TSTP Solution File: NUM042-1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM042-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n027.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 : Tue Aug 22 10:50:53 EDT 2023
% Result : Unsatisfiable 264.54s 238.05s
% Output : CNFRefutation 264.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 87
% Syntax : Number of formulae : 102 ( 8 unt; 79 typ; 0 def)
% Number of atoms : 41 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 16 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 63 ( 63 usr; 19 con; 0-3 aty)
% Number of variables : 47 (; 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ section > maps > homomorphism > compatible > well_ordering > transitive > subclass > member > irreflexive > connected > asymmetric > single_valued_class > operation > one_to_one > inductive > function > segment > restrict > recursion > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordinal_multiply > ordinal_add > ordered_pair > not_well_ordering > not_subclass_element > least > intersection > image > cross_product > compose > apply > #nlpp > symmetrization_of > sum_class > successor > singleton > single_valued3 > single_valued2 > single_valued1 > second > rotate > rest_of > regular > recursion_equation_functions > range_of > power_class > inverse > integer_of > flip > first > domain_of > diagonalise > compose_class > complement > cantor > x > universal_class > union_of_range_map > successor_relation > subset_relation > singleton_relation > rest_relation > ordinal_numbers > omega > null_class > limit_ordinals > kind_1_ordinals > identity_relation > element_relation > domain_relation > composition_function > choice > application_function > add_relation
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(omega,type,
omega: $i ).
tff(null_class,type,
null_class: $i ).
tff(limit_ordinals,type,
limit_ordinals: $i ).
tff(kind_1_ordinals,type,
kind_1_ordinals: $i ).
tff(rotate,type,
rotate: $i > $i ).
tff(rest_relation,type,
rest_relation: $i ).
tff(subclass,type,
subclass: ( $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(single_valued_class,type,
single_valued_class: $i > $o ).
tff(operation,type,
operation: $i > $o ).
tff(sum_class,type,
sum_class: $i > $i ).
tff(single_valued3,type,
single_valued3: $i > $i ).
tff(x,type,
x: $i ).
tff(maps,type,
maps: ( $i * $i * $i ) > $o ).
tff(compose_class,type,
compose_class: $i > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(compatible,type,
compatible: ( $i * $i * $i ) > $o ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(regular,type,
regular: $i > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(singleton_relation,type,
singleton_relation: $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(element_relation,type,
element_relation: $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(second,type,
second: $i > $i ).
tff(union_of_range_map,type,
union_of_range_map: $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff(symmetric_difference,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(application_function,type,
application_function: $i ).
tff(flip,type,
flip: $i > $i ).
tff(power_class,type,
power_class: $i > $i ).
tff(transitive,type,
transitive: ( $i * $i ) > $o ).
tff(well_ordering,type,
well_ordering: ( $i * $i ) > $o ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(ordinal_numbers,type,
ordinal_numbers: $i ).
tff(choice,type,
choice: $i ).
tff(connected,type,
connected: ( $i * $i ) > $o ).
tff(subset_relation,type,
subset_relation: $i ).
tff(ordinal_multiply,type,
ordinal_multiply: ( $i * $i ) > $i ).
tff(restrict,type,
restrict: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(section,type,
section: ( $i * $i * $i ) > $o ).
tff(ordinal_add,type,
ordinal_add: ( $i * $i ) > $i ).
tff(recursion,type,
recursion: ( $i * $i * $i ) > $i ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(irreflexive,type,
irreflexive: ( $i * $i ) > $o ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
tff(first,type,
first: $i > $i ).
tff(integer_of,type,
integer_of: $i > $i ).
tff(diagonalise,type,
diagonalise: $i > $i ).
tff(homomorphism,type,
homomorphism: ( $i * $i * $i ) > $o ).
tff(single_valued2,type,
single_valued2: $i > $i ).
tff(least,type,
least: ( $i * $i ) > $i ).
tff(cantor,type,
cantor: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff(inductive,type,
inductive: $i > $o ).
tff(recursion_equation_functions,type,
recursion_equation_functions: $i > $i ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff(add_relation,type,
add_relation: $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(composition_function,type,
composition_function: $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(domain_relation,type,
domain_relation: $i ).
tff(rest_of,type,
rest_of: $i > $i ).
tff(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(segment,type,
segment: ( $i * $i * $i ) > $i ).
tff(symmetrization_of,type,
symmetrization_of: $i > $i ).
tff(single_valued1,type,
single_valued1: $i > $i ).
tff(successor,type,
successor: $i > $i ).
tff(asymmetric,type,
asymmetric: ( $i * $i ) > $o ).
tff(successor_relation,type,
successor_relation: $i ).
tff(identity_relation,type,
identity_relation: $i ).
tff(not_homomorphism1,type,
not_homomorphism1: ( $i * $i * $i ) > $i ).
tff(universal_class,type,
universal_class: $i ).
tff(not_well_ordering,type,
not_well_ordering: ( $i * $i ) > $i ).
tff(f_1114,axiom,
subclass(x,complement(identity_relation)),
file(unknown,unknown) ).
tff(f_234,axiom,
! [Xr,X,Y] : ( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_191,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_63,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_808,axiom,
! [X,Y] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) ),
file(unknown,unknown) ).
tff(f_1116,axiom,
~ irreflexive(x,domain_of(symmetrization_of(x))),
file(unknown,unknown) ).
