%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM560+2 : 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 : n017.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 08:17:24 AM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 4 unt; 0 def)
% Number of atoms : 51 ( 8 equ)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 60 ( 19 ~; 13 |; 22 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xF,xy))
<=> ( sdtlpdtrp0(xF,W0) = xy
& aElementOf0(W0,szDzozmdt0(xF)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) )
=> ( aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
| ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xF,xy))
=> aElementOf0(W0,szDzozmdt0(xF)) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xF,xy))
<=> ( sdtlpdtrp0(xF,W0) = xy
& aElementOf0(W0,szDzozmdt0(xF)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) )
=> ( aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
| ! [W0] :
( aElementOf0(W0,sdtlbdtrb0(xF,xy))
=> aElementOf0(W0,szDzozmdt0(xF)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(nnf_65,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& ? [W0] :
( ~ aElementOf0(W0,szDzozmdt0(xF))
& aElementOf0(W0,sdtlbdtrb0(xF,xy)) )
& ! [X0] :
( ( sdtlpdtrp0(xF,X0) != xy
| ~ aElementOf0(X0,szDzozmdt0(xF))
| aElementOf0(X0,sdtlbdtrb0(xF,xy)) )
& ( ( sdtlpdtrp0(xF,X0) = xy
& aElementOf0(X0,szDzozmdt0(xF)) )
| ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) ),
inference(fof_nnf,[status(thm)],[m___neg]) ).
fof(sk_m___neg_sk,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& ~ aElementOf0(sK0,szDzozmdt0(xF))
& aElementOf0(sK0,sdtlbdtrb0(xF,xy))
& ! [X0] :
( ( sdtlpdtrp0(xF,X0) != xy
| ~ aElementOf0(X0,szDzozmdt0(xF))
| aElementOf0(X0,sdtlbdtrb0(xF,xy)) )
& ( ( sdtlpdtrp0(xF,X0) = xy
& aElementOf0(X0,szDzozmdt0(xF)) )
| ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(W0,sK0)],[nnf_65]) ).
fof(sk_m___neg,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& ~ aElementOf0(sK0,szDzozmdt0(xF))
& aElementOf0(sK0,sdtlbdtrb0(xF,xy))
& ! [VAR_0] :
( sdtlpdtrp0(xF,VAR_0) != xy
| ~ aElementOf0(VAR_0,szDzozmdt0(xF))
| aElementOf0(VAR_0,sdtlbdtrb0(xF,xy)) )
& ! [VAR_0] :
( sdtlpdtrp0(xF,VAR_0) = xy
| ~ aElementOf0(VAR_0,sdtlbdtrb0(xF,xy)) )
& ! [VAR_0] :
( aElementOf0(VAR_0,szDzozmdt0(xF))
| ~ aElementOf0(VAR_0,sdtlbdtrb0(xF,xy)) )
& aSet0(sdtlbdtrb0(xF,xy)) ),
inference(cnf_transformation,[status(thm)],[sk_m___neg_sk]) ).
cnf(c_198,negated_conjecture,
( aElementOf0(A,szDzozmdt0(xF))
| ~ aElementOf0(A,sdtlbdtrb0(xF,xy)) ),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_201,negated_conjecture,
aElementOf0(sK0,sdtlbdtrb0(xF,xy)),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_202,negated_conjecture,
~ aElementOf0(sK0,szDzozmdt0(xF)),
inference(split_conjunct,[status(thm)],[sk_m___neg]) ).
cnf(c_320,negated_conjecture,
aElementOf0(sK0,szDzozmdt0(xF)),
inference(resolve,[status(thm)],[c_201,c_198]) ).
cnf(c_319,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_202,c_320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM560+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 03:09:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3851113 was started by sandbox on n017,
% 0.09/0.35 % Sat Sep 26 03:09:33 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.42
% 0.14/0.42 % SZS status Theorem for theBenchmark
% 0.14/0.42
% 0.14/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/0.42 % Length of proof is 5.
% 0.14/0.42 % Level of proof is 2.
% 0.14/0.42 % Maximum clause weight is 9.000.
% 0.14/0.42 % Given clauses 106.
% 0.14/0.42
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------