TSTP Solution File: SEU032+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 12:35:43 EDT 2023

% Result   : Theorem 0.19s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   73 (   9 unt;   0 def)
%            Number of atoms       :  223 (  41 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  254 ( 104   ~; 103   |;  22   &)
%                                         (  11 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   16 (  14 usr;  12 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   23 (;  22   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( relation(function_inverse(A))
        & function(function_inverse(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( one_to_one(A)
       => ( relation_rng(A) = relation_dom(function_inverse(A))
          & relation_dom(A) = relation_rng(function_inverse(A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f38,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( one_to_one(A)
       => ( relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A))
          & relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f39,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( one_to_one(A)
       => one_to_one(function_inverse(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f40,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B] :
          ( ( relation(B)
            & function(B) )
         => ( ( one_to_one(A)
              & relation_rng(A) = relation_dom(B)
              & relation_composition(A,B) = identity_relation(relation_dom(A)) )
           => B = function_inverse(A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f41,conjecture,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( one_to_one(A)
       => function_inverse(function_inverse(A)) = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f42,negated_conjecture,
    ~ ! [A] :
        ( ( relation(A)
          & function(A) )
       => ( one_to_one(A)
         => function_inverse(function_inverse(A)) = A ) ),
    inference(negated_conjecture,[status(cth)],[f41]) ).

fof(f56,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ( relation(function_inverse(A))
        & function(function_inverse(A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | relation(function_inverse(X0)) ),
    inference(cnf_transformation,[status(esa)],[f56]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | function(function_inverse(X0)) ),
    inference(cnf_transformation,[status(esa)],[f56]) ).

fof(f137,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ~ one_to_one(A)
      | ( relation_rng(A) = relation_dom(function_inverse(A))
        & relation_dom(A) = relation_rng(function_inverse(A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f36]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0)
      | relation_rng(X0) = relation_dom(function_inverse(X0)) ),
    inference(cnf_transformation,[status(esa)],[f137]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0)
      | relation_dom(X0) = relation_rng(function_inverse(X0)) ),
    inference(cnf_transformation,[status(esa)],[f137]) ).

fof(f143,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ~ one_to_one(A)
      | ( relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A))
        & relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f38]) ).

fof(f145,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0)
      | relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) ),
    inference(cnf_transformation,[status(esa)],[f143]) ).

fof(f146,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ~ one_to_one(A)
      | one_to_one(function_inverse(A)) ),
    inference(pre_NNF_transformation,[status(esa)],[f39]) ).

fof(f147,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0)
      | one_to_one(function_inverse(X0)) ),
    inference(cnf_transformation,[status(esa)],[f146]) ).

fof(f148,plain,
    ! [A] :
      ( ~ relation(A)
      | ~ function(A)
      | ! [B] :
          ( ~ relation(B)
          | ~ function(B)
          | ~ one_to_one(A)
          | relation_rng(A) != relation_dom(B)
          | relation_composition(A,B) != identity_relation(relation_dom(A))
          | B = function_inverse(A) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f40]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ~ relation(X1)
      | ~ function(X1)
      | ~ one_to_one(X0)
      | relation_rng(X0) != relation_dom(X1)
      | relation_composition(X0,X1) != identity_relation(relation_dom(X0))
      | X1 = function_inverse(X0) ),
    inference(cnf_transformation,[status(esa)],[f148]) ).

fof(f150,plain,
    ? [A] :
      ( relation(A)
      & function(A)
      & one_to_one(A)
      & function_inverse(function_inverse(A)) != A ),
    inference(pre_NNF_transformation,[status(esa)],[f42]) ).

fof(f151,plain,
    ( relation(sk0_11)
    & function(sk0_11)
    & one_to_one(sk0_11)
    & function_inverse(function_inverse(sk0_11)) != sk0_11 ),
    inference(skolemization,[status(esa)],[f150]) ).

fof(f152,plain,
    relation(sk0_11),
    inference(cnf_transformation,[status(esa)],[f151]) ).

fof(f153,plain,
    function(sk0_11),
    inference(cnf_transformation,[status(esa)],[f151]) ).

fof(f154,plain,
    one_to_one(sk0_11),
    inference(cnf_transformation,[status(esa)],[f151]) ).

fof(f155,plain,
    function_inverse(function_inverse(sk0_11)) != sk0_11,
    inference(cnf_transformation,[status(esa)],[f151]) ).

fof(f168,plain,
    ( spl0_1
  <=> one_to_one(sk0_11) ),
    introduced(split_symbol_definition) ).

