%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM069-1 : 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 : n018.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 01:44:20 PM UTC 2026
% Result : Unsatisfiable 48.80s 7.65s
% Output : CNFRefutation 48.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 25
% Syntax : Number of clauses : 134 ( 43 unt; 32 nHn; 86 RR)
% Number of literals : 265 ( 63 equ; 110 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 233 ( 53 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(domain2,axiom,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',domain2) ).
cnf(cartesian_product4,axiom,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(cartesian_product3,axiom,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
cnf(cartesian_product1,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(prove_corollary_to_well_ordering_property3_2,negated_conjecture,
member(ordered_pair(u,v),cross_product(y,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property3_2) ).
cnf(cartesian_product2,axiom,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
cnf(unordered_pairs_in_universal,axiom,
member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
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(prove_corollary_to_well_ordering_property3_4,negated_conjecture,
member(v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property3_4) ).
cnf(prove_corollary_to_well_ordering_property3_3,negated_conjecture,
member(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property3_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(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_pair3,axiom,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
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_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(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(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(c_0_25,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
cnf(c_0_26,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_27,plain,
( ~ member(X3,X1)
| ~ subclass(X1,X2)
| member(X3,X2) ),
c_0_25 ).
cnf(c_0_28,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_29,plain,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
c_0_26 ).
cnf(c_0_30,axiom,
( member(regular(X1),X1)
| X1 = null_class ),
regularity1 ).
cnf(c_0_31,plain,
( ~ member(X1,X2)
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class ),
inference(fof_simplification,[status(thm)],[domain2]) ).
cnf(c_0_33,plain,
( ~ member(regular(complement(X1)),X1)
| complement(X1) = null_class ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( member(regular(X1),universal_class)
| X1 = null_class ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_35,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
inference(fof_simplification,[status(thm)],[cartesian_product4]) ).
cnf(c_0_36,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_37,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_38,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection3]) ).
cnf(c_0_39,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| restrict(X2,singleton(X1),universal_class) = null_class ),
c_0_32 ).
cnf(c_0_40,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_41,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
inference(fof_simplification,[status(thm)],[cartesian_product3]) ).
cnf(c_0_43,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[cartesian_product1]) ).
cnf(c_0_44,plain,
( ~ member(X1,cross_product(X2,X3))
| ordered_pair(first(X1),second(X1)) = X1 ),
c_0_35 ).
cnf(c_0_45,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_37]) ).
cnf(c_0_46,negated_conjecture,
member(ordered_pair(u,v),cross_product(y,y)),
prove_corollary_to_well_ordering_property3_2 ).
cnf(c_0_47,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_38 ).
cnf(c_0_48,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(X2))
| intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)) = null_class ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_37]),c_0_40]) ).
cnf(c_0_49,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_31]) ).
cnf(c_0_50,plain,
( ~ member(X3,X4)
| ~ member(X1,X2)
| member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
c_0_42 ).
cnf(c_0_51,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X1,X3) ),
c_0_43 ).
cnf(c_0_52,plain,
( ~ member(X1,cross_product(X2,X3))
| unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1 ),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(y,y)),
inference(rw,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_54,plain,
( ~ member(X3,X2)
| ~ member(X1,universal_class)
| ~ member(X3,cross_product(unordered_pair(X1,X1),universal_class))
| member(X1,domain_of(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_55,plain,
( ~ member(X1,X2)
| ~ member(X3,X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4)) ),
inference(rw,[status(thm)],[c_0_50,c_0_45]) ).
cnf(c_0_56,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,X4) ),
inference(fof_simplification,[status(thm)],[cartesian_product2]) ).
cnf(c_0_57,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4))
| member(X1,X3) ),
inference(rw,[status(thm)],[c_0_51,c_0_45]) ).
cnf(c_0_58,negated_conjecture,
unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))),unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))) = unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
( ~ member(X4,universal_class)
| ~ member(X1,universal_class)
| ~ member(X3,unordered_pair(X1,X1))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2)
| member(X1,domain_of(X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,axiom,
member(unordered_pair(X1,X2),universal_class),
unordered_pairs_in_universal ).
cnf(c_0_61,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_62,plain,
( ~ member(ordered_pair(X1,X2),cross_product(X3,X4))
| member(X2,X4) ),
c_0_56 ).
cnf(c_0_63,negated_conjecture,
( ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X1,X2))
| member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
( ~ member(X1,universal_class)
| ~ member(X2,unordered_pair(X1,X1))
| member(X1,domain_of(universal_class)) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_65,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
c_0_61 ).
cnf(c_0_66,negated_conjecture,
member(v,u),
prove_corollary_to_well_ordering_property3_4 ).
cnf(c_0_67,plain,
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4))
| member(X2,X4) ),
inference(rw,[status(thm)],[c_0_62,c_0_45]) ).
