0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n006.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   : 1200
0.12/0.33	% DateTime   : Tue Jul 13 16:14:40 EDT 2021
0.12/0.33	% CPUTime    : 
0.76/1.02	============================== Prover9 ===============================
0.76/1.02	Prover9 (32) version 2009-11A, November 2009.
0.76/1.02	Process 14617 was started by sandbox on n006.cluster.edu,
0.76/1.02	Tue Jul 13 16:14:41 2021
0.76/1.02	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_14463_n006.cluster.edu".
0.76/1.02	============================== end of head ===========================
0.76/1.02	
0.76/1.02	============================== INPUT =================================
0.76/1.02	
0.76/1.02	% Reading from file /tmp/Prover9_14463_n006.cluster.edu
0.76/1.02	
0.76/1.02	set(prolog_style_variables).
0.76/1.02	set(auto2).
0.76/1.02	    % set(auto2) -> set(auto).
0.76/1.02	    % set(auto) -> set(auto_inference).
0.76/1.02	    % set(auto) -> set(auto_setup).
0.76/1.02	    % set(auto_setup) -> set(predicate_elim).
0.76/1.02	    % set(auto_setup) -> assign(eq_defs, unfold).
0.76/1.02	    % set(auto) -> set(auto_limits).
0.76/1.02	    % set(auto_limits) -> assign(max_weight, "100.000").
0.76/1.02	    % set(auto_limits) -> assign(sos_limit, 20000).
0.76/1.02	    % set(auto) -> set(auto_denials).
0.76/1.02	    % set(auto) -> set(auto_process).
0.76/1.02	    % set(auto2) -> assign(new_constants, 1).
0.76/1.02	    % set(auto2) -> assign(fold_denial_max, 3).
0.76/1.02	    % set(auto2) -> assign(max_weight, "200.000").
0.76/1.02	    % set(auto2) -> assign(max_hours, 1).
0.76/1.02	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.76/1.02	    % set(auto2) -> assign(max_seconds, 0).
0.76/1.02	    % set(auto2) -> assign(max_minutes, 5).
0.76/1.02	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.76/1.02	    % set(auto2) -> set(sort_initial_sos).
0.76/1.02	    % set(auto2) -> assign(sos_limit, -1).
0.76/1.02	    % set(auto2) -> assign(lrs_ticks, 3000).
0.76/1.02	    % set(auto2) -> assign(max_megs, 400).
0.76/1.02	    % set(auto2) -> assign(stats, some).
0.76/1.02	    % set(auto2) -> clear(echo_input).
0.76/1.02	    % set(auto2) -> set(quiet).
0.76/1.02	    % set(auto2) -> clear(print_initial_clauses).
0.76/1.02	    % set(auto2) -> clear(print_given).
0.76/1.02	assign(lrs_ticks,-1).
0.76/1.02	assign(sos_limit,10000).
0.76/1.02	assign(order,kbo).
0.76/1.02	set(lex_order_vars).
0.76/1.02	clear(print_given).
0.76/1.02	
0.76/1.02	% formulas(sos).  % not echoed (77 formulas)
0.76/1.02	
0.76/1.02	============================== end of input ==========================
0.76/1.02	
0.76/1.02	% From the command line: assign(max_seconds, 1200).
0.76/1.02	
0.76/1.02	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.76/1.02	
0.76/1.02	% Formulas that are not ordinary clauses:
0.76/1.02	1 implies_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))) # label(implies_3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	2 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) <-> cn1 # label(cn1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	3 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	4 (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) <-> implies_2 # label(implies_2) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	5 (all X all Y (is_a_theorem(implies(X,Y)) & is_a_theorem(X) -> is_a_theorem(Y))) <-> modus_ponens # label(modus_ponens) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	6 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	7 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) <-> equivalence_2 # label(equivalence_2) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	8 equivalence_3 <-> (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) # label(equivalence_3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	9 equivalence_1 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) # label(equivalence_1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	10 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	11 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	12 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	13 and_3 <-> (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) # label(and_3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	14 kn3 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) # label(kn3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	15 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	16 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	17 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	18 (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) <-> r5 # label(r5) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	19 r4 <-> (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) # label(r4) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	20 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	21 (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) <-> modus_tollens # label(modus_tollens) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	22 (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) <-> or_3 # label(or_3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	23 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	24 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	25 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	26 (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) <-> substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	27 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	28 op_implies_and -> (all X all Y implies(X,Y) = not(and(X,not(Y)))) # label(op_implies_and) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	29 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	30 op_equiv -> (all X all Y and(implies(X,Y),implies(Y,X)) = equiv(X,Y)) # label(op_equiv) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	31 op_and -> (all X all Y not(or(not(X),not(Y))) = and(X,Y)) # label(op_and) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	32 (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),and(possibly(P),possibly(Q))))) <-> axiom_s2 # label(axiom_s2) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	33 (all X all Y all Z is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))) <-> axiom_m3 # label(axiom_m3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	34 (all X all Y (is_a_theorem(X) & is_a_theorem(strict_implies(X,Y)) -> is_a_theorem(Y))) <-> modus_ponens_strict_implies # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	35 (all X is_a_theorem(implies(X,necessarily(possibly(X))))) <-> axiom_B # label(axiom_B) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	36 (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) <-> axiom_m9 # label(axiom_m9) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	37 axiom_m7 <-> (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),P))) # label(axiom_m7) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	38 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	39 (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) <-> axiom_m10 # label(axiom_m10) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	40 axiom_s4 <-> (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_s4) # label(axiom) # label(non_clause).  [assumption].
