0.00/0.06	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.06	% Command    : tptp2X_and_run_prover9 %d %s
0.02/0.29	% Computer   : n146.star.cs.uiowa.edu
0.02/0.29	% Model      : x86_64 x86_64
0.02/0.29	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.29	% Memory     : 32218.625MB
0.02/0.29	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.30	% CPULimit   : 300
0.02/0.30	% DateTime   : Sat Jul 14 04:16:44 CDT 2018
0.02/0.30	% CPUTime    : 
0.26/0.54	============================== Prover9 ===============================
0.26/0.54	Prover9 (32) version 2009-11A, November 2009.
0.26/0.54	Process 25761 was started by sandbox2 on n146.star.cs.uiowa.edu,
0.26/0.54	Sat Jul 14 04:16:44 2018
0.26/0.54	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25702_n146.star.cs.uiowa.edu".
0.26/0.54	============================== end of head ===========================
0.26/0.54	
0.26/0.54	============================== INPUT =================================
0.26/0.54	
0.26/0.54	% Reading from file /tmp/Prover9_25702_n146.star.cs.uiowa.edu
0.26/0.54	
0.26/0.54	set(prolog_style_variables).
0.26/0.54	set(auto2).
0.26/0.54	    % set(auto2) -> set(auto).
0.26/0.54	    % set(auto) -> set(auto_inference).
0.26/0.54	    % set(auto) -> set(auto_setup).
0.26/0.54	    % set(auto_setup) -> set(predicate_elim).
0.26/0.54	    % set(auto_setup) -> assign(eq_defs, unfold).
0.26/0.54	    % set(auto) -> set(auto_limits).
0.26/0.54	    % set(auto_limits) -> assign(max_weight, "100.000").
0.26/0.54	    % set(auto_limits) -> assign(sos_limit, 20000).
0.26/0.54	    % set(auto) -> set(auto_denials).
0.26/0.54	    % set(auto) -> set(auto_process).
0.26/0.54	    % set(auto2) -> assign(new_constants, 1).
0.26/0.54	    % set(auto2) -> assign(fold_denial_max, 3).
0.26/0.54	    % set(auto2) -> assign(max_weight, "200.000").
0.26/0.54	    % set(auto2) -> assign(max_hours, 1).
0.26/0.54	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.26/0.54	    % set(auto2) -> assign(max_seconds, 0).
0.26/0.54	    % set(auto2) -> assign(max_minutes, 5).
0.26/0.54	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.26/0.54	    % set(auto2) -> set(sort_initial_sos).
0.26/0.54	    % set(auto2) -> assign(sos_limit, -1).
0.26/0.54	    % set(auto2) -> assign(lrs_ticks, 3000).
0.26/0.54	    % set(auto2) -> assign(max_megs, 400).
0.26/0.54	    % set(auto2) -> assign(stats, some).
0.26/0.54	    % set(auto2) -> clear(echo_input).
0.26/0.54	    % set(auto2) -> set(quiet).
0.26/0.54	    % set(auto2) -> clear(print_initial_clauses).
0.26/0.54	    % set(auto2) -> clear(print_given).
0.26/0.54	assign(lrs_ticks,-1).
0.26/0.54	assign(sos_limit,10000).
0.26/0.54	assign(order,kbo).
0.26/0.54	set(lex_order_vars).
0.26/0.54	clear(print_given).
0.26/0.54	
0.26/0.54	% formulas(sos).  % not echoed (17 formulas)
0.26/0.54	
0.26/0.54	============================== end of input ==========================
0.26/0.54	
0.26/0.54	% From the command line: assign(max_seconds, 300).
0.26/0.54	
0.26/0.54	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.26/0.54	
0.26/0.54	% Formulas that are not ordinary clauses:
0.26/0.54	1 (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].
0.26/0.54	2 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
0.26/0.54	3 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
0.26/0.54	4 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
0.26/0.54	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].
0.26/0.54	6 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.26/0.54	7 (all X0 all X1 join(converse(X0),converse(X1)) = converse(join(X0,X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
0.26/0.54	8 (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].
0.26/0.54	9 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.26/0.54	10 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
0.26/0.54	11 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
0.26/0.54	12 (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].
0.26/0.54	13 (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].
