%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM504+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/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 : n014.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 07:56:10 PM UTC 2025
% Result : Theorem 9.87s 3.28s
% Output : CNFRefutation 10.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 22 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 68 ( 20 ~; 17 |; 26 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 28 ( 28 usr; 16 con; 0-3 aty)
% Number of variables : 19 ( 13 !; 6 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_17 > #skF_11 > #skF_6 > #skF_15 > #skF_10 > #skF_16 > #skF_14 > #skF_13 > #skF_5 > #skF_9 > #skF_7 > #skF_3 > #skF_2 > #skF_8 > #skF_1 > #skF_12
%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('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz00,type,
sz00: $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $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('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
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('#skF_12',type,
'#skF_12': $i ).
tff(f_615,hypothesis,
( ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm) )
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sdtasdt0(xn,xm),W0) = sdtasdt0(xp,xm) ) )
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ( sdtasdt0(xp,xm) != sdtasdt0(xp,xk) )
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(sdtasdt0(xp,xm),W0) = sdtasdt0(xp,xk) ) )
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2414) ).
tff(f_579,hypothesis,
( aNaturalNumber0(xr)
& ? [W0] :
( aNaturalNumber0(W0)
& ( xk = sdtasdt0(xr,W0) ) )
& doDivides0(xr,xk)
& ( xr != sz00 )
& ( xr != sz10 )
& ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xr = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xr) ) )
=> ( ( W0 = sz10 )
| ( W0 = xr ) ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
tff(f_590,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xr,W0) = xk ) )
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtasdt0(xn,xm) = sdtasdt0(xr,W0) ) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
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_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(f_540,hypothesis,
( aNaturalNumber0(xk)
& ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
& ( xk = sdtsldt0(sdtasdt0(xn,xm),xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
tff(f_189,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
tff(c_503,plain,
sdtasdt0(xp,xm) != sdtasdt0(xn,xm),
inference(cnfTransformation,[status(thm)],[f_615]) ).
tff(c_467,plain,
aNaturalNumber0(xr),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_477,plain,
aNaturalNumber0('#skF_13'),
inference(cnfTransformation,[status(thm)],[f_590]) ).
tff(c_475,plain,
sdtasdt0(xr,'#skF_13') = sdtasdt0(xn,xm),
inference(cnfTransformation,[status(thm)],[f_590]) ).
tff(c_1201,plain,
! [W0_123,W1_124] :
( aNaturalNumber0(sdtasdt0(W0_123,W1_124))
| ~ aNaturalNumber0(W1_124)
| ~ aNaturalNumber0(W0_123) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_1282,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0('#skF_13')
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_475,c_1201]) ).
tff(c_1352,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_467,c_477,c_1282]) ).
tff(c_501,plain,
aNaturalNumber0('#skF_17'),
inference(cnfTransformation,[status(thm)],[f_615]) ).
tff(c_499,plain,
sdtpldt0(sdtasdt0(xn,xm),'#skF_17') = sdtasdt0(xp,xm),
inference(cnfTransformation,[status(thm)],[f_615]) ).
tff(c_1452,plain,
! [W0_125,W1_126] :
( aNaturalNumber0(sdtpldt0(W0_125,W1_126))
| ~ aNaturalNumber0(W1_126)
| ~ aNaturalNumber0(W0_125) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_1479,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0('#skF_17')
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm),theory(equality)],[c_499,c_1452]) ).
tff(c_1528,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_1352,c_501,c_1479]) ).
tff(c_497,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnfTransformation,[status(thm)],[f_615]) ).
tff(c_443,plain,
sdtasdt0(xp,xk) = sdtasdt0(xn,xm),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_489,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnfTransformation,[status(thm)],[f_615]) ).
tff(c_506,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)),
inference(demodulation,[status(thm),theory(equality)],[c_443,c_489]) ).
tff(c_3571,plain,
! [W1_157,W0_158] :
( ( W1_157 = W0_158 )
| ~ sdtlseqdt0(W1_157,W0_158)
| ~ sdtlseqdt0(W0_158,W1_157)
| ~ aNaturalNumber0(W1_157)
| ~ aNaturalNumber0(W0_158) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_3611,plain,
( ( sdtasdt0(xp,xm) = sdtasdt0(xn,xm) )
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[status(thm)],[c_506,c_3571]) ).
tff(c_3690,plain,
sdtasdt0(xp,xm) = sdtasdt0(xn,xm),
inference(demodulation,[status(thm),theory(equality)],[c_1352,c_1528,c_497,c_3611]) ).
tff(c_3692,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_503,c_3690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM504+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % 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
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 13:03:49 EDT 2025
% 0.14/0.34 % CPUTime :
% 9.87/3.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.87/3.28
% 9.87/3.28 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------