TSTP Solution File: SET050-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET050-6 : TPTP v8.1.2. 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 : n032.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 : Tue Aug 22 10:55:42 EDT 2023
% Result : Unsatisfiable 5.67s 2.36s
% Output : CNFRefutation 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 57
% Syntax : Number of formulae : 68 ( 10 unt; 51 typ; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 39 >; 26 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 12 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 > v > 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(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(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(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(v,type,
v: $i ).
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_110,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_647,axiom,
~ member(x,unordered_pair(x,y)),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_645,axiom,
member(ordered_pair(x,y),cross_product(u,v)),
file(unknown,unknown) ).
tff(f_137,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(c_333,plain,
! [X_220,Y_221] :
( member(X_220,unordered_pair(X_220,Y_221))
| ~ member(X_220,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_186,plain,
~ member(x,unordered_pair(x,y)),
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_340,plain,
~ member(x,universal_class),
inference(resolution,[status(thm)],[c_333,c_186]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_184,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_1506,plain,
! [U_351,X_352,V_353,Y_354] :
( member(U_351,X_352)
| ~ member(ordered_pair(U_351,V_353),cross_product(X_352,Y_354)) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_1515,plain,
member(x,u),
inference(resolution,[status(thm)],[c_184,c_1506]) ).
tff(c_2,plain,
! [U_3,Y_2,X_1] :
( member(U_3,Y_2)
| ~ member(U_3,X_1)
| ~ subclass(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_1519,plain,
! [Y_355] :
( member(x,Y_355)
| ~ subclass(u,Y_355) ),
inference(resolution,[status(thm)],[c_1515,c_2]) ).
tff(c_1527,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[c_8,c_1519]) ).
tff(c_1536,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_340,c_1527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET050-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % 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
% 0.14/0.32 % Computer : n032.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Thu Aug 3 16:23:21 EDT 2023
% 0.14/0.32 % CPUTime :
% 5.67/2.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/2.36
% 5.67/2.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.07/2.39
% 6.07/2.39 Inference rules
% 6.07/2.39 ----------------------
% 6.07/2.39 #Ref : 0
% 6.07/2.39 #Sup : 303
% 6.07/2.39 #Fact : 0
% 6.07/2.39 #Define : 0
% 6.07/2.39 #Split : 12
% 6.07/2.39 #Chain : 0
% 6.07/2.39 #Close : 0
% 6.07/2.39
% 6.07/2.39 Ordering : KBO
% 6.07/2.39
% 6.07/2.39 Simplification rules
% 6.07/2.39 ----------------------
% 6.07/2.39 #Subsume : 33
% 6.07/2.39 #Demod : 35
% 6.07/2.39 #Tautology : 62
% 6.07/2.39 #SimpNegUnit : 2
% 6.07/2.39 #BackRed : 1
% 6.07/2.39
% 6.07/2.39 #Partial instantiations: 0
% 6.07/2.39 #Strategies tried : 1
% 6.07/2.39
% 6.07/2.39 Timing (in seconds)
% 6.07/2.39 ----------------------
% 6.07/2.40 Preprocessing : 0.68
% 6.07/2.40 Parsing : 0.35
% 6.07/2.40 CNF conversion : 0.05
% 6.07/2.40 Main loop : 0.69
% 6.07/2.40 Inferencing : 0.24
% 6.07/2.40 Reduction : 0.21
% 6.07/2.40 Demodulation : 0.15
% 6.07/2.40 BG Simplification : 0.05
% 6.07/2.40 Subsumption : 0.15
% 6.07/2.40 Abstraction : 0.02
% 6.07/2.40 MUC search : 0.00
% 6.07/2.40 Cooper : 0.00
% 6.07/2.40 Total : 1.41
% 6.07/2.40 Index Insertion : 0.00
% 6.07/2.40 Index Deletion : 0.00
% 6.07/2.40 Index Matching : 0.00
% 6.07/2.40 BG Taut test : 0.00
%------------------------------------------------------------------------------