TSTP Solution File: SET099-6 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET099-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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  : 300s
% DateTime : Thu Aug 31 14:33:02 EDT 2023

% Result   : Unsatisfiable 64.07s 64.15s
% Output   : CNFRefutation 64.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   66
% Syntax   : Number of formulae    :  141 (  26 unt;  48 typ;   0 def)
%            Number of atoms       :  177 (  55 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  152 (  68   ~;  84   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   65 (  39   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   39 (  39 usr;   9 con; 0-3 aty)
%            Number of variables   :  114 (  16 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    subclass: ( $i * $i ) > $o ).

tff(decl_23,type,
    member: ( $i * $i ) > $o ).

tff(decl_24,type,
    not_subclass_element: ( $i * $i ) > $i ).

tff(decl_25,type,
    universal_class: $i ).

tff(decl_26,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_27,type,
    singleton: $i > $i ).

tff(decl_28,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(decl_29,type,
    cross_product: ( $i * $i ) > $i ).

tff(decl_30,type,
    first: $i > $i ).

tff(decl_31,type,
    second: $i > $i ).

tff(decl_32,type,
    element_relation: $i ).

tff(decl_33,type,
    intersection: ( $i * $i ) > $i ).

tff(decl_34,type,
    complement: $i > $i ).

tff(decl_35,type,
    union: ( $i * $i ) > $i ).

tff(decl_36,type,
    symmetric_difference: ( $i * $i ) > $i ).

tff(decl_37,type,
    restrict: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    null_class: $i ).

tff(decl_39,type,
    domain_of: $i > $i ).

tff(decl_40,type,
    rotate: $i > $i ).

tff(decl_41,type,
    flip: $i > $i ).

tff(decl_42,type,
    inverse: $i > $i ).

tff(decl_43,type,
    range_of: $i > $i ).

tff(decl_44,type,
    domain: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    range: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    image: ( $i * $i ) > $i ).

tff(decl_47,type,
    successor: $i > $i ).

tff(decl_48,type,
    successor_relation: $i ).

tff(decl_49,type,
    inductive: $i > $o ).

tff(decl_50,type,
    omega: $i ).

tff(decl_51,type,
    sum_class: $i > $i ).

tff(decl_52,type,
    power_class: $i > $i ).

tff(decl_53,type,
    compose: ( $i * $i ) > $i ).

tff(decl_54,type,
    single_valued_class: $i > $o ).

tff(decl_55,type,
    identity_relation: $i ).

tff(decl_56,type,
    function: $i > $o ).

tff(decl_57,type,
    regular: $i > $i ).

tff(decl_58,type,
    apply: ( $i * $i ) > $i ).

tff(decl_59,type,
    choice: $i ).

tff(decl_60,type,
    one_to_one: $i > $o ).

tff(decl_61,type,
    subset_relation: $i ).

tff(decl_62,type,
    diagonalise: $i > $i ).

tff(decl_63,type,
    cantor: $i > $i ).

tff(decl_64,type,
    operation: $i > $o ).

tff(decl_65,type,
    compatible: ( $i * $i * $i ) > $o ).

tff(decl_66,type,
    homomorphism: ( $i * $i * $i ) > $o ).

tff(decl_67,type,
    not_homomorphism1: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    not_homomorphism2: ( $i * $i * $i ) > $i ).

tff(decl_69,type,
    x: $i ).

cnf(subclass_members,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).

cnf(class_elements_are_sets,axiom,
    subclass(X1,universal_class),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(complement1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).

cnf(regularity1,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).

cnf(prove_corollary_2_to_number_of_elements_in_class_1,negated_conjecture,
    not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).

cnf(singleton_set,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).

cnf(not_subclass_members1,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).

cnf(intersection1,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).

cnf(intersection2,axiom,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).

cnf(subclass_implies_equal,axiom,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).

cnf(unordered_pair_member,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).

cnf(unordered_pair2,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).

cnf(intersection3,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).

cnf(regularity2,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).

cnf(not_subclass_members2,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).

cnf(prove_corollary_2_to_number_of_elements_in_class_3,negated_conjecture,
    x != null_class,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_3) ).

cnf(complement2,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).

cnf(prove_corollary_2_to_number_of_elements_in_class_2,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_2) ).

cnf(c_0_18,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    subclass_members ).

cnf(c_0_19,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_20,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    complement1 ).

cnf(c_0_21,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    regularity1 ).

cnf(c_0_22,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
    prove_corollary_2_to_number_of_elements_in_class_1 ).

cnf(c_0_24,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_25,plain,
    ( complement(X1) = null_class
    | ~ member(regular(complement(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    ( X1 = null_class
    | member(regular(X1),universal_class) ),
    inference(spm,[status(thm)],[c_0_22,c_0_21]) ).

