%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET082-6 : 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 : n017.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 08:37:53 PM UTC 2025
% Result : Unsatisfiable 11.80s 3.82s
% Output : CNFRefutation 11.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 21 ~; 26 |; 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 : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 9 con; 0-3 aty)
% Number of variables : 37 ( 37 !; 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_647,axiom,
singleton(x) != null_class,
file(unknown,unknown) ).
tff(f_482,axiom,
function(choice),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_119,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file(unknown,unknown) ).
tff(f_489,axiom,
! [Y] :
( ~ member(Y,universal_class)
| ( Y = null_class )
| member(apply(choice,Y),Y) ),
file(unknown,unknown) ).
tff(f_102,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file(unknown,unknown) ).
tff(f_464,axiom,
! [Xf,X] :
( ~ function(Xf)
| ~ member(X,universal_class)
| member(image(Xf,X),universal_class) ),
file(unknown,unknown) ).
tff(f_478,axiom,
! [Xf,Y] : ( sum_class(image(Xf,singleton(Y))) = apply(Xf,Y) ),
file(unknown,unknown) ).
tff(f_390,axiom,
! [X] :
( ~ member(X,universal_class)
| member(sum_class(X),universal_class) ),
file(unknown,unknown) ).
tff(f_645,axiom,
~ member(x,universal_class),
file(unknown,unknown) ).
tff(c_186,plain,
singleton(x) != null_class,
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_138,plain,
function(choice),
inference(cnfTransformation,[status(thm)],[f_482]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_216,plain,
! [X_183,Y_184] : member(unordered_pair(X_183,Y_184),universal_class),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_218,plain,
! [X_24] : member(singleton(X_24),universal_class),
inference(superposition,[status(thm),theory(equality)],[c_24,c_216]) ).
tff(c_1442,plain,
! [Y_339] :
( member(apply(choice,Y_339),Y_339)
| ( null_class = Y_339 )
| ~ member(Y_339,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_489]) ).
tff(c_815,plain,
! [Y_276,U_277,X_278] :
( ( Y_276 = U_277 )
| ( X_278 = U_277 )
| ~ member(U_277,unordered_pair(X_278,Y_276)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_840,plain,
! [X_24,U_277] :
( ( X_24 = U_277 )
| ( X_24 = U_277 )
| ~ member(U_277,singleton(X_24)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_815]) ).
tff(c_1454,plain,
! [X_24] :
( ( apply(choice,singleton(X_24)) = X_24 )
| ( singleton(X_24) = null_class )
| ~ member(singleton(X_24),universal_class) ),
inference(resolution,[status(thm)],[c_1442,c_840]) ).
tff(c_1480,plain,
! [X_24] :
( ( apply(choice,singleton(X_24)) = X_24 )
| ( singleton(X_24) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_1454]) ).
tff(c_130,plain,
! [Xf_129,X_130] :
( member(image(Xf_129,X_130),universal_class)
| ~ member(X_130,universal_class)
| ~ function(Xf_129) ),
inference(cnfTransformation,[status(thm)],[f_464]) ).
tff(c_386,plain,
! [Xf_237,Y_238] : ( sum_class(image(Xf_237,singleton(Y_238))) = apply(Xf_237,Y_238) ),
inference(cnfTransformation,[status(thm)],[f_478]) ).
tff(c_108,plain,
! [X_111] :
( member(sum_class(X_111),universal_class)
| ~ member(X_111,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_390]) ).
tff(c_9172,plain,
! [Xf_741,Y_742] :
( member(apply(Xf_741,Y_742),universal_class)
| ~ member(image(Xf_741,singleton(Y_742)),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_386,c_108]) ).
tff(c_9183,plain,
! [Xf_129,Y_742] :
( member(apply(Xf_129,Y_742),universal_class)
| ~ member(singleton(Y_742),universal_class)
| ~ function(Xf_129) ),
inference(resolution,[status(thm)],[c_130,c_9172]) ).
tff(c_9188,plain,
! [Xf_743,Y_744] :
( member(apply(Xf_743,Y_744),universal_class)
| ~ function(Xf_743) ),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_9183]) ).
tff(c_9205,plain,
! [X_24] :
( member(X_24,universal_class)
| ~ function(choice)
| ( singleton(X_24) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_1480,c_9188]) ).
tff(c_9210,plain,
! [X_745] :
( member(X_745,universal_class)
| ( singleton(X_745) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_9205]) ).
tff(c_184,plain,
~ member(x,universal_class),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_9245,plain,
singleton(x) = null_class,
inference(resolution,[status(thm)],[c_9210,c_184]) ).
tff(c_9265,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_186,c_9245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET082-6 : 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 : n017.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 19:58:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 11.80/3.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.80/3.83
% 11.80/3.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------