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   : n026.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 12:15:50 EDT 2019
0.12/0.33	% CPUTime    : 
0.42/0.99	============================== Prover9 ===============================
0.42/0.99	Prover9 (32) version 2009-11A, November 2009.
0.42/0.99	Process 31712 was started by sandbox on n026.cluster.edu,
0.42/0.99	Thu Aug 29 12:15:51 2019
0.42/0.99	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_31558_n026.cluster.edu".
0.42/0.99	============================== end of head ===========================
0.42/0.99	
0.42/0.99	============================== INPUT =================================
0.42/0.99	
0.42/0.99	% Reading from file /tmp/Prover9_31558_n026.cluster.edu
0.42/0.99	
0.42/0.99	set(prolog_style_variables).
0.42/0.99	set(auto2).
0.42/0.99	    % set(auto2) -> set(auto).
0.42/0.99	    % set(auto) -> set(auto_inference).
0.42/0.99	    % set(auto) -> set(auto_setup).
0.42/0.99	    % set(auto_setup) -> set(predicate_elim).
0.42/0.99	    % set(auto_setup) -> assign(eq_defs, unfold).
0.42/0.99	    % set(auto) -> set(auto_limits).
0.42/0.99	    % set(auto_limits) -> assign(max_weight, "100.000").
0.42/0.99	    % set(auto_limits) -> assign(sos_limit, 20000).
0.42/0.99	    % set(auto) -> set(auto_denials).
0.42/0.99	    % set(auto) -> set(auto_process).
0.42/0.99	    % set(auto2) -> assign(new_constants, 1).
0.42/0.99	    % set(auto2) -> assign(fold_denial_max, 3).
0.42/0.99	    % set(auto2) -> assign(max_weight, "200.000").
0.42/0.99	    % set(auto2) -> assign(max_hours, 1).
0.42/0.99	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.42/0.99	    % set(auto2) -> assign(max_seconds, 0).
0.42/0.99	    % set(auto2) -> assign(max_minutes, 5).
0.42/0.99	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.42/0.99	    % set(auto2) -> set(sort_initial_sos).
0.42/0.99	    % set(auto2) -> assign(sos_limit, -1).
0.42/0.99	    % set(auto2) -> assign(lrs_ticks, 3000).
0.42/0.99	    % set(auto2) -> assign(max_megs, 400).
0.42/0.99	    % set(auto2) -> assign(stats, some).
0.42/0.99	    % set(auto2) -> clear(echo_input).
0.42/0.99	    % set(auto2) -> set(quiet).
0.42/0.99	    % set(auto2) -> clear(print_initial_clauses).
0.42/0.99	    % set(auto2) -> clear(print_given).
0.42/0.99	assign(lrs_ticks,-1).
0.42/0.99	assign(sos_limit,10000).
0.42/0.99	assign(order,kbo).
0.42/0.99	set(lex_order_vars).
0.42/0.99	clear(print_given).
0.42/0.99	
0.42/0.99	% formulas(sos).  % not echoed (19 formulas)
0.42/0.99	
0.42/0.99	============================== end of input ==========================
0.42/0.99	
0.42/0.99	% From the command line: assign(max_seconds, 180).
0.42/0.99	
0.42/0.99	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.42/0.99	
0.42/0.99	% Formulas that are not ordinary clauses:
0.42/0.99	1 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.42/0.99	2 (all A A = addition(A,A)) # label(idempotence) # label(axiom) # label(non_clause).  [assumption].
0.42/0.99	3 (all A star(A) = addition(one,multiplication(star(A),A))) # label(star_unfold2) # label(axiom) # label(non_clause).  [assumption].
0.42/0.99	4 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.42/0.99	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].
0.42/0.99	6 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
0.42/0.99	7 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.42/0.99	8 (all A all B (addition(A,B) = B <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.42/0.99	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].
0.42/0.99	10 (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].
0.42/0.99	11 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause).  [assumption].
0.42/0.99	12 (all A A = addition(A,zero)) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.42/0.99	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].
0.42/0.99	14 (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].
0.97/1.28	15 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	16 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	17 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	18 (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].
