TSTP Solution File: SEU223+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 12:36:20 EDT 2023

% Result   : Theorem 0.12s 0.37s
% Output   : CNFRefutation 0.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   44 (   8 unt;   0 def)
%            Number of atoms       :  157 (  34 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  187 (  74   ~;  70   |;  28   &)
%                                         (   6 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   63 (;  55   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f69,axiom,
    ! [A,B] :
      ( relation(A)
     => relation(relation_dom_restriction(A,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f91,axiom,
    ! [A,B] :
      ( ( relation(A)
        & function(A) )
     => ( relation(relation_dom_restriction(A,B))
        & function(relation_dom_restriction(A,B)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f216,lemma,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ! [C] :
          ( ( relation(C)
            & function(C) )
         => ( B = relation_dom_restriction(C,A)
          <=> ( relation_dom(B) = set_intersection2(relation_dom(C),A)
              & ! [D] :
                  ( in(D,relation_dom(B))
                 => apply(B,D) = apply(C,D) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f220,conjecture,
    ! [A,B,C] :
      ( ( relation(C)
        & function(C) )
     => ( in(B,relation_dom(relation_dom_restriction(C,A)))
       => apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f221,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( relation(C)
          & function(C) )
       => ( in(B,relation_dom(relation_dom_restriction(C,A)))
         => apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
    inference(negated_conjecture,[status(cth)],[f220]) ).

fof(f521,plain,
    ! [A,B] :
      ( ~ relation(A)
      | relation(relation_dom_restriction(A,B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f69]) ).

fof(f522,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] : relation(relation_dom_restriction(A,B)) ),
    inference(miniscoping,[status(esa)],[f521]) ).

fof(f523,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | relation(relation_dom_restriction(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f522]) ).

fof(f568,plain,
    ! [A,B] :
      ( ~ relation(A)
      | ~ function(A)
      | ( relation(relation_dom_restriction(A,B))
        & function(relation_dom_restriction(A,B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f91]) ).

fof(f569,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ( ! [B] : relation(relation_dom_restriction(A,B))
        & ! [B] : function(relation_dom_restriction(A,B)) ) ),
    inference(miniscoping,[status(esa)],[f568]) ).

fof(f571,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | function(relation_dom_restriction(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f569]) ).

fof(f942,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( B = relation_dom_restriction(C,A)
          <=> ( relation_dom(B) = set_intersection2(relation_dom(C),A)
              & ! [D] :
                  ( ~ in(D,relation_dom(B))
                  | apply(B,D) = apply(C,D) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f216]) ).

fof(f943,plain,
    ! [A,B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( ( B != relation_dom_restriction(C,A)
              | ( relation_dom(B) = set_intersection2(relation_dom(C),A)
                & ! [D] :
                    ( ~ in(D,relation_dom(B))
                    | apply(B,D) = apply(C,D) ) ) )
            & ( B = relation_dom_restriction(C,A)
              | relation_dom(B) != set_intersection2(relation_dom(C),A)
              | ? [D] :
                  ( in(D,relation_dom(B))
                  & apply(B,D) != apply(C,D) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f942]) ).

fof(f944,plain,
    ! [B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( ! [A] :
                ( B != relation_dom_restriction(C,A)
                | ( relation_dom(B) = set_intersection2(relation_dom(C),A)
                  & ! [D] :
                      ( ~ in(D,relation_dom(B))
                      | apply(B,D) = apply(C,D) ) ) )
            & ! [A] :
                ( B = relation_dom_restriction(C,A)
                | relation_dom(B) != set_intersection2(relation_dom(C),A)
                | ? [D] :
                    ( in(D,relation_dom(B))
                    & apply(B,D) != apply(C,D) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f943]) ).

fof(f945,plain,
    ! [B] :
      ( ~ relation(B)
      | ~ function(B)
      | ! [C] :
          ( ~ relation(C)
          | ~ function(C)
          | ( ! [A] :
                ( B != relation_dom_restriction(C,A)
                | ( relation_dom(B) = set_intersection2(relation_dom(C),A)
                  & ! [D] :
                      ( ~ in(D,relation_dom(B))
                      | apply(B,D) = apply(C,D) ) ) )
            & ! [A] :
                ( B = relation_dom_restriction(C,A)
                | relation_dom(B) != set_intersection2(relation_dom(C),A)
                | ( in(sk0_78(A,C,B),relation_dom(B))
                  & apply(B,sk0_78(A,C,B)) != apply(C,sk0_78(A,C,B)) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f944]) ).

