%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET074-6 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/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 08:37:50 PM UTC 2025
% Result : Unsatisfiable 6.14s 2.36s
% Output : CNFRefutation 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 10 con; 0-3 aty)
% Number of variables : 21 ( 21 !; 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 > inverse > flip > first > domain_of > diagonalise > complement > cantor > y > x > universal_class > 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(x,type,
x: $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(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(y,type,
y: $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(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_644,axiom,
member(y,universal_class),
file(unknown,unknown) ).
tff(f_645,axiom,
unordered_pair(x,y) = null_class,
file(unknown,unknown) ).
tff(f_116,axiom,
! [Y,X] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_474,axiom,
! [X] :
( ( X = null_class )
| ( intersection(X,regular(X)) = null_class ) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_207,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(c_184,plain,
member(y,universal_class),
inference(cnfTransformation,[status(thm)],[f_644]) ).
tff(c_186,plain,
unordered_pair(x,y) = null_class,
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_332,plain,
! [Y_216,X_217] :
( member(Y_216,unordered_pair(X_217,Y_216))
| ~ member(Y_216,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_338,plain,
( member(y,null_class)
| ~ member(y,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_186,c_332]) ).
tff(c_340,plain,
member(y,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_184,c_338]) ).
tff(c_134,plain,
! [X_132] :
( ( intersection(X_132,regular(X_132)) = null_class )
| ( null_class = X_132 ) ),
inference(cnfTransformation,[status(thm)],[f_474]) ).
tff(c_518,plain,
! [Z_248,X_249,Y_250] :
( member(Z_248,X_249)
| ~ member(Z_248,intersection(X_249,Y_250)) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_591,plain,
! [Z_259,X_260] :
( member(Z_259,X_260)
| ~ member(Z_259,null_class)
| ( null_class = X_260 ) ),
inference(superposition,[status(thm),theory(equality)],[c_134,c_518]) ).
tff(c_641,plain,
! [X_264] :
( member(y,X_264)
| ( null_class = X_264 ) ),
inference(resolution,[status(thm)],[c_340,c_591]) ).
tff(c_48,plain,
! [Z_55,X_56] :
( ~ member(Z_55,X_56)
| ~ member(Z_55,complement(X_56)) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_661,plain,
! [X_265] :
( ~ member(y,X_265)
| ( complement(X_265) = null_class ) ),
inference(resolution,[status(thm)],[c_641,c_48]) ).
tff(c_700,plain,
complement(null_class) = null_class,
inference(resolution,[status(thm)],[c_340,c_661]) ).
tff(c_1180,plain,
! [Z_280] :
( ~ member(Z_280,null_class)
| ~ member(Z_280,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_700,c_48]) ).
tff(c_1188,plain,
~ member(y,null_class),
inference(resolution,[status(thm)],[c_340,c_1180]) ).
tff(c_1203,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_340,c_1188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET074-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n026.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 19:57:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 6.14/2.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.14/2.37
% 6.14/2.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------