TSTP Solution File: SET624+3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET624+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 12:34:51 EDT 2023

% Result   : Theorem 1.73s 0.58s
% Output   : CNFRefutation 2.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   64 (   1 unt;   0 def)
%            Number of atoms       :  181 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  196 (  79   ~;  91   |;  15   &)
%                                         (   9 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  101 (;  92   !;   9   ?)

% 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] :
      ( intersect(B,C)
    <=> ? [D] :
          ( member(D,B)
          & member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f7,negated_conjecture,
    ~ ! [B,C,D] :
        ( intersect(B,union(C,D))
      <=> ( intersect(B,C)
          | intersect(B,D) ) ),
    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] :
      ( ( ~ intersect(B,C)
        | ? [D] :
            ( member(D,B)
            & member(D,C) ) )
      & ( intersect(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | ~ member(D,C) ) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f14,plain,
    ( ! [B,C] :
        ( ~ intersect(B,C)
        | ? [D] :
            ( member(D,B)
            & member(D,C) ) )
    & ! [B,C] :
        ( intersect(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | ~ member(D,C) ) ) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f15,plain,
    ( ! [B,C] :
        ( ~ intersect(B,C)
        | ( member(sk0_0(C,B),B)
          & member(sk0_0(C,B),C) ) )
    & ! [B,C] :
        ( intersect(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | ~ member(D,C) ) ) ),
    inference(skolemization,[status(esa)],[f14]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ~ intersect(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ~ intersect(X0,X1)
      | member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( intersect(X0,X1)
      | ~ member(X2,X0)
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f20,plain,
    ! [B,C] :
      ( ~ intersect(B,C)
      | intersect(C,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ intersect(X0,X1)
      | intersect(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f29,plain,
    ? [B,C,D] :
      ( intersect(B,union(C,D))
    <~> ( intersect(B,C)
        | intersect(B,D) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f30,plain,
    ? [B,C,D] :
      ( ( intersect(B,union(C,D))
        | intersect(B,C)
        | intersect(B,D) )
      & ( ~ intersect(B,union(C,D))
        | ( ~ intersect(B,C)
          & ~ intersect(B,D) ) ) ),
    inference(NNF_transformation,[status(esa)],[f29]) ).

fof(f31,plain,
    ( ( intersect(sk0_2,union(sk0_3,sk0_4))
      | intersect(sk0_2,sk0_3)
      | intersect(sk0_2,sk0_4) )
    & ( ~ intersect(sk0_2,union(sk0_3,sk0_4))
      | ( ~ intersect(sk0_2,sk0_3)
        & ~ intersect(sk0_2,sk0_4) ) ) ),
    inference(skolemization,[status(esa)],[f30]) ).

fof(f32,plain,
    ( intersect(sk0_2,union(sk0_3,sk0_4))
    | intersect(sk0_2,sk0_3)
    | intersect(sk0_2,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ( ~ intersect(sk0_2,union(sk0_3,sk0_4))
    | ~ intersect(sk0_2,sk0_3) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f34,plain,
    ( ~ intersect(sk0_2,union(sk0_3,sk0_4))
    | ~ intersect(sk0_2,sk0_4) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f35,plain,
    ( spl0_0
  <=> intersect(sk0_2,union(sk0_3,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f36,plain,
    ( intersect(sk0_2,union(sk0_3,sk0_4))
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f35]) ).

fof(f37,plain,
    ( ~ intersect(sk0_2,union(sk0_3,sk0_4))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f35]) ).

fof(f38,plain,
    ( spl0_1
  <=> intersect(sk0_2,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f41,plain,
    ( spl0_2
  <=> intersect(sk0_2,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f42,plain,
    ( intersect(sk0_2,sk0_4)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f41]) ).

fof(f44,plain,
    ( spl0_0
    | spl0_1
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f32,f35,f38,f41]) ).

fof(f45,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f33,f35,f38]) ).

fof(f46,plain,
    ( ~ spl0_0
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f34,f35,f41]) ).

fof(f54,plain,
    ! [X0,X1,X2,X3] :
      ( intersect(X0,union(X1,X2))
      | ~ member(X3,X0)
      | ~ member(X3,X1) ),
    inference(resolution,[status(thm)],[f18,f11]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ~ intersect(union(X0,X1),X2)
      | member(sk0_0(X2,union(X0,X1)),X0)
      | member(sk0_0(X2,union(X0,X1)),X1) ),
    inference(resolution,[status(thm)],[f16,f10]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( ~ intersect(X0,X1)
      | intersect(X2,X1)
      | ~ member(sk0_0(X1,X0),X2) ),
    inference(resolution,[status(thm)],[f17,f18]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( ~ intersect(union(X0,X1),X2)
      | intersect(X1,X2)
      | ~ intersect(union(X0,X1),X2)
      | member(sk0_0(X2,union(X0,X1)),X0) ),
    inference(resolution,[status(thm)],[f74,f67]) ).

