%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET098-7 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n021.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 08:37:58 PM UTC 2025
% Result : Unsatisfiable 256.66s 232.05s
% Output : CNFRefutation 256.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 9 con; 0-3 aty)
% Number of variables : 14 ( 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ 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 > second > rotate > regular > range_of > power_class > member_of1 > member_of > inverse > flip > first > domain_of > diagonalise > complement > cantor > x > universal_class > successor_relation > subset_relation > omega > null_class > identity_relation > element_relation > choice
%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(x,type,
x: $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(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(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(member_of1,type,
member_of1: $i > $i ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(member_of,type,
member_of: $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(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(domain_of,type,
domain_of: $i > $i ).
tff(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $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_723,axiom,
! [Z] : ~ member(Z,null_class),
file(unknown,unknown) ).
tff(f_955,axiom,
singleton(not_subclass_element(x,null_class)) != x,
file(unknown,unknown) ).
tff(f_957,axiom,
x != null_class,
file(unknown,unknown) ).
tff(f_737,axiom,
! [Z] :
( ( Z = null_class )
| member(not_subclass_element(Z,null_class),Z) ),
file(unknown,unknown) ).
tff(f_191,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_953,axiom,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file(unknown,unknown) ).
tff(f_951,axiom,
! [X] :
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
| ( singleton(not_subclass_element(X,null_class)) = X )
| ( X = null_class ) ),
file(unknown,unknown) ).
tff(c_206,plain,
! [Z_207] : ~ member(Z_207,null_class),
inference(cnfTransformation,[status(thm)],[f_723]) ).
tff(c_286,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(cnfTransformation,[status(thm)],[f_955]) ).
tff(c_288,plain,
x != null_class,
inference(cnfTransformation,[status(thm)],[f_957]) ).
tff(c_212,plain,
! [Z_210] :
( member(not_subclass_element(Z_210,null_class),Z_210)
| ( null_class = Z_210 ) ),
inference(cnfTransformation,[status(thm)],[f_737]) ).
tff(c_1238,plain,
! [Z_386,Y_387,X_388] :
( member(Z_386,Y_387)
| ~ member(Z_386,intersection(X_388,Y_387)) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_485354,plain,
! [X_5974,Y_5975] :
( member(not_subclass_element(intersection(X_5974,Y_5975),null_class),Y_5975)
| ( intersection(X_5974,Y_5975) = null_class ) ),
inference(resolution,[status(thm)],[c_212,c_1238]) ).
tff(c_284,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
inference(cnfTransformation,[status(thm)],[f_953]) ).
tff(c_485600,plain,
intersection(complement(singleton(not_subclass_element(x,null_class))),x) = null_class,
inference(resolution,[status(thm)],[c_485354,c_284]) ).
tff(c_282,plain,
! [X_269] :
( ( null_class = X_269 )
| ( singleton(not_subclass_element(X_269,null_class)) = X_269 )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X_269,null_class))),X_269),null_class),intersection(complement(singleton(not_subclass_element(X_269,null_class))),X_269)) ),
inference(cnfTransformation,[status(thm)],[f_951]) ).
tff(c_488106,plain,
( ( x = null_class )
| ( singleton(not_subclass_element(x,null_class)) = x )
| member(not_subclass_element(null_class,null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(superposition,[status(thm),theory(equality)],[c_485600,c_282]) ).
tff(c_488140,plain,
( ( x = null_class )
| ( singleton(not_subclass_element(x,null_class)) = x )
| member(not_subclass_element(null_class,null_class),null_class) ),
inference(demodulation,[status(thm),theory(equality)],[c_485600,c_488106]) ).
tff(c_488142,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_206,c_286,c_288,c_488140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET098-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.00/0.08 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.07/0.28 % Computer : n021.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Tue Apr 8 20:02:13 EDT 2025
% 0.07/0.28 % CPUTime :
% 256.66/232.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 256.66/232.05
% 256.66/232.05 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------