0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : tptp2X_and_run_prover9 %d %s
0.02/0.23	% Computer   : n068.star.cs.uiowa.edu
0.02/0.23	% Model      : x86_64 x86_64
0.02/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.23	% Memory     : 32218.625MB
0.02/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.23	% CPULimit   : 300
0.02/0.23	% DateTime   : Sat Jul 14 05:18:40 CDT 2018
0.02/0.24	% CPUTime    : 
0.07/0.44	============================== Prover9 ===============================
0.07/0.44	Prover9 (32) version 2009-11A, November 2009.
0.07/0.44	Process 55059 was started by sandbox on n068.star.cs.uiowa.edu,
0.07/0.44	Sat Jul 14 05:18:40 2018
0.07/0.44	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_55027_n068.star.cs.uiowa.edu".
0.07/0.44	============================== end of head ===========================
0.07/0.44	
0.07/0.44	============================== INPUT =================================
0.07/0.44	
0.07/0.44	% Reading from file /tmp/Prover9_55027_n068.star.cs.uiowa.edu
0.07/0.44	
0.07/0.44	set(prolog_style_variables).
0.07/0.44	set(auto2).
0.07/0.44	    % set(auto2) -> set(auto).
0.07/0.44	    % set(auto) -> set(auto_inference).
0.07/0.44	    % set(auto) -> set(auto_setup).
0.07/0.44	    % set(auto_setup) -> set(predicate_elim).
0.07/0.44	    % set(auto_setup) -> assign(eq_defs, unfold).
0.07/0.44	    % set(auto) -> set(auto_limits).
0.07/0.44	    % set(auto_limits) -> assign(max_weight, "100.000").
0.07/0.44	    % set(auto_limits) -> assign(sos_limit, 20000).
0.07/0.44	    % set(auto) -> set(auto_denials).
0.07/0.44	    % set(auto) -> set(auto_process).
0.07/0.44	    % set(auto2) -> assign(new_constants, 1).
0.07/0.44	    % set(auto2) -> assign(fold_denial_max, 3).
0.07/0.44	    % set(auto2) -> assign(max_weight, "200.000").
0.07/0.44	    % set(auto2) -> assign(max_hours, 1).
0.07/0.44	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.07/0.44	    % set(auto2) -> assign(max_seconds, 0).
0.07/0.44	    % set(auto2) -> assign(max_minutes, 5).
0.07/0.44	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.07/0.44	    % set(auto2) -> set(sort_initial_sos).
0.07/0.44	    % set(auto2) -> assign(sos_limit, -1).
0.07/0.44	    % set(auto2) -> assign(lrs_ticks, 3000).
0.07/0.44	    % set(auto2) -> assign(max_megs, 400).
0.07/0.44	    % set(auto2) -> assign(stats, some).
0.07/0.44	    % set(auto2) -> clear(echo_input).
0.07/0.44	    % set(auto2) -> set(quiet).
0.07/0.44	    % set(auto2) -> clear(print_initial_clauses).
0.07/0.44	    % set(auto2) -> clear(print_given).
0.07/0.44	assign(lrs_ticks,-1).
0.07/0.44	assign(sos_limit,10000).
0.07/0.44	assign(order,kbo).
0.07/0.44	set(lex_order_vars).
0.07/0.44	clear(print_given).
0.07/0.44	
0.07/0.44	% formulas(sos).  % not echoed (19 formulas)
0.07/0.44	
0.07/0.44	============================== end of input ==========================
0.07/0.44	
0.07/0.44	% From the command line: assign(max_seconds, 300).
0.07/0.44	
0.07/0.44	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.07/0.44	
0.07/0.44	% Formulas that are not ordinary clauses:
0.07/0.44	1 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	2 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(distributivity1) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	3 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	4 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	5 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	6 (all A all B all C (leq(C,addition(multiplication(A,C),B)) -> leq(C,multiplication(strong_iteration(A),B)))) # label(infty_coinduction) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	8 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	9 (all A addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A)) # label(isolation) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	10 (all A addition(multiplication(A,strong_iteration(A)),one) = strong_iteration(A)) # label(infty_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	11 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	13 (all A all B all C (leq(addition(multiplication(C,A),B),C) -> leq(multiplication(B,star(A)),C))) # label(star_induction2) # label(axiom) # label(non_clause).  [assumption].
