0.10/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n014.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 180
0.12/0.33	% DateTime   : Thu Aug 29 09:51:09 EDT 2019
0.12/0.33	% CPUTime    : 
0.67/0.99	============================== Prover9 ===============================
0.67/0.99	Prover9 (32) version 2009-11A, November 2009.
0.67/0.99	Process 31573 was started by sandbox on n014.cluster.edu,
0.67/0.99	Thu Aug 29 09:51:09 2019
0.67/0.99	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_31420_n014.cluster.edu".
0.67/0.99	============================== end of head ===========================
0.67/0.99	
0.67/0.99	============================== INPUT =================================
0.67/0.99	
0.67/0.99	% Reading from file /tmp/Prover9_31420_n014.cluster.edu
0.67/0.99	
0.67/0.99	set(prolog_style_variables).
0.67/0.99	set(auto2).
0.67/0.99	    % set(auto2) -> set(auto).
0.67/0.99	    % set(auto) -> set(auto_inference).
0.67/0.99	    % set(auto) -> set(auto_setup).
0.67/0.99	    % set(auto_setup) -> set(predicate_elim).
0.67/0.99	    % set(auto_setup) -> assign(eq_defs, unfold).
0.67/0.99	    % set(auto) -> set(auto_limits).
0.67/0.99	    % set(auto_limits) -> assign(max_weight, "100.000").
0.67/0.99	    % set(auto_limits) -> assign(sos_limit, 20000).
0.67/0.99	    % set(auto) -> set(auto_denials).
0.67/0.99	    % set(auto) -> set(auto_process).
0.67/0.99	    % set(auto2) -> assign(new_constants, 1).
0.67/0.99	    % set(auto2) -> assign(fold_denial_max, 3).
0.67/0.99	    % set(auto2) -> assign(max_weight, "200.000").
0.67/0.99	    % set(auto2) -> assign(max_hours, 1).
0.67/0.99	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.67/0.99	    % set(auto2) -> assign(max_seconds, 0).
0.67/0.99	    % set(auto2) -> assign(max_minutes, 5).
0.67/0.99	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.67/0.99	    % set(auto2) -> set(sort_initial_sos).
0.67/0.99	    % set(auto2) -> assign(sos_limit, -1).
0.67/0.99	    % set(auto2) -> assign(lrs_ticks, 3000).
0.67/0.99	    % set(auto2) -> assign(max_megs, 400).
0.67/0.99	    % set(auto2) -> assign(stats, some).
0.67/0.99	    % set(auto2) -> clear(echo_input).
0.67/0.99	    % set(auto2) -> set(quiet).
0.67/0.99	    % set(auto2) -> clear(print_initial_clauses).
0.67/0.99	    % set(auto2) -> clear(print_given).
0.67/0.99	assign(lrs_ticks,-1).
0.67/0.99	assign(sos_limit,10000).
0.67/0.99	assign(order,kbo).
0.67/0.99	set(lex_order_vars).
0.67/0.99	clear(print_given).
0.67/0.99	
0.67/0.99	% formulas(sos).  % not echoed (17 formulas)
0.67/0.99	
0.67/0.99	============================== end of input ==========================
0.67/0.99	
0.67/0.99	% From the command line: assign(max_seconds, 180).
0.67/0.99	
0.67/0.99	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.67/0.99	
0.67/0.99	% Formulas that are not ordinary clauses:
0.67/0.99	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].
0.67/0.99	2 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	3 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	4 (all X0 meet(X0,complement(X0)) = zero) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	5 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	6 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	7 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	8 (all X0 all X1 all X2 composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2))) # label(composition_associativity) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	9 (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].
0.67/0.99	10 (all X0 all X1 join(X1,X0) = join(X0,X1)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	11 (all X0 X0 = converse(converse(X0))) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	12 (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].
0.67/0.99	13 (all X0 all X1 complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))) # label(converse_cancellativity) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	14 (all X0 all X1 all X2 meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2) = join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2))) # label(modular_law_1) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	15 (all X0 all X1 all X2 meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2) = join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2))) # label(modular_law_2) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	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].
