TSTP Solution File: NUM069-1 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : NUM069-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n002.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 : Tue May 21 01:18:14 EDT 2024
% Result : Unsatisfiable 17.58s 2.70s
% Output : CNFRefutation 17.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 27
% Syntax : Number of clauses : 157 ( 41 unt; 41 nHn; 115 RR)
% Number of literals : 328 ( 89 equ; 129 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 255 ( 62 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cartesian_product4,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
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(cartesian_product1,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
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_product3,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
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(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(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(limit_ordinals,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',limit_ordinals) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
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(cartesian_product2,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
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(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(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(well_ordering3,axiom,
( member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering3) ).
cnf(prove_corollary_to_well_ordering_property3_1,negated_conjecture,
well_ordering(element_relation,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property3_1) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(equal_implies_subclass2,axiom,
( subclass(X2,X1)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',equal_implies_subclass2) ).
cnf(c_0_27,plain,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(fof_simplification,[status(thm)],[cartesian_product4]) ).
cnf(c_0_28,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_29,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_30,plain,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(fof_simplification,[status(thm)],[cartesian_product1]) ).
cnf(c_0_31,plain,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
c_0_27 ).
cnf(c_0_32,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_28,c_0_29]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
member(ordered_pair(u,v),cross_product(y,y)),
prove_corollary_to_well_ordering_property3_2 ).
cnf(c_0_34,plain,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
c_0_30 ).
cnf(c_0_35,plain,
( unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1
| ~ member(X1,cross_product(X2,X3)) ),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,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_33,c_0_32]) ).
cnf(c_0_37,plain,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
inference(fof_simplification,[status(thm)],[cartesian_product3]) ).
cnf(c_0_38,plain,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
inference(fof_simplification,[status(thm)],[subclass_members]) ).
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,
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_41,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_35,c_0_36]) ).
cnf(c_0_42,plain,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
c_0_37 ).
cnf(c_0_43,plain,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
c_0_38 ).
cnf(c_0_44,negated_conjecture,
member(v,u),
prove_corollary_to_well_ordering_property3_4 ).
cnf(c_0_45,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
c_0_39 ).
cnf(c_0_46,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection1]) ).
cnf(c_0_47,negated_conjecture,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X1,X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4))
| ~ member(X3,X4)
| ~ member(X1,X2) ),
inference(rw,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_49,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(fof_simplification,[status(thm)],[unordered_pair2]) ).
cnf(c_0_50,negated_conjecture,
( member(v,X1)
| ~ subclass(u,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_52,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ member(X1,X4)
| ~ subclass(intersection(X4,X3),X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_45]) ).
cnf(c_0_53,plain,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
inference(fof_simplification,[status(thm)],[complement1]) ).
cnf(c_0_54,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
c_0_46 ).
cnf(c_0_55,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
limit_ordinals ).
cnf(c_0_56,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[intersection2]) ).
cnf(c_0_57,negated_conjecture,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(v,X2)
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_58,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
c_0_49 ).
cnf(c_0_59,negated_conjecture,
member(v,universal_class),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
( member(X1,universal_class)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_61,negated_conjecture,
member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),y),
inference(spm,[status(thm)],[c_0_47,c_0_36]) ).
cnf(c_0_62,negated_conjecture,
member(u,v),
prove_corollary_to_well_ordering_property3_3 ).
cnf(c_0_63,plain,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
c_0_53 ).
cnf(c_0_64,plain,
( member(X1,complement(kind_1_ordinals))
| ~ member(X1,limit_ordinals) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,plain,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
c_0_56 ).
cnf(c_0_66,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_67,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(fof_simplification,[status(thm)],[unordered_pair_member]) ).
cnf(c_0_68,plain,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(fof_simplification,[status(thm)],[cartesian_product2]) ).
cnf(c_0_69,negated_conjecture,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(u,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_70,negated_conjecture,
( member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),universal_class)
| ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,plain,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
inference(fof_simplification,[status(thm)],[complement2]) ).
cnf(c_0_72,negated_conjecture,
( member(u,X1)
| ~ subclass(v,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_62]) ).
