%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU115+1 : TPTP v9.3.1. Released v3.2.0.
% 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 08:45:03 AM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 21 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 4 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
fof(t27_finsub_1,axiom,
! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
file('theBenchmark.p',t27_finsub_1) ).
fof(t28_finsub_1,conjecture,
finite_subsets(empty_set) = singleton(empty_set),
file('theBenchmark.p',t28_finsub_1) ).
fof(t28_finsub_1_neg,negated_conjecture,
finite_subsets(empty_set) != singleton(empty_set),
inference(assume_negation,[status(cth)],[t28_finsub_1]) ).
cnf(c_50,plain,
( finite(A)
| ~ empty(A) ),
inference(clausify,[status(thm)],[cc1_finset_1]) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
cnf(c_75,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc1_xboole_0]) ).
cnf(c_79,plain,
( finite_subsets(A) = powerset(A)
| ~ finite(A) ),
inference(clausify,[status(thm)],[t27_finsub_1]) ).
fof(t1_zfmisc_1,axiom,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
cnf(c_80,plain,
powerset(empty_set) = singleton(empty_set),
inference(clausify,[status(thm)],[t1_zfmisc_1]) ).
cnf(c_81,plain,
singleton(empty_set) = powerset(empty_set),
inference(copy,[status(thm)],[c_80]) ).
cnf(c_82,negated_conjecture,
singleton(empty_set) != finite_subsets(empty_set),
inference(clausify,[status(thm)],[t28_finsub_1_neg]) ).
cnf(c_140,negated_conjecture,
powerset(empty_set) != finite_subsets(empty_set),
inference(paramod,[status(thm)],[c_81,c_82]) ).
cnf(c_83,negated_conjecture,
finite_subsets(empty_set) != powerset(empty_set),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_119,plain,
finite(empty_set),
inference(resolve,[status(thm)],[c_75,c_50]) ).
cnf(c_141,negated_conjecture,
~ finite(empty_set),
inference(resolve,[status(thm)],[c_79,c_83]) ).
cnf(c_139,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_119,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU115+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 08:32:18 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 280849 was started by sandbox2 on n017,
% 0.17/0.44 % Sat Sep 26 08:32:18 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.17/0.48 % Length of proof is 12.
% 0.17/0.48 % Level of proof is 3.
% 0.17/0.48 % Maximum clause weight is 7.000.
% 0.17/0.48 % Given clauses 38.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------