0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : tptp2X_and_run_prover9 %d %s
0.03/0.23	% Computer   : n163.star.cs.uiowa.edu
0.03/0.23	% Model      : x86_64 x86_64
0.03/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.23	% Memory     : 32218.625MB
0.03/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.23	% CPULimit   : 300
0.03/0.23	% DateTime   : Sat Jul 14 05:44:39 CDT 2018
0.03/0.23	% CPUTime    : 
0.06/0.47	============================== Prover9 ===============================
0.06/0.47	Prover9 (32) version 2009-11A, November 2009.
0.06/0.47	Process 58188 was started by sandbox on n163.star.cs.uiowa.edu,
0.06/0.47	Sat Jul 14 05:44:40 2018
0.06/0.47	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_58156_n163.star.cs.uiowa.edu".
0.06/0.47	============================== end of head ===========================
0.06/0.47	
0.06/0.47	============================== INPUT =================================
0.06/0.47	
0.06/0.47	% Reading from file /tmp/Prover9_58156_n163.star.cs.uiowa.edu
0.06/0.47	
0.06/0.47	set(prolog_style_variables).
0.06/0.47	set(auto2).
0.06/0.47	    % set(auto2) -> set(auto).
0.06/0.47	    % set(auto) -> set(auto_inference).
0.06/0.47	    % set(auto) -> set(auto_setup).
0.06/0.47	    % set(auto_setup) -> set(predicate_elim).
0.06/0.47	    % set(auto_setup) -> assign(eq_defs, unfold).
0.06/0.47	    % set(auto) -> set(auto_limits).
0.06/0.47	    % set(auto_limits) -> assign(max_weight, "100.000").
0.06/0.47	    % set(auto_limits) -> assign(sos_limit, 20000).
0.06/0.47	    % set(auto) -> set(auto_denials).
0.06/0.47	    % set(auto) -> set(auto_process).
0.06/0.47	    % set(auto2) -> assign(new_constants, 1).
0.06/0.47	    % set(auto2) -> assign(fold_denial_max, 3).
0.06/0.47	    % set(auto2) -> assign(max_weight, "200.000").
0.06/0.47	    % set(auto2) -> assign(max_hours, 1).
0.06/0.47	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.06/0.47	    % set(auto2) -> assign(max_seconds, 0).
0.06/0.47	    % set(auto2) -> assign(max_minutes, 5).
0.06/0.47	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.06/0.47	    % set(auto2) -> set(sort_initial_sos).
0.06/0.47	    % set(auto2) -> assign(sos_limit, -1).
0.06/0.47	    % set(auto2) -> assign(lrs_ticks, 3000).
0.06/0.47	    % set(auto2) -> assign(max_megs, 400).
0.06/0.47	    % set(auto2) -> assign(stats, some).
0.06/0.47	    % set(auto2) -> clear(echo_input).
0.06/0.47	    % set(auto2) -> set(quiet).
0.06/0.47	    % set(auto2) -> clear(print_initial_clauses).
0.06/0.47	    % set(auto2) -> clear(print_given).
0.06/0.47	assign(lrs_ticks,-1).
0.06/0.47	assign(sos_limit,10000).
0.06/0.47	assign(order,kbo).
0.06/0.47	set(lex_order_vars).
0.06/0.47	clear(print_given).
0.06/0.47	
0.06/0.47	% formulas(sos).  % not echoed (82 formulas)
0.06/0.47	
0.06/0.47	============================== end of input ==========================
0.06/0.47	
0.06/0.47	% From the command line: assign(max_seconds, 300).
0.06/0.47	
0.06/0.47	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.06/0.47	
0.06/0.47	% Formulas that are not ordinary clauses:
0.06/0.47	1 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	2 (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].
0.06/0.47	3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	4 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].
0.06/0.47	5 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].
0.06/0.47	6 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	7 (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].
0.06/0.47	8 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].
0.06/0.47	9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	11 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	12 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].
0.06/0.47	13 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].
0.06/0.47	14 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	15 (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].