14.03/14.33	14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) # label(modular_law_1) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	15 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) # label(modular_law_2) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	16 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) # label(dedekind_law) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	17 -(all X0 all X1 (one = join(X0,one) & join(X1,one) = one -> composition(X0,X1) = meet(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
14.03/14.33	
14.03/14.33	============================== end of process non-clausal formulas ===
14.03/14.33	
14.03/14.33	============================== PROCESS INITIAL CLAUSES ===============
14.03/14.33	
14.03/14.33	============================== PREDICATE ELIMINATION =================
14.03/14.33	
14.03/14.33	============================== end predicate elimination =============
14.03/14.33	
14.03/14.33	Auto_denials:
14.03/14.33	  % copying label goals to answer in negative clause
14.03/14.33	
14.03/14.33	Term ordering decisions:
14.03/14.33	Function symbol KB weights:  one=1. top=1. zero=1. c1=1. c2=1. composition=1. join=1. meet=1. converse=1. complement=1.
14.03/14.33	
14.03/14.33	============================== end of process initial clauses ========
14.03/14.33	
14.03/14.33	============================== CLAUSES FOR SEARCH ====================
14.03/14.33	
14.03/14.33	============================== end of clauses for search =============
14.03/14.33	
14.03/14.33	============================== SEARCH ================================
14.03/14.33	
14.03/14.33	% Starting search at 0.01 seconds.
14.03/14.33	
14.03/14.33	Low Water (keep): wt=84.000, iters=3340
14.03/14.33	
14.03/14.33	Low Water (keep): wt=82.000, iters=3758
14.03/14.33	
14.03/14.33	Low Water (keep): wt=80.000, iters=3770
14.03/14.33	
14.03/14.33	Low Water (keep): wt=69.000, iters=3365
14.03/14.33	
14.03/14.33	Low Water (keep): wt=68.000, iters=3437
14.03/14.33	
14.03/14.33	Low Water (keep): wt=67.000, iters=3370
14.03/14.33	
14.03/14.33	Low Water (keep): wt=66.000, iters=3371
14.03/14.33	
14.03/14.33	Low Water (keep): wt=65.000, iters=3398
14.03/14.33	
14.03/14.33	Low Water (keep): wt=64.000, iters=3454
14.03/14.33	
14.03/14.33	Low Water (keep): wt=61.000, iters=3334
14.03/14.33	
14.03/14.33	Low Water (keep): wt=59.000, iters=3343
14.03/14.33	
14.03/14.33	Low Water (keep): wt=58.000, iters=3371
14.03/14.33	
14.03/14.33	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 46 (0.00 of 2.42 sec).
14.03/14.33	
14.03/14.33	Low Water (keep): wt=57.000, iters=3461
14.03/14.33	
14.03/14.33	Low Water (keep): wt=55.000, iters=3425
14.03/14.33	
14.03/14.33	Low Water (keep): wt=53.000, iters=3684
14.03/14.33	
14.03/14.33	Low Water (keep): wt=51.000, iters=3546
14.03/14.33	
14.03/14.33	Low Water (keep): wt=49.000, iters=3383
14.03/14.33	
14.03/14.33	Low Water (keep): wt=46.000, iters=3335
14.03/14.33	
14.03/14.33	Low Water (keep): wt=43.000, iters=3333
14.03/14.33	
14.03/14.33	Low Water (keep): wt=42.000, iters=3336
14.03/14.33	
14.03/14.33	Low Water (keep): wt=39.000, iters=3462
14.03/14.33	
14.03/14.33	Low Water (keep): wt=38.000, iters=3395
14.03/14.33	
14.03/14.33	Low Water (keep): wt=37.000, iters=3341
14.03/14.33	
14.03/14.33	Low Water (keep): wt=35.000, iters=3370
14.03/14.33	
14.03/14.33	Low Water (keep): wt=33.000, iters=3356
14.03/14.33	
14.03/14.33	Low Water (keep): wt=31.000, iters=3334
14.03/14.33	
14.03/14.33	Low Water (displace): id=4838, wt=171.000
14.03/14.33	
14.03/14.33	Low Water (displace): id=4741, wt=166.000
14.03/14.33	
14.03/14.33	Low Water (displace): id=5992, wt=157.000
14.03/14.33	
14.03/14.33	Low Water (displace): id=11951, wt=15.000
14.03/14.33	
14.03/14.33	Low Water (keep): wt=30.000, iters=3380
14.03/14.33	
14.03/14.33	Low Water (displace): id=11981, wt=14.000
14.03/14.33	
14.03/14.33	Low Water (displace): id=11996, wt=13.000
14.03/14.33	
14.03/14.33	Low Water (displace): id=12011, wt=12.000
14.03/14.33	
14.03/14.33	Low Water (keep): wt=29.000, iters=3378
14.03/14.33	
14.03/14.33	Low Water (keep): wt=28.000, iters=3341
14.03/14.33	
14.03/14.33	Low Water (keep): wt=27.000, iters=3411
14.03/14.33	
14.03/14.33	Low Water (keep): wt=26.000, iters=3378
14.03/14.33	
14.03/14.33	Low Water (keep): wt=25.000, iters=3335
14.03/14.33	
14.03/14.33	Low Water (keep): wt=24.000, iters=3393
14.03/14.33	
14.03/14.33	Low Water (keep): wt=23.000, iters=3333
14.03/14.33	
14.03/14.33	Low Water (keep): wt=22.000, iters=3335
14.03/14.33	
14.03/14.33	Low Water (keep): wt=21.000, iters=3358
14.03/14.33	
14.03/14.33	Low Water (keep): wt=20.000, iters=3346
14.03/14.33	
14.03/14.33	Low Water (keep): wt=19.000, iters=3335
14.03/14.33	
14.03/14.33	Low Water (keep): wt=18.000, iters=3333
14.03/14.33	
14.03/14.33	Low Water (keep): wt=17.000, iters=3343
14.03/14.33	
14.03/14.33	============================== PROOF =================================
14.03/14.33	% SZS status Theorem
14.03/14.33	% SZS output start Refutation
14.03/14.33	
14.03/14.33	% Proof 1 at 13.62 (+ 0.18) seconds: goals.
