0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% 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   : 180
0.12/0.33	% DateTime   : Thu Aug 29 13:59:03 EDT 2019
0.12/0.33	% CPUTime    : 
0.41/0.99	============================== Prover9 ===============================
0.41/0.99	Prover9 (32) version 2009-11A, November 2009.
0.41/0.99	Process 15882 was started by sandbox on n005.cluster.edu,
0.41/0.99	Thu Aug 29 13:59:04 2019
0.41/0.99	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_15725_n005.cluster.edu".
0.41/0.99	============================== end of head ===========================
0.41/0.99	
0.41/0.99	============================== INPUT =================================
0.41/0.99	
0.41/0.99	% Reading from file /tmp/Prover9_15725_n005.cluster.edu
0.41/0.99	
0.41/0.99	set(prolog_style_variables).
0.41/0.99	set(auto2).
0.41/0.99	    % set(auto2) -> set(auto).
0.41/0.99	    % set(auto) -> set(auto_inference).
0.41/0.99	    % set(auto) -> set(auto_setup).
0.41/0.99	    % set(auto_setup) -> set(predicate_elim).
0.41/0.99	    % set(auto_setup) -> assign(eq_defs, unfold).
0.41/0.99	    % set(auto) -> set(auto_limits).
0.41/0.99	    % set(auto_limits) -> assign(max_weight, "100.000").
0.41/0.99	    % set(auto_limits) -> assign(sos_limit, 20000).
0.41/0.99	    % set(auto) -> set(auto_denials).
0.41/0.99	    % set(auto) -> set(auto_process).
0.41/0.99	    % set(auto2) -> assign(new_constants, 1).
0.41/0.99	    % set(auto2) -> assign(fold_denial_max, 3).
0.41/0.99	    % set(auto2) -> assign(max_weight, "200.000").
0.41/0.99	    % set(auto2) -> assign(max_hours, 1).
0.41/0.99	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.41/0.99	    % set(auto2) -> assign(max_seconds, 0).
0.41/0.99	    % set(auto2) -> assign(max_minutes, 5).
0.41/0.99	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.41/0.99	    % set(auto2) -> set(sort_initial_sos).
0.41/0.99	    % set(auto2) -> assign(sos_limit, -1).
0.41/0.99	    % set(auto2) -> assign(lrs_ticks, 3000).
0.41/0.99	    % set(auto2) -> assign(max_megs, 400).
0.41/0.99	    % set(auto2) -> assign(stats, some).
0.41/0.99	    % set(auto2) -> clear(echo_input).
0.41/0.99	    % set(auto2) -> set(quiet).
0.41/0.99	    % set(auto2) -> clear(print_initial_clauses).
0.41/0.99	    % set(auto2) -> clear(print_given).
0.41/0.99	assign(lrs_ticks,-1).
0.41/0.99	assign(sos_limit,10000).
0.41/0.99	assign(order,kbo).
0.41/0.99	set(lex_order_vars).
0.41/0.99	clear(print_given).
0.41/0.99	
0.41/0.99	% formulas(sos).  % not echoed (17 formulas)
0.41/0.99	
0.41/0.99	============================== end of input ==========================
0.41/0.99	
0.41/0.99	% From the command line: assign(max_seconds, 180).
0.41/0.99	
0.41/0.99	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.41/0.99	
0.41/0.99	% Formulas that are not ordinary clauses:
0.41/0.99	1 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	2 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	3 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	5 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	6 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	7 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	8 (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].
0.41/0.99	9 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	10 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	11 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	12 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.41/0.99	13 (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].
0.41/0.99	14 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	15 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	16 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	
3.23/3.54	============================== end of process non-clausal formulas ===
3.23/3.54	
3.23/3.54	============================== PROCESS INITIAL CLAUSES ===============
3.23/3.54	
3.23/3.54	============================== PREDICATE ELIMINATION =================
3.23/3.54	
3.23/3.54	============================== end predicate elimination =============
3.23/3.54	
3.23/3.54	Auto_denials:
3.23/3.54	  % copying label a to answer in negative clause
3.23/3.54	
3.23/3.54	Term ordering decisions:
3.23/3.54	
3.23/3.54	% Assigning unary symbol star kb_weight 0 and highest precedence (8).
