%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET099-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:13:35 PM UTC 2026
% Result : Unsatisfiable 11.56s 2.48s
% Output : CNFRefutation 11.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of clauses : 107 ( 28 unt; 30 nHn; 79 RR)
% Number of literals : 209 ( 62 equ; 87 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subclass_members,axiom,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(complement1,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(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(regularity1,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
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(intersection1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(not_subclass_members1,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(intersection2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(subclass_implies_equal,axiom,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(unordered_pair_member,axiom,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(unordered_pair2,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(intersection3,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(regularity2,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(not_subclass_members2,axiom,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,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,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
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,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_19,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_20,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_18 ).
cnf(c_0_21,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_22,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_19 ).
cnf(c_0_23,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_24,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,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_26,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_27,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_29,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_30,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_31,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_25,c_0_26]) ).
cnf(c_0_32,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_33,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_29 ).
cnf(c_0_35,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),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).
cnf(c_0_37,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_32 ).
cnf(c_0_38,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_33]),c_0_24]) ).
cnf(c_0_39,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),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
c_0_36 ).
cnf(c_0_41,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),x) ),
inference(spm,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_42,plain,
subclass(null_class,X1),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_43,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_44,negated_conjecture,
( ~ member(not_subclass_element(x,null_class),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_22,c_0_39]) ).
cnf(c_0_45,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_46,negated_conjecture,
( member(not_subclass_element(x,null_class),x)
| intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_47,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_48,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_43 ).
cnf(c_0_49,negated_conjecture,
( ~ member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_44]),c_0_42])]) ).
cnf(c_0_50,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_45 ).
cnf(c_0_51,negated_conjecture,
( member(not_subclass_element(x,null_class),x)
| not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class) ),
inference(spm,[status(thm)],[c_0_31,c_0_46]) ).
cnf(c_0_52,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_47 ).
cnf(c_0_53,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
regularity2 ).
cnf(c_0_54,plain,
( unordered_pair(X1,X2) = null_class
| regular(unordered_pair(X1,X2)) = X2
| regular(unordered_pair(X1,X2)) = X1 ),
inference(spm,[status(thm)],[c_0_48,c_0_23]) ).
cnf(c_0_55,negated_conjecture,
( ~ member(not_subclass_element(x,null_class),universal_class)
| 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_49,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
( member(not_subclass_element(x,null_class),universal_class)
| not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_51]) ).
cnf(c_0_57,plain,
( ~ member(X2,X1)
| ~ member(X2,regular(X1))
| X1 = null_class ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_38]) ).
cnf(c_0_58,plain,
( unordered_pair(X1,X1) = null_class
| regular(unordered_pair(X1,X1)) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_54])]) ).
cnf(c_0_59,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_31,c_0_55]),c_0_56]) ).
cnf(c_0_60,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_61,plain,
( ~ member(X2,X1)
| ~ member(X2,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( ~ member(not_subclass_element(null_class,null_class),unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| subclass(intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x),null_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_59]),c_0_59]),c_0_59]),c_0_59]),c_0_59]) ).
cnf(c_0_63,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_60 ).
cnf(c_0_64,plain,
( subclass(intersection(X1,X2),X3)
| member(not_subclass_element(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_65,plain,
( ~ member(regular(unordered_pair(X1,X1)),X1)
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_61,c_0_23]) ).
cnf(c_0_66,negated_conjecture,
x != null_class,
inference(fof_simplification,[status(thm)],[prove_corollary_2_to_number_of_elements_in_class_3]) ).
cnf(c_0_67,negated_conjecture,
( ~ member(not_subclass_element(null_class,null_class),unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)))
| ~ member(X1,intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_62]),c_0_38]) ).
cnf(c_0_68,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( member(not_subclass_element(null_class,null_class),x)
| intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x) = null_class ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_59]),c_0_59]),c_0_59]) ).
cnf(c_0_70,plain,
null_class = unordered_pair(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_65,c_0_28]) ).
cnf(c_0_71,negated_conjecture,
x != null_class,
c_0_66 ).
cnf(c_0_72,negated_conjecture,
( subclass(x,null_class)
| member(not_subclass_element(null_class,null_class),x) ),
inference(spm,[status(thm)],[c_0_30,c_0_59]) ).
cnf(c_0_73,negated_conjecture,
( ~ member(not_subclass_element(null_class,null_class),universal_class)
| ~ member(X1,intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x)) ),
inference(spm,[status(thm)],[c_0_67,c_0_50]) ).
cnf(c_0_74,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_75,plain,
( ~ subclass(X2,intersection(X1,X2))
| intersection(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_40,c_0_68]) ).
cnf(c_0_76,negated_conjecture,
( member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),x)
| 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) ),
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_69,c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]) ).
cnf(c_0_77,negated_conjecture,
x != unordered_pair(universal_class,universal_class),
inference(rw,[status(thm)],[c_0_71,c_0_70]) ).
