%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET558-6 : 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 : n009.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 08:38:43 PM UTC 2025
% Result : Unsatisfiable 7.50s 2.76s
% Output : CNFRefutation 7.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 15 con; 0-3 aty)
% Number of variables : 8 ( 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ maps > 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 > single_valued3 > single_valued2 > single_valued1 > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > compose_class > complement > cantor > xh > xf2 > xf1 > universal_class > successor_relation > subset_relation > singleton_relation > omega > null_class > identity_relation > element_relation > domain_relation > composition_function > choice > application_function
%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(single_valued3,type,
single_valued3: $i > $i ).
tff(maps,type,
maps: ( $i * $i * $i ) > $o ).
tff(compose_class,type,
compose_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(xh,type,
xh: $i ).
tff(regular,type,
regular: $i > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(singleton_relation,type,
singleton_relation: $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(application_function,type,
application_function: $i ).
tff(flip,type,
flip: $i > $i ).
tff(power_class,type,
power_class: $i > $i ).
tff(xf2,type,
xf2: $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(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(single_valued2,type,
single_valued2: $i > $i ).
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(xf1,type,
xf1: $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(composition_function,type,
composition_function: $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(domain_relation,type,
domain_relation: $i ).
tff(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(single_valued1,type,
single_valued1: $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_781,axiom,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
file(unknown,unknown) ).
tff(f_778,axiom,
operation(xf1),
file(unknown,unknown) ).
tff(f_779,axiom,
compatible(xh,xf1,xf2),
file(unknown,unknown) ).
tff(f_576,axiom,
! [Xh,Xf1,Xf2] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ),
file(unknown,unknown) ).
tff(f_544,axiom,
! [Xf] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) ),
file(unknown,unknown) ).
tff(c_230,plain,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
inference(cnfTransformation,[status(thm)],[f_781]) ).
tff(c_226,plain,
operation(xf1),
inference(cnfTransformation,[status(thm)],[f_778]) ).
tff(c_228,plain,
compatible(xh,xf1,xf2),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_962,plain,
! [Xf1_338,Xh_339,Xf2_340] :
( ( domain_of(domain_of(Xf1_338)) = domain_of(Xh_339) )
| ~ compatible(Xh_339,Xf1_338,Xf2_340) ),
inference(cnfTransformation,[status(thm)],[f_576]) ).
tff(c_965,plain,
domain_of(domain_of(xf1)) = domain_of(xh),
inference(resolution,[status(thm)],[c_228,c_962]) ).
tff(c_2167,plain,
! [Xf_448] :
( ( cross_product(domain_of(domain_of(Xf_448)),domain_of(domain_of(Xf_448))) = domain_of(Xf_448) )
| ~ operation(Xf_448) ),
inference(cnfTransformation,[status(thm)],[f_544]) ).
tff(c_2196,plain,
( ( cross_product(domain_of(xh),domain_of(domain_of(xf1))) = domain_of(xf1) )
| ~ operation(xf1) ),
inference(superposition,[status(thm),theory(equality)],[c_965,c_2167]) ).
tff(c_2225,plain,
cross_product(domain_of(xh),domain_of(xh)) = domain_of(xf1),
inference(demodulation,[status(thm),theory(equality)],[c_226,c_965,c_2196]) ).
tff(c_2227,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_230,c_2225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET558-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 8 21:12:56 EDT 2025
% 0.14/0.35 % CPUTime :
% 7.50/2.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.50/2.76
% 7.50/2.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------