0.00/0.10	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.10	% Command  : tptp2X_and_run_prover9 %d %s
0.09/0.30	% Computer : n028.cluster.edu
0.09/0.30	% Model    : x86_64 x86_64
0.09/0.30	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.30	% Memory   : 8042.1875MB
0.09/0.30	% OS       : Linux 3.10.0-693.el7.x86_64
0.09/0.30	% CPULimit : 1440
0.09/0.30	% WCLimit  : 180
0.09/0.30	% DateTime : Mon Jul  3 08:12:43 EDT 2023
0.09/0.30	% CPUTime  : 
0.68/0.99	============================== Prover9 ===============================
0.68/0.99	Prover9 (32) version 2009-11A, November 2009.
0.68/0.99	Process 17098 was started by sandbox2 on n028.cluster.edu,
0.68/0.99	Mon Jul  3 08:12:44 2023
0.68/0.99	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_16945_n028.cluster.edu".
0.68/0.99	============================== end of head ===========================
0.68/0.99	
0.68/0.99	============================== INPUT =================================
0.68/0.99	
0.68/0.99	% Reading from file /tmp/Prover9_16945_n028.cluster.edu
0.68/0.99	
0.68/0.99	set(prolog_style_variables).
0.68/0.99	set(auto2).
0.68/0.99	    % set(auto2) -> set(auto).
0.68/0.99	    % set(auto) -> set(auto_inference).
0.68/0.99	    % set(auto) -> set(auto_setup).
0.68/0.99	    % set(auto_setup) -> set(predicate_elim).
0.68/0.99	    % set(auto_setup) -> assign(eq_defs, unfold).
0.68/0.99	    % set(auto) -> set(auto_limits).
0.68/0.99	    % set(auto_limits) -> assign(max_weight, "100.000").
0.68/0.99	    % set(auto_limits) -> assign(sos_limit, 20000).
0.68/0.99	    % set(auto) -> set(auto_denials).
0.68/0.99	    % set(auto) -> set(auto_process).
0.68/0.99	    % set(auto2) -> assign(new_constants, 1).
0.68/0.99	    % set(auto2) -> assign(fold_denial_max, 3).
0.68/0.99	    % set(auto2) -> assign(max_weight, "200.000").
0.68/0.99	    % set(auto2) -> assign(max_hours, 1).
0.68/0.99	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.68/0.99	    % set(auto2) -> assign(max_seconds, 0).
0.68/0.99	    % set(auto2) -> assign(max_minutes, 5).
0.68/0.99	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.68/0.99	    % set(auto2) -> set(sort_initial_sos).
0.68/0.99	    % set(auto2) -> assign(sos_limit, -1).
0.68/0.99	    % set(auto2) -> assign(lrs_ticks, 3000).
0.68/0.99	    % set(auto2) -> assign(max_megs, 400).
0.68/0.99	    % set(auto2) -> assign(stats, some).
0.68/0.99	    % set(auto2) -> clear(echo_input).
0.68/0.99	    % set(auto2) -> set(quiet).
0.68/0.99	    % set(auto2) -> clear(print_initial_clauses).
0.68/0.99	    % set(auto2) -> clear(print_given).
0.68/0.99	assign(lrs_ticks,-1).
0.68/0.99	assign(sos_limit,10000).
0.68/0.99	assign(order,kbo).
0.68/0.99	set(lex_order_vars).
0.68/0.99	clear(print_given).
0.68/0.99	
0.68/0.99	% formulas(sos).  % not echoed (19 formulas)
0.68/0.99	
0.68/0.99	============================== end of input ==========================
0.68/0.99	
0.68/0.99	% From the command line: assign(max_seconds, 1440).
0.68/0.99	
0.68/0.99	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.68/0.99	
0.68/0.99	% Formulas that are not ordinary clauses:
0.68/0.99	1 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(distributivity2) # label(axiom) # label(non_clause).  [assumption].
0.68/0.99	2 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause).  [assumption].