cnf(c_0_78,negated_conjecture,
( subclass(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)],[c_0_72,c_0_70]),c_0_70]),c_0_70]) ).
cnf(c_0_79,negated_conjecture,
( ~ member(X1,x)
| ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),universal_class)
| ~ 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))))) ),
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_73,c_0_52]),c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]),c_0_70]) ).
cnf(c_0_80,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_74 ).
cnf(c_0_81,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_75,c_0_76]),c_0_77]),c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( ~ member(X1,x)
| ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),universal_class)
| 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)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_24]) ).
cnf(c_0_83,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_24,c_0_81]) ).
cnf(c_0_84,plain,
( subclass(intersection(X1,X2),X3)
| member(not_subclass_element(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_85,plain,
( subclass(unordered_pair(X1,X2),X3)
| not_subclass_element(unordered_pair(X1,X2),X3) = X2
| not_subclass_element(unordered_pair(X1,X2),X3) = X1 ),
inference(spm,[status(thm)],[c_0_48,c_0_30]) ).
cnf(c_0_86,negated_conjecture,
( ~ member(X1,x)
| 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)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83])]) ).
cnf(c_0_87,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_63,c_0_84]) ).
cnf(c_0_88,plain,
( subclass(unordered_pair(X1,X1),X2)
| not_subclass_element(unordered_pair(X1,X1),X2) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_85])]) ).
cnf(c_0_89,plain,
( ~ member(not_subclass_element(X1,intersection(X2,X3)),X2)
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
| subclass(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_63,c_0_52]) ).
cnf(c_0_90,negated_conjecture,
( ~ member(X1,x)
| X1 = not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)) ),
inference(spm,[status(thm)],[c_0_48,c_0_86]) ).
cnf(c_0_91,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
inference(fof_simplification,[status(thm)],[prove_corollary_2_to_number_of_elements_in_class_2]) ).
cnf(c_0_92,plain,
( ~ subclass(X1,intersection(X1,X2))
| intersection(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_40,c_0_87]) ).
cnf(c_0_93,plain,
( ~ member(X1,X2)
| subclass(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_88]) ).
cnf(c_0_94,plain,
( ~ member(not_subclass_element(X1,intersection(X2,X1)),X2)
| subclass(X1,intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_89,c_0_30]) ).
cnf(c_0_95,negated_conjecture,
( subclass(x,X1)
| not_subclass_element(x,X1) = not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)) ),
inference(spm,[status(thm)],[c_0_90,c_0_30]) ).
cnf(c_0_96,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
c_0_91 ).
cnf(c_0_97,plain,
( ~ member(X1,intersection(unordered_pair(X1,X1),X2))
| intersection(unordered_pair(X1,X1),X2) = unordered_pair(X1,X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_98,negated_conjecture,
( ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),X1)
| subclass(x,intersection(X1,x)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(rw,[status(thm)],[c_0_96,c_0_26]) ).
cnf(c_0_100,plain,
( ~ member(X1,X2)
| ~ member(X1,unordered_pair(X1,X1))
| intersection(unordered_pair(X1,X1),X2) = unordered_pair(X1,X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_52]) ).
cnf(c_0_101,negated_conjecture,
( ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),X1)
| intersection(X1,x) = x ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_98]),c_0_68])]) ).
cnf(c_0_102,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_99,c_0_59]),c_0_59]) ).
cnf(c_0_103,plain,
( ~ member(X1,X2)
| intersection(unordered_pair(X1,X1),X2) = unordered_pair(X1,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_50]),c_0_24]) ).
cnf(c_0_104,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_101,c_0_50]),c_0_83])]) ).
cnf(c_0_105,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_102,c_0_70]) ).
cnf(c_0_106,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_81])]),c_0_105]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET099-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:52:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 11.56/2.48 % Version: 3.5.1
% 11.56/2.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 11.56/2.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.56/2.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 11.56/2.48 % Starting new_bool_3 with 300s (1) cores
% 11.56/2.48 % Starting new_bool_1 with 300s (1) cores
% 11.56/2.48 % Starting sh5l with 300s (1) cores
% 11.56/2.48 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2595418 completed with status 0
% 11.56/2.48 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 11.56/2.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 11.56/2.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.56/2.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 11.56/2.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.56/2.48 % No SInE strategy applied
% 11.56/2.48 % Search class: FGHSM-FFLM31-DFFFFFNN
% 11.56/2.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 11.56/2.48 % Starting SubtermCWHack with 136s (1) cores
% 11.56/2.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 11.56/2.48 % Starting new_bool_3 with 311s (1) cores
% 11.56/2.48 % Starting new_bool_1 with 308s (1) cores
% 11.56/2.48 % Starting sh5l with 304s (1) cores
% 11.56/2.48 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2595426 completed with status 0
% 11.56/2.48 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 11.56/2.48 % Preprocessing class: FSLSSMSMSSSNFFN.
