TSTP Solution File: NUM069-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM069-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:26:22 EDT 2023
% Result : Unsatisfiable 1.83s 1.96s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 108
% Syntax : Number of formulae : 227 ( 42 unt; 81 typ; 0 def)
% Number of atoms : 298 ( 85 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 264 ( 112 ~; 152 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 60 >; 43 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 65 ( 65 usr; 21 con; 0-3 aty)
% Number of variables : 214 ( 54 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subclass: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(decl_25,type,
universal_class: $i ).
tff(decl_26,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_27,type,
singleton: $i > $i ).
tff(decl_28,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_29,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_30,type,
first: $i > $i ).
tff(decl_31,type,
second: $i > $i ).
tff(decl_32,type,
element_relation: $i ).
tff(decl_33,type,
intersection: ( $i * $i ) > $i ).
tff(decl_34,type,
complement: $i > $i ).
tff(decl_35,type,
union: ( $i * $i ) > $i ).
tff(decl_36,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(decl_37,type,
restrict: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
null_class: $i ).
tff(decl_39,type,
domain_of: $i > $i ).
tff(decl_40,type,
rotate: $i > $i ).
tff(decl_41,type,
flip: $i > $i ).
tff(decl_42,type,
inverse: $i > $i ).
tff(decl_43,type,
range_of: $i > $i ).
tff(decl_44,type,
domain: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
range: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
image: ( $i * $i ) > $i ).
tff(decl_47,type,
successor: $i > $i ).
tff(decl_48,type,
successor_relation: $i ).
tff(decl_49,type,
inductive: $i > $o ).
tff(decl_50,type,
omega: $i ).
tff(decl_51,type,
sum_class: $i > $i ).
tff(decl_52,type,
power_class: $i > $i ).
tff(decl_53,type,
compose: ( $i * $i ) > $i ).
tff(decl_54,type,
single_valued_class: $i > $o ).
tff(decl_55,type,
identity_relation: $i ).
tff(decl_56,type,
function: $i > $o ).
tff(decl_57,type,
regular: $i > $i ).
tff(decl_58,type,
apply: ( $i * $i ) > $i ).
tff(decl_59,type,
choice: $i ).
tff(decl_60,type,
one_to_one: $i > $o ).
tff(decl_61,type,
subset_relation: $i ).
tff(decl_62,type,
diagonalise: $i > $i ).
tff(decl_63,type,
cantor: $i > $i ).
tff(decl_64,type,
operation: $i > $o ).
tff(decl_65,type,
compatible: ( $i * $i * $i ) > $o ).
tff(decl_66,type,
homomorphism: ( $i * $i * $i ) > $o ).
tff(decl_67,type,
not_homomorphism1: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
compose_class: $i > $i ).
tff(decl_70,type,
composition_function: $i ).
tff(decl_71,type,
domain_relation: $i ).
tff(decl_72,type,
single_valued1: $i > $i ).
tff(decl_73,type,
single_valued2: $i > $i ).
tff(decl_74,type,
single_valued3: $i > $i ).
tff(decl_75,type,
singleton_relation: $i ).
tff(decl_76,type,
application_function: $i ).
tff(decl_77,type,
maps: ( $i * $i * $i ) > $o ).
tff(decl_78,type,
symmetrization_of: $i > $i ).
tff(decl_79,type,
irreflexive: ( $i * $i ) > $o ).
tff(decl_80,type,
connected: ( $i * $i ) > $o ).
tff(decl_81,type,
transitive: ( $i * $i ) > $o ).
tff(decl_82,type,
asymmetric: ( $i * $i ) > $o ).
tff(decl_83,type,
segment: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
well_ordering: ( $i * $i ) > $o ).
tff(decl_85,type,
least: ( $i * $i ) > $i ).
tff(decl_86,type,
not_well_ordering: ( $i * $i ) > $i ).
tff(decl_87,type,
section: ( $i * $i * $i ) > $o ).
tff(decl_88,type,
ordinal_numbers: $i ).
tff(decl_89,type,
kind_1_ordinals: $i ).
tff(decl_90,type,
limit_ordinals: $i ).
tff(decl_91,type,
rest_of: $i > $i ).
tff(decl_92,type,
rest_relation: $i ).
tff(decl_93,type,
recursion_equation_functions: $i > $i ).
tff(decl_94,type,
union_of_range_map: $i ).
tff(decl_95,type,
recursion: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
ordinal_add: ( $i * $i ) > $i ).
tff(decl_97,type,
add_relation: $i ).
tff(decl_98,type,
ordinal_multiply: ( $i * $i ) > $i ).
tff(decl_99,type,
integer_of: $i > $i ).
tff(decl_100,type,
y: $i ).
tff(decl_101,type,
u: $i ).
tff(decl_102,type,
v: $i ).
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_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(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_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(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(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(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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
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(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(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(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(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(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(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(equal_implies_subclass2,axiom,
( subclass(X2,X1)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',equal_implies_subclass2) ).
