0.09/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.09/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.10/0.31	% Computer   : n027.cluster.edu
0.10/0.31	% Model      : x86_64 x86_64
0.10/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory     : 8042.1875MB
0.10/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 960
0.10/0.31	% DateTime   : Thu Jul  2 06:56:01 EDT 2020
0.10/0.31	% CPUTime    : 
0.75/1.06	============================== Prover9 ===============================
0.75/1.06	Prover9 (32) version 2009-11A, November 2009.
0.75/1.06	Process 12178 was started by sandbox2 on n027.cluster.edu,
0.75/1.06	Thu Jul  2 06:56:02 2020
0.75/1.06	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_12019_n027.cluster.edu".
0.75/1.06	============================== end of head ===========================
0.75/1.06	
0.75/1.06	============================== INPUT =================================
0.75/1.06	
0.75/1.06	% Reading from file /tmp/Prover9_12019_n027.cluster.edu
0.75/1.06	
0.75/1.06	set(prolog_style_variables).
0.75/1.06	set(auto2).
0.75/1.06	    % set(auto2) -> set(auto).
0.75/1.06	    % set(auto) -> set(auto_inference).
0.75/1.06	    % set(auto) -> set(auto_setup).
0.75/1.06	    % set(auto_setup) -> set(predicate_elim).
0.75/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.75/1.06	    % set(auto) -> set(auto_limits).
0.75/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.75/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.75/1.06	    % set(auto) -> set(auto_denials).
0.75/1.06	    % set(auto) -> set(auto_process).
0.75/1.06	    % set(auto2) -> assign(new_constants, 1).
0.75/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.75/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.75/1.06	    % set(auto2) -> assign(max_hours, 1).
0.75/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.75/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.75/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.75/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.75/1.06	    % set(auto2) -> set(sort_initial_sos).
0.75/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.75/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.75/1.06	    % set(auto2) -> assign(max_megs, 400).
0.75/1.06	    % set(auto2) -> assign(stats, some).
0.75/1.06	    % set(auto2) -> clear(echo_input).
0.75/1.06	    % set(auto2) -> set(quiet).
0.75/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.75/1.06	    % set(auto2) -> clear(print_given).
0.75/1.06	assign(lrs_ticks,-1).
0.75/1.06	assign(sos_limit,10000).
0.75/1.06	assign(order,kbo).
0.75/1.06	set(lex_order_vars).
0.75/1.06	clear(print_given).
0.75/1.06	
0.75/1.06	% formulas(sos).  % not echoed (89 formulas)
0.75/1.06	
0.75/1.06	============================== end of input ==========================
0.75/1.06	
0.75/1.06	% From the command line: assign(max_seconds, 960).
0.75/1.06	
0.75/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.75/1.06	
0.75/1.06	% Formulas that are not ordinary clauses:
0.75/1.06	1 (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].
0.75/1.06	2 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause).  [assumption].
0.75/1.06	3 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.75/1.06	4 (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].
0.75/1.06	5 or_3 <-> (all X all Y all Z is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))) # label(or_3) # label(axiom) # label(non_clause).  [assumption].
0.75/1.06	6 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause).  [assumption].
0.75/1.06	7 (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].
0.75/1.06	8 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause).  [assumption].
0.75/1.06	9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause).  [assumption].
0.75/1.06	10 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause).  [assumption].
0.75/1.06	11 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
0.75/1.06	12 (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].
0.75/1.06	13 (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].
0.75/1.06	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].
0.75/1.07	15 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	16 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].
0.75/1.07	17 (all X all Y is_a_theorem(implies(X,or(X,Y)))) <-> or_1 # label(or_1) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	19 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	20 (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].
0.75/1.07	21 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	22 (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].
0.75/1.07	23 (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].
0.75/1.07	24 (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) <-> modus_ponens # label(modus_ponens) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	25 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].
0.75/1.07	26 (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].
0.75/1.07	27 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	28 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].
0.75/1.07	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].
0.75/1.07	30 op_implies_and -> (all X all Y not(and(X,not(Y))) = implies(X,Y)) # label(op_implies_and) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	31 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	32 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].
0.75/1.07	33 (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_4 # label(axiom_4) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	34 (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].
0.75/1.07	35 (all X is_a_theorem(implies(necessarily(X),X))) <-> axiom_M # label(axiom_M) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	36 substitution_strict_equiv <-> (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> X = Y)) # label(substitution_strict_equiv) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	37 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].
0.75/1.07	38 (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_s4 # label(axiom_s4) # label(axiom) # label(non_clause).  [assumption].
0.75/1.07	39 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].
0.75/1.07	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].
0.75/1.07	41 (all X is_a_theorem(strict_implies(X,and(X,X)))) <-> axiom_m4 # label(axiom_m4) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	42 axiom_m2 <-> (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) # label(axiom_m2) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	43 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	44 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].
