0.07/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n005.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   : 960
0.12/0.33	% DateTime   : Thu Jul  2 07:20:21 EDT 2020
0.12/0.33	% CPUTime    : 
0.71/0.99	============================== Prover9 ===============================
0.71/0.99	Prover9 (32) version 2009-11A, November 2009.
0.71/0.99	Process 28985 was started by sandbox2 on n005.cluster.edu,
0.71/0.99	Thu Jul  2 07:20:21 2020
0.71/0.99	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_28830_n005.cluster.edu".
0.71/0.99	============================== end of head ===========================
0.71/0.99	
0.71/0.99	============================== INPUT =================================
0.71/0.99	
0.71/0.99	% Reading from file /tmp/Prover9_28830_n005.cluster.edu
0.71/0.99	
0.71/0.99	set(prolog_style_variables).
0.71/0.99	set(auto2).
0.71/0.99	    % set(auto2) -> set(auto).
0.71/0.99	    % set(auto) -> set(auto_inference).
0.71/0.99	    % set(auto) -> set(auto_setup).
0.71/0.99	    % set(auto_setup) -> set(predicate_elim).
0.71/0.99	    % set(auto_setup) -> assign(eq_defs, unfold).
0.71/0.99	    % set(auto) -> set(auto_limits).
0.71/0.99	    % set(auto_limits) -> assign(max_weight, "100.000").
0.71/0.99	    % set(auto_limits) -> assign(sos_limit, 20000).
0.71/0.99	    % set(auto) -> set(auto_denials).
0.71/0.99	    % set(auto) -> set(auto_process).
0.71/0.99	    % set(auto2) -> assign(new_constants, 1).
0.71/0.99	    % set(auto2) -> assign(fold_denial_max, 3).
0.71/0.99	    % set(auto2) -> assign(max_weight, "200.000").
0.71/0.99	    % set(auto2) -> assign(max_hours, 1).
0.71/0.99	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.71/0.99	    % set(auto2) -> assign(max_seconds, 0).
0.71/0.99	    % set(auto2) -> assign(max_minutes, 5).
0.71/0.99	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.71/0.99	    % set(auto2) -> set(sort_initial_sos).
0.71/0.99	    % set(auto2) -> assign(sos_limit, -1).
0.71/0.99	    % set(auto2) -> assign(lrs_ticks, 3000).
0.71/0.99	    % set(auto2) -> assign(max_megs, 400).
0.71/0.99	    % set(auto2) -> assign(stats, some).
0.71/0.99	    % set(auto2) -> clear(echo_input).
0.71/0.99	    % set(auto2) -> set(quiet).
0.71/0.99	    % set(auto2) -> clear(print_initial_clauses).
0.71/0.99	    % set(auto2) -> clear(print_given).
0.71/0.99	assign(lrs_ticks,-1).
0.71/0.99	assign(sos_limit,10000).
0.71/0.99	assign(order,kbo).
0.71/0.99	set(lex_order_vars).
0.71/0.99	clear(print_given).
0.71/0.99	
0.71/0.99	% formulas(sos).  % not echoed (17 formulas)
0.71/0.99	
0.71/0.99	============================== end of input ==========================
0.71/0.99	
0.71/0.99	% From the command line: assign(max_seconds, 960).
0.71/0.99	
0.71/0.99	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.71/0.99	
0.71/0.99	% Formulas that are not ordinary clauses:
0.71/0.99	1 (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].
0.71/0.99	2 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
0.71/0.99	3 (all X0 all X1 join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause).  [assumption].
0.71/0.99	4 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
0.71/0.99	5 (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].
0.71/0.99	6 (all X0 all X1 complement(join(complement(X0),complement(X1))) = meet(X0,X1)) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
0.71/0.99	7 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.71/0.99	8 (all X0 X0 = converse(converse(X0))) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.71/0.99	9 (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].
0.71/0.99	10 (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].
0.71/0.99	11 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
0.71/0.99	12 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
0.71/0.99	13 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
5.28/5.56	14 (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].
5.28/5.56	15 (all X0 all X1 all X2 composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) = join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))))) # label(dedekind_law) # label(axiom) # label(non_clause).  [assumption].
5.28/5.56	16 (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].
