%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM487+1 : TPTP v9.0.0. 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 : n016.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 : Wed Apr 9 07:56:06 PM UTC 2025
% Result : Theorem 14.74s 4.55s
% Output : CNFRefutation 14.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 37 unt; 0 typ; 3 def)
% Number of atoms : 167 ( 49 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 160 ( 67 ~; 61 |; 18 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 38 ( 37 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
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_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_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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_67,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
tff(f_449,negated_conjecture,
~ ( ( xr != xn )
& sdtlseqdt0(xr,xn) ),
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_443,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
tff(f_444,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
tff(f_175,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
tff(f_53,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
tff(f_162,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
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_163,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_11123,plain,
! [W0_256] :
( ( sdtasdt0(sz10,W0_256) = W0_256 )
| ~ aNaturalNumber0(W0_256) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_11144,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_11123]) ).
tff(c_12241,plain,
! [W1_283,W0_284] :
( sdtlseqdt0(W1_283,sdtasdt0(W1_283,W0_284))
| ( sz00 = W0_284 )
| ~ aNaturalNumber0(W1_283)
| ~ aNaturalNumber0(W0_284) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_12280,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_11144,c_12241]) ).
tff(c_12358,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_12280]) ).
tff(c_12512,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_12358]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_12581,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_12512,c_153]) ).
tff(c_12601,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_163,c_12581]) ).
tff(c_12603,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_12358]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_10931,plain,
! [W0_251] :
( ( sdtpldt0(W0_251,sz00) = W0_251 )
| ~ aNaturalNumber0(W0_251) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_10949,plain,
sdtpldt0(xn,sz00) = xn,
inference(resolution,[status(thm)],[c_147,c_10931]) ).
tff(c_159,plain,
( ~ sdtlseqdt0(xr,xn)
| ( xr = xn ) ),
inference(cnfTransformation,[status(thm)],[f_449]) ).
tff(c_164,plain,
~ sdtlseqdt0(xr,xn),
inference(splitLeft,[status(thm)],[c_159]) ).
tff(c_889,plain,
! [W1_119,W0_120] :
( sdtlseqdt0(W1_119,W0_120)
| sdtlseqdt0(W0_120,W1_119)
| ~ aNaturalNumber0(W1_119)
| ~ aNaturalNumber0(W0_120) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_892,plain,
( sdtlseqdt0(xn,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_889,c_164]) ).
tff(c_898,plain,
( sdtlseqdt0(xn,xr)
| ~ aNaturalNumber0(xr) ),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_892]) ).
tff(c_902,plain,
~ aNaturalNumber0(xr),
inference(splitLeft,[status(thm)],[c_898]) ).
tff(c_155,plain,
sdtlseqdt0(xp,xn),
inference(cnfTransformation,[status(thm)],[f_443]) ).
tff(c_157,plain,
sdtmndt0(xn,xp) = xr,
inference(cnfTransformation,[status(thm)],[f_444]) ).
tff(c_1395,plain,
! [W1_129,W0_130] :
( aNaturalNumber0(sdtmndt0(W1_129,W0_130))
| ~ sdtlseqdt0(W0_130,W1_129)
| ~ aNaturalNumber0(W1_129)
| ~ aNaturalNumber0(W0_130) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_1429,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_1395]) ).
tff(c_1442,plain,
aNaturalNumber0(xr),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_1429]) ).
tff(c_1444,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_902,c_1442]) ).
tff(c_1446,plain,
aNaturalNumber0(xr),
inference(splitRight,[status(thm)],[c_898]) ).
tff(c_10663,plain,
! [W0_246,W1_247] :
( ( sdtpldt0(W0_246,sdtmndt0(W1_247,W0_246)) = W1_247 )
| ~ sdtlseqdt0(W0_246,W1_247)
| ~ aNaturalNumber0(W1_247)
| ~ aNaturalNumber0(W0_246) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_10682,plain,
( ( sdtpldt0(xp,xr) = xn )
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_157,c_10663]) ).
tff(c_10686,plain,
sdtpldt0(xp,xr) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_10682]) ).
tff(c_14,plain,
! [W1_7,W0_6] :
( ( sdtpldt0(W1_7,W0_6) = sdtpldt0(W0_6,W1_7) )
| ~ aNaturalNumber0(W1_7)
| ~ aNaturalNumber0(W0_6) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_1878,plain,
! [W0_135] :
( ( sdtpldt0(xr,W0_135) = sdtpldt0(W0_135,xr) )
| ~ aNaturalNumber0(W0_135) ),
inference(resolution,[status(thm)],[c_1446,c_14]) ).
