 0.84/1.13  13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
% 0.84/1.13  14 -(all X0 all X1 all X2 join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(meet(X0,converse(X1)),X2)) = composition(meet(X0,converse(X1)),X2)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.84/1.13  15 composition(A,one) = A # label(composition_identity) # label(axiom).  [clausify(6)].
% 0.84/1.13  16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom).  [clausify(8)].
% 0.84/1.13  17 join(A,complement(A)) = top # label(def_top) # label(axiom).  [clausify(12)].
% 0.84/1.13  18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom).  [clausify(13)].
% 0.84/1.13  19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom).  [clausify(1)].
% 0.84/1.13  20 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom).  [clausify(4)].
% 0.84/1.13  21 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom).  [clausify(9)].
% 0.84/1.13  22 join(converse(A),converse(B)) = converse(join(A,B)).  [copy(21),flip(a)].
% 0.84/1.13  23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom).  [clausify(10)].
% 0.84/1.13  24 composition(converse(A),converse(B)) = converse(composition(B,A)).  [copy(23),flip(a)].
% 0.84/1.13  25 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom).  [clausify(2)].
% 0.84/1.13  26 join(A,join(B,C)) = join(C,join(A,B)).  [copy(25),rewrite([19(2)]),flip(a)].
% 0.84/1.13  27 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom).  [clausify(5)].
% 0.84/1.13  28 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom).  [clausify(7)].
% 0.84/1.13  29 join(composition(A,B),composition(C,B)) = composition(join(A,C),B).  [copy(28),flip(a)].
% 0.84/1.13  30 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom).  [clausify(11)].
% 0.84/1.13  31 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(30),rewrite([19(7)]),flip(a)].
% 0.84/1.13  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)].
% 0.84/1.13  33 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(32),rewrite([19(6),19(8)]),rewrite([19(6)])].
% 0.84/1.13  34 composition(meet(c1,converse(c2)),c3) != join(composition(meet(c1,converse(c2)),meet(c2,c3)),composition(meet(c1,converse(c2)),c3)) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(14)].
% 0.84/1.13  35 join(composition(complement(join(complement(c1),complement(converse(c2)))),c3),composition(complement(join(complement(c1),complement(converse(c2)))),complement(join(complement(c2),complement(c3))))) != composition(complement(join(complement(c1),complement(converse(c2)))),c3) # answer(goals).  [copy(34),rewrite([20(4),20(13),20(19),20(27),19(33)]),flip(a)].
% 0.84/1.13  36 complement(top) = zero.  [back_rewrite(18),rewrite([20(2),17(4)])].
% 0.84/1.13  39 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(16(a,1),24(a,1,2)),flip(a)].
% 0.84/1.13  40 join(A,join(B,complement(A))) = join(B,top).  [para(17(a,1),26(a,2,2)),rewrite([19(2)])].
% 0.84/1.13  41 composition(A,composition(one,B)) = composition(A,B).  [para(15(a,1),27(a,1,1)),flip(a)].
% 0.84/1.13  43 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)).  [para(24(a,1),29(a,1,1)),rewrite([19(7)])].
% 0.84/1.13  52 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(17(a,1),33(a,1,1,1)),rewrite([36(2)])].
% 0.84/1.13  60 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A.  [para(36(a,1),33(a,1,2,1,1))].
% 0.84/1.13  73 composition(converse(one),A) = A.  [para(15(a,1),39(a,1,1)),rewrite([16(2)]),flip(a)].
% 0.84/1.13  74 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)).  [para(39(a,1),22(a,1,1)),rewrite([19(7)]),flip(a)].
% 0.84/1.13  79 converse(one) = one.  [para(73(a,1),15(a,1)),flip(a)].
% 0.84/1.13  83 join(complement(A),complement(composition(one,A))) = complement(A).  [para(73(a,1),31(a,1,2))].
% 0.84/1.13  84 composition(one,A) = A.  [para(73(a,1),41(a,2)),rewrite([79(2),41(4)])].
% 0.84/1.13  85 join(complement(A),complement(A)) = complement(A).  [back_rewrite(83),rewrite([84(3)])].
% 0.84/1.13  86 join(zero,complement(complement(A))) = A.  [back_rewrite(52),rewrite([85(4)])].
% 0.84/1.13  91 join(top,complement(A)) = top.  [para(85(a,1),40(a,1,2)),rewrite([17(2),19(4)]),flip(a)].
% 0.84/1.13  92 join(zero,complement(join(zero,complement(A)))) = A.  [back_rewrite(60),rewrite([91(3),36(2)])].
% 0.84/1.13  141 join(zero,complement(A)) = complement(A).  [para(86(a,1),92(a,1,2,1))].
% 0.84/1.13  142 complement(complement(A)) = A.  [back_rewrite(92),rewrite([141(4),141(4)])].
% 0.84/1.13  150 join(A,A) = A.  [para(142(a,1),85(a,1,1)),rewrite([142(2),142(3)])].
% 0.84/1.13  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)].
% 0.84/1.14  155 join(A,complement(join(B,complement(A)))) = A.  [para(33(a,1),154(a,1,2)),rewrite([19(4),33(12)])].
% 0.84/1.14  676 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)).  [para(43(a,1),74(a,1,1)),rewrite([22(3),24(4),16(4),16(4),16(6)]),flip(a)].
% 0.84/1.14  708 $F # answer(goals).  [back_rewrite(35),rewrite([676(24),155(15)]),xx(a)].
% 0.84/1.14  
% 0.84/1.14  % SZS output end Refutation
% 0.84/1.14  ============================== end of proof ==========================
% 0.84/1.14  
% 0.84/1.14  ============================== STATISTICS ============================
% 0.84/1.14  
% 0.84/1.14  Given=125. Generated=4387. Kept=686. proofs=1.
% 0.84/1.14  Usable=98. Sos=409. Demods=522. Limbo=32, Disabled=161. Hints=0.
% 0.84/1.14  Megabytes=0.88.
% 0.84/1.14  User_CPU=0.13, System_CPU=0.01, Wall_clock=0.
% 0.84/1.14  
% 0.84/1.14  ============================== end of statistics =====================
% 0.84/1.14  
% 0.84/1.14  ============================== end of search =========================
% 0.84/1.14  
% 0.84/1.14  THEOREM PROVED
% 0.84/1.14  % SZS status Theorem
% 0.84/1.14  
% 0.84/1.14  Exiting with 1 proof.
% 0.84/1.14  
% 0.84/1.14  Process 8993 exit (max_proofs) Fri Jul  8 12:29:59 2022
% 0.84/1.14  Prover9 interrupted
%------------------------------------------------------------------------------