%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM501+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Fri Jul 25 12:28:20 PM UTC 2025
% Result : Theorem 115.75s 14.93s
% Output : CNFRefutation 115.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 18 unt; 0 def)
% Number of atoms : 80 ( 23 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 68 ( 23 ~; 22 |; 19 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
( ? [W0] :
( aNaturalNumber0(W0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,W0) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,W0) )
| doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(122,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) != sdtasdt0(xr,X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aNaturalNumber0(sdtasdt0(sK14,xp))
| sdtasdt0(xn,xm) != sdtasdt0(xr,sdtasdt0(sK14,xp)) ),
inference(instantiation,[status(thm)],[122]) ).
fof(mMulComm,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
cnf(9,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf,[status(esa)],[mMulComm]) ).
cnf(l104,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| sdtasdt0(xp,xk) = sdtasdt0(xk,xp) ),
inference(instantiation,[status(thm)],[9]) ).
fof(m__2306,plain,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
cnf(107,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf,[status(esa)],[m__2306]) ).
cnf(l149,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(instantiation,[status(thm)],[107]) ).
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/sandbox2/benchmark/theBenchmark.p',m__2342) ).
cnf(115,plain,
xk = sdtasdt0(xr,sK14),
inference(cnf,[status(esa)],[m__2342]) ).
cnf(l152,plain,
xk = sdtasdt0(xr,sK14),
inference(instantiation,[status(thm)],[115]) ).
cnf(106,plain,
aNaturalNumber0(xk),
inference(cnf,[status(esa)],[m__2306]) ).
cnf(l118,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
fof(m__1837,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
cnf(70,plain,
aNaturalNumber0(xp),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l108,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
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/sandbox2/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(l14,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sK14)
| ~ aNaturalNumber0(xp)
| sdtasdt0(sdtasdt0(xr,sK14),xp) = sdtasdt0(xr,sdtasdt0(sK14,xp)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(114,plain,
aNaturalNumber0(sK14),
inference(cnf,[status(esa)],[m__2342]) ).
cnf(l212,plain,
aNaturalNumber0(sK14),
inference(instantiation,[status(thm)],[114]) ).
cnf(l261,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(113,plain,
aNaturalNumber0(xr),
inference(cnf,[status(esa)],[m__2342]) ).
cnf(l266,plain,
aNaturalNumber0(xr),
inference(instantiation,[status(thm)],[113]) ).
cnf(l21,plain,
( ~ aNaturalNumber0(sK14)
| ~ aNaturalNumber0(xp)
| sdtasdt0(sK14,xp) = sdtasdt0(xp,sK14) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l75,plain,
aNaturalNumber0(sK14),
inference(instantiation,[status(thm)],[114]) ).
cnf(l41,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
fof(mSortsB_02,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
cnf(4,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf,[status(esa)],[mSortsB_02]) ).
cnf(l236,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK14)
| aNaturalNumber0(sdtasdt0(xp,sK14)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l251,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l239,plain,
aNaturalNumber0(sK14),
inference(instantiation,[status(thm)],[114]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l104,l149,l152,l118,l108,l14,l212,l261,l266,l21,l75,l41,l236,l251,l239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : NUM501+3 : TPTP v9.0.0. Released v4.0.0.
% 0.05/0.10 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.30 % Computer : n018.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Jul 21 12:30:19 EDT 2025
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % launching worker at depth: 5
% 0.10/0.31 % launching worker at depth: 4
% 0.10/0.31 % launching worker at depth: 6
% 0.10/0.31 % launching worker at depth: 2
% 0.10/0.31 % launching worker at depth: 3
% 0.10/0.31 % launching worker at depth: 1
% 0.10/0.31 % launching worker at depth: 7
% 0.10/0.31 % launching worker at depth: 8
% 0.14/0.32 % launching worker at depth: 9
% 0.14/0.33 % launching worker at depth: 10
% 3.51/0.77 % launching worker at depth: 11
% 115.75/14.93 % SZS status Theorem for theBenchmark
% 115.75/14.93 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------