TSTP Solution File: SET183+3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET183+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 12:34:13 EDT 2023

% Result   : Theorem 0.16s 0.32s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   44 (  10 unt;   0 def)
%            Number of atoms       :  117 (  17 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  115 (  42   ~;  47   |;  18   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   83 (;  79   !;   4   ?)

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

fof(f2,axiom,
    ! [B,C] : subset(intersection(B,C),B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f5,axiom,
    ! [B,C] : intersection(B,C) = intersection(C,B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,conjecture,
    ! [B,C] :
      ( subset(B,C)
     => intersection(B,C) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    ~ ! [B,C] :
        ( subset(B,C)
       => intersection(B,C) = B ),
    inference(negated_conjecture,[status(cth)],[f8]) ).

fof(f10,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)],[f1]) ).

fof(f11,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)],[f10]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f15,plain,
    ! [X0,X1] : subset(intersection(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f16,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f17,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)],[f16]) ).

fof(f18,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)],[f17]) ).

fof(f19,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)],[f18]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f23,plain,
    ! [B,C] :
      ( ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
      & ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

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

fof(f27,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f28,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f37,plain,
    ? [B,C] :
      ( subset(B,C)
      & intersection(B,C) != B ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f38,plain,
    ( subset(sk0_2,sk0_3)
    & intersection(sk0_2,sk0_3) != sk0_2 ),
    inference(skolemization,[status(esa)],[f37]) ).

fof(f39,plain,
    subset(sk0_2,sk0_3),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f40,plain,
    intersection(sk0_2,sk0_3) != sk0_2,
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f43,plain,
    ! [X0,X1] : subset(intersection(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f28,f15]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( X0 = intersection(X1,X0)
      | ~ subset(X0,intersection(X1,X0)) ),
    inference(resolution,[status(thm)],[f27,f43]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( X0 = intersection(X1,X0)
      | ~ subset(X0,intersection(X0,X1)) ),
    inference(paramodulation,[status(thm)],[f28,f49]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),intersection(X2,X0))
      | ~ member(sk0_0(X1,X0),X2) ),
    inference(resolution,[status(thm)],[f21,f14]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
      | ~ subset(X0,X2)
      | member(sk0_0(X1,X0),X2) ),
    inference(resolution,[status(thm)],[f21,f20]) ).

fof(f77,plain,
    ! [X0] :
      ( subset(sk0_2,X0)
      | member(sk0_0(X0,sk0_2),sk0_3) ),
    inference(resolution,[status(thm)],[f68,f39]) ).

fof(f122,plain,
    ! [X0] :
      ( subset(sk0_2,X0)
      | member(sk0_0(X0,sk0_2),intersection(sk0_3,sk0_2))
      | subset(sk0_2,X0) ),
    inference(resolution,[status(thm)],[f67,f77]) ).

fof(f123,plain,
    ! [X0] :
      ( subset(sk0_2,X0)
      | member(sk0_0(X0,sk0_2),intersection(sk0_2,sk0_3))
      | subset(sk0_2,X0) ),
    inference(forward_demodulation,[status(thm)],[f28,f122]) ).

fof(f124,plain,
    ! [X0] :
      ( subset(sk0_2,X0)
      | member(sk0_0(X0,sk0_2),intersection(sk0_2,sk0_3)) ),
    inference(duplicate_literals_removal,[status(esa)],[f123]) ).

fof(f175,plain,
    ( spl0_3
  <=> subset(sk0_2,intersection(sk0_2,sk0_3)) ),
    introduced(split_symbol_definition) ).

fof(f176,plain,
    ( subset(sk0_2,intersection(sk0_2,sk0_3))
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f175]) ).

fof(f178,plain,
    ( subset(sk0_2,intersection(sk0_2,sk0_3))
    | subset(sk0_2,intersection(sk0_2,sk0_3)) ),
    inference(resolution,[status(thm)],[f124,f22]) ).

fof(f179,plain,
    spl0_3,
    inference(split_clause,[status(thm)],[f178,f175]) ).

fof(f184,plain,
    ( sk0_2 = intersection(sk0_3,sk0_2)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f176,f61]) ).

fof(f185,plain,
    ( sk0_2 = intersection(sk0_2,sk0_3)
    | ~ spl0_3 ),
    inference(forward_demodulation,[status(thm)],[f28,f184]) ).

fof(f186,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f185,f40]) ).

fof(f187,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f186]) ).

fof(f188,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f179,f187]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : SET183+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.31  % Computer : n028.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Tue May 30 10:33:32 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.16/0.31  % Drodi V3.5.1
% 0.16/0.32  % Refutation found
% 0.16/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.33  % Elapsed time: 0.022060 seconds
% 0.16/0.33  % CPU time: 0.039748 seconds
% 0.16/0.33  % Memory used: 14.466 MB
%------------------------------------------------------------------------------