TSTP Solution File: SET347+4 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET347+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 : n029.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 10:56:21 EDT 2023
% Result : Theorem 3.54s 1.91s
% Output : CNFRefutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 20
% Syntax : Number of formulae : 32 ( 9 unt; 15 typ; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 6 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 22 (; 21 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_3 > #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_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(empty_set,type,
empty_set: $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_116,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI38) ).
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_105,axiom,
! [X,A] :
( member(X,sum(A))
<=> ? [Y] :
( member(Y,A)
& member(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
tff(f_81,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
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(c_60,plain,
~ equal_set(sum(empty_set),empty_set),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_6,plain,
! [A_1,B_2] :
( member('#skF_1'(A_1,B_2),A_1)
| subset(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_335,plain,
! [X_101,A_102] :
( member('#skF_2'(X_101,A_102),A_102)
| ~ member(X_101,sum(A_102)) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_30,plain,
! [X_16] : ~ member(X_16,empty_set),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_378,plain,
! [X_103] : ~ member(X_103,sum(empty_set)),
inference(resolution,[status(thm)],[c_335,c_30]) ).
tff(c_394,plain,
! [B_104] : subset(sum(empty_set),B_104),
inference(resolution,[status(thm)],[c_6,c_378]) ).
tff(c_100,plain,
! [A_68,B_69] :
( member('#skF_1'(A_68,B_69),A_68)
| subset(A_68,B_69) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_135,plain,
! [B_69] : subset(empty_set,B_69),
inference(resolution,[status(thm)],[c_100,c_30]) ).
tff(c_268,plain,
! [A_92,B_93] :
( equal_set(A_92,B_93)
| ~ subset(B_93,A_92)
| ~ subset(A_92,B_93) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_280,plain,
! [B_69] :
( equal_set(B_69,empty_set)
| ~ subset(B_69,empty_set) ),
inference(resolution,[status(thm)],[c_135,c_268]) ).
tff(c_398,plain,
equal_set(sum(empty_set),empty_set),
inference(resolution,[status(thm)],[c_394,c_280]) ).
tff(c_404,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET347+4 : TPTP v8.1.2. Released v2.2.0.
% 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
% 0.16/0.35 % Computer : n029.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu Aug 3 17:10:52 EDT 2023
% 0.16/0.35 % CPUTime :
% 3.54/1.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.54/1.92
% 3.54/1.92 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.65/1.94
% 3.65/1.94 Inference rules
% 3.65/1.94 ----------------------
% 3.65/1.94 #Ref : 0
% 3.65/1.94 #Sup : 67
% 3.65/1.94 #Fact : 0
% 3.65/1.94 #Define : 0
% 3.65/1.94 #Split : 0
% 3.65/1.94 #Chain : 0
% 3.65/1.94 #Close : 0
% 3.65/1.94
% 3.65/1.94 Ordering : KBO
% 3.65/1.94
% 3.65/1.94 Simplification rules
% 3.65/1.94 ----------------------
% 3.65/1.94 #Subsume : 0
% 3.65/1.94 #Demod : 11
% 3.65/1.94 #Tautology : 14
% 3.65/1.94 #SimpNegUnit : 1
% 3.65/1.94 #BackRed : 0
% 3.65/1.94
% 3.65/1.94 #Partial instantiations: 0
% 3.65/1.94 #Strategies tried : 1
% 3.65/1.94
% 3.65/1.94 Timing (in seconds)
% 3.65/1.94 ----------------------
% 3.65/1.95 Preprocessing : 0.49
% 3.65/1.95 Parsing : 0.26
% 3.65/1.95 CNF conversion : 0.04
% 3.65/1.95 Main loop : 0.34
% 3.65/1.95 Inferencing : 0.14
% 3.65/1.95 Reduction : 0.09
% 3.65/1.95 Demodulation : 0.06
% 3.65/1.95 BG Simplification : 0.02
% 3.65/1.95 Subsumption : 0.07
% 3.65/1.95 Abstraction : 0.01
% 3.65/1.95 MUC search : 0.00
% 3.65/1.95 Cooper : 0.00
% 3.65/1.95 Total : 0.88
% 3.65/1.95 Index Insertion : 0.00
% 3.65/1.95 Index Deletion : 0.00
% 3.65/1.95 Index Matching : 0.00
% 3.65/1.95 BG Taut test : 0.00
%------------------------------------------------------------------------------