TSTP Solution File: NUM030-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM030-1 : 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 : n020.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 10:26:13 EDT 2023
% Result : Unsatisfiable 66.06s 66.23s
% Output : CNFRefutation 66.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 92
% Syntax : Number of formulae : 122 ( 20 unt; 79 typ; 0 def)
% Number of atoms : 72 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 26 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 65 ( 6 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(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(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(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(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
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(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(prove_symmetrization_property3_1,negated_conjecture,
symmetrization_of(x) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_1) ).
cnf(symmetrization,axiom,
union(X1,inverse(X1)) = symmetrization_of(X1),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',symmetrization) ).
cnf(inverse,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(prove_symmetrization_property3_2,negated_conjecture,
~ subclass(inverse(x),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetrization_property3_2) ).
cnf(c_0_13,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_14,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_15,plain,
( member(X1,universal_class)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,axiom,
( member(not_subclass_element(X1,X2),X1)
| subclass(X1,X2) ),
not_subclass_members1 ).
cnf(c_0_17,axiom,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),X2) ),
not_subclass_members2 ).
cnf(c_0_18,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_19,plain,
( member(not_subclass_element(X1,X2),universal_class)
| subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_21,plain,
( member(not_subclass_element(X1,complement(X2)),X2)
| subclass(X1,complement(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,plain,
( subclass(X1,complement(complement(X2)))
| ~ member(not_subclass_element(X1,complement(complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( subclass(complement(X1),X2)
| ~ member(not_subclass_element(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_24,axiom,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
subclass_implies_equal ).
cnf(c_0_25,plain,
subclass(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_26,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_23,c_0_18]),c_0_19]) ).
cnf(c_0_27,plain,
( complement(complement(X1)) = X1
| ~ subclass(complement(complement(X1)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
subclass(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_29,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_30,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_31,negated_conjecture,
symmetrization_of(x) = x,
prove_symmetrization_property3_1 ).
cnf(c_0_32,axiom,
union(X1,inverse(X1)) = symmetrization_of(X1),
symmetrization ).
cnf(c_0_33,axiom,
domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
inverse ).
cnf(c_0_34,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_35,plain,
( subclass(X1,X2)
| ~ member(not_subclass_element(X1,X2),complement(X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_36,plain,
( member(not_subclass_element(X1,complement(intersection(X2,X3))),X3)
| subclass(X1,complement(intersection(X2,X3))) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_37,negated_conjecture,
complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))) = x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
~ subclass(inverse(x),x),
prove_symmetrization_property3_2 ).
cnf(c_0_39,plain,
subclass(X1,complement(intersection(X2,complement(X1)))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))) = complement(x),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
~ subclass(domain_of(flip(cross_product(x,universal_class))),x),
inference(rw,[status(thm)],[c_0_38,c_0_33]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_29]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM030-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 15:23:30 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 66.06/66.23 % Version : CSE_E---1.5
% 66.06/66.23 % Problem : theBenchmark.p
% 66.06/66.23 % Proof found
% 66.06/66.23 % SZS status Theorem for theBenchmark.p
% 66.06/66.23 % SZS output start Proof
% See solution above
% 66.06/66.24 % Total time : 65.558000 s
% 66.06/66.24 % SZS output end Proof
% 66.06/66.24 % Total time : 65.568000 s
%------------------------------------------------------------------------------