0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.11/0.33	% Computer   : n021.cluster.edu
0.11/0.33	% Model      : x86_64 x86_64
0.11/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory     : 8042.1875MB
0.11/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit   : 1200
0.11/0.33	% DateTime   : Tue Jul 13 17:07:41 EDT 2021
0.11/0.33	% CPUTime    : 
0.47/1.01	============================== Prover9 ===============================
0.47/1.01	Prover9 (32) version 2009-11A, November 2009.
0.47/1.01	Process 27112 was started by sandbox on n021.cluster.edu,
0.47/1.01	Tue Jul 13 17:07:41 2021
0.47/1.01	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_26765_n021.cluster.edu".
0.47/1.01	============================== end of head ===========================
0.47/1.01	
0.47/1.01	============================== INPUT =================================
0.47/1.01	
0.47/1.01	% Reading from file /tmp/Prover9_26765_n021.cluster.edu
0.47/1.01	
0.47/1.01	set(prolog_style_variables).
0.47/1.01	set(auto2).
0.47/1.01	    % set(auto2) -> set(auto).
0.47/1.01	    % set(auto) -> set(auto_inference).
0.47/1.01	    % set(auto) -> set(auto_setup).
0.47/1.01	    % set(auto_setup) -> set(predicate_elim).
0.47/1.01	    % set(auto_setup) -> assign(eq_defs, unfold).
0.47/1.01	    % set(auto) -> set(auto_limits).
0.47/1.01	    % set(auto_limits) -> assign(max_weight, "100.000").
0.47/1.01	    % set(auto_limits) -> assign(sos_limit, 20000).
0.47/1.01	    % set(auto) -> set(auto_denials).
0.47/1.01	    % set(auto) -> set(auto_process).
0.47/1.01	    % set(auto2) -> assign(new_constants, 1).
0.47/1.01	    % set(auto2) -> assign(fold_denial_max, 3).
0.47/1.01	    % set(auto2) -> assign(max_weight, "200.000").
0.47/1.01	    % set(auto2) -> assign(max_hours, 1).
0.47/1.01	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.47/1.01	    % set(auto2) -> assign(max_seconds, 0).
0.47/1.01	    % set(auto2) -> assign(max_minutes, 5).
0.47/1.01	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.47/1.01	    % set(auto2) -> set(sort_initial_sos).
0.47/1.01	    % set(auto2) -> assign(sos_limit, -1).
0.47/1.01	    % set(auto2) -> assign(lrs_ticks, 3000).
0.47/1.01	    % set(auto2) -> assign(max_megs, 400).
0.47/1.01	    % set(auto2) -> assign(stats, some).
0.47/1.01	    % set(auto2) -> clear(echo_input).
0.47/1.01	    % set(auto2) -> set(quiet).
0.47/1.01	    % set(auto2) -> clear(print_initial_clauses).
0.47/1.01	    % set(auto2) -> clear(print_given).
0.47/1.01	assign(lrs_ticks,-1).
0.47/1.01	assign(sos_limit,10000).
0.47/1.01	assign(order,kbo).
0.47/1.01	set(lex_order_vars).
0.47/1.01	clear(print_given).
0.47/1.01	
0.47/1.01	% formulas(sos).  % not echoed (44 formulas)
0.47/1.01	
0.47/1.01	============================== end of input ==========================
0.47/1.01	
0.47/1.01	% From the command line: assign(max_seconds, 1200).
0.47/1.01	
0.47/1.01	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.47/1.01	
0.47/1.01	% Formulas that are not ordinary clauses:
0.47/1.01	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].
0.47/1.01	2 (all X subclass(X,universal_class)) # label(class_elements_are_sets) # label(axiom) # label(non_clause).  [assumption].
0.47/1.01	3 (all X all Y member(unordered_pair(X,Y),universal_class)) # label(unordered_pair) # label(axiom) # label(non_clause).  [assumption].
0.47/1.01	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].
0.47/1.01	5 (all X unordered_pair(X,X) = singleton(X)) # label(singleton_set_defn) # label(axiom) # label(non_clause).  [assumption].
0.47/1.01	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].
0.47/1.01	7 (all U (member(U,universal_class) -> member(power_class(U),universal_class))) # label(power_class) # label(axiom) # label(non_clause).  [assumption].
0.47/1.01	8 (all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(rotate) # label(axiom) # label(non_clause).  [assumption].
0.47/1.01	9 (all XF all Y sum_class(image(XF,singleton(Y))) = apply(XF,Y)) # label(apply_defn) # label(axiom) # label(non_clause).  [assumption].
