TSTP Solution File: SEU217+2 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU217+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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 : Tue Apr 30 20:41:32 EDT 2024

% Result   : Theorem 0.17s 0.35s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   34 (   8 unt;   0 def)
%            Number of atoms       :  150 (  59 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  186 (  70   ~;  70   |;  32   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-2 aty)
%            Number of variables   :   85 (  79   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [A,B] :
      ( relation(B)
     => ( B = identity_relation(A)
      <=> ! [C,D] :
            ( in(ordered_pair(C,D),B)
          <=> ( in(C,A)
              & C = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f27,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B,C] :
          ( ( in(B,relation_dom(A))
           => ( C = apply(A,B)
            <=> in(ordered_pair(B,C),A) ) )
          & ( ~ in(B,relation_dom(A))
           => ( C = apply(A,B)
            <=> C = empty_set ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f62,axiom,
    ! [A] : relation(identity_relation(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f78,axiom,
    ! [A] :
      ( relation(identity_relation(A))
      & function(identity_relation(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f165,conjecture,
    ! [A,B] :
      ( in(B,A)
     => apply(identity_relation(A),B) = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f166,negated_conjecture,
    ~ ! [A,B] :
        ( in(B,A)
       => apply(identity_relation(A),B) = B ),
    inference(negated_conjecture,[status(cth)],[f165]) ).

fof(f206,lemma,
    ! [A] :
      ( relation_dom(identity_relation(A)) = A
      & relation_rng(identity_relation(A)) = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f235,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ( B = identity_relation(A)
      <=> ! [C,D] :
            ( in(ordered_pair(C,D),B)
          <=> ( in(C,A)
              & C = D ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f236,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ( ( B != identity_relation(A)
          | ! [C,D] :
              ( ( ~ in(ordered_pair(C,D),B)
                | ( in(C,A)
                  & C = D ) )
              & ( in(ordered_pair(C,D),B)
                | ~ in(C,A)
                | C != D ) ) )
        & ( B = identity_relation(A)
          | ? [C,D] :
              ( ( ~ in(ordered_pair(C,D),B)
                | ~ in(C,A)
                | C != D )
              & ( in(ordered_pair(C,D),B)
                | ( in(C,A)
                  & C = D ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f235]) ).

fof(f237,plain,
    ! [B] :
      ( ~ relation(B)
      | ( ! [A] :
            ( B != identity_relation(A)
            | ( ! [C,D] :
                  ( ~ in(ordered_pair(C,D),B)
                  | ( in(C,A)
                    & C = D ) )
              & ! [C,D] :
                  ( in(ordered_pair(C,D),B)
                  | ~ in(C,A)
                  | C != D ) ) )
        & ! [A] :
            ( B = identity_relation(A)
            | ? [C,D] :
                ( ( ~ in(ordered_pair(C,D),B)
                  | ~ in(C,A)
                  | C != D )
                & ( in(ordered_pair(C,D),B)
                  | ( in(C,A)
                    & C = D ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f236]) ).

fof(f238,plain,
    ! [B] :
      ( ~ relation(B)
      | ( ! [A] :
            ( B != identity_relation(A)
            | ( ! [C,D] :
                  ( ~ in(ordered_pair(C,D),B)
                  | ( in(C,A)
                    & C = D ) )
              & ! [C,D] :
                  ( in(ordered_pair(C,D),B)
                  | ~ in(C,A)
                  | C != D ) ) )
        & ! [A] :
            ( B = identity_relation(A)
            | ( ( ~ in(ordered_pair(sk0_0(A,B),sk0_1(A,B)),B)
                | ~ in(sk0_0(A,B),A)
                | sk0_0(A,B) != sk0_1(A,B) )
              & ( in(ordered_pair(sk0_0(A,B),sk0_1(A,B)),B)
                | ( in(sk0_0(A,B),A)
                  & sk0_0(A,B) = sk0_1(A,B) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f237]) ).

fof(f240,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X0 != identity_relation(X1)
      | ~ in(ordered_pair(X2,X3),X0)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f238]) ).

fof(f392,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ! [B,C] :
          ( ( ~ in(B,relation_dom(A))
            | ( C = apply(A,B)
            <=> in(ordered_pair(B,C),A) ) )
          & ( in(B,relation_dom(A))
            | ( C = apply(A,B)
            <=> C = empty_set ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f27]) ).

fof(f393,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ! [B,C] :
          ( ( ~ in(B,relation_dom(A))
            | ( ( C != apply(A,B)
                | in(ordered_pair(B,C),A) )
              & ( C = apply(A,B)
                | ~ in(ordered_pair(B,C),A) ) ) )
          & ( in(B,relation_dom(A))
            | ( ( C != apply(A,B)
                | C = empty_set )
              & ( C = apply(A,B)
                | C != empty_set ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f392]) ).

