%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU275+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 12:36:33 EDT 2023

% Result   : Theorem 0.09s 0.31s
% Output   : CNFRefutation 0.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   53 (  17 unt;   0 def)
%            Number of atoms       :  123 (   0 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  112 (  42   ~;  42   |;  15   &)
%                                         (   8 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   15 (  14 usr;   7 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   21 (;  20   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A] :
      ( relation(A)
     => ( well_ordering(A)
      <=> ( reflexive(A)
          & transitive(A)
          & antisymmetric(A)
          & connected(A)
          & well_founded_relation(A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] : relation(inclusion_relation(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A] : reflexive(inclusion_relation(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A] : transitive(inclusion_relation(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A] :
      ( ordinal(A)
     => connected(inclusion_relation(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A] : antisymmetric(inclusion_relation(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A] :
      ( ordinal(A)
     => well_founded_relation(inclusion_relation(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ! [A] :
      ( ordinal(A)
     => well_ordering(inclusion_relation(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ! [A] :
        ( ordinal(A)
       => well_ordering(inclusion_relation(A)) ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f18,plain,
    ! [A] :
      ( ~ relation(A)
      | ( well_ordering(A)
      <=> ( reflexive(A)
          & transitive(A)
          & antisymmetric(A)
          & connected(A)
          & well_founded_relation(A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f19,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ( ~ well_ordering(A)
          | ( reflexive(A)
            & transitive(A)
            & antisymmetric(A)
            & connected(A)
            & well_founded_relation(A) ) )
        & ( well_ordering(A)
          | ~ reflexive(A)
          | ~ transitive(A)
          | ~ antisymmetric(A)
          | ~ connected(A)
          | ~ well_founded_relation(A) ) ) ),
    inference(NNF_transformation,[status(esa)],[f18]) ).

fof(f25,plain,
    ! [X0] :
      ( ~ relation(X0)
      | well_ordering(X0)
      | ~ reflexive(X0)
      | ~ transitive(X0)
      | ~ antisymmetric(X0)
      | ~ connected(X0)
      | ~ well_founded_relation(X0) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f26,plain,
    ! [X0] : relation(inclusion_relation(X0)),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f31,plain,
    ! [X0] : reflexive(inclusion_relation(X0)),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f32,plain,
    ! [X0] : transitive(inclusion_relation(X0)),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f33,plain,
    ! [A] :
      ( ~ ordinal(A)
      | connected(inclusion_relation(A)) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f34,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | connected(inclusion_relation(X0)) ),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f35,plain,
    ! [X0] : antisymmetric(inclusion_relation(X0)),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f36,plain,
    ! [A] :
      ( ~ ordinal(A)
      | well_founded_relation(inclusion_relation(A)) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f37,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | well_founded_relation(inclusion_relation(X0)) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    ? [A] :
      ( ordinal(A)
      & ~ well_ordering(inclusion_relation(A)) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f39,plain,
    ( ordinal(sk0_1)
    & ~ well_ordering(inclusion_relation(sk0_1)) ),
    inference(skolemization,[status(esa)],[f38]) ).

fof(f40,plain,
    ordinal(sk0_1),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f41,plain,
    ~ well_ordering(inclusion_relation(sk0_1)),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f42,plain,
    ( spl0_0
  <=> relation(inclusion_relation(sk0_1)) ),
    introduced(split_symbol_definition) ).

fof(f44,plain,
    ( ~ relation(inclusion_relation(sk0_1))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f42]) ).

fof(f45,plain,
    ( spl0_1
  <=> reflexive(inclusion_relation(sk0_1)) ),
    introduced(split_symbol_definition) ).

fof(f47,plain,
    ( ~ reflexive(inclusion_relation(sk0_1))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f45]) ).

fof(f48,plain,
    ( spl0_2
  <=> transitive(inclusion_relation(sk0_1)) ),
    introduced(split_symbol_definition) ).

fof(f50,plain,
    ( ~ transitive(inclusion_relation(sk0_1))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f48]) ).

fof(f51,plain,
    ( spl0_3
  <=> antisymmetric(inclusion_relation(sk0_1)) ),
    introduced(split_symbol_definition) ).

fof(f53,plain,
    ( ~ antisymmetric(inclusion_relation(sk0_1))
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f51]) ).

fof(f54,plain,
    ( spl0_4
  <=> connected(inclusion_relation(sk0_1)) ),
    introduced(split_symbol_definition) ).

fof(f56,plain,
    ( ~ connected(inclusion_relation(sk0_1))
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f54]) ).

fof(f57,plain,
    ( spl0_5
  <=> well_founded_relation(inclusion_relation(sk0_1)) ),
    introduced(split_symbol_definition) ).

fof(f59,plain,
    ( ~ well_founded_relation(inclusion_relation(sk0_1))
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f57]) ).

fof(f60,plain,
    ( ~ relation(inclusion_relation(sk0_1))
    | ~ reflexive(inclusion_relation(sk0_1))
    | ~ transitive(inclusion_relation(sk0_1))
    | ~ antisymmetric(inclusion_relation(sk0_1))
    | ~ connected(inclusion_relation(sk0_1))
    | ~ well_founded_relation(inclusion_relation(sk0_1)) ),
    inference(resolution,[status(thm)],[f25,f41]) ).

fof(f61,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_4
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f60,f42,f45,f48,f51,f54,f57]) ).

fof(f66,plain,
    ( ~ ordinal(sk0_1)
    | spl0_5 ),
    inference(resolution,[status(thm)],[f59,f37]) ).

fof(f67,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f66,f40]) ).

fof(f68,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f67]) ).

fof(f69,plain,
    ( ~ ordinal(sk0_1)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f56,f34]) ).

fof(f70,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f69,f40]) ).

fof(f71,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f70]) ).

fof(f72,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f53,f35]) ).

fof(f73,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f72]) ).

fof(f74,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f50,f32]) ).

fof(f75,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f74]) ).

fof(f76,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f44,f26]) ).

fof(f77,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f76]) ).

fof(f78,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f47,f31]) ).

fof(f79,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f78]) ).

fof(f80,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f61,f68,f71,f73,f75,f77,f79]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SEU275+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n027.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue May 30 09:28:32 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.5.1
% 0.09/0.31  % Refutation found
% 0.09/0.31  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53  % Elapsed time: 0.010084 seconds
% 0.14/0.53  % CPU time: 0.012254 seconds
% 0.14/0.53  % Memory used: 1.825 MB
%------------------------------------------------------------------------------