%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET105-7 : 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 : n023.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 08:38:00 PM UTC 2025
% Result : Unsatisfiable 11.42s 3.62s
% Output : CNFRefutation 11.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 10 con; 0-3 aty)
% Number of variables : 31 ( 31 !; 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 > 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(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(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_753,axiom,
! [Y,X] :
( member(Y,universal_class)
| ( unordered_pair(X,Y) = singleton(X) ) ),
file(unknown,unknown) ).
tff(f_983,axiom,
~ member(x,universal_class),
file(unknown,unknown) ).
tff(f_743,axiom,
! [X,Y] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
file(unknown,unknown) ).
tff(f_847,axiom,
! [X] :
( member(X,universal_class)
| ( singleton(X) = null_class ) ),
file(unknown,unknown) ).
tff(f_128,axiom,
! [X,Y] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
file(unknown,unknown) ).
tff(f_985,axiom,
~ member(y,universal_class),
file(unknown,unknown) ).
tff(f_970,axiom,
! [X,Y] : ( unordered_pair(X,Y) = union(singleton(X),singleton(Y)) ),
file(unknown,unknown) ).
tff(f_316,axiom,
! [X] : ( union(X,singleton(X)) = successor(X) ),
file(unknown,unknown) ).
tff(f_981,axiom,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
file(unknown,unknown) ).
tff(c_1398,plain,
! [X_389,Y_390] :
( ( unordered_pair(X_389,Y_390) = singleton(X_389) )
| member(Y_390,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_753]) ).
tff(c_298,plain,
~ member(x,universal_class),
inference(cnfTransformation,[status(thm)],[f_983]) ).
tff(c_1489,plain,
! [X_391] : ( unordered_pair(X_391,x) = singleton(X_391) ),
inference(resolution,[status(thm)],[c_1398,c_298]) ).
tff(c_216,plain,
! [Y_212,X_211] : ( unordered_pair(Y_212,X_211) = unordered_pair(X_211,Y_212) ),
inference(cnfTransformation,[status(thm)],[f_743]) ).
tff(c_1512,plain,
! [X_391] : ( unordered_pair(x,X_391) = singleton(X_391) ),
inference(superposition,[status(thm),theory(equality)],[c_1489,c_216]) ).
tff(c_462,plain,
! [X_318] :
( ( singleton(X_318) = null_class )
| member(X_318,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_847]) ).
tff(c_469,plain,
singleton(x) = null_class,
inference(resolution,[status(thm)],[c_462,c_298]) ).
tff(c_4800,plain,
! [X_536,Y_537] : ( unordered_pair(singleton(X_536),unordered_pair(X_536,singleton(Y_537))) = ordered_pair(X_536,Y_537) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_4918,plain,
! [Y_537] : ( unordered_pair(null_class,unordered_pair(x,singleton(Y_537))) = ordered_pair(x,Y_537) ),
inference(superposition,[status(thm),theory(equality)],[c_469,c_4800]) ).
tff(c_4956,plain,
! [Y_537] : ( unordered_pair(null_class,singleton(singleton(Y_537))) = ordered_pair(x,Y_537) ),
inference(demodulation,[status(thm),theory(equality)],[c_1512,c_4918]) ).
tff(c_300,plain,
~ member(y,universal_class),
inference(cnfTransformation,[status(thm)],[f_985]) ).
tff(c_1561,plain,
! [X_392] : ( unordered_pair(X_392,y) = singleton(X_392) ),
inference(resolution,[status(thm)],[c_1398,c_300]) ).
tff(c_1614,plain,
! [Y_212] : ( unordered_pair(y,Y_212) = singleton(Y_212) ),
inference(superposition,[status(thm),theory(equality)],[c_216,c_1561]) ).
tff(c_470,plain,
singleton(y) = null_class,
inference(resolution,[status(thm)],[c_462,c_300]) ).
tff(c_4912,plain,
! [Y_537] : ( unordered_pair(null_class,unordered_pair(y,singleton(Y_537))) = ordered_pair(y,Y_537) ),
inference(superposition,[status(thm),theory(equality)],[c_470,c_4800]) ).
tff(c_4955,plain,
! [Y_537] : ( unordered_pair(null_class,singleton(singleton(Y_537))) = ordered_pair(y,Y_537) ),
inference(demodulation,[status(thm),theory(equality)],[c_1614,c_4912]) ).
tff(c_8956,plain,
! [Y_537] : ( ordered_pair(y,Y_537) = ordered_pair(x,Y_537) ),
inference(demodulation,[status(thm),theory(equality)],[c_4956,c_4955]) ).
tff(c_5084,plain,
! [Y_548] : ( unordered_pair(null_class,singleton(singleton(Y_548))) = ordered_pair(y,Y_548) ),
inference(demodulation,[status(thm),theory(equality)],[c_1614,c_4912]) ).
tff(c_5170,plain,
unordered_pair(null_class,singleton(null_class)) = ordered_pair(y,x),
inference(superposition,[status(thm),theory(equality)],[c_469,c_5084]) ).
tff(c_5167,plain,
unordered_pair(null_class,singleton(null_class)) = ordered_pair(y,y),
inference(superposition,[status(thm),theory(equality)],[c_470,c_5084]) ).
tff(c_5559,plain,
ordered_pair(y,y) = ordered_pair(y,x),
inference(demodulation,[status(thm),theory(equality)],[c_5170,c_5167]) ).
tff(c_9104,plain,
ordered_pair(x,y) = ordered_pair(x,x),
inference(demodulation,[status(thm),theory(equality)],[c_8956,c_8956,c_5559]) ).
tff(c_1157,plain,
! [X_376,Y_377] : ( union(singleton(X_376),singleton(Y_377)) = unordered_pair(X_376,Y_377) ),
inference(cnfTransformation,[status(thm)],[f_970]) ).
tff(c_86,plain,
! [X_101] : ( union(X_101,singleton(X_101)) = successor(X_101) ),
inference(cnfTransformation,[status(thm)],[f_316]) ).
tff(c_1164,plain,
! [X_376] : ( unordered_pair(X_376,singleton(X_376)) = successor(singleton(X_376)) ),
inference(superposition,[status(thm),theory(equality)],[c_1157,c_86]) ).
tff(c_5467,plain,
successor(singleton(null_class)) = ordered_pair(y,y),
inference(superposition,[status(thm),theory(equality)],[c_5167,c_1164]) ).
tff(c_296,plain,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
inference(cnfTransformation,[status(thm)],[f_981]) ).
tff(c_1264,plain,
successor(singleton(null_class)) != ordered_pair(x,y),
inference(demodulation,[status(thm),theory(equality)],[c_1164,c_296]) ).
tff(c_5520,plain,
ordered_pair(y,y) != ordered_pair(x,y),
inference(demodulation,[status(thm),theory(equality)],[c_5467,c_1264]) ).
tff(c_5680,plain,
ordered_pair(y,x) != ordered_pair(x,y),
inference(demodulation,[status(thm),theory(equality)],[c_5559,c_5520]) ).
tff(c_9102,plain,
ordered_pair(x,y) != ordered_pair(x,x),
inference(demodulation,[status(thm),theory(equality)],[c_8956,c_5680]) ).
tff(c_9381,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9104,c_9102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET105-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.13 % 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
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 20:03:54 EDT 2025
% 0.13/0.35 % CPUTime :
% 11.42/3.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.42/3.63
% 11.42/3.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------