14.03/14.33	% Length of proof is 164.
14.03/14.33	% Level of proof is 34.
14.03/14.33	% Maximum clause weight is 48.000.
14.03/14.33	% Given clauses 1469.
14.03/14.33	
14.03/14.33	1 (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].
14.03/14.33	2 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	3 (all X0 top = join(X0,complement(X0))) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	4 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	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].
14.03/14.33	6 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	7 (all X0 all X1 join(converse(X0),converse(X1)) = converse(join(X0,X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	8 (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].
14.03/14.33	9 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	10 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	11 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	12 (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].
14.03/14.33	13 (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].
14.03/14.33	14 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) # label(modular_law_1) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	16 (all X0 all X1 all X2 join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) # label(dedekind_law) # label(axiom) # label(non_clause).  [assumption].
14.03/14.33	17 -(all X0 all X1 (one = join(X0,one) & join(X1,one) = one -> composition(X0,X1) = meet(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
14.03/14.33	18 converse(converse(A)) = A # label(converse_idempotence) # label(axiom).  [clausify(6)].
14.03/14.33	19 composition(A,one) = A # label(composition_identity) # label(axiom).  [clausify(10)].
14.03/14.33	20 join(c1,one) = one # label(goals) # label(negated_conjecture).  [clausify(17)].
14.03/14.33	21 join(c2,one) = one # label(goals) # label(negated_conjecture).  [clausify(17)].
14.03/14.33	22 meet(A,complement(A)) = zero # label(def_zero) # label(axiom).  [clausify(2)].
14.03/14.33	23 join(A,complement(A)) = top # label(def_top) # label(axiom).  [clausify(3)].
14.03/14.33	24 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom).  [clausify(9)].
14.03/14.33	25 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom).  [clausify(4)].
14.03/14.33	26 composition(converse(A),converse(B)) = converse(composition(B,A)).  [copy(25),flip(a)].
14.03/14.33	27 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom).  [clausify(7)].
14.03/14.33	28 join(converse(A),converse(B)) = converse(join(A,B)).  [copy(27),flip(a)].
14.03/14.33	29 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom).  [clausify(11)].
14.03/14.33	30 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom).  [clausify(5)].
14.03/14.33	31 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom).  [clausify(13)].
14.03/14.33	32 join(A,join(B,C)) = join(C,join(A,B)).  [copy(31),rewrite([24(2)]),flip(a)].
14.03/14.33	33 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity) # label(axiom).  [clausify(8)].
14.03/14.33	34 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(33),rewrite([24(6)])].
14.03/14.33	35 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom).  [clausify(12)].
14.03/14.33	36 join(composition(A,B),composition(C,B)) = composition(join(A,C),B).  [copy(35),flip(a)].
14.03/14.33	37 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom).  [clausify(1)].
14.03/14.33	38 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(37),rewrite([24(6),24(8)]),rewrite([24(6)])].
14.03/14.33	39 meet(composition(A,meet(B,composition(converse(A),C))),C) = join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) # label(modular_law_1) # label(axiom).  [clausify(14)].
14.03/14.33	40 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(C),complement(composition(converse(B),A)))))))).  [copy(39),rewrite([29(3),29(8),24(10),29(13),24(15),29(19),29(24),24(26)]),flip(a)].
14.03/14.33	43 composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))) # label(dedekind_law) # label(axiom).  [clausify(16)].
