%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET063-6 : 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 : 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 08:37:46 PM UTC 2025
% Result : Unsatisfiable 7.18s 2.76s
% Output : CNFRefutation 7.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 39 ( 39 usr; 9 con; 0-3 aty)
% Number of variables : 26 ( 26 !; 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 > 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(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_646,axiom,
x != null_class,
file(unknown,unknown) ).
tff(f_644,axiom,
subclass(x,null_class),
file(unknown,unknown) ).
tff(f_470,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_207,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(c_186,plain,
x != null_class,
inference(cnfTransformation,[status(thm)],[f_646]) ).
tff(c_184,plain,
subclass(x,null_class),
inference(cnfTransformation,[status(thm)],[f_644]) ).
tff(c_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_627,plain,
! [U_265,Y_266,X_267] :
( member(U_265,Y_266)
| ~ member(U_265,X_267)
| ~ subclass(X_267,Y_266) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_662,plain,
! [X_131,Y_266] :
( member(regular(X_131),Y_266)
| ~ subclass(X_131,Y_266)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_132,c_627]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_1216,plain,
! [X_331,Y_332] :
( member(regular(X_331),Y_332)
| ~ subclass(X_331,Y_332)
| ( null_class = X_331 ) ),
inference(resolution,[status(thm)],[c_132,c_627]) ).
tff(c_237,plain,
! [Z_201,X_202] :
( ~ member(Z_201,X_202)
| ~ member(Z_201,complement(X_202)) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_246,plain,
! [X_202] :
( ~ member(regular(complement(X_202)),X_202)
| ( complement(X_202) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_237]) ).
tff(c_1266,plain,
! [Y_333] :
( ~ subclass(complement(Y_333),Y_333)
| ( complement(Y_333) = null_class ) ),
inference(resolution,[status(thm)],[c_1216,c_246]) ).
tff(c_1288,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[c_8,c_1266]) ).
tff(c_48,plain,
! [Z_55,X_56] :
( ~ member(Z_55,X_56)
| ~ member(Z_55,complement(X_56)) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_1332,plain,
! [Z_336] :
( ~ member(Z_336,universal_class)
| ~ member(Z_336,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1288,c_48]) ).
tff(c_1339,plain,
! [X_131] :
( ~ member(regular(X_131),null_class)
| ~ subclass(X_131,universal_class)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_662,c_1332]) ).
tff(c_1631,plain,
! [X_359] :
( ~ member(regular(X_359),null_class)
| ( null_class = X_359 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1339]) ).
tff(c_1646,plain,
! [X_360] :
( ~ subclass(X_360,null_class)
| ( null_class = X_360 ) ),
inference(resolution,[status(thm)],[c_662,c_1631]) ).
tff(c_1661,plain,
x = null_class,
inference(resolution,[status(thm)],[c_184,c_1646]) ).
tff(c_1669,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_186,c_1661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET063-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.08 % 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
% 0.09/0.27 % Computer : n023.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Tue Apr 8 19:56:09 EDT 2025
% 0.09/0.28 % CPUTime :
% 7.18/2.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.18/2.77
% 7.18/2.77 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------