TSTP Solution File: SET518-6 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET518-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n018.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 : Sat May  4 09:18:55 EDT 2024

% Result   : Unsatisfiable 127.17s 21.82s
% Output   : CNFRefutation 127.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   21
% Syntax   : Number of clauses     :  128 (  38 unt;  35 nHn;  71 RR)
%            Number of literals    :  255 (  70 equ; 103 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :  230 (  27 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',subclass_members) ).

cnf(complement1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',complement1) ).

cnf(regularity1,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',regularity1) ).

cnf(class_elements_are_sets,axiom,
    subclass(X1,universal_class),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',class_elements_are_sets) ).

cnf(domain1,axiom,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',domain1) ).

cnf(intersection2,axiom,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',intersection2) ).

cnf(singleton_set,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',singleton_set) ).

cnf(restriction1,axiom,
    intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',restriction1) ).

cnf(restriction2,axiom,
    intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',restriction2) ).

cnf(not_subclass_members2,axiom,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',not_subclass_members2) ).

cnf(intersection3,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',intersection3) ).

cnf(intersection1,axiom,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',intersection1) ).

cnf(not_subclass_members1,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',not_subclass_members1) ).

cnf(unordered_pair_member,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',unordered_pair_member) ).

cnf(subclass_implies_equal,axiom,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',subclass_implies_equal) ).

cnf(regularity2,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',regularity2) ).

cnf(unordered_pair2,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',unordered_pair2) ).

cnf(prove_no_cycles_length_2_2,negated_conjecture,
    member(y,x),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',prove_no_cycles_length_2_2) ).

cnf(prove_no_cycles_length_2_1,negated_conjecture,
    member(x,y),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',prove_no_cycles_length_2_1) ).

cnf(complement2,axiom,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',complement2) ).

cnf(unordered_pair3,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p',unordered_pair3) ).

cnf(c_0_21,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_members]) ).

cnf(c_0_22,plain,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    inference(fof_simplification,[status(thm)],[complement1]) ).

cnf(c_0_23,plain,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    c_0_21 ).

cnf(c_0_24,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    regularity1 ).

cnf(c_0_25,plain,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    c_0_22 ).

cnf(c_0_26,plain,
    ( X1 = null_class
    | member(regular(X1),X2)
    | ~ subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_27,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_28,plain,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    inference(fof_simplification,[status(thm)],[domain1]) ).

cnf(c_0_29,plain,
    ( complement(X1) = null_class
    | ~ member(regular(complement(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_24]) ).

cnf(c_0_30,plain,
    ( X1 = null_class
    | member(regular(X1),universal_class) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(fof_simplification,[status(thm)],[intersection2]) ).

cnf(c_0_32,plain,
    ( restrict(X1,singleton(X2),universal_class) != null_class
    | ~ member(X2,domain_of(X1)) ),
    c_0_28 ).

cnf(c_0_33,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_34,axiom,
    intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
    restriction1 ).

cnf(c_0_35,axiom,
    intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
    restriction2 ).

cnf(c_0_36,plain,
    complement(universal_class) = null_class,
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_37,plain,
    ( member(X1,X3)
    | ~ member(X1,intersection(X2,X3)) ),
    c_0_31 ).

cnf(c_0_38,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).

cnf(c_0_39,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(fof_simplification,[status(thm)],[intersection3]) ).

cnf(c_0_40,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_32,c_0_33]),c_0_34]) ).

cnf(c_0_41,plain,
    intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
    inference(rw,[status(thm)],[c_0_35,c_0_34]) ).

cnf(c_0_42,plain,
    ( ~ member(X1,null_class)
    | ~ member(X1,universal_class) ),
    inference(spm,[status(thm)],[c_0_25,c_0_36]) ).

cnf(c_0_43,plain,
    ( intersection(X1,X2) = null_class
    | member(regular(intersection(X1,X2)),X2) ),
    inference(spm,[status(thm)],[c_0_37,c_0_24]) ).

cnf(c_0_44,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(fof_simplification,[status(thm)],[intersection1]) ).

cnf(c_0_45,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),X2) ),
    c_0_38 ).

cnf(c_0_46,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    c_0_39 ).

cnf(c_0_47,axiom,
    ( member(not_subclass_element(X1,X2),X1)
    | subclass(X1,X2) ),
    not_subclass_members1 ).

cnf(c_0_48,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).

cnf(c_0_49,plain,
    ( intersection(cross_product(unordered_pair(X1,X1),universal_class),X2) != null_class
    | ~ member(X1,domain_of(X2)) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_50,plain,
    intersection(X1,null_class) = null_class,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_30]) ).