0.07/0.44	14 (all A star(A) = addition(one,multiplication(A,star(A)))) # label(star_unfold1) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	15 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(distributivity2) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	16 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	17 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	18 (all A all B all C (leq(addition(multiplication(A,C),B),C) -> leq(multiplication(star(A),B),C))) # label(star_induction1) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	19 -(all X0 (leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) & leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
2.93/3.16	
2.93/3.16	============================== end of process non-clausal formulas ===
2.93/3.16	
2.93/3.16	============================== PROCESS INITIAL CLAUSES ===============
2.93/3.16	
2.93/3.16	============================== PREDICATE ELIMINATION =================
2.93/3.16	
2.93/3.16	============================== end predicate elimination =============
2.93/3.16	
2.93/3.16	Auto_denials:
2.93/3.16	  % copying label goals to answer in negative clause
2.93/3.16	
2.93/3.16	Term ordering decisions:
2.93/3.16	Function symbol KB weights:  one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
2.93/3.16	
2.93/3.16	============================== end of process initial clauses ========
2.93/3.16	
2.93/3.16	============================== CLAUSES FOR SEARCH ====================
2.93/3.16	
2.93/3.16	============================== end of clauses for search =============
2.93/3.16	
2.93/3.16	============================== SEARCH ================================
2.93/3.16	
2.93/3.16	% Starting search at 0.01 seconds.
2.93/3.16	
2.93/3.16	Low Water (keep): wt=54.000, iters=3472
2.93/3.16	
2.93/3.16	Low Water (keep): wt=36.000, iters=3334
2.93/3.16	
2.93/3.16	Low Water (keep): wt=35.000, iters=3363
2.93/3.16	
2.93/3.16	Low Water (keep): wt=33.000, iters=3390
2.93/3.16	
2.93/3.16	Low Water (keep): wt=31.000, iters=3451
2.93/3.16	
2.93/3.16	Low Water (keep): wt=29.000, iters=3335
2.93/3.16	
2.93/3.16	Low Water (keep): wt=28.000, iters=3396
2.93/3.16	
2.93/3.16	Low Water (keep): wt=27.000, iters=3355
2.93/3.16	
2.93/3.16	Low Water (keep): wt=25.000, iters=3343
2.93/3.16	
2.93/3.16	Low Water (keep): wt=24.000, iters=3349
2.93/3.16	
2.93/3.16	Low Water (keep): wt=23.000, iters=3391
2.93/3.16	
2.93/3.16	Low Water (keep): wt=22.000, iters=3350
2.93/3.16	
2.93/3.16	Low Water (keep): wt=21.000, iters=3352
2.93/3.16	
2.93/3.16	Low Water (keep): wt=20.000, iters=3342
2.93/3.16	
2.93/3.16	Low Water (keep): wt=19.000, iters=3335
2.93/3.16	
2.93/3.16	Low Water (displace): id=5734, wt=43.000
2.93/3.16	
2.93/3.16	Low Water (displace): id=12920, wt=18.000
2.93/3.16	
2.93/3.16	Low Water (displace): id=12925, wt=17.000
2.93/3.16	
2.93/3.16	Low Water (keep): wt=18.000, iters=3338
2.93/3.16	
2.93/3.16	============================== PROOF =================================
2.93/3.16	% SZS status Theorem
2.93/3.16	% SZS output start Refutation
2.93/3.16	
2.93/3.16	% Proof 1 at 2.67 (+ 0.06) seconds: goals.
2.93/3.16	% Length of proof is 124.
2.93/3.16	% Level of proof is 16.
2.93/3.16	% Maximum clause weight is 23.000.
2.93/3.16	% Given clauses 1188.
2.93/3.16	
2.93/3.16	1 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	2 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(distributivity1) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	3 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	4 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	5 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	6 (all A all B all C (leq(C,addition(multiplication(A,C),B)) -> leq(C,multiplication(strong_iteration(A),B)))) # label(infty_coinduction) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	8 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	9 (all A addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A)) # label(isolation) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	10 (all A addition(multiplication(A,strong_iteration(A)),one) = strong_iteration(A)) # label(infty_unfold1) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	11 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	12 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	14 (all A star(A) = addition(one,multiplication(A,star(A)))) # label(star_unfold1) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	15 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(distributivity2) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	16 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	17 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	18 (all A all B all C (leq(addition(multiplication(A,C),B),C) -> leq(multiplication(star(A),B),C))) # label(star_induction1) # label(axiom) # label(non_clause).  [assumption].
