TSTP Solution File: SET091+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 04:27:05 EDT 2022
% Result : Theorem 0.91s 1.19s
% Output : Refutation 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET091+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.13/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.36 % Computer : n016.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 600
% 0.13/0.36 % DateTime : Sun Jul 10 09:58:41 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.48/1.05 ============================== Prover9 ===============================
% 0.48/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.48/1.05 Process 25255 was started by sandbox on n016.cluster.edu,
% 0.48/1.05 Sun Jul 10 09:58:41 2022
% 0.48/1.05 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25102_n016.cluster.edu".
% 0.48/1.05 ============================== end of head ===========================
% 0.48/1.05
% 0.48/1.05 ============================== INPUT =================================
% 0.48/1.05
% 0.48/1.05 % Reading from file /tmp/Prover9_25102_n016.cluster.edu
% 0.48/1.05
% 0.48/1.05 set(prolog_style_variables).
% 0.48/1.05 set(auto2).
% 0.48/1.05 % set(auto2) -> set(auto).
% 0.48/1.05 % set(auto) -> set(auto_inference).
% 0.48/1.05 % set(auto) -> set(auto_setup).
% 0.48/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.48/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/1.05 % set(auto) -> set(auto_limits).
% 0.48/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/1.05 % set(auto) -> set(auto_denials).
% 0.48/1.05 % set(auto) -> set(auto_process).
% 0.48/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.48/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.48/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.48/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.48/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.48/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.48/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.48/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.48/1.05 % set(auto2) -> assign(stats, some).
% 0.48/1.05 % set(auto2) -> clear(echo_input).
% 0.48/1.05 % set(auto2) -> set(quiet).
% 0.48/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.48/1.05 % set(auto2) -> clear(print_given).
% 0.48/1.05 assign(lrs_ticks,-1).
% 0.48/1.05 assign(sos_limit,10000).
% 0.48/1.05 assign(order,kbo).
% 0.48/1.05 set(lex_order_vars).
% 0.48/1.05 clear(print_given).
% 0.48/1.05
% 0.48/1.05 % formulas(sos). % not echoed (48 formulas)
% 0.48/1.05
% 0.48/1.05 ============================== end of input ==========================
% 0.48/1.05
% 0.48/1.05 % From the command line: assign(max_seconds, 300).
% 0.48/1.05
% 0.48/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/1.05
% 0.48/1.05 % Formulas that are not ordinary clauses:
% 0.48/1.05 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].
% 0.48/1.05 2 (all X subclass(X,universal_class)) # label(class_elements_are_sets) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 3 (all X all Y (X = Y <-> subclass(X,Y) & subclass(Y,X))) # label(extensionality) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 5 (all X all Y member(unordered_pair(X,Y),universal_class)) # label(unordered_pair) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 6 (all X singleton(X) = unordered_pair(X,X)) # label(singleton_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 13 (all X all Z (member(Z,complement(X)) <-> member(Z,universal_class) & -member(Z,X))) # label(complement) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 15 (all X -member(X,null_class)) # label(null_class_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 18 (all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(rotate) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 20 (all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(flip) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 22 (all X successor(X) = union(X,singleton(X))) # label(successor_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 24 (all Y inverse(Y) = domain_of(flip(cross_product(Y,universal_class)))) # label(inverse_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 25 (all Z range_of(Z) = domain_of(inverse(Z))) # label(range_of_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 26 (all X all XR image(XR,X) = range_of(restrict(XR,X,universal_class))) # label(image_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 27 (all X (inductive(X) <-> member(null_class,X) & subclass(image(successor_relation,X),X))) # label(inductive_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 28 (exists X (member(X,universal_class) & inductive(X) & (all Y (inductive(Y) -> subclass(X,Y))))) # label(infinity) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 30 (all X (member(X,universal_class) -> member(sum_class(X),universal_class))) # label(sum_class) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 32 (all U (member(U,universal_class) -> member(power_class(U),universal_class))) # label(power_class) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 33 (all XR all YR subclass(compose(YR,XR),cross_product(universal_class,universal_class))) # label(compose_defn1) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 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].
% 0.48/1.05 40 (all XF all Y apply(XF,Y) = sum_class(image(XF,singleton(Y)))) # label(apply_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 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].