0.06/0.47	16 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	19 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	20 (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].
0.06/0.47	21 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].
0.06/0.47	22 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	23 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	24 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	25 (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].
0.06/0.47	26 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].
0.06/0.47	27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	28 op_and -> (all X all Y and(X,Y) = not(or(not(X),not(Y)))) # label(op_and) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	29 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].
0.06/0.47	30 op_implies_or -> (all X all Y or(not(X),Y) = implies(X,Y)) # label(op_implies_or) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	31 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].
0.06/0.47	32 axiom_m6 <-> (all X is_a_theorem(strict_implies(X,possibly(X)))) # label(axiom_m6) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	33 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].
0.06/0.47	34 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].
0.06/0.47	35 (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) <-> axiom_m9 # label(axiom_m9) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	36 (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].
0.06/0.47	37 (all X all Y (is_a_theorem(strict_equiv(X,Y)) -> Y = X)) <-> substitution_strict_equiv # label(substitution_strict_equiv) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	38 (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) <-> axiom_m10 # label(axiom_m10) # label(axiom) # label(non_clause).  [assumption].
0.06/0.47	39 (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].
0.06/0.47	40 (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].
0.06/0.47	41 (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_4 # label(axiom_4) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	42 (all X all Y (is_a_theorem(strict_implies(X,Y)) & is_a_theorem(X) -> is_a_theorem(Y))) <-> modus_ponens_strict_implies # label(modus_ponens_strict_implies) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	43 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].
0.06/0.49	44 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	45 (all X all Y is_a_theorem(strict_implies(and(X,Y),and(Y,X)))) <-> axiom_m1 # label(axiom_m1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	46 axiom_m4 <-> (all X is_a_theorem(strict_implies(X,and(X,X)))) # label(axiom_m4) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	47 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	48 (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_s4 # label(axiom_s4) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	49 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	50 (all P all Q is_a_theorem(strict_implies(strict_implies(P,Q),strict_implies(possibly(P),possibly(Q))))) <-> axiom_m8 # label(axiom_m8) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	51 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	52 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].
0.06/0.49	53 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].
0.06/0.49	54 (all X all Y is_a_theorem(strict_implies(and(X,Y),X))) <-> axiom_m2 # label(axiom_m2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	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].
0.06/0.49	56 op_necessarily -> (all X not(possibly(not(X))) = necessarily(X)) # label(op_necessarily) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	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].
0.06/0.49	58 op_possibly -> (all X not(necessarily(not(X))) = possibly(X)) # label(op_possibly) # label(axiom) # label(non_clause).  [assumption].
0.06/0.49	
0.06/0.49	============================== end of process non-clausal formulas ===
0.06/0.49	
0.06/0.49	============================== PROCESS INITIAL CLAUSES ===============
0.06/0.49	
0.06/0.49	============================== PREDICATE ELIMINATION =================
0.06/0.49	
0.06/0.49	============================== end predicate elimination =============
0.06/0.49	
0.06/0.49	Auto_denials:  (non-Horn, no changes).
0.06/0.49	
0.06/0.49	Term ordering decisions:
0.06/0.49	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.
0.06/0.49	
0.06/0.49	============================== end of process initial clauses ========
0.06/0.49	
0.06/0.49	============================== CLAUSES FOR SEARCH ====================
6.17/6.36	
6.17/6.36	============================== end of clauses for search =============
6.17/6.36	
6.17/6.36	============================== SEARCH ================================
6.17/6.36	
6.17/6.36	% Starting search at 0.03 seconds.
