TSTP Solution File: SET103+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET103+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 : n029.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 10:55:59 EDT 2023
% Result : Theorem 8.42s 3.00s
% Output : CNFRefutation 8.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 46
% Syntax : Number of formulae : 66 ( 13 unt; 40 typ; 0 def)
% Number of atoms : 49 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 10 ~; 19 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 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 : 36 (; 35 !; 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_100,axiom,
! [X] : ( singleton(X) = unordered_pair(X,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
tff(f_97,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
tff(f_380,negated_conjecture,
~ ! [X,Y] :
( ( unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(X,Y) )
| member(Y,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_1_of_ordered_pair) ).
tff(f_103,axiom,
! [X,Y] : ( ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
tff(c_188,plain,
! [X_100] : ( unordered_pair(X_100,X_100) = singleton(X_100) ),
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_193,plain,
! [X_100] : member(singleton(X_100),universal_class),
inference(superposition,[status(thm),theory(equality)],[c_188,c_24]) ).
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_26,plain,
! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_1864,plain,
! [Y_259,U_260,X_261] :
( ( Y_259 = U_260 )
| ( X_261 = U_260 )
| ~ member(U_260,unordered_pair(X_261,Y_259)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_3625,plain,
! [X_380,U_381] :
( ( X_380 = U_381 )
| ( X_380 = U_381 )
| ~ member(U_381,singleton(X_380)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1864]) ).
tff(c_3629,plain,
! [X_380] :
( ( apply('#skF_7',singleton(X_380)) = X_380 )
| ( singleton(X_380) = null_class )
| ~ member(singleton(X_380),universal_class) ),
inference(resolution,[status(thm)],[c_176,c_3625]) ).
tff(c_4607,plain,
! [X_458] :
( ( apply('#skF_7',singleton(X_458)) = X_458 )
| ( singleton(X_458) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_193,c_3629]) ).
tff(c_4613,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_4607,c_176]) ).
tff(c_4885,plain,
! [X_462] :
( member(X_462,singleton(X_462))
| ( singleton(X_462) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_193,c_4613]) ).
tff(c_587,plain,
! [U_184,X_185,Y_186] :
( member(U_184,universal_class)
| ~ member(U_184,unordered_pair(X_185,Y_186)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_615,plain,
! [U_184,X_14] :
( member(U_184,universal_class)
| ~ member(U_184,singleton(X_14)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_587]) ).
tff(c_4951,plain,
! [X_463] :
( member(X_463,universal_class)
| ( singleton(X_463) = null_class ) ),
inference(resolution,[status(thm)],[c_4885,c_615]) ).
tff(c_180,plain,
~ member('#skF_9',universal_class),
inference(cnfTransformation,[status(thm)],[f_380]) ).
tff(c_5015,plain,
singleton('#skF_9') = null_class,
inference(resolution,[status(thm)],[c_4951,c_180]) ).
tff(c_28,plain,
! [X_15,Y_16] : ( unordered_pair(singleton(X_15),unordered_pair(X_15,singleton(Y_16))) = ordered_pair(X_15,Y_16) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_5055,plain,
! [X_15] : ( unordered_pair(singleton(X_15),unordered_pair(X_15,null_class)) = ordered_pair(X_15,'#skF_9') ),
inference(superposition,[status(thm),theory(equality)],[c_5015,c_28]) ).
tff(c_182,plain,
unordered_pair(singleton('#skF_8'),unordered_pair('#skF_8',null_class)) != ordered_pair('#skF_8','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_380]) ).
tff(c_5614,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5055,c_182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET103+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
% 0.14/0.35 % Computer : n029.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 16:56:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 8.42/3.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.42/3.01
% 8.42/3.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.76/3.04
% 8.76/3.04 Inference rules
% 8.76/3.04 ----------------------
% 8.76/3.04 #Ref : 0
% 8.76/3.04 #Sup : 1173
% 8.76/3.04 #Fact : 0
% 8.76/3.04 #Define : 0
% 8.76/3.04 #Split : 24
% 8.76/3.04 #Chain : 0
% 8.76/3.04 #Close : 0
% 8.76/3.04
% 8.76/3.04 Ordering : KBO
% 8.76/3.04
% 8.76/3.04 Simplification rules
% 8.76/3.04 ----------------------
% 8.76/3.04 #Subsume : 250
% 8.76/3.04 #Demod : 332
% 8.76/3.04 #Tautology : 169
% 8.76/3.04 #SimpNegUnit : 24
% 8.76/3.04 #BackRed : 119
% 8.76/3.04
% 8.76/3.04 #Partial instantiations: 0
% 8.76/3.04 #Strategies tried : 1
% 8.76/3.04
% 8.76/3.04 Timing (in seconds)
% 8.76/3.04 ----------------------
% 8.76/3.04 Preprocessing : 0.66
% 8.76/3.04 Parsing : 0.33
% 8.76/3.04 CNF conversion : 0.05
% 8.76/3.04 Main loop : 1.34
% 8.76/3.04 Inferencing : 0.44
% 8.76/3.04 Reduction : 0.43
% 8.76/3.04 Demodulation : 0.27
% 8.76/3.04 BG Simplification : 0.05
% 8.76/3.04 Subsumption : 0.30
% 8.76/3.04 Abstraction : 0.05
% 8.76/3.04 MUC search : 0.00
% 8.76/3.04 Cooper : 0.00
% 8.76/3.04 Total : 2.04
% 8.76/3.04 Index Insertion : 0.00
% 8.76/3.04 Index Deletion : 0.00
% 8.76/3.04 Index Matching : 0.00
% 8.76/3.04 BG Taut test : 0.00
%------------------------------------------------------------------------------