%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM574+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 : n010.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 08:17:27 AM UTC 2026
% Result : Theorem 77.58s 11.33s
% Output : CNFRefutation 77.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 14 unt; 0 def)
% Number of atoms : 122 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 36 ~; 46 |; 12 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefSub) ).
fof(mSubRefl,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('theBenchmark.p',mSubRefl) ).
fof(mNATSet,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('theBenchmark.p',mNATSet) ).
fof(mNatExtra,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ? [W1] :
( W0 = szszuzczcdt0(W1)
& aElementOf0(W1,szNzAzT0) )
| W0 = sz00 ) ),
file('theBenchmark.p',mNatExtra) ).
fof(mZeroLess,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('theBenchmark.p',mZeroLess) ).
fof(mLessASymm,axiom,
! [W0,W1] :
( ( aElementOf0(W1,szNzAzT0)
& aElementOf0(W0,szNzAzT0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mLessASymm) ).
fof(m__3671,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( isCountable0(sdtlpdtrp0(xN,W0))
& aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) ),
file('theBenchmark.p',m__3671) ).
fof(m__3786,axiom,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('theBenchmark.p',m__3786) ).
fof(m__3786_02,axiom,
( ( ? [W0] :
( szszuzczcdt0(W0) = xi
& aElementOf0(W0,szNzAzT0) )
& sdtlseqdt0(xj,xi) )
=> ( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
file('theBenchmark.p',m__3786_02) ).
fof(m__,conjecture,
( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdtlseqdt0(xj,xi)
=> aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_88,plain,
( aSet0(B)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSub]) ).
cnf(c_93,plain,
( aSubsetOf0(A,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mSubRefl]) ).
cnf(c_120,plain,
aSet0(szNzAzT0),
inference(clausify,[status(thm)],[mNATSet]) ).
fof(nnf_25,plain,
! [W0] :
( ? [W1] :
( szszuzczcdt0(W1) = W0
& aElementOf0(W1,szNzAzT0) )
| sz00 = W0
| ~ aElementOf0(W0,szNzAzT0) ),
inference(fof_nnf,[status(thm)],[mNatExtra]) ).
fof(sk_mNatExtra_sk,plain,
! [W0] :
( ( szszuzczcdt0(sK0(W0)) = W0
& aElementOf0(sK0(W0),szNzAzT0) )
| sz00 = W0
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W1,sK0(W0))],[nnf_25]) ).
fof(sk_mNatExtra,plain,
( ! [VAR_0] :
( szszuzczcdt0(sK0(VAR_0)) = VAR_0
| sz00 = VAR_0
| ~ aElementOf0(VAR_0,szNzAzT0) )
& ! [VAR_0] :
( aElementOf0(sK0(VAR_0),szNzAzT0)
| sz00 = VAR_0
| ~ aElementOf0(VAR_0,szNzAzT0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mNatExtra_sk]) ).
cnf(c_126,plain,
( aElementOf0(sK0(A),szNzAzT0)
| sz00 = A
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_mNatExtra]) ).
cnf(c_127,plain,
( szszuzczcdt0(sK0(A)) = A
| sz00 = A
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_mNatExtra]) ).
cnf(c_129,plain,
( sdtlseqdt0(sz00,A)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mZeroLess]) ).
cnf(c_135,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElementOf0(B,szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[mLessASymm]) ).
cnf(c_242,plain,
( aSubsetOf0(sdtlpdtrp0(xN,A),szNzAzT0)
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m__3671]) ).
cnf(c_244,plain,
aElementOf0(xj,szNzAzT0),
inference(clausify,[status(thm)],[m__3786]) ).
cnf(c_245,plain,
aElementOf0(xi,szNzAzT0),
inference(clausify,[status(thm)],[m__3786]) ).
cnf(c_247,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| szszuzczcdt0(A) != xi
| ~ aElementOf0(A,szNzAzT0)
| ~ sdtlseqdt0(xj,xi) ),
inference(clausify,[status(thm)],[m__3786_02]) ).
cnf(c_248,negated_conjecture,
sdtlseqdt0(xj,xi),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_249,negated_conjecture,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_13415,negated_conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| szszuzczcdt0(A) != xi
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_248,c_247]) ).
cnf(c_279,negated_conjecture,
( szszuzczcdt0(A) != xi
| ~ aElementOf0(A,szNzAzT0) ),
inference(resolve,[status(thm)],[c_249,c_13415]) ).
cnf(c_575,plain,
sdtlseqdt0(sz00,xj),
inference(resolve,[status(thm)],[c_244,c_129]) ).
cnf(c_598,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0),
inference(resolve,[status(thm)],[c_245,c_242]) ).