0.97/1.28	19 -(all X0 strong_iteration(one) = strong_iteration(star(X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.97/1.28	
0.97/1.28	============================== end of process non-clausal formulas ===
0.97/1.28	
0.97/1.28	============================== PROCESS INITIAL CLAUSES ===============
0.97/1.28	
0.97/1.28	============================== PREDICATE ELIMINATION =================
0.97/1.28	
0.97/1.28	============================== end predicate elimination =============
0.97/1.28	
0.97/1.28	Auto_denials:
0.97/1.28	  % copying label goals to answer in negative clause
0.97/1.28	
0.97/1.28	Term ordering decisions:
0.97/1.28	Function symbol KB weights:  one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
0.97/1.28	
0.97/1.28	============================== end of process initial clauses ========
0.97/1.28	
0.97/1.28	============================== CLAUSES FOR SEARCH ====================
0.97/1.28	
0.97/1.28	============================== end of clauses for search =============
0.97/1.28	
0.97/1.28	============================== SEARCH ================================
0.97/1.28	
0.97/1.28	% Starting search at 0.01 seconds.
0.97/1.28	
0.97/1.28	============================== PROOF =================================
0.97/1.28	% SZS status Theorem
0.97/1.28	% SZS output start Refutation
0.97/1.28	
0.97/1.28	% Proof 1 at 0.29 (+ 0.02) seconds: goals.
0.97/1.28	% Length of proof is 90.
0.97/1.28	% Level of proof is 15.
0.97/1.28	% Maximum clause weight is 17.000.
0.97/1.28	% Given clauses 393.
0.97/1.28	
0.97/1.28	1 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	2 (all A A = addition(A,A)) # label(idempotence) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	3 (all A star(A) = addition(one,multiplication(star(A),A))) # label(star_unfold2) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	4 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	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].
0.97/1.28	6 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	7 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	8 (all A all B (addition(A,B) = B <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	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].
0.97/1.28	11 (all A strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero))) # label(isolation) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	12 (all A A = addition(A,zero)) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	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].
0.97/1.28	14 (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].
0.97/1.28	15 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	16 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	17 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.97/1.28	18 (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].
0.97/1.28	19 -(all X0 strong_iteration(one) = strong_iteration(star(X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.97/1.28	20 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [clausify(1)].
0.97/1.28	21 addition(A,A) = A # label(idempotence) # label(axiom).  [clausify(2)].
0.97/1.28	22 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(12)].
0.97/1.28	23 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(15)].
0.97/1.28	24 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(16)].
0.97/1.28	25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(17)].
0.97/1.28	26 star(A) = addition(one,multiplication(star(A),A)) # label(star_unfold2) # label(axiom).  [clausify(3)].
0.97/1.28	27 addition(one,multiplication(star(A),A)) = star(A).  [copy(26),flip(a)].
0.97/1.28	28 strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) # label(infty_unfold1) # label(axiom).  [clausify(4)].
0.97/1.28	29 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A).  [copy(28),rewrite([25(5)]),flip(a)].
0.97/1.28	30 star(A) = addition(one,multiplication(A,star(A))) # label(star_unfold1) # label(axiom).  [clausify(7)].
0.97/1.28	31 addition(one,multiplication(A,star(A))) = star(A).  [copy(30),flip(a)].
0.97/1.28	32 strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)) # label(isolation) # label(axiom).  [clausify(11)].
0.97/1.28	33 addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A).  [copy(32),flip(a)].
0.97/1.28	34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(6)].
0.97/1.28	35 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(34),rewrite([25(2)]),flip(a)].
0.97/1.28	36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(13)].
0.97/1.28	37 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(distributivity1) # label(axiom).  [clausify(5)].
0.97/1.28	38 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(distributivity2) # label(axiom).  [clausify(14)].
0.97/1.28	39 strong_iteration(star(c1)) != strong_iteration(one) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(19)].
0.97/1.28	40 addition(A,B) != B | leq(A,B) # label(order) # label(axiom).  [clausify(8)].
0.97/1.28	41 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom).  [clausify(8)].
0.97/1.28	42 -leq(addition(multiplication(A,B),C),A) | leq(multiplication(C,star(B)),A) # label(star_induction2) # label(axiom).  [clausify(9)].