fof(f170,plain,
    ( ~ one_to_one(sk0_11)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f168]) ).

fof(f529,plain,
    ( spl0_15
  <=> relation(sk0_11) ),
    introduced(split_symbol_definition) ).

fof(f531,plain,
    ( ~ relation(sk0_11)
    | spl0_15 ),
    inference(component_clause,[status(thm)],[f529]) ).

fof(f532,plain,
    ( spl0_16
  <=> function(sk0_11) ),
    introduced(split_symbol_definition) ).

fof(f534,plain,
    ( ~ function(sk0_11)
    | spl0_16 ),
    inference(component_clause,[status(thm)],[f532]) ).

fof(f535,plain,
    ( spl0_17
  <=> relation_rng(sk0_11) = relation_dom(function_inverse(sk0_11)) ),
    introduced(split_symbol_definition) ).

fof(f536,plain,
    ( relation_rng(sk0_11) = relation_dom(function_inverse(sk0_11))
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f535]) ).

fof(f538,plain,
    ( ~ relation(sk0_11)
    | ~ function(sk0_11)
    | relation_rng(sk0_11) = relation_dom(function_inverse(sk0_11)) ),
    inference(resolution,[status(thm)],[f138,f154]) ).

fof(f539,plain,
    ( ~ spl0_15
    | ~ spl0_16
    | spl0_17 ),
    inference(split_clause,[status(thm)],[f538,f529,f532,f535]) ).

fof(f542,plain,
    ( $false
    | spl0_16 ),
    inference(forward_subsumption_resolution,[status(thm)],[f534,f153]) ).

fof(f543,plain,
    spl0_16,
    inference(contradiction_clause,[status(thm)],[f542]) ).

fof(f544,plain,
    ( $false
    | spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f531,f152]) ).

fof(f545,plain,
    spl0_15,
    inference(contradiction_clause,[status(thm)],[f544]) ).

fof(f565,plain,
    ( spl0_21
  <=> relation(function_inverse(sk0_11)) ),
    introduced(split_symbol_definition) ).

fof(f567,plain,
    ( ~ relation(function_inverse(sk0_11))
    | spl0_21 ),
    inference(component_clause,[status(thm)],[f565]) ).

fof(f570,plain,
    ( ~ relation(sk0_11)
    | ~ function(sk0_11)
    | spl0_21 ),
    inference(resolution,[status(thm)],[f567,f57]) ).

fof(f571,plain,
    ( ~ spl0_15
    | ~ spl0_16
    | spl0_21 ),
    inference(split_clause,[status(thm)],[f570,f529,f532,f565]) ).

fof(f1214,plain,
    ( spl0_55
  <=> relation_dom(sk0_11) = relation_rng(function_inverse(sk0_11)) ),
    introduced(split_symbol_definition) ).

fof(f1215,plain,
    ( relation_dom(sk0_11) = relation_rng(function_inverse(sk0_11))
    | ~ spl0_55 ),
    inference(component_clause,[status(thm)],[f1214]) ).

fof(f1217,plain,
    ( ~ relation(sk0_11)
    | ~ function(sk0_11)
    | relation_dom(sk0_11) = relation_rng(function_inverse(sk0_11)) ),
    inference(resolution,[status(thm)],[f139,f154]) ).

fof(f1218,plain,
    ( ~ spl0_15
    | ~ spl0_16
    | spl0_55 ),
    inference(split_clause,[status(thm)],[f1217,f529,f532,f1214]) ).

fof(f1469,plain,
    ( spl0_77
  <=> function(function_inverse(sk0_11)) ),
    introduced(split_symbol_definition) ).

fof(f1471,plain,
    ( ~ function(function_inverse(sk0_11))
    | spl0_77 ),
    inference(component_clause,[status(thm)],[f1469]) ).

fof(f1484,plain,
    ( ~ relation(sk0_11)
    | ~ function(sk0_11)
    | spl0_77 ),
    inference(resolution,[status(thm)],[f1471,f58]) ).

fof(f1485,plain,
    ( ~ spl0_15
    | ~ spl0_16
    | spl0_77 ),
    inference(split_clause,[status(thm)],[f1484,f529,f532,f1469]) ).

fof(f2136,plain,
    ( spl0_97
  <=> relation_composition(function_inverse(sk0_11),sk0_11) = identity_relation(relation_rng(sk0_11)) ),
    introduced(split_symbol_definition) ).

fof(f2137,plain,
    ( relation_composition(function_inverse(sk0_11),sk0_11) = identity_relation(relation_rng(sk0_11))
    | ~ spl0_97 ),
    inference(component_clause,[status(thm)],[f2136]) ).

