%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM450+6 : 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 : n021.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 12:28:11 PM UTC 2025
% Result : Theorem 48.21s 6.43s
% Output : CNFRefutation 48.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 171 ( 27 equ)
% Maximal formula atoms : 56 ( 6 avg)
% Number of connectives : 182 ( 38 ~; 38 |; 75 &)
% ( 11 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 21 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
? [W0] :
( aInteger0(W0)
& W0 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,W0))
& ! [W1] :
( ( aElementOf0(W1,szAzrzSzezqlpdtcmdtrp0(sz10,W0))
=> ( aInteger0(W1)
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W0,W2) = sdtpldt0(W1,smndt0(sz10)) )
& aDivisorOf0(W0,sdtpldt0(W1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(W1,sz10,W0) ) )
& ( ( aInteger0(W1)
& ( ? [W2] :
( aInteger0(W2)
& sdtasdt0(W0,W2) = sdtpldt0(W1,smndt0(sz10)) )
| aDivisorOf0(W0,sdtpldt0(W1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(W1,sz10,W0) ) )
=> aElementOf0(W1,szAzrzSzezqlpdtcmdtrp0(sz10,W0)) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [W1] :
( aElementOf0(W1,sbsmnsldt0(xS))
<=> ( aInteger0(W1)
& ? [W2] :
( aElementOf0(W2,xS)
& aElementOf0(W1,W2) ) ) ) )
=> ( ! [W1] :
( aElementOf0(W1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W1)
& ~ aElementOf0(W1,sbsmnsldt0(xS)) ) )
=> ( ! [W1] :
( aElementOf0(W1,szAzrzSzezqlpdtcmdtrp0(sz10,W0))
=> aElementOf0(W1,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,W0),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ? [W0] :
( aInteger0(W0)
& W0 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,W0))
& ! [W1] :
( ( aElementOf0(W1,szAzrzSzezqlpdtcmdtrp0(sz10,W0))
=> ( aInteger0(W1)
& ? [W2] :
( aInteger0(W2)
& sdtasdt0(W0,W2) = sdtpldt0(W1,smndt0(sz10)) )
& aDivisorOf0(W0,sdtpldt0(W1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(W1,sz10,W0) ) )
& ( ( aInteger0(W1)
& ( ? [W2] :
( aInteger0(W2)
& sdtasdt0(W0,W2) = sdtpldt0(W1,smndt0(sz10)) )
| aDivisorOf0(W0,sdtpldt0(W1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(W1,sz10,W0) ) )
=> aElementOf0(W1,szAzrzSzezqlpdtcmdtrp0(sz10,W0)) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [W1] :
( aElementOf0(W1,sbsmnsldt0(xS))
<=> ( aInteger0(W1)
& ? [W2] :
( aElementOf0(W2,xS)
& aElementOf0(W1,W2) ) ) ) )
=> ( ! [W1] :
( aElementOf0(W1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W1)
& ~ aElementOf0(W1,sbsmnsldt0(xS)) ) )
=> ( ! [W1] :
( aElementOf0(W1,szAzrzSzezqlpdtcmdtrp0(sz10,W0))
=> aElementOf0(W1,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,W0),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(209,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| X0 = sz00
| aElementOf0(X1,sbsmnsldt0(xS))
| aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
( ~ aInteger0(sK32(smndt0(sz10)))
| ~ aInteger0(sz10)
| sK32(smndt0(sz10)) = sz00
| aElementOf0(sz10,sbsmnsldt0(xS))
| aElementOf0(sz10,stldt0(sbsmnsldt0(xS))) ),
inference(instantiation,[status(thm)],[209]) ).
fof(m__2079,plain,
( aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( aInteger0(W0)
& ? [W1] :
( aElementOf0(W1,xS)
& aElementOf0(W0,W1) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( W0 = sz10
| W0 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).
cnf(142,plain,
( ~ aElementOf0(X0,sbsmnsldt0(xS))
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ),
inference(cnf,[status(esa)],[m__2079]) ).
cnf(l153,plain,
( ~ aElementOf0(sz10,sbsmnsldt0(xS))
| ~ aElementOf0(sz10,stldt0(sbsmnsldt0(xS))) ),
inference(instantiation,[status(thm)],[142]) ).
