%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM551+3 : 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 : n003.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 0.22s 0.53s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 5 unt; 0 def)
% Number of atoms : 28 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 5 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 4 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn 2 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(m__2291,axiom,
( sbrdtbr0(xQ) = xk
& isFinite0(xQ)
& aSet0(xQ) ),
file('theBenchmark.p',m__2291) ).
fof(m__2313,axiom,
~ ( xQ = slcrc0
| ~ ? [W0] : aElementOf0(W0,xQ) ),
file('theBenchmark.p',m__2313) ).
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_64,negated_conjecture,
( ~ aElementOf0(A,xQ)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
fof(nnf_62,plain,
( xQ != slcrc0
& ? [W0] : aElementOf0(W0,xQ) ),
inference(fof_nnf,[status(thm)],[m__2313]) ).
fof(sk_m__2313,plain,
( xQ != slcrc0
& aElementOf0(sK0,xQ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_62]) ).
cnf(c_66,plain,
aElementOf0(sK0,xQ),
inference(split_conjunct,[status(thm)],[sk_m__2313]) ).
cnf(c_70,plain,
aSet0(xQ),
inference(clausify,[status(thm)],[m__2291]) ).
cnf(c_206,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_231,plain,
~ aElement0(sK0),
inference(resolve,[status(thm)],[c_66,c_64]) ).
cnf(c_491,plain,
( aElement0(sK0)
| ~ aSet0(xQ) ),
inference(resolve,[status(thm)],[c_206,c_66]) ).
cnf(c_492,plain,
aElement0(sK0),
inference(resolve,[status(thm)],[c_70,c_491]) ).
cnf(c_490,plain,
$false,
inference(resolve,[status(thm)],[c_231,c_492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM551+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n003.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 03:13:55 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 1903567 was started by sandbox on n003,
% 0.15/0.44 % Sat Sep 26 03:13:55 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.46
% 0.15/0.46 % From the command line: assign(max_seconds, 300).
% 0.22/0.53
% 0.22/0.53 % SZS status Theorem for theBenchmark
% 0.22/0.53
% 0.22/0.53 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.22/0.53 % Length of proof is 10.
% 0.22/0.53 % Level of proof is 3.
% 0.22/0.53 % Maximum clause weight is 12.000.
% 0.22/0.53 % Given clauses 139.
% 0.22/0.53
% 0.22/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------