%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET054+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 08:35:30 AM UTC 2026
% Result : Theorem 0.11s 0.61s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 7 unt; 0 def)
% Number of atoms : 12 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 1 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 8 ( 0 sgn 4 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(extensionality,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('theBenchmark.p',extensionality) ).
fof(reflexivity_of_subclass,conjecture,
! [X] : subclass(X,X),
file('theBenchmark.p',reflexivity_of_subclass) ).
fof(reflexivity_of_subclass_neg,negated_conjecture,
~ ! [X] : subclass(X,X),
inference(assume_negation,[status(cth)],[reflexivity_of_subclass]) ).
fof(nnf_42,plain,
? [X] : ~ subclass(X,X),
inference(fof_nnf,[status(thm)],[reflexivity_of_subclass_neg]) ).
fof(sk_reflexivity_of_subclass_neg,plain,
~ subclass(sK0,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
~ subclass(sK0,sK0),
inference(split_conjunct,[status(thm)],[sk_reflexivity_of_subclass_neg]) ).
cnf(c_134,plain,
( subclass(A,B)
| A != B ),
inference(clausify,[status(thm)],[extensionality]) ).
cnf(c_295,plain,
subclass(A,A),
inference(xxres,[status(thm)],[c_134]) ).
cnf(c_296,plain,
$false,
inference(resolve,[status(thm)],[c_295,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET054+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.56 % Computer : n007.cluster.edu
% 0.11/0.56 % Model : x86_64 x86_64
% 0.11/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.56 % Memory : 8046.5625MB
% 0.11/0.56 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Sat Sep 26 06:57:55 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.56 % Process 3062745 was started by sandbox on n007,
% 0.11/0.56 % Sat Sep 26 06:57:55 2026
% 0.11/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.58
% 0.11/0.58 % From the command line: assign(max_seconds, 300).
% 0.11/0.61
% 0.11/0.61 % SZS status Theorem for theBenchmark
% 0.11/0.61
% 0.11/0.61 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.11/0.61 % Length of proof is 6.
% 0.11/0.61 % Level of proof is 3.
% 0.11/0.61 % Maximum clause weight is 6.000.
% 0.11/0.61 % Given clauses 44.
% 0.11/0.61
% 0.11/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------