%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM551+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 : n011.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 08:17:22 AM UTC 2026
% Result : Theorem 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 53 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 53 ( 21 ~; 18 |; 11 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 19 ( 0 sgn 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mDefEmp,axiom,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('theBenchmark.p',mDefEmp) ).
fof(m__2291,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('theBenchmark.p',m__2291) ).
fof(m__,conjecture,
? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_62,negated_conjecture,
( ~ aElementOf0(A,xQ)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__2313,axiom,
xQ != slcrc0,
file('theBenchmark.p',m__2313) ).
cnf(c_63,plain,
xQ != slcrc0,
inference(clausify,[status(thm)],[m__2313]) ).
cnf(c_67,plain,
aSet0(xQ),
inference(clausify,[status(thm)],[m__2291]) ).
fof(nnf_5,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| slcrc0 = W0 )
& ( ( ! [X0] : ~ aElementOf0(X0,W0)
& aSet0(W0) )
| slcrc0 != W0 ) ),
inference(fof_nnf,[status(thm)],[mDefEmp]) ).
fof(sk_mDefEmp_sk,plain,
! [W0] :
( ( aElementOf0(sK0(W0),W0)
| ~ aSet0(W0)
| slcrc0 = W0 )
& ( ( ! [X0] : ~ aElementOf0(X0,W0)
& aSet0(W0) )
| slcrc0 != W0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W1,sK0(W0))],[nnf_5]) ).
fof(sk_mDefEmp,plain,
( ! [VAR_0] :
( aElementOf0(sK0(VAR_0),VAR_0)
| ~ aSet0(VAR_0)
| slcrc0 = VAR_0 )
& ! [VAR_0,VAR_1] :
( ~ aElementOf0(VAR_1,VAR_0)
| slcrc0 != VAR_0 )
& ! [VAR_0] :
( aSet0(VAR_0)
| slcrc0 != VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_mDefEmp_sk]) ).
cnf(c_177,plain,
( aElementOf0(sK0(A),A)
| ~ aSet0(A)
| slcrc0 = A ),
inference(split_conjunct,[status(thm)],[sk_mDefEmp]) ).
cnf(c_180,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_1007,plain,
( aElementOf0(sK0(xQ),xQ)
| slcrc0 = xQ ),
inference(resolve,[status(thm)],[c_177,c_67]) ).
cnf(c_1008,plain,
( aElementOf0(sK0(xQ),xQ)
| xQ = slcrc0 ),
inference(copy,[status(thm)],[c_1007]) ).
cnf(c_369,plain,
aElementOf0(sK0(xQ),xQ),
inference(resolve,[status(thm)],[c_63,c_1008]) ).
cnf(c_1009,plain,
( aElement0(sK0(xQ))
| ~ aSet0(xQ) ),
inference(resolve,[status(thm)],[c_369,c_180]) ).
cnf(c_994,plain,
aElement0(sK0(xQ)),
inference(resolve,[status(thm)],[c_67,c_1009]) ).
cnf(c_1010,negated_conjecture,
~ aElement0(sK0(xQ)),
inference(resolve,[status(thm)],[c_369,c_62]) ).
cnf(c_1006,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_994,c_1010]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM551+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 03:12:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3660645 was started by sandbox2 on n011,
% 0.09/0.37 % Sat Sep 26 03:12:29 2026
% 0.09/0.37 % 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).
% 0.09/0.45
% 0.09/0.45 % SZS status Theorem for theBenchmark
% 0.09/0.45
% 0.09/0.45 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.09/0.45 % Length of proof is 12.
% 0.09/0.45 % Level of proof is 4.
% 0.09/0.45 % Maximum clause weight is 19.000.
% 0.09/0.45 % Given clauses 209.
% 0.09/0.45
% 0.09/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------