0.75/1.09	45 (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) <-> axiom_m9 # label(axiom_m9) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	46 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].
0.75/1.09	47 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].
0.75/1.09	48 (all X is_a_theorem(implies(X,necessarily(possibly(X))))) <-> axiom_B # label(axiom_B) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	49 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	50 axiom_m10 <-> (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) # label(axiom_m10) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	51 (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].
0.75/1.09	52 axiom_m5 <-> (all X all Y all Z is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))) # label(axiom_m5) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	53 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	54 modus_ponens_strict_implies <-> (all X all Y (is_a_theorem(strict_implies(X,Y)) & is_a_theorem(X) -> is_a_theorem(Y))) # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	55 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	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].
0.75/1.09	57 op_possibly -> (all X possibly(X) = not(necessarily(not(X)))) # label(op_possibly) # label(axiom) # label(non_clause).  [assumption].
0.75/1.09	58 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].
0.75/1.09	
0.75/1.09	============================== end of process non-clausal formulas ===
0.75/1.09	
0.75/1.09	============================== PROCESS INITIAL CLAUSES ===============
0.75/1.09	
0.75/1.09	============================== PREDICATE ELIMINATION =================
0.75/1.09	
0.75/1.09	============================== end predicate elimination =============
0.75/1.09	
0.75/1.09	Auto_denials:  (non-Horn, no changes).
0.75/1.09	
0.75/1.09	Term ordering decisions:
0.75/1.09	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.
0.75/1.09	
0.75/1.09	============================== end of process initial clauses ========
0.75/1.09	
0.75/1.09	============================== CLAUSES FOR SEARCH ====================
3.80/4.15	
3.80/4.15	============================== end of clauses for search =============
3.80/4.15	
3.80/4.15	============================== SEARCH ================================
3.80/4.15	
3.80/4.15	% Starting search at 0.04 seconds.
3.80/4.15	
3.80/4.15	Low Water (keep): wt=30.000, iters=3375
3.80/4.15	
3.80/4.15	Low Water (keep): wt=28.000, iters=3366
3.80/4.15	
3.80/4.15	Low Water (keep): wt=24.000, iters=3341
3.80/4.15	
3.80/4.15	Low Water (keep): wt=22.000, iters=3380
3.80/4.15	
3.80/4.15	Low Water (keep): wt=21.000, iters=3356
3.80/4.15	
3.80/4.15	Low Water (keep): wt=20.000, iters=3338
3.80/4.15	
3.80/4.15	Low Water (keep): wt=19.000, iters=3390
3.80/4.15	
3.80/4.15	Low Water (keep): wt=17.000, iters=3333
3.80/4.15	
3.80/4.15	Low Water (keep): wt=16.000, iters=3347
3.80/4.15	
3.80/4.15	Low Water (keep): wt=15.000, iters=3340
3.80/4.15	
3.80/4.15	Low Water (keep): wt=14.000, iters=3347
3.80/4.15	
3.80/4.15	Low Water (keep): wt=13.000, iters=3419
3.80/4.15	
3.80/4.15	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 3.00 sec).
3.80/4.15	
3.80/4.15	============================== PROOF =================================
3.80/4.15	% SZS status Theorem
3.80/4.15	% SZS output start Refutation
3.80/4.15	
3.80/4.15	% Proof 1 at 3.07 (+ 0.02) seconds.
3.80/4.15	% Length of proof is 36.
3.80/4.15	% Level of proof is 8.
3.80/4.15	% Maximum clause weight is 12.000.
3.80/4.15	% Given clauses 554.
3.80/4.15	
3.80/4.15	24 (all X all Y (is_a_theorem(X) & is_a_theorem(implies(X,Y)) -> is_a_theorem(Y))) <-> modus_ponens # label(modus_ponens) # label(axiom) # label(non_clause).  [assumption].
3.80/4.15	32 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].
3.80/4.15	35 (all X is_a_theorem(implies(necessarily(X),X))) <-> axiom_M # label(axiom_M) # label(axiom) # label(non_clause).  [assumption].
3.80/4.15	43 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause).  [assumption].
3.80/4.15	54 modus_ponens_strict_implies <-> (all X all Y (is_a_theorem(strict_implies(X,Y)) & is_a_theorem(X) -> is_a_theorem(Y))) # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause).  [assumption].
3.80/4.15	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].
3.80/4.15	109 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) | -modus_ponens # label(modus_ponens) # label(axiom).  [clausify(24)].
3.80/4.15	133 modus_ponens # label(hilbert_modus_ponens) # label(axiom).  [assumption].
3.80/4.15	137 -axiom_K | is_a_theorem(implies(necessarily(implies(A,B)),implies(necessarily(A),necessarily(B)))) # label(axiom_K) # label(axiom).  [clausify(32)].
