TSTP Solution File: SET072+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET072+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 : n024.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 10:55:49 EDT 2023
% Result : Theorem 5.44s 2.28s
% Output : CNFRefutation 5.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 44
% Syntax : Number of formulae : 64 ( 13 unt; 41 typ; 0 def)
% Number of atoms : 40 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 9 ~; 12 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 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 : 36 ( 36 usr; 10 con; 0-3 aty)
% Number of variables : 17 (; 17 !; 0 ?; 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_10 > #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('#skF_10',type,
'#skF_10': $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_384,negated_conjecture,
~ ! [X,Y,Z] :
( ( member(X,universal_class)
& member(Y,universal_class)
& ( unordered_pair(X,Z) = unordered_pair(Y,Z) ) )
=> ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation) ).
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_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,
'#skF_9' != '#skF_8',
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_186,plain,
member('#skF_8',universal_class),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_26,plain,
! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_184,plain,
member('#skF_9',universal_class),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_182,plain,
unordered_pair('#skF_9','#skF_10') = unordered_pair('#skF_8','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_343,plain,
! [X_135,Y_136] :
( member(X_135,unordered_pair(X_135,Y_136))
| ~ member(X_135,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_349,plain,
( member('#skF_9',unordered_pair('#skF_8','#skF_10'))
| ~ member('#skF_9',universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_182,c_343]) ).
tff(c_351,plain,
member('#skF_9',unordered_pair('#skF_8','#skF_10')),
inference(demodulation,[status(thm),theory(equality)],[c_184,c_349]) ).
tff(c_1090,plain,
! [Y_226,U_227,X_228] :
( ( Y_226 = U_227 )
| ( X_228 = U_227 )
| ~ member(U_227,unordered_pair(X_228,Y_226)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_1108,plain,
( ( '#skF_10' = '#skF_9' )
| ( '#skF_9' = '#skF_8' ) ),
inference(resolution,[status(thm)],[c_351,c_1090]) ).
tff(c_1133,plain,
'#skF_10' = '#skF_9',
inference(negUnitSimplification,[status(thm)],[c_180,c_1108]) ).
tff(c_1139,plain,
unordered_pair('#skF_9','#skF_9') = unordered_pair('#skF_8','#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_1133,c_1133,c_182]) ).
tff(c_1140,plain,
unordered_pair('#skF_8','#skF_9') = singleton('#skF_9'),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_1139]) ).
tff(c_22,plain,
! [X_10,Y_11] :
( member(X_10,unordered_pair(X_10,Y_11))
| ~ member(X_10,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_1176,plain,
( member('#skF_8',singleton('#skF_9'))
| ~ member('#skF_8',universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1140,c_22]) ).
tff(c_1184,plain,
member('#skF_8',singleton('#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_186,c_1176]) ).
tff(c_1125,plain,
! [U_227] :
( ( U_227 = '#skF_10' )
| ( U_227 = '#skF_9' )
| ~ member(U_227,unordered_pair('#skF_8','#skF_10')) ),
inference(superposition,[status(thm),theory(equality)],[c_182,c_1090]) ).
tff(c_1486,plain,
! [U_244] :
( ( U_244 = '#skF_9' )
| ( U_244 = '#skF_9' )
| ~ member(U_244,singleton('#skF_9')) ),
inference(demodulation,[status(thm),theory(equality)],[c_1140,c_1133,c_1133,c_1125]) ).
tff(c_1489,plain,
'#skF_9' = '#skF_8',
inference(resolution,[status(thm)],[c_1184,c_1486]) ).
tff(c_1520,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_180,c_180,c_1489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET072+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.14 % 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
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 16:17:45 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.44/2.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/2.28
% 5.44/2.28 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.44/2.31
% 5.44/2.31 Inference rules
% 5.44/2.31 ----------------------
% 5.44/2.31 #Ref : 0
% 5.44/2.31 #Sup : 298
% 5.44/2.31 #Fact : 0
% 5.44/2.31 #Define : 0
% 5.44/2.31 #Split : 7
% 5.44/2.31 #Chain : 0
% 5.44/2.31 #Close : 0
% 5.44/2.31
% 5.44/2.31 Ordering : KBO
% 5.44/2.31
% 5.44/2.31 Simplification rules
% 5.44/2.31 ----------------------
% 5.44/2.31 #Subsume : 49
% 5.44/2.31 #Demod : 41
% 5.44/2.31 #Tautology : 59
% 5.44/2.31 #SimpNegUnit : 3
% 5.44/2.31 #BackRed : 3
% 5.44/2.31
% 5.44/2.31 #Partial instantiations: 0
% 5.44/2.31 #Strategies tried : 1
% 5.44/2.31
% 5.44/2.31 Timing (in seconds)
% 5.44/2.31 ----------------------
% 5.44/2.31 Preprocessing : 0.63
% 5.44/2.31 Parsing : 0.32
% 5.44/2.31 CNF conversion : 0.05
% 5.44/2.31 Main loop : 0.57
% 5.44/2.31 Inferencing : 0.20
% 5.44/2.31 Reduction : 0.18
% 5.44/2.31 Demodulation : 0.12
% 5.44/2.31 BG Simplification : 0.04
% 5.44/2.31 Subsumption : 0.12
% 5.44/2.31 Abstraction : 0.02
% 5.44/2.31 MUC search : 0.00
% 5.44/2.31 Cooper : 0.00
% 5.44/2.31 Total : 1.24
% 5.44/2.31 Index Insertion : 0.00
% 5.44/2.31 Index Deletion : 0.00
% 5.44/2.31 Index Matching : 0.00
% 5.44/2.31 BG Taut test : 0.00
%------------------------------------------------------------------------------