%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM520+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 : n020.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 12:28:23 PM UTC 2025
% Result : Theorem 75.41s 9.82s
% Output : CNFRefutation 75.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 28 unt; 0 def)
% Number of atoms : 132 ( 65 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 122 ( 45 ~; 44 |; 23 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 10 !; 6 ?)
% 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(112,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)],[112]) ).
fof(mDefQuot,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00
& doDivides0(W0,W1) )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
cnf(50,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X2 != sdtsldt0(X1,X0)
| ~ doDivides0(X0,X1)
| aNaturalNumber0(X2)
| X0 = sz00 ),
inference(cnf,[status(esa)],[mDefQuot]) ).
cnf(l1,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 != sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| aNaturalNumber0(sz00)
| xp = sz00 ),
inference(instantiation,[status(thm)],[50]) ).
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(19,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X0 = sz00
| X1 = X2 ),
inference(cnf,[status(esa)],[mMulCanc]) ).
cnf(l32,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sz10)
| sdtasdt0(xn,xk) != sdtasdt0(xn,sz10)
| xn = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[19]) ).
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(13,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf,[status(esa)],[m_MulZero]) ).
cnf(l9,plain,
( ~ aNaturalNumber0(xp)
| sdtasdt0(xp,sz00) = sz00 ),
inference(instantiation,[status(thm)],[13]) ).
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(l69,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(68,plain,
aNaturalNumber0(xn),
inference(cnf,[status(esa)],[m__1837]) ).
cnf(l118,plain,
aNaturalNumber0(xn),
inference(instantiation,[status(thm)],[68]) ).
fof(m__2306,plain,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
cnf(108,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf,[status(esa)],[m__2306]) ).
cnf(l313,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(instantiation,[status(thm)],[108]) ).
fof(m__2327,plain,
~ ( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
cnf(111,plain,
( xk = sz00
| xk = sz10 ),
inference(cnf,[status(esa)],[m__2327]) ).
cnf(l359,plain,
( xk = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[111]) ).
fof(m__1860,plain,
( xp != sz00
& xp != sz10
& ! [W0] :
( ( aNaturalNumber0(W0)
& ( ? [W1] :
( aNaturalNumber0(W1)
& xp = sdtasdt0(W0,W1) )
| doDivides0(W0,xp) ) )
=> ( W0 = sz10
| W0 = xp ) )
& isPrime0(xp)
& ? [W0] :
( aNaturalNumber0(W0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,W0) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
cnf(93,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf,[status(esa)],[m__1860]) ).
cnf(l294,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(instantiation,[status(thm)],[93]) ).
fof(m__2315,plain,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
cnf(110,plain,
xk != sz10,
inference(cnf,[status(esa)],[m__2315]) ).
cnf(l673,plain,
xk != sz10,
inference(instantiation,[status(thm)],[110]) ).
cnf(l183,plain,
( xk = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[111]) ).
cnf(l292,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(106,plain,
aNaturalNumber0(xk),
inference(cnf,[status(esa)],[m__2306]) ).
cnf(l126,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
cnf(109,plain,
xk != sz00,
inference(cnf,[status(esa)],[m__2315]) ).
cnf(l515,plain,
xk != sz00,
inference(instantiation,[status(thm)],[109]) ).
cnf(92,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK11),
inference(cnf,[status(esa)],[m__1860]) ).
cnf(l322,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK11),
inference(instantiation,[status(thm)],[92]) ).
cnf(87,plain,
xp != sz10,
inference(cnf,[status(esa)],[m__1860]) ).
cnf(l315,plain,
xp != sz10,
inference(instantiation,[status(thm)],[87]) ).
cnf(l137,plain,
( xk = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[111]) ).
cnf(l443,plain,
( xk = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[111]) ).
cnf(l810,plain,
xk != sz00,
inference(instantiation,[status(thm)],[109]) ).
cnf(l144,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
cnf(l120,plain,
xk != sz10,
inference(instantiation,[status(thm)],[110]) ).
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(l320,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK11)
| aNaturalNumber0(sdtasdt0(xp,sK11)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l419,plain,
aNaturalNumber0(xp),
inference(instantiation,[status(thm)],[70]) ).
cnf(l465,plain,
( xk = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[111]) ).
cnf(91,plain,
aNaturalNumber0(sK11),
inference(cnf,[status(esa)],[m__1860]) ).
cnf(l333,plain,
aNaturalNumber0(sK11),
inference(instantiation,[status(thm)],[91]) ).
cnf(l538,plain,
xk != sz00,
inference(instantiation,[status(thm)],[109]) ).
cnf(l811,plain,
xk != sz10,
inference(instantiation,[status(thm)],[110]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l32,l9,l69,l118,l313,l359,l294,l673,l183,l292,l126,l515,l322,l315,l137,l443,l810,l144,l120,l320,l419,l465,l333,l538,l811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM520+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Mon Jul 21 12:38:34 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.37 % launching worker at depth: 10
% 3.05/0.75 % launching worker at depth: 11
% 75.41/9.82 % SZS status Theorem for theBenchmark
% 75.41/9.82 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------