TSTP Solution File: SET594+3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n017.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 12:34:45 EDT 2023

% Result   : Theorem 3.89s 0.85s
% Output   : CNFRefutation 3.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   38 (   5 unt;   0 def)
%            Number of atoms       :  109 (   5 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  109 (  38   ~;  46   |;  17   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   82 (;  77   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [B,C,D] :
      ( member(D,union(B,C))
    <=> ( member(D,B)
        | member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [B,C,D] :
      ( member(D,intersection(B,C))
    <=> ( member(D,B)
        & member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,conjecture,
    ! [B,C,D] :
      ( union(intersection(B,C),intersection(B,D)) = B
     => subset(B,union(C,D)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ ! [B,C,D] :
        ( union(intersection(B,C),intersection(B,D)) = B
       => subset(B,union(C,D)) ),
    inference(negated_conjecture,[status(cth)],[f9]) ).

fof(f11,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f12,plain,
    ! [B,C] :
      ( ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
      & ( subset(B,C)
        | ? [D] :
            ( member(D,B)
            & ~ member(D,C) ) ) ),
    inference(NNF_transformation,[status(esa)],[f11]) ).

fof(f13,plain,
    ( ! [B,C] :
        ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
    & ! [B,C] :
        ( subset(B,C)
        | ? [D] :
            ( member(D,B)
            & ~ member(D,C) ) ) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f14,plain,
    ( ! [B,C] :
        ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
    & ! [B,C] :
        ( subset(B,C)
        | ( member(sk0_0(C,B),B)
          & ~ member(sk0_0(C,B),C) ) ) ),
    inference(skolemization,[status(esa)],[f13]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f18,plain,
    ! [B,C,D] :
      ( ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) )
      & ( member(D,union(B,C))
        | ( ~ member(D,B)
          & ~ member(D,C) ) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f19,plain,
    ( ! [B,C,D] :
        ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) )
    & ! [B,C,D] :
        ( member(D,union(B,C))
        | ( ~ member(D,B)
          & ~ member(D,C) ) ) ),
    inference(miniscoping,[status(esa)],[f18]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f23,plain,
    ! [B,C,D] :
      ( ( ~ member(D,intersection(B,C))
        | ( member(D,B)
          & member(D,C) ) )
      & ( member(D,intersection(B,C))
        | ~ member(D,B)
        | ~ member(D,C) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f24,plain,
    ( ! [B,C,D] :
        ( ~ member(D,intersection(B,C))
        | ( member(D,B)
          & member(D,C) ) )
    & ! [B,C,D] :
        ( member(D,intersection(B,C))
        | ~ member(D,B)
        | ~ member(D,C) ) ),
    inference(miniscoping,[status(esa)],[f23]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f43,plain,
    ? [B,C,D] :
      ( union(intersection(B,C),intersection(B,D)) = B
      & ~ subset(B,union(C,D)) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f44,plain,
    ( union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = sk0_2
    & ~ subset(sk0_2,union(sk0_3,sk0_4)) ),
    inference(skolemization,[status(esa)],[f43]) ).

fof(f45,plain,
    union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = sk0_2,
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f46,plain,
    ~ subset(sk0_2,union(sk0_3,sk0_4)),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ member(X0,sk0_2)
      | member(X0,intersection(sk0_2,sk0_3))
      | member(X0,intersection(sk0_2,sk0_4)) ),
    inference(paramodulation,[status(thm)],[f45,f20]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( subset(X0,union(X1,X2))
      | ~ member(sk0_0(union(X1,X2),X0),X2) ),
    inference(resolution,[status(thm)],[f17,f22]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( subset(X0,union(X1,X2))
      | ~ member(sk0_0(union(X1,X2),X0),X1) ),
    inference(resolution,[status(thm)],[f17,f21]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ member(X0,sk0_2)
      | member(X0,intersection(sk0_2,sk0_3))
      | member(X0,sk0_4) ),
    inference(resolution,[status(thm)],[f59,f26]) ).

fof(f178,plain,
    ! [X0] :
      ( member(sk0_0(X0,sk0_2),intersection(sk0_2,sk0_3))
      | member(sk0_0(X0,sk0_2),sk0_4)
      | subset(sk0_2,X0) ),
    inference(resolution,[status(thm)],[f139,f16]) ).

fof(f189,plain,
    ! [X0] :
      ( member(sk0_0(X0,sk0_2),sk0_4)
      | subset(sk0_2,X0)
      | member(sk0_0(X0,sk0_2),sk0_3) ),
    inference(resolution,[status(thm)],[f178,f26]) ).

fof(f795,plain,
    ! [X0] :
      ( subset(sk0_2,union(X0,sk0_4))
      | subset(sk0_2,union(X0,sk0_4))
      | member(sk0_0(union(X0,sk0_4),sk0_2),sk0_3) ),
    inference(resolution,[status(thm)],[f70,f189]) ).

fof(f796,plain,
    ! [X0] :
      ( subset(sk0_2,union(X0,sk0_4))
      | member(sk0_0(union(X0,sk0_4),sk0_2),sk0_3) ),
    inference(duplicate_literals_removal,[status(esa)],[f795]) ).

fof(f938,plain,
    ( spl0_36
  <=> subset(sk0_2,union(sk0_3,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f939,plain,
    ( subset(sk0_2,union(sk0_3,sk0_4))
    | ~ spl0_36 ),
    inference(component_clause,[status(thm)],[f938]) ).

fof(f941,plain,
    ( subset(sk0_2,union(sk0_3,sk0_4))
    | subset(sk0_2,union(sk0_3,sk0_4)) ),
    inference(resolution,[status(thm)],[f71,f796]) ).

fof(f942,plain,
    spl0_36,
    inference(split_clause,[status(thm)],[f941,f938]) ).

fof(f970,plain,
    ( $false
    | ~ spl0_36 ),
    inference(forward_subsumption_resolution,[status(thm)],[f939,f46]) ).

fof(f971,plain,
    ~ spl0_36,
    inference(contradiction_clause,[status(thm)],[f970]) ).

fof(f972,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f942,f971]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n017.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 09:40:10 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 3.89/0.85  % Refutation found
% 3.89/0.85  % SZS status Theorem for theBenchmark: Theorem is valid
% 3.89/0.85  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.89/0.87  % Elapsed time: 0.529520 seconds
% 3.89/0.87  % CPU time: 4.018348 seconds
% 3.89/0.87  % Memory used: 79.779 MB
%------------------------------------------------------------------------------