2.93/3.16	19 -(all X0 (leq(multiplication(strong_iteration(X0),strong_iteration(X0)),strong_iteration(X0)) & leq(strong_iteration(X0),multiplication(strong_iteration(X0),strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
2.93/3.16	20 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(1)].
2.93/3.16	21 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(5)].
2.93/3.16	22 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(7)].
2.93/3.16	23 addition(A,A) = A # label(idempotence) # label(axiom).  [clausify(8)].
2.93/3.16	24 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [clausify(17)].
2.93/3.16	25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(11)].
2.93/3.16	26 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom).  [clausify(10)].
2.93/3.16	27 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A).  [copy(26),rewrite([25(5)]),flip(a)].
2.93/3.16	28 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom).  [clausify(12)].
2.93/3.16	29 addition(one,multiplication(star(A),A)) = star(A).  [copy(28),flip(a)].
2.93/3.16	30 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom).  [clausify(14)].
2.93/3.16	31 addition(one,multiplication(A,star(A))) = star(A).  [copy(30),flip(a)].
2.93/3.16	32 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom).  [clausify(9)].
2.93/3.16	33 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A).  [copy(32),flip(a)].
2.93/3.16	34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(3)].
2.93/3.16	35 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(34),rewrite([25(2)]),flip(a)].
2.93/3.16	36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(16)].
2.93/3.16	37 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(distributivity1) # label(axiom).  [clausify(2)].
2.93/3.16	38 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(distributivity2) # label(axiom).  [clausify(15)].
2.93/3.16	39 -leq(multiplication(strong_iteration(c1),strong_iteration(c1)),strong_iteration(c1)) | -leq(strong_iteration(c1),multiplication(strong_iteration(c1),strong_iteration(c1))) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(19)].
2.93/3.16	40 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom).  [clausify(4)].
2.93/3.16	41 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(4)].
2.93/3.16	42 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom).  [clausify(6)].
2.93/3.16	43 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)).  [copy(42),rewrite([25(2)])].
2.93/3.16	46 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom).  [clausify(18)].
2.93/3.16	47 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C).  [copy(46),rewrite([25(2)])].
2.93/3.16	49 strong_iteration(zero) = one.  [para(24(a,1),27(a,1,2)),rewrite([22(3)]),flip(a)].
2.93/3.16	52 addition(A,addition(A,B)) = addition(A,B).  [para(35(a,1),23(a,1)),rewrite([25(1),25(2),35(2,R),23(1),25(3)])].
2.93/3.16	53 addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)).  [para(36(a,1),27(a,1,2))].
2.93/3.16	54 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)).  [para(36(a,1),31(a,1,2))].
2.93/3.16	55 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)).  [para(21(a,1),37(a,1,1)),rewrite([25(4)])].
2.93/3.16	56 addition(A,multiplication(A,multiplication(B,strong_iteration(B)))) = multiplication(A,strong_iteration(B)).  [para(27(a,1),37(a,2,2)),rewrite([21(2)])].
2.93/3.16	57 addition(A,multiplication(A,multiplication(star(B),B))) = multiplication(A,star(B)).  [para(29(a,1),37(a,2,2)),rewrite([21(2)])].
2.93/3.16	59 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A).  [para(20(a,1),38(a,1,1)),rewrite([25(4)])].
2.93/3.16	60 addition(zero,multiplication(A,B)) = multiplication(A,B).  [para(22(a,1),38(a,2,1)),rewrite([24(3),25(3)])].
2.93/3.16	61 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A).  [para(27(a,1),38(a,2,1)),rewrite([20(2),36(3)])].
2.93/3.16	62 addition(A,multiplication(star(B),multiplication(B,A))) = multiplication(star(B),A).  [para(29(a,1),38(a,2,1)),rewrite([20(2),36(3)])].
2.93/3.16	63 addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A).  [para(31(a,1),38(a,2,1)),rewrite([20(2),36(3)])].
2.93/3.16	65 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C).  [para(36(a,1),38(a,1,1)),rewrite([25(6)])].
2.93/3.16	66 addition(multiplication(A,B),multiplication(C,multiplication(D,B))) = multiplication(addition(A,multiplication(C,D)),B).  [para(36(a,1),38(a,1,2))].
2.93/3.16	67 leq(A,A).  [hyper(41,b,23,a)].
2.93/3.16	107 leq(A,addition(A,B)).  [hyper(41,b,52,a)].
2.93/3.16	108 addition(one,strong_iteration(A)) = strong_iteration(A).  [para(27(a,1),52(a,1,2)),rewrite([27(7)])].
