TSTP Solution File: SEU128+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU128+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n024.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 0.10s 0.33s
% Output   : CNFRefutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   34 (   6 unt;   0 def)
%            Number of atoms       :  125 (   8 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  139 (  48   ~;  55   |;  28   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :   79 (  72   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,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(f12,conjecture,
    ! [A,B,C] :
      ( ( subset(A,B)
        & subset(A,C) )
     => subset(A,set_intersection2(B,C)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( subset(A,B)
          & subset(A,C) )
       => subset(A,set_intersection2(B,C)) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f21,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f22,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)],[f21]) ).

fof(f23,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)],[f22]) ).

fof(f24,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_0(B,A),A)
          & ~ in(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f28,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)],[f4]) ).

fof(f29,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)],[f28]) ).

fof(f30,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_1(C,B,A),C)
            | ~ in(sk0_1(C,B,A),A)
            | ~ in(sk0_1(C,B,A),B) )
          & ( in(sk0_1(C,B,A),C)
            | ( in(sk0_1(C,B,A),A)
              & in(sk0_1(C,B,A),B) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f29]) ).

fof(f33,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | in(X3,X0)
      | ~ in(X3,X1)
      | ~ in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f46,plain,
    ? [A,B,C] :
      ( subset(A,B)
      & subset(A,C)
      & ~ subset(A,set_intersection2(B,C)) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f47,plain,
    ( subset(sk0_4,sk0_5)
    & subset(sk0_4,sk0_6)
    & ~ subset(sk0_4,set_intersection2(sk0_5,sk0_6)) ),
    inference(skolemization,[status(esa)],[f46]) ).

fof(f48,plain,
    subset(sk0_4,sk0_5),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f49,plain,
    subset(sk0_4,sk0_6),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f50,plain,
    ~ subset(sk0_4,set_intersection2(sk0_5,sk0_6)),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( in(X0,set_intersection2(X1,X2))
      | ~ in(X0,X1)
      | ~ in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f33]) ).

fof(f72,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
      | ~ subset(X0,X2)
      | in(sk0_0(X1,X0),X2) ),
    inference(resolution,[status(thm)],[f26,f25]) ).

fof(f90,plain,
    ! [X0] :
      ( subset(sk0_4,X0)
      | in(sk0_0(X0,sk0_4),sk0_6) ),
    inference(resolution,[status(thm)],[f72,f49]) ).

fof(f91,plain,
    ! [X0] :
      ( subset(sk0_4,X0)
      | in(sk0_0(X0,sk0_4),sk0_5) ),
    inference(resolution,[status(thm)],[f72,f48]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( subset(sk0_4,X0)
      | in(sk0_0(X0,sk0_4),set_intersection2(X1,sk0_6))
      | ~ in(sk0_0(X0,sk0_4),X1) ),
    inference(resolution,[status(thm)],[f90,f62]) ).

fof(f153,plain,
    ! [X0] :
      ( subset(sk0_4,X0)
      | in(sk0_0(X0,sk0_4),set_intersection2(sk0_5,sk0_6))
      | subset(sk0_4,X0) ),
    inference(resolution,[status(thm)],[f99,f91]) ).

fof(f154,plain,
    ! [X0] :
      ( subset(sk0_4,X0)
      | in(sk0_0(X0,sk0_4),set_intersection2(sk0_5,sk0_6)) ),
    inference(duplicate_literals_removal,[status(esa)],[f153]) ).

fof(f163,plain,
    ( spl0_2
  <=> subset(sk0_4,set_intersection2(sk0_5,sk0_6)) ),
    introduced(split_symbol_definition) ).

fof(f164,plain,
    ( subset(sk0_4,set_intersection2(sk0_5,sk0_6))
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f163]) ).

fof(f166,plain,
    ( subset(sk0_4,set_intersection2(sk0_5,sk0_6))
    | subset(sk0_4,set_intersection2(sk0_5,sk0_6)) ),
    inference(resolution,[status(thm)],[f154,f27]) ).

fof(f167,plain,
    spl0_2,
    inference(split_clause,[status(thm)],[f166,f163]) ).

fof(f173,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f164,f50]) ).

fof(f174,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f173]) ).

fof(f175,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f167,f174]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEU128+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n024.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Mon Apr 29 19:46:21 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.6.0
% 0.10/0.33  % Refutation found
% 0.10/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.35  % Elapsed time: 0.020974 seconds
% 0.16/0.35  % CPU time: 0.032043 seconds
% 0.16/0.35  % Total memory used: 13.060 MB
% 0.16/0.35  % Net memory used: 12.994 MB
%------------------------------------------------------------------------------