%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM482+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 : n012.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 07:56:05 PM UTC 2025
% Result : Theorem 6.24s 2.43s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 36 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 34 ( 14 ~; 10 |; 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 : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 7 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xk > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $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(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(sdtsldt0,type,
sdtsldt0: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_404,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
tff(f_435,negated_conjecture,
~ ( isPrime0(xk)
=> ? [W0] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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_137,plain,
aNaturalNumber0(xk),
inference(cnfTransformation,[status(thm)],[f_404]) ).
tff(c_151,plain,
isPrime0(xk),
inference(cnfTransformation,[status(thm)],[f_435]) ).
tff(c_274,plain,
! [W0_103] :
( ( sdtasdt0(W0_103,sz10) = W0_103 )
| ~ aNaturalNumber0(W0_103) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_288,plain,
sdtasdt0(xk,sz10) = xk,
inference(resolution,[status(thm)],[c_137,c_274]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2449,plain,
! [W0_160,W2_161] :
( doDivides0(W0_160,sdtasdt0(W0_160,W2_161))
| ~ aNaturalNumber0(W2_161)
| ~ aNaturalNumber0(sdtasdt0(W0_160,W2_161))
| ~ aNaturalNumber0(W0_160) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_2464,plain,
( doDivides0(xk,xk)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtasdt0(xk,sz10))
| ~ aNaturalNumber0(xk) ),
inference(superposition,[status(thm),theory(equality)],[c_288,c_2449]) ).
tff(c_2495,plain,
doDivides0(xk,xk),
inference(demodulation,[status(thm),theory(equality)],[c_137,c_137,c_288,c_8,c_2464]) ).
tff(c_149,plain,
! [W0_95] :
( ~ isPrime0(W0_95)
| ~ doDivides0(W0_95,xk)
| ~ aNaturalNumber0(W0_95) ),
inference(cnfTransformation,[status(thm)],[f_435]) ).
tff(c_2512,plain,
( ~ isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_2495,c_149]) ).
tff(c_2516,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_137,c_151,c_2512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM482+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % 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
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 8 12:50:45 EDT 2025
% 0.12/0.33 % CPUTime :
% 6.24/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.24/2.43
% 6.24/2.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------