2.93/3.16	109 addition(one,star(A)) = star(A).  [para(29(a,1),52(a,1,2)),rewrite([29(7)])].
2.93/3.16	111 leq(A,multiplication(strong_iteration(B),A)).  [hyper(43,a,107,a)].
2.93/3.16	114 leq(multiplication(A,B),multiplication(A,addition(B,C))).  [para(37(a,1),107(a,2))].
2.93/3.16	116 -leq(multiplication(strong_iteration(c1),strong_iteration(c1)),strong_iteration(c1)) # answer(goals).  [back_unit_del(39),unit_del(b,111)].
2.93/3.16	121 addition(A,multiplication(A,multiplication(B,multiplication(C,strong_iteration(multiplication(B,C)))))) = multiplication(A,strong_iteration(multiplication(B,C))).  [para(53(a,1),37(a,2,2)),rewrite([21(2)])].
2.93/3.16	124 -leq(multiplication(A,strong_iteration(multiplication(B,A))),strong_iteration(multiplication(B,A))) | leq(multiplication(A,strong_iteration(multiplication(B,A))),strong_iteration(B)).  [para(53(a,1),43(a,2)),rewrite([21(12)])].
2.93/3.16	127 multiplication(strong_iteration(c1),strong_iteration(c1)) != strong_iteration(c1) # answer(goals).  [ur(41,a,116,a),rewrite([25(8),55(8),25(6),108(6)])].
2.93/3.16	135 addition(A,multiplication(A,multiplication(B,multiplication(C,star(multiplication(B,C)))))) = multiplication(A,star(multiplication(B,C))).  [para(54(a,1),37(a,2,2)),rewrite([21(2)])].
2.93/3.16	138 -leq(multiplication(A,star(multiplication(B,A))),star(multiplication(B,A))) | leq(multiplication(A,star(multiplication(B,A))),strong_iteration(B)).  [para(54(a,1),43(a,2)),rewrite([21(12)])].
2.93/3.16	172 addition(A,multiplication(A,zero)) = A.  [para(24(a,1),56(a,1,2,2)),rewrite([49(5),21(5)])].
2.93/3.16	173 addition(A,addition(B,multiplication(A,multiplication(C,strong_iteration(C))))) = addition(B,multiplication(A,strong_iteration(C))).  [para(56(a,1),35(a,2,2)),rewrite([25(4)])].
2.93/3.16	181 addition(A,addition(B,multiplication(A,zero))) = addition(A,B).  [para(172(a,1),35(a,2,2)),rewrite([25(3),25(5)])].
2.93/3.16	191 leq(A,multiplication(A,star(B))).  [para(57(a,1),107(a,2))].
2.93/3.16	192 leq(multiplication(A,B),multiplication(A,multiplication(B,star(C)))).  [para(36(a,1),191(a,2))].
2.93/3.16	197 leq(multiplication(A,zero),multiplication(A,multiplication(B,C))).  [para(60(a,1),114(a,2,2))].
2.93/3.16	199 leq(multiplication(A,B),addition(A,multiplication(A,B))).  [para(55(a,2),114(a,2))].
2.93/3.16	233 -leq(multiplication(addition(A,one),B),B) | leq(multiplication(star(A),B),B).  [para(59(a,1),47(a,1))].
2.93/3.16	239 multiplication(addition(A,one),zero) = multiplication(A,zero).  [para(59(a,1),60(a,1))].
2.93/3.16	240 multiplication(addition(A,one),A) = multiplication(A,addition(A,one)).  [para(59(a,1),55(a,1))].
2.93/3.16	258 multiplication(A,multiplication(strong_iteration(A),zero)) = multiplication(strong_iteration(A),zero).  [para(61(a,1),60(a,1)),flip(a)].
2.93/3.16	259 multiplication(A,addition(one,multiplication(strong_iteration(A),A))) = multiplication(strong_iteration(A),A).  [para(61(a,1),55(a,1)),rewrite([25(6)]),flip(a)].
2.93/3.16	261 leq(multiplication(A,zero),multiplication(A,B)).  [para(20(a,1),197(a,2,2))].
2.93/3.16	282 leq(multiplication(A,strong_iteration(A)),strong_iteration(A)).  [para(53(a,1),199(a,2)),rewrite([20(3),20(4),20(4)])].
2.93/3.16	283 leq(multiplication(A,star(A)),star(A)).  [para(54(a,1),199(a,2)),rewrite([20(3),20(4),20(4)])].
