TSTP Solution File: NUM523+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM523+1 : 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/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 : n031.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 10:51:58 EDT 2023
% Result : Theorem 13.93s 4.46s
% Output : CNFRefutation 14.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 25
% Syntax : Number of formulae : 50 ( 19 unt; 18 typ; 1 def)
% Number of atoms : 71 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 29 ~; 22 |; 12 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 15 (; 14 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff(sz10,type,
sz10: $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz00,type,
sz00: $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(xp,type,
xp: $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(xm,type,
xm: $i ).
tff(sdtsldt0,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xn,type,
xn: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_474,negated_conjecture,
~ ( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_446,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_469,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
tff(f_307,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
tff(f_470,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
tff(f_432,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( isPrime0(W2)
& doDivides0(W2,sdtasdt0(W0,W1)) )
=> ( doDivides0(W2,W0)
| doDivides0(W2,W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPDP) ).
tff(c_163,plain,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(cnfTransformation,[status(thm)],[f_474]) ).
tff(c_168,plain,
~ doDivides0(xp,sdtasdt0(xn,xn)),
inference(splitLeft,[status(thm)],[c_163]) ).
tff(c_151,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_153,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_12,plain,
! [W0_4,W1_5] :
( aNaturalNumber0(sdtasdt0(W0_4,W1_5))
| ~ aNaturalNumber0(W1_5)
| ~ aNaturalNumber0(W0_4) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_159,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnfTransformation,[status(thm)],[f_469]) ).
tff(c_579,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_12]) ).
tff(c_583,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_579]) ).
tff(c_585,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitLeft,[status(thm)],[c_583]) ).
tff(c_588,plain,
~ aNaturalNumber0(xm),
inference(resolution,[status(thm)],[c_12,c_585]) ).
tff(c_592,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_153,c_588]) ).
tff(c_593,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(splitRight,[status(thm)],[c_583]) ).
tff(c_594,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitRight,[status(thm)],[c_583]) ).
tff(c_4153,plain,
! [W0_184,W2_185] :
( doDivides0(W0_184,sdtasdt0(W0_184,W2_185))
| ~ aNaturalNumber0(W2_185)
| ~ aNaturalNumber0(sdtasdt0(W0_184,W2_185))
| ~ aNaturalNumber0(W0_184) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_4225,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_4153]) ).
tff(c_4321,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_593,c_159,c_594,c_4225]) ).
tff(c_4323,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_168,c_4321]) ).
tff(c_4324,plain,
~ doDivides0(xp,xn),
inference(splitRight,[status(thm)],[c_163]) ).
tff(c_155,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_161,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_4325,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(splitRight,[status(thm)],[c_163]) ).
tff(c_15511,plain,
! [W2_342,W1_343,W0_344] :
( doDivides0(W2_342,W1_343)
| doDivides0(W2_342,W0_344)
| ~ doDivides0(W2_342,sdtasdt0(W0_344,W1_343))
| ~ isPrime0(W2_342)
| ~ aNaturalNumber0(W2_342)
| ~ aNaturalNumber0(W1_343)
| ~ aNaturalNumber0(W0_344) ),
inference(cnfTransformation,[status(thm)],[f_432]) ).
tff(c_15702,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_4325,c_15511]) ).
tff(c_15831,plain,
doDivides0(xp,xn),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_151,c_161,c_15702]) ).
tff(c_15833,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4324,c_15831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM523+1 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.14 % 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
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 15:19:44 EDT 2023
% 0.15/0.36 % CPUTime :
% 13.93/4.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.93/4.46
% 13.93/4.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.08/4.49
% 14.08/4.49 Inference rules
% 14.08/4.49 ----------------------
% 14.08/4.49 #Ref : 7
% 14.08/4.49 #Sup : 3327
% 14.08/4.49 #Fact : 4
% 14.08/4.49 #Define : 0
% 14.08/4.49 #Split : 20
% 14.08/4.49 #Chain : 0
% 14.08/4.49 #Close : 0
% 14.08/4.49
% 14.08/4.49 Ordering : KBO
% 14.08/4.49
% 14.08/4.49 Simplification rules
% 14.08/4.49 ----------------------
% 14.08/4.49 #Subsume : 184
% 14.08/4.49 #Demod : 5212
% 14.08/4.49 #Tautology : 1258
% 14.08/4.49 #SimpNegUnit : 455
% 14.08/4.49 #BackRed : 391
% 14.08/4.49
% 14.08/4.49 #Partial instantiations: 0
% 14.08/4.49 #Strategies tried : 1
% 14.08/4.49
% 14.08/4.49 Timing (in seconds)
% 14.08/4.49 ----------------------
% 14.08/4.49 Preprocessing : 0.67
% 14.08/4.49 Parsing : 0.34
% 14.08/4.49 CNF conversion : 0.05
% 14.08/4.49 Main loop : 2.63
% 14.08/4.49 Inferencing : 0.67
% 14.08/4.49 Reduction : 1.19
% 14.08/4.49 Demodulation : 0.93
% 14.08/4.49 BG Simplification : 0.08
% 14.08/4.49 Subsumption : 0.52
% 14.08/4.49 Abstraction : 0.08
% 14.08/4.49 MUC search : 0.00
% 14.08/4.49 Cooper : 0.00
% 14.08/4.49 Total : 3.34
% 14.08/4.49 Index Insertion : 0.00
% 14.08/4.49 Index Deletion : 0.00
% 14.08/4.49 Index Matching : 0.00
% 14.08/4.49 BG Taut test : 0.00
%------------------------------------------------------------------------------