%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM441+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /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 08:17:00 AM UTC 2026
% Result : Theorem 0.14s 5.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 193 ( 15 equ)
% Maximal formula atoms : 64 ( 10 avg)
% Number of connectives : 199 ( 25 ~; 27 |; 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 : 50 ( 0 sgn 35 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mInterOpen,axiom,
! [W0,W1] :
( ( isOpen0(W1)
& isOpen0(W0)
& aSubsetOf0(W1,cS1395)
& aSubsetOf0(W0,cS1395) )
=> isOpen0(sdtslmnbsdt0(W0,W1)) ),
file('theBenchmark.p',mInterOpen) ).
fof(m__1826,axiom,
( isClosed0(xB)
& isOpen0(stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xB))
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xB)) )
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB))
& isClosed0(xA)
& isOpen0(stldt0(xA))
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> ? [W1] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(xA))
& ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(xA)) )
& ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1))
& W1 != sz00
& aInteger0(W1) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA))
& aSubsetOf0(xB,cS1395)
& ! [W0] :
( aElementOf0(W0,xB)
=> aElementOf0(W0,cS1395) )
& aSet0(xB)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& aSubsetOf0(xA,cS1395)
& ! [W0] :
( aElementOf0(W0,xA)
=> aElementOf0(W0,cS1395) )
& aSet0(xA)
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395) ),
file('theBenchmark.p',m__1826) ).
fof(m__1883,axiom,
( stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB))
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aElementOf0(W0,stldt0(xB))
& aElementOf0(W0,stldt0(xA))
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB))
& aSubsetOf0(stldt0(xB),cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
=> aElementOf0(W0,cS1395) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xB))
<=> ( ~ aElementOf0(W0,xB)
& aInteger0(W0) ) )
& aSet0(stldt0(xB))
& aSubsetOf0(stldt0(xA),cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
=> aElementOf0(W0,cS1395) )
& ! [W0] :
( aElementOf0(W0,cS1395)
<=> aInteger0(W0) )
& aSet0(cS1395)
& ! [W0] :
( aElementOf0(W0,stldt0(xA))
<=> ( ~ aElementOf0(W0,xA)
& aInteger0(W0) ) )
& aSet0(stldt0(xA)) ),
file('theBenchmark.p',m__1883) ).
fof(m__,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( isClosed0(sdtbsmnsldt0(xA,xB))
| ( ( ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [W1] :
( ( ( ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB)))
| ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) )
& W1 != sz00
& aInteger0(W1) ) ) ) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,sdtbsmnsldt0(xA,xB))
<=> ( ( aElementOf0(W0,xB)
| aElementOf0(W0,xA) )
& aInteger0(W0) ) )
& aSet0(sdtbsmnsldt0(xA,xB)) )
=> ( isClosed0(sdtbsmnsldt0(xA,xB))
| ( ( ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( ~ aElementOf0(W0,sdtbsmnsldt0(xA,xB))
& aInteger0(W0) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB))) )
=> ( isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
| ! [W0] :
( aElementOf0(W0,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [W1] :
( ( ( ! [W2] :
( ( ( ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
| aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
| ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) ) )
& aInteger0(W2) )
=> aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
& ( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> ( sdteqdtlpzmzozddtrp0(W2,W0,W1)
& aDivisorOf0(W1,sdtpldt0(W2,smndt0(W0)))
& ? [W3] :
( sdtasdt0(W1,W3) = sdtpldt0(W2,smndt0(W0))
& aInteger0(W3) )
& aInteger0(W2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(W0,W1)) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0,W1),stldt0(sdtbsmnsldt0(xA,xB)))
| ! [W2] :
( aElementOf0(W2,szAzrzSzezqlpdtcmdtrp0(W0,W1))
=> aElementOf0(W2,stldt0(sdtbsmnsldt0(xA,xB))) ) ) )
& W1 != sz00
& aInteger0(W1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_46,negated_conjecture,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_81,plain,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(clausify,[status(thm)],[m__1883]) ).
cnf(c_82,plain,
sdtslmnbsdt0(stldt0(xA),stldt0(xB)) = stldt0(sdtbsmnsldt0(xA,xB)),
inference(copy,[status(thm)],[c_81]) ).
cnf(c_92,plain,
aSubsetOf0(stldt0(xB),cS1395),
inference(clausify,[status(thm)],[m__1883]) ).
cnf(c_97,plain,
aSubsetOf0(stldt0(xA),cS1395),
inference(clausify,[status(thm)],[m__1883]) ).
cnf(c_102,plain,
isOpen0(stldt0(xB)),
inference(clausify,[status(thm)],[m__1826]) ).
cnf(c_117,plain,
isOpen0(stldt0(xA)),
inference(clausify,[status(thm)],[m__1826]) ).
cnf(c_137,plain,
( isOpen0(sdtslmnbsdt0(A,B))
| ~ isOpen0(B)
| ~ isOpen0(A)
| ~ aSubsetOf0(B,cS1395)
| ~ aSubsetOf0(A,cS1395) ),
inference(clausify,[status(thm)],[mInterOpen]) ).
cnf(c_386,plain,
( isOpen0(sdtslmnbsdt0(stldt0(xA),A))
| ~ isOpen0(A)
| ~ isOpen0(stldt0(xA))
| ~ aSubsetOf0(A,cS1395) ),
inference(resolve,[status(thm)],[c_137,c_97]) ).
cnf(c_387,plain,
( isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ isOpen0(stldt0(xB))
| ~ isOpen0(stldt0(xA)) ),
inference(resolve,[status(thm)],[c_386,c_92]) ).
cnf(c_388,plain,
( isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB)))
| ~ isOpen0(stldt0(xB)) ),
inference(resolve,[status(thm)],[c_387,c_117]) ).
cnf(c_389,plain,
isOpen0(sdtslmnbsdt0(stldt0(xA),stldt0(xB))),
inference(resolve,[status(thm)],[c_388,c_102]) ).
cnf(c_390,plain,
isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(paramod,[status(thm)],[c_82,c_389]) ).
cnf(c_385,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_46,c_390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM441+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n009.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 02:45:34 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3219444 was started by sandbox2 on n009,
% 0.10/5.38 % Sat Sep 26 02:45:34 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.40
% 0.14/5.40 % From the command line: assign(max_seconds, 300).
% 0.14/5.47
% 0.14/5.47 % SZS status Theorem for theBenchmark
% 0.14/5.47
% 0.14/5.47 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.14/5.47 % Length of proof is 13.
% 0.14/5.47 % Level of proof is 3.
% 0.14/5.47 % Maximum clause weight is 25.000.
% 0.14/5.47 % Given clauses 82.
% 0.14/5.47
% 0.14/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------