0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n016.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   : 1200
0.12/0.33	% DateTime   : Tue Jul 13 16:17:08 EDT 2021
0.12/0.33	% CPUTime    : 
0.74/1.00	============================== Prover9 ===============================
0.74/1.00	Prover9 (32) version 2009-11A, November 2009.
0.74/1.00	Process 22308 was started by sandbox on n016.cluster.edu,
0.74/1.00	Tue Jul 13 16:17:08 2021
0.74/1.00	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_22155_n016.cluster.edu".
0.74/1.00	============================== end of head ===========================
0.74/1.00	
0.74/1.00	============================== INPUT =================================
0.74/1.00	
0.74/1.00	% Reading from file /tmp/Prover9_22155_n016.cluster.edu
0.74/1.00	
0.74/1.00	set(prolog_style_variables).
0.74/1.00	set(auto2).
0.74/1.00	    % set(auto2) -> set(auto).
0.74/1.00	    % set(auto) -> set(auto_inference).
0.74/1.00	    % set(auto) -> set(auto_setup).
0.74/1.00	    % set(auto_setup) -> set(predicate_elim).
0.74/1.00	    % set(auto_setup) -> assign(eq_defs, unfold).
0.74/1.00	    % set(auto) -> set(auto_limits).
0.74/1.00	    % set(auto_limits) -> assign(max_weight, "100.000").
0.74/1.00	    % set(auto_limits) -> assign(sos_limit, 20000).
0.74/1.00	    % set(auto) -> set(auto_denials).
0.74/1.00	    % set(auto) -> set(auto_process).
0.74/1.00	    % set(auto2) -> assign(new_constants, 1).
0.74/1.00	    % set(auto2) -> assign(fold_denial_max, 3).
0.74/1.00	    % set(auto2) -> assign(max_weight, "200.000").
0.74/1.00	    % set(auto2) -> assign(max_hours, 1).
0.74/1.00	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.74/1.00	    % set(auto2) -> assign(max_seconds, 0).
0.74/1.00	    % set(auto2) -> assign(max_minutes, 5).
0.74/1.00	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.74/1.00	    % set(auto2) -> set(sort_initial_sos).
0.74/1.00	    % set(auto2) -> assign(sos_limit, -1).
0.74/1.00	    % set(auto2) -> assign(lrs_ticks, 3000).
0.74/1.00	    % set(auto2) -> assign(max_megs, 400).
0.74/1.00	    % set(auto2) -> assign(stats, some).
0.74/1.00	    % set(auto2) -> clear(echo_input).
0.74/1.00	    % set(auto2) -> set(quiet).
0.74/1.00	    % set(auto2) -> clear(print_initial_clauses).
0.74/1.00	    % set(auto2) -> clear(print_given).
0.74/1.00	assign(lrs_ticks,-1).
0.74/1.00	assign(sos_limit,10000).
0.74/1.00	assign(order,kbo).
0.74/1.00	set(lex_order_vars).
0.74/1.00	clear(print_given).
0.74/1.00	
0.74/1.00	% formulas(sos).  % not echoed (43 formulas)
0.74/1.00	
0.74/1.00	============================== end of input ==========================
0.74/1.00	
0.74/1.00	% From the command line: assign(max_seconds, 1200).
0.74/1.00	
0.74/1.00	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.74/1.00	
0.74/1.00	% Formulas that are not ordinary clauses:
0.74/1.00	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].
0.74/1.00	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].
0.74/1.00	3 (all X all Y is_a_theorem(implies(and(X,Y),X))) <-> and_1 # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.00	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].
0.74/1.00	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].
0.74/1.00	6 (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) <-> cn2 # label(cn2) # label(axiom) # label(non_clause).  [assumption].
0.74/1.00	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].
0.74/1.00	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].
0.74/1.00	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].
0.74/1.00	10 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.00	11 and_2 <-> (all X all Y is_a_theorem(implies(and(X,Y),Y))) # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.74/1.00	12 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.74/1.00	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].
0.74/1.00	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].