3.23/3.54	Function symbol KB weights:  zero=1. one=1. a=1. multiplication=1. addition=1. star=0.
3.23/3.54	
3.23/3.54	============================== end of process initial clauses ========
3.23/3.54	
3.23/3.54	============================== CLAUSES FOR SEARCH ====================
3.23/3.54	
3.23/3.54	============================== end of clauses for search =============
3.23/3.54	
3.23/3.54	============================== SEARCH ================================
3.23/3.54	
3.23/3.54	% Starting search at 0.01 seconds.
3.23/3.54	
3.23/3.54	Low Water (keep): wt=36.000, iters=3378
3.23/3.54	
3.23/3.54	Low Water (keep): wt=35.000, iters=3363
3.23/3.54	
3.23/3.54	Low Water (keep): wt=33.000, iters=3371
3.23/3.54	
3.23/3.54	Low Water (keep): wt=32.000, iters=3479
3.23/3.54	
3.23/3.54	Low Water (keep): wt=31.000, iters=3425
3.23/3.54	
3.23/3.54	Low Water (keep): wt=29.000, iters=3342
3.23/3.54	
3.23/3.54	Low Water (keep): wt=28.000, iters=3364
3.23/3.54	
3.23/3.54	Low Water (keep): wt=27.000, iters=3409
3.23/3.54	
3.23/3.54	Low Water (keep): wt=26.000, iters=3364
3.23/3.54	
3.23/3.54	Low Water (keep): wt=25.000, iters=3386
3.23/3.54	
3.23/3.54	Low Water (keep): wt=24.000, iters=3379
3.23/3.54	
3.23/3.54	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 50 (0.00 of 0.91 sec).
3.23/3.54	
3.23/3.54	Low Water (keep): wt=23.000, iters=3349
3.23/3.54	
3.23/3.54	Low Water (keep): wt=22.000, iters=3360
3.23/3.54	
3.23/3.54	Low Water (keep): wt=21.000, iters=3403
3.23/3.54	
3.23/3.54	Low Water (keep): wt=20.000, iters=3338
3.23/3.54	
3.23/3.54	Low Water (keep): wt=19.000, iters=3350
3.23/3.54	
3.23/3.54	Low Water (displace): id=5659, wt=46.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=5635, wt=44.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6315, wt=43.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=5881, wt=42.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6327, wt=41.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6311, wt=40.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6250, wt=39.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6289, wt=38.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6229, wt=37.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6171, wt=36.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6113, wt=35.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6363, wt=34.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=6421, wt=33.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=11766, wt=18.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=11801, wt=15.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=12393, wt=14.000
3.23/3.54	
3.23/3.54	Low Water (displace): id=12398, wt=13.000
3.23/3.54	
3.23/3.54	Low Water (keep): wt=18.000, iters=3336
3.23/3.54	
3.23/3.54	Low Water (displace): id=13254, wt=12.000
3.23/3.54	
3.23/3.54	Low Water (keep): wt=17.000, iters=3338
3.23/3.54	
3.23/3.54	Low Water (keep): wt=16.000, iters=3340
3.23/3.54	
3.23/3.54	============================== PROOF =================================
3.23/3.54	% SZS status Theorem
3.23/3.54	% SZS output start Refutation
3.23/3.54	
3.23/3.54	% Proof 1 at 2.49 (+ 0.08) seconds: a.
3.23/3.54	% Length of proof is 143.
3.23/3.54	% Level of proof is 32.
3.23/3.54	% Maximum clause weight is 22.000.
3.23/3.54	% Given clauses 1485.
3.23/3.54	
3.23/3.54	1 (all A all B all C (leq(addition(multiplication(A,B),C),B) -> leq(multiplication(star(A),C),B))) # label(star_induction_left) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	2 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	5 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	6 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	7 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	8 (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].
3.23/3.54	9 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	10 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	12 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	13 (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].
3.23/3.54	15 (all A all B all C (leq(addition(multiplication(A,B),C),A) -> leq(multiplication(C,star(B)),A))) # label(star_induction_right) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	16 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
3.23/3.54	18 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(4)].
