TSTP Solution File: SET071-7 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET071-7 : 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 : n027.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 10:55:49 EDT 2023
% Result : Unsatisfiable 6.18s 2.45s
% Output : CNFRefutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 59
% Syntax : Number of formulae : 90 ( 25 unt; 49 typ; 0 def)
% Number of atoms : 62 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 16 ~; 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 : 40 ( 40 usr; 10 con; 0-3 aty)
% Number of variables : 35 (; 35 !; 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 > 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(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_762,axiom,
~ member(x,universal_class),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_744,axiom,
! [X,Y] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
file(unknown,unknown) ).
tff(f_758,axiom,
! [X,Y] :
( member(X,universal_class)
| ( unordered_pair(X,Y) = singleton(Y) ) ),
file(unknown,unknown) ).
tff(f_764,axiom,
~ member(y,universal_class),
file(unknown,unknown) ).
tff(f_760,axiom,
unordered_pair(x,y) != null_class,
file(unknown,unknown) ).
tff(f_471,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_124,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_103,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(c_228,plain,
~ member(x,universal_class),
inference(cnfTransformation,[status(thm)],[f_762]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_72]) ).
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_744]) ).
tff(c_593,plain,
! [X_291,Y_292] :
( ( unordered_pair(X_291,Y_292) = singleton(Y_292) )
| member(X_291,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_758]) ).
tff(c_649,plain,
! [Y_293] : ( unordered_pair(x,Y_293) = singleton(Y_293) ),
inference(resolution,[status(thm)],[c_593,c_228]) ).
tff(c_781,plain,
! [X_297] : ( unordered_pair(X_297,x) = singleton(X_297) ),
inference(superposition,[status(thm),theory(equality)],[c_216,c_649]) ).
tff(c_230,plain,
~ member(y,universal_class),
inference(cnfTransformation,[status(thm)],[f_764]) ).
tff(c_645,plain,
! [Y_292] : ( unordered_pair(y,Y_292) = singleton(Y_292) ),
inference(resolution,[status(thm)],[c_593,c_230]) ).
tff(c_788,plain,
singleton(y) = singleton(x),
inference(superposition,[status(thm),theory(equality)],[c_781,c_645]) ).
tff(c_644,plain,
! [Y_292] : ( unordered_pair(x,Y_292) = singleton(Y_292) ),
inference(resolution,[status(thm)],[c_593,c_228]) ).
tff(c_226,plain,
unordered_pair(x,y) != null_class,
inference(cnfTransformation,[status(thm)],[f_760]) ).
tff(c_648,plain,
singleton(y) != null_class,
inference(demodulation,[status(thm),theory(equality)],[c_644,c_226]) ).
tff(c_855,plain,
singleton(x) != null_class,
inference(demodulation,[status(thm),theory(equality)],[c_788,c_648]) ).
tff(c_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_471]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_1625,plain,
! [Y_344,U_345,X_346] :
( ( Y_344 = U_345 )
| ( X_346 = U_345 )
| ~ member(U_345,unordered_pair(X_346,Y_344)) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_1893,plain,
! [X_361,U_362] :
( ( X_361 = U_362 )
| ( X_361 = U_362 )
| ~ member(U_362,singleton(X_361)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_1625]) ).
tff(c_1929,plain,
! [X_366] :
( ( regular(singleton(X_366)) = X_366 )
| ( singleton(X_366) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_1893]) ).
tff(c_1944,plain,
( ( regular(singleton(x)) = y )
| ( singleton(y) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_788,c_1929]) ).
tff(c_1947,plain,
( ( regular(singleton(x)) = y )
| ( singleton(x) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_788,c_1944]) ).
tff(c_1948,plain,
regular(singleton(x)) = y,
inference(negUnitSimplification,[status(thm)],[c_855,c_1947]) ).
tff(c_1925,plain,
! [X_361] :
( ( regular(singleton(X_361)) = X_361 )
| ( singleton(X_361) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_1893]) ).
tff(c_1952,plain,
( ( y = x )
| ( singleton(x) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_1948,c_1925]) ).
tff(c_1964,plain,
y = x,
inference(negUnitSimplification,[status(thm)],[c_855,c_1952]) ).
tff(c_1958,plain,
( member(y,singleton(x))
| ( singleton(x) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_1948,c_132]) ).
tff(c_1966,plain,
member(y,singleton(x)),
inference(negUnitSimplification,[status(thm)],[c_855,c_1958]) ).
tff(c_2026,plain,
member(x,singleton(x)),
inference(demodulation,[status(thm),theory(equality)],[c_1964,c_1966]) ).
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_2078,plain,
! [Y_374] :
( member(x,Y_374)
| ~ subclass(singleton(x),Y_374) ),
inference(resolution,[status(thm)],[c_2026,c_2]) ).
tff(c_2101,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[c_8,c_2078]) ).
tff(c_2118,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_228,c_2101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET071-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % 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
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 3 16:37:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 6.18/2.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.18/2.45
% 6.18/2.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.54/2.48
% 6.54/2.48 Inference rules
% 6.54/2.48 ----------------------
% 6.54/2.48 #Ref : 0
% 6.54/2.48 #Sup : 447
% 6.54/2.48 #Fact : 0
% 6.54/2.48 #Define : 0
% 6.54/2.48 #Split : 6
% 6.54/2.48 #Chain : 0
% 6.54/2.48 #Close : 0
% 6.54/2.48
% 6.54/2.48 Ordering : KBO
% 6.54/2.48
% 6.54/2.48 Simplification rules
% 6.54/2.48 ----------------------
% 6.54/2.48 #Subsume : 61
% 6.54/2.48 #Demod : 122
% 6.54/2.48 #Tautology : 187
% 6.54/2.48 #SimpNegUnit : 22
% 6.54/2.48 #BackRed : 16
% 6.54/2.48
% 6.54/2.48 #Partial instantiations: 0
% 6.54/2.48 #Strategies tried : 1
% 6.54/2.48
% 6.54/2.48 Timing (in seconds)
% 6.54/2.48 ----------------------
% 6.54/2.49 Preprocessing : 0.71
% 6.54/2.49 Parsing : 0.36
% 6.57/2.49 CNF conversion : 0.05
% 6.57/2.49 Main loop : 0.71
% 6.57/2.49 Inferencing : 0.24
% 6.57/2.49 Reduction : 0.23
% 6.57/2.49 Demodulation : 0.16
% 6.57/2.49 BG Simplification : 0.05
% 6.57/2.49 Subsumption : 0.14
% 6.57/2.49 Abstraction : 0.03
% 6.57/2.49 MUC search : 0.00
% 6.57/2.49 Cooper : 0.00
% 6.57/2.49 Total : 1.47
% 6.57/2.49 Index Insertion : 0.00
% 6.57/2.49 Index Deletion : 0.00
% 6.57/2.49 Index Matching : 0.00
% 6.57/2.49 BG Taut test : 0.00
%------------------------------------------------------------------------------