0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.11/0.32	% Computer   : n012.cluster.edu
0.11/0.32	% Model      : x86_64 x86_64
0.11/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory     : 8042.1875MB
0.11/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 1200
0.11/0.32	% DateTime   : Tue Jul 13 16:11:31 EDT 2021
0.11/0.32	% CPUTime    : 
0.54/0.87	============================== Prover9 ===============================
0.54/0.87	Prover9 (32) version 2009-11A, November 2009.
0.54/0.87	Process 7918 was started by sandbox2 on n012.cluster.edu,
0.54/0.87	Tue Jul 13 16:11:31 2021
0.54/0.87	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_7764_n012.cluster.edu".
0.54/0.87	============================== end of head ===========================
0.54/0.87	
0.54/0.87	============================== INPUT =================================
0.54/0.87	
0.54/0.87	% Reading from file /tmp/Prover9_7764_n012.cluster.edu
0.54/0.87	
0.54/0.87	set(prolog_style_variables).
0.54/0.87	set(auto2).
0.54/0.87	    % set(auto2) -> set(auto).
0.54/0.87	    % set(auto) -> set(auto_inference).
0.54/0.87	    % set(auto) -> set(auto_setup).
0.54/0.87	    % set(auto_setup) -> set(predicate_elim).
0.54/0.87	    % set(auto_setup) -> assign(eq_defs, unfold).
0.54/0.87	    % set(auto) -> set(auto_limits).
0.54/0.87	    % set(auto_limits) -> assign(max_weight, "100.000").
0.54/0.87	    % set(auto_limits) -> assign(sos_limit, 20000).
0.54/0.87	    % set(auto) -> set(auto_denials).
0.54/0.87	    % set(auto) -> set(auto_process).
0.54/0.87	    % set(auto2) -> assign(new_constants, 1).
0.54/0.87	    % set(auto2) -> assign(fold_denial_max, 3).
0.54/0.87	    % set(auto2) -> assign(max_weight, "200.000").
0.54/0.87	    % set(auto2) -> assign(max_hours, 1).
0.54/0.87	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.54/0.87	    % set(auto2) -> assign(max_seconds, 0).
0.54/0.87	    % set(auto2) -> assign(max_minutes, 5).
0.54/0.87	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.54/0.87	    % set(auto2) -> set(sort_initial_sos).
0.54/0.87	    % set(auto2) -> assign(sos_limit, -1).
0.54/0.87	    % set(auto2) -> assign(lrs_ticks, 3000).
0.54/0.87	    % set(auto2) -> assign(max_megs, 400).
0.54/0.87	    % set(auto2) -> assign(stats, some).
0.54/0.87	    % set(auto2) -> clear(echo_input).
0.54/0.87	    % set(auto2) -> set(quiet).
0.54/0.87	    % set(auto2) -> clear(print_initial_clauses).
0.54/0.87	    % set(auto2) -> clear(print_given).
0.54/0.87	assign(lrs_ticks,-1).
0.54/0.87	assign(sos_limit,10000).
0.54/0.87	assign(order,kbo).
0.54/0.87	set(lex_order_vars).
0.54/0.87	clear(print_given).
0.54/0.87	
0.54/0.87	% formulas(sos).  % not echoed (45 formulas)
0.54/0.87	
0.54/0.87	============================== end of input ==========================
0.54/0.87	
0.54/0.87	% From the command line: assign(max_seconds, 1200).
0.54/0.87	
0.54/0.87	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.54/0.87	
0.54/0.87	% Formulas that are not ordinary clauses:
0.54/0.87	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].
0.54/0.87	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].
0.54/0.87	3 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.54/0.87	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].
0.54/0.87	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].
0.54/0.87	6 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause).  [assumption].
0.54/0.87	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].
0.54/0.87	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].
0.54/0.87	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].
0.54/0.87	10 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause).  [assumption].
0.54/0.87	11 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.54/0.87	12 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.54/0.87	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].
0.54/0.87	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].
1.54/1.84	15 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause).  [assumption].
1.54/1.84	16 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause).  [assumption].
1.54/1.84	17 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
1.54/1.84	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].
1.54/1.84	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].
1.54/1.84	20 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause).  [assumption].
1.54/1.84	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].
1.54/1.84	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].
1.54/1.84	23 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
1.54/1.84	24 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
1.54/1.84	25 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause).  [assumption].
1.54/1.84	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].
1.54/1.84	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].
1.54/1.84	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].
1.54/1.84	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].
1.54/1.84	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].
1.54/1.84	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].
