TSTP Solution File: SEU020+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU020+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 12:35:42 EDT 2023

% Result   : Theorem 0.14s 0.31s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   54 (  18 unt;   0 def)
%            Number of atoms       :  149 (  14 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  150 (  55   ~;  55   |;  23   &)
%                                         (   7 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   8 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (;  20   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f29,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B] :
          ( ( relation(B)
            & function(B) )
         => ( relation_dom(relation_composition(B,A)) = relation_dom(B)
           => subset(relation_rng(B),relation_dom(A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B] :
          ( ( relation(B)
            & function(B) )
         => ( ( one_to_one(relation_composition(B,A))
              & subset(relation_rng(B),relation_dom(A)) )
           => one_to_one(B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f34,axiom,
    ! [A] : one_to_one(identity_relation(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f35,conjecture,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( ? [B] :
            ( relation(B)
            & function(B)
            & relation_composition(A,B) = identity_relation(relation_dom(A)) )
       => one_to_one(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,negated_conjecture,
    ~ ! [A] :
        ( ( relation(A)
          & function(A) )
       => ( ? [B] :
              ( relation(B)
              & function(B)
              & relation_composition(A,B) = identity_relation(relation_dom(A)) )
         => one_to_one(A) ) ),
    inference(negated_conjecture,[status(cth)],[f35]) ).

fof(f39,axiom,
    ! [A] :
      ( relation_dom(identity_relation(A)) = A
      & relation_rng(identity_relation(A)) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f109,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ! [B] :
          ( ~ relation(B)
          | ~ function(B)
          | relation_dom(relation_composition(B,A)) != relation_dom(B)
          | subset(relation_rng(B),relation_dom(A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f29]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X1)
      | ~ function(X1)
      | relation_dom(relation_composition(X1,X0)) != relation_dom(X1)
      | subset(relation_rng(X1),relation_dom(X0)) ),
    inference(cnf_transformation,[status(esa)],[f109]) ).

fof(f117,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ! [B] :
          ( ~ relation(B)
          | ~ function(B)
          | ~ one_to_one(relation_composition(B,A))
          | ~ subset(relation_rng(B),relation_dom(A))
          | one_to_one(B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f32]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X1)
      | ~ function(X1)
      | ~ one_to_one(relation_composition(X1,X0))
      | ~ subset(relation_rng(X1),relation_dom(X0))
      | one_to_one(X1) ),
    inference(cnf_transformation,[status(esa)],[f117]) ).

fof(f122,plain,
    ! [X0] : one_to_one(identity_relation(X0)),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f123,plain,
    ? [A] :
      ( relation(A)
      & function(A)
      & ? [B] :
          ( relation(B)
          & function(B)
          & relation_composition(A,B) = identity_relation(relation_dom(A)) )
      & ~ one_to_one(A) ),
    inference(pre_NNF_transformation,[status(esa)],[f36]) ).

fof(f124,plain,
    ( relation(sk0_9)
    & function(sk0_9)
    & relation(sk0_10)
    & function(sk0_10)
    & relation_composition(sk0_9,sk0_10) = identity_relation(relation_dom(sk0_9))
    & ~ one_to_one(sk0_9) ),
    inference(skolemization,[status(esa)],[f123]) ).

fof(f125,plain,
    relation(sk0_9),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f126,plain,
    function(sk0_9),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f127,plain,
    relation(sk0_10),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f128,plain,
    function(sk0_10),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f129,plain,
    relation_composition(sk0_9,sk0_10) = identity_relation(relation_dom(sk0_9)),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f130,plain,
    ~ one_to_one(sk0_9),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f136,plain,
    ( ! [A] : relation_dom(identity_relation(A)) = A
    & ! [A] : relation_rng(identity_relation(A)) = A ),
    inference(miniscoping,[status(esa)],[f39]) ).

fof(f137,plain,
    ! [X0] : relation_dom(identity_relation(X0)) = X0,
    inference(cnf_transformation,[status(esa)],[f136]) ).

fof(f147,plain,
    one_to_one(relation_composition(sk0_9,sk0_10)),
    inference(paramodulation,[status(thm)],[f129,f122]) ).

fof(f148,plain,
    relation_dom(relation_composition(sk0_9,sk0_10)) = relation_dom(sk0_9),
    inference(paramodulation,[status(thm)],[f129,f137]) ).