0.76/1.02	41 axiom_m1 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),and(Y,X)))) # label(axiom_m1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	42 adjunction <-> (all X all Y (is_a_theorem(Y) & is_a_theorem(X) -> is_a_theorem(and(X,Y)))) # label(adjunction) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	43 axiom_m2 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) # label(axiom_m2) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	44 axiom_s3 <-> (all X all Y is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X)))))) # label(axiom_s3) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	45 (all X is_a_theorem(strict_implies(X,possibly(X)))) <-> axiom_m6 # label(axiom_m6) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	46 substitution_strict_equiv <-> (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> Y = X)) # label(substitution_strict_equiv) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	47 (all X all Y all Z is_a_theorem(implies(and(necessarily(implies(X,Y)),necessarily(implies(Y,Z))),necessarily(implies(X,Z))))) <-> axiom_s1 # label(axiom_s1) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	48 (all X all Y all Z is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))) <-> axiom_m5 # label(axiom_m5) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	49 axiom_4 <-> (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) # label(axiom_4) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	50 (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) <-> necessitation # label(necessitation) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	51 (all X is_a_theorem(strict_implies(X,and(X,X)))) <-> axiom_m4 # label(axiom_m4) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	52 axiom_m8 <-> (all P all Q is_a_theorem(strict_implies(strict_implies(P,Q),strict_implies(possibly(P),possibly(Q))))) # label(axiom_m8) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	53 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	54 axiom_K <-> (all X all Y is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))) # label(axiom_K) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	55 op_strict_equiv -> (all X all Y and(strict_implies(X,Y),strict_implies(Y,X)) = strict_equiv(X,Y)) # label(op_strict_equiv) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	56 op_strict_implies -> (all X all Y necessarily(implies(X,Y)) = strict_implies(X,Y)) # label(op_strict_implies) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	57 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	58 op_possibly -> (all X possibly(X) = not(necessarily(not(X)))) # label(op_possibly) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	
0.76/1.06	============================== end of process non-clausal formulas ===
0.76/1.06	
0.76/1.06	============================== PROCESS INITIAL CLAUSES ===============
0.76/1.06	
0.76/1.06	============================== PREDICATE ELIMINATION =================
0.76/1.06	
0.76/1.06	============================== end predicate elimination =============
0.76/1.06	
0.76/1.06	Auto_denials:  (non-Horn, no changes).
0.76/1.06	
0.76/1.06	Term ordering decisions:
0.76/1.06	Function symbol KB weights:  c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. c56=1. c57=1. c58=1. c59=1. c60=1. c61=1. c62=1. c63=1. c64=1. c65=1. c66=1. c67=1. c68=1. c69=1. c70=1. c71=1. c72=1. c73=1. c74=1. c75=1. c76=1. c77=1. c78=1. c79=1. c80=1. c81=1. c82=1. c83=1. c84=1. c85=1. c86=1. c87=1. c88=1. c89=1. c90=1. c91=1. c92=1. c93=1. c94=1. implies=1. and=1. strict_implies=1. or=1. equiv=1. strict_equiv=1. necessarily=1. possibly=1. not=1.
0.76/1.06	
0.76/1.06	============================== end of process initial clauses ========
0.76/1.06	
0.76/1.06	============================== CLAUSES FOR SEARCH =================Alarm clock 
119.71/120.05	Prover9 interrupted
119.71/120.06	EOF