3.23/3.54	19 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(5)].
3.23/3.54	22 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(16)].
3.23/3.54	23 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(6)].
3.23/3.54	24 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom).  [clausify(9)].
3.23/3.54	25 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom).  [clausify(10)].
3.23/3.54	26 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(8)].
3.23/3.54	27 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(26),rewrite([23(2)]),flip(a)].
3.23/3.54	28 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(13)].
3.23/3.54	29 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom).  [clausify(2)].
3.23/3.54	30 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom).  [clausify(7)].
3.23/3.54	31 -leq(multiplication(a,multiplication(a,multiplication(a,multiplication(a,multiplication(a,a))))),star(a)) # label(a) # label(negated_conjecture) # answer(a).  [assumption].
3.23/3.54	32 addition(A,B) != B | leq(A,B) # label(order) # label(axiom).  [clausify(12)].
3.23/3.54	33 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom).  [clausify(12)].
3.23/3.54	34 -leq(addition(multiplication(A,B),C),B) | leq(multiplication(star(A),C),B) # label(star_induction_left) # label(axiom).  [clausify(1)].
3.23/3.54	35 -leq(addition(A,multiplication(B,C)),C) | leq(multiplication(star(B),A),C).  [copy(34),rewrite([23(2)])].
3.23/3.54	36 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction_right) # label(axiom).  [clausify(15)].
3.23/3.54	37 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B).  [copy(36),rewrite([23(2)])].
3.23/3.54	40 addition(A,addition(A,B)) = addition(A,B).  [para(27(a,1),19(a,1)),rewrite([23(1),23(2),27(2,R),19(1),23(3)])].
3.23/3.54	41 leq(addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))),star(multiplication(A,B))).  [para(28(a,1),24(a,1,2))].
3.23/3.54	43 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)).  [para(22(a,1),29(a,1,1)),rewrite([23(4)])].
3.23/3.54	44 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A).  [para(18(a,1),30(a,1,1)),rewrite([23(4)])].
3.23/3.54	48 leq(A,A).  [hyper(32,a,19,a)].
3.23/3.54	52 addition(A,addition(B,C)) != addition(A,C) | leq(B,addition(A,C)).  [para(27(a,1),32(a,1)),rewrite([23(3),23(5)])].
3.23/3.54	53 addition(A,addition(B,C)) != addition(A,B) | leq(C,addition(A,B)).  [para(27(a,2),32(a,1))].
3.23/3.54	56 addition(star(A),addition(one,multiplication(star(A),A))) = star(A).  [hyper(33,b,25,a),rewrite([23(6)])].
3.23/3.54	57 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A).  [hyper(33,b,24,a),rewrite([23(6)])].
3.23/3.54	60 -leq(multiplication(A,B),B) | leq(multiplication(star(A),multiplication(A,B)),B).  [para(19(a,1),35(a,1))].
3.23/3.54	63 -leq(addition(A,multiplication(B,multiplication(C,D))),D) | leq(multiplication(star(multiplication(B,C)),A),D).  [para(28(a,1),35(a,1,2))].
3.23/3.54	64 -leq(multiplication(A,addition(B,C)),C) | leq(multiplication(star(A),multiplication(A,B)),C).  [para(29(a,1),35(a,1))].
3.23/3.54	68 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A).  [para(19(a,1),37(a,1)),rewrite([28(5)])].
3.23/3.54	79 leq(A,addition(A,B)).  [hyper(32,a,40,a)].
3.23/3.54	80 leq(multiplication(A,B),multiplication(A,addition(B,C))).  [para(29(a,1),79(a,2))].
3.23/3.54	103 addition(A,addition(B,multiplication(A,C))) = addition(B,multiplication(A,addition(C,one))).  [para(43(a,1),27(a,2,2)),rewrite([23(2)])].
3.23/3.54	120 leq(addition(one,multiplication(A,multiplication(addition(B,one),star(addition(A,multiplication(A,B)))))),star(multiplication(A,addition(B,one)))).  [para(43(a,2),41(a,1,2,2,2,1))].