14.03/14.33	44 join(complement(join(complement(A),complement(composition(B,C)))),composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(C))))),complement(join(complement(C),complement(composition(converse(B),A))))).  [copy(43),rewrite([29(3),29(9),29(15),24(17),29(21),29(27)]),flip(a)].
14.03/14.33	45 composition(c1,c2) != meet(c1,c2) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(17)].
14.03/14.33	46 complement(join(complement(c1),complement(c2))) != composition(c1,c2) # answer(goals).  [copy(45),rewrite([29(6)]),flip(a)].
14.03/14.33	47 join(one,c2) = one.  [back_rewrite(21),rewrite([24(3)])].
14.03/14.33	48 join(one,c1) = one.  [back_rewrite(20),rewrite([24(3)])].
14.03/14.33	49 complement(top) = zero.  [back_rewrite(22),rewrite([29(2),23(4)])].
14.03/14.33	50 converse(composition(A,converse(B))) = composition(B,converse(A)).  [para(18(a,1),26(a,1,1)),flip(a)].
14.03/14.33	51 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(18(a,1),26(a,1,2)),flip(a)].
14.03/14.33	52 converse(join(A,converse(B))) = join(B,converse(A)).  [para(18(a,1),28(a,1,1)),rewrite([24(4)]),flip(a)].
14.03/14.33	53 composition(A,composition(one,B)) = composition(A,B).  [para(19(a,1),30(a,1,1)),flip(a)].
14.03/14.33	55 join(A,join(B,complement(A))) = join(B,top).  [para(23(a,1),32(a,2,2)),rewrite([24(2)])].
14.03/14.33	57 join(complement(one),composition(converse(A),complement(A))) = complement(one).  [para(19(a,1),34(a,1,2,2,1))].
14.03/14.33	61 join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(C,converse(B)),converse(A)).  [para(26(a,1),36(a,1,1)),rewrite([24(7)])].
14.03/14.33	65 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(23(a,1),38(a,1,1,1)),rewrite([49(2)])].
14.03/14.33	69 join(complement(A),complement(join(join(B,complement(A)),complement(join(complement(B),complement(A)))))) = join(complement(B),complement(A)).  [para(38(a,1),38(a,1,2,1)),rewrite([24(10)])].
14.03/14.33	70 join(complement(join(complement(A),complement(composition(converse(B),C)))),complement(join(complement(A),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A))))))))) = complement(join(complement(A),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A)))))))).  [para(18(a,1),40(a,1,2,1,2,1,2,1,2,1,1)),rewrite([18(23)])].
14.03/14.33	71 join(complement(join(complement(A),complement(B))),complement(join(complement(A),complement(composition(B,complement(join(complement(one),complement(composition(converse(B),A))))))))) = complement(join(complement(A),complement(composition(B,complement(join(complement(one),complement(composition(converse(B),A)))))))).  [para(19(a,1),40(a,1,1,1,2,1))].
14.03/14.33	88 join(complement(join(complement(A),complement(B))),composition(complement(join(complement(B),complement(composition(A,converse(one))))),complement(join(complement(one),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,converse(one))))),complement(join(complement(one),complement(composition(converse(B),A))))).  [para(19(a,1),44(a,1,1,1,2,1))].
14.03/14.33	97 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A.  [para(49(a,1),38(a,1,2,1,1))].
14.03/14.33	106 converse(composition(A,composition(converse(B),C))) = composition(converse(C),composition(B,converse(A))).  [para(50(a,1),26(a,1,2)),rewrite([30(7)]),flip(a)].
14.03/14.33	107 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)).  [para(50(a,1),28(a,1,1)),rewrite([24(7)]),flip(a)].
14.03/14.33	119 composition(converse(one),A) = A.  [para(19(a,1),51(a,1,1)),rewrite([18(2)]),flip(a)].
14.03/14.33	120 converse(join(A,composition(converse(B),C))) = join(composition(converse(C),B),converse(A)).  [para(51(a,1),28(a,1,1)),rewrite([24(7)]),flip(a)].
14.03/14.33	127 converse(one) = one.  [para(119(a,1),19(a,1)),flip(a)].
14.03/14.33	129 join(complement(A),composition(one,complement(A))) = complement(A).  [para(119(a,1),34(a,1,2,2,1)),rewrite([127(3),127(3)])].
14.03/14.33	145 composition(one,A) = A.  [para(119(a,1),53(a,2)),rewrite([127(2),53(4)])].
14.03/14.33	146 join(complement(join(complement(A),complement(B))),composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(B),A)))))) = composition(complement(join(complement(A),complement(B))),complement(join(complement(one),complement(composition(converse(B),A))))).  [back_rewrite(88),rewrite([127(7),19(7),24(7),127(20),19(20),24(20)])].
