0.02/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.10	% Command    : tptp2X_and_run_prover9 %d %s
0.10/0.31	% Computer   : n016.cluster.edu
0.10/0.31	% Model      : x86_64 x86_64
0.10/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory     : 8042.1875MB
0.10/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 1200
0.10/0.31	% DateTime   : Tue Jul 13 16:54:53 EDT 2021
0.10/0.31	% CPUTime    : 
0.74/1.06	============================== Prover9 ===============================
0.74/1.06	Prover9 (32) version 2009-11A, November 2009.
0.74/1.06	Process 23009 was started by sandbox on n016.cluster.edu,
0.74/1.06	Tue Jul 13 16:54:53 2021
0.74/1.06	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_22833_n016.cluster.edu".
0.74/1.06	============================== end of head ===========================
0.74/1.06	
0.74/1.06	============================== INPUT =================================
0.74/1.06	
0.74/1.06	% Reading from file /tmp/Prover9_22833_n016.cluster.edu
0.74/1.06	
0.74/1.06	set(prolog_style_variables).
0.74/1.06	set(auto2).
0.74/1.06	    % set(auto2) -> set(auto).
0.74/1.06	    % set(auto) -> set(auto_inference).
0.74/1.06	    % set(auto) -> set(auto_setup).
0.74/1.06	    % set(auto_setup) -> set(predicate_elim).
0.74/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.74/1.06	    % set(auto) -> set(auto_limits).
0.74/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.74/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.74/1.06	    % set(auto) -> set(auto_denials).
0.74/1.06	    % set(auto) -> set(auto_process).
0.74/1.06	    % set(auto2) -> assign(new_constants, 1).
0.74/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.74/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.74/1.06	    % set(auto2) -> assign(max_hours, 1).
0.74/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.74/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.74/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.74/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.74/1.06	    % set(auto2) -> set(sort_initial_sos).
0.74/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.74/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.74/1.06	    % set(auto2) -> assign(max_megs, 400).
0.74/1.06	    % set(auto2) -> assign(stats, some).
0.74/1.06	    % set(auto2) -> clear(echo_input).
0.74/1.06	    % set(auto2) -> set(quiet).
0.74/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.74/1.06	    % set(auto2) -> clear(print_given).
0.74/1.06	assign(lrs_ticks,-1).
0.74/1.06	assign(sos_limit,10000).
0.74/1.06	assign(order,kbo).
0.74/1.06	set(lex_order_vars).
0.74/1.06	clear(print_given).
0.74/1.06	
0.74/1.06	% formulas(sos).  % not echoed (44 formulas)
0.74/1.06	
0.74/1.06	============================== end of input ==========================
0.74/1.06	
0.74/1.06	% From the command line: assign(max_seconds, 1200).
0.74/1.06	
0.74/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.74/1.06	
0.74/1.06	% Formulas that are not ordinary clauses:
0.74/1.06	1 (all X all Y all Z (member(Z,X) & member(Z,Y) <-> member(Z,intersection(X,Y)))) # label(intersection) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	2 (all X subclass(X,universal_class)) # label(class_elements_are_sets) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	3 (all X all Y member(unordered_pair(X,Y),universal_class)) # label(unordered_pair) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	4 (all U all V all W all 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) <-> member(ordered_pair(ordered_pair(U,V),W),flip(X)))) # label(flip_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	5 (all X unordered_pair(X,X) = singleton(X)) # label(singleton_set_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	6 (all X all U all V all W (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) <-> member(ordered_pair(ordered_pair(U,V),W),rotate(X)))) # label(rotate_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	7 (all U (member(U,universal_class) -> member(power_class(U),universal_class))) # label(power_class) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	8 (all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(rotate) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	9 (all XF all Y sum_class(image(XF,singleton(Y))) = apply(XF,Y)) # label(apply_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	10 (all X all Y ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))) # label(ordered_pair_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	11 (all X all XF (member(X,universal_class) & function(XF) -> member(image(XF,X),universal_class))) # label(replacement) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	12 (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].
0.74/1.06	13 (all X all Y (disjoint(X,Y) <-> (all U -(member(U,X) & member(U,Y))))) # label(disjoint_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	14 (all U all V all X all Y (member(V,Y) & member(U,X) <-> member(ordered_pair(U,V),cross_product(X,Y)))) # label(cross_product_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	15 (all Y domain_of(flip(cross_product(Y,universal_class))) = inverse(Y)) # label(inverse_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	16 (all X all XR all Y restrict(XR,X,Y) = intersection(XR,cross_product(X,Y))) # label(restrict_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	17 (all Z range_of(Z) = domain_of(inverse(Z))) # label(range_of_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	18 (all X (inductive(X) <-> subclass(image(successor_relation,X),X) & member(null_class,X))) # label(inductive_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	19 (all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(flip) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	20 (all XF (function(XF) <-> subclass(XF,cross_product(universal_class,universal_class)) & subclass(compose(XF,inverse(XF)),identity_relation))) # label(function_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	21 (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].
