0.00/0.04	% 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   : n013.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 04:57:55 CDT 2018
0.03/0.24	% CPUTime    : 
0.06/0.45	============================== Prover9 ===============================
0.06/0.45	Prover9 (32) version 2009-11A, November 2009.
0.06/0.45	Process 52473 was started by sandbox2 on n013.star.cs.uiowa.edu,
0.06/0.45	Sat Jul 14 04:57:55 2018
0.06/0.45	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_52441_n013.star.cs.uiowa.edu".
0.06/0.45	============================== end of head ===========================
0.06/0.45	
0.06/0.45	============================== INPUT =================================
0.06/0.45	
0.06/0.45	% Reading from file /tmp/Prover9_52441_n013.star.cs.uiowa.edu
0.06/0.45	
0.06/0.45	set(prolog_style_variables).
0.06/0.45	set(auto2).
0.06/0.45	    % set(auto2) -> set(auto).
0.06/0.45	    % set(auto) -> set(auto_inference).
0.06/0.45	    % set(auto) -> set(auto_setup).
0.06/0.45	    % set(auto_setup) -> set(predicate_elim).
0.06/0.45	    % set(auto_setup) -> assign(eq_defs, unfold).
0.06/0.45	    % set(auto) -> set(auto_limits).
0.06/0.45	    % set(auto_limits) -> assign(max_weight, "100.000").
0.06/0.45	    % set(auto_limits) -> assign(sos_limit, 20000).
0.06/0.45	    % set(auto) -> set(auto_denials).
0.06/0.45	    % set(auto) -> set(auto_process).
0.06/0.45	    % set(auto2) -> assign(new_constants, 1).
0.06/0.45	    % set(auto2) -> assign(fold_denial_max, 3).
0.06/0.45	    % set(auto2) -> assign(max_weight, "200.000").
0.06/0.45	    % set(auto2) -> assign(max_hours, 1).
0.06/0.45	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.06/0.45	    % set(auto2) -> assign(max_seconds, 0).
0.06/0.45	    % set(auto2) -> assign(max_minutes, 5).
0.06/0.45	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.06/0.45	    % set(auto2) -> set(sort_initial_sos).
0.06/0.45	    % set(auto2) -> assign(sos_limit, -1).
0.06/0.45	    % set(auto2) -> assign(lrs_ticks, 3000).
0.06/0.45	    % set(auto2) -> assign(max_megs, 400).
0.06/0.45	    % set(auto2) -> assign(stats, some).
0.06/0.45	    % set(auto2) -> clear(echo_input).
0.06/0.45	    % set(auto2) -> set(quiet).
0.06/0.45	    % set(auto2) -> clear(print_initial_clauses).
0.06/0.45	    % set(auto2) -> clear(print_given).
0.06/0.45	assign(lrs_ticks,-1).
0.06/0.45	assign(sos_limit,10000).
0.06/0.45	assign(order,kbo).
0.06/0.45	set(lex_order_vars).
0.06/0.45	clear(print_given).
0.06/0.45	
0.06/0.45	% formulas(sos).  % not echoed (45 formulas)
0.06/0.45	
0.06/0.45	============================== end of input ==========================
0.06/0.45	
0.06/0.45	% From the command line: assign(max_seconds, 300).
0.06/0.45	
0.06/0.45	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.06/0.45	
0.06/0.45	% Formulas that are not ordinary clauses:
0.06/0.45	1 (all X all Y is_a_theorem(implies(and(X,Y),Y))) <-> and_2 # label(and_2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.45	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].
0.06/0.45	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].
0.06/0.45	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].
0.06/0.45	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].
0.06/0.45	6 (all P is_a_theorem(implies(P,and(P,P)))) <-> kn1 # label(kn1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.45	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].
0.06/0.45	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].
0.06/0.45	9 cn2 <-> (all P all Q is_a_theorem(implies(P,implies(not(P),Q)))) # label(cn2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.45	10 or_1 <-> (all X all Y is_a_theorem(implies(X,or(X,Y)))) # label(or_1) # label(axiom) # label(non_clause).  [assumption].
0.06/0.45	11 (all X all Y is_a_theorem(implies(Y,or(X,Y)))) <-> or_2 # label(or_2) # label(axiom) # label(non_clause).  [assumption].
0.06/0.45	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].
0.06/0.45	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].
0.06/0.45	14 (all P is_a_theorem(implies(or(P,P),P))) <-> r1 # label(r1) # label(axiom) # label(non_clause).  [assumption].
0.36/0.57	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].