14.03/14.33	148 join(complement(A),complement(A)) = complement(A).  [back_rewrite(129),rewrite([145(4)])].
14.03/14.33	152 join(zero,complement(complement(A))) = A.  [back_rewrite(65),rewrite([148(4)])].
14.03/14.33	155 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)).  [para(52(a,1),28(a,1,1)),rewrite([24(7),32(7,R),24(6)]),flip(a)].
14.03/14.33	156 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))).  [para(52(a,1),28(a,1,2)),rewrite([32(4,R),24(3),28(3),155(7)]),flip(a)].
14.03/14.33	162 join(join(A,B),converse(C)) = join(A,join(B,converse(C))).  [para(52(a,1),52(a,2,2)),rewrite([156(4),52(4),32(6,R),24(5)])].
14.03/14.33	163 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))).  [back_rewrite(155),rewrite([162(8),28(7)])].
14.03/14.33	164 converse(join(A,one)) = join(one,converse(A)).  [para(127(a,1),28(a,1,1)),rewrite([24(5)]),flip(a)].
14.03/14.33	180 composition(join(one,converse(A)),converse(B)) = converse(composition(B,join(A,one))).  [para(164(a,1),26(a,1,1))].
14.03/14.33	182 converse(join(A,join(B,one))) = join(one,converse(join(A,B))).  [para(164(a,1),28(a,1,1)),rewrite([162(5),28(4),24(7),32(7,R),24(6)]),flip(a)].
14.03/14.33	193 join(top,complement(A)) = top.  [para(148(a,1),55(a,1,2)),rewrite([23(2),24(4)]),flip(a)].
14.03/14.33	194 join(zero,complement(join(zero,complement(A)))) = A.  [back_rewrite(97),rewrite([193(3),49(2)])].
14.03/14.33	195 join(top,top) = join(A,top).  [para(193(a,1),55(a,1,2)),flip(a)].
14.03/14.33	204 join(A,top) = join(B,top).  [para(195(a,1),55(a,2)),rewrite([193(3)])].
14.03/14.33	205 join(A,top) = c_0.  [new_symbol(204)].
14.03/14.33	208 join(A,join(B,complement(A))) = c_0.  [back_rewrite(55),rewrite([205(5)])].
14.03/14.33	213 c_0 = top.  [para(40(a,1),208(a,1,2)),rewrite([23(22)]),flip(a)].
14.03/14.33	214 join(A,join(B,complement(A))) = top.  [back_rewrite(208),rewrite([213(4)])].
14.03/14.33	216 join(A,top) = top.  [back_rewrite(205),rewrite([213(3)])].
14.03/14.33	224 join(zero,complement(A)) = complement(A).  [para(152(a,1),194(a,1,2,1))].
14.03/14.33	225 complement(complement(A)) = A.  [back_rewrite(194),rewrite([224(4),224(4)])].
14.03/14.33	226 join(A,zero) = A.  [back_rewrite(152),rewrite([225(3),24(2)])].
14.03/14.33	249 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B).  [para(225(a,1),38(a,1,1,1,2)),rewrite([225(5),24(4)])].
14.03/14.33	258 join(A,A) = A.  [para(225(a,1),148(a,1,1)),rewrite([225(2),225(3)])].
14.03/14.33	260 join(complement(one),composition(converse(complement(A)),A)) = complement(one).  [para(225(a,1),57(a,1,2,2))].
14.03/14.33	267 join(A,join(A,B)) = join(A,B).  [para(258(a,1),32(a,1)),rewrite([24(3),32(4,R),24(3),32(3,R),258(2)]),flip(a)].
14.03/14.33	273 join(A,complement(join(B,complement(A)))) = A.  [para(38(a,1),267(a,1,2)),rewrite([24(4),38(12)])].
14.03/14.33	278 join(complement(A),complement(join(A,B))) = complement(A).  [para(225(a,1),273(a,1,2,1,2)),rewrite([24(2)])].
14.03/14.33	289 join(complement(converse(A)),complement(converse(join(A,B)))) = complement(converse(A)).  [para(28(a,1),278(a,1,2,1))].
14.03/14.33	290 join(complement(composition(A,B)),complement(composition(join(A,C),B))) = complement(composition(A,B)).  [para(36(a,1),278(a,1,2,1))].
14.03/14.33	304 converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))).  [para(145(a,1),61(a,1,2)),rewrite([24(4),28(4),180(8)]),flip(a)].
14.03/14.33	334 join(complement(one),converse(complement(one))) = complement(one).  [para(19(a,1),260(a,1,2))].
