TSTP Solution File: SET085-7 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET085-7 : 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 : n022.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 10:55:54 EDT 2023
% Result : Unsatisfiable 6.06s 2.40s
% Output : CNFRefutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 60
% Syntax : Number of formulae : 86 ( 22 unt; 50 typ; 0 def)
% Number of atoms : 50 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 41 ( 41 usr; 11 con; 0-3 aty)
% Number of variables : 21 (; 21 !; 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 > z > 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(z,type,
z: $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_869,axiom,
x != y,
file(unknown,unknown) ).
tff(f_871,axiom,
x != z,
file(unknown,unknown) ).
tff(f_867,axiom,
member(x,universal_class),
file(unknown,unknown) ).
tff(f_835,axiom,
! [X] :
( ~ member(X,universal_class)
| ( singleton(X) != null_class ) ),
file(unknown,unknown) ).
tff(f_848,axiom,
! [X] :
( member(X,universal_class)
| ( singleton(X) = null_class ) ),
file(unknown,unknown) ).
tff(f_866,axiom,
unordered_pair(y,z) = singleton(x),
file(unknown,unknown) ).
tff(f_117,axiom,
! [Y,X] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_758,axiom,
! [X,Y] :
( member(X,universal_class)
| ( unordered_pair(X,Y) = singleton(Y) ) ),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_843,axiom,
! [Y,X] :
( ~ member(Y,singleton(X))
| ( Y = X ) ),
file(unknown,unknown) ).
tff(c_262,plain,
y != x,
inference(cnfTransformation,[status(thm)],[f_869]) ).
tff(c_264,plain,
z != x,
inference(cnfTransformation,[status(thm)],[f_871]) ).
tff(c_260,plain,
member(x,universal_class),
inference(cnfTransformation,[status(thm)],[f_867]) ).
tff(c_363,plain,
! [X_272] :
( ( singleton(X_272) != null_class )
| ~ member(X_272,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_835]) ).
tff(c_392,plain,
singleton(x) != null_class,
inference(resolution,[status(thm)],[c_260,c_363]) ).
tff(c_252,plain,
! [X_247] :
( ( singleton(X_247) = null_class )
| member(X_247,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_848]) ).
tff(c_258,plain,
unordered_pair(y,z) = singleton(x),
inference(cnfTransformation,[status(thm)],[f_866]) ).
tff(c_816,plain,
! [Y_332,X_333] :
( member(Y_332,unordered_pair(X_333,Y_332))
| ~ member(Y_332,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_828,plain,
( member(z,singleton(x))
| ~ member(z,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_258,c_816]) ).
tff(c_980,plain,
~ member(z,universal_class),
inference(splitLeft,[status(thm)],[c_828]) ).
tff(c_984,plain,
singleton(z) = null_class,
inference(resolution,[status(thm)],[c_252,c_980]) ).
tff(c_1188,plain,
! [X_364,Y_365] :
( ( unordered_pair(X_364,Y_365) = singleton(Y_365) )
| member(X_364,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_758]) ).
tff(c_722,plain,
! [X_324,Y_325] :
( member(X_324,unordered_pair(X_324,Y_325))
| ~ member(X_324,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_734,plain,
( member(y,singleton(x))
| ~ member(y,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_258,c_722]) ).
tff(c_829,plain,
~ member(y,universal_class),
inference(splitLeft,[status(thm)],[c_734]) ).
tff(c_1366,plain,
! [Y_369] : ( unordered_pair(y,Y_369) = singleton(Y_369) ),
inference(resolution,[status(thm)],[c_1188,c_829]) ).
tff(c_1413,plain,
singleton(z) = singleton(x),
inference(superposition,[status(thm),theory(equality)],[c_1366,c_258]) ).
tff(c_1445,plain,
singleton(x) = null_class,
inference(demodulation,[status(thm),theory(equality)],[c_984,c_1413]) ).
tff(c_1447,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_392,c_1445]) ).
tff(c_1448,plain,
member(z,singleton(x)),
inference(splitRight,[status(thm)],[c_828]) ).
tff(c_250,plain,
! [Y_245,X_246] :
( ( Y_245 = X_246 )
| ~ member(Y_245,singleton(X_246)) ),
inference(cnfTransformation,[status(thm)],[f_843]) ).
tff(c_1460,plain,
z = x,
inference(resolution,[status(thm)],[c_1448,c_250]) ).
tff(c_1464,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_264,c_1460]) ).
tff(c_1465,plain,
member(y,singleton(x)),
inference(splitRight,[status(thm)],[c_734]) ).
tff(c_1473,plain,
y = x,
inference(resolution,[status(thm)],[c_1465,c_250]) ).
tff(c_1477,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_262,c_1473]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET085-7 : 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 : n022.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 16:24:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 6.06/2.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.06/2.41
% 6.06/2.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.06/2.43
% 6.06/2.43 Inference rules
% 6.06/2.43 ----------------------
% 6.06/2.43 #Ref : 0
% 6.06/2.44 #Sup : 294
% 6.06/2.44 #Fact : 0
% 6.06/2.44 #Define : 0
% 6.06/2.44 #Split : 6
% 6.06/2.44 #Chain : 0
% 6.06/2.44 #Close : 0
% 6.06/2.44
% 6.06/2.44 Ordering : KBO
% 6.06/2.44
% 6.06/2.44 Simplification rules
% 6.06/2.44 ----------------------
% 6.06/2.44 #Subsume : 55
% 6.06/2.44 #Demod : 94
% 6.06/2.44 #Tautology : 139
% 6.06/2.44 #SimpNegUnit : 8
% 6.06/2.44 #BackRed : 4
% 6.06/2.44
% 6.06/2.44 #Partial instantiations: 0
% 6.06/2.44 #Strategies tried : 1
% 6.06/2.44
% 6.06/2.44 Timing (in seconds)
% 6.06/2.44 ----------------------
% 6.06/2.44 Preprocessing : 0.74
% 6.06/2.44 Parsing : 0.36
% 6.06/2.44 CNF conversion : 0.05
% 6.06/2.44 Main loop : 0.63
% 6.06/2.44 Inferencing : 0.21
% 6.06/2.44 Reduction : 0.22
% 6.06/2.44 Demodulation : 0.15
% 6.06/2.44 BG Simplification : 0.05
% 6.06/2.44 Subsumption : 0.12
% 6.06/2.44 Abstraction : 0.02
% 6.06/2.44 MUC search : 0.00
% 6.06/2.44 Cooper : 0.00
% 6.06/2.44 Total : 1.42
% 6.06/2.44 Index Insertion : 0.00
% 6.06/2.44 Index Deletion : 0.00
% 6.06/2.44 Index Matching : 0.00
% 6.06/2.44 BG Taut test : 0.00
%------------------------------------------------------------------------------