2.93/3.16	290 multiplication(addition(A,one),strong_iteration(A)) = strong_iteration(A).  [hyper(40,a,282,a),rewrite([25(4),59(4)])].
2.93/3.16	293 multiplication(addition(A,one),star(A)) = star(A).  [hyper(40,a,283,a),rewrite([25(4),59(4)])].
2.93/3.16	299 multiplication(star(A),multiplication(A,B)) = multiplication(A,multiplication(star(A),B)).  [para(63(a,1),37(a,1)),rewrite([62(7)])].
2.93/3.16	303 multiplication(star(A),A) = multiplication(A,star(A)).  [para(63(a,1),55(a,1)),rewrite([25(6),29(6)])].
2.93/3.16	348 addition(A,addition(multiplication(A,B),multiplication(C,multiplication(D,addition(B,one))))) = multiplication(addition(A,multiplication(C,D)),addition(B,one)).  [para(55(a,2),65(a,1,2)),rewrite([35(7,R)])].
2.93/3.16	366 addition(A,strong_iteration(A)) = strong_iteration(A).  [para(290(a,1),55(a,1,2)),rewrite([25(4),35(4),25(3),35(4,R),25(3),108(3),25(7),108(7),290(6)])].
2.93/3.16	376 addition(multiplication(A,B),multiplication(C,zero)) = multiplication(addition(A,multiplication(C,zero)),B).  [para(24(a,1),66(a,1,2,2))].
2.93/3.16	394 addition(A,addition(B,strong_iteration(A))) = addition(B,strong_iteration(A)).  [para(366(a,1),35(a,2,2)),rewrite([25(2)])].
2.93/3.16	422 addition(A,star(A)) = star(A).  [para(293(a,1),55(a,1,2)),rewrite([25(4),35(4),25(3),35(4,R),25(3),109(3),25(7),109(7),293(6)])].
2.93/3.16	426 leq(multiplication(A,zero),star(A)).  [para(293(a,1),261(a,2)),rewrite([239(4)])].
2.93/3.16	431 leq(multiplication(A,multiplication(B,zero)),star(multiplication(A,B))).  [para(36(a,1),426(a,1))].
2.93/3.16	435 leq(multiplication(A,B),multiplication(A,star(B))).  [para(422(a,1),114(a,2,2))].
2.93/3.16	448 leq(multiplication(A,addition(A,one)),star(A)).  [para(293(a,1),435(a,2)),rewrite([240(3)])].
2.93/3.16	477 leq(addition(A,multiplication(A,A)),star(A)).  [para(55(a,2),448(a,1))].
2.93/3.16	479 addition(A,addition(star(A),multiplication(A,A))) = star(A).  [hyper(40,a,477,a),rewrite([25(4),35(4,R),25(3)])].
2.93/3.16	504 addition(multiplication(A,multiplication(B,C)),multiplication(C,star(C))) = multiplication(addition(star(C),multiplication(A,B)),C).  [para(303(a,1),65(a,1,2))].
2.93/3.16	1026 leq(multiplication(A,addition(B,one)),multiplication(A,star(B))).  [para(293(a,1),192(a,2,2))].
2.93/3.16	1124 multiplication(addition(one,multiplication(A,B)),strong_iteration(multiplication(A,B))) = strong_iteration(multiplication(A,B)).  [para(290(a,1),121(a,2)),rewrite([25(3),25(6),55(12),25(9),53(9)])].
2.93/3.16	1270 leq(addition(A,multiplication(A,B)),multiplication(A,star(B))).  [para(55(a,2),1026(a,1))].
2.93/3.16	1373 leq(strong_iteration(A),star(multiplication(A,strong_iteration(A)))).  [para(53(a,1),1270(a,1)),rewrite([20(2),20(4),20(6)])].
2.93/3.16	1384 addition(strong_iteration(A),star(multiplication(A,strong_iteration(A)))) = star(multiplication(A,strong_iteration(A))).  [hyper(40,a,1373,a)].
2.93/3.16	1398 multiplication(addition(one,multiplication(A,B)),star(multiplication(A,B))) = star(multiplication(A,B)).  [para(293(a,1),135(a,2)),rewrite([25(3),25(6),55(12),25(9),54(9)])].
2.93/3.16	1640 leq(multiplication(strong_iteration(A),zero),star(multiplication(A,strong_iteration(A)))).  [para(258(a,1),431(a,1))].
