0.08/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.14	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.35	% Computer   : n021.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 1200
0.13/0.35	% DateTime   : Tue Jul 13 16:13:26 EDT 2021
0.13/0.36	% CPUTime    : 
0.79/1.06	============================== Prover9 ===============================
0.79/1.06	Prover9 (32) version 2009-11A, November 2009.
0.79/1.06	Process 4663 was started by sandbox2 on n021.cluster.edu,
0.79/1.06	Tue Jul 13 16:13:26 2021
0.79/1.06	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_4509_n021.cluster.edu".
0.79/1.06	============================== end of head ===========================
0.79/1.06	
0.79/1.06	============================== INPUT =================================
0.79/1.06	
0.79/1.06	% Reading from file /tmp/Prover9_4509_n021.cluster.edu
0.79/1.06	
0.79/1.06	set(prolog_style_variables).
0.79/1.06	set(auto2).
0.79/1.06	    % set(auto2) -> set(auto).
0.79/1.06	    % set(auto) -> set(auto_inference).
0.79/1.06	    % set(auto) -> set(auto_setup).
0.79/1.06	    % set(auto_setup) -> set(predicate_elim).
0.79/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.79/1.06	    % set(auto) -> set(auto_limits).
0.79/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.79/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.79/1.06	    % set(auto) -> set(auto_denials).
0.79/1.06	    % set(auto) -> set(auto_process).
0.79/1.06	    % set(auto2) -> assign(new_constants, 1).
0.79/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.79/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.79/1.06	    % set(auto2) -> assign(max_hours, 1).
0.79/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.79/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.79/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.79/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.79/1.06	    % set(auto2) -> set(sort_initial_sos).
0.79/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.79/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.79/1.06	    % set(auto2) -> assign(max_megs, 400).
0.79/1.06	    % set(auto2) -> assign(stats, some).
0.79/1.06	    % set(auto2) -> clear(echo_input).
0.79/1.06	    % set(auto2) -> set(quiet).
0.79/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.79/1.06	    % set(auto2) -> clear(print_given).
0.79/1.06	assign(lrs_ticks,-1).
0.79/1.06	assign(sos_limit,10000).
0.79/1.06	assign(order,kbo).
0.79/1.06	set(lex_order_vars).
0.79/1.06	clear(print_given).
0.79/1.06	
0.79/1.06	% formulas(sos).  % not echoed (18 formulas)
0.79/1.06	
0.79/1.06	============================== end of input ==========================
0.79/1.06	
0.79/1.06	% From the command line: assign(max_seconds, 1200).
0.79/1.06	
0.79/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.79/1.06	
0.79/1.06	% Formulas that are not ordinary clauses:
0.79/1.06	1 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.79/1.06	2 (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].
0.79/1.06	3 (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].
0.79/1.06	4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.79/1.06	5 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.79/1.06	6 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.79/1.06	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].
0.79/1.06	8 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.79/1.06	9 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.79/1.06	10 (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].
0.79/1.06	11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.79/1.06	12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.79/1.06	13 (all X0 all X1 addition(domain(X0),domain(X1)) = domain(addition(X0,X1))) # label(domain5) # label(axiom) # label(non_clause).  [assumption].
0.79/1.06	14 (all X0 multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0))) # label(domain1) # label(axiom) # label(non_clause).  [assumption].
0.79/1.07	15 (all X0 all X1 domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1)))) # label(domain2) # label(axiom) # label(non_clause).  [assumption].
0.79/1.07	16 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause).  [assumption].
0.79/1.07	17 -(all X0 all X1 (addition(domain(X0),domain(X1)) = domain(X1) -> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.79/1.07	
0.79/1.07	============================== end of process non-clausal formulas ===
0.79/1.07	
0.79/1.07	============================== PROCESS INITIAL CLAUSES ===============
0.79/1.07	
0.79/1.07	============================== PREDICATE ELIMINATION =================
0.79/1.07	18 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom).  [clausify(8)].
0.79/1.07	19 addition(A,B) != B | leq(A,B) # label(order) # label(axiom).  [clausify(8)].
0.79/1.07	
0.79/1.07	============================== end predicate elimination =============
0.79/1.07	
0.79/1.07	Auto_denials:
0.79/1.07	  % copying label goals to answer in negative clause
0.79/1.07	
0.79/1.07	Term ordering decisions:
0.79/1.07	
0.79/1.07	% Assigning unary symbol domain kb_weight 0 and highest precedence (8).
