TSTP Solution File: NUM441+6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM441+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 : n015.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 10:51:41 EDT 2023
% Result : Theorem 16.20s 5.04s
% Output : CNFRefutation 16.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 53
% Syntax : Number of formulae : 63 ( 8 unt; 49 typ; 0 def)
% Number of atoms : 157 ( 11 equ)
% Maximal formula atoms : 64 ( 11 avg)
% Number of connectives : 164 ( 21 ~; 19 |; 89 &)
% ( 15 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 43 >; 35 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 6 con; 0-3 aty)
% Number of variables : 41 (; 32 !; 9 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aSubsetOf0 > aElementOf0 > aDivisorOf0 > isPrime0 > isOpen0 > isFinite0 > isClosed0 > aSet0 > aInteger0 > szAzrzSzezqlpdtcmdtrp0 > sdtslmnbsdt0 > sdtpldt0 > sdtbsmnsldt0 > sdtasdt0 > #nlpp > stldt0 > smndt0 > sbsmnsldt0 > xB > xA > sz10 > sz00 > cS1395 > #skF_11 > #skF_2 > #skF_18 > #skF_6 > #skF_19 > #skF_17 > #skF_22 > #skF_12 > #skF_8 > #skF_4 > #skF_3 > #skF_13 > #skF_14 > #skF_5 > #skF_10 > #skF_7 > #skF_26 > #skF_15 > #skF_23 > #skF_25 > #skF_24 > #skF_1 > #skF_21 > #skF_9 > #skF_20 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(aInteger0,type,
aInteger0: $i > $o ).
tff(sbsmnsldt0,type,
sbsmnsldt0: $i > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $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_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('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff(sz00,type,
sz00: $i ).
tff('#skF_8',type,
'#skF_8': $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(xB,type,
xB: $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_26',type,
'#skF_26': $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('#skF_25',type,
'#skF_25': ( $i * $i ) > $i ).
tff(aDivisorOf0,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff('#skF_24',type,
'#skF_24': $i ).
tff(xA,type,
xA: $i ).
tff(sdteqdtlpzmzozddtrp0,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_707,negated_conjecture,
~ ( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [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(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_637,hypothesis,
( aSet0(stldt0(xA))
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& aElementOf0(W0,stldt0(xA))
& aElementOf0(W0,stldt0(xB)) ) )
& ( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
tff(f_542,hypothesis,
( aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xA)
& ! [W0] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xB)
& ! [W0] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> ? [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(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> ? [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(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB)) ) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1826) ).
tff(f_393,axiom,
! [W0,W1] :
( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mInterOpen) ).
tff(c_440,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(cnfTransformation,[status(thm)],[f_707]) ).
tff(c_390,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(cnfTransformation,[status(thm)],[f_637]) ).
tff(c_376,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(cnfTransformation,[status(thm)],[f_637]) ).
tff(c_272,plain,
isOpen0(stldt0(xA)),
inference(cnfTransformation,[status(thm)],[f_542]) ).
tff(c_264,plain,
isOpen0(stldt0(xB)),
inference(cnfTransformation,[status(thm)],[f_542]) ).
tff(c_362,plain,
sdtslmnbsdt0(stldt0(xA),stldt0(xB)) = stldt0(sdtbsmnsldt0(xA,xB)),
inference(cnfTransformation,[status(thm)],[f_637]) ).
tff(c_14553,plain,
! [W0_572,W1_573] :
( isOpen0(sdtslmnbsdt0(W0_572,W1_573))
| ~ isOpen0(W1_573)
| ~ isOpen0(W0_572)
| ~ aSubsetOf0(W1_573,cS1395)
| ~ aSubsetOf0(W0_572,cS1395) ),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_14556,plain,
( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(superposition,[status(thm),theory(equality)],[c_362,c_14553]) ).
tff(c_14558,plain,
isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(demodulation,[status(thm),theory(equality)],[c_390,c_376,c_272,c_264,c_14556]) ).
tff(c_14560,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_440,c_14558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 15:25:44 EDT 2023
% 0.14/0.36 % CPUTime :
% 16.20/5.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.20/5.04
% 16.20/5.04 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.26/5.07
% 16.26/5.07 Inference rules
% 16.26/5.07 ----------------------
% 16.26/5.07 #Ref : 0
% 16.26/5.07 #Sup : 3198
% 16.26/5.07 #Fact : 0
% 16.26/5.07 #Define : 0
% 16.26/5.07 #Split : 55
% 16.26/5.07 #Chain : 0
% 16.26/5.07 #Close : 0
% 16.26/5.07
% 16.26/5.07 Ordering : KBO
% 16.26/5.07
% 16.26/5.07 Simplification rules
% 16.26/5.07 ----------------------
% 16.26/5.07 #Subsume : 179
% 16.26/5.07 #Demod : 2271
% 16.26/5.07 #Tautology : 1378
% 16.26/5.07 #SimpNegUnit : 85
% 16.26/5.07 #BackRed : 46
% 16.26/5.07
% 16.26/5.07 #Partial instantiations: 0
% 16.26/5.07 #Strategies tried : 1
% 16.26/5.07
% 16.26/5.07 Timing (in seconds)
% 16.26/5.07 ----------------------
% 16.26/5.08 Preprocessing : 0.88
% 16.26/5.08 Parsing : 0.42
% 16.26/5.08 CNF conversion : 0.09
% 16.26/5.08 Main loop : 3.04
% 16.26/5.08 Inferencing : 0.86
% 16.26/5.08 Reduction : 1.22
% 16.26/5.08 Demodulation : 0.92
% 16.26/5.08 BG Simplification : 0.11
% 16.26/5.08 Subsumption : 0.66
% 16.26/5.08 Abstraction : 0.08
% 16.26/5.08 MUC search : 0.00
% 16.26/5.08 Cooper : 0.00
% 16.26/5.08 Total : 3.98
% 16.26/5.08 Index Insertion : 0.00
% 16.26/5.08 Index Deletion : 0.00
% 16.26/5.08 Index Matching : 0.00
% 16.26/5.08 BG Taut test : 0.00
%------------------------------------------------------------------------------