%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET507-6 : TPTP v9.0.0. 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 : n023.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 : Wed Apr 9 08:38:39 PM UTC 2025
% Result : Unsatisfiable 7.04s 2.59s
% Output : CNFRefutation 7.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 46 ( 46 usr; 12 con; 0-3 aty)
% Number of variables : 31 ( 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ maps > homomorphism > compatible > subclass > member > single_valued_class > operation > one_to_one > inductive > function > restrict > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordered_pair > not_subclass_element > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > single_valued3 > single_valued2 > single_valued1 > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > compose_class > complement > cantor > universal_class > successor_relation > subset_relation > singleton_relation > omega > null_class > identity_relation > element_relation > domain_relation > composition_function > choice > application_function
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(omega,type,
omega: $i ).
tff(null_class,type,
null_class: $i ).
tff(rotate,type,
rotate: $i > $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(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,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(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(choice,type,
choice: $i ).
tff(subset_relation,type,
subset_relation: $i ).
tff(restrict,type,
restrict: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
tff(first,type,
first: $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(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(domain,type,
domain: ( $i * $i * $i ) > $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(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(single_valued1,type,
single_valued1: $i > $i ).
tff(successor,type,
successor: $i > $i ).
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(f_80,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_778,axiom,
subclass(universal_class,null_class),
file(unknown,unknown) ).
tff(f_100,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file(unknown,unknown) ).
tff(f_383,axiom,
member(omega,universal_class),
file(unknown,unknown) ).
tff(f_483,axiom,
! [X] :
( ( X = null_class )
| ( intersection(X,regular(X)) = null_class ) ),
file(unknown,unknown) ).
tff(f_194,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_216,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_226,plain,
subclass(universal_class,null_class),
inference(cnfTransformation,[status(thm)],[f_778]) ).
tff(c_418,plain,
! [Y_282,X_283] :
( ( Y_282 = X_283 )
| ~ subclass(Y_282,X_283)
| ~ subclass(X_283,Y_282) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_448,plain,
( ( universal_class = null_class )
| ~ subclass(null_class,universal_class) ),
inference(resolution,[status(thm)],[c_226,c_418]) ).
tff(c_468,plain,
universal_class = null_class,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_448]) ).
tff(c_22,plain,
! [X_22,Y_23] : member(unordered_pair(X_22,Y_23),universal_class),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_483,plain,
! [X_22,Y_23] : member(unordered_pair(X_22,Y_23),null_class),
inference(demodulation,[status(thm),theory(equality)],[c_468,c_22]) ).
tff(c_104,plain,
member(omega,universal_class),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_488,plain,
member(omega,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_468,c_104]) ).
tff(c_134,plain,
! [X_132] :
( ( intersection(X_132,regular(X_132)) = null_class )
| ( null_class = X_132 ) ),
inference(cnfTransformation,[status(thm)],[f_483]) ).
tff(c_371,plain,
! [Z_265,X_266,Y_267] :
( member(Z_265,X_266)
| ~ member(Z_265,intersection(X_266,Y_267)) ),
inference(cnfTransformation,[status(thm)],[f_194]) ).
tff(c_1669,plain,
! [Z_375,X_376] :
( member(Z_375,X_376)
| ~ member(Z_375,null_class)
| ( null_class = X_376 ) ),
inference(superposition,[status(thm),theory(equality)],[c_134,c_371]) ).
tff(c_1698,plain,
! [X_377] :
( member(omega,X_377)
| ( null_class = X_377 ) ),
inference(resolution,[status(thm)],[c_488,c_1669]) ).
tff(c_48,plain,
! [Z_55,X_56] :
( ~ member(Z_55,X_56)
| ~ member(Z_55,complement(X_56)) ),
inference(cnfTransformation,[status(thm)],[f_216]) ).
tff(c_1829,plain,
! [X_385] :
( ~ member(omega,X_385)
| ( complement(X_385) = null_class ) ),
inference(resolution,[status(thm)],[c_1698,c_48]) ).
tff(c_1871,plain,
complement(null_class) = null_class,
inference(resolution,[status(thm)],[c_488,c_1829]) ).
tff(c_2332,plain,
! [Z_402] :
( ~ member(Z_402,null_class)
| ~ member(Z_402,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1871,c_48]) ).
tff(c_2347,plain,
! [X_22,Y_23] : ~ member(unordered_pair(X_22,Y_23),null_class),
inference(resolution,[status(thm)],[c_483,c_2332]) ).
tff(c_2372,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_483,c_2347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET507-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n023.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 : Tue Apr 8 21:05:39 EDT 2025
% 0.13/0.34 % CPUTime :
% 7.04/2.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.04/2.60
% 7.04/2.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------