TSTP Solution File: SET082+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n027.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 : Theorem 6.69s 2.81s
% Output : CNFRefutation 7.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 44
% Syntax : Number of formulae : 63 ( 10 unt; 39 typ; 0 def)
% Number of atoms : 49 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 12 ~; 20 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 31 >; 16 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 8 con; 0-3 aty)
% Number of variables : 31 (; 30 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subclass > member > disjoint > inductive > function > restrict > unordered_pair > union > ordered_pair > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > range_of > power_class > inverse > flip > first > domain_of > complement > universal_class > successor_relation > null_class > identity_relation > element_relation > #skF_4 > #skF_7 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_5 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(null_class,type,
null_class: $i ).
tff(rotate,type,
rotate: $i > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(subclass,type,
subclass: ( $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(sum_class,type,
sum_class: $i > $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
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('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $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(restrict,type,
restrict: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff(first,type,
first: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(inductive,type,
inductive: $i > $o ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(successor,type,
successor: $i > $i ).
tff(successor_relation,type,
successor_relation: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(identity_relation,type,
identity_relation: $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff(universal_class,type,
universal_class: $i ).
tff(f_381,negated_conjecture,
~ ! [X] :
( ~ member(X,universal_class)
=> ( singleton(X) = null_class ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
tff(f_100,axiom,
! [X] : ( singleton(X) = unordered_pair(X,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
tff(f_97,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
tff(f_372,axiom,
? [XF] :
( function(XF)
& ! [Y] :
( member(Y,universal_class)
=> ( ( Y = null_class )
| member(apply(XF,Y),Y) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',choice) ).
tff(f_87,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
tff(c_180,plain,
singleton('#skF_8') != null_class,
inference(cnfTransformation,[status(thm)],[f_381]) ).
tff(c_204,plain,
! [X_103] : ( unordered_pair(X_103,X_103) = singleton(X_103) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_24,plain,
! [X_12,Y_13] : member(unordered_pair(X_12,Y_13),universal_class),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_209,plain,
! [X_103] : member(singleton(X_103),universal_class),
inference(superposition,[status(thm),theory(equality)],[c_204,c_24]) ).
tff(c_3275,plain,
! [Y_349] :
( member(apply('#skF_7',Y_349),Y_349)
| ( null_class = Y_349 )
| ~ member(Y_349,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_26,plain,
! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_2146,plain,
! [Y_284,U_285,X_286] :
( ( Y_284 = U_285 )
| ( X_286 = U_285 )
| ~ member(U_285,unordered_pair(X_286,Y_284)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_2171,plain,
! [X_14,U_285] :
( ( X_14 = U_285 )
| ( X_14 = U_285 )
| ~ member(U_285,singleton(X_14)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_2146]) ).
tff(c_3292,plain,
! [X_14] :
( ( apply('#skF_7',singleton(X_14)) = X_14 )
| ( singleton(X_14) = null_class )
| ~ member(singleton(X_14),universal_class) ),
inference(resolution,[status(thm)],[c_3275,c_2171]) ).
tff(c_4647,plain,
! [X_458] :
( ( apply('#skF_7',singleton(X_458)) = X_458 )
| ( singleton(X_458) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_209,c_3292]) ).
tff(c_176,plain,
! [Y_94] :
( member(apply('#skF_7',Y_94),Y_94)
| ( null_class = Y_94 )
| ~ member(Y_94,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_372]) ).
tff(c_4653,plain,
! [X_458] :
( member(X_458,singleton(X_458))
| ( singleton(X_458) = null_class )
| ~ member(singleton(X_458),universal_class)
| ( singleton(X_458) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_4647,c_176]) ).
tff(c_4665,plain,
! [X_463] :
( member(X_463,singleton(X_463))
| ( singleton(X_463) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_209,c_4653]) ).
tff(c_344,plain,
! [U_138,X_139,Y_140] :
( member(U_138,universal_class)
| ~ member(U_138,unordered_pair(X_139,Y_140)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_350,plain,
! [U_138,X_14] :
( member(U_138,universal_class)
| ~ member(U_138,singleton(X_14)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_344]) ).
tff(c_4713,plain,
! [X_464] :
( member(X_464,universal_class)
| ( singleton(X_464) = null_class ) ),
inference(resolution,[status(thm)],[c_4665,c_350]) ).
tff(c_182,plain,
~ member('#skF_8',universal_class),
inference(cnfTransformation,[status(thm)],[f_381]) ).
tff(c_4753,plain,
singleton('#skF_8') = null_class,
inference(resolution,[status(thm)],[c_4713,c_182]) ).
tff(c_4770,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_180,c_4753]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET082+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n027.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 16:34:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 6.69/2.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.69/2.82
% 6.69/2.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.27/2.86
% 7.27/2.86 Inference rules
% 7.27/2.86 ----------------------
% 7.27/2.86 #Ref : 0
% 7.27/2.86 #Sup : 1004
% 7.27/2.86 #Fact : 0
% 7.27/2.86 #Define : 0
% 7.27/2.86 #Split : 23
% 7.27/2.86 #Chain : 0
% 7.27/2.86 #Close : 0
% 7.27/2.86
% 7.27/2.86 Ordering : KBO
% 7.27/2.86
% 7.27/2.86 Simplification rules
% 7.27/2.86 ----------------------
% 7.27/2.86 #Subsume : 181
% 7.27/2.86 #Demod : 176
% 7.27/2.86 #Tautology : 156
% 7.27/2.86 #SimpNegUnit : 11
% 7.27/2.86 #BackRed : 3
% 7.27/2.86
% 7.27/2.86 #Partial instantiations: 0
% 7.27/2.86 #Strategies tried : 1
% 7.27/2.86
% 7.27/2.86 Timing (in seconds)
% 7.27/2.86 ----------------------
% 7.27/2.86 Preprocessing : 0.65
% 7.27/2.86 Parsing : 0.34
% 7.27/2.86 CNF conversion : 0.05
% 7.27/2.86 Main loop : 1.05
% 7.27/2.86 Inferencing : 0.37
% 7.27/2.86 Reduction : 0.31
% 7.27/2.86 Demodulation : 0.21
% 7.27/2.86 BG Simplification : 0.05
% 7.27/2.86 Subsumption : 0.24
% 7.27/2.86 Abstraction : 0.04
% 7.27/2.86 MUC search : 0.00
% 7.27/2.86 Cooper : 0.00
% 7.27/2.86 Total : 1.77
% 7.27/2.86 Index Insertion : 0.00
% 7.27/2.86 Index Deletion : 0.00
% 7.27/2.86 Index Matching : 0.00
% 7.27/2.87 BG Taut test : 0.00
%------------------------------------------------------------------------------