TSTP Solution File: SET755+4 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 12:35:08 EDT 2023

% Result   : Theorem 134.20s 17.33s
% Output   : CNFRefutation 134.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   42 (   6 unt;   0 def)
%            Number of atoms       :  148 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  173 (  67   ~;  69   |;  31   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :  142 (; 127   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( member(X,A)
         => member(X,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ! [F,B,X] :
      ( member(X,inverse_image2(F,B))
    <=> ? [Y] :
          ( member(Y,B)
          & apply(F,X,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f29,conjecture,
    ! [F,A,B,X,Y] :
      ( ( maps(F,A,B)
        & subset(X,B)
        & subset(Y,B)
        & subset(X,Y) )
     => subset(inverse_image2(F,X),inverse_image2(F,Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    ~ ! [F,A,B,X,Y] :
        ( ( maps(F,A,B)
          & subset(X,B)
          & subset(Y,B)
          & subset(X,Y) )
       => subset(inverse_image2(F,X),inverse_image2(F,Y)) ),
    inference(negated_conjecture,[status(cth)],[f29]) ).

fof(f31,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( ~ member(X,A)
          | member(X,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f32,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
      & ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(miniscoping,[status(esa)],[f32]) ).

fof(f34,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( member(sk0_0(B,A),A)
          & ~ member(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f33]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f189,plain,
    ! [F,B,X] :
      ( ( ~ member(X,inverse_image2(F,B))
        | ? [Y] :
            ( member(Y,B)
            & apply(F,X,Y) ) )
      & ( member(X,inverse_image2(F,B))
        | ! [Y] :
            ( ~ member(Y,B)
            | ~ apply(F,X,Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f24]) ).

fof(f190,plain,
    ( ! [F,B,X] :
        ( ~ member(X,inverse_image2(F,B))
        | ? [Y] :
            ( member(Y,B)
            & apply(F,X,Y) ) )
    & ! [F,B,X] :
        ( member(X,inverse_image2(F,B))
        | ! [Y] :
            ( ~ member(Y,B)
            | ~ apply(F,X,Y) ) ) ),
    inference(miniscoping,[status(esa)],[f189]) ).

fof(f191,plain,
    ( ! [F,B,X] :
        ( ~ member(X,inverse_image2(F,B))
        | ( member(sk0_25(X,B,F),B)
          & apply(F,X,sk0_25(X,B,F)) ) )
    & ! [F,B,X] :
        ( member(X,inverse_image2(F,B))
        | ! [Y] :
            ( ~ member(Y,B)
            | ~ apply(F,X,Y) ) ) ),
    inference(skolemization,[status(esa)],[f190]) ).

fof(f192,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,inverse_image2(X1,X2))
      | member(sk0_25(X0,X2,X1),X2) ),
    inference(cnf_transformation,[status(esa)],[f191]) ).

fof(f193,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,inverse_image2(X1,X2))
      | apply(X1,X0,sk0_25(X0,X2,X1)) ),
    inference(cnf_transformation,[status(esa)],[f191]) ).

fof(f194,plain,
    ! [X0,X1,X2,X3] :
      ( member(X0,inverse_image2(X1,X2))
      | ~ member(X3,X2)
      | ~ apply(X1,X0,X3) ),
    inference(cnf_transformation,[status(esa)],[f191]) ).

fof(f244,plain,
    ? [F,A,B,X,Y] :
      ( maps(F,A,B)
      & subset(X,B)
      & subset(Y,B)
      & subset(X,Y)
      & ~ subset(inverse_image2(F,X),inverse_image2(F,Y)) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f245,plain,
    ? [F,X,Y] :
      ( ? [B] :
          ( ? [A] : maps(F,A,B)
          & subset(X,B)
          & subset(Y,B) )
      & subset(X,Y)
      & ~ subset(inverse_image2(F,X),inverse_image2(F,Y)) ),
    inference(miniscoping,[status(esa)],[f244]) ).

fof(f246,plain,
    ( maps(sk0_39,sk0_43,sk0_42)
    & subset(sk0_40,sk0_42)
    & subset(sk0_41,sk0_42)
    & subset(sk0_40,sk0_41)
    & ~ subset(inverse_image2(sk0_39,sk0_40),inverse_image2(sk0_39,sk0_41)) ),
    inference(skolemization,[status(esa)],[f245]) ).

fof(f250,plain,
    subset(sk0_40,sk0_41),
    inference(cnf_transformation,[status(esa)],[f246]) ).

fof(f251,plain,
    ~ subset(inverse_image2(sk0_39,sk0_40),inverse_image2(sk0_39,sk0_41)),
    inference(cnf_transformation,[status(esa)],[f246]) ).

fof(f271,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
      | ~ subset(X0,X2)
      | member(sk0_0(X1,X0),X2) ),
    inference(resolution,[status(thm)],[f36,f35]) ).

fof(f272,plain,
    ! [X0,X1,X2,X3] :
      ( subset(X0,X1)
      | ~ subset(X0,X2)
      | ~ subset(X2,X3)
      | member(sk0_0(X1,X0),X3) ),
    inference(resolution,[status(thm)],[f271,f35]) ).

