%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET099-7 : 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/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 : n024.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 08:37:58 PM UTC 2025
% Result : Unsatisfiable 61.41s 45.84s
% Output : CNFRefutation 61.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 52 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 36 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 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; 9 con; 0-3 aty)
% Number of variables : 73 ( 73 !; 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 > member_of1 > member_of > 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(member_of1,type,
member_of1: $i > $i ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(member_of,type,
member_of: $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_954,axiom,
singleton(not_subclass_element(x,null_class)) != x,
file(unknown,unknown) ).
tff(f_956,axiom,
x != null_class,
file(unknown,unknown) ).
tff(f_952,axiom,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file(unknown,unknown) ).
tff(f_951,axiom,
! [X] :
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X))
| ( singleton(not_subclass_element(X,null_class)) = X )
| ( X = null_class ) ),
file(unknown,unknown) ).
tff(f_150,axiom,
! [U,X,V,Y] :
( ~ member(U,X)
| ~ member(V,Y)
| member(ordered_pair(U,V),cross_product(X,Y)) ),
file(unknown,unknown) ).
tff(f_660,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
file(unknown,unknown) ).
tff(f_743,axiom,
! [X,Y] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
file(unknown,unknown) ).
tff(f_119,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file(unknown,unknown) ).
tff(f_128,axiom,
! [X,Y] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
file(unknown,unknown) ).
tff(f_116,axiom,
! [Y,X] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_834,axiom,
! [X] :
( ~ member(X,universal_class)
| ( singleton(X) != null_class ) ),
file(unknown,unknown) ).
tff(f_817,axiom,
! [X] : member(singleton(X),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_842,axiom,
! [Y,X] :
( ~ member(Y,singleton(X))
| ( Y = X ) ),
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(c_286,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(cnfTransformation,[status(thm)],[f_954]) ).
tff(c_288,plain,
x != null_class,
inference(cnfTransformation,[status(thm)],[f_956]) ).
tff(c_284,plain,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(cnfTransformation,[status(thm)],[f_952]) ).
tff(c_106416,plain,
! [X_2233] :
( ( null_class = X_2233 )
| ( singleton(not_subclass_element(X_2233,null_class)) = X_2233 )
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X_2233,null_class))),X_2233),null_class),intersection(complement(singleton(not_subclass_element(X_2233,null_class))),X_2233)) ),
inference(cnfTransformation,[status(thm)],[f_951]) ).
tff(c_106440,plain,
( ( x = null_class )
| ( singleton(not_subclass_element(x,null_class)) = x )
| member(not_subclass_element(x,null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(superposition,[status(thm),theory(equality)],[c_284,c_106416]) ).
tff(c_106466,plain,
member(not_subclass_element(x,null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
inference(negUnitSimplification,[status(thm)],[c_286,c_288,c_106440]) ).
tff(c_104419,plain,
! [U_2157,V_2158,X_2159,Y_2160] :
( member(ordered_pair(U_2157,V_2158),cross_product(X_2159,Y_2160))
| ~ member(V_2158,Y_2160)
| ~ member(U_2157,X_2159) ),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_188,plain,
! [U_185,V_186,X_187,Y_188] :
( member(U_185,universal_class)
| ~ member(ordered_pair(U_185,V_186),cross_product(X_187,Y_188)) ),
inference(cnfTransformation,[status(thm)],[f_660]) ).
tff(c_104452,plain,
! [U_2157,V_2158,Y_2160,X_2159] :
( member(U_2157,universal_class)
| ~ member(V_2158,Y_2160)
| ~ member(U_2157,X_2159) ),
inference(resolution,[status(thm)],[c_104419,c_188]) ).
tff(c_105180,plain,
! [V_2158,Y_2160] : ~ member(V_2158,Y_2160),
inference(splitLeft,[status(thm)],[c_104452]) ).
tff(c_216,plain,
! [Y_212,X_211] : ( unordered_pair(Y_212,X_211) = unordered_pair(X_211,Y_212) ),
inference(cnfTransformation,[status(thm)],[f_743]) ).
