%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET044+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:41:42 PM UTC 2026
% Result : Theorem 2.09s 6.13s
% Output : Proof 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 43 ( 18 ~; 13 |; 6 &)
% ( 4 <=>; 2 =>; 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 : 25 ( 0 sgn 12 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ? [Y] :
! [X] :
( element(X,Y)
<=> element(X,X) )
=> ~ ! [X1] :
? [Y1] :
! [Z] :
( element(Z,Y1)
<=> ~ element(Z,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel40) ).
fof(f0_neg,negated_conjecture,
~ ( ? [Y] :
! [X] :
( element(X,Y)
<=> element(X,X) )
=> ~ ! [X1] :
? [Y1] :
! [Z] :
( element(Z,Y1)
<=> ~ element(Z,X1) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ! [X1] :
? [Y1] :
! [Z] :
( ( element(Z,X1)
| element(Z,Y1) )
& ( ~ element(Z,X1)
| ~ element(Z,Y1) ) )
& ? [Y] :
! [X] :
( ( ~ element(X,X)
| element(X,Y) )
& ( element(X,X)
| ~ element(X,Y) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Z,X1] :
( ( element(Z,X1)
| element(Z,sk1(X1)) )
& ( ~ element(Z,X1)
| ~ element(Z,sk1(X1)) )
& ( ~ element(X,X)
| element(X,sk0) )
& ( element(X,X)
| ~ element(X,sk0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c3,plain,
( element(X4,X2)
| element(X4,sk1(X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c1,plain,
( ~ element(X1,X1)
| element(X1,sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p4,plain,
( element(sk1(X0),sk0)
| element(sk1(X0),X0) ),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(p5,plain,
element(sk1(sk0),sk0),
inference(factoring,[status(thm)],[p4]) ).
cnf(c0,plain,
( element(X1,X1)
| ~ element(X1,sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p7,plain,
element(sk1(sk0),sk1(sk0)),
inference(resolution,[status(thm)],[p5,c0]) ).
cnf(c2,plain,
( ~ element(X4,X2)
| ~ element(X4,sk1(X2)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p8,plain,
~ element(sk1(sk0),sk0),
inference(resolution,[status(thm)],[p7,c2]) ).
cnf(p9,plain,
$false,
inference(resolution,[status(thm)],[p8,p5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET044+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n013.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 09:24:41 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.09/6.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.09/6.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------