0.36/0.57	16 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
0.36/0.57	17 and_1 <-> (all X all Y is_a_theorem(implies(and(X,Y),X))) # label(and_1) # label(axiom) # label(non_clause).  [assumption].
0.36/0.57	18 (all P is_a_theorem(implies(implies(not(P),P),P))) <-> cn3 # label(cn3) # label(axiom) # label(non_clause).  [assumption].
0.36/0.57	19 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	22 (all X all Y is_a_theorem(implies(X,implies(Y,X)))) <-> implies_1 # label(implies_1) # label(axiom) # label(non_clause).  [assumption].
0.36/0.57	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].
0.36/0.57	24 (all P all Q is_a_theorem(implies(and(P,Q),P))) <-> kn2 # label(kn2) # label(axiom) # label(non_clause).  [assumption].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	
0.36/0.57	============================== end of process non-clausal formulas ===
0.36/0.57	
0.36/0.57	============================== PROCESS INITIAL CLAUSES ===============
0.36/0.57	
0.36/0.57	============================== PREDICATE ELIMINATION =================
0.36/0.57	
0.36/0.57	============================== end predicate elimination =============
0.36/0.57	
0.36/0.57	Auto_denials:  (non-Horn, no changes).
0.36/0.57	
0.36/0.57	Term ordering decisions:
0.36/0.57	
0.36/0.57	% Assigning unary symbol not kb_weight 0 and highest precedence (93).
0.36/0.57	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.
0.36/0.57	
0.36/0.57	============================== end of process initial clauses ========
0.36/0.57	
0.36/0.57	============================== CLAUSES FOR SEARCH ====================
0.36/0.57	
0.36/0.57	============================== end of clauses for search =============
0.36/0.57	
0.36/0.57	============================== SEARCH ================================
0.36/0.57	
0.36/0.57	% Starting search at 0.01 seconds.
0.36/0.57	
0.36/0.57	============================== PROOF =================================
0.36/0.57	% SZS status Theorem
0.36/0.57	% SZS output start Refutation
0.36/0.57	
0.36/0.57	% Proof 1 at 0.12 (+ 0.00) seconds.
0.36/0.57	% Length of proof is 48.
0.36/0.57	% Level of proof is 9.
0.36/0.57	% Maximum clause weight is 13.000.
0.36/0.57	% Given clauses 157.
0.36/0.57	
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	16 r2 <-> (all P all Q is_a_theorem(implies(Q,or(P,Q)))) # label(r2) # label(axiom) # label(non_clause).  [assumption].
0.36/0.57	19 r3 <-> (all P all Q is_a_theorem(implies(or(P,Q),or(Q,P)))) # label(r3) # label(axiom) # label(non_clause).  [assumption].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	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].
0.36/0.57	33 op_equiv # label(principia_op_equiv) # label(axiom).  [assumption].
0.36/0.57	34 r2 # label(principia_r2) # label(axiom).  [assumption].
0.36/0.57	36 r3 # label(principia_r3) # label(axiom).  [assumption].
0.36/0.57	37 modus_ponens # label(principia_modus_ponens) # label(axiom).  [assumption].
0.36/0.57	39 op_implies_or # label(principia_op_implies_or) # label(axiom).  [assumption].
0.36/0.57	40 op_and # label(principia_op_and) # label(axiom).  [assumption].
0.36/0.57	42 op_or # label(hilbert_op_or) # label(axiom).  [assumption].
0.36/0.57	43 op_implies_and # label(hilbert_op_implies_and) # label(axiom).  [assumption].
0.36/0.57	44 -equivalence_2 # label(hilbert_equivalence_2) # label(negated_conjecture).  [assumption].
0.36/0.57	55 -r2 | is_a_theorem(implies(A,or(B,A))) # label(r2) # label(axiom).  [clausify(16)].
0.36/0.57	56 is_a_theorem(implies(A,or(B,A))).  [copy(55),unit_del(a,34)].
0.36/0.57	70 -is_a_theorem(implies(equiv(c3,c4),implies(c4,c3))) | equivalence_2 # label(equivalence_2) # label(axiom).  [clausify(2)].
0.36/0.57	71 -is_a_theorem(implies(equiv(c3,c4),implies(c4,c3))).  [copy(70),unit_del(b,44)].
0.36/0.57	72 -modus_ponens | -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B) # label(modus_ponens) # label(axiom).  [clausify(12)].
0.36/0.57	73 -is_a_theorem(A) | -is_a_theorem(implies(A,B)) | is_a_theorem(B).  [copy(72),unit_del(a,37)].
