TSTP Solution File: SET020+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET020+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 : n008.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 10:55:34 EDT 2023
% Result : Theorem 10.54s 3.62s
% Output : CNFRefutation 10.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 43
% Syntax : Number of formulae : 57 ( 9 unt; 41 typ; 0 def)
% Number of atoms : 32 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 29 ( 13 ~; 9 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 9 (; 9 !; 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_387,negated_conjecture,
~ ! [U,V,X] :
( ( member(U,universal_class)
& member(V,universal_class)
& ( X = ordered_pair(U,V) ) )
=> ( ( first(X) = U )
& ( second(X) = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
tff(f_128,axiom,
! [X,Y] :
( ( member(X,universal_class)
& member(Y,universal_class) )
=> ( ( first(ordered_pair(X,Y)) = X )
& ( second(ordered_pair(X,Y)) = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',first_second) ).
tff(c_180,plain,
( ( second('#skF_10') != '#skF_9' )
| ( first('#skF_10') != '#skF_8' ) ),
inference(cnfTransformation,[status(thm)],[f_387]) ).
tff(c_195,plain,
first('#skF_10') != '#skF_8',
inference(splitLeft,[status(thm)],[c_180]) ).
tff(c_186,plain,
member('#skF_8',universal_class),
inference(cnfTransformation,[status(thm)],[f_387]) ).
tff(c_184,plain,
member('#skF_9',universal_class),
inference(cnfTransformation,[status(thm)],[f_387]) ).
tff(c_182,plain,
ordered_pair('#skF_8','#skF_9') = '#skF_10',
inference(cnfTransformation,[status(thm)],[f_387]) ).
tff(c_5536,plain,
! [X_475,Y_476] :
( ( first(ordered_pair(X_475,Y_476)) = X_475 )
| ~ member(Y_476,universal_class)
| ~ member(X_475,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_5548,plain,
( ( first('#skF_10') = '#skF_8' )
| ~ member('#skF_9',universal_class)
| ~ member('#skF_8',universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_182,c_5536]) ).
tff(c_5552,plain,
first('#skF_10') = '#skF_8',
inference(demodulation,[status(thm),theory(equality)],[c_186,c_184,c_5548]) ).
tff(c_5554,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_195,c_5552]) ).
tff(c_5555,plain,
second('#skF_10') != '#skF_9',
inference(splitRight,[status(thm)],[c_180]) ).
tff(c_11762,plain,
! [X_903,Y_904] :
( ( second(ordered_pair(X_903,Y_904)) = Y_904 )
| ~ member(Y_904,universal_class)
| ~ member(X_903,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_11774,plain,
( ( second('#skF_10') = '#skF_9' )
| ~ member('#skF_9',universal_class)
| ~ member('#skF_8',universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_182,c_11762]) ).
tff(c_11778,plain,
second('#skF_10') = '#skF_9',
inference(demodulation,[status(thm),theory(equality)],[c_186,c_184,c_11774]) ).
tff(c_11780,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5555,c_11778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.14 % 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
% 0.17/0.35 % Computer : n008.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 3 16:53:49 EDT 2023
% 0.17/0.35 % CPUTime :
% 10.54/3.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.54/3.62
% 10.54/3.62 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.54/3.64
% 10.54/3.64 Inference rules
% 10.54/3.64 ----------------------
% 10.54/3.64 #Ref : 0
% 10.54/3.64 #Sup : 2519
% 10.54/3.64 #Fact : 0
% 10.54/3.64 #Define : 0
% 10.54/3.64 #Split : 90
% 10.54/3.64 #Chain : 0
% 10.54/3.64 #Close : 0
% 10.54/3.64
% 10.54/3.64 Ordering : KBO
% 10.54/3.64
% 10.54/3.64 Simplification rules
% 10.54/3.64 ----------------------
% 10.54/3.64 #Subsume : 500
% 10.54/3.65 #Demod : 444
% 10.54/3.65 #Tautology : 338
% 10.54/3.65 #SimpNegUnit : 28
% 10.54/3.65 #BackRed : 7
% 10.54/3.65
% 10.54/3.65 #Partial instantiations: 0
% 10.54/3.65 #Strategies tried : 1
% 10.54/3.65
% 10.54/3.65 Timing (in seconds)
% 10.54/3.65 ----------------------
% 10.54/3.65 Preprocessing : 0.67
% 10.54/3.65 Parsing : 0.34
% 10.54/3.65 CNF conversion : 0.05
% 10.54/3.65 Main loop : 1.90
% 10.54/3.65 Inferencing : 0.63
% 10.54/3.65 Reduction : 0.62
% 10.54/3.65 Demodulation : 0.41
% 10.54/3.65 BG Simplification : 0.06
% 10.54/3.65 Subsumption : 0.42
% 10.54/3.65 Abstraction : 0.05
% 10.54/3.65 MUC search : 0.00
% 10.54/3.65 Cooper : 0.00
% 10.54/3.65 Total : 2.61
% 10.54/3.65 Index Insertion : 0.00
% 10.54/3.65 Index Deletion : 0.00
% 10.54/3.65 Index Matching : 0.00
% 10.54/3.65 BG Taut test : 0.00
%------------------------------------------------------------------------------