TSTP Solution File: NUM450+6 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% 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 : n023.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 10:51:42 EDT 2023
% Result : Theorem 7.02s 2.58s
% Output : CNFRefutation 7.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 60
% Syntax : Number of formulae : 77 ( 7 unt; 57 typ; 0 def)
% Number of atoms : 125 ( 20 equ)
% Maximal formula atoms : 56 ( 6 avg)
% Number of connectives : 131 ( 26 ~; 21 |; 61 &)
% ( 9 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 51 >; 39 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 6 con; 0-3 aty)
% Number of variables : 38 (; 25 !; 13 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aSubsetOf0 > aElementOf0 > aDivisorOf0 > isPrime0 > isOpen0 > isFinite0 > isClosed0 > aSet0 > aInteger0 > szAzrzSzezqlpdtcmdtrp0 > sdtslmnbsdt0 > sdtpldt0 > sdtbsmnsldt0 > sdtasdt0 > #nlpp > stldt0 > smndt0 > sbsmnsldt0 > xS > sz10 > sz00 > cS2076 > cS2043 > cS1395 > #skF_25 > #skF_11 > #skF_2 > #skF_18 > #skF_24 > #skF_26 > #skF_6 > #skF_19 > #skF_17 > #skF_22 > #skF_32 > #skF_12 > #skF_8 > #skF_31 > #skF_4 > #skF_3 > #skF_13 > #skF_14 > #skF_28 > #skF_5 > #skF_10 > #skF_7 > #skF_33 > #skF_15 > #skF_23 > #skF_27 > #skF_29 > #skF_21 > #skF_1 > #skF_9 > #skF_30 > #skF_20 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(aInteger0,type,
aInteger0: $i > $o ).
tff(sbsmnsldt0,type,
sbsmnsldt0: $i > $i ).
tff('#skF_25',type,
'#skF_25': $i > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(cS2043,type,
cS2043: $i ).
tff(stldt0,type,
stldt0: $i > $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff(isClosed0,type,
isClosed0: $i > $o ).
tff('#skF_24',type,
'#skF_24': $i > $i ).
tff('#skF_26',type,
'#skF_26': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(szAzrzSzezqlpdtcmdtrp0,type,
szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(cS1395,type,
cS1395: $i ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': $i > $i ).
tff(cS2076,type,
cS2076: $i ).
tff('#skF_32',type,
'#skF_32': ( $i * $i ) > $i ).
tff(xS,type,
xS: $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff(sz00,type,
sz00: $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtslmnbsdt0,type,
sdtslmnbsdt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff('#skF_28',type,
'#skF_28': $i > $i ).
tff(smndt0,type,
smndt0: $i > $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(isOpen0,type,
isOpen0: $i > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff('#skF_33',type,
'#skF_33': $i > $i ).
tff(sdtbsmnsldt0,type,
sdtbsmnsldt0: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i ) > $i ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff(aDivisorOf0,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff('#skF_27',type,
'#skF_27': $i > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i ) > $i ).
tff(sdteqdtlpzmzozddtrp0,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': $i > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_543,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( aInteger0(W0)
& ? [W1] :
( aElementOf0(W1,xS)
& aElementOf0(W0,W1) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( ( W0 = sz10 )
| ( W0 = smndt0(sz10) ) ) )
& ( stldt0(sbsmnsldt0(xS)) = cS2076 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).
tff(f_677,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( aInteger0(W0)
& ? [W1] :
( aElementOf0(W1,xS)
& aElementOf0(W0,W1) ) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
=> ? [W1] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sbsmnsldt0(xS))) ) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( aInteger0(W0)
& ? [W1] :
( aElementOf0(W1,xS)
& aElementOf0(W0,W1) ) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
=> ? [W1] :
( aInteger0(W1)
& ( W1 != sz00 )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3] :
( aInteger0(W3)
& ( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) ) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sbsmnsldt0(xS))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).
tff(f_739,negated_conjecture,
~ ? [W0] :
( aInteger0(W0)
& ( W0 != sz00 )
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,W0))
& ! [W1] :
( ( aElementOf0(W1,szAzrzSzezqlpdtcmdtrp0(sz10,W0))
=> ( aInteger0(W1)
& ? [W2] :
( aInteger0(W2)
& ( sdtasdt0(W0,W2) = sdtpldt0(W1,smndt0(sz10)) ) )
& aDivisorOf0(W0,sdtpldt0(W1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(W1,sz10,W0) ) )
& ( ( aInteger0(W1)
& ( ? [W2] :
( aInteger0(W2)
& ( sdtasdt0(W0,W2) = sdtpldt0(W1,smndt0(sz10)) ) )
| aDivisorOf0(W0,sdtpldt0(W1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(W1,sz10,W0) ) )
=> aElementOf0(W1,szAzrzSzezqlpdtcmdtrp0(sz10,W0)) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [W1] :
( aElementOf0(W1,sbsmnsldt0(xS))
<=> ( aInteger0(W1)
& ? [W2] :
( aElementOf0(W2,xS)
& aElementOf0(W1,W2) ) ) ) )
=> ( ! [W1] :
( aElementOf0(W1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W1)
& ~ aElementOf0(W1,sbsmnsldt0(xS)) ) )
=> ( ! [W1] :
( aElementOf0(W1,szAzrzSzezqlpdtcmdtrp0(sz10,W0))
=> aElementOf0(W1,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,W0),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(c_322,plain,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_336,plain,
aElementOf0(sz10,stldt0(sbsmnsldt0(xS))),
inference(cnfTransformation,[status(thm)],[f_543]) ).
