%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM500+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 : n022.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 12:28:19 PM UTC 2025
% Result : Theorem 5.26s 1.03s
% Output : CNFRefutation 5.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 26 unt; 0 def)
% Number of atoms : 134 ( 59 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 141 ( 57 ~; 54 |; 25 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 5 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
? [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/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ? [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(113,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| xk != sdtasdt0(X0,X1)
| sP3(X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aNaturalNumber0(sK6(xk))
| ~ aNaturalNumber0(sK3(sK6(xk),xk))
| xk != sdtasdt0(sK6(xk),sK3(sK6(xk),xk))
| sP3(sK6(xk)) ),
inference(instantiation,[status(thm)],[113]) ).
fof(mPrimDiv,plain,
! [W0] :
( ( aNaturalNumber0(W0)
& W0 != sz00
& W0 != sz10 )
=> ? [W1] :
( aNaturalNumber0(W1)
& doDivides0(W1,W0)
& isPrime0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
cnf(65,plain,
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(sK6(X0))
| X0 = sz00
| X0 = sz10 ),
inference(cnf,[status(esa)],[mPrimDiv]) ).
cnf(l3,plain,
( ~ aNaturalNumber0(xk)
| aNaturalNumber0(sK6(xk))
| xk = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[65]) ).
cnf(115,plain,
( ~ isPrime0(X0)
| ~ sP3(X0) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l2,plain,
( ~ isPrime0(sK6(xk))
| ~ sP3(sK6(xk)) ),
inference(instantiation,[status(thm)],[115]) ).
cnf(67,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| isPrime0(sK6(X0)) ),
inference(cnf,[status(esa)],[mPrimDiv]) ).
cnf(l15,plain,
( ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10
| isPrime0(sK6(xk)) ),
inference(instantiation,[status(thm)],[67]) ).
fof(m__2315,plain,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
cnf(110,plain,
xk != sz10,
inference(cnf,[status(esa)],[m__2315]) ).
cnf(l105,plain,
xk != sz10,
inference(instantiation,[status(thm)],[110]) ).
fof(m__2327,plain,
( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
cnf(111,plain,
xk != sz00,
inference(cnf,[status(esa)],[m__2327]) ).
cnf(l22,plain,
xk != sz00,
inference(instantiation,[status(thm)],[111]) ).
cnf(109,plain,
xk != sz00,
inference(cnf,[status(esa)],[m__2315]) ).
cnf(l96,plain,
xk != sz00,
inference(instantiation,[status(thm)],[109]) ).
cnf(112,plain,
xk != sz10,
inference(cnf,[status(esa)],[m__2327]) ).
cnf(l60,plain,
xk != sz10,
inference(instantiation,[status(thm)],[112]) ).
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(106,plain,
aNaturalNumber0(xk),
inference(cnf,[status(esa)],[m__2306]) ).
cnf(l117,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
cnf(l95,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
fof(mDefDiv,plain,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& W1 = sdtasdt0(W0,W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
cnf(48,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X0,X1)
| X1 = sdtasdt0(X0,sK3(X0,X1)) ),
inference(cnf,[status(esa)],[mDefDiv]) ).
cnf(l5,plain,
( ~ aNaturalNumber0(sK6(xk))
| ~ aNaturalNumber0(xk)
| ~ doDivides0(sK6(xk),xk)
| xk = sdtasdt0(sK6(xk),sK3(sK6(xk),xk)) ),
inference(instantiation,[status(thm)],[48]) ).
cnf(l8,plain,
( ~ aNaturalNumber0(xk)
| aNaturalNumber0(sK6(xk))
| xk = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[65]) ).
cnf(47,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X0,X1)
| aNaturalNumber0(sK3(X0,X1)) ),
inference(cnf,[status(esa)],[mDefDiv]) ).
cnf(l1,plain,
( ~ aNaturalNumber0(sK6(xk))
| ~ aNaturalNumber0(xk)
| ~ doDivides0(sK6(xk),xk)
| aNaturalNumber0(sK3(sK6(xk),xk)) ),
inference(instantiation,[status(thm)],[47]) ).
cnf(66,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| doDivides0(sK6(X0),X0) ),
inference(cnf,[status(esa)],[mPrimDiv]) ).
cnf(l29,plain,
( ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10
| doDivides0(sK6(xk),xk) ),
inference(instantiation,[status(thm)],[66]) ).
cnf(l48,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
cnf(l10,plain,
xk != sz10,
inference(instantiation,[status(thm)],[112]) ).
cnf(l59,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
cnf(l35,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
cnf(l9,plain,
xk != sz00,
inference(instantiation,[status(thm)],[111]) ).
cnf(l23,plain,
( ~ aNaturalNumber0(xk)
| xk = sz00
| xk = sz10
| doDivides0(sK6(xk),xk) ),
inference(instantiation,[status(thm)],[66]) ).
cnf(l52,plain,
xk != sz10,
inference(instantiation,[status(thm)],[112]) ).
cnf(l12,plain,
( ~ aNaturalNumber0(xk)
| aNaturalNumber0(sK6(xk))
| xk = sz00
| xk = sz10 ),
inference(instantiation,[status(thm)],[65]) ).
cnf(l19,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
cnf(l40,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
cnf(l38,plain,
aNaturalNumber0(xk),
inference(instantiation,[status(thm)],[106]) ).
cnf(l34,plain,
xk != sz10,
inference(instantiation,[status(thm)],[110]) ).
cnf(l39,plain,
xk != sz00,
inference(instantiation,[status(thm)],[111]) ).
cnf(l51,plain,
xk != sz00,
inference(instantiation,[status(thm)],[111]) ).
cnf(l80,plain,
xk != sz00,
inference(instantiation,[status(thm)],[109]) ).
cnf(l67,plain,
xk != sz10,
inference(instantiation,[status(thm)],[112]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l3,l2,l15,l105,l22,l96,l60,l117,l95,l5,l8,l1,l29,l48,l10,l59,l35,l9,l23,l52,l12,l19,l40,l38,l34,l39,l51,l80,l67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM500+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n022.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 12:30:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 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: 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
% 0.18/0.46 % launching worker at depth: 10
% 5.26/1.03 % SZS status Theorem for theBenchmark
% 5.26/1.03 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------