0.68/0.99	3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.68/0.99	4 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.68/0.99	5 (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].
0.68/0.99	6 (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].
0.68/0.99	7 (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].
0.68/0.99	8 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.68/0.99	9 (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].
0.68/0.99	10 (all A star(A) = addition(one,multiplication(A,star(A)))) # label(star_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.68/0.99	11 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.68/0.99	12 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.68/0.99	13 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	14 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	15 (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].
31.64/32.00	16 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	17 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	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].
31.64/32.00	19 -(all X0 multiplication(strong_iteration(X0),strong_iteration(X0)) = strong_iteration(X0)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
31.64/32.00	
31.64/32.00	============================== end of process non-clausal formulas ===
31.64/32.00	
31.64/32.00	============================== PROCESS INITIAL CLAUSES ===============
31.64/32.00	
31.64/32.00	============================== PREDICATE ELIMINATION =================
31.64/32.00	
31.64/32.00	============================== end predicate elimination =============
31.64/32.00	
31.64/32.00	Auto_denials:
31.64/32.00	  % copying label goals to answer in negative clause
31.64/32.00	
31.64/32.00	Term ordering decisions:
31.64/32.00	Function symbol KB weights:  one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
31.64/32.00	
31.64/32.00	============================== end of process initial clauses ========
31.64/32.00	
31.64/32.00	============================== CLAUSES FOR SEARCH ====================
31.64/32.00	
31.64/32.00	============================== end of clauses for search =============
31.64/32.00	
31.64/32.00	============================== SEARCH ================================
31.64/32.00	
31.64/32.00	% Starting search at 0.01 seconds.
31.64/32.00	
31.64/32.00	Low Water (keep): wt=41.000, iters=3388
31.64/32.00	
31.64/32.00	Low Water (keep): wt=36.000, iters=3380
31.64/32.00	
31.64/32.00	Low Water (keep): wt=35.000, iters=3346
31.64/32.00	
31.64/32.00	Low Water (keep): wt=34.000, iters=3372
31.64/32.00	
31.64/32.00	Low Water (keep): wt=33.000, iters=3355
31.64/32.00	
31.64/32.00	Low Water (keep): wt=31.000, iters=3340
31.64/32.00	
31.64/32.00	Low Water (keep): wt=28.000, iters=3391
31.64/32.00	
31.64/32.00	Low Water (keep): wt=27.000, iters=3348
31.64/32.00	
31.64/32.00	Low Water (keep): wt=25.000, iters=3378
31.64/32.00	
31.64/32.00	Low Water (keep): wt=23.000, iters=3341
31.64/32.00	
31.64/32.00	Low Water (keep): wt=22.000, iters=3394
31.64/32.00	
31.64/32.00	Low Water (keep): wt=21.000, iters=3361
31.64/32.00	
31.64/32.00	Low Water (keep): wt=20.000, iters=3338
31.64/32.00	
31.64/32.00	Low Water (keep): wt=19.000, iters=3345
31.64/32.00	
31.64/32.00	Low Water (displace): id=5894, wt=72.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=6241, wt=71.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=5982, wt=56.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=3763, wt=54.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=6663, wt=53.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=3813, wt=52.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=6701, wt=50.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=6854, wt=49.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=6826, wt=47.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=3824, wt=46.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=6700, wt=44.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=6477, wt=43.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=13192, wt=18.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=13214, wt=17.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=13324, wt=15.000
31.64/32.00	
31.64/32.00	Low Water (keep): wt=18.000, iters=3333
31.64/32.00	
31.64/32.00	Low Water (displace): id=14122, wt=14.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=14127, wt=13.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=14131, wt=12.000
31.64/32.00	
31.64/32.00	Low Water (displace): id=14165, wt=11.000
31.64/32.00	
31.64/32.00	Low Water (keep): wt=17.000, iters=3348
31.64/32.00	
31.64/32.00	Low Water (keep): wt=16.000, iters=3340
31.64/32.00	
31.64/32.00	Low Water (keep): wt=15.000, iters=3333
31.64/32.00	
31.64/32.00	Low Water (keep): wt=14.000, iters=3349
31.64/32.00	
31.64/32.00	============================== PROOF =================================
31.64/32.00	% SZS status Theorem
31.64/32.00	% SZS output start Refutation
31.64/32.00	
31.64/32.00	% Proof 1 at 30.00 (+ 0.95) seconds: goals.