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(c_0_27,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_28,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_29,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| ~ member(X1,cross_product(X2,X3)) ),
cartesian_product4 ).
cnf(c_0_30,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_27,c_0_28]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
member(ordered_pair(u,v),cross_product(y,y)),
prove_corollary_to_well_ordering_property3_2 ).
cnf(c_0_32,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product1 ).
cnf(c_0_33,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_29,c_0_30]) ).
cnf(c_0_34,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_31,c_0_30]) ).
cnf(c_0_35,axiom,
( member(X2,X4)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product2 ).
cnf(c_0_36,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_32,c_0_30]) ).
cnf(c_0_37,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_33,c_0_34]) ).
cnf(c_0_38,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
cnf(c_0_39,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_40,negated_conjecture,
member(v,u),
prove_corollary_to_well_ordering_property3_4 ).
cnf(c_0_41,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_42,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_35,c_0_30]) ).
cnf(c_0_43,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_36,c_0_37]) ).
cnf(c_0_44,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_38,c_0_30]) ).
cnf(c_0_45,negated_conjecture,
( member(v,X1)
| ~ subclass(u,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_47,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ member(X1,X4)
| ~ subclass(intersection(X4,X3),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_48,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_49,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
limit_ordinals ).
cnf(c_0_50,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_42,c_0_37]) ).
cnf(c_0_51,negated_conjecture,
member(u,v),
prove_corollary_to_well_ordering_property3_3 ).
cnf(c_0_52,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_43,c_0_44]) ).
cnf(c_0_53,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_54,negated_conjecture,
member(v,universal_class),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,plain,
( member(X1,universal_class)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
member(first(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),y),
inference(spm,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_57,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_58,plain,
( member(X1,complement(kind_1_ordinals))
| ~ member(X1,limit_ordinals) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_60,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_61,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_50,c_0_44]) ).
cnf(c_0_62,negated_conjecture,
( member(u,X1)
| ~ subclass(v,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_51]) ).
cnf(c_0_63,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_52,c_0_53]),c_0_54])]) ).
cnf(c_0_64,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_55,c_0_56]) ).
cnf(c_0_65,plain,
( ~ member(X1,kind_1_ordinals)
| ~ member(X1,limit_ordinals) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_68,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_69,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),u)
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_40]) ).
cnf(c_0_70,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_62,c_0_46]) ).
cnf(c_0_71,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_57,c_0_63]) ).
cnf(c_0_72,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_64,c_0_56]) ).
cnf(c_0_73,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_74,plain,
( intersection(X1,limit_ordinals) = null_class
| ~ member(regular(intersection(X1,limit_ordinals)),kind_1_ordinals) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_60]) ).
cnf(c_0_76,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_77,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_67,c_0_68]) ).
cnf(c_0_78,negated_conjecture,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_53]),c_0_70])]) ).
cnf(c_0_79,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_71,c_0_53]),c_0_72])]) ).
cnf(c_0_80,negated_conjecture,
( member(u,complement(X1))
| member(u,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_70]) ).
cnf(c_0_81,plain,
intersection(kind_1_ordinals,limit_ordinals) = null_class,
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_82,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_76,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
member(v,y),
inference(spm,[status(thm)],[c_0_42,c_0_34]) ).
cnf(c_0_84,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_76,c_0_77]) ).
cnf(c_0_85,negated_conjecture,
member(u,y),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_86,negated_conjecture,
( member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ subclass(u,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_78]) ).
cnf(c_0_87,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_79,c_0_80]) ).
cnf(c_0_88,plain,
( member(X1,limit_ordinals)
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_59,c_0_81]) ).
cnf(c_0_89,plain,
( member(X1,kind_1_ordinals)
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_48,c_0_81]) ).
cnf(c_0_90,axiom,
( member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3) ),
well_ordering3 ).
cnf(c_0_91,negated_conjecture,
well_ordering(element_relation,y),
prove_corollary_to_well_ordering_property3_1 ).
cnf(c_0_92,negated_conjecture,
( not_subclass_element(unordered_pair(X1,v),y) = X1
| subclass(unordered_pair(X1,v),y) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_93,negated_conjecture,
( not_subclass_element(unordered_pair(u,X1),y) = X1
| subclass(unordered_pair(u,X1),y) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_94,negated_conjecture,
( ~ member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),X1)
| ~ subclass(u,complement(X1)) ),
inference(spm,[status(thm)],[c_0_57,c_0_86]) ).
cnf(c_0_95,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_67,c_0_87]) ).
cnf(c_0_96,axiom,
( subclass(X2,X1)
| X1 != X2 ),
equal_implies_subclass2 ).
cnf(c_0_97,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_98,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_88]),c_0_89]) ).
cnf(c_0_99,negated_conjecture,
( member(least(element_relation,X1),X1)
| ~ member(X2,X1)
| ~ subclass(X1,y) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_100,negated_conjecture,
( v = u
| subclass(unordered_pair(u,v),y) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_101,negated_conjecture,
~ subclass(u,complement(u)),
inference(spm,[status(thm)],[c_0_94,c_0_78]) ).
