TSTP Solution File: SET083+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 04:26:58 EDT 2022
% Result : Theorem 0.69s 1.08s
% Output : Refutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET083+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n019.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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 19:53:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/0.95 ============================== Prover9 ===============================
% 0.42/0.95 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.95 Process 5605 was started by sandbox2 on n019.cluster.edu,
% 0.42/0.95 Sat Jul 9 19:53:39 2022
% 0.42/0.95 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5452_n019.cluster.edu".
% 0.42/0.95 ============================== end of head ===========================
% 0.42/0.95
% 0.42/0.95 ============================== INPUT =================================
% 0.42/0.95
% 0.42/0.95 % Reading from file /tmp/Prover9_5452_n019.cluster.edu
% 0.42/0.95
% 0.42/0.95 set(prolog_style_variables).
% 0.42/0.95 set(auto2).
% 0.42/0.95 % set(auto2) -> set(auto).
% 0.42/0.95 % set(auto) -> set(auto_inference).
% 0.42/0.95 % set(auto) -> set(auto_setup).
% 0.42/0.95 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.95 % set(auto) -> set(auto_limits).
% 0.42/0.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.95 % set(auto) -> set(auto_denials).
% 0.42/0.95 % set(auto) -> set(auto_process).
% 0.42/0.95 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.95 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.95 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.95 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.95 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.95 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.95 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.95 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.95 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.95 % set(auto2) -> assign(stats, some).
% 0.42/0.95 % set(auto2) -> clear(echo_input).
% 0.42/0.95 % set(auto2) -> set(quiet).
% 0.42/0.95 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.95 % set(auto2) -> clear(print_given).
% 0.42/0.95 assign(lrs_ticks,-1).
% 0.42/0.95 assign(sos_limit,10000).
% 0.42/0.95 assign(order,kbo).
% 0.42/0.95 set(lex_order_vars).
% 0.42/0.95 clear(print_given).
% 0.42/0.95
% 0.42/0.95 % formulas(sos). % not echoed (44 formulas)
% 0.42/0.95
% 0.42/0.95 ============================== end of input ==========================
% 0.42/0.95
% 0.42/0.95 % From the command line: assign(max_seconds, 300).
% 0.42/0.95
% 0.42/0.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.95
% 0.42/0.95 % Formulas that are not ordinary clauses:
% 0.42/0.95 1 (all X all Y (subclass(X,Y) <-> (all U (member(U,X) -> member(U,Y))))) # label(subclass_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 2 (all X subclass(X,universal_class)) # label(class_elements_are_sets) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 3 (all X all Y (X = Y <-> subclass(X,Y) & subclass(Y,X))) # label(extensionality) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 4 (all U all X all Y (member(U,unordered_pair(X,Y)) <-> member(U,universal_class) & (U = X | U = Y))) # label(unordered_pair_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 5 (all X all Y member(unordered_pair(X,Y),universal_class)) # label(unordered_pair) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 6 (all X singleton(X) = unordered_pair(X,X)) # label(singleton_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 7 (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].
% 0.42/0.95 8 (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].
% 0.42/0.95 9 (all X all Y (member(X,universal_class) & member(Y,universal_class) -> first(ordered_pair(X,Y)) = X & second(ordered_pair(X,Y)) = Y)) # label(first_second) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 10 (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].
% 0.42/0.95 11 (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].
% 0.42/0.95 12 (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].
% 0.42/0.95 13 (all X all Z (member(Z,complement(X)) <-> member(Z,universal_class) & -member(Z,X))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 14 (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].
% 0.42/0.95 15 (all X -member(X,null_class)) # label(null_class_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 16 (all X all Z (member(Z,domain_of(X)) <-> member(Z,universal_class) & restrict(X,singleton(Z),universal_class) != null_class)) # label(domain_of) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 17 (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].
% 0.42/0.95 18 (all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(rotate) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 19 (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].
% 0.42/0.95 20 (all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(flip) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 21 (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].
% 0.42/0.95 22 (all X successor(X) = union(X,singleton(X))) # label(successor_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 23 (all X all Y (member(ordered_pair(X,Y),successor_relation) <-> member(X,universal_class) & member(Y,universal_class) & successor(X) = Y)) # label(successor_relation_defn2) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 24 (all Y inverse(Y) = domain_of(flip(cross_product(Y,universal_class)))) # label(inverse_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 25 (all Z range_of(Z) = domain_of(inverse(Z))) # label(range_of_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 26 (all X all XR image(XR,X) = range_of(restrict(XR,X,universal_class))) # label(image_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 27 (all X (inductive(X) <-> member(null_class,X) & subclass(image(successor_relation,X),X))) # label(inductive_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 28 (exists X (member(X,universal_class) & inductive(X) & (all Y (inductive(Y) -> subclass(X,Y))))) # label(infinity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 29 (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].
