%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU115+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:38:28 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 49 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 15 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ) ).
fof(fc1_xboole_0,axiom,
empty(empty_set) ).
fof(t28_finsub_1,conjecture,
finite_subsets(empty_set) = singleton(empty_set) ).
fof(t27_finsub_1,axiom,
! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ) ).
fof(t1_zfmisc_1,axiom,
powerset(empty_set) = singleton(empty_set) ).
fof(subgoal_0,plain,
finite_subsets(empty_set) = singleton(empty_set),
inference(strip,[],[t28_finsub_1]) ).
fof(negate_0_0,plain,
finite_subsets(empty_set) != singleton(empty_set),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
empty(empty_set),
inference(canonicalize,[],[fc1_xboole_0]) ).
fof(normalize_0_1,plain,
! [A] :
( ~ empty(A)
| finite(A) ),
inference(canonicalize,[],[cc1_finset_1]) ).
fof(normalize_0_2,plain,
! [A] :
( ~ empty(A)
| finite(A) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ finite(A)
| finite_subsets(A) = powerset(A) ),
inference(canonicalize,[],[t27_finsub_1]) ).
fof(normalize_0_4,plain,
! [A] :
( ~ finite(A)
| finite_subsets(A) = powerset(A) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
finite_subsets(empty_set) != singleton(empty_set),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
powerset(empty_set) = singleton(empty_set),
inference(canonicalize,[],[t1_zfmisc_1]) ).
cnf(refute_0_0,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
( ~ empty(A)
| finite(A) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ empty(empty_set)
| finite(empty_set) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_3,plain,
finite(empty_set),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ finite(A)
| finite_subsets(A) = powerset(A) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_5,plain,
( ~ finite(empty_set)
| finite_subsets(empty_set) = powerset(empty_set) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_6,plain,
finite_subsets(empty_set) = powerset(empty_set),
inference(resolve,[$cnf( finite(empty_set) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
finite_subsets(empty_set) != singleton(empty_set),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_8,plain,
powerset(empty_set) = singleton(empty_set),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_9,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_10,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_11,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( powerset(empty_set) != singleton(empty_set)
| singleton(empty_set) = powerset(empty_set) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(powerset(empty_set))),bind(Y,$fot(singleton(empty_set)))]]) ).
cnf(refute_0_13,plain,
singleton(empty_set) = powerset(empty_set),
inference(resolve,[$cnf( $equal(powerset(empty_set),singleton(empty_set)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( finite_subsets(empty_set) != powerset(empty_set)
| singleton(empty_set) != powerset(empty_set)
| finite_subsets(empty_set) = singleton(empty_set) ),
introduced(tautology,[equality,[$cnf( ~ $equal(finite_subsets(empty_set),singleton(empty_set)) ),[1],$fot(powerset(empty_set))]]) ).
cnf(refute_0_15,plain,
( finite_subsets(empty_set) != powerset(empty_set)
| finite_subsets(empty_set) = singleton(empty_set) ),
inference(resolve,[$cnf( $equal(singleton(empty_set),powerset(empty_set)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
finite_subsets(empty_set) != powerset(empty_set),
inference(resolve,[$cnf( $equal(finite_subsets(empty_set),singleton(empty_set)) )],[refute_0_15,refute_0_7]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( $equal(finite_subsets(empty_set),powerset(empty_set)) )],[refute_0_6,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU115+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 08:50:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------