TSTP Solution File: SET126-6 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET126-6 : 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 : n031.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 14:33:13 EDT 2023

% Result   : Unsatisfiable 42.97s 43.04s
% Output   : CNFRefutation 42.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   69
% Syntax   : Number of formulae    :  149 (  40 unt;  49 typ;   0 def)
%            Number of atoms       :  177 (  56 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  138 (  61   ~;  77   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   67 (  40   >;  27   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;   9 con; 0-3 aty)
%            Number of variables   :  177 (  15 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,
    set_builder: ( $i * $i ) > $i ).

tff(decl_70,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(regularity1,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).

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

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

cnf(domain1,axiom,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain1) ).

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

cnf(restriction1,axiom,
    intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).

cnf(restriction2,axiom,
    intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction2) ).

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

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

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(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(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(definition_of_set_builder,axiom,
    union(singleton(X1),X2) = set_builder(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_set_builder) ).

cnf(prove_set_builder_and_singleton_1,negated_conjecture,
    set_builder(x,null_class) != singleton(x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_builder_and_singleton_1) ).

cnf(union,axiom,
    complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).

cnf(c_0_20,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    subclass_members ).

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

cnf(c_0_22,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    complement1 ).

cnf(c_0_23,plain,
    ( X1 = null_class
    | member(regular(X1),X2)
    | ~ subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_25,plain,
    ( complement(X1) = null_class
    | ~ member(regular(complement(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_21]) ).

cnf(c_0_26,plain,
    ( X1 = null_class
    | member(regular(X1),universal_class) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_27,axiom,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    domain1 ).

cnf(c_0_28,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_29,axiom,
    intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
    restriction1 ).

cnf(c_0_30,axiom,
    intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
    restriction2 ).

cnf(c_0_31,plain,
    complement(universal_class) = null_class,
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

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

cnf(c_0_33,plain,
    ( intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != null_class
    | ~ member(X2,domain_of(X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_34,plain,
    intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
    inference(rw,[status(thm)],[c_0_30,c_0_29]) ).

cnf(c_0_35,plain,
    ( ~ member(X1,null_class)
    | ~ member(X1,universal_class) ),
    inference(spm,[status(thm)],[c_0_22,c_0_31]) ).

cnf(c_0_36,plain,
    ( intersection(X1,X2) = null_class
    | member(regular(intersection(X1,X2)),X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_21]) ).

cnf(c_0_37,plain,
    ( intersection(cross_product(unordered_pair(X1,X1),universal_class),X2) != null_class
    | ~ member(X1,domain_of(X2)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_38,plain,
    intersection(X1,null_class) = null_class,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26]) ).

cnf(c_0_39,plain,
    ~ member(X1,domain_of(null_class)),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_40,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    complement2 ).

cnf(c_0_41,plain,
    domain_of(null_class) = null_class,
    inference(spm,[status(thm)],[c_0_39,c_0_21]) ).

cnf(c_0_42,plain,
    ( X1 = null_class
    | member(regular(X1),complement(X2))
    | member(regular(X1),X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_26]) ).

cnf(c_0_43,plain,
    ~ member(X1,null_class),
    inference(rw,[status(thm)],[c_0_39,c_0_41]) ).

cnf(c_0_44,plain,
    ( complement(complement(X1)) = null_class
    | member(regular(complement(complement(X1))),X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_42]) ).

cnf(c_0_45,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    unordered_pair_member ).

cnf(c_0_46,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    not_subclass_members2 ).

cnf(c_0_47,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    intersection3 ).

cnf(c_0_48,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_49,plain,
    complement(complement(null_class)) = null_class,
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_50,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_45,c_0_21]) ).

cnf(c_0_51,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_46,c_0_47]) ).

cnf(c_0_52,plain,
    ( member(not_subclass_element(X1,X2),X3)
    | subclass(X1,X2)
    | ~ subclass(X1,X3) ),
    inference(spm,[status(thm)],[c_0_20,c_0_48]) ).

cnf(c_0_53,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    intersection1 ).

cnf(c_0_54,plain,
    ( X1 = null_class
    | member(regular(X1),complement(null_class)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_49]),c_0_43]) ).

cnf(c_0_55,plain,
    ( regular(unordered_pair(X1,X1)) = X1
    | unordered_pair(X1,X1) = null_class ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_50])]) ).

cnf(c_0_56,plain,
    ( subclass(X1,intersection(X2,X1))
    | ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_48]) ).

cnf(c_0_57,plain,
    ( member(not_subclass_element(X1,X2),universal_class)
    | subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_52,c_0_24]) ).

cnf(c_0_58,plain,
    ( member(not_subclass_element(intersection(X1,X2),X3),X2)
    | subclass(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_32,c_0_48]) ).

cnf(c_0_59,plain,
    ( intersection(X1,X2) = null_class
    | member(regular(intersection(X1,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_53,c_0_21]) ).

cnf(c_0_60,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    unordered_pair2 ).

cnf(c_0_61,plain,
    ( unordered_pair(X1,X1) = null_class
    | member(X1,complement(null_class)) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_62,plain,
    ( member(not_subclass_element(intersection(X1,X2),X3),X1)
    | subclass(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_53,c_0_48]) ).

cnf(c_0_63,axiom,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    subclass_implies_equal ).

cnf(c_0_64,plain,
    subclass(X1,intersection(universal_class,X1)),
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_65,plain,
    subclass(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_46,c_0_58]) ).

