%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM523+3 : 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/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 : n026.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 07:56:14 PM UTC 2025
% Result : Theorem 16.88s 5.42s
% Output : CNFRefutation 16.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 25 unt; 0 typ; 1 def)
% Number of atoms : 102 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 102 ( 44 ~; 34 |; 18 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 22 ( 18 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_6 > #skF_5 > #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('#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(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_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_486,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
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_518,negated_conjecture,
~ ( ( ? [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__) ).
tff(f_504,hypothesis,
( ( xp != sz10 )
& ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xp = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xp) ) )
=> ( ( W0 = sz10 )
| ( W0 = xp ) ) )
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
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_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_171,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnfTransformation,[status(thm)],[f_486]) ).
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_151,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_19343,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_171,c_12]) ).
tff(c_19347,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_19343]) ).
tff(c_19423,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitLeft,[status(thm)],[c_19347]) ).
tff(c_19426,plain,
~ aNaturalNumber0(xm),
inference(resolution,[status(thm)],[c_12,c_19423]) ).
tff(c_19430,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_153,c_19426]) ).
tff(c_19432,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitRight,[status(thm)],[c_19347]) ).
tff(c_181,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ doDivides0(xp,xn) ),
inference(cnfTransformation,[status(thm)],[f_518]) ).
tff(c_192,plain,
~ doDivides0(xp,xn),
inference(splitLeft,[status(thm)],[c_181]) ).
tff(c_155,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_173,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_504]) ).
tff(c_185,plain,
! [W0_109] :
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ( sdtasdt0(xp,W0_109) != xn )
| ~ aNaturalNumber0(W0_109) ),
inference(cnfTransformation,[status(thm)],[f_518]) ).
tff(c_294,plain,
~ doDivides0(xp,sdtasdt0(xn,xn)),
inference(splitLeft,[status(thm)],[c_185]) ).
tff(c_562,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_171,c_12]) ).
tff(c_566,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_562]) ).
tff(c_688,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitLeft,[status(thm)],[c_566]) ).
tff(c_691,plain,
~ aNaturalNumber0(xm),
inference(resolution,[status(thm)],[c_12,c_688]) ).
tff(c_695,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_153,c_691]) ).
tff(c_696,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(splitRight,[status(thm)],[c_566]) ).
tff(c_697,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitRight,[status(thm)],[c_566]) ).
tff(c_4746,plain,
! [W0_186,W2_187] :
( doDivides0(W0_186,sdtasdt0(W0_186,W2_187))
| ~ aNaturalNumber0(W2_187)
| ~ aNaturalNumber0(sdtasdt0(W0_186,W2_187))
| ~ aNaturalNumber0(W0_186) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_4858,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_171,c_4746]) ).
tff(c_4979,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_696,c_171,c_697,c_4858]) ).
tff(c_4981,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_294,c_4979]) ).
tff(c_4983,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(splitRight,[status(thm)],[c_185]) ).
tff(c_18632,plain,
! [W2_366,W1_367,W0_368] :
( doDivides0(W2_366,W1_367)
| doDivides0(W2_366,W0_368)
| ~ doDivides0(W2_366,sdtasdt0(W0_368,W1_367))
| ~ isPrime0(W2_366)
| ~ aNaturalNumber0(W2_366)
| ~ aNaturalNumber0(W1_367)
| ~ aNaturalNumber0(W0_368) ),
inference(cnfTransformation,[status(thm)],[f_432]) ).
tff(c_18823,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_4983,c_18632]) ).
tff(c_18968,plain,
doDivides0(xp,xn),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_151,c_173,c_18823]) ).
tff(c_18970,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_192,c_18968]) ).
tff(c_18972,plain,
doDivides0(xp,xn),
inference(splitRight,[status(thm)],[c_181]) ).
tff(c_183,plain,
! [W0_108] :
( ( sdtasdt0(xp,W0_108) != sdtasdt0(xn,xn) )
| ~ aNaturalNumber0(W0_108)
| ~ doDivides0(xp,xn) ),
inference(cnfTransformation,[status(thm)],[f_518]) ).
tff(c_19009,plain,
! [W0_108] :
( ( sdtasdt0(xp,W0_108) != sdtasdt0(xn,xn) )
| ~ aNaturalNumber0(W0_108) ),
inference(demodulation,[status(thm),theory(equality)],[c_18972,c_183]) ).
tff(c_19478,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) != sdtasdt0(xn,xn),
inference(resolution,[status(thm)],[c_19432,c_19009]) ).
tff(c_19490,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_171,c_19478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM523+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.14 % 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
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 8 13:16:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 16.88/5.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.88/5.42
% 16.88/5.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------