TSTP Solution File: SET386-6 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET386-6 : 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 : n031.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 10:56:24 EDT 2023
% Result : Unsatisfiable 12.88s 4.34s
% Output : CNFRefutation 12.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 63
% Syntax : Number of formulae : 74 ( 10 unt; 57 typ; 0 def)
% Number of atoms : 24 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 72 ( 44 >; 28 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 13 con; 0-3 aty)
% Number of variables : 28 (; 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ maps > 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 > single_valued3 > single_valued2 > single_valued1 > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > compose_class > complement > cantor > x > universal_class > successor_relation > subset_relation > singleton_relation > omega > null_class > identity_relation > element_relation > domain_relation > composition_function > choice > application_function
%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(single_valued3,type,
single_valued3: $i > $i ).
tff(x,type,
x: $i ).
tff(maps,type,
maps: ( $i * $i * $i ) > $o ).
tff(compose_class,type,
compose_class: $i > $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(singleton_relation,type,
singleton_relation: $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(application_function,type,
application_function: $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(single_valued2,type,
single_valued2: $i > $i ).
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(composition_function,type,
composition_function: $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(domain_relation,type,
domain_relation: $i ).
tff(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(single_valued1,type,
single_valued1: $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_781,axiom,
~ subclass(x,cross_product(universal_class,universal_class)),
file(unknown,unknown) ).
tff(f_779,axiom,
restrict(x,universal_class,universal_class) = x,
file(unknown,unknown) ).
tff(f_240,axiom,
! [X,Y,Xr] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
file(unknown,unknown) ).
tff(f_71,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_195,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_76,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(c_228,plain,
~ subclass(x,cross_product(universal_class,universal_class)),
inference(cnfTransformation,[status(thm)],[f_781]) ).
tff(c_226,plain,
restrict(x,universal_class,universal_class) = x,
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_58,plain,
! [X_66,Y_67,Xr_68] : ( intersection(cross_product(X_66,Y_67),Xr_68) = restrict(Xr_68,X_66,Y_67) ),
inference(cnfTransformation,[status(thm)],[f_240]) ).
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_71]) ).
tff(c_617,plain,
! [Z_299,X_300,Y_301] :
( member(Z_299,X_300)
| ~ member(Z_299,intersection(X_300,Y_301)) ),
inference(cnfTransformation,[status(thm)],[f_195]) ).
tff(c_10230,plain,
! [X_844,Y_845,Y_846] :
( member(not_subclass_element(intersection(X_844,Y_845),Y_846),X_844)
| subclass(intersection(X_844,Y_845),Y_846) ),
inference(resolution,[status(thm)],[c_4,c_617]) ).
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_76]) ).
tff(c_10385,plain,
! [X_847,Y_848] : subclass(intersection(X_847,Y_848),X_847),
inference(resolution,[status(thm)],[c_10230,c_6]) ).
tff(c_10575,plain,
! [Xr_855,X_856,Y_857] : subclass(restrict(Xr_855,X_856,Y_857),cross_product(X_856,Y_857)),
inference(superposition,[status(thm),theory(equality)],[c_58,c_10385]) ).
tff(c_10605,plain,
subclass(x,cross_product(universal_class,universal_class)),
inference(superposition,[status(thm),theory(equality)],[c_226,c_10575]) ).
tff(c_10614,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_228,c_10605]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : SET386-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.16 % 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
% 0.16/0.37 % Computer : n031.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu Aug 3 17:29:15 EDT 2023
% 0.16/0.37 % CPUTime :
% 12.88/4.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.88/4.35
% 12.88/4.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.88/4.38
% 12.88/4.38 Inference rules
% 12.88/4.38 ----------------------
% 12.88/4.38 #Ref : 0
% 12.88/4.38 #Sup : 2595
% 12.88/4.38 #Fact : 0
% 12.88/4.38 #Define : 0
% 12.88/4.38 #Split : 71
% 12.88/4.38 #Chain : 0
% 12.88/4.38 #Close : 0
% 12.88/4.38
% 12.88/4.38 Ordering : KBO
% 12.88/4.38
% 12.88/4.38 Simplification rules
% 12.88/4.38 ----------------------
% 12.88/4.38 #Subsume : 571
% 12.88/4.38 #Demod : 697
% 12.88/4.38 #Tautology : 439
% 12.88/4.38 #SimpNegUnit : 32
% 12.88/4.38 #BackRed : 126
% 12.88/4.38
% 12.88/4.38 #Partial instantiations: 0
% 12.88/4.38 #Strategies tried : 1
% 12.88/4.38
% 12.88/4.38 Timing (in seconds)
% 12.88/4.38 ----------------------
% 12.88/4.38 Preprocessing : 0.73
% 12.88/4.38 Parsing : 0.39
% 12.88/4.38 CNF conversion : 0.05
% 12.88/4.38 Main loop : 2.55
% 12.88/4.38 Inferencing : 0.76
% 12.88/4.38 Reduction : 0.91
% 12.88/4.38 Demodulation : 0.60
% 12.88/4.38 BG Simplification : 0.08
% 12.88/4.38 Subsumption : 0.60
% 12.88/4.38 Abstraction : 0.06
% 12.88/4.38 MUC search : 0.00
% 12.88/4.38 Cooper : 0.00
% 12.88/4.38 Total : 3.33
% 12.88/4.38 Index Insertion : 0.00
% 12.88/4.38 Index Deletion : 0.00
% 12.88/4.38 Index Matching : 0.00
% 12.88/4.38 BG Taut test : 0.00
%------------------------------------------------------------------------------