0.11/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% 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   : 1200
0.12/0.33	% DateTime   : Tue Jul 13 16:37:34 EDT 2021
0.12/0.33	% CPUTime    : 
0.71/1.00	============================== Prover9 ===============================
0.71/1.00	Prover9 (32) version 2009-11A, November 2009.
0.71/1.00	Process 25190 was started by sandbox2 on n014.cluster.edu,
0.71/1.00	Tue Jul 13 16:37:35 2021
0.71/1.00	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_25020_n014.cluster.edu".
0.71/1.00	============================== end of head ===========================
0.71/1.00	
0.71/1.00	============================== INPUT =================================
0.71/1.00	
0.71/1.00	% Reading from file /tmp/Prover9_25020_n014.cluster.edu
0.71/1.00	
0.71/1.00	set(prolog_style_variables).
0.71/1.00	set(auto2).
0.71/1.00	    % set(auto2) -> set(auto).
0.71/1.00	    % set(auto) -> set(auto_inference).
0.71/1.00	    % set(auto) -> set(auto_setup).
0.71/1.00	    % set(auto_setup) -> set(predicate_elim).
0.71/1.00	    % set(auto_setup) -> assign(eq_defs, unfold).
0.71/1.00	    % set(auto) -> set(auto_limits).
0.71/1.00	    % set(auto_limits) -> assign(max_weight, "100.000").
0.71/1.00	    % set(auto_limits) -> assign(sos_limit, 20000).
0.71/1.00	    % set(auto) -> set(auto_denials).
0.71/1.00	    % set(auto) -> set(auto_process).
0.71/1.00	    % set(auto2) -> assign(new_constants, 1).
0.71/1.00	    % set(auto2) -> assign(fold_denial_max, 3).
0.71/1.00	    % set(auto2) -> assign(max_weight, "200.000").
0.71/1.00	    % set(auto2) -> assign(max_hours, 1).
0.71/1.00	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.71/1.00	    % set(auto2) -> assign(max_seconds, 0).
0.71/1.00	    % set(auto2) -> assign(max_minutes, 5).
0.71/1.00	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.71/1.00	    % set(auto2) -> set(sort_initial_sos).
0.71/1.00	    % set(auto2) -> assign(sos_limit, -1).
0.71/1.00	    % set(auto2) -> assign(lrs_ticks, 3000).
0.71/1.00	    % set(auto2) -> assign(max_megs, 400).
0.71/1.00	    % set(auto2) -> assign(stats, some).
0.71/1.00	    % set(auto2) -> clear(echo_input).
0.71/1.00	    % set(auto2) -> set(quiet).
0.71/1.00	    % set(auto2) -> clear(print_initial_clauses).
0.71/1.00	    % set(auto2) -> clear(print_given).
0.71/1.00	assign(lrs_ticks,-1).
0.71/1.00	assign(sos_limit,10000).
0.71/1.00	assign(order,kbo).
0.71/1.00	set(lex_order_vars).
0.71/1.00	clear(print_given).
0.71/1.00	
0.71/1.00	% formulas(sos).  % not echoed (17 formulas)
0.71/1.00	
0.71/1.00	============================== end of input ==========================
0.71/1.00	
0.71/1.00	% From the command line: assign(max_seconds, 1200).
0.71/1.00	
0.71/1.00	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.71/1.00	
0.71/1.00	% Formulas that are not ordinary clauses:
0.71/1.00	1 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.71/1.00	2 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
0.71/1.00	3 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
0.71/1.00	4 (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].
0.71/1.00	5 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
0.71/1.00	6 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
0.71/1.00	7 (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].
0.71/1.00	8 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
0.71/1.00	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].
0.71/1.00	10 (all X0 all X1 all X2 join(join(X0,X1),X2) = join(X0,join(X1,X2))) # label(maddux2_join_associativity) # label(axiom) # label(non_clause).  [assumption].
0.71/1.00	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].
0.71/1.00	12 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.71/1.00	13 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	14 (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].
3.34/3.63	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].
3.34/3.63	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].
3.34/3.63	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].