0.47/1.01	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].
0.47/1.01	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].
0.75/1.01	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].
0.75/1.01	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].
0.75/1.01	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].
0.75/1.01	15 (all Y domain_of(flip(cross_product(Y,universal_class))) = inverse(Y)) # label(inverse_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	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].
0.75/1.01	17 (all Z range_of(Z) = domain_of(inverse(Z))) # label(range_of_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	18 (all X (inductive(X) <-> subclass(image(successor_relation,X),X) & member(null_class,X))) # label(inductive_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	19 (all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(flip) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	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].
0.75/1.01	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].
0.75/1.01	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].
0.75/1.01	23 (all X all Z (member(Z,universal_class) & -member(Z,X) <-> member(Z,complement(X)))) # label(complement) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	24 (all X -member(X,null_class)) # label(null_class_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	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].
0.75/1.01	26 (all XR all YR subclass(compose(YR,XR),cross_product(universal_class,universal_class))) # label(compose_defn1) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	27 (exists X (inductive(X) & (all Y (inductive(Y) -> subclass(X,Y))) & member(X,universal_class))) # label(infinity) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	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].
0.75/1.01	29 (all X successor(X) = union(X,singleton(X))) # label(successor_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	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].
0.75/1.01	31 (all X all Y (subclass(Y,X) & subclass(X,Y) <-> X = Y)) # label(extensionality) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	32 (all X all XR image(XR,X) = range_of(restrict(XR,X,universal_class))) # label(image_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.01	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].
0.75/1.01	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].
0.75/1.01	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].
0.75/1.01	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].
0.75/1.03	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].
0.75/1.03	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].
0.75/1.03	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].
0.75/1.03	40 (all X (member(X,universal_class) -> member(sum_class(X),universal_class))) # label(sum_class) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	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].
0.75/1.03	42 -(all X all Y (member(X,universal_class) & singleton(Y) = singleton(X) -> Y = X)) # label(singleton_identified_by_element1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.75/1.03	
0.75/1.03	============================== end of process non-clausal formulas ===
0.75/1.03	
0.75/1.03	============================== PROCESS INITIAL CLAUSES ===============
0.75/1.03	
0.75/1.03	============================== PREDICATE ELIMINATION =================
0.75/1.03	43 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function_defn) # label(axiom).  [clausify(20)].
0.75/1.03	44 function(c1) # label(choice) # label(axiom).  [clausify(22)].
0.75/1.03	Derived: subclass(c1,cross_product(universal_class,universal_class)).  [resolve(43,a,44,a)].
0.75/1.03	45 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom).  [clausify(20)].
0.75/1.03	Derived: subclass(compose(c1,inverse(c1)),identity_relation).  [resolve(45,a,44,a)].
0.75/1.03	46 -member(A,universal_class) | -function(B) | member(image(B,A),universal_class) # label(replacement) # label(axiom).  [clausify(11)].
0.75/1.03	Derived: -member(A,universal_class) | member(image(c1,A),universal_class).  [resolve(46,b,44,a)].
0.75/1.03	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)].
0.75/1.03	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)].
0.75/1.03	48 -inductive(A) | member(null_class,A) # label(inductive_defn) # label(axiom).  [clausify(18)].
0.75/1.03	49 inductive(c2) # label(infinity) # label(axiom).  [clausify(27)].
0.75/1.03	Derived: member(null_class,c2).  [resolve(48,a,49,a)].
0.75/1.03	50 -inductive(A) | subclass(c2,A) # label(infinity) # label(axiom).  [clausify(27)].
0.75/1.03	Derived: subclass(c2,c2).  [resolve(50,a,49,a)].
0.75/1.03	51 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive_defn) # label(axiom).  [clausify(18)].
0.75/1.03	Derived: subclass(image(successor_relation,c2),c2).  [resolve(51,a,49,a)].
0.75/1.03	52 inductive(A) | -subclass(image(successor_relation,A),A) | -member(null_class,A) # label(inductive_defn) # label(axiom).  [clausify(18)].
0.75/1.03	Derived: -subclass(image(successor_relation,A),A) | -member(null_class,A) | subclass(c2,A).  [resolve(52,a,50,a)].
0.75/1.03	53 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint_defn) # label(axiom).  [clausify(13)].
0.75/1.03	54 null_class = A | disjoint(f4(A),A) # label(regularity) # label(axiom).  [clausify(37)].