3.23/3.54	143 -leq(multiplication(addition(A,one),B),B) | leq(multiplication(star(A),B),B).  [para(44(a,1),35(a,1))].
3.23/3.54	197 leq(A,addition(B,A)).  [para(19(a,1),52(a,1,2)),xx(a)].
3.23/3.54	203 leq(A,addition(B,addition(A,C))).  [para(40(a,1),52(a,1,2)),xx(a)].
3.23/3.54	210 leq(addition(A,B),addition(A,addition(B,C))).  [para(27(a,1),197(a,2)),rewrite([23(2),27(3,R),23(2)])].
3.23/3.54	211 leq(multiplication(A,B),addition(C,multiplication(A,addition(B,D)))).  [para(29(a,1),203(a,2,2))].
3.23/3.54	212 leq(multiplication(A,B),addition(C,multiplication(addition(A,D),B))).  [para(30(a,1),203(a,2,2))].
3.23/3.54	213 leq(A,addition(B,multiplication(A,addition(C,one)))).  [para(43(a,1),203(a,2,2))].
3.23/3.54	214 leq(A,addition(B,multiplication(addition(C,one),A))).  [para(44(a,1),203(a,2,2))].
3.23/3.54	219 addition(A,multiplication(addition(B,C),D)) != addition(A,multiplication(B,D)) | leq(multiplication(C,D),addition(A,multiplication(B,D))).  [para(30(a,1),53(a,1,2))].
3.23/3.54	248 addition(A,addition(B,multiplication(addition(C,one),A))) = addition(B,multiplication(addition(C,one),A)).  [hyper(33,b,214,a)].
3.23/3.54	249 leq(A,multiplication(addition(B,one),addition(A,C))).  [para(29(a,1),214(a,2)),rewrite([23(3)])].
3.23/3.54	288 leq(one,star(A)).  [para(56(a,1),203(a,2))].
3.23/3.54	290 addition(star(A),one) != star(A) | leq(multiplication(star(A),A),addition(star(A),one)).  [para(56(a,1),53(a,1)),flip(a)].
3.23/3.54	291 leq(addition(star(A),one),star(A)).  [para(56(a,1),210(a,2))].
3.23/3.54	294 addition(one,star(A)) = star(A).  [hyper(33,b,288,a)].
3.23/3.54	295 addition(star(A),one) = star(A).  [hyper(33,b,291,a),rewrite([23(5),40(5)])].
3.23/3.54	296 leq(multiplication(star(A),A),star(A)).  [back_rewrite(290),rewrite([295(3),295(8)]),xx(a)].
3.23/3.54	297 addition(A,multiplication(A,star(B))) = multiplication(A,star(B)).  [para(294(a,1),29(a,2,2)),rewrite([22(2)])].
3.23/3.54	300 leq(A,multiplication(A,star(B))).  [para(294(a,1),80(a,2,2)),rewrite([22(2)])].
3.23/3.54	306 leq(one,multiplication(addition(A,one),star(B))).  [para(294(a,1),249(a,2,2))].
3.23/3.54	307 leq(multiplication(A,B),multiplication(A,multiplication(B,star(C)))).  [para(28(a,1),300(a,2))].
3.23/3.54	309 addition(star(A),multiplication(A,star(A))) = star(A).  [para(57(a,1),27(a,1)),rewrite([295(6),23(5)]),flip(a)].
3.23/3.54	311 addition(one,multiplication(addition(A,one),star(addition(A,one)))) = star(addition(A,one)).  [para(44(a,2),57(a,1,2,2)),rewrite([44(12),248(12)])].
3.23/3.54	314 leq(multiplication(A,star(A)),star(A)).  [para(57(a,1),53(a,1)),rewrite([295(4),295(8)]),xx(a)].
3.23/3.54	318 leq(A,addition(B,multiplication(A,star(C)))).  [para(295(a,1),213(a,2,2,2))].
3.23/3.54	326 addition(star(A),multiplication(star(A),A)) = star(A).  [hyper(33,b,296,a),rewrite([23(4)])].