% 0.48/1.05 42 (all Y (member(Y,universal_class) -> member(member_of(singleton(Y)),universal_class))) # label(member_singleton_universal) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 43 (all Y (member(Y,universal_class) -> singleton(member_of(singleton(Y))) = singleton(Y))) # label(member_singleton_singleton) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 44 (all X (member(member_of(X),universal_class) | member_of(X) = X)) # label(member_universal_self) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 45 (all X (singleton(member_of(X)) = X | member_of(X) = X)) # label(singleton_self) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.05 46 -(all X all U (-(exists Y (member(Y,universal_class) & X = singleton(Y))) & X = U -> member_of(X) = U)) # label(member_when_not_a_singleton) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.48/1.05
% 0.48/1.05 ============================== end of process non-clausal formulas ===
% 0.48/1.05
% 0.48/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.48/1.05
% 0.48/1.05 ============================== PREDICATE ELIMINATION =================
% 0.48/1.05 47 -inductive(A) | member(null_class,A) # label(inductive_defn) # label(axiom). [clausify(27)].
% 0.48/1.05 48 inductive(c1) # label(infinity) # label(axiom). [clausify(28)].
% 0.48/1.05 Derived: member(null_class,c1). [resolve(47,a,48,a)].
% 0.48/1.05 49 -inductive(A) | subclass(c1,A) # label(infinity) # label(axiom). [clausify(28)].
% 0.48/1.05 Derived: subclass(c1,c1). [resolve(49,a,48,a)].
% 0.48/1.05 50 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive_defn) # label(axiom). [clausify(27)].
% 0.48/1.05 Derived: subclass(image(successor_relation,c1),c1). [resolve(50,a,48,a)].
% 0.48/1.05 51 inductive(A) | -member(null_class,A) | -subclass(image(successor_relation,A),A) # label(inductive_defn) # label(axiom). [clausify(27)].
% 0.48/1.05 Derived: -member(null_class,A) | -subclass(image(successor_relation,A),A) | subclass(c1,A). [resolve(51,a,49,a)].
% 0.48/1.05 52 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function_defn) # label(axiom). [clausify(36)].
% 0.48/1.05 53 function(c2) # label(choice) # label(axiom). [clausify(41)].
% 0.48/1.05 Derived: subclass(c2,cross_product(universal_class,universal_class)). [resolve(52,a,53,a)].
% 0.48/1.05 54 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom). [clausify(36)].
% 0.48/1.05 Derived: subclass(compose(c2,inverse(c2)),identity_relation). [resolve(54,a,53,a)].
% 0.48/1.05 55 -member(A,universal_class) | -function(B) | member(image(B,A),universal_class) # label(replacement) # label(axiom). [clausify(37)].
% 0.48/1.05 Derived: -member(A,universal_class) | member(image(c2,A),universal_class). [resolve(55,b,53,a)].
% 0.48/1.05 56 function(A) | -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom). [clausify(36)].
% 0.48/1.05 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(56,a,55,b)].
% 0.48/1.05 57 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint_defn) # label(axiom). [clausify(38)].
% 0.48/1.05 58 null_class = A | disjoint(f5(A),A) # label(regularity) # label(axiom). [clausify(39)].
% 0.91/1.19 59 disjoint(A,B) | member(f4(A,B),A) # label(disjoint_defn) # label(axiom). [clausify(38)].
% 0.91/1.19 60 disjoint(A,B) | member(f4(A,B),B) # label(disjoint_defn) # label(axiom). [clausify(38)].
% 0.91/1.19 Derived: -member(A,f5(B)) | -member(A,B) | null_class = B. [resolve(57,a,58,b)].
% 0.91/1.19 Derived: -member(A,B) | -member(A,C) | member(f4(B,C),B). [resolve(57,a,59,a)].
% 0.91/1.19 Derived: -member(A,B) | -member(A,C) | member(f4(B,C),C). [resolve(57,a,60,a)].
% 0.91/1.19
% 0.91/1.19 ============================== end predicate elimination =============
% 0.91/1.19
% 0.91/1.19 Auto_denials: (non-Horn, no changes).
% 0.91/1.19
% 0.91/1.19 Term ordering decisions:
% 0.91/1.19 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. 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. f5=1. restrict=1.