1.54/1.84	
1.54/1.84	============================== end of process non-clausal formulas ===
1.54/1.84	
1.54/1.84	============================== PROCESS INITIAL CLAUSES ===============
1.54/1.84	
1.54/1.84	============================== PREDICATE ELIMINATION =================
1.54/1.84	
1.54/1.84	============================== end predicate elimination =============
1.54/1.84	
1.54/1.84	Auto_denials:  (non-Horn, no changes).
1.54/1.84	
1.54/1.84	Term ordering decisions:
1.54/1.84	
1.54/1.84	% Assigning unary symbol not kb_weight 0 and highest precedence (94).
1.54/1.84	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. implies=1. or=1. and=1. equiv=1. not=0.
1.54/1.84	
1.54/1.84	============================== end of process initial clauses ========
1.54/1.84	
1.54/1.84	============================== CLAUSES FOR SEARCH ====================
1.54/1.84	
1.54/1.84	============================== end of clauses for search =============
1.54/1.84	
1.54/1.84	============================== SEARCH ================================
1.54/1.84	
1.54/1.84	% Starting search at 0.01 seconds.
1.54/1.84	
1.54/1.84	Low Water (keep): wt=28.000, iters=3537
1.54/1.84	
1.54/1.84	Low Water (keep): wt=24.000, iters=3438
1.54/1.84	
1.54/1.84	Low Water (keep): wt=23.000, iters=3479
1.54/1.84	
1.54/1.84	Low Water (keep): wt=22.000, iters=3493
1.54/1.84	
1.54/1.84	Low Water (keep): wt=20.000, iters=3346
1.54/1.84	
1.54/1.84	Low Water (keep): wt=19.000, iters=3342
1.54/1.84	
1.54/1.84	Low Water (keep): wt=18.000, iters=3367
1.54/1.84	
1.54/1.84	Low Water (keep): wt=17.000, iters=3444
1.54/1.84	
1.54/1.84	Low Water (keep): wt=16.000, iters=3405
1.54/1.84	
1.54/1.84	Low Water (keep): wt=15.000, iters=3335
2.61/2.99	
2.61/2.99	Low Water (displace): id=2800, wt=43.000
2.61/2.99	
2.61/2.99	Low Water (displace): id=1180, wt=37.000
2.61/2.99	
2.61/2.99	Low Water (displace): id=5343, wt=30.000
2.61/2.99	
2.61/2.99	Low Water (displace): id=11461, wt=14.000
2.61/2.99	
2.61/2.99	Low Water (displace): id=11918, wt=13.000
2.61/2.99	
2.61/2.99	Low Water (displace): id=14131, wt=12.000
2.61/2.99	
2.61/2.99	Low Water (displace): id=14672, wt=10.000
2.61/2.99	
2.61/2.99	Low Water (keep): wt=14.000, iters=3341
2.61/2.99	
2.61/2.99	============================== PROOF =================================
2.61/2.99	% SZS status Theorem
2.61/2.99	% SZS output start Refutation
2.61/2.99	
2.61/2.99	% Proof 1 at 2.04 (+ 0.08) seconds.
2.61/2.99	% Length of proof is 47.
2.61/2.99	% Level of proof is 13.
2.61/2.99	% Maximum clause weight is 13.000.
2.61/2.99	% Given clauses 734.
2.61/2.99	
2.61/2.99	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].
2.61/2.99	10 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause).  [assumption].
2.61/2.99	12 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
2.61/2.99	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].
2.61/2.99	24 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
2.61/2.99	25 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause).  [assumption].
2.61/2.99	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].
2.61/2.99	32 r3 # label(principia_r3) # label(axiom).  [assumption].
2.61/2.99	34 r5 # label(principia_r5) # label(axiom).  [assumption].
2.61/2.99	36 r1 # label(principia_r1) # label(axiom).  [assumption].
2.61/2.99	37 r2 # label(principia_r2) # label(axiom).  [assumption].
2.61/2.99	38 modus_ponens # label(principia_modus_ponens) # label(axiom).  [assumption].
2.61/2.99	40 op_implies_or # label(principia_op_implies_or) # label(axiom).  [assumption].
2.61/2.99	44 -cn3 # label(luka_cn3) # label(negated_conjecture).  [assumption].
2.61/2.99	47 is_a_theorem(implies(or(A,A),A)) | -r1 # label(r1) # label(axiom).  [clausify(10)].
2.61/2.99	48 is_a_theorem(implies(or(A,A),A)).  [copy(47),unit_del(b,36)].
2.61/2.99	61 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom).  [clausify(24)].
2.61/2.99	62 is_a_theorem(implies(A,or(B,A))).  [copy(61),unit_del(a,37)].
2.61/2.99	66 cn3 | -is_a_theorem(implies(implies(not(c53),c53),c53)) # label(cn3) # label(axiom).  [clausify(25)].
2.61/2.99	67 -is_a_theorem(implies(implies(not(c53),c53),c53)).  [copy(66),unit_del(a,44)].
