%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM604+1 : 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 : n017.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 08:17:32 AM UTC 2026
% Result : Theorem 11.30s 2.09s
% Output : CNFRefutation 11.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 20 unt; 0 def)
% Number of atoms : 89 ( 21 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 72 ( 28 ~; 25 |; 10 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mCountNFin_01,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> W0 != slcrc0 ),
file('theBenchmark.p',mCountNFin_01) ).
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('theBenchmark.p',mNATSet) ).
fof(mDefMin,axiom,
! [W0] :
( ( W0 != slcrc0
& aSubsetOf0(W0,szNzAzT0) )
=> ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,W0) ) ) ),
file('theBenchmark.p',mDefMin) ).
fof(m__3435,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('theBenchmark.p',m__3435) ).
fof(m__3671,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) ),
file('theBenchmark.p',m__3671) ).
fof(m__4660,axiom,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) )
& szDzozmdt0(xe) = szNzAzT0
& aFunction0(xe) ),
file('theBenchmark.p',m__4660) ).
fof(m__5034,axiom,
( sdtlpdtrp0(xe,xi) = xx
& aElementOf0(xi,szNzAzT0) ),
file('theBenchmark.p',m__5034) ).
fof(m__,conjecture,
aElementOf0(xx,xS),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ aElementOf0(xx,xS),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_99,plain,
( slcrc0 != A
| ~ isCountable0(A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mCountNFin_01]) ).
cnf(c_100,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_101,plain,
( aElementOf0(C,A)
| ~ aElementOf0(C,B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_132,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
cnf(c_162,plain,
( aElementOf0(B,A)
| szmzizndt0(A) != B
| slcrc0 = A
| ~ aSubsetOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mDefMin]) ).
cnf(c_235,plain,
aSubsetOf0(xS,szNzAzT0),
inference(clausify,[status(thm)],[m__3435]) ).
cnf(c_254,plain,
( aSubsetOf0(sdtlpdtrp0(xN,A),szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__3671]) ).
cnf(c_255,plain,
( isCountable0(sdtlpdtrp0(xN,A))
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__3671]) ).
cnf(c_277,plain,
( sdtlpdtrp0(xe,A) = szmzizndt0(sdtlpdtrp0(xN,A))
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__4660]) ).
cnf(c_292,plain,
aElementOf0(xi,szNzAzT0),
inference(clausify,[status(thm)],[m__5034]) ).
cnf(c_293,plain,
sdtlpdtrp0(xe,xi) = xx,
inference(clausify,[status(thm)],[m__5034]) ).
fof(m__5045,axiom,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
file('theBenchmark.p',m__5045) ).
cnf(c_294,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),xS),
inference(clausify,[status(thm)],[m__5045]) ).
cnf(c_295,negated_conjecture,
~ aElementOf0(xx,xS),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_437,plain,
( aElementOf0(szmzizndt0(A),A)
| slcrc0 = A
| ~ aSubsetOf0(A,szNzAzT0) ),
inference(xxres,[status(thm)],[c_162]) ).
cnf(c_11450,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_235,c_100]) ).
cnf(c_750,plain,
aSet0(xS),
inference(resolve,[status(thm)],[c_132,c_11450]) ).
cnf(c_11451,plain,
sdtlpdtrp0(xe,xi) = szmzizndt0(sdtlpdtrp0(xN,xi)),
inference(resolve,[status(thm)],[c_292,c_277]) ).
cnf(c_11452,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xi)),
inference(paramod,[status(thm)],[c_293,c_11451]) ).
cnf(c_1418,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = xx,
inference(copy,[status(thm)],[c_11452]) ).
cnf(c_1434,plain,
isCountable0(sdtlpdtrp0(xN,xi)),
inference(resolve,[status(thm)],[c_292,c_255]) ).
cnf(c_1435,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0),
inference(resolve,[status(thm)],[c_292,c_254]) ).
cnf(c_11453,plain,
( aSet0(sdtlpdtrp0(xN,xi))
| ~ aSet0(xS) ),
inference(resolve,[status(thm)],[c_294,c_100]) ).
cnf(c_1544,plain,
aSet0(sdtlpdtrp0(xN,xi)),
inference(resolve,[status(thm)],[c_750,c_11453]) ).
cnf(c_1838,plain,
( aElementOf0(B,xS)
| ~ aElementOf0(B,A)
| ~ aSubsetOf0(A,xS) ),
inference(resolve,[status(thm)],[c_750,c_101]) ).
cnf(c_11454,plain,
( slcrc0 != sdtlpdtrp0(xN,xi)
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(resolve,[status(thm)],[c_1434,c_99]) ).
cnf(c_11455,plain,
( sdtlpdtrp0(xN,xi) != slcrc0
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(copy,[status(thm)],[c_11454]) ).
cnf(c_6356,plain,
sdtlpdtrp0(xN,xi) != slcrc0,
inference(resolve,[status(thm)],[c_1544,c_11455]) ).
cnf(c_11456,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| slcrc0 = sdtlpdtrp0(xN,xi) ),
inference(resolve,[status(thm)],[c_1435,c_437]) ).
cnf(c_11457,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xi))
| slcrc0 = sdtlpdtrp0(xN,xi) ),
inference(paramod,[status(thm)],[c_1418,c_11456]) ).
cnf(c_11458,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xi))
| sdtlpdtrp0(xN,xi) = slcrc0 ),
inference(copy,[status(thm)],[c_11457]) ).
cnf(c_9658,plain,
aElementOf0(xx,sdtlpdtrp0(xN,xi)),
inference(resolve,[status(thm)],[c_6356,c_11458]) ).
cnf(c_11459,plain,
( aElementOf0(xx,xS)
| ~ aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(resolve,[status(thm)],[c_9658,c_1838]) ).
cnf(c_11460,plain,
aElementOf0(xx,xS),
inference(resolve,[status(thm)],[c_294,c_11459]) ).
cnf(c_11449,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_295,c_11460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM604+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 03:20:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3872329 was started by sandbox2 on n017,
% 0.09/0.36 % Sat Sep 26 03:20:32 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 11.30/2.09
% 11.30/2.09 % given #500 (F,wt=15): 6020 sdtmndt0(xS,sz00) != szNzAzT0. [resolve(2149,a,750,a)].
% 11.30/2.09
% 11.30/2.09 % SZS status Theorem for theBenchmark
% 11.30/2.09
% 11.30/2.09 % Proof 1 at 1.20 (+ 0.34) seconds.
% 11.30/2.09 % Length of proof is 32.
% 11.30/2.09 % Level of proof is 6.
% 11.30/2.09 % Maximum clause weight is 26.000.
% 11.30/2.09 % Given clauses 814.
% 11.30/2.09
% 11.30/2.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------