TSTP Solution File: SET098-6 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET098-6 : 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 : n017.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 63.65s 63.85s
% Output : CNFRefutation 63.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 64
% Syntax : Number of formulae : 127 ( 29 unt; 48 typ; 0 def)
% Number of atoms : 145 ( 46 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 124 ( 58 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 1 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 : 103 ( 8 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/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(prove_corollary_1_to_number_of_elements_in_class_1,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(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(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
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(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(prove_corollary_1_to_number_of_elements_in_class_3,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_3) ).
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(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(prove_corollary_1_to_number_of_elements_in_class_2,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_2) ).
cnf(c_0_16,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_17,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_18,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_19,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_20,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
prove_corollary_1_to_number_of_elements_in_class_1 ).
cnf(c_0_24,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_25,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_26,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_27,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
~ member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),x),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_27]),c_0_20]) ).
cnf(c_0_31,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_32,negated_conjecture,
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_28,c_0_29]) ).
cnf(c_0_33,plain,
subclass(null_class,X1),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_34,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_35,negated_conjecture,
intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) = null_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(X1,complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ~ member(X1,x) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_30]) ).
cnf(c_0_37,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_38,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_39,negated_conjecture,
( member(X1,unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ member(X1,x) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_20]) ).
cnf(c_0_40,negated_conjecture,
( X1 = not_subclass_element(x,null_class)
| ~ member(X1,x) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
x != null_class,
prove_corollary_1_to_number_of_elements_in_class_3 ).
cnf(c_0_42,negated_conjecture,
not_subclass_element(x,null_class) = regular(x),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_19]),c_0_41]) ).
cnf(c_0_43,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_44,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_45,negated_conjecture,
( X1 = regular(x)
| ~ member(X1,x) ),
inference(rw,[status(thm)],[c_0_40,c_0_42]) ).
cnf(c_0_46,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_47,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_48,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_38,c_0_19]) ).
cnf(c_0_49,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_37]),c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( not_subclass_element(x,X1) = regular(x)
| subclass(x,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_51,plain,
( member(not_subclass_element(complement(complement(X1)),X2),X1)
| subclass(complement(complement(X1)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_44]) ).
cnf(c_0_52,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_47]),c_0_30]) ).
cnf(c_0_53,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_48])]) ).
cnf(c_0_54,negated_conjecture,
( member(regular(x),X1)
| subclass(x,complement(X1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_43,c_0_51]) ).
cnf(c_0_56,plain,
( subclass(X1,complement(complement(X2)))
| ~ member(not_subclass_element(X1,complement(complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_49]) ).
cnf(c_0_57,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X2,unordered_pair(X1,X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_43,c_0_29]) ).
cnf(c_0_59,negated_conjecture,
( subclass(x,complement(complement(X1)))
| ~ member(regular(x),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_54]) ).
cnf(c_0_60,plain,
( complement(complement(X1)) = X1
| ~ subclass(X1,complement(complement(X1))) ),
inference(spm,[status(thm)],[c_0_31,c_0_55]) ).
cnf(c_0_61,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_56,c_0_26]) ).
cnf(c_0_62,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(regular(unordered_pair(X1,X1)),X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_19]) ).
cnf(c_0_63,plain,
( intersection(X1,X2) = X2
| ~ subclass(X2,intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
prove_corollary_1_to_number_of_elements_in_class_2 ).
cnf(c_0_65,negated_conjecture,
( complement(complement(X1)) = x
| ~ member(regular(x),X1)
| ~ subclass(complement(complement(X1)),x) ),
inference(spm,[status(thm)],[c_0_31,c_0_59]) ).
cnf(c_0_66,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
cnf(c_0_67,plain,
null_class = unordered_pair(universal_class,universal_class),
inference(spm,[status(thm)],[c_0_62,c_0_22]) ).
cnf(c_0_68,negated_conjecture,
~ subclass(x,null_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_35]),c_0_41]) ).
cnf(c_0_69,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(rw,[status(thm)],[c_0_64,c_0_24]) ).
cnf(c_0_70,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_38,c_0_26]) ).
cnf(c_0_71,negated_conjecture,
( X1 = x
| ~ member(regular(x),X1)
| ~ subclass(X1,x) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_66]) ).
cnf(c_0_72,negated_conjecture,
not_subclass_element(x,unordered_pair(universal_class,universal_class)) = regular(x),
inference(rw,[status(thm)],[c_0_42,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
member(regular(x),x),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_42]),c_0_68]) ).
cnf(c_0_74,negated_conjecture,
unordered_pair(regular(x),regular(x)) != x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_42]),c_0_42]) ).
cnf(c_0_75,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_70])]) ).
cnf(c_0_76,negated_conjecture,
~ subclass(unordered_pair(regular(x),regular(x)),x),
inference(sr,[status(thm)],[inference(cn,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_39]),c_0_67]),c_0_72]),c_0_67]),c_0_72]),c_0_67]),c_0_72]),c_0_67]),c_0_72]),c_0_73])]),c_0_74]) ).
cnf(c_0_77,plain,
( subclass(unordered_pair(X1,X1),X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_75]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_73])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET098-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 08:46:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 63.65/63.85 % Version : CSE_E---1.5
% 63.65/63.85 % Problem : theBenchmark.p
% 63.65/63.85 % Proof found
% 63.65/63.85 % SZS status Theorem for theBenchmark.p
% 63.65/63.85 % SZS output start Proof
% See solution above
% 63.65/63.86 % Total time : 63.281000 s
% 63.65/63.86 % SZS output end Proof
% 63.65/63.86 % Total time : 63.288000 s
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