5.28/5.56	17 -(all X0 all X1 join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)) = complement(X0)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
5.28/5.56	
5.28/5.56	============================== end of process non-clausal formulas ===
5.28/5.56	
5.28/5.56	============================== PROCESS INITIAL CLAUSES ===============
5.28/5.56	
5.28/5.56	============================== PREDICATE ELIMINATION =================
5.28/5.56	
5.28/5.56	============================== end predicate elimination =============
5.28/5.56	
5.28/5.56	Auto_denials:
5.28/5.56	  % copying label goals to answer in negative clause
5.28/5.56	
5.28/5.56	Term ordering decisions:
5.28/5.56	Function symbol KB weights:  one=1. top=1. zero=1. c1=1. c2=1. composition=1. join=1. meet=1. converse=1. complement=1.
5.28/5.56	
5.28/5.56	============================== end of process initial clauses ========
5.28/5.56	
5.28/5.56	============================== CLAUSES FOR SEARCH ====================
5.28/5.56	
5.28/5.56	============================== end of clauses for search =============
5.28/5.56	
5.28/5.56	============================== SEARCH ================================
5.28/5.56	
5.28/5.56	% Starting search at 0.01 seconds.
5.28/5.56	
5.28/5.56	Low Water (keep): wt=86.000, iters=3408
5.28/5.56	
5.28/5.56	Low Water (keep): wt=77.000, iters=3340
5.28/5.56	
5.28/5.56	Low Water (keep): wt=76.000, iters=3442
5.28/5.56	
5.28/5.56	Low Water (keep): wt=74.000, iters=3361
5.28/5.56	
5.28/5.56	Low Water (keep): wt=73.000, iters=3348
5.28/5.56	
5.28/5.56	Low Water (keep): wt=72.000, iters=3345
5.28/5.56	
5.28/5.56	Low Water (keep): wt=71.000, iters=3370
5.28/5.56	
5.28/5.56	Low Water (keep): wt=70.000, iters=3337
5.28/5.56	
5.28/5.56	Low Water (keep): wt=69.000, iters=3343
5.28/5.56	
5.28/5.56	Low Water (keep): wt=68.000, iters=3441
5.28/5.56	
5.28/5.56	Low Water (keep): wt=67.000, iters=3401
5.28/5.56	
5.28/5.56	Low Water (keep): wt=66.000, iters=3400
5.28/5.56	
5.28/5.56	Low Water (keep): wt=64.000, iters=3397
5.28/5.56	
5.28/5.56	Low Water (keep): wt=63.000, iters=3451
5.28/5.56	
5.28/5.56	Low Water (keep): wt=62.000, iters=3496
5.28/5.56	
5.28/5.56	Low Water (keep): wt=61.000, iters=3447
5.28/5.56	
5.28/5.56	Low Water (keep): wt=60.000, iters=3369
5.28/5.56	
5.28/5.56	Low Water (keep): wt=59.000, iters=3356
5.28/5.56	
5.28/5.56	Low Water (keep): wt=57.000, iters=3390
5.28/5.56	
5.28/5.56	Low Water (keep): wt=56.000, iters=3409
5.28/5.56	
5.28/5.56	Low Water (keep): wt=54.000, iters=3376
5.28/5.56	
5.28/5.56	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 2.57 sec).
