TSTP Solution File: NUM145-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM145-1 : 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 : n022.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 10:26:40 EDT 2023
% Result : Unsatisfiable 57.07s 57.16s
% Output : CNFRefutation 57.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 108
% Syntax : Number of formulae : 235 ( 55 unt; 79 typ; 0 def)
% Number of atoms : 291 ( 73 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 242 ( 107 ~; 135 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 103 ( 60 >; 43 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 63 ( 63 usr; 19 con; 0-3 aty)
% Number of variables : 253 ( 36 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,
symmetrization_of: $i > $i ).
tff(decl_79,type,
irreflexive: ( $i * $i ) > $o ).
tff(decl_80,type,
connected: ( $i * $i ) > $o ).
tff(decl_81,type,
transitive: ( $i * $i ) > $o ).
tff(decl_82,type,
asymmetric: ( $i * $i ) > $o ).
tff(decl_83,type,
segment: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
well_ordering: ( $i * $i ) > $o ).
tff(decl_85,type,
least: ( $i * $i ) > $i ).
tff(decl_86,type,
not_well_ordering: ( $i * $i ) > $i ).
tff(decl_87,type,
section: ( $i * $i * $i ) > $o ).
tff(decl_88,type,
ordinal_numbers: $i ).
tff(decl_89,type,
kind_1_ordinals: $i ).
tff(decl_90,type,
limit_ordinals: $i ).
tff(decl_91,type,
rest_of: $i > $i ).
tff(decl_92,type,
rest_relation: $i ).
tff(decl_93,type,
recursion_equation_functions: $i > $i ).
tff(decl_94,type,
union_of_range_map: $i ).
tff(decl_95,type,
recursion: ( $i * $i * $i ) > $i ).
tff(decl_96,type,
ordinal_add: ( $i * $i ) > $i ).
tff(decl_97,type,
add_relation: $i ).
tff(decl_98,type,
ordinal_multiply: ( $i * $i ) > $i ).
tff(decl_99,type,
integer_of: $i > $i ).
tff(decl_100,type,
x: $i ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(limit_ordinals,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',limit_ordinals) ).
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(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(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(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(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(successor,axiom,
union(X1,singleton(X1)) = successor(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_corollary_1,negated_conjecture,
member(successor(x),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(prove_corollary_2,negated_conjecture,
~ member(x,successor(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2) ).
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(equal_implies_subclass2,axiom,
( subclass(X2,X1)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',equal_implies_subclass2) ).
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(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(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(domain2,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',domain2) ).
cnf(restriction1,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(cartesian_product3,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).
cnf(cartesian_product1,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
cnf(rest_of4,axiom,
( member(ordered_pair(X1,X3),rest_of(X2))
| ~ member(X1,domain_of(X2))
| restrict(X2,X1,universal_class) != X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',rest_of4) ).
cnf(omega_in_universal,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_in_universal) ).
cnf(c_0_29,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_30,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
limit_ordinals ).
cnf(c_0_31,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_32,plain,
( member(X1,complement(kind_1_ordinals))
| ~ member(X1,limit_ordinals) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_34,plain,
( ~ member(X1,kind_1_ordinals)
| ~ member(X1,limit_ordinals) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_36,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_37,plain,
( intersection(limit_ordinals,X1) = null_class
| ~ member(regular(intersection(limit_ordinals,X1)),kind_1_ordinals) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_39,plain,
intersection(limit_ordinals,kind_1_ordinals) = null_class,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
( member(X1,limit_ordinals)
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_41,plain,
( ~ member(X1,kind_1_ordinals)
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_42,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_43,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_44,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_45,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_39]),c_0_41]) ).
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_42,c_0_33]) ).
cnf(c_0_47,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_48,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_49,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_50,plain,
( X1 = null_class
| member(regular(X1),X2)
| ~ subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_33]) ).
cnf(c_0_51,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
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_48,c_0_49]) ).
cnf(c_0_53,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_54,plain,
( X1 = null_class
| member(regular(X1),universal_class) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X1,universal_class)
| ~ member(X1,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_54,c_0_49]) ).
cnf(c_0_57,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X1,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_58,plain,
unordered_pair(universal_class,universal_class) = null_class,
inference(spm,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_59,plain,
( regular(unordered_pair(X1,X2)) = X2
| unordered_pair(X1,X2) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_54,c_0_46]) ).
