%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET045+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 : 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 : Sun Sep 27 08:35:28 AM UTC 2026
% Result : Theorem 0.04s 0.31s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 42 ( 20 ~; 14 |; 7 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 29 ( 2 sgn 16 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel41_1,axiom,
! [Z] :
? [Y] :
! [X] :
( element(X,Y)
<=> ( ~ element(X,X)
& element(X,Z) ) ),
file('theBenchmark.p',pel41_1) ).
fof(pel41,conjecture,
~ ? [Z] :
! [X] : element(X,Z),
file('theBenchmark.p',pel41) ).
fof(pel41_neg,negated_conjecture,
~ ~ ? [Z] :
! [X] : element(X,Z),
inference(assume_negation,[status(cth)],[pel41]) ).
fof(nnf_1,plain,
! [Z] :
? [Y] :
! [X] :
( ( element(X,X)
| ~ element(X,Z)
| element(X,Y) )
& ( ( ~ element(X,X)
& element(X,Z) )
| ~ element(X,Y) ) ),
inference(fof_nnf,[status(thm)],[pel41_1]) ).
fof(sk_pel41_1_sk,plain,
! [Z,X] :
( ( element(X,X)
| ~ element(X,Z)
| element(X,sK0(Z)) )
& ( ( ~ element(X,X)
& element(X,Z) )
| ~ element(X,sK0(Z)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(Z))],[nnf_1]) ).
fof(sk_pel41_1,plain,
( ! [VAR_0,VAR_1] :
( element(VAR_0,VAR_0)
| ~ element(VAR_0,VAR_1)
| element(VAR_0,sK0(VAR_1)) )
& ! [VAR_0,VAR_1] :
( ~ element(VAR_0,VAR_0)
| ~ element(VAR_0,sK0(VAR_1)) )
& ! [VAR_0,VAR_1] :
( element(VAR_0,VAR_1)
| ~ element(VAR_0,sK0(VAR_1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel41_1_sk]) ).
cnf(c_4,plain,
( ~ element(A,A)
| ~ element(A,sK0(B)) ),
inference(split_conjunct,[status(thm)],[sk_pel41_1]) ).
cnf(c_5,plain,
( element(A,A)
| ~ element(A,B)
| element(A,sK0(B)) ),
inference(split_conjunct,[status(thm)],[sk_pel41_1]) ).
fof(nnf_2,plain,
? [Z] :
! [X] : element(X,Z),
inference(fof_nnf,[status(thm)],[pel41_neg]) ).
fof(sk_pel41_neg,plain,
! [X] : element(X,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Z,sK1)],[nnf_2]) ).
cnf(c_6,negated_conjecture,
element(A,sK1),
inference(split_conjunct,[status(thm)],[sk_pel41_neg]) ).
cnf(c_7,plain,
~ element(sK0(A),sK0(A)),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_10,plain,
( ~ element(sK0(A),A)
| element(sK0(A),sK0(A)) ),
inference(factor,[status(thm)],[c_5]) ).
cnf(c_8,plain,
~ element(sK0(A),A),
inference(resolve,[status(thm)],[c_7,c_10]) ).
cnf(c_9,plain,
$false,
inference(resolve,[status(thm)],[c_8,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET045+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sat Sep 26 06:59:05 UTC 2026
% 0.04/0.29 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 4142289 was started by sandbox2 on n012,
% 0.04/0.30 % Sat Sep 26 06:59:05 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/0.30
% 0.04/0.30 % From the command line: assign(max_seconds, 300).
% 0.04/0.31
% 0.04/0.31 % SZS status Theorem for theBenchmark
% 0.04/0.31
% 0.04/0.31 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/0.31 % Length of proof is 8.
% 0.04/0.31 % Level of proof is 4.
% 0.04/0.31 % Maximum clause weight is 10.000.
% 0.04/0.31 % Given clauses 0.
% 0.04/0.31
% 0.04/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------