%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM441+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:12:44 AM UTC 2026
% Result : Theorem 21.60s 5.18s
% Output : CNFRefutation 21.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 196 ( 14 equ)
% Maximal formula atoms : 64 ( 10 avg)
% Number of connectives : 211 ( 33 ~; 31 |; 103 &)
% ( 17 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 8 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(mInterOpen,axiom,
! [X0,X1] :
( ( isOpen0(X1)
& isOpen0(X0)
& aSubsetOf0(X1,cS1395)
& aSubsetOf0(X0,cS1395) )
=> isOpen0(sdtslmnbsdt0(X0,X1)) ) ).
fof(m__1826,hypothesis,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xB))
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(xB)) )
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& X1 != sz00
& aInteger0(X1) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
=> ? [X1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(xA))
& ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(xA)) )
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1))
& X1 != sz00
& aInteger0(X1) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [X0] :
( aElementOf0(X0,xB)
=> aElementOf0(X0,cS1395) )
& aSet0(xB)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [X0] :
( aElementOf0(X0,xA)
=> aElementOf0(X0,cS1395) )
& aSet0(xA)
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395) ) ).
fof(m__1883,hypothesis,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(X0,stldt0(xB))
& aElementOf0(X0,stldt0(xA))
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
=> aElementOf0(X0,cS1395) )
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xB))
<=> ( ~ aElementOf0(X0,xB)
& aInteger0(X0) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
=> aElementOf0(X0,cS1395) )
& ! [X0] :
( aElementOf0(X0,cS1395)
<=> aInteger0(X0) )
& aSet0(cS1395)
& ! [X0] :
( aElementOf0(X0,stldt0(xA))
<=> ( ~ aElementOf0(X0,xA)
& aInteger0(X0) ) )
& aSet0(stldt0(xA)) ) ).
fof(m__,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( isClosed0(sdtbsmnsldt0(xA,xB))
| ( ( ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) )
& X1 != sz00
& aInteger0(X1) ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(X0,xB)
| aElementOf0(X0,xA) )
& aInteger0(X0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( isClosed0(sdtbsmnsldt0(xA,xB))
| ( ( ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(X0,sdtbsmnsldt0(xA,xB))
& aInteger0(X0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X0] :
( aElementOf0(X0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,X0,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(X0)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(X0))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(X0,X1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X0,X1),stldt0(sdtbsmnsldt0(xA,xB)))
| ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X0,X1))
=> aElementOf0(X2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) )
& X1 != sz00
& aInteger0(X1) ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c127,plain,
( ~ aSubsetOf0(X0,cS1395)
| ~ isOpen0(X0)
| ~ aSubsetOf0(X1,cS1395)
| ~ isOpen0(X1)
| isOpen0(sdtslmnbsdt0(X0,X1)) ),
inference(clausification,[status(esa)],[mInterOpen]) ).
cnf(c145,plain,
isOpen0(stldt0(xA)),
inference(clausification,[status(esa)],[m__1826]) ).
cnf(c152,plain,
isOpen0(stldt0(xB)),
inference(clausification,[status(esa)],[m__1826]) ).
cnf(c190,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(clausification,[status(esa)],[m__1883]) ).
cnf(c199,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(clausification,[status(esa)],[m__1883]) ).
cnf(c219,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(clausification,[status(esa)],[m__1883]) ).
cnf(c231,plain,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395)
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ),
inference(superposition,[status(thm)],[c219,c127]) ).
cnf(d1,plain,
( ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(resolution,[status(thm)],[c231,d0]) ).
cnf(d2,plain,
( ~ isOpen0(stldt0(xB))
| ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(resolution,[status(thm)],[c145,d1]) ).
cnf(d3,plain,
( ~ aSubsetOf0(stldt0(xB),cS1395)
| ~ aSubsetOf0(stldt0(xA),cS1395) ),
inference(resolution,[status(thm)],[c152,d2]) ).
cnf(d4,plain,
~ aSubsetOf0(stldt0(xB),cS1395),
inference(resolution,[status(thm)],[c190,d3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c199,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM441+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 02:45:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.60/5.18 % SZS status Theorem for theBenchmark.p
% 21.60/5.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------