0.02/0.09	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.09	% Command    : tptp2X_and_run_prover9 %d %s
0.09/0.29	% Computer   : n013.cluster.edu
0.09/0.29	% Model      : x86_64 x86_64
0.09/0.29	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.29	% Memory     : 8042.1875MB
0.09/0.29	% OS         : Linux 3.10.0-693.el7.x86_64
0.09/0.29	% CPULimit   : 1200
0.09/0.29	% DateTime   : Tue Jul 13 16:13:33 EDT 2021
0.09/0.29	% CPUTime    : 
0.70/0.98	============================== Prover9 ===============================
0.70/0.98	Prover9 (32) version 2009-11A, November 2009.
0.70/0.98	Process 14902 was started by sandbox on n013.cluster.edu,
0.70/0.98	Tue Jul 13 16:13:34 2021
0.70/0.98	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_14749_n013.cluster.edu".
0.70/0.98	============================== end of head ===========================
0.70/0.98	
0.70/0.98	============================== INPUT =================================
0.70/0.98	
0.70/0.98	% Reading from file /tmp/Prover9_14749_n013.cluster.edu
0.70/0.98	
0.70/0.98	set(prolog_style_variables).
0.70/0.98	set(auto2).
0.70/0.98	    % set(auto2) -> set(auto).
0.70/0.98	    % set(auto) -> set(auto_inference).
0.70/0.98	    % set(auto) -> set(auto_setup).
0.70/0.98	    % set(auto_setup) -> set(predicate_elim).
0.70/0.98	    % set(auto_setup) -> assign(eq_defs, unfold).
0.70/0.98	    % set(auto) -> set(auto_limits).
0.70/0.98	    % set(auto_limits) -> assign(max_weight, "100.000").
0.70/0.98	    % set(auto_limits) -> assign(sos_limit, 20000).
0.70/0.98	    % set(auto) -> set(auto_denials).
0.70/0.98	    % set(auto) -> set(auto_process).
0.70/0.98	    % set(auto2) -> assign(new_constants, 1).
0.70/0.98	    % set(auto2) -> assign(fold_denial_max, 3).
0.70/0.98	    % set(auto2) -> assign(max_weight, "200.000").
0.70/0.98	    % set(auto2) -> assign(max_hours, 1).
0.70/0.98	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.70/0.98	    % set(auto2) -> assign(max_seconds, 0).
0.70/0.98	    % set(auto2) -> assign(max_minutes, 5).
0.70/0.98	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.70/0.98	    % set(auto2) -> set(sort_initial_sos).
0.70/0.98	    % set(auto2) -> assign(sos_limit, -1).
0.70/0.98	    % set(auto2) -> assign(lrs_ticks, 3000).
0.70/0.98	    % set(auto2) -> assign(max_megs, 400).
0.70/0.98	    % set(auto2) -> assign(stats, some).
0.70/0.98	    % set(auto2) -> clear(echo_input).
0.70/0.98	    % set(auto2) -> set(quiet).
0.70/0.98	    % set(auto2) -> clear(print_initial_clauses).
0.70/0.98	    % set(auto2) -> clear(print_given).
0.70/0.98	assign(lrs_ticks,-1).
0.70/0.98	assign(sos_limit,10000).
0.70/0.98	assign(order,kbo).
0.70/0.98	set(lex_order_vars).
0.70/0.98	clear(print_given).
0.70/0.98	
0.70/0.98	% formulas(sos).  % not echoed (43 formulas)
0.70/0.98	
0.70/0.98	============================== end of input ==========================
0.70/0.98	
0.70/0.98	% From the command line: assign(max_seconds, 1200).
0.70/0.98	
0.70/0.98	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.70/0.98	
0.70/0.98	% Formulas that are not ordinary clauses:
0.70/0.98	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].
0.70/0.98	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].
0.70/0.98	3 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.70/0.98	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].
0.70/0.98	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].
0.70/0.98	6 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause).  [assumption].
0.70/0.98	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].
0.70/0.98	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].
0.70/0.98	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].
