%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET090-7 : 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/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 : n026.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 : Unsatisfiable 16.33s 5.22s
% Output : CNFRefutation 16.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 40 ( 40 usr; 9 con; 0-3 aty)
% Number of variables : 11 ( 11 !; 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_of > inverse > flip > first > domain_of > diagonalise > complement > cantor > universal_class > u > 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(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(u,type,
u: $i ).
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(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_900,axiom,
member_of(singleton(u)) != u,
file(unknown,unknown) ).
tff(f_897,axiom,
! [X] :
( ( singleton(member_of(X)) = X )
| ( member_of(X) = X ) ),
file(unknown,unknown) ).
tff(f_898,axiom,
member(u,universal_class),
file(unknown,unknown) ).
tff(f_864,axiom,
! [X,Y] :
( ( singleton(X) != singleton(Y) )
| ~ member(Y,universal_class)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_889,axiom,
! [Y] :
( ~ member(Y,universal_class)
| ( singleton(member_of(singleton(Y))) = singleton(Y) ) ),
file(unknown,unknown) ).
tff(c_270,plain,
member_of(singleton(u)) != u,
inference(cnfTransformation,[status(thm)],[f_900]) ).
tff(c_266,plain,
! [X_258] :
( ( member_of(X_258) = X_258 )
| ( singleton(member_of(X_258)) = X_258 ) ),
inference(cnfTransformation,[status(thm)],[f_897]) ).
tff(c_268,plain,
member(u,universal_class),
inference(cnfTransformation,[status(thm)],[f_898]) ).
tff(c_1762,plain,
! [Y_409,X_410] :
( ( Y_409 = X_410 )
| ~ member(Y_409,universal_class)
| ( singleton(Y_409) != singleton(X_410) ) ),
inference(cnfTransformation,[status(thm)],[f_864]) ).
tff(c_1844,plain,
! [X_413] :
( ( u = X_413 )
| ( singleton(u) != singleton(X_413) ) ),
inference(resolution,[status(thm)],[c_268,c_1762]) ).
tff(c_1847,plain,
! [X_258] :
( ( member_of(X_258) = u )
| ( singleton(u) != X_258 )
| ( member_of(X_258) = X_258 ) ),
inference(superposition,[status(thm),theory(equality)],[c_266,c_1844]) ).
tff(c_11032,plain,
( ( member_of(singleton(u)) = u )
| ( member_of(singleton(u)) = singleton(u) ) ),
inference(reflexivity,[status(thm),theory(equality)],[c_1847]) ).
tff(c_11033,plain,
member_of(singleton(u)) = singleton(u),
inference(negUnitSimplification,[status(thm)],[c_270,c_11032]) ).
tff(c_11035,plain,
singleton(u) != u,
inference(demodulation,[status(thm),theory(equality)],[c_11033,c_270]) ).
tff(c_262,plain,
! [Y_256] :
( ( singleton(member_of(singleton(Y_256))) = singleton(Y_256) )
| ~ member(Y_256,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_889]) ).
tff(c_11054,plain,
( ( singleton(singleton(u)) = singleton(u) )
| ~ member(u,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_11033,c_262]) ).
tff(c_11080,plain,
singleton(singleton(u)) = singleton(u),
inference(demodulation,[status(thm),theory(equality)],[c_268,c_11054]) ).
tff(c_1823,plain,
! [X_410] :
( ( u = X_410 )
| ( singleton(u) != singleton(X_410) ) ),
inference(resolution,[status(thm)],[c_268,c_1762]) ).
tff(c_11215,plain,
singleton(u) = u,
inference(superposition,[status(thm),theory(equality)],[c_11080,c_1823]) ).
tff(c_11317,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_11035,c_11215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : SET090-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.09 % 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
% 0.08/0.29 % Computer : n026.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Tue Apr 8 19:59:23 EDT 2025
% 0.08/0.29 % CPUTime :
% 16.33/5.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.33/5.23
% 16.33/5.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------