TSTP Solution File: SET016+4 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 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 : n021.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 10:55:32 EDT 2023
% Result : Theorem 4.11s 1.95s
% Output : CNFRefutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of formulae : 44 ( 13 unt; 19 typ; 0 def)
% Number of atoms : 42 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 9 ~; 10 |; 1 &)
% ( 4 <=>; 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 : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 33 (; 33 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(equal_set,type,
equal_set: ( $i * $i ) > $o ).
tff(power_set,type,
power_set: $i > $i ).
tff(product,type,
product: $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(sum,type,
sum: $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_119,negated_conjecture,
~ ! [A,B,U,V] :
( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
=> ( A = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI50a) ).
tff(f_62,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
tff(f_98,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( ( X = A )
| ( X = B ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
tff(f_56,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
tff(f_92,axiom,
! [X,A] :
( member(X,singleton(A))
<=> ( X = A ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
tff(c_60,plain,
'#skF_6' != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_62,plain,
equal_set(unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5')),unordered_pair(singleton('#skF_6'),unordered_pair('#skF_6','#skF_7'))),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_10,plain,
! [B_7,A_6] :
( subset(B_7,A_6)
| ~ equal_set(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_46,plain,
! [X_22,B_24] : member(X_22,unordered_pair(X_22,B_24)),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_146,plain,
! [X_75,B_76,A_77] :
( member(X_75,B_76)
| ~ member(X_75,A_77)
| ~ subset(A_77,B_76) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_188,plain,
! [X_86,B_87,B_88] :
( member(X_86,B_87)
| ~ subset(unordered_pair(X_86,B_88),B_87) ),
inference(resolution,[status(thm)],[c_46,c_146]) ).
tff(c_230,plain,
! [X_95,A_96,B_97] :
( member(X_95,A_96)
| ~ equal_set(A_96,unordered_pair(X_95,B_97)) ),
inference(resolution,[status(thm)],[c_10,c_188]) ).
tff(c_234,plain,
member(singleton('#skF_6'),unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_62,c_230]) ).
tff(c_514,plain,
! [X_123,B_124,A_125] :
( ( X_123 = B_124 )
| ( X_123 = A_125 )
| ~ member(X_123,unordered_pair(A_125,B_124)) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_539,plain,
( ( unordered_pair('#skF_4','#skF_5') = singleton('#skF_6') )
| ( singleton('#skF_6') = singleton('#skF_4') ) ),
inference(resolution,[status(thm)],[c_234,c_514]) ).
tff(c_741,plain,
singleton('#skF_6') = singleton('#skF_4'),
inference(splitLeft,[status(thm)],[c_539]) ).
tff(c_40,plain,
! [X_20] : member(X_20,singleton(X_20)),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_763,plain,
member('#skF_6',singleton('#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_741,c_40]) ).
tff(c_38,plain,
! [X_20,A_21] :
( ( X_20 = A_21 )
| ~ member(X_20,singleton(A_21)) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_773,plain,
'#skF_6' = '#skF_4',
inference(resolution,[status(thm)],[c_763,c_38]) ).
tff(c_779,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_773]) ).
tff(c_780,plain,
unordered_pair('#skF_4','#skF_5') = singleton('#skF_6'),
inference(splitRight,[status(thm)],[c_539]) ).
tff(c_837,plain,
member('#skF_4',singleton('#skF_6')),
inference(superposition,[status(thm),theory(equality)],[c_780,c_46]) ).
tff(c_906,plain,
'#skF_6' = '#skF_4',
inference(resolution,[status(thm)],[c_837,c_38]) ).
tff(c_913,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % 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
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 16:27:51 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.11/1.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.11/1.96
% 4.11/1.96 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.11/1.98
% 4.11/1.98 Inference rules
% 4.11/1.98 ----------------------
% 4.11/1.98 #Ref : 0
% 4.11/1.98 #Sup : 187
% 4.11/1.98 #Fact : 0
% 4.11/1.98 #Define : 0
% 4.11/1.98 #Split : 1
% 4.11/1.98 #Chain : 0
% 4.11/1.98 #Close : 0
% 4.11/1.98
% 4.11/1.98 Ordering : KBO
% 4.11/1.98
% 4.11/1.98 Simplification rules
% 4.11/1.98 ----------------------
% 4.11/1.98 #Subsume : 0
% 4.11/1.98 #Demod : 39
% 4.11/1.98 #Tautology : 41
% 4.11/1.98 #SimpNegUnit : 2
% 4.11/1.98 #BackRed : 10
% 4.11/1.98
% 4.11/1.98 #Partial instantiations: 0
% 4.11/1.98 #Strategies tried : 1
% 4.11/1.98
% 4.11/1.98 Timing (in seconds)
% 4.11/1.98 ----------------------
% 4.11/1.99 Preprocessing : 0.48
% 4.11/1.99 Parsing : 0.24
% 4.11/1.99 CNF conversion : 0.03
% 4.11/1.99 Main loop : 0.48
% 4.11/1.99 Inferencing : 0.18
% 4.11/1.99 Reduction : 0.13
% 4.11/1.99 Demodulation : 0.09
% 4.11/1.99 BG Simplification : 0.02
% 4.11/1.99 Subsumption : 0.10
% 4.11/1.99 Abstraction : 0.02
% 4.11/1.99 MUC search : 0.00
% 4.11/1.99 Cooper : 0.00
% 4.11/1.99 Total : 1.00
% 4.11/1.99 Index Insertion : 0.00
% 4.11/1.99 Index Deletion : 0.00
% 4.11/1.99 Index Matching : 0.00
% 4.11/1.99 BG Taut test : 0.00
%------------------------------------------------------------------------------