TSTP Solution File: SET062-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET062-6 : 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 : n021.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 10:55:46 EDT 2023
% Result : Unsatisfiable 9.83s 3.44s
% Output : CNFRefutation 9.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 56
% Syntax : Number of formulae : 83 ( 8 unt; 48 typ; 0 def)
% Number of atoms : 67 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 29 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 39 ( 39 usr; 9 con; 0-3 aty)
% Number of variables : 55 (; 55 !; 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 > 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(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_61,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_470,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_191,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_207,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(f_185,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_645,axiom,
~ subclass(null_class,x),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_4,Y_5] :
( subclass(X_4,Y_5)
| member(not_subclass_element(X_4,Y_5),X_4) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_519,plain,
! [Z_249,Y_250,X_251] :
( member(Z_249,Y_250)
| ~ member(Z_249,intersection(X_251,Y_250)) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_3847,plain,
! [X_531,Y_532] :
( member(regular(intersection(X_531,Y_532)),Y_532)
| ( intersection(X_531,Y_532) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_519]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_706,plain,
! [U_280,Y_281,X_282] :
( member(U_280,Y_281)
| ~ member(U_280,X_282)
| ~ subclass(X_282,Y_281) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_741,plain,
! [X_131,Y_281] :
( member(regular(X_131),Y_281)
| ~ subclass(X_131,Y_281)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_132,c_706]) ).
tff(c_1212,plain,
! [X_326,Y_327] :
( member(regular(X_326),Y_327)
| ~ subclass(X_326,Y_327)
| ( null_class = X_326 ) ),
inference(resolution,[status(thm)],[c_132,c_706]) ).
tff(c_234,plain,
! [Z_200,X_201] :
( ~ member(Z_200,X_201)
| ~ member(Z_200,complement(X_201)) ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_243,plain,
! [X_201] :
( ~ member(regular(complement(X_201)),X_201)
| ( complement(X_201) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_234]) ).
tff(c_1267,plain,
! [Y_328] :
( ~ subclass(complement(Y_328),Y_328)
| ( complement(Y_328) = null_class ) ),
inference(resolution,[status(thm)],[c_1212,c_243]) ).
tff(c_1289,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[c_8,c_1267]) ).
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_1387,plain,
! [Z_334] :
( ~ member(Z_334,universal_class)
| ~ member(Z_334,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1289,c_48]) ).
tff(c_1391,plain,
! [X_131] :
( ~ member(regular(X_131),null_class)
| ~ subclass(X_131,universal_class)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_741,c_1387]) ).
tff(c_1439,plain,
! [X_131] :
( ~ member(regular(X_131),null_class)
| ( null_class = X_131 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1391]) ).
tff(c_3960,plain,
! [X_533] : ( intersection(X_533,null_class) = null_class ),
inference(resolution,[status(thm)],[c_3847,c_1439]) ).
tff(c_42,plain,
! [Z_46,X_47,Y_48] :
( member(Z_46,X_47)
| ~ member(Z_46,intersection(X_47,Y_48)) ),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_4973,plain,
! [Z_571,X_572] :
( member(Z_571,X_572)
| ~ member(Z_571,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_3960,c_42]) ).
tff(c_6224,plain,
! [Y_608,X_609] :
( member(not_subclass_element(null_class,Y_608),X_609)
| subclass(null_class,Y_608) ),
inference(resolution,[status(thm)],[c_4,c_4973]) ).
tff(c_475,plain,
! [X_242,Y_243] :
( subclass(X_242,Y_243)
| member(not_subclass_element(X_242,Y_243),X_242) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_3143,plain,
! [X_513,Y_514] :
( ~ member(not_subclass_element(complement(X_513),Y_514),X_513)
| subclass(complement(X_513),Y_514) ),
inference(resolution,[status(thm)],[c_475,c_48]) ).
tff(c_3186,plain,
! [Y_514] :
( ~ member(not_subclass_element(null_class,Y_514),universal_class)
| subclass(complement(universal_class),Y_514) ),
inference(superposition,[status(thm),theory(equality)],[c_1289,c_3143]) ).
tff(c_3216,plain,
! [Y_514] :
( ~ member(not_subclass_element(null_class,Y_514),universal_class)
| subclass(null_class,Y_514) ),
inference(demodulation,[status(thm),theory(equality)],[c_1289,c_3186]) ).
tff(c_6323,plain,
! [Y_608] : subclass(null_class,Y_608),
inference(resolution,[status(thm)],[c_6224,c_3216]) ).
tff(c_184,plain,
~ subclass(null_class,x),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_6347,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6323,c_184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET062-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.14 % 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
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 16:18:21 EDT 2023
% 0.14/0.35 % CPUTime :
% 9.83/3.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.83/3.45
% 9.83/3.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.83/3.48
% 9.83/3.48 Inference rules
% 9.83/3.48 ----------------------
% 9.83/3.48 #Ref : 0
% 9.83/3.48 #Sup : 1468
% 9.83/3.48 #Fact : 0
% 9.83/3.48 #Define : 0
% 9.83/3.48 #Split : 43
% 9.83/3.48 #Chain : 0
% 9.83/3.48 #Close : 0
% 9.83/3.48
% 9.83/3.48 Ordering : KBO
% 9.83/3.48
% 9.83/3.48 Simplification rules
% 9.83/3.48 ----------------------
% 9.83/3.48 #Subsume : 287
% 9.83/3.48 #Demod : 366
% 9.83/3.48 #Tautology : 207
% 9.83/3.48 #SimpNegUnit : 14
% 9.83/3.48 #BackRed : 98
% 9.83/3.48
% 9.83/3.48 #Partial instantiations: 0
% 9.83/3.48 #Strategies tried : 1
% 9.83/3.48
% 9.83/3.48 Timing (in seconds)
% 9.83/3.48 ----------------------
% 9.83/3.49 Preprocessing : 0.71
% 9.83/3.49 Parsing : 0.38
% 9.83/3.49 CNF conversion : 0.05
% 9.83/3.49 Main loop : 1.62
% 9.83/3.49 Inferencing : 0.56
% 9.83/3.49 Reduction : 0.53
% 9.83/3.49 Demodulation : 0.36
% 9.83/3.49 BG Simplification : 0.06
% 9.83/3.49 Subsumption : 0.34
% 9.83/3.49 Abstraction : 0.05
% 9.83/3.49 MUC search : 0.00
% 9.83/3.49 Cooper : 0.00
% 9.83/3.49 Total : 2.39
% 9.83/3.49 Index Insertion : 0.00
% 9.83/3.49 Index Deletion : 0.00
% 9.83/3.49 Index Matching : 0.00
% 9.83/3.49 BG Taut test : 0.00
%------------------------------------------------------------------------------