TSTP Solution File: SET065+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET065+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 : n002.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 10:55:47 EDT 2023
% Result : Theorem 4.62s 2.25s
% Output : CNFRefutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 43
% Syntax : Number of formulae : 52 ( 7 unt; 38 typ; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 6 |; 3 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 31 >; 16 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 7 con; 0-3 aty)
% Number of variables : 16 (; 15 !; 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_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(first,type,
first: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $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_377,negated_conjecture,
~ member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
tff(f_70,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
tff(f_252,axiom,
! [X] :
( inductive(X)
<=> ( member(null_class,X)
& subclass(image(successor_relation,X),X) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',inductive_defn) ).
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_262,axiom,
? [X] :
( member(X,universal_class)
& inductive(X)
& ! [Y] :
( inductive(Y)
=> subclass(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',infinity) ).
tff(c_180,plain,
~ member(null_class,universal_class),
inference(cnfTransformation,[status(thm)],[f_377]) ).
tff(c_8,plain,
! [X_6] : subclass(X_6,universal_class),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_116,plain,
! [X_59] :
( member(null_class,X_59)
| ~ inductive(X_59) ),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_943,plain,
! [U_212,Y_213,X_214] :
( member(U_212,Y_213)
| ~ member(U_212,X_214)
| ~ subclass(X_214,Y_213) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_1337,plain,
! [Y_238,X_239] :
( member(null_class,Y_238)
| ~ subclass(X_239,Y_238)
| ~ inductive(X_239) ),
inference(resolution,[status(thm)],[c_116,c_943]) ).
tff(c_1373,plain,
! [X_6] :
( member(null_class,universal_class)
| ~ inductive(X_6) ),
inference(resolution,[status(thm)],[c_8,c_1337]) ).
tff(c_1392,plain,
! [X_6] : ~ inductive(X_6),
inference(negUnitSimplification,[status(thm)],[c_180,c_1373]) ).
tff(c_120,plain,
inductive('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_1395,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1392,c_120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET065+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/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
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 17:06:01 EDT 2023
% 0.15/0.36 % CPUTime :
% 4.62/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.62/2.25
% 4.62/2.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.62/2.28
% 4.62/2.28 Inference rules
% 4.62/2.28 ----------------------
% 4.62/2.28 #Ref : 0
% 4.62/2.28 #Sup : 263
% 4.62/2.28 #Fact : 0
% 4.62/2.28 #Define : 0
% 4.62/2.28 #Split : 2
% 4.62/2.28 #Chain : 0
% 4.62/2.28 #Close : 0
% 4.62/2.28
% 4.62/2.28 Ordering : KBO
% 4.62/2.28
% 4.62/2.28 Simplification rules
% 4.62/2.28 ----------------------
% 4.62/2.28 #Subsume : 58
% 4.62/2.28 #Demod : 24
% 4.62/2.28 #Tautology : 47
% 4.62/2.28 #SimpNegUnit : 10
% 4.62/2.28 #BackRed : 1
% 4.62/2.28
% 4.62/2.28 #Partial instantiations: 0
% 4.62/2.28 #Strategies tried : 1
% 4.62/2.28
% 4.62/2.28 Timing (in seconds)
% 4.62/2.28 ----------------------
% 4.62/2.28 Preprocessing : 0.65
% 4.62/2.28 Parsing : 0.33
% 4.62/2.28 CNF conversion : 0.05
% 4.62/2.28 Main loop : 0.56
% 4.62/2.28 Inferencing : 0.19
% 4.62/2.28 Reduction : 0.16
% 4.62/2.28 Demodulation : 0.11
% 4.62/2.28 BG Simplification : 0.04
% 4.62/2.28 Subsumption : 0.12
% 4.62/2.28 Abstraction : 0.02
% 4.62/2.28 MUC search : 0.00
% 4.62/2.28 Cooper : 0.00
% 4.62/2.28 Total : 1.25
% 4.62/2.28 Index Insertion : 0.00
% 4.62/2.28 Index Deletion : 0.00
% 4.62/2.28 Index Matching : 0.00
% 4.62/2.28 BG Taut test : 0.00
%------------------------------------------------------------------------------