6.17/6.36	
6.17/6.36	Low Water (keep): wt=28.000, iters=3616
6.17/6.36	
6.17/6.36	Low Water (keep): wt=20.000, iters=3483
6.17/6.36	
6.17/6.36	Low Water (keep): wt=19.000, iters=3425
6.17/6.36	
6.17/6.36	Low Water (keep): wt=18.000, iters=3458
6.17/6.36	
6.17/6.36	Low Water (keep): wt=17.000, iters=3340
6.17/6.36	
6.17/6.36	Low Water (keep): wt=16.000, iters=3485
6.17/6.36	
6.17/6.36	Low Water (keep): wt=15.000, iters=3337
6.17/6.36	
6.17/6.36	Low Water (keep): wt=14.000, iters=3438
6.17/6.36	
6.17/6.36	Low Water (keep): wt=13.000, iters=3502
6.17/6.36	
6.17/6.36	Low Water (keep): wt=12.000, iters=3341
6.17/6.36	
6.17/6.36	Low Water (displace): id=8856, wt=32.000
6.17/6.36	
6.17/6.36	Low Water (displace): id=8057, wt=30.000
6.17/6.36	
6.17/6.36	Low Water (displace): id=14493, wt=10.000
6.17/6.36	
6.17/6.36	Low Water (keep): wt=11.000, iters=3333
6.17/6.36	
6.17/6.36	Low Water (displace): id=14530, wt=9.000
6.17/6.36	
6.17/6.36	============================== PROOF =================================
6.17/6.36	% SZS status Theorem
6.17/6.36	% SZS output start Refutation
6.17/6.36	
6.17/6.36	% Proof 1 at 5.82 (+ 0.08) seconds.
6.17/6.36	% Length of proof is 79.
6.17/6.36	% Level of proof is 12.
6.17/6.36	% Maximum clause weight is 15.000.
6.17/6.36	% Given clauses 1946.
6.17/6.36	
6.17/6.36	3 substitution_of_equivalents <-> (all X all Y (is_a_theorem(equiv(X,Y)) -> Y = X)) # label(substitution_of_equivalents) # label(axiom) # label(non_clause).  [assumption].
6.17/6.36	12 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].
6.17/6.36	15 (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].
6.17/6.36	17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause).  [assumption].
6.17/6.36	21 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].
6.17/6.36	23 modus_tollens <-> (all X all Y is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) # label(modus_tollens) # label(axiom) # label(non_clause).  [assumption].
6.17/6.36	25 (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].
6.17/6.36	26 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].
6.17/6.36	27 op_or -> (all X all Y or(X,Y) = not(and(not(X),not(Y)))) # label(op_or) # label(axiom) # label(non_clause).  [assumption].
6.17/6.36	29 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].
6.17/6.36	44 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause).  [assumption].
6.17/6.36	47 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause).  [assumption].
6.17/6.36	51 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause).  [assumption].
6.17/6.36	58 op_possibly -> (all X not(necessarily(not(X))) = possibly(X)) # label(op_possibly) # label(axiom) # label(non_clause).  [assumption].
6.17/6.36	63 -substitution_of_equivalents | -is_a_theorem(equiv(A,B)) | B = A # label(substitution_of_equivalents) # label(axiom).  [clausify(3)].
6.17/6.36	82 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom).  [clausify(12)].
6.17/6.36	91 is_a_theorem(implies(A,implies(B,and(A,B)))) | -and_3 # label(and_3) # label(axiom).  [clausify(15)].
6.17/6.36	94 -and_1 | is_a_theorem(implies(and(A,B),A)) # label(and_1) # label(axiom).  [clausify(17)].
6.17/6.36	102 -or_3 | is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))) # label(or_3) # label(axiom).  [clausify(21)].
6.17/6.36	106 -modus_tollens | is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))) # label(modus_tollens) # label(axiom).  [clausify(23)].
6.17/6.36	111 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))) | -equivalence_3 # label(equivalence_3) # label(axiom).  [clausify(25)].
6.17/6.36	112 -implies_2 | is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))) # label(implies_2) # label(axiom).  [clausify(26)].
6.17/6.36	114 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom).  [clausify(27)].
6.17/6.36	115 -op_or | not(and(not(A),not(B))) = or(A,B).  [copy(114),flip(b)].
6.17/6.36	117 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom).  [clausify(29)].
6.17/6.36	122 and_3 # label(hilbert_and_3) # label(axiom).  [assumption].
