0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n022.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   : 180
0.12/0.33	% DateTime   : Thu Aug 29 09:42:13 EDT 2019
0.12/0.34	% CPUTime    : 
0.42/1.03	============================== Prover9 ===============================
0.42/1.03	Prover9 (32) version 2009-11A, November 2009.
0.42/1.03	Process 10099 was started by sandbox on n022.cluster.edu,
0.42/1.03	Thu Aug 29 09:42:14 2019
0.42/1.03	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_9946_n022.cluster.edu".
0.42/1.03	============================== end of head ===========================
0.42/1.03	
0.42/1.03	============================== INPUT =================================
0.42/1.03	
0.42/1.03	% Reading from file /tmp/Prover9_9946_n022.cluster.edu
0.42/1.03	
0.42/1.03	set(prolog_style_variables).
0.42/1.03	set(auto2).
0.42/1.03	    % set(auto2) -> set(auto).
0.42/1.03	    % set(auto) -> set(auto_inference).
0.42/1.03	    % set(auto) -> set(auto_setup).
0.42/1.03	    % set(auto_setup) -> set(predicate_elim).
0.42/1.03	    % set(auto_setup) -> assign(eq_defs, unfold).
0.42/1.03	    % set(auto) -> set(auto_limits).
0.42/1.03	    % set(auto_limits) -> assign(max_weight, "100.000").
0.42/1.03	    % set(auto_limits) -> assign(sos_limit, 20000).
0.42/1.03	    % set(auto) -> set(auto_denials).
0.42/1.03	    % set(auto) -> set(auto_process).
0.42/1.03	    % set(auto2) -> assign(new_constants, 1).
0.42/1.03	    % set(auto2) -> assign(fold_denial_max, 3).
0.42/1.03	    % set(auto2) -> assign(max_weight, "200.000").
0.42/1.03	    % set(auto2) -> assign(max_hours, 1).
0.42/1.03	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.42/1.03	    % set(auto2) -> assign(max_seconds, 0).
0.42/1.03	    % set(auto2) -> assign(max_minutes, 5).
0.42/1.03	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.42/1.03	    % set(auto2) -> set(sort_initial_sos).
0.42/1.03	    % set(auto2) -> assign(sos_limit, -1).
0.42/1.03	    % set(auto2) -> assign(lrs_ticks, 3000).
0.42/1.03	    % set(auto2) -> assign(max_megs, 400).
0.42/1.03	    % set(auto2) -> assign(stats, some).
0.42/1.03	    % set(auto2) -> clear(echo_input).
0.42/1.03	    % set(auto2) -> set(quiet).
0.42/1.03	    % set(auto2) -> clear(print_initial_clauses).
0.42/1.03	    % set(auto2) -> clear(print_given).
0.42/1.03	assign(lrs_ticks,-1).
0.42/1.03	assign(sos_limit,10000).
0.42/1.03	assign(order,kbo).
0.42/1.03	set(lex_order_vars).
0.42/1.03	clear(print_given).
0.42/1.03	
0.42/1.03	% formulas(sos).  % not echoed (89 formulas)
0.42/1.03	
0.42/1.03	============================== end of input ==========================
0.42/1.03	
0.42/1.03	% From the command line: assign(max_seconds, 180).
0.42/1.03	
0.42/1.03	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.42/1.03	
0.42/1.03	% Formulas that are not ordinary clauses:
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	10 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	11 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	12 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	13 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	14 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	15 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	16 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	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].
0.42/1.03	18 (all P all Q is_a_theorem(implies(Q,or(P,Q)))) <-> r2 # label(r2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	22 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	23 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	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].
0.42/1.03	25 r1 <-> (all P is_a_theorem(implies(or(P,P),P))) # label(r1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	26 kn2 <-> (all P all Q is_a_theorem(implies(and(P,Q),P))) # label(kn2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	35 axiom_B <-> (all X is_a_theorem(implies(X,necessarily(possibly(X))))) # label(axiom_B) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	36 (all X is_a_theorem(strict_implies(X,possibly(X)))) <-> axiom_m6 # label(axiom_m6) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	37 (all X is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_s4 # label(axiom_s4) # label(axiom) # label(non_clause).  [assumption].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	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].
0.42/1.03	41 necessitation <-> (all X (is_a_theorem(X) -> is_a_theorem(necessarily(X)))) # label(necessitation) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	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].
0.76/1.06	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].
0.76/1.06	44 (all X is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))) <-> axiom_4 # label(axiom_4) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	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].
0.76/1.06	46 (all X is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))) <-> axiom_m10 # label(axiom_m10) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	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].
