TSTP Solution File: SET594+3 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% 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 : n025.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 20:39:54 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   41 (   7 unt;   0 def)
%            Number of atoms       :  113 (   7 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  112 (  40   ~;  47   |;  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   :   86 (  81   !;   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(f5,axiom,
    ! [B,C] : union(B,C) = union(C,B),
    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(f33,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

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(f61,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(f76,plain,
    ! [X0] :
      ( ~ member(X0,sk0_2)
      | member(X0,intersection(sk0_2,sk0_3))
      | member(X0,sk0_4) ),
    inference(resolution,[status(thm)],[f61,f26]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( subset(X0,union(X1,X2))
      | ~ member(sk0_0(union(X1,X2),X0),X2) ),
    inference(resolution,[status(thm)],[f17,f22]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( subset(X0,union(X1,X2))
      | ~ member(sk0_0(union(X1,X2),X0),X1) ),
    inference(resolution,[status(thm)],[f17,f21]) ).

fof(f249,plain,
    ! [X0] :
      ( ~ member(X0,sk0_2)
      | member(X0,sk0_4)
      | member(X0,sk0_3) ),
    inference(resolution,[status(thm)],[f76,f26]) ).

fof(f256,plain,
    ! [X0] :
      ( member(sk0_0(X0,sk0_2),sk0_4)
      | member(sk0_0(X0,sk0_2),sk0_3)
      | subset(sk0_2,X0) ),
    inference(resolution,[status(thm)],[f249,f16]) ).

fof(f306,plain,
    ! [X0] :
      ( member(sk0_0(union(sk0_4,X0),sk0_2),sk0_3)
      | subset(sk0_2,union(sk0_4,X0))
      | subset(sk0_2,union(sk0_4,X0)) ),
    inference(resolution,[status(thm)],[f256,f91]) ).

fof(f307,plain,
    ! [X0] :
      ( member(sk0_0(union(sk0_4,X0),sk0_2),sk0_3)
      | subset(sk0_2,union(sk0_4,X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f306]) ).

fof(f478,plain,
    ( spl0_27
  <=> subset(sk0_2,union(sk0_4,sk0_3)) ),
    introduced(split_symbol_definition) ).

fof(f479,plain,
    ( subset(sk0_2,union(sk0_4,sk0_3))
    | ~ spl0_27 ),
    inference(component_clause,[status(thm)],[f478]) ).

fof(f481,plain,
    ( subset(sk0_2,union(sk0_4,sk0_3))
    | subset(sk0_2,union(sk0_4,sk0_3)) ),
    inference(resolution,[status(thm)],[f307,f90]) ).

fof(f482,plain,
    spl0_27,
    inference(split_clause,[status(thm)],[f481,f478]) ).

fof(f486,plain,
    ( subset(sk0_2,union(sk0_3,sk0_4))
    | ~ spl0_27 ),
    inference(forward_demodulation,[status(thm)],[f33,f479]) ).

fof(f487,plain,
    ( $false
    | ~ spl0_27 ),
    inference(forward_subsumption_resolution,[status(thm)],[f486,f46]) ).

fof(f488,plain,
    ~ spl0_27,
    inference(contradiction_clause,[status(thm)],[f487]) ).

fof(f489,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f482,f488]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31  % Computer : n025.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 : Mon Apr 29 21:43:40 EDT 2024
% 0.09/0.31  % CPUTime  : 
% 0.15/0.31  % Drodi V3.6.0
% 0.15/0.39  % Refutation found
% 0.15/0.39  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.41  % Elapsed time: 0.085856 seconds
% 0.15/0.41  % CPU time: 0.600292 seconds
% 0.15/0.41  % Total memory used: 65.106 MB
% 0.15/0.41  % Net memory used: 64.610 MB
%------------------------------------------------------------------------------