%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM615+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 : 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 08:17:35 AM UTC 2026
% Result : Theorem 28.07s 4.74s
% Output : CNFRefutation 28.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 20 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 14 ( 4 ~; 3 |; 7 &)
% ( 0 <=>; 0 =>; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 0 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__5182,axiom,
? [W0] :
( sdtlpdtrp0(xe,W0) = xp
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('theBenchmark.p',m__5182) ).
fof(m__,conjecture,
? [W0] :
( sdtlpdtrp0(xe,W0) = xp
& ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xd)) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ? [W0] :
( sdtlpdtrp0(xe,W0) = xp
& ( aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ( sdtlpdtrp0(xd,W0) = szDzizrdt0(xd)
& aElementOf0(W0,szDzozmdt0(xd)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_99,plain,
? [W0] :
( sdtlpdtrp0(xe,W0) = xp
& aElementOf0(W0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(fof_nnf,[status(thm)],[m__5182]) ).
fof(sk_m__5182,plain,
( sdtlpdtrp0(xe,sK0) = xp
& aElementOf0(sK0,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_99]) ).
cnf(c_978,plain,
aElementOf0(sK0,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(split_conjunct,[status(thm)],[sk_m__5182]) ).
cnf(c_979,plain,
sdtlpdtrp0(xe,sK0) = xp,
inference(split_conjunct,[status(thm)],[sk_m__5182]) ).
cnf(c_987,negated_conjecture,
( sdtlpdtrp0(xe,A) != xp
| ~ aElementOf0(A,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_5816,negated_conjecture,
sdtlpdtrp0(xe,sK0) != xp,
inference(resolve,[status(thm)],[c_987,c_978]) ).
cnf(c_5815,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_979,c_5816]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM615+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 03:27:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3682960 was started by sandbox on n011,
% 0.11/0.37 % Sat Sep 26 03:27:59 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.34/0.63
% 0.34/0.63 % From the command line: assign(max_seconds, 300).
% 28.07/4.74
% 28.07/4.74 % given #500 (I,wt=37): 900 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 28.07/4.74
% 28.07/4.74 % SZS status Theorem for theBenchmark
% 28.07/4.74
% 28.07/4.74 % Proof 1 at 3.88 (+ 0.15) seconds.
% 28.07/4.74 % Length of proof is 6.
% 28.07/4.74 % Level of proof is 2.
% 28.07/4.74 % Maximum clause weight is 26.000.
% 28.07/4.74 % Given clauses 580.
% 28.07/4.74
% 28.07/4.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------