cnf(c_0_27,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_28,negated_conjecture,
    not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
    inference(rw,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,plain,
    complement(universal_class) = null_class,
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    intersection1 ).

cnf(c_0_31,negated_conjecture,
    ( member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x))
    | subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,axiom,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    intersection2 ).

cnf(c_0_33,plain,
    ~ member(X1,null_class),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_22]) ).

cnf(c_0_34,negated_conjecture,
    ( member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
    | subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,axiom,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    subclass_implies_equal ).

cnf(c_0_36,negated_conjecture,
    ( member(not_subclass_element(x,null_class),x)
    | subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) ),
    inference(spm,[status(thm)],[c_0_32,c_0_31]) ).

cnf(c_0_37,plain,
    subclass(null_class,X1),
    inference(spm,[status(thm)],[c_0_33,c_0_27]) ).

cnf(c_0_38,negated_conjecture,
    ( subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class)
    | ~ member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))) ),
    inference(spm,[status(thm)],[c_0_20,c_0_34]) ).

cnf(c_0_39,negated_conjecture,
    ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class
    | member(not_subclass_element(x,null_class),x) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).

cnf(c_0_40,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    unordered_pair_member ).

cnf(c_0_41,negated_conjecture,
    ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class
    | ~ member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_38]),c_0_37])]) ).

cnf(c_0_42,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    unordered_pair2 ).

cnf(c_0_43,negated_conjecture,
    ( not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class)
    | member(not_subclass_element(x,null_class),x) ),
    inference(spm,[status(thm)],[c_0_28,c_0_39]) ).

cnf(c_0_44,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    intersection3 ).

cnf(c_0_45,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    regularity2 ).

cnf(c_0_46,plain,
    ( regular(unordered_pair(X1,X2)) = X1
    | regular(unordered_pair(X1,X2)) = X2
    | unordered_pair(X1,X2) = null_class ),
    inference(spm,[status(thm)],[c_0_40,c_0_21]) ).

cnf(c_0_47,negated_conjecture,
    ( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class
    | ~ member(not_subclass_element(x,null_class),universal_class) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_48,negated_conjecture,
    ( not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class)
    | member(not_subclass_element(x,null_class),universal_class) ),
    inference(spm,[status(thm)],[c_0_22,c_0_43]) ).

cnf(c_0_49,plain,
    ( X1 = null_class
    | ~ member(X2,regular(X1))
    | ~ member(X2,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_33]) ).

cnf(c_0_50,plain,
    ( regular(unordered_pair(X1,X1)) = X1
    | unordered_pair(X1,X1) = null_class ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_46])]) ).

cnf(c_0_51,negated_conjecture,
    not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_48]) ).

cnf(c_0_52,plain,
    ( unordered_pair(X1,X1) = null_class
    | ~ member(X2,unordered_pair(X1,X1))
    | ~ member(X2,X1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_53,negated_conjecture,
    ( subclass(intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x),null_class)
    | ~ member(not_subclass_element(null_class,null_class),unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_51]),c_0_51]),c_0_51]),c_0_51]),c_0_51]) ).

cnf(c_0_54,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    not_subclass_members2 ).

cnf(c_0_55,plain,
    ( member(not_subclass_element(intersection(X1,X2),X3),X2)
    | subclass(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_32,c_0_27]) ).

cnf(c_0_56,plain,
    ( unordered_pair(X1,X1) = null_class
    | ~ member(regular(unordered_pair(X1,X1)),X1) ),
    inference(spm,[status(thm)],[c_0_52,c_0_21]) ).

cnf(c_0_57,negated_conjecture,
    ( ~ member(X1,intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x))
    | ~ member(not_subclass_element(null_class,null_class),unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_53]),c_0_33]) ).

cnf(c_0_58,plain,
    subclass(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_59,negated_conjecture,
    ( intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x) = null_class
    | member(not_subclass_element(null_class,null_class),x) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_51]),c_0_51]),c_0_51]) ).

cnf(c_0_60,plain,
    null_class = unordered_pair(universal_class,universal_class),
    inference(spm,[status(thm)],[c_0_56,c_0_26]) ).

cnf(c_0_61,negated_conjecture,
    x != null_class,
    prove_corollary_2_to_number_of_elements_in_class_3 ).

cnf(c_0_62,negated_conjecture,
    ( member(not_subclass_element(null_class,null_class),x)
    | subclass(x,null_class) ),
    inference(spm,[status(thm)],[c_0_27,c_0_51]) ).

cnf(c_0_63,negated_conjecture,
    ( ~ member(X1,intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x))
    | ~ member(not_subclass_element(null_class,null_class),universal_class) ),
    inference(spm,[status(thm)],[c_0_57,c_0_42]) ).