cnf(c_0_51,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    c_0_44 ).

cnf(c_0_52,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_45,c_0_46]) ).

cnf(c_0_53,plain,
    ( member(not_subclass_element(X1,X2),X3)
    | subclass(X1,X2)
    | ~ subclass(X1,X3) ),
    inference(spm,[status(thm)],[c_0_23,c_0_47]) ).

cnf(c_0_54,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    c_0_48 ).

cnf(c_0_55,plain,
    ~ member(X1,domain_of(null_class)),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_56,plain,
    ( intersection(X1,X2) = null_class
    | member(regular(intersection(X1,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_51,c_0_24]) ).

cnf(c_0_57,plain,
    ( member(not_subclass_element(intersection(X1,X2),X3),X1)
    | subclass(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_47]) ).

cnf(c_0_58,plain,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).

cnf(c_0_59,plain,
    ( subclass(X1,intersection(X2,X1))
    | ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_52,c_0_47]) ).

cnf(c_0_60,plain,
    ( member(not_subclass_element(X1,X2),universal_class)
    | subclass(X1,X2) ),
    inference(spm,[status(thm)],[c_0_53,c_0_27]) ).

cnf(c_0_61,plain,
    ( member(not_subclass_element(intersection(X1,X2),X3),X2)
    | subclass(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_37,c_0_47]) ).

cnf(c_0_62,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    regularity2 ).

cnf(c_0_63,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_54,c_0_24]) ).

cnf(c_0_64,plain,
    domain_of(null_class) = null_class,
    inference(spm,[status(thm)],[c_0_55,c_0_24]) ).

cnf(c_0_65,plain,
    ( intersection(complement(X1),X2) = null_class
    | ~ member(regular(intersection(complement(X1),X2)),X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_56]) ).

cnf(c_0_66,plain,
    ( intersection(X1,intersection(X2,X3)) = null_class
    | member(regular(intersection(X1,intersection(X2,X3))),X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_43]) ).

cnf(c_0_67,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_52,c_0_57]) ).

cnf(c_0_68,plain,
    ( X1 = X2
    | ~ subclass(X1,X2)
    | ~ subclass(X2,X1) ),
    c_0_58 ).

cnf(c_0_69,plain,
    subclass(X1,intersection(universal_class,X1)),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_70,plain,
    subclass(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_45,c_0_61]) ).

cnf(c_0_71,plain,
    ( X1 = null_class
    | member(X2,null_class)
    | ~ member(X2,regular(X1))
    | ~ member(X2,X1) ),
    inference(spm,[status(thm)],[c_0_46,c_0_62]) ).

cnf(c_0_72,plain,
    ( regular(unordered_pair(X1,X1)) = X1
    | unordered_pair(X1,X1) = null_class ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_63])]) ).

cnf(c_0_73,plain,
    ~ member(X1,null_class),
    inference(rw,[status(thm)],[c_0_55,c_0_64]) ).

cnf(c_0_74,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    inference(fof_simplification,[status(thm)],[unordered_pair2]) ).

cnf(c_0_75,plain,
    intersection(complement(X1),intersection(X1,X2)) = null_class,
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_76,plain,
    subclass(intersection(X1,X2),intersection(X2,X1)),
    inference(spm,[status(thm)],[c_0_67,c_0_61]) ).

cnf(c_0_77,plain,
    intersection(universal_class,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).

cnf(c_0_78,plain,
    ( unordered_pair(X1,X1) = null_class
    | ~ member(X2,unordered_pair(X1,X1))
    | ~ member(X2,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).

cnf(c_0_79,plain,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    c_0_74 ).

cnf(c_0_80,plain,
    ( ~ member(X1,intersection(X2,X3))
    | ~ member(X1,complement(X2)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_75]),c_0_73]) ).

cnf(c_0_81,plain,
    subclass(X1,intersection(X1,universal_class)),
    inference(spm,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_82,plain,
    subclass(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_45,c_0_57]) ).

cnf(c_0_83,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_54,c_0_47]) ).

cnf(c_0_84,negated_conjecture,
    member(y,x),
    prove_no_cycles_length_2_2 ).

cnf(c_0_85,plain,
    ( unordered_pair(X1,X1) = null_class
    | ~ member(X1,universal_class)
    | ~ member(X1,X1) ),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_86,plain,
    ( unordered_pair(X1,X1) = null_class
    | member(X1,universal_class) ),
    inference(spm,[status(thm)],[c_0_30,c_0_72]) ).

