TSTP Solution File: SET200+3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 12:34:16 EDT 2023

% Result   : Theorem 0.09s 0.41s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   41 (  10 unt;   0 def)
%            Number of atoms       :  102 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  101 (  40   ~;  37   |;  16   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   72 (;  66   !;   6   ?)

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

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

fof(f6,conjecture,
    ! [B,C,D,E] :
      ( ( subset(B,C)
        & subset(D,E) )
     => subset(union(B,D),union(C,E)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,negated_conjecture,
    ~ ! [B,C,D,E] :
        ( ( subset(B,C)
          & subset(D,E) )
       => subset(union(B,D),union(C,E)) ),
    inference(negated_conjecture,[status(cth)],[f6]) ).

fof(f8,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)],[f1]) ).

fof(f9,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)],[f8]) ).

fof(f10,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f13,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f14,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)],[f13]) ).

fof(f15,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)],[f14]) ).

fof(f16,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)],[f15]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f29,plain,
    ? [B,C,D,E] :
      ( subset(B,C)
      & subset(D,E)
      & ~ subset(union(B,D),union(C,E)) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f30,plain,
    ( subset(sk0_2,sk0_3)
    & subset(sk0_4,sk0_5)
    & ~ subset(union(sk0_2,sk0_4),union(sk0_3,sk0_5)) ),
    inference(skolemization,[status(esa)],[f29]) ).

fof(f31,plain,
    subset(sk0_2,sk0_3),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f32,plain,
    subset(sk0_4,sk0_5),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f33,plain,
    ~ subset(union(sk0_2,sk0_4),union(sk0_3,sk0_5)),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ member(X0,sk0_4)
      | member(X0,sk0_5) ),
    inference(resolution,[status(thm)],[f17,f32]) ).

fof(f41,plain,
    ! [X0] :
      ( ~ member(X0,sk0_2)
      | member(X0,sk0_3) ),
    inference(resolution,[status(thm)],[f17,f31]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( subset(union(X0,X1),X2)
      | member(sk0_0(X2,union(X0,X1)),X0)
      | member(sk0_0(X2,union(X0,X1)),X1) ),
    inference(resolution,[status(thm)],[f18,f10]) ).

fof(f43,plain,
    ( spl0_0
  <=> member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f44,plain,
    ( member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_2)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f43]) ).

fof(f46,plain,
    ( spl0_1
  <=> member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f47,plain,
    ( member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_4)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f46]) ).

fof(f49,plain,
    ( member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_2)
    | member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_4) ),
    inference(resolution,[status(thm)],[f42,f33]) ).

fof(f50,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f49,f43,f46]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( subset(X0,union(X1,X2))
      | ~ member(sk0_0(union(X1,X2),X0),X2) ),
    inference(resolution,[status(thm)],[f19,f12]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( subset(X0,union(X1,X2))
      | ~ member(sk0_0(union(X1,X2),X0),X1) ),
    inference(resolution,[status(thm)],[f19,f11]) ).

fof(f124,plain,
    ~ member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_5),
    inference(resolution,[status(thm)],[f89,f33]) ).

fof(f128,plain,
    ~ member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_3),
    inference(resolution,[status(thm)],[f90,f33]) ).

fof(f142,plain,
    ~ member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_4),
    inference(resolution,[status(thm)],[f124,f40]) ).

fof(f146,plain,
    ~ member(sk0_0(union(sk0_3,sk0_5),union(sk0_2,sk0_4)),sk0_2),
    inference(resolution,[status(thm)],[f128,f41]) ).

fof(f147,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f146,f44]) ).

fof(f148,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f147]) ).

fof(f149,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f47,f142]) ).

fof(f150,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f149]) ).

fof(f151,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f50,f148,f150]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31  % Computer : n031.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Tue May 30 10:42:37 EDT 2023
% 0.09/0.32  % CPUTime  : 
% 0.09/0.32  % Drodi V3.5.1
% 0.09/0.41  % Refutation found
% 0.09/0.41  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43  % Elapsed time: 0.109570 seconds
% 0.15/0.43  % CPU time: 0.317172 seconds
% 0.15/0.43  % Memory used: 53.226 MB
%------------------------------------------------------------------------------