3.34/3.63	
3.34/3.63	============================== end of process non-clausal formulas ===
3.34/3.63	
3.34/3.63	============================== PROCESS INITIAL CLAUSES ===============
3.34/3.63	
3.34/3.63	============================== PREDICATE ELIMINATION =================
3.34/3.63	
3.34/3.63	============================== end predicate elimination =============
3.34/3.63	
3.34/3.63	Auto_denials:
3.34/3.63	  % copying label goals to answer in negative clause
3.34/3.63	
3.34/3.63	Term ordering decisions:
3.34/3.63	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.
3.34/3.63	
3.34/3.63	============================== end of process initial clauses ========
3.34/3.63	
3.34/3.63	============================== CLAUSES FOR SEARCH ====================
3.34/3.63	
3.34/3.63	============================== end of clauses for search =============
3.34/3.63	
3.34/3.63	============================== SEARCH ================================
3.34/3.63	
3.34/3.63	% Starting search at 0.01 seconds.
3.34/3.63	
3.34/3.63	Low Water (keep): wt=157.000, iters=3403
3.34/3.63	
3.34/3.63	Low Water (keep): wt=131.000, iters=3385
3.34/3.63	
3.34/3.63	Low Water (keep): wt=83.000, iters=3353
3.34/3.63	
3.34/3.63	Low Water (keep): wt=81.000, iters=3396
3.34/3.63	
3.34/3.63	Low Water (keep): wt=80.000, iters=3454
3.34/3.63	
3.34/3.63	Low Water (keep): wt=78.000, iters=3415
3.34/3.63	
3.34/3.63	Low Water (keep): wt=76.000, iters=3381
3.34/3.63	
3.34/3.63	Low Water (keep): wt=74.000, iters=3343
3.34/3.63	
3.34/3.63	Low Water (keep): wt=73.000, iters=3383
3.34/3.63	
3.34/3.63	Low Water (keep): wt=72.000, iters=3352
3.34/3.63	
3.34/3.63	Low Water (keep): wt=71.000, iters=3414
3.34/3.63	
3.34/3.63	Low Water (keep): wt=70.000, iters=3358
3.34/3.63	
3.34/3.63	Low Water (keep): wt=69.000, iters=3341
3.34/3.63	
3.34/3.63	Low Water (keep): wt=68.000, iters=3401
3.34/3.63	
3.34/3.63	Low Water (keep): wt=65.000, iters=3450
3.34/3.63	
3.34/3.63	Low Water (keep): wt=64.000, iters=3348
3.34/3.63	
3.34/3.63	Low Water (keep): wt=63.000, iters=3375
3.34/3.63	
3.34/3.63	Low Water (keep): wt=62.000, iters=3338
3.34/3.63	
3.34/3.63	Low Water (keep): wt=61.000, iters=3440
3.34/3.63	
3.34/3.63	Low Water (keep): wt=60.000, iters=3385
3.34/3.63	
3.34/3.63	Low Water (keep): wt=59.000, iters=3385
3.34/3.63	
3.34/3.63	Low Water (keep): wt=58.000, iters=3448
3.34/3.63	
3.34/3.63	Low Water (keep): wt=57.000, iters=3444
3.34/3.63	
3.34/3.63	Low Water (keep): wt=56.000, iters=3455
3.34/3.63	
3.34/3.63	Low Water (keep): wt=55.000, iters=3395
3.34/3.63	
3.34/3.63	Low Water (keep): wt=53.000, iters=3342
3.34/3.63	
3.34/3.63	Low Water (keep): wt=52.000, iters=3366
3.34/3.63	
3.34/3.63	Low Water (keep): wt=51.000, iters=3445
3.34/3.63	
3.34/3.63	Low Water (keep): wt=50.000, iters=3365
3.34/3.63	
3.34/3.63	Low Water (keep): wt=49.000, iters=3381
3.34/3.63	
3.34/3.63	Low Water (keep): wt=48.000, iters=3385
3.34/3.63	
3.34/3.63	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 2.39 sec).
