TSTP Solution File: SET067+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET067+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 : n016.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 10:55:48 EDT 2023
% Result : Theorem 10.23s 3.54s
% Output : CNFRefutation 10.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 44
% Syntax : Number of formulae : 63 ( 11 unt; 40 typ; 0 def)
% Number of atoms : 40 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 12 ~; 13 |; 1 &)
% ( 2 <=>; 1 =>; 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 : 28 (; 28 !; 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_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_378,negated_conjecture,
~ ! [X,Y] : subclass(unordered_pair(X,X),unordered_pair(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pair_contains_other) ).
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_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_26,plain,
! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_180,plain,
~ subclass(unordered_pair('#skF_8','#skF_8'),unordered_pair('#skF_8','#skF_9')),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_181,plain,
~ subclass(singleton('#skF_8'),unordered_pair('#skF_8','#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_180]) ).
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_2581,plain,
! [Y_314,U_315,X_316] :
( ( Y_314 = U_315 )
| ( X_316 = U_315 )
| ~ member(U_315,unordered_pair(X_316,Y_314)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_3224,plain,
! [X_356,U_357] :
( ( X_356 = U_357 )
| ( X_356 = U_357 )
| ~ member(U_357,singleton(X_356)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_2581]) ).
tff(c_8975,plain,
! [X_701,Y_702] :
( ( '#skF_1'(singleton(X_701),Y_702) = X_701 )
| subclass(singleton(X_701),Y_702) ),
inference(resolution,[status(thm)],[c_6,c_3224]) ).
tff(c_9004,plain,
'#skF_1'(singleton('#skF_8'),unordered_pair('#skF_8','#skF_9')) = '#skF_8',
inference(resolution,[status(thm)],[c_8975,c_181]) ).
tff(c_9011,plain,
( member('#skF_8',singleton('#skF_8'))
| subclass(singleton('#skF_8'),unordered_pair('#skF_8','#skF_9')) ),
inference(superposition,[status(thm),theory(equality)],[c_9004,c_6]) ).
tff(c_9015,plain,
member('#skF_8',singleton('#skF_8')),
inference(negUnitSimplification,[status(thm)],[c_181,c_9011]) ).
tff(c_451,plain,
! [U_162,X_163,Y_164] :
( member(U_162,universal_class)
| ~ member(U_162,unordered_pair(X_163,Y_164)) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_468,plain,
! [U_162,X_14] :
( member(U_162,universal_class)
| ~ member(U_162,singleton(X_14)) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_451]) ).
tff(c_9037,plain,
member('#skF_8',universal_class),
inference(resolution,[status(thm)],[c_9015,c_468]) ).
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_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_9008,plain,
( ~ member('#skF_8',unordered_pair('#skF_8','#skF_9'))
| subclass(singleton('#skF_8'),unordered_pair('#skF_8','#skF_9')) ),
inference(superposition,[status(thm),theory(equality)],[c_9004,c_4]) ).
tff(c_9014,plain,
~ member('#skF_8',unordered_pair('#skF_8','#skF_9')),
inference(negUnitSimplification,[status(thm)],[c_181,c_9008]) ).
tff(c_9061,plain,
~ member('#skF_8',universal_class),
inference(resolution,[status(thm)],[c_22,c_9014]) ).
tff(c_9065,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9037,c_9061]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET067+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 : n016.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 17:01:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 10.23/3.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.23/3.55
% 10.23/3.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.23/3.57
% 10.23/3.57 Inference rules
% 10.23/3.57 ----------------------
% 10.23/3.57 #Ref : 0
% 10.23/3.57 #Sup : 1873
% 10.23/3.57 #Fact : 0
% 10.23/3.57 #Define : 0
% 10.23/3.57 #Split : 41
% 10.23/3.57 #Chain : 0
% 10.23/3.57 #Close : 0
% 10.23/3.57
% 10.23/3.57 Ordering : KBO
% 10.23/3.57
% 10.23/3.58 Simplification rules
% 10.23/3.58 ----------------------
% 10.23/3.58 #Subsume : 422
% 10.23/3.58 #Demod : 515
% 10.23/3.58 #Tautology : 216
% 10.23/3.58 #SimpNegUnit : 29
% 10.23/3.58 #BackRed : 163
% 10.23/3.58
% 10.23/3.58 #Partial instantiations: 0
% 10.23/3.58 #Strategies tried : 1
% 10.23/3.58
% 10.23/3.58 Timing (in seconds)
% 10.23/3.58 ----------------------
% 10.23/3.58 Preprocessing : 0.74
% 10.23/3.58 Parsing : 0.36
% 10.23/3.58 CNF conversion : 0.06
% 10.23/3.58 Main loop : 1.71
% 10.23/3.58 Inferencing : 0.56
% 10.23/3.58 Reduction : 0.54
% 10.23/3.58 Demodulation : 0.35
% 10.23/3.58 BG Simplification : 0.06
% 10.23/3.58 Subsumption : 0.42
% 10.23/3.58 Abstraction : 0.05
% 10.23/3.58 MUC search : 0.00
% 10.23/3.58 Cooper : 0.00
% 10.23/3.58 Total : 2.50
% 10.23/3.58 Index Insertion : 0.00
% 10.23/3.58 Index Deletion : 0.00
% 10.23/3.58 Index Matching : 0.00
% 10.23/3.58 BG Taut test : 0.00
%------------------------------------------------------------------------------