TSTP Solution File: SET096-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET096-6 : 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 : n002.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 10:55:57 EDT 2023
% Result : Unsatisfiable 7.22s 2.63s
% Output : CNFRefutation 7.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 59
% Syntax : Number of formulae : 84 ( 14 unt; 49 typ; 0 def)
% Number of atoms : 66 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 23 ~; 31 |; 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 : 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 > 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_648,axiom,
singleton(y) != x,
file(unknown,unknown) ).
tff(f_644,axiom,
subclass(x,singleton(y)),
file(unknown,unknown) ).
tff(f_91,axiom,
! [X,Y] :
( ~ subclass(X,Y)
| ~ subclass(Y,X)
| ( X = Y ) ),
file(unknown,unknown) ).
tff(f_646,axiom,
x != null_class,
file(unknown,unknown) ).
tff(f_470,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_102,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(c_188,plain,
singleton(y) != x,
inference(cnfTransformation,[status(thm)],[f_648]) ).
tff(c_184,plain,
subclass(x,singleton(y)),
inference(cnfTransformation,[status(thm)],[f_644]) ).
tff(c_444,plain,
! [Y_248,X_249] :
( ( Y_248 = X_249 )
| ~ subclass(Y_248,X_249)
| ~ subclass(X_249,Y_248) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_466,plain,
( ( singleton(y) = x )
| ~ subclass(singleton(y),x) ),
inference(resolution,[status(thm)],[c_184,c_444]) ).
tff(c_483,plain,
~ subclass(singleton(y),x),
inference(negUnitSimplification,[status(thm)],[c_188,c_466]) ).
tff(c_186,plain,
x != null_class,
inference(cnfTransformation,[status(thm)],[f_646]) ).
tff(c_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_743,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_1525,plain,
! [X_363,Y_364] :
( member(regular(X_363),Y_364)
| ~ subclass(X_363,Y_364)
| ( null_class = X_363 ) ),
inference(resolution,[status(thm)],[c_132,c_743]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_606,plain,
! [Y_262,U_263,X_264] :
( ( Y_262 = U_263 )
| ( X_264 = U_263 )
| ~ member(U_263,unordered_pair(X_264,Y_262)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_627,plain,
! [X_24,U_263] :
( ( X_24 = U_263 )
| ( X_24 = U_263 )
| ~ member(U_263,singleton(X_24)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_606]) ).
tff(c_2341,plain,
! [X_408,X_409] :
( ( regular(X_408) = X_409 )
| ~ subclass(X_408,singleton(X_409))
| ( null_class = X_408 ) ),
inference(resolution,[status(thm)],[c_1525,c_627]) ).
tff(c_2352,plain,
( ( regular(x) = y )
| ( x = null_class ) ),
inference(resolution,[status(thm)],[c_184,c_2341]) ).
tff(c_2361,plain,
regular(x) = y,
inference(negUnitSimplification,[status(thm)],[c_186,c_2352]) ).
tff(c_2389,plain,
( member(y,x)
| ( x = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_2361,c_132]) ).
tff(c_2396,plain,
member(y,x),
inference(negUnitSimplification,[status(thm)],[c_186,c_2389]) ).
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_662,plain,
! [X_271,U_272] :
( ( X_271 = U_272 )
| ( X_271 = U_272 )
| ~ member(U_272,singleton(X_271)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_606]) ).
tff(c_2676,plain,
! [X_442,Y_443] :
( ( not_subclass_element(singleton(X_442),Y_443) = X_442 )
| subclass(singleton(X_442),Y_443) ),
inference(resolution,[status(thm)],[c_4,c_662]) ).
tff(c_2711,plain,
not_subclass_element(singleton(y),x) = y,
inference(resolution,[status(thm)],[c_2676,c_483]) ).
tff(c_6,plain,
! [X_6,Y_7] :
( subclass(X_6,Y_7)
| ~ member(not_subclass_element(X_6,Y_7),Y_7) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_2722,plain,
( subclass(singleton(y),x)
| ~ member(y,x) ),
inference(superposition,[status(thm),theory(equality)],[c_2711,c_6]) ).
tff(c_2729,plain,
subclass(singleton(y),x),
inference(demodulation,[status(thm),theory(equality)],[c_2396,c_2722]) ).
tff(c_2731,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_483,c_2729]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET096-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Aug 3 16:31:01 EDT 2023
% 0.11/0.34 % CPUTime :
% 7.22/2.63 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.48/2.63
% 7.48/2.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.58/2.66
% 7.58/2.66 Inference rules
% 7.58/2.66 ----------------------
% 7.58/2.66 #Ref : 0
% 7.58/2.66 #Sup : 603
% 7.58/2.66 #Fact : 0
% 7.58/2.66 #Define : 0
% 7.58/2.66 #Split : 24
% 7.58/2.66 #Chain : 0
% 7.58/2.66 #Close : 0
% 7.58/2.66
% 7.58/2.66 Ordering : KBO
% 7.58/2.66
% 7.58/2.66 Simplification rules
% 7.58/2.66 ----------------------
% 7.58/2.66 #Subsume : 72
% 7.58/2.66 #Demod : 88
% 7.58/2.66 #Tautology : 107
% 7.58/2.66 #SimpNegUnit : 13
% 7.58/2.66 #BackRed : 9
% 7.58/2.66
% 7.58/2.66 #Partial instantiations: 0
% 7.58/2.66 #Strategies tried : 1
% 7.58/2.66
% 7.58/2.66 Timing (in seconds)
% 7.58/2.66 ----------------------
% 7.58/2.67 Preprocessing : 0.68
% 7.58/2.67 Parsing : 0.35
% 7.58/2.67 CNF conversion : 0.05
% 7.58/2.67 Main loop : 0.93
% 7.58/2.67 Inferencing : 0.32
% 7.58/2.67 Reduction : 0.30
% 7.58/2.67 Demodulation : 0.21
% 7.58/2.67 BG Simplification : 0.05
% 7.58/2.67 Subsumption : 0.19
% 7.58/2.67 Abstraction : 0.03
% 7.58/2.67 MUC search : 0.00
% 7.58/2.67 Cooper : 0.00
% 7.58/2.67 Total : 1.66
% 7.58/2.67 Index Insertion : 0.00
% 7.58/2.67 Index Deletion : 0.00
% 7.58/2.67 Index Matching : 0.00
% 7.58/2.67 BG Taut test : 0.00
%------------------------------------------------------------------------------