TSTP Solution File: NUM190-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM190-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 10:26:49 EDT 2023
% Result : Unsatisfiable 0.18s 0.61s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 85
% Syntax : Number of formulae : 101 ( 11 unt; 78 typ; 0 def)
% Number of atoms : 37 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 14 |; 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 : 62 ( 62 usr; 18 con; 0-3 aty)
% Number of variables : 21 ( 3 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 ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
cnf(prove_omega_is_not_null_1,negated_conjecture,
omega = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_omega_is_not_null_1) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(inductive1,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inductive1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(omega_in_universal,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',omega_in_universal) ).
cnf(c_0_7,axiom,
inductive(omega),
omega_is_inductive1 ).
cnf(c_0_8,negated_conjecture,
omega = null_class,
prove_omega_is_not_null_1 ).
cnf(c_0_9,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_10,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_11,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
inductive1 ).
cnf(c_0_12,plain,
inductive(null_class),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( X1 = null_class
| member(X2,X1)
| ~ member(X2,null_class) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
member(null_class,null_class),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_16,plain,
( X1 = null_class
| member(null_class,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( complement(X1) = null_class
| ~ member(null_class,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
member(omega,universal_class),
omega_in_universal ).
cnf(c_0_19,plain,
( ~ member(X1,null_class)
| ~ member(null_class,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_20,plain,
member(null_class,universal_class),
inference(rw,[status(thm)],[c_0_18,c_0_8]) ).
cnf(c_0_21,plain,
~ member(null_class,X1),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_22,plain,
$false,
inference(sr,[status(thm)],[c_0_20,c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM190-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 16:59:50 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.58 start to proof: theBenchmark
% 0.18/0.61 % Version : CSE_E---1.5
% 0.18/0.61 % Problem : theBenchmark.p
% 0.18/0.61 % Proof found
% 0.18/0.61 % SZS status Theorem for theBenchmark.p
% 0.18/0.61 % SZS output start Proof
% See solution above
% 0.18/0.62 % Total time : 0.019000 s
% 0.18/0.62 % SZS output end Proof
% 0.18/0.62 % Total time : 0.024000 s
%------------------------------------------------------------------------------