0.03/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.11	% Command  : tptp2X_and_run_prover9 %d %s
0.11/0.32	% Computer : n003.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 : 1440
0.11/0.32	% WCLimit  : 180
0.11/0.32	% DateTime : Mon Jul  3 10:21:31 EDT 2023
0.11/0.32	% CPUTime  : 
0.37/1.06	============================== Prover9 ===============================
0.37/1.06	Prover9 (32) version 2009-11A, November 2009.
0.37/1.06	Process 25096 was started by sandbox2 on n003.cluster.edu,
0.37/1.06	Mon Jul  3 10:21:31 2023
0.37/1.06	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_24943_n003.cluster.edu".
0.37/1.06	============================== end of head ===========================
0.37/1.06	
0.37/1.06	============================== INPUT =================================
0.37/1.06	
0.37/1.06	% Reading from file /tmp/Prover9_24943_n003.cluster.edu
0.37/1.06	
0.37/1.06	set(prolog_style_variables).
0.37/1.06	set(auto2).
0.37/1.06	    % set(auto2) -> set(auto).
0.37/1.06	    % set(auto) -> set(auto_inference).
0.37/1.06	    % set(auto) -> set(auto_setup).
0.37/1.06	    % set(auto_setup) -> set(predicate_elim).
0.37/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.37/1.06	    % set(auto) -> set(auto_limits).
0.37/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.37/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.37/1.06	    % set(auto) -> set(auto_denials).
0.37/1.06	    % set(auto) -> set(auto_process).
0.37/1.06	    % set(auto2) -> assign(new_constants, 1).
0.37/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.37/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.37/1.06	    % set(auto2) -> assign(max_hours, 1).
0.37/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.37/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.37/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.37/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.37/1.06	    % set(auto2) -> set(sort_initial_sos).
0.37/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.37/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.37/1.06	    % set(auto2) -> assign(max_megs, 400).
0.37/1.06	    % set(auto2) -> assign(stats, some).
0.37/1.06	    % set(auto2) -> clear(echo_input).
0.37/1.06	    % set(auto2) -> set(quiet).
0.37/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.37/1.06	    % set(auto2) -> clear(print_given).
0.37/1.06	assign(lrs_ticks,-1).
0.37/1.06	assign(sos_limit,10000).
0.37/1.06	assign(order,kbo).
0.37/1.06	set(lex_order_vars).
0.37/1.06	clear(print_given).
0.37/1.06	
0.37/1.06	% formulas(sos).  % not echoed (44 formulas)
0.37/1.06	
0.37/1.06	============================== end of input ==========================
0.37/1.06	
0.37/1.06	% From the command line: assign(max_seconds, 1440).
0.37/1.06	
0.37/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.37/1.06	
0.37/1.06	% Formulas that are not ordinary clauses:
0.37/1.06	1 (all X subclass(X,universal_class)) # label(class_elements_are_sets) # label(axiom) # label(non_clause).  [assumption].
0.37/1.06	2 (all X all Y member(unordered_pair(X,Y),universal_class)) # label(unordered_pair) # label(axiom) # label(non_clause).  [assumption].
0.37/1.06	3 (all XR all YR subclass(compose(YR,XR),cross_product(universal_class,universal_class))) # label(compose_defn1) # label(axiom) # label(non_clause).  [assumption].
0.37/1.06	4 (all U all V all X all Y (member(ordered_pair(U,V),cross_product(X,Y)) <-> member(U,X) & member(V,Y))) # label(cross_product_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.06	5 (exists XF ((all Y (member(Y,universal_class) -> member(apply(XF,Y),Y) | null_class = Y)) & function(XF))) # label(choice) # label(axiom) # label(non_clause).  [assumption].