cnf(c_0_73,plain,
( ~ member(X1,kind_1_ordinals)
| ~ member(X1,limit_ordinals) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_74,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[not_subclass_members2]) ).
cnf(c_0_76,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
c_0_67 ).
cnf(c_0_77,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_78,plain,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
c_0_68 ).
cnf(c_0_79,negated_conjecture,
( ~ member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(u,complement(X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_69]) ).
cnf(c_0_80,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_70,c_0_61]) ).
cnf(c_0_81,plain,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
c_0_71 ).
cnf(c_0_82,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_72,c_0_51]) ).
cnf(c_0_83,plain,
( intersection(X1,limit_ordinals) = null_class
| ~ member(regular(intersection(X1,limit_ordinals)),kind_1_ordinals) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_84,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_66]) ).
cnf(c_0_85,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
c_0_75 ).
cnf(c_0_86,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_76,c_0_77]) ).
cnf(c_0_87,plain,
( member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_78,c_0_32]) ).
cnf(c_0_88,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_79,c_0_58]),c_0_80])]) ).
cnf(c_0_89,negated_conjecture,
( member(u,complement(X1))
| member(u,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,plain,
intersection(kind_1_ordinals,limit_ordinals) = null_class,
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,plain,
( member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3) ),
inference(fof_simplification,[status(thm)],[well_ordering3]) ).
cnf(c_0_92,plain,
( not_subclass_element(unordered_pair(X1,X2),X3) = X1
| subclass(unordered_pair(X1,X2),X3)
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,negated_conjecture,
member(v,y),
inference(spm,[status(thm)],[c_0_87,c_0_36]) ).
cnf(c_0_94,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_85,c_0_86]) ).
cnf(c_0_95,negated_conjecture,
member(u,y),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_96,negated_conjecture,
member(u,unordered_pair(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,plain,
( member(X1,limit_ordinals)
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_65,c_0_90]) ).
cnf(c_0_98,plain,
( member(X1,kind_1_ordinals)
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_54,c_0_90]) ).
cnf(c_0_99,plain,
( member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3) ),
c_0_91 ).
cnf(c_0_100,negated_conjecture,
well_ordering(element_relation,y),
prove_corollary_to_well_ordering_property3_1 ).
cnf(c_0_101,negated_conjecture,
( not_subclass_element(unordered_pair(X1,v),y) = X1
| subclass(unordered_pair(X1,v),y) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_102,negated_conjecture,
( not_subclass_element(unordered_pair(u,X1),y) = X1
| subclass(unordered_pair(u,X1),y) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_103,negated_conjecture,
( first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u
| u = X1 ),
inference(spm,[status(thm)],[c_0_76,c_0_96]) ).
cnf(c_0_104,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_105,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_97]),c_0_98]) ).
cnf(c_0_106,negated_conjecture,
( member(least(element_relation,X1),X1)
| ~ member(X2,X1)
| ~ subclass(X1,y) ),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_107,negated_conjecture,
( v = u
| subclass(unordered_pair(u,v),y) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_108,negated_conjecture,
first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))) = u,
inference(ef,[status(thm)],[c_0_103]) ).
cnf(c_0_109,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v))),cross_product(X2,X1)) ),
inference(spm,[status(thm)],[c_0_87,c_0_41]) ).
cnf(c_0_110,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_104]),c_0_105]) ).
cnf(c_0_111,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_76,c_0_66]) ).
cnf(c_0_112,negated_conjecture,
( v = u
| member(least(element_relation,unordered_pair(u,v)),unordered_pair(u,v))
| ~ member(X1,unordered_pair(u,v)) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
member(u,unordered_pair(u,X1)),
inference(spm,[status(thm)],[c_0_96,c_0_108]) ).
cnf(c_0_114,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(v,X1)
| ~ member(u,X2) ),
inference(spm,[status(thm)],[c_0_109,c_0_48]) ).
cnf(c_0_115,plain,
( regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class
| ~ member(X3,unordered_pair(X1,X2))
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( v = u
| member(least(element_relation,unordered_pair(u,v)),unordered_pair(u,v)) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_117,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(v,X1))
| ~ member(u,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_58]),c_0_59])]) ).
