%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET083-6 : 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 : n027.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 6.35s 2.49s
% Output : CNFRefutation 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 21 ~; 28 |; 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 : 36 ( 36 !; 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_645,axiom,
member(x,universal_class),
file(unknown,unknown) ).
tff(f_644,axiom,
singleton(x) = singleton(y),
file(unknown,unknown) ).
tff(f_470,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
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_109,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_474,axiom,
! [X] :
( ( X = null_class )
| ( intersection(X,regular(X)) = null_class ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_207,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(f_647,axiom,
x != y,
file(unknown,unknown) ).
tff(c_186,plain,
member(x,universal_class),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_184,plain,
singleton(y) = singleton(x),
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_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_888,plain,
! [Y_277,U_278,X_279] :
( ( Y_277 = U_278 )
| ( X_279 = U_278 )
| ~ member(U_278,unordered_pair(X_279,Y_277)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_997,plain,
! [X_292,U_293] :
( ( X_292 = U_293 )
| ( X_292 = U_293 )
| ~ member(U_293,singleton(X_292)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_888]) ).
tff(c_1032,plain,
! [X_294] :
( ( regular(singleton(X_294)) = X_294 )
| ( singleton(X_294) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_997]) ).
tff(c_1047,plain,
( ( regular(singleton(x)) = y )
| ( singleton(y) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_1032]) ).
tff(c_1050,plain,
( ( regular(singleton(x)) = y )
| ( singleton(x) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_184,c_1047]) ).
tff(c_1054,plain,
singleton(x) = null_class,
inference(splitLeft,[status(thm)],[c_1050]) ).
tff(c_389,plain,
! [X_231,Y_232] :
( member(X_231,unordered_pair(X_231,Y_232))
| ~ member(X_231,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_392,plain,
! [X_24] :
( member(X_24,singleton(X_24))
| ~ member(X_24,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_389]) ).
tff(c_1106,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1054,c_392]) ).
tff(c_1116,plain,
member(x,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_186,c_1106]) ).
tff(c_134,plain,
! [X_132] :
( ( intersection(X_132,regular(X_132)) = null_class )
| ( null_class = X_132 ) ),
inference(cnfTransformation,[status(thm)],[f_474]) ).
tff(c_360,plain,
! [Z_220,X_221,Y_222] :
( member(Z_220,X_221)
| ~ member(Z_220,intersection(X_221,Y_222)) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_363,plain,
! [Z_220,X_132] :
( member(Z_220,X_132)
| ~ member(Z_220,null_class)
| ( null_class = X_132 ) ),
inference(superposition,[status(thm),theory(equality)],[c_134,c_360]) ).
tff(c_1166,plain,
! [X_304] :
( member(x,X_304)
| ( null_class = X_304 ) ),
inference(resolution,[status(thm)],[c_1116,c_363]) ).
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_1352,plain,
! [X_321] :
( ~ member(x,X_321)
| ( complement(X_321) = null_class ) ),
inference(resolution,[status(thm)],[c_1166,c_48]) ).
tff(c_1383,plain,
complement(null_class) = null_class,
inference(resolution,[status(thm)],[c_1116,c_1352]) ).
tff(c_1796,plain,
! [Z_329] :
( ~ member(Z_329,null_class)
| ~ member(Z_329,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1383,c_48]) ).
tff(c_1801,plain,
~ member(x,null_class),
inference(resolution,[status(thm)],[c_1116,c_1796]) ).
tff(c_1824,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1116,c_1801]) ).
tff(c_1826,plain,
singleton(x) != null_class,
inference(splitRight,[status(thm)],[c_1050]) ).
tff(c_188,plain,
y != x,
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_1825,plain,
regular(singleton(x)) = y,
inference(splitRight,[status(thm)],[c_1050]) ).
tff(c_1029,plain,
! [X_292] :
( ( regular(singleton(X_292)) = X_292 )
| ( singleton(X_292) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_997]) ).
tff(c_1859,plain,
( ( y = x )
| ( singleton(x) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_1825,c_1029]) ).
tff(c_1872,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1826,c_188,c_1859]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET083-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.13 % 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 : n027.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 19:58:36 EDT 2025
% 0.14/0.35 % CPUTime :
% 6.35/2.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.63/2.49
% 6.63/2.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------