0.37/1.06	6 (all XR all YR all U all V (member(ordered_pair(U,V),compose(YR,XR)) <-> member(V,image(YR,image(XR,singleton(U)))) & member(U,universal_class))) # label(compose_defn2) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	7 (all X all Z (member(Z,complement(X)) <-> -member(Z,X) & member(Z,universal_class))) # label(complement) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	8 (all X (inductive(X) <-> subclass(image(successor_relation,X),X) & member(null_class,X))) # label(inductive_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	9 (all U all X all Y (member(U,unordered_pair(X,Y)) <-> (U = Y | X = U) & member(U,universal_class))) # label(unordered_pair_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	10 (all X all Y ((all U (member(U,X) -> member(U,Y))) <-> subclass(X,Y))) # label(subclass_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	11 (all U all V all W all X (member(ordered_pair(ordered_pair(U,V),W),flip(X)) <-> member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)) & member(ordered_pair(ordered_pair(V,U),W),X))) # label(flip_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	12 (all X union(X,singleton(X)) = successor(X)) # label(successor_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	13 (all X (X != null_class -> (exists U (member(U,universal_class) & disjoint(U,X) & member(U,X))))) # label(regularity) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	14 (all X all XR image(XR,X) = range_of(restrict(XR,X,universal_class))) # label(image_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	15 (all U (member(U,universal_class) -> member(power_class(U),universal_class))) # label(power_class) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	16 (all Z (member(Z,identity_relation) <-> (exists X (member(X,universal_class) & ordered_pair(X,X) = Z)))) # label(identity_relation) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	17 (all X all Y (disjoint(X,Y) <-> (all U -(member(U,X) & member(U,Y))))) # label(disjoint_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	18 (all Z domain_of(inverse(Z)) = range_of(Z)) # label(range_of_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	19 (all X (member(X,universal_class) -> member(sum_class(X),universal_class))) # label(sum_class) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	20 (all X all Y (member(Y,universal_class) & member(X,universal_class) -> second(ordered_pair(X,Y)) = Y & first(ordered_pair(X,Y)) = X)) # label(first_second) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	21 (all X all Y (member(ordered_pair(X,Y),successor_relation) <-> member(X,universal_class) & member(Y,universal_class) & Y = successor(X))) # label(successor_relation_defn2) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	22 (all X all XR all Y intersection(XR,cross_product(X,Y)) = restrict(XR,X,Y)) # label(restrict_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	23 (all X all Y unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y)) # label(ordered_pair_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	24 (all X all Y (subclass(Y,X) & subclass(X,Y) <-> Y = X)) # label(extensionality) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	25 (all X all Y all Z (member(Z,X) | member(Z,Y) <-> member(Z,union(X,Y)))) # label(union_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	26 (all X unordered_pair(X,X) = singleton(X)) # label(singleton_set_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	27 (all X all Y (member(ordered_pair(X,Y),element_relation) <-> member(Y,universal_class) & member(X,Y))) # label(element_relation_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	28 (all X all Y all Z (member(Z,intersection(X,Y)) <-> member(Z,X) & member(Z,Y))) # label(intersection) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	29 (all X -member(X,null_class)) # label(null_class_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	30 (all X all XF (member(X,universal_class) & function(XF) -> member(image(XF,X),universal_class))) # label(replacement) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	31 (all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(flip) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	32 (all XF all Y apply(XF,Y) = sum_class(image(XF,singleton(Y)))) # label(apply_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	33 (all XF (function(XF) <-> subclass(compose(XF,inverse(XF)),identity_relation) & subclass(XF,cross_product(universal_class,universal_class)))) # label(function_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	34 (all X all Y all Z (member(Z,cross_product(X,Y)) -> Z = ordered_pair(first(Z),second(Z)))) # label(cross_product) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	35 (all Y domain_of(flip(cross_product(Y,universal_class))) = inverse(Y)) # label(inverse_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.07	36 (all X all U all V all W (member(ordered_pair(ordered_pair(U,V),W),rotate(X)) <-> member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)) & member(ordered_pair(ordered_pair(V,W),U),X))) # label(rotate_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.08	37 (all X all Z (member(Z,universal_class) & restrict(X,singleton(Z),universal_class) != null_class <-> member(Z,domain_of(X)))) # label(domain_of) # label(axiom) # label(non_clause).  [assumption].
0.37/1.08	38 (exists X (member(X,universal_class) & inductive(X) & (all Y (inductive(Y) -> subclass(X,Y))))) # label(infinity) # label(axiom) # label(non_clause).  [assumption].
0.37/1.08	39 (all U all X (member(U,sum_class(X)) <-> (exists Y (member(U,Y) & member(Y,X))))) # label(sum_class_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.08	40 (all U all X (member(U,universal_class) & subclass(U,X) <-> member(U,power_class(X)))) # label(power_class_defn) # label(axiom) # label(non_clause).  [assumption].