3.24/3.57	17 -(all X0 all X1 all X2 (join(composition(complement(X0),X1),complement(X2)) = complement(X2) -> X0 = join(composition(X2,converse(X1)),X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
3.24/3.57	
3.24/3.57	============================== end of process non-clausal formulas ===
3.24/3.57	
3.24/3.57	============================== PROCESS INITIAL CLAUSES ===============
3.24/3.57	
3.24/3.57	============================== PREDICATE ELIMINATION =================
3.24/3.57	
3.24/3.57	============================== end predicate elimination =============
3.24/3.57	
3.24/3.57	Auto_denials:
3.24/3.57	  % copying label goals to answer in negative clause
3.24/3.57	
3.24/3.57	Term ordering decisions:
3.24/3.57	Function symbol KB weights:  one=1. top=1. zero=1. c1=1. c2=1. c3=1. composition=1. join=1. meet=1. converse=1. complement=1.
3.24/3.57	
3.24/3.57	============================== end of process initial clauses ========
3.24/3.57	
3.24/3.57	============================== CLAUSES FOR SEARCH ====================
3.24/3.57	
3.24/3.57	============================== end of clauses for search =============
3.24/3.57	
3.24/3.57	============================== SEARCH ================================
3.24/3.57	
3.24/3.57	% Starting search at 0.01 seconds.
3.24/3.57	
3.24/3.57	Low Water (keep): wt=157.000, iters=3401
3.24/3.57	
3.24/3.57	Low Water (keep): wt=131.000, iters=3383
3.24/3.57	
3.24/3.57	Low Water (keep): wt=83.000, iters=3352
3.24/3.57	
3.24/3.57	Low Water (keep): wt=81.000, iters=3395
3.24/3.57	
3.24/3.57	Low Water (keep): wt=80.000, iters=3453
3.24/3.57	
3.24/3.57	Low Water (keep): wt=78.000, iters=3413
3.24/3.57	
3.24/3.57	Low Water (keep): wt=76.000, iters=3380
3.24/3.57	
3.24/3.57	Low Water (keep): wt=74.000, iters=3341
3.24/3.57	
3.24/3.57	Low Water (keep): wt=73.000, iters=3382
3.24/3.57	
3.24/3.57	Low Water (keep): wt=72.000, iters=3351
3.24/3.57	
3.24/3.57	Low Water (keep): wt=71.000, iters=3413
3.24/3.57	
3.24/3.57	Low Water (keep): wt=70.000, iters=3356
3.24/3.57	
3.24/3.57	Low Water (keep): wt=69.000, iters=3340
3.24/3.57	
3.24/3.57	Low Water (keep): wt=68.000, iters=3400
3.24/3.57	
3.24/3.57	Low Water (keep): wt=65.000, iters=3449
3.24/3.57	
3.24/3.57	Low Water (keep): wt=64.000, iters=3346
3.24/3.57	
3.24/3.57	Low Water (keep): wt=63.000, iters=3374
3.24/3.57	
3.24/3.57	Low Water (keep): wt=62.000, iters=3337
3.24/3.57	
3.24/3.57	Low Water (keep): wt=61.000, iters=3440
3.24/3.57	
3.24/3.57	Low Water (keep): wt=60.000, iters=3385
3.24/3.57	
3.24/3.57	Low Water (keep): wt=59.000, iters=3385
3.24/3.57	
3.24/3.57	Low Water (keep): wt=58.000, iters=3448
3.24/3.57	
3.24/3.57	Low Water (keep): wt=57.000, iters=3443
3.24/3.57	
3.24/3.57	Low Water (keep): wt=56.000, iters=3455
3.24/3.57	
3.24/3.57	Low Water (keep): wt=54.000, iters=3394
3.24/3.57	
3.24/3.57	Low Water (keep): wt=53.000, iters=3439
3.24/3.57	
3.24/3.57	Low Water (keep): wt=52.000, iters=3370
3.24/3.57	
3.24/3.57	Low Water (keep): wt=51.000, iters=3447
3.24/3.57	
3.24/3.57	Low Water (keep): wt=50.000, iters=3423
3.24/3.57	
3.24/3.57	Low Water (keep): wt=49.000, iters=3381
3.24/3.57	
3.24/3.57	Low Water (keep): wt=48.000, iters=3384
3.24/3.57	
3.24/3.57	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 2.35 sec).
