TSTP Solution File: SEU337+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU337+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 : 300s
% DateTime : Wed May 31 12:36:45 EDT 2023
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 118 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 41 ~; 43 |; 9 &)
% ( 10 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 (; 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f169,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f260,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f404,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( closed_subsets(B,A)
<=> open_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f410,conjecture,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( open_subsets(B,A)
<=> closed_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f411,negated_conjecture,
~ ! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( open_subsets(B,A)
<=> closed_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f410]) ).
fof(f1305,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| element(complements_of_subsets(A,B),powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(esa)],[f169]) ).
fof(f1306,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
inference(cnf_transformation,[status(esa)],[f1305]) ).
fof(f1573,plain,
! [A,B] :
( ~ element(B,powerset(powerset(A)))
| complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
inference(pre_NNF_transformation,[status(esa)],[f260]) ).
fof(f1574,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f1573]) ).
fof(f2411,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(powerset(the_carrier(A))))
| ( closed_subsets(B,A)
<=> open_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f404]) ).
fof(f2412,plain,
! [A] :
( ~ top_str(A)
| ! [B] :
( ~ element(B,powerset(powerset(the_carrier(A))))
| ( ( ~ closed_subsets(B,A)
| open_subsets(complements_of_subsets(the_carrier(A),B),A) )
& ( closed_subsets(B,A)
| ~ open_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f2411]) ).
fof(f2413,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ closed_subsets(X1,X0)
| open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[status(esa)],[f2412]) ).
fof(f2414,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| closed_subsets(X1,X0)
| ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[status(esa)],[f2412]) ).
fof(f2432,plain,
? [A] :
( top_str(A)
& ? [B] :
( element(B,powerset(powerset(the_carrier(A))))
& ( open_subsets(B,A)
<~> closed_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f411]) ).
fof(f2433,plain,
? [A] :
( top_str(A)
& ? [B] :
( element(B,powerset(powerset(the_carrier(A))))
& ( open_subsets(B,A)
| closed_subsets(complements_of_subsets(the_carrier(A),B),A) )
& ( ~ open_subsets(B,A)
| ~ closed_subsets(complements_of_subsets(the_carrier(A),B),A) ) ) ),
inference(NNF_transformation,[status(esa)],[f2432]) ).
fof(f2434,plain,
( top_str(sk0_329)
& element(sk0_330,powerset(powerset(the_carrier(sk0_329))))
& ( open_subsets(sk0_330,sk0_329)
| closed_subsets(complements_of_subsets(the_carrier(sk0_329),sk0_330),sk0_329) )
& ( ~ open_subsets(sk0_330,sk0_329)
| ~ closed_subsets(complements_of_subsets(the_carrier(sk0_329),sk0_330),sk0_329) ) ),
inference(skolemization,[status(esa)],[f2433]) ).
fof(f2435,plain,
top_str(sk0_329),
inference(cnf_transformation,[status(esa)],[f2434]) ).
fof(f2436,plain,
element(sk0_330,powerset(powerset(the_carrier(sk0_329)))),
inference(cnf_transformation,[status(esa)],[f2434]) ).
fof(f2437,plain,
( open_subsets(sk0_330,sk0_329)
| closed_subsets(complements_of_subsets(the_carrier(sk0_329),sk0_330),sk0_329) ),
inference(cnf_transformation,[status(esa)],[f2434]) ).
fof(f2438,plain,
( ~ open_subsets(sk0_330,sk0_329)
| ~ closed_subsets(complements_of_subsets(the_carrier(sk0_329),sk0_330),sk0_329) ),
inference(cnf_transformation,[status(esa)],[f2434]) ).
fof(f3349,plain,
( spl0_31
<=> open_subsets(sk0_330,sk0_329) ),
introduced(split_symbol_definition) ).
fof(f3352,plain,
( spl0_32
<=> closed_subsets(complements_of_subsets(the_carrier(sk0_329),sk0_330),sk0_329) ),
introduced(split_symbol_definition) ).
fof(f3355,plain,
( spl0_31
| spl0_32 ),
inference(split_clause,[status(thm)],[f2437,f3349,f3352]) ).
fof(f3356,plain,
( ~ spl0_31
| ~ spl0_32 ),
inference(split_clause,[status(thm)],[f2438,f3349,f3352]) ).
fof(f3544,plain,
( spl0_54
<=> top_str(sk0_329) ),
introduced(split_symbol_definition) ).
fof(f3546,plain,
( ~ top_str(sk0_329)
| spl0_54 ),
inference(component_clause,[status(thm)],[f3544]) ).
