%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM482+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n027.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 : Fri Jul 25 12:28:16 PM UTC 2025
% Result : Theorem 8.30s 1.39s
% Output : CNFRefutation 8.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 81 ( 28 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 79 ( 22 ~; 24 |; 25 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 7 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
( ( ! [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/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ( ( ! [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) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(80,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| xk != sdtasdt0(X0,X1)
| sP0(X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sz10)
| xk != sdtasdt0(xk,sz10)
| sP0(xk) ),
inference(instantiation,[status(thm)],[80]) ).
cnf(82,plain,
( ~ isPrime0(X0)
| ~ sP0(X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l6,plain,
( ~ isPrime0(xk)
| ~ sP0(xk) ),
inference(instantiation,[status(thm)],[82]) ).
fof(mSortsC_01,plain,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
cnf(1,plain,
aNaturalNumber0(sz10),
inference(cnf,[status(esa)],[mSortsC_01]) ).
cnf(l1,plain,
aNaturalNumber0(sz10),
inference(instantiation,[status(thm)],[1]) ).
fof(m__1716,plain,
aNaturalNumber0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716) ).
cnf(65,plain,
aNaturalNumber0(xk),
inference(cnf,[status(esa)],[m__1716]) ).
cnf(l3,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[65]) ).
fof(mMulComm,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
cnf(9,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf,[status(esa)],[mMulComm]) ).
cnf(l16,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| sdtasdt0(sz10,xk) = sdtasdt0(xk,sz10) ),
inference(instantiation,[status(thm)],[9]) ).
fof(m_MulUnit,plain,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtasdt0(W0,sz10) = W0
& W0 = sdtasdt0(sz10,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
cnf(12,plain,
( ~ aNaturalNumber0(X0)
| X0 = sdtasdt0(sz10,X0) ),
inference(cnf,[status(esa)],[m_MulUnit]) ).
cnf(l9,plain,
( ~ aNaturalNumber0(xk)
| xk = sdtasdt0(sz10,xk) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l70,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[65]) ).
cnf(l68,plain,
aNaturalNumber0(sz10),
inference(instantiation,[status(thm)],[1]) ).
cnf(79,plain,
isPrime0(xk),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l35,plain,
isPrime0(xk),
inference(instantiation,[status(thm)],[79]) ).
cnf(l20,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[65]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l6,l1,l3,l16,l9,l70,l68,l35,l20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM482+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n027.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Jul 21 12:23:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.35 % launching worker at depth: 9
% 0.12/0.38 % launching worker at depth: 10
% 8.30/1.39 % SZS status Theorem for theBenchmark
% 8.30/1.39 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------