3.24/3.57	
3.24/3.57	Low Water (keep): wt=44.000, iters=3401
3.24/3.57	
3.24/3.57	Low Water (keep): wt=43.000, iters=3361
3.24/3.57	
3.24/3.57	Low Water (keep): wt=39.000, iters=3359
3.24/3.57	
3.24/3.57	Low Water (keep): wt=38.000, iters=3458
3.24/3.57	
3.24/3.57	Low Water (keep): wt=36.000, iters=3388
3.24/3.57	
3.24/3.57	Low Water (keep): wt=35.000, iters=3346
3.24/3.57	
3.24/3.57	Low Water (keep): wt=25.000, iters=4737
3.24/3.57	
3.24/3.57	Low Water (keep): wt=22.000, iters=3892
3.24/3.57	
3.24/3.57	Low Water (keep): wt=21.000, iters=3551
3.24/3.57	
3.24/3.57	============================== PROOF =================================
3.24/3.57	% SZS status Theorem
3.24/3.57	% SZS output start Refutation
3.24/3.57	
3.24/3.57	% Proof 1 at 2.55 (+ 0.05) seconds: goals.
3.24/3.57	% Length of proof is 107.
3.24/3.57	% Level of proof is 31.
3.24/3.57	% Maximum clause weight is 49.000.
3.24/3.57	% Given clauses 526.
3.24/3.57	
3.24/3.57	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].
3.24/3.57	2 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	3 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	4 (all X0 meet(X0,complement(X0)) = zero) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	5 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	6 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	7 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	8 (all X0 all X1 all X2 composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2))) # label(composition_associativity) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	9 (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].
3.24/3.57	10 (all X0 all X1 join(X1,X0) = join(X0,X1)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	11 (all X0 X0 = converse(converse(X0))) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	12 (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].
3.24/3.57	13 (all X0 all X1 complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1))) # label(converse_cancellativity) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	14 (all X0 all X1 all X2 meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2) = join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2))) # label(modular_law_1) # label(axiom) # label(non_clause).  [assumption].
3.24/3.57	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].
3.24/3.57	17 -(all X0 all X1 all X2 (join(composition(complement(X0),X1),complement(X2)) = complement(X2) -> X0 = join(composition(X2,converse(X1)),X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
3.24/3.57	18 composition(A,one) = A # label(composition_identity) # label(axiom).  [clausify(2)].
3.24/3.57	19 converse(converse(A)) = A # label(converse_idempotence) # label(axiom).  [clausify(11)].
3.24/3.57	20 meet(A,complement(A)) = zero # label(def_zero) # label(axiom).  [clausify(4)].
3.24/3.57	21 join(A,complement(A)) = top # label(def_top) # label(axiom).  [clausify(7)].
3.24/3.57	22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom).  [clausify(10)].
3.24/3.57	23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom).  [clausify(3)].
3.24/3.57	24 composition(converse(A),converse(B)) = converse(composition(B,A)).  [copy(23),flip(a)].
3.24/3.57	25 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom).  [clausify(5)].
3.24/3.57	26 converse(join(A,B)) = join(converse(A),converse(B)) # label(converse_additivity) # label(axiom).  [clausify(6)].
3.24/3.57	27 join(converse(A),converse(B)) = converse(join(A,B)).  [copy(26),flip(a)].
3.24/3.57	28 join(composition(complement(c1),c2),complement(c3)) = complement(c3) # label(goals) # label(negated_conjecture).  [clausify(17)].
3.24/3.57	29 join(complement(c3),composition(complement(c1),c2)) = complement(c3).  [copy(28),rewrite([22(7)])].
