TSTP Solution File: REL046+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : REL046+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 19:54:30 EDT 2022

% Result   : Theorem 0.97s 1.27s
% Output   : Refutation 0.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : REL046+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.33  % Computer : n020.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 10:39:13 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.44/1.00  ============================== Prover9 ===============================
% 0.44/1.00  Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.00  Process 29002 was started by sandbox2 on n020.cluster.edu,
% 0.44/1.00  Fri Jul  8 10:39:14 2022
% 0.44/1.00  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28833_n020.cluster.edu".
% 0.44/1.00  ============================== end of head ===========================
% 0.44/1.00  
% 0.44/1.00  ============================== INPUT =================================
% 0.44/1.00  
% 0.44/1.00  % Reading from file /tmp/Prover9_28833_n020.cluster.edu
% 0.44/1.00  
% 0.44/1.00  set(prolog_style_variables).
% 0.44/1.00  set(auto2).
% 0.44/1.00      % set(auto2) -> set(auto).
% 0.44/1.00      % set(auto) -> set(auto_inference).
% 0.44/1.00      % set(auto) -> set(auto_setup).
% 0.44/1.00      % set(auto_setup) -> set(predicate_elim).
% 0.44/1.00      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.00      % set(auto) -> set(auto_limits).
% 0.44/1.00      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.00      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.00      % set(auto) -> set(auto_denials).
% 0.44/1.00      % set(auto) -> set(auto_process).
% 0.44/1.00      % set(auto2) -> assign(new_constants, 1).
% 0.44/1.00      % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.00      % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.00      % set(auto2) -> assign(max_hours, 1).
% 0.44/1.00      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.00      % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.00      % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.00      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.00      % set(auto2) -> set(sort_initial_sos).
% 0.44/1.00      % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.00      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.00      % set(auto2) -> assign(max_megs, 400).
% 0.44/1.00      % set(auto2) -> assign(stats, some).
% 0.44/1.00      % set(auto2) -> clear(echo_input).
% 0.44/1.00      % set(auto2) -> set(quiet).
% 0.44/1.00      % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.00      % set(auto2) -> clear(print_given).
% 0.44/1.00  assign(lrs_ticks,-1).
% 0.44/1.00  assign(sos_limit,10000).
% 0.44/1.00  assign(order,kbo).
% 0.44/1.00  set(lex_order_vars).
% 0.44/1.00  clear(print_given).
% 0.44/1.00  
% 0.44/1.00  % formulas(sos).  % not echoed (14 formulas)
% 0.44/1.00  
% 0.44/1.00  ============================== end of input ==========================
% 0.44/1.00  
% 0.44/1.00  % From the command line: assign(max_seconds, 300).
% 0.44/1.00  
% 0.44/1.00  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.00  
% 0.44/1.00  % Formulas that are not ordinary clauses:
% 0.44/1.00  1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.00  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].
% 0.44/1.00  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].
% 0.44/1.00  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].
% 0.44/1.00  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].
% 0.44/1.00  6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.00  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].
% 0.44/1.00  8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.00  9 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.00  10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.00  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].
% 0.44/1.00  12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
% 0.44/1.00  13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
% 0.97/1.27  14 -(all X0 all X1 all X2 (join(X0,meet(X1,X2)) = meet(X1,X2) -> join(X0,X1) = X1 & join(X0,X2) = X2)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.97/1.27  
% 0.97/1.27  ============================== end of process non-clausal formulas ===
% 0.97/1.27  
% 0.97/1.27  ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.27  
% 0.97/1.27  ============================== PREDICATE ELIMINATION =================
% 0.97/1.27  
% 0.97/1.27  ============================== end predicate elimination =============
% 0.97/1.27  
% 0.97/1.27  Auto_denials:
% 0.97/1.27    % copying label goals to answer in negative clause
% 0.97/1.27  
% 0.97/1.27  Term ordering decisions:
% 0.97/1.27  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.
