%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM609+3 : 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 : n013.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 08:17:33 AM UTC 2026
% Result : Theorem 27.77s 4.11s
% Output : CNFRefutation 27.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 26 ( 2 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 24 ( 8 ~; 3 |; 9 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn 4 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__5164,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( W0 != szmzizndt0(xQ)
& aElementOf0(W0,xQ)
& aElement0(W0) ) )
& ! [W0] :
( aElementOf0(W0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),W0) )
& aSet0(xP) ),
file('theBenchmark.p',m__5164) ).
fof(m__,conjecture,
( aSubsetOf0(xP,xQ)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( aSubsetOf0(xP,xQ)
| ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xQ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_970,plain,
( aElementOf0(A,xQ)
| ~ aElementOf0(A,xP) ),
inference(clausify,[status(thm)],[m__5164]) ).
fof(nnf_100,plain,
( ~ aSubsetOf0(xP,xQ)
& ? [W0] :
( ~ aElementOf0(W0,xQ)
& aElementOf0(W0,xP) ) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg,plain,
( ~ aSubsetOf0(xP,xQ)
& ~ aElementOf0(sK0,xQ)
& aElementOf0(sK0,xP) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_100]) ).
cnf(c_976,negated_conjecture,
aElementOf0(sK0,xP),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_977,negated_conjecture,
~ aElementOf0(sK0,xQ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_4363,negated_conjecture,
aElementOf0(sK0,xQ),
inference(resolve,[status(thm)],[c_976,c_970]) ).
cnf(c_4362,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_977,c_4363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM609+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.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 03:25:51 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1834212 was started by sandbox2 on n013,
% 0.11/0.38 % Sat Sep 26 03:25:51 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.49
% 0.15/0.49 % From the command line: assign(max_seconds, 300).
% 27.77/4.11
% 27.77/4.11 % given #500 (I,wt=37): 896 -aElementOf0(A,szNzAzT0) | -aElementOf0(B,f39(A)) | aElementOf0(B,sdtmndt0(sdtlpdtrp0(xN,A),szmzizndt0(sdtlpdtrp0(xN,A)))) # tptp_name(m__4411). [clausify(83)].
% 27.77/4.11
% 27.77/4.11 % SZS status Theorem for theBenchmark
% 27.77/4.11
% 27.77/4.11 % Proof 1 at 3.37 (+ 0.10) seconds.
% 27.77/4.11 % Length of proof is 6.
% 27.77/4.11 % Level of proof is 2.
% 27.77/4.11 % Maximum clause weight is 11.000.
% 27.77/4.11 % Given clauses 574.
% 27.77/4.11
% 27.77/4.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------