%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET084+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 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 : Theorem 5.30s 2.21s
% Output : CNFRefutation 5.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 7 ~; 8 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 9 con; 0-3 aty)
% Number of variables : 15 ( 15 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subclass > member > disjoint > inductive > function > restrict > unordered_pair > union > ordered_pair > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > range_of > power_class > inverse > flip > first > domain_of > complement > universal_class > successor_relation > null_class > identity_relation > element_relation > #skF_4 > #skF_7 > #skF_3 > #skF_2 > #skF_9 > #skF_8 > #skF_1 > #skF_5 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(null_class,type,
null_class: $i ).
tff(rotate,type,
rotate: $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(subclass,type,
subclass: ( $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(sum_class,type,
sum_class: $i > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
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('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $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(restrict,type,
restrict: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(first,type,
first: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(inductive,type,
inductive: $i > $o ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(successor,type,
successor: $i > $i ).
tff(successor_relation,type,
successor_relation: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(identity_relation,type,
identity_relation: $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(universal_class,type,
universal_class: $i ).
tff(f_382,negated_conjecture,
~ ! [X,Y] :
( ( ( singleton(X) = singleton(Y) )
& member(Y,universal_class) )
=> ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element2) ).
tff(f_100,axiom,
! [X] : ( singleton(X) = unordered_pair(X,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
tff(f_87,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
tff(c_180,plain,
'#skF_9' != '#skF_8',
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_182,plain,
member('#skF_9',universal_class),
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_184,plain,
singleton('#skF_9') = singleton('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_26,plain,
! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_374,plain,
! [Y_146,X_147] :
( member(Y_146,unordered_pair(X_147,Y_146))
| ~ member(Y_146,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_378,plain,
! [X_148] :
( member(X_148,singleton(X_148))
| ~ member(X_148,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_374]) ).
tff(c_381,plain,
( member('#skF_9',singleton('#skF_8'))
| ~ member('#skF_9',universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_378]) ).
tff(c_383,plain,
member('#skF_9',singleton('#skF_8')),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_381]) ).
tff(c_982,plain,
! [Y_219,U_220,X_221] :
( ( Y_219 = U_220 )
| ( X_221 = U_220 )
| ~ member(U_220,unordered_pair(X_221,Y_219)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_1386,plain,
! [X_234,U_235] :
( ( X_234 = U_235 )
| ( X_234 = U_235 )
| ~ member(U_235,singleton(X_234)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_982]) ).
tff(c_1409,plain,
'#skF_9' = '#skF_8',
inference(resolution,[status(thm)],[c_383,c_1386]) ).
tff(c_1432,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_180,c_180,c_1409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET084+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n027.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 19:58:51 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.30/2.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.30/2.21
% 5.30/2.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------