TSTP Solution File: SEU128+2 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU128+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 20:41:06 EDT 2024

% Result   : Theorem 69.34s 9.15s
% Output   : CNFRefutation 69.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   39 (   6 unt;   0 def)
%            Number of atoms       :  133 (   8 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  149 (  55   ~;  57   |;  28   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   75 (  68   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B,C] :
      ( C = set_intersection2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f24,conjecture,
    ! [A,B,C] :
      ( ( subset(A,B)
        & subset(A,C) )
     => subset(A,set_intersection2(B,C)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f25,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( subset(A,B)
          & subset(A,C) )
       => subset(A,set_intersection2(B,C)) ),
    inference(negated_conjecture,[status(cth)],[f24]) ).

fof(f61,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f62,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
      & ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f61]) ).

fof(f63,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(miniscoping,[status(esa)],[f62]) ).

fof(f64,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_2(B,A),A)
          & ~ in(sk0_2(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f63]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_2(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_2(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f68,plain,
    ! [A,B,C] :
      ( ( C != set_intersection2(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
            & ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
      & ( C = set_intersection2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & in(D,B) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f8]) ).

fof(f69,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_intersection2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & in(D,B) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f68]) ).

fof(f70,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_intersection2(A,B)
        | ( ( ~ in(sk0_3(C,B,A),C)
            | ~ in(sk0_3(C,B,A),A)
            | ~ in(sk0_3(C,B,A),B) )
          & ( in(sk0_3(C,B,A),C)
            | ( in(sk0_3(C,B,A),A)
              & in(sk0_3(C,B,A),B) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f69]) ).

fof(f73,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | in(X3,X0)
      | ~ in(X3,X1)
      | ~ in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f70]) ).

fof(f103,plain,
    ? [A,B,C] :
      ( subset(A,B)
      & subset(A,C)
      & ~ subset(A,set_intersection2(B,C)) ),
    inference(pre_NNF_transformation,[status(esa)],[f25]) ).

fof(f104,plain,
    ( subset(sk0_6,sk0_7)
    & subset(sk0_6,sk0_8)
    & ~ subset(sk0_6,set_intersection2(sk0_7,sk0_8)) ),
    inference(skolemization,[status(esa)],[f103]) ).

fof(f105,plain,
    subset(sk0_6,sk0_7),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f106,plain,
    subset(sk0_6,sk0_8),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f107,plain,
    ~ subset(sk0_6,set_intersection2(sk0_7,sk0_8)),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f146,plain,
    ! [X0,X1,X2] :
      ( in(X0,set_intersection2(X1,X2))
      | ~ in(X0,X1)
      | ~ in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f73]) ).

fof(f177,plain,
    ! [X0] :
      ( ~ in(X0,sk0_6)
      | in(X0,sk0_8) ),
    inference(resolution,[status(thm)],[f65,f106]) ).

fof(f178,plain,
    ! [X0] :
      ( ~ in(X0,sk0_6)
      | in(X0,sk0_7) ),
    inference(resolution,[status(thm)],[f65,f105]) ).

fof(f1881,plain,
    ! [X0,X1,X2] :
      ( subset(X0,set_intersection2(X1,X2))
      | ~ in(sk0_2(set_intersection2(X1,X2),X0),X1)
      | ~ in(sk0_2(set_intersection2(X1,X2),X0),X2) ),
    inference(resolution,[status(thm)],[f67,f146]) ).

fof(f8115,plain,
    ( spl0_109
  <=> in(sk0_2(set_intersection2(sk0_7,sk0_8),sk0_6),sk0_7) ),
    introduced(split_symbol_definition) ).

fof(f8117,plain,
    ( ~ in(sk0_2(set_intersection2(sk0_7,sk0_8),sk0_6),sk0_7)
    | spl0_109 ),
    inference(component_clause,[status(thm)],[f8115]) ).

fof(f8118,plain,
    ( spl0_110
  <=> in(sk0_2(set_intersection2(sk0_7,sk0_8),sk0_6),sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f8120,plain,
    ( ~ in(sk0_2(set_intersection2(sk0_7,sk0_8),sk0_6),sk0_8)
    | spl0_110 ),
    inference(component_clause,[status(thm)],[f8118]) ).

fof(f8121,plain,
    ( ~ in(sk0_2(set_intersection2(sk0_7,sk0_8),sk0_6),sk0_7)
    | ~ in(sk0_2(set_intersection2(sk0_7,sk0_8),sk0_6),sk0_8) ),
    inference(resolution,[status(thm)],[f1881,f107]) ).

fof(f8122,plain,
    ( ~ spl0_109
    | ~ spl0_110 ),
    inference(split_clause,[status(thm)],[f8121,f8115,f8118]) ).

fof(f8963,plain,
    ( ~ in(sk0_2(set_intersection2(sk0_7,sk0_8),sk0_6),sk0_6)
    | spl0_109 ),
    inference(resolution,[status(thm)],[f8117,f178]) ).

fof(f9187,plain,
    ( subset(sk0_6,set_intersection2(sk0_7,sk0_8))
    | spl0_109 ),
    inference(resolution,[status(thm)],[f8963,f66]) ).

fof(f9188,plain,
    ( $false
    | spl0_109 ),
    inference(forward_subsumption_resolution,[status(thm)],[f9187,f107]) ).

fof(f9189,plain,
    spl0_109,
    inference(contradiction_clause,[status(thm)],[f9188]) ).

fof(f9190,plain,
    ( ~ in(sk0_2(set_intersection2(sk0_7,sk0_8),sk0_6),sk0_6)
    | spl0_110 ),
    inference(resolution,[status(thm)],[f8120,f177]) ).

fof(f11407,plain,
    ( subset(sk0_6,set_intersection2(sk0_7,sk0_8))
    | spl0_110 ),
    inference(resolution,[status(thm)],[f9190,f66]) ).

fof(f11408,plain,
    ( $false
    | spl0_110 ),
    inference(forward_subsumption_resolution,[status(thm)],[f11407,f107]) ).

fof(f11409,plain,
    spl0_110,
    inference(contradiction_clause,[status(thm)],[f11408]) ).

fof(f11410,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f8122,f9189,f11409]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU128+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n010.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Apr 29 19:35:50 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 69.34/9.15  % Refutation found
% 69.34/9.15  % SZS status Theorem for theBenchmark: Theorem is valid
% 69.34/9.15  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 70.33/9.27  % Elapsed time: 8.904695 seconds
% 70.33/9.27  % CPU time: 70.176547 seconds
% 70.33/9.27  % Total memory used: 369.002 MB
% 70.33/9.27  % Net memory used: 357.475 MB
%------------------------------------------------------------------------------