tff(c_22,plain,
! [X_22,Y_23] : member(unordered_pair(X_22,Y_23),universal_class),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_3507,plain,
! [X_501,Y_502] : ( unordered_pair(singleton(X_501),unordered_pair(X_501,singleton(Y_502))) = ordered_pair(X_501,Y_502) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_20,plain,
! [Y_20,X_21] :
( member(Y_20,unordered_pair(X_21,Y_20))
| ~ member(Y_20,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_3539,plain,
! [X_501,Y_502] :
( member(unordered_pair(X_501,singleton(Y_502)),ordered_pair(X_501,Y_502))
| ~ member(unordered_pair(X_501,singleton(Y_502)),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_3507,c_20]) ).
tff(c_3841,plain,
! [X_517,Y_518] : member(unordered_pair(X_517,singleton(Y_518)),ordered_pair(X_517,Y_518)),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_3539]) ).
tff(c_3882,plain,
! [Y_518,Y_212] : member(unordered_pair(singleton(Y_518),Y_212),ordered_pair(Y_212,Y_518)),
inference(superposition,[status(thm),theory(equality)],[c_216,c_3841]) ).
tff(c_105257,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_105180,c_3882]) ).
tff(c_105258,plain,
! [U_2157,X_2159] :
( member(U_2157,universal_class)
| ~ member(U_2157,X_2159) ),
inference(splitRight,[status(thm)],[c_104452]) ).
tff(c_227664,plain,
member(not_subclass_element(x,null_class),universal_class),
inference(resolution,[status(thm)],[c_106466,c_105258]) ).
tff(c_246,plain,
! [X_244] :
( ( singleton(X_244) != null_class )
| ~ member(X_244,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_834]) ).
tff(c_227707,plain,
singleton(not_subclass_element(x,null_class)) != null_class,
inference(resolution,[status(thm)],[c_227664,c_246]) ).
tff(c_240,plain,
! [X_240] : member(singleton(X_240),universal_class),
inference(cnfTransformation,[status(thm)],[f_817]) ).
tff(c_3048,plain,
! [Y_486] :
( member(apply(choice,Y_486),Y_486)
| ( null_class = Y_486 )
| ~ member(Y_486,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_489]) ).
tff(c_250,plain,
! [Y_245,X_246] :
( ( Y_245 = X_246 )
| ~ member(Y_245,singleton(X_246)) ),
inference(cnfTransformation,[status(thm)],[f_842]) ).
tff(c_3077,plain,
! [X_246] :
( ( apply(choice,singleton(X_246)) = X_246 )
| ( singleton(X_246) = null_class )
| ~ member(singleton(X_246),universal_class) ),
inference(resolution,[status(thm)],[c_3048,c_250]) ).
tff(c_3259,plain,
! [X_494] :
( ( apply(choice,singleton(X_494)) = X_494 )
| ( singleton(X_494) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_240,c_3077]) ).
tff(c_140,plain,
! [Y_135] :
( member(apply(choice,Y_135),Y_135)
| ( null_class = Y_135 )
| ~ member(Y_135,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_489]) ).
tff(c_3265,plain,
! [X_494] :
( member(X_494,singleton(X_494))
| ( singleton(X_494) = null_class )
| ~ member(singleton(X_494),universal_class)
| ( singleton(X_494) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_3259,c_140]) ).
tff(c_3280,plain,
! [X_494] :
( member(X_494,singleton(X_494))
| ( singleton(X_494) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_240,c_3265]) ).
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_227669,plain,
member(not_subclass_element(x,null_class),complement(singleton(not_subclass_element(x,null_class)))),
inference(resolution,[status(thm)],[c_106466,c_42]) ).
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_229128,plain,
~ member(not_subclass_element(x,null_class),singleton(not_subclass_element(x,null_class))),
inference(resolution,[status(thm)],[c_227669,c_48]) ).
tff(c_229148,plain,
singleton(not_subclass_element(x,null_class)) = null_class,
inference(resolution,[status(thm)],[c_3280,c_229128]) ).
tff(c_229162,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_227707,c_229148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET099-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.12/0.13 % 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 : n024.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 20:02:06 EDT 2025
% 0.13/0.34 % CPUTime :
% 61.41/45.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 61.41/45.85
% 61.41/45.85 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------