TSTP Solution File: SET510-6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET510-6 : 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 : n028.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 14:34:24 EDT 2023
% Result : Unsatisfiable 0.19s 0.65s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 70
% Syntax : Number of formulae : 105 ( 18 unt; 56 typ; 0 def)
% Number of atoms : 89 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 38 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 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 : 46 ( 46 usr; 12 con; 0-3 aty)
% Number of variables : 81 ( 9 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 ).
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(regularity1,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
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(restriction2,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
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(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
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(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(prove_corollary_to_singleton_is_null_class_1,negated_conjecture,
singleton(universal_class) != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_singleton_is_null_class_1) ).
cnf(c_0_14,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_15,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_16,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_17,plain,
( X1 = null_class
| member(regular(X1),X2)
| ~ subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_19,plain,
( complement(X1) = null_class
| ~ member(regular(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_20,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
( restrict(X1,singleton(X2),universal_class) != null_class
| ~ member(X2,domain_of(X1)) ),
domain1 ).
cnf(c_0_22,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_23,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_24,axiom,
intersection(cross_product(X1,X2),X3) = restrict(X3,X1,X2),
restriction2 ).
cnf(c_0_25,plain,
complement(universal_class) = null_class,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_27,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_21,c_0_22]),c_0_23]) ).
cnf(c_0_28,plain,
intersection(cross_product(X1,X2),X3) = intersection(X3,cross_product(X1,X2)),
inference(rw,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_29,plain,
( ~ member(X1,null_class)
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_30,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_31,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_32,plain,
( intersection(cross_product(unordered_pair(X1,X1),universal_class),X2) != null_class
| ~ member(X1,domain_of(X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
intersection(X1,null_class) = null_class,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_20]) ).
cnf(c_0_34,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_31,c_0_15]) ).
cnf(c_0_35,plain,
~ member(X1,domain_of(null_class)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_37,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_34])]) ).
cnf(c_0_38,plain,
domain_of(null_class) = null_class,
inference(spm,[status(thm)],[c_0_35,c_0_15]) ).
cnf(c_0_39,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_40,plain,
( intersection(unordered_pair(X1,X1),X1) = null_class
| unordered_pair(X1,X1) = null_class ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
~ member(X1,null_class),
inference(rw,[status(thm)],[c_0_35,c_0_38]) ).
cnf(c_0_42,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X2,unordered_pair(X1,X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_43,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_44,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
singleton(universal_class) != null_class,
prove_corollary_to_singleton_is_null_class_1 ).
cnf(c_0_46,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X1,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
unordered_pair(universal_class,universal_class) != null_class,
inference(rw,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_48,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_44]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET510-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 14:06:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.65 % Version : CSE_E---1.5
% 0.19/0.65 % Problem : theBenchmark.p
% 0.19/0.65 % Proof found
% 0.19/0.65 % SZS status Theorem for theBenchmark.p
% 0.19/0.65 % SZS output start Proof
% See solution above
% 0.19/0.66 % Total time : 0.074000 s
% 0.19/0.66 % SZS output end Proof
% 0.19/0.66 % Total time : 0.078000 s
%------------------------------------------------------------------------------