cnf(c_0_60,axiom,
union(X1,singleton(X1)) = successor(X1),
successor ).
cnf(c_0_61,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_62,plain,
~ member(universal_class,universal_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_58]),c_0_45]) ).
cnf(c_0_63,plain,
( unordered_pair(X1,X2) = null_class
| member(X1,universal_class)
| member(X2,universal_class) ),
inference(spm,[status(thm)],[c_0_54,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
member(successor(x),universal_class),
prove_corollary_1 ).
cnf(c_0_65,plain,
union(X1,unordered_pair(X1,X1)) = successor(X1),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_67,negated_conjecture,
~ member(x,successor(x)),
prove_corollary_2 ).
cnf(c_0_68,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_69,plain,
( unordered_pair(X1,universal_class) = null_class
| member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,negated_conjecture,
member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),universal_class),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_71,axiom,
( subclass(X2,X1)
| X1 != X2 ),
equal_implies_subclass2 ).
cnf(c_0_72,negated_conjecture,
~ member(x,complement(intersection(complement(x),complement(unordered_pair(x,x))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_65]),c_0_66]) ).
cnf(c_0_73,plain,
( unordered_pair(X1,universal_class) = null_class
| member(X1,complement(X2))
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_75,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_76,negated_conjecture,
( member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),X1)
| ~ subclass(universal_class,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_70]) ).
cnf(c_0_77,plain,
subclass(X1,X1),
inference(er,[status(thm)],[c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( unordered_pair(x,universal_class) = null_class
| member(x,intersection(complement(x),complement(unordered_pair(x,x)))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_79,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_74,c_0_43]) ).
cnf(c_0_80,plain,
( member(not_subclass_element(X1,X2),X3)
| subclass(X1,X2)
| ~ subclass(X1,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
( member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),complement(X1))
| member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_76]),c_0_77])]) ).
cnf(c_0_82,negated_conjecture,
( unordered_pair(x,universal_class) = null_class
| member(x,complement(unordered_pair(x,x))) ),
inference(spm,[status(thm)],[c_0_36,c_0_78]) ).
cnf(c_0_83,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X1)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_75]) ).
cnf(c_0_84,plain,
( subclass(X1,intersection(X2,X1))
| ~ member(not_subclass_element(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_75]) ).
cnf(c_0_85,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_51]) ).
cnf(c_0_86,plain,
( member(not_subclass_element(intersection(X1,X2),X3),X2)
| subclass(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_75]) ).
cnf(c_0_87,negated_conjecture,
( ~ member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),X1)
| ~ subclass(universal_class,complement(X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_76]) ).
cnf(c_0_88,negated_conjecture,
( unordered_pair(complement(intersection(complement(x),complement(unordered_pair(x,x)))),complement(intersection(complement(x),complement(unordered_pair(x,x))))) = null_class
| member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),intersection(complement(x),complement(unordered_pair(x,x)))) ),
inference(spm,[status(thm)],[c_0_57,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
( unordered_pair(x,universal_class) = null_class
| ~ member(x,unordered_pair(x,x)) ),
inference(spm,[status(thm)],[c_0_31,c_0_82]) ).
cnf(c_0_90,plain,
( member(not_subclass_element(universal_class,X1),complement(X2))
| member(not_subclass_element(universal_class,X1),X2)
| subclass(universal_class,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_75]) ).
cnf(c_0_91,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_79,c_0_83]) ).
cnf(c_0_92,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_93,plain,
subclass(X1,intersection(universal_class,X1)),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_94,plain,
subclass(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_74,c_0_86]) ).
cnf(c_0_95,negated_conjecture,
( ~ member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),X1)
| ~ member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),X2)
| ~ subclass(universal_class,complement(intersection(X2,X1))) ),
inference(spm,[status(thm)],[c_0_87,c_0_43]) ).
cnf(c_0_96,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_97,plain,
( intersection(complement(X1),X2) = null_class
| ~ member(regular(intersection(complement(X1),X2)),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_35]) ).
cnf(c_0_98,negated_conjecture,
member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),intersection(complement(x),complement(unordered_pair(x,x)))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_88]),c_0_70])]),c_0_45]) ).
cnf(c_0_99,negated_conjecture,
unordered_pair(x,universal_class) = null_class,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_53]),c_0_69]) ).