5.28/5.56	
5.28/5.56	Low Water (keep): wt=53.000, iters=3348
5.28/5.56	
5.28/5.56	Low Water (keep): wt=51.000, iters=3377
5.28/5.56	
5.28/5.56	Low Water (keep): wt=48.000, iters=3349
5.28/5.56	
5.28/5.56	Low Water (keep): wt=47.000, iters=3569
5.28/5.56	
5.28/5.56	Low Water (keep): wt=45.000, iters=3494
5.28/5.56	
5.28/5.56	Low Water (keep): wt=38.000, iters=3351
5.28/5.56	
5.28/5.56	Low Water (keep): wt=35.000, iters=3346
5.28/5.56	
5.28/5.56	Low Water (keep): wt=34.000, iters=3355
5.28/5.56	
5.28/5.56	Low Water (keep): wt=33.000, iters=3390
5.28/5.56	
5.28/5.56	Low Water (keep): wt=32.000, iters=3352
5.28/5.56	
5.28/5.56	Low Water (keep): wt=31.000, iters=3349
5.28/5.56	
5.28/5.56	Low Water (keep): wt=30.000, iters=3413
5.28/5.56	
5.28/5.56	Low Water (keep): wt=29.000, iters=3370
5.28/5.56	
5.28/5.56	Low Water (keep): wt=28.000, iters=3376
5.28/5.56	
5.28/5.56	Low Water (keep): wt=27.000, iters=3351
5.28/5.56	
5.28/5.56	Low Water (keep): wt=26.000, iters=3376
5.28/5.56	
5.28/5.56	Low Water (keep): wt=25.000, iters=3409
5.28/5.56	
5.28/5.56	Low Water (displace): id=4733, wt=87.000
5.28/5.56	
5.28/5.56	Low Water (displace): id=5890, wt=86.000
5.28/5.56	
5.28/5.56	Low Water (keep): wt=24.000, iters=3345
5.28/5.56	
5.28/5.56	Low Water (displace): id=16581, wt=23.000
5.28/5.56	
5.28/5.56	Low Water (displace): id=16586, wt=22.000
5.28/5.56	
5.28/5.56	Low Water (displace): id=16600, wt=21.000
5.28/5.56	
5.28/5.56	Low Water (displace): id=16656, wt=18.000
5.28/5.56	
5.28/5.56	Low Water (keep): wt=23.000, iters=3342
5.28/5.56	
5.28/5.56	Low Water (displace): id=16996, wt=17.000
5.28/5.56	
5.28/5.56	Low Water (displace): id=17095, wt=16.000
5.28/5.56	
5.28/5.56	Low Water (keep): wt=22.000, iters=3335
5.28/5.56	
5.28/5.56	Low Water (displace): id=18018, wt=14.000
5.28/5.56	
5.28/5.56	Low Water (keep): wt=21.000, iters=3334
5.43/5.71	
5.43/5.71	Low Water (displace): id=18443, wt=13.000
5.43/5.71	
5.43/5.71	============================== PROOF =================================
5.43/5.71	% SZS status Theorem
5.43/5.71	% SZS output start Refutation
5.43/5.71	
5.43/5.71	% Proof 1 at 4.64 (+ 0.09) seconds: goals.
5.43/5.71	% Length of proof is 125.
5.43/5.71	% Level of proof is 34.
5.43/5.71	% Maximum clause weight is 48.000.
5.43/5.71	% Given clauses 749.
5.43/5.71	
5.43/5.71	1 (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].
5.43/5.71	2 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	3 (all X0 all X1 join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0) # label(maddux3_a_kind_of_de_Morgan) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	4 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	5 (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].
5.43/5.71	6 (all X0 all X1 complement(join(complement(X0),complement(X1))) = meet(X0,X1)) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	7 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	8 (all X0 X0 = converse(converse(X0))) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	9 (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].
5.43/5.71	10 (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].
5.43/5.71	11 (all X0 X0 = composition(X0,one)) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	12 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	13 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	14 (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].
5.43/5.71	15 (all X0 all X1 all X2 composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) = join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))))) # label(dedekind_law) # label(axiom) # label(non_clause).  [assumption].
5.43/5.71	17 -(all X0 all X1 join(composition(complement(composition(X0,X1)),converse(X1)),complement(X0)) = complement(X0)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
5.43/5.71	18 converse(converse(A)) = A # label(converse_idempotence) # label(axiom).  [clausify(8)].
5.43/5.71	19 composition(A,one) = A # label(composition_identity) # label(axiom).  [clausify(11)].
5.43/5.71	20 join(A,complement(A)) = top # label(def_top) # label(axiom).  [clausify(4)].
5.43/5.71	21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom).  [clausify(12)].
5.43/5.71	22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom).  [clausify(7)].
5.43/5.71	23 converse(composition(A,B)) = composition(converse(B),converse(A)) # label(converse_multiplicativity) # label(axiom).  [clausify(2)].
5.43/5.71	24 composition(converse(A),converse(B)) = converse(composition(B,A)).  [copy(23),flip(a)].
5.43/5.71	25 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom).  [clausify(6)].