cnf(c_0_118,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(fof_simplification,[status(thm)],[unordered_pair3]) ).
cnf(c_0_119,negated_conjecture,
( regular(unordered_pair(u,v)) = v
| unordered_pair(u,v) = null_class
| v = u
| ~ member(least(element_relation,unordered_pair(u,v)),u) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_120,negated_conjecture,
( least(element_relation,unordered_pair(u,v)) = u
| least(element_relation,unordered_pair(u,v)) = v
| v = u ),
inference(spm,[status(thm)],[c_0_76,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(v,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_58]),c_0_82])]) ).
cnf(c_0_122,plain,
( not_subclass_element(unordered_pair(X1,X1),X2) = X1
| subclass(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_86])]) ).
cnf(c_0_123,negated_conjecture,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),y),
inference(spm,[status(thm)],[c_0_109,c_0_36]) ).
cnf(c_0_124,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
c_0_118 ).
cnf(c_0_125,negated_conjecture,
( least(element_relation,unordered_pair(u,v)) = u
| regular(unordered_pair(u,v)) = v
| unordered_pair(u,v) = null_class
| v = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_44])]) ).
cnf(c_0_126,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ subclass(unordered_pair(v,X2),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_121]) ).
cnf(c_0_127,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_122]) ).
cnf(c_0_128,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ subclass(y,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_123]) ).
cnf(c_0_129,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(X1,v))
| ~ member(u,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_124]),c_0_59])]) ).
cnf(c_0_130,plain,
( regular(unordered_pair(X1,X2)) = X1
| unordered_pair(X1,X2) = null_class
| ~ member(X3,unordered_pair(X1,X2))
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_131,negated_conjecture,
( least(element_relation,unordered_pair(u,v)) = u
| unordered_pair(u,v) = null_class
| v = u
| ~ member(X1,unordered_pair(u,v))
| ~ member(X1,v) ),
inference(spm,[status(thm)],[c_0_110,c_0_125]) ).
cnf(c_0_132,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(v,X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_133,negated_conjecture,
( X1 = null_class
| ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ subclass(y,regular(X1)) ),
inference(spm,[status(thm)],[c_0_110,c_0_128]) ).
cnf(c_0_134,negated_conjecture,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),unordered_pair(X1,v)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_58]),c_0_82])]) ).
cnf(c_0_135,plain,
( subclass(X2,X1)
| X1 != X2 ),
inference(fof_simplification,[status(thm)],[equal_implies_subclass2]) ).
cnf(c_0_136,negated_conjecture,
( regular(unordered_pair(u,v)) = u
| unordered_pair(u,v) = null_class
| v = u
| ~ member(least(element_relation,unordered_pair(u,v)),v) ),
inference(spm,[status(thm)],[c_0_130,c_0_116]) ).
cnf(c_0_137,negated_conjecture,
( least(element_relation,unordered_pair(u,v)) = u
| unordered_pair(u,v) = null_class
| v = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_113]),c_0_62])]) ).
cnf(c_0_138,negated_conjecture,
( ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ member(v,complement(X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_132]) ).
cnf(c_0_139,negated_conjecture,
( unordered_pair(X1,v) = null_class
| ~ subclass(y,regular(unordered_pair(X1,v))) ),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_140,plain,
( subclass(X2,X1)
| X1 != X2 ),
c_0_135 ).
cnf(c_0_141,negated_conjecture,
( regular(unordered_pair(u,v)) = u
| unordered_pair(u,v) = null_class
| v = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_62])]) ).
cnf(c_0_142,negated_conjecture,
~ member(v,complement(unordered_pair(X1,v))),
inference(spm,[status(thm)],[c_0_138,c_0_134]) ).
cnf(c_0_143,negated_conjecture,
( member(v,complement(X1))
| member(v,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_59]) ).
cnf(c_0_144,negated_conjecture,
( regular(unordered_pair(X1,v)) = v
| unordered_pair(X1,v) = null_class
| ~ subclass(y,X1) ),
inference(spm,[status(thm)],[c_0_139,c_0_111]) ).
