%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM491+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/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 : n002.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 07:56:07 PM UTC 2025
% Result : Theorem 8.25s 2.80s
% Output : CNFRefutation 8.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 42 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 39 ( 16 ~; 13 |; 6 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 14 ( 13 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xr,type,
xr: $i ).
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/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(f_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_453,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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_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(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_621,plain,
! [W1_112,W0_113] :
( ( sdtasdt0(W1_112,W0_113) = sdtasdt0(W0_113,W1_112) )
| ~ aNaturalNumber0(W1_112)
| ~ aNaturalNumber0(W0_113) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_2202,plain,
! [W0_142] :
( ( sdtasdt0(xm,W0_142) = sdtasdt0(W0_142,xm) )
| ~ aNaturalNumber0(W0_142) ),
inference(resolution,[status(thm)],[c_145,c_621]) ).
tff(c_2250,plain,
sdtasdt0(xp,xm) = sdtasdt0(xm,xp),
inference(resolution,[status(thm)],[c_143,c_2202]) ).
tff(c_169,plain,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnfTransformation,[status(thm)],[f_453]) ).
tff(c_2316,plain,
~ doDivides0(xp,sdtasdt0(xm,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_2250,c_169]) ).
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_2320,plain,
( aNaturalNumber0(sdtasdt0(xm,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_2250,c_12]) ).
tff(c_2324,plain,
aNaturalNumber0(sdtasdt0(xm,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_145,c_2320]) ).
tff(c_5526,plain,
! [W0_208,W2_209] :
( doDivides0(W0_208,sdtasdt0(W0_208,W2_209))
| ~ aNaturalNumber0(W2_209)
| ~ aNaturalNumber0(sdtasdt0(W0_208,W2_209))
| ~ aNaturalNumber0(W0_208) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_5547,plain,
( doDivides0(xp,sdtasdt0(xm,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_2250,c_5526]) ).
tff(c_5648,plain,
doDivides0(xp,sdtasdt0(xm,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_2324,c_2250,c_145,c_5547]) ).
tff(c_5650,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2316,c_5648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM491+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 12:57:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 8.25/2.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.25/2.81
% 8.25/2.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------