% 0.97/1.27  
% 0.97/1.27  ============================== end of process initial clauses ========
% 0.97/1.27  
% 0.97/1.27  ============================== CLAUSES FOR SEARCH ====================
% 0.97/1.27  
% 0.97/1.27  ============================== end of clauses for search =============
% 0.97/1.27  
% 0.97/1.27  ============================== SEARCH ================================
% 0.97/1.27  
% 0.97/1.27  % Starting search at 0.01 seconds.
% 0.97/1.27  
% 0.97/1.27  ============================== PROOF =================================
% 0.97/1.27  % SZS status Theorem
% 0.97/1.27  % SZS output start Refutation
% 0.97/1.27  
% 0.97/1.27  % Proof 1 at 0.27 (+ 0.01) seconds: goals.
% 0.97/1.27  % Length of proof is 76.
% 0.97/1.27  % Level of proof is 22.
% 0.97/1.27  % Maximum clause weight is 21.000.
% 0.97/1.27  % Given clauses 243.
% 0.97/1.27  
% 0.97/1.27  1 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
% 0.97/1.27  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].
% 0.97/1.27  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].
% 0.97/1.27  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].
% 0.97/1.27  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].
% 0.97/1.27  6 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
% 0.97/1.27  8 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
% 0.97/1.27  10 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
% 0.97/1.27  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].
% 0.97/1.27  12 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
% 0.97/1.27  13 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
% 0.97/1.27  14 -(all X0 all X1 all X2 (join(X0,meet(X1,X2)) = meet(X1,X2) -> join(X0,X1) = X1 & join(X0,X2) = X2)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.97/1.27  15 composition(A,one) = A # label(composition_identity) # label(axiom).  [clausify(6)].
% 0.97/1.27  16 converse(converse(A)) = A # label(converse_idempotence) # label(axiom).  [clausify(8)].
% 0.97/1.27  17 join(A,complement(A)) = top # label(def_top) # label(axiom).  [clausify(12)].
% 0.97/1.27  18 meet(A,complement(A)) = zero # label(def_zero) # label(axiom).  [clausify(13)].
% 0.97/1.27  19 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom).  [clausify(1)].
% 0.97/1.27  20 meet(c2,c3) = join(c1,meet(c2,c3)) # label(goals) # label(negated_conjecture).  [clausify(14)].
% 0.97/1.27  21 join(c1,meet(c2,c3)) = meet(c2,c3).  [copy(20),flip(a)].
% 0.97/1.27  22 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom).  [clausify(4)].
% 0.97/1.27  25 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom).  [clausify(10)].
% 0.97/1.27  26 composition(converse(A),converse(B)) = converse(composition(B,A)).  [copy(25),flip(a)].
% 0.97/1.27  27 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom).  [clausify(2)].
% 0.97/1.27  28 join(A,join(B,C)) = join(C,join(A,B)).  [copy(27),rewrite([19(2)]),flip(a)].
% 0.97/1.27  29 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom).  [clausify(5)].
% 0.97/1.27  32 complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)) # label(converse_cancellativity) # label(axiom).  [clausify(11)].
% 0.97/1.27  33 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(32),rewrite([19(7)]),flip(a)].
% 0.97/1.27  34 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom).  [clausify(3)].
% 0.97/1.27  35 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(34),rewrite([19(6),19(8)]),rewrite([19(6)])].
% 0.97/1.27  36 join(c1,c2) != c2 | join(c1,c3) != c3 # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(14)].
% 0.97/1.27  37 join(c1,complement(join(complement(c2),complement(c3)))) = complement(join(complement(c2),complement(c3))).  [back_rewrite(21),rewrite([22(4),22(11)])].
% 0.97/1.27  38 complement(top) = zero.  [back_rewrite(18),rewrite([22(2),17(4)])].
% 0.97/1.27  41 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(16(a,1),26(a,1,2)),flip(a)].