cnf(c_0_64,plain,
    ( intersection(X1,X2) = X2
    | ~ subclass(X2,intersection(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_35,c_0_58]) ).

cnf(c_0_65,negated_conjecture,
    ( intersection(complement(unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)))),x) = unordered_pair(universal_class,universal_class)
    | member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),x) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]) ).

cnf(c_0_66,negated_conjecture,
    x != unordered_pair(universal_class,universal_class),
    inference(rw,[status(thm)],[c_0_61,c_0_60]) ).

cnf(c_0_67,negated_conjecture,
    ( member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),x)
    | subclass(x,unordered_pair(universal_class,universal_class)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_60]),c_0_60]),c_0_60]) ).

cnf(c_0_68,negated_conjecture,
    ( ~ member(X1,complement(unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)))))
    | ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),universal_class)
    | ~ member(X1,x) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_44]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]) ).

cnf(c_0_69,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    complement2 ).

cnf(c_0_70,negated_conjecture,
    member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),x),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67]) ).

cnf(c_0_71,negated_conjecture,
    ( member(X1,unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))))
    | ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),universal_class)
    | ~ member(X1,x) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_22]) ).

cnf(c_0_72,negated_conjecture,
    member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),universal_class),
    inference(spm,[status(thm)],[c_0_22,c_0_70]) ).

cnf(c_0_73,negated_conjecture,
    ( member(X1,unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))))
    | ~ member(X1,x) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).

cnf(c_0_74,plain,
    ( subclass(X1,intersection(X2,X3))
    | ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
    | ~ member(not_subclass_element(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_54,c_0_44]) ).

cnf(c_0_75,negated_conjecture,
    ( X1 = not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))
    | ~ member(X1,x) ),
    inference(spm,[status(thm)],[c_0_40,c_0_73]) ).

cnf(c_0_76,plain,
    ( member(not_subclass_element(intersection(X1,X2),X3),X1)
    | subclass(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_30,c_0_27]) ).

cnf(c_0_77,plain,
    ( not_subclass_element(unordered_pair(X1,X2),X3) = X1
    | not_subclass_element(unordered_pair(X1,X2),X3) = X2
    | subclass(unordered_pair(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_40,c_0_27]) ).

cnf(c_0_78,plain,
    ( subclass(X1,intersection(X2,X1))
    | ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_74,c_0_27]) ).

cnf(c_0_79,negated_conjecture,
    ( not_subclass_element(x,X1) = not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))
    | subclass(x,X1) ),
    inference(spm,[status(thm)],[c_0_75,c_0_27]) ).

cnf(c_0_80,negated_conjecture,
    singleton(not_subclass_element(x,null_class)) != x,
    prove_corollary_2_to_number_of_elements_in_class_2 ).

cnf(c_0_81,plain,
    subclass(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_54,c_0_76]) ).

cnf(c_0_82,plain,
    ( not_subclass_element(unordered_pair(X1,X1),X2) = X1
    | subclass(unordered_pair(X1,X1),X2) ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_77])]) ).

cnf(c_0_83,negated_conjecture,
    ( subclass(x,intersection(X1,x))
    | ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),X1) ),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_84,negated_conjecture,
    unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
    inference(rw,[status(thm)],[c_0_80,c_0_24]) ).

cnf(c_0_85,plain,
    ( intersection(X1,X2) = X1
    | ~ subclass(X1,intersection(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_35,c_0_81]) ).

cnf(c_0_86,plain,
    ( subclass(unordered_pair(X1,X1),X2)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_54,c_0_82]) ).

cnf(c_0_87,negated_conjecture,
    ( intersection(X1,x) = x
    | ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_83]),c_0_58])]) ).

cnf(c_0_88,negated_conjecture,
    unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)) != x,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_51]),c_0_51]) ).

cnf(c_0_89,plain,
    ( intersection(unordered_pair(X1,X1),X2) = unordered_pair(X1,X1)
    | ~ member(X1,intersection(unordered_pair(X1,X1),X2)) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_90,negated_conjecture,
    intersection(unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),X1),x) = x,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_42]),c_0_72])]) ).

cnf(c_0_91,negated_conjecture,
    unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))) != x,
    inference(spm,[status(thm)],[c_0_88,c_0_60]) ).

cnf(c_0_92,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_70])]),c_0_91]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET099-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 09:35:10 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 64.07/64.15  % Version  : CSE_E---1.5
% 64.07/64.15  % Problem  : theBenchmark.p
% 64.07/64.15  % Proof found
% 64.07/64.15  % SZS status Theorem for theBenchmark.p
% 64.07/64.15  % SZS output start Proof
% See solution above
% 64.15/64.16  % Total time : 63.580000 s
% 64.15/64.16  % SZS output end Proof
% 64.15/64.16  % Total time : 63.588000 s
%------------------------------------------------------------------------------