3.34/3.63	
3.34/3.63	Low Water (keep): wt=44.000, iters=3401
3.34/3.63	
3.34/3.63	Low Water (keep): wt=43.000, iters=3361
3.34/3.63	
3.34/3.63	Low Water (keep): wt=39.000, iters=3360
3.34/3.63	
3.34/3.63	Low Water (keep): wt=38.000, iters=3458
3.34/3.63	
3.34/3.63	Low Water (keep): wt=36.000, iters=3388
3.34/3.63	
3.34/3.63	Low Water (keep): wt=35.000, iters=3347
3.34/3.63	
3.34/3.63	Low Water (keep): wt=25.000, iters=4737
3.34/3.63	
3.34/3.63	Low Water (keep): wt=22.000, iters=3892
3.34/3.63	
3.34/3.63	Low Water (keep): wt=21.000, iters=3551
3.34/3.63	
3.34/3.63	============================== PROOF =================================
3.34/3.63	% SZS status Theorem
3.34/3.63	% SZS output start Refutation
3.34/3.63	
3.34/3.63	% Proof 1 at 2.60 (+ 0.05) seconds: goals.
3.34/3.63	% Length of proof is 105.
3.34/3.63	% Level of proof is 30.
3.34/3.63	% Maximum clause weight is 49.000.
3.34/3.63	% Given clauses 526.
3.34/3.63	
3.34/3.63	1 (all X0 converse(converse(X0)) = X0) # label(converse_idempotence) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	2 (all X0 all X1 meet(X0,X1) = complement(join(complement(X0),complement(X1)))) # label(maddux4_definiton_of_meet) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	3 (all X0 join(X0,complement(X0)) = top) # label(def_top) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	4 (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].
3.34/3.63	5 (all X0 composition(X0,one) = X0) # label(composition_identity) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	6 (all X0 zero = meet(X0,complement(X0))) # label(def_zero) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	7 (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].
3.34/3.63	8 (all X0 all X1 converse(composition(X0,X1)) = composition(converse(X1),converse(X0))) # label(converse_multiplicativity) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	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].
3.34/3.63	10 (all X0 all X1 all X2 join(join(X0,X1),X2) = join(X0,join(X1,X2))) # label(maddux2_join_associativity) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	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].
3.34/3.63	12 (all X0 all X1 join(X0,X1) = join(X1,X0)) # label(maddux1_join_commutativity) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	13 (all X0 all X1 converse(join(X0,X1)) = join(converse(X0),converse(X1))) # label(converse_additivity) # label(axiom) # label(non_clause).  [assumption].
3.34/3.63	14 (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].
3.34/3.63	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].
3.34/3.63	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].
3.34/3.63	18 converse(converse(A)) = A # label(converse_idempotence) # label(axiom).  [clausify(1)].
3.34/3.63	19 composition(A,one) = A # label(composition_identity) # label(axiom).  [clausify(5)].
3.34/3.63	20 join(A,complement(A)) = top # label(def_top) # label(axiom).  [clausify(3)].
3.34/3.63	21 meet(A,complement(A)) = zero # label(def_zero) # label(axiom).  [clausify(6)].
3.34/3.63	22 join(A,B) = join(B,A) # label(maddux1_join_commutativity) # label(axiom).  [clausify(12)].
3.34/3.63	23 meet(A,B) = complement(join(complement(A),complement(B))) # label(maddux4_definiton_of_meet) # label(axiom).  [clausify(2)].
3.34/3.63	24 composition(converse(A),converse(B)) = converse(composition(B,A)) # label(converse_multiplicativity) # label(axiom).  [clausify(8)].
3.34/3.63	25 join(converse(A),converse(B)) = converse(join(A,B)) # label(converse_additivity) # label(axiom).  [clausify(13)].
3.34/3.63	26 join(composition(complement(c1),c2),complement(c3)) = complement(c3) # label(goals) # label(negated_conjecture).  [clausify(17)].
3.34/3.63	27 join(complement(c3),composition(complement(c1),c2)) = complement(c3).  [copy(26),rewrite([22(7)])].
3.34/3.63	28 composition(composition(A,B),C) = composition(A,composition(B,C)) # label(composition_associativity) # label(axiom).  [clausify(4)].
3.34/3.63	29 join(join(A,B),C) = join(A,join(B,C)) # label(maddux2_join_associativity) # label(axiom).  [clausify(10)].