14.03/14.33	344 converse(complement(one)) = complement(one).  [para(334(a,1),28(a,2,1)),rewrite([18(7),24(6),334(6)]),flip(a)].
14.03/14.33	353 converse(top) = top.  [para(344(a,1),164(a,2,2)),rewrite([24(4),23(4),23(6)])].
14.03/14.33	360 join(top,converse(A)) = top.  [para(353(a,1),28(a,1,1)),rewrite([24(5),216(5),353(5)])].
14.03/14.33	364 join(top,composition(A,converse(B))) = top.  [para(50(a,1),360(a,1,2))].
14.03/14.33	372 join(top,composition(A,B)) = top.  [para(18(a,1),364(a,1,2,2))].
14.03/14.33	446 join(complement(A),complement(join(B,A))) = complement(A).  [para(273(a,1),69(a,2)),rewrite([225(2),225(4),225(8),69(13)])].
14.03/14.33	447 join(A,complement(join(complement(A),complement(B)))) = A.  [para(69(a,1),278(a,1,2,1)),rewrite([225(2),24(3),225(7)])].
14.03/14.33	499 join(complement(A),join(join(complement(A),complement(composition(converse(B),C))),complement(composition(converse(B),complement(join(complement(C),complement(composition(B,A)))))))) = join(complement(A),complement(composition(converse(B),C))).  [para(70(a,1),278(a,1,2,1)),rewrite([225(7),225(17),32(16,R),24(15),225(23)])].
14.03/14.33	713 join(complement(one),complement(c2)) = complement(c2).  [para(47(a,1),446(a,1,2,1)),rewrite([24(5)])].
14.03/14.33	714 join(complement(one),complement(c1)) = complement(c1).  [para(48(a,1),446(a,1,2,1)),rewrite([24(5)])].
14.03/14.33	750 join(A,join(complement(A),complement(B))) = top.  [para(447(a,1),214(a,1,2)),rewrite([24(4)])].
14.03/14.33	760 join(one,complement(c1)) = top.  [para(714(a,1),750(a,1,2))].
14.03/14.33	790 join(zero,c1) = c1.  [para(760(a,1),38(a,1,1,1)),rewrite([49(2),714(6),225(4)])].
14.03/14.33	2351 join(composition(A,B),composition(A,C)) = composition(A,join(B,C)).  [para(61(a,1),120(a,1,1)),rewrite([28(3),26(4),18(4),18(4),18(6)]),flip(a)].
14.03/14.33	4271 join(one,join(c2,converse(A))) = join(one,converse(A)).  [para(47(a,1),162(a,1,1)),flip(a)].
14.03/14.33	4272 join(one,join(c1,converse(A))) = join(one,converse(A)).  [para(48(a,1),162(a,1,1)),flip(a)].
14.03/14.33	5521 join(A,join(one,converse(c2))) = join(A,one).  [para(4271(a,1),28(a,2,1)),rewrite([127(2),52(5),32(5,R),24(4),52(9),127(7)])].
14.03/14.33	5529 join(one,converse(c2)) = one.  [para(258(a,1),5521(a,2)),rewrite([267(6)])].
14.03/14.33	5530 join(A,composition(converse(c2),A)) = A.  [para(5529(a,1),36(a,2,1)),rewrite([145(2),145(6)])].
14.03/14.33	5532 join(complement(one),complement(converse(c2))) = complement(converse(c2)).  [para(5529(a,1),446(a,1,2,1)),rewrite([24(6)])].
14.03/14.33	5564 join(one,converse(c1)) = one.  [para(790(a,1),182(a,2,2,1)),rewrite([24(4),48(4),24(3),226(3),127(2)]),flip(a)].
14.03/14.33	5744 join(A,composition(converse(c1),A)) = A.  [para(5564(a,1),36(a,2,1)),rewrite([145(2),145(6)])].
14.03/14.33	5746 join(complement(one),complement(converse(c1))) = complement(converse(c1)).  [para(5564(a,1),446(a,1,2,1)),rewrite([24(6)])].
14.03/14.33	5753 join(complement(A),complement(composition(converse(c2),A))) = complement(composition(converse(c2),A)).  [para(5530(a,1),446(a,1,2,1)),rewrite([24(6)])].
14.03/14.33	5755 join(A,composition(A,c2)) = A.  [para(5530(a,1),107(a,1,1)),rewrite([18(2),18(3),18(4),24(3)]),flip(a)].
14.03/14.33	5766 join(A,composition(A,c1)) = A.  [para(5744(a,1),107(a,1,1)),rewrite([18(2),18(3),18(4),24(3)]),flip(a)].
