%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET067-6 : 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/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 : n018.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 08:37:47 PM UTC 2025
% Result : Unsatisfiable 6.85s 2.50s
% Output : CNFRefutation 6.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 17 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 10 con; 0-3 aty)
% Number of variables : 33 ( 33 !; 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 > inverse > flip > first > domain_of > diagonalise > complement > cantor > y > 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(y,type,
y: $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(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_110,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_646,axiom,
~ subclass(singleton(x),unordered_pair(x,y)),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_124,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_103,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(c_18,plain,
! [X_18,Y_19] :
( member(X_18,unordered_pair(X_18,Y_19))
| ~ member(X_18,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_184,plain,
~ subclass(singleton(x),unordered_pair(x,y)),
inference(cnfTransformation,[status(thm)],[f_646]) ).
tff(c_4,plain,
! [X_4,Y_5] :
( subclass(X_4,Y_5)
| member(not_subclass_element(X_4,Y_5),X_4) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_611,plain,
! [Y_264,U_265,X_266] :
( ( Y_264 = U_265 )
| ( X_266 = U_265 )
| ~ member(U_265,unordered_pair(X_266,Y_264)) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_640,plain,
! [X_267,U_268] :
( ( X_267 = U_268 )
| ( X_267 = U_268 )
| ~ member(U_268,singleton(X_267)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_611]) ).
tff(c_2341,plain,
! [X_422,Y_423] :
( ( not_subclass_element(singleton(X_422),Y_423) = X_422 )
| subclass(singleton(X_422),Y_423) ),
inference(resolution,[status(thm)],[c_4,c_640]) ).
tff(c_2367,plain,
not_subclass_element(singleton(x),unordered_pair(x,y)) = x,
inference(resolution,[status(thm)],[c_2341,c_184]) ).
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_67]) ).
tff(c_2374,plain,
( subclass(singleton(x),unordered_pair(x,y))
| ~ member(x,unordered_pair(x,y)) ),
inference(superposition,[status(thm),theory(equality)],[c_2367,c_6]) ).
tff(c_2378,plain,
~ member(x,unordered_pair(x,y)),
inference(negUnitSimplification,[status(thm)],[c_184,c_2374]) ).
tff(c_2391,plain,
~ member(x,universal_class),
inference(resolution,[status(thm)],[c_18,c_2378]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_2371,plain,
( subclass(singleton(x),unordered_pair(x,y))
| member(x,singleton(x)) ),
inference(superposition,[status(thm),theory(equality)],[c_2367,c_4]) ).
tff(c_2377,plain,
member(x,singleton(x)),
inference(negUnitSimplification,[status(thm)],[c_184,c_2371]) ).
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_58]) ).
tff(c_2410,plain,
! [Y_428] :
( member(x,Y_428)
| ~ subclass(singleton(x),Y_428) ),
inference(resolution,[status(thm)],[c_2377,c_2]) ).
tff(c_2422,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[c_8,c_2410]) ).
tff(c_2432,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2391,c_2422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET067-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.12/0.13 % 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
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 19:56:32 EDT 2025
% 0.20/0.35 % CPUTime :
% 6.85/2.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.85/2.50
% 6.85/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------