% 11.56/2.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.56/2.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 11.56/2.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.56/2.48 % No SInE strategy applied
% 11.56/2.48 % Search class: FGHSM-FFLM31-DFFFFFNN
% 11.56/2.48 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 11.56/2.48 % Starting SubtermCWHack with 136s (1) cores
% 11.56/2.48 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 11.56/2.48 % Preprocessing time : 0.004 s
% 11.56/2.48 % Presaturation interreduction done
% 11.56/2.48
% 11.56/2.48 % Proof found!
% 11.56/2.48 % SZS status Unsatisfiable
% 11.56/2.48 % SZS output start CNFRefutation
% See solution above
% 11.56/2.48 % Parsed axioms : 94
% 11.56/2.48 % Removed by relevancy pruning/SinE : 0
% 11.56/2.48 % Initial clauses : 94
% 11.56/2.48 % Removed in clause preprocessing : 15
% 11.56/2.48 % Initial clauses in saturation : 79
% 11.56/2.48 % Processed clauses : 5009
% 11.56/2.48 % ...of these trivial : 22
% 11.56/2.48 % ...subsumed : 3662
% 11.56/2.48 % ...remaining for further processing : 1325
% 11.56/2.48 % Other redundant clauses eliminated : 9
% 11.56/2.48 % Clauses deleted for lack of memory : 0
% 11.56/2.48 % Backward-subsumed : 105
% 11.56/2.48 % Backward-rewritten : 275
% 11.56/2.48 % Generated clauses : 23164
% 11.56/2.48 % ...of the previous two non-redundant : 19385
% 11.56/2.48 % ...aggressively subsumed : 0
% 11.56/2.48 % Contextual simplify-reflections : 35
% 11.56/2.48 % Paramodulations : 23147
% 11.56/2.48 % Factorizations : 7
% 11.56/2.48 % NegExts : 0
% 11.56/2.48 % Equation resolutions : 9
% 11.56/2.48 % Disequality decompositions : 0
% 11.56/2.48 % Total rewrite steps : 99596
% 11.56/2.48 % ...of those cached : 99008
% 11.56/2.48 % Propositional unsat checks : 0
% 11.56/2.48 % Propositional check models : 0
% 11.56/2.48 % Propositional check unsatisfiable : 0
% 11.56/2.48 % Propositional clauses : 0
% 11.56/2.48 % Propositional clauses after purity: 0
% 11.56/2.48 % Propositional unsat core size : 0
% 11.56/2.48 % Propositional preprocessing time : 0.000
% 11.56/2.48 % Propositional encoding time : 0.000
% 11.56/2.48 % Propositional solver time : 0.000
% 11.56/2.48 % Success case prop preproc time : 0.000
% 11.56/2.48 % Success case prop encoding time : 0.000
% 11.56/2.48 % Success case prop solver time : 0.000
% 11.56/2.48 % Current number of processed clauses : 863
% 11.56/2.48 % Positive orientable unit clauses : 75
% 11.56/2.48 % Positive unorientable unit clauses: 1
% 11.56/2.48 % Negative unit clauses : 17
% 11.56/2.48 % Non-unit-clauses : 770
% 11.56/2.48 % Current number of unprocessed clauses: 13685
% 11.56/2.48 % ...number of literals in the above : 57768
% 11.56/2.48 % Current number of archived formulas : 0
% 11.56/2.48 % Current number of archived clauses : 474
% 11.56/2.48 % Clause-clause subsumption calls (NU) : 102205
% 11.56/2.48 % Rec. Clause-clause subsumption calls : 57699
% 11.56/2.48 % Non-unit clause-clause subsumptions : 2887
% 11.56/2.48 % Unit Clause-clause subsumption calls : 2965
% 11.56/2.48 % Rewrite failures with RHS unbound : 0
% 11.56/2.48 % BW rewrite match attempts : 196
% 11.56/2.48 % BW rewrite match successes : 92
% 11.56/2.48 % Condensation attempts : 0
% 11.56/2.48 % Condensation successes : 0
% 11.56/2.48 % Termbank termtop insertions : 2404167
% 11.56/2.48 % Search garbage collected termcells : 158
% 11.56/2.48
% 11.56/2.48 % -------------------------------------------------
% 11.56/2.48 % User time : 1.926 s
% 11.56/2.48 % System time : 0.034 s
% 11.56/2.48 % Total time : 1.960 s
% 11.56/2.48 % Maximum resident set size: 3720 pages
% 11.56/2.48
% 11.56/2.48 % -------------------------------------------------
% 11.56/2.48 % User time : 9.488 s
% 11.56/2.48 % System time : 0.339 s
% 11.56/2.48 % Total time : 9.827 s
% 11.56/2.48 % Maximum resident set size: 4608 pages
% 11.56/2.48 % E exiting
%------------------------------------------------------------------------------