0.70/0.98	10 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause).  [assumption].
0.70/0.98	11 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.70/0.98	12 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.70/0.98	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].
0.70/0.98	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].
1.25/1.60	15 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause).  [assumption].
1.25/1.60	16 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause).  [assumption].
1.25/1.60	17 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
1.25/1.60	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].
1.25/1.60	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].
1.25/1.60	20 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause).  [assumption].
1.25/1.60	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].
1.25/1.60	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].
1.25/1.60	23 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
1.25/1.60	24 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
1.25/1.60	25 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause).  [assumption].
1.25/1.60	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].
1.25/1.60	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].
1.25/1.60	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].
1.25/1.60	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].
1.25/1.60	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].
1.25/1.60	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].
1.25/1.60	
1.25/1.60	============================== end of process non-clausal formulas ===
1.25/1.60	
1.25/1.60	============================== PROCESS INITIAL CLAUSES ===============
1.25/1.60	
1.25/1.60	============================== PREDICATE ELIMINATION =================
1.25/1.60	
1.25/1.60	============================== end predicate elimination =============
1.25/1.60	
1.25/1.60	Auto_denials:  (non-Horn, no changes).
1.25/1.60	
1.25/1.60	Term ordering decisions:
1.25/1.60	
1.25/1.60	% Assigning unary symbol not kb_weight 0 and highest precedence (94).
1.25/1.60	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.
1.25/1.60	
1.25/1.60	============================== end of process initial clauses ========
1.25/1.60	
1.25/1.60	============================== CLAUSES FOR SEARCH ====================
1.25/1.60	
1.25/1.60	============================== end of clauses for search =============
1.25/1.60	
1.25/1.60	============================== SEARCH ================================
1.25/1.60	
1.25/1.60	% Starting search at 0.01 seconds.
1.25/1.60	
1.25/1.60	Low Water (keep): wt=37.000, iters=3438
1.25/1.60	
1.25/1.60	Low Water (keep): wt=31.000, iters=3353
1.25/1.60	
1.25/1.60	Low Water (keep): wt=30.000, iters=3639
1.25/1.60	
1.25/1.60	Low Water (keep): wt=25.000, iters=3390
1.25/1.60	
1.25/1.60	Low Water (keep): wt=24.000, iters=3402
1.25/1.60	
1.25/1.60	Low Water (keep): wt=23.000, iters=3361
1.25/1.60	
1.25/1.60	Low Water (keep): wt=22.000, iters=3391
1.25/1.60	
1.25/1.60	Low Water (keep): wt=21.000, iters=3427
1.25/1.60	
1.25/1.60	Low Water (keep): wt=20.000, iters=3415
1.25/1.60	
1.25/1.60	Low Water (keep): wt=19.000, iters=3351
3.61/3.91	
3.61/3.91	Low Water (keep): wt=18.000, iters=3498
3.61/3.91	
3.61/3.91	Low Water (keep): wt=17.000, iters=3348
3.61/3.91	
3.61/3.91	Low Water (keep): wt=16.000, iters=3354
3.61/3.91	
3.61/3.91	Low Water (keep): wt=15.000, iters=3436
3.61/3.91	
3.61/3.91	Low Water (displace): id=3269, wt=51.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=3276, wt=49.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=1613, wt=47.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=2743, wt=45.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=3268, wt=43.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=3279, wt=41.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=3463, wt=40.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=3270, wt=39.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=3229, wt=38.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=3277, wt=37.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=3280, wt=35.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=10666, wt=14.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=11360, wt=13.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=11394, wt=12.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=11422, wt=11.000
3.61/3.91	
3.61/3.91	Low Water (displace): id=11616, wt=10.000
3.61/3.91	
3.61/3.91	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 117 (0.00 of 1.56 sec).
3.61/3.91	
3.61/3.91	============================== PROOF =================================
3.61/3.91	% SZS status Theorem
3.61/3.91	% SZS output start Refutation
3.61/3.91	
3.61/3.91	% Proof 1 at 2.80 (+ 0.13) seconds.