3.23/3.54	353 addition(one,multiplication(addition(A,one),star(B))) = multiplication(addition(A,one),star(B)).  [hyper(33,b,306,a)].
3.23/3.54	355 multiplication(addition(A,one),star(addition(A,one))) = star(addition(A,one)).  [back_rewrite(311),rewrite([353(8)])].
3.23/3.54	394 -leq(multiplication(A,addition(one,multiplication(B,C))),C) | leq(multiplication(star(multiplication(A,B)),A),C).  [para(43(a,1),63(a,1)),rewrite([23(3)])].
3.23/3.54	428 -leq(multiplication(A,star(B)),star(B)) | leq(multiplication(star(A),A),star(B)).  [para(294(a,1),64(a,1,2)),rewrite([22(7)])].
3.23/3.54	482 multiplication(addition(A,one),star(A)) = star(A).  [para(309(a,1),44(a,1)),flip(a)].
3.23/3.55	487 leq(A,star(A)).  [para(309(a,1),318(a,2))].
3.23/3.55	492 addition(A,star(A)) = star(A).  [hyper(33,b,487,a)].
3.23/3.55	597 multiplication(star(A),star(star(A))) = star(star(A)).  [para(295(a,1),482(a,1,1))].
3.23/3.55	602 leq(multiplication(A,addition(B,one)),multiplication(A,star(B))).  [para(482(a,1),307(a,2,2))].
3.23/3.55	653 multiplication(star(A),addition(A,one)) = star(A).  [para(326(a,1),43(a,1)),flip(a)].
3.23/3.55	692 multiplication(star(star(A)),star(A)) = star(star(A)).  [para(295(a,1),653(a,1,2))].
3.23/3.55	844 leq(A,addition(B,addition(C,multiplication(A,addition(D,one))))).  [para(103(a,1),203(a,2,2))].
3.23/3.55	1356 multiplication(star(star(A)),multiplication(star(A),B)) = multiplication(star(star(A)),B).  [para(692(a,1),28(a,1,1)),flip(a)].
3.23/3.55	1371 leq(multiplication(star(star(A)),addition(A,one)),star(star(A))).  [para(692(a,1),602(a,2))].
3.23/3.55	1901 leq(multiplication(A,B),addition(C,multiplication(A,star(B)))).  [para(492(a,1),211(a,2,2,2))].
3.23/3.55	1903 leq(multiplication(star(addition(A,B)),A),star(addition(A,B))).  [para(326(a,1),211(a,2))].
3.23/3.55	1931 leq(multiplication(A,B),multiplication(addition(A,C),star(B))).  [para(30(a,1),1901(a,2)),rewrite([23(2)])].
3.23/3.55	1935 leq(multiplication(A,A),star(A)).  [para(309(a,1),1901(a,2))].
3.23/3.55	1951 addition(star(A),multiplication(A,A)) = star(A).  [hyper(33,b,1935,a),rewrite([23(3)])].
3.23/3.55	1990 leq(multiplication(addition(A,B),A),star(addition(A,B))).  [para(1951(a,1),211(a,2))].
3.23/3.55	2036 leq(multiplication(A,B),multiplication(star(A),star(B))).  [para(492(a,1),1931(a,2,1))].
3.23/3.55	2142 leq(multiplication(addition(A,B),B),star(addition(A,B))).  [para(23(a,1),1990(a,1,1)),rewrite([23(3)])].
3.23/3.55	2312 leq(multiplication(addition(A,one),star(star(A))),star(star(A))).  [para(482(a,1),120(a,1,2,2,2,1,2)),rewrite([295(6),23(8),27(8,R),294(7),492(6),597(7),353(7),295(10),482(9)])].
3.23/3.55	2333 leq(multiplication(A,star(addition(A,B))),star(addition(A,B))).  [para(309(a,1),212(a,2))].
3.23/3.55	3834 leq(multiplication(star(A),star(addition(A,one))),star(addition(A,one))).  [hyper(143,a,314,a)].
3.23/3.55	4192 leq(A,addition(B,addition(C,multiplication(A,star(D))))).  [para(295(a,1),844(a,2,2,2,2))].