2.61/2.99	70 -is_a_theorem(implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B) | -modus_ponens # label(modus_ponens) # label(axiom).  [clausify(5)].
2.61/2.99	71 -is_a_theorem(implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B).  [copy(70),unit_del(d,38)].
2.61/2.99	76 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom).  [clausify(12)].
2.61/2.99	77 is_a_theorem(implies(or(A,B),or(B,A))).  [copy(76),unit_del(a,32)].
2.61/2.99	81 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom).  [clausify(27)].
2.61/2.99	82 or(not(A),B) = implies(A,B).  [copy(81),unit_del(a,40)].
2.61/2.99	100 is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))) | -r5 # label(r5) # label(axiom).  [clausify(18)].
2.61/2.99	101 is_a_theorem(implies(implies(A,B),implies(or(C,A),or(C,B)))).  [copy(100),unit_del(b,34)].
2.61/2.99	115 -is_a_theorem(or(A,B)) | is_a_theorem(or(B,A)).  [resolve(77,a,71,a)].
2.61/2.99	120 is_a_theorem(implies(or(A,not(B)),implies(B,A))).  [para(82(a,1),77(a,1,2))].
2.61/2.99	131 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(or(C,A),or(C,B))).  [resolve(101,a,71,a)].
2.61/2.99	183 -is_a_theorem(implies(A,B)) | is_a_theorem(or(B,not(A))).  [para(82(a,1),115(a,1))].
2.61/2.99	511 -is_a_theorem(or(A,not(B))) | is_a_theorem(implies(B,A)).  [resolve(120,a,71,a)].
2.61/2.99	541 -is_a_theorem(or(c53,not(implies(not(c53),c53)))).  [ur(71,a,120,a,c,67,a)].
2.61/2.99	1121 -is_a_theorem(implies(A,not(B))) | is_a_theorem(implies(B,not(A))).  [para(82(a,1),511(a,1))].
2.61/2.99	2434 is_a_theorem(implies(or(A,or(B,B)),or(A,B))).  [resolve(131,a,48,a)].
2.61/2.99	5236 -is_a_theorem(or(A,or(B,B))) | is_a_theorem(or(A,B)).  [resolve(2434,a,71,a)].
2.61/2.99	6187 -is_a_theorem(implies(A,or(B,B))) | is_a_theorem(implies(A,B)).  [para(82(a,1),5236(a,1)),rewrite([82(5)])].
2.61/2.99	7340 is_a_theorem(implies(A,A)).  [resolve(6187,a,62,a)].
2.61/2.99	7352 is_a_theorem(implies(A,not(not(A)))).  [resolve(7340,a,1121,a)].
2.61/2.99	7353 is_a_theorem(or(A,not(A))).  [resolve(7340,a,183,a)].
2.61/2.99	7685 -is_a_theorem(implies(or(A,not(A)),or(c53,not(implies(not(c53),c53))))).  [ur(71,b,7353,a,c,541,a)].
2.61/2.99	8286 is_a_theorem(implies(or(A,B),or(A,not(not(B))))).  [resolve(7352,a,131,a)].
2.61/2.99	17204 is_a_theorem(implies(implies(not(A),A),not(not(A)))).  [resolve(8286,a,6187,a),rewrite([82(3)])].
2.61/2.99	17238 is_a_theorem(implies(not(A),not(implies(not(A),A)))).  [resolve(17204,a,1121,a)].
2.61/2.99	17331 is_a_theorem(implies(or(A,not(B)),or(A,not(implies(not(B),B))))).  [resolve(17238,a,131,a)].
2.61/2.99	17332 $F.  [resolve(17331,a,7685,a)].
2.61/2.99	
2.61/2.99	% SZS output end Refutation
2.61/2.99	============================== end of proof ==========================
2.61/2.99	
2.61/2.99	============================== STATISTICS ============================
2.61/2.99	
2.61/2.99	Given=734. Generated=108382. Kept=17285. proofs=1.
2.61/2.99	Usable=704. Sos=9999. Demods=11. Limbo=15, Disabled=6640. Hints=0.
2.61/2.99	Megabytes=12.06.
2.61/2.99	User_CPU=2.04, System_CPU=0.08, Wall_clock=2.
2.61/2.99	
2.61/2.99	============================== end of statistics =====================
2.61/2.99	
2.61/2.99	============================== end of search =========================
2.61/2.99	
2.61/2.99	THEOREM PROVED
2.61/2.99	% SZS status Theorem
2.61/2.99	
2.61/2.99	Exiting with 1 proof.
2.61/2.99	
2.61/2.99	Process 7918 exit (max_proofs) Tue Jul 13 16:11:33 2021
2.61/2.99	Prover9 interrupted
2.61/2.99	EOF