cnf(c_0_68,negated_conjecture,
( ~ member(u,X1)
| ~ member(v,X2)
| member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_55]) ).
cnf(c_0_69,plain,
( ~ member(X1,universal_class)
| member(X1,domain_of(universal_class)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
member(v,universal_class),
inference(spm,[status(thm)],[c_0_31,c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X2,X1))
| member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_58]) ).
cnf(c_0_72,negated_conjecture,
member(u,v),
prove_corollary_to_well_ordering_property3_3 ).
cnf(c_0_73,negated_conjecture,
( ~ member(u,X1)
| member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),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_74,negated_conjecture,
member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),y),
inference(spm,[status(thm)],[c_0_63,c_0_53]) ).
cnf(c_0_75,negated_conjecture,
( ~ member(u,X2)
| ~ member(v,X1)
| member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_55]) ).
cnf(c_0_76,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_31,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( ~ member(u,complement(X1))
| ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class),
inference(spm,[status(thm)],[c_0_31,c_0_74]) ).
cnf(c_0_79,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_80,negated_conjecture,
( ~ member(v,X1)
| member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_69]),c_0_76])]) ).
cnf(c_0_81,negated_conjecture,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),y),
inference(spm,[status(thm)],[c_0_71,c_0_53]) ).
cnf(c_0_82,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_83,negated_conjecture,
~ member(u,complement(unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_65]),c_0_78])]) ).
cnf(c_0_84,plain,
( ~ member(X1,universal_class)
| member(X1,X2)
| member(X1,complement(X2)) ),
c_0_79 ).
cnf(c_0_85,negated_conjecture,
( ~ member(v,complement(X1))
| ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_80]) ).
cnf(c_0_86,negated_conjecture,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class),
inference(spm,[status(thm)],[c_0_31,c_0_81]) ).
cnf(c_0_87,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
c_0_82 ).
cnf(c_0_88,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
inference(fof_simplification,[status(thm)],[unordered_pair3]) ).
cnf(c_0_89,negated_conjecture,
member(u,unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_76])]) ).
cnf(c_0_90,negated_conjecture,
~ member(v,complement(unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_65]),c_0_86])]) ).
cnf(c_0_91,axiom,
( intersection(X1,regular(X1)) = null_class
| X1 = null_class ),
regularity2 ).
cnf(c_0_92,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_87,c_0_30]) ).
cnf(c_0_93,axiom,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),X1) ),
not_subclass_members1 ).
cnf(c_0_94,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_95,plain,
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X2,X1)) ),
c_0_88 ).
cnf(c_0_96,negated_conjecture,
( u = X1
| first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u ),
inference(spm,[status(thm)],[c_0_87,c_0_89]) ).
cnf(c_0_97,negated_conjecture,
member(v,unordered_pair(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_84]),c_0_70])]) ).
cnf(c_0_98,plain,
( ~ member(X2,X1)
| ~ member(X2,regular(X1))
| X1 = null_class ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_91]),c_0_49]) ).
cnf(c_0_99,plain,
( unordered_pair(X1,X1) = null_class
| regular(unordered_pair(X1,X1)) = X1 ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_92])]) ).
cnf(c_0_100,plain,
( ~ member(not_subclass_element(complement(X1),X2),X1)
| subclass(complement(X1),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_93]) ).
cnf(c_0_101,plain,
( subclass(X1,X2)
| member(not_subclass_element(X1,X2),universal_class) ),
inference(spm,[status(thm)],[c_0_31,c_0_93]) ).
cnf(c_0_102,plain,
( ~ member(not_subclass_element(X1,X2),X2)
| subclass(X1,X2) ),
c_0_94 ).
cnf(c_0_103,negated_conjecture,
~ member(u,complement(unordered_pair(X1,first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_95]),c_0_78])]) ).
cnf(c_0_104,negated_conjecture,
first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u,
inference(ef,[status(thm)],[c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( v = X1
| second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = v ),
inference(spm,[status(thm)],[c_0_87,c_0_97]) ).
cnf(c_0_106,plain,
( ~ member(X2,X1)
| ~ member(X2,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_107,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
inference(fof_simplification,[status(thm)],[subclass_implies_equal]) ).
cnf(c_0_108,plain,
( subclass(complement(complement(X1)),X2)
| member(not_subclass_element(complement(complement(X1)),X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_84]),c_0_101]) ).
cnf(c_0_109,plain,
( subclass(X1,complement(X2))
| member(not_subclass_element(X1,complement(X2)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_84]),c_0_101]) ).
cnf(c_0_110,negated_conjecture,
~ member(u,complement(unordered_pair(X1,u))),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_111,negated_conjecture,
~ member(u,complement(y)),
inference(spm,[status(thm)],[c_0_77,c_0_74]) ).