cnf(c_0_87,plain,
    ( subclass(intersection(X1,X2),X3)
    | ~ member(not_subclass_element(intersection(X1,X2),X3),complement(X1)) ),
    inference(spm,[status(thm)],[c_0_80,c_0_47]) ).

cnf(c_0_88,plain,
    intersection(X1,universal_class) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_81]),c_0_82])]) ).

cnf(c_0_89,plain,
    ( not_subclass_element(unordered_pair(X1,X2),X3) = X2
    | subclass(unordered_pair(X1,X2),X3)
    | ~ member(X1,X3) ),
    inference(spm,[status(thm)],[c_0_45,c_0_83]) ).

cnf(c_0_90,negated_conjecture,
    member(x,y),
    prove_no_cycles_length_2_1 ).

cnf(c_0_91,plain,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    inference(fof_simplification,[status(thm)],[complement2]) ).

cnf(c_0_92,negated_conjecture,
    ( member(y,X1)
    | ~ subclass(x,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_84]) ).

cnf(c_0_93,plain,
    ( unordered_pair(X1,X1) = null_class
    | ~ member(X1,X1) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_94,plain,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    inference(fof_simplification,[status(thm)],[unordered_pair3]) ).

cnf(c_0_95,plain,
    ( subclass(X1,X2)
    | ~ member(not_subclass_element(X1,X2),complement(X1)) ),
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_96,negated_conjecture,
    ( not_subclass_element(unordered_pair(x,X1),y) = X1
    | subclass(unordered_pair(x,X1),y) ),
    inference(spm,[status(thm)],[c_0_89,c_0_90]) ).

cnf(c_0_97,plain,
    ( member(X1,complement(X2))
    | member(X1,X2)
    | ~ member(X1,universal_class) ),
    c_0_91 ).

cnf(c_0_98,negated_conjecture,
    member(y,universal_class),
    inference(spm,[status(thm)],[c_0_92,c_0_27]) ).

cnf(c_0_99,plain,
    ( unordered_pair(intersection(X1,X2),intersection(X1,X2)) = null_class
    | ~ member(intersection(X1,X2),X2)
    | ~ member(intersection(X1,X2),X1) ),
    inference(spm,[status(thm)],[c_0_93,c_0_46]) ).

cnf(c_0_100,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_77]) ).

cnf(c_0_101,plain,
    subclass(X1,intersection(X1,X1)),
    inference(spm,[status(thm)],[c_0_59,c_0_47]) ).

cnf(c_0_102,plain,
    ( member(X1,X2)
    | ~ member(X1,X3)
    | ~ member(X1,X4)
    | ~ subclass(intersection(X4,X3),X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_46]) ).

cnf(c_0_103,plain,
    subclass(null_class,X1),
    inference(spm,[status(thm)],[c_0_73,c_0_47]) ).

cnf(c_0_104,plain,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    c_0_94 ).

cnf(c_0_105,negated_conjecture,
    ( subclass(unordered_pair(x,X1),y)
    | ~ member(X1,complement(unordered_pair(x,X1))) ),
    inference(spm,[status(thm)],[c_0_95,c_0_96]) ).

cnf(c_0_106,negated_conjecture,
    ( member(y,complement(X1))
    | member(y,X1) ),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_107,plain,
    ( ~ member(intersection(X1,X2),X2)
    | ~ member(intersection(X1,X2),X1) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_99]),c_0_73]),c_0_100]) ).

cnf(c_0_108,plain,
    intersection(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_101]),c_0_82])]) ).

cnf(c_0_109,plain,
    ( intersection(X1,complement(X2)) = null_class
    | ~ member(regular(intersection(X1,complement(X2))),X2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_43]) ).

cnf(c_0_110,plain,
    ( X1 = null_class
    | member(X2,X3)
    | ~ member(X2,regular(X1))
    | ~ member(X2,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_62]),c_0_103])]) ).

cnf(c_0_111,plain,
    ( member(X1,X2)
    | ~ member(X1,universal_class)
    | ~ subclass(unordered_pair(X3,X1),X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_104]) ).

cnf(c_0_112,negated_conjecture,
    ( member(y,unordered_pair(x,y))
    | subclass(unordered_pair(x,y),y) ),
    inference(spm,[status(thm)],[c_0_105,c_0_106]) ).

cnf(c_0_113,plain,
    ~ member(X1,X1),
    inference(spm,[status(thm)],[c_0_107,c_0_108]) ).

