%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET044+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% 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(pel40,conjecture,
( ? [Y] :
! [X] :
( element(X,Y)
<=> element(X,X) )
=> ~ ! [X1] :
? [Y1] :
! [Z] :
( element(Z,Y1)
<=> ~ element(Z,X1) ) ),
file('theBenchmark.p',pel40) ).
fof(pel40_neg,negated_conjecture,
~ ( ? [Y] :
! [X] :
( element(X,Y)
<=> element(X,X) )
=> ~ ! [X1] :
? [Y1] :
! [Z] :
( element(Z,Y1)
<=> ~ element(Z,X1) ) ),
inference(assume_negation,[status(cth)],[pel40]) ).
fof(nnf_1,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(fof_nnf,[status(thm)],[pel40_neg]) ).
fof(sk_pel40_neg,plain,
( ! [X1,Z] :
( ( element(Z,X1)
| element(Z,sK1(X1)) )
& ( ~ element(Z,X1)
| ~ element(Z,sK1(X1)) ) )
& ! [X] :
( ( ~ element(X,X)
| element(X,sK0) )
& ( element(X,X)
| ~ element(X,sK0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(Y,sK0),skolemize(Y1,sK1(X1))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( element(A,A)
| ~ element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel40_neg]) ).
cnf(c_3,negated_conjecture,
( ~ element(A,A)
| element(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel40_neg]) ).
cnf(c_4,negated_conjecture,
( ~ element(A,B)
| ~ element(A,sK1(B)) ),
inference(split_conjunct,[status(thm)],[sk_pel40_neg]) ).
cnf(c_5,negated_conjecture,
( element(A,B)
| element(A,sK1(B)) ),
inference(split_conjunct,[status(thm)],[sk_pel40_neg]) ).
cnf(c_6,plain,
( element(sK1(A),sK0)
| element(sK1(A),A) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_7,plain,
element(sK1(sK0),sK0),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_9,plain,
element(sK1(sK0),sK1(sK0)),
inference(resolve,[status(thm)],[c_7,c_2]) ).
cnf(c_11,negated_conjecture,
~ element(sK1(sK0),sK1(sK0)),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_10,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_9,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET044+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 06:57:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 3060848 was started by sandbox on n007,
% 0.09/0.38 % Sat Sep 26 06:57:08 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 9.
% 0.09/0.39 % Level of proof is 5.
% 0.09/0.39 % Maximum clause weight is 8.000.
% 0.09/0.39 % Given clauses 6.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------