0.97/1.28	43 -leq(addition(A,multiplication(B,C)),B) | leq(multiplication(A,star(C)),B).  [copy(42),rewrite([25(2)])].
0.97/1.28	46 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom).  [clausify(18)].
0.97/1.28	47 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)).  [copy(46),rewrite([25(2)])].
0.97/1.28	49 strong_iteration(zero) = one.  [para(20(a,1),29(a,1,2)),rewrite([22(3)]),flip(a)].
0.97/1.28	52 addition(A,addition(A,B)) = addition(A,B).  [para(35(a,1),21(a,1)),rewrite([25(1),25(2),35(2,R),21(1),25(3)])].
0.97/1.28	53 addition(one,multiplication(A,multiplication(B,strong_iteration(multiplication(A,B))))) = strong_iteration(multiplication(A,B)).  [para(36(a,1),29(a,1,2))].
0.97/1.28	54 addition(one,multiplication(A,multiplication(B,star(multiplication(A,B))))) = star(multiplication(A,B)).  [para(36(a,1),31(a,1,2))].
0.97/1.28	55 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)).  [para(24(a,1),37(a,1,1)),rewrite([25(4)])].
0.97/1.28	60 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A).  [para(23(a,1),38(a,1,1)),rewrite([25(4)])].
0.97/1.28	62 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A).  [para(29(a,1),38(a,2,1)),rewrite([23(2),36(3)])].
0.97/1.28	63 addition(A,multiplication(B,multiplication(star(B),A))) = multiplication(star(B),A).  [para(31(a,1),38(a,2,1)),rewrite([23(2),36(3)])].
0.97/1.28	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)])].
0.97/1.28	68 leq(A,A).  [hyper(40,a,21,a)].
0.97/1.28	75 addition(A,addition(B,C)) != addition(A,C) | leq(B,addition(A,C)).  [para(35(a,1),40(a,1)),rewrite([25(3),25(5)])].
0.97/1.28	80 -leq(multiplication(A,B),A) | leq(multiplication(A,multiplication(B,star(B))),A).  [para(21(a,1),43(a,1)),rewrite([36(5)])].
0.97/1.28	122 leq(A,addition(A,B)).  [hyper(40,a,52,a)].
0.97/1.28	123 addition(one,star(A)) = star(A).  [para(27(a,1),52(a,1,2)),rewrite([27(7)])].
0.97/1.28	131 leq(multiplication(A,B),multiplication(A,addition(B,C))).  [para(37(a,1),122(a,2))].
0.97/1.28	218 leq(multiplication(A,B),addition(A,multiplication(A,B))).  [para(55(a,2),131(a,2))].
0.97/1.28	294 leq(multiplication(A,star(A)),star(A)).  [para(54(a,1),218(a,2)),rewrite([23(3),23(4),23(4)])].
0.97/1.28	303 multiplication(addition(A,one),star(A)) = star(A).  [hyper(41,b,294,a),rewrite([25(4),60(4)])].
0.97/1.28	336 multiplication(star(A),A) = multiplication(A,star(A)).  [para(63(a,1),55(a,1)),rewrite([25(6),27(6)])].
0.97/1.28	452 addition(A,star(A)) = star(A).  [para(303(a,1),55(a,1,2)),rewrite([25(4),35(4),25(3),35(4,R),25(3),123(3),25(7),123(7),303(6)])].
0.97/1.28	486 leq(A,addition(B,addition(A,C))).  [para(52(a,1),75(a,1,2)),xx(a)].
0.97/1.28	536 leq(A,addition(B,multiplication(strong_iteration(C),A))).  [para(62(a,1),486(a,2,2))].
0.97/1.28	537 leq(A,addition(B,multiplication(star(C),A))).  [para(63(a,1),486(a,2,2))].
0.97/1.28	602 leq(A,multiplication(strong_iteration(strong_iteration(B)),C)).  [hyper(47,a,536,a)].
0.97/1.28	613 leq(A,strong_iteration(strong_iteration(B))).  [para(24(a,1),602(a,2))].
0.97/1.28	614 leq(A,multiplication(strong_iteration(one),B)).  [para(49(a,1),602(a,2,1,1))].