fof(f94,plain,
    ! [X0,X1,X2] :
      ( ~ intersect(union(X0,X1),X2)
      | intersect(X1,X2)
      | member(sk0_0(X2,union(X0,X1)),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f93]) ).

fof(f97,plain,
    ! [X0,X1,X2,X3] :
      ( ~ intersect(X0,X1)
      | intersect(union(X2,X3),X1)
      | ~ member(sk0_0(X1,X0),X3) ),
    inference(resolution,[status(thm)],[f74,f12]) ).

fof(f172,plain,
    ! [X0] :
      ( ~ member(X0,sk0_2)
      | ~ member(X0,sk0_3)
      | spl0_0 ),
    inference(resolution,[status(thm)],[f37,f54]) ).

fof(f178,plain,
    ! [X0] :
      ( ~ member(sk0_0(sk0_3,X0),sk0_2)
      | ~ intersect(X0,sk0_3)
      | spl0_0 ),
    inference(resolution,[status(thm)],[f172,f17]) ).

fof(f188,plain,
    ( ~ intersect(sk0_2,sk0_3)
    | ~ intersect(sk0_2,sk0_3)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f178,f16]) ).

fof(f189,plain,
    ( ~ spl0_1
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f188,f38,f35]) ).

fof(f192,plain,
    ( intersect(union(sk0_3,sk0_4),sk0_2)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f36,f21]) ).

fof(f494,plain,
    ! [X0,X1,X2] :
      ( ~ intersect(union(X0,X1),X2)
      | intersect(X1,X2)
      | ~ intersect(union(X0,X1),X2)
      | intersect(X0,X2) ),
    inference(resolution,[status(thm)],[f94,f74]) ).

fof(f495,plain,
    ! [X0,X1,X2] :
      ( ~ intersect(union(X0,X1),X2)
      | intersect(X1,X2)
      | intersect(X0,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f494]) ).

fof(f522,plain,
    ! [X0,X1,X2] :
      ( ~ intersect(X0,X1)
      | intersect(union(X2,X0),X1)
      | ~ intersect(X0,X1) ),
    inference(resolution,[status(thm)],[f97,f16]) ).

fof(f523,plain,
    ! [X0,X1,X2] :
      ( ~ intersect(X0,X1)
      | intersect(union(X2,X0),X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f522]) ).

fof(f556,plain,
    ! [X0,X1,X2] :
      ( ~ intersect(X0,X1)
      | intersect(X1,union(X2,X0)) ),
    inference(resolution,[status(thm)],[f523,f21]) ).

fof(f793,plain,
    ( spl0_5
  <=> intersect(sk0_4,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f794,plain,
    ( intersect(sk0_4,sk0_2)
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f793]) ).

fof(f865,plain,
    ( spl0_13
  <=> intersect(sk0_3,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f866,plain,
    ( intersect(sk0_3,sk0_2)
    | ~ spl0_13 ),
    inference(component_clause,[status(thm)],[f865]) ).

fof(f868,plain,
    ( intersect(sk0_4,sk0_2)
    | intersect(sk0_3,sk0_2)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f495,f192]) ).

fof(f869,plain,
    ( spl0_5
    | spl0_13
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f868,f793,f865,f35]) ).

fof(f1669,plain,
    ( intersect(sk0_4,sk0_2)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f42,f21]) ).

fof(f1680,plain,
    ( ~ intersect(sk0_4,sk0_2)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f37,f556]) ).

fof(f1681,plain,
    ( $false
    | ~ spl0_2
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1680,f1669]) ).

fof(f1682,plain,
    ( ~ spl0_2
    | spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f1681]) ).

fof(f1686,plain,
    ( intersect(sk0_2,sk0_4)
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f794,f21]) ).

fof(f1687,plain,
    ( spl0_2
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f1686,f41,f793]) ).

fof(f1688,plain,
    ( intersect(sk0_2,sk0_3)
    | ~ spl0_13 ),
    inference(resolution,[status(thm)],[f866,f21]) ).

fof(f1689,plain,
    ( spl0_1
    | ~ spl0_13 ),
    inference(split_clause,[status(thm)],[f1688,f38,f865]) ).

fof(f1690,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f44,f45,f46,f189,f869,f1682,f1687,f1689]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET624+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 10:22:08 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 1.73/0.58  % Refutation found
% 1.73/0.58  % SZS status Theorem for theBenchmark: Theorem is valid
% 1.73/0.58  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.05/0.60  % Elapsed time: 0.247414 seconds
% 2.05/0.60  % CPU time: 1.818858 seconds
% 2.05/0.60  % Memory used: 68.147 MB
%------------------------------------------------------------------------------