cnf(c_0_102,negated_conjecture,
( u = X1
| member(u,unordered_pair(u,X2)) ),
inference(spm,[status(thm)],[c_0_87,c_0_95]) ).
cnf(c_0_103,plain,
subclass(X1,X1),
inference(er,[status(thm)],[c_0_96]) ).
cnf(c_0_104,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_97]),c_0_98]) ).
cnf(c_0_105,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_67,c_0_60]) ).
cnf(c_0_106,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_99,c_0_100]) ).
cnf(c_0_107,negated_conjecture,
member(u,unordered_pair(u,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103])]) ).
cnf(c_0_108,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_104,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
( v = u
| member(least(element_relation,unordered_pair(u,v)),unordered_pair(u,v)) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_110,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_61,c_0_53]),c_0_54])]) ).
cnf(c_0_111,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_108,c_0_109]) ).
cnf(c_0_112,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_67,c_0_109]) ).
cnf(c_0_113,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_110,c_0_53]),c_0_70])]) ).
cnf(c_0_114,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_77])]) ).
cnf(c_0_115,negated_conjecture,
member(second(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(v,v)))),y),
inference(spm,[status(thm)],[c_0_50,c_0_34]) ).
cnf(c_0_116,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_117,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_111,c_0_112]),c_0_40])]) ).
cnf(c_0_118,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_39,c_0_113]) ).
cnf(c_0_119,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_114]) ).
cnf(c_0_120,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_39,c_0_115]) ).
cnf(c_0_121,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_61,c_0_116]),c_0_54])]) ).
cnf(c_0_122,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_104,c_0_105]) ).
cnf(c_0_123,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_104,c_0_117]) ).
cnf(c_0_124,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_118,c_0_119]) ).
cnf(c_0_125,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_104,c_0_120]) ).
cnf(c_0_126,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_121,c_0_53]),c_0_70])]) ).
cnf(c_0_127,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_122,c_0_109]) ).
cnf(c_0_128,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_123,c_0_107]),c_0_51])]) ).
cnf(c_0_129,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_57,c_0_124]) ).
cnf(c_0_130,negated_conjecture,
( unordered_pair(X1,v) = null_class
| ~ subclass(y,regular(unordered_pair(X1,v))) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_131,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_127,c_0_128]),c_0_51])]) ).
cnf(c_0_132,negated_conjecture,
~ member(v,complement(unordered_pair(X1,v))),
inference(spm,[status(thm)],[c_0_129,c_0_126]) ).
cnf(c_0_133,negated_conjecture,
( member(v,complement(X1))
| member(v,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_54]) ).
cnf(c_0_134,negated_conjecture,
( regular(unordered_pair(X1,v)) = v
| unordered_pair(X1,v) = null_class
| ~ subclass(y,X1) ),
inference(spm,[status(thm)],[c_0_130,c_0_105]) ).
cnf(c_0_135,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_104,c_0_131]) ).
cnf(c_0_136,negated_conjecture,
member(v,unordered_pair(X1,v)),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
( regular(unordered_pair(y,v)) = v
| unordered_pair(y,v) = null_class ),
inference(spm,[status(thm)],[c_0_134,c_0_103]) ).
cnf(c_0_138,negated_conjecture,
( unordered_pair(u,v) = null_class
| v = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_40])]) ).
cnf(c_0_139,negated_conjecture,
( unordered_pair(y,v) = null_class
| ~ member(X1,unordered_pair(y,v))
| ~ member(X1,v) ),
inference(spm,[status(thm)],[c_0_104,c_0_137]) ).
cnf(c_0_140,negated_conjecture,
( unordered_pair(y,v) = null_class
| member(v,unordered_pair(y,v)) ),
inference(spm,[status(thm)],[c_0_60,c_0_137]) ).
cnf(c_0_141,negated_conjecture,
v = u,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_138]),c_0_70])]),c_0_98]) ).
cnf(c_0_142,negated_conjecture,
( unordered_pair(y,v) = null_class
| ~ member(v,v) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_143,negated_conjecture,
member(u,u),
inference(rw,[status(thm)],[c_0_40,c_0_141]) ).
cnf(c_0_144,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_142,c_0_141]),c_0_141]),c_0_141]),c_0_143])]) ).
cnf(c_0_145,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_144]),c_0_70])]),c_0_98]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM069-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 12:39:08 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 1.83/1.96 % Version : CSE_E---1.5
% 1.83/1.96 % Problem : theBenchmark.p
% 1.83/1.96 % Proof found
% 1.83/1.96 % SZS status Theorem for theBenchmark.p
% 1.83/1.96 % SZS output start Proof
% See solution above
% 1.83/1.97 % Total time : 1.395000 s
% 1.83/1.97 % SZS output end Proof
% 1.83/1.97 % Total time : 1.401000 s
%------------------------------------------------------------------------------