% 0.42/0.95 30 (all X (member(X,universal_class) -> member(sum_class(X),universal_class))) # label(sum_class) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 31 (all U all X (member(U,power_class(X)) <-> member(U,universal_class) & subclass(U,X))) # label(power_class_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 32 (all U (member(U,universal_class) -> member(power_class(U),universal_class))) # label(power_class) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 33 (all XR all YR subclass(compose(YR,XR),cross_product(universal_class,universal_class))) # label(compose_defn1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 34 (all XR all YR all U all V (member(ordered_pair(U,V),compose(YR,XR)) <-> member(U,universal_class) & member(V,image(YR,image(XR,singleton(U)))))) # label(compose_defn2) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.95 35 (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].
% 0.42/0.95 36 (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].
% 0.42/0.97 37 (all X all XF (member(X,universal_class) & function(XF) -> member(image(XF,X),universal_class))) # label(replacement) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 38 (all X all Y (disjoint(X,Y) <-> (all U -(member(U,X) & member(U,Y))))) # label(disjoint_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 39 (all X (X != null_class -> (exists U (member(U,universal_class) & member(U,X) & disjoint(U,X))))) # label(regularity) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 40 (all XF all Y apply(XF,Y) = sum_class(image(XF,singleton(Y)))) # label(apply_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 41 (exists XF (function(XF) & (all Y (member(Y,universal_class) -> Y = null_class | member(apply(XF,Y),Y))))) # label(choice) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 42 -(all X all Y (singleton(X) = singleton(Y) & member(X,universal_class) -> X = Y)) # label(singleton_identified_by_element1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.97
% 0.42/0.97 ============================== end of process non-clausal formulas ===
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.97
% 0.42/0.97 ============================== PREDICATE ELIMINATION =================
% 0.42/0.97 43 -inductive(A) | member(null_class,A) # label(inductive_defn) # label(axiom). [clausify(27)].
% 0.42/0.97 44 inductive(c1) # label(infinity) # label(axiom). [clausify(28)].
% 0.42/0.97 Derived: member(null_class,c1). [resolve(43,a,44,a)].
% 0.42/0.97 45 -inductive(A) | subclass(c1,A) # label(infinity) # label(axiom). [clausify(28)].
% 0.42/0.97 Derived: subclass(c1,c1). [resolve(45,a,44,a)].
% 0.42/0.97 46 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive_defn) # label(axiom). [clausify(27)].
% 0.42/0.97 Derived: subclass(image(successor_relation,c1),c1). [resolve(46,a,44,a)].
% 0.42/0.97 47 inductive(A) | -member(null_class,A) | -subclass(image(successor_relation,A),A) # label(inductive_defn) # label(axiom). [clausify(27)].
% 0.42/0.97 Derived: -member(null_class,A) | -subclass(image(successor_relation,A),A) | subclass(c1,A). [resolve(47,a,45,a)].
% 0.42/0.97 48 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function_defn) # label(axiom). [clausify(36)].
% 0.42/0.97 49 function(c2) # label(choice) # label(axiom). [clausify(41)].
% 0.42/0.97 Derived: subclass(c2,cross_product(universal_class,universal_class)). [resolve(48,a,49,a)].
% 0.42/0.97 50 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom). [clausify(36)].
% 0.42/0.97 Derived: subclass(compose(c2,inverse(c2)),identity_relation). [resolve(50,a,49,a)].
% 0.42/0.97 51 -member(A,universal_class) | -function(B) | member(image(B,A),universal_class) # label(replacement) # label(axiom). [clausify(37)].
% 0.42/0.97 Derived: -member(A,universal_class) | member(image(c2,A),universal_class). [resolve(51,b,49,a)].
% 0.42/0.97 52 function(A) | -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom). [clausify(36)].
% 0.42/0.97 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(52,a,51,b)].
% 0.42/0.97 53 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint_defn) # label(axiom). [clausify(38)].
% 0.42/0.97 54 null_class = A | disjoint(f5(A),A) # label(regularity) # label(axiom). [clausify(39)].
% 0.42/0.97 55 disjoint(A,B) | member(f4(A,B),A) # label(disjoint_defn) # label(axiom). [clausify(38)].
% 0.42/0.97 56 disjoint(A,B) | member(f4(A,B),B) # label(disjoint_defn) # label(axiom). [clausify(38)].