cnf(c_0_66,plain,
    ( intersection(complement(X1),X2) = null_class
    | ~ member(regular(intersection(complement(X1),X2)),X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_59]) ).

cnf(c_0_67,plain,
    ( intersection(X1,intersection(X2,X3)) = null_class
    | member(regular(intersection(X1,intersection(X2,X3))),X2) ),
    inference(spm,[status(thm)],[c_0_53,c_0_36]) ).

cnf(c_0_68,plain,
    ( member(X1,complement(null_class))
    | ~ member(X1,universal_class) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_43]) ).

cnf(c_0_69,plain,
    ( member(not_subclass_element(intersection(universal_class,X1),X2),complement(X3))
    | member(not_subclass_element(intersection(universal_class,X1),X2),X3)
    | subclass(intersection(universal_class,X1),X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_62]) ).

cnf(c_0_70,plain,
    intersection(universal_class,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]) ).

cnf(c_0_71,plain,
    intersection(complement(X1),intersection(X1,X2)) = null_class,
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_72,axiom,
    union(singleton(X1),X2) = set_builder(X1,X2),
    definition_of_set_builder ).

cnf(c_0_73,plain,
    ( subclass(X1,complement(null_class))
    | ~ member(not_subclass_element(X1,complement(null_class)),universal_class) ),
    inference(spm,[status(thm)],[c_0_46,c_0_68]) ).

cnf(c_0_74,plain,
    ( subclass(complement(X1),X2)
    | ~ member(not_subclass_element(complement(X1),X2),X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_48]) ).

cnf(c_0_75,plain,
    ( member(not_subclass_element(X1,X2),complement(X3))
    | member(not_subclass_element(X1,X2),X3)
    | subclass(X1,X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_70]),c_0_70]) ).

cnf(c_0_76,plain,
    ( ~ member(X1,intersection(X2,X3))
    | ~ member(X1,complement(X2)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_71]),c_0_43]) ).

cnf(c_0_77,plain,
    subclass(X1,intersection(X1,X1)),
    inference(spm,[status(thm)],[c_0_56,c_0_48]) ).

cnf(c_0_78,plain,
    subclass(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_46,c_0_62]) ).

cnf(c_0_79,negated_conjecture,
    set_builder(x,null_class) != singleton(x),
    prove_set_builder_and_singleton_1 ).

cnf(c_0_80,plain,
    union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
    inference(rw,[status(thm)],[c_0_72,c_0_28]) ).

cnf(c_0_81,axiom,
    complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
    union ).

cnf(c_0_82,plain,
    subclass(universal_class,complement(null_class)),
    inference(spm,[status(thm)],[c_0_73,c_0_48]) ).

cnf(c_0_83,plain,
    ( subclass(intersection(X1,X2),intersection(X3,X1))
    | ~ member(not_subclass_element(intersection(X1,X2),intersection(X3,X1)),X3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_62]) ).

cnf(c_0_84,plain,
    ( member(not_subclass_element(complement(complement(X1)),X2),X1)
    | subclass(complement(complement(X1)),X2) ),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_85,plain,
    ( subclass(intersection(X1,X2),X3)
    | ~ member(not_subclass_element(intersection(X1,X2),X3),complement(X1)) ),
    inference(spm,[status(thm)],[c_0_76,c_0_48]) ).

cnf(c_0_86,plain,
    intersection(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_77]),c_0_78])]) ).

cnf(c_0_87,negated_conjecture,
    complement(intersection(complement(unordered_pair(x,x)),complement(null_class))) != unordered_pair(x,x),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_28]),c_0_80]),c_0_81]) ).

cnf(c_0_88,plain,
    complement(null_class) = universal_class,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_82]),c_0_24])]) ).

cnf(c_0_89,plain,
    subclass(intersection(X1,X2),intersection(X2,X1)),
    inference(spm,[status(thm)],[c_0_83,c_0_58]) ).

cnf(c_0_90,plain,
    subclass(complement(complement(X1)),X1),
    inference(spm,[status(thm)],[c_0_46,c_0_84]) ).

cnf(c_0_91,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),complement(X1)) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_92,plain,
    ( member(not_subclass_element(X1,complement(X2)),X2)
    | subclass(X1,complement(X2)) ),
    inference(spm,[status(thm)],[c_0_46,c_0_75]) ).

cnf(c_0_93,negated_conjecture,
    complement(intersection(complement(unordered_pair(x,x)),universal_class)) != unordered_pair(x,x),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_94,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_89]),c_0_89])]) ).

cnf(c_0_95,plain,
    ( complement(complement(X1)) = X1
    | ~ subclass(X1,complement(complement(X1))) ),
    inference(spm,[status(thm)],[c_0_63,c_0_90]) ).

cnf(c_0_96,plain,
    subclass(X1,complement(complement(X1))),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_97,negated_conjecture,
    complement(complement(unordered_pair(x,x))) != unordered_pair(x,x),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_70]) ).

cnf(c_0_98,plain,
    complement(complement(X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]) ).

cnf(c_0_99,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET126-6 : 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
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 09:49:23 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 42.97/43.04  % Version  : CSE_E---1.5
% 42.97/43.04  % Problem  : theBenchmark.p
% 42.97/43.04  % Proof found
% 42.97/43.04  % SZS status Theorem for theBenchmark.p
% 42.97/43.04  % SZS output start Proof
% See solution above
% 42.97/43.05  % Total time : 42.483000 s
% 42.97/43.05  % SZS output end Proof
% 42.97/43.05  % Total time : 42.488000 s
%------------------------------------------------------------------------------