31.64/32.00	% Length of proof is 85.
31.64/32.00	% Level of proof is 16.
31.64/32.00	% Maximum clause weight is 23.000.
31.64/32.00	% Given clauses 5003.
31.64/32.00	
31.64/32.00	1 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(distributivity2) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	2 (all A addition(one,multiplication(star(A),A)) = star(A)) # label(star_unfold2) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	4 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	5 (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].
31.64/32.00	6 (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].
31.64/32.00	7 (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].
31.64/32.00	8 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	10 (all A star(A) = addition(one,multiplication(A,star(A)))) # label(star_unfold1) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	11 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	12 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	13 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	14 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	16 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	17 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause).  [assumption].
31.64/32.00	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].
31.64/32.00	19 -(all X0 multiplication(strong_iteration(X0),strong_iteration(X0)) = strong_iteration(X0)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
31.64/32.00	20 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [clausify(4)].
31.64/32.00	21 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(12)].
31.64/32.00	22 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(14)].
31.64/32.00	23 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(16)].
31.64/32.00	24 addition(A,A) = A # label(idempotence) # label(axiom).  [clausify(17)].
31.64/32.00	25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(3)].
31.64/32.00	26 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom).  [clausify(2)].
31.64/32.00	27 addition(one,multiplication(star(A),A)) = star(A).  [copy(26),flip(a)].
31.64/32.00	28 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom).  [clausify(8)].
31.64/32.00	29 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A).  [copy(28),rewrite([25(5)]),flip(a)].
31.64/32.00	30 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom).  [clausify(10)].
31.64/32.00	31 addition(one,multiplication(A,star(A))) = star(A).  [copy(30),flip(a)].
31.64/32.00	32 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom).  [clausify(13)].
31.64/32.00	33 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A).  [copy(32),flip(a)].
31.64/32.00	34 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(6)].
31.64/32.00	35 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(7)].
31.64/32.00	36 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(35),rewrite([25(2)]),flip(a)].
31.64/32.00	37 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(distributivity2) # label(axiom).  [clausify(1)].
31.64/32.00	38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(distributivity1) # label(axiom).  [clausify(5)].
31.64/32.00	39 strong_iteration(c1) != multiplication(strong_iteration(c1),strong_iteration(c1)) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(19)].
31.64/32.00	40 multiplication(strong_iteration(c1),strong_iteration(c1)) != strong_iteration(c1) # answer(goals).  [copy(39),flip(a)].
31.64/32.00	41 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom).  [clausify(11)].
31.64/32.00	42 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(11)].
31.64/32.00	47 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction1) # label(axiom).  [clausify(18)].
31.64/32.00	48 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C).  [copy(47),rewrite([25(2)])].
31.64/32.00	53 addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)).  [para(34(a,1),29(a,1,2))].
31.64/32.00	54 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)).  [para(34(a,1),31(a,1,2))].
31.64/32.00	55 addition(A,addition(A,B)) = addition(A,B).  [para(36(a,1),24(a,1)),rewrite([25(1),25(2),36(2,R),24(1),25(3)])].
31.64/32.00	58 addition(A,multiplication(star(B),multiplication(B,A))) = multiplication(star(B),A).  [para(27(a,1),37(a,2,1)),rewrite([21(2),34(3)])].
31.64/32.00	59 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A).  [para(29(a,1),37(a,2,1)),rewrite([21(2),34(3)])].
31.64/32.00	60 addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A).  [para(31(a,1),37(a,2,1)),rewrite([21(2),34(3)])].
31.64/32.00	62 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C).  [para(34(a,1),37(a,1,1)),rewrite([25(6)])].