fof(f2139,plain,
    ( ~ relation(sk0_11)
    | ~ function(sk0_11)
    | relation_composition(function_inverse(sk0_11),sk0_11) = identity_relation(relation_rng(sk0_11)) ),
    inference(resolution,[status(thm)],[f145,f154]) ).

fof(f2140,plain,
    ( ~ spl0_15
    | ~ spl0_16
    | spl0_97 ),
    inference(split_clause,[status(thm)],[f2139,f529,f532,f2136]) ).

fof(f2273,plain,
    ( spl0_130
  <=> one_to_one(function_inverse(sk0_11)) ),
    introduced(split_symbol_definition) ).

fof(f2275,plain,
    ( ~ one_to_one(function_inverse(sk0_11))
    | spl0_130 ),
    inference(component_clause,[status(thm)],[f2273]) ).

fof(f2276,plain,
    ( spl0_131
  <=> relation_composition(function_inverse(sk0_11),sk0_11) = identity_relation(relation_dom(function_inverse(sk0_11))) ),
    introduced(split_symbol_definition) ).

fof(f2278,plain,
    ( relation_composition(function_inverse(sk0_11),sk0_11) != identity_relation(relation_dom(function_inverse(sk0_11)))
    | spl0_131 ),
    inference(component_clause,[status(thm)],[f2276]) ).

fof(f2279,plain,
    ( spl0_132
  <=> sk0_11 = function_inverse(function_inverse(sk0_11)) ),
    introduced(split_symbol_definition) ).

fof(f2280,plain,
    ( sk0_11 = function_inverse(function_inverse(sk0_11))
    | ~ spl0_132 ),
    inference(component_clause,[status(thm)],[f2279]) ).

fof(f2282,plain,
    ( ~ relation(function_inverse(sk0_11))
    | ~ function(function_inverse(sk0_11))
    | ~ relation(sk0_11)
    | ~ function(sk0_11)
    | ~ one_to_one(function_inverse(sk0_11))
    | relation_composition(function_inverse(sk0_11),sk0_11) != identity_relation(relation_dom(function_inverse(sk0_11)))
    | sk0_11 = function_inverse(function_inverse(sk0_11))
    | ~ spl0_55 ),
    inference(resolution,[status(thm)],[f149,f1215]) ).

fof(f2283,plain,
    ( ~ spl0_21
    | ~ spl0_77
    | ~ spl0_15
    | ~ spl0_16
    | ~ spl0_130
    | ~ spl0_131
    | spl0_132
    | ~ spl0_55 ),
    inference(split_clause,[status(thm)],[f2282,f565,f1469,f529,f532,f2273,f2276,f2279,f1214]) ).

fof(f2510,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f170,f154]) ).

fof(f2511,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f2510]) ).

fof(f2536,plain,
    ( ~ relation(sk0_11)
    | ~ function(sk0_11)
    | ~ one_to_one(sk0_11)
    | spl0_130 ),
    inference(resolution,[status(thm)],[f2275,f147]) ).

fof(f2537,plain,
    ( ~ spl0_15
    | ~ spl0_16
    | ~ spl0_1
    | spl0_130 ),
    inference(split_clause,[status(thm)],[f2536,f529,f532,f168,f2273]) ).

fof(f2718,plain,
    ( relation_composition(function_inverse(sk0_11),sk0_11) != identity_relation(relation_rng(sk0_11))
    | spl0_131
    | ~ spl0_17 ),
    inference(paramodulation,[status(thm)],[f536,f2278]) ).

fof(f2719,plain,
    ( $false
    | ~ spl0_97
    | spl0_131
    | ~ spl0_17 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2718,f2137]) ).

fof(f2720,plain,
    ( ~ spl0_97
    | spl0_131
    | ~ spl0_17 ),
    inference(contradiction_clause,[status(thm)],[f2719]) ).

fof(f2721,plain,
    ( $false
    | ~ spl0_132 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2280,f155]) ).

fof(f2722,plain,
    ~ spl0_132,
    inference(contradiction_clause,[status(thm)],[f2721]) ).

fof(f2723,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f539,f543,f545,f571,f1218,f1485,f2140,f2283,f2511,f2537,f2720,f2722]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 09:08:12 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 0.19/0.38  % Refutation found
% 0.19/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.39  % Elapsed time: 0.049876 seconds
% 0.19/0.39  % CPU time: 0.245617 seconds
% 0.19/0.39  % Memory used: 20.744 MB
%------------------------------------------------------------------------------