%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET018-7 : 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 : n022.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 08:37:31 PM UTC 2025
% Result : Unsatisfiable 10.33s 3.37s
% Output : CNFRefutation 10.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 44 ( 44 usr; 12 con; 0-3 aty)
% Number of variables : 13 ( 13 !; 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_of1 > member_of > inverse > flip > first > domain_of > diagonalise > complement > cantor > z > y > x > w > 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(w,type,
w: $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(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(member_of1,type,
member_of1: $i > $i ).
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(z,type,
z: $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_1110,axiom,
x != z,
file(unknown,unknown) ).
tff(f_1104,axiom,
ordered_pair(w,x) = ordered_pair(y,z),
file(unknown,unknown) ).
tff(f_1105,axiom,
member(x,universal_class),
file(unknown,unknown) ).
tff(f_1020,axiom,
! [W,X,Y,Z] :
( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(X,universal_class)
| ( X = Z ) ),
file(unknown,unknown) ).
tff(c_340,plain,
z != x,
inference(cnfTransformation,[status(thm)],[f_1110]) ).
tff(c_336,plain,
ordered_pair(y,z) = ordered_pair(w,x),
inference(cnfTransformation,[status(thm)],[f_1104]) ).
tff(c_338,plain,
member(x,universal_class),
inference(cnfTransformation,[status(thm)],[f_1105]) ).
tff(c_5385,plain,
! [Z_628,X_629,Y_630,W_631] :
( ( Z_628 = X_629 )
| ~ member(X_629,universal_class)
| ( ordered_pair(Y_630,Z_628) != ordered_pair(W_631,X_629) ) ),
inference(cnfTransformation,[status(thm)],[f_1020]) ).
tff(c_5894,plain,
! [Z_658,Y_659,W_660] :
( ( x = Z_658 )
| ( ordered_pair(Y_659,Z_658) != ordered_pair(W_660,x) ) ),
inference(resolution,[status(thm)],[c_338,c_5385]) ).
tff(c_5903,plain,
! [W_660] :
( ( z = x )
| ( ordered_pair(w,x) != ordered_pair(W_660,x) ) ),
inference(superposition,[status(thm),theory(equality)],[c_336,c_5894]) ).
tff(c_5904,plain,
! [W_660] : ( ordered_pair(w,x) != ordered_pair(W_660,x) ),
inference(negUnitSimplification,[status(thm)],[c_340,c_5903]) ).
tff(c_5908,plain,
$false,
inference(reflexivity,[status(thm),theory(equality)],[c_5904]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET018-7 : TPTP v9.0.0. Bugfixed v7.3.0.
% 0.03/0.12 % 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
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Apr 8 19:43:20 EDT 2025
% 0.12/0.32 % CPUTime :
% 10.33/3.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.33/3.38
% 10.33/3.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------