6.17/6.36	123 op_or # label(hilbert_op_or) # label(axiom).  [assumption].
6.17/6.36	125 and_1 # label(hilbert_and_1) # label(axiom).  [assumption].
6.17/6.36	126 substitution_of_equivalents # label(substitution_of_equivalents) # label(axiom).  [assumption].
6.17/6.36	127 implies_2 # label(hilbert_implies_2) # label(axiom).  [assumption].
6.17/6.36	130 op_implies_and # label(hilbert_op_implies_and) # label(axiom).  [assumption].
6.17/6.36	132 or_3 # label(hilbert_or_3) # label(axiom).  [assumption].
6.17/6.36	135 modus_tollens # label(hilbert_modus_tollens) # label(axiom).  [assumption].
6.17/6.36	137 modus_ponens # label(hilbert_modus_ponens) # label(axiom).  [assumption].
6.17/6.36	138 equivalence_3 # label(hilbert_equivalence_3) # label(axiom).  [assumption].
6.17/6.36	167 is_a_theorem(implies(possibly(A),necessarily(possibly(A)))) | -axiom_5 # label(axiom_5) # label(axiom).  [clausify(44)].
6.17/6.36	172 -axiom_M | is_a_theorem(implies(necessarily(A),A)) # label(axiom_M) # label(axiom).  [clausify(47)].
6.17/6.36	182 axiom_B | -is_a_theorem(implies(c88,necessarily(possibly(c88)))) # label(axiom_B) # label(axiom).  [clausify(51)].
6.17/6.36	196 -op_possibly | possibly(A) = not(necessarily(not(A))) # label(op_possibly) # label(axiom).  [clausify(58)].
6.17/6.36	197 -op_possibly | not(necessarily(not(A))) = possibly(A).  [copy(196),flip(b)].
6.17/6.36	199 axiom_M # label(km5_axiom_M) # label(axiom).  [assumption].
6.17/6.36	200 axiom_5 # label(km5_axiom_5) # label(axiom).  [assumption].
6.17/6.36	201 op_possibly # label(km5_op_possibly) # label(axiom).  [assumption].
6.17/6.36	203 -axiom_B # label(km4b_axiom_B) # label(negated_conjecture).  [assumption].
6.17/6.36	205 is_a_theorem(implies(A,implies(B,and(A,B)))).  [back_unit_del(91),unit_del(b,122)].
6.17/6.36	206 not(and(not(A),not(B))) = or(A,B).  [back_unit_del(115),unit_del(a,123)].
6.17/6.36	208 is_a_theorem(implies(and(A,B),A)).  [back_unit_del(94),unit_del(a,125)].
6.17/6.36	209 -is_a_theorem(equiv(A,B)) | B = A.  [back_unit_del(63),unit_del(a,126)].
6.17/6.36	210 is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))).  [back_unit_del(112),unit_del(a,127)].
6.17/6.36	213 not(and(A,not(B))) = implies(A,B).  [back_unit_del(117),unit_del(a,130)].
6.17/6.36	215 is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))).  [back_unit_del(102),unit_del(a,132)].
6.17/6.36	218 is_a_theorem(implies(implies(not(A),not(B)),implies(B,A))).  [back_unit_del(106),unit_del(a,135)].
6.17/6.36	220 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B).  [back_unit_del(82),unit_del(a,137)].
6.17/6.36	221 is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))).  [back_unit_del(111),unit_del(b,138)].
6.17/6.36	224 is_a_theorem(implies(necessarily(A),A)).  [back_unit_del(172),unit_del(a,199)].
6.17/6.36	225 is_a_theorem(implies(possibly(A),necessarily(possibly(A)))).  [back_unit_del(167),unit_del(b,200)].
6.17/6.36	226 not(necessarily(not(A))) = possibly(A).  [back_unit_del(197),unit_del(a,201)].
6.17/6.36	228 -is_a_theorem(implies(c88,necessarily(possibly(c88)))).  [back_unit_del(182),unit_del(a,203)].