fof(m__2144,plain,
( aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( aInteger0(W0)
& ? [W1] :
( aElementOf0(W1,xS)
& aElementOf0(W0,W1) ) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
=> ? [W1] :
( aInteger0(W1)
& W1 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3] :
( aInteger0(W3)
& sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3] :
( aInteger0(W3)
& sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sbsmnsldt0(xS))) ) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ! [W0] :
( aElementOf0(W0,sbsmnsldt0(xS))
<=> ( aInteger0(W0)
& ? [W1] :
( aElementOf0(W1,xS)
& aElementOf0(W0,W1) ) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sbsmnsldt0(xS)) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sbsmnsldt0(xS)))
=> ? [W1] :
( aInteger0(W1)
& W1 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& ! [W2] :
( ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( aInteger0(W2)
& ? [W3] :
( aInteger0(W3)
& sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
& ( ( aInteger0(W2)
& ( ? [W3] :
( aInteger0(W3)
& sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0)) )
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| sdteqdtlpzmzozddtrp0(W2,W0,W1) ) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) ) )
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sbsmnsldt0(xS))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).
cnf(180,plain,
( ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
| aInteger0(sK32(X0)) ),
inference(cnf,[status(esa)],[m__2144]) ).
cnf(l7,plain,
( ~ aElementOf0(smndt0(sz10),stldt0(sbsmnsldt0(xS)))
| aInteger0(sK32(smndt0(sz10))) ),
inference(instantiation,[status(thm)],[180]) ).
fof(mIntOne,plain,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
cnf(1,plain,
aInteger0(sz10),
inference(cnf,[status(esa)],[mIntOne]) ).
cnf(l1,plain,
aInteger0(sz10),
inference(instantiation,[status(thm)],[1]) ).
cnf(181,plain,
( sK32(X0) != sz00
| ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ),
inference(cnf,[status(esa)],[m__2144]) ).
cnf(l2,plain,
( sK32(smndt0(sz10)) != sz00
| ~ aElementOf0(smndt0(sz10),stldt0(sbsmnsldt0(xS))) ),
inference(instantiation,[status(thm)],[181]) ).
cnf(145,plain,
( X0 != sz10
| aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ),
inference(cnf,[status(esa)],[m__2079]) ).
cnf(l157,plain,
( sz10 != sz10
| aElementOf0(sz10,stldt0(sbsmnsldt0(xS))) ),
inference(instantiation,[status(thm)],[145]) ).
cnf(l222,plain,
( ~ aElementOf0(sz10,stldt0(sbsmnsldt0(xS)))
| aInteger0(sK32(sz10)) ),
inference(instantiation,[status(thm)],[180]) ).
cnf(146,plain,
( X0 != smndt0(sz10)
| aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ),
inference(cnf,[status(esa)],[m__2079]) ).
cnf(l26,plain,
( smndt0(sz10) != smndt0(sz10)
| aElementOf0(smndt0(sz10),stldt0(sbsmnsldt0(xS))) ),
inference(instantiation,[status(thm)],[146]) ).
cnf(l3,plain,
( smndt0(sz10) != smndt0(sz10)
| aElementOf0(smndt0(sz10),stldt0(sbsmnsldt0(xS))) ),
inference(instantiation,[status(thm)],[146]) ).
cnf(212,plain,
( ~ aInteger0(X0)
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X0),stldt0(sbsmnsldt0(xS)))
| X0 = sz00 ),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l245,plain,
( ~ aInteger0(sK32(sz10))
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,sK32(sz10)),stldt0(sbsmnsldt0(xS)))
| sK32(sz10) = sz00 ),
inference(instantiation,[status(thm)],[212]) ).
cnf(192,plain,
( ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,sK32(X0)),stldt0(sbsmnsldt0(xS))) ),
inference(cnf,[status(esa)],[m__2144]) ).
cnf(l260,plain,
( ~ aElementOf0(sz10,stldt0(sbsmnsldt0(xS)))
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,sK32(sz10)),stldt0(sbsmnsldt0(xS))) ),
inference(instantiation,[status(thm)],[192]) ).
cnf(l280,plain,
( sK32(sz10) != sz00
| ~ aElementOf0(sz10,stldt0(sbsmnsldt0(xS))) ),
inference(instantiation,[status(thm)],[181]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l153,l7,l1,l2,l157,l222,l26,l3,l245,l260,l280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM450+6 : 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 : n021.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 12:09:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 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: 1
% 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
% 0.12/0.35 % launching worker at depth: 9
% 2.36/0.64 % launching worker at depth: 10
% 48.21/6.43 % SZS status Theorem for theBenchmark
% 48.21/6.43 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------