%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM568+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:17:26 AM UTC 2026
% Result : Theorem 0.24s 0.55s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 47 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 38 ( 13 ~; 18 |; 6 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn 5 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mNatExtra,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ? [W1] :
( W0 = szszuzczcdt0(W1)
& aElementOf0(W1,szNzAzT0) )
| W0 = sz00 ) ),
file('theBenchmark.p',mNatExtra) ).
fof(m__,conjecture,
? [W0] :
( szszuzczcdt0(W0) = xK
& aElementOf0(W0,szNzAzT0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( szszuzczcdt0(W0) = xK
& aElementOf0(W0,szNzAzT0) ),
inference(assume_negation,[status(cth)],[m__]) ).
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_120,plain,
( aElementOf0(sK0(A),szNzAzT0)
| sz00 = A
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_mNatExtra]) ).
cnf(c_121,plain,
( szszuzczcdt0(sK0(A)) = A
| sz00 = A
| ~ aElementOf0(A,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[sk_mNatExtra]) ).
fof(m__3418,axiom,
aElementOf0(xK,szNzAzT0),
file('theBenchmark.p',m__3418) ).
cnf(c_219,plain,
aElementOf0(xK,szNzAzT0),
inference(clausify,[status(thm)],[m__3418]) ).
fof(m__3462,axiom,
xK != sz00,
file('theBenchmark.p',m__3462) ).
cnf(c_231,plain,
xK != sz00,
inference(clausify,[status(thm)],[m__3462]) ).
cnf(c_232,negated_conjecture,
( szszuzczcdt0(A) != xK
| ~ aElementOf0(A,szNzAzT0) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_734,plain,
( szszuzczcdt0(sK0(xK)) = xK
| sz00 = xK ),
inference(resolve,[status(thm)],[c_219,c_121]) ).
cnf(c_735,plain,
( szszuzczcdt0(sK0(xK)) = xK
| xK = sz00 ),
inference(copy,[status(thm)],[c_734]) ).
cnf(c_364,plain,
szszuzczcdt0(sK0(xK)) = xK,
inference(resolve,[status(thm)],[c_231,c_735]) ).
cnf(c_736,plain,
( aElementOf0(sK0(xK),szNzAzT0)
| sz00 = xK ),
inference(resolve,[status(thm)],[c_219,c_120]) ).
cnf(c_737,plain,
( aElementOf0(sK0(xK),szNzAzT0)
| xK = sz00 ),
inference(copy,[status(thm)],[c_736]) ).
cnf(c_365,plain,
aElementOf0(sK0(xK),szNzAzT0),
inference(resolve,[status(thm)],[c_231,c_737]) ).
cnf(c_738,negated_conjecture,
szszuzczcdt0(sK0(xK)) != xK,
inference(resolve,[status(thm)],[c_365,c_232]) ).
cnf(c_739,negated_conjecture,
xK != xK,
inference(paramod,[status(thm)],[c_364,c_738]) ).
cnf(c_733,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM568+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 03:15:21 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 692022 was started by sandbox on n004,
% 0.17/0.43 % Sat Sep 26 03:15:21 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 0.24/0.55
% 0.24/0.55 % SZS status Theorem for theBenchmark
% 0.24/0.55
% 0.24/0.55 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.24/0.55 % Length of proof is 10.
% 0.24/0.55 % Level of proof is 3.
% 0.24/0.55 % Maximum clause weight is 11.000.
% 0.24/0.55 % Given clauses 226.
% 0.24/0.55
% 0.24/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------