5.43/5.71	26 join(converse(A),converse(B)) = converse(join(A,B)) # label(converse_additivity) # label(axiom).  [clausify(13)].
5.43/5.71	27 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom).  [clausify(9)].
5.43/5.71	28 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom).  [clausify(10)].
5.43/5.71	29 join(A,join(B,C)) = join(C,join(A,B)).  [copy(28),rewrite([22(2)]),flip(a)].
5.43/5.71	30 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity) # label(axiom).  [clausify(1)].
5.43/5.71	31 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(30),rewrite([22(6)])].
5.43/5.71	32 join(composition(A,B),composition(C,B)) = composition(join(A,C),B) # label(composition_distributivity) # label(axiom).  [clausify(5)].
5.43/5.71	33 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom).  [clausify(3)].
5.43/5.71	34 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(33),rewrite([22(6),22(8)]),rewrite([22(6)])].
5.43/5.71	35 meet(composition(meet(A,composition(B,converse(C))),C),B) = join(meet(composition(A,C),B),meet(composition(meet(A,composition(B,converse(C))),C),B)) # label(modular_law_2) # label(axiom).  [clausify(14)].
5.43/5.71	36 join(complement(join(complement(A),complement(composition(B,C)))),complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C))))) = complement(join(complement(A),complement(composition(complement(join(complement(B),complement(composition(A,converse(C))))),C)))).  [copy(35),rewrite([25(3),25(8),22(10),25(13),22(15),25(19),25(24),22(26)]),flip(a)].
5.43/5.71	39 join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))) # label(dedekind_law) # label(axiom).  [clausify(15)].
5.43/5.71	40 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(39),rewrite([25(2),22(4),25(8),25(14),25(22),25(28)])].
5.43/5.71	41 join(composition(complement(composition(c1,c2)),converse(c2)),complement(c1)) != complement(c1) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(17)].
5.43/5.71	42 join(complement(c1),composition(complement(composition(c1,c2)),converse(c2))) != complement(c1) # answer(goals).  [copy(41),rewrite([22(10)])].
5.43/5.71	43 complement(top) = zero.  [back_rewrite(21),rewrite([25(2),20(4)])].
5.43/5.71	44 converse(composition(A,converse(B))) = composition(B,converse(A)).  [para(18(a,1),24(a,1,1)),flip(a)].
5.43/5.71	45 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(18(a,1),24(a,1,2)),flip(a)].
5.43/5.71	46 converse(join(A,converse(B))) = join(B,converse(A)).  [para(18(a,1),26(a,1,1)),rewrite([22(4)]),flip(a)].
5.43/5.71	47 composition(A,composition(one,B)) = composition(A,B).  [para(19(a,1),27(a,1,1)),flip(a)].
5.43/5.71	49 join(A,join(B,complement(A))) = join(B,top).  [para(20(a,1),29(a,2,2)),rewrite([22(2)])].
5.43/5.71	50 join(complement(A),composition(B,complement(composition(converse(B),A)))) = complement(A).  [para(18(a,1),31(a,1,2,1))].
5.43/5.71	51 join(complement(one),composition(converse(A),complement(A))) = complement(one).  [para(19(a,1),31(a,1,2,2,1))].
5.43/5.71	53 join(converse(complement(A)),composition(converse(complement(composition(B,A))),B)) = converse(complement(A)).  [para(31(a,1),26(a,2,1)),rewrite([45(7)])].
5.43/5.71	57 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C).  [para(27(a,1),32(a,1,1)),rewrite([22(6)])].
5.43/5.71	59 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(20(a,1),34(a,1,1,1)),rewrite([43(2)])].
5.43/5.71	89 join(zero,composition(converse(A),complement(composition(A,top)))) = zero.  [para(43(a,1),31(a,1,1)),rewrite([43(9)])].
5.43/5.71	91 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A.  [para(43(a,1),34(a,1,2,1,1))].
5.43/5.71	101 converse(join(A,composition(B,converse(C)))) = join(composition(C,converse(B)),converse(A)).  [para(44(a,1),26(a,1,1)),rewrite([22(7)]),flip(a)].
5.43/5.71	113 composition(converse(one),A) = A.  [para(19(a,1),45(a,1,1)),rewrite([18(2)]),flip(a)].
