TSTP Solution File: NUM066-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM066-1 : 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 : n003.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 10:26:21 EDT 2023
% Result : Unsatisfiable 10.39s 10.45s
% Output : CNFRefutation 10.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 99
% Syntax : Number of formulae : 139 ( 20 unt; 81 typ; 0 def)
% Number of atoms : 128 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 141 ( 71 ~; 70 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 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 : 115 ( 12 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(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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
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(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(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(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_property1_1,negated_conjecture,
well_ordering(element_relation,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_1) ).
cnf(element_relation3,axiom,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',element_relation3) ).
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_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(prove_corollary_to_well_ordering_property1_2,negated_conjecture,
subclass(u,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_2) ).
cnf(well_ordering5,axiom,
( ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3)
| ~ member(ordered_pair(X4,least(X1,X3)),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',well_ordering5) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(prove_corollary_to_well_ordering_property1_3,negated_conjecture,
member(v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_3) ).
cnf(prove_corollary_to_well_ordering_property1_4,negated_conjecture,
member(v,least(element_relation,u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_4) ).
cnf(c_0_18,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_19,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_20,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_21,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_22,plain,
( subclass(X1,intersection(X2,X3))
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X3)
| ~ member(not_subclass_element(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( member(not_subclass_element(X1,X2),X3)
| subclass(X1,X2)
| ~ subclass(X1,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_25,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_26,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_27,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_28,plain,
( subclass(X1,intersection(X2,X1))
| ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_29,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_31,axiom,
( member(least(X1,X3),X3)
| ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3) ),
well_ordering3 ).
cnf(c_0_32,negated_conjecture,
well_ordering(element_relation,y),
prove_corollary_to_well_ordering_property1_1 ).
cnf(c_0_33,axiom,
( member(ordered_pair(X1,X2),element_relation)
| ~ member(ordered_pair(X1,X2),cross_product(universal_class,universal_class))
| ~ member(X1,X2) ),
element_relation3 ).
cnf(c_0_34,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_26,c_0_27]),c_0_27]) ).
cnf(c_0_35,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
cnf(c_0_36,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_37,plain,
subclass(X1,intersection(universal_class,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_39,negated_conjecture,
( member(least(element_relation,X1),X1)
| ~ member(X2,X1)
| ~ subclass(X1,y) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
subclass(u,y),
prove_corollary_to_well_ordering_property1_2 ).
cnf(c_0_41,axiom,
( ~ well_ordering(X1,X2)
| ~ subclass(X3,X2)
| ~ member(X4,X3)
| ~ member(ordered_pair(X4,least(X1,X3)),X1) ),
well_ordering5 ).
cnf(c_0_42,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation)
| ~ member(X1,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_34]) ).
cnf(c_0_43,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_35,c_0_34]) ).
cnf(c_0_44,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_45,plain,
intersection(universal_class,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_46,negated_conjecture,
( member(least(element_relation,u),u)
| ~ member(X1,u) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
member(v,u),
prove_corollary_to_well_ordering_property1_3 ).
cnf(c_0_48,plain,
( ~ subclass(X3,X2)
| ~ member(X4,X3)
| ~ well_ordering(X1,X2)
| ~ member(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(least(X1,X3),least(X1,X3)))),X1) ),
inference(rw,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_49,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),element_relation)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,negated_conjecture,
member(least(element_relation,u),u),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
( ~ well_ordering(element_relation,X1)
| ~ member(least(element_relation,X2),universal_class)
| ~ member(X3,least(element_relation,X2))
| ~ member(X3,X2)
| ~ subclass(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( member(least(element_relation,u),X1)
| ~ subclass(u,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( ~ well_ordering(element_relation,X1)
| ~ member(X2,least(element_relation,u))
| ~ member(X2,u)
| ~ subclass(u,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_24])]) ).
cnf(c_0_55,negated_conjecture,
member(v,least(element_relation,u)),
prove_corollary_to_well_ordering_property1_4 ).
cnf(c_0_56,negated_conjecture,
( ~ well_ordering(element_relation,X1)
| ~ subclass(u,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_47])]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_32]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM066-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n003.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 13:24:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.62 start to proof: theBenchmark
% 10.39/10.45 % Version : CSE_E---1.5
% 10.39/10.45 % Problem : theBenchmark.p
% 10.39/10.45 % Proof found
% 10.39/10.45 % SZS status Theorem for theBenchmark.p
% 10.39/10.45 % SZS output start Proof
% See solution above
% 10.39/10.46 % Total time : 9.825000 s
% 10.39/10.46 % SZS output end Proof
% 10.39/10.46 % Total time : 9.832000 s
%------------------------------------------------------------------------------