%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM521+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 : n019.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 7.46s 2.66s
% Output : CNFRefutation 7.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 58 ( 25 ~; 19 |; 12 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 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 : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 12 ( 8 !; 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_9 > #skF_7 > #skF_3 > #skF_2 > #skF_8 > #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_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(f_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(f_67,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
tff(f_509,hypothesis,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xp,W0) = xn ) )
| sdtlseqdt0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
tff(f_516,hypothesis,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xp,W0) = xm ) )
| sdtlseqdt0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
tff(f_212,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
tff(f_536,hypothesis,
~ ( ( xn != xp )
& ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xn,W0) = xp ) )
| sdtlseqdt0(xn,xp) )
& ( xm != xp )
& ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xp ) )
| sdtlseqdt0(xm,xp) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_537,plain,
! [W0_119] :
( ( sdtpldt0(W0_119,sz00) = W0_119 )
| ~ aNaturalNumber0(W0_119) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_561,plain,
sdtpldt0(xp,sz00) = xp,
inference(resolution,[status(thm)],[c_143,c_537]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_656,plain,
! [W0_122] :
( ( sdtpldt0(xp,W0_122) != xn )
| ~ aNaturalNumber0(W0_122) ),
inference(cnfTransformation,[status(thm)],[f_509]) ).
tff(c_665,plain,
sdtpldt0(xp,sz00) != xn,
inference(resolution,[status(thm)],[c_4,c_656]) ).
tff(c_678,plain,
xp != xn,
inference(demodulation,[status(thm),theory(equality)],[c_561,c_665]) ).
tff(c_595,plain,
! [W0_120] :
( ( sdtpldt0(xp,W0_120) != xm )
| ~ aNaturalNumber0(W0_120) ),
inference(cnfTransformation,[status(thm)],[f_516]) ).
tff(c_604,plain,
sdtpldt0(xp,sz00) != xm,
inference(resolution,[status(thm)],[c_4,c_595]) ).
tff(c_617,plain,
xp != xm,
inference(demodulation,[status(thm),theory(equality)],[c_561,c_604]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_1649,plain,
! [W1_143,W0_144] :
( sdtlseqdt0(W1_143,W0_144)
| sdtlseqdt0(W0_144,W1_143)
| ~ aNaturalNumber0(W1_143)
| ~ aNaturalNumber0(W0_144) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_421,plain,
~ sdtlseqdt0(xp,xm),
inference(cnfTransformation,[status(thm)],[f_516]) ).
tff(c_1655,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_1649,c_421]) ).
tff(c_1667,plain,
sdtlseqdt0(xm,xp),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_143,c_1655]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_417,plain,
~ sdtlseqdt0(xp,xn),
inference(cnfTransformation,[status(thm)],[f_509]) ).
tff(c_1652,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_1649,c_417]) ).
tff(c_1664,plain,
sdtlseqdt0(xn,xp),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_143,c_1652]) ).
tff(c_425,plain,
( ~ sdtlseqdt0(xn,xp)
| ~ sdtlseqdt0(xm,xp)
| ( xp = xm )
| ( xp = xn ) ),
inference(cnfTransformation,[status(thm)],[f_536]) ).
tff(c_2130,plain,
( ( xp = xm )
| ( xp = xn ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1667,c_1664,c_425]) ).
tff(c_2131,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_678,c_617,c_2130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM521+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
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 8 13:14:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.46/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.46/2.66
% 7.46/2.66 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------