3.24/3.57	30 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom).  [clausify(8)].
3.24/3.57	31 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom).  [clausify(12)].
3.24/3.57	32 join(A,join(B,C)) = join(C,join(A,B)).  [copy(31),rewrite([22(2)]),flip(a)].
3.24/3.57	33 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom).  [clausify(9)].
3.24/3.57	34 join(composition(A,B),composition(C,B)) = composition(join(A,C),B).  [copy(33),flip(a)].
3.24/3.57	35 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity) # label(axiom).  [clausify(13)].
3.24/3.57	36 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(35),rewrite([22(6)])].
3.24/3.57	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)].
3.24/3.57	38 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(37),rewrite([22(6),22(8)]),rewrite([22(6)])].
3.24/3.57	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)].
3.24/3.57	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([25(3),25(8),22(10),25(13),22(15),25(19),25(24),22(26)]),flip(a)].
3.24/3.57	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)].
3.24/3.57	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([25(3),25(9),25(15),22(17),25(21),25(27)]),flip(a)].
3.24/3.57	45 join(composition(c3,converse(c2)),c1) != c1 # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(17)].
3.24/3.57	46 join(c1,composition(c3,converse(c2))) != c1 # answer(goals).  [copy(45),rewrite([22(6)])].
3.24/3.57	47 complement(top) = zero.  [back_rewrite(20),rewrite([25(2),21(4)])].
3.24/3.57	48 converse(composition(A,converse(B))) = composition(B,converse(A)).  [para(19(a,1),24(a,1,1)),flip(a)].
3.24/3.57	49 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(19(a,1),24(a,1,2)),flip(a)].
3.24/3.57	51 composition(A,composition(one,B)) = composition(A,B).  [para(18(a,1),30(a,1,1)),flip(a)].
3.24/3.57	53 join(A,join(B,complement(A))) = join(B,top).  [para(21(a,1),32(a,2,2)),rewrite([22(2)])].
3.24/3.57	57 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C).  [para(30(a,1),34(a,1,1)),rewrite([22(6)])].
3.24/3.57	59 join(complement(one),composition(converse(A),complement(A))) = complement(one).  [para(18(a,1),36(a,1,2,2,1))].
3.24/3.57	64 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(21(a,1),38(a,1,1,1)),rewrite([47(2)])].
3.24/3.57	87 join(complement(join(complement(A),complement(composition(B,converse(C))))),composition(complement(join(complement(B),complement(composition(A,C)))),complement(join(complement(converse(C)),complement(composition(converse(B),A)))))) = composition(complement(join(complement(B),complement(composition(A,C)))),complement(join(complement(converse(C)),complement(composition(converse(B),A))))).  [para(19(a,1),44(a,1,2,1,1,2,1,2)),rewrite([19(23)])].
3.24/3.57	94 join(zero,composition(converse(A),complement(composition(A,top)))) = zero.  [para(47(a,1),36(a,1,1)),rewrite([47(9)])].
3.24/3.57	96 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A.  [para(47(a,1),38(a,1,2,1,1))].
3.24/3.57	118 composition(converse(one),A) = A.  [para(18(a,1),49(a,1,1)),rewrite([19(2)]),flip(a)].
3.24/3.57	126 converse(one) = one.  [para(118(a,1),18(a,1)),flip(a)].
3.24/3.57	128 composition(join(A,one),B) = join(B,composition(A,B)).  [para(118(a,1),34(a,1,1)),rewrite([126(4),22(4)]),flip(a)].
3.24/3.57	130 join(complement(A),complement(composition(one,A))) = complement(A).  [para(118(a,1),36(a,1,2))].
3.24/3.57	144 composition(one,A) = A.  [para(118(a,1),51(a,2)),rewrite([126(2),51(4)])].
3.24/3.57	150 join(complement(A),complement(A)) = complement(A).  [back_rewrite(130),rewrite([144(3)])].
3.24/3.57	151 join(zero,complement(complement(A))) = A.  [back_rewrite(64),rewrite([150(4)])].