6.17/6.36	231 implies(not(A),B) = or(A,B).  [back_rewrite(206),rewrite([213(4)])].
6.17/6.36	233 is_a_theorem(implies(or(A,not(B)),implies(B,A))).  [back_rewrite(218),rewrite([231(3)])].
6.17/6.36	274 -is_a_theorem(implies(A,implies(A,B))) | is_a_theorem(implies(A,B)).  [resolve(220,b,210,a)].
6.17/6.36	279 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,A),equiv(A,B))).  [resolve(221,a,220,b)].
6.17/6.36	338 or(and(A,not(B)),C) = implies(implies(A,B),C).  [para(213(a,1),231(a,1,1)),flip(a)].
6.17/6.36	353 -is_a_theorem(or(A,not(B))) | is_a_theorem(implies(B,A)).  [resolve(233,a,220,b)].
6.17/6.36	3072 is_a_theorem(implies(implies(A,B),implies(or(A,A),B))).  [resolve(274,a,215,a)].
6.17/6.36	3073 is_a_theorem(implies(A,and(A,A))).  [resolve(274,a,205,a)].
6.17/6.36	3337 is_a_theorem(implies(implies(and(A,A),A),equiv(A,and(A,A)))).  [resolve(279,a,3073,a)].
6.17/6.36	3363 is_a_theorem(implies(implies(necessarily(possibly(A)),possibly(A)),equiv(possibly(A),necessarily(possibly(A))))).  [resolve(279,a,225,a)].
6.17/6.36	14995 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(or(A,A),B)).  [resolve(3072,a,220,b)].
6.17/6.36	15144 is_a_theorem(equiv(A,and(A,A))).  [resolve(3337,a,220,b),unit_del(a,208)].
6.17/6.36	15160 and(A,A) = A.  [resolve(15144,a,209,a)].
6.17/6.36	15169 implies(or(A,A),B) = or(not(A),B).  [para(15160(a,1),338(a,1,1)),rewrite([231(4)]),flip(a)].
6.17/6.36	15186 -is_a_theorem(implies(A,B)) | is_a_theorem(or(not(A),B)).  [back_rewrite(14995),rewrite([15169(4)])].
6.17/6.36	16645 is_a_theorem(equiv(possibly(A),necessarily(possibly(A)))).  [resolve(3363,a,220,b),unit_del(a,224)].
6.17/6.36	16661 necessarily(possibly(A)) = possibly(A).  [resolve(16645,a,209,a)].
6.17/6.36	16695 -is_a_theorem(implies(c88,possibly(c88))).  [back_rewrite(228),rewrite([16661(4)])].
6.17/6.36	18720 is_a_theorem(or(not(necessarily(A)),A)).  [resolve(15186,a,224,a)].
6.17/6.36	18740 is_a_theorem(implies(A,possibly(A))).  [resolve(18720,a,353,a),rewrite([226(3)])].
6.17/6.36	18741 $F.  [resolve(18740,a,16695,a)].
6.17/6.36	
6.17/6.36	% SZS output end Refutation
6.17/6.36	============================== end of proof ==========================
6.17/6.36	
6.17/6.36	============================== STATISTICS ============================
6.17/6.36	
6.17/6.36	Given=1946. Generated=98887. Kept=18677. proofs=1.
6.17/6.36	Usable=1605. Sos=9998. Demods=46. Limbo=10, Disabled=7203. Hints=0.
6.17/6.36	Megabytes=20.16.
6.17/6.36	User_CPU=5.82, System_CPU=0.08, Wall_clock=6.
6.17/6.36	
6.17/6.36	============================== end of statistics =====================
6.17/6.36	
6.17/6.36	============================== end of search =========================
6.17/6.36	
6.17/6.36	THEOREM PROVED
6.17/6.36	% SZS status Theorem
6.17/6.36	
6.17/6.36	Exiting with 1 proof.
6.17/6.36	
6.17/6.36	Process 58188 exit (max_proofs) Sat Jul 14 05:44:46 2018
6.17/6.36	Prover9 interrupted
6.17/6.37	EOF