TSTP Solution File: SEU140+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU140+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 12:35:56 EDT 2023

% Result   : Theorem 0.10s 0.40s
% Output   : CNFRefutation 0.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   47 (   6 unt;   0 def)
%            Number of atoms       :  139 (   9 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  152 (  60   ~;  53   |;  30   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   4 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   78 (;  67   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A,B] :
      ( proper_subset(A,B)
    <=> ( subset(A,B)
        & A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f43,lemma,
    ! [A,B] :
      ( ~ ( ~ disjoint(A,B)
          & ! [C] :
              ~ ( in(C,A)
                & in(C,B) ) )
      & ~ ( ? [C] :
              ( in(C,A)
              & in(C,B) )
          & disjoint(A,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f51,conjecture,
    ! [A,B,C] :
      ( ( subset(A,B)
        & disjoint(B,C) )
     => disjoint(A,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f52,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( subset(A,B)
          & disjoint(B,C) )
       => disjoint(A,C) ),
    inference(negated_conjecture,[status(cth)],[f51]) ).

fof(f83,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f84,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)],[f83]) ).

fof(f85,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)],[f84]) ).

fof(f86,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)],[f85]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f86]) ).

fof(f112,plain,
    ! [A,B] :
      ( ( ~ proper_subset(A,B)
        | ( subset(A,B)
          & A != B ) )
      & ( proper_subset(A,B)
        | ~ subset(A,B)
        | A = B ) ),
    inference(NNF_transformation,[status(esa)],[f12]) ).

fof(f113,plain,
    ( ! [A,B] :
        ( ~ proper_subset(A,B)
        | ( subset(A,B)
          & A != B ) )
    & ! [A,B] :
        ( proper_subset(A,B)
        | ~ subset(A,B)
        | A = B ) ),
    inference(miniscoping,[status(esa)],[f112]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ~ proper_subset(X0,X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( proper_subset(X0,X1)
      | ~ subset(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f173,plain,
    ! [A,B] :
      ( ( disjoint(A,B)
        | ? [C] :
            ( in(C,A)
            & in(C,B) ) )
      & ( ! [C] :
            ( ~ in(C,A)
            | ~ in(C,B) )
        | ~ disjoint(A,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f43]) ).

fof(f174,plain,
    ( ! [A,B] :
        ( disjoint(A,B)
        | ? [C] :
            ( in(C,A)
            & in(C,B) ) )
    & ! [A,B] :
        ( ! [C] :
            ( ~ in(C,A)
            | ~ in(C,B) )
        | ~ disjoint(A,B) ) ),
    inference(miniscoping,[status(esa)],[f173]) ).

fof(f175,plain,
    ( ! [A,B] :
        ( disjoint(A,B)
        | ( in(sk0_8(B,A),A)
          & in(sk0_8(B,A),B) ) )
    & ! [A,B] :
        ( ! [C] :
            ( ~ in(C,A)
            | ~ in(C,B) )
        | ~ disjoint(A,B) ) ),
    inference(skolemization,[status(esa)],[f174]) ).

fof(f176,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | in(sk0_8(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f175]) ).

fof(f177,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | in(sk0_8(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f175]) ).

fof(f178,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,X1)
      | ~ in(X0,X2)
      | ~ disjoint(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f175]) ).

fof(f193,plain,
    ? [A,B,C] :
      ( subset(A,B)
      & disjoint(B,C)
      & ~ disjoint(A,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f52]) ).

fof(f194,plain,
    ? [A,C] :
      ( ? [B] :
          ( subset(A,B)
          & disjoint(B,C) )
      & ~ disjoint(A,C) ),
    inference(miniscoping,[status(esa)],[f193]) ).

fof(f195,plain,
    ( subset(sk0_10,sk0_12)
    & disjoint(sk0_12,sk0_11)
    & ~ disjoint(sk0_10,sk0_11) ),
    inference(skolemization,[status(esa)],[f194]) ).

fof(f196,plain,
    subset(sk0_10,sk0_12),
    inference(cnf_transformation,[status(esa)],[f195]) ).

fof(f197,plain,
    disjoint(sk0_12,sk0_11),
    inference(cnf_transformation,[status(esa)],[f195]) ).

