TSTP Solution File: SET577+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET577+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n016.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 20:39:51 EDT 2024

% Result   : Theorem 0.20s 0.57s
% Output   : CNFRefutation 1.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   77 (  11 unt;   0 def)
%            Number of atoms       :  218 (  21 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  218 (  77   ~; 100   |;  25   &)
%                                         (  13 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   7 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  122 ( 111   !;  11   ?)

% 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] :
      ( B = C
    <=> ( subset(B,C)
        & subset(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [B,C] : union(B,C) = union(C,B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f7,conjecture,
    ! [B,C,D] :
      ( ! [E] :
          ( member(E,B)
        <=> ( member(E,C)
            | member(E,D) ) )
     => B = union(C,D) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,negated_conjecture,
    ~ ! [B,C,D] :
        ( ! [E] :
            ( member(E,B)
          <=> ( member(E,C)
              | member(E,D) ) )
       => B = union(C,D) ),
    inference(negated_conjecture,[status(cth)],[f7]) ).

fof(f9,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(f10,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)],[f9]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f14,plain,
    ! [B,C] :
      ( ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
      & ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

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

fof(f18,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f19,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f20,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f21,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)],[f20]) ).

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

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

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f35,plain,
    ? [B,C,D] :
      ( ! [E] :
          ( member(E,B)
        <=> ( member(E,C)
            | member(E,D) ) )
      & B != union(C,D) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f36,plain,
    ? [B,C,D] :
      ( ! [E] :
          ( ( ~ member(E,B)
            | member(E,C)
            | member(E,D) )
          & ( member(E,B)
            | ( ~ member(E,C)
              & ~ member(E,D) ) ) )
      & B != union(C,D) ),
    inference(NNF_transformation,[status(esa)],[f35]) ).

fof(f37,plain,
    ? [B,C,D] :
      ( ! [E] :
          ( ~ member(E,B)
          | member(E,C)
          | member(E,D) )
      & ! [E] :
          ( member(E,B)
          | ( ~ member(E,C)
            & ~ member(E,D) ) )
      & B != union(C,D) ),
    inference(miniscoping,[status(esa)],[f36]) ).

fof(f38,plain,
    ( ! [E] :
        ( ~ member(E,sk0_2)
        | member(E,sk0_3)
        | member(E,sk0_4) )
    & ! [E] :
        ( member(E,sk0_2)
        | ( ~ member(E,sk0_3)
          & ~ member(E,sk0_4) ) )
    & sk0_2 != union(sk0_3,sk0_4) ),
    inference(skolemization,[status(esa)],[f37]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ member(X0,sk0_2)
      | member(X0,sk0_3)
      | member(X0,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f40,plain,
    ! [X0] :
      ( member(X0,sk0_2)
      | ~ member(X0,sk0_3) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f41,plain,
    ! [X0] :
      ( member(X0,sk0_2)
      | ~ member(X0,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f42,plain,
    sk0_2 != union(sk0_3,sk0_4),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f51,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)],[f25,f11]) ).

fof(f52,plain,
    ! [X0] :
      ( subset(sk0_2,X0)
      | member(sk0_0(X0,sk0_2),sk0_3)
      | member(sk0_0(X0,sk0_2),sk0_4) ),
    inference(resolution,[status(thm)],[f25,f39]) ).

fof(f53,plain,
    ! [X0] :
      ( subset(sk0_4,X0)
      | member(sk0_0(X0,sk0_4),sk0_2) ),
    inference(resolution,[status(thm)],[f25,f41]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( subset(union(X0,X1),X1)
      | subset(union(X0,X1),X1)
      | member(sk0_0(X1,union(X0,X1)),X0) ),
    inference(resolution,[status(thm)],[f26,f51]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( subset(union(X0,X1),X1)
      | member(sk0_0(X1,union(X0,X1)),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f71]) ).

fof(f73,plain,
    ( spl0_2
  <=> subset(sk0_4,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f74,plain,
    ( subset(sk0_4,sk0_2)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f73]) ).

fof(f76,plain,
    ( subset(sk0_4,sk0_2)
    | subset(sk0_4,sk0_2) ),
    inference(resolution,[status(thm)],[f26,f53]) ).

fof(f77,plain,
    spl0_2,
    inference(split_clause,[status(thm)],[f76,f73]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( subset(X0,union(X1,X2))
      | ~ member(sk0_0(union(X1,X2),X0),X2) ),
    inference(resolution,[status(thm)],[f26,f13]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( subset(X0,union(X1,X2))
      | ~ member(sk0_0(union(X1,X2),X0),X1) ),
    inference(resolution,[status(thm)],[f26,f12]) ).

fof(f99,plain,
    ! [X0] :
      ( subset(union(sk0_3,X0),X0)
      | member(sk0_0(X0,union(sk0_3,X0)),sk0_2) ),
    inference(resolution,[status(thm)],[f72,f40]) ).

fof(f110,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)],[f80,f52]) ).

fof(f111,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)],[f110]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1,X0))
      | subset(X0,union(X1,X0)) ),
    inference(resolution,[status(thm)],[f80,f25]) ).

fof(f119,plain,
    ! [X0,X1] : subset(X0,union(X1,X0)),
    inference(duplicate_literals_removal,[status(esa)],[f118]) ).

fof(f127,plain,
    ! [X0,X1] : subset(X0,union(X0,X1)),
    inference(paramodulation,[status(thm)],[f19,f119]) ).

