%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM505+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 : n003.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 9.73s 3.28s
% Output : CNFRefutation 9.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 32 ( 12 ~; 9 |; 9 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 25 ( 25 usr; 13 con; 0-3 aty)
% Number of variables : 6 ( 4 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_11 > #skF_6 > #skF_10 > #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_11',type,
'#skF_11': $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('#skF_10',type,
'#skF_10': $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_608,negated_conjecture,
~ ( ~ ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xp,W0) = xk ) )
| sdtlseqdt0(xp,xk) )
=> ( ( xk != xp )
& ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xk,W0) = xp ) )
| sdtlseqdt0(xk,xp) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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(c_487,plain,
( ~ sdtlseqdt0(xk,xp)
| ( xp = xk ) ),
inference(cnfTransformation,[status(thm)],[f_608]) ).
tff(c_494,plain,
~ sdtlseqdt0(xk,xp),
inference(splitLeft,[status(thm)],[c_487]) ).
tff(c_445,plain,
aNaturalNumber0(xk),
inference(cnfTransformation,[status(thm)],[f_540]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_3867,plain,
! [W1_153,W0_154] :
( sdtlseqdt0(W1_153,W0_154)
| sdtlseqdt0(W0_154,W1_153)
| ~ aNaturalNumber0(W1_153)
| ~ aNaturalNumber0(W0_154) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_483,plain,
~ sdtlseqdt0(xp,xk),
inference(cnfTransformation,[status(thm)],[f_608]) ).
tff(c_3877,plain,
( sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_3867,c_483]) ).
tff(c_3896,plain,
sdtlseqdt0(xk,xp),
inference(demodulation,[status(thm),theory(equality)],[c_445,c_143,c_3877]) ).
tff(c_3898,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_494,c_3896]) ).
tff(c_3899,plain,
xp = xk,
inference(splitRight,[status(thm)],[c_487]) ).
tff(c_3904,plain,
~ sdtlseqdt0(xk,xk),
inference(demodulation,[status(thm),theory(equality)],[c_3899,c_483]) ).
tff(c_3900,plain,
sdtlseqdt0(xk,xp),
inference(splitRight,[status(thm)],[c_487]) ).
tff(c_3964,plain,
sdtlseqdt0(xk,xk),
inference(demodulation,[status(thm),theory(equality)],[c_3899,c_3900]) ).
tff(c_3965,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3904,c_3964]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15 % Problem : NUM505+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.16 % 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
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8042.1875MB
% 0.12/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Tue Apr 8 13:04:19 EDT 2025
% 0.12/0.37 % CPUTime :
% 9.73/3.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.73/3.29
% 9.73/3.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------