0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n029.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 17:07:40 EDT 2021
0.12/0.33	% CPUTime    : 
0.42/1.01	============================== Prover9 ===============================
0.42/1.01	Prover9 (32) version 2009-11A, November 2009.
0.42/1.01	Process 9087 was started by sandbox2 on n029.cluster.edu,
0.42/1.01	Tue Jul 13 17:07:40 2021
0.42/1.01	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_8934_n029.cluster.edu".
0.42/1.01	============================== end of head ===========================
0.42/1.01	
0.42/1.01	============================== INPUT =================================
0.42/1.01	
0.42/1.01	% Reading from file /tmp/Prover9_8934_n029.cluster.edu
0.42/1.01	
0.42/1.01	set(prolog_style_variables).
0.42/1.01	set(auto2).
0.42/1.01	    % set(auto2) -> set(auto).
0.42/1.01	    % set(auto) -> set(auto_inference).
0.42/1.01	    % set(auto) -> set(auto_setup).
0.42/1.01	    % set(auto_setup) -> set(predicate_elim).
0.42/1.01	    % set(auto_setup) -> assign(eq_defs, unfold).
0.42/1.01	    % set(auto) -> set(auto_limits).
0.42/1.01	    % set(auto_limits) -> assign(max_weight, "100.000").
0.42/1.01	    % set(auto_limits) -> assign(sos_limit, 20000).
0.42/1.01	    % set(auto) -> set(auto_denials).
0.42/1.01	    % set(auto) -> set(auto_process).
0.42/1.01	    % set(auto2) -> assign(new_constants, 1).
0.42/1.01	    % set(auto2) -> assign(fold_denial_max, 3).
0.42/1.01	    % set(auto2) -> assign(max_weight, "200.000").
0.42/1.01	    % set(auto2) -> assign(max_hours, 1).
0.42/1.01	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.42/1.01	    % set(auto2) -> assign(max_seconds, 0).
0.42/1.01	    % set(auto2) -> assign(max_minutes, 5).
0.42/1.01	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.42/1.01	    % set(auto2) -> set(sort_initial_sos).
0.42/1.01	    % set(auto2) -> assign(sos_limit, -1).
0.42/1.01	    % set(auto2) -> assign(lrs_ticks, 3000).
0.42/1.01	    % set(auto2) -> assign(max_megs, 400).
0.42/1.01	    % set(auto2) -> assign(stats, some).
0.42/1.01	    % set(auto2) -> clear(echo_input).
0.42/1.01	    % set(auto2) -> set(quiet).
0.42/1.01	    % set(auto2) -> clear(print_initial_clauses).
0.42/1.01	    % set(auto2) -> clear(print_given).
0.42/1.01	assign(lrs_ticks,-1).
0.42/1.01	assign(sos_limit,10000).
0.42/1.01	assign(order,kbo).
0.42/1.01	set(lex_order_vars).
0.42/1.01	clear(print_given).
0.42/1.01	
0.42/1.01	% formulas(sos).  % not echoed (48 formulas)
0.42/1.01	
0.42/1.01	============================== end of input ==========================
0.42/1.01	
0.42/1.01	% From the command line: assign(max_seconds, 1200).
0.42/1.01	
0.42/1.01	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.42/1.01	
0.42/1.01	% Formulas that are not ordinary clauses:
0.42/1.01	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].
0.42/1.01	2 (all X subclass(X,universal_class)) # label(class_elements_are_sets) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	3 (all X all Y member(unordered_pair(X,Y),universal_class)) # label(unordered_pair) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	5 (all X unordered_pair(X,X) = singleton(X)) # label(singleton_set_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	7 (all U (member(U,universal_class) -> member(power_class(U),universal_class))) # label(power_class) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	8 (all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(rotate) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	9 (all XF all Y sum_class(image(XF,singleton(Y))) = apply(XF,Y)) # label(apply_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	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].
0.42/1.01	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].
0.42/1.01	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].
0.42/1.01	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].
0.42/1.01	15 (all Y domain_of(flip(cross_product(Y,universal_class))) = inverse(Y)) # label(inverse_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	17 (all Z range_of(Z) = domain_of(inverse(Z))) # label(range_of_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	18 (all X (inductive(X) <-> subclass(image(successor_relation,X),X) & member(null_class,X))) # label(inductive_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	19 (all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(flip) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	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].
0.42/1.01	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].
