%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM482+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 : 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 07:56:05 PM UTC 2025
% Result : Theorem 4.71s 2.00s
% Output : CNFRefutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 15 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 40 ( 12 ~; 11 |; 13 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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; 3 con; 0-2 aty)
% Number of variables : 10 ( 6 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xk > sz10 > sz00 > #skF_7 > #skF_5 > #skF_4 > #skF_3 > #skF_2 > #skF_1 > #skF_6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_5',type,
'#skF_5': $i > $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('#skF_6',type,
'#skF_6': $i > $i ).
tff(f_404,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
tff(f_499,negated_conjecture,
~ ( ( ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xk) ) )
=> ( ( W0 = sz10 )
| ( W0 = xk ) ) )
& isPrime0(xk) )
=> ? [W0] :
( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& ( xk = sdtasdt0(W0,W1) ) )
| doDivides0(W0,xk) )
& ( ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1] :
( ( aNaturalNumber0(W1)
& ? [W2] :
( aNaturalNumber0(W2)
& ( W0 = sdtasdt0(W1,W2) ) )
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) )
| isPrime0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
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(c_137,plain,
aNaturalNumber0(xk),
inference(cnfTransformation,[status(thm)],[f_404]) ).
tff(c_161,plain,
isPrime0(xk),
inference(cnfTransformation,[status(thm)],[f_499]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_347,plain,
! [W0_130] :
( ( sdtasdt0(W0_130,sz10) = W0_130 )
| ~ aNaturalNumber0(W0_130) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_359,plain,
sdtasdt0(xk,sz10) = xk,
inference(resolution,[status(thm)],[c_137,c_347]) ).
tff(c_165,plain,
! [W0_113,W1_118] :
( ( sdtasdt0(W0_113,W1_118) != xk )
| ~ aNaturalNumber0(W1_118)
| ~ isPrime0(W0_113)
| ~ aNaturalNumber0(W0_113) ),
inference(cnfTransformation,[status(thm)],[f_499]) ).
tff(c_364,plain,
( ~ aNaturalNumber0(sz10)
| ~ isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[status(thm),theory(equality)],[c_359,c_165]) ).
tff(c_370,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_137,c_161,c_8,c_364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM482+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % 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
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 12:52:02 EDT 2025
% 0.13/0.34 % CPUTime :
% 4.71/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.71/2.00
% 4.71/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------