TSTP Solution File: SET190-6 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET190-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 14:33:32 EDT 2023
% Result : Unsatisfiable 48.48s 48.75s
% Output : CNFRefutation 48.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 75
% Syntax : Number of formulae : 141 ( 33 unt; 58 typ; 0 def)
% Number of atoms : 147 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 118 ( 54 ~; 64 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 44 >; 28 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 48 ( 48 usr; 14 con; 0-3 aty)
% Number of variables : 134 ( 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,
x: $i ).
tff(decl_79,type,
y: $i ).
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
cnf(not_subclass_members2,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(prove_subclass_property7_1,negated_conjecture,
subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property7_1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(subclass_implies_equal,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
cnf(domain1,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(prove_subclass_property7_2,negated_conjecture,
union(complement(x),y) != universal_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property7_2) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(c_0_17,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_18,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_19,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_20,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_21,plain,
( member(not_subclass_element(X1,X2),X3)
| subclass(X1,X2)
| ~ subclass(X1,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
subclass(x,y),
prove_subclass_property7_1 ).
cnf(c_0_23,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_24,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_19,c_0_20]) ).
cnf(c_0_25,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_26,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_27,negated_conjecture,
( member(not_subclass_element(x,X1),y)
| subclass(x,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_29,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_30,plain,
( X1 = null_class
| member(regular(X1),X2)
| ~ subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_31,plain,
( subclass(X1,intersection(X2,X1))
| ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_32,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_33,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_34,negated_conjecture,
( subclass(x,intersection(X1,y))
| ~ member(not_subclass_element(x,intersection(X1,y)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_35,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_36,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_37,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_38,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_39,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_40,plain,
subclass(X1,intersection(universal_class,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_42,negated_conjecture,
subclass(x,intersection(x,y)),
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
cnf(c_0_43,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
cnf(c_0_44,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
( member(not_subclass_element(intersection(universal_class,X1),X2),complement(X3))
| member(not_subclass_element(intersection(universal_class,X1),X2),X3)
| subclass(intersection(universal_class,X1),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_35]) ).
cnf(c_0_46,plain,
intersection(universal_class,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_47,plain,
( subclass(intersection(X1,X2),intersection(X3,X1))
| ~ member(not_subclass_element(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_48,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_49,negated_conjecture,
intersection(x,y) = x,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_42]),c_0_43])]) ).
cnf(c_0_50,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_51,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
domain1 ).
cnf(c_0_52,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_53,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_54,plain,
( ~ member(X1,null_class)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_29,c_0_44]) ).
cnf(c_0_55,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_56,plain,
( member(not_subclass_element(X1,X2),complement(X3))
| member(not_subclass_element(X1,X2),X3)
| subclass(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_46]),c_0_46]) ).
cnf(c_0_57,negated_conjecture,
union(complement(x),y) != universal_class,
prove_subclass_property7_2 ).
cnf(c_0_58,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_59,plain,
subclass(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_47,c_0_33]) ).
cnf(c_0_60,plain,
( intersection(X1,complement(X2)) = null_class
| ~ member(regular(intersection(X1,complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_61,negated_conjecture,
( member(X1,y)
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_26,c_0_49]) ).
cnf(c_0_62,plain,
( intersection(complement(X1),X2) = null_class
| ~ member(regular(intersection(complement(X1),X2)),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_50]) ).
cnf(c_0_63,plain,
( X1 = null_class
| member(regular(X1),complement(X2))
| member(regular(X1),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
cnf(c_0_64,plain,
( intersection(X1,cross_product(unordered_pair(X2,X2),universal_class)) != null_class
| ~ member(X2,domain_of(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_65,plain,
intersection(null_class,X1) = null_class,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_37]) ).
cnf(c_0_66,plain,
( member(not_subclass_element(complement(complement(X1)),X2),X1)
| subclass(complement(complement(X1)),X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,negated_conjecture,
complement(intersection(complement(complement(x)),complement(y))) != universal_class,
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_68,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_59]),c_0_59])]) ).
cnf(c_0_69,negated_conjecture,
( intersection(X1,complement(y)) = null_class
| ~ member(regular(intersection(X1,complement(y))),x) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,plain,
( intersection(complement(complement(X1)),X2) = null_class
| member(regular(intersection(complement(complement(X1)),X2)),X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,plain,
~ member(X1,domain_of(null_class)),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_19,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
complement(intersection(complement(y),complement(complement(x)))) != universal_class,
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
intersection(complement(y),complement(complement(x))) = null_class,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_68]) ).
cnf(c_0_75,plain,
domain_of(null_class) = null_class,
inference(spm,[status(thm)],[c_0_71,c_0_23]) ).
cnf(c_0_76,plain,
( complement(complement(X1)) = X1
| ~ subclass(X1,complement(complement(X1))) ),
inference(spm,[status(thm)],[c_0_39,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
complement(null_class) != universal_class,
inference(rw,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,plain,
~ member(X1,null_class),
inference(rw,[status(thm)],[c_0_71,c_0_75]) ).
cnf(c_0_79,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_56]) ).
cnf(c_0_80,plain,
~ subclass(universal_class,complement(null_class)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_44]),c_0_77]) ).
cnf(c_0_81,plain,
subclass(X1,complement(null_class)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_82,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET190-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.32 % Computer : n015.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Aug 26 11:50:07 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.16/0.52 start to proof: theBenchmark
% 48.48/48.75 % Version : CSE_E---1.5
% 48.48/48.75 % Problem : theBenchmark.p
% 48.48/48.75 % Proof found
% 48.48/48.75 % SZS status Theorem for theBenchmark.p
% 48.48/48.75 % SZS output start Proof
% See solution above
% 48.54/48.75 % Total time : 48.043000 s
% 48.54/48.75 % SZS output end Proof
% 48.54/48.75 % Total time : 48.049000 s
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