fof(f394,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ( ! [B] :
            ( ~ in(B,relation_dom(A))
            | ( ! [C] :
                  ( C != apply(A,B)
                  | in(ordered_pair(B,C),A) )
              & ! [C] :
                  ( C = apply(A,B)
                  | ~ in(ordered_pair(B,C),A) ) ) )
        & ! [B] :
            ( in(B,relation_dom(A))
            | ( ! [C] :
                  ( C != apply(A,B)
                  | C = empty_set )
              & ! [C] :
                  ( C = apply(A,B)
                  | C != empty_set ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f393]) ).

fof(f395,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ in(X1,relation_dom(X0))
      | X2 != apply(X0,X1)
      | in(ordered_pair(X1,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f394]) ).

fof(f483,plain,
    ! [X0] : relation(identity_relation(X0)),
    inference(cnf_transformation,[status(esa)],[f62]) ).

fof(f512,plain,
    ( ! [A] : relation(identity_relation(A))
    & ! [A] : function(identity_relation(A)) ),
    inference(miniscoping,[status(esa)],[f78]) ).

fof(f514,plain,
    ! [X0] : function(identity_relation(X0)),
    inference(cnf_transformation,[status(esa)],[f512]) ).

fof(f765,plain,
    ? [A,B] :
      ( in(B,A)
      & apply(identity_relation(A),B) != B ),
    inference(pre_NNF_transformation,[status(esa)],[f166]) ).

fof(f766,plain,
    ( in(sk0_67,sk0_66)
    & apply(identity_relation(sk0_66),sk0_67) != sk0_67 ),
    inference(skolemization,[status(esa)],[f765]) ).

fof(f767,plain,
    in(sk0_67,sk0_66),
    inference(cnf_transformation,[status(esa)],[f766]) ).

fof(f768,plain,
    apply(identity_relation(sk0_66),sk0_67) != sk0_67,
    inference(cnf_transformation,[status(esa)],[f766]) ).

fof(f872,plain,
    ( ! [A] : relation_dom(identity_relation(A)) = A
    & ! [A] : relation_rng(identity_relation(A)) = A ),
    inference(miniscoping,[status(esa)],[f206]) ).

fof(f873,plain,
    ! [X0] : relation_dom(identity_relation(X0)) = X0,
    inference(cnf_transformation,[status(esa)],[f872]) ).

fof(f942,plain,
    ! [X0,X1,X2] :
      ( ~ relation(identity_relation(X0))
      | ~ in(ordered_pair(X1,X2),identity_relation(X0))
      | X1 = X2 ),
    inference(destructive_equality_resolution,[status(esa)],[f240]) ).

fof(f979,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ in(X1,relation_dom(X0))
      | in(ordered_pair(X1,apply(X0,X1)),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f395]) ).

fof(f1011,plain,
    ! [X0,X1,X2] :
      ( ~ in(ordered_pair(X0,X1),identity_relation(X2))
      | X0 = X1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f942,f483]) ).

fof(f1016,plain,
    ! [X0,X1] :
      ( ~ relation(identity_relation(X0))
      | ~ function(identity_relation(X0))
      | ~ in(X1,relation_dom(identity_relation(X0)))
      | X1 = apply(identity_relation(X0),X1) ),
    inference(resolution,[status(thm)],[f979,f1011]) ).

fof(f1017,plain,
    ! [X0,X1] :
      ( ~ relation(identity_relation(X0))
      | ~ function(identity_relation(X0))
      | ~ in(X1,X0)
      | X1 = apply(identity_relation(X0),X1) ),
    inference(forward_demodulation,[status(thm)],[f873,f1016]) ).

fof(f1018,plain,
    ! [X0,X1] :
      ( ~ function(identity_relation(X0))
      | ~ in(X1,X0)
      | X1 = apply(identity_relation(X0),X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1017,f483]) ).

fof(f1028,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | X0 = apply(identity_relation(X1),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1018,f514]) ).

fof(f1029,plain,
    ~ in(sk0_67,sk0_66),
    inference(resolution,[status(thm)],[f1028,f768]) ).

fof(f1030,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f1029,f767]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU217+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n014.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon Apr 29 19:34:34 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.17/0.35  % Drodi V3.6.0
% 0.17/0.35  % Refutation found
% 0.17/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.38  % Elapsed time: 0.037480 seconds
% 0.17/0.38  % CPU time: 0.049319 seconds
% 0.17/0.38  % Total memory used: 19.032 MB
% 0.17/0.38  % Net memory used: 18.956 MB
%------------------------------------------------------------------------------