TSTP Solution File: SET081-7 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET081-7 : 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 : n012.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 10:55:53 EDT 2023
% Result : Unsatisfiable 7.44s 2.93s
% Output : CNFRefutation 7.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 57
% Syntax : Number of formulae : 74 ( 17 unt; 49 typ; 0 def)
% Number of atoms : 37 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 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 : 24 (; 24 !; 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_349,axiom,
! [X] :
( ~ inductive(X)
| member(null_class,X) ),
file(unknown,unknown) ).
tff(f_723,axiom,
! [Z] : ~ member(Z,null_class),
file(unknown,unknown) ).
tff(f_839,axiom,
y != x,
file(unknown,unknown) ).
tff(f_747,axiom,
! [X,Y] : subclass(singleton(X),unordered_pair(X,Y)),
file(unknown,unknown) ).
tff(f_837,axiom,
member(y,singleton(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_102,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file(unknown,unknown) ).
tff(f_368,axiom,
inductive(omega),
file(unknown,unknown) ).
tff(c_265,plain,
! [X_253] :
( member(null_class,X_253)
| ~ inductive(X_253) ),
inference(cnfTransformation,[status(thm)],[f_349]) ).
tff(c_206,plain,
! [Z_207] : ~ member(Z_207,null_class),
inference(cnfTransformation,[status(thm)],[f_723]) ).
tff(c_270,plain,
~ inductive(null_class),
inference(resolution,[status(thm)],[c_265,c_206]) ).
tff(c_252,plain,
y != x,
inference(cnfTransformation,[status(thm)],[f_839]) ).
tff(c_218,plain,
! [X_213,Y_214] : subclass(singleton(X_213),unordered_pair(X_213,Y_214)),
inference(cnfTransformation,[status(thm)],[f_747]) ).
tff(c_250,plain,
member(y,singleton(x)),
inference(cnfTransformation,[status(thm)],[f_837]) ).
tff(c_1239,plain,
! [U_370,Y_371,X_372] :
( member(U_370,Y_371)
| ~ member(U_370,X_372)
| ~ subclass(X_372,Y_371) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1535,plain,
! [Y_384] :
( member(y,Y_384)
| ~ subclass(singleton(x),Y_384) ),
inference(resolution,[status(thm)],[c_250,c_1239]) ).
tff(c_1643,plain,
! [Y_388] : member(y,unordered_pair(x,Y_388)),
inference(resolution,[status(thm)],[c_218,c_1535]) ).
tff(c_16,plain,
! [Y_17,U_15,X_16] :
( ( Y_17 = U_15 )
| ( X_16 = U_15 )
| ~ member(U_15,unordered_pair(X_16,Y_17)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_1646,plain,
! [Y_388] :
( ( y = Y_388 )
| ( y = x ) ),
inference(resolution,[status(thm)],[c_1643,c_16]) ).
tff(c_1701,plain,
y = omega,
inference(negUnitSimplification,[status(thm)],[c_252,c_1646]) ).
tff(c_1673,plain,
! [Y_388] : ( y = Y_388 ),
inference(negUnitSimplification,[status(thm)],[c_252,c_1646]) ).
tff(c_3376,plain,
omega = null_class,
inference(superposition,[status(thm),theory(equality)],[c_1701,c_1673]) ).
tff(c_100,plain,
inductive(omega),
inference(cnfTransformation,[status(thm)],[f_368]) ).
tff(c_3377,plain,
inductive(null_class),
inference(superposition,[status(thm),theory(equality)],[c_3376,c_100]) ).
tff(c_3415,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_270,c_3377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET081-7 : 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
% 0.13/0.34 % Computer : n012.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 16:06:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.44/2.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.44/2.93
% 7.44/2.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.44/2.96
% 7.44/2.96 Inference rules
% 7.44/2.96 ----------------------
% 7.44/2.96 #Ref : 0
% 7.44/2.96 #Sup : 1141
% 7.44/2.96 #Fact : 0
% 7.44/2.96 #Define : 0
% 7.44/2.96 #Split : 4
% 7.44/2.96 #Chain : 0
% 7.44/2.96 #Close : 0
% 7.44/2.96
% 7.44/2.96 Ordering : KBO
% 7.44/2.96
% 7.44/2.96 Simplification rules
% 7.44/2.96 ----------------------
% 7.44/2.96 #Subsume : 166
% 7.44/2.96 #Demod : 85
% 7.44/2.96 #Tautology : 150
% 7.44/2.96 #SimpNegUnit : 2
% 7.44/2.96 #BackRed : 1
% 7.44/2.96
% 7.44/2.96 #Partial instantiations: 2376
% 7.44/2.96 #Strategies tried : 1
% 7.44/2.96
% 7.44/2.96 Timing (in seconds)
% 7.44/2.96 ----------------------
% 7.44/2.97 Preprocessing : 0.83
% 7.44/2.97 Parsing : 0.42
% 7.44/2.97 CNF conversion : 0.05
% 7.44/2.97 Main loop : 1.02
% 7.44/2.97 Inferencing : 0.41
% 7.44/2.97 Reduction : 0.32
% 7.44/2.97 Demodulation : 0.23
% 7.44/2.97 BG Simplification : 0.06
% 7.44/2.97 Subsumption : 0.18
% 7.44/2.97 Abstraction : 0.03
% 7.44/2.97 MUC search : 0.00
% 7.44/2.97 Cooper : 0.00
% 7.44/2.97 Total : 1.91
% 7.44/2.97 Index Insertion : 0.00
% 7.44/2.97 Index Deletion : 0.00
% 7.44/2.97 Index Matching : 0.00
% 7.44/2.97 BG Taut test : 0.00
%------------------------------------------------------------------------------