0.79/1.07	Function symbol KB weights:  zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. domain=0.
0.79/1.07	
0.79/1.07	============================== end of process initial clauses ========
0.79/1.07	
0.79/1.07	============================== CLAUSES FOR SEARCH ====================
0.79/1.07	
0.79/1.07	============================== end of clauses for search =============
0.79/1.07	
0.79/1.07	============================== SEARCH ================================
0.79/1.07	
0.79/1.07	% Starting search at 0.01 seconds.
0.79/1.07	
0.79/1.07	============================== PROOF =================================
0.79/1.07	% SZS status Theorem
0.79/1.07	% SZS output start Refutation
0.79/1.07	
0.79/1.07	% Proof 1 at 0.03 (+ 0.00) seconds: goals.
0.79/1.07	% Length of proof is 23.
0.79/1.07	% Level of proof is 7.
0.79/1.07	% Maximum clause weight is 13.000.
0.79/1.07	% Given clauses 31.
0.79/1.07	
0.79/1.07	4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.79/1.07	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].
0.79/1.07	9 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.79/1.07	14 (all X0 multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0))) # label(domain1) # label(axiom) # label(non_clause).  [assumption].
0.79/1.07	16 (all X0 addition(domain(X0),one) = one) # label(domain3) # label(axiom) # label(non_clause).  [assumption].
0.79/1.07	17 -(all X0 all X1 (addition(domain(X0),domain(X1)) = domain(X1) -> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.79/1.07	22 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(4)].
0.79/1.07	27 addition(domain(A),one) = one # label(domain3) # label(axiom).  [clausify(16)].
0.79/1.07	28 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(9)].
0.79/1.07	29 domain(c2) = addition(domain(c1),domain(c2)) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.79/1.07	30 addition(domain(c1),domain(c2)) = domain(c2).  [copy(29),flip(a)].
0.79/1.07	36 addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A) # label(domain1) # label(axiom).  [clausify(14)].
0.79/1.07	38 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom).  [clausify(7)].
0.79/1.07	39 addition(c1,multiplication(domain(c2),c1)) != multiplication(domain(c2),c1) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(17)].
0.79/1.07	41 addition(one,domain(A)) = one.  [para(28(a,1),27(a,1))].
0.79/1.07	61 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A).  [para(22(a,1),38(a,1,1)),rewrite([28(4)])].
0.79/1.07	62 addition(A,multiplication(domain(B),A)) = A.  [para(27(a,1),38(a,2,1)),rewrite([22(4),28(3),22(5)])].
0.79/1.07	69 multiplication(domain(c2),c1) != c1 # answer(goals).  [back_rewrite(39),rewrite([61(6),28(4),41(4),22(3)]),flip(a)].
0.79/1.07	70 multiplication(domain(A),A) = A.  [back_rewrite(36),rewrite([62(3)]),flip(a)].
0.79/1.07	72 addition(A,multiplication(B,A)) = multiplication(addition(B,domain(A)),A).  [para(70(a,1),38(a,1,1)),rewrite([28(4)])].
0.79/1.07	74 multiplication(addition(domain(A),domain(B)),A) = A.  [back_rewrite(62),rewrite([72(3),28(3)])].
0.79/1.07	89 multiplication(domain(c2),c1) = c1.  [para(30(a,1),74(a,1,1))].
0.79/1.07	90 $F # answer(goals).  [resolve(89,a,69,a)].
0.79/1.07	
0.79/1.07	% SZS output end Refutation
0.79/1.07	============================== end of proof ==========================
0.79/1.07	
0.79/1.07	============================== STATISTICS ============================
0.79/1.07	
0.79/1.07	Given=31. Generated=486. Kept=68. proofs=1.
0.79/1.07	Usable=30. Sos=24. Demods=53. Limbo=1, Disabled=32. Hints=0.
0.79/1.07	Megabytes=0.10.
0.79/1.07	User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
0.79/1.07	
0.79/1.07	============================== end of statistics =====================
0.79/1.07	
0.79/1.07	============================== end of search =========================
0.79/1.07	
0.79/1.07	THEOREM PROVED
0.79/1.07	% SZS status Theorem
0.79/1.07	
0.79/1.07	Exiting with 1 proof.
0.79/1.07	
0.79/1.07	Process 4663 exit (max_proofs) Tue Jul 13 16:13:26 2021
0.79/1.07	Prover9 interrupted
0.81/1.08	EOF