fof(f177,plain,
    ( spl0_4
  <=> relation(sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f179,plain,
    ( ~ relation(sk0_9)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f177]) ).

fof(f206,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f179,f125]) ).

fof(f207,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f206]) ).

fof(f223,plain,
    ( spl0_8
  <=> relation(sk0_10) ),
    introduced(split_symbol_definition) ).

fof(f225,plain,
    ( ~ relation(sk0_10)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f223]) ).

fof(f230,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f225,f127]) ).

fof(f231,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f230]) ).

fof(f297,plain,
    ( spl0_13
  <=> function(sk0_10) ),
    introduced(split_symbol_definition) ).

fof(f299,plain,
    ( ~ function(sk0_10)
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f297]) ).

fof(f300,plain,
    ( spl0_14
  <=> function(sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f302,plain,
    ( ~ function(sk0_9)
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f300]) ).

fof(f303,plain,
    ( spl0_15
  <=> subset(relation_rng(sk0_9),relation_dom(sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f304,plain,
    ( subset(relation_rng(sk0_9),relation_dom(sk0_10))
    | ~ spl0_15 ),
    inference(component_clause,[status(thm)],[f303]) ).

fof(f306,plain,
    ( ~ relation(sk0_10)
    | ~ function(sk0_10)
    | ~ relation(sk0_9)
    | ~ function(sk0_9)
    | subset(relation_rng(sk0_9),relation_dom(sk0_10)) ),
    inference(resolution,[status(thm)],[f110,f148]) ).

fof(f307,plain,
    ( ~ spl0_8
    | ~ spl0_13
    | ~ spl0_4
    | ~ spl0_14
    | spl0_15 ),
    inference(split_clause,[status(thm)],[f306,f223,f297,f177,f300,f303]) ).

fof(f313,plain,
    ( $false
    | spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f302,f126]) ).

fof(f314,plain,
    spl0_14,
    inference(contradiction_clause,[status(thm)],[f313]) ).

fof(f315,plain,
    ( $false
    | spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f299,f128]) ).

fof(f316,plain,
    spl0_13,
    inference(contradiction_clause,[status(thm)],[f315]) ).

fof(f324,plain,
    ( spl0_17
  <=> one_to_one(relation_composition(sk0_9,sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f326,plain,
    ( ~ one_to_one(relation_composition(sk0_9,sk0_10))
    | spl0_17 ),
    inference(component_clause,[status(thm)],[f324]) ).

fof(f327,plain,
    ( spl0_18
  <=> one_to_one(sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f328,plain,
    ( one_to_one(sk0_9)
    | ~ spl0_18 ),
    inference(component_clause,[status(thm)],[f327]) ).

fof(f330,plain,
    ( ~ relation(sk0_10)
    | ~ function(sk0_10)
    | ~ relation(sk0_9)
    | ~ function(sk0_9)
    | ~ one_to_one(relation_composition(sk0_9,sk0_10))
    | one_to_one(sk0_9)
    | ~ spl0_15 ),
    inference(resolution,[status(thm)],[f304,f118]) ).

fof(f331,plain,
    ( ~ spl0_8
    | ~ spl0_13
    | ~ spl0_4
    | ~ spl0_14
    | ~ spl0_17
    | spl0_18
    | ~ spl0_15 ),
    inference(split_clause,[status(thm)],[f330,f223,f297,f177,f300,f324,f327,f303]) ).

fof(f332,plain,
    ( $false
    | spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f326,f147]) ).

fof(f333,plain,
    spl0_17,
    inference(contradiction_clause,[status(thm)],[f332]) ).

fof(f334,plain,
    ( $false
    | ~ spl0_18 ),
    inference(forward_subsumption_resolution,[status(thm)],[f328,f130]) ).

fof(f335,plain,
    ~ spl0_18,
    inference(contradiction_clause,[status(thm)],[f334]) ).

fof(f336,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f207,f231,f307,f314,f316,f331,f333,f335]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SEU020+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n003.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 09:20:53 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.5.1
% 0.14/0.31  % Refutation found
% 0.14/0.31  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.55  % Elapsed time: 0.033937 seconds
% 0.14/0.55  % CPU time: 0.017390 seconds
% 0.14/0.55  % Memory used: 3.831 MB
%------------------------------------------------------------------------------