tff(c_486,plain,
aElementOf0(sz10,cS2076),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_336]) ).
tff(c_374,plain,
! [W0_227] :
( aInteger0('#skF_25'(W0_227))
| ~ aElementOf0(W0_227,stldt0(sbsmnsldt0(xS))) ),
inference(cnfTransformation,[status(thm)],[f_677]) ).
tff(c_481,plain,
! [W0_227] :
( aInteger0('#skF_25'(W0_227))
| ~ aElementOf0(W0_227,cS2076) ),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_374]) ).
tff(c_372,plain,
! [W0_227] :
( ( '#skF_25'(W0_227) != sz00 )
| ~ aElementOf0(W0_227,stldt0(sbsmnsldt0(xS))) ),
inference(cnfTransformation,[status(thm)],[f_677]) ).
tff(c_621,plain,
! [W0_319] :
( ( '#skF_25'(W0_319) != sz00 )
| ~ aElementOf0(W0_319,cS2076) ),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_372]) ).
tff(c_629,plain,
'#skF_25'(sz10) != sz00,
inference(resolution,[status(thm)],[c_486,c_621]) ).
tff(c_366,plain,
! [W0_227] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0_227,'#skF_25'(W0_227)),stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(W0_227,stldt0(sbsmnsldt0(xS))) ),
inference(cnfTransformation,[status(thm)],[f_677]) ).
tff(c_1734,plain,
! [W0_395] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0_395,'#skF_25'(W0_395)),cS2076)
| ~ aElementOf0(W0_395,cS2076) ),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_322,c_366]) ).
tff(c_438,plain,
! [W0_287] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,W0_287),stldt0(sbsmnsldt0(xS)))
| ( sz00 = W0_287 )
| ~ aInteger0(W0_287) ),
inference(cnfTransformation,[status(thm)],[f_739]) ).
tff(c_498,plain,
! [W0_287] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,W0_287),cS2076)
| ( sz00 = W0_287 )
| ~ aInteger0(W0_287) ),
inference(demodulation,[status(thm),theory(equality)],[c_322,c_438]) ).
tff(c_1738,plain,
( ( '#skF_25'(sz10) = sz00 )
| ~ aInteger0('#skF_25'(sz10))
| ~ aElementOf0(sz10,cS2076) ),
inference(resolution,[status(thm)],[c_1734,c_498]) ).
tff(c_1744,plain,
( ( '#skF_25'(sz10) = sz00 )
| ~ aInteger0('#skF_25'(sz10)) ),
inference(demodulation,[status(thm),theory(equality)],[c_486,c_1738]) ).
tff(c_1745,plain,
~ aInteger0('#skF_25'(sz10)),
inference(negUnitSimplification,[status(thm)],[c_629,c_1744]) ).
tff(c_1751,plain,
~ aElementOf0(sz10,cS2076),
inference(resolution,[status(thm)],[c_481,c_1745]) ).
tff(c_1755,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_486,c_1751]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % 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
% 0.14/0.35 % Computer : n023.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 15:15:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 7.02/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.02/2.58
% 7.02/2.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.09/2.61
% 7.09/2.61 Inference rules
% 7.09/2.61 ----------------------
% 7.09/2.61 #Ref : 0
% 7.09/2.61 #Sup : 261
% 7.09/2.61 #Fact : 0
% 7.09/2.61 #Define : 0
% 7.09/2.61 #Split : 0
% 7.09/2.61 #Chain : 0
% 7.09/2.61 #Close : 0
% 7.09/2.61
% 7.09/2.61 Ordering : KBO
% 7.09/2.61
% 7.09/2.61 Simplification rules
% 7.09/2.61 ----------------------
% 7.09/2.61 #Subsume : 22
% 7.09/2.61 #Demod : 275
% 7.09/2.61 #Tautology : 160
% 7.09/2.61 #SimpNegUnit : 1
% 7.09/2.61 #BackRed : 0
% 7.09/2.61
% 7.09/2.61 #Partial instantiations: 0
% 7.09/2.61 #Strategies tried : 1
% 7.09/2.61
% 7.09/2.61 Timing (in seconds)
% 7.09/2.61 ----------------------
% 7.18/2.61 Preprocessing : 0.86
% 7.18/2.61 Parsing : 0.41
% 7.18/2.61 CNF conversion : 0.09
% 7.18/2.61 Main loop : 0.69
% 7.18/2.61 Inferencing : 0.18
% 7.18/2.61 Reduction : 0.23
% 7.18/2.61 Demodulation : 0.16
% 7.18/2.61 BG Simplification : 0.08
% 7.18/2.61 Subsumption : 0.17
% 7.18/2.61 Abstraction : 0.03
% 7.18/2.61 MUC search : 0.00
% 7.18/2.61 Cooper : 0.00
% 7.18/2.61 Total : 1.60
% 7.18/2.61 Index Insertion : 0.00
% 7.18/2.61 Index Deletion : 0.00
% 7.18/2.62 Index Matching : 0.00
% 7.18/2.62 BG Taut test : 0.00
%------------------------------------------------------------------------------