0.42/1.01	23 (all X all Z (member(Z,universal_class) & -member(Z,X) <-> member(Z,complement(X)))) # label(complement) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	24 (all X -member(X,null_class)) # label(null_class_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	26 (all XR all YR subclass(compose(YR,XR),cross_product(universal_class,universal_class))) # label(compose_defn1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	27 (exists X (inductive(X) & (all Y (inductive(Y) -> subclass(X,Y))) & member(X,universal_class))) # label(infinity) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	29 (all X successor(X) = union(X,singleton(X))) # label(successor_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	31 (all X all Y (subclass(Y,X) & subclass(X,Y) <-> X = Y)) # label(extensionality) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	32 (all X all XR image(XR,X) = range_of(restrict(XR,X,universal_class))) # label(image_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	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].
0.42/1.01	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].
0.42/1.01	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].
0.74/1.01	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].
0.74/1.01	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].
0.74/1.01	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].
0.74/1.01	40 (all X (member(X,universal_class) -> member(sum_class(X),universal_class))) # label(sum_class) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	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].
0.74/1.01	42 (all X (X = member_of(X) | member(member_of(X),universal_class))) # label(member_universal_self) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	43 (all Y (member(Y,universal_class) -> singleton(member_of(singleton(Y))) = singleton(Y))) # label(member_singleton_singleton) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	44 (all X (singleton(member_of(X)) = X | X = member_of(X))) # label(singleton_self) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	45 (all Y (member(Y,universal_class) -> member(member_of(singleton(Y)),universal_class))) # label(member_singleton_universal) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	46 -(all X all U (X = U & -(exists Y (member(Y,universal_class) & X = singleton(Y))) -> member_of(X) = U)) # label(member_when_not_a_singleton) # label(negated_conjecture) # label(non_clause).  [assumption].
0.74/1.01	
0.74/1.01	============================== end of process non-clausal formulas ===
0.74/1.01	
0.74/1.01	============================== PROCESS INITIAL CLAUSES ===============
0.74/1.01	
0.74/1.01	============================== PREDICATE ELIMINATION =================
0.74/1.01	47 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function_defn) # label(axiom).  [clausify(20)].
0.74/1.01	48 function(c1) # label(choice) # label(axiom).  [clausify(22)].
0.74/1.01	Derived: subclass(c1,cross_product(universal_class,universal_class)).  [resolve(47,a,48,a)].
0.74/1.01	49 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom).  [clausify(20)].
0.74/1.01	Derived: subclass(compose(c1,inverse(c1)),identity_relation).  [resolve(49,a,48,a)].
0.74/1.01	50 -member(A,universal_class) | -function(B) | member(image(B,A),universal_class) # label(replacement) # label(axiom).  [clausify(11)].
0.74/1.01	Derived: -member(A,universal_class) | member(image(c1,A),universal_class).  [resolve(50,b,48,a)].
0.74/1.01	51 function(A) | -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom).  [clausify(20)].
0.74/1.01	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(51,a,50,b)].
0.74/1.01	52 -inductive(A) | member(null_class,A) # label(inductive_defn) # label(axiom).  [clausify(18)].
0.74/1.01	53 inductive(c2) # label(infinity) # label(axiom).  [clausify(27)].
0.74/1.01	Derived: member(null_class,c2).  [resolve(52,a,53,a)].
0.74/1.01	54 -inductive(A) | subclass(c2,A) # label(infinity) # label(axiom).  [clausify(27)].
0.74/1.01	Derived: subclass(c2,c2).  [resolve(54,a,53,a)].
0.74/1.01	55 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive_defn) # label(axiom).  [clausify(18)].
0.74/1.01	Derived: subclass(image(successor_relation,c2),c2).  [resolve(55,a,53,a)].
0.74/1.01	56 inductive(A) | -subclass(image(successor_relation,A),A) | -member(null_class,A) # label(inductive_defn) # label(axiom).  [clausify(18)].
0.74/1.01	Derived: -subclass(image(successor_relation,A),A) | -member(null_class,A) | subclass(c2,A).  [resolve(56,a,54,a)].
0.74/1.01	57 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint_defn) # label(axiom).  [clausify(13)].
0.74/1.01	58 null_class = A | disjoint(f4(A),A) # label(regularity) # label(axiom).  [clausify(37)].
0.74/1.11	59 disjoint(A,B) | member(f1(A,B),A) # label(disjoint_defn) # label(axiom).  [clausify(13)].
0.74/1.11	60 disjoint(A,B) | member(f1(A,B),B) # label(disjoint_defn) # label(axiom).  [clausify(13)].
0.74/1.11	Derived: -member(A,f4(B)) | -member(A,B) | null_class = B.  [resolve(57,a,58,b)].
0.74/1.11	Derived: -member(A,B) | -member(A,C) | member(f1(B,C),B).  [resolve(57,a,59,a)].
