%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET091+1 : TPTP v9.0.0. Bugfixed v7.3.0.
% 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 : n013.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 08:37:55 PM UTC 2025
% Result : Theorem 6.11s 2.53s
% Output : CNFRefutation 6.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 16 ( 7 ~; 6 |; 2 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 9 con; 0-3 aty)
% Number of variables : 9 ( 8 !; 1 ?; 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 > member_of > 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(member_of,type,
member_of: $i > $i ).
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_392,axiom,
! [X] :
( ( singleton(member_of(X)) = X )
| ( member_of(X) = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_self) ).
tff(f_388,axiom,
! [X] :
( member(member_of(X),universal_class)
| ( member_of(X) = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_universal_self) ).
tff(f_405,negated_conjecture,
~ ! [X,U] :
( ( ~ ? [Y] :
( member(Y,universal_class)
& ( X = singleton(Y) ) )
& ( X = U ) )
=> ( member_of(X) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_when_not_a_singleton) ).
tff(c_186,plain,
! [X_98] :
( ( member_of(X_98) = X_98 )
| ( singleton(member_of(X_98)) = X_98 ) ),
inference(cnfTransformation,[status(thm)],[f_392]) ).
tff(c_407,plain,
! [X_145] :
( ( member_of(X_145) = X_145 )
| member(member_of(X_145),universal_class) ),
inference(cnfTransformation,[status(thm)],[f_388]) ).
tff(c_192,plain,
! [Y_100] :
( ( singleton(Y_100) != '#skF_8' )
| ~ member(Y_100,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_435,plain,
! [X_150] :
( ( singleton(member_of(X_150)) != '#skF_8' )
| ( member_of(X_150) = X_150 ) ),
inference(resolution,[status(thm)],[c_407,c_192]) ).
tff(c_966,plain,
member_of('#skF_8') = '#skF_8',
inference(superposition,[status(thm),theory(equality)],[c_186,c_435]) ).
tff(c_190,plain,
'#skF_9' = '#skF_8',
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_188,plain,
member_of('#skF_8') != '#skF_9',
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_193,plain,
member_of('#skF_8') != '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_190,c_188]) ).
tff(c_969,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_966,c_193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET091+1 : TPTP v9.0.0. Bugfixed v7.3.0.
% 0.00/0.10 % 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
% 0.10/0.30 % Computer : n013.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Apr 8 19:59:17 EDT 2025
% 0.10/0.30 % CPUTime :
% 6.11/2.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.11/2.54
% 6.11/2.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------