TSTP Solution File: SET083+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET083+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 : n005.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 6.41s 2.51s
% Output : CNFRefutation 6.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 48
% Syntax : Number of formulae : 80 ( 19 unt; 40 typ; 0 def)
% Number of atoms : 71 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 24 ~; 21 |; 5 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 40 (; 39 !; 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_172,axiom,
! [X] : ~ member(X,null_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
tff(f_382,negated_conjecture,
~ ! [X,Y] :
( ( ( singleton(X) = singleton(Y) )
& member(X,universal_class) )
=> ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_identified_by_element1) ).
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_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(f_224,axiom,
! [X] : ( successor(X) = union(X,singleton(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',successor_defn) ).
tff(f_209,axiom,
! [X,Y,Z] :
( member(Z,union(X,Y))
<=> ( member(Z,X)
| member(Z,Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',union_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(c_64,plain,
! [X_36] : ~ member(X_36,null_class),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_184,plain,
singleton('#skF_9') = singleton('#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_26,plain,
! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_1734,plain,
! [Y_251,U_252,X_253] :
( ( Y_251 = U_252 )
| ( X_253 = U_252 )
| ~ member(U_252,unordered_pair(X_253,Y_251)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_2194,plain,
! [X_289,U_290] :
( ( X_289 = U_290 )
| ( X_289 = U_290 )
| ~ member(U_290,singleton(X_289)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1734]) ).
tff(c_2249,plain,
! [X_291] :
( ( '#skF_6'(singleton(X_291)) = X_291 )
| ( singleton(X_291) = null_class ) ),
inference(resolution,[status(thm)],[c_170,c_2194]) ).
tff(c_2267,plain,
( ( '#skF_6'(singleton('#skF_8')) = '#skF_9' )
| ( singleton('#skF_9') = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_2249]) ).
tff(c_2270,plain,
( ( '#skF_6'(singleton('#skF_8')) = '#skF_9' )
| ( singleton('#skF_8') = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_184,c_2267]) ).
tff(c_2291,plain,
singleton('#skF_8') = null_class,
inference(splitLeft,[status(thm)],[c_2270]) ).
tff(c_182,plain,
member('#skF_8',universal_class),
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_374,plain,
! [Y_146,X_147] :
( member(Y_146,unordered_pair(X_147,Y_146))
| ~ member(Y_146,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_377,plain,
! [X_14] :
( member(X_14,singleton(X_14))
| ~ member(X_14,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_374]) ).
tff(c_94,plain,
! [X_52] : ( union(X_52,singleton(X_52)) = successor(X_52) ),
inference(cnfTransformation,[status(thm)],[f_224]) ).
tff(c_506,plain,
! [Z_164,Y_165,X_166] :
( ~ member(Z_164,Y_165)
| member(Z_164,union(X_166,Y_165)) ),
inference(cnfTransformation,[status(thm)],[f_209]) ).
tff(c_512,plain,
! [Z_164,X_52] :
( ~ member(Z_164,singleton(X_52))
| member(Z_164,successor(X_52)) ),
inference(superposition,[status(thm),theory(equality)],[c_94,c_506]) ).
tff(c_1416,plain,
! [U_234,Y_235,X_236] :
( ~ member(U_234,Y_235)
| ~ member(U_234,X_236)
| ~ disjoint(X_236,Y_235) ),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_1492,plain,
! [X_237] :
( ~ member('#skF_8',X_237)
| ~ disjoint(X_237,universal_class) ),
inference(resolution,[status(thm)],[c_182,c_1416]) ).
tff(c_1701,plain,
! [X_247] :
( ~ disjoint(successor(X_247),universal_class)
| ~ member('#skF_8',singleton(X_247)) ),
inference(resolution,[status(thm)],[c_512,c_1492]) ).
tff(c_1708,plain,
( ~ disjoint(successor('#skF_9'),universal_class)
| ~ member('#skF_8',singleton('#skF_8')) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_1701]) ).
tff(c_1787,plain,
~ member('#skF_8',singleton('#skF_8')),
inference(splitLeft,[status(thm)],[c_1708]) ).
tff(c_1790,plain,
~ member('#skF_8',universal_class),
inference(resolution,[status(thm)],[c_377,c_1787]) ).
tff(c_1794,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_182,c_1790]) ).
tff(c_1796,plain,
member('#skF_8',singleton('#skF_8')),
inference(splitRight,[status(thm)],[c_1708]) ).
tff(c_2295,plain,
member('#skF_8',null_class),
inference(demodulation,[status(thm),theory(equality)],[c_2291,c_1796]) ).
tff(c_2309,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_64,c_2295]) ).
tff(c_2311,plain,
singleton('#skF_8') != null_class,
inference(splitRight,[status(thm)],[c_2270]) ).
tff(c_180,plain,
'#skF_9' != '#skF_8',
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_2310,plain,
'#skF_6'(singleton('#skF_8')) = '#skF_9',
inference(splitRight,[status(thm)],[c_2270]) ).
tff(c_2246,plain,
! [X_289] :
( ( '#skF_6'(singleton(X_289)) = X_289 )
| ( singleton(X_289) = null_class ) ),
inference(resolution,[status(thm)],[c_170,c_2194]) ).
tff(c_2315,plain,
( ( '#skF_9' = '#skF_8' )
| ( singleton('#skF_8') = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_2310,c_2246]) ).
tff(c_2331,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2311,c_180,c_2315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET083+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/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
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 16:08:12 EDT 2023
% 0.13/0.35 % CPUTime :
% 6.41/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.41/2.52
% 6.41/2.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.41/2.55
% 6.41/2.55 Inference rules
% 6.41/2.55 ----------------------
% 6.41/2.55 #Ref : 0
% 6.41/2.55 #Sup : 464
% 6.41/2.55 #Fact : 0
% 6.41/2.55 #Define : 0
% 6.41/2.55 #Split : 16
% 6.41/2.55 #Chain : 0
% 6.41/2.55 #Close : 0
% 6.41/2.55
% 6.41/2.55 Ordering : KBO
% 6.41/2.55
% 6.41/2.55 Simplification rules
% 6.41/2.55 ----------------------
% 6.41/2.55 #Subsume : 111
% 6.41/2.55 #Demod : 91
% 6.41/2.55 #Tautology : 88
% 6.41/2.55 #SimpNegUnit : 3
% 6.41/2.55 #BackRed : 13
% 6.41/2.55
% 6.41/2.55 #Partial instantiations: 0
% 6.41/2.55 #Strategies tried : 1
% 6.41/2.55
% 6.41/2.55 Timing (in seconds)
% 6.41/2.55 ----------------------
% 6.41/2.56 Preprocessing : 0.66
% 6.41/2.56 Parsing : 0.33
% 6.41/2.56 CNF conversion : 0.05
% 6.41/2.56 Main loop : 0.83
% 6.41/2.56 Inferencing : 0.28
% 6.41/2.56 Reduction : 0.26
% 6.41/2.56 Demodulation : 0.18
% 6.41/2.56 BG Simplification : 0.04
% 6.41/2.56 Subsumption : 0.18
% 6.41/2.56 Abstraction : 0.03
% 6.41/2.56 MUC search : 0.00
% 6.41/2.56 Cooper : 0.00
% 6.41/2.56 Total : 1.54
% 6.41/2.56 Index Insertion : 0.00
% 6.41/2.56 Index Deletion : 0.00
% 6.41/2.56 Index Matching : 0.00
% 6.41/2.56 BG Taut test : 0.00
%------------------------------------------------------------------------------