0.12/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.14/0.35	% Computer   : n029.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 1200
0.14/0.35	% DateTime   : Tue Jul 13 16:17:55 EDT 2021
0.14/0.35	% CPUTime    : 
0.50/1.07	============================== Prover9 ===============================
0.50/1.07	Prover9 (32) version 2009-11A, November 2009.
0.50/1.07	Process 21062 was started by sandbox2 on n029.cluster.edu,
0.50/1.07	Tue Jul 13 16:17:55 2021
0.50/1.07	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_20909_n029.cluster.edu".
0.50/1.07	============================== end of head ===========================
0.50/1.07	
0.50/1.07	============================== INPUT =================================
0.50/1.07	
0.50/1.07	% Reading from file /tmp/Prover9_20909_n029.cluster.edu
0.50/1.07	
0.50/1.07	set(prolog_style_variables).
0.50/1.07	set(auto2).
0.50/1.07	    % set(auto2) -> set(auto).
0.50/1.07	    % set(auto) -> set(auto_inference).
0.50/1.07	    % set(auto) -> set(auto_setup).
0.50/1.07	    % set(auto_setup) -> set(predicate_elim).
0.50/1.07	    % set(auto_setup) -> assign(eq_defs, unfold).
0.50/1.07	    % set(auto) -> set(auto_limits).
0.50/1.07	    % set(auto_limits) -> assign(max_weight, "100.000").
0.50/1.07	    % set(auto_limits) -> assign(sos_limit, 20000).
0.50/1.07	    % set(auto) -> set(auto_denials).
0.50/1.07	    % set(auto) -> set(auto_process).
0.50/1.07	    % set(auto2) -> assign(new_constants, 1).
0.50/1.07	    % set(auto2) -> assign(fold_denial_max, 3).
0.50/1.07	    % set(auto2) -> assign(max_weight, "200.000").
0.50/1.07	    % set(auto2) -> assign(max_hours, 1).
0.50/1.07	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.50/1.07	    % set(auto2) -> assign(max_seconds, 0).
0.50/1.07	    % set(auto2) -> assign(max_minutes, 5).
0.50/1.07	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.50/1.07	    % set(auto2) -> set(sort_initial_sos).
0.50/1.07	    % set(auto2) -> assign(sos_limit, -1).
0.50/1.07	    % set(auto2) -> assign(lrs_ticks, 3000).
0.50/1.07	    % set(auto2) -> assign(max_megs, 400).
0.50/1.07	    % set(auto2) -> assign(stats, some).
0.50/1.07	    % set(auto2) -> clear(echo_input).
0.50/1.07	    % set(auto2) -> set(quiet).
0.50/1.07	    % set(auto2) -> clear(print_initial_clauses).
0.50/1.07	    % set(auto2) -> clear(print_given).
0.50/1.07	assign(lrs_ticks,-1).
0.50/1.07	assign(sos_limit,10000).
0.50/1.07	assign(order,kbo).
0.50/1.07	set(lex_order_vars).
0.50/1.07	clear(print_given).
0.50/1.07	
0.50/1.07	% formulas(sos).  % not echoed (17 formulas)
0.50/1.07	
0.50/1.07	============================== end of input ==========================
0.50/1.07	
0.50/1.07	% From the command line: assign(max_seconds, 1200).
0.50/1.07	
0.50/1.07	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.50/1.07	
0.50/1.07	% Formulas that are not ordinary clauses:
0.50/1.07	1 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.50/1.07	2 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.50/1.07	3 (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].
0.50/1.07	4 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.50/1.07	5 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.50/1.07	6 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause).  [assumption].
0.50/1.07	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].
0.50/1.07	8 (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].
0.50/1.07	9 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.50/1.07	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].
0.50/1.07	11 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.50/1.07	12 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.50/1.07	13 (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].
0.50/1.07	14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause).  [assumption].
0.96/1.25	15 (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].
0.96/1.25	16 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.96/1.25	
0.96/1.25	============================== end of process non-clausal formulas ===
0.96/1.25	
0.96/1.25	============================== PROCESS INITIAL CLAUSES ===============
0.96/1.25	
0.96/1.25	============================== PREDICATE ELIMINATION =================
0.96/1.25	
0.96/1.25	============================== end predicate elimination =============
0.96/1.25	
0.96/1.25	Auto_denials:
0.96/1.25	  % copying label a to answer in negative clause
0.96/1.25	
0.96/1.25	Term ordering decisions:
0.96/1.25	
0.96/1.25	% Assigning unary symbol star kb_weight 0 and highest precedence (8).
0.96/1.25	Function symbol KB weights:  zero=1. one=1. a=1. multiplication=1. addition=1. star=0.
0.96/1.25	
0.96/1.25	============================== end of process initial clauses ========
0.96/1.25	
0.96/1.25	============================== CLAUSES FOR SEARCH ====================
0.96/1.25	
0.96/1.25	============================== end of clauses for search =============
0.96/1.25	
0.96/1.25	============================== SEARCH ================================
0.96/1.25	
0.96/1.25	% Starting search at 0.01 seconds.
0.96/1.25	
0.96/1.25	============================== PROOF =================================
0.96/1.25	% SZS status Theorem
0.96/1.25	% SZS output start Refutation
0.96/1.25	
0.96/1.25	% Proof 1 at 0.19 (+ 0.01) seconds: a.
0.96/1.25	% Length of proof is 44.
0.96/1.25	% Level of proof is 13.
0.96/1.25	% Maximum clause weight is 16.000.
0.96/1.25	% Given clauses 222.
0.96/1.25	
0.96/1.25	2 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.96/1.25	3 (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].