0.37/1.08	41 (all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(rotate) # label(axiom) # label(non_clause).  [assumption].
0.37/1.08	42 -(all X ((exists Y singleton(Y) = X) | (exists V (member(V,X) & (exists W (member(W,X) & member(W,intersection(complement(singleton(V)),X)))))) | null_class = X)) # label(corollary_1_to_number_of_elements_in_class) # label(negated_conjecture) # label(non_clause).  [assumption].
0.37/1.08	
0.37/1.08	============================== end of process non-clausal formulas ===
0.37/1.08	
0.37/1.08	============================== PROCESS INITIAL CLAUSES ===============
0.37/1.08	
0.37/1.08	============================== PREDICATE ELIMINATION =================
0.37/1.08	43 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function_defn) # label(axiom).  [clausify(33)].
0.37/1.08	44 function(c1) # label(choice) # label(axiom).  [clausify(5)].
0.37/1.08	Derived: subclass(c1,cross_product(universal_class,universal_class)).  [resolve(43,a,44,a)].
0.37/1.08	45 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom).  [clausify(33)].
0.37/1.08	Derived: subclass(compose(c1,inverse(c1)),identity_relation).  [resolve(45,a,44,a)].
0.37/1.08	46 -member(A,universal_class) | -function(B) | member(image(B,A),universal_class) # label(replacement) # label(axiom).  [clausify(30)].
0.37/1.08	Derived: -member(A,universal_class) | member(image(c1,A),universal_class).  [resolve(46,b,44,a)].
0.37/1.08	47 function(A) | -subclass(compose(A,inverse(A)),identity_relation) | -subclass(A,cross_product(universal_class,universal_class)) # label(function_defn) # label(axiom).  [clausify(33)].
0.37/1.08	Derived: -subclass(compose(A,inverse(A)),identity_relation) | -subclass(A,cross_product(universal_class,universal_class)) | -member(B,universal_class) | member(image(A,B),universal_class).  [resolve(47,a,46,b)].
0.37/1.08	48 -inductive(A) | member(null_class,A) # label(inductive_defn) # label(axiom).  [clausify(8)].
0.37/1.08	49 inductive(c2) # label(infinity) # label(axiom).  [clausify(38)].
0.37/1.08	Derived: member(null_class,c2).  [resolve(48,a,49,a)].
0.37/1.08	50 -inductive(A) | subclass(c2,A) # label(infinity) # label(axiom).  [clausify(38)].
0.37/1.08	Derived: subclass(c2,c2).  [resolve(50,a,49,a)].
0.37/1.08	51 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive_defn) # label(axiom).  [clausify(8)].
0.37/1.08	Derived: subclass(image(successor_relation,c2),c2).  [resolve(51,a,49,a)].
0.37/1.08	52 inductive(A) | -subclass(image(successor_relation,A),A) | -member(null_class,A) # label(inductive_defn) # label(axiom).  [clausify(8)].
0.37/1.08	Derived: -subclass(image(successor_relation,A),A) | -member(null_class,A) | subclass(c2,A).  [resolve(52,a,50,a)].
0.37/1.08	53 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint_defn) # label(axiom).  [clausify(17)].
0.37/1.08	54 null_class = A | disjoint(f2(A),A) # label(regularity) # label(axiom).  [clausify(13)].
0.37/1.08	55 disjoint(A,B) | member(f4(A,B),A) # label(disjoint_defn) # label(axiom).  [clausify(17)].
0.37/1.08	56 disjoint(A,B) | member(f4(A,B),B) # label(disjoint_defn) # label(axiom).  [clausify(17)].
0.37/1.08	Derived: -member(A,f2(B)) | -member(A,B) | null_class = B.  [resolve(53,a,54,b)].
0.37/1.08	Derived: -member(A,B) | -member(A,C) | member(f4(B,C),B).  [resolve(53,a,55,a)].
0.37/1.08	Derived: -member(A,B) | -member(A,C) | member(f4(B,C),C).  [resolve(53,a,56,a)].
0.37/1.08	
0.37/1.08	============================== end predicate elimination =============
0.37/1.08	
0.37/1.08	Auto_denials:  (noAlarm clock 
179.35/180.05	Prover9 interrupted
179.35/180.05	EOF