14.03/14.33	5787 join(complement(A),complement(composition(A,c1))) = complement(composition(A,c1)).  [para(5766(a,1),446(a,1,2,1)),rewrite([24(5)])].
14.03/14.33	5800 composition(converse(c2),c2) = converse(c2).  [para(5532(a,1),146(a,1,1,1)),rewrite([225(4),5532(8),225(6),18(9),19(9),713(9),225(7),5755(7),5532(8),225(6),18(9),19(9),713(9),225(7)]),flip(a)].
14.03/14.33	5829 converse(c2) = c2.  [para(5800(a,1),26(a,2,1)),rewrite([18(5),5800(4),18(5)])].
14.03/14.33	5830 composition(c2,composition(c2,A)) = composition(c2,A).  [para(5800(a,1),30(a,1,1)),rewrite([5829(2),5829(4)]),flip(a)].
14.03/14.33	5865 converse(composition(A,c2)) = composition(c2,converse(A)).  [para(5800(a,1),106(a,1,1,2)),rewrite([5829(2),5829(5),5830(8)])].
14.03/14.33	5894 join(complement(A),complement(composition(c2,A))) = complement(composition(c2,A)).  [back_rewrite(5753),rewrite([5829(3),5829(7)])].
14.03/14.33	5896 join(A,composition(c2,A)) = A.  [back_rewrite(5530),rewrite([5829(2)])].
14.03/14.33	5903 converse(composition(c2,A)) = composition(converse(A),c2).  [para(5829(a,1),26(a,1,2)),flip(a)].
14.03/14.33	6414 composition(converse(c1),c1) = converse(c1).  [para(5746(a,1),146(a,1,1,1)),rewrite([225(4),5746(8),225(6),18(9),19(9),714(9),225(7),5766(7),5746(8),225(6),18(9),19(9),714(9),225(7)]),flip(a)].
14.03/14.33	6462 converse(c1) = c1.  [para(6414(a,1),26(a,2,1)),rewrite([18(5),6414(4),18(5)])].
14.03/14.33	6463 composition(c1,composition(c1,A)) = composition(c1,A).  [para(6414(a,1),30(a,1,1)),rewrite([6462(2),6462(4)]),flip(a)].
14.03/14.33	6498 converse(composition(A,c1)) = composition(c1,converse(A)).  [para(6414(a,1),106(a,1,1,2)),rewrite([6462(2),6462(5),6463(8)])].
14.03/14.33	10184 join(complement(converse(A)),converse(join(A,B))) = top.  [para(289(a,1),214(a,1,2)),rewrite([24(5)])].
14.03/14.33	10244 join(A,join(B,converse(complement(converse(A))))) = top.  [para(10184(a,1),28(a,2,1)),rewrite([18(6),32(5),24(4),32(5,R),24(4),353(7)])].
14.03/14.33	10343 join(A,converse(complement(converse(A)))) = top.  [para(258(a,1),10244(a,1,2))].
14.03/14.33	10376 join(complement(converse(A)),converse(join(B,A))) = top.  [para(10343(a,1),163(a,1,1,2)),rewrite([216(2),353(2)]),flip(a)].
14.03/14.33	10528 join(converse(A),complement(composition(c2,converse(A)))) = top.  [para(5755(a,1),10376(a,1,2,1)),rewrite([5865(3),24(6)])].
14.03/14.33	10530 join(converse(A),complement(composition(converse(A),c2))) = top.  [para(5896(a,1),10376(a,1,2,1)),rewrite([5903(3),24(6)])].
14.03/14.33	10666 join(A,converse(complement(composition(c2,converse(A))))) = top.  [para(10528(a,1),28(a,2,1)),rewrite([18(2),353(8)])].
14.03/14.33	10771 join(A,complement(composition(A,c2))) = top.  [para(18(a,1),10530(a,1,1)),rewrite([18(2)])].
14.03/14.33	10852 join(A,join(B,complement(composition(A,c2)))) = top.  [para(10771(a,1),32(a,2,2)),rewrite([24(4),216(7)])].
14.03/14.33	11009 join(one,converse(complement(composition(c2,c1)))) = top.  [para(10666(a,1),4272(a,1,2)),rewrite([216(3),6462(5)]),flip(a)].
14.03/14.33	11014 join(one,complement(composition(c2,c1))) = top.  [para(11009(a,1),28(a,2,1)),rewrite([127(2),18(7),353(8)])].
14.03/14.33	11086 complement(join(complement(one),complement(composition(c2,c1)))) = composition(c2,c1).  [para(11014(a,1),38(a,1,1,1)),rewrite([49(2),224(10)])].