0.96/1.25	5 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.96/1.25	6 (all A leq(addition(one,multiplication(A,star(A))),star(A))) # label(star_unfold_right) # label(axiom) # label(non_clause).  [assumption].
0.96/1.25	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].
0.96/1.25	12 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.96/1.25	14 (all A leq(addition(one,multiplication(star(A),A)),star(A))) # label(star_unfold_left) # label(axiom) # label(non_clause).  [assumption].
0.96/1.25	15 (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].
0.96/1.25	16 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.96/1.25	18 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(2)].
0.96/1.25	20 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(5)].
0.96/1.25	23 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(12)].
0.96/1.25	24 leq(addition(one,multiplication(A,star(A))),star(A)) # label(star_unfold_right) # label(axiom).  [clausify(6)].
0.96/1.25	25 leq(addition(one,multiplication(star(A),A)),star(A)) # label(star_unfold_left) # label(axiom).  [clausify(14)].
0.96/1.25	26 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(7)].
0.96/1.25	27 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(26),rewrite([23(2)]),flip(a)].
0.96/1.25	29 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom).  [clausify(3)].
0.96/1.25	30 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom).  [clausify(15)].
0.96/1.25	31 -leq(multiplication(a,a),star(a)) # label(a) # label(negated_conjecture) # answer(a).  [assumption].
0.96/1.25	32 addition(A,B) != B | leq(A,B) # label(order) # label(axiom).  [clausify(16)].
0.96/1.25	33 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom).  [clausify(16)].
0.96/1.25	40 addition(A,addition(A,B)) = addition(A,B).  [para(27(a,1),20(a,1)),rewrite([23(1),23(2),27(2,R),20(1),23(3)])].
0.96/1.25	46 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)).  [para(18(a,1),30(a,1,1)),rewrite([23(4)])].
0.96/1.25	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)])].
0.96/1.25	53 addition(A,addition(B,C)) != addition(A,B) | leq(C,addition(A,B)).  [para(27(a,2),32(a,1))].
0.96/1.25	56 addition(star(A),addition(one,multiplication(star(A),A))) = star(A).  [hyper(33,b,25,a),rewrite([23(6)])].
0.96/1.25	57 addition(star(A),addition(one,multiplication(A,star(A)))) = star(A).  [hyper(33,b,24,a),rewrite([23(6)])].
0.96/1.25	197 leq(A,addition(B,A)).  [para(20(a,1),52(a,1,2)),xx(a)].
0.96/1.25	203 leq(A,addition(B,addition(A,C))).  [para(40(a,1),52(a,1,2)),xx(a)].
0.96/1.25	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)])].
0.96/1.25	212 leq(multiplication(A,B),addition(C,multiplication(addition(A,D),B))).  [para(29(a,1),203(a,2,2))].
0.96/1.25	216 leq(A,addition(B,multiplication(A,addition(C,one)))).  [para(46(a,1),203(a,2,2))].
0.96/1.25	291 addition(star(A),one) != star(A) | leq(multiplication(star(A),A),addition(star(A),one)).  [para(56(a,1),53(a,1)),flip(a)].
0.96/1.25	292 leq(addition(star(A),one),star(A)).  [para(56(a,1),210(a,2))].
0.96/1.25	296 addition(star(A),one) = star(A).  [hyper(33,b,292,a),rewrite([23(5),40(5)])].
0.96/1.25	297 leq(multiplication(star(A),A),star(A)).  [back_rewrite(291),rewrite([296(3),296(8)]),xx(a)].
0.96/1.25	309 addition(star(A),multiplication(A,star(A))) = star(A).  [para(57(a,1),27(a,1)),rewrite([296(6),23(5)]),flip(a)].
0.96/1.25	321 leq(A,addition(B,multiplication(A,star(C)))).  [para(296(a,1),216(a,2,2,2))].
0.96/1.25	327 addition(star(A),multiplication(star(A),A)) = star(A).  [hyper(33,b,297,a),rewrite([23(4)])].
0.96/1.25	488 leq(A,star(A)).  [para(309(a,1),321(a,2))].
0.96/1.25	493 addition(A,star(A)) = star(A).  [hyper(33,b,488,a)].
0.96/1.25	1741 leq(multiplication(A,B),addition(C,multiplication(star(A),B))).  [para(493(a,1),212(a,2,2,1))].
0.96/1.25	1770 leq(multiplication(A,A),star(A)).  [para(327(a,1),1741(a,2))].
0.96/1.25	1771 $F # answer(a).  [resolve(1770,a,31,a)].
0.96/1.25	
0.96/1.25	% SZS output end Refutation
0.96/1.25	============================== end of proof ==========================
0.96/1.25	
0.96/1.25	============================== STATISTICS ============================
0.96/1.25	
0.96/1.25	Given=222. Generated=5540. Kept=1751. proofs=1.
0.96/1.25	Usable=195. Sos=1430. Demods=213. Limbo=8, Disabled=135. Hints=0.
0.96/1.25	Megabytes=1.67.
0.96/1.25	User_CPU=0.19, System_CPU=0.01, Wall_clock=1.
0.96/1.25	
0.96/1.25	============================== end of statistics =====================
0.96/1.25	
0.96/1.25	============================== end of search =========================
0.96/1.25	
0.96/1.25	THEOREM PROVED
0.96/1.25	% SZS status Theorem
0.96/1.25	
0.96/1.25	Exiting with 1 proof.
0.96/1.25	
0.96/1.25	Process 21062 exit (max_proofs) Tue Jul 13 16:17:56 2021
0.96/1.25	Prover9 interrupted
0.96/1.26	EOF