%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM521+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 : n018.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 07:56:13 PM UTC 2025
% Result : Theorem 5.14s 2.20s
% Output : CNFRefutation 5.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 9 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 13 |; 7 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 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 : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 5 ( 5 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xp > xn > xm > sz10 > sz00 > #skF_4 > #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(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_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(f_444,hypothesis,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
tff(f_446,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
tff(f_456,hypothesis,
~ ( ( xn != xp )
& sdtlseqdt0(xn,xp)
& ( xm != xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_72,plain,
! [W1_50] :
( sdtlseqdt0(W1_50,W1_50)
| ~ aNaturalNumber0(W1_50) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_616,plain,
! [W1_112,W0_113] :
( sdtlseqdt0(W1_112,W0_113)
| sdtlseqdt0(W0_113,W1_112)
| ~ aNaturalNumber0(W1_112)
| ~ aNaturalNumber0(W0_113) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_155,plain,
~ sdtlseqdt0(xp,xn),
inference(cnfTransformation,[status(thm)],[f_444]) ).
tff(c_622,plain,
( sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_616,c_155]) ).
tff(c_634,plain,
sdtlseqdt0(xn,xp),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_143,c_622]) ).
tff(c_157,plain,
~ sdtlseqdt0(xp,xm),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_619,plain,
( sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_616,c_157]) ).
tff(c_631,plain,
sdtlseqdt0(xm,xp),
inference(demodulation,[status(thm),theory(equality)],[c_145,c_143,c_619]) ).
tff(c_159,plain,
( ~ sdtlseqdt0(xm,xp)
| ( xp = xm )
| ~ sdtlseqdt0(xn,xp)
| ( xp = xn ) ),
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_817,plain,
( ( xp = xm )
| ( xp = xn ) ),
inference(demodulation,[status(thm),theory(equality)],[c_634,c_631,c_159]) ).
tff(c_818,plain,
xp = xn,
inference(splitLeft,[status(thm)],[c_817]) ).
tff(c_822,plain,
sdtlseqdt0(xn,xn),
inference(demodulation,[status(thm),theory(equality)],[c_818,c_634]) ).
tff(c_832,plain,
~ sdtlseqdt0(xn,xn),
inference(demodulation,[status(thm),theory(equality)],[c_818,c_155]) ).
tff(c_862,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_822,c_832]) ).
tff(c_863,plain,
xp = xm,
inference(splitRight,[status(thm)],[c_817]) ).
tff(c_877,plain,
~ sdtlseqdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_863,c_157]) ).
tff(c_934,plain,
~ aNaturalNumber0(xm),
inference(resolution,[status(thm)],[c_72,c_877]) ).
tff(c_938,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_145,c_934]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : NUM521+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.14 % 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
% 0.12/0.36 % Computer : n018.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Tue Apr 8 13:14:47 EDT 2025
% 0.12/0.36 % CPUTime :
% 5.14/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.14/2.21
% 5.14/2.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------