% 0.91/1.19
% 0.91/1.19 ============================== end of process initial clauses ========
% 0.91/1.19
% 0.91/1.19 ============================== CLAUSES FOR SEARCH ====================
% 0.91/1.19
% 0.91/1.19 ============================== end of clauses for search =============
% 0.91/1.19
% 0.91/1.19 ============================== SEARCH ================================
% 0.91/1.19
% 0.91/1.19 % Starting search at 0.03 seconds.
% 0.91/1.19
% 0.91/1.19 ============================== PROOF =================================
% 0.91/1.19 % SZS status Theorem
% 0.91/1.19 % SZS output start Refutation
% 0.91/1.19
% 0.91/1.19 % Proof 1 at 0.16 (+ 0.00) seconds.
% 0.91/1.19 % Length of proof is 15.
% 0.91/1.19 % Level of proof is 4.
% 0.91/1.19 % Maximum clause weight is 11.000.
% 0.91/1.19 % Given clauses 148.
% 0.91/1.19
% 0.91/1.19 6 (all X singleton(X) = unordered_pair(X,X)) # label(singleton_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.19 44 (all X (member(member_of(X),universal_class) | member_of(X) = X)) # label(member_universal_self) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.19 45 (all X (singleton(member_of(X)) = X | member_of(X) = X)) # label(singleton_self) # label(axiom) # label(non_clause). [assumption].
% 0.91/1.19 46 -(all X all U (-(exists Y (member(Y,universal_class) & X = singleton(Y))) & X = U -> member_of(X) = U)) # label(member_when_not_a_singleton) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.91/1.19 63 c4 = c3 # label(member_when_not_a_singleton) # label(negated_conjecture). [clausify(46)].
% 0.91/1.19 67 singleton(A) = unordered_pair(A,A) # label(singleton_set_defn) # label(axiom). [clausify(6)].
% 0.91/1.19 78 member(member_of(A),universal_class) | member_of(A) = A # label(member_universal_self) # label(axiom). [clausify(44)].
% 0.91/1.19 83 singleton(member_of(A)) = A | member_of(A) = A # label(singleton_self) # label(axiom). [clausify(45)].
% 0.91/1.19 84 unordered_pair(member_of(A),member_of(A)) = A | member_of(A) = A. [copy(83),rewrite([67(2)])].
% 0.91/1.19 89 member_of(c3) != c4 # label(member_when_not_a_singleton) # label(negated_conjecture). [clausify(46)].
% 0.91/1.19 90 member_of(c3) != c3. [copy(89),rewrite([63(3)])].
% 0.91/1.19 92 -member(A,universal_class) | singleton(A) != c3 # label(member_when_not_a_singleton) # label(negated_conjecture). [clausify(46)].
% 0.91/1.19 93 -member(A,universal_class) | unordered_pair(A,A) != c3. [copy(92),rewrite([67(3)])].
% 0.91/1.19 217 unordered_pair(member_of(A),member_of(A)) != c3 | member_of(A) = A. [resolve(93,a,78,a)].
% 0.91/1.19 1297 $F. [resolve(217,a,84,a),merge(b),unit_del(a,90)].
% 0.91/1.19
% 0.91/1.19 % SZS output end Refutation
% 0.91/1.19 ============================== end of proof ==========================
% 0.91/1.19
% 0.91/1.19 ============================== STATISTICS ============================
% 0.91/1.19
% 0.91/1.19 Given=148. Generated=1690. Kept=1195. proofs=1.
% 0.91/1.19 Usable=141. Sos=982. Demods=44. Limbo=0, Disabled=179. Hints=0.
% 0.91/1.19 Megabytes=2.24.
% 0.91/1.19 User_CPU=0.16, System_CPU=0.00, Wall_clock=1.
% 0.91/1.19
% 0.91/1.19 ============================== end of statistics =====================
% 0.91/1.19
% 0.91/1.19 ============================== end of search =========================
% 0.91/1.19
% 0.91/1.19 THEOREM PROVED
% 0.91/1.19 % SZS status Theorem
% 0.91/1.19
% 0.91/1.19 Exiting with 1 proof.
% 0.91/1.19
% 0.91/1.19 Process 25255 exit (max_proofs) Sun Jul 10 09:58:42 2022
% 0.91/1.19 Prover9 interrupted
%------------------------------------------------------------------------------