%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET168-6 : 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 : n006.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 08:38:10 PM UTC 2025
% Result : Unsatisfiable 101.68s 82.18s
% Output : CNFRefutation 101.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 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 : 49 ( 49 usr; 15 con; 0-3 aty)
% Number of variables : 33 ( 33 !; 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 > z > y > x > 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(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,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(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(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(z,type,
z: $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_778,axiom,
member(x,z),
file(unknown,unknown) ).
tff(f_80,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_228,axiom,
! [X,Y] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
file(unknown,unknown) ).
tff(f_223,axiom,
! [Z,X] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_200,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_780,axiom,
~ member(x,union(y,z)),
file(unknown,unknown) ).
tff(f_216,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(c_226,plain,
member(x,z),
inference(cnfTransformation,[status(thm)],[f_778]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_960,plain,
! [U_341,Y_342,X_343] :
( member(U_341,Y_342)
| ~ member(U_341,X_343)
| ~ subclass(X_343,Y_342) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_1356,plain,
! [Y_373] :
( member(x,Y_373)
| ~ subclass(z,Y_373) ),
inference(resolution,[status(thm)],[c_226,c_960]) ).
tff(c_1370,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[c_8,c_1356]) ).
tff(c_52,plain,
! [X_59,Y_60] : ( complement(intersection(complement(X_59),complement(Y_60))) = union(X_59,Y_60) ),
inference(cnfTransformation,[status(thm)],[f_228]) ).
tff(c_1442,plain,
! [Z_380,X_381] :
( member(Z_380,X_381)
| member(Z_380,complement(X_381))
| ~ member(Z_380,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_223]) ).
tff(c_285347,plain,
! [Z_6960,X_6961,Y_6962] :
( member(Z_6960,intersection(complement(X_6961),complement(Y_6962)))
| member(Z_6960,union(X_6961,Y_6962))
| ~ member(Z_6960,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_52,c_1442]) ).
tff(c_44,plain,
! [Z_49,Y_51,X_50] :
( member(Z_49,Y_51)
| ~ member(Z_49,intersection(X_50,Y_51)) ),
inference(cnfTransformation,[status(thm)],[f_200]) ).
tff(c_317754,plain,
! [Z_7605,Y_7606,X_7607] :
( member(Z_7605,complement(Y_7606))
| member(Z_7605,union(X_7607,Y_7606))
| ~ member(Z_7605,universal_class) ),
inference(resolution,[status(thm)],[c_285347,c_44]) ).
tff(c_228,plain,
~ member(x,union(y,z)),
inference(cnfTransformation,[status(thm)],[f_780]) ).
tff(c_317845,plain,
( member(x,complement(z))
| ~ member(x,universal_class) ),
inference(resolution,[status(thm)],[c_317754,c_228]) ).
tff(c_317931,plain,
member(x,complement(z)),
inference(demodulation,[status(thm),theory(equality)],[c_1370,c_317845]) ).
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_317952,plain,
~ member(x,z),
inference(resolution,[status(thm)],[c_317931,c_48]) ).
tff(c_317962,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_226,c_317952]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET168-6 : 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 : n006.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 20:13:52 EDT 2025
% 0.13/0.34 % CPUTime :
% 101.68/82.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 101.68/82.18
% 101.68/82.18 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------