31.64/32.00	63 addition(multiplication(A,B),multiplication(C,multiplication(D,B))) = multiplication(addition(A,multiplication(C,D)),B).  [para(34(a,1),37(a,1,2))].
31.64/32.00	64 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)).  [para(23(a,1),38(a,1,1)),rewrite([25(4)])].
31.64/32.00	66 addition(A,multiplication(A,multiplication(B,strong_iteration(B)))) = multiplication(A,strong_iteration(B)).  [para(29(a,1),38(a,2,2)),rewrite([23(2)])].
31.64/32.00	97 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B).  [para(24(a,1),48(a,1))].
31.64/32.00	108 leq(A,addition(A,B)).  [hyper(42,b,55,a)].
31.64/32.00	109 addition(one,star(A)) = star(A).  [para(27(a,1),55(a,1,2)),rewrite([27(7)])].
31.64/32.00	110 addition(one,strong_iteration(A)) = strong_iteration(A).  [para(29(a,1),55(a,1,2)),rewrite([29(7)])].
31.64/32.00	111 addition(star(A),strong_iteration(A)) = strong_iteration(A).  [para(33(a,1),55(a,1,2)),rewrite([33(8)])].
31.64/32.00	117 leq(multiplication(A,B),multiplication(A,addition(B,C))).  [para(38(a,1),108(a,2))].
31.64/32.00	118 addition(one,multiplication(A,zero)) = strong_iteration(multiplication(A,zero)).  [para(20(a,1),53(a,1,2,2))].
31.64/32.00	127 strong_iteration(multiplication(A,zero)) = star(multiplication(A,zero)).  [para(20(a,1),54(a,1,2,2)),rewrite([118(4)])].
31.64/32.00	138 addition(A,multiplication(A,strong_iteration(B))) = multiplication(A,strong_iteration(B)).  [para(110(a,1),38(a,2,2)),rewrite([23(2)])].
31.64/32.00	200 multiplication(star(A),multiplication(A,B)) = multiplication(A,multiplication(star(A),B)).  [para(60(a,1),38(a,1)),rewrite([58(7)])].
31.64/32.00	205 -leq(multiplication(A,B),B) | leq(multiplication(A,multiplication(star(A),B)),B).  [back_rewrite(97),rewrite([200(5)])].
31.64/32.00	211 multiplication(star(multiplication(A,zero)),B) = addition(B,multiplication(A,zero)).  [para(127(a,1),59(a,1,2,2,1)),rewrite([34(7),20(6),127(6)]),flip(a)].
31.64/32.00	254 addition(multiplication(A,B),multiplication(C,zero)) = multiplication(addition(A,multiplication(C,zero)),B).  [para(20(a,1),63(a,1,2,2))].
31.64/32.00	274 multiplication(addition(A,multiplication(A,B)),B) = multiplication(A,multiplication(B,addition(B,one))).  [para(64(a,1),37(a,1)),rewrite([34(4)]),flip(a)].
31.64/32.00	295 leq(multiplication(A,B),addition(A,multiplication(A,B))).  [para(64(a,2),117(a,2))].
31.64/32.00	300 addition(A,addition(multiplication(A,B),multiplication(C,multiplication(D,addition(B,one))))) = multiplication(addition(A,multiplication(C,D)),addition(B,one)).  [para(64(a,2),62(a,1,2)),rewrite([36(7,R)])].
31.64/32.00	303 multiplication(addition(A,multiplication(A,multiplication(B,C))),B) = multiplication(A,multiplication(B,addition(one,multiplication(C,B)))).  [para(64(a,1),63(a,1)),rewrite([25(4),34(5),34(7)]),flip(a)].
31.64/32.00	311 leq(multiplication(A,strong_iteration(A)),strong_iteration(A)).  [para(53(a,1),295(a,2)),rewrite([21(3),21(4),21(4)])].
31.64/32.00	312 leq(multiplication(A,star(A)),star(A)).  [para(54(a,1),295(a,2)),rewrite([21(3),21(4),21(4)])].