3.61/3.91	% Length of proof is 56.
3.61/3.91	% Level of proof is 21.
3.61/3.91	% Maximum clause weight is 16.000.
3.61/3.91	% Given clauses 770.
3.61/3.91	
3.61/3.91	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].
3.61/3.91	6 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause).  [assumption].
3.61/3.91	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].
3.61/3.91	15 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause).  [assumption].
3.61/3.91	20 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause).  [assumption].
3.61/3.91	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].
3.61/3.91	33 op_implies_and # label(rosser_op_implies_and) # label(axiom).  [assumption].
3.61/3.91	34 modus_ponens # label(rosser_modus_ponens) # label(axiom).  [assumption].
3.61/3.91	36 kn1 # label(rosser_kn1) # label(axiom).  [assumption].
3.61/3.91	37 kn2 # label(rosser_kn2) # label(axiom).  [assumption].
3.61/3.91	38 kn3 # label(rosser_kn3) # label(axiom).  [assumption].
3.61/3.91	41 -cn2 # label(luka_cn2) # label(negated_conjecture).  [assumption].
3.61/3.91	48 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom).  [clausify(15)].
3.61/3.91	49 is_a_theorem(implies(A,and(A,A))).  [copy(48),unit_del(a,36)].
3.61/3.91	55 is_a_theorem(implies(and(A,B),A)) | -kn2 # label(kn2) # label(axiom).  [clausify(20)].
3.61/3.91	56 is_a_theorem(implies(and(A,B),A)).  [copy(55),unit_del(b,37)].
3.61/3.91	61 -is_a_theorem(implies(c13,implies(not(c13),c14))) | cn2 # label(cn2) # label(axiom).  [clausify(6)].
3.61/3.91	62 -is_a_theorem(implies(c13,implies(not(c13),c14))).  [copy(61),unit_del(b,41)].
3.61/3.91	67 -is_a_theorem(implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B) | -modus_ponens # label(modus_ponens) # label(axiom).  [clausify(5)].
3.61/3.91	68 -is_a_theorem(implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B).  [copy(67),unit_del(d,34)].
3.61/3.91	78 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom).  [clausify(28)].
3.61/3.91	79 not(and(A,not(B))) = implies(A,B).  [copy(78),unit_del(a,33)].
3.61/3.91	104 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom).  [clausify(14)].
3.61/3.91	105 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))).  [copy(104),unit_del(a,38)].
3.61/3.91	132 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))).  [resolve(105,a,68,a)].
3.61/3.91	275 is_a_theorem(implies(not(and(A,B)),not(and(B,and(A,C))))).  [resolve(132,a,56,a)].
3.61/3.91	276 is_a_theorem(implies(not(and(and(A,A),B)),not(and(B,A)))).  [resolve(132,a,49,a)].
3.61/3.91	280 -is_a_theorem(not(and(A,B))) | is_a_theorem(not(and(B,and(A,C)))).  [resolve(275,a,68,a)].
3.61/3.91	357 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))).  [resolve(276,a,68,a)].
3.61/3.91	407 -is_a_theorem(implies(and(A,A),B)) | is_a_theorem(not(and(not(B),A))).  [para(79(a,1),357(a,1))].
3.61/3.91	703 is_a_theorem(not(and(not(A),A))).  [resolve(407,a,56,a)].
3.61/3.91	706 is_a_theorem(not(and(A,and(not(A),B)))).  [resolve(703,a,280,a)].
3.61/3.91	736 is_a_theorem(implies(not(not(A)),A)).  [para(79(a,1),703(a,1))].
3.61/3.91	739 is_a_theorem(implies(not(and(A,B)),implies(B,not(A)))).  [resolve(736,a,132,a),rewrite([79(6)])].
3.61/3.91	741 -is_a_theorem(not(not(A))) | is_a_theorem(A).  [resolve(736,a,68,a)].
3.61/3.91	918 is_a_theorem(not(and(and(not(A),B),and(A,C)))).  [resolve(706,a,280,a)].