1.47/1.76	15 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	16 or_2 <-> (all X all Y is_a_theorem(implies(Y,or(X,Y)))) # label(or_2) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	17 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	20 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	23 implies_1 <-> (all X all Y is_a_theorem(implies(X,implies(Y,X)))) # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	24 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	25 cn3 <-> (all P is_a_theorem(implies(implies(not(P),P),P))) # label(cn3) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	
1.47/1.76	============================== end of process non-clausal formulas ===
1.47/1.76	
1.47/1.76	============================== PROCESS INITIAL CLAUSES ===============
1.47/1.76	
1.47/1.76	============================== PREDICATE ELIMINATION =================
1.47/1.76	
1.47/1.76	============================== end predicate elimination =============
1.47/1.76	
1.47/1.76	Auto_denials:  (non-Horn, no changes).
1.47/1.76	
1.47/1.76	Term ordering decisions:
1.47/1.76	
1.47/1.76	% Assigning unary symbol not kb_weight 0 and highest precedence (93).
1.47/1.76	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.
1.47/1.76	
1.47/1.76	============================== end of process initial clauses ========
1.47/1.76	
1.47/1.76	============================== CLAUSES FOR SEARCH ====================
1.47/1.76	
1.47/1.76	============================== end of clauses for search =============
1.47/1.76	
1.47/1.76	============================== SEARCH ================================
1.47/1.76	
1.47/1.76	% Starting search at 0.02 seconds.
1.47/1.76	
1.47/1.76	Low Water (keep): wt=33.000, iters=3501
1.47/1.76	
1.47/1.76	Low Water (keep): wt=32.000, iters=3586
1.47/1.76	
1.47/1.76	Low Water (keep): wt=30.000, iters=3408
1.47/1.76	
1.47/1.76	Low Water (keep): wt=28.000, iters=3336
1.47/1.76	
1.47/1.76	Low Water (keep): wt=27.000, iters=3390
1.47/1.76	
1.47/1.76	Low Water (keep): wt=26.000, iters=3346
1.47/1.76	
1.47/1.76	Low Water (keep): wt=25.000, iters=3495
1.47/1.76	
1.47/1.76	============================== PROOF =================================
1.47/1.76	% SZS status Theorem
1.47/1.76	% SZS output start Refutation
1.47/1.76	
1.47/1.76	% Proof 1 at 0.76 (+ 0.02) seconds.
1.47/1.76	% Length of proof is 67.
1.47/1.76	% Level of proof is 14.
1.47/1.76	% Maximum clause weight is 16.000.
1.47/1.76	% Given clauses 392.
1.47/1.76	
1.47/1.76	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].
1.47/1.76	12 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	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].
1.47/1.76	15 kn1 <-> (all P is_a_theorem(implies(P,and(P,P)))) # label(kn1) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	20 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause).  [assumption].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	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].
1.47/1.76	33 op_implies_and # label(rosser_op_implies_and) # label(axiom).  [assumption].
1.47/1.76	34 modus_ponens # label(rosser_modus_ponens) # label(axiom).  [assumption].
1.47/1.76	35 op_or # label(rosser_op_or) # label(axiom).  [assumption].
1.47/1.76	36 kn1 # label(rosser_kn1) # label(axiom).  [assumption].
1.47/1.76	37 kn2 # label(rosser_kn2) # label(axiom).  [assumption].
1.47/1.76	38 kn3 # label(rosser_kn3) # label(axiom).  [assumption].
1.47/1.76	40 op_and # label(principia_op_and) # label(axiom).  [assumption].
1.47/1.76	41 op_implies_or # label(principia_op_implies_or) # label(axiom).  [assumption].
1.47/1.76	42 -r3 # label(principia_r3) # label(negated_conjecture).  [assumption].
1.47/1.76	49 -kn1 | is_a_theorem(implies(A,and(A,A))) # label(kn1) # label(axiom).  [clausify(15)].
1.47/1.76	50 is_a_theorem(implies(A,and(A,A))).  [copy(49),unit_del(a,36)].