cnf(c_0_145,plain,
subclass(X1,X1),
inference(er,[status(thm)],[c_0_140]) ).
cnf(c_0_146,negated_conjecture,
( unordered_pair(u,v) = null_class
| v = u
| ~ member(X1,unordered_pair(u,v))
| ~ member(X1,u) ),
inference(spm,[status(thm)],[c_0_110,c_0_141]) ).
cnf(c_0_147,negated_conjecture,
member(v,unordered_pair(X1,v)),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_148,negated_conjecture,
( regular(unordered_pair(y,v)) = v
| unordered_pair(y,v) = null_class ),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_149,negated_conjecture,
( unordered_pair(u,v) = null_class
| v = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_44])]) ).
cnf(c_0_150,negated_conjecture,
( unordered_pair(y,v) = null_class
| ~ member(X1,unordered_pair(y,v))
| ~ member(X1,v) ),
inference(spm,[status(thm)],[c_0_110,c_0_148]) ).
cnf(c_0_151,negated_conjecture,
( unordered_pair(y,v) = null_class
| member(v,unordered_pair(y,v)) ),
inference(spm,[status(thm)],[c_0_66,c_0_148]) ).
cnf(c_0_152,negated_conjecture,
v = u,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_149]),c_0_82])]),c_0_105]) ).
cnf(c_0_153,negated_conjecture,
( unordered_pair(y,v) = null_class
| ~ member(v,v) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_154,negated_conjecture,
member(u,u),
inference(rw,[status(thm)],[c_0_44,c_0_152]) ).
cnf(c_0_155,negated_conjecture,
unordered_pair(y,u) = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_152]),c_0_152]),c_0_152]),c_0_154])]) ).
cnf(c_0_156,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_155]),c_0_82])]),c_0_105]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : NUM069-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.05/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 05:35:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.44 Running first-order model finding
% 0.20/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.58/2.70 # Version: 3.1.0
% 17.58/2.70 # Preprocessing class: FSLSSMSMSSSNFFN.
% 17.58/2.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.58/2.70 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 17.58/2.70 # Starting new_bool_3 with 300s (1) cores
% 17.58/2.70 # Starting new_bool_1 with 300s (1) cores
% 17.58/2.70 # Starting sh5l with 300s (1) cores
% 17.58/2.70 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 28119 completed with status 0
% 17.58/2.70 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 17.58/2.70 # Preprocessing class: FSLSSMSMSSSNFFN.
% 17.58/2.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.58/2.70 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 17.58/2.70 # No SInE strategy applied
% 17.58/2.70 # Search class: FGHSM-FFLM31-DFFFFFNN
% 17.58/2.70 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 17.58/2.70 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 17.58/2.70 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 17.58/2.70 # Starting new_bool_1 with 308s (1) cores
% 17.58/2.70 # Starting sh5l with 304s (1) cores
% 17.58/2.70 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 17.58/2.70 # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 28130 completed with status 0
% 17.58/2.70 # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 17.58/2.70 # Preprocessing class: FSLSSMSMSSSNFFN.
% 17.58/2.70 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.58/2.70 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 17.58/2.70 # No SInE strategy applied
% 17.58/2.70 # Search class: FGHSM-FFLM31-DFFFFFNN
% 17.58/2.70 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 17.58/2.70 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 313s (1) cores
% 17.58/2.70 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 17.58/2.70 # Starting new_bool_1 with 308s (1) cores
% 17.58/2.70 # Starting sh5l with 304s (1) cores
% 17.58/2.70 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 17.58/2.70 # Preprocessing time : 0.003 s
% 17.58/2.70 # Presaturation interreduction done
% 17.58/2.70
% 17.58/2.70 # Proof found!