cnf(c_0_114,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_76]),c_0_76])]) ).

cnf(c_0_115,plain,
    intersection(X1,complement(X1)) = null_class,
    inference(spm,[status(thm)],[c_0_109,c_0_56]) ).

cnf(c_0_116,plain,
    ( regular(unordered_pair(X1,X2)) = X2
    | unordered_pair(X1,X2) = null_class
    | member(X3,X4)
    | ~ member(X3,unordered_pair(X1,X2))
    | ~ member(X3,X1) ),
    inference(spm,[status(thm)],[c_0_110,c_0_63]) ).

cnf(c_0_117,negated_conjecture,
    member(y,unordered_pair(x,y)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_98])]),c_0_113]) ).

cnf(c_0_118,plain,
    ( X1 = null_class
    | subclass(intersection(X1,regular(X1)),null_class) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_62]),c_0_114]) ).

cnf(c_0_119,plain,
    ~ member(X1,domain_of(complement(cross_product(unordered_pair(X1,X1),universal_class)))),
    inference(spm,[status(thm)],[c_0_49,c_0_115]) ).

cnf(c_0_120,negated_conjecture,
    ( regular(unordered_pair(x,y)) = y
    | unordered_pair(x,y) = null_class
    | member(y,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_84])]) ).

cnf(c_0_121,plain,
    ( X1 = null_class
    | ~ member(X2,regular(X1))
    | ~ member(X2,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_118]),c_0_73]) ).

cnf(c_0_122,negated_conjecture,
    ( regular(unordered_pair(x,y)) = y
    | unordered_pair(x,y) = null_class ),
    inference(spm,[status(thm)],[c_0_119,c_0_120]) ).

cnf(c_0_123,negated_conjecture,
    ( member(x,X1)
    | ~ subclass(y,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_90]) ).

cnf(c_0_124,negated_conjecture,
    ( unordered_pair(x,y) = null_class
    | ~ member(X1,unordered_pair(x,y))
    | ~ member(X1,y) ),
    inference(spm,[status(thm)],[c_0_121,c_0_122]) ).

cnf(c_0_125,negated_conjecture,
    member(x,universal_class),
    inference(spm,[status(thm)],[c_0_123,c_0_27]) ).

cnf(c_0_126,negated_conjecture,
    unordered_pair(x,y) = null_class,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_79]),c_0_90]),c_0_125])]) ).

