0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.34	% Computer   : n005.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 1200
0.12/0.34	% DateTime   : Tue Jul 13 16:02:18 EDT 2021
0.12/0.34	% CPUTime    : 
0.72/1.01	============================== Prover9 ===============================
0.72/1.01	Prover9 (32) version 2009-11A, November 2009.
0.72/1.01	Process 28046 was started by sandbox on n005.cluster.edu,
0.72/1.01	Tue Jul 13 16:02:19 2021
0.72/1.01	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_27858_n005.cluster.edu".
0.72/1.01	============================== end of head ===========================
0.72/1.01	
0.72/1.01	============================== INPUT =================================
0.72/1.01	
0.72/1.01	% Reading from file /tmp/Prover9_27858_n005.cluster.edu
0.72/1.01	
0.72/1.01	set(prolog_style_variables).
0.72/1.01	set(auto2).
0.72/1.01	    % set(auto2) -> set(auto).
0.72/1.01	    % set(auto) -> set(auto_inference).
0.72/1.01	    % set(auto) -> set(auto_setup).
0.72/1.01	    % set(auto_setup) -> set(predicate_elim).
0.72/1.01	    % set(auto_setup) -> assign(eq_defs, unfold).
0.72/1.01	    % set(auto) -> set(auto_limits).
0.72/1.01	    % set(auto_limits) -> assign(max_weight, "100.000").
0.72/1.01	    % set(auto_limits) -> assign(sos_limit, 20000).
0.72/1.01	    % set(auto) -> set(auto_denials).
0.72/1.01	    % set(auto) -> set(auto_process).
0.72/1.01	    % set(auto2) -> assign(new_constants, 1).
0.72/1.01	    % set(auto2) -> assign(fold_denial_max, 3).
0.72/1.01	    % set(auto2) -> assign(max_weight, "200.000").
0.72/1.01	    % set(auto2) -> assign(max_hours, 1).
0.72/1.01	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.72/1.01	    % set(auto2) -> assign(max_seconds, 0).
0.72/1.01	    % set(auto2) -> assign(max_minutes, 5).
0.72/1.01	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.72/1.01	    % set(auto2) -> set(sort_initial_sos).
0.72/1.01	    % set(auto2) -> assign(sos_limit, -1).
0.72/1.01	    % set(auto2) -> assign(lrs_ticks, 3000).
0.72/1.01	    % set(auto2) -> assign(max_megs, 400).
0.72/1.01	    % set(auto2) -> assign(stats, some).
0.72/1.01	    % set(auto2) -> clear(echo_input).
0.72/1.01	    % set(auto2) -> set(quiet).
0.72/1.01	    % set(auto2) -> clear(print_initial_clauses).
0.72/1.01	    % set(auto2) -> clear(print_given).
0.72/1.01	assign(lrs_ticks,-1).
0.72/1.01	assign(sos_limit,10000).
0.72/1.01	assign(order,kbo).
0.72/1.01	set(lex_order_vars).
0.72/1.01	clear(print_given).
0.72/1.01	
0.72/1.01	% formulas(sos).  % not echoed (19 formulas)
0.72/1.01	
0.72/1.01	============================== end of input ==========================
0.72/1.01	
0.72/1.01	% From the command line: assign(max_seconds, 1200).
0.72/1.01	
0.72/1.01	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.72/1.01	
0.72/1.01	% Formulas that are not ordinary clauses:
0.72/1.01	1 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.72/1.01	2 (all A addition(star(A),multiplication(strong_iteration(A),zero)) = strong_iteration(A)) # label(isolation) # label(axiom) # label(non_clause).  [assumption].
0.72/1.01	3 (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].
0.72/1.01	4 (all A star(A) = addition(one,multiplication(star(A),A))) # label(star_unfold2) # label(axiom) # label(non_clause).  [assumption].
0.72/1.01	5 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.72/1.01	6 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.72/1.01	7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.72/1.01	8 (all A addition(one,multiplication(A,star(A))) = star(A)) # label(star_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.72/1.01	9 (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].
0.72/1.01	10 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause).  [assumption].
0.72/1.01	11 (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].
0.72/1.01	12 (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].
0.72/1.01	13 (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].
0.72/1.01	14 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	15 (all A all B all C multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C))) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	16 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	17 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	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].
0.75/1.09	19 -(all X0 (leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) & leq(strong_iteration(one),strong_iteration(strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.75/1.09	
0.75/1.09	============================== end of process non-clausal formulas ===
0.75/1.09	
0.75/1.09	============================== PROCESS INITIAL CLAUSES ===============
0.75/1.09	
0.75/1.09	============================== PREDICATE ELIMINATION =================
0.75/1.09	
0.75/1.09	============================== end predicate elimination =============
0.75/1.09	
0.75/1.09	Auto_denials:
0.75/1.09	  % copying label goals to answer in negative clause
0.75/1.09	
0.75/1.09	Term ordering decisions:
0.75/1.09	Function symbol KB weights:  one=1. zero=1. c1=1. multiplication=1. addition=1. star=1. strong_iteration=1.
0.75/1.09	
0.75/1.09	============================== end of process initial clauses ========
0.75/1.09	
0.75/1.09	============================== CLAUSES FOR SEARCH ====================
0.75/1.09	
0.75/1.09	============================== end of clauses for search =============
0.75/1.09	
0.75/1.09	============================== SEARCH ================================
0.75/1.09	
0.75/1.09	% Starting search at 0.01 seconds.