0.75/1.03	55 disjoint(A,B) | member(f1(A,B),A) # label(disjoint_defn) # label(axiom).  [clausify(13)].
0.75/1.03	56 disjoint(A,B) | member(f1(A,B),B) # label(disjoint_defn) # label(axiom).  [clausify(13)].
0.75/1.03	Derived: -member(A,f4(B)) | -member(A,B) | null_class = B.  [resolve(53,a,54,b)].
0.75/1.03	Derived: -member(A,B) | -member(A,C) | member(f1(B,C),B).  [resolve(53,a,55,a)].
0.75/1.03	Derived: -member(A,B) | -member(A,C) | member(f1(B,C),C).  [resolve(53,a,56,a)].
0.75/1.03	
0.75/1.03	============================== end predicate elimination =============
0.75/1.03	
0.75/1.03	Auto_denials:  (non-Horn, no changes).
0.75/1.03	
0.75/1.03	Term ordering decisions:
0.75/1.03	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.
0.75/1.13	
0.75/1.13	============================== end of process initial clauses ========
0.75/1.13	
0.75/1.13	============================== CLAUSES FOR SEARCH ====================
0.75/1.13	
0.75/1.13	============================== end of clauses for search =============
0.75/1.13	
0.75/1.13	============================== SEARCH ================================
0.75/1.13	
0.75/1.13	% Starting search at 0.03 seconds.
0.75/1.13	
0.75/1.13	============================== PROOF =================================
0.75/1.13	% SZS status Theorem
0.75/1.13	% SZS output start Refutation
0.75/1.13	
0.75/1.13	% Proof 1 at 0.13 (+ 0.01) seconds.
0.75/1.13	% Length of proof is 12.
0.75/1.13	% Level of proof is 4.
0.75/1.13	% Maximum clause weight is 11.000.
0.75/1.13	% Given clauses 148.
0.75/1.13	
0.75/1.13	5 (all X unordered_pair(X,X) = singleton(X)) # label(singleton_set_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.13	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].
0.75/1.13	42 -(all X all Y (member(X,universal_class) & singleton(Y) = singleton(X) -> Y = X)) # label(singleton_identified_by_element1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.75/1.13	59 member(c3,universal_class) # label(singleton_identified_by_element1) # label(negated_conjecture).  [clausify(42)].
0.75/1.13	63 singleton(c4) = singleton(c3) # label(singleton_identified_by_element1) # label(negated_conjecture).  [clausify(42)].
0.75/1.13	64 singleton(A) = unordered_pair(A,A) # label(singleton_set_defn) # label(axiom).  [clausify(5)].
0.75/1.13	83 c4 != c3 # label(singleton_identified_by_element1) # label(negated_conjecture).  [clausify(42)].
0.75/1.13	135 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_defn) # label(axiom).  [clausify(39)].
0.75/1.13	137 member(A,unordered_pair(B,C)) | -member(A,universal_class) | A != C # label(unordered_pair_defn) # label(axiom).  [clausify(39)].
0.75/1.13	182 unordered_pair(c4,c4) = unordered_pair(c3,c3).  [back_rewrite(63),rewrite([64(2),64(5)])].
0.75/1.13	319 -member(c3,unordered_pair(c3,c3)).  [ur(135,b,83,a(flip),c,83,a(flip)),rewrite([182(4)])].
0.75/1.13	1162 $F.  [ur(137,a,319,a,c,xx),unit_del(a,59)].
0.75/1.13	
0.75/1.13	% SZS output end Refutation
0.75/1.13	============================== end of proof ==========================
0.75/1.13	
0.75/1.13	============================== STATISTICS ============================
0.75/1.13	
0.75/1.13	Given=148. Generated=1740. Kept=1069. proofs=1.
0.75/1.13	Usable=140. Sos=884. Demods=34. Limbo=1, Disabled=147. Hints=0.
0.75/1.13	Megabytes=1.79.
0.75/1.13	User_CPU=0.13, System_CPU=0.01, Wall_clock=0.
0.75/1.13	
0.75/1.13	============================== end of statistics =====================
0.75/1.13	
0.75/1.13	============================== end of search =========================
0.75/1.13	
0.75/1.13	THEOREM PROVED
0.75/1.13	% SZS status Theorem
0.75/1.13	
0.75/1.13	Exiting with 1 proof.
0.75/1.13	
0.75/1.13	Process 27112 exit (max_proofs) Tue Jul 13 17:07:41 2021
0.75/1.13	Prover9 interrupted
0.75/1.13	EOF