3.61/3.91	1173 -is_a_theorem(not(and(A,B))) | is_a_theorem(implies(B,not(A))).  [resolve(739,a,68,a)].
3.61/3.91	1779 is_a_theorem(implies(and(A,B),not(and(not(A),C)))).  [resolve(1173,a,918,a)].
3.61/3.91	1786 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(B),not(A))).  [para(79(a,1),1173(a,1))].
3.61/3.91	2675 is_a_theorem(implies(and(A,B),implies(not(A),C))).  [para(79(a,1),1779(a,1,2))].
3.61/3.91	2679 is_a_theorem(not(and(not(implies(not(A),B)),A))).  [resolve(2675,a,407,a)].
3.61/3.91	3021 -is_a_theorem(implies(not(and(not(implies(not(A),B)),A)),implies(c13,implies(not(c13),c14)))).  [ur(68,b,2679,a,c,62,a)].
3.61/3.91	4884 is_a_theorem(implies(not(A),not(and(A,B)))).  [resolve(1786,a,56,a)].
3.61/3.91	4885 is_a_theorem(implies(not(and(A,A)),not(A))).  [resolve(1786,a,49,a)].
3.61/3.91	4965 is_a_theorem(implies(not(A),implies(A,B))).  [para(79(a,1),4884(a,1,2))].
3.61/3.91	4972 is_a_theorem(implies(not(and(implies(A,B),C)),implies(C,A))).  [resolve(4965,a,132,a),rewrite([79(6)])].
3.61/3.91	5389 -is_a_theorem(not(and(A,A))) | is_a_theorem(not(A)).  [resolve(4885,a,68,a)].
3.61/3.91	5492 -is_a_theorem(implies(not(A),A)) | is_a_theorem(not(not(A))).  [para(79(a,1),5389(a,1))].
3.61/3.91	11508 -is_a_theorem(not(and(implies(A,B),C))) | is_a_theorem(implies(C,A)).  [resolve(4972,a,68,a)].
3.61/3.91	11527 is_a_theorem(implies(implies(implies(A,B),C),implies(not(C),A))).  [para(79(a,1),4972(a,1,1))].
3.61/3.91	13796 -is_a_theorem(implies(implies(A,B),C)) | is_a_theorem(implies(not(C),A)).  [para(79(a,1),11508(a,1))].
3.61/3.91	14826 is_a_theorem(implies(not(implies(not(A),B)),implies(B,C))).  [resolve(13796,a,11527,a)].
3.61/3.91	15595 is_a_theorem(not(not(implies(not(A),not(A))))).  [resolve(14826,a,5492,a)].
3.61/3.91	15626 is_a_theorem(implies(not(A),not(A))).  [resolve(15595,a,741,a)].
3.61/3.91	15653 is_a_theorem(implies(not(and(not(A),B)),implies(B,A))).  [resolve(15626,a,132,a),rewrite([79(6)])].
3.61/3.91	15654 $F.  [resolve(15653,a,3021,a)].
3.61/3.91	
3.61/3.91	% SZS output end Refutation
3.61/3.91	============================== end of proof ==========================
3.61/3.91	
3.61/3.91	============================== STATISTICS ============================
3.61/3.91	
3.61/3.91	Given=770. Generated=140501. Kept=15604. proofs=1.
3.61/3.91	Usable=765. Sos=9999. Demods=5. Limbo=9, Disabled=4902. Hints=0.
3.61/3.91	Megabytes=13.77.
3.61/3.91	User_CPU=2.80, System_CPU=0.13, Wall_clock=2.
3.61/3.91	
3.61/3.91	============================== end of statistics =====================
3.61/3.91	
3.61/3.91	============================== end of search =========================
3.61/3.91	
3.61/3.91	THEOREM PROVED
3.61/3.91	% SZS status Theorem
3.61/3.91	
3.61/3.91	Exiting with 1 proof.
3.61/3.91	
3.61/3.91	Process 14902 exit (max_proofs) Tue Jul 13 16:13:36 2021
3.61/3.91	Prover9 interrupted
3.61/3.91	EOF