0.75/1.09	
0.75/1.09	============================== PROOF =================================
0.75/1.09	% SZS status Theorem
0.75/1.09	% SZS output start Refutation
0.75/1.09	
0.75/1.09	% Proof 1 at 0.09 (+ 0.01) seconds: goals.
0.75/1.09	% Length of proof is 38.
0.75/1.09	% Level of proof is 8.
0.75/1.09	% Maximum clause weight is 14.000.
0.75/1.09	% Given clauses 152.
0.75/1.09	
0.75/1.09	5 (all A strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one)) # label(infty_unfold1) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	7 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	9 (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].
0.75/1.09	10 (all A addition(A,A) = A) # label(idempotence) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	13 (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].
0.75/1.09	14 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	15 (all A all B all C multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C))) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	16 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	17 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	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].
0.75/1.09	19 -(all X0 (leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) & leq(strong_iteration(one),strong_iteration(strong_iteration(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.75/1.09	22 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(7)].
0.75/1.09	23 addition(A,A) = A # label(idempotence) # label(axiom).  [clausify(10)].
0.75/1.09	24 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(16)].
0.75/1.09	25 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(17)].
0.75/1.09	27 addition(multiplication(A,strong_iteration(A)),one) = strong_iteration(A) # label(infty_unfold1) # label(axiom).  [clausify(5)].
0.75/1.09	28 addition(one,multiplication(A,strong_iteration(A))) = strong_iteration(A).  [copy(27),rewrite([25(4)])].
0.75/1.09	31 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(13)].
0.75/1.09	32 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(31),rewrite([25(2)]),flip(a)].
0.75/1.09	33 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(15)].
0.75/1.09	34 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(distributivity2) # label(axiom).  [clausify(9)].
0.75/1.09	36 -leq(strong_iteration(strong_iteration(c1)),strong_iteration(one)) | -leq(strong_iteration(one),strong_iteration(strong_iteration(c1))) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(19)].
0.75/1.09	37 addition(A,B) != B | leq(A,B) # label(order) # label(axiom).  [clausify(14)].
0.75/1.09	43 -leq(A,addition(multiplication(B,A),C)) | leq(A,multiplication(strong_iteration(B),C)) # label(infty_coinduction) # label(axiom).  [clausify(18)].
0.75/1.09	44 -leq(A,addition(B,multiplication(C,A))) | leq(A,multiplication(strong_iteration(C),B)).  [copy(43),rewrite([25(2)])].
0.75/1.09	49 addition(A,addition(A,B)) = addition(A,B).  [para(32(a,1),23(a,1)),rewrite([25(1),25(2),32(2,R),23(1),25(3)])].
0.75/1.09	55 addition(A,multiplication(B,multiplication(strong_iteration(B),A))) = multiplication(strong_iteration(B),A).  [para(28(a,1),34(a,2,1)),rewrite([22(2),33(3)])].
0.75/1.09	71 addition(A,addition(B,C)) != addition(A,C) | leq(B,addition(A,C)).  [para(32(a,1),37(a,1)),rewrite([25(3),25(5)])].
0.75/1.09	92 -leq(A,addition(A,B)) | leq(A,multiplication(strong_iteration(one),B)).  [para(22(a,1),44(a,2,2)),rewrite([25(1)])].
0.75/1.09	118 leq(A,addition(A,B)).  [hyper(37,a,49,a)].
0.75/1.09	122 leq(A,multiplication(strong_iteration(one),B)).  [back_unit_del(92),unit_del(a,118)].
0.75/1.09	138 leq(A,strong_iteration(one)).  [para(24(a,1),122(a,2))].
0.75/1.09	139 -leq(strong_iteration(one),strong_iteration(strong_iteration(c1))) # answer(goals).  [back_unit_del(36),unit_del(a,138)].
0.75/1.09	491 leq(A,addition(B,addition(A,C))).  [para(49(a,1),71(a,1,2)),xx(a)].
0.75/1.09	540 leq(A,addition(B,multiplication(strong_iteration(C),A))).  [para(55(a,1),491(a,2,2))].
0.75/1.09	703 leq(A,multiplication(strong_iteration(strong_iteration(B)),C)).  [hyper(44,a,540,a)].
0.75/1.09	714 leq(A,strong_iteration(strong_iteration(B))).  [para(24(a,1),703(a,2))].
0.75/1.09	715 $F # answer(goals).  [resolve(714,a,139,a)].
0.75/1.09	
0.75/1.09	% SZS output end Refutation
0.75/1.09	============================== end of proof ==========================
0.75/1.09	
0.75/1.09	============================== STATISTICS ============================
0.75/1.09	
0.75/1.09	Given=152. Generated=2721. Kept=690. proofs=1.
0.75/1.09	Usable=128. Sos=455. Demods=150. Limbo=1, Disabled=125. Hints=0.
0.75/1.09	Megabytes=0.63.
0.75/1.09	User_CPU=0.09, System_CPU=0.01, Wall_clock=0.
0.75/1.09	
0.75/1.09	============================== end of statistics =====================
0.75/1.09	
0.75/1.09	============================== end of search =========================
0.75/1.09	
0.75/1.09	THEOREM PROVED
0.75/1.09	% SZS status Theorem
0.75/1.09	
0.75/1.09	Exiting with 1 proof.
0.75/1.09	
0.75/1.09	Process 28046 exit (max_proofs) Tue Jul 13 16:02:19 2021
0.75/1.09	Prover9 interrupted
0.75/1.09	EOF