TSTP Solution File: SET075-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET075-6 : 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/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 : n020.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 10:55:50 EDT 2023
% Result : Unsatisfiable 6.08s 2.43s
% Output : CNFRefutation 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 60
% Syntax : Number of formulae : 83 ( 14 unt; 51 typ; 0 def)
% Number of atoms : 53 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 22 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 39 >; 26 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 12 con; 0-3 aty)
% Number of variables : 38 (; 38 !; 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_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_71,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_644,axiom,
member(ordered_pair(x,y),cross_product(u,v)),
file(unknown,unknown) ).
tff(f_142,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,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_186,plain,
unordered_pair(x,y) = null_class,
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_340,plain,
! [Y_222,X_223] :
( member(Y_222,unordered_pair(X_223,Y_222))
| ~ member(Y_222,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_346,plain,
( member(y,null_class)
| ~ member(y,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_186,c_340]) ).
tff(c_347,plain,
~ member(y,universal_class),
inference(splitLeft,[status(thm)],[c_346]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_184,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(cnfTransformation,[status(thm)],[f_644]) ).
tff(c_1216,plain,
! [V_315,Y_316,U_317,X_318] :
( member(V_315,Y_316)
| ~ member(ordered_pair(U_317,V_315),cross_product(X_318,Y_316)) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_1220,plain,
member(y,v),
inference(resolution,[status(thm)],[c_184,c_1216]) ).
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_57]) ).
tff(c_1224,plain,
! [Y_319] :
( member(y,Y_319)
| ~ subclass(v,Y_319) ),
inference(resolution,[status(thm)],[c_1220,c_2]) ).
tff(c_1232,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[c_8,c_1224]) ).
tff(c_1241,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_347,c_1232]) ).
tff(c_1242,plain,
member(y,null_class),
inference(splitRight,[status(thm)],[c_346]) ).
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_1399,plain,
! [Z_342,X_343,Y_344] :
( member(Z_342,X_343)
| ~ member(Z_342,intersection(X_343,Y_344)) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_1486,plain,
! [Z_355,X_356] :
( member(Z_355,X_356)
| ~ member(Z_355,null_class)
| ( null_class = X_356 ) ),
inference(superposition,[status(thm),theory(equality)],[c_134,c_1399]) ).
tff(c_1503,plain,
! [X_357] :
( member(y,X_357)
| ( null_class = X_357 ) ),
inference(resolution,[status(thm)],[c_1242,c_1486]) ).
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_1560,plain,
! [X_361] :
( ~ member(y,X_361)
| ( complement(X_361) = null_class ) ),
inference(resolution,[status(thm)],[c_1503,c_48]) ).
tff(c_1600,plain,
complement(null_class) = null_class,
inference(resolution,[status(thm)],[c_1242,c_1560]) ).
tff(c_2064,plain,
! [Z_372] :
( ~ member(Z_372,null_class)
| ~ member(Z_372,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1600,c_48]) ).
tff(c_2072,plain,
~ member(y,null_class),
inference(resolution,[status(thm)],[c_1242,c_2064]) ).
tff(c_2087,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1242,c_2072]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET075-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15 % 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
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 16:36:52 EDT 2023
% 0.14/0.36 % CPUTime :
% 6.08/2.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.08/2.44
% 6.08/2.44 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.46/2.47
% 6.46/2.47 Inference rules
% 6.46/2.47 ----------------------
% 6.46/2.47 #Ref : 0
% 6.46/2.47 #Sup : 453
% 6.46/2.47 #Fact : 0
% 6.46/2.47 #Define : 0
% 6.46/2.47 #Split : 15
% 6.46/2.47 #Chain : 0
% 6.46/2.47 #Close : 0
% 6.46/2.47
% 6.46/2.47 Ordering : KBO
% 6.46/2.47
% 6.46/2.47 Simplification rules
% 6.46/2.47 ----------------------
% 6.46/2.47 #Subsume : 30
% 6.46/2.47 #Demod : 80
% 6.46/2.47 #Tautology : 119
% 6.46/2.47 #SimpNegUnit : 2
% 6.46/2.47 #BackRed : 20
% 6.46/2.47
% 6.46/2.47 #Partial instantiations: 0
% 6.46/2.47 #Strategies tried : 1
% 6.46/2.47
% 6.46/2.47 Timing (in seconds)
% 6.46/2.47 ----------------------
% 6.46/2.47 Preprocessing : 0.69
% 6.46/2.47 Parsing : 0.37
% 6.46/2.47 CNF conversion : 0.04
% 6.46/2.47 Main loop : 0.70
% 6.46/2.47 Inferencing : 0.24
% 6.46/2.47 Reduction : 0.21
% 6.46/2.47 Demodulation : 0.15
% 6.46/2.47 BG Simplification : 0.05
% 6.46/2.47 Subsumption : 0.16
% 6.46/2.47 Abstraction : 0.03
% 6.46/2.47 MUC search : 0.00
% 6.46/2.47 Cooper : 0.00
% 6.46/2.47 Total : 1.44
% 6.46/2.47 Index Insertion : 0.00
% 6.46/2.47 Index Deletion : 0.00
% 6.46/2.47 Index Matching : 0.00
% 6.46/2.47 BG Taut test : 0.00
%------------------------------------------------------------------------------