TSTP Solution File: SET096+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET096+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/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 : n028.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 10:55:57 EDT 2023
% Result : Theorem 14.45s 5.30s
% Output : CNFRefutation 14.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 47
% Syntax : Number of formulae : 77 ( 12 unt; 40 typ; 0 def)
% Number of atoms : 78 ( 25 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 66 ( 25 ~; 29 |; 5 &)
% ( 4 <=>; 3 =>; 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 : 35 ( 35 usr; 9 con; 0-3 aty)
% Number of variables : 49 (; 48 !; 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_9 > #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('#skF_9',type,
'#skF_9': $i ).
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_382,negated_conjecture,
~ ! [X,Y] :
( subclass(X,singleton(Y))
=> ( ( X = null_class )
| ( singleton(Y) = X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
tff(f_78,axiom,
! [X,Y] :
( ( X = Y )
<=> ( subclass(X,Y)
& subclass(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',extensionality) ).
tff(f_359,axiom,
! [X] :
( ( X != null_class )
=> ? [U] :
( member(U,universal_class)
& member(U,X)
& disjoint(U,X) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',regularity) ).
tff(f_67,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
tff(f_346,axiom,
! [X,Y] :
( disjoint(X,Y)
<=> ! [U] :
~ ( member(U,X)
& member(U,Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',disjoint_defn) ).
tff(f_100,axiom,
! [X] : ( singleton(X) = unordered_pair(X,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
tff(f_87,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( ( U = X )
| ( U = Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
tff(c_180,plain,
singleton('#skF_9') != '#skF_8',
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_184,plain,
subclass('#skF_8',singleton('#skF_9')),
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_495,plain,
! [Y_166,X_167] :
( ( Y_166 = X_167 )
| ~ subclass(Y_166,X_167)
| ~ subclass(X_167,Y_166) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_513,plain,
( ( singleton('#skF_9') = '#skF_8' )
| ~ subclass(singleton('#skF_9'),'#skF_8') ),
inference(resolution,[status(thm)],[c_184,c_495]) ).
tff(c_528,plain,
~ subclass(singleton('#skF_9'),'#skF_8'),
inference(negUnitSimplification,[status(thm)],[c_180,c_513]) ).
tff(c_182,plain,
null_class != '#skF_8',
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_170,plain,
! [X_89] :
( member('#skF_6'(X_89),X_89)
| ( null_class = X_89 ) ),
inference(cnfTransformation,[status(thm)],[f_359]) ).
tff(c_2188,plain,
! [U_281,Y_282,X_283] :
( member(U_281,Y_282)
| ~ member(U_281,X_283)
| ~ subclass(X_283,Y_282) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_2249,plain,
! [X_89,Y_282] :
( member('#skF_6'(X_89),Y_282)
| ~ subclass(X_89,Y_282)
| ( null_class = X_89 ) ),
inference(resolution,[status(thm)],[c_170,c_2188]) ).
tff(c_2530,plain,
! [U_293,Y_294,X_295] :
( ~ member(U_293,Y_294)
| ~ member(U_293,X_295)
| ~ disjoint(X_295,Y_294) ),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_6542,plain,
! [X_563,X_564] :
( ~ member('#skF_6'(X_563),X_564)
| ~ disjoint(X_564,X_563)
| ( null_class = X_563 ) ),
inference(resolution,[status(thm)],[c_170,c_2530]) ).
tff(c_6698,plain,
! [Y_571,X_572] :
( ~ disjoint(Y_571,X_572)
| ~ subclass(X_572,Y_571)
| ( null_class = X_572 ) ),
inference(resolution,[status(thm)],[c_2249,c_6542]) ).
tff(c_6737,plain,
( ~ disjoint(singleton('#skF_9'),'#skF_8')
| ( null_class = '#skF_8' ) ),
inference(resolution,[status(thm)],[c_184,c_6698]) ).
tff(c_6761,plain,
~ disjoint(singleton('#skF_9'),'#skF_8'),
inference(negUnitSimplification,[status(thm)],[c_182,c_6737]) ).
tff(c_166,plain,
! [X_84,Y_85] :
( member('#skF_5'(X_84,Y_85),X_84)
| disjoint(X_84,Y_85) ),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_26,plain,
! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_824,plain,
! [Y_206,U_207,X_208] :
( ( Y_206 = U_207 )
| ( X_208 = U_207 )
| ~ member(U_207,unordered_pair(X_208,Y_206)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_2138,plain,
! [X_278,U_279] :
( ( X_278 = U_279 )
| ( X_278 = U_279 )
| ~ member(U_279,singleton(X_278)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_824]) ).