cnf(c_0_127,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_126]),c_0_73]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem    : SET518-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.15  % Command    : run_E %s %d THM
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 10:26:01 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.23/0.51  Running first-order theorem proving
% 0.23/0.51  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.VfYvV7wS4o/E---3.1_25130.p
% 127.17/21.82  # Version: 3.1.0
% 127.17/21.82  # Preprocessing class: FSLSSMSMSSSNFFN.
% 127.17/21.82  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 127.17/21.82  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 127.17/21.82  # Starting new_bool_3 with 300s (1) cores
% 127.17/21.82  # Starting new_bool_1 with 300s (1) cores
% 127.17/21.82  # Starting sh5l with 300s (1) cores
% 127.17/21.82  # new_bool_3 with pid 25261 completed with status 8
% 127.17/21.82  # new_bool_1 with pid 25262 completed with status 8
% 127.17/21.82  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 25260 completed with status 0
% 127.17/21.82  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 127.17/21.82  # Preprocessing class: FSLSSMSMSSSNFFN.
% 127.17/21.82  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 127.17/21.82  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 127.17/21.82  # No SInE strategy applied
% 127.17/21.82  # Search class: FGHSM-FFLM31-DFFFFFNN
% 127.17/21.82  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 127.17/21.82  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 127.17/21.82  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 127.17/21.82  # Starting new_bool_1 with 308s (1) cores
% 127.17/21.82  # Starting sh5l with 304s (1) cores
% 127.17/21.82  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 127.17/21.82  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 25272 completed with status 0
% 127.17/21.82  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 127.17/21.82  # Preprocessing class: FSLSSMSMSSSNFFN.
% 127.17/21.82  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 127.17/21.82  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 127.17/21.82  # No SInE strategy applied
% 127.17/21.82  # Search class: FGHSM-FFLM31-DFFFFFNN
% 127.17/21.82  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 127.17/21.82  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 127.17/21.82  # Preprocessing time       : 0.004 s
% 127.17/21.82  # Presaturation interreduction done
% 127.17/21.82  
% 127.17/21.82  # Proof found!
% 127.17/21.82  # SZS status Unsatisfiable
% 127.17/21.82  # SZS output start CNFRefutation
% See solution above
% 127.17/21.82  # Parsed axioms                        : 114
% 127.17/21.82  # Removed by relevancy pruning/SinE    : 0
% 127.17/21.82  # Initial clauses                      : 114
% 127.17/21.82  # Removed in clause preprocessing      : 17
% 127.17/21.82  # Initial clauses in saturation        : 97
% 127.17/21.82  # Processed clauses                    : 62003
% 127.17/21.82  # ...of these trivial                  : 214
% 127.17/21.82  # ...subsumed                          : 53930
% 127.17/21.82  # ...remaining for further processing  : 7859
% 127.17/21.82  # Other redundant clauses eliminated   : 30
% 127.17/21.82  # Clauses deleted for lack of memory   : 0
% 127.17/21.82  # Backward-subsumed                    : 737
% 127.17/21.82  # Backward-rewritten                   : 276
% 127.17/21.82  # Generated clauses                    : 624086
% 127.17/21.82  # ...of the previous two non-redundant : 540926
% 127.17/21.82  # ...aggressively subsumed             : 0
% 127.17/21.82  # Contextual simplify-reflections      : 154
% 127.17/21.82  # Paramodulations                      : 623981
% 127.17/21.82  # Factorizations                       : 66
% 127.17/21.82  # NegExts                              : 0
% 127.17/21.82  # Equation resolutions                 : 31
% 127.17/21.82  # Disequality decompositions           : 0
% 127.17/21.82  # Total rewrite steps                  : 338652
% 127.17/21.82  # ...of those cached                   : 331059
% 127.17/21.82  # Propositional unsat checks           : 1
% 127.17/21.82  #    Propositional check models        : 0
% 127.17/21.82  #    Propositional check unsatisfiable : 0
% 127.17/21.82  #    Propositional clauses             : 0
% 127.17/21.82  #    Propositional clauses after purity: 0
% 127.17/21.82  #    Propositional unsat core size     : 0
% 127.17/21.82  #    Propositional preprocessing time  : 0.000
% 127.17/21.82  #    Propositional encoding time       : 0.635
% 127.17/21.82  #    Propositional solver time         : 0.272
% 127.17/21.82  #    Success case prop preproc time    : 0.000
% 127.17/21.82  #    Success case prop encoding time   : 0.000
% 127.17/21.82  #    Success case prop solver time     : 0.000
% 127.17/21.82  # Current number of processed clauses  : 6738
% 127.17/21.82  #    Positive orientable unit clauses  : 187
% 127.17/21.82  #    Positive unorientable unit clauses: 1
% 127.17/21.82  #    Negative unit clauses             : 194
% 127.17/21.82  #    Non-unit-clauses                  : 6356
% 127.17/21.82  # Current number of unprocessed clauses: 474347
% 127.17/21.82  # ...number of literals in the above   : 1981412
% 127.17/21.82  # Current number of archived formulas  : 0
% 127.17/21.82  # Current number of archived clauses   : 1134
% 127.17/21.82  # Clause-clause subsumption calls (NU) : 8040739
% 127.17/21.82  # Rec. Clause-clause subsumption calls : 3053571
% 127.17/21.82  # Non-unit clause-clause subsumptions  : 25506
% 127.17/21.82  # Unit Clause-clause subsumption calls : 68760
% 127.17/21.82  # Rewrite failures with RHS unbound    : 0
% 127.17/21.82  # BW rewrite match attempts            : 1174
% 127.17/21.82  # BW rewrite match successes           : 484
% 127.17/21.82  # Condensation attempts                : 0
% 127.17/21.82  # Condensation successes               : 0
% 127.17/21.82  # Termbank termtop insertions          : 39943689
% 127.17/21.82  # Search garbage collected termcells   : 183
% 127.17/21.82  
% 127.17/21.82  # -------------------------------------------------
% 127.17/21.82  # User time                : 20.694 s
% 127.17/21.82  # System time              : 0.408 s
% 127.17/21.82  # Total time               : 21.102 s
% 127.17/21.82  # Maximum resident set size: 2008 pages
% 127.17/21.82  
% 127.17/21.82  # -------------------------------------------------
% 127.17/21.82  # User time                : 104.528 s
% 127.17/21.82  # System time              : 1.092 s
% 127.17/21.82  # Total time               : 105.621 s
% 127.17/21.82  # Maximum resident set size: 1788 pages
% 127.17/21.82  % E---3.1 exiting
% 127.17/21.82  % E exiting
%------------------------------------------------------------------------------