cnf(c_0_112,negated_conjecture,
( member(v,unordered_pair(v,X2))
| v = X1 ),
inference(spm,[status(thm)],[c_0_97,c_0_105]) ).
cnf(c_0_113,plain,
( ~ member(X1,X1)
| unordered_pair(X1,X1) = null_class ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_65]),c_0_31]) ).
cnf(c_0_114,plain,
( member(X1,universal_class)
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_34,c_0_99]) ).
cnf(c_0_115,plain,
( ~ subclass(X2,X1)
| ~ subclass(X1,X2)
| X1 = X2 ),
c_0_107 ).
cnf(c_0_116,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_102,c_0_108]) ).
cnf(c_0_117,plain,
( ~ member(not_subclass_element(X1,complement(complement(X2))),X2)
| subclass(X1,complement(complement(X2))) ),
inference(spm,[status(thm)],[c_0_29,c_0_109]) ).
cnf(c_0_118,plain,
( ~ member(X3,X1)
| ~ member(X3,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = null_class
| regular(unordered_pair(X1,X2)) = X2 ),
inference(spm,[status(thm)],[c_0_98,c_0_92]) ).
cnf(c_0_119,negated_conjecture,
member(u,unordered_pair(X1,u)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_84]),c_0_76])]) ).
cnf(c_0_120,plain,
( ~ member(X3,X2)
| ~ member(X3,unordered_pair(X1,X2))
| unordered_pair(X1,X2) = null_class
| regular(unordered_pair(X1,X2)) = X1 ),
inference(spm,[status(thm)],[c_0_98,c_0_92]) ).
cnf(c_0_121,negated_conjecture,
member(v,unordered_pair(v,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_72])]) ).
cnf(c_0_122,plain,
( member(complement(X1),X1)
| unordered_pair(complement(X1),complement(X1)) = null_class ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_84]),c_0_114]) ).
cnf(c_0_123,plain,
( ~ subclass(X1,complement(complement(X1)))
| complement(complement(X1)) = X1 ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_124,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_117,c_0_93]) ).
cnf(c_0_125,negated_conjecture,
( ~ member(u,X1)
| unordered_pair(X1,u) = null_class
| regular(unordered_pair(X1,u)) = u ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_126,negated_conjecture,
( ~ member(v,X1)
| unordered_pair(v,X1) = null_class
| regular(unordered_pair(v,X1)) = v ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_127,plain,
( ~ member(complement(X1),universal_class)
| member(complement(X1),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_122]),c_0_49]) ).
cnf(c_0_128,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_129,negated_conjecture,
( v = u
| unordered_pair(v,u) = null_class ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_72]),c_0_66])]) ).
cnf(c_0_130,plain,
( ~ member(X1,universal_class)
| member(X1,complement(X1)) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_131,negated_conjecture,
v = u,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_129]),c_0_70])]),c_0_49]) ).
cnf(c_0_132,plain,
~ member(X1,X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_130]),c_0_31]) ).
cnf(c_0_133,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_131]),c_0_132]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM069-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n018.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 02:04:29 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 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
% 48.80/7.65 % Version: 3.5.1
% 48.80/7.65 % Preprocessing class: FSLSSMSMSSSNFFN.
% 48.80/7.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.80/7.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 48.80/7.65 % Starting new_bool_3 with 300s (1) cores
% 48.80/7.65 % Starting new_bool_1 with 300s (1) cores
% 48.80/7.65 % Starting sh5l with 300s (1) cores
% 48.80/7.65 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 739013 completed with status 0
% 48.80/7.65 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 48.80/7.65 % Preprocessing class: FSLSSMSMSSSNFFN.
% 48.80/7.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.80/7.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 48.80/7.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 48.80/7.65 % No SInE strategy applied
% 48.80/7.65 % Search class: FGHSM-FFLM31-DFFFFFNN
% 48.80/7.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 48.80/7.65 % Starting SubtermCWHack with 136s (1) cores
% 48.80/7.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 48.80/7.65 % Starting new_bool_3 with 311s (1) cores
% 48.80/7.65 % Starting new_bool_1 with 308s (1) cores
% 48.80/7.65 % Starting sh5l with 304s (1) cores
% 48.80/7.65 % sh5l with pid 739024 completed with status 0
% 48.80/7.65 % Result found by sh5l
% 48.80/7.65 % Preprocessing class: FSLSSMSMSSSNFFN.
