TSTP Solution File: SET098-7 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET098-7 : 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 : n024.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 0.19s 0.66s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 67
% Syntax : Number of formulae : 104 ( 19 unt; 50 typ; 0 def)
% Number of atoms : 99 ( 53 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 75 ( 30 ~; 45 |; 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 : 67 ( 41 >; 26 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 9 con; 0-3 aty)
% Number of variables : 67 ( 7 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,
member_of: $i > $i ).
tff(decl_70,type,
member_of1: $i > $i ).
tff(decl_71,type,
x: $i ).
cnf(only_member_in_singleton,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(existence_of_null_class,axiom,
~ member(X1,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
cnf(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(null_class_is_unique,axiom,
( X1 = null_class
| member(not_subclass_element(X1,null_class),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_unique) ).
cnf(equality1,axiom,
( X1 = X2
| member(not_subclass_element(X1,X2),X1)
| member(not_subclass_element(X2,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).
cnf(unordered_pair_equals_singleton1,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
cnf(singleton_is_null_class,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
cnf(corollary_to_unordered_pair_axiom1,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X1,X2) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
cnf(number_of_elements_in_class,axiom,
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1))
| singleton(not_subclass_element(X1,null_class)) = X1
| X1 = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',number_of_elements_in_class) ).
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(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(commutativity_of_unordered_pair,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
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(c_0_17,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
only_member_in_singleton ).
cnf(c_0_18,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_19,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_20,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_21,axiom,
~ member(X1,null_class),
existence_of_null_class ).
cnf(c_0_22,plain,
( X1 = X2
| ~ member(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_24,axiom,
( X1 = null_class
| member(not_subclass_element(X1,null_class),X1) ),
null_class_is_unique ).
cnf(c_0_25,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,axiom,
( X1 = X2
| member(not_subclass_element(X1,X2),X1)
| member(not_subclass_element(X2,X1),X2) ),
equality1 ).
cnf(c_0_28,plain,
( not_subclass_element(unordered_pair(X1,X1),null_class) = X1
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_29,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
unordered_pair_equals_singleton1 ).
cnf(c_0_30,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X2,unordered_pair(X1,X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,unordered_pair(X1,X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_21]) ).
cnf(c_0_32,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
singleton_is_null_class ).
cnf(c_0_33,axiom,
( ~ member(X1,universal_class)
| unordered_pair(X1,X2) != null_class ),
corollary_to_unordered_pair_axiom1 ).
cnf(c_0_34,plain,
( unordered_pair(X2,X1) = unordered_pair(X2,X2)
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_35,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X1,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_37,axiom,
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(singleton(not_subclass_element(X1,null_class))),X1))
| singleton(not_subclass_element(X1,null_class)) = X1
| X1 = null_class ),
number_of_elements_in_class ).
cnf(c_0_38,plain,
( unordered_pair(X1,X2) = unordered_pair(X1,X1)
| unordered_pair(X2,X3) != null_class ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
unordered_pair(universal_class,universal_class) = null_class,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,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_41,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_42,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
prove_corollary_1_to_number_of_elements_in_class_2 ).
cnf(c_0_43,plain,
( X1 = null_class
| unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class)) = X1
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(unordered_pair(not_subclass_element(X1,null_class),not_subclass_element(X1,null_class))),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_44,plain,
unordered_pair(X1,universal_class) = unordered_pair(X1,X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
commutativity_of_unordered_pair ).
cnf(c_0_46,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_40,c_0_18]) ).
cnf(c_0_47,plain,
( intersection(X1,X2) = null_class
| member(not_subclass_element(intersection(X1,X2),null_class),X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_24]) ).
cnf(c_0_48,negated_conjecture,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(rw,[status(thm)],[c_0_42,c_0_18]) ).
cnf(c_0_49,plain,
( unordered_pair(universal_class,not_subclass_element(X1,null_class)) = X1
| X1 = null_class
| member(not_subclass_element(intersection(complement(unordered_pair(universal_class,not_subclass_element(X1,null_class))),X1),null_class),intersection(complement(unordered_pair(universal_class,not_subclass_element(X1,null_class))),X1)) ),
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_43,c_0_44]),c_0_45]),c_0_44]),c_0_45]),c_0_44]),c_0_45]) ).
cnf(c_0_50,negated_conjecture,
intersection(complement(unordered_pair(universal_class,not_subclass_element(x,null_class))),x) = null_class,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_44]),c_0_45]) ).
cnf(c_0_51,negated_conjecture,
unordered_pair(universal_class,not_subclass_element(x,null_class)) != x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_44]),c_0_45]) ).
cnf(c_0_52,negated_conjecture,
x != null_class,
prove_corollary_1_to_number_of_elements_in_class_3 ).
cnf(c_0_53,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET098-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 10:22:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.66 % Version : CSE_E---1.5
% 0.19/0.66 % Problem : theBenchmark.p
% 0.19/0.66 % Proof found
% 0.19/0.66 % SZS status Theorem for theBenchmark.p
% 0.19/0.66 % SZS output start Proof
% See solution above
% 0.19/0.67 % Total time : 0.091000 s
% 0.19/0.67 % SZS output end Proof
% 0.19/0.67 % Total time : 0.096000 s
%------------------------------------------------------------------------------