cnf(c_0_100,plain,
( member(not_subclass_element(universal_class,complement(X1)),X1)
| subclass(universal_class,complement(X1)) ),
inference(spm,[status(thm)],[c_0_74,c_0_90]) ).
cnf(c_0_101,plain,
subclass(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_91,c_0_86]) ).
cnf(c_0_102,plain,
intersection(universal_class,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94])]) ).
cnf(c_0_103,negated_conjecture,
( ~ member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),X1)
| ~ subclass(universal_class,complement(intersection(X1,unordered_pair(X2,complement(intersection(complement(x),complement(unordered_pair(x,x)))))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_70])]) ).
cnf(c_0_104,plain,
intersection(complement(X1),X1) = null_class,
inference(spm,[status(thm)],[c_0_97,c_0_38]) ).
cnf(c_0_105,axiom,
( restrict(X2,singleton(X1),universal_class) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
domain2 ).
cnf(c_0_106,axiom,
intersection(X1,cross_product(X2,X3)) = restrict(X1,X2,X3),
restriction1 ).
cnf(c_0_107,negated_conjecture,
member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),complement(x)),
inference(spm,[status(thm)],[c_0_29,c_0_98]) ).
cnf(c_0_108,negated_conjecture,
~ member(x,universal_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_99]),c_0_45]) ).
cnf(c_0_109,plain,
subclass(universal_class,complement(null_class)),
inference(spm,[status(thm)],[c_0_45,c_0_100]) ).
cnf(c_0_110,plain,
subclass(X1,intersection(X1,universal_class)),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_111,plain,
subclass(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_74,c_0_83]) ).
cnf(c_0_112,negated_conjecture,
( ~ member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),complement(unordered_pair(X1,complement(intersection(complement(x),complement(unordered_pair(x,x)))))))
| ~ subclass(universal_class,complement(null_class)) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_113,plain,
( intersection(X1,complement(X2)) = null_class
| ~ member(regular(intersection(X1,complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_114,plain,
( intersection(intersection(X1,X2),X3) = null_class
| member(regular(intersection(intersection(X1,X2),X3)),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_115,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_116,plain,
( intersection(X2,cross_product(unordered_pair(X1,X1),universal_class)) = null_class
| member(X1,domain_of(X2))
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_61]),c_0_106]) ).
cnf(c_0_117,negated_conjecture,
( member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),X1)
| ~ subclass(complement(x),X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_107]) ).
cnf(c_0_118,negated_conjecture,
unordered_pair(x,x) = null_class,
inference(spm,[status(thm)],[c_0_108,c_0_56]) ).
cnf(c_0_119,plain,
complement(null_class) = universal_class,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_109]),c_0_51])]) ).
cnf(c_0_120,plain,
intersection(X1,universal_class) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_110]),c_0_111])]) ).
cnf(c_0_121,negated_conjecture,
~ member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),complement(unordered_pair(X1,complement(intersection(complement(x),complement(unordered_pair(x,x))))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_109])]) ).
cnf(c_0_122,plain,
intersection(intersection(X1,X2),complement(X1)) = null_class,
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_123,axiom,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4) ),
cartesian_product3 ).
cnf(c_0_124,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_61]),c_0_61]) ).
cnf(c_0_125,negated_conjecture,
( intersection(X1,cross_product(unordered_pair(complement(complement(x)),complement(complement(x))),universal_class)) = null_class
| member(complement(complement(x)),domain_of(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_51])]),c_0_118]),c_0_119]),c_0_120]),c_0_118]),c_0_119]),c_0_120]),c_0_118]),c_0_119]),c_0_120]) ).
cnf(c_0_126,negated_conjecture,
member(complement(intersection(complement(x),complement(unordered_pair(x,x)))),unordered_pair(X1,complement(intersection(complement(x),complement(unordered_pair(x,x)))))),
inference(spm,[status(thm)],[c_0_121,c_0_81]) ).
cnf(c_0_127,plain,
( ~ member(X1,intersection(X2,X3))
| ~ member(X1,complement(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_122]),c_0_45]) ).
cnf(c_0_128,axiom,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
cartesian_product1 ).