3.80/4.15	144 is_a_theorem(implies(necessarily(A),A)) | -axiom_M # label(axiom_M) # label(axiom).  [clausify(35)].
3.80/4.15	162 -necessitation | -is_a_theorem(A) | is_a_theorem(necessarily(A)) # label(necessitation) # label(axiom).  [clausify(43)].
3.80/4.15	186 modus_ponens_strict_implies | is_a_theorem(strict_implies(c93,c94)) # label(modus_ponens_strict_implies) # label(axiom).  [clausify(54)].
3.80/4.15	187 modus_ponens_strict_implies | is_a_theorem(c93) # label(modus_ponens_strict_implies) # label(axiom).  [clausify(54)].
3.80/4.15	188 modus_ponens_strict_implies | -is_a_theorem(c94) # label(modus_ponens_strict_implies) # label(axiom).  [clausify(54)].
3.80/4.15	191 -op_strict_implies | strict_implies(A,B) = necessarily(implies(A,B)) # label(op_strict_implies) # label(axiom).  [clausify(56)].
3.80/4.15	192 -op_strict_implies | necessarily(implies(A,B)) = strict_implies(A,B).  [copy(191),flip(b)].
3.80/4.15	197 axiom_M # label(km4b_axiom_M) # label(axiom).  [assumption].
3.80/4.15	201 necessitation # label(km4b_necessitation) # label(axiom).  [assumption].
3.80/4.15	202 axiom_K # label(km4b_axiom_K) # label(axiom).  [assumption].
3.80/4.15	205 op_strict_implies # label(s1_0_op_strict_implies) # label(axiom).  [assumption].
3.80/4.15	206 -modus_ponens_strict_implies # label(s1_0_modus_ponens_strict_implies) # label(negated_conjecture).  [assumption].
3.80/4.15	221 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B).  [back_unit_del(109),unit_del(d,133)].
3.80/4.15	226 is_a_theorem(implies(necessarily(A),A)).  [back_unit_del(144),unit_del(b,197)].
3.80/4.15	230 -is_a_theorem(A) | is_a_theorem(necessarily(A)).  [back_unit_del(162),unit_del(a,201)].
3.80/4.15	231 is_a_theorem(implies(necessarily(implies(A,B)),implies(necessarily(A),necessarily(B)))).  [back_unit_del(137),unit_del(a,202)].
3.80/4.15	233 necessarily(implies(A,B)) = strict_implies(A,B).  [back_unit_del(192),unit_del(a,205)].
3.80/4.15	234 -is_a_theorem(c94).  [back_unit_del(188),unit_del(a,206)].
3.80/4.15	235 is_a_theorem(c93).  [back_unit_del(187),unit_del(a,206)].
3.80/4.15	236 is_a_theorem(strict_implies(c93,c94)).  [back_unit_del(186),unit_del(a,206)].
3.80/4.15	246 is_a_theorem(implies(strict_implies(A,B),implies(necessarily(A),necessarily(B)))).  [back_rewrite(231),rewrite([233(2)])].
3.80/4.15	320 -is_a_theorem(necessarily(A)) | is_a_theorem(A).  [resolve(226,a,221,b)].
3.80/4.15	361 is_a_theorem(necessarily(c93)).  [resolve(235,a,230,a)].
3.80/4.15	379 -is_a_theorem(strict_implies(A,B)) | is_a_theorem(implies(necessarily(A),necessarily(B))).  [resolve(246,a,221,b)].
3.80/4.15	10457 is_a_theorem(implies(necessarily(c93),necessarily(c94))).  [resolve(379,a,236,a)].
3.80/4.15	10475 is_a_theorem(necessarily(c94)).  [resolve(10457,a,221,b),unit_del(a,361)].
3.80/4.15	10490 $F.  [resolve(10475,a,320,a),unit_del(a,234)].
3.80/4.15	
3.80/4.15	% SZS output end Refutation
3.80/4.15	============================== end of proof ==========================
3.80/4.15	
3.80/4.15	============================== STATISTICS ============================
3.80/4.15	
3.80/4.15	Given=554. Generated=19446. Kept=10427. proofs=1.
3.80/4.15	Usable=540. Sos=9597. Demods=29. Limbo=12, Disabled=425. Hints=0.
3.80/4.15	Megabytes=12.90.
3.80/4.15	User_CPU=3.07, System_CPU=0.02, Wall_clock=3.
3.80/4.15	
3.80/4.15	============================== end of statistics =====================
3.80/4.15	
3.80/4.15	============================== end of search =========================
3.80/4.15	
3.80/4.15	THEOREM PROVED
3.80/4.15	% SZS status Theorem
3.80/4.15	
3.80/4.15	Exiting with 1 proof.
3.80/4.15	
3.80/4.15	Process 12178 exit (max_proofs) Thu Jul  2 06:56:05 2020
3.80/4.15	Prover9 interrupted
3.80/4.15	EOF