1.47/1.76	56 is_a_theorem(implies(and(A,B),A)) | -kn2 # label(kn2) # label(axiom).  [clausify(20)].
1.47/1.76	57 is_a_theorem(implies(and(A,B),A)).  [copy(56),unit_del(b,37)].
1.47/1.76	68 -is_a_theorem(implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B) | -modus_ponens # label(modus_ponens) # label(axiom).  [clausify(5)].
1.47/1.76	69 -is_a_theorem(implies(A,B)) | -is_a_theorem(A) | is_a_theorem(B).  [copy(68),unit_del(d,34)].
1.47/1.76	74 r3 | -is_a_theorem(implies(or(c24,c25),or(c25,c24))) # label(r3) # label(axiom).  [clausify(12)].
1.47/1.76	75 -is_a_theorem(implies(or(c24,c25),or(c25,c24))).  [copy(74),unit_del(a,42)].
1.47/1.76	78 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom).  [clausify(27)].
1.47/1.76	79 or(not(A),B) = implies(A,B).  [copy(78),unit_del(a,41)].
1.47/1.76	80 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom).  [clausify(28)].
1.47/1.76	81 not(and(A,not(B))) = implies(A,B).  [copy(80),unit_del(a,33)].
1.47/1.76	86 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom).  [clausify(29)].
1.47/1.76	87 or(A,B) = implies(not(A),B).  [copy(86),rewrite([81(6)]),unit_del(a,35)].
1.47/1.76	88 -op_and | not(or(not(A),not(B))) = and(A,B) # label(op_and) # label(axiom).  [clausify(31)].
1.47/1.76	89 not(implies(not(not(A)),not(B))) = and(A,B).  [copy(88),rewrite([87(4)]),unit_del(a,40)].
1.47/1.76	106 -kn3 | is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))) # label(kn3) # label(axiom).  [clausify(14)].
1.47/1.76	107 is_a_theorem(implies(implies(A,B),implies(not(and(B,C)),not(and(C,A))))).  [copy(106),unit_del(a,38)].
1.47/1.76	114 implies(not(not(A)),B) = implies(A,B).  [back_rewrite(79),rewrite([87(2)])].
1.47/1.76	115 -is_a_theorem(implies(implies(not(c24),c25),implies(not(c25),c24))).  [back_rewrite(75),rewrite([87(3),87(7)])].
1.47/1.76	124 not(implies(A,not(B))) = and(A,B).  [back_rewrite(89),rewrite([114(4)])].
1.47/1.76	125 -is_a_theorem(and(A,B)) | is_a_theorem(A).  [resolve(69,a,57,a)].
1.47/1.76	126 -is_a_theorem(A) | is_a_theorem(and(A,A)).  [resolve(69,a,50,a)].
1.47/1.76	131 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(not(and(B,C)),not(and(C,A)))).  [resolve(107,a,69,a)].
1.47/1.76	132 is_a_theorem(implies(implies(A,B),implies(implies(B,C),not(and(not(C),A))))).  [para(81(a,1),107(a,1,2,1))].
1.47/1.76	136 is_a_theorem(implies(A,and(not(not(A)),not(not(A))))).  [para(114(a,1),50(a,1))].
1.47/1.76	137 -is_a_theorem(implies(A,B)) | -is_a_theorem(not(not(A))) | is_a_theorem(B).  [para(114(a,1),69(a,1))].
1.47/1.76	138 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C).  [para(81(a,1),114(a,1,1,1))].
1.47/1.76	145 -is_a_theorem(and(implies(implies(not(c24),c25),implies(not(c25),c24)),A)).  [ur(69,a,57,a,c,115,a)].
1.47/1.76	146 not(and(A,and(B,C))) = implies(A,implies(B,not(C))).  [para(124(a,1),81(a,1,1,2))].
1.47/1.76	147 not(implies(A,implies(B,C))) = and(A,and(B,not(C))).  [para(81(a,1),124(a,1,1,2))].
