%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : TOP002-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 09:52:56 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lemma_1b_2,axiom,
~ element_of_collection(empty_set,top_of_basis(f)),
file('theBenchmark.p',lemma_1b_2) ).
cnf(c_1,plain,
~ element_of_collection(empty_set,top_of_basis(f)),
inference(clausify,[status(thm)],[lemma_1b_2]) ).
fof(topology_generated_40,axiom,
! [VAR_0,VAR_1] :
( element_of_set(f11(VAR_1,VAR_0),VAR_0)
| element_of_collection(VAR_0,top_of_basis(VAR_1)) ),
file('theBenchmark.p',topology_generated_40) ).
cnf(c_2,plain,
( element_of_set(f11(B,A),A)
| element_of_collection(A,top_of_basis(B)) ),
inference(clausify,[status(thm)],[topology_generated_40]) ).
fof(set_theory_6,axiom,
! [VAR_0] : ~ element_of_set(VAR_0,empty_set),
file('theBenchmark.p',set_theory_6) ).
cnf(c_3,plain,
~ element_of_set(A,empty_set),
inference(clausify,[status(thm)],[set_theory_6]) ).
cnf(c_4,plain,
element_of_set(f11(f,empty_set),empty_set),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_5,plain,
$false,
inference(resolve,[status(thm)],[c_3,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP002-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 20:25:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1574811 was started by sandbox2 on n017,
% 0.09/0.36 % Sat Sep 26 20:25:05 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 5.
% 0.09/0.38 % Level of proof is 2.
% 0.09/0.38 % Maximum clause weight is 0.000.
% 0.09/0.38 % Given clauses 0.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------