cnf(c_0_129,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4))
| ~ member(X3,X4)
| ~ member(X1,X2) ),
inference(rw,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_130,negated_conjecture,
( cross_product(unordered_pair(complement(complement(x)),complement(complement(x))),universal_class) = null_class
| member(complement(complement(x)),domain_of(universal_class)) ),
inference(spm,[status(thm)],[c_0_102,c_0_125]) ).
cnf(c_0_131,negated_conjecture,
member(complement(intersection(complement(x),universal_class)),unordered_pair(X1,complement(intersection(complement(x),universal_class)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_118]),c_0_119]),c_0_119]) ).
cnf(c_0_132,plain,
( subclass(intersection(X1,X2),X3)
| ~ member(not_subclass_element(intersection(X1,X2),X3),complement(X1)) ),
inference(spm,[status(thm)],[c_0_127,c_0_75]) ).
cnf(c_0_133,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)],[inference(spm,[status(thm)],[c_0_68,c_0_83]),c_0_102]),c_0_102]),c_0_102]) ).
cnf(c_0_134,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_75]) ).
cnf(c_0_135,axiom,
( member(ordered_pair(X1,X3),rest_of(X2))
| ~ member(X1,domain_of(X2))
| restrict(X2,X1,universal_class) != X3 ),
rest_of4 ).
cnf(c_0_136,plain,
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_128,c_0_124]) ).
cnf(c_0_137,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_102]) ).
cnf(c_0_138,negated_conjecture,
( member(complement(complement(x)),domain_of(universal_class))
| ~ member(X1,unordered_pair(complement(complement(x)),complement(complement(x))))
| ~ member(X2,universal_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_45]) ).
cnf(c_0_139,negated_conjecture,
member(complement(complement(x)),unordered_pair(X1,complement(complement(x)))),
inference(spm,[status(thm)],[c_0_131,c_0_120]) ).
cnf(c_0_140,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),complement(X1)) ),
inference(spm,[status(thm)],[c_0_132,c_0_120]) ).
cnf(c_0_141,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(spm,[status(thm)],[c_0_74,c_0_133]) ).
cnf(c_0_142,plain,
( member(not_subclass_element(complement(complement(X1)),X2),X1)
| subclass(complement(complement(X1)),X2) ),
inference(spm,[status(thm)],[c_0_134,c_0_133]) ).
cnf(c_0_143,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),rest_of(X2))
| intersection(X2,cross_product(X1,universal_class)) != X3
| ~ member(X1,domain_of(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_106]),c_0_124]) ).
cnf(c_0_144,plain,
( member(X1,universal_class)
| ~ member(unordered_pair(null_class,unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_56]),c_0_137]) ).
cnf(c_0_145,negated_conjecture,
( member(unordered_pair(null_class,unordered_pair(x,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(x,X2)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_129,c_0_118]) ).
cnf(c_0_146,negated_conjecture,
( member(complement(complement(x)),domain_of(universal_class))
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_147,axiom,
member(omega,universal_class),
omega_in_universal ).
cnf(c_0_148,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_149,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_74,c_0_142]) ).
cnf(c_0_150,plain,
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(intersection(X2,cross_product(X1,universal_class)),intersection(X2,cross_product(X1,universal_class))))),rest_of(X2))
| ~ member(X1,domain_of(X2)) ),
inference(er,[status(thm)],[c_0_143]) ).
cnf(c_0_151,negated_conjecture,
( ~ member(x,X1)
| ~ member(X2,X3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_108]) ).
cnf(c_0_152,negated_conjecture,
member(complement(complement(x)),domain_of(universal_class)),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_153,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_148]),c_0_149])]) ).
cnf(c_0_154,negated_conjecture,
~ member(x,domain_of(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_118]),c_0_151]) ).
cnf(c_0_155,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153]),c_0_154]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM145-1 : 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
% 0.12/0.34 % Computer : n022.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 : Fri Aug 25 12:30:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 57.07/57.16 % Version : CSE_E---1.5
% 57.07/57.16 % Problem : theBenchmark.p
% 57.07/57.16 % Proof found
% 57.07/57.16 % SZS status Theorem for theBenchmark.p
% 57.07/57.16 % SZS output start Proof
% See solution above
% 57.17/57.17 % Total time : 56.573000 s
% 57.17/57.17 % SZS output end Proof
% 57.17/57.17 % Total time : 56.582000 s
%------------------------------------------------------------------------------