TSTP Solution File: NUM078-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM078-1 : 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 : n002.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 10:26:23 EDT 2023
% Result : Unsatisfiable 0.88s 1.01s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 92
% Syntax : Number of formulae : 124 ( 12 unt; 80 typ; 0 def)
% Number of atoms : 85 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 75 ( 34 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 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 : 64 ( 64 usr; 20 con; 0-3 aty)
% Number of variables : 64 ( 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 ).
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,
y: $i ).
tff(decl_101,type,
u: $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(prove_corollary_2_to_well_ordering_property7_3,negated_conjecture,
member(u,intersection(u,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_well_ordering_property7_3) ).
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(c_0_12,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_13,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
limit_ordinals ).
cnf(c_0_14,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_15,plain,
( member(X1,complement(kind_1_ordinals))
| ~ member(X1,limit_ordinals) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
( X1 = null_class
| member(regular(X1),X1) ),
regularity1 ).
cnf(c_0_17,plain,
( ~ member(X1,kind_1_ordinals)
| ~ member(X1,limit_ordinals) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_19,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_20,plain,
( intersection(limit_ordinals,X1) = null_class
| ~ member(regular(intersection(limit_ordinals,X1)),kind_1_ordinals) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( intersection(X1,X2) = null_class
| member(regular(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_22,plain,
intersection(limit_ordinals,kind_1_ordinals) = null_class,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( member(X1,limit_ordinals)
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_24,plain,
( ~ member(X1,kind_1_ordinals)
| ~ member(X1,null_class) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_25,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_26,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_27,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_28,plain,
~ member(X1,null_class),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_24]) ).
cnf(c_0_29,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_25,c_0_16]) ).
cnf(c_0_30,plain,
( X1 = null_class
| ~ member(X2,regular(X1))
| ~ member(X2,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_31,plain,
( regular(unordered_pair(X1,X1)) = X1
| unordered_pair(X1,X1) = null_class ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
member(u,intersection(u,y)),
prove_corollary_2_to_well_ordering_property7_3 ).
cnf(c_0_33,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X2,unordered_pair(X1,X1))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,unordered_pair(X1,X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_31]) ).
cnf(c_0_35,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_36,negated_conjecture,
member(u,u),
inference(spm,[status(thm)],[c_0_12,c_0_32]) ).
cnf(c_0_37,plain,
( unordered_pair(X1,X1) = null_class
| ~ member(X1,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( member(u,X1)
| ~ subclass(u,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_40,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_41,negated_conjecture,
unordered_pair(u,u) = null_class,
inference(spm,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM078-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.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 : Fri Aug 25 09:09:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.88/1.01 % Version : CSE_E---1.5
% 0.88/1.01 % Problem : theBenchmark.p
% 0.88/1.01 % Proof found
% 0.88/1.01 % SZS status Theorem for theBenchmark.p
% 0.88/1.01 % SZS output start Proof
% See solution above
% 0.88/1.01 % Total time : 0.425000 s
% 0.88/1.01 % SZS output end Proof
% 0.88/1.01 % Total time : 0.431000 s
%------------------------------------------------------------------------------