3.23/3.55	4209 leq(A,addition(B,multiplication(addition(A,C),star(D)))).  [para(30(a,1),4192(a,2,2)),rewrite([23(1)])].
3.23/3.55	4240 leq(A,star(addition(A,B))).  [para(309(a,1),4209(a,2))].
3.23/3.55	4260 addition(A,star(addition(A,B))) = star(addition(A,B)).  [hyper(33,b,4240,a)].
3.23/3.55	6784 leq(multiplication(star(star(A)),star(addition(A,one))),star(star(A))).  [hyper(68,a,1371,a),rewrite([355(8)])].
3.23/3.55	6975 multiplication(star(addition(A,B)),addition(A,one)) = star(addition(A,B)).  [hyper(33,b,1903,a),rewrite([23(6),43(6)])].
3.23/3.55	7513 multiplication(addition(A,one),star(addition(A,B))) = star(addition(A,B)).  [hyper(33,b,2333,a),rewrite([23(6),44(6)])].
3.23/3.55	9534 leq(multiplication(A,star(addition(B,A))),star(addition(B,A))).  [para(309(a,1),219(a,1)),rewrite([44(8),7513(7),44(14),7513(13)]),xx(a)].
3.23/3.55	13474 -leq(addition(one,multiplication(A,B)),B) | leq(star(A),B).  [para(18(a,1),394(a,1)),rewrite([18(6),22(7)])].
3.23/3.55	13485 -leq(star(A),star(A)) | leq(star(addition(A,one)),star(A)).  [para(482(a,1),13474(a,1,2)),rewrite([294(3)])].
3.23/3.55	13805 leq(multiplication(star(star(A)),star(addition(A,one))),star(addition(A,one))).  [hyper(60,a,3834,a),rewrite([1356(8)])].
3.23/3.55	13862 leq(multiplication(star(A),A),star(addition(A,B))).  [hyper(428,a,9534,a),rewrite([23(3)])].
3.23/3.55	13863 leq(star(addition(A,one)),star(star(A))).  [hyper(428,a,2312,a),rewrite([6975(6)])].
3.23/3.55	13865 addition(star(star(A)),star(addition(A,one))) = star(star(A)).  [hyper(33,b,13863,a),rewrite([23(6)])].
3.23/3.55	13870 leq(star(addition(A,one)),star(addition(A,addition(B,one)))).  [para(43(a,2),13862(a,1)),rewrite([43(8),6975(6),23(6),27(6,R),23(5)])].
3.23/3.55	13941 leq(star(addition(A,one)),star(addition(A,star(B)))).  [para(295(a,1),13870(a,2,1,2))].
3.23/3.55	13944 leq(star(addition(A,one)),star(star(addition(A,B)))).  [para(4260(a,1),13941(a,2,1))].
3.23/3.55	13949 leq(star(addition(A,one)),star(star(multiplication(A,addition(B,one))))).  [para(43(a,1),13944(a,2,1,1))].
3.23/3.55	14481 multiplication(star(star(A)),star(addition(A,one))) = star(star(A)).  [hyper(33,b,6784,a),rewrite([23(9),297(9)])].
3.23/3.55	14482 leq(star(star(A)),star(addition(A,one))).  [back_rewrite(13805),rewrite([14481(6)])].
3.23/3.55	14483 star(addition(A,one)) = star(star(A)).  [hyper(33,b,14482,a),rewrite([13865(6)]),flip(a)].
3.23/3.55	14503 leq(star(star(A)),star(star(multiplication(A,addition(B,one))))).  [back_rewrite(13949),rewrite([14483(3)])].
3.23/3.55	14505 leq(star(star(A)),star(star(addition(A,B)))).  [back_rewrite(13944),rewrite([14483(3)])].
3.23/3.55	14523 -leq(star(A),star(A)) | leq(star(star(A)),star(A)).  [back_rewrite(13485),rewrite([14483(6)])].
3.23/3.55	14786 leq(star(star(multiplication(A,B))),star(star(multiplication(A,addition(B,C))))).  [para(29(a,1),14505(a,2,1,1))].