0.36/0.57	76 -r3 | is_a_theorem(implies(or(A,B),or(B,A))) # label(r3) # label(axiom).  [clausify(19)].
0.36/0.57	77 is_a_theorem(implies(or(A,B),or(B,A))).  [copy(76),unit_del(a,36)].
0.36/0.57	81 -op_implies_or | or(not(A),B) = implies(A,B) # label(op_implies_or) # label(axiom).  [clausify(30)].
0.36/0.57	82 or(not(A),B) = implies(A,B).  [copy(81),unit_del(a,39)].
0.36/0.57	83 -op_implies_and | not(and(A,not(B))) = implies(A,B) # label(op_implies_and) # label(axiom).  [clausify(29)].
0.36/0.57	84 not(and(A,not(B))) = implies(A,B).  [copy(83),unit_del(a,43)].
0.36/0.57	89 -op_or | or(A,B) = not(and(not(A),not(B))) # label(op_or) # label(axiom).  [clausify(27)].
0.36/0.57	90 or(A,B) = implies(not(A),B).  [copy(89),rewrite([84(6)]),unit_del(a,42)].
0.36/0.57	91 -op_and | not(or(not(A),not(B))) = and(A,B) # label(op_and) # label(axiom).  [clausify(28)].
0.36/0.57	92 not(implies(not(not(A)),not(B))) = and(A,B).  [copy(91),rewrite([90(4)]),unit_del(a,40)].
0.36/0.57	93 -op_equiv | equiv(A,B) = and(implies(A,B),implies(B,A)) # label(op_equiv) # label(axiom).  [clausify(31)].
0.36/0.57	94 and(implies(A,B),implies(B,A)) = equiv(A,B).  [copy(93),flip(b),unit_del(a,33)].
0.36/0.57	114 implies(not(not(A)),B) = implies(A,B).  [back_rewrite(82),rewrite([90(2)])].
0.36/0.57	115 is_a_theorem(implies(implies(not(A),B),implies(not(B),A))).  [back_rewrite(77),rewrite([90(1),90(3)])].
0.36/0.57	116 is_a_theorem(implies(A,implies(not(B),A))).  [back_rewrite(56),rewrite([90(1)])].
0.36/0.57	120 not(implies(A,not(B))) = and(A,B).  [back_rewrite(92),rewrite([114(4)])].
0.36/0.57	132 implies(not(implies(A,B)),C) = implies(and(A,not(B)),C).  [para(84(a,1),114(a,1,1,1))].
0.36/0.57	139 -is_a_theorem(implies(not(A),B)) | is_a_theorem(implies(not(B),A)).  [resolve(115,a,73,b)].
0.36/0.57	149 is_a_theorem(implies(A,implies(B,A))).  [para(114(a,1),116(a,1,2))].
0.36/0.57	201 is_a_theorem(implies(A,implies(B,not(not(A))))).  [para(114(a,1),149(a,1))].
0.36/0.57	748 implies(and(A,not(not(B))),C) = implies(and(A,B),C).  [para(120(a,1),132(a,1,1)),flip(a)].
0.36/0.57	1320 is_a_theorem(implies(and(A,B),B)).  [resolve(139,a,201,a),rewrite([120(5),748(4)])].
0.36/0.57	1577 is_a_theorem(implies(equiv(A,B),implies(B,A))).  [para(94(a,1),1320(a,1,1))].
0.36/0.57	1578 $F.  [resolve(1577,a,71,a)].
0.36/0.57	
0.36/0.57	% SZS output end Refutation
0.36/0.57	============================== end of proof ==========================
0.36/0.57	
0.36/0.57	============================== STATISTICS ============================
0.36/0.57	
0.36/0.57	Given=157. Generated=2867. Kept=1527. proofs=1.
0.36/0.57	Usable=135. Sos=1134. Demods=42. Limbo=116, Disabled=215. Hints=0.
0.36/0.57	Megabytes=1.54.
0.36/0.57	User_CPU=0.12, System_CPU=0.00, Wall_clock=0.
0.36/0.57	
0.36/0.57	============================== end of statistics =====================
0.36/0.57	
0.36/0.57	============================== end of search =========================
0.36/0.57	
0.36/0.57	THEOREM PROVED
0.36/0.57	% SZS status Theorem
0.36/0.57	
0.36/0.57	Exiting with 1 proof.
0.36/0.57	
0.36/0.57	Process 52473 exit (max_proofs) Sat Jul 14 04:57:55 2018
0.36/0.57	Prover9 interrupted
0.36/0.57	EOF