1.47/1.76	148 implies(not(and(A,B)),C) = implies(implies(A,not(B)),C).  [para(124(a,1),114(a,1,1,1))].
1.47/1.76	149 and(not(not(A)),B) = and(A,B).  [para(114(a,1),124(a,1,1)),rewrite([124(3)]),flip(a)].
1.47/1.76	154 -is_a_theorem(implies(A,B)) | is_a_theorem(implies(implies(B,not(C)),not(and(C,A)))).  [back_rewrite(131),rewrite([148(7)])].
1.47/1.76	156 is_a_theorem(implies(A,and(A,not(not(A))))).  [back_rewrite(136),rewrite([149(5)])].
1.47/1.76	171 is_a_theorem(and(implies(and(A,B),A),implies(and(A,B),A))).  [resolve(126,a,57,a)].
1.47/1.76	225 is_a_theorem(implies(A,and(A,not(not(not(not(A))))))).  [para(114(a,1),156(a,1)),rewrite([149(7)])].
1.47/1.76	248 is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(not(C),not(A))))).  [para(114(a,1),132(a,1,1)),rewrite([81(7)])].
1.47/1.76	286 -is_a_theorem(and(A,B)) | is_a_theorem(not(not(A))).  [para(149(a,1),125(a,1))].
1.47/1.76	323 -is_a_theorem(implies(implies(not(c24),c25),implies(not(c25),not(not(c24))))).  [ur(137,a,156,a,c,145,a),rewrite([147(10),146(11)])].
1.47/1.76	550 is_a_theorem(implies(A,and(A,not(not(not(not(not(not(A))))))))).  [para(114(a,1),225(a,1)),rewrite([149(9)])].
1.47/1.76	611 implies(and(A,not(not(B))),C) = implies(and(A,B),C).  [para(124(a,1),138(a,1,1)),flip(a)].
1.47/1.76	1193 is_a_theorem(not(not(implies(and(A,B),A)))).  [resolve(171,a,286,a)].
1.47/1.76	1231 is_a_theorem(not(and(and(not(A),B),A))).  [para(124(a,1),1193(a,1,1))].
1.47/1.76	1913 is_a_theorem(implies(implies(and(A,A),not(B)),not(and(B,A)))).  [resolve(154,a,550,a),rewrite([611(9),611(7),611(5)])].
1.47/1.76	3075 -is_a_theorem(not(and(and(A,A),B))) | is_a_theorem(not(and(B,A))).  [resolve(1913,a,137,a),rewrite([124(4)])].
1.47/1.76	8151 is_a_theorem(implies(A,A)).  [resolve(3075,a,1231,a),rewrite([81(3)])].
1.47/1.76	8353 -is_a_theorem(implies(implies(A,A),implies(implies(not(c24),c25),implies(not(c25),not(not(c24)))))).  [ur(69,b,8151,a,c,323,a)].
1.47/1.76	8354 $F.  [resolve(8353,a,248,a)].
1.47/1.76	
1.47/1.76	% SZS output end Refutation
1.47/1.76	============================== end of proof ==========================
1.47/1.76	
1.47/1.76	============================== STATISTICS ============================
1.47/1.76	
1.47/1.76	Given=392. Generated=21286. Kept=8303. proofs=1.
1.47/1.76	Usable=346. Sos=6581. Demods=184. Limbo=187, Disabled=1260. Hints=0.
1.47/1.76	Megabytes=9.75.
1.47/1.76	User_CPU=0.76, System_CPU=0.02, Wall_clock=1.
1.47/1.76	
1.47/1.76	============================== end of statistics =====================
1.47/1.76	
1.47/1.76	============================== end of search =========================
1.47/1.76	
1.47/1.76	THEOREM PROVED
1.47/1.76	% SZS status Theorem
1.47/1.76	
1.47/1.76	Exiting with 1 proof.
1.47/1.76	
1.47/1.76	Process 22308 exit (max_proofs) Tue Jul 13 16:17:09 2021
1.47/1.76	Prover9 interrupted
1.47/1.76	EOF