TSTP Solution File: SET587+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 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 20:39:53 EDT 2024

% Result   : Theorem 0.11s 0.36s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   49 (   4 unt;   0 def)
%            Number of atoms       :  141 (  19 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  153 (  61   ~;  64   |;  18   &)
%                                         (   8 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   85 (  79   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [B,C,D] :
      ( member(D,difference(B,C))
    <=> ( member(D,B)
        & ~ member(D,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [B] : ~ member(B,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [B,C] :
      ( B = C
    <=> ( subset(B,C)
        & subset(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,conjecture,
    ! [B,C] :
      ( difference(B,C) = empty_set
    <=> subset(B,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ ! [B,C] :
        ( difference(B,C) = empty_set
      <=> subset(B,C) ),
    inference(negated_conjecture,[status(cth)],[f9]) ).

fof(f16,plain,
    ! [B,C,D] :
      ( ( ~ member(D,difference(B,C))
        | ( member(D,B)
          & ~ member(D,C) ) )
      & ( member(D,difference(B,C))
        | ~ member(D,B)
        | member(D,C) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f17,plain,
    ( ! [B,C,D] :
        ( ~ member(D,difference(B,C))
        | ( member(D,B)
          & ~ member(D,C) ) )
    & ! [B,C,D] :
        ( member(D,difference(B,C))
        | ~ member(D,B)
        | member(D,C) ) ),
    inference(miniscoping,[status(esa)],[f16]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,difference(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,difference(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X1,X2))
      | ~ member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f21,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f22,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

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

fof(f24,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)],[f23]) ).

fof(f25,plain,
    ( ! [B,C] :
        ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
    & ! [B,C] :
        ( subset(B,C)
        | ( member(sk0_1(C,B),B)
          & ~ member(sk0_1(C,B),C) ) ) ),
    inference(skolemization,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_1(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f29,plain,
    ! [B,C] :
      ( ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
      & ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(NNF_transformation,[status(esa)],[f5]) ).

fof(f30,plain,
    ( ! [B,C] :
        ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
    & ! [B,C] :
        ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(miniscoping,[status(esa)],[f29]) ).

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

fof(f47,plain,
    ? [B,C] :
      ( difference(B,C) = empty_set
    <~> subset(B,C) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f48,plain,
    ? [B,C] :
      ( ( difference(B,C) = empty_set
        | subset(B,C) )
      & ( difference(B,C) != empty_set
        | ~ subset(B,C) ) ),
    inference(NNF_transformation,[status(esa)],[f47]) ).

fof(f49,plain,
    ( ( difference(sk0_4,sk0_5) = empty_set
      | subset(sk0_4,sk0_5) )
    & ( difference(sk0_4,sk0_5) != empty_set
      | ~ subset(sk0_4,sk0_5) ) ),
    inference(skolemization,[status(esa)],[f48]) ).

fof(f50,plain,
    ( difference(sk0_4,sk0_5) = empty_set
    | subset(sk0_4,sk0_5) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    ( difference(sk0_4,sk0_5) != empty_set
    | ~ subset(sk0_4,sk0_5) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f52,plain,
    ( spl0_0
  <=> difference(sk0_4,sk0_5) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f53,plain,
    ( difference(sk0_4,sk0_5) = empty_set
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f52]) ).

fof(f55,plain,
    ( spl0_1
  <=> subset(sk0_4,sk0_5) ),
    introduced(split_symbol_definition) ).

fof(f56,plain,
    ( subset(sk0_4,sk0_5)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f55]) ).

fof(f58,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f50,f52,f55]) ).

fof(f59,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f51,f52,f55]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( subset(difference(X0,X1),X2)
      | ~ member(sk0_1(X2,difference(X0,X1)),X1) ),
    inference(resolution,[status(thm)],[f27,f19]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( subset(difference(X0,X1),X2)
      | member(sk0_1(X2,difference(X0,X1)),X0) ),
    inference(resolution,[status(thm)],[f27,f18]) ).

fof(f65,plain,
    ! [X0] : subset(empty_set,X0),
    inference(resolution,[status(thm)],[f27,f21]) ).

fof(f70,plain,
    ! [X0] :
      ( X0 = empty_set
      | ~ subset(X0,empty_set) ),
    inference(resolution,[status(thm)],[f65,f33]) ).

fof(f234,plain,
    ! [X0] :
      ( member(X0,empty_set)
      | ~ member(X0,sk0_4)
      | member(X0,sk0_5)
      | ~ spl0_0 ),
    inference(paramodulation,[status(thm)],[f53,f20]) ).

fof(f235,plain,
    ! [X0] :
      ( ~ member(X0,sk0_4)
      | member(X0,sk0_5)
      | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f234,f21]) ).

fof(f241,plain,
    ! [X0] :
      ( member(sk0_1(X0,sk0_4),sk0_5)
      | subset(sk0_4,X0)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f235,f27]) ).

fof(f278,plain,
    ( subset(sk0_4,sk0_5)
    | subset(sk0_4,sk0_5)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f241,f28]) ).

fof(f279,plain,
    ( spl0_1
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f278,f55,f52]) ).

fof(f280,plain,
    ! [X0] :
      ( ~ member(X0,sk0_4)
      | member(X0,sk0_5)
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f56,f26]) ).

fof(f291,plain,
    ! [X0,X1] :
      ( member(sk0_1(X0,difference(sk0_4,X1)),sk0_5)
      | subset(difference(sk0_4,X1),X0)
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f280,f64]) ).

fof(f297,plain,
    ! [X0] :
      ( subset(difference(sk0_4,sk0_5),X0)
      | subset(difference(sk0_4,sk0_5),X0)
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f291,f63]) ).

fof(f298,plain,
    ! [X0] :
      ( subset(difference(sk0_4,sk0_5),X0)
      | ~ spl0_1 ),
    inference(duplicate_literals_removal,[status(esa)],[f297]) ).

fof(f303,plain,
    ( difference(sk0_4,sk0_5) = empty_set
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f298,f70]) ).

fof(f304,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f303,f52,f55]) ).

fof(f307,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f58,f59,f279,f304]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET587+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n010.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon Apr 29 21:13:50 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  % Drodi V3.6.0
% 0.11/0.36  % Refutation found
% 0.11/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.36  % Elapsed time: 0.024841 seconds
% 0.11/0.36  % CPU time: 0.088621 seconds
% 0.11/0.36  % Total memory used: 18.813 MB
% 0.11/0.36  % Net memory used: 18.668 MB
%------------------------------------------------------------------------------