TSTP Solution File: SET077+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET077+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 : n010.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 3.96s 1.90s
% Output : CNFRefutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 42
% Syntax : Number of formulae : 47 ( 8 unt; 39 typ; 0 def)
% Number of atoms : 8 ( 2 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 8 con; 0-3 aty)
% Number of variables : 8 (; 8 !; 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_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(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_97,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
tff(f_378,negated_conjecture,
~ ! [X] : member(singleton(X),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletons_are_sets) ).
tff(c_186,plain,
! [X_100] : ( unordered_pair(X_100,X_100) = singleton(X_100) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_24,plain,
! [X_12,Y_13] : member(unordered_pair(X_12,Y_13),universal_class),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_191,plain,
! [X_100] : member(singleton(X_100),universal_class),
inference(superposition,[status(thm),theory(equality)],[c_186,c_24]) ).
tff(c_180,plain,
~ member(singleton('#skF_8'),universal_class),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_199,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_191,c_180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET077+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
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 16:38:43 EDT 2023
% 0.15/0.35 % CPUTime :
% 3.96/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.96/1.90
% 3.96/1.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.96/1.92
% 3.96/1.92 Inference rules
% 3.96/1.92 ----------------------
% 3.96/1.92 #Ref : 0
% 3.96/1.92 #Sup : 3
% 3.96/1.92 #Fact : 0
% 3.96/1.92 #Define : 0
% 3.96/1.92 #Split : 0
% 3.96/1.92 #Chain : 0
% 3.96/1.92 #Close : 0
% 3.96/1.92
% 3.96/1.92 Ordering : KBO
% 3.96/1.92
% 3.96/1.92 Simplification rules
% 3.96/1.92 ----------------------
% 3.96/1.92 #Subsume : 0
% 3.96/1.92 #Demod : 2
% 3.96/1.92 #Tautology : 3
% 3.96/1.92 #SimpNegUnit : 0
% 3.96/1.92 #BackRed : 1
% 3.96/1.92
% 3.96/1.92 #Partial instantiations: 0
% 3.96/1.92 #Strategies tried : 1
% 3.96/1.92
% 3.96/1.92 Timing (in seconds)
% 3.96/1.92 ----------------------
% 3.96/1.93 Preprocessing : 0.64
% 3.96/1.93 Parsing : 0.33
% 3.96/1.93 CNF conversion : 0.05
% 3.96/1.93 Main loop : 0.22
% 3.96/1.93 Inferencing : 0.04
% 3.96/1.93 Reduction : 0.09
% 3.96/1.93 Demodulation : 0.07
% 3.96/1.93 BG Simplification : 0.03
% 3.96/1.93 Subsumption : 0.06
% 3.96/1.93 Abstraction : 0.01
% 3.96/1.93 MUC search : 0.00
% 3.96/1.93 Cooper : 0.00
% 3.96/1.93 Total : 0.91
% 3.96/1.93 Index Insertion : 0.00
% 3.96/1.93 Index Deletion : 0.00
% 3.96/1.93 Index Matching : 0.00
% 3.96/1.93 BG Taut test : 0.00
%------------------------------------------------------------------------------