0.97/1.28	616 -leq(A,one) | leq(multiplication(A,star(A)),one).  [para(23(a,1),80(a,1)),rewrite([23(6)])].
0.97/1.28	624 leq(A,strong_iteration(one)).  [para(49(a,1),613(a,2,1))].
0.97/1.28	626 addition(A,strong_iteration(one)) = strong_iteration(one).  [hyper(41,b,624,a)].
0.97/1.28	627 addition(A,multiplication(strong_iteration(one),B)) = multiplication(strong_iteration(one),B).  [hyper(41,b,614,a)].
0.97/1.28	659 leq(A,multiplication(strong_iteration(star(B)),C)).  [hyper(47,a,537,a)].
0.97/1.28	661 leq(A,multiplication(star(B),addition(A,C))).  [para(37(a,1),537(a,2)),rewrite([25(2)])].
0.97/1.28	670 leq(A,strong_iteration(star(B))).  [para(24(a,1),659(a,2))].
0.97/1.28	671 addition(A,strong_iteration(star(B))) = strong_iteration(star(B)).  [hyper(41,b,670,a)].
0.97/1.28	984 multiplication(star(A),addition(A,one)) = star(A).  [para(336(a,1),55(a,1,2)),rewrite([60(4),303(4)]),flip(a)].
0.97/1.28	1222 leq(star(one),one).  [hyper(616,a,68,a),rewrite([23(4)])].
0.97/1.28	1225 star(one) = one.  [hyper(41,b,1222,a),rewrite([25(4),452(4)])].
0.97/1.28	1245 multiplication(strong_iteration(one),zero) = strong_iteration(one).  [para(1225(a,1),33(a,1,1)),rewrite([627(6)])].
0.97/1.28	1246 multiplication(strong_iteration(one),A) = strong_iteration(one).  [para(1245(a,1),36(a,1,1)),rewrite([20(7),1245(7)])].
0.97/1.28	1253 addition(strong_iteration(one),multiplication(A,B)) = strong_iteration(one).  [para(1245(a,1),65(a,2,1,2)),rewrite([20(4),1246(4),626(7),1246(7)])].
0.97/1.28	1355 leq(A,multiplication(star(B),strong_iteration(star(C)))).  [para(671(a,1),661(a,2,2))].
0.97/1.28	1390 addition(A,multiplication(star(B),strong_iteration(star(C)))) = multiplication(star(B),strong_iteration(star(C))).  [hyper(41,b,1355,a)].
0.97/1.28	1599 multiplication(star(A),multiplication(addition(A,one),B)) = multiplication(star(A),B).  [para(984(a,1),36(a,1,1)),flip(a)].
0.97/1.28	1604 multiplication(star(A),strong_iteration(star(A))) = strong_iteration(star(A)).  [para(984(a,1),53(a,1,2,2,2,1)),rewrite([1599(8),1390(6),984(8)])].
0.97/1.28	3060 strong_iteration(star(A)) = strong_iteration(one).  [para(1604(a,1),1253(a,1,2)),rewrite([671(5)])].
0.97/1.28	3061 $F # answer(goals).  [resolve(3060,a,39,a)].
0.97/1.28	
0.97/1.28	% SZS output end Refutation
0.97/1.28	============================== end of proof ==========================
0.97/1.28	
0.97/1.28	============================== STATISTICS ============================
0.97/1.28	
0.97/1.28	Given=393. Generated=11623. Kept=3033. proofs=1.
0.97/1.28	Usable=357. Sos=2393. Demods=438. Limbo=14, Disabled=288. Hints=0.
0.97/1.28	Megabytes=2.87.
0.97/1.28	User_CPU=0.29, System_CPU=0.02, Wall_clock=0.
0.97/1.28	
0.97/1.28	============================== end of statistics =====================
0.97/1.28	
0.97/1.28	============================== end of search =========================
0.97/1.28	
0.97/1.28	THEOREM PROVED
0.97/1.28	% SZS status Theorem
0.97/1.28	
0.97/1.28	Exiting with 1 proof.
0.97/1.28	
0.97/1.28	Process 31712 exit (max_proofs) Thu Aug 29 12:15:51 2019
0.97/1.28	Prover9 interrupted
0.97/1.29	EOF