fof(f198,plain,
    ~ disjoint(sk0_10,sk0_11),
    inference(cnf_transformation,[status(esa)],[f195]) ).

fof(f223,plain,
    ( spl0_0
  <=> sk0_12 = sk0_10 ),
    introduced(split_symbol_definition) ).

fof(f224,plain,
    ( sk0_12 = sk0_10
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f223]) ).

fof(f237,plain,
    ! [X0] :
      ( ~ in(X0,sk0_12)
      | ~ in(X0,sk0_11) ),
    inference(resolution,[status(thm)],[f178,f197]) ).

fof(f2380,plain,
    ( spl0_31
  <=> proper_subset(sk0_10,sk0_12) ),
    introduced(split_symbol_definition) ).

fof(f2381,plain,
    ( proper_subset(sk0_10,sk0_12)
    | ~ spl0_31 ),
    inference(component_clause,[status(thm)],[f2380]) ).

fof(f2383,plain,
    ( proper_subset(sk0_10,sk0_12)
    | sk0_10 = sk0_12 ),
    inference(resolution,[status(thm)],[f116,f196]) ).

fof(f2384,plain,
    ( spl0_31
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f2383,f2380,f223]) ).

fof(f2583,plain,
    ( disjoint(sk0_10,sk0_11)
    | ~ spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f224,f197]) ).

fof(f2584,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2583,f198]) ).

fof(f2585,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f2584]) ).

fof(f2586,plain,
    ( subset(sk0_10,sk0_12)
    | ~ spl0_31 ),
    inference(resolution,[status(thm)],[f2381,f114]) ).

fof(f2592,plain,
    ! [X0] :
      ( ~ in(X0,sk0_10)
      | in(X0,sk0_12)
      | ~ spl0_31 ),
    inference(resolution,[status(thm)],[f2586,f87]) ).

fof(f3635,plain,
    ! [X0] :
      ( disjoint(sk0_10,X0)
      | in(sk0_8(X0,sk0_10),sk0_12)
      | ~ spl0_31 ),
    inference(resolution,[status(thm)],[f176,f2592]) ).

fof(f3730,plain,
    ! [X0] :
      ( disjoint(sk0_10,X0)
      | ~ in(sk0_8(X0,sk0_10),sk0_11)
      | ~ spl0_31 ),
    inference(resolution,[status(thm)],[f3635,f237]) ).

fof(f3746,plain,
    ( spl0_61
  <=> disjoint(sk0_10,sk0_11) ),
    introduced(split_symbol_definition) ).

fof(f3747,plain,
    ( disjoint(sk0_10,sk0_11)
    | ~ spl0_61 ),
    inference(component_clause,[status(thm)],[f3746]) ).

fof(f3749,plain,
    ( disjoint(sk0_10,sk0_11)
    | disjoint(sk0_10,sk0_11)
    | ~ spl0_31 ),
    inference(resolution,[status(thm)],[f3730,f177]) ).

fof(f3750,plain,
    ( spl0_61
    | ~ spl0_31 ),
    inference(split_clause,[status(thm)],[f3749,f3746,f2380]) ).

fof(f3751,plain,
    ( $false
    | ~ spl0_61 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3747,f198]) ).

fof(f3752,plain,
    ~ spl0_61,
    inference(contradiction_clause,[status(thm)],[f3751]) ).

fof(f3753,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f2384,f2585,f3750,f3752]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem  : SEU140+2 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33  % Computer : n015.cluster.edu
% 0.10/0.33  % Model    : x86_64 x86_64
% 0.10/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33  % Memory   : 8042.1875MB
% 0.10/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33  % CPULimit : 300
% 0.10/0.33  % WCLimit  : 300
% 0.10/0.33  % DateTime : Tue May 30 09:33:49 EDT 2023
% 0.10/0.33  % CPUTime  : 
% 0.10/0.34  % Drodi V3.5.1
% 0.10/0.40  % Refutation found
% 0.10/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.33/0.62  % Elapsed time: 0.073595 seconds
% 0.33/0.62  % CPU time: 0.174174 seconds
% 0.33/0.62  % Memory used: 16.575 MB
%------------------------------------------------------------------------------