0.74/1.06	22 (exists XF (function(XF) & (all Y (member(Y,universal_class) -> member(apply(XF,Y),Y) | Y = null_class)))) # label(choice) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	23 (all X all Z (member(Z,universal_class) & -member(Z,X) <-> member(Z,complement(X)))) # label(complement) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	24 (all X -member(X,null_class)) # label(null_class_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	25 (all X all Y (member(Y,universal_class) & member(X,universal_class) -> X = first(ordered_pair(X,Y)) & Y = second(ordered_pair(X,Y)))) # label(first_second) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	26 (all XR all YR subclass(compose(YR,XR),cross_product(universal_class,universal_class))) # label(compose_defn1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	27 (exists X (inductive(X) & (all Y (inductive(Y) -> subclass(X,Y))) & member(X,universal_class))) # label(infinity) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	28 (all X all Y all Z (member(Z,cross_product(X,Y)) -> ordered_pair(first(Z),second(Z)) = Z)) # label(cross_product) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	29 (all X successor(X) = union(X,singleton(X))) # label(successor_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	30 (all Z (member(Z,identity_relation) <-> (exists X (member(X,universal_class) & Z = ordered_pair(X,X))))) # label(identity_relation) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	31 (all X all Y (subclass(Y,X) & subclass(X,Y) <-> X = Y)) # label(extensionality) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	32 (all X all XR image(XR,X) = range_of(restrict(XR,X,universal_class))) # label(image_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	33 (all XR all YR all U all V (member(U,universal_class) & member(V,image(YR,image(XR,singleton(U)))) <-> member(ordered_pair(U,V),compose(YR,XR)))) # label(compose_defn2) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	34 (all X all Y all Z (member(Z,union(X,Y)) <-> member(Z,X) | member(Z,Y))) # label(union_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	35 (all X all Y (member(Y,universal_class) & Y = successor(X) & member(X,universal_class) <-> member(ordered_pair(X,Y),successor_relation))) # label(successor_relation_defn2) # label(axiom) # label(non_clause).  [assumption].
0.74/1.06	36 (all X all Y (member(X,Y) & member(Y,universal_class) <-> member(ordered_pair(X,Y),element_relation))) # label(element_relation_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.07	37 (all X (null_class != X -> (exists U (member(U,universal_class) & member(U,X) & disjoint(U,X))))) # label(regularity) # label(axiom) # label(non_clause).  [assumption].
0.74/1.07	38 (all U all X (subclass(U,X) & member(U,universal_class) <-> member(U,power_class(X)))) # label(power_class_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.07	39 (all U all X all Y (member(U,unordered_pair(X,Y)) <-> member(U,universal_class) & (U = X | Y = U))) # label(unordered_pair_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.07	40 (all X (member(X,universal_class) -> member(sum_class(X),universal_class))) # label(sum_class) # label(axiom) # label(non_clause).  [assumption].
0.74/1.07	41 (all X all Y (subclass(X,Y) <-> (all U (member(U,X) -> member(U,Y))))) # label(subclass_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.07	42 -(all X all Y (singleton(Y) = singleton(X) & member(Y,universal_class) -> Y = X)) # label(singleton_identified_by_element2) # label(negated_conjecture) # label(non_clause).  [assumption].
0.74/1.07	
0.74/1.07	============================== end of process non-clausal formulas ===
0.74/1.07	
0.74/1.07	============================== PROCESS INITIAL CLAUSES ===============
0.74/1.07	
0.74/1.07	============================== PREDICATE ELIMINATION =================
0.74/1.07	43 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function_defn) # label(axiom).  [clausify(20)].
0.74/1.07	44 function(c1) # label(choice) # label(axiom).  [clausify(22)].
0.74/1.07	Derived: subclass(c1,cross_product(universal_class,universal_class)).  [resolve(43,a,44,a)].
0.74/1.07	45 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom).  [clausify(20)].
0.74/1.07	Derived: subclass(compose(c1,inverse(c1)),identity_relation).  [resolve(45,a,44,a)].
0.74/1.07	46 -member(A,universal_class) | -function(B) | member(image(B,A),universal_class) # label(replacement) # label(axiom).  [clausify(11)].
0.74/1.07	Derived: -member(A,universal_class) | member(image(c1,A),universal_class).  [resolve(46,b,44,a)].
0.74/1.07	47 function(A) | -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom).  [clausify(20)].
0.74/1.07	Derived: -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | -member(B,universal_class) | member(image(A,B),universal_class).  [resolve(47,a,46,b)].
