TSTP Solution File: SET101-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET101-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n007.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 10:55:58 EDT 2023
% Result : Unsatisfiable 4.74s 2.30s
% Output : CNFRefutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 54
% Syntax : Number of formulae : 63 ( 11 unt; 49 typ; 0 def)
% Number of atoms : 17 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 39 >; 26 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 10 con; 0-3 aty)
% Number of variables : 19 (; 19 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ homomorphism > compatible > subclass > member > single_valued_class > operation > one_to_one > inductive > function > restrict > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordered_pair > not_subclass_element > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > complement > cantor > y > x > universal_class > successor_relation > subset_relation > omega > null_class > identity_relation > element_relation > choice
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(omega,type,
omega: $i ).
tff(null_class,type,
null_class: $i ).
tff(rotate,type,
rotate: $i > $i ).
tff(subclass,type,
subclass: ( $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(single_valued_class,type,
single_valued_class: $i > $o ).
tff(operation,type,
operation: $i > $o ).
tff(sum_class,type,
sum_class: $i > $i ).
tff(x,type,
x: $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(compatible,type,
compatible: ( $i * $i * $i ) > $o ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(regular,type,
regular: $i > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
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(symmetric_difference,type,
symmetric_difference: ( $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(choice,type,
choice: $i ).
tff(y,type,
y: $i ).
tff(subset_relation,type,
subset_relation: $i ).
tff(restrict,type,
restrict: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
tff(first,type,
first: $i > $i ).
tff(diagonalise,type,
diagonalise: $i > $i ).
tff(homomorphism,type,
homomorphism: ( $i * $i * $i ) > $o ).
tff(cantor,type,
cantor: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff(inductive,type,
inductive: $i > $o ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(successor,type,
successor: $i > $i ).
tff(successor_relation,type,
successor_relation: $i ).
tff(identity_relation,type,
identity_relation: $i ).
tff(not_homomorphism1,type,
not_homomorphism1: ( $i * $i * $i ) > $i ).
tff(universal_class,type,
universal_class: $i ).
tff(f_123,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_119,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file(unknown,unknown) ).
tff(f_128,axiom,
! [X,Y] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
file(unknown,unknown) ).
tff(f_109,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_645,axiom,
~ member(singleton(x),ordered_pair(x,y)),
file(unknown,unknown) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_211,plain,
! [X_184,Y_185] : member(unordered_pair(X_184,Y_185),universal_class),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_213,plain,
! [X_24] : member(singleton(X_24),universal_class),
inference(superposition,[status(thm),theory(equality)],[c_24,c_211]) ).
tff(c_1019,plain,
! [X_305,Y_306] : ( unordered_pair(singleton(X_305),unordered_pair(X_305,singleton(Y_306))) = ordered_pair(X_305,Y_306) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
tff(c_18,plain,
! [X_18,Y_19] :
( member(X_18,unordered_pair(X_18,Y_19))
| ~ member(X_18,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_1033,plain,
! [X_305,Y_306] :
( member(singleton(X_305),ordered_pair(X_305,Y_306))
| ~ member(singleton(X_305),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1019,c_18]) ).
tff(c_1048,plain,
! [X_305,Y_306] : member(singleton(X_305),ordered_pair(X_305,Y_306)),
inference(demodulation,[status(thm),theory(equality)],[c_213,c_1033]) ).
tff(c_184,plain,
~ member(singleton(x),ordered_pair(x,y)),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_1058,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1048,c_184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET101-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 15:55:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.74/2.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.74/2.31
% 4.74/2.31 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.74/2.35
% 4.74/2.35 Inference rules
% 4.74/2.35 ----------------------
% 4.74/2.35 #Ref : 0
% 4.74/2.35 #Sup : 198
% 4.74/2.35 #Fact : 0
% 4.74/2.35 #Define : 0
% 4.74/2.35 #Split : 8
% 4.74/2.35 #Chain : 0
% 4.74/2.35 #Close : 0
% 4.74/2.35
% 4.74/2.35 Ordering : KBO
% 4.74/2.35
% 4.74/2.35 Simplification rules
% 4.74/2.35 ----------------------
% 4.74/2.35 #Subsume : 27
% 4.74/2.35 #Demod : 22
% 4.74/2.35 #Tautology : 50
% 4.74/2.35 #SimpNegUnit : 1
% 4.74/2.35 #BackRed : 2
% 4.74/2.35
% 4.74/2.35 #Partial instantiations: 0
% 4.74/2.35 #Strategies tried : 1
% 4.74/2.35
% 4.74/2.35 Timing (in seconds)
% 4.74/2.35 ----------------------
% 4.74/2.35 Preprocessing : 0.70
% 4.74/2.35 Parsing : 0.37
% 4.74/2.35 CNF conversion : 0.05
% 4.74/2.35 Main loop : 0.54
% 4.74/2.35 Inferencing : 0.17
% 4.74/2.35 Reduction : 0.18
% 4.74/2.35 Demodulation : 0.12
% 4.74/2.35 BG Simplification : 0.04
% 4.74/2.35 Subsumption : 0.11
% 4.74/2.35 Abstraction : 0.02
% 4.74/2.35 MUC search : 0.00
% 4.74/2.35 Cooper : 0.00
% 4.74/2.35 Total : 1.31
% 4.74/2.35 Index Insertion : 0.00
% 4.74/2.35 Index Deletion : 0.00
% 4.74/2.36 Index Matching : 0.00
% 4.74/2.36 BG Taut test : 0.00
%------------------------------------------------------------------------------