3.24/3.57	163 converse(join(A,one)) = join(one,converse(A)).  [para(126(a,1),27(a,1,1)),rewrite([22(5)]),flip(a)].
3.24/3.57	208 join(top,complement(A)) = top.  [para(150(a,1),53(a,1,2)),rewrite([21(2),22(4)]),flip(a)].
3.24/3.57	209 join(zero,complement(join(zero,complement(A)))) = A.  [back_rewrite(96),rewrite([208(3),47(2)])].
3.24/3.57	210 join(top,top) = join(A,top).  [para(208(a,1),53(a,1,2)),flip(a)].
3.24/3.57	215 join(A,top) = join(B,top).  [para(210(a,1),53(a,2)),rewrite([208(3)])].
3.24/3.57	216 join(A,top) = c_0.  [new_symbol(215)].
3.24/3.57	219 join(A,join(B,complement(A))) = c_0.  [back_rewrite(53),rewrite([216(5)])].
3.24/3.57	233 c_0 = top.  [para(40(a,1),219(a,1,2)),rewrite([21(22)]),flip(a)].
3.24/3.57	236 join(A,top) = top.  [back_rewrite(216),rewrite([233(3)])].
3.24/3.57	251 join(zero,complement(A)) = complement(A).  [para(151(a,1),209(a,1,2,1))].
3.24/3.57	252 complement(complement(A)) = A.  [back_rewrite(209),rewrite([251(4),251(4)])].
3.24/3.57	283 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B).  [para(252(a,1),38(a,1,1,1,2)),rewrite([252(5),22(4)])].
3.24/3.57	291 complement(zero) = top.  [para(47(a,1),252(a,1,1))].
3.24/3.57	292 join(A,A) = A.  [para(252(a,1),150(a,1,1)),rewrite([252(2),252(3)])].
3.24/3.57	304 join(A,join(A,B)) = join(A,B).  [para(292(a,1),32(a,1)),rewrite([22(3),32(4,R),22(3),32(3,R),292(2)]),flip(a)].
3.24/3.57	305 join(A,complement(join(B,complement(A)))) = A.  [para(38(a,1),304(a,1,2)),rewrite([22(4),38(12)])].
3.24/3.57	308 join(A,join(B,complement(join(C,complement(A))))) = join(A,B).  [para(305(a,1),32(a,2,2)),rewrite([22(4),22(6)])].
3.24/3.57	327 join(complement(one),composition(converse(complement(A)),A)) = complement(one).  [para(252(a,1),59(a,1,2,2))].
3.24/3.57	342 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero.  [para(163(a,1),94(a,1,2,1))].
3.24/3.57	378 join(complement(one),converse(complement(one))) = complement(one).  [para(18(a,1),327(a,1,2))].
3.24/3.57	382 converse(complement(one)) = complement(one).  [para(378(a,1),27(a,2,1)),rewrite([19(7),22(6),378(6)]),flip(a)].
3.24/3.57	396 converse(top) = top.  [para(382(a,1),163(a,2,2)),rewrite([22(4),21(4),21(6)])].
3.24/3.57	404 join(top,converse(A)) = top.  [para(396(a,1),27(a,1,1)),rewrite([22(5),236(5),396(5)])].
3.24/3.57	409 join(top,composition(A,converse(B))) = top.  [para(48(a,1),404(a,1,2))].
3.24/3.57	411 join(top,composition(A,B)) = top.  [para(19(a,1),409(a,1,2,2))].
3.24/3.57	412 composition(join(A,one),top) = top.  [para(396(a,1),409(a,1,2,2)),rewrite([128(4,R)])].
3.24/3.57	413 composition(join(one,converse(A)),zero) = zero.  [back_rewrite(342),rewrite([412(8),47(6),128(7,R),22(5),304(5)])].
3.24/3.57	445 composition(top,zero) = zero.  [para(382(a,1),413(a,1,1,2)),rewrite([21(4)])].