3.34/3.63	30 join(A,join(B,C)) = join(C,join(A,B)).  [copy(29),rewrite([22(2)]),flip(a)].
3.34/3.63	31 composition(join(A,B),C) = join(composition(A,C),composition(B,C)) # label(composition_distributivity) # label(axiom).  [clausify(9)].
3.34/3.63	32 join(composition(A,B),composition(C,B)) = composition(join(A,C),B).  [copy(31),flip(a)].
3.34/3.63	33 join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) # label(converse_cancellativity) # label(axiom).  [clausify(11)].
3.34/3.63	34 join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A).  [copy(33),rewrite([22(6)])].
3.34/3.63	35 join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A # label(maddux3_a_kind_of_de_Morgan) # label(axiom).  [clausify(7)].
3.34/3.63	36 join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B.  [copy(35),rewrite([22(6),22(8)]),rewrite([22(6)])].
3.34/3.63	37 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(15)].
3.34/3.63	38 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(37),rewrite([23(3),23(8),22(10),23(13),22(15),23(19),23(24),22(26)]),flip(a)].
3.34/3.63	41 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(14)].
3.34/3.63	42 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(41),rewrite([23(3),23(9),23(15),22(17),23(21),23(27)]),flip(a)].
3.34/3.63	43 join(composition(c3,converse(c2)),c1) != c1 # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(17)].
3.34/3.63	44 join(c1,composition(c3,converse(c2))) != c1 # answer(goals).  [copy(43),rewrite([22(6)])].
3.34/3.63	45 complement(top) = zero.  [back_rewrite(21),rewrite([23(2),20(4)])].
3.34/3.63	46 converse(composition(A,converse(B))) = composition(B,converse(A)).  [para(18(a,1),24(a,1,1)),flip(a)].
3.34/3.63	47 converse(composition(converse(A),B)) = composition(converse(B),A).  [para(18(a,1),24(a,1,2)),flip(a)].
3.34/3.63	49 composition(A,composition(one,B)) = composition(A,B).  [para(19(a,1),28(a,1,1)),flip(a)].
3.34/3.63	51 join(A,join(B,complement(A))) = join(B,top).  [para(20(a,1),30(a,2,2)),rewrite([22(2)])].
3.34/3.63	55 join(composition(A,composition(B,C)),composition(D,C)) = composition(join(D,composition(A,B)),C).  [para(28(a,1),32(a,1,1)),rewrite([22(6)])].
3.34/3.63	58 join(complement(one),composition(converse(A),complement(A))) = complement(one).  [para(19(a,1),34(a,1,2,2,1))].
3.34/3.63	62 join(zero,complement(join(complement(A),complement(A)))) = A.  [para(20(a,1),36(a,1,1,1)),rewrite([45(2)])].
3.34/3.63	83 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(18(a,1),42(a,1,2,1,1,2,1,2)),rewrite([18(23)])].
3.34/3.63	92 join(zero,composition(converse(A),complement(composition(A,top)))) = zero.  [para(45(a,1),34(a,1,1)),rewrite([45(9)])].
3.34/3.63	94 join(complement(join(top,complement(A))),complement(join(zero,complement(A)))) = A.  [para(45(a,1),36(a,1,2,1,1))].
3.34/3.63	116 composition(converse(one),A) = A.  [para(19(a,1),47(a,1,1)),rewrite([18(2)]),flip(a)].
3.34/3.63	124 converse(one) = one.  [para(116(a,1),19(a,1)),flip(a)].
3.34/3.63	126 composition(join(A,one),B) = join(B,composition(A,B)).  [para(116(a,1),32(a,1,1)),rewrite([124(4),22(4)]),flip(a)].
3.34/3.63	128 join(complement(A),complement(composition(one,A))) = complement(A).  [para(116(a,1),34(a,1,2))].
3.34/3.63	142 composition(one,A) = A.  [para(116(a,1),49(a,2)),rewrite([124(2),49(4)])].
3.34/3.63	148 join(complement(A),complement(A)) = complement(A).  [back_rewrite(128),rewrite([142(3)])].
3.34/3.63	149 join(zero,complement(complement(A))) = A.  [back_rewrite(62),rewrite([148(4)])].