fof(f947,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X1)
      | ~ function(X1)
      | X0 != relation_dom_restriction(X1,X2)
      | ~ in(X3,relation_dom(X0))
      | apply(X0,X3) = apply(X1,X3) ),
    inference(cnf_transformation,[status(esa)],[f945]) ).

fof(f955,plain,
    ? [A,B,C] :
      ( relation(C)
      & function(C)
      & in(B,relation_dom(relation_dom_restriction(C,A)))
      & apply(relation_dom_restriction(C,A),B) != apply(C,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f221]) ).

fof(f956,plain,
    ? [C] :
      ( relation(C)
      & function(C)
      & ? [A,B] :
          ( in(B,relation_dom(relation_dom_restriction(C,A)))
          & apply(relation_dom_restriction(C,A),B) != apply(C,B) ) ),
    inference(miniscoping,[status(esa)],[f955]) ).

fof(f957,plain,
    ( relation(sk0_79)
    & function(sk0_79)
    & in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80)))
    & apply(relation_dom_restriction(sk0_79,sk0_80),sk0_81) != apply(sk0_79,sk0_81) ),
    inference(skolemization,[status(esa)],[f956]) ).

fof(f958,plain,
    relation(sk0_79),
    inference(cnf_transformation,[status(esa)],[f957]) ).

fof(f959,plain,
    function(sk0_79),
    inference(cnf_transformation,[status(esa)],[f957]) ).

fof(f960,plain,
    in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80))),
    inference(cnf_transformation,[status(esa)],[f957]) ).

fof(f961,plain,
    apply(relation_dom_restriction(sk0_79,sk0_80),sk0_81) != apply(sk0_79,sk0_81),
    inference(cnf_transformation,[status(esa)],[f957]) ).

fof(f1110,plain,
    ! [X0,X1,X2] :
      ( ~ relation(relation_dom_restriction(X0,X1))
      | ~ function(relation_dom_restriction(X0,X1))
      | ~ relation(X0)
      | ~ function(X0)
      | ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
      | apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f947]) ).

fof(f1117,plain,
    ( spl0_0
  <=> relation(sk0_79) ),
    introduced(split_symbol_definition) ).

fof(f1119,plain,
    ( ~ relation(sk0_79)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f1117]) ).

fof(f1125,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1119,f958]) ).

fof(f1126,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f1125]) ).

fof(f1156,plain,
    ! [X0,X1,X2] :
      ( ~ function(relation_dom_restriction(X0,X1))
      | ~ relation(X0)
      | ~ function(X0)
      | ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
      | apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1110,f523]) ).

fof(f1157,plain,
    ( spl0_3
  <=> function(relation_dom_restriction(sk0_79,sk0_80)) ),
    introduced(split_symbol_definition) ).

fof(f1159,plain,
    ( ~ function(relation_dom_restriction(sk0_79,sk0_80))
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f1157]) ).

fof(f1160,plain,
    ( spl0_4
  <=> function(sk0_79) ),
    introduced(split_symbol_definition) ).

fof(f1162,plain,
    ( ~ function(sk0_79)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f1160]) ).

fof(f1163,plain,
    ( spl0_5
  <=> in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80))) ),
    introduced(split_symbol_definition) ).

fof(f1165,plain,
    ( ~ in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80)))
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f1163]) ).

fof(f1166,plain,
    ( ~ function(relation_dom_restriction(sk0_79,sk0_80))
    | ~ relation(sk0_79)
    | ~ function(sk0_79)
    | ~ in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80))) ),
    inference(resolution,[status(thm)],[f1156,f961]) ).

fof(f1167,plain,
    ( ~ spl0_3
    | ~ spl0_0
    | ~ spl0_4
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f1166,f1157,f1117,f1160,f1163]) ).

fof(f1168,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1165,f960]) ).

fof(f1169,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f1168]) ).

fof(f1170,plain,
    ( ~ relation(sk0_79)
    | ~ function(sk0_79)
    | spl0_3 ),
    inference(resolution,[status(thm)],[f1159,f571]) ).

fof(f1171,plain,
    ( ~ spl0_0
    | ~ spl0_4
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f1170,f1117,f1160,f1157]) ).

fof(f1172,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1162,f959]) ).

fof(f1173,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f1172]) ).

fof(f1174,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1126,f1167,f1169,f1171,f1173]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue May 30 09:09:21 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.36  % Drodi V3.5.1
% 0.12/0.37  % Refutation found
% 0.12/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.34/0.60  % Elapsed time: 0.040341 seconds
% 0.34/0.60  % CPU time: 0.083607 seconds
% 0.34/0.60  % Memory used: 21.233 MB
%------------------------------------------------------------------------------