TSTP Solution File: NUM505+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM505+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/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 10:51:55 EDT 2023
% Result : Theorem 8.66s 3.09s
% Output : CNFRefutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 70 ( 26 unt; 20 typ; 2 def)
% Number of atoms : 109 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 99 ( 40 ~; 31 |; 16 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 21 (; 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff(xr,type,
xr: $i ).
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_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(f_403,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
tff(f_278,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
tff(f_442,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
tff(f_481,negated_conjecture,
~ ( ~ sdtlseqdt0(xp,xk)
=> ( ( xk != xp )
& sdtlseqdt0(xk,xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_212,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
tff(f_456,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
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_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_135,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_193,plain,
~ isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_270,plain,
! [W0_101] :
( ( sdtasdt0(sz10,W0_101) = W0_101 )
| ~ aNaturalNumber0(W0_101) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_292,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_270]) ).
tff(c_1256,plain,
! [W1_126,W0_127] :
( sdtlseqdt0(W1_126,sdtasdt0(W1_126,W0_127))
| ( sz00 = W0_127 )
| ~ aNaturalNumber0(W1_126)
| ~ aNaturalNumber0(W0_127) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_1313,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_292,c_1256]) ).
tff(c_1381,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_1313]) ).
tff(c_3810,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_1381]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_3832,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_3810,c_153]) ).
tff(c_3845,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_193,c_3832]) ).
tff(c_3847,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_1381]) ).
tff(c_187,plain,
( ~ sdtlseqdt0(xk,xp)
| ( xp = xk ) ),
inference(cnfTransformation,[status(thm)],[f_481]) ).
tff(c_194,plain,
~ sdtlseqdt0(xk,xp),
inference(splitLeft,[status(thm)],[c_187]) ).
tff(c_1135,plain,
! [W1_122,W0_123] :
( sdtlseqdt0(W1_122,W0_123)
| sdtlseqdt0(W0_123,W1_122)
| ~ aNaturalNumber0(W1_122)
| ~ aNaturalNumber0(W0_123) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_189,plain,
~ sdtlseqdt0(xp,xk),
inference(cnfTransformation,[status(thm)],[f_481]) ).
tff(c_1145,plain,
( sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_1135,c_189]) ).
tff(c_1164,plain,
( sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_1145]) ).
tff(c_1165,plain,
~ aNaturalNumber0(xk),
inference(negUnitSimplification,[status(thm)],[c_194,c_1164]) ).
tff(c_151,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_167,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_4851,plain,
! [W1_202,W0_203] :
( aNaturalNumber0(sdtsldt0(W1_202,W0_203))
| ~ doDivides0(W0_203,W1_202)
| ( sz00 = W0_203 )
| ~ aNaturalNumber0(W1_202)
| ~ aNaturalNumber0(W0_203) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_4885,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_4851]) ).
tff(c_4898,plain,
( aNaturalNumber0(xk)
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_151,c_4885]) ).
tff(c_4899,plain,
~ aNaturalNumber0(sdtasdt0(xn,xm)),
inference(negUnitSimplification,[status(thm)],[c_3847,c_1165,c_4898]) ).
tff(c_4902,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_12,c_4899]) ).
tff(c_4906,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_4902]) ).
tff(c_4907,plain,
xp = xk,
inference(splitRight,[status(thm)],[c_187]) ).
tff(c_4910,plain,
~ sdtlseqdt0(xk,xk),
inference(demodulation,[status(thm),theory(equality)],[c_4907,c_189]) ).
tff(c_4908,plain,
sdtlseqdt0(xk,xp),
inference(splitRight,[status(thm)],[c_187]) ).
tff(c_4919,plain,
sdtlseqdt0(xk,xk),
inference(demodulation,[status(thm),theory(equality)],[c_4907,c_4908]) ).
tff(c_4920,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4910,c_4919]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM505+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % 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 14:49:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 8.66/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.66/3.10
% 8.66/3.10 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.04/3.16
% 9.04/3.16 Inference rules
% 9.04/3.16 ----------------------
% 9.04/3.16 #Ref : 0
% 9.04/3.16 #Sup : 914
% 9.04/3.16 #Fact : 2
% 9.04/3.16 #Define : 0
% 9.04/3.16 #Split : 17
% 9.04/3.16 #Chain : 0
% 9.04/3.16 #Close : 0
% 9.04/3.16
% 9.04/3.16 Ordering : KBO
% 9.04/3.16
% 9.04/3.16 Simplification rules
% 9.04/3.16 ----------------------
% 9.04/3.16 #Subsume : 90
% 9.04/3.16 #Demod : 1510
% 9.04/3.16 #Tautology : 591
% 9.04/3.16 #SimpNegUnit : 177
% 9.04/3.16 #BackRed : 281
% 9.04/3.16
% 9.04/3.16 #Partial instantiations: 0
% 9.04/3.16 #Strategies tried : 1
% 9.04/3.16
% 9.04/3.16 Timing (in seconds)
% 9.04/3.16 ----------------------
% 9.04/3.16 Preprocessing : 0.70
% 9.04/3.16 Parsing : 0.36
% 9.04/3.16 CNF conversion : 0.05
% 9.04/3.16 Main loop : 1.25
% 9.04/3.16 Inferencing : 0.39
% 9.04/3.16 Reduction : 0.46
% 9.04/3.16 Demodulation : 0.33
% 9.04/3.16 BG Simplification : 0.06
% 9.04/3.16 Subsumption : 0.25
% 9.04/3.16 Abstraction : 0.05
% 9.04/3.16 MUC search : 0.00
% 9.04/3.17 Cooper : 0.00
% 9.04/3.17 Total : 2.04
% 9.04/3.17 Index Insertion : 0.00
% 9.04/3.17 Index Deletion : 0.00
% 9.04/3.17 Index Matching : 0.00
% 9.04/3.17 BG Taut test : 0.00
%------------------------------------------------------------------------------