%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM518+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 : n028.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 12:28:22 PM UTC 2025
% Result : Theorem 263.21s 33.35s
% Output : CNFRefutation 263.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 18 unt; 0 def)
% Number of atoms : 140 ( 33 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 125 ( 40 ~; 45 |; 33 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 11 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
( ? [W0] :
( aNaturalNumber0(W0)
& xn = sdtasdt0(xp,W0) )
| doDivides0(xp,xn)
| ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xp,W0) )
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& xn = sdtasdt0(xp,W0) )
| doDivides0(xp,xn)
| ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xp,W0) )
| doDivides0(xp,xm) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(161,plain,
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xp,X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aNaturalNumber0(sdtasdt0(sK23,xr))
| xn != sdtasdt0(xp,sdtasdt0(sK23,xr)) ),
inference(instantiation,[status(thm)],[161]) ).
fof(mMulAsso,plain,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
cnf(10,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf,[status(esa)],[mMulAsso]) ).
cnf(l63,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK23)
| ~ aNaturalNumber0(xr)
| sdtasdt0(sdtasdt0(xp,sK23),xr) = sdtasdt0(xp,sdtasdt0(sK23,xr)) ),
inference(instantiation,[status(thm)],[10]) ).
fof(m__1837,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
cnf(70,plain,
aNaturalNumber0(xp),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l83,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
fof(m__2645,plain,
( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [W0] :
( aNaturalNumber0(W0)
& sdtsldt0(xn,xr) = sdtasdt0(xp,W0) )
& doDivides0(xp,sdtsldt0(xn,xr)) )
| ( ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xp,W0) )
& doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2645) ).
cnf(154,plain,
( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| sP4 ),
inference(cnf,[status(esa)],[m__2645]) ).
cnf(l17,plain,
( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| sP4 ),
inference(instantiation,[status(thm)],[154]) ).
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(l32,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtasdt0(xr,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xr) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(158,plain,
( doDivides0(xp,xm)
| ~ sP4 ),
inference(cnf,[status(esa)],[m__2645]) ).
cnf(l271,plain,
( doDivides0(xp,xm)
| ~ sP4 ),
inference(instantiation,[status(thm)],[158]) ).
fof(m__2504,plain,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn )
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [W0] :
( aNaturalNumber0(W0)
& sdtpldt0(sdtsldt0(xn,xr),W0) = xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2504) ).
cnf(143,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf,[status(esa)],[m__2504]) ).
cnf(l289,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(instantiation,[status(thm)],[143]) ).
fof(m__2342,plain,
( aNaturalNumber0(xr)
& ? [W0] :
( aNaturalNumber0(W0)
& xk = sdtasdt0(xr,W0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& xr = sdtasdt0(W0,W1) )
| doDivides0(W0,xr) ) )
=> ( W0 = sz10
| W0 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
cnf(113,plain,
aNaturalNumber0(xr),
inference(cnf,[status(esa)],[m__2342]) ).
cnf(l294,plain,
aNaturalNumber0(xr),
inference(instantiation,[status(thm)],[113]) ).
cnf(155,plain,
( aNaturalNumber0(sK23)
| sP4 ),
inference(cnf,[status(esa)],[m__2645]) ).
cnf(l200,plain,
( aNaturalNumber0(sK23)
| sP4 ),
inference(instantiation,[status(thm)],[155]) ).
fof(m_AddZero,plain,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
cnf(7,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf,[status(esa)],[m_AddZero]) ).
cnf(l57,plain,
( ~ aNaturalNumber0(sK23)
| sdtpldt0(sK23,sz00) = sK23 ),
inference(instantiation,[status(thm)],[7]) ).
fof(mSortsB_02,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
cnf(4,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf,[status(esa)],[mSortsB_02]) ).
cnf(l6,plain,
( ~ aNaturalNumber0(sdtpldt0(sK23,sz00))
| ~ aNaturalNumber0(xr)
| aNaturalNumber0(sdtasdt0(sdtpldt0(sK23,sz00),xr)) ),
inference(instantiation,[status(thm)],[4]) ).
fof(mSortsB,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
cnf(3,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf,[status(esa)],[mSortsB]) ).
cnf(l7,plain,
( ~ aNaturalNumber0(sK23)
| ~ aNaturalNumber0(sz00)
| aNaturalNumber0(sdtpldt0(sK23,sz00)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(164,plain,
~ doDivides0(xp,xm),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l407,plain,
~ doDivides0(xp,xm),
inference(instantiation,[status(thm)],[164]) ).
fof(mSortsC,plain,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
cnf(0,plain,
aNaturalNumber0(sz00),
inference(cnf,[status(esa)],[mSortsC]) ).
cnf(l25,plain,
aNaturalNumber0(sz00),
inference(instantiation,[status(thm)],[0]) ).
cnf(l214,plain,
( doDivides0(xp,xm)
| ~ sP4 ),
inference(instantiation,[status(thm)],[158]) ).
cnf(l86,plain,
( aNaturalNumber0(sK23)
| sP4 ),
inference(instantiation,[status(thm)],[155]) ).
cnf(l570,plain,
( aNaturalNumber0(sK23)
| sP4 ),
inference(instantiation,[status(thm)],[155]) ).
cnf(l51,plain,
aNaturalNumber0(xr),
inference(instantiation,[status(thm)],[113]) ).
cnf(156,plain,
( sdtsldt0(xn,xr) = sdtasdt0(xp,sK23)
| sP4 ),
inference(cnf,[status(esa)],[m__2645]) ).
cnf(l150,plain,
( sdtsldt0(xn,xr) = sdtasdt0(xp,sK23)
| sP4 ),
inference(instantiation,[status(thm)],[156]) ).
cnf(l447,plain,
~ doDivides0(xp,xm),
inference(instantiation,[status(thm)],[164]) ).
cnf(l87,plain,
aNaturalNumber0(xr),
inference(instantiation,[status(thm)],[113]) ).
cnf(l174,plain,
( doDivides0(xp,xm)
| ~ sP4 ),
inference(instantiation,[status(thm)],[158]) ).
cnf(l444,plain,
~ doDivides0(xp,xm),
inference(instantiation,[status(thm)],[164]) ).
cnf(l722,plain,
( doDivides0(xp,xm)
| ~ sP4 ),
inference(instantiation,[status(thm)],[158]) ).
cnf(l723,plain,
~ doDivides0(xp,xm),
inference(instantiation,[status(thm)],[164]) ).
cnf(l684,plain,
( doDivides0(xp,xm)
| ~ sP4 ),
inference(instantiation,[status(thm)],[158]) ).
cnf(l837,plain,
~ doDivides0(xp,xm),
inference(instantiation,[status(thm)],[164]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l63,l83,l17,l32,l271,l289,l294,l200,l57,l6,l7,l407,l25,l214,l86,l570,l51,l150,l447,l87,l174,l444,l722,l723,l684,l837]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM518+3 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n028.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 : Mon Jul 21 12:37:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 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: 6
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.36 % launching worker at depth: 9
% 0.18/0.43 % launching worker at depth: 10
% 10.61/1.67 % launching worker at depth: 11
% 263.21/33.35 % SZS status Theorem for theBenchmark
% 263.21/33.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------