TSTP Solution File: NUM525+3 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM525+3 : 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 : n003.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 10:51:59 EDT 2023
% Result : Theorem 19.30s 7.44s
% Output : CNFRefutation 19.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 31
% Syntax : Number of formulae : 63 ( 22 unt; 23 typ; 1 def)
% Number of atoms : 88 ( 43 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 83 ( 35 ~; 25 |; 18 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 15 >; 13 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 22 (; 20 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xq > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_6 > #skF_7 > #skF_5 > #skF_8 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xq,type,
xq: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $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('#skF_7',type,
'#skF_7': $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_8',type,
'#skF_8': $i ).
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_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_517,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xn) = sdtasdt0(xp,W0) ) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [W0] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xp,W0) ) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
tff(f_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_81,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
tff(f_522,hypothesis,
( aNaturalNumber0(xq)
& ( xn = sdtasdt0(xp,xq) )
& ( xq = sdtsldt0(xn,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
tff(f_323,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
tff(f_486,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
tff(f_524,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(c_155,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_191,plain,
aNaturalNumber0('#skF_8'),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_151,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_957,plain,
! [W1_123,W0_124] :
( ( sdtasdt0(W1_123,W0_124) = sdtasdt0(W0_124,W1_123) )
| ~ aNaturalNumber0(W1_123)
| ~ aNaturalNumber0(W0_124) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_994,plain,
! [W0_125] :
( ( sdtasdt0(xp,W0_125) = sdtasdt0(W0_125,xp) )
| ~ aNaturalNumber0(W0_125) ),
inference(resolution,[status(thm)],[c_151,c_957]) ).
tff(c_1045,plain,
sdtasdt0(xp,'#skF_8') = sdtasdt0('#skF_8',xp),
inference(resolution,[status(thm)],[c_191,c_994]) ).
tff(c_189,plain,
sdtasdt0(xp,'#skF_8') = sdtasdt0(xn,xn),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_1189,plain,
sdtasdt0(xn,xn) = sdtasdt0('#skF_8',xp),
inference(demodulation,[status(thm),theory(equality)],[c_1045,c_189]) ).
tff(c_185,plain,
aNaturalNumber0('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_183,plain,
sdtasdt0(xp,'#skF_7') = xn,
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_18598,plain,
! [W0_406,W1_407,W2_408] :
( ( sdtasdt0(sdtasdt0(W0_406,W1_407),W2_408) = sdtasdt0(W0_406,sdtasdt0(W1_407,W2_408)) )
| ~ aNaturalNumber0(W2_408)
| ~ aNaturalNumber0(W1_407)
| ~ aNaturalNumber0(W0_406) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_18763,plain,
! [W2_408] :
( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_408)) = sdtasdt0(xn,W2_408) )
| ~ aNaturalNumber0(W2_408)
| ~ aNaturalNumber0('#skF_7')
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_183,c_18598]) ).
tff(c_18844,plain,
! [W2_408] :
( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_408)) = sdtasdt0(xn,W2_408) )
| ~ aNaturalNumber0(W2_408) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_185,c_18763]) ).
tff(c_28761,plain,
! [W0_496] :
( ( sdtasdt0(xn,W0_496) = sdtasdt0(W0_496,xn) )
| ~ aNaturalNumber0(W0_496) ),
inference(resolution,[status(thm)],[c_155,c_957]) ).
tff(c_28880,plain,
sdtasdt0(xn,'#skF_7') = sdtasdt0('#skF_7',xn),
inference(resolution,[status(thm)],[c_185,c_28761]) ).
tff(c_36027,plain,
! [W2_513] :
( ( sdtasdt0(xp,sdtasdt0('#skF_7',W2_513)) = sdtasdt0(xn,W2_513) )
| ~ aNaturalNumber0(W2_513) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_185,c_18763]) ).
tff(c_145,plain,
xp != sz00,
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_181,plain,
doDivides0(xp,xn),
inference(cnfTransformation,[status(thm)],[f_517]) ).
tff(c_193,plain,
sdtsldt0(xn,xp) = xq,
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_25031,plain,
! [W0_463,W2_464] :
( ( sdtsldt0(sdtasdt0(W0_463,W2_464),W0_463) = W2_464 )
| ~ aNaturalNumber0(W2_464)
| ~ doDivides0(W0_463,sdtasdt0(W0_463,W2_464))
| ( sz00 = W0_463 )
| ~ aNaturalNumber0(sdtasdt0(W0_463,W2_464))
| ~ aNaturalNumber0(W0_463) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_25145,plain,
( ( sdtsldt0(sdtasdt0(xp,'#skF_7'),xp) = '#skF_7' )
| ~ aNaturalNumber0('#skF_7')
| ~ doDivides0(xp,xn)
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,'#skF_7'))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_183,c_25031]) ).
