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
0.03/0.23	% Computer   : n144.star.cs.uiowa.edu
0.03/0.23	% Model      : x86_64 x86_64
0.03/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.23	% Memory     : 32218.625MB
0.03/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.23	% CPULimit   : 300
0.03/0.23	% DateTime   : Sat Jul 14 05:06:55 CDT 2018
0.03/0.23	% CPUTime    : 
0.06/0.43	============================== Prover9 ===============================
0.06/0.43	Prover9 (32) version 2009-11A, November 2009.
0.06/0.43	Process 1254 was started by sandbox2 on n144.star.cs.uiowa.edu,
0.06/0.43	Sat Jul 14 05:06:55 2018
0.06/0.43	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1221_n144.star.cs.uiowa.edu".
0.06/0.43	============================== end of head ===========================
0.06/0.43	
0.06/0.43	============================== INPUT =================================
0.06/0.43	
0.06/0.43	% Reading from file /tmp/Prover9_1221_n144.star.cs.uiowa.edu
0.06/0.43	
0.06/0.43	set(prolog_style_variables).
0.06/0.43	set(auto2).
0.06/0.43	    % set(auto2) -> set(auto).
0.06/0.43	    % set(auto) -> set(auto_inference).
0.06/0.43	    % set(auto) -> set(auto_setup).
0.06/0.43	    % set(auto_setup) -> set(predicate_elim).
0.06/0.43	    % set(auto_setup) -> assign(eq_defs, unfold).
0.06/0.43	    % set(auto) -> set(auto_limits).
0.06/0.43	    % set(auto_limits) -> assign(max_weight, "100.000").
0.06/0.43	    % set(auto_limits) -> assign(sos_limit, 20000).
0.06/0.43	    % set(auto) -> set(auto_denials).
0.06/0.43	    % set(auto) -> set(auto_process).
0.06/0.43	    % set(auto2) -> assign(new_constants, 1).
0.06/0.43	    % set(auto2) -> assign(fold_denial_max, 3).
0.06/0.43	    % set(auto2) -> assign(max_weight, "200.000").
0.06/0.43	    % set(auto2) -> assign(max_hours, 1).
0.06/0.43	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.06/0.43	    % set(auto2) -> assign(max_seconds, 0).
0.06/0.43	    % set(auto2) -> assign(max_minutes, 5).
0.06/0.43	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.06/0.43	    % set(auto2) -> set(sort_initial_sos).
0.06/0.43	    % set(auto2) -> assign(sos_limit, -1).
0.06/0.43	    % set(auto2) -> assign(lrs_ticks, 3000).
0.06/0.43	    % set(auto2) -> assign(max_megs, 400).
0.06/0.43	    % set(auto2) -> assign(stats, some).
0.06/0.43	    % set(auto2) -> clear(echo_input).
0.06/0.43	    % set(auto2) -> set(quiet).
0.06/0.43	    % set(auto2) -> clear(print_initial_clauses).
0.06/0.43	    % set(auto2) -> clear(print_given).
0.06/0.43	assign(lrs_ticks,-1).
0.06/0.43	assign(sos_limit,10000).
0.06/0.43	assign(order,kbo).
0.06/0.43	set(lex_order_vars).
0.06/0.43	clear(print_given).
0.06/0.43	
0.06/0.43	% formulas(sos).  % not echoed (17 formulas)
0.06/0.43	
0.06/0.43	============================== end of input ==========================
0.06/0.43	
0.06/0.43	% From the command line: assign(max_seconds, 300).
0.06/0.43	
0.06/0.43	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.06/0.43	
0.06/0.43	% Formulas that are not ordinary clauses:
0.06/0.43	1 (all A all B (addition(A,B) = B <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.06/0.43	2 (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].
0.06/0.43	3 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.06/0.43	4 (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].
0.06/0.43	5 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.06/0.43	6 (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].
0.06/0.43	7 (all A zero = multiplication(A,zero)) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.06/0.43	8 (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].
