TSTP Solution File: SET099-6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET099-6 : 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 : n029.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 14:33:02 EDT 2023
% Result : Unsatisfiable 64.07s 64.15s
% Output : CNFRefutation 64.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 66
% Syntax : Number of formulae : 141 ( 26 unt; 48 typ; 0 def)
% Number of atoms : 177 ( 55 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 152 ( 68 ~; 84 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 39 >; 26 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 9 con; 0-3 aty)
% Number of variables : 114 ( 16 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,
x: $i ).
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(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(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(prove_corollary_2_to_number_of_elements_in_class_1,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(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(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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
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(prove_corollary_2_to_number_of_elements_in_class_3,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_3) ).
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(prove_corollary_2_to_number_of_elements_in_class_2,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_2) ).
cnf(c_0_18,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_19,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_20,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_21,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_22,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
prove_corollary_2_to_number_of_elements_in_class_1 ).
cnf(c_0_24,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_25,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_28,negated_conjecture,
not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_31,negated_conjecture,
( member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x))
| subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_33,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_22]) ).
cnf(c_0_34,negated_conjecture,
( member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_36,negated_conjecture,
( member(not_subclass_element(x,null_class),x)
| subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_37,plain,
subclass(null_class,X1),
inference(spm,[status(thm)],[c_0_33,c_0_27]) ).
cnf(c_0_38,negated_conjecture,
( subclass(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class)
| ~ member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))) ),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class
| member(not_subclass_element(x,null_class),x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_40,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_41,negated_conjecture,
( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class
| ~ member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_38]),c_0_37])]) ).
cnf(c_0_42,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_43,negated_conjecture,
( not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class)
| member(not_subclass_element(x,null_class),x) ),
inference(spm,[status(thm)],[c_0_28,c_0_39]) ).
cnf(c_0_44,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_45,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_46,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_40,c_0_21]) ).
cnf(c_0_47,negated_conjecture,
( intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class
| ~ member(not_subclass_element(x,null_class),universal_class) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class)
| member(not_subclass_element(x,null_class),universal_class) ),
inference(spm,[status(thm)],[c_0_22,c_0_43]) ).
cnf(c_0_49,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_33]) ).
cnf(c_0_50,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_46])]) ).
cnf(c_0_51,negated_conjecture,
not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_47]),c_0_48]) ).
cnf(c_0_52,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X2,unordered_pair(X1,X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( subclass(intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x),null_class)
| ~ member(not_subclass_element(null_class,null_class),unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_51]),c_0_51]),c_0_51]),c_0_51]),c_0_51]) ).
cnf(c_0_54,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_55,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_56,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(regular(unordered_pair(X1,X1)),X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_21]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(X1,intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x))
| ~ member(not_subclass_element(null_class,null_class),unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_53]),c_0_33]) ).
cnf(c_0_58,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
( intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x) = null_class
| member(not_subclass_element(null_class,null_class),x) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_51]),c_0_51]),c_0_51]) ).
cnf(c_0_60,plain,
null_class = unordered_pair(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_56,c_0_26]) ).
cnf(c_0_61,negated_conjecture,
x != null_class,
prove_corollary_2_to_number_of_elements_in_class_3 ).
cnf(c_0_62,negated_conjecture,
( member(not_subclass_element(null_class,null_class),x)
| subclass(x,null_class) ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(X1,intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x))
| ~ member(not_subclass_element(null_class,null_class),universal_class) ),
inference(spm,[status(thm)],[c_0_57,c_0_42]) ).
cnf(c_0_64,plain,
( intersection(X1,X2) = X2
| ~ subclass(X2,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
( intersection(complement(unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)))),x) = unordered_pair(universal_class,universal_class)
| member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),x) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]) ).
cnf(c_0_66,negated_conjecture,
x != unordered_pair(universal_class,universal_class),
inference(rw,[status(thm)],[c_0_61,c_0_60]) ).
cnf(c_0_67,negated_conjecture,
( member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),x)
| subclass(x,unordered_pair(universal_class,universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_60]),c_0_60]),c_0_60]) ).
cnf(c_0_68,negated_conjecture,
( ~ member(X1,complement(unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)))))
| ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),universal_class)
| ~ member(X1,x) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_44]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]),c_0_60]) ).
cnf(c_0_69,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_70,negated_conjecture,
member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),x),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]),c_0_67]) ).
cnf(c_0_71,negated_conjecture,
( member(X1,unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))))
| ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),universal_class)
| ~ member(X1,x) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_22]) ).
cnf(c_0_72,negated_conjecture,
member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),universal_class),
inference(spm,[status(thm)],[c_0_22,c_0_70]) ).
cnf(c_0_73,negated_conjecture,
( member(X1,unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))))
| ~ member(X1,x) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
cnf(c_0_74,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_54,c_0_44]) ).
cnf(c_0_75,negated_conjecture,
( X1 = not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_40,c_0_73]) ).
cnf(c_0_76,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
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_40,c_0_27]) ).
cnf(c_0_78,plain,
( subclass(X1,intersection(X2,X1))
| ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_27]) ).
cnf(c_0_79,negated_conjecture,
( not_subclass_element(x,X1) = not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))
| subclass(x,X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_27]) ).
cnf(c_0_80,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
prove_corollary_2_to_number_of_elements_in_class_2 ).
cnf(c_0_81,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_54,c_0_76]) ).
cnf(c_0_82,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_83,negated_conjecture,
( subclass(x,intersection(X1,x))
| ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(rw,[status(thm)],[c_0_80,c_0_24]) ).
cnf(c_0_85,plain,
( intersection(X1,X2) = X1
| ~ subclass(X1,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_81]) ).
cnf(c_0_86,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_82]) ).
cnf(c_0_87,negated_conjecture,
( intersection(X1,x) = x
| ~ member(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_83]),c_0_58])]) ).
cnf(c_0_88,negated_conjecture,
unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class)) != x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_51]),c_0_51]) ).
cnf(c_0_89,plain,
( intersection(unordered_pair(X1,X1),X2) = unordered_pair(X1,X1)
| ~ member(X1,intersection(unordered_pair(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_90,negated_conjecture,
intersection(unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),X1),x) = x,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_42]),c_0_72])]) ).
cnf(c_0_91,negated_conjecture,
unordered_pair(not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class)),not_subclass_element(unordered_pair(universal_class,universal_class),unordered_pair(universal_class,universal_class))) != x,
inference(spm,[status(thm)],[c_0_88,c_0_60]) ).
cnf(c_0_92,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_70])]),c_0_91]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET099-6 : 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
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 09:35:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 64.07/64.15 % Version : CSE_E---1.5
% 64.07/64.15 % Problem : theBenchmark.p
% 64.07/64.15 % Proof found
% 64.07/64.15 % SZS status Theorem for theBenchmark.p
% 64.07/64.15 % SZS output start Proof
% See solution above
% 64.15/64.16 % Total time : 63.580000 s
% 64.15/64.16 % SZS output end Proof
% 64.15/64.16 % Total time : 63.588000 s
%------------------------------------------------------------------------------