tff(c_25250,plain,
( ( xq = '#skF_7' )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_183,c_181,c_185,c_193,c_183,c_25145]) ).
tff(c_25251,plain,
xq = '#skF_7',
inference(negUnitSimplification,[status(thm)],[c_145,c_25250]) ).
tff(c_171,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnfTransformation,[status(thm)],[f_486]) ).
tff(c_199,plain,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xp,sdtasdt0(xm,xm)),
inference(cnfTransformation,[status(thm)],[f_524]) ).
tff(c_200,plain,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0(xn,xn),
inference(demodulation,[status(thm),theory(equality)],[c_171,c_199]) ).
tff(c_1308,plain,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0(xq,xq))) != sdtasdt0('#skF_8',xp),
inference(demodulation,[status(thm),theory(equality)],[c_1189,c_200]) ).
tff(c_25296,plain,
sdtasdt0(xp,sdtasdt0(xp,sdtasdt0('#skF_7','#skF_7'))) != sdtasdt0('#skF_8',xp),
inference(demodulation,[status(thm),theory(equality)],[c_25251,c_25251,c_1308]) ).
tff(c_36048,plain,
( ( sdtasdt0(xp,sdtasdt0(xn,'#skF_7')) != sdtasdt0('#skF_8',xp) )
| ~ aNaturalNumber0('#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_36027,c_25296]) ).
tff(c_36141,plain,
sdtasdt0(xp,sdtasdt0('#skF_7',xn)) != sdtasdt0('#skF_8',xp),
inference(demodulation,[status(thm),theory(equality)],[c_185,c_28880,c_36048]) ).
tff(c_36206,plain,
( ( sdtasdt0(xn,xn) != sdtasdt0('#skF_8',xp) )
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_18844,c_36141]) ).
tff(c_36209,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_155,c_1189,c_36206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM525+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % 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
% 0.14/0.36 % Computer : n003.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 14:37:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 19.30/7.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.30/7.45
% 19.30/7.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.30/7.48
% 19.30/7.48 Inference rules
% 19.30/7.48 ----------------------
% 19.30/7.48 #Ref : 19
% 19.30/7.48 #Sup : 7410
% 19.30/7.48 #Fact : 2
% 19.30/7.48 #Define : 0
% 19.30/7.48 #Split : 43
% 19.30/7.48 #Chain : 0
% 19.30/7.48 #Close : 0
% 19.30/7.48
% 19.30/7.48 Ordering : KBO
% 19.30/7.48
% 19.30/7.48 Simplification rules
% 19.30/7.48 ----------------------
% 19.30/7.48 #Subsume : 346
% 19.30/7.48 #Demod : 13506
% 19.30/7.48 #Tautology : 2649
% 19.30/7.48 #SimpNegUnit : 1591
% 19.30/7.48 #BackRed : 1077
% 19.30/7.48
% 19.30/7.48 #Partial instantiations: 0
% 19.30/7.48 #Strategies tried : 1
% 19.30/7.48
% 19.30/7.48 Timing (in seconds)
% 19.30/7.48 ----------------------
% 19.30/7.48 Preprocessing : 0.68
% 19.30/7.48 Parsing : 0.34
% 19.30/7.48 CNF conversion : 0.05
% 19.30/7.48 Main loop : 5.71
% 19.30/7.48 Inferencing : 1.15
% 19.30/7.48 Reduction : 2.92
% 19.30/7.48 Demodulation : 2.39
% 19.30/7.48 BG Simplification : 0.13
% 19.30/7.48 Subsumption : 1.10
% 19.30/7.48 Abstraction : 0.13
% 19.30/7.48 MUC search : 0.00
% 19.30/7.48 Cooper : 0.00
% 19.30/7.48 Total : 6.45
% 19.30/7.48 Index Insertion : 0.00
% 19.30/7.48 Index Deletion : 0.00
% 19.30/7.48 Index Matching : 0.00
% 19.30/7.48 BG Taut test : 0.00
%------------------------------------------------------------------------------