% 48.80/7.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.80/7.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 48.80/7.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 48.80/7.65 % No SInE strategy applied
% 48.80/7.65 % Search class: FGHSM-FFLM31-DFFFFFNN
% 48.80/7.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 48.80/7.65 % Starting SubtermCWHack with 136s (1) cores
% 48.80/7.65 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 48.80/7.65 % Starting new_bool_3 with 311s (1) cores
% 48.80/7.65 % Starting new_bool_1 with 308s (1) cores
% 48.80/7.65 % Starting sh5l with 304s (1) cores
% 48.80/7.65 % Preprocessing time : 0.006 s
% 48.80/7.65 % Presaturation interreduction done
% 48.80/7.65
% 48.80/7.65 % Proof found!
% 48.80/7.65 % SZS status Unsatisfiable
% 48.80/7.65 % SZS output start CNFRefutation
% See solution above
% 48.80/7.65 % Parsed axioms : 162
% 48.80/7.65 % Removed by relevancy pruning/SinE : 0
% 48.80/7.65 % Initial clauses : 162
% 48.80/7.65 % Removed in clause preprocessing : 19
% 48.80/7.65 % Initial clauses in saturation : 143
% 48.80/7.65 % Processed clauses : 16141
% 48.80/7.65 % ...of these trivial : 43
% 48.80/7.65 % ...subsumed : 11893
% 48.80/7.65 % ...remaining for further processing : 4205
% 48.80/7.65 % Other redundant clauses eliminated : 32
% 48.80/7.65 % Clauses deleted for lack of memory : 0
% 48.80/7.65 % Backward-subsumed : 1022
% 48.80/7.65 % Backward-rewritten : 425
% 48.80/7.65 % Generated clauses : 111794
% 48.80/7.65 % ...of the previous two non-redundant : 100986
% 48.80/7.65 % ...aggressively subsumed : 0
% 48.80/7.65 % Contextual simplify-reflections : 73
% 48.80/7.65 % Paramodulations : 111741
% 48.80/7.65 % Factorizations : 21
% 48.80/7.65 % NegExts : 0
% 48.80/7.65 % Equation resolutions : 32
% 48.80/7.65 % Disequality decompositions : 0
% 48.80/7.65 % Total rewrite steps : 39156
% 48.80/7.65 % ...of those cached : 37898
% 48.80/7.65 % Propositional unsat checks : 0
% 48.80/7.65 % Propositional check models : 0
% 48.80/7.65 % Propositional check unsatisfiable : 0
% 48.80/7.65 % Propositional clauses : 0
% 48.80/7.65 % Propositional clauses after purity: 0
% 48.80/7.65 % Propositional unsat core size : 0
% 48.80/7.65 % Propositional preprocessing time : 0.000
% 48.80/7.65 % Propositional encoding time : 0.000
% 48.80/7.65 % Propositional solver time : 0.000
% 48.80/7.65 % Success case prop preproc time : 0.000
% 48.80/7.65 % Success case prop encoding time : 0.000
% 48.80/7.65 % Success case prop solver time : 0.000
% 48.80/7.65 % Current number of processed clauses : 2610
% 48.80/7.65 % Positive orientable unit clauses : 197
% 48.80/7.65 % Positive unorientable unit clauses: 4
% 48.80/7.65 % Negative unit clauses : 83
% 48.80/7.65 % Non-unit-clauses : 2326
% 48.80/7.65 % Current number of unprocessed clauses: 79065
% 48.80/7.65 % ...number of literals in the above : 304495
% 48.80/7.65 % Current number of archived formulas : 0
% 48.80/7.65 % Current number of archived clauses : 1608
% 48.80/7.65 % Clause-clause subsumption calls (NU) : 1082097
% 48.80/7.65 % Rec. Clause-clause subsumption calls : 566638
% 48.80/7.65 % Non-unit clause-clause subsumptions : 8934
% 48.80/7.65 % Unit Clause-clause subsumption calls : 35477
% 48.80/7.65 % Rewrite failures with RHS unbound : 89
% 48.80/7.65 % BW rewrite match attempts : 616
% 48.80/7.65 % BW rewrite match successes : 76
% 48.80/7.65 % Condensation attempts : 16141
% 48.80/7.65 % Condensation successes : 830
% 48.80/7.65 % Termbank termtop insertions : 4194974
% 48.80/7.65 % Search garbage collected termcells : 285
% 48.80/7.65
% 48.80/7.65 % -------------------------------------------------
% 48.80/7.65 % User time : 6.707 s
% 48.80/7.65 % System time : 0.134 s
% 48.80/7.65 % Total time : 6.840 s
% 48.80/7.65 % Maximum resident set size: 3996 pages
% 48.80/7.65
% 48.80/7.65 % -------------------------------------------------
% 48.80/7.65 % User time : 33.443 s
% 48.80/7.65 % System time : 1.040 s
% 48.80/7.65 % Total time : 34.483 s
% 48.80/7.65 % Maximum resident set size: 4608 pages
% 48.80/7.65 % E exiting
%------------------------------------------------------------------------------