0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.33	% Computer   : n011.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 180
0.13/0.33	% DateTime   : Thu Aug 29 09:23:42 EDT 2019
0.13/0.33	% CPUTime    : 
0.73/1.02	============================== Prover9 ===============================
0.73/1.02	Prover9 (32) version 2009-11A, November 2009.
0.73/1.02	Process 14622 was started by sandbox2 on n011.cluster.edu,
0.73/1.02	Thu Aug 29 09:23:43 2019
0.73/1.02	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 180 -f /tmp/Prover9_14468_n011.cluster.edu".
0.73/1.02	============================== end of head ===========================
0.73/1.02	
0.73/1.02	============================== INPUT =================================
0.73/1.02	
0.73/1.02	% Reading from file /tmp/Prover9_14468_n011.cluster.edu
0.73/1.02	
0.73/1.02	set(prolog_style_variables).
0.73/1.02	set(auto2).
0.73/1.02	    % set(auto2) -> set(auto).
0.73/1.02	    % set(auto) -> set(auto_inference).
0.73/1.02	    % set(auto) -> set(auto_setup).
0.73/1.02	    % set(auto_setup) -> set(predicate_elim).
0.73/1.02	    % set(auto_setup) -> assign(eq_defs, unfold).
0.73/1.02	    % set(auto) -> set(auto_limits).
0.73/1.02	    % set(auto_limits) -> assign(max_weight, "100.000").
0.73/1.02	    % set(auto_limits) -> assign(sos_limit, 20000).
0.73/1.02	    % set(auto) -> set(auto_denials).
0.73/1.02	    % set(auto) -> set(auto_process).
0.73/1.02	    % set(auto2) -> assign(new_constants, 1).
0.73/1.02	    % set(auto2) -> assign(fold_denial_max, 3).
0.73/1.02	    % set(auto2) -> assign(max_weight, "200.000").
0.73/1.02	    % set(auto2) -> assign(max_hours, 1).
0.73/1.02	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.73/1.02	    % set(auto2) -> assign(max_seconds, 0).
0.73/1.02	    % set(auto2) -> assign(max_minutes, 5).
0.73/1.02	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.73/1.02	    % set(auto2) -> set(sort_initial_sos).
0.73/1.02	    % set(auto2) -> assign(sos_limit, -1).
0.73/1.02	    % set(auto2) -> assign(lrs_ticks, 3000).
0.73/1.02	    % set(auto2) -> assign(max_megs, 400).
0.73/1.02	    % set(auto2) -> assign(stats, some).
0.73/1.02	    % set(auto2) -> clear(echo_input).
0.73/1.02	    % set(auto2) -> set(quiet).
0.73/1.02	    % set(auto2) -> clear(print_initial_clauses).
0.73/1.02	    % set(auto2) -> clear(print_given).
0.73/1.02	assign(lrs_ticks,-1).
0.73/1.02	assign(sos_limit,10000).
0.73/1.02	assign(order,kbo).
0.73/1.02	set(lex_order_vars).
0.73/1.02	clear(print_given).
0.73/1.02	
0.73/1.02	% formulas(sos).  % not echoed (89 formulas)
0.73/1.02	
0.73/1.02	============================== end of input ==========================
0.73/1.02	
0.73/1.02	% From the command line: assign(max_seconds, 180).
0.73/1.02	
0.73/1.02	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.73/1.02	
0.73/1.02	% Formulas that are not ordinary clauses:
0.73/1.02	1 (all X all Y is_a_theorem(implies(X,implies(Y,and(X,Y))))) <-> and_3 # label(and_3) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	2 r5 <-> (all P all Q all R is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))) # label(r5) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> X = Y)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	4 (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))) <-> kn3 # label(kn3) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	5 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].
0.73/1.02	6 cn1 <-> (all P all Q all R is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))) # label(cn1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	7 (all X all Y is_a_theorem(implies(equiv(X,Y),implies(X,Y)))) <-> equivalence_1 # label(equivalence_1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	8 (all X all Y is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))) <-> equivalence_3 # label(equivalence_3) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	9 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	10 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	11 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	12 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	13 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	14 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	15 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	16 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	17 implies_2 <-> (all X all Y is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))) # label(implies_2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	18 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	19 (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].
0.73/1.02	20 (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].
0.73/1.02	21 equivalence_2 <-> (all X all Y is_a_theorem(implies(equiv(X,Y),implies(Y,X)))) # label(equivalence_2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	22 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	23 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	24 (all P all Q all R is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))) <-> r4 # label(r4) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	25 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	26 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	27 op_and -> (all X all Y not(or(not(X),not(Y))) = and(X,Y)) # label(op_and) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	28 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	29 op_equiv -> (all X all Y equiv(X,Y) = and(implies(X,Y),implies(Y,X))) # label(op_equiv) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	30 op_implies_or -> (all X all Y implies(X,Y) = or(not(X),Y)) # label(op_implies_or) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	31 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].
0.73/1.02	32 (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].