cnf(c_13416,plain,
( szszuzczcdt0(sK0(xi)) = xi
| sz00 = xi ),
inference(resolve,[status(thm)],[c_245,c_127]) ).
cnf(c_628,plain,
( szszuzczcdt0(sK0(xi)) = xi
| xi = sz00 ),
inference(copy,[status(thm)],[c_13416]) ).
cnf(c_13417,plain,
( aElementOf0(sK0(xi),szNzAzT0)
| sz00 = xi ),
inference(resolve,[status(thm)],[c_245,c_126]) ).
cnf(c_629,plain,
( aElementOf0(sK0(xi),szNzAzT0)
| xi = sz00 ),
inference(copy,[status(thm)],[c_13417]) ).
cnf(c_13418,negated_conjecture,
( xj = xi
| ~ sdtlseqdt0(xi,xj)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolve,[status(thm)],[c_248,c_135]) ).
cnf(c_13419,negated_conjecture,
( xj = xi
| ~ sdtlseqdt0(xi,xj)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolve,[status(thm)],[c_245,c_13418]) ).
cnf(c_651,negated_conjecture,
( xj = xi
| ~ sdtlseqdt0(xi,xj) ),
inference(resolve,[status(thm)],[c_244,c_13419]) ).
cnf(c_13420,plain,
( aSet0(sdtlpdtrp0(xN,xi))
| ~ aSet0(szNzAzT0) ),
inference(resolve,[status(thm)],[c_598,c_88]) ).
cnf(c_2944,plain,
aSet0(sdtlpdtrp0(xN,xi)),
inference(resolve,[status(thm)],[c_120,c_13420]) ).
cnf(c_2988,plain,
aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xi)),
inference(resolve,[status(thm)],[c_2944,c_93]) ).
cnf(c_13421,plain,
( xj = xi
| ~ sdtlseqdt0(sz00,xj)
| aElementOf0(sK0(xi),szNzAzT0) ),
inference(paramod,[status(thm)],[c_629,c_651]) ).
cnf(c_7736,plain,
( xj = xi
| aElementOf0(sK0(xi),szNzAzT0) ),
inference(resolve,[status(thm)],[c_575,c_13421]) ).
cnf(c_13422,plain,
( xj = xi
| ~ sdtlseqdt0(sz00,xj)
| szszuzczcdt0(sK0(xi)) = xi ),
inference(paramod,[status(thm)],[c_628,c_651]) ).
cnf(c_10199,plain,
( xj = xi
| szszuzczcdt0(sK0(xi)) = xi ),
inference(resolve,[status(thm)],[c_575,c_13422]) ).
cnf(c_13423,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xi))
| aElementOf0(sK0(xi),szNzAzT0) ),
inference(paramod,[status(thm)],[c_7736,c_249]) ).
cnf(c_13175,plain,
aElementOf0(sK0(xi),szNzAzT0),
inference(resolve,[status(thm)],[c_2988,c_13423]) ).
cnf(c_13225,plain,
szszuzczcdt0(sK0(xi)) != xi,
inference(resolve,[status(thm)],[c_13175,c_279]) ).
cnf(c_13302,plain,
xj = xi,
inference(resolve,[status(thm)],[c_13225,c_10199]) ).
cnf(c_13424,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xi)),
inference(paramod,[status(thm)],[c_13302,c_249]) ).
cnf(c_13414,plain,
$false,
inference(resolve,[status(thm)],[c_2988,c_13424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM574+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n010.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 03:17:15 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.46 % Process 2363817 was started by sandbox2 on n010,
% 0.20/0.46 % Sat Sep 26 03:17:15 2026
% 0.20/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.24/0.50
% 0.24/0.50 % From the command line: assign(max_seconds, 300).
% 77.58/11.33
% 77.58/11.33 % given #500 (T,wt=14): 2154 isFinite0(slbdtsldtrb0(slcrc0,xK)). [resolve(357,b,85,a),unit_del(a,280)].
% 77.58/11.33
% 77.58/11.33 % given #1000 (F,wt=21): 5293 sdtmndt0(slbdtrb0(xj),xK) != szNzAzT0. [resolve(5266,a,2714,a)].
% 77.58/11.33
% 77.58/11.33 % SZS status Theorem for theBenchmark
% 77.58/11.33
% 77.58/11.33 % Proof 1 at 1.87 (+ 0.56) seconds.
% 77.58/11.33 % Length of proof is 37.
% 77.58/11.33 % Level of proof is 8.
% 77.58/11.33 % Maximum clause weight is 27.000.
% 77.58/11.33 % Given clauses 1425.
% 77.58/11.33
% 77.58/11.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------