% 0.97/1.27  42 join(A,join(B,complement(A))) = join(B,top).  [para(17(a,1),28(a,2,2)),rewrite([19(2)])].
% 0.97/1.27  43 composition(A,composition(one,B)) = composition(A,B).  [para(15(a,1),29(a,1,1)),flip(a)].
% 0.97/1.27  54 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(17(a,1),35(a,1,1,1)),rewrite([38(2)])].
% 0.97/1.27  58 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)).  [para(35(a,1),35(a,1,2,1)),rewrite([19(10)])].
% 0.97/1.27  63 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A.  [para(38(a,1),35(a,1,2,1,1))].
% 0.97/1.27  76 composition(converse(one),A) = A.  [para(15(a,1),41(a,1,1)),rewrite([16(2)]),flip(a)].
% 0.97/1.27  80 join(A,join(B,join(C,complement(A)))) = join(B,join(C,top)).  [para(42(a,1),28(a,2,2)),rewrite([19(3),28(3,R),19(2),28(7,R),19(6)])].
% 0.97/1.27  82 join(top,c1) = top.  [para(37(a,1),42(a,1,2)),rewrite([17(12),19(4)]),flip(a)].
% 0.97/1.27  83 converse(one) = one.  [para(76(a,1),15(a,1)),flip(a)].
% 0.97/1.27  87 join(complement(A),complement(composition(one,A))) = complement(A).  [para(76(a,1),33(a,1,2))].
% 0.97/1.27  88 composition(one,A) = A.  [para(76(a,1),43(a,2)),rewrite([83(2),43(4)])].
% 0.97/1.27  89 join(complement(A),complement(A)) = complement(A).  [back_rewrite(87),rewrite([88(3)])].
% 0.97/1.27  90 join(zero,complement(complement(A))) = A.  [back_rewrite(54),rewrite([89(4)])].
% 0.97/1.27  95 join(top,complement(A)) = top.  [para(89(a,1),42(a,1,2)),rewrite([17(2),19(4)]),flip(a)].
% 0.97/1.27  96 join(zero,complement(join(zero,complement(A)))) = A.  [back_rewrite(63),rewrite([95(3),38(2)])].
% 0.97/1.27  97 join(top,top) = join(A,top).  [para(95(a,1),42(a,1,2)),flip(a)].
% 0.97/1.27  108 join(A,top) = join(B,top).  [para(97(a,1),42(a,2)),rewrite([95(3)])].
% 0.97/1.27  109 join(A,top) = c_0.  [new_symbol(108)].
% 0.97/1.27  111 join(A,join(B,join(C,complement(A)))) = join(B,c_0).  [back_rewrite(80),rewrite([109(6)])].
% 0.97/1.27  112 join(A,join(B,complement(A))) = c_0.  [back_rewrite(42),rewrite([109(5)])].
% 0.97/1.27  117 c_0 = top.  [para(37(a,1),112(a,1,2)),rewrite([17(12)]),flip(a)].
% 0.97/1.27  118 join(A,join(B,complement(A))) = top.  [back_rewrite(112),rewrite([117(4)])].
% 0.97/1.27  119 join(A,join(B,join(C,complement(A)))) = top.  [back_rewrite(111),rewrite([117(5),109(6),117(5)])].
% 0.97/1.27  120 join(A,top) = top.  [back_rewrite(109),rewrite([117(3)])].
% 0.97/1.27  145 join(zero,complement(A)) = complement(A).  [para(90(a,1),96(a,1,2,1))].
% 0.97/1.27  146 complement(complement(A)) = A.  [back_rewrite(96),rewrite([145(4),145(4)])].
% 0.97/1.27  153 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B).  [para(146(a,1),35(a,1,1,1,2)),rewrite([146(5),19(4)])].
% 0.97/1.27  155 join(A,A) = A.  [para(146(a,1),89(a,1,1)),rewrite([146(2),146(3)])].