fof(f273,plain,
    ! [X0,X1,X2,X3,X4] :
      ( subset(X0,X1)
      | ~ subset(X0,X2)
      | ~ subset(X2,X3)
      | ~ subset(X3,X4)
      | member(sk0_0(X1,X0),X4) ),
    inference(resolution,[status(thm)],[f272,f35]) ).

fof(f302,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,inverse_image2(X1,X2))
      | ~ subset(X2,X3)
      | member(sk0_25(X0,X2,X1),X3) ),
    inference(resolution,[status(thm)],[f192,f35]) ).

fof(f310,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( subset(X0,X1)
      | ~ subset(X0,X2)
      | ~ subset(X2,X3)
      | ~ subset(X3,X4)
      | ~ subset(X4,X5)
      | member(sk0_0(X1,X0),X5) ),
    inference(resolution,[status(thm)],[f273,f35]) ).

fof(f315,plain,
    ! [X0] :
      ( subset(X0,X0)
      | subset(X0,X0) ),
    inference(resolution,[status(thm)],[f37,f36]) ).

fof(f316,plain,
    ! [X0] : subset(X0,X0),
    inference(duplicate_literals_removal,[status(esa)],[f315]) ).

fof(f321,plain,
    ! [X0,X1,X2,X3] :
      ( subset(X0,inverse_image2(X1,X2))
      | ~ member(X3,X2)
      | ~ apply(X1,sk0_0(inverse_image2(X1,X2),X0),X3) ),
    inference(resolution,[status(thm)],[f37,f194]) ).

fof(f352,plain,
    ! [X0,X1,X2,X3] :
      ( subset(X0,inverse_image2(X1,X2))
      | ~ member(sk0_25(sk0_0(inverse_image2(X1,X2),X0),X3,X1),X2)
      | ~ member(sk0_0(inverse_image2(X1,X2),X0),inverse_image2(X1,X3)) ),
    inference(resolution,[status(thm)],[f321,f193]) ).

fof(f370,plain,
    ! [X0,X1,X2,X3,X4] :
      ( subset(X0,X1)
      | ~ subset(X0,X2)
      | ~ subset(X2,X3)
      | ~ subset(X3,X4)
      | ~ subset(X4,X1)
      | subset(X0,X1) ),
    inference(resolution,[status(thm)],[f310,f37]) ).

fof(f371,plain,
    ! [X0,X1,X2,X3,X4] :
      ( subset(X0,X1)
      | ~ subset(X0,X2)
      | ~ subset(X2,X3)
      | ~ subset(X3,X4)
      | ~ subset(X4,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f370]) ).

fof(f397,plain,
    ! [X0,X1,X2] :
      ( subset(X0,sk0_41)
      | ~ subset(X0,X1)
      | ~ subset(X1,X2)
      | ~ subset(X2,sk0_40) ),
    inference(resolution,[status(thm)],[f371,f250]) ).

fof(f7309,plain,
    ! [X0,X1,X2,X3] :
      ( subset(X0,inverse_image2(X1,X2))
      | ~ member(sk0_0(inverse_image2(X1,X2),X0),inverse_image2(X1,X3))
      | ~ member(sk0_0(inverse_image2(X1,X2),X0),inverse_image2(X1,X3))
      | ~ subset(X3,X2) ),
    inference(resolution,[status(thm)],[f352,f302]) ).

fof(f7310,plain,
    ! [X0,X1,X2,X3] :
      ( subset(X0,inverse_image2(X1,X2))
      | ~ member(sk0_0(inverse_image2(X1,X2),X0),inverse_image2(X1,X3))
      | ~ subset(X3,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f7309]) ).

fof(f10434,plain,
    ! [X0] :
      ( subset(X0,sk0_41)
      | ~ subset(X0,sk0_40) ),
    inference(resolution,[status(thm)],[f397,f316]) ).

fof(f11625,plain,
    subset(sk0_40,sk0_41),
    inference(resolution,[status(thm)],[f10434,f316]) ).

fof(f21703,plain,
    ! [X0,X1,X2] :
      ( subset(inverse_image2(X0,X1),inverse_image2(X0,X2))
      | ~ subset(X1,X2)
      | subset(inverse_image2(X0,X1),inverse_image2(X0,X2)) ),
    inference(resolution,[status(thm)],[f7310,f36]) ).

fof(f21704,plain,
    ! [X0,X1,X2] :
      ( subset(inverse_image2(X0,X1),inverse_image2(X0,X2))
      | ~ subset(X1,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f21703]) ).

fof(f21718,plain,
    ~ subset(sk0_40,sk0_41),
    inference(resolution,[status(thm)],[f21704,f251]) ).

fof(f21719,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f21718,f11625]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.09/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n003.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue May 30 10:16:23 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.5.1
% 134.20/17.33  % Refutation found
% 134.20/17.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 134.20/17.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 135.27/17.42  % Elapsed time: 17.086179 seconds
% 135.27/17.42  % CPU time: 135.403099 seconds
% 135.27/17.42  % Memory used: 545.395 MB
%------------------------------------------------------------------------------