0.06/0.43	9 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause).  [assumption].
0.06/0.43	10 (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].
0.06/0.43	11 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.06/0.43	12 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause).  [assumption].
0.06/0.43	13 (all A A = addition(A,zero)) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.06/0.43	14 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.34/0.58	15 (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].
0.34/0.58	16 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.34/0.58	
0.34/0.58	============================== end of process non-clausal formulas ===
0.34/0.58	
0.34/0.58	============================== PROCESS INITIAL CLAUSES ===============
0.34/0.58	
0.34/0.58	============================== PREDICATE ELIMINATION =================
0.34/0.58	
0.34/0.58	============================== end predicate elimination =============
0.34/0.58	
0.34/0.58	Auto_denials:
0.34/0.58	  % copying label a to answer in negative clause
0.34/0.58	
0.34/0.58	Term ordering decisions:
0.34/0.58	
0.34/0.58	% Assigning unary symbol star kb_weight 0 and highest precedence (8).
0.34/0.58	Function symbol KB weights:  zero=1. one=1. a=1. multiplication=1. addition=1. star=0.
0.34/0.58	
0.34/0.58	============================== end of process initial clauses ========
0.34/0.58	
0.34/0.58	============================== CLAUSES FOR SEARCH ====================
0.34/0.58	
0.34/0.58	============================== end of clauses for search =============
0.34/0.58	
0.34/0.58	============================== SEARCH ================================
0.34/0.58	
0.34/0.58	% Starting search at 0.01 seconds.
0.34/0.58	
0.34/0.58	============================== PROOF =================================
0.34/0.58	% SZS status Theorem
0.34/0.58	% SZS output start Refutation
0.34/0.58	
0.34/0.58	% Proof 1 at 0.15 (+ 0.00) seconds: a.
0.34/0.58	% Length of proof is 46.
0.34/0.58	% Level of proof is 13.
0.34/0.58	% Maximum clause weight is 16.000.
0.34/0.58	% Given clauses 222.
0.34/0.58	
0.34/0.58	1 (all A all B (addition(A,B) = B <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.34/0.58	3 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.34/0.58	5 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.34/0.58	6 (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].
0.34/0.58	8 (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].
0.34/0.58	9 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause).  [assumption].
0.34/0.58	12 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause).  [assumption].
0.34/0.58	15 (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].
0.34/0.58	16 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.34/0.58	17 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(3)].
0.34/0.58	18 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(5)].
0.34/0.58	23 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(16)].
0.34/0.58	24 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom).  [clausify(9)].
0.34/0.58	25 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom).  [clausify(12)].
0.34/0.58	27 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(15)].
0.34/0.58	28 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(27),rewrite([23(2)]),flip(a)].
0.34/0.58	29 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom).  [clausify(6)].
0.34/0.58	30 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)).  [copy(29),flip(a)].
0.34/0.58	31 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom).  [clausify(8)].
0.34/0.58	32 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B).  [copy(31),flip(a)].
0.34/0.58	33 -leq(multiplication(a,a),star(a)) # label(a) # label(negated_conjecture) # answer(a).  [assumption].
0.34/0.58	34 addition(A,B) != B | leq(A,B) # label(order) # label(axiom).  [clausify(1)].
0.34/0.58	35 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom).  [clausify(1)].
0.34/0.58	43 addition(A,addition(A,B)) = addition(A,B).  [para(28(a,1),17(a,1)),rewrite([23(1),23(2),28(2,R),17(1),23(3)])].
0.34/0.58	46 multiplication(addition(A,one),B) = addition(B,multiplication(A,B)).  [para(18(a,1),32(a,1,1)),rewrite([23(4)]),flip(a)].
0.34/0.58	54 addition(A,addition(B,C)) != addition(A,C) | leq(B,addition(A,C)).  [para(28(a,1),34(a,1)),rewrite([23(3),23(5)])].