3.23/3.55	14787 leq(star(star(multiplication(A,B))),star(star(multiplication(addition(A,C),B)))).  [para(30(a,1),14505(a,2,1,1))].
3.23/3.55	14793 leq(star(star(A)),star(A)).  [hyper(14523,a,48,a)].
3.23/3.55	14794 star(star(A)) = star(A).  [hyper(33,b,14793,a),rewrite([23(4),492(4)])].
3.23/3.55	14797 leq(star(multiplication(A,B)),star(multiplication(addition(A,C),B))).  [back_rewrite(14787),rewrite([14794(3),14794(6)])].
3.23/3.55	14798 leq(star(multiplication(A,B)),star(multiplication(A,addition(B,C)))).  [back_rewrite(14786),rewrite([14794(3),14794(6)])].
3.23/3.55	14980 leq(star(A),star(multiplication(A,addition(B,one)))).  [back_rewrite(14503),rewrite([14794(2),14794(6)])].
3.23/3.55	15336 addition(star(A),star(multiplication(A,addition(B,one)))) = star(multiplication(A,addition(B,one))).  [hyper(33,b,14980,a)].
3.23/3.55	15439 leq(star(multiplication(A,B)),star(multiplication(star(A),B))).  [para(492(a,1),14797(a,2,1,1))].
3.23/3.55	15673 leq(star(multiplication(A,addition(A,one))),star(A)).  [para(653(a,1),15439(a,2,1)),rewrite([14794(6)])].
3.23/3.55	15692 star(multiplication(A,addition(A,one))) = star(A).  [hyper(33,b,15673,a),rewrite([23(6),15336(6)])].
3.23/3.55	16259 leq(star(multiplication(A,A)),star(A)).  [para(15692(a,1),14798(a,2))].
3.23/3.55	16260 addition(star(A),star(multiplication(A,A))) = star(A).  [hyper(33,b,16259,a),rewrite([23(4)])].
3.23/3.55	16511 leq(multiplication(star(A),star(multiplication(A,A))),star(A)).  [para(16260(a,1),2142(a,1,1)),rewrite([16260(8),14794(6)])].
3.23/3.55	16726 multiplication(star(A),star(multiplication(A,A))) = star(A).  [hyper(33,b,16511,a),rewrite([23(6),297(6)])].
3.23/3.55	16766 leq(multiplication(A,multiplication(A,A)),star(A)).  [para(16726(a,1),2036(a,2))].
3.23/3.55	16807 addition(star(A),multiplication(A,multiplication(A,A))) = star(A).  [hyper(33,b,16766,a),rewrite([23(4)])].
3.23/3.55	17720 leq(multiplication(A,multiplication(A,A)),addition(B,star(A))).  [para(16807(a,1),53(a,1,2)),xx(a)].
3.23/3.55	17744 leq(multiplication(A,multiplication(A,multiplication(A,multiplication(A,multiplication(A,A))))),star(A)).  [para(16260(a,1),17720(a,2)),rewrite([28(4),28(5)])].
3.23/3.55	17745 $F # answer(a).  [resolve(17744,a,31,a)].
3.23/3.55	
3.23/3.55	% SZS output end Refutation
3.23/3.55	============================== end of proof ==========================
3.23/3.55	
3.23/3.55	============================== STATISTICS ============================
3.23/3.55	
3.23/3.55	Given=1485. Generated=124714. Kept=17725. proofs=1.
3.23/3.55	Usable=1115. Sos=9999. Demods=493. Limbo=0, Disabled=6628. Hints=0.
3.23/3.55	Megabytes=12.40.
3.23/3.55	User_CPU=2.49, System_CPU=0.08, Wall_clock=2.
3.23/3.55	
3.23/3.55	============================== end of statistics =====================
3.23/3.55	
3.23/3.55	============================== end of search =========================
3.23/3.55	
3.23/3.55	THEOREM PROVED
3.23/3.55	% SZS status Theorem
3.23/3.55	
3.23/3.55	Exiting with 1 proof.
3.23/3.55	
3.23/3.55	Process 15882 exit (max_proofs) Thu Aug 29 13:59:06 2019
3.23/3.55	Prover9 interrupted
3.23/3.55	EOF