0.76/1.06	48 (all X is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) <-> axiom_m9 # label(axiom_m9) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	49 (all X is_a_theorem(strict_implies(X,and(X,X)))) <-> axiom_m4 # label(axiom_m4) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	50 (all X is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <-> axiom_5 # label(axiom_5) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	51 axiom_M <-> (all X is_a_theorem(implies(necessarily(X),X))) # label(axiom_M) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	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].
0.76/1.06	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].
0.76/1.06	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].
0.76/1.06	55 op_necessarily -> (all X necessarily(X) = not(possibly(not(X)))) # label(op_necessarily) # label(axiom) # label(non_clause).  [assumption].
0.76/1.06	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].
0.76/1.06	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].
0.76/1.06	58 op_possibly -> (all X not(necessarily(not(X))) = possibly(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 ====================
1.01/1.30	
1.01/1.30	============================== end of clauses for search =============
1.01/1.30	
1.01/1.30	============================== SEARCH ================================
1.01/1.30	
1.01/1.30	% Starting search at 0.05 seconds.
1.01/1.30	
1.01/1.30	============================== PROOF =================================
1.01/1.30	% SZS status Theorem
1.01/1.30	% SZS output start Refutation
1.01/1.30	
1.01/1.30	% Proof 1 at 0.28 (+ 0.00) seconds.
1.01/1.30	% Length of proof is 20.
1.01/1.30	% Level of proof is 6.
1.01/1.30	% Maximum clause weight is 9.000.
1.01/1.30	% Given clauses 392.
1.01/1.30	
1.01/1.30	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].
1.01/1.30	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].
1.01/1.30	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].
1.01/1.30	60 is_a_theorem(implies(A,implies(B,and(A,B)))) | -and_3 # label(and_3) # label(axiom).  [clausify(1)].
1.01/1.30	76 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom).  [clausify(9)].
1.01/1.30	124 and_3 # label(hilbert_and_3) # label(axiom).  [assumption].
1.01/1.30	128 modus_ponens # label(hilbert_modus_ponens) # label(axiom).  [assumption].
1.01/1.30	143 adjunction | is_a_theorem(c61) # label(adjunction) # label(axiom).  [clausify(34)].
1.01/1.30	144 adjunction | is_a_theorem(c62) # label(adjunction) # label(axiom).  [clausify(34)].
1.01/1.30	145 adjunction | -is_a_theorem(and(c61,c62)) # label(adjunction) # label(axiom).  [clausify(34)].
1.01/1.30	206 -adjunction # label(s1_0_adjunction) # label(negated_conjecture).  [assumption].
1.01/1.30	211 is_a_theorem(implies(A,implies(B,and(A,B)))).  [back_unit_del(60),unit_del(b,124)].
1.01/1.30	215 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B).  [back_unit_del(76),unit_del(a,128)].
1.01/1.30	233 -is_a_theorem(and(c61,c62)).  [back_unit_del(145),unit_del(a,206)].
1.01/1.30	234 is_a_theorem(c62).  [back_unit_del(144),unit_del(a,206)].
1.01/1.30	235 is_a_theorem(c61).  [back_unit_del(143),unit_del(a,206)].
1.01/1.30	251 -is_a_theorem(A) | is_a_theorem(implies(B,and(A,B))).  [resolve(215,b,211,a)].
1.01/1.30	441 is_a_theorem(implies(A,and(c61,A))).  [resolve(251,a,235,a)].
1.01/1.30	1228 -is_a_theorem(A) | is_a_theorem(and(c61,A)).  [resolve(441,a,215,b)].
1.01/1.30	2469 $F.  [resolve(1228,a,234,a),unit_del(a,233)].
1.01/1.30	
1.01/1.30	% SZS output end Refutation
1.01/1.30	============================== end of proof ==========================
1.01/1.30	
1.01/1.30	============================== STATISTICS ============================
1.01/1.30	
1.01/1.30	Given=392. Generated=3010. Kept=2406. proofs=1.
1.01/1.30	Usable=384. Sos=1667. Demods=39. Limbo=243, Disabled=259. Hints=0.
1.01/1.30	Megabytes=2.73.
1.01/1.30	User_CPU=0.28, System_CPU=0.00, Wall_clock=0.
1.01/1.30	
1.01/1.30	============================== end of statistics =====================
1.01/1.30	
1.01/1.30	============================== end of search =========================
1.01/1.30	
1.01/1.30	THEOREM PROVED
1.01/1.30	% SZS status Theorem
1.01/1.30	
1.01/1.30	Exiting with 1 proof.
1.01/1.30	
1.01/1.30	Process 10099 exit (max_proofs) Thu Aug 29 09:42:14 2019
1.01/1.30	Prover9 interrupted
1.01/1.30	EOF