% 0.42/0.97 Derived: -member(A,f5(B)) | -member(A,B) | null_class = B. [resolve(53,a,54,b)].
% 0.42/0.97 Derived: -member(A,B) | -member(A,C) | member(f4(B,C),B). [resolve(53,a,55,a)].
% 0.42/0.97 Derived: -member(A,B) | -member(A,C) | member(f4(B,C),C). [resolve(53,a,56,a)].
% 0.42/0.97
% 0.42/0.97 ============================== end predicate elimination =============
% 0.42/0.97
% 0.42/0.97 Auto_denials: (non-Horn, no changes).
% 0.42/0.97
% 0.42/0.97 Term ordering decisions:
% 0.42/0.97 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. f4=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. f5=1. restrict=1.
% 0.69/1.08
% 0.69/1.08 ============================== end of process initial clauses ========
% 0.69/1.08
% 0.69/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.69/1.08
% 0.69/1.08 ============================== end of clauses for search =============
% 0.69/1.08
% 0.69/1.08 ============================== SEARCH ================================
% 0.69/1.08
% 0.69/1.08 % Starting search at 0.03 seconds.
% 0.69/1.08
% 0.69/1.08 ============================== PROOF =================================
% 0.69/1.08 % SZS status Theorem
% 0.69/1.08 % SZS output start Refutation
% 0.69/1.08
% 0.69/1.08 % Proof 1 at 0.13 (+ 0.00) seconds.
% 0.69/1.08 % Length of proof is 12.
% 0.69/1.08 % Level of proof is 4.
% 0.69/1.08 % Maximum clause weight is 11.000.
% 0.69/1.08 % Given clauses 147.
% 0.69/1.08
% 0.69/1.08 4 (all U all X all Y (member(U,unordered_pair(X,Y)) <-> member(U,universal_class) & (U = X | U = Y))) # label(unordered_pair_defn) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.08 6 (all X singleton(X) = unordered_pair(X,X)) # label(singleton_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.08 42 -(all X all Y (singleton(X) = singleton(Y) & member(X,universal_class) -> X = Y)) # label(singleton_identified_by_element1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.69/1.08 59 member(c3,universal_class) # label(singleton_identified_by_element1) # label(negated_conjecture). [clausify(42)].
% 0.69/1.08 63 singleton(c4) = singleton(c3) # label(singleton_identified_by_element1) # label(negated_conjecture). [clausify(42)].
% 0.69/1.08 64 singleton(A) = unordered_pair(A,A) # label(singleton_set_defn) # label(axiom). [clausify(6)].
% 0.69/1.08 83 c4 != c3 # label(singleton_identified_by_element1) # label(negated_conjecture). [clausify(42)].
% 0.69/1.08 127 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_defn) # label(axiom). [clausify(4)].
% 0.69/1.08 129 member(A,unordered_pair(B,C)) | -member(A,universal_class) | A != C # label(unordered_pair_defn) # label(axiom). [clausify(4)].
% 0.69/1.08 182 unordered_pair(c4,c4) = unordered_pair(c3,c3). [back_rewrite(63),rewrite([64(2),64(5)])].
% 0.69/1.08 286 -member(c3,unordered_pair(c3,c3)). [ur(127,b,83,a(flip),c,83,a(flip)),rewrite([182(4)])].
% 0.69/1.08 1165 $F. [ur(129,a,286,a,c,xx),unit_del(a,59)].
% 0.69/1.08
% 0.69/1.08 % SZS output end Refutation
% 0.69/1.08 ============================== end of proof ==========================
% 0.69/1.08
% 0.69/1.08 ============================== STATISTICS ============================
% 0.69/1.08
% 0.69/1.08 Given=147. Generated=1645. Kept=1072. proofs=1.
% 0.69/1.08 Usable=140. Sos=884. Demods=33. Limbo=5, Disabled=146. Hints=0.
% 0.69/1.08 Megabytes=1.79.
% 0.69/1.08 User_CPU=0.13, System_CPU=0.00, Wall_clock=0.
% 0.69/1.08
% 0.69/1.08 ============================== end of statistics =====================
% 0.69/1.08
% 0.69/1.08 ============================== end of search =========================
% 0.69/1.08
% 0.69/1.08 THEOREM PROVED
% 0.69/1.08 % SZS status Theorem
% 0.69/1.08
% 0.69/1.08 Exiting with 1 proof.
% 0.69/1.08
% 0.69/1.08 Process 5605 exit (max_proofs) Sat Jul 9 19:53:39 2022
% 0.69/1.08 Prover9 interrupted
%------------------------------------------------------------------------------