5.43/5.71	121 converse(one) = one.  [para(113(a,1),19(a,1)),flip(a)].
5.43/5.71	123 join(complement(A),composition(one,complement(A))) = complement(A).  [para(113(a,1),31(a,1,2,2,1)),rewrite([121(3),121(3)])].
5.43/5.71	125 join(A,composition(B,A)) = composition(join(B,one),A).  [para(113(a,1),32(a,1,1)),rewrite([121(4),22(4)])].
5.43/5.71	139 composition(one,A) = A.  [para(113(a,1),47(a,2)),rewrite([121(2),47(4)])].
5.43/5.71	142 join(complement(A),complement(A)) = complement(A).  [back_rewrite(123),rewrite([139(4)])].
5.43/5.71	146 join(zero,complement(complement(A))) = A.  [back_rewrite(59),rewrite([142(4)])].
5.43/5.71	149 converse(join(A,join(B,converse(C)))) = join(join(C,converse(A)),converse(B)).  [para(46(a,1),26(a,1,1)),rewrite([22(7),29(7,R),22(6)]),flip(a)].
5.43/5.71	150 join(join(A,converse(B)),converse(C)) = join(A,converse(join(B,C))).  [para(46(a,1),26(a,1,2)),rewrite([29(4,R),22(3),26(3),149(7)]),flip(a)].
5.43/5.71	156 join(join(A,B),converse(C)) = join(A,join(B,converse(C))).  [para(46(a,1),46(a,2,2)),rewrite([150(4),46(4),29(6,R),22(5)])].
5.43/5.71	157 converse(join(A,join(B,converse(C)))) = join(C,converse(join(A,B))).  [back_rewrite(149),rewrite([156(8),26(7)])].
5.43/5.71	158 converse(join(A,one)) = join(one,converse(A)).  [para(121(a,1),26(a,1,1)),rewrite([22(5)]),flip(a)].
5.43/5.71	187 join(top,complement(A)) = top.  [para(142(a,1),49(a,1,2)),rewrite([20(2),22(4)]),flip(a)].
5.43/5.71	188 join(zero,complement(join(zero,complement(A)))) = A.  [back_rewrite(91),rewrite([187(3),43(2)])].
5.43/5.71	189 join(top,top) = join(A,top).  [para(187(a,1),49(a,1,2)),flip(a)].
5.43/5.71	190 join(complement(one),composition(A,complement(converse(A)))) = complement(one).  [para(19(a,1),50(a,1,2,2,1))].
5.43/5.71	198 join(A,top) = join(B,top).  [para(189(a,1),49(a,2)),rewrite([187(3)])].
5.43/5.71	199 join(A,top) = c_0.  [new_symbol(198)].
5.43/5.71	202 join(A,join(B,complement(A))) = c_0.  [back_rewrite(49),rewrite([199(5)])].
5.43/5.71	207 c_0 = top.  [para(36(a,1),202(a,1,2)),rewrite([20(22)]),flip(a)].
5.43/5.71	208 join(A,join(B,complement(A))) = top.  [back_rewrite(202),rewrite([207(4)])].
5.43/5.71	210 join(A,top) = top.  [back_rewrite(199),rewrite([207(3)])].
5.43/5.71	218 join(zero,complement(A)) = complement(A).  [para(146(a,1),188(a,1,2,1))].
5.43/5.71	219 complement(complement(A)) = A.  [back_rewrite(188),rewrite([218(4),218(4)])].
5.43/5.71	243 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B).  [para(219(a,1),34(a,1,1,1,2)),rewrite([219(5),22(4)])].
5.43/5.71	251 complement(zero) = top.  [para(43(a,1),219(a,1,1))].
5.43/5.71	252 join(A,A) = A.  [para(219(a,1),142(a,1,1)),rewrite([219(2),219(3)])].
5.43/5.71	254 join(complement(one),composition(converse(complement(A)),A)) = complement(one).  [para(219(a,1),51(a,1,2,2))].
5.43/5.71	261 join(A,join(A,B)) = join(A,B).  [para(252(a,1),29(a,1)),rewrite([22(3),29(4,R),22(3),29(3,R),252(2)]),flip(a)].