0.74/1.07	48 -inductive(A) | member(null_class,A) # label(inductive_defn) # label(axiom).  [clausify(18)].
0.74/1.07	49 inductive(c2) # label(infinity) # label(axiom).  [clausify(27)].
0.74/1.07	Derived: member(null_class,c2).  [resolve(48,a,49,a)].
0.74/1.07	50 -inductive(A) | subclass(c2,A) # label(infinity) # label(axiom).  [clausify(27)].
0.74/1.07	Derived: subclass(c2,c2).  [resolve(50,a,49,a)].
0.74/1.07	51 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive_defn) # label(axiom).  [clausify(18)].
0.74/1.07	Derived: subclass(image(successor_relation,c2),c2).  [resolve(51,a,49,a)].
0.74/1.07	52 inductive(A) | -subclass(image(successor_relation,A),A) | -member(null_class,A) # label(inductive_defn) # label(axiom).  [clausify(18)].
0.74/1.07	Derived: -subclass(image(successor_relation,A),A) | -member(null_class,A) | subclass(c2,A).  [resolve(52,a,50,a)].
0.74/1.07	53 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint_defn) # label(axiom).  [clausify(13)].
0.74/1.07	54 null_class = A | disjoint(f4(A),A) # label(regularity) # label(axiom).  [clausify(37)].
0.74/1.07	55 disjoint(A,B) | member(f1(A,B),A) # label(disjoint_defn) # label(axiom).  [clausify(13)].
0.74/1.07	56 disjoint(A,B) | member(f1(A,B),B) # label(disjoint_defn) # label(axiom).  [clausify(13)].
0.74/1.07	Derived: -member(A,f4(B)) | -member(A,B) | null_class = B.  [resolve(53,a,54,b)].
0.74/1.07	Derived: -member(A,B) | -member(A,C) | member(f1(B,C),B).  [resolve(53,a,55,a)].
0.74/1.07	Derived: -member(A,B) | -member(A,C) | member(f1(B,C),C).  [resolve(53,a,56,a)].
0.74/1.07	
0.74/1.07	============================== end predicate elimination =============
0.74/1.07	
0.74/1.07	Auto_denials:  (non-Horn, no changes).
0.74/1.07	
0.74/1.07	Term ordering decisions:
0.74/1.07	Function symbol KB weights:  universal_class=1. null_class=1. successor_relation=1. identity_relation=1. element_relation=1. c1=1. c2=1. c3=1. c4=1. ordered_pair=1. cross_product=1. image=1. unordered_pair=1. compose=1. intersection=1. union=1. apply=1. f1=1. f2=1. f5=1. singleton=1. flip=1. sum_class=1. domain_of=1. inverse=1. power_class=1. rotate=1. successor=1. complement=1. first=1. range_of=1. second=1. f3=1. f4=1. restrict=1.
0.87/1.18	
0.87/1.18	============================== end of process initial clauses ========
0.87/1.18	
0.87/1.18	============================== CLAUSES FOR SEARCH ====================
0.87/1.18	
0.87/1.18	============================== end of clauses for search =============
0.87/1.18	
0.87/1.18	============================== SEARCH ================================
0.87/1.18	
0.87/1.18	% Starting search at 0.02 seconds.
0.87/1.18	
0.87/1.18	============================== PROOF =================================
0.87/1.18	% SZS status Theorem
0.87/1.18	% SZS output start Refutation
0.87/1.18	
0.87/1.18	% Proof 1 at 0.13 (+ 0.00) seconds.
0.87/1.18	% Length of proof is 31.
0.87/1.18	% Level of proof is 7.
0.87/1.18	% Maximum clause weight is 19.000.
0.87/1.18	% Given clauses 154.
0.87/1.18	
0.87/1.18	5 (all X unordered_pair(X,X) = singleton(X)) # label(singleton_set_defn) # label(axiom) # label(non_clause).  [assumption].
0.87/1.18	7 (all U (member(U,universal_class) -> member(power_class(U),universal_class))) # label(power_class) # label(axiom) # label(non_clause).  [assumption].
0.87/1.18	10 (all X all Y ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))) # label(ordered_pair_defn) # label(axiom) # label(non_clause).  [assumption].
0.87/1.18	14 (all U all V all X all Y (member(V,Y) & member(U,X) <-> member(ordered_pair(U,V),cross_product(X,Y)))) # label(cross_product_defn) # label(axiom) # label(non_clause).  [assumption].
0.87/1.18	27 (exists X (inductive(X) & (all Y (inductive(Y) -> subclass(X,Y))) & member(X,universal_class))) # label(infinity) # label(axiom) # label(non_clause).  [assumption].
0.87/1.18	39 (all U all X all Y (member(U,unordered_pair(X,Y)) <-> member(U,universal_class) & (U = X | Y = U))) # label(unordered_pair_defn) # label(axiom) # label(non_clause).  [assumption].