fof(f3552,plain,
( $false
| spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f3546,f2435]) ).
fof(f3553,plain,
spl0_54,
inference(contradiction_clause,[status(thm)],[f3552]) ).
fof(f3556,plain,
complements_of_subsets(the_carrier(sk0_329),complements_of_subsets(the_carrier(sk0_329),sk0_330)) = sk0_330,
inference(resolution,[status(thm)],[f1574,f2436]) ).
fof(f3567,plain,
element(complements_of_subsets(the_carrier(sk0_329),sk0_330),powerset(powerset(the_carrier(sk0_329)))),
inference(resolution,[status(thm)],[f1306,f2436]) ).
fof(f3594,plain,
( spl0_62
<=> open_subsets(complements_of_subsets(the_carrier(sk0_329),complements_of_subsets(the_carrier(sk0_329),sk0_330)),sk0_329) ),
introduced(split_symbol_definition) ).
fof(f3595,plain,
( open_subsets(complements_of_subsets(the_carrier(sk0_329),complements_of_subsets(the_carrier(sk0_329),sk0_330)),sk0_329)
| ~ spl0_62 ),
inference(component_clause,[status(thm)],[f3594]) ).
fof(f3597,plain,
( ~ top_str(sk0_329)
| ~ closed_subsets(complements_of_subsets(the_carrier(sk0_329),sk0_330),sk0_329)
| open_subsets(complements_of_subsets(the_carrier(sk0_329),complements_of_subsets(the_carrier(sk0_329),sk0_330)),sk0_329) ),
inference(resolution,[status(thm)],[f2413,f3567]) ).
fof(f3598,plain,
( ~ spl0_54
| ~ spl0_32
| spl0_62 ),
inference(split_clause,[status(thm)],[f3597,f3544,f3352,f3594]) ).
fof(f3604,plain,
( open_subsets(sk0_330,sk0_329)
| ~ spl0_62 ),
inference(forward_demodulation,[status(thm)],[f3556,f3595]) ).
fof(f3650,plain,
( spl0_71
<=> empty_set = empty_set ),
introduced(split_symbol_definition) ).
fof(f3652,plain,
( empty_set != empty_set
| spl0_71 ),
inference(component_clause,[status(thm)],[f3650]) ).
fof(f3686,plain,
( $false
| spl0_71 ),
inference(trivial_equality_resolution,[status(esa)],[f3652]) ).
fof(f3687,plain,
spl0_71,
inference(contradiction_clause,[status(thm)],[f3686]) ).
fof(f3747,plain,
( spl0_31
| ~ spl0_62 ),
inference(split_clause,[status(thm)],[f3604,f3349,f3594]) ).
fof(f3749,plain,
( spl0_82
<=> element(complements_of_subsets(the_carrier(sk0_329),sk0_330),powerset(powerset(the_carrier(sk0_329)))) ),
introduced(split_symbol_definition) ).
fof(f3751,plain,
( ~ element(complements_of_subsets(the_carrier(sk0_329),sk0_330),powerset(powerset(the_carrier(sk0_329))))
| spl0_82 ),
inference(component_clause,[status(thm)],[f3749]) ).
fof(f3752,plain,
( ~ top_str(sk0_329)
| ~ element(complements_of_subsets(the_carrier(sk0_329),sk0_330),powerset(powerset(the_carrier(sk0_329))))
| closed_subsets(complements_of_subsets(the_carrier(sk0_329),sk0_330),sk0_329)
| ~ open_subsets(sk0_330,sk0_329) ),
inference(paramodulation,[status(thm)],[f3556,f2414]) ).
fof(f3753,plain,
( ~ spl0_54
| ~ spl0_82
| spl0_32
| ~ spl0_31 ),
inference(split_clause,[status(thm)],[f3752,f3544,f3749,f3352,f3349]) ).
fof(f3754,plain,
( $false
| spl0_82 ),
inference(forward_subsumption_resolution,[status(thm)],[f3751,f3567]) ).
fof(f3755,plain,
spl0_82,
inference(contradiction_clause,[status(thm)],[f3754]) ).
fof(f3756,plain,
$false,
inference(sat_refutation,[status(thm)],[f3355,f3356,f3553,f3598,f3687,f3747,f3753,f3755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU337+2 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n013.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 09:11:50 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.15/0.37 % Drodi V3.5.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.095825 seconds
% 0.15/0.42 % CPU time: 0.249225 seconds
% 0.15/0.42 % Memory used: 59.100 MB
%------------------------------------------------------------------------------