5.43/5.71	265 join(converse(A),composition(converse(complement(composition(B,complement(A)))),B)) = converse(A).  [para(219(a,1),53(a,1,1,1)),rewrite([219(9)])].
5.43/5.71	267 join(A,complement(join(B,complement(A)))) = A.  [para(34(a,1),261(a,1,2)),rewrite([22(4),34(12)])].
5.43/5.71	272 join(complement(A),complement(join(A,B))) = complement(A).  [para(219(a,1),267(a,1,2,1,2)),rewrite([22(2)])].
5.43/5.71	292 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero.  [para(158(a,1),89(a,1,2,1))].
5.43/5.71	321 join(complement(A),complement(composition(join(B,one),A))) = complement(A).  [para(125(a,1),272(a,1,2,1))].
5.43/5.71	328 join(complement(one),converse(complement(one))) = complement(one).  [para(19(a,1),254(a,1,2))].
5.43/5.71	338 converse(complement(one)) = complement(one).  [para(328(a,1),26(a,2,1)),rewrite([18(7),22(6),328(6)]),flip(a)].
5.43/5.71	347 converse(top) = top.  [para(338(a,1),158(a,2,2)),rewrite([22(4),20(4),20(6)])].
5.43/5.71	354 join(top,converse(A)) = top.  [para(347(a,1),26(a,1,1)),rewrite([22(5),210(5),347(5)])].
5.43/5.71	358 join(top,composition(A,converse(B))) = top.  [para(44(a,1),354(a,1,2))].
5.43/5.71	366 join(top,composition(A,B)) = top.  [para(18(a,1),358(a,1,2,2))].
5.43/5.71	367 composition(join(A,one),top) = top.  [para(347(a,1),358(a,1,2,2)),rewrite([125(4)])].
5.43/5.71	368 composition(join(one,converse(A)),zero) = zero.  [back_rewrite(292),rewrite([367(8),43(6),125(7),22(5),261(5)])].
5.43/5.71	391 composition(top,zero) = zero.  [para(338(a,1),368(a,1,1,2)),rewrite([20(4)])].
5.43/5.71	401 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)).  [para(391(a,1),40(a,1,1,1,2,1)),rewrite([251(3),22(3),187(3),43(2),43(3),218(7),219(6),251(6),347(7),187(9),43(6),27(6),43(9),218(13),219(12),251(12),347(13),187(15),43(12),27(12)])].
5.43/5.71	406 join(zero,composition(A,composition(B,zero))) = zero.  [para(391(a,1),57(a,1,2)),rewrite([22(5),366(8),391(8)])].
5.43/5.71	408 composition(A,composition(converse(zero),zero)) = zero.  [back_rewrite(401),rewrite([406(7)]),flip(a)].
5.43/5.71	475 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B).  [para(408(a,1),27(a,1,1)),rewrite([27(7)]),flip(a)].
5.43/5.71	476 composition(A,zero) = zero.  [para(408(a,1),27(a,1)),rewrite([408(6)]),flip(a)].
5.43/5.71	477 composition(converse(zero),A) = converse(zero).  [para(408(a,1),45(a,1,1)),rewrite([476(6)]),flip(a)].
5.43/5.71	482 composition(zero,A) = composition(B,converse(zero)).  [back_rewrite(475),rewrite([477(5)]),flip(a)].
5.43/5.71	516 converse(zero) = zero.  [para(477(a,1),476(a,1))].
5.43/5.71	523 composition(zero,A) = zero.  [back_rewrite(482),rewrite([516(4),476(4)])].
5.43/5.71	3570 join(complement(A),composition(join(B,one),A)) = top.  [para(321(a,1),208(a,1,2)),rewrite([22(5)])].
5.43/5.71	3648 join(A,composition(join(B,one),complement(A))) = top.  [para(219(a,1),3570(a,1,1))].
5.43/5.71	3651 join(A,join(B,composition(join(C,one),complement(A)))) = top.  [para(3648(a,1),29(a,2,2)),rewrite([22(5),210(8)])].
5.43/5.71	7742 join(complement(A),composition(join(one,converse(B)),A)) = top.  [para(50(a,1),3651(a,1,2)),rewrite([158(3),22(6)])].