0.87/1.18	42 -(all X all Y (singleton(Y) = singleton(X) & member(Y,universal_class) -> Y = X)) # label(singleton_identified_by_element2) # label(negated_conjecture) # label(non_clause).  [assumption].
0.87/1.18	58 member(c2,universal_class) # label(infinity) # label(axiom).  [clausify(27)].
0.87/1.18	59 member(c4,universal_class) # label(singleton_identified_by_element2) # label(negated_conjecture).  [clausify(42)].
0.87/1.18	63 singleton(c4) = singleton(c3) # label(singleton_identified_by_element2) # label(negated_conjecture).  [clausify(42)].
0.87/1.18	64 singleton(A) = unordered_pair(A,A) # label(singleton_set_defn) # label(axiom).  [clausify(5)].
0.87/1.18	80 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))) # label(ordered_pair_defn) # label(axiom).  [clausify(10)].
0.87/1.18	81 ordered_pair(A,B) = unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))).  [copy(80),rewrite([64(2),64(3)])].
0.87/1.18	83 c4 != c3 # label(singleton_identified_by_element2) # label(negated_conjecture).  [clausify(42)].
0.87/1.18	89 -member(A,universal_class) | member(power_class(A),universal_class) # label(power_class) # label(axiom).  [clausify(7)].
0.87/1.18	116 member(A,B) | -member(ordered_pair(C,A),cross_product(D,B)) # label(cross_product_defn) # label(axiom).  [clausify(14)].
0.87/1.18	117 member(A,B) | -member(unordered_pair(unordered_pair(C,C),unordered_pair(C,unordered_pair(A,A))),cross_product(D,B)).  [copy(116),rewrite([81(2)])].
0.87/1.18	135 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_defn) # label(axiom).  [clausify(39)].
0.87/1.18	137 member(A,unordered_pair(B,C)) | -member(A,universal_class) | A != C # label(unordered_pair_defn) # label(axiom).  [clausify(39)].
0.87/1.18	144 -member(A,B) | -member(C,D) | member(ordered_pair(C,A),cross_product(D,B)) # label(cross_product_defn) # label(axiom).  [clausify(14)].
0.87/1.18	145 -member(A,B) | -member(C,D) | member(unordered_pair(unordered_pair(C,C),unordered_pair(C,unordered_pair(A,A))),cross_product(D,B)).  [copy(144),rewrite([81(3)])].
0.87/1.18	182 unordered_pair(c4,c4) = unordered_pair(c3,c3).  [back_rewrite(63),rewrite([64(2),64(5)])].
0.87/1.18	213 member(power_class(c2),universal_class).  [resolve(89,a,58,a)].
0.87/1.18	319 -member(c3,unordered_pair(c3,c3)).  [ur(135,b,83,a(flip),c,83,a(flip)),rewrite([182(4)])].
0.87/1.18	355 -member(A,B) | member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(c3,c3))),cross_product(B,universal_class)).  [resolve(145,a,59,a),rewrite([182(5)])].
0.87/1.18	575 member(power_class(power_class(c2)),universal_class).  [resolve(213,a,89,a)].
0.87/1.18	1164 -member(c3,universal_class).  [ur(137,a,319,a,c,xx)].
0.87/1.18	1309 member(power_class(power_class(power_class(c2))),universal_class).  [resolve(575,a,89,a)].
0.87/1.18	1352 -member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(c3,c3))),cross_product(B,universal_class)).  [ur(117,a,1164,a)].
0.87/1.18	1358 -member(A,B).  [back_unit_del(355),unit_del(b,1352)].
0.87/1.18	1359 $F.  [resolve(1358,a,1309,a)].
0.87/1.18	
0.87/1.18	% SZS output end Refutation
0.87/1.18	============================== end of proof ==========================
0.87/1.18	
0.87/1.18	============================== STATISTICS ============================
0.87/1.18	
0.87/1.18	Given=154. Generated=1973. Kept=1266. proofs=1.
0.87/1.18	Usable=146. Sos=1067. Demods=42. Limbo=6, Disabled=149. Hints=0.
0.87/1.18	Megabytes=2.07.
0.87/1.18	User_CPU=0.13, System_CPU=0.01, Wall_clock=0.
0.87/1.18	
0.87/1.18	============================== end of statistics =====================
0.87/1.18	
0.87/1.18	============================== end of search =========================
0.87/1.18	
0.87/1.18	THEOREM PROVED
0.87/1.18	% SZS status Theorem
0.87/1.18	
0.87/1.18	Exiting with 1 proof.
0.87/1.18	
0.87/1.18	Process 23009 exit (max_proofs) Tue Jul 13 16:54:53 2021
0.87/1.18	Prover9 interrupted
0.87/1.19	EOF