14.03/14.33	11087 join(complement(one),complement(composition(c2,c1))) = complement(composition(c2,c1)).  [para(11014(a,1),69(a,1,2,1,1)),rewrite([11086(13),372(9),49(6),24(6),224(6)]),flip(a)].
14.03/14.33	11089 complement(join(one,composition(c2,c1))) = complement(one).  [para(11014(a,1),249(a,1,2,1)),rewrite([24(5),49(8),24(8),224(8)])].
14.03/14.33	11091 join(one,composition(c2,c1)) = one.  [para(11089(a,1),38(a,1,1,1,2)),rewrite([11089(11),38(10)]),flip(a)].
14.03/14.33	11092 join(one,composition(c1,c2)) = one.  [para(11091(a,1),28(a,2,1)),rewrite([127(2),6498(5),5829(4),127(7)])].
14.03/14.33	11099 join(complement(one),complement(composition(c1,c2))) = complement(composition(c1,c2)).  [para(11092(a,1),446(a,1,2,1)),rewrite([24(7)])].
14.03/14.33	11184 composition(A,join(B,one)) = join(A,composition(A,B)).  [para(304(a,1),18(a,1,1)),rewrite([18(4)]),flip(a)].
14.03/14.33	11527 join(join(A,B),complement(composition(A,c2))) = top.  [para(290(a,1),10852(a,1,2))].
14.03/14.33	11974 join(join(A,B),complement(composition(B,c2))) = top.  [para(24(a,1),11527(a,1,1))].
14.03/14.33	12222 join(one,complement(composition(c2,composition(c1,c2)))) = top.  [para(11091(a,1),11974(a,1,1)),rewrite([30(6)])].
14.03/14.33	12644 complement(join(complement(one),complement(composition(c2,composition(c1,c2))))) = composition(c2,composition(c1,c2)).  [para(12222(a,1),38(a,1,1,1)),rewrite([49(2),224(12)])].
14.03/14.33	12645 join(complement(one),complement(composition(c2,composition(c1,c2)))) = complement(composition(c2,composition(c1,c2))).  [para(12222(a,1),69(a,1,2,1,1)),rewrite([12644(17),372(13),49(8),24(8),224(8)]),flip(a)].
14.03/14.33	25293 composition(c2,composition(c1,c2)) = composition(c2,c1).  [para(11087(a,1),71(a,1,1,1)),rewrite([225(5),6498(14),5829(13),19(15),11099(15),225(13),30(12),6463(11),12645(12),225(10),2351(9),11184(6,R),24(5),47(5),19(4),6498(14),5829(13),19(15),11099(15),225(13),30(12),6463(11),12645(12),225(10)]),flip(a)].
14.03/14.33	25299 join(complement(c1),complement(c2)) = complement(composition(c2,c1)).  [para(11087(a,1),499(a,1,2,2,1,2,1)),rewrite([5829(6),19(7),5829(9),225(13),5830(12),24(12),32(12),24(11),5894(11),5787(9),5894(7),5829(8),19(9)]),flip(a)].
14.03/14.33	25311 composition(c2,c1) != composition(c1,c2) # answer(goals).  [back_rewrite(46),rewrite([25299(5),225(5)])].
14.03/14.33	25312 composition(c2,c1) = composition(c1,c2).  [para(25293(a,1),26(a,2,1)),rewrite([5865(4),6462(3),5829(5),30(5),25293(5),6498(7),5829(6)])].
14.03/14.33	25313 $F # answer(goals).  [resolve(25312,a,25311,a)].
14.03/14.33	
14.03/14.33	% SZS output end Refutation
14.03/14.33	============================== end of proof ==========================
14.03/14.33	
14.03/14.33	============================== STATISTICS ============================
14.03/14.33	
14.03/14.33	Given=1469. Generated=335748. Kept=25285. proofs=1.
14.03/14.33	Usable=1030. Sos=9930. Demods=10701. Limbo=0, Disabled=14343. Hints=0.
14.03/14.33	Megabytes=30.54.
14.03/14.33	User_CPU=13.62, System_CPU=0.18, Wall_clock=14.
14.03/14.33	
14.03/14.33	============================== end of statistics =====================
14.03/14.33	
14.03/14.33	============================== end of search =========================
14.03/14.33	
14.03/14.33	THEOREM PROVED
14.03/14.33	% SZS status Theorem
14.03/14.33	
14.03/14.33	Exiting with 1 proof.
14.03/14.33	
14.03/14.33	Process 25761 exit (max_proofs) Sat Jul 14 04:16:58 2018
14.03/14.33	Prover9 interrupted
14.03/14.34	EOF