% 17.58/2.70 # SZS status Unsatisfiable
% 17.58/2.70 # SZS output start CNFRefutation
% See solution above
% 17.58/2.70 # Parsed axioms : 162
% 17.58/2.70 # Removed by relevancy pruning/SinE : 0
% 17.58/2.70 # Initial clauses : 162
% 17.58/2.70 # Removed in clause preprocessing : 19
% 17.58/2.70 # Initial clauses in saturation : 143
% 17.58/2.70 # Processed clauses : 12159
% 17.58/2.70 # ...of these trivial : 34
% 17.58/2.70 # ...subsumed : 7690
% 17.58/2.70 # ...remaining for further processing : 4435
% 17.58/2.70 # Other redundant clauses eliminated : 27
% 17.58/2.70 # Clauses deleted for lack of memory : 0
% 17.58/2.70 # Backward-subsumed : 283
% 17.58/2.70 # Backward-rewritten : 1160
% 17.58/2.70 # Generated clauses : 62388
% 17.58/2.70 # ...of the previous two non-redundant : 56449
% 17.58/2.70 # ...aggressively subsumed : 0
% 17.58/2.70 # Contextual simplify-reflections : 70
% 17.58/2.70 # Paramodulations : 62341
% 17.58/2.70 # Factorizations : 20
% 17.58/2.70 # NegExts : 0
% 17.58/2.70 # Equation resolutions : 27
% 17.58/2.70 # Disequality decompositions : 0
% 17.58/2.70 # Total rewrite steps : 16747
% 17.58/2.70 # ...of those cached : 15784
% 17.58/2.70 # Propositional unsat checks : 0
% 17.58/2.70 # Propositional check models : 0
% 17.58/2.70 # Propositional check unsatisfiable : 0
% 17.58/2.70 # Propositional clauses : 0
% 17.58/2.70 # Propositional clauses after purity: 0
% 17.58/2.71 # Propositional unsat core size : 0
% 17.58/2.71 # Propositional preprocessing time : 0.000
% 17.58/2.71 # Propositional encoding time : 0.000
% 17.58/2.71 # Propositional solver time : 0.000
% 17.58/2.71 # Success case prop preproc time : 0.000
% 17.58/2.71 # Success case prop encoding time : 0.000
% 17.58/2.71 # Success case prop solver time : 0.000
% 17.58/2.71 # Current number of processed clauses : 2844
% 17.58/2.71 # Positive orientable unit clauses : 148
% 17.58/2.71 # Positive unorientable unit clauses: 3
% 17.58/2.71 # Negative unit clauses : 54
% 17.58/2.71 # Non-unit-clauses : 2639
% 17.58/2.71 # Current number of unprocessed clauses: 42718
% 17.58/2.71 # ...number of literals in the above : 160852
% 17.58/2.71 # Current number of archived formulas : 0
% 17.58/2.71 # Current number of archived clauses : 1604
% 17.58/2.71 # Clause-clause subsumption calls (NU) : 1279806
% 17.58/2.71 # Rec. Clause-clause subsumption calls : 548580
% 17.58/2.71 # Non-unit clause-clause subsumptions : 4813
% 17.58/2.71 # Unit Clause-clause subsumption calls : 21763
% 17.58/2.71 # Rewrite failures with RHS unbound : 0
% 17.58/2.71 # BW rewrite match attempts : 450
% 17.58/2.71 # BW rewrite match successes : 57
% 17.58/2.71 # Condensation attempts : 0
% 17.58/2.71 # Condensation successes : 0
% 17.58/2.71 # Termbank termtop insertions : 1533165
% 17.58/2.71 # Search garbage collected termcells : 285
% 17.58/2.71
% 17.58/2.71 # -------------------------------------------------
% 17.58/2.71 # User time : 2.101 s
% 17.58/2.71 # System time : 0.067 s
% 17.58/2.71 # Total time : 2.168 s
% 17.58/2.71 # Maximum resident set size: 2196 pages
% 17.58/2.71
% 17.58/2.71 # -------------------------------------------------
% 17.58/2.71 # User time : 10.520 s
% 17.58/2.71 # System time : 0.160 s
% 17.58/2.71 # Total time : 10.681 s
% 17.58/2.71 # Maximum resident set size: 1840 pages
% 17.58/2.71 % E---3.1 exiting
%------------------------------------------------------------------------------