%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM441+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 : n025.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 12:28:10 PM UTC 2025
% Result : Theorem 91.42s 11.83s
% Output : CNFRefutation 91.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 192 ( 15 equ)
% Maximal formula atoms : 64 ( 9 avg)
% Number of connectives : 196 ( 24 ~; 25 |; 103 &)
% ( 17 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 7 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 : 49 ( 0 sgn 35 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,plain,
( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [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(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m___negated,plain,
~ ( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [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(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(215,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(cnf,[status(esa)],[m___negated]) ).
cnf(l0,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(instantiation,[status(thm)],[215]) ).
fof(m__1883,plain,
( aSet0(stldt0(xA))
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(W0)
& ( aElementOf0(W0,xA)
| aElementOf0(W0,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB)) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(W0)
& aElementOf0(W0,stldt0(xA))
& aElementOf0(W0,stldt0(xB)) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
cnf(192,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(cnf,[status(esa)],[m__1883]) ).
cnf(l18,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(instantiation,[status(thm)],[192]) ).
fof(mInterOpen,plain,
! [W0,W1] :
( ( aSubsetOf0(W0,cS1395)
& aSubsetOf0(W1,cS1395)
& isOpen0(W0)
& isOpen0(W1) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mInterOpen) ).
cnf(104,plain,
( ~ aSubsetOf0(X0,cS1395)
| ~ aSubsetOf0(X1,cS1395)
| ~ isOpen0(X0)
| ~ isOpen0(X1)
| isOpen0(sdtslmnbsdt0(X0,X1)) ),
inference(cnf,[status(esa)],[mInterOpen]) ).
cnf(l2,plain,
( ~ aSubsetOf0(stldt0(xA),cS1395)
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ isOpen0(stldt0(xA))
| ~ isOpen0(stldt0(xB))
| isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB))) ),
inference(instantiation,[status(thm)],[104]) ).
cnf(163,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(cnf,[status(esa)],[m__1883]) ).
cnf(l6,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(instantiation,[status(thm)],[163]) ).
fof(m__1826,plain,
( aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xA)
& ! [W0] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(xB)
& ! [W0] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xA) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> ? [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(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( aInteger0(W0)
& ~ aElementOf0(W0,xB) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> ? [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(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB)) ) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1826) ).
cnf(134,plain,
isOpen0(stldt0(xA)),
inference(cnf,[status(esa)],[m__1826]) ).
cnf(l4,plain,
isOpen0(stldt0(xA)),
inference(instantiation,[status(thm)],[134]) ).
cnf(172,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(cnf,[status(esa)],[m__1883]) ).
cnf(l9,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(instantiation,[status(thm)],[172]) ).
cnf(153,plain,
isOpen0(stldt0(xB)),
inference(cnf,[status(esa)],[m__1826]) ).
cnf(l24,plain,
isOpen0(stldt0(xB)),
inference(instantiation,[status(thm)],[153]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l18,l2,l6,l4,l9,l24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM441+6 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 21 12:05:19 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.34 % launching worker at depth: 5
% 0.20/0.34 % launching worker at depth: 6
% 0.20/0.34 % launching worker at depth: 2
% 0.20/0.34 % launching worker at depth: 4
% 0.20/0.34 % launching worker at depth: 3
% 0.20/0.34 % launching worker at depth: 1
% 0.20/0.34 % launching worker at depth: 7
% 0.20/0.34 % launching worker at depth: 8
% 0.20/0.36 % launching worker at depth: 9
% 4.18/0.86 % launching worker at depth: 10
% 91.42/11.83 % SZS status Theorem for theBenchmark
% 91.42/11.83 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------