% 0.97/1.27  159 join(A,join(A,B)) = join(A,B).  [para(155(a,1),28(a,1)),rewrite([19(3),28(4,R),19(3),28(3,R),155(2)]),flip(a)].
% 0.97/1.27  160 join(A,complement(join(B,complement(A)))) = A.  [para(35(a,1),159(a,1,2)),rewrite([19(4),35(12)])].
% 0.97/1.27  174 join(complement(A),complement(join(A,B))) = complement(A).  [para(146(a,1),160(a,1,2,1,2)),rewrite([19(2)])].
% 0.97/1.27  185 join(complement(c1),join(complement(c2),complement(c3))) = complement(c1).  [para(37(a,1),174(a,1,2,1)),rewrite([146(9)])].
% 0.97/1.27  298 join(A,complement(join(complement(A),complement(B)))) = A.  [para(58(a,1),174(a,1,2,1)),rewrite([146(2),19(3),146(7)])].
% 0.97/1.27  593 join(A,join(complement(A),complement(B))) = top.  [para(298(a,1),118(a,1,2)),rewrite([19(4)])].
% 0.97/1.27  595 join(A,join(B,join(complement(A),complement(C)))) = top.  [para(593(a,1),28(a,2,2)),rewrite([19(4),120(7)])].
% 0.97/1.27  985 join(c3,complement(c1)) = top.  [para(185(a,1),119(a,1,2))].
% 0.97/1.27  987 complement(join(complement(c1),complement(c3))) = c1.  [para(985(a,1),35(a,1,1,1)),rewrite([38(2),19(6),145(8)])].
% 0.97/1.27  990 join(complement(c1),complement(c3)) = complement(c1).  [para(985(a,1),58(a,1,2,1,1)),rewrite([19(8),987(9),82(5),38(4),19(4),145(4),19(7)]),flip(a)].
% 0.97/1.27  1029 join(c1,c3) = c3.  [para(990(a,1),160(a,1,2,1)),rewrite([146(4),19(3)])].
% 0.97/1.27  1034 join(c1,c2) != c2 # answer(goals).  [back_rewrite(36),rewrite([1029(8)]),xx(b)].
% 0.97/1.27  1883 join(c2,complement(c1)) = top.  [para(185(a,1),595(a,1,2))].
% 0.97/1.27  1954 complement(join(c1,c2)) = complement(c2).  [para(1883(a,1),153(a,1,2,1)),rewrite([38(6),19(6),145(6)])].
% 0.97/1.27  1969 $F # answer(goals).  [para(1954(a,1),35(a,1,1,1,2)),rewrite([1954(9),35(10)]),flip(a),unit_del(a,1034)].
% 0.97/1.27  
% 0.97/1.27  % SZS output end Refutation
% 0.97/1.27  ============================== end of proof ==========================
% 0.97/1.27  
% 0.97/1.27  ============================== STATISTICS ============================
% 0.97/1.27  
% 0.97/1.27  Given=243. Generated=13350. Kept=1947. proofs=1.
% 0.97/1.27  Usable=191. Sos=1480. Demods=1573. Limbo=1, Disabled=290. Hints=0.
% 0.97/1.27  Megabytes=2.64.
% 0.97/1.27  User_CPU=0.27, System_CPU=0.01, Wall_clock=0.
% 0.97/1.27  
% 0.97/1.27  ============================== end of statistics =====================
% 0.97/1.27  
% 0.97/1.27  ============================== end of search =========================
% 0.97/1.27  
% 0.97/1.27  THEOREM PROVED
% 0.97/1.27  % SZS status Theorem
% 0.97/1.27  
% 0.97/1.27  Exiting with 1 proof.
% 0.97/1.27  
% 0.97/1.27  Process 29002 exit (max_proofs) Fri Jul  8 10:39:14 2022
% 0.97/1.27  Prover9 interrupted
%------------------------------------------------------------------------------