TSTP Solution File: SET238-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET238-6 : 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 : n026.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 10:56:14 EDT 2023
% Result : Unsatisfiable 10.58s 3.51s
% Output : CNFRefutation 10.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 65
% Syntax : Number of formulae : 75 ( 10 unt; 60 typ; 0 def)
% Number of atoms : 20 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 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 : 72 ( 44 >; 28 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 50 ( 50 usr; 16 con; 0-3 aty)
% Number of variables : 22 (; 22 !; 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 > z > y > xr > 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(xr,type,
xr: $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(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(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(z,type,
z: $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_779,axiom,
member(z,restrict(xr,x,y)),
file(unknown,unknown) ).
tff(f_238,axiom,
! [Xr,X,Y] : ( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
file(unknown,unknown) ).
tff(f_201,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file(unknown,unknown) ).
tff(f_169,axiom,
! [Z,X,Y] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
file(unknown,unknown) ).
tff(f_781,axiom,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
file(unknown,unknown) ).
tff(c_226,plain,
member(z,restrict(xr,x,y)),
inference(cnfTransformation,[status(thm)],[f_779]) ).
tff(c_721,plain,
! [Xr_315,X_316,Y_317] : ( intersection(Xr_315,cross_product(X_316,Y_317)) = restrict(Xr_315,X_316,Y_317) ),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_44,plain,
! [Z_49,Y_51,X_50] :
( member(Z_49,Y_51)
| ~ member(Z_49,intersection(X_50,Y_51)) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_6084,plain,
! [Z_688,X_689,Y_690,Xr_691] :
( member(Z_688,cross_product(X_689,Y_690))
| ~ member(Z_688,restrict(Xr_691,X_689,Y_690)) ),
inference(superposition,[status(thm),theory(equality)],[c_721,c_44]) ).
tff(c_6139,plain,
member(z,cross_product(x,y)),
inference(resolution,[status(thm)],[c_226,c_6084]) ).
tff(c_34,plain,
! [Z_39,X_40,Y_41] :
( ( ordered_pair(first(Z_39),second(Z_39)) = Z_39 )
| ~ member(Z_39,cross_product(X_40,Y_41)) ),
inference(cnfTransformation,[status(thm)],[f_169]) ).
tff(c_6144,plain,
ordered_pair(first(z),second(z)) = z,
inference(resolution,[status(thm)],[c_6139,c_34]) ).
tff(c_228,plain,
~ member(ordered_pair(first(z),second(z)),restrict(xr,x,y)),
inference(cnfTransformation,[status(thm)],[f_781]) ).
tff(c_6146,plain,
~ member(z,restrict(xr,x,y)),
inference(demodulation,[status(thm),theory(equality)],[c_6144,c_228]) ).
tff(c_6149,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_226,c_6146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET238-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 17:08:31 EDT 2023
% 0.13/0.35 % CPUTime :
% 10.58/3.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.58/3.52
% 10.58/3.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.80/3.54
% 10.80/3.54 Inference rules
% 10.80/3.54 ----------------------
% 10.80/3.54 #Ref : 0
% 10.80/3.54 #Sup : 1422
% 10.80/3.54 #Fact : 0
% 10.80/3.54 #Define : 0
% 10.80/3.54 #Split : 57
% 10.80/3.54 #Chain : 0
% 10.80/3.54 #Close : 0
% 10.80/3.54
% 10.80/3.54 Ordering : KBO
% 10.80/3.54
% 10.80/3.54 Simplification rules
% 10.80/3.54 ----------------------
% 10.80/3.54 #Subsume : 333
% 10.80/3.55 #Demod : 374
% 10.80/3.55 #Tautology : 252
% 10.80/3.55 #SimpNegUnit : 20
% 10.80/3.55 #BackRed : 101
% 10.80/3.55
% 10.80/3.55 #Partial instantiations: 0
% 10.80/3.55 #Strategies tried : 1
% 10.80/3.55
% 10.80/3.55 Timing (in seconds)
% 10.80/3.55 ----------------------
% 10.80/3.55 Preprocessing : 0.77
% 10.80/3.55 Parsing : 0.42
% 10.80/3.55 CNF conversion : 0.05
% 10.80/3.55 Main loop : 1.72
% 10.80/3.55 Inferencing : 0.56
% 10.80/3.55 Reduction : 0.58
% 10.80/3.55 Demodulation : 0.39
% 10.80/3.55 BG Simplification : 0.08
% 10.80/3.55 Subsumption : 0.37
% 10.80/3.55 Abstraction : 0.05
% 10.80/3.55 MUC search : 0.00
% 10.80/3.55 Cooper : 0.00
% 10.80/3.55 Total : 2.54
% 10.80/3.55 Index Insertion : 0.00
% 10.80/3.55 Index Deletion : 0.00
% 10.80/3.55 Index Matching : 0.00
% 10.80/3.55 BG Taut test : 0.00
%------------------------------------------------------------------------------