0.74/1.11	Derived: -member(A,B) | -member(A,C) | member(f1(B,C),C).  [resolve(57,a,60,a)].
0.74/1.11	
0.74/1.11	============================== end predicate elimination =============
0.74/1.11	
0.74/1.11	Auto_denials:  (non-Horn, no changes).
0.74/1.11	
0.74/1.11	Term ordering decisions:
0.74/1.11	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. member_of=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.
0.74/1.11	
0.74/1.11	============================== end of process initial clauses ========
0.74/1.11	
0.74/1.11	============================== CLAUSES FOR SEARCH ====================
0.74/1.11	
0.74/1.11	============================== end of clauses for search =============
0.74/1.11	
0.74/1.11	============================== SEARCH ================================
0.74/1.11	
0.74/1.11	% Starting search at 0.02 seconds.
0.74/1.11	
0.74/1.11	============================== PROOF =================================
0.74/1.11	% SZS status Theorem
0.74/1.11	% SZS output start Refutation
0.74/1.11	
0.74/1.11	% Proof 1 at 0.10 (+ 0.00) seconds.
0.74/1.11	% Length of proof is 15.
0.74/1.11	% Level of proof is 4.
0.74/1.11	% Maximum clause weight is 11.000.
0.74/1.11	% Given clauses 148.
0.74/1.11	
0.74/1.11	5 (all X unordered_pair(X,X) = singleton(X)) # label(singleton_set_defn) # label(axiom) # label(non_clause).  [assumption].
0.74/1.11	42 (all X (X = member_of(X) | member(member_of(X),universal_class))) # label(member_universal_self) # label(axiom) # label(non_clause).  [assumption].
0.74/1.11	44 (all X (singleton(member_of(X)) = X | X = member_of(X))) # label(singleton_self) # label(axiom) # label(non_clause).  [assumption].
0.74/1.11	46 -(all X all U (X = U & -(exists Y (member(Y,universal_class) & X = singleton(Y))) -> member_of(X) = U)) # label(member_when_not_a_singleton) # label(negated_conjecture) # label(non_clause).  [assumption].
0.74/1.11	63 c4 = c3 # label(member_when_not_a_singleton) # label(negated_conjecture).  [clausify(46)].
0.74/1.11	67 singleton(A) = unordered_pair(A,A) # label(singleton_set_defn) # label(axiom).  [clausify(5)].
0.74/1.11	78 member_of(A) = A | member(member_of(A),universal_class) # label(member_universal_self) # label(axiom).  [clausify(42)].
0.74/1.11	83 singleton(member_of(A)) = A | member_of(A) = A # label(singleton_self) # label(axiom).  [clausify(44)].
0.74/1.11	84 unordered_pair(member_of(A),member_of(A)) = A | member_of(A) = A.  [copy(83),rewrite([67(2)])].
0.74/1.11	89 member_of(c3) != c4 # label(member_when_not_a_singleton) # label(negated_conjecture).  [clausify(46)].
0.74/1.11	90 member_of(c3) != c3.  [copy(89),rewrite([63(3)])].
0.74/1.11	92 -member(A,universal_class) | singleton(A) != c3 # label(member_when_not_a_singleton) # label(negated_conjecture).  [clausify(46)].
0.74/1.11	93 -member(A,universal_class) | unordered_pair(A,A) != c3.  [copy(92),rewrite([67(3)])].
0.74/1.11	217 unordered_pair(member_of(A),member_of(A)) != c3 | member_of(A) = A.  [resolve(93,a,78,b)].
0.74/1.11	1297 $F.  [resolve(217,a,84,a),merge(b),unit_del(a,90)].
0.74/1.11	
0.74/1.11	% SZS output end Refutation
0.74/1.11	============================== end of proof ==========================
0.74/1.11	
0.74/1.11	============================== STATISTICS ============================
0.74/1.11	
0.74/1.11	Given=148. Generated=1690. Kept=1195. proofs=1.
0.74/1.11	Usable=141. Sos=982. Demods=44. Limbo=0, Disabled=179. Hints=0.
0.74/1.11	Megabytes=2.25.
0.74/1.11	User_CPU=0.10, System_CPU=0.00, Wall_clock=1.
0.74/1.11	
0.74/1.11	============================== end of statistics =====================
0.74/1.11	
0.74/1.11	============================== end of search =========================
0.74/1.11	
0.74/1.11	THEOREM PROVED
0.74/1.11	% SZS status Theorem
0.74/1.11	
0.74/1.11	Exiting with 1 proof.
0.74/1.11	
0.74/1.11	Process 9087 exit (max_proofs) Tue Jul 13 17:07:41 2021
0.74/1.11	Prover9 interrupted
0.74/1.11	EOF