%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET065+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 : n018.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 08:37:46 PM UTC 2025
% Result : Theorem 5.42s 2.23s
% Output : CNFRefutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 6 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 7 con; 0-3 aty)
% Number of variables : 16 ( 15 !; 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 > 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_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(first,type,
first: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $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_377,negated_conjecture,
~ member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
tff(f_70,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
tff(f_252,axiom,
! [X] :
( inductive(X)
<=> ( member(null_class,X)
& subclass(image(successor_relation,X),X) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',inductive_defn) ).
tff(f_67,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
tff(f_262,axiom,
? [X] :
( member(X,universal_class)
& inductive(X)
& ! [Y] :
( inductive(Y)
=> subclass(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',infinity) ).
tff(c_180,plain,
~ member(null_class,universal_class),
inference(cnfTransformation,[status(thm)],[f_377]) ).
tff(c_8,plain,
! [X_6] : subclass(X_6,universal_class),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_116,plain,
! [X_59] :
( member(null_class,X_59)
| ~ inductive(X_59) ),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_943,plain,
! [U_212,Y_213,X_214] :
( member(U_212,Y_213)
| ~ member(U_212,X_214)
| ~ subclass(X_214,Y_213) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_1337,plain,
! [Y_238,X_239] :
( member(null_class,Y_238)
| ~ subclass(X_239,Y_238)
| ~ inductive(X_239) ),
inference(resolution,[status(thm)],[c_116,c_943]) ).
tff(c_1373,plain,
! [X_6] :
( member(null_class,universal_class)
| ~ inductive(X_6) ),
inference(resolution,[status(thm)],[c_8,c_1337]) ).
tff(c_1392,plain,
! [X_6] : ~ inductive(X_6),
inference(negUnitSimplification,[status(thm)],[c_180,c_1373]) ).
tff(c_120,plain,
inductive('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_1395,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1392,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET065+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.12/0.13 % 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 : n018.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 19:55:47 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.42/2.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.42/2.23
% 5.42/2.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------