%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 : Fri Sep 25 02:43:56 PM UTC 2026
% Result : Theorem 2.25s 0.66s
% Output : Proof 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 3 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 39 ( 18 ~; 13 |; 6 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 17 ( 0 sgn 6 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
~ ? [Y] :
! [X] :
( element(X,Y)
<=> ~ ? [Z] :
( element(Z,X)
& element(X,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm25) ).
fof(f0_neg,negated_conjecture,
~ ~ ? [Y] :
! [X] :
( element(X,Y)
<=> ~ ? [Z] :
( element(Z,X)
& element(X,Z) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [Y] :
! [X] :
( ( ? [Z] :
( element(Z,X)
& element(X,Z) )
| element(X,Y) )
& ( ! [Z] :
( ~ element(Z,X)
| ~ element(X,Z) )
| ~ element(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Z] :
( ( ( element(sk1(X),X)
& element(X,sk1(X)) )
| element(X,sk0) )
& ( ~ element(Z,X)
| ~ element(X,Z)
| ~ element(X,sk0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c0,plain,
( ~ element(X2,X1)
| ~ element(X1,X2)
| ~ element(X1,sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p3,plain,
( ~ element(sk0,X0)
| ~ element(X0,sk0) ),
inference(factoring,[status(thm)],[c0]) ).
cnf(c2,plain,
( element(sk1(X1),X1)
| element(X1,sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p7,plain,
( element(sk0,sk0)
| ~ element(sk0,sk1(sk0)) ),
inference(resolution,[status(thm)],[p3,c2]) ).
cnf(c1,plain,
( element(X1,sk1(X1))
| element(X1,sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p9,plain,
( element(sk0,sk0)
| element(sk0,sk0) ),
inference(resolution,[status(thm)],[p7,c1]) ).
cnf(p10,plain,
element(sk0,sk0),
inference(factoring,[status(thm)],[p9]) ).
cnf(p6,plain,
~ element(sk0,sk0),
inference(factoring,[status(thm)],[p3]) ).
cnf(p11,plain,
$false,
inference(resolution,[status(thm)],[p10,p6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Thu Sep 24 11:57:05 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.25/0.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.25/0.66 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------