0.34/0.58	55 addition(A,addition(B,C)) != addition(A,B) | leq(C,addition(A,B)).  [para(28(a,2),34(a,1))].
0.34/0.58	58 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A).  [hyper(35,b,25,a),rewrite([23(6)])].
0.34/0.58	59 addition(star(A),addition(one,multiplication(star(A),A))) = star(A).  [hyper(35,b,24,a),rewrite([23(6)])].
0.34/0.58	199 leq(A,addition(B,A)).  [para(17(a,1),54(a,1,2)),xx(a)].
0.34/0.58	205 leq(A,addition(B,addition(A,C))).  [para(43(a,1),54(a,1,2)),xx(a)].
0.34/0.58	212 leq(addition(A,B),addition(A,addition(B,C))).  [para(28(a,1),199(a,2)),rewrite([23(2),28(3,R),23(2)])].
0.34/0.58	213 leq(multiplication(A,B),addition(C,multiplication(A,addition(B,D)))).  [para(30(a,1),205(a,2,2))].
0.34/0.58	216 leq(A,addition(B,multiplication(addition(C,one),A))).  [para(46(a,2),205(a,2,2))].
0.34/0.58	292 addition(star(A),one) != star(A) | leq(multiplication(A,star(A)),addition(star(A),one)).  [para(58(a,1),55(a,1)),flip(a)].
0.34/0.58	293 leq(addition(star(A),one),star(A)).  [para(58(a,1),212(a,2))].
0.34/0.58	297 addition(star(A),one) = star(A).  [hyper(35,b,293,a),rewrite([23(5),43(5)])].
0.34/0.58	298 leq(multiplication(A,star(A)),star(A)).  [back_rewrite(292),rewrite([297(3),297(8)]),xx(a)].
0.34/0.58	311 addition(star(A),multiplication(star(A),A)) = star(A).  [para(59(a,1),28(a,1)),rewrite([297(6),23(5)]),flip(a)].
0.34/0.58	322 leq(A,addition(B,multiplication(star(C),A))).  [para(297(a,1),216(a,2,2,1))].
0.34/0.58	328 addition(star(A),multiplication(A,star(A))) = star(A).  [hyper(35,b,298,a),rewrite([23(4)])].
0.34/0.58	479 leq(A,star(A)).  [para(311(a,1),322(a,2))].
0.34/0.58	484 addition(A,star(A)) = star(A).  [hyper(35,b,479,a)].
0.34/0.58	1894 leq(multiplication(A,B),addition(C,multiplication(A,star(B)))).  [para(484(a,1),213(a,2,2,2))].
0.34/0.58	1934 leq(multiplication(A,A),star(A)).  [para(328(a,1),1894(a,2))].
0.34/0.58	1935 $F # answer(a).  [resolve(1934,a,33,a)].
0.34/0.58	
0.34/0.58	% SZS output end Refutation
0.34/0.58	============================== end of proof ==========================
0.34/0.58	
0.34/0.58	============================== STATISTICS ============================
0.34/0.58	
0.34/0.58	Given=222. Generated=5851. Kept=1913. proofs=1.
0.34/0.58	Usable=194. Sos=1592. Demods=229. Limbo=6, Disabled=138. Hints=0.
0.34/0.58	Megabytes=1.87.
0.34/0.58	User_CPU=0.15, System_CPU=0.00, Wall_clock=0.
0.34/0.58	
0.34/0.58	============================== end of statistics =====================
0.34/0.58	
0.34/0.58	============================== end of search =========================
0.34/0.58	
0.34/0.58	THEOREM PROVED
0.34/0.58	% SZS status Theorem
0.34/0.58	
0.34/0.58	Exiting with 1 proof.
0.34/0.58	
0.34/0.58	Process 1254 exit (max_proofs) Sat Jul 14 05:06:55 2018
0.34/0.58	Prover9 interrupted
0.34/0.58	EOF