3.24/3.57	449 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)).  [para(445(a,1),44(a,1,1,1,2,1)),rewrite([291(3),22(3),208(3),47(2),47(3),251(7),252(6),291(6),396(7),208(9),47(6),30(6),47(9),251(13),252(12),291(12),396(13),208(15),47(12),30(12)])].
3.24/3.57	453 join(zero,composition(A,composition(B,zero))) = zero.  [para(445(a,1),57(a,1,2)),rewrite([22(5),411(8),445(8)])].
3.24/3.57	456 composition(A,composition(converse(zero),zero)) = zero.  [back_rewrite(449),rewrite([453(7)]),flip(a)].
3.24/3.57	547 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B).  [para(456(a,1),30(a,1,1)),rewrite([30(7)]),flip(a)].
3.24/3.57	548 composition(A,zero) = zero.  [para(456(a,1),30(a,1)),rewrite([456(6)]),flip(a)].
3.24/3.57	549 composition(converse(zero),A) = converse(zero).  [para(456(a,1),49(a,1,1)),rewrite([548(6)]),flip(a)].
3.24/3.57	554 composition(zero,A) = composition(B,converse(zero)).  [back_rewrite(547),rewrite([549(5)]),flip(a)].
3.24/3.57	587 converse(zero) = zero.  [para(549(a,1),548(a,1))].
3.24/3.57	595 composition(zero,A) = zero.  [back_rewrite(554),rewrite([587(4),548(4)])].
3.24/3.57	11619 join(A,complement(join(A,B))) = join(A,complement(B)).  [para(283(a,1),308(a,1,2)),flip(a)].
3.24/3.57	11634 join(complement(c3),complement(composition(complement(c1),c2))) = top.  [para(29(a,1),11619(a,1,2,1)),rewrite([252(5),22(4),21(4)]),flip(a)].
3.24/3.57	11796 complement(join(c1,complement(composition(c3,converse(c2))))) = zero.  [para(11634(a,1),87(a,1,2,1,1)),rewrite([252(3),47(10),595(21),22(10),251(10),11634(16),47(10),595(21)])].
3.24/3.57	11813 complement(join(c1,composition(c3,converse(c2)))) = complement(c1).  [para(11796(a,1),283(a,1,2)),rewrite([22(6),22(9),251(9)])].
3.24/3.57	11814 join(c1,composition(c3,converse(c2))) = join(zero,c1).  [para(11796(a,1),11619(a,1,2)),rewrite([22(3),252(10)]),flip(a)].
3.24/3.57	11815 complement(join(zero,c1)) = complement(c1).  [back_rewrite(11813),rewrite([11814(6)])].
3.24/3.57	11816 join(zero,c1) != c1 # answer(goals).  [back_rewrite(46),rewrite([11814(6)])].
3.24/3.57	11837 join(zero,c1) = c1.  [para(11815(a,1),38(a,1,1,1,2)),rewrite([11815(9),38(10)]),flip(a)].
3.24/3.57	11838 $F # answer(goals).  [resolve(11837,a,11816,a)].
3.24/3.57	
3.24/3.57	% SZS output end Refutation
3.24/3.57	============================== end of proof ==========================
3.24/3.57	
3.24/3.57	============================== STATISTICS ============================
3.24/3.57	
3.24/3.57	Given=526. Generated=74320. Kept=11809. proofs=1.
3.24/3.57	Usable=430. Sos=9703. Demods=9833. Limbo=1, Disabled=1692. Hints=0.
3.24/3.57	Megabytes=25.09.
3.24/3.57	User_CPU=2.55, System_CPU=0.05, Wall_clock=3.
3.24/3.57	
3.24/3.57	============================== end of statistics =====================
3.24/3.57	
3.24/3.57	============================== end of search =========================
3.24/3.57	
3.24/3.57	THEOREM PROVED
3.24/3.57	% SZS status Theorem
3.24/3.57	
3.24/3.57	Exiting with 1 proof.
3.24/3.57	
3.24/3.57	Process 31573 exit (max_proofs) Thu Aug 29 09:51:12 2019
3.24/3.57	Prover9 interrupted
3.24/3.57	EOF