2.93/3.16	1683 addition(multiplication(strong_iteration(A),zero),star(multiplication(A,strong_iteration(A)))) = star(multiplication(A,strong_iteration(A))).  [hyper(40,a,1640,a)].
2.93/3.16	5959 leq(multiplication(star(A),strong_iteration(A)),strong_iteration(A)).  [para(290(a,1),233(a,1)),unit_del(a,67)].
2.93/3.16	6014 multiplication(star(A),strong_iteration(A)) = strong_iteration(A).  [hyper(40,a,5959,a),rewrite([25(5),59(5),25(3),109(3)])].
2.93/3.16	6061 addition(star(A),multiplication(A,strong_iteration(A))) = strong_iteration(A).  [para(6014(a,1),56(a,2)),rewrite([299(5),6014(4)])].
2.93/3.16	7314 leq(strong_iteration(multiplication(strong_iteration(A),A)),strong_iteration(A)).  [para(259(a,1),124(a,1,2,1)),rewrite([1124(8),259(8),259(16),1124(15)]),unit_del(a,67)].
2.93/3.16	7322 leq(star(multiplication(strong_iteration(A),A)),strong_iteration(A)).  [para(259(a,1),138(a,1,2,1)),rewrite([1398(8),259(8),259(16),1398(15)]),unit_del(a,67)].
2.93/3.16	7354 addition(strong_iteration(A),strong_iteration(multiplication(strong_iteration(A),A))) = strong_iteration(A).  [hyper(40,a,7314,a),rewrite([25(5)])].
2.93/3.16	7381 addition(strong_iteration(A),star(multiplication(strong_iteration(A),A))) = strong_iteration(A).  [hyper(40,a,7322,a),rewrite([25(5)])].
2.93/3.16	9139 addition(star(multiplication(A,strong_iteration(A))),multiplication(A,multiplication(strong_iteration(A),strong_iteration(A)))) = star(multiplication(A,strong_iteration(A))).  [para(479(a,1),173(a,1)),rewrite([36(10)]),flip(a)].
2.93/3.16	9928 addition(star(A),multiplication(strong_iteration(A),B)) = multiplication(strong_iteration(A),addition(B,one)).  [para(33(a,1),348(a,2,1)),rewrite([24(8),376(7),33(6)])].
2.93/3.16	11659 multiplication(strong_iteration(A),addition(A,one)) = strong_iteration(A).  [para(7354(a,1),394(a,1,2)),rewrite([25(4),55(4),7354(9)])].
2.93/3.16	11917 addition(strong_iteration(A),addition(multiplication(strong_iteration(A),zero),star(multiplication(strong_iteration(A),A)))) = strong_iteration(A).  [para(7381(a,1),181(a,2)),rewrite([25(8)])].
2.93/3.16	13124 multiplication(strong_iteration(A),A) = multiplication(A,strong_iteration(A)).  [para(6061(a,1),504(a,2,1)),rewrite([25(6),37(6),9928(4),11659(4)]),flip(a)].
2.93/3.16	13141 star(multiplication(A,strong_iteration(A))) = strong_iteration(A).  [back_rewrite(11917),rewrite([13124(6),1683(8),1384(5)])].
2.93/3.16	13186 multiplication(strong_iteration(A),strong_iteration(A)) = strong_iteration(A).  [back_rewrite(9139),rewrite([13141(3),61(6),13141(6)])].
2.93/3.16	13187 $F # answer(goals).  [resolve(13186,a,127,a)].
2.93/3.16	
2.93/3.16	% SZS output end Refutation
2.93/3.16	============================== end of proof ==========================
2.93/3.16	
2.93/3.16	============================== STATISTICS ============================
2.93/3.16	
2.93/3.16	Given=1188. Generated=100414. Kept=13159. proofs=1.
2.93/3.16	Usable=959. Sos=9689. Demods=1517. Limbo=45, Disabled=2485. Hints=0.
2.93/3.16	Megabytes=11.37.
2.93/3.16	User_CPU=2.67, System_CPU=0.06, Wall_clock=3.
2.93/3.16	
2.93/3.16	============================== end of statistics =====================
2.93/3.16	
2.93/3.16	============================== end of search =========================
2.93/3.16	
2.93/3.16	THEOREM PROVED
2.93/3.16	% SZS status Theorem
2.93/3.16	
2.93/3.16	Exiting with 1 proof.
2.93/3.16	
2.93/3.16	Process 55059 exit (max_proofs) Sat Jul 14 05:18:43 2018
2.93/3.16	Prover9 interrupted
2.93/3.16	EOF