3.34/3.63	161 converse(join(A,one)) = join(one,converse(A)).  [para(124(a,1),25(a,1,1)),rewrite([22(5)]),flip(a)].
3.34/3.63	206 join(top,complement(A)) = top.  [para(148(a,1),51(a,1,2)),rewrite([20(2),22(4)]),flip(a)].
3.34/3.63	207 join(zero,complement(join(zero,complement(A)))) = A.  [back_rewrite(94),rewrite([206(3),45(2)])].
3.34/3.63	208 join(top,top) = join(A,top).  [para(206(a,1),51(a,1,2)),flip(a)].
3.34/3.63	213 join(A,top) = join(B,top).  [para(208(a,1),51(a,2)),rewrite([206(3)])].
3.34/3.63	214 join(A,top) = c_0.  [new_symbol(213)].
3.34/3.63	217 join(A,join(B,complement(A))) = c_0.  [back_rewrite(51),rewrite([214(5)])].
3.34/3.63	231 c_0 = top.  [para(38(a,1),217(a,1,2)),rewrite([20(22)]),flip(a)].
3.34/3.63	234 join(A,top) = top.  [back_rewrite(214),rewrite([231(3)])].
3.34/3.63	249 join(zero,complement(A)) = complement(A).  [para(149(a,1),207(a,1,2,1))].
3.34/3.63	250 complement(complement(A)) = A.  [back_rewrite(207),rewrite([249(4),249(4)])].
3.34/3.63	281 join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B).  [para(250(a,1),36(a,1,1,1,2)),rewrite([250(5),22(4)])].
3.34/3.63	289 complement(zero) = top.  [para(45(a,1),250(a,1,1))].
3.34/3.63	290 join(A,A) = A.  [para(250(a,1),148(a,1,1)),rewrite([250(2),250(3)])].
3.34/3.63	302 join(A,join(A,B)) = join(A,B).  [para(290(a,1),30(a,1)),rewrite([22(3),30(4,R),22(3),30(3,R),290(2)]),flip(a)].
3.34/3.63	303 join(A,complement(join(B,complement(A)))) = A.  [para(36(a,1),302(a,1,2)),rewrite([22(4),36(12)])].
3.34/3.63	306 join(A,join(B,complement(join(C,complement(A))))) = join(A,B).  [para(303(a,1),30(a,2,2)),rewrite([22(4),22(6)])].
3.34/3.63	325 join(complement(one),composition(converse(complement(A)),A)) = complement(one).  [para(250(a,1),58(a,1,2,2))].
3.34/3.63	340 join(zero,composition(join(one,converse(A)),complement(composition(join(A,one),top)))) = zero.  [para(161(a,1),92(a,1,2,1))].
3.34/3.63	376 join(complement(one),converse(complement(one))) = complement(one).  [para(19(a,1),325(a,1,2))].
3.34/3.63	380 converse(complement(one)) = complement(one).  [para(376(a,1),25(a,2,1)),rewrite([18(7),22(6),376(6)]),flip(a)].
3.34/3.63	394 converse(top) = top.  [para(380(a,1),161(a,2,2)),rewrite([22(4),20(4),20(6)])].
3.34/3.63	402 join(top,converse(A)) = top.  [para(394(a,1),25(a,1,1)),rewrite([22(5),234(5),394(5)])].
3.34/3.63	407 join(top,composition(A,converse(B))) = top.  [para(46(a,1),402(a,1,2))].
3.34/3.63	409 join(top,composition(A,B)) = top.  [para(18(a,1),407(a,1,2,2))].
3.34/3.63	410 composition(join(A,one),top) = top.  [para(394(a,1),407(a,1,2,2)),rewrite([126(4,R)])].
3.34/3.63	411 composition(join(one,converse(A)),zero) = zero.  [back_rewrite(340),rewrite([410(8),45(6),126(7,R),22(5),302(5)])].
3.34/3.63	443 composition(top,zero) = zero.  [para(380(a,1),411(a,1,1,2)),rewrite([20(4)])].