0.73/1.02	33 (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),P))) <-> axiom_m7 # label(axiom_m7) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	34 adjunction <-> (all X all Y (is_a_theorem(X) & is_a_theorem(Y) -> is_a_theorem(and(X,Y)))) # label(adjunction) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	35 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	36 (all X is_a_theorem(strict_implies(X,possibly(X)))) <-> axiom_m6 # label(axiom_m6) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	37 (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_s4 # label(axiom_s4) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	38 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].
0.73/1.02	39 (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> X = Y)) <-> substitution_strict_equiv # label(substitution_strict_equiv) # label(axiom) # label(non_clause).  [assumption].
0.73/1.02	40 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].
0.73/1.02	41 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	42 (all X all Y is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))) <-> axiom_K # label(axiom_K) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	43 axiom_s1 <-> (all X all Y all Z is_a_theorem(implies(and(necessarily(implies(X,Y)),necessarily(implies(Y,Z))),necessarily(implies(X,Z))))) # label(axiom_s1) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	44 (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_4 # label(axiom_4) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	45 axiom_s2 <-> (all P all Q is_a_theorem(strict_implies(possibly(and(P,Q)),and(possibly(P),possibly(Q))))) # label(axiom_s2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	46 (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) <-> axiom_m10 # label(axiom_m10) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	47 modus_ponens_strict_implies <-> (all X all Y (is_a_theorem(X) & is_a_theorem(strict_implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	48 (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) <-> axiom_m9 # label(axiom_m9) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	49 (all X is_a_theorem(strict_implies(X,and(X,X)))) <-> axiom_m4 # label(axiom_m4) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	50 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	51 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	52 axiom_m2 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) # label(axiom_m2) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	53 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].
0.73/1.06	54 axiom_m3 <-> (all X all Y all Z is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))) # label(axiom_m3) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	55 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	56 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].
0.73/1.06	57 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].
0.73/1.06	58 op_possibly -> (all X not(necessarily(not(X))) = possibly(X)) # label(op_possibly) # label(axiom) # label(non_clause).  [assumption].
0.73/1.06	
0.73/1.06	============================== end of process non-clausal formulas ===
0.73/1.06	
0.73/1.06	============================== PROCESS INITIAL CLAUSES ===============
0.73/1.06	
0.73/1.06	============================== PREDICATE ELIMINATION =================
0.73/1.06	
0.73/1.06	============================== end predicate elimination =============
0.73/1.06	
0.73/1.06	Auto_denials:  (non-Horn, no changes).
0.73/1.06	
0.73/1.06	Term ordering decisions:
0.73/1.06	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.
0.73/1.06	
0.73/1.06	============================== end of process initial clauses ========
0.73/1.06	
0.73/1.06	============================== CLAUSES FOR SEARCH ====================
2.75/3.02	
2.75/3.02	============================== end of clauses for search =============
2.75/3.02	
2.75/3.02	============================== SEARCH ================================
2.75/3.02	
2.75/3.02	% Starting search at 0.05 seconds.
2.75/3.02	
2.75/3.02	Low Water (keep): wt=25.000, iters=3398
2.75/3.02	
2.75/3.02	Low Water (keep): wt=22.000, iters=3425
2.75/3.02	
2.75/3.02	Low Water (keep): wt=21.000, iters=3416
2.75/3.02	
2.75/3.02	Low Water (keep): wt=20.000, iters=3383
2.75/3.02	
2.75/3.02	Low Water (keep): wt=19.000, iters=3367
2.75/3.02	
2.75/3.02	Low Water (keep): wt=17.000, iters=3387
2.75/3.02	
2.75/3.02	Low Water (keep): wt=16.000, iters=3338
2.75/3.02	
2.75/3.02	Low Water (keep): wt=15.000, iters=3341
2.75/3.02	
2.75/3.02	Low Water (keep): wt=14.000, iters=3368
2.75/3.02	
2.75/3.02	Low Water (keep): wt=13.000, iters=3363
2.75/3.02	
2.75/3.02	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 37 (0.00 of 1.94 sec).
2.75/3.02	
2.75/3.02	============================== PROOF =================================
2.75/3.02	% SZS status Theorem
2.75/3.02	% SZS output start Refutation
2.75/3.02	
2.75/3.02	% Proof 1 at 1.99 (+ 0.02) seconds.
2.75/3.02	% Length of proof is 35.
2.75/3.02	% Level of proof is 7.
2.75/3.02	% Maximum clause weight is 12.000.
2.75/3.02	% Given clauses 549.
2.75/3.02	
2.75/3.02	9 modus_ponens <-> (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens) # label(axiom) # label(non_clause).  [assumption].
2.75/3.02	41 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause).  [assumption].
2.75/3.02	42 (all X all Y is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))) <-> axiom_K # label(axiom_K) # label(axiom) # label(non_clause).  [assumption].
2.75/3.02	47 modus_ponens_strict_implies <-> (all X all Y (is_a_theorem(X) & is_a_theorem(strict_implies(X,Y)) -> is_a_theorem(Y))) # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause).  [assumption].
2.75/3.02	51 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause).  [assumption].
