%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM519+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 : n024.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 155.27s 19.83s
% Output : CNFRefutation 155.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 23 unt; 0 def)
% Number of atoms : 153 ( 43 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 142 ( 52 ~; 57 |; 25 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 9 !; 10 ?)
% 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(141,plain,
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xp,X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aNaturalNumber0(sz00)
| xn != sdtasdt0(xp,sz00) ),
inference(instantiation,[status(thm)],[141]) ).
fof(mMulCanc,plain,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)
| sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )
=> W1 = W2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
cnf(20,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X0 = sz00
| X1 = X2 ),
inference(cnf,[status(esa)],[mMulCanc]) ).
cnf(l3,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xr,sK18))
| sdtasdt0(xn,xn) != sdtasdt0(sdtasdt0(xr,sK18),xn)
| xn = sz00
| xn = sdtasdt0(xr,sK18) ),
inference(instantiation,[status(thm)],[20]) ).
fof(m_MulZero,plain,
! [W0] :
( aNaturalNumber0(W0)
=> ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
cnf(14,plain,
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf,[status(esa)],[m_MulZero]) ).
cnf(l26,plain,
( ~ aNaturalNumber0(xp)
| sz00 = sdtasdt0(sz00,xp) ),
inference(instantiation,[status(thm)],[14]) ).
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(l28,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
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(l30,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| sdtasdt0(sz00,xp) = sdtasdt0(xp,sz00) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l100,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(68,plain,
aNaturalNumber0(xn),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l120,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
fof(mSortsC,plain,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
cnf(0,plain,
aNaturalNumber0(sz00),
inference(cnf,[status(esa)],[mSortsC]) ).
cnf(l74,plain,
aNaturalNumber0(sz00),
inference(instantiation,[status(thm)],[0]) ).
fof(m__2449,plain,
( ( ? [W0] :
( aNaturalNumber0(W0)
& xn = sdtasdt0(xr,W0) )
& doDivides0(xr,xn) )
| ( ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xr,W0) )
& doDivides0(xr,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2449) ).
cnf(132,plain,
( xn = sdtasdt0(xr,sK18)
| sP3 ),
inference(cnf,[status(esa)],[m__2449]) ).
cnf(l156,plain,
( xn = sdtasdt0(xr,sK18)
| sP3 ),
inference(instantiation,[status(thm)],[132]) ).
cnf(l139,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(134,plain,
( doDivides0(xr,xm)
| ~ sP3 ),
inference(cnf,[status(esa)],[m__2449]) ).
cnf(l484,plain,
( doDivides0(xr,xm)
| ~ sP3 ),
inference(instantiation,[status(thm)],[134]) ).
cnf(l160,plain,
( xn = sdtasdt0(xr,sK18)
| sP3 ),
inference(instantiation,[status(thm)],[132]) ).
cnf(l798,plain,
( doDivides0(xr,xm)
| ~ sP3 ),
inference(instantiation,[status(thm)],[134]) ).
cnf(l190,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xr,sK18))
| sdtasdt0(xn,xn) != sdtasdt0(sdtasdt0(xr,sK18),xn)
| xn = sz00
| xn = sdtasdt0(xr,sK18) ),
inference(instantiation,[status(thm)],[20]) ).
fof(m__2698,plain,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& xm = sdtasdt0(xr,W0) )
| doDivides0(xr,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2698) ).
cnf(140,plain,
~ doDivides0(xr,xm),
inference(cnf,[status(esa)],[m__2698]) ).
cnf(l609,plain,
~ doDivides0(xr,xm),
inference(instantiation,[status(thm)],[140]) ).
fof(m__2487,plain,
~ ( ? [W0] :
( aNaturalNumber0(W0)
& xn = sdtasdt0(xr,W0) )
| doDivides0(xr,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
cnf(137,plain,
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xr,X0) ),
inference(cnf,[status(esa)],[m__2487]) ).
cnf(l199,plain,
( ~ aNaturalNumber0(sK18)
| xn != sdtasdt0(xr,sK18) ),
inference(instantiation,[status(thm)],[137]) ).
cnf(l115,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l188,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l1040,plain,
~ doDivides0(xr,xm),
inference(instantiation,[status(thm)],[140]) ).
cnf(131,plain,
( aNaturalNumber0(sK18)
| sP3 ),
inference(cnf,[status(esa)],[m__2449]) ).
cnf(l311,plain,
( aNaturalNumber0(sK18)
| sP3 ),
inference(instantiation,[status(thm)],[131]) ).
cnf(l288,plain,
( ~ aNaturalNumber0(sK18)
| xn != sdtasdt0(xr,sK18) ),
inference(instantiation,[status(thm)],[137]) ).
cnf(l1067,plain,
( doDivides0(xr,xm)
| ~ sP3 ),
inference(instantiation,[status(thm)],[134]) ).
cnf(l226,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l282,plain,
( xn = sdtasdt0(xr,sK18)
| sP3 ),
inference(instantiation,[status(thm)],[132]) ).
cnf(l1076,plain,
~ doDivides0(xr,xm),
inference(instantiation,[status(thm)],[140]) ).
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(l222,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sK18)
| aNaturalNumber0(sdtasdt0(xr,sK18)) ),
inference(instantiation,[status(thm)],[4]) ).
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(l271,plain,
aNaturalNumber0(xr),
inference(instantiation,[status(thm)],[113]) ).
cnf(l246,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
cnf(l223,plain,
( aNaturalNumber0(sK18)
| sP3 ),
inference(instantiation,[status(thm)],[131]) ).
cnf(l315,plain,
( aNaturalNumber0(sK18)
| sP3 ),
inference(instantiation,[status(thm)],[131]) ).
cnf(l1136,plain,
( doDivides0(xr,xm)
| ~ sP3 ),
inference(instantiation,[status(thm)],[134]) ).
cnf(l307,plain,
( doDivides0(xr,xm)
| ~ sP3 ),
inference(instantiation,[status(thm)],[134]) ).
cnf(l1137,plain,
~ doDivides0(xr,xm),
inference(instantiation,[status(thm)],[140]) ).
cnf(l1097,plain,
~ doDivides0(xr,xm),
inference(instantiation,[status(thm)],[140]) ).
cnf(l663,plain,
( doDivides0(xr,xm)
| ~ sP3 ),
inference(instantiation,[status(thm)],[134]) ).
cnf(l1135,plain,
~ doDivides0(xr,xm),
inference(instantiation,[status(thm)],[140]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l3,l26,l28,l30,l100,l120,l74,l156,l139,l484,l160,l798,l190,l609,l199,l115,l188,l1040,l311,l288,l1067,l226,l282,l1076,l222,l271,l246,l223,l315,l1136,l307,l1137,l1097,l663,l1135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM519+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n024.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 12:38:34 EDT 2025
% 0.12/0.33 % 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: 2
% 0.12/0.34 % launching worker at depth: 4
% 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
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.36 % launching worker at depth: 10
% 3.82/0.89 % launching worker at depth: 11
% 155.27/19.83 % SZS status Theorem for theBenchmark
% 155.27/19.83 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------