tff(c_8647,plain,
! [X_651,Y_652] :
( ( '#skF_5'(singleton(X_651),Y_652) = X_651 )
| disjoint(singleton(X_651),Y_652) ),
inference(resolution,[status(thm)],[c_166,c_2138]) ).
tff(c_8726,plain,
'#skF_5'(singleton('#skF_9'),'#skF_8') = '#skF_9',
inference(resolution,[status(thm)],[c_8647,c_6761]) ).
tff(c_164,plain,
! [X_84,Y_85] :
( member('#skF_5'(X_84,Y_85),Y_85)
| disjoint(X_84,Y_85) ),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_8916,plain,
( member('#skF_9','#skF_8')
| disjoint(singleton('#skF_9'),'#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_8726,c_164]) ).
tff(c_8922,plain,
member('#skF_9','#skF_8'),
inference(negUnitSimplification,[status(thm)],[c_6761,c_8916]) ).
tff(c_6,plain,
! [X_1,Y_2] :
( member('#skF_1'(X_1,Y_2),X_1)
| subclass(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_19823,plain,
! [X_1013,Y_1014] :
( ( '#skF_1'(singleton(X_1013),Y_1014) = X_1013 )
| subclass(singleton(X_1013),Y_1014) ),
inference(resolution,[status(thm)],[c_6,c_2138]) ).
tff(c_19906,plain,
'#skF_1'(singleton('#skF_9'),'#skF_8') = '#skF_9',
inference(resolution,[status(thm)],[c_19823,c_528]) ).
tff(c_4,plain,
! [X_1,Y_2] :
( ~ member('#skF_1'(X_1,Y_2),Y_2)
| subclass(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_19920,plain,
( ~ member('#skF_9','#skF_8')
| subclass(singleton('#skF_9'),'#skF_8') ),
inference(superposition,[status(thm),theory(equality)],[c_19906,c_4]) ).
tff(c_19931,plain,
subclass(singleton('#skF_9'),'#skF_8'),
inference(demodulation,[status(thm),theory(equality)],[c_8922,c_19920]) ).
tff(c_19933,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_528,c_19931]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET096+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.14 % 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
% 0.18/0.36 % Computer : n028.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Thu Aug 3 17:09:09 EDT 2023
% 0.18/0.36 % CPUTime :
% 14.45/5.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.45/5.30
% 14.45/5.30 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.45/5.33
% 14.45/5.33 Inference rules
% 14.45/5.33 ----------------------
% 14.45/5.33 #Ref : 0
% 14.45/5.33 #Sup : 4473
% 14.45/5.33 #Fact : 0
% 14.45/5.33 #Define : 0
% 14.45/5.33 #Split : 81
% 14.45/5.33 #Chain : 0
% 14.45/5.33 #Close : 0
% 14.45/5.33
% 14.45/5.33 Ordering : KBO
% 14.45/5.33
% 14.45/5.33 Simplification rules
% 14.45/5.33 ----------------------
% 14.45/5.33 #Subsume : 1278
% 14.45/5.33 #Demod : 968
% 14.45/5.33 #Tautology : 578
% 14.45/5.33 #SimpNegUnit : 141
% 14.45/5.33 #BackRed : 169
% 14.45/5.33
% 14.45/5.33 #Partial instantiations: 0
% 14.45/5.33 #Strategies tried : 1
% 14.45/5.33
% 14.45/5.33 Timing (in seconds)
% 14.45/5.33 ----------------------
% 14.45/5.34 Preprocessing : 0.65
% 14.45/5.34 Parsing : 0.33
% 14.45/5.34 CNF conversion : 0.05
% 14.45/5.34 Main loop : 3.62
% 14.45/5.34 Inferencing : 0.92
% 14.45/5.34 Reduction : 1.28
% 14.45/5.34 Demodulation : 0.78
% 14.45/5.34 BG Simplification : 0.07
% 14.45/5.34 Subsumption : 1.04
% 14.45/5.34 Abstraction : 0.07
% 14.45/5.34 MUC search : 0.00
% 14.45/5.34 Cooper : 0.00
% 14.45/5.34 Total : 4.32
% 14.45/5.34 Index Insertion : 0.00
% 14.45/5.34 Index Deletion : 0.00
% 14.45/5.34 Index Matching : 0.00
% 14.45/5.34 BG Taut test : 0.00
%------------------------------------------------------------------------------