TSTP Solution File: SET800+4 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% 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 : n017.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 10:57:02 EDT 2023
% Result : Theorem 8.73s 3.09s
% Output : CNFRefutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 52
% Syntax : Number of formulae : 67 ( 9 unt; 48 typ; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 33 ( 10 ~; 8 |; 6 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 99 ( 41 >; 58 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 34 ( 34 usr; 7 con; 0-4 aty)
% Number of variables : 36 (; 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ least_upper_bound > greatest_lower_bound > upper_bound > min > max > lower_bound > least > greatest > apply > total_order > subset > order > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_13 > #skF_11 > #skF_6 > #skF_17 > #skF_20 > #skF_25 > #skF_12 > #skF_18 > #skF_19 > #skF_3 > #skF_10 > #skF_8 > #skF_21 > #skF_15 > #skF_14 > #skF_22 > #skF_2 > #skF_24 > #skF_23 > #skF_7 > #skF_1 > #skF_9 > #skF_5 > #skF_4 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(equal_set,type,
equal_set: ( $i * $i ) > $o ).
tff(upper_bound,type,
upper_bound: ( $i * $i * $i ) > $o ).
tff(power_set,type,
power_set: $i > $i ).
tff(greatest_lower_bound,type,
greatest_lower_bound: ( $i * $i * $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff(product,type,
product: $i > $i ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(apply,type,
apply: ( $i * $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(least_upper_bound,type,
least_upper_bound: ( $i * $i * $i * $i ) > $o ).
tff(sum,type,
sum: $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i * $i ) > $i ).
tff(total_order,type,
total_order: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(greatest,type,
greatest: ( $i * $i * $i ) > $o ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(lower_bound,type,
lower_bound: ( $i * $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff(min,type,
min: ( $i * $i * $i ) > $o ).
tff(least,type,
least: ( $i * $i * $i ) > $o ).
tff('#skF_22',type,
'#skF_22': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(order,type,
order: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(max,type,
max: ( $i * $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_282,negated_conjecture,
~ ! [R,E] :
( order(R,E)
=> ! [X1,X2] :
( ( subset(X1,E)
& subset(X2,E)
& subset(X1,X2) )
=> ! [M1,M2] :
( ( greatest_lower_bound(M1,X1,R,E)
& greatest_lower_bound(M2,X2,R,E) )
=> apply(R,M2,M1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV12) ).
tff(f_263,axiom,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( member(A,X)
& lower_bound(A,R,X)
& ! [M] :
( ( member(M,E)
& lower_bound(M,R,X) )
=> apply(R,M,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest_lower_bound) ).
tff(f_57,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_197,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',lower_bound) ).
tff(c_270,plain,
~ apply('#skF_20','#skF_25','#skF_24'),
inference(cnfTransformation,[status(thm)],[f_282]) ).
tff(c_272,plain,
greatest_lower_bound('#skF_25','#skF_23','#skF_20','#skF_21'),
inference(cnfTransformation,[status(thm)],[f_282]) ).
tff(c_1305,plain,
! [A_239,R_240,X_241,E_242] :
( lower_bound(A_239,R_240,X_241)
| ~ greatest_lower_bound(A_239,X_241,R_240,E_242) ),
inference(cnfTransformation,[status(thm)],[f_263]) ).
tff(c_1313,plain,
lower_bound('#skF_25','#skF_20','#skF_23'),
inference(resolution,[status(thm)],[c_272,c_1305]) ).
tff(c_276,plain,
subset('#skF_22','#skF_23'),
inference(cnfTransformation,[status(thm)],[f_282]) ).
tff(c_274,plain,
greatest_lower_bound('#skF_24','#skF_22','#skF_20','#skF_21'),
inference(cnfTransformation,[status(thm)],[f_282]) ).
tff(c_313,plain,
! [A_173,X_174,R_175,E_176] :
( member(A_173,X_174)
| ~ greatest_lower_bound(A_173,X_174,R_175,E_176) ),
inference(cnfTransformation,[status(thm)],[f_263]) ).
tff(c_320,plain,
member('#skF_24','#skF_22'),
inference(resolution,[status(thm)],[c_274,c_313]) ).
tff(c_381,plain,
! [X_183,B_184,A_185] :
( member(X_183,B_184)
| ~ member(X_183,A_185)
| ~ subset(A_185,B_184) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_433,plain,
! [B_187] :
( member('#skF_24',B_187)
| ~ subset('#skF_22',B_187) ),
inference(resolution,[status(thm)],[c_320,c_381]) ).
tff(c_456,plain,
member('#skF_24','#skF_23'),
inference(resolution,[status(thm)],[c_276,c_433]) ).
tff(c_3440,plain,
! [R_360,M_361,X_362,E_363] :
( apply(R_360,M_361,X_362)
| ~ member(X_362,E_363)
| ~ lower_bound(M_361,R_360,E_363) ),
inference(cnfTransformation,[status(thm)],[f_197]) ).
tff(c_4887,plain,
! [R_431,M_432] :
( apply(R_431,M_432,'#skF_24')
| ~ lower_bound(M_432,R_431,'#skF_23') ),
inference(resolution,[status(thm)],[c_456,c_3440]) ).
tff(c_4890,plain,
apply('#skF_20','#skF_25','#skF_24'),
inference(resolution,[status(thm)],[c_1313,c_4887]) ).
tff(c_4894,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_270,c_4890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 15:43:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 8.73/3.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.73/3.09
% 8.73/3.09 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.04/3.12
% 9.04/3.12 Inference rules
% 9.04/3.12 ----------------------
% 9.04/3.12 #Ref : 0
% 9.04/3.12 #Sup : 1059
% 9.04/3.12 #Fact : 0
% 9.04/3.12 #Define : 0
% 9.04/3.12 #Split : 21
% 9.04/3.12 #Chain : 0
% 9.04/3.12 #Close : 0
% 9.04/3.12
% 9.04/3.12 Ordering : KBO
% 9.04/3.12
% 9.04/3.12 Simplification rules
% 9.04/3.12 ----------------------
% 9.04/3.12 #Subsume : 78
% 9.04/3.12 #Demod : 110
% 9.04/3.12 #Tautology : 131
% 9.04/3.12 #SimpNegUnit : 1
% 9.04/3.12 #BackRed : 0
% 9.04/3.12
% 9.04/3.12 #Partial instantiations: 0
% 9.04/3.12 #Strategies tried : 1
% 9.04/3.12
% 9.04/3.12 Timing (in seconds)
% 9.04/3.12 ----------------------
% 9.04/3.13 Preprocessing : 0.66
% 9.04/3.13 Parsing : 0.31
% 9.04/3.13 CNF conversion : 0.06
% 9.04/3.13 Main loop : 1.41
% 9.04/3.13 Inferencing : 0.44
% 9.04/3.13 Reduction : 0.46
% 9.04/3.13 Demodulation : 0.28
% 9.04/3.13 BG Simplification : 0.07
% 9.04/3.13 Subsumption : 0.35
% 9.04/3.13 Abstraction : 0.04
% 9.04/3.13 MUC search : 0.00
% 9.04/3.13 Cooper : 0.00
% 9.04/3.13 Total : 2.12
% 9.04/3.13 Index Insertion : 0.00
% 9.04/3.13 Index Deletion : 0.00
% 9.04/3.13 Index Matching : 0.00
% 9.04/3.13 BG Taut test : 0.00
%------------------------------------------------------------------------------