tff(c_318,plain,
subclass(x,complement(identity_relation)),
inference(cnfTransformation,[status(thm)],[f_1114]) ).
tff(c_56,plain,
! [Xr_63,X_64,Y_65] : ( intersection(Xr_63,cross_product(X_64,Y_65)) = restrict(Xr_63,X_64,Y_65) ),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_1357,plain,
! [X_439,Y_440] :
( subclass(X_439,Y_440)
| member(not_subclass_element(X_439,Y_440),X_439) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_42,plain,
! [Z_46,X_47,Y_48] :
( member(Z_46,X_47)
| ~ member(Z_46,intersection(X_47,Y_48)) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_453074,plain,
! [X_11258,Y_11259,Y_11260] :
( member(not_subclass_element(intersection(X_11258,Y_11259),Y_11260),X_11258)
| subclass(intersection(X_11258,Y_11259),Y_11260) ),
inference(resolution,[status(thm)],[c_1357,c_42]) ).
tff(c_2,plain,
! [U_3,Y_2,X_1] :
( member(U_3,Y_2)
| ~ member(U_3,X_1)
| ~ subclass(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_740643,plain,
! [X_15235,Y_15236,Y_15237,Y_15238] :
( member(not_subclass_element(intersection(X_15235,Y_15236),Y_15237),Y_15238)
| ~ subclass(X_15235,Y_15238)
| subclass(intersection(X_15235,Y_15236),Y_15237) ),
inference(resolution,[status(thm)],[c_453074,c_2]) ).
tff(c_6,plain,
! [X_6,Y_7] :
( subclass(X_6,Y_7)
| ~ member(not_subclass_element(X_6,Y_7),Y_7) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_742198,plain,
! [X_15245,Y_15246,Y_15247] :
( ~ subclass(X_15245,Y_15246)
| subclass(intersection(X_15245,Y_15247),Y_15246) ),
inference(resolution,[status(thm)],[c_740643,c_6]) ).
tff(c_750656,plain,
! [Xr_15296,Y_15297,X_15298,Y_15299] :
( ~ subclass(Xr_15296,Y_15297)
| subclass(restrict(Xr_15296,X_15298,Y_15299),Y_15297) ),
inference(superposition,[status(thm),theory(equality)],[c_56,c_742198]) ).
tff(c_230,plain,
! [X_218,Y_219] :
( irreflexive(X_218,Y_219)
| ~ subclass(restrict(X_218,Y_219,Y_219),complement(identity_relation)) ),
inference(cnfTransformation,[status(thm)],[f_808]) ).
tff(c_750979,plain,
! [Xr_15300,Y_15301] :
( irreflexive(Xr_15300,Y_15301)
| ~ subclass(Xr_15300,complement(identity_relation)) ),
inference(resolution,[status(thm)],[c_750656,c_230]) ).
tff(c_751188,plain,
! [Y_15301] : irreflexive(x,Y_15301),
inference(resolution,[status(thm)],[c_318,c_750979]) ).
tff(c_320,plain,
~ irreflexive(x,domain_of(symmetrization_of(x))),
inference(cnfTransformation,[status(thm)],[f_1116]) ).
tff(c_751193,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_751188,c_320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM042-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 15:13:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 264.54/238.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 264.54/238.06
% 264.54/238.06 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 264.64/238.09
% 264.64/238.09 Inference rules
% 264.64/238.09 ----------------------
% 264.64/238.09 #Ref : 13
% 264.64/238.09 #Sup : 204438
% 264.64/238.09 #Fact : 10
% 264.64/238.09 #Define : 0
% 264.64/238.09 #Split : 1539
% 264.64/238.09 #Chain : 0
% 264.64/238.09 #Close : 0
% 264.64/238.09
% 264.64/238.09 Ordering : KBO
% 264.64/238.09
% 264.64/238.09 Simplification rules
% 264.64/238.09 ----------------------
% 264.64/238.09 #Subsume : 74447
% 264.64/238.09 #Demod : 52637
% 264.64/238.09 #Tautology : 19733
% 264.64/238.09 #SimpNegUnit : 3967
% 264.64/238.09 #BackRed : 2941
% 264.64/238.09
% 264.64/238.09 #Partial instantiations: 0
% 264.64/238.09 #Strategies tried : 1
% 264.64/238.09
% 264.64/238.09 Timing (in seconds)
% 264.64/238.09 ----------------------
% 264.64/238.09 Preprocessing : 0.81
% 264.64/238.09 Parsing : 0.44
% 264.64/238.09 CNF conversion : 0.06
% 264.64/238.09 Main loop : 236.19
% 264.64/238.09 Inferencing : 28.08
% 264.64/238.09 Reduction : 101.93
% 264.64/238.09 Demodulation : 70.94
% 264.64/238.09 BG Simplification : 0.86
% 264.64/238.09 Subsumption : 78.73
% 264.64/238.09 Abstraction : 1.47
% 264.64/238.09 MUC search : 0.00
% 264.64/238.09 Cooper : 0.00
% 264.64/238.09 Total : 237.06
% 264.64/238.09 Index Insertion : 0.00
% 264.64/238.09 Index Deletion : 0.00
% 264.64/238.09 Index Matching : 0.00
% 264.64/238.09 BG Taut test : 0.00
%------------------------------------------------------------------------------