fof(f260,plain,
    ( spl0_8
  <=> subset(union(sk0_3,sk0_2),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f261,plain,
    ( subset(union(sk0_3,sk0_2),sk0_2)
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f260]) ).

fof(f263,plain,
    ( subset(union(sk0_3,sk0_2),sk0_2)
    | subset(union(sk0_3,sk0_2),sk0_2) ),
    inference(resolution,[status(thm)],[f99,f26]) ).

fof(f264,plain,
    spl0_8,
    inference(split_clause,[status(thm)],[f263,f260]) ).

fof(f275,plain,
    ( subset(union(sk0_2,sk0_3),sk0_2)
    | ~ spl0_8 ),
    inference(forward_demodulation,[status(thm)],[f19,f261]) ).

fof(f278,plain,
    ( spl0_11
  <=> sk0_2 = union(sk0_2,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f279,plain,
    ( sk0_2 = union(sk0_2,sk0_3)
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f278]) ).

fof(f281,plain,
    ( spl0_12
  <=> subset(sk0_2,union(sk0_2,sk0_3)) ),
    introduced(split_symbol_definition) ).

fof(f283,plain,
    ( ~ subset(sk0_2,union(sk0_2,sk0_3))
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f281]) ).

fof(f284,plain,
    ( sk0_2 = union(sk0_2,sk0_3)
    | ~ subset(sk0_2,union(sk0_2,sk0_3))
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f275,f18]) ).

fof(f285,plain,
    ( spl0_11
    | ~ spl0_12
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f284,f278,f281,f260]) ).

fof(f286,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f283,f127]) ).

fof(f287,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f286]) ).

fof(f290,plain,
    ! [X0] :
      ( ~ member(X0,sk0_4)
      | member(X0,sk0_2)
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f74,f24]) ).

fof(f334,plain,
    ! [X0,X1] :
      ( member(sk0_0(X0,union(X1,sk0_4)),sk0_2)
      | subset(union(X1,sk0_4),X0)
      | member(sk0_0(X0,union(X1,sk0_4)),X1)
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f290,f51]) ).

fof(f785,plain,
    ! [X0,X1] :
      ( subset(union(X0,sk0_4),union(sk0_2,X1))
      | member(sk0_0(union(sk0_2,X1),union(X0,sk0_4)),X0)
      | subset(union(X0,sk0_4),union(sk0_2,X1))
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f334,f81]) ).

fof(f786,plain,
    ! [X0,X1] :
      ( subset(union(X0,sk0_4),union(sk0_2,X1))
      | member(sk0_0(union(sk0_2,X1),union(X0,sk0_4)),X0)
      | ~ spl0_2 ),
    inference(duplicate_literals_removal,[status(esa)],[f785]) ).

fof(f2318,plain,
    ! [X0] :
      ( subset(union(X0,sk0_4),union(sk0_2,X0))
      | subset(union(X0,sk0_4),union(sk0_2,X0))
      | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f786,f80]) ).

fof(f2319,plain,
    ! [X0] :
      ( subset(union(X0,sk0_4),union(sk0_2,X0))
      | ~ spl0_2 ),
    inference(duplicate_literals_removal,[status(esa)],[f2318]) ).

fof(f2371,plain,
    ( subset(union(sk0_3,sk0_4),sk0_2)
    | ~ spl0_2
    | ~ spl0_11 ),
    inference(paramodulation,[status(thm)],[f279,f2319]) ).

fof(f2383,plain,
    ( spl0_43
  <=> sk0_2 = union(sk0_3,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f2384,plain,
    ( sk0_2 = union(sk0_3,sk0_4)
    | ~ spl0_43 ),
    inference(component_clause,[status(thm)],[f2383]) ).

fof(f2386,plain,
    ( spl0_44
  <=> subset(sk0_2,union(sk0_3,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f2389,plain,
    ( sk0_2 = union(sk0_3,sk0_4)
    | ~ subset(sk0_2,union(sk0_3,sk0_4))
    | ~ spl0_2
    | ~ spl0_11 ),
    inference(resolution,[status(thm)],[f2371,f18]) ).

fof(f2390,plain,
    ( spl0_43
    | ~ spl0_44
    | ~ spl0_2
    | ~ spl0_11 ),
    inference(split_clause,[status(thm)],[f2389,f2383,f2386,f73,f278]) ).

fof(f2391,plain,
    ( $false
    | ~ spl0_43 ),
    inference(forward_subsumption_resolution,[status(thm)],[f2384,f42]) ).

fof(f2392,plain,
    ~ spl0_43,
    inference(contradiction_clause,[status(thm)],[f2391]) ).

fof(f2702,plain,
    ( subset(sk0_2,union(sk0_3,sk0_4))
    | subset(sk0_2,union(sk0_3,sk0_4)) ),
    inference(resolution,[status(thm)],[f111,f81]) ).

fof(f2703,plain,
    spl0_44,
    inference(split_clause,[status(thm)],[f2702,f2386]) ).

fof(f2714,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f77,f264,f285,f287,f2390,f2392,f2703]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET577+3 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 22:07:10 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.20/0.57  % Refutation found
% 0.20/0.57  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.57  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.58/0.58  % Elapsed time: 0.226956 seconds
% 1.58/0.58  % CPU time: 1.668662 seconds
% 1.58/0.58  % Total memory used: 74.910 MB
% 1.58/0.58  % Net memory used: 74.214 MB
%------------------------------------------------------------------------------