%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET027-7 : 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 : n004.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 08:37:35 PM UTC 2025
% Result : Unsatisfiable 82.93s 64.08s
% Output : CNFRefutation 82.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 29 ~; 35 |; 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 : 41 ( 41 usr; 11 con; 0-3 aty)
% Number of variables : 64 ( 64 !; 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 > z > 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(z,type,
z: $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_675,axiom,
~ subclass(x,z),
file(unknown,unknown) ).
tff(f_672,axiom,
subclass(x,y),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_199,axiom,
! [Z,X,Y] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_191,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_673,axiom,
subclass(y,z),
file(unknown,unknown) ).
tff(c_198,plain,
~ subclass(x,z),
inference(cnfTransformation,[status(thm)],[f_675]) ).
tff(c_194,plain,
subclass(x,y),
inference(cnfTransformation,[status(thm)],[f_672]) ).
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_61]) ).
tff(c_597,plain,
! [U_276,Y_277,X_278] :
( member(U_276,Y_277)
| ~ member(U_276,X_278)
| ~ subclass(X_278,Y_277) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_626,plain,
! [X_4,Y_5,Y_277] :
( member(not_subclass_element(X_4,Y_5),Y_277)
| ~ subclass(X_4,Y_277)
| subclass(X_4,Y_5) ),
inference(resolution,[status(thm)],[c_4,c_597]) ).
tff(c_1660,plain,
! [Z_382,X_383,Y_384] :
( member(Z_382,intersection(X_383,Y_384))
| ~ member(Z_382,Y_384)
| ~ member(Z_382,X_383) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
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_66]) ).
tff(c_247403,plain,
! [X_6443,X_6444,Y_6445] :
( subclass(X_6443,intersection(X_6444,Y_6445))
| ~ member(not_subclass_element(X_6443,intersection(X_6444,Y_6445)),Y_6445)
| ~ member(not_subclass_element(X_6443,intersection(X_6444,Y_6445)),X_6444) ),
inference(resolution,[status(thm)],[c_1660,c_6]) ).
tff(c_268286,plain,
! [X_6968,X_6969] :
( ~ member(not_subclass_element(X_6968,intersection(X_6969,X_6968)),X_6969)
| subclass(X_6968,intersection(X_6969,X_6968)) ),
inference(resolution,[status(thm)],[c_4,c_247403]) ).
tff(c_279129,plain,
! [X_7069,Y_7070] :
( ~ subclass(X_7069,Y_7070)
| subclass(X_7069,intersection(Y_7070,X_7069)) ),
inference(resolution,[status(thm)],[c_626,c_268286]) ).
tff(c_478,plain,
! [Z_254,Y_255,X_256] :
( member(Z_254,Y_255)
| ~ member(Z_254,intersection(X_256,Y_255)) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_228762,plain,
! [X_6035,Y_6036,Y_6037] :
( member(not_subclass_element(intersection(X_6035,Y_6036),Y_6037),Y_6036)
| subclass(intersection(X_6035,Y_6036),Y_6037) ),
inference(resolution,[status(thm)],[c_4,c_478]) ).
tff(c_228953,plain,
! [X_6038,Y_6039] : subclass(intersection(X_6038,Y_6039),Y_6039),
inference(resolution,[status(thm)],[c_228762,c_6]) ).
tff(c_14,plain,
! [Y_14,X_13] :
( ( Y_14 = X_13 )
| ~ subclass(Y_14,X_13)
| ~ subclass(X_13,Y_14) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_229020,plain,
! [X_6038,Y_6039] :
( ( intersection(X_6038,Y_6039) = Y_6039 )
| ~ subclass(Y_6039,intersection(X_6038,Y_6039)) ),
inference(resolution,[status(thm)],[c_228953,c_14]) ).
tff(c_279611,plain,
! [Y_7071,X_7072] :
( ( intersection(Y_7071,X_7072) = X_7072 )
| ~ subclass(X_7072,Y_7071) ),
inference(resolution,[status(thm)],[c_279129,c_229020]) ).
tff(c_279846,plain,
intersection(y,x) = x,
inference(resolution,[status(thm)],[c_194,c_279611]) ).
tff(c_457,plain,
! [X_251,Y_252] :
( subclass(X_251,Y_252)
| member(not_subclass_element(X_251,Y_252),X_251) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_42,plain,
! [Z_46,X_47,Y_48] :
( member(Z_46,X_47)
| ~ member(Z_46,intersection(X_47,Y_48)) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_472,plain,
! [X_47,Y_48,Y_252] :
( member(not_subclass_element(intersection(X_47,Y_48),Y_252),X_47)
| subclass(intersection(X_47,Y_48),Y_252) ),
inference(resolution,[status(thm)],[c_457,c_42]) ).
tff(c_279936,plain,
! [Y_252] :
( member(not_subclass_element(x,Y_252),y)
| subclass(intersection(y,x),Y_252) ),
inference(superposition,[status(thm),theory(equality)],[c_279846,c_472]) ).
tff(c_279981,plain,
! [Y_252] :
( member(not_subclass_element(x,Y_252),y)
| subclass(x,Y_252) ),
inference(demodulation,[status(thm),theory(equality)],[c_279846,c_279936]) ).
tff(c_196,plain,
subclass(y,z),
inference(cnfTransformation,[status(thm)],[f_673]) ).
tff(c_279851,plain,
intersection(z,y) = y,
inference(resolution,[status(thm)],[c_196,c_279611]) ).
tff(c_281318,plain,
! [Z_7074] :
( member(Z_7074,z)
| ~ member(Z_7074,y) ),
inference(superposition,[status(thm),theory(equality)],[c_279851,c_42]) ).
tff(c_290985,plain,
! [X_7182] :
( subclass(X_7182,z)
| ~ member(not_subclass_element(X_7182,z),y) ),
inference(resolution,[status(thm)],[c_281318,c_6]) ).
tff(c_290989,plain,
subclass(x,z),
inference(resolution,[status(thm)],[c_279981,c_290985]) ).
tff(c_291020,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_198,c_198,c_290989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET027-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.08/0.13 % 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
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 19:46:37 EDT 2025
% 0.13/0.35 % CPUTime :
% 82.93/64.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 82.93/64.08
% 82.93/64.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------