2.75/3.02	57 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].
2.75/3.02	76 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom).  [clausify(9)].
2.75/3.02	128 modus_ponens # label(hilbert_modus_ponens) # label(axiom).  [assumption].
2.75/3.02	159 -necessitation | -is_a_theorem(A) | is_a_theorem(necessarily(A)) # label(necessitation) # label(axiom).  [clausify(41)].
2.75/3.02	163 is_a_theorem(implies(necessarily(implies(A,B)),implies(necessarily(A),necessarily(B)))) | -axiom_K # label(axiom_K) # label(axiom).  [clausify(42)].
2.75/3.02	173 modus_ponens_strict_implies | is_a_theorem(c82) # label(modus_ponens_strict_implies) # label(axiom).  [clausify(47)].
2.75/3.02	174 modus_ponens_strict_implies | is_a_theorem(strict_implies(c82,c83)) # label(modus_ponens_strict_implies) # label(axiom).  [clausify(47)].
2.75/3.02	175 modus_ponens_strict_implies | -is_a_theorem(c83) # label(modus_ponens_strict_implies) # label(axiom).  [clausify(47)].
2.75/3.02	182 -axiom_M | is_a_theorem(implies(necessarily(A),A)) # label(axiom_M) # label(axiom).  [clausify(51)].
2.75/3.02	194 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B) # label(op_strict_implies) # label(axiom).  [clausify(57)].
2.75/3.02	198 axiom_M # label(km4b_axiom_M) # label(axiom).  [assumption].
2.75/3.02	199 necessitation # label(km4b_necessitation) # label(axiom).  [assumption].
2.75/3.02	200 axiom_K # label(km4b_axiom_K) # label(axiom).  [assumption].
2.75/3.02	205 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom).  [assumption].
2.75/3.02	206 -modus_ponens_strict_implies # label(s1_0_modus_ponens_strict_implies) # label(negated_conjecture).  [assumption].
2.75/3.02	215 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B).  [back_unit_del(76),unit_del(a,128)].
2.75/3.02	227 is_a_theorem(implies(necessarily(A),A)).  [back_unit_del(182),unit_del(a,198)].
2.75/3.02	228 -is_a_theorem(A) | is_a_theorem(necessarily(A)).  [back_unit_del(159),unit_del(a,199)].
2.75/3.02	229 is_a_theorem(implies(necessarily(implies(A,B)),implies(necessarily(A),necessarily(B)))).  [back_unit_del(163),unit_del(b,200)].
2.75/3.02	233 necessarily(implies(A,B)) = strict_implies(A,B).  [back_unit_del(194),unit_del(a,205)].
2.75/3.02	234 -is_a_theorem(c83).  [back_unit_del(175),unit_del(a,206)].
2.75/3.02	235 is_a_theorem(strict_implies(c82,c83)).  [back_unit_del(174),unit_del(a,206)].
2.75/3.02	236 is_a_theorem(c82).  [back_unit_del(173),unit_del(a,206)].
2.75/3.02	246 is_a_theorem(implies(strict_implies(A,B),implies(necessarily(A),necessarily(B)))).  [back_rewrite(229),rewrite([233(2)])].
2.75/3.02	325 -is_a_theorem(necessarily(A)) | is_a_theorem(A).  [resolve(227,a,215,b)].
2.75/3.02	365 is_a_theorem(necessarily(c82)).  [resolve(236,a,228,a)].
2.75/3.02	379 -is_a_theorem(strict_implies(A,B)) | is_a_theorem(implies(necessarily(A),necessarily(B))).  [resolve(246,a,215,b)].
2.75/3.02	10141 is_a_theorem(implies(necessarily(c82),necessarily(c83))).  [resolve(379,a,235,a)].
2.75/3.02	10159 is_a_theorem(necessarily(c83)).  [resolve(10141,a,215,b),unit_del(a,365)].
2.75/3.02	10171 $F.  [resolve(10159,a,325,a),unit_del(a,234)].
2.75/3.02	
2.75/3.02	% SZS output end Refutation
2.75/3.02	============================== end of proof ==========================
2.75/3.02	
2.75/3.02	============================== STATISTICS ============================
2.75/3.02	
2.75/3.02	Given=549. Generated=19244. Kept=10108. proofs=1.
2.75/3.02	Usable=535. Sos=9267. Demods=24. Limbo=9, Disabled=444. Hints=0.
2.75/3.02	Megabytes=12.83.
2.75/3.02	User_CPU=1.99, System_CPU=0.02, Wall_clock=2.
2.75/3.02	
2.75/3.02	============================== end of statistics =====================
2.75/3.02	
2.75/3.02	============================== end of search =========================
2.75/3.02	
2.75/3.02	THEOREM PROVED
2.75/3.02	% SZS status Theorem
2.75/3.02	
2.75/3.02	Exiting with 1 proof.
2.75/3.02	
2.75/3.02	Process 14622 exit (max_proofs) Thu Aug 29 09:23:45 2019
2.75/3.02	Prover9 interrupted
2.75/3.02	EOF