TSTP Solution File: SET076+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET076+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 : n032.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 10:55:51 EDT 2023
% Result : Theorem 35.67s 23.62s
% Output : CNFRefutation 35.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 44
% Syntax : Number of formulae : 60 ( 9 unt; 41 typ; 0 def)
% Number of atoms : 35 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 6 ~; 10 |; 2 &)
% ( 2 <=>; 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 : 36 ( 36 usr; 10 con; 0-3 aty)
% Number of variables : 19 (; 19 !; 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_382,negated_conjecture,
~ ! [X,Y,Z] :
( ( member(X,Z)
& member(Y,Z) )
=> subclass(unordered_pair(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
tff(f_67,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
tff(c_180,plain,
~ subclass(unordered_pair('#skF_8','#skF_9'),'#skF_10'),
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_182,plain,
member('#skF_9','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_184,plain,
member('#skF_8','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_382]) ).
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_849,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_83573,plain,
! [X_2188,Y_2189,Y_2190] :
( ( '#skF_1'(unordered_pair(X_2188,Y_2189),Y_2190) = Y_2189 )
| ( '#skF_1'(unordered_pair(X_2188,Y_2189),Y_2190) = X_2188 )
| subclass(unordered_pair(X_2188,Y_2189),Y_2190) ),
inference(resolution,[status(thm)],[c_6,c_849]) ).
tff(c_83645,plain,
( ( '#skF_1'(unordered_pair('#skF_8','#skF_9'),'#skF_10') = '#skF_9' )
| ( '#skF_1'(unordered_pair('#skF_8','#skF_9'),'#skF_10') = '#skF_8' ) ),
inference(resolution,[status(thm)],[c_83573,c_180]) ).
tff(c_83769,plain,
'#skF_1'(unordered_pair('#skF_8','#skF_9'),'#skF_10') = '#skF_8',
inference(splitLeft,[status(thm)],[c_83645]) ).
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_83793,plain,
( ~ member('#skF_8','#skF_10')
| subclass(unordered_pair('#skF_8','#skF_9'),'#skF_10') ),
inference(superposition,[status(thm),theory(equality)],[c_83769,c_4]) ).
tff(c_83805,plain,
subclass(unordered_pair('#skF_8','#skF_9'),'#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_184,c_83793]) ).
tff(c_83807,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_180,c_83805]) ).
tff(c_83808,plain,
'#skF_1'(unordered_pair('#skF_8','#skF_9'),'#skF_10') = '#skF_9',
inference(splitRight,[status(thm)],[c_83645]) ).
tff(c_83833,plain,
( ~ member('#skF_9','#skF_10')
| subclass(unordered_pair('#skF_8','#skF_9'),'#skF_10') ),
inference(superposition,[status(thm),theory(equality)],[c_83808,c_4]) ).
tff(c_83845,plain,
subclass(unordered_pair('#skF_8','#skF_9'),'#skF_10'),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_83833]) ).
tff(c_83847,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_180,c_83845]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET076+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.12 % 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
% 0.12/0.31 % Computer : n032.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Thu Aug 3 16:59:21 EDT 2023
% 0.12/0.31 % CPUTime :
% 35.67/23.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.67/23.63
% 35.67/23.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 35.67/23.65
% 35.67/23.65 Inference rules
% 35.67/23.65 ----------------------
% 35.67/23.65 #Ref : 0
% 35.67/23.65 #Sup : 20432
% 35.67/23.65 #Fact : 6
% 35.67/23.65 #Define : 0
% 35.67/23.65 #Split : 128
% 35.67/23.65 #Chain : 0
% 35.67/23.65 #Close : 0
% 35.67/23.65
% 35.67/23.65 Ordering : KBO
% 35.67/23.65
% 35.67/23.65 Simplification rules
% 35.67/23.65 ----------------------
% 35.67/23.65 #Subsume : 5690
% 35.67/23.65 #Demod : 6080
% 35.67/23.65 #Tautology : 3437
% 35.67/23.65 #SimpNegUnit : 610
% 35.67/23.65 #BackRed : 293
% 35.67/23.65
% 35.67/23.65 #Partial instantiations: 0
% 35.67/23.65 #Strategies tried : 1
% 35.67/23.65
% 35.67/23.65 Timing (in seconds)
% 35.67/23.65 ----------------------
% 35.67/23.66 Preprocessing : 0.69
% 35.67/23.66 Parsing : 0.35
% 35.67/23.66 CNF conversion : 0.05
% 35.67/23.66 Main loop : 21.94
% 35.67/23.66 Inferencing : 3.14
% 35.67/23.66 Reduction : 9.72
% 35.67/23.66 Demodulation : 6.45
% 35.67/23.66 BG Simplification : 0.12
% 35.67/23.66 Subsumption : 7.68
% 35.67/23.66 Abstraction : 0.18
% 35.67/23.66 MUC search : 0.00
% 35.67/23.66 Cooper : 0.00
% 35.67/23.66 Total : 22.67
% 35.67/23.66 Index Insertion : 0.00
% 35.67/23.66 Index Deletion : 0.00
% 35.67/23.66 Index Matching : 0.00
% 35.67/23.66 BG Taut test : 0.00
%------------------------------------------------------------------------------