tff(c_1944,plain,
sdtpldt0(xr,xp) = sdtpldt0(xp,xr),
inference(resolution,[status(thm)],[c_143,c_1878]) ).
tff(c_10872,plain,
sdtpldt0(xr,xp) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_10686,c_1944]) ).
tff(c_52,plain,
! [W0_34,W2_38] :
( sdtlseqdt0(W0_34,sdtpldt0(W0_34,W2_38))
| ~ aNaturalNumber0(W2_38)
| ~ aNaturalNumber0(sdtpldt0(W0_34,W2_38))
| ~ aNaturalNumber0(W0_34) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_10904,plain,
( sdtlseqdt0(xr,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xr,xp))
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_10872,c_52]) ).
tff(c_10915,plain,
sdtlseqdt0(xr,xn),
inference(demodulation,[status(thm),theory(equality)],[c_1446,c_147,c_10872,c_143,c_10904]) ).
tff(c_10917,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_164,c_10915]) ).
tff(c_10918,plain,
xr = xn,
inference(splitRight,[status(thm)],[c_159]) ).
tff(c_10919,plain,
sdtlseqdt0(xr,xn),
inference(splitRight,[status(thm)],[c_159]) ).
tff(c_10924,plain,
sdtlseqdt0(xn,xn),
inference(demodulation,[status(thm),theory(equality)],[c_10918,c_10919]) ).
tff(c_18199,plain,
! [W0_409,W2_410] :
( ( sdtmndt0(sdtpldt0(W0_409,W2_410),W0_409) = W2_410 )
| ~ aNaturalNumber0(W2_410)
| ~ sdtlseqdt0(W0_409,sdtpldt0(W0_409,W2_410))
| ~ aNaturalNumber0(sdtpldt0(W0_409,W2_410))
| ~ aNaturalNumber0(W0_409) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_18260,plain,
( ( sdtmndt0(sdtpldt0(xn,sz00),xn) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(sdtpldt0(xn,sz00))
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_10949,c_18199]) ).
tff(c_18290,plain,
sdtmndt0(xn,xn) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_147,c_10949,c_10924,c_4,c_10949,c_18260]) ).
tff(c_11364,plain,
! [W1_264,W0_265] :
( ( sdtpldt0(W1_264,W0_265) = sdtpldt0(W0_265,W1_264) )
| ~ aNaturalNumber0(W1_264)
| ~ aNaturalNumber0(W0_265) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_11813,plain,
! [W0_276] :
( ( sdtpldt0(xn,W0_276) = sdtpldt0(W0_276,xn) )
| ~ aNaturalNumber0(W0_276) ),
inference(resolution,[status(thm)],[c_147,c_11364]) ).
tff(c_11859,plain,
sdtpldt0(xp,xn) = sdtpldt0(xn,xp),
inference(resolution,[status(thm)],[c_143,c_11813]) ).
tff(c_10925,plain,
sdtmndt0(xn,xp) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_10918,c_157]) ).
tff(c_14642,plain,
! [W0_342,W1_343] :
( ( sdtpldt0(W0_342,sdtmndt0(W1_343,W0_342)) = W1_343 )
| ~ sdtlseqdt0(W0_342,W1_343)
| ~ aNaturalNumber0(W1_343)
| ~ aNaturalNumber0(W0_342) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_14661,plain,
( ( sdtpldt0(xp,xn) = xn )
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_10925,c_14642]) ).
tff(c_14665,plain,
sdtpldt0(xn,xp) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_147,c_155,c_11859,c_14661]) ).
tff(c_18218,plain,
( ( sdtmndt0(sdtpldt0(xn,xp),xn) = xp )
| ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(sdtpldt0(xn,xp))
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_14665,c_18199]) ).
tff(c_18271,plain,
sdtmndt0(xn,xn) = xp,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_147,c_14665,c_10924,c_143,c_14665,c_18218]) ).
tff(c_18650,plain,
xp = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_18290,c_18271]) ).
tff(c_18651,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_12603,c_18650]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM487+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 12:54:23 EDT 2025
% 0.13/0.34 % CPUTime :
% 14.74/4.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.74/4.56
% 14.74/4.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------