5.43/5.71	7752 join(converse(complement(converse(A))),composition(A,join(B,one))) = top.  [para(7742(a,1),101(a,1,1)),rewrite([347(2),46(5),121(3),22(8)]),flip(a)].
5.43/5.71	9380 join(A,converse(complement(converse(A)))) = top.  [para(252(a,1),7752(a,1,2,2)),rewrite([19(5),22(4)])].
5.43/5.71	9411 join(complement(converse(A)),converse(join(B,A))) = top.  [para(9380(a,1),157(a,1,1,2)),rewrite([210(2),347(2)]),flip(a)].
5.43/5.71	9415 complement(join(complement(A),converse(complement(converse(A))))) = complement(converse(complement(converse(A)))).  [para(9380(a,1),243(a,1,1,1)),rewrite([43(2),22(6),218(8)])].
5.43/5.71	9474 join(complement(one),complement(composition(converse(complement(A)),A))) = top.  [para(51(a,1),9411(a,1,2,1)),rewrite([45(4),338(7),22(7)])].
5.43/5.71	9481 join(complement(one),complement(converse(composition(A,complement(converse(A)))))) = top.  [para(190(a,1),9411(a,1,2,1)),rewrite([338(8),22(8)])].
5.43/5.71	9568 complement(join(complement(A),complement(converse(complement(converse(A)))))) = zero.  [para(9474(a,1),36(a,1,2,1,2,1,1,1)),rewrite([139(6),22(6),43(13),523(13),251(13),22(13),187(13),43(9),22(9),218(9),24(18),9481(19),43(13),523(13),251(13),22(13),187(13),43(9)])].
5.43/5.71	9711 complement(join(A,complement(converse(complement(converse(A)))))) = converse(complement(converse(A))).  [para(9568(a,1),34(a,1,1)),rewrite([219(3),218(8)])].
5.43/5.71	9727 complement(converse(complement(converse(A)))) = A.  [para(9568(a,1),243(a,1,2)),rewrite([22(5),9415(6),22(6),218(6),219(6)])].
5.43/5.71	9728 converse(complement(converse(A))) = complement(A).  [back_rewrite(9711),rewrite([9727(4),252(1)]),flip(a)].
5.43/5.71	9765 complement(converse(A)) = converse(complement(A)).  [para(9728(a,1),18(a,1,1)),flip(a)].
5.43/5.71	9768 converse(complement(composition(A,converse(B)))) = complement(composition(B,converse(A))).  [para(44(a,1),9728(a,1,1,1))].
5.43/5.71	12401 join(A,composition(complement(composition(complement(A),converse(B))),B)) = A.  [para(18(a,1),265(a,1,1)),rewrite([9765(2),9768(5),18(8)])].
5.43/5.71	16481 join(A,composition(complement(composition(complement(A),B)),converse(B))) = A.  [para(18(a,1),12401(a,1,2,1,1,2))].
5.43/5.71	18487 join(complement(A),composition(complement(composition(A,B)),converse(B))) = complement(A).  [para(219(a,1),16481(a,1,2,1,1,1))].
5.43/5.71	18488 $F # answer(goals).  [resolve(18487,a,42,a)].
5.43/5.71	
5.43/5.71	% SZS output end Refutation
5.43/5.71	============================== end of proof ==========================
5.43/5.71	
5.43/5.71	============================== STATISTICS ============================
5.43/5.71	
5.43/5.71	Given=749. Generated=147452. Kept=18462. proofs=1.
5.43/5.71	Usable=566. Sos=9999. Demods=10263. Limbo=3, Disabled=7910. Hints=0.
5.43/5.71	Megabytes=28.58.
5.43/5.71	User_CPU=4.64, System_CPU=0.09, Wall_clock=5.
5.43/5.71	
5.43/5.71	============================== end of statistics =====================
5.43/5.71	
5.43/5.71	============================== end of search =========================
5.43/5.71	
5.43/5.71	THEOREM PROVED
5.43/5.71	% SZS status Theorem
5.43/5.71	
5.43/5.71	Exiting with 1 proof.
5.43/5.71	
5.43/5.71	Process 28985 exit (max_proofs) Thu Jul  2 07:20:26 2020
5.43/5.71	Prover9 interrupted
5.43/5.71	EOF