31.64/32.00	333 addition(A,multiplication(A,multiplication(B,zero))) = multiplication(A,star(multiplication(B,zero))).  [para(127(a,1),66(a,1,2,2,2)),rewrite([34(6),20(5),127(7)])].
31.64/32.00	4543 leq(multiplication(A,multiplication(star(A),star(A))),star(A)).  [hyper(205,a,312,a)].
31.64/32.00	4544 leq(multiplication(A,multiplication(star(A),strong_iteration(A))),strong_iteration(A)).  [hyper(205,a,311,a)].
31.64/32.00	6004 multiplication(star(A),star(A)) = star(A).  [hyper(41,a,4543,a),rewrite([25(6),60(6)])].
31.64/32.00	6104 multiplication(star(A),strong_iteration(A)) = strong_iteration(A).  [hyper(41,a,4544,a),rewrite([25(6),60(6)])].
31.64/32.00	6118 multiplication(star(A),multiplication(strong_iteration(A),B)) = multiplication(strong_iteration(A),B).  [para(6104(a,1),34(a,1,1)),flip(a)].
31.64/32.00	10777 addition(star(A),multiplication(strong_iteration(A),B)) = multiplication(strong_iteration(A),addition(B,one)).  [para(33(a,1),300(a,2,1)),rewrite([20(8),254(7),33(6)])].
31.64/32.00	19565 multiplication(star(A),star(multiplication(strong_iteration(A),zero))) = strong_iteration(A).  [para(6118(a,1),333(a,1,2)),rewrite([10777(5),25(4),22(4),23(3)]),flip(a)].
31.64/32.00	19617 multiplication(strong_iteration(A),star(multiplication(strong_iteration(A),zero))) = strong_iteration(A).  [para(19565(a,1),274(a,1,1,2)),rewrite([111(3),25(17),109(17),6004(16),19565(12)])].
31.64/32.00	19620 multiplication(A,multiplication(strong_iteration(B),star(B))) = multiplication(A,strong_iteration(B)).  [para(19565(a,1),303(a,1,1,2,2)),rewrite([138(3),34(4),211(12),10777(11),25(10),22(10),23(9),110(8),6104(7)])].
31.64/32.00	24893 multiplication(strong_iteration(A),star(A)) = strong_iteration(A).  [para(19620(a,1),21(a,1)),rewrite([21(3)]),flip(a)].
31.64/32.00	24917 multiplication(strong_iteration(A),multiplication(star(A),B)) = multiplication(strong_iteration(A),B).  [para(24893(a,1),34(a,1,1)),flip(a)].
31.64/32.00	27601 multiplication(strong_iteration(A),strong_iteration(A)) = strong_iteration(A).  [para(19565(a,1),24917(a,1,2)),rewrite([19617(9)])].
31.64/32.00	27602 $F # answer(goals).  [resolve(27601,a,40,a)].
31.64/32.00	
31.64/32.00	% SZS output end Refutation
31.64/32.00	============================== end of proof ==========================
31.64/32.00	
31.64/32.00	============================== STATISTICS ============================
31.64/32.00	
31.64/32.00	Given=5003. Generated=1058001. Kept=27573. proofs=1.
31.64/32.00	Usable=4072. Sos=9941. Demods=884. Limbo=9, Disabled=13570. Hints=0.
31.64/32.00	Megabytes=17.51.
31.64/32.00	User_CPU=30.00, System_CPU=0.95, Wall_clock=31.
31.64/32.00	
31.64/32.00	============================== end of statistics =====================
31.64/32.00	
31.64/32.00	============================== end of search =========================
31.64/32.00	
31.64/32.00	THEOREM PROVED
31.64/32.00	% SZS status Theorem
31.64/32.00	
31.64/32.00	Exiting with 1 proof.
31.64/32.00	
31.64/32.00	Process 17098 exit (max_proofs) Mon Jul  3 08:13:15 2023
31.64/32.00	Prover9 interrupted
31.64/32.00	EOF