%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET046+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:35:29 AM UTC 2026
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 52 ( 24 ~; 18 |; 8 &)
% ( 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 : 21 ( 0 sgn 10 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel42,conjecture,
~ ? [Y] :
! [X] :
( element(X,Y)
<=> ~ ? [Z] :
( element(Z,X)
& element(X,Z) ) ),
file('theBenchmark.p',pel42) ).
fof(pel42_neg,negated_conjecture,
~ ~ ? [Y] :
! [X] :
( element(X,Y)
<=> ~ ? [Z] :
( element(Z,X)
& element(X,Z) ) ),
inference(assume_negation,[status(cth)],[pel42]) ).
fof(nnf_1,plain,
? [Y] :
! [X] :
( ( ? [Z] :
( element(Z,X)
& element(X,Z) )
| element(X,Y) )
& ( ! [X0] :
( ~ element(X0,X)
| ~ element(X,X0) )
| ~ element(X,Y) ) ),
inference(fof_nnf,[status(thm)],[pel42_neg]) ).
fof(sk_pel42_neg_sk,plain,
! [X] :
( ( ( element(sK1(X),X)
& element(X,sK1(X)) )
| element(X,sK0) )
& ( ! [X0] :
( ~ element(X0,X)
| ~ element(X,X0) )
| ~ element(X,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(Y,sK0),skolemize(Z,sK1(X))],[nnf_1]) ).
fof(sk_pel42_neg,plain,
( ! [VAR_0] :
( element(sK1(VAR_0),VAR_0)
| element(VAR_0,sK0) )
& ! [VAR_0] :
( element(VAR_0,sK1(VAR_0))
| element(VAR_0,sK0) )
& ! [VAR_0,VAR_1] :
( ~ element(VAR_1,VAR_0)
| ~ element(VAR_0,VAR_1)
| ~ element(VAR_0,sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel42_neg_sk]) ).
cnf(c_2,negated_conjecture,
( ~ element(B,A)
| ~ element(A,B)
| ~ element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel42_neg]) ).
cnf(c_3,negated_conjecture,
( element(A,sK1(A))
| element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel42_neg]) ).
cnf(c_4,negated_conjecture,
( element(sK1(A),A)
| element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel42_neg]) ).
cnf(c_16,plain,
( ~ element(sK0,sK0)
| ~ element(sK0,sK0) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_6,plain,
~ element(sK0,sK0),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_8,plain,
( ~ element(sK1(A),A)
| ~ element(sK1(A),sK0)
| element(A,sK0) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_17,plain,
( ~ element(sK1(sK0),sK0)
| element(sK0,sK0) ),
inference(factor,[status(thm)],[c_8]) ).
cnf(c_9,plain,
~ element(sK1(sK0),sK0),
inference(resolve,[status(thm)],[c_6,c_17]) ).
cnf(c_18,negated_conjecture,
element(sK0,sK0),
inference(resolve,[status(thm)],[c_9,c_4]) ).
cnf(c_15,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_6,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET046+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n014.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 06:59:16 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2441820 was started by sandbox2 on n014,
% 0.07/0.35 % Sat Sep 26 06:59:16 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.36
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36
% 0.12/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.36 % Length of proof is 8.
% 0.12/0.36 % Level of proof is 4.
% 0.12/0.36 % Maximum clause weight is 11.000.
% 0.12/0.36 % Given clauses 8.
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------