3.34/3.63	447 join(zero,composition(A,composition(converse(zero),zero))) = composition(A,composition(converse(zero),zero)).  [para(443(a,1),42(a,1,1,1,2,1)),rewrite([289(3),22(3),206(3),45(2),45(3),249(7),250(6),289(6),394(7),206(9),45(6),28(6),45(9),249(13),250(12),289(12),394(13),206(15),45(12),28(12)])].
3.34/3.63	451 join(zero,composition(A,composition(B,zero))) = zero.  [para(443(a,1),55(a,1,2)),rewrite([22(5),409(8),443(8)])].
3.34/3.63	454 composition(A,composition(converse(zero),zero)) = zero.  [back_rewrite(447),rewrite([451(7)]),flip(a)].
3.34/3.63	539 composition(A,composition(converse(zero),composition(zero,B))) = composition(zero,B).  [para(454(a,1),28(a,1,1)),rewrite([28(7)]),flip(a)].
3.34/3.63	540 composition(A,zero) = zero.  [para(454(a,1),28(a,1)),rewrite([454(6)]),flip(a)].
3.34/3.63	541 composition(converse(zero),A) = converse(zero).  [para(454(a,1),47(a,1,1)),rewrite([540(6)]),flip(a)].
3.34/3.63	547 composition(zero,A) = composition(B,converse(zero)).  [back_rewrite(539),rewrite([541(5)]),flip(a)].
3.34/3.63	581 converse(zero) = zero.  [para(541(a,1),540(a,1))].
3.34/3.63	589 composition(zero,A) = zero.  [back_rewrite(547),rewrite([581(4),540(4)])].
3.34/3.63	11622 join(A,complement(join(A,B))) = join(A,complement(B)).  [para(281(a,1),306(a,1,2)),flip(a)].
3.34/3.63	11637 join(complement(c3),complement(composition(complement(c1),c2))) = top.  [para(27(a,1),11622(a,1,2,1)),rewrite([250(5),22(4),20(4)]),flip(a)].
3.34/3.63	11799 complement(join(c1,complement(composition(c3,converse(c2))))) = zero.  [para(11637(a,1),83(a,1,2,1,1)),rewrite([250(3),45(10),589(21),22(10),249(10),11637(16),45(10),589(21)])].
3.34/3.63	11816 complement(join(c1,composition(c3,converse(c2)))) = complement(c1).  [para(11799(a,1),281(a,1,2)),rewrite([22(6),22(9),249(9)])].
3.34/3.63	11817 join(c1,composition(c3,converse(c2))) = join(zero,c1).  [para(11799(a,1),11622(a,1,2)),rewrite([22(3),250(10)]),flip(a)].
3.34/3.63	11818 complement(join(zero,c1)) = complement(c1).  [back_rewrite(11816),rewrite([11817(6)])].
3.34/3.63	11819 join(zero,c1) != c1 # answer(goals).  [back_rewrite(44),rewrite([11817(6)])].
3.34/3.63	11840 join(zero,c1) = c1.  [para(11818(a,1),36(a,1,1,1,2)),rewrite([11818(9),36(10)]),flip(a)].
3.34/3.63	11841 $F # answer(goals).  [resolve(11840,a,11819,a)].
3.34/3.63	
3.34/3.63	% SZS output end Refutation
3.34/3.63	============================== end of proof ==========================
3.34/3.63	
3.34/3.63	============================== STATISTICS ============================
3.34/3.63	
3.34/3.63	Given=526. Generated=74344. Kept=11814. proofs=1.
3.34/3.63	Usable=430. Sos=9702. Demods=9832. Limbo=1, Disabled=1698. Hints=0.
3.34/3.63	Megabytes=25.10.
3.34/3.63	User_CPU=2.60, System_CPU=0.05, Wall_clock=2.
3.34/3.63	
3.34/3.63	============================== end of statistics =====================
3.34/3.63	
3.34/3.63	============================== end of search =========================
3.34/3.63	
3.34/3.63	THEOREM PROVED
3.34/3.63	% SZS status Theorem
3.34/3.63	
3.34/3.63	Exiting with 1 proof.
3.34/3.63